From 12f54e0b9773c9c34654f684b3acfabdecf6cfe9 Mon Sep 17 00:00:00 2001
From: Donald Pinckney <donald_pinckney@icloud.com>
Date: Fri, 5 Feb 2016 01:50:25 -0800
Subject: [PATCH 0001/1679] Write initial structs for Graph

---
 Graph/Graph.playground/Contents.swift        | 21 ++++++++++++++++++++
 Graph/Graph.playground/contents.xcplayground |  4 ++++
 Graph/Graph.playground/timeline.xctimeline   |  6 ++++++
 Graph/README.markdown                        |  6 ++++++
 4 files changed, 37 insertions(+)
 create mode 100644 Graph/Graph.playground/Contents.swift
 create mode 100644 Graph/Graph.playground/contents.xcplayground
 create mode 100644 Graph/Graph.playground/timeline.xctimeline
 create mode 100644 Graph/README.markdown

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
new file mode 100644
index 000000000..c1b1dccbb
--- /dev/null
+++ b/Graph/Graph.playground/Contents.swift
@@ -0,0 +1,21 @@
+public struct GraphEdge<T> {
+    let from: GraphVertex<T>
+    let to: GraphVertex<T>
+    let weight: Int
+}
+
+public struct GraphVertex<T> {
+    public var data: T
+    private var edges: [GraphEdge<T>] // This is a simple adjacency list, rather than matrix
+    
+    public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+        edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
+    }
+    
+    public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+        edges.append(GraphEdge(from: self, to: otherVertex, weight: weight))
+        otherVertex.edges.append(GraphEdge(from: otherVertex, to: self, weight: weight))
+    }
+}
+
+
diff --git a/Graph/Graph.playground/contents.xcplayground b/Graph/Graph.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Graph/Graph.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Graph/Graph.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Graph/README.markdown b/Graph/README.markdown
new file mode 100644
index 000000000..30327f474
--- /dev/null
+++ b/Graph/README.markdown
@@ -0,0 +1,6 @@
+# Graph
+
+YAY Graphs!
+TODO: Write stuff here.
+
+*Written by Donald Pinckney*

From 7d1fbb8e28a4d107dbdd4e455332904c9d54ddc0 Mon Sep 17 00:00:00 2001
From: Donald Pinckney <donald_pinckney@icloud.com>
Date: Fri, 5 Feb 2016 01:58:00 -0800
Subject: [PATCH 0002/1679] Reformatted code to match style guide

---
 Graph/Graph.playground/Contents.swift | 49 +++++++++++++++++++--------
 1 file changed, 35 insertions(+), 14 deletions(-)

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index c1b1dccbb..1aa1d1444 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,21 +1,42 @@
 public struct GraphEdge<T> {
-    let from: GraphVertex<T>
-    let to: GraphVertex<T>
-    let weight: Int
+  let from: GraphVertex<T>
+  let to: GraphVertex<T>
+  let weight: Int
 }
 
 public struct GraphVertex<T> {
-    public var data: T
-    private var edges: [GraphEdge<T>] // This is a simple adjacency list, rather than matrix
-    
-    public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Int = 0) {
-        edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
-    }
-    
-    public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Int = 0) {
-        edges.append(GraphEdge(from: self, to: otherVertex, weight: weight))
-        otherVertex.edges.append(GraphEdge(from: otherVertex, to: self, weight: weight))
-    }
+  public var data: T
+  private var edges: [GraphEdge<T>] = [] // This is a simple adjacency list, rather than matrix
+  
+  public init(data: T) {
+    self.data = data
+  }
+  
+  // Creates a directed edge self -----> dest
+  public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+    edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
+  }
+  
+  // Creates an undirected edge by making 2 directed edges: self ----> other, and other ----> self
+  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+    edges.append(GraphEdge(from: self, to: otherVertex, weight: weight))
+    otherVertex.edges.append(GraphEdge(from: otherVertex, to: self, weight: weight))
+  }
 }
 
 
+
+
+var v1 = GraphVertex(data: 1)
+var v2 = GraphVertex(data: 2)
+var v3 = GraphVertex(data: 3)
+var v4 = GraphVertex(data: 4)
+
+// v1 ---> v2 ---> v3 ---> v4
+// ^                       |
+// |                       V
+// -----------<------------|
+v1.connectTo(v2)
+v2.connectTo(v3)
+v3.connectTo(v4)
+v4.connectTo(v1)

From 10154dc6e05c1c4586c6600708ce6ba69e22518f Mon Sep 17 00:00:00 2001
From: Donald Pinckney <donald_pinckney@icloud.com>
Date: Fri, 5 Feb 2016 02:39:45 -0800
Subject: [PATCH 0003/1679] Add adjacency matrix implementation

---
 .../Contents.swift                            |  0
 .../contents.xcplayground                     |  0
 .../timeline.xctimeline                       |  0
 .../Contents.swift                            | 59 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 .../timeline.xctimeline                       |  6 ++
 6 files changed, 69 insertions(+)
 rename Graph/{Graph.playground => Graph Adjacency List.playground}/Contents.swift (100%)
 rename Graph/{Graph.playground => Graph Adjacency List.playground}/contents.xcplayground (100%)
 rename Graph/{Graph.playground => Graph Adjacency List.playground}/timeline.xctimeline (100%)
 create mode 100644 Graph/Graph Adjacency Matrix.playground/Contents.swift
 create mode 100644 Graph/Graph Adjacency Matrix.playground/contents.xcplayground
 create mode 100644 Graph/Graph Adjacency Matrix.playground/timeline.xctimeline

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph Adjacency List.playground/Contents.swift
similarity index 100%
rename from Graph/Graph.playground/Contents.swift
rename to Graph/Graph Adjacency List.playground/Contents.swift
diff --git a/Graph/Graph.playground/contents.xcplayground b/Graph/Graph Adjacency List.playground/contents.xcplayground
similarity index 100%
rename from Graph/Graph.playground/contents.xcplayground
rename to Graph/Graph Adjacency List.playground/contents.xcplayground
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph Adjacency List.playground/timeline.xctimeline
similarity index 100%
rename from Graph/Graph.playground/timeline.xctimeline
rename to Graph/Graph Adjacency List.playground/timeline.xctimeline
diff --git a/Graph/Graph Adjacency Matrix.playground/Contents.swift b/Graph/Graph Adjacency Matrix.playground/Contents.swift
new file mode 100644
index 000000000..2d634e0c0
--- /dev/null
+++ b/Graph/Graph Adjacency Matrix.playground/Contents.swift	
@@ -0,0 +1,59 @@
+
+
+public struct GraphVertex<T> {
+  public var data: T
+  let uniqueID: Int
+}
+
+public struct Graph<T> {
+  
+  private var adjacencyMatrix: [[Int?]] = [] // row-major
+  
+  public init() { } // Silence default constructor
+  
+  public mutating func createVertex(data: T) -> GraphVertex<T> {
+    let vertex = GraphVertex(data: data, uniqueID: adjacencyMatrix.count)
+    
+    // Expand each existing row to the right one column
+    for i in 0..<adjacencyMatrix.count {
+      adjacencyMatrix[i].append(nil)
+    }
+    
+    // Add one new row at the bottom
+    let newRow = [Int?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+    adjacencyMatrix.append(newRow)
+    
+    return vertex
+  }
+  
+  // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
+  public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+    adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID] = weight
+  }
+  
+  // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
+  public mutating func connect(someVertex: GraphVertex<T>, withVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+    adjacencyMatrix[someVertex.uniqueID][withVertex.uniqueID] = weight
+    adjacencyMatrix[withVertex.uniqueID][someVertex.uniqueID] = weight
+
+  }
+}
+
+
+
+
+var graph = Graph<Int>()
+let v1 = graph.createVertex(1)
+let v2 = graph.createVertex(2)
+let v3 = graph.createVertex(3)
+let v4 = graph.createVertex(4)
+
+// v1 ---> v2 ---> v3 ---> v4
+// ^                       |
+// |                       V
+// -----------<------------|
+
+graph.connect(v1, toDestinationVertex: v2)
+graph.connect(v2, toDestinationVertex: v3)
+graph.connect(v3, toDestinationVertex: v4)
+graph.connect(v4, toDestinationVertex: v1)
diff --git a/Graph/Graph Adjacency Matrix.playground/contents.xcplayground b/Graph/Graph Adjacency Matrix.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Graph/Graph Adjacency Matrix.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Graph/Graph Adjacency Matrix.playground/timeline.xctimeline b/Graph/Graph Adjacency Matrix.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Graph/Graph Adjacency Matrix.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>

From ebc45083d18197c3826cd72fa9bd07e0bec1b32c Mon Sep 17 00:00:00 2001
From: Donald Pinckney <donald_pinckney@icloud.com>
Date: Fri, 5 Feb 2016 21:43:28 -0800
Subject: [PATCH 0004/1679] Combine playgrounds into 1 playground with pages

---
 .../contents.xcplayground                     |  4 --
 .../Contents.swift                            | 29 ++++++--
 .../timeline.xctimeline                       |  0
 .../Contents.swift                            | 71 +++++++++++++++++++
 .../timeline.xctimeline                       |  6 ++
 Graph/Graph.playground/contents.xcplayground  |  7 ++
 6 files changed, 106 insertions(+), 11 deletions(-)
 delete mode 100644 Graph/Graph Adjacency List.playground/contents.xcplayground
 rename Graph/{Graph Adjacency List.playground => Graph.playground/Pages/Adjacency List.xcplaygroundpage}/Contents.swift (58%)
 rename Graph/{Graph Adjacency List.playground => Graph.playground/Pages/Adjacency List.xcplaygroundpage}/timeline.xctimeline (100%)
 create mode 100644 Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
 create mode 100644 Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Graph/Graph.playground/contents.xcplayground

diff --git a/Graph/Graph Adjacency List.playground/contents.xcplayground b/Graph/Graph Adjacency List.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Graph/Graph Adjacency List.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Graph/Graph Adjacency List.playground/Contents.swift b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
similarity index 58%
rename from Graph/Graph Adjacency List.playground/Contents.swift
rename to Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
index 1aa1d1444..17c0514ea 100644
--- a/Graph/Graph Adjacency List.playground/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
@@ -1,24 +1,34 @@
+/*
+
+A graph implementation, using an adjacency list.
+
+In an adjacency list implementation, each vertex stores an array of edges, indicating to which vertices it has an edge (note the directionality).  The edge stores the source and destination vertices, as well as a weight.
+
+Connected vertices in this implementation is O(1).
+
+*/
+
 public struct GraphEdge<T> {
-  let from: GraphVertex<T>
-  let to: GraphVertex<T>
-  let weight: Int
+  public let from: GraphVertex<T>
+  public let to: GraphVertex<T>
+  public let weight: Double
 }
 
 public struct GraphVertex<T> {
   public var data: T
-  private var edges: [GraphEdge<T>] = [] // This is a simple adjacency list, rather than matrix
+  public private(set) var edges: [GraphEdge<T>] = [] // This is a simple adjacency list, rather than matrix
   
   public init(data: T) {
     self.data = data
   }
   
   // Creates a directed edge self -----> dest
-  public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+  public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
     edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
   }
   
   // Creates an undirected edge by making 2 directed edges: self ----> other, and other ----> self
-  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Int = 0) {
+  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Double = 0) {
     edges.append(GraphEdge(from: self, to: otherVertex, weight: weight))
     otherVertex.edges.append(GraphEdge(from: otherVertex, to: self, weight: weight))
   }
@@ -26,17 +36,22 @@ public struct GraphVertex<T> {
 
 
 
-
+// Create 4 separate vertices
 var v1 = GraphVertex(data: 1)
 var v2 = GraphVertex(data: 2)
 var v3 = GraphVertex(data: 3)
 var v4 = GraphVertex(data: 4)
 
+// Setup a cycle like so:
 // v1 ---> v2 ---> v3 ---> v4
 // ^                       |
 // |                       V
 // -----------<------------|
+
 v1.connectTo(v2)
 v2.connectTo(v3)
 v3.connectTo(v4)
 v4.connectTo(v1)
+
+
+//: [Next](@next)
diff --git a/Graph/Graph Adjacency List.playground/timeline.xctimeline b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/timeline.xctimeline
similarity index 100%
rename from Graph/Graph Adjacency List.playground/timeline.xctimeline
rename to Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/timeline.xctimeline
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..4fffc4d40
--- /dev/null
+++ b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,71 @@
+//: [Previous](@previous)
+/*
+
+A graph implementation, using an adjacency matrix.
+
+In an adjacency matrix implementation, each vertex is associated with an index from 0..<V (V being the number of vertices). Then a matrix (a 2D array) is stored for the entire graph, with each entry indicating if the corresponding vertices are connected, and the weight.  For example, if matrix[3][5] = 4.6, then vertex #3 is connected to vertex #5, with a weight of 4.6.  Note that vertex #5 is not necessarily connected to vertex #3.
+
+Creating a new vertex must expand the adjacency matrix in this implementation, so creating a new vertex is O(V).  
+Connecting vertices os O(1).
+
+*/
+
+public struct GraphVertex<T> {
+    public var data: T
+    private let uniqueID: Int
+}
+
+public struct Graph<T> {
+    
+    // nil entries are used to mark that two vertices are NOT connected.
+    private var adjacencyMatrix: [[Double?]] = []
+    
+    public init() { }
+    
+    public mutating func createVertex(data: T) -> GraphVertex<T> {
+        let vertex = GraphVertex(data: data, uniqueID: adjacencyMatrix.count)
+        
+        // Expand each existing row to the right one column
+        for i in 0..<adjacencyMatrix.count {
+            adjacencyMatrix[i].append(nil)
+        }
+        
+        // Add one new row at the bottom
+        let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+        adjacencyMatrix.append(newRow)
+        
+        return vertex
+    }
+    
+    // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
+    public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+        adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID] = weight
+    }
+    
+    // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
+    public mutating func connect(someVertex: GraphVertex<T>, withVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+        adjacencyMatrix[someVertex.uniqueID][withVertex.uniqueID] = weight
+        adjacencyMatrix[withVertex.uniqueID][someVertex.uniqueID] = weight
+        
+    }
+}
+
+
+
+// Create 4 separate vertices
+var graph = Graph<Int>()
+let v1 = graph.createVertex(1)
+let v2 = graph.createVertex(2)
+let v3 = graph.createVertex(3)
+let v4 = graph.createVertex(4)
+
+// Setup a cycle like so:
+// v1 ---> v2 ---> v3 ---> v4
+// ^                       |
+// |                       V
+// -----------<------------|
+
+graph.connect(v1, toDestinationVertex: v2)
+graph.connect(v2, toDestinationVertex: v3)
+graph.connect(v3, toDestinationVertex: v4)
+graph.connect(v4, toDestinationVertex: v1)
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Graph/Graph.playground/contents.xcplayground b/Graph/Graph.playground/contents.xcplayground
new file mode 100644
index 000000000..32b5a98b9
--- /dev/null
+++ b/Graph/Graph.playground/contents.xcplayground
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='6.0' target-platform='ios' display-mode='rendered'>
+    <pages>
+        <page name='Adjacency List'/>
+        <page name='Adjacency Matrix'/>
+    </pages>
+</playground>
\ No newline at end of file

From 743b2f640d79e8c602e7dbc7dd1330b10f36cd4f Mon Sep 17 00:00:00 2001
From: Artur Antonov <artu-antonov@yandex.ru>
Date: Tue, 9 Feb 2016 21:14:11 +0300
Subject: [PATCH 0005/1679] Add Union-Find data structure implementation

---
 UnionFindDS/README.markdown                   |   3 +
 .../UnioinFindDS.playground/Contents.swift    | 106 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../timeline.xctimeline                       |   6 +
 UnionFindDS/UnionFindDS.swift                 |  51 +++++++++
 5 files changed, 170 insertions(+)
 create mode 100644 UnionFindDS/README.markdown
 create mode 100644 UnionFindDS/UnioinFindDS.playground/Contents.swift
 create mode 100644 UnionFindDS/UnioinFindDS.playground/contents.xcplayground
 create mode 100644 UnionFindDS/UnioinFindDS.playground/timeline.xctimeline
 create mode 100644 UnionFindDS/UnionFindDS.swift

diff --git a/UnionFindDS/README.markdown b/UnionFindDS/README.markdown
new file mode 100644
index 000000000..5ae638efc
--- /dev/null
+++ b/UnionFindDS/README.markdown
@@ -0,0 +1,3 @@
+# Union Find Data Structure
+
+TODO
diff --git a/UnionFindDS/UnioinFindDS.playground/Contents.swift b/UnionFindDS/UnioinFindDS.playground/Contents.swift
new file mode 100644
index 000000000..cb59acdbc
--- /dev/null
+++ b/UnionFindDS/UnioinFindDS.playground/Contents.swift
@@ -0,0 +1,106 @@
+//: Playground - noun: a place where people can play
+
+public class UnionFindDS<T: Hashable> {
+  
+  private var index = [T:Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  
+  public func addSetWithElement(element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private func findSetByIndexOfElement(index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = findSetByIndexOfElement(parent[index])
+      return parent[index]
+    }
+  }
+  
+  public func findSetOfElement(element: T) -> Int {
+    let indexOfElement = index[element]!
+    return findSetByIndexOfElement(indexOfElement)
+  }
+  
+  public func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
+    let firstSet = findSetOfElement(firstElement)
+    let secondSet = findSetOfElement(secondElement)
+    if (firstSet != secondSet) {
+      if (size[firstSet] < size[secondSet]) {
+        parent[firstSet] = secondSet;
+        size[secondSet] += size[firstSet]
+      } else {
+        parent[secondSet] = firstSet;
+        size[firstSet] += size[secondSet]
+      }
+    }
+  }
+}
+
+
+let dsu = UnionFindDS<Int>()
+
+for i in 1...10 {
+  dsu.addSetWithElement(i)
+}
+// now our dsu contains 10 independent sets
+
+// let's divide our numbers into two sets by divisibility by 2
+for i in 3...10 {
+  if i % 2 == 0 {
+    dsu.unionSetsWithElement(2, andSecondElement: i)
+  } else {
+    dsu.unionSetsWithElement(1, andSecondElement: i)
+  }
+}
+
+// check our division
+print(dsu.findSetOfElement(2) == dsu.findSetOfElement(4))
+print(dsu.findSetOfElement(4) == dsu.findSetOfElement(6))
+print(dsu.findSetOfElement(6) == dsu.findSetOfElement(8))
+print(dsu.findSetOfElement(8) == dsu.findSetOfElement(10))
+
+print(dsu.findSetOfElement(1) == dsu.findSetOfElement(3))
+print(dsu.findSetOfElement(3) == dsu.findSetOfElement(5))
+print(dsu.findSetOfElement(5) == dsu.findSetOfElement(7))
+print(dsu.findSetOfElement(7) == dsu.findSetOfElement(9))
+
+print(dsu.findSetOfElement(8) == dsu.findSetOfElement(9))
+print(dsu.findSetOfElement(4) == dsu.findSetOfElement(3))
+
+
+let dsuForStrings = UnionFindDS<String>()
+let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
+
+dsuForStrings.addSetWithElement("a")
+dsuForStrings.addSetWithElement("b")
+
+// In that example we divide strings by its first letter
+for word in words {
+  dsuForStrings.addSetWithElement(word)
+  if word.hasPrefix("a") {
+    dsuForStrings.unionSetsWithElement("a", andSecondElement: word)
+  } else if word.hasPrefix("b") {
+    dsuForStrings.unionSetsWithElement("b", andSecondElement: word)
+  }
+}
+
+print(dsuForStrings.findSetOfElement("a") == dsuForStrings.findSetOfElement("all"))
+print(dsuForStrings.findSetOfElement("all") == dsuForStrings.findSetOfElement("awesome"))
+print(dsuForStrings.findSetOfElement("amazing") == dsuForStrings.findSetOfElement("afternoon"))
+
+print(dsuForStrings.findSetOfElement("b") == dsuForStrings.findSetOfElement("boy"))
+print(dsuForStrings.findSetOfElement("best") == dsuForStrings.findSetOfElement("boy"))
+print(dsuForStrings.findSetOfElement("border") == dsuForStrings.findSetOfElement("best"))
+
+print(dsuForStrings.findSetOfElement("amazing") == dsuForStrings.findSetOfElement("boy"))
+print(dsuForStrings.findSetOfElement("all") == dsuForStrings.findSetOfElement("border"))
+
+
+
+
diff --git a/UnionFindDS/UnioinFindDS.playground/contents.xcplayground b/UnionFindDS/UnioinFindDS.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/UnionFindDS/UnioinFindDS.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/UnionFindDS/UnioinFindDS.playground/timeline.xctimeline b/UnionFindDS/UnioinFindDS.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/UnionFindDS/UnioinFindDS.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/UnionFindDS/UnionFindDS.swift b/UnionFindDS/UnionFindDS.swift
new file mode 100644
index 000000000..0e3a982f2
--- /dev/null
+++ b/UnionFindDS/UnionFindDS.swift
@@ -0,0 +1,51 @@
+/*
+  Union-Find Data Structure
+
+  Performance:
+    adding new set is almost O(1)
+    finding set of element is almost O(1)
+    union sets is almost O(1)
+*/
+
+
+public class UnionFindDS<T: Hashable> {
+  
+  private var index = [T:Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  
+  public func addSetWithElement(element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private func findSetByIndexOfElement(index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = findSetByIndexOfElement(parent[index])
+      return parent[index]
+    }
+  }
+  
+  public func findSetOfElement(element: T) -> Int {
+    let indexOfElement = index[element]!
+    return findSetByIndexOfElement(indexOfElement)
+  }
+  
+  public func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
+    let firstSet = findSetOfElement(firstElement)
+    let secondSet = findSetOfElement(secondElement)
+    if (firstSet != secondSet) {
+      if (size[firstSet] < size[secondSet]) {
+        parent[firstSet] = secondSet;
+        size[secondSet] += size[firstSet]
+      } else {
+        parent[secondSet] = firstSet;
+        size[firstSet] += size[secondSet]
+      }
+    }
+  }
+}
\ No newline at end of file

From 5d262b9eef21eca8c58bdac34205804d8f350ffb Mon Sep 17 00:00:00 2001
From: Artur Antonov <artu-antonov@yandex.ru>
Date: Wed, 10 Feb 2016 23:51:01 +0300
Subject: [PATCH 0006/1679] Rename UnionFindDS to UnionFind and make it struct

---
 {UnionFindDS => UnionFind}/README.markdown         |  0
 .../UnioinFind.playground}/Contents.swift          | 14 +++++++-------
 .../UnioinFind.playground}/contents.xcplayground   |  0
 .../UnioinFind.playground}/timeline.xctimeline     |  0
 .../UnionFindDS.swift => UnionFind/UnionFind.swift | 10 +++++-----
 5 files changed, 12 insertions(+), 12 deletions(-)
 rename {UnionFindDS => UnionFind}/README.markdown (100%)
 rename {UnionFindDS/UnioinFindDS.playground => UnionFind/UnioinFind.playground}/Contents.swift (88%)
 rename {UnionFindDS/UnioinFindDS.playground => UnionFind/UnioinFind.playground}/contents.xcplayground (100%)
 rename {UnionFindDS/UnioinFindDS.playground => UnionFind/UnioinFind.playground}/timeline.xctimeline (100%)
 rename UnionFindDS/UnionFindDS.swift => UnionFind/UnionFind.swift (75%)

diff --git a/UnionFindDS/README.markdown b/UnionFind/README.markdown
similarity index 100%
rename from UnionFindDS/README.markdown
rename to UnionFind/README.markdown
diff --git a/UnionFindDS/UnioinFindDS.playground/Contents.swift b/UnionFind/UnioinFind.playground/Contents.swift
similarity index 88%
rename from UnionFindDS/UnioinFindDS.playground/Contents.swift
rename to UnionFind/UnioinFind.playground/Contents.swift
index cb59acdbc..2b2a68aea 100644
--- a/UnionFindDS/UnioinFindDS.playground/Contents.swift
+++ b/UnionFind/UnioinFind.playground/Contents.swift
@@ -1,19 +1,19 @@
 //: Playground - noun: a place where people can play
 
-public class UnionFindDS<T: Hashable> {
+public struct UnionFind<T: Hashable> {
   
   private var index = [T:Int]()
   private var parent = [Int]()
   private var size = [Int]()
   
   
-  public func addSetWithElement(element: T) {
+  public mutating func addSetWithElement(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
   
-  private func findSetByIndexOfElement(index: Int) -> Int {
+  private mutating func findSetByIndexOfElement(index: Int) -> Int {
     if parent[index] == index {
       return index
     } else {
@@ -22,12 +22,12 @@ public class UnionFindDS<T: Hashable> {
     }
   }
   
-  public func findSetOfElement(element: T) -> Int {
+  public mutating func findSetOfElement(element: T) -> Int {
     let indexOfElement = index[element]!
     return findSetByIndexOfElement(indexOfElement)
   }
   
-  public func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
+  public mutating func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
     let firstSet = findSetOfElement(firstElement)
     let secondSet = findSetOfElement(secondElement)
     if (firstSet != secondSet) {
@@ -43,7 +43,7 @@ public class UnionFindDS<T: Hashable> {
 }
 
 
-let dsu = UnionFindDS<Int>()
+var dsu = UnionFind<Int>()
 
 for i in 1...10 {
   dsu.addSetWithElement(i)
@@ -74,7 +74,7 @@ print(dsu.findSetOfElement(8) == dsu.findSetOfElement(9))
 print(dsu.findSetOfElement(4) == dsu.findSetOfElement(3))
 
 
-let dsuForStrings = UnionFindDS<String>()
+var dsuForStrings = UnionFind<String>()
 let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
 
 dsuForStrings.addSetWithElement("a")
diff --git a/UnionFindDS/UnioinFindDS.playground/contents.xcplayground b/UnionFind/UnioinFind.playground/contents.xcplayground
similarity index 100%
rename from UnionFindDS/UnioinFindDS.playground/contents.xcplayground
rename to UnionFind/UnioinFind.playground/contents.xcplayground
diff --git a/UnionFindDS/UnioinFindDS.playground/timeline.xctimeline b/UnionFind/UnioinFind.playground/timeline.xctimeline
similarity index 100%
rename from UnionFindDS/UnioinFindDS.playground/timeline.xctimeline
rename to UnionFind/UnioinFind.playground/timeline.xctimeline
diff --git a/UnionFindDS/UnionFindDS.swift b/UnionFind/UnionFind.swift
similarity index 75%
rename from UnionFindDS/UnionFindDS.swift
rename to UnionFind/UnionFind.swift
index 0e3a982f2..617d20951 100644
--- a/UnionFindDS/UnionFindDS.swift
+++ b/UnionFind/UnionFind.swift
@@ -8,20 +8,20 @@
 */
 
 
-public class UnionFindDS<T: Hashable> {
+public struct UnionFind<T: Hashable> {
   
   private var index = [T:Int]()
   private var parent = [Int]()
   private var size = [Int]()
   
   
-  public func addSetWithElement(element: T) {
+  public mutating func addSetWithElement(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
   
-  private func findSetByIndexOfElement(index: Int) -> Int {
+  private mutating func findSetByIndexOfElement(index: Int) -> Int {
     if parent[index] == index {
       return index
     } else {
@@ -30,12 +30,12 @@ public class UnionFindDS<T: Hashable> {
     }
   }
   
-  public func findSetOfElement(element: T) -> Int {
+  public mutating func findSetOfElement(element: T) -> Int {
     let indexOfElement = index[element]!
     return findSetByIndexOfElement(indexOfElement)
   }
   
-  public func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
+  public mutating func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
     let firstSet = findSetOfElement(firstElement)
     let secondSet = findSetOfElement(secondElement)
     if (firstSet != secondSet) {

From 1ff10bc01972bc57f3313f2d721b7212e965c6f8 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 11 Feb 2016 13:06:09 +1300
Subject: [PATCH 0007/1679] Adding placeholder readme for BFS

---
 Breadth-First Search/README.markdown | 3 +++
 1 file changed, 3 insertions(+)
 create mode 100644 Breadth-First Search/README.markdown

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
new file mode 100644
index 000000000..c1d74ec99
--- /dev/null
+++ b/Breadth-First Search/README.markdown	
@@ -0,0 +1,3 @@
+# Breadth-First Search
+
+TODO

From b3bb50a9ae6b18058aa9cc0045c0967fb9f3d423 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 11 Feb 2016 13:07:36 +1300
Subject: [PATCH 0008/1679] Linking to BFS from main readme

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 1b5ff2a85..719b1bb7c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -157,7 +157,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 ### Graphs
 
 - Graph
-- Breadth-First Search (BFS)
+- [Breadth-First Search (BFS)](Breadth-First Search/)
 - Depth-First Search (DFS)
 - Shortest Path
 - Minimum Spanning Tree

From 1ce7af4778c5ff36036f1fd54d27bca8ae51f721 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 11 Feb 2016 22:08:39 +1300
Subject: [PATCH 0009/1679] Added titles in readme and added draft BFS
 playground

---
 .../Contents.swift                            | 113 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../timeline.xctimeline                       |   6 +
 Breadth-First Search/Images/Animated_BFS.gif  | Bin 0 -> 33276 bytes
 Breadth-First Search/README.markdown          |  20 +++-
 5 files changed, 142 insertions(+), 1 deletion(-)
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/timeline.xctimeline
 create mode 100644 Breadth-First Search/Images/Animated_BFS.gif

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
new file mode 100644
index 000000000..706cb2b97
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -0,0 +1,113 @@
+public class Graph {
+  private var canvas: Array<Node>
+
+  init() {
+    canvas = Array<Node>()
+  }
+
+  func addNode(key: String) -> Node {
+    let childNode: Node = Node(key: key)
+    canvas.append(childNode)
+    return childNode
+  }
+
+  func addEdge(source: Node, neighbor: Node) {
+    let newEdge = Edge(neighbor: neighbor)
+    newEdge.neighbor = neighbor
+    source.neighbors.append(newEdge)
+  }
+}
+
+public class Node {
+  var key: String
+  var neighbors: Array<Edge>
+
+  init(key: String) {
+    self.key = key
+    self.neighbors = Array<Edge>()
+  }
+}
+
+public class Edge {
+  var neighbor: Node
+  init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public class Queue<T> {
+  private var top: QueueNode<T>! = QueueNode<T>()
+
+  func enQueue(key: T) {
+    if (top == nil) {
+      top = QueueNode<T>()
+    }
+
+    if (top.key == nil) {
+      top.key = key;
+      return
+    }
+
+    let childToUse: QueueNode<T> = QueueNode<T>()
+    var current: QueueNode = top
+    while (current.next != nil) {
+      current = current.next!
+    }
+
+    childToUse.key = key;
+    current.next = childToUse;
+  }
+
+  func deQueue() -> QueueNode<T> {
+    let itemToDeQueue = top
+    top = itemToDeQueue.next
+    return itemToDeQueue
+  }
+
+  var isEmpty: Bool {
+    get { return top == nil }
+  }
+}
+
+class QueueNode<T> {
+  var key: T?
+  var next: QueueNode?
+}
+
+func breadthFirstSearch(graph: Graph, root: Node) {
+
+  let q = Queue<Node>()
+  q.enQueue(root)
+  print(root.key)
+
+  while !q.isEmpty {
+    let current = q.deQueue()
+    for edge in current.key!.neighbors {
+      let neighbor = edge.neighbor
+      q.enQueue(neighbor)
+
+      print(neighbor.key)
+    }
+  }
+}
+
+let graph = Graph()
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeD)
+graph.addEdge(nodeB, neighbor: nodeE)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeG)
+graph.addEdge(nodeE, neighbor: nodeH)
+
+breadthFirstSearch(graph, root: nodeA)
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/timeline.xctimeline b/Breadth-First Search/BreadthFirstSearch.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Breadth-First Search/Images/Animated_BFS.gif b/Breadth-First Search/Images/Animated_BFS.gif
new file mode 100644
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diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index c1d74ec99..7f5a314e0 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,3 +1,21 @@
 # Breadth-First Search
 
-TODO
+Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root  and explores the neighbor nodes first, before moving to the next level neighbors.
+
+## Animated example
+
+![Animated example of a breadth-first search](Images/Animated_BFS.gif)
+
+## The code
+
+```swift
+func breadthFirstSearch() {
+
+}
+```
+
+## See also
+
+[Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search)
+
+*Written by [Chris Pilcher](https://github.com/chris-pilcher)*

From d49eb998a664dcc060084bf1d92086efd0d3465a Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 11 Feb 2016 22:47:00 +1300
Subject: [PATCH 0010/1679] Renaming variables in BFS playground

---
 .../Contents.swift                            | 83 ++++++++++---------
 Breadth-First Search/README.markdown          |  2 +-
 2 files changed, 43 insertions(+), 42 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
index 706cb2b97..a6318d8c9 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -1,67 +1,68 @@
-public class Graph {
-  private var canvas: Array<Node>
+class Graph {
+  private var nodes = [Node]()
 
-  init() {
-    canvas = Array<Node>()
-  }
-
-  func addNode(key: String) -> Node {
-    let childNode: Node = Node(key: key)
-    canvas.append(childNode)
-    return childNode
+  func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
   }
 
   func addEdge(source: Node, neighbor: Node) {
-    let newEdge = Edge(neighbor: neighbor)
-    newEdge.neighbor = neighbor
-    source.neighbors.append(newEdge)
+    let edge = Edge(neighbor: neighbor)
+    edge.neighbor = neighbor
+    source.neighbors.append(edge)
   }
 }
 
-public class Node {
-  var key: String
-  var neighbors: Array<Edge>
+class Node {
+  private var label: String
+  private var neighbors: [Edge]
 
-  init(key: String) {
-    self.key = key
-    self.neighbors = Array<Edge>()
+  init(label: String) {
+    self.label = label
+    neighbors = []
   }
 }
 
-public class Edge {
-  var neighbor: Node
+class Edge {
+  private var neighbor: Node
+
   init(neighbor: Node) {
     self.neighbor = neighbor
   }
 }
 
-public class Queue<T> {
-  private var top: QueueNode<T>! = QueueNode<T>()
+class Queue<T> {
+  private var top: QueueNode<T>!
 
-  func enQueue(key: T) {
+  func enqueue(item: T) {
     if (top == nil) {
       top = QueueNode<T>()
     }
 
-    if (top.key == nil) {
-      top.key = key;
+    if (top.item == nil) {
+      top.item = item;
       return
     }
 
-    let childToUse: QueueNode<T> = QueueNode<T>()
+    let childToUse = QueueNode<T>()
     var current: QueueNode = top
-    while (current.next != nil) {
+    while current.next != nil {
       current = current.next!
     }
 
-    childToUse.key = key;
+    childToUse.item = item;
     current.next = childToUse;
   }
 
-  func deQueue() -> QueueNode<T> {
-    let itemToDeQueue = top
-    top = itemToDeQueue.next
-    return itemToDeQueue
+  func dequeue() -> QueueNode<T>? {
+    guard !isEmpty else {
+      return nil
+    }
+
+    let itemToDequeue = top
+    top = itemToDequeue.next
+    return itemToDequeue
   }
 
   var isEmpty: Bool {
@@ -70,23 +71,23 @@ public class Queue<T> {
 }
 
 class QueueNode<T> {
-  var key: T?
+  var item: T?
   var next: QueueNode?
 }
 
 func breadthFirstSearch(graph: Graph, root: Node) {
+  print("Performing breadth-first search on '\(root.label)'")
 
   let q = Queue<Node>()
-  q.enQueue(root)
-  print(root.key)
+  q.enqueue(root)
 
   while !q.isEmpty {
-    let current = q.deQueue()
-    for edge in current.key!.neighbors {
-      let neighbor = edge.neighbor
-      q.enQueue(neighbor)
+    let current = q.dequeue()
+    for edge in current!.item!.neighbors {
+      let neighborNode = edge.neighbor
+      q.enqueue(neighborNode)
 
-      print(neighbor.key)
+      print(neighborNode.label)
     }
   }
 }
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 7f5a314e0..b1278df8b 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,6 +1,6 @@
 # Breadth-First Search
 
-Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root  and explores the neighbor nodes first, before moving to the next level neighbors.
+Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root and explores the neighbor nodes first, before moving to the next level neighbors.
 
 ## Animated example
 

From 55d329deddfb6a4ec491edaf54905794e98fbe40 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 11 Feb 2016 23:26:02 +1300
Subject: [PATCH 0011/1679] Adding code to readme

---
 Breadth-First Search/README.markdown | 145 ++++++++++++++++++++++++++-
 1 file changed, 144 insertions(+), 1 deletion(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index b1278df8b..bbb7fa376 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -8,14 +8,157 @@ Breadth-first search (BFS) is an algorithm for traversing or searching tree or g
 
 ## The code
 
+Before we can code the breadth-first search algorithm we need to:
+* Create an implementation of the graph
+* Create an implementation of a queue
+
+### Graph implementation
+
+A graph is made up of nodes and edges. In the [animated example](#animated-example) the nodes are represented as circles and the edges are represented as lines.
+
+Implementation of a node:
+```swift
+class Node {
+  private var label: String
+  private var neighbors: [Edge]
+
+  init(label: String) {
+    self.label = label
+    neighbors = []
+  }
+}
+```
+
+Implementation of an edge:
 ```swift
-func breadthFirstSearch() {
+class Edge {
+  private var neighbor: Node
 
+  init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
 }
 ```
 
+Implementation of a graph:
+```swift
+class Graph {
+  private var nodes = [Node]()
+
+  func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    edge.neighbor = neighbor
+    source.neighbors.append(edge)
+  }
+}
+```
+
+### Queue implementation
+
+Implementation of simple queue:
+
+```swift
+class Queue<T> {
+  private var top: QueueNode<T>!
+
+  func enqueue(item: T) {
+    if (top == nil) {
+      top = QueueNode<T>()
+    }
+
+    if (top.item == nil) {
+      top.item = item;
+      return
+    }
+
+    let childToUse = QueueNode<T>()
+    var current: QueueNode = top
+    while current.next != nil {
+      current = current.next!
+    }
+
+    childToUse.item = item;
+    current.next = childToUse;
+  }
+
+  func dequeue() -> QueueNode<T>? {
+    guard !isEmpty else {
+      return nil
+    }
+
+    let itemToDequeue = top
+    top = itemToDequeue.next
+    return itemToDequeue
+  }
+
+  var isEmpty: Bool {
+    get { return top == nil }
+  }
+}
+
+class QueueNode<T> {
+  var item: T?
+  var next: QueueNode?
+}
+```
+
+### Breadth-first search algorithm
+
+Simple implementation of breadth-first search using queues:
+```swift
+func breadthFirstSearch(graph: Graph, root: Node) {
+  print("Performing breadth-first search on '\(root.label)'")
+
+  let q = Queue<Node>()
+  q.enqueue(root)
+
+  while !q.isEmpty {
+    let current = q.dequeue()
+    for edge in current!.item!.neighbors {
+      let neighborNode = edge.neighbor
+      q.enqueue(neighborNode)
+
+      print(neighborNode.label)
+    }
+  }
+}
+```
+
+Put this code in a playground and test it like so:
+```swift
+let graph = Graph() // Representing the graph from the animated example
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeD)
+graph.addEdge(nodeB, neighbor: nodeE)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeG)
+graph.addEdge(nodeE, neighbor: nodeH)
+
+breadthFirstSearch(graph, root: nodeA) // This will output: Performing breadth-first search on 'a', b, c, d, e, f, g, h
+
+```
+
 ## See also
 
 [Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search)
 
+[Queues](http://waynewbishop.com/swift/stacks-queues) & [Graphs](http://waynewbishop.com/swift/graphs) by Wayne Bishop
+
 *Written by [Chris Pilcher](https://github.com/chris-pilcher)*

From 475024e409f01bb6c657849955c09c59731e7992 Mon Sep 17 00:00:00 2001
From: Artur Antonov <artu-antonov@yandex.ru>
Date: Thu, 11 Feb 2016 17:00:39 +0300
Subject: [PATCH 0012/1679] Make some methods safer, rename the directory to
 Union-Find

---
 {UnionFind => Union-Find}/README.markdown     |  0
 .../UnioinFind.playground/Contents.swift      | 27 ++++++++++---------
 .../contents.xcplayground                     |  0
 .../UnioinFind.playground/timeline.xctimeline |  0
 {UnionFind => Union-Find}/UnionFind.swift     | 27 ++++++++++---------
 5 files changed, 30 insertions(+), 24 deletions(-)
 rename {UnionFind => Union-Find}/README.markdown (100%)
 rename {UnionFind => Union-Find}/UnioinFind.playground/Contents.swift (83%)
 rename {UnionFind => Union-Find}/UnioinFind.playground/contents.xcplayground (100%)
 rename {UnionFind => Union-Find}/UnioinFind.playground/timeline.xctimeline (100%)
 rename {UnionFind => Union-Find}/UnionFind.swift (58%)

diff --git a/UnionFind/README.markdown b/Union-Find/README.markdown
similarity index 100%
rename from UnionFind/README.markdown
rename to Union-Find/README.markdown
diff --git a/UnionFind/UnioinFind.playground/Contents.swift b/Union-Find/UnioinFind.playground/Contents.swift
similarity index 83%
rename from UnionFind/UnioinFind.playground/Contents.swift
rename to Union-Find/UnioinFind.playground/Contents.swift
index 2b2a68aea..d7cd8fd19 100644
--- a/UnionFind/UnioinFind.playground/Contents.swift
+++ b/Union-Find/UnioinFind.playground/Contents.swift
@@ -22,21 +22,24 @@ public struct UnionFind<T: Hashable> {
     }
   }
   
-  public mutating func findSetOfElement(element: T) -> Int {
-    let indexOfElement = index[element]!
-    return findSetByIndexOfElement(indexOfElement)
+  public mutating func findSetOfElement(element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return findSetByIndexOfElement(indexOfElement)
+    } else {
+      return nil
+    }
   }
   
   public mutating func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
-    let firstSet = findSetOfElement(firstElement)
-    let secondSet = findSetOfElement(secondElement)
-    if (firstSet != secondSet) {
-      if (size[firstSet] < size[secondSet]) {
-        parent[firstSet] = secondSet;
-        size[secondSet] += size[firstSet]
-      } else {
-        parent[secondSet] = firstSet;
-        size[firstSet] += size[secondSet]
+    if let firstSet = findSetOfElement(firstElement), secondSet = findSetOfElement(secondElement) {
+      if (firstSet != secondSet) {
+        if (size[firstSet] < size[secondSet]) {
+          parent[firstSet] = secondSet;
+          size[secondSet] += size[firstSet]
+        } else {
+          parent[secondSet] = firstSet;
+          size[firstSet] += size[secondSet]
+        }
       }
     }
   }
diff --git a/UnionFind/UnioinFind.playground/contents.xcplayground b/Union-Find/UnioinFind.playground/contents.xcplayground
similarity index 100%
rename from UnionFind/UnioinFind.playground/contents.xcplayground
rename to Union-Find/UnioinFind.playground/contents.xcplayground
diff --git a/UnionFind/UnioinFind.playground/timeline.xctimeline b/Union-Find/UnioinFind.playground/timeline.xctimeline
similarity index 100%
rename from UnionFind/UnioinFind.playground/timeline.xctimeline
rename to Union-Find/UnioinFind.playground/timeline.xctimeline
diff --git a/UnionFind/UnionFind.swift b/Union-Find/UnionFind.swift
similarity index 58%
rename from UnionFind/UnionFind.swift
rename to Union-Find/UnionFind.swift
index 617d20951..193dd1d87 100644
--- a/UnionFind/UnionFind.swift
+++ b/Union-Find/UnionFind.swift
@@ -30,21 +30,24 @@ public struct UnionFind<T: Hashable> {
     }
   }
   
-  public mutating func findSetOfElement(element: T) -> Int {
-    let indexOfElement = index[element]!
-    return findSetByIndexOfElement(indexOfElement)
+  public mutating func findSetOfElement(element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return findSetByIndexOfElement(indexOfElement)
+    } else {
+      return nil
+    }
   }
   
   public mutating func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
-    let firstSet = findSetOfElement(firstElement)
-    let secondSet = findSetOfElement(secondElement)
-    if (firstSet != secondSet) {
-      if (size[firstSet] < size[secondSet]) {
-        parent[firstSet] = secondSet;
-        size[secondSet] += size[firstSet]
-      } else {
-        parent[secondSet] = firstSet;
-        size[firstSet] += size[secondSet]
+    if let firstSet = findSetOfElement(firstElement), secondSet = findSetOfElement(secondElement) {
+      if (firstSet != secondSet) {
+        if (size[firstSet] < size[secondSet]) {
+          parent[firstSet] = secondSet;
+          size[secondSet] += size[firstSet]
+        } else {
+          parent[secondSet] = firstSet;
+          size[firstSet] += size[secondSet]
+        }
       }
     }
   }

From 4419a0d67f1cb54d4ad639fe32d3474bd066e61d Mon Sep 17 00:00:00 2001
From: Artur Antonov <artu-antonov@yandex.ru>
Date: Fri, 12 Feb 2016 19:01:03 +0300
Subject: [PATCH 0013/1679] Simplify method names

---
 .../UnioinFind.playground/Contents.swift      | 85 +++++++++++--------
 Union-Find/UnionFind.swift                    | 30 ++++---
 2 files changed, 67 insertions(+), 48 deletions(-)

diff --git a/Union-Find/UnioinFind.playground/Contents.swift b/Union-Find/UnioinFind.playground/Contents.swift
index d7cd8fd19..fe53241b9 100644
--- a/Union-Find/UnioinFind.playground/Contents.swift
+++ b/Union-Find/UnioinFind.playground/Contents.swift
@@ -7,102 +7,113 @@ public struct UnionFind<T: Hashable> {
   private var size = [Int]()
   
   
-  public mutating func addSetWithElement(element: T) {
+  public mutating func addSetWith(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
   
-  private mutating func findSetByIndexOfElement(index: Int) -> Int {
+  private mutating func setByIndex(index: Int) -> Int {
     if parent[index] == index {
       return index
     } else {
-      parent[index] = findSetByIndexOfElement(parent[index])
+      parent[index] = setByIndex(parent[index])
       return parent[index]
     }
   }
   
-  public mutating func findSetOfElement(element: T) -> Int? {
+  public mutating func setOf(element: T) -> Int? {
     if let indexOfElement = index[element] {
-      return findSetByIndexOfElement(indexOfElement)
+      return setByIndex(indexOfElement)
     } else {
       return nil
     }
   }
   
-  public mutating func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
-    if let firstSet = findSetOfElement(firstElement), secondSet = findSetOfElement(secondElement) {
-      if (firstSet != secondSet) {
-        if (size[firstSet] < size[secondSet]) {
-          parent[firstSet] = secondSet;
+  public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
           size[secondSet] += size[firstSet]
         } else {
-          parent[secondSet] = firstSet;
+          parent[secondSet] = firstSet
           size[firstSet] += size[secondSet]
         }
       }
     }
   }
+  
+  public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
+    }
+  }
 }
 
 
 var dsu = UnionFind<Int>()
 
 for i in 1...10 {
-  dsu.addSetWithElement(i)
+  dsu.addSetWith(i)
 }
 // now our dsu contains 10 independent sets
 
 // let's divide our numbers into two sets by divisibility by 2
 for i in 3...10 {
   if i % 2 == 0 {
-    dsu.unionSetsWithElement(2, andSecondElement: i)
+    dsu.unionSetsContaining(2, and: i)
   } else {
-    dsu.unionSetsWithElement(1, andSecondElement: i)
+    dsu.unionSetsContaining(1, and: i)
   }
 }
 
 // check our division
-print(dsu.findSetOfElement(2) == dsu.findSetOfElement(4))
-print(dsu.findSetOfElement(4) == dsu.findSetOfElement(6))
-print(dsu.findSetOfElement(6) == dsu.findSetOfElement(8))
-print(dsu.findSetOfElement(8) == dsu.findSetOfElement(10))
+print(dsu.inSameSet(2, and: 4))
+print(dsu.inSameSet(4, and: 6))
+print(dsu.inSameSet(6, and: 8))
+print(dsu.inSameSet(8, and: 10))
+
+
+print(dsu.inSameSet(1, and: 3))
+print(dsu.inSameSet(3, and: 5))
+print(dsu.inSameSet(5, and: 7))
+print(dsu.inSameSet(7, and: 9))
+
 
-print(dsu.findSetOfElement(1) == dsu.findSetOfElement(3))
-print(dsu.findSetOfElement(3) == dsu.findSetOfElement(5))
-print(dsu.findSetOfElement(5) == dsu.findSetOfElement(7))
-print(dsu.findSetOfElement(7) == dsu.findSetOfElement(9))
+print(dsu.inSameSet(7, and: 4))
+print(dsu.inSameSet(3, and: 6))
 
-print(dsu.findSetOfElement(8) == dsu.findSetOfElement(9))
-print(dsu.findSetOfElement(4) == dsu.findSetOfElement(3))
 
 
 var dsuForStrings = UnionFind<String>()
 let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
 
-dsuForStrings.addSetWithElement("a")
-dsuForStrings.addSetWithElement("b")
+dsuForStrings.addSetWith("a")
+dsuForStrings.addSetWith("b")
 
 // In that example we divide strings by its first letter
 for word in words {
-  dsuForStrings.addSetWithElement(word)
+  dsuForStrings.addSetWith(word)
   if word.hasPrefix("a") {
-    dsuForStrings.unionSetsWithElement("a", andSecondElement: word)
+    dsuForStrings.unionSetsContaining("a", and: word)
   } else if word.hasPrefix("b") {
-    dsuForStrings.unionSetsWithElement("b", andSecondElement: word)
+    dsuForStrings.unionSetsContaining("b", and: word)
   }
 }
 
-print(dsuForStrings.findSetOfElement("a") == dsuForStrings.findSetOfElement("all"))
-print(dsuForStrings.findSetOfElement("all") == dsuForStrings.findSetOfElement("awesome"))
-print(dsuForStrings.findSetOfElement("amazing") == dsuForStrings.findSetOfElement("afternoon"))
+print(dsuForStrings.inSameSet("a", and: "all"))
+print(dsuForStrings.inSameSet("all", and: "awesome"))
+print(dsuForStrings.inSameSet("amazing", and: "afternoon"))
 
-print(dsuForStrings.findSetOfElement("b") == dsuForStrings.findSetOfElement("boy"))
-print(dsuForStrings.findSetOfElement("best") == dsuForStrings.findSetOfElement("boy"))
-print(dsuForStrings.findSetOfElement("border") == dsuForStrings.findSetOfElement("best"))
+print(dsuForStrings.inSameSet("b", and: "boy"))
+print(dsuForStrings.inSameSet("best", and: "boy"))
+print(dsuForStrings.inSameSet("border", and: "best"))
 
-print(dsuForStrings.findSetOfElement("amazing") == dsuForStrings.findSetOfElement("boy"))
-print(dsuForStrings.findSetOfElement("all") == dsuForStrings.findSetOfElement("border"))
+print(dsuForStrings.inSameSet("amazing", and: "boy"))
+print(dsuForStrings.inSameSet("all", and: "border"))
 
 
 
diff --git a/Union-Find/UnionFind.swift b/Union-Find/UnionFind.swift
index 193dd1d87..88583cb9a 100644
--- a/Union-Find/UnionFind.swift
+++ b/Union-Find/UnionFind.swift
@@ -15,40 +15,48 @@ public struct UnionFind<T: Hashable> {
   private var size = [Int]()
   
   
-  public mutating func addSetWithElement(element: T) {
+  public mutating func addSetWith(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
   
-  private mutating func findSetByIndexOfElement(index: Int) -> Int {
+  private mutating func setByIndex(index: Int) -> Int {
     if parent[index] == index {
       return index
     } else {
-      parent[index] = findSetByIndexOfElement(parent[index])
+      parent[index] = setByIndex(parent[index])
       return parent[index]
     }
   }
   
-  public mutating func findSetOfElement(element: T) -> Int? {
+  public mutating func setOf(element: T) -> Int? {
     if let indexOfElement = index[element] {
-      return findSetByIndexOfElement(indexOfElement)
+      return setByIndex(indexOfElement)
     } else {
       return nil
     }
   }
   
-  public mutating func unionSetsWithElement(firstElement: T, andSecondElement secondElement: T) {
-    if let firstSet = findSetOfElement(firstElement), secondSet = findSetOfElement(secondElement) {
-      if (firstSet != secondSet) {
-        if (size[firstSet] < size[secondSet]) {
-          parent[firstSet] = secondSet;
+  public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
           size[secondSet] += size[firstSet]
         } else {
-          parent[secondSet] = firstSet;
+          parent[secondSet] = firstSet
           size[firstSet] += size[secondSet]
         }
       }
     }
   }
+  
+  public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
+    }
+  }
 }
\ No newline at end of file

From 8ce99ee123232357f01bc8cc99bfac546b9eb0ab Mon Sep 17 00:00:00 2001
From: Artur Antonov <artu-antonov@yandex.ru>
Date: Fri, 12 Feb 2016 22:27:57 +0300
Subject: [PATCH 0014/1679] Add description with illustrations

---
 Union-Find/Images/AfterFind.png   | Bin 0 -> 10347 bytes
 Union-Find/Images/AfterUnion.png  | Bin 0 -> 26331 bytes
 Union-Find/Images/BeforeFind.png  | Bin 0 -> 11685 bytes
 Union-Find/Images/BeforeUnion.png | Bin 0 -> 22581 bytes
 Union-Find/README.markdown        | 152 +++++++++++++++++++++++++++++-
 5 files changed, 150 insertions(+), 2 deletions(-)
 create mode 100644 Union-Find/Images/AfterFind.png
 create mode 100644 Union-Find/Images/AfterUnion.png
 create mode 100644 Union-Find/Images/BeforeFind.png
 create mode 100644 Union-Find/Images/BeforeUnion.png

diff --git a/Union-Find/Images/AfterFind.png b/Union-Find/Images/AfterFind.png
new file mode 100644
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diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 5ae638efc..a0d80dd1a 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -1,3 +1,151 @@
-# Union Find Data Structure
+# Union-Find data structure
 
-TODO
+Union-Find data structure (also known as disjoint-set data structure) is data structure that can keep track of a set of elements partitioned into a number of disjoint (non-overlapping) subsets. It supports three basic operations:
+  1. Find(**A**): Determine which subset an element **A** is in
+  2. Union(**A**, **B**): Join two subsets that contain **A** and **B** into a single subset
+  3. AddSet(**A**): Add a new subset containing just that element **A**
+
+The most common application of this data structure is keeping track of the connected components of an undirected graph. It is also used for implementing efficient version of Kruskal's algorithm to find the minimum spanning tree of a graph.
+
+## Implementation
+
+Union-Find can be implemented in many ways but we'll look at the most efficient.
+
+Every Union-Find data structure is just value of type `UnionFind`
+
+```swift
+public struct UnionFind<T: Hashable> {
+  private var index = [T:Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+}
+```
+
+Our Union-Find data structure is actually a forest where each subset represented by a [tree](../Tree/). For our purposes we only need to keep parent of each node. To do this we use array `parent` where `parent[i]` is index of parent of node with number **i**. In a that forest, the unique number of each subset is the index of value of root of that subset's tree.
+
+So let's look at the implementation of basic operations:
+
+### Add set
+
+```swift
+public mutating func addSetWith(element: T) {
+  index[element] = parent.count  // 1
+  parent.append(parent.count)  //2
+  size.append(1)  // 3
+}
+```
+
+1. We save index of new element in `index` dictionary because we need `parent` array only containing values in range 0..<parent.count.
+
+2. Then we add that index to `parent` array. It's pointing itself because the tree that represent new set containing only one node which obviously is a root of that tree.
+
+3. `size[i]` is a count of nodes in tree which root is node with number `i` We'll be using that in Union method.
+
+
+### Find
+
+```swift
+private mutating func setByIndex(index: Int) -> Int {
+  if parent[index] == index {  // 1
+    return index
+  } else {
+    parent[index] = setByIndex(parent[index])  // 2
+    return parent[index]  // 3
+  }
+}
+
+public mutating func setOf(element: T) -> Int? {
+  if let indexOfElement = index[element] {
+    return setByIndex(indexOfElement)
+  } else {
+    return nil
+  }
+}
+```
+
+`setOf(element: T)` is a helper method to get index corresponding to `element` and if it exists we return value of actual method `setByIndex(index: Int)`
+
+1. First, we check if current index represent a node that is root. That means we find number that represent the set of element we search for.
+
+2. Otherwise we recursively call our method on parent of current node. And then we do **very important thing**: we cache index of root node, so when we call this method again it will executed faster because of cached indexes. Without that optimization method's complexity is **O(n)** but now in combination with the size optimization (we'll look at that in Union section) it is almost **O(1)**.
+
+3. We return our cached root as result.
+
+Here's illustration of what I mean
+
+Before first call `setOf(4)`:
+
+![BeforeFind](Images/BeforeFind.png)
+
+After:
+
+![AfterFind](Images/AfterFind.png)
+
+Indexes of elements are marked in red.
+
+
+### Union
+
+```swift
+public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
+  if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {  // 1
+    if firstSet != secondSet {  // 2
+      if size[firstSet] < size[secondSet] {  // 3
+        parent[firstSet] = secondSet  // 4
+        size[secondSet] += size[firstSet]  // 5
+      } else {
+        parent[secondSet] = firstSet
+        size[firstSet] += size[secondSet]
+      }
+    }
+  }
+}
+```
+
+1. We find sets of each element.
+
+2. Check that sets are not equal because if they are it makes no sense to union them.
+
+3. This is where our size optimization comes in. We want to keep trees as small as possible so we always attach the smaller tree to the root of the larger tree. To determine small tree we compare trees by its sizes.
+
+4. Here we attach the smaller tree to the root of the larger tree.
+
+5. We keep sizes of trees in actual states so we update size of larger tree.
+
+Union with optimizations also takes almost **O(1)** time.
+
+As always, some illustrations for better understanding
+
+Before calling `unionSetsContaining(4, and: 7)`:
+
+![BeforeUnion](Images/BeforeUnion.png)
+
+After:
+
+![AfterUnion](Images/AfterUnion.png)
+
+Note that during union caching optimization was performed because of calling `setOf` in the beginning of method.
+
+
+
+There are also helper method to just check that two elements is in the same set:
+
+```swift
+public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
+  if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+    return firstSet == secondSet
+  } else {
+    return false
+  }
+}
+```
+
+
+See the playground for more examples of how to use this handy data structure.
+
+
+## See also
+
+[Union-Find at wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
+
+*Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From 58392bcb5e804953b7b2da3370eb921f1b4f6f37 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 12 Feb 2016 21:17:22 +0100
Subject: [PATCH 0015/1679] Add run-length encoding

---
 README.markdown                               |   2 +-
 Run-Length Encoding/README.markdown           | 139 ++++
 .../RLE Tests/RLE.xcodeproj/project.pbxproj   | 394 ++++++++++
 .../RLE Tests/RLE/AppDelegate.swift           |  27 +
 .../AppIcon.appiconset/Contents.json          |  58 ++
 .../RLE Tests/RLE/Base.lproj/MainMenu.xib     | 680 ++++++++++++++++++
 Run-Length Encoding/RLE Tests/RLE/Info.plist  |  34 +
 Run-Length Encoding/RLE Tests/RLE/RLE.swift   |  70 ++
 .../RLE Tests/RLETests/Info.plist             |  24 +
 .../RLE Tests/RLETests/RLETests.swift         | 111 +++
 .../RLE.playground/Contents.swift             |  82 +++
 .../RLE.playground/contents.xcplayground      |   4 +
 .../RLE.playground/timeline.xctimeline        |   6 +
 Run-Length Encoding/RLE.swift                 |  60 ++
 14 files changed, 1690 insertions(+), 1 deletion(-)
 create mode 100644 Run-Length Encoding/README.markdown
 create mode 100644 Run-Length Encoding/RLE Tests/RLE.xcodeproj/project.pbxproj
 create mode 100644 Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift
 create mode 100644 Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib
 create mode 100644 Run-Length Encoding/RLE Tests/RLE/Info.plist
 create mode 100644 Run-Length Encoding/RLE Tests/RLE/RLE.swift
 create mode 100644 Run-Length Encoding/RLE Tests/RLETests/Info.plist
 create mode 100644 Run-Length Encoding/RLE Tests/RLETests/RLETests.swift
 create mode 100644 Run-Length Encoding/RLE.playground/Contents.swift
 create mode 100644 Run-Length Encoding/RLE.playground/contents.xcplayground
 create mode 100644 Run-Length Encoding/RLE.playground/timeline.xctimeline
 create mode 100644 Run-Length Encoding/RLE.swift

diff --git a/README.markdown b/README.markdown
index 1b5ff2a85..eb2bda765 100644
--- a/README.markdown
+++ b/README.markdown
@@ -79,7 +79,7 @@ Bad sorting algorithms (don't use these!):
 
 ### Compression
 
-- Run-Length Encoding (RLE)
+- [Run-Length Encoding (RLE)](Run-Length Encoding)
 - Huffman Encoding
 
 ### Miscellaneous
diff --git a/Run-Length Encoding/README.markdown b/Run-Length Encoding/README.markdown
new file mode 100644
index 000000000..0f6041885
--- /dev/null
+++ b/Run-Length Encoding/README.markdown	
@@ -0,0 +1,139 @@
+# Run-Length Encoding (RLE)
+
+RLE is probably the simplest way to do compression. Let's say you have data that looks like this:
+
+	aaaaabbbcdeeeeeeef...
+	
+then RLE encodes it as follows:
+
+	5a3b1c1d7e1f...
+
+Instead of repeating bytes, you first write how often that byte occurs and then the byte's actual value. If the data has a lot of "byte runs", that is lots of repeating bytes, then RLE can save quite a bit of space. It works quite well on images.
+
+There are many different ways you can implement RLE. Here's an extension of `NSData` that does a version of RLE inspired by the old [PCX image file format](https://en.wikipedia.org/wiki/PCX).
+
+The rules are these:
+
+- Each byte run, i.e. when a certain byte value occurs more than once in a row, is compressed using two bytes: the first byte records the number of repetitions, the second records the actual value. The first byte is stored as: `191 + count`. This means encoded byte runs can never be more than 64 bytes long.
+
+- A single byte in the range 0 - 191 is not compressed and is copied without change.
+
+- A single byte in the range 192 - 255 is represented by two bytes: first the byte 192 (meaning a run of 1 byte), followed by the actual value.
+
+Here is the compression code. It returns a new `NSData` object containing the run-length encoded bytes:
+
+```swift
+extension NSData {
+  public func compressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+      
+      while ptr < end {                        // 1
+        var count = 0
+        var byte = ptr.memory
+        var next = byte
+        
+        while next == byte && ptr < end && count < 64 {   // 2
+          ptr = ptr.advancedBy(1)
+          next = ptr.memory
+          count += 1
+        }
+      
+        if count > 1 || byte >= 192 {          // 3
+          var size = 191 + UInt8(count)
+          data.appendBytes(&size, length: 1)
+          data.appendBytes(&byte, length: 1)
+        } else {                               // 4
+          data.appendBytes(&byte, length: 1)
+        }
+      }
+    }
+    return data
+  }
+}
+```
+
+How it works:
+
+1. We use an `UnsafePointer` to step through the bytes of the original `NSData` object.
+
+2. At this point we've read the current byte value into the `byte` variable. If the next byte is the same, then we keep reading until we find a byte value that is different, or we reach the end of the data. We also stop if the run is 64 bytes because that's the maximum we can encode.
+
+3. Here, we have to decide how to encode the bytes we just read. The first possibility is that we've read a run of 2 or more bytes (up to 64). In that case we write out two bytes: the length of the run followed by the byte value. But it's also possible we've read a single byte with a value >= 192. That will also be encoded with two bytes.
+
+4. The third possibility is that we've read a single byte < 192. That simply gets copied to the output verbatim.
+
+You can test it like this in a playground:
+
+```swift
+let originalString = "aaaaabbbcdeeeeeeef"
+let utf8 = originalString.dataUsingEncoding(NSUTF8StringEncoding)!
+let compressed = utf8.compressRLE()
+```
+
+The compressed `NSData` object should be `<c461c262 6364c665 66>`. Let's decode that by hand to see what has happened:
+
+	c4    This is 196 in decimal. It means the next byte appears 5 times.
+	61    The data byte "a".
+	c2    The next byte appears 3 times.
+	62    The data byte "b".
+	63    The data byte "c". Because this is < 192, it's a single data byte.
+	64    The data byte "d". Also appears just once.
+	c6    The next byte will appear 7 times.
+	65    The data byte "e".
+	66    The data byte "f". Appears just once.
+
+So that's 9 bytes encoded versus 18 original. That's a savings of 50%. Of course, this was only a simple test case... If you get unlucky and there are no byte runs at all in your original data, then this method will actually make the encoded data twice as large! So it really depends on the input data.
+
+Here is the decompression code:
+
+```swift
+  public func decompressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+
+      while ptr < end {
+        var byte = ptr.memory                 // 1
+        ptr = ptr.advancedBy(1)
+        
+        if byte < 192 {                       // 2
+          data.appendBytes(&byte, length: 1)
+
+        } else if ptr < end {                 // 3
+          var value = ptr.memory
+          ptr = ptr.advancedBy(1)
+
+          for _ in 0 ..< byte - 191 {
+            data.appendBytes(&value, length: 1)
+          }
+        }
+      }
+    }
+    return data
+  }
+```
+
+1. Again this uses an `UnsafePointer` to read the `NSData`. Here we read the next byte; this is either a single value less than 192, or the start of a byte run.
+
+2. If it's a single value, then it's just a matter of copying it to the output.
+
+3. But if the byte is the start of a run, we have to first read the actual data value and then write it out repeatedly.
+
+To turn the compressed data back into the original, you'd do:
+
+```swift
+let decompressed = compressed.decompressRLE()
+let restoredString = String(data: decompressed, encoding: NSUTF8StringEncoding)
+```
+
+And now `originalString == restoredString` must be true!
+
+Footnote: The original PCX implementation is slightly different. There, a byte value of 192 (0xC0) means that the following byte will be repeated 0 times. This also limits the maximum run size to 63 bytes. Because it makes no sense to store bytes that don't occur, in my implementation 192 means the next byte appears once, and the maximum run length is 64 bytes.
+
+This was probably a trade-off when they designed the PCX format way back when. If you look at it in binary, the upper two bits indicate whether a byte is compressed. (If both bits are set then the byte value is 192 or more.) To get the run length you can simply do `byte & 0x3F`, giving you a value in the range 0 to 63. 
+
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Run-Length Encoding/RLE Tests/RLE.xcodeproj/project.pbxproj b/Run-Length Encoding/RLE Tests/RLE.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..394f2c196
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLE.xcodeproj/project.pbxproj	
@@ -0,0 +1,394 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B1BFA9B1C6E5CD70051C9A4 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B1BFA9A1C6E5CD70051C9A4 /* AppDelegate.swift */; };
+		7B1BFA9D1C6E5CD70051C9A4 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 7B1BFA9C1C6E5CD70051C9A4 /* Assets.xcassets */; };
+		7B1BFAA01C6E5CD70051C9A4 /* MainMenu.xib in Resources */ = {isa = PBXBuildFile; fileRef = 7B1BFA9E1C6E5CD70051C9A4 /* MainMenu.xib */; };
+		7B1BFAAB1C6E5CD70051C9A4 /* RLETests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B1BFAAA1C6E5CD70051C9A4 /* RLETests.swift */; };
+		7B1BFAB61C6E5D000051C9A4 /* RLE.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B1BFAB51C6E5D000051C9A4 /* RLE.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
+		7B1BFAA71C6E5CD70051C9A4 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 7B1BFA8F1C6E5CD70051C9A4 /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = 7B1BFA961C6E5CD70051C9A4;
+			remoteInfo = RLE;
+		};
+/* End PBXContainerItemProxy section */
+
+/* Begin PBXFileReference section */
+		7B1BFA971C6E5CD70051C9A4 /* RLE.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = RLE.app; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B1BFA9A1C6E5CD70051C9A4 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
+		7B1BFA9C1C6E5CD70051C9A4 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
+		7B1BFA9F1C6E5CD70051C9A4 /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.xib; name = Base; path = Base.lproj/MainMenu.xib; sourceTree = "<group>"; };
+		7B1BFAA11C6E5CD70051C9A4 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
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+/* End PBXFileReference section */
+
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+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		7B1BFAA31C6E5CD70051C9A4 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
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+			);
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+			);
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+			sourceTree = "<group>";
+		};
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+			isa = PBXGroup;
+			children = (
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+			);
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+		};
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+			isa = PBXGroup;
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+			);
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+			sourceTree = "<group>";
+		};
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+
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+			);
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+			);
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+		};
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+				7B1BFAA41C6E5CD70051C9A4 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				7B1BFAA81C6E5CD70051C9A4 /* PBXTargetDependency */,
+			);
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+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B1BFA8F1C6E5CD70051C9A4 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B1BFA961C6E5CD70051C9A4 = {
+						CreatedOnToolsVersion = 7.2;
+					};
+					7B1BFAA51C6E5CD70051C9A4 = {
+						CreatedOnToolsVersion = 7.2;
+						TestTargetID = 7B1BFA961C6E5CD70051C9A4;
+					};
+				};
+			};
+			buildConfigurationList = 7B1BFA921C6E5CD70051C9A4 /* Build configuration list for PBXProject "RLE" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
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+			productRefGroup = 7B1BFA981C6E5CD70051C9A4 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B1BFA961C6E5CD70051C9A4 /* RLE */,
+				7B1BFAA51C6E5CD70051C9A4 /* RLETests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B1BFA951C6E5CD70051C9A4 /* Resources */ = {
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+			buildActionMask = 2147483647;
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+				7B1BFA9D1C6E5CD70051C9A4 /* Assets.xcassets in Resources */,
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+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
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+			files = (
+			);
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+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B1BFA931C6E5CD70051C9A4 /* Sources */ = {
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+			buildActionMask = 2147483647;
+			files = (
+				7B1BFA9B1C6E5CD70051C9A4 /* AppDelegate.swift in Sources */,
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+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		7B1BFAA21C6E5CD70051C9A4 /* Sources */ = {
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+			buildActionMask = 2147483647;
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+				7B1BFAAB1C6E5CD70051C9A4 /* RLETests.swift in Sources */,
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+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin PBXTargetDependency section */
+		7B1BFAA81C6E5CD70051C9A4 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			target = 7B1BFA961C6E5CD70051C9A4 /* RLE */;
+			targetProxy = 7B1BFAA71C6E5CD70051C9A4 /* PBXContainerItemProxy */;
+		};
+/* End PBXTargetDependency section */
+
+/* Begin PBXVariantGroup section */
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+			isa = PBXVariantGroup;
+			children = (
+				7B1BFA9F1C6E5CD70051C9A4 /* Base */,
+			);
+			name = MainMenu.xib;
+			sourceTree = "<group>";
+		};
+/* End PBXVariantGroup section */
+
+/* Begin XCBuildConfiguration section */
+		7B1BFAAD1C6E5CD70051C9A4 /* Debug */ = {
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+			buildSettings = {
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+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
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+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
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+			name = Debug;
+		};
+		7B1BFAAE1C6E5CD70051C9A4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
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+				CLANG_ENABLE_OBJC_ARC = YES;
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+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
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+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B1BFAB01C6E5CD70051C9A4 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = RLE/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLE;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		7B1BFAB11C6E5CD70051C9A4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = RLE/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLE;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+		7B1BFAB31C6E5CD70051C9A4 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = RLETests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLETests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/RLE.app/Contents/MacOS/RLE";
+			};
+			name = Debug;
+		};
+		7B1BFAB41C6E5CD70051C9A4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = RLETests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLETests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/RLE.app/Contents/MacOS/RLE";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B1BFA921C6E5CD70051C9A4 /* Build configuration list for PBXProject "RLE" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B1BFAAD1C6E5CD70051C9A4 /* Debug */,
+				7B1BFAAE1C6E5CD70051C9A4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B1BFAAF1C6E5CD70051C9A4 /* Build configuration list for PBXNativeTarget "RLE" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B1BFAB01C6E5CD70051C9A4 /* Debug */,
+				7B1BFAB11C6E5CD70051C9A4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B1BFAB21C6E5CD70051C9A4 /* Build configuration list for PBXNativeTarget "RLETests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B1BFAB31C6E5CD70051C9A4 /* Debug */,
+				7B1BFAB41C6E5CD70051C9A4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B1BFA8F1C6E5CD70051C9A4 /* Project object */;
+}
diff --git a/Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift b/Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift
new file mode 100644
index 000000000..4ae9f8243
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift	
@@ -0,0 +1,27 @@
+//
+//  AppDelegate.swift
+//  RLE
+//
+//  Created by Matthijs Hollemans on 12-02-16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import Cocoa
+
+@NSApplicationMain
+class AppDelegate: NSObject, NSApplicationDelegate {
+
+  @IBOutlet weak var window: NSWindow!
+
+
+  func applicationDidFinishLaunching(aNotification: NSNotification) {
+    // Insert code here to initialize your application
+  }
+
+  func applicationWillTerminate(aNotification: NSNotification) {
+    // Insert code here to tear down your application
+  }
+
+
+}
+
diff --git a/Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json b/Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..2db2b1c7c
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json	
@@ -0,0 +1,58 @@
+{
+  "images" : [
+    {
+      "idiom" : "mac",
+      "size" : "16x16",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "16x16",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "32x32",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "32x32",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "128x128",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "128x128",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "256x256",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "256x256",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "512x512",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "512x512",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib b/Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib
new file mode 100644
index 000000000..6f60cc595
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib	
@@ -0,0 +1,680 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
+    </dependencies>
+    <objects>
+        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
+            <connections>
+                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
+            </connections>
+        </customObject>
+        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
+        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
+        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
+            <connections>
+                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
+            </connections>
+        </customObject>
+        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
+        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
+            <items>
+                <menuItem title="RLE" id="1Xt-HY-uBw">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="RLE" systemMenu="apple" id="uQy-DD-JDr">
+                        <items>
+                            <menuItem title="About RLE" id="5kV-Vb-QxS">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
+                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
+                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
+                            <menuItem title="Services" id="NMo-om-nkz">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
+                            <menuItem title="Hide RLE" keyEquivalent="h" id="Olw-nP-bQN">
+                                <connections>
+                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
+                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                <connections>
+                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Show All" id="Kd2-mp-pUS">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
+                            <menuItem title="Quit RLE" keyEquivalent="q" id="4sb-4s-VLi">
+                                <connections>
+                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="File" id="dMs-cI-mzQ">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="File" id="bib-Uj-vzu">
+                        <items>
+                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
+                                <connections>
+                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
+                                <connections>
+                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Open Recent" id="tXI-mr-wws">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
+                                    <items>
+                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
+                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
+                                <connections>
+                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
+                                <connections>
+                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
+                                <connections>
+                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
+                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
+                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
+                                <connections>
+                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
+                                <connections>
+                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Edit" id="5QF-Oa-p0T">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
+                        <items>
+                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
+                                <connections>
+                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
+                                <connections>
+                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
+                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
+                                <connections>
+                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
+                                <connections>
+                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
+                                <connections>
+                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
+                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                <connections>
+                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Delete" id="pa3-QI-u2k">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
+                                <connections>
+                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
+                            <menuItem title="Find" id="4EN-yA-p0u">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
+                                    <items>
+                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
+                                            <connections>
+                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
+                                    <items>
+                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
+                                            <connections>
+                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
+                                            <connections>
+                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
+                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Substitutions" id="9ic-FL-obx">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
+                                    <items>
+                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
+                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smart Links" id="cwL-P1-jid">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
+                                    <items>
+                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Speech" id="xrE-MZ-jX0">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
+                                    <items>
+                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Format" id="jxT-CU-nIS">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
+                        <items>
+                            <menuItem title="Font" id="Gi5-1S-RQB">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
+                                    <items>
+                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
+                                            <connections>
+                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
+                                            <connections>
+                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
+                                            <connections>
+                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
+                                            <connections>
+                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
+                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
+                                            <connections>
+                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
+                                            <connections>
+                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
+                                        <menuItem title="Kern" id="jBQ-r6-VK2">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
+                                                <items>
+                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use None" id="cDB-IK-hbR">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Tighten" id="46P-cB-AYj">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
+                                                <items>
+                                                    <menuItem title="Use Default" id="agt-UL-0e3">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use None" id="J7y-lM-qPV">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use All" id="xQD-1f-W4t">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
+                                                <items>
+                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Subscript" id="I0S-gh-46l">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Raise" id="2h7-ER-AoG">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Lower" id="1tx-W0-xDw">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
+                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
+                                            <connections>
+                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
+                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="pasteFont:" target="-1" id="JfD-CL-leO"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Text" id="Fal-I4-PZk">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Text" id="d9c-me-L2H">
+                                    <items>
+                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
+                                            <connections>
+                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
+                                            <connections>
+                                                <action selector="alignCenter:" target="-1" id="spX-mk-kcS"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Justify" id="J5U-5w-g23">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="alignJustified:" target="-1" id="ljL-7U-jND"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
+                                            <connections>
+                                                <action selector="alignRight:" target="-1" id="r48-bG-YeY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
+                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
+                                                <items>
+                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                    </menuItem>
+                                                    <menuItem id="YGs-j5-SAR">
+                                                        <string key="title">	Default</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="Lbh-J2-qVU">
+                                                        <string key="title">	Left to Right</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="jFq-tB-4Kx">
+                                                        <string key="title">	Right to Left</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
+                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                    </menuItem>
+                                                    <menuItem id="Nop-cj-93Q">
+                                                        <string key="title">	Default</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeTextWritingDirectionNatural:" target="-1" id="lPI-Se-ZHp"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="BgM-ve-c93">
+                                                        <string key="title">	Left to Right</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeTextWritingDirectionLeftToRight:" target="-1" id="caW-Bv-w94"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="RB4-Sm-HuC">
+                                                        <string key="title">	Right to Left</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeTextWritingDirectionRightToLeft:" target="-1" id="EXD-6r-ZUu"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="fKy-g9-1gm"/>
+                                        <menuItem title="Show Ruler" id="vLm-3I-IUL">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleRuler:" target="-1" id="FOx-HJ-KwY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Copy Ruler" keyEquivalent="c" id="MkV-Pr-PK5">
+                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="copyRuler:" target="-1" id="71i-fW-3W2"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Paste Ruler" keyEquivalent="v" id="LVM-kO-fVI">
+                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="pasteRuler:" target="-1" id="cSh-wd-qM2"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="View" id="H8h-7b-M4v">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="View" id="HyV-fh-RgO">
+                        <items>
+                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
+                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                <connections>
+                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="runToolbarCustomizationPalette:" target="-1" id="pQI-g3-MTW"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Window" id="aUF-d1-5bR">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
+                        <items>
+                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
+                                <connections>
+                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Zoom" id="R4o-n2-Eq4">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
+                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Help" id="wpr-3q-Mcd">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
+                        <items>
+                            <menuItem title="RLE Help" keyEquivalent="?" id="FKE-Sm-Kum">
+                                <connections>
+                                    <action selector="showHelp:" target="-1" id="y7X-2Q-9no"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+            </items>
+        </menu>
+        <window title="RLE" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" releasedWhenClosed="NO" animationBehavior="default" id="QvC-M9-y7g">
+            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
+            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
+            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
+            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
+            <view key="contentView" id="EiT-Mj-1SZ">
+                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
+                <autoresizingMask key="autoresizingMask"/>
+            </view>
+        </window>
+    </objects>
+</document>
diff --git a/Run-Length Encoding/RLE Tests/RLE/Info.plist b/Run-Length Encoding/RLE Tests/RLE/Info.plist
new file mode 100644
index 000000000..0dca3caa8
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLE/Info.plist	
@@ -0,0 +1,34 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIconFile</key>
+	<string></string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSMinimumSystemVersion</key>
+	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
+	<key>NSHumanReadableCopyright</key>
+	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
+	<key>NSMainNibFile</key>
+	<string>MainMenu</string>
+	<key>NSPrincipalClass</key>
+	<string>NSApplication</string>
+</dict>
+</plist>
diff --git a/Run-Length Encoding/RLE Tests/RLE/RLE.swift b/Run-Length Encoding/RLE Tests/RLE/RLE.swift
new file mode 100644
index 000000000..f26299cf1
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLE/RLE.swift	
@@ -0,0 +1,70 @@
+import Foundation
+
+extension NSData {
+  /*
+    Compresses the NSData using run-length encoding.
+  */
+  public func compressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+      
+      while ptr < end {
+        var count = 0
+        var byte = ptr.memory
+        var next = byte
+        
+        // Is the next byte the same? Keep reading until we find a different
+        // value, or we reach the end of the data, or the run is 64 bytes.
+        while next == byte && ptr < end && count < 64 {
+          ptr = ptr.advancedBy(1)
+          next = ptr.memory
+          count += 1
+        }
+
+        if count > 1 || byte >= 192 {         // byte run of up to 64 repeats
+          var size = 191 + UInt8(count)
+          data.appendBytes(&size, length: 1)
+          data.appendBytes(&byte, length: 1)
+        } else {                              // single byte between 0 and 192
+          data.appendBytes(&byte, length: 1)
+        }
+      }
+    }
+    return data
+  }
+  
+  /*
+    Converts a run-length encoded NSData back to the original.
+  */
+  public func decompressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+
+      while ptr < end {
+        // Read the next byte. This is either a single value less than 192, 
+        // or the start of a byte run.
+        var byte = ptr.memory
+        ptr = ptr.advancedBy(1)
+        
+        if byte < 192 {                       // single value
+          data.appendBytes(&byte, length: 1)
+
+        } else if ptr < end {                 // byte run
+          // Read the actual data value.
+          var value = ptr.memory
+          ptr = ptr.advancedBy(1)
+
+          // And write it out repeatedly.
+          for _ in 0 ..< byte - 191 {
+            data.appendBytes(&value, length: 1)
+          }
+        }
+      }
+    }
+    return data
+  }
+}
diff --git a/Run-Length Encoding/RLE Tests/RLETests/Info.plist b/Run-Length Encoding/RLE Tests/RLETests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLETests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Run-Length Encoding/RLE Tests/RLETests/RLETests.swift b/Run-Length Encoding/RLE Tests/RLETests/RLETests.swift
new file mode 100644
index 000000000..99616a8c2
--- /dev/null
+++ b/Run-Length Encoding/RLE Tests/RLETests/RLETests.swift	
@@ -0,0 +1,111 @@
+import XCTest
+@testable import RLE
+
+class RLETests: XCTestCase {
+  private var showExtraOutput = false
+
+  private func dumpData(data: NSData) {
+    if showExtraOutput {
+      var ptr = UnsafePointer<UInt8>(data.bytes)
+      for _ in 0..<data.length {
+        print(String(format: "%02x", ptr.memory))
+        ptr = ptr.advancedBy(1)
+      }
+    }
+  }
+
+  private func encodeAndDecode(bytes: [UInt8]) {
+    var bytes = bytes
+
+    let data1 = NSMutableData(bytes: &bytes, length: bytes.count)
+    print("data1 is \(data1.length) bytes")
+    dumpData(data1)
+
+    let rleData = data1.compressRLE()
+    print("encoded data is \(rleData.length) bytes")
+    dumpData(rleData)
+
+    let data2 = rleData.decompressRLE()
+    print("data2 is \(data2.length) bytes")
+    dumpData(data2)
+
+    XCTAssertEqual(data1, data2)
+    print("")
+  }
+
+  func testEmpty() {
+    let bytes: [UInt8] = []
+    encodeAndDecode(bytes)
+  }
+  
+  func testOneByteWithLowValue() {
+    let bytes: [UInt8] = [ 0x80 ]
+    encodeAndDecode(bytes)
+  }
+  
+  func testOneByteWithHighValue() {
+    let bytes: [UInt8] = [ 0xD0 ]
+    encodeAndDecode(bytes)
+  }
+  
+  func testSimpleCases() {
+    let bytes: [UInt8] = [
+      0x00,
+      0x20, 0x20, 0x20, 0x20, 0x20,
+      0x30,
+      0x00, 0x00,
+      0xC0,
+      0xC1,
+      0xC0, 0xC0, 0xC0,
+      0xFF, 0xFF, 0xFF, 0xFF
+    ]
+    encodeAndDecode(bytes)
+  }
+
+  func testBufferWithoutSpans() {
+    // There is nothing that can be encoded in this buffer, so the encoded
+    // data ends up being longer.
+
+    var bytes: [UInt8] = []
+    for i in 0..<1024 {
+      bytes.append(UInt8(i % 256))
+    }
+    encodeAndDecode(bytes)
+  }
+
+  func bufferWithSpans(spanSize: Int) {
+    if showExtraOutput {
+      print("span size \(spanSize)")
+    }
+
+    let length = spanSize * 32
+    var bytes: [UInt8] = .init(count: length, repeatedValue: 0)
+
+    for t in 0.stride(to: length, by: spanSize) {
+      for i in 0..<spanSize {
+        bytes[t + i] = UInt8(t % 256)
+      }
+    }
+    encodeAndDecode(bytes)
+  }
+
+  func testBufferWithSpans() {
+    bufferWithSpans(4)
+    bufferWithSpans(63)
+    bufferWithSpans(64)
+    bufferWithSpans(65)
+    bufferWithSpans(66)
+    bufferWithSpans(80)
+  }
+  
+  func testRandomBytes() {
+    for _ in 0..<10 {
+      let length = 1 + Int(arc4random_uniform(2048))
+      var bytes: [UInt8] = []
+      for _ in 0..<length {
+        bytes.append(UInt8(arc4random() % 256))
+      }
+      encodeAndDecode(bytes)
+    }
+  }
+}
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
new file mode 100644
index 000000000..b79cdf9e6
--- /dev/null
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -0,0 +1,82 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+extension NSData {
+  /*
+    Compresses the NSData using run-length encoding.
+  */
+  public func compressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+      
+      while ptr < end {
+        var count = 0
+        var byte = ptr.memory
+        var next = byte
+        
+        // Is the next byte the same? Keep reading until we find a different
+        // value, or we reach the end of the data, or the run is 64 bytes.
+        while next == byte && ptr < end && count < 64 {
+          ptr = ptr.advancedBy(1)
+          next = ptr.memory
+          count += 1
+        }
+
+        if count > 1 || byte >= 192 {         // byte run of up to 64 repeats
+          var size = 191 + UInt8(count)
+          data.appendBytes(&size, length: 1)
+          data.appendBytes(&byte, length: 1)
+        } else {                              // single byte between 0 and 192
+          data.appendBytes(&byte, length: 1)
+        }
+      }
+    }
+    return data
+  }
+  
+  /*
+    Converts a run-length encoded NSData back to the original.
+  */
+  public func decompressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+
+      while ptr < end {
+        // Read the next byte. This is either a single value less than 192, 
+        // or the start of a byte run.
+        var byte = ptr.memory
+        ptr = ptr.advancedBy(1)
+        
+        if byte < 192 {                       // single value
+          data.appendBytes(&byte, length: 1)
+
+        } else if ptr < end {                 // byte run
+          // Read the actual data value.
+          var value = ptr.memory
+          ptr = ptr.advancedBy(1)
+
+          // And write it out repeatedly.
+          for _ in 0 ..< byte - 191 {
+            data.appendBytes(&value, length: 1)
+          }
+        }
+      }
+    }
+    return data
+  }
+}
+
+
+
+let originalString = "aaaaabbbcdeeeeeeef"
+let utf8 = originalString.dataUsingEncoding(NSUTF8StringEncoding)!
+let compressed = utf8.compressRLE()
+
+let decompressed = compressed.decompressRLE()
+let restoredString = String(data: decompressed, encoding: NSUTF8StringEncoding)
+originalString == restoredString
diff --git a/Run-Length Encoding/RLE.playground/contents.xcplayground b/Run-Length Encoding/RLE.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Run-Length Encoding/RLE.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Run-Length Encoding/RLE.playground/timeline.xctimeline b/Run-Length Encoding/RLE.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Run-Length Encoding/RLE.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Run-Length Encoding/RLE.swift b/Run-Length Encoding/RLE.swift
new file mode 100644
index 000000000..ee25af997
--- /dev/null
+++ b/Run-Length Encoding/RLE.swift	
@@ -0,0 +1,60 @@
+import Foundation
+
+extension NSData {
+  /*
+    Helper method that reads the next run of bytes. Returns the size of the
+    run (between 1 and 64), the byte value, and the updated read pointer.
+  */
+  private func readRun(start start: UnsafePointer<UInt8>, end: UnsafePointer<UInt8>) -> (Int, UInt8, UnsafePointer<UInt8>) {
+    var ptr = start
+    var count = 0
+
+    // Read the current byte.
+    let previous = ptr.memory
+    var current = previous
+
+    // Is the next byte the same? Then keep reading until we find another
+    // byte, or we reach the end of the data, or the run is 64 bytes.
+    while current == previous && ptr < end && count < 64 {
+      ptr = ptr.advancedBy(1)
+      current = ptr.memory
+      count += 1
+    }
+    
+    return (count, previous, ptr)
+  }
+
+  /*
+    Compresses the NSData using run-length encoding.
+  */
+  public func compressRLE() -> NSData {
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+      
+      while ptr < end {
+        var (count, byte, out) = readRun(start: ptr, end: end)
+
+        if count == 0 {                        // end-of-file
+          out = end
+        } else if count > 1 || byte >= 192 {   // byte run, up to 64 repeats
+          var pair: [UInt8] = [191 + UInt8(count), byte]
+          data.appendBytes(&pair, length: 2)
+        } else {                               // single byte between 0 and 192
+          data.appendBytes(&byte, length: 1)
+        }
+        ptr = out
+      }
+    }
+    return data
+  }
+  
+
+  /*
+    Converts a run-length encoded NSData back to the original.
+  */
+  public func decompressRLE() -> NSData {
+    return NSData()
+  }
+}

From 0cfd81d52c09aa01def16a835f3617ad0645f514 Mon Sep 17 00:00:00 2001
From: Artur Antonov <artu-antonov@yandex.ru>
Date: Sat, 13 Feb 2016 00:10:22 +0300
Subject: [PATCH 0016/1679] Fix images with union

---
 Union-Find/Images/AfterUnion.png  | Bin 26331 -> 26672 bytes
 Union-Find/Images/BeforeUnion.png | Bin 22581 -> 22881 bytes
 Union-Find/README.markdown        |   6 +++---
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Union-Find/Images/AfterUnion.png b/Union-Find/Images/AfterUnion.png
index aa75eefd882b0945d694acda6dadfdd11649a04c..10c1f2d7eacdd8c650ea908a24dfa74b8fa602b6 100644
GIT binary patch
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diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index a0d80dd1a..0ea8907e2 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -67,7 +67,7 @@ public mutating func setOf(element: T) -> Int? {
 
 1. First, we check if current index represent a node that is root. That means we find number that represent the set of element we search for.
 
-2. Otherwise we recursively call our method on parent of current node. And then we do **very important thing**: we cache index of root node, so when we call this method again it will executed faster because of cached indexes. Without that optimization method's complexity is **O(n)** but now in combination with the size optimization (we'll look at that in Union section) it is almost **O(1)**.
+2. Otherwise we recursively call our method on parent of current node. And then we do **very important thing**: we cache index of root node, so when we call this method again it will executed faster because of cached indexes. Without that optimization method's complexity is **O(n)** but now in combination with the size optimization (I'll cover that in Union section) it is almost **O(1)**.
 
 3. We return our cached root as result.
 
@@ -116,7 +116,7 @@ Union with optimizations also takes almost **O(1)** time.
 
 As always, some illustrations for better understanding
 
-Before calling `unionSetsContaining(4, and: 7)`:
+Before calling `unionSetsContaining(4, and: 3)`:
 
 ![BeforeUnion](Images/BeforeUnion.png)
 
@@ -128,7 +128,7 @@ Note that during union caching optimization was performed because of calling `se
 
 
 
-There are also helper method to just check that two elements is in the same set:
+There is also helper method to just check that two elements is in the same set:
 
 ```swift
 public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {

From 3b1b11c59c8dfcf5231fb842c61bc249de7b927e Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 13 Feb 2016 14:14:37 +0100
Subject: [PATCH 0017/1679] Add the Monty Hall problem

---
 .../MontyHall.playground/Contents.swift       | 53 +++++++++++++
 .../contents.xcplayground                     |  4 +
 .../MontyHall.playground/timeline.xctimeline  |  6 ++
 Monty Hall Problem/README.markdown            | 74 +++++++++++++++++++
 README.markdown                               |  1 +
 5 files changed, 138 insertions(+)
 create mode 100644 Monty Hall Problem/MontyHall.playground/Contents.swift
 create mode 100644 Monty Hall Problem/MontyHall.playground/contents.xcplayground
 create mode 100644 Monty Hall Problem/MontyHall.playground/timeline.xctimeline
 create mode 100644 Monty Hall Problem/README.markdown

diff --git a/Monty Hall Problem/MontyHall.playground/Contents.swift b/Monty Hall Problem/MontyHall.playground/Contents.swift
new file mode 100644
index 000000000..930dad714
--- /dev/null
+++ b/Monty Hall Problem/MontyHall.playground/Contents.swift	
@@ -0,0 +1,53 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+func random(n: Int) -> Int {
+  return Int(arc4random_uniform(UInt32(n)))
+}
+
+let numberOfDoors = 3
+
+var rounds = 0
+var winOriginalChoice = 0
+var winChangedMind = 0
+
+func playRound() {
+  // The door with the prize.
+  let prizeDoor = random(numberOfDoors)
+
+  // The door the player chooses.
+  let chooseDoor = random(numberOfDoors)
+
+  // The door that Monty opens. This must be empty and not the one the player chose.
+  var openDoor = -1
+  repeat {
+    openDoor = random(numberOfDoors)
+  } while openDoor == prizeDoor || openDoor == chooseDoor
+
+  // What happens when the player changes his mind and picks the other door.
+  var changeMind = -1
+  repeat {
+    changeMind = random(numberOfDoors)
+  } while changeMind == openDoor || changeMind == chooseDoor
+
+  // Figure out which choice was the winner.
+  if chooseDoor == prizeDoor {
+    winOriginalChoice += 1
+  }
+  if changeMind == prizeDoor {
+    winChangedMind += 1
+  }
+
+  rounds += 1
+}
+
+// Run the simulation a large number of times.
+for i in 1...5000 {
+  playRound()
+}
+
+let stubbornPct = Double(winOriginalChoice)/Double(rounds)
+let changedMindPct = Double(winChangedMind)/Double(rounds)
+
+print(String(format: "Played %d rounds, stubborn: %g%% vs changed mind: %g%%", rounds, stubbornPct, changedMindPct))
diff --git a/Monty Hall Problem/MontyHall.playground/contents.xcplayground b/Monty Hall Problem/MontyHall.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Monty Hall Problem/MontyHall.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Monty Hall Problem/MontyHall.playground/timeline.xctimeline b/Monty Hall Problem/MontyHall.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Monty Hall Problem/MontyHall.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Monty Hall Problem/README.markdown b/Monty Hall Problem/README.markdown
new file mode 100644
index 000000000..701299d63
--- /dev/null
+++ b/Monty Hall Problem/README.markdown	
@@ -0,0 +1,74 @@
+# The Monty Hall Problem
+
+Congrats! You've reached the final round of the popular [Monty Hall game show](https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal). Monty, the show host, gives you the choice between 3 doors. Behind one of the doors is a prize (a new car? a trip to Hawaii? a microwave oven?), the other two are empty.
+
+After you make your choice, Monty decides to make things a bit more interesting and opens one of the two doors that you didn't pick. Of course, the one he opens is empty. There are now two doors left, behind one of which is the coveted prize.
+
+Now Monty gives you the opportunity to change your mind. Should you stick with your original choice, should you pick the other door, or doesn't it matter?
+
+You'd think that changing your answer wouldn't improve your chances... but it does!
+
+This is a very nonintuitive result. Maybe you have trouble believing this is true. Don't worry, when this problem was first proposed many mathematicians didn't believe it either, so you're in good company.
+
+There's a simple way to verify this claim: we can write a program to test it out! We should be able to show who wins more often by playing the game a large number of times.
+
+Here's the code (see the [playground](MontyHall.playground/Contents.swift) for the full thing). First, we randomly choose the door that has the prize:
+
+```swift
+  let prizeDoor = random(3)
+```
+
+We also randomly pick the choice of the player:
+
+```swift
+  let chooseDoor = random(3)
+```
+
+Next, Monty opens one of the empty doors. Obviously, he won't choose the door that the player chose or the one with the prize.
+
+```swift
+  var openDoor = -1
+  repeat {
+    openDoor = random(numberOfDoors)
+  } while openDoor == prizeDoor || openDoor == chooseDoor
+```  
+
+There are only two closed doors left, one of which has the prize. What happens when the player changes his mind and picks the other door?
+
+```swift
+  var changeMind = -1
+  repeat {
+    changeMind = random(3)
+  } while changeMind == openDoor || changeMind == chooseDoor
+```
+
+Now we see which choice was the right one:
+
+```swift
+  if chooseDoor == prizeDoor {
+    winOriginalChoice += 1
+  }
+  if changeMind == prizeDoor {
+    winChangedMind += 1
+  }
+```
+
+If the prize is behind the player's original door choice, we increment `winOriginalChoice`. If the prize is behind the other door, then the player would have won if he changed his mind, and so we increment `winChangedMind`.
+
+And that's all there is to it.
+
+If you run the above code 1000 times or so, you'll find that the probability of choosing the prize without changing your mind is about 33%. But if you *do* change your mind, the probability of winning is 67% -- that is twice as large!
+
+Try it out in the playground if you still don't believe it. ;-)
+
+Here's why: When you first make a choice, your chances of picking the prize are 1 out of 3, or 33%
+
+After Monty opens one of the doors, this gives you new information. However, it doesn't change the probability of your original choice being the winner. That chance remains 33% because you made that choice when you didn't know yet what was behind this open door.
+
+Since probabilities always need to add up to 100%, the chance that the prize is behind the other door is now 100 - 33 = 67%. So, as strange as it may sound, you're better of switching doors!
+
+This is hard to wrap your head around, but easily shown using a simulation that runs a significant number of times. Probability is weird.
+
+[Monty Hall Problem on Wikipedia](https://en.wikipedia.org/wiki/Monty_Hall_problem)
+
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/README.markdown b/README.markdown
index eb2bda765..5eba20eb5 100644
--- a/README.markdown
+++ b/README.markdown
@@ -169,6 +169,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 
 - [Two-Sum Problem](Two-Sum Problem/)
 - [Fizz Buzz](Fizz Buzz/)
+- [Monty Hall Problem](Monty Hall Problem/)
 
 ## Learn more!
 

From a424764784a35fd5880a320098ebc2706ef17b71 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 13 Feb 2016 14:15:39 +0100
Subject: [PATCH 0018/1679] Small readme fix

---
 Monty Hall Problem/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Monty Hall Problem/README.markdown b/Monty Hall Problem/README.markdown
index 701299d63..f227a9b29 100644
--- a/Monty Hall Problem/README.markdown	
+++ b/Monty Hall Problem/README.markdown	
@@ -29,7 +29,7 @@ Next, Monty opens one of the empty doors. Obviously, he won't choose the door th
 ```swift
   var openDoor = -1
   repeat {
-    openDoor = random(numberOfDoors)
+    openDoor = random(3)
   } while openDoor == prizeDoor || openDoor == chooseDoor
 ```  
 

From d9313352c34b456ac02f230c8af6b4b55098123e Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 13 Feb 2016 15:41:48 +0100
Subject: [PATCH 0019/1679] Tweaks to union-find

---
 README.markdown                               |   2 +-
 Union-Find/README.markdown                    | 177 +++++++++++-------
 .../Contents.swift                            |   6 +-
 .../contents.xcplayground                     |   0
 .../timeline.xctimeline                       |   0
 Union-Find/UnionFind.swift                    |   7 +-
 6 files changed, 116 insertions(+), 76 deletions(-)
 rename Union-Find/{UnioinFind.playground => UnionFind.playground}/Contents.swift (98%)
 rename Union-Find/{UnioinFind.playground => UnionFind.playground}/contents.xcplayground (100%)
 rename Union-Find/{UnioinFind.playground => UnionFind.playground}/timeline.xctimeline (100%)

diff --git a/README.markdown b/README.markdown
index 5eba20eb5..a81f8a7ce 100644
--- a/README.markdown
+++ b/README.markdown
@@ -43,7 +43,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
 - [k-th Largest Element](Kth Largest Element/). Find the *k*th largest element in an array, such as the median.
 - [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
-- Union-Find
+- [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
 
 ### String Search
 
diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 0ea8907e2..66937cf69 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -1,59 +1,88 @@
-# Union-Find data structure
+# Union-Find
 
-Union-Find data structure (also known as disjoint-set data structure) is data structure that can keep track of a set of elements partitioned into a number of disjoint (non-overlapping) subsets. It supports three basic operations:
-  1. Find(**A**): Determine which subset an element **A** is in
-  2. Union(**A**, **B**): Join two subsets that contain **A** and **B** into a single subset
-  3. AddSet(**A**): Add a new subset containing just that element **A**
+Union-Find is a data structure that can keep track of a set of elements partitioned into a number of disjoint (non-overlapping) subsets. It is also known as disjoint-set data structure.
 
-The most common application of this data structure is keeping track of the connected components of an undirected graph. It is also used for implementing efficient version of Kruskal's algorithm to find the minimum spanning tree of a graph.
+What do we mean by this? For example, the Union-Find data structure could be keeping track of the following sets:
+
+	[ a, b, f, k ]
+	[ e ]
+	[ g, d, c ]
+	[ i, j ]
+
+These sets are disjoint because they have no members in common. 
+
+Union-Find supports three basic operations:
+
+1. **Find(A)**: Determine which subset an element **A** is in. For example, `find(d)` would return the subset `[ g, d, c ]`.
+
+2. **Union(A, B)**: Join two subsets that contain **A** and **B** into a single subset. For example, `union(d, j)` would combine `[ g, d, c ]` and `[ i, j ]` into the larger set `[ g, d, c, i, j ]`.
+
+3. **AddSet(A)**: Add a new subset containing just that element **A**. For example, `addSet(h)` would add a new set `[ h ]`.
+
+The most common application of this data structure is keeping track of the connected components of an undirected [graph](../Graph/). It is also used for implementing an efficient version of Kruskal's algorithm to find the minimum spanning tree of a graph.
 
 ## Implementation
 
 Union-Find can be implemented in many ways but we'll look at the most efficient.
 
-Every Union-Find data structure is just value of type `UnionFind`
-
 ```swift
 public struct UnionFind<T: Hashable> {
-  private var index = [T:Int]()
+  private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
 }
 ```
 
-Our Union-Find data structure is actually a forest where each subset represented by a [tree](../Tree/). For our purposes we only need to keep parent of each node. To do this we use array `parent` where `parent[i]` is index of parent of node with number **i**. In a that forest, the unique number of each subset is the index of value of root of that subset's tree.
+Our Union-Find data structure is actually a forest where each subset is represented by a [tree](../Tree/).
+
+For our purposes we only need to keep track of the parent of each tree node, not the node's children. To do this we use the array `parent` so that `parent[i]` is the index of node `i`'s parent.
 
-So let's look at the implementation of basic operations:
+Example: If `parent` looks like this,
 
-### Add set
+	parent [ 1, 1, 1, 0, 2, 0, 6, 6, 6 ]
+	     i   0  1  2  3  4  5  6  7  8
+	
+then the tree structure looks like:
+	
+	      1              6
+	    /   \           / \
+	  0       2        7   8
+	 / \     /
+	3   5   4
+
+There are two trees in this forest, each of which corresponds to one set of elements. (Note: due to the limitations of ASCII art the trees are shown here as binary trees but that is not necessarily the case.)
+
+We give each subset a unique number to identify it. That number is the index of  the root node of that subset's tree. In the example, node `1` is the root of the first tree and `6` is the root of the second tree.
+
+Note that the `parent[]` of a root node points to itself. So `parent[1] = 1` and `parent[6] = 6`. That's how we can tell something is a root node.
+
+So in this example we have two subsets, the first with the label `1` and the second with the label `6`. The **Find** operation actually returns the set's label, not its contents.
+
+## Add set
+
+Let's look at the implementation of these basic operations, starting with adding a new set.
 
 ```swift
 public mutating func addSetWith(element: T) {
   index[element] = parent.count  // 1
-  parent.append(parent.count)  //2
-  size.append(1)  // 3
+  parent.append(parent.count)    // 2
+  size.append(1)                 // 3
 }
 ```
 
-1. We save index of new element in `index` dictionary because we need `parent` array only containing values in range 0..<parent.count.
+When you add a new element, this actually adds a new subset containing just that element.
 
-2. Then we add that index to `parent` array. It's pointing itself because the tree that represent new set containing only one node which obviously is a root of that tree.
+1. We save the index of the new element in the `index` dictionary. That lets us look up the element quickly later on.
 
-3. `size[i]` is a count of nodes in tree which root is node with number `i` We'll be using that in Union method.
+2. Then we add that index to the `parent` array to build a new tree for this  set. Here, `parent[i]` is pointing to itself because the tree that represents the new set contains only one node, which of course is the root of that tree.
 
+3. `size[i]` is the count of nodes in the tree whose root is at index `i`. For the new set this is 1 because it only contains the one element. We'll be using the `size` array in the Union operation.
 
-### Find
+## Find
 
-```swift
-private mutating func setByIndex(index: Int) -> Int {
-  if parent[index] == index {  // 1
-    return index
-  } else {
-    parent[index] = setByIndex(parent[index])  // 2
-    return parent[index]  // 3
-  }
-}
+Often we want to determine whether we already have a set that contains a given element. That's what the **Find** operation does. In our `UnionFind` data structure it is called `setOf()`:
 
+```swift
 public mutating func setOf(element: T) -> Int? {
   if let indexOfElement = index[element] {
     return setByIndex(indexOfElement)
@@ -63,36 +92,66 @@ public mutating func setOf(element: T) -> Int? {
 }
 ```
 
-`setOf(element: T)` is a helper method to get index corresponding to `element` and if it exists we return value of actual method `setByIndex(index: Int)`
+This looks up the element's index in the `index` dictionary and then uses a helper method to find the set that this element belongs to:
+
+```swift
+private mutating func setByIndex(index: Int) -> Int {
+  if parent[index] == index {  // 1
+    return index
+  } else {
+    parent[index] = setByIndex(parent[index])  // 2
+    return parent[index]       // 3
+  }
+}
+```
+
+Because we're dealing with a tree structure, this is a recursive method.
 
-1. First, we check if current index represent a node that is root. That means we find number that represent the set of element we search for.
+Recall that each set is represented by a tree and that the index of the root node serves as the number that identifies the set. We're going to find the root node of the tree that the element we're searching for belongs to, and return its index.
 
-2. Otherwise we recursively call our method on parent of current node. And then we do **very important thing**: we cache index of root node, so when we call this method again it will executed faster because of cached indexes. Without that optimization method's complexity is **O(n)** but now in combination with the size optimization (I'll cover that in Union section) it is almost **O(1)**.
+1. First, we check if the given index represents a root node (i.e. a node whose `parent` points back to the node itself). If so, we're done. 
 
-3. We return our cached root as result.
+2. Otherwise we recursively call this method on the parent of the current node. And then we do a **very important thing**: we overwrite the parent of the current node with the index of root node, in effect reconnecting the node directly to the root of the tree. The next time we call this method, it will execute faster because the path to the root of the tree is now much shorter. Without that optimization, this method's complexity is **O(n)** but now in combination with the size optimization (covered in the Union section) it is almost **O(1)**.
 
-Here's illustration of what I mean
+3. We return the index of the root node as the result.
 
-Before first call `setOf(4)`:
+Here's illustration of what I mean. Let's say the tree looks like this:
 
 ![BeforeFind](Images/BeforeFind.png)
 
-After:
+We call `setOf(4)`. To find the root node we have to first go to node `2` and then to node `7`. (The indexes of the elements are marked in red.)
+
+During the call to `setOf(4)`, the tree is reorganized to look like this:
 
 ![AfterFind](Images/AfterFind.png)
 
-Indexes of elements are marked in red.
+Now if we need to call `setOf(4)` again, we no longer have to go through node `2` to get to the root. So as you use the Union-Find data structure, it optimizes itself. Pretty cool!
 
+There is also a helper method to check that two elements are in the same set:
 
-### Union
+```swift
+public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
+  if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+    return firstSet == secondSet
+  } else {
+    return false
+  }
+}
+```
+
+Since this calls `setOf()` it also optimizes the tree.
+
+## Union
+
+The final operation is **Union**, which combines two sets into one larger set.
 
 ```swift
 public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
   if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {  // 1
-    if firstSet != secondSet {  // 2
+    if firstSet != secondSet {               // 2
       if size[firstSet] < size[secondSet] {  // 3
-        parent[firstSet] = secondSet  // 4
-        size[secondSet] += size[firstSet]  // 5
+        parent[firstSet] = secondSet         // 4
+        size[secondSet] += size[firstSet]    // 5
       } else {
         parent[secondSet] = firstSet
         size[firstSet] += size[secondSet]
@@ -102,50 +161,34 @@ public mutating func unionSetsContaining(firstElement: T, and secondElement: T)
 }
 ```
 
-1. We find sets of each element.
+Here is how it works:
 
-2. Check that sets are not equal because if they are it makes no sense to union them.
+1. We find the sets that each element belongs to. Remember that this gives us two integers: the indices of the root nodes in the `parent` array.
 
-3. This is where our size optimization comes in. We want to keep trees as small as possible so we always attach the smaller tree to the root of the larger tree. To determine small tree we compare trees by its sizes.
+2. Check that the sets are not equal because if they are it makes no sense to union them.
 
-4. Here we attach the smaller tree to the root of the larger tree.
-
-5. We keep sizes of trees in actual states so we update size of larger tree.
+3. This is where the size optimization comes in. We want to keep the trees as shallow as possible so we always attach the smaller tree to the root of the larger tree. To determine which is the smaller tree we compare trees by their sizes.
 
-Union with optimizations also takes almost **O(1)** time.
+4. Here we attach the smaller tree to the root of the larger tree.
 
-As always, some illustrations for better understanding
+5. Update the size of larger tree because it just had a bunch of nodes added to it.
 
-Before calling `unionSetsContaining(4, and: 3)`:
+An illustration may help to better understand this. Let's say we have these two sets, each with its own tree:
 
 ![BeforeUnion](Images/BeforeUnion.png)
 
-After:
+Now we call `unionSetsContaining(4, and: 3)`. The smaller tree is attached to the larger one:
 
 ![AfterUnion](Images/AfterUnion.png)
 
-Note that during union caching optimization was performed because of calling `setOf` in the beginning of method.
+Note that, because we call `setOf()` in the beginning of the method, the larger tree was also optimized in the process -- node `3` now hangs directly off the root.
 
+Union with optimizations also takes almost **O(1)** time.
 
-
-There is also helper method to just check that two elements is in the same set:
-
-```swift
-public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
-  if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
-    return firstSet == secondSet
-  } else {
-    return false
-  }
-}
-```
-
+## See also
 
 See the playground for more examples of how to use this handy data structure.
 
-
-## See also
-
-[Union-Find at wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
+[Union-Find at Wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*
diff --git a/Union-Find/UnioinFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
similarity index 98%
rename from Union-Find/UnioinFind.playground/Contents.swift
rename to Union-Find/UnionFind.playground/Contents.swift
index fe53241b9..dd57514cd 100644
--- a/Union-Find/UnioinFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,12 +1,10 @@
 //: Playground - noun: a place where people can play
 
 public struct UnionFind<T: Hashable> {
-  
-  private var index = [T:Int]()
+  private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
   
-  
   public mutating func addSetWith(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
@@ -54,6 +52,8 @@ public struct UnionFind<T: Hashable> {
 }
 
 
+
+
 var dsu = UnionFind<Int>()
 
 for i in 1...10 {
diff --git a/Union-Find/UnioinFind.playground/contents.xcplayground b/Union-Find/UnionFind.playground/contents.xcplayground
similarity index 100%
rename from Union-Find/UnioinFind.playground/contents.xcplayground
rename to Union-Find/UnionFind.playground/contents.xcplayground
diff --git a/Union-Find/UnioinFind.playground/timeline.xctimeline b/Union-Find/UnionFind.playground/timeline.xctimeline
similarity index 100%
rename from Union-Find/UnioinFind.playground/timeline.xctimeline
rename to Union-Find/UnionFind.playground/timeline.xctimeline
diff --git a/Union-Find/UnionFind.swift b/Union-Find/UnionFind.swift
index 88583cb9a..f1500e6c9 100644
--- a/Union-Find/UnionFind.swift
+++ b/Union-Find/UnionFind.swift
@@ -7,14 +7,11 @@
     union sets is almost O(1)
 */
 
-
 public struct UnionFind<T: Hashable> {
-  
-  private var index = [T:Int]()
+  private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
   
-  
   public mutating func addSetWith(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
@@ -51,7 +48,7 @@ public struct UnionFind<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
       return firstSet == secondSet

From ef637c843fd296919153e7e9bcbda11005825f7c Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 15 Feb 2016 21:47:20 +1300
Subject: [PATCH 0020/1679] BFS. Manually stepping through animated example.
 Removed Queue and Graph from readme.

---
 .../Contents.swift                            |  51 +++----
 Breadth-First Search/README.markdown          | 138 ++++++------------
 2 files changed, 59 insertions(+), 130 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
index a6318d8c9..a9fabb1c9 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -32,58 +32,43 @@ class Edge {
   }
 }
 
-class Queue<T> {
-  private var top: QueueNode<T>!
+struct Queue<T> {
+  var array = [T]()
 
-  func enqueue(item: T) {
-    if (top == nil) {
-      top = QueueNode<T>()
-    }
-
-    if (top.item == nil) {
-      top.item = item;
-      return
-    }
+  var isEmpty: Bool {
+    return array.isEmpty
+  }
 
-    let childToUse = QueueNode<T>()
-    var current: QueueNode = top
-    while current.next != nil {
-      current = current.next!
-    }
+  var count: Int {
+    return array.count
+  }
 
-    childToUse.item = item;
-    current.next = childToUse;
+  mutating func enqueue(element: T) {
+    array.append(element)
   }
 
-  func dequeue() -> QueueNode<T>? {
-    guard !isEmpty else {
+  mutating func dequeue() -> T? {
+    if isEmpty {
       return nil
+    } else {
+      return array.removeFirst()
     }
-
-    let itemToDequeue = top
-    top = itemToDequeue.next
-    return itemToDequeue
   }
 
-  var isEmpty: Bool {
-    get { return top == nil }
+  func peek() -> T? {
+    return array.first
   }
 }
 
-class QueueNode<T> {
-  var item: T?
-  var next: QueueNode?
-}
-
 func breadthFirstSearch(graph: Graph, root: Node) {
   print("Performing breadth-first search on '\(root.label)'")
 
-  let q = Queue<Node>()
+  var q = Queue<Node>()
   q.enqueue(root)
 
   while !q.isEmpty {
     let current = q.dequeue()
-    for edge in current!.item!.neighbors {
+    for edge in current!.neighbors {
       let neighborNode = edge.neighbor
       q.enqueue(neighborNode)
 
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index bbb7fa376..21f2e8a97 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -6,111 +6,57 @@ Breadth-first search (BFS) is an algorithm for traversing or searching tree or g
 
 ![Animated example of a breadth-first search](Images/Animated_BFS.gif)
 
-## The code
-
-Before we can code the breadth-first search algorithm we need to:
-* Create an implementation of the graph
-* Create an implementation of a queue
-
-### Graph implementation
-
-A graph is made up of nodes and edges. In the [animated example](#animated-example) the nodes are represented as circles and the edges are represented as lines.
+Let's follow the animated example by using a [queue](../Queue/).
 
-Implementation of a node:
+Start with the root node ``a`` and add it to a queue.
 ```swift
-class Node {
-  private var label: String
-  private var neighbors: [Edge]
-
-  init(label: String) {
-    self.label = label
-    neighbors = []
-  }
-}
+queue.enqueue(a)
 ```
-
-Implementation of an edge:
+The queue is now ``[ a ]``. Dequeue ``a`` and enqueue the neighbor nodes ``b`` and ``c``.
 ```swift
-class Edge {
-  private var neighbor: Node
-
-  init(neighbor: Node) {
-    self.neighbor = neighbor
-  }
-}
+queue.dequeue(a)
+queue.enqueue(b)
+queue.enqueue(c)
 ```
-
-Implementation of a graph:
+The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue the neighbor nodes ``d`` and ``e``.
 ```swift
-class Graph {
-  private var nodes = [Node]()
-
-  func addNode(label: String) -> Node {
-    let node = Node(label: label)
-    nodes.append(node)
-    return node
-  }
-
-  func addEdge(source: Node, neighbor: Node) {
-    let edge = Edge(neighbor: neighbor)
-    edge.neighbor = neighbor
-    source.neighbors.append(edge)
-  }
-}
+queue.dequeue(b)
+queue.enqueue(d)
+queue.enqueue(e)
 ```
-
-### Queue implementation
-
-Implementation of simple queue:
-
+The queue is now ``[ c, d, e ]``. Dequeue ``c`` and enqueue the neighbor nodes ``f`` and ``g``.
 ```swift
-class Queue<T> {
-  private var top: QueueNode<T>!
-
-  func enqueue(item: T) {
-    if (top == nil) {
-      top = QueueNode<T>()
-    }
-
-    if (top.item == nil) {
-      top.item = item;
-      return
-    }
-
-    let childToUse = QueueNode<T>()
-    var current: QueueNode = top
-    while current.next != nil {
-      current = current.next!
-    }
-
-    childToUse.item = item;
-    current.next = childToUse;
-  }
-
-  func dequeue() -> QueueNode<T>? {
-    guard !isEmpty else {
-      return nil
-    }
-
-    let itemToDequeue = top
-    top = itemToDequeue.next
-    return itemToDequeue
-  }
-
-  var isEmpty: Bool {
-    get { return top == nil }
-  }
-}
-
-class QueueNode<T> {
-  var item: T?
-  var next: QueueNode?
-}
+queue.dequeue(c)
+queue.enqueue(f)
+queue.enqueue(g)
 ```
+The queue is now ``[ d, e, f, g ]``. Dequeue ``d`` which has no neighbor nodes.
+```swift
+queue.dequeue(d)
+```
+The queue is now ``[ e, f, g ]``. Dequeue ``e`` which enqueue the single neighbor node ``h``.
+```swift
+queue.dequeue(e)
+queue.enqueue(h)
+```
+The queue is now ``[ f, g, h ]``. Dequeue ``f`` which has no neighbor nodes.
+```swift
+queue.dequeue(f)
+```
+The queue is now ``[ g, h ]``. Dequeue ``g`` which has no neighbor nodes.
+```swift
+queue.dequeue(g)
+```
+The queue is now ``[ h ]``. Dequeue ``h`` which has no neighbor nodes.
+```swift
+queue.dequeue(h)
+```
+The queue is now empty which means all nodes have been explored.
 
-### Breadth-first search algorithm
+## The code
+
+Simple implementation of breadth-first search using a queue:
 
-Simple implementation of breadth-first search using queues:
 ```swift
 func breadthFirstSearch(graph: Graph, root: Node) {
   print("Performing breadth-first search on '\(root.label)'")
@@ -157,8 +103,6 @@ breadthFirstSearch(graph, root: nodeA) // This will output: Performing breadth-f
 
 ## See also
 
-[Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search)
-
-[Queues](http://waynewbishop.com/swift/stacks-queues) & [Graphs](http://waynewbishop.com/swift/graphs) by Wayne Bishop
+[Graphs](../Graph/), [Queues](../Queue/), [Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search).
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher)*

From 0ca1a40a0d7e5fa3879693730c905881cad22012 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 15 Feb 2016 21:55:32 +1300
Subject: [PATCH 0021/1679] BFS. Typo and adding ToDos for future sections.

---
 Breadth-First Search/README.markdown | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 21f2e8a97..878605fdf 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -34,7 +34,7 @@ The queue is now ``[ d, e, f, g ]``. Dequeue ``d`` which has no neighbor nodes.
 ```swift
 queue.dequeue(d)
 ```
-The queue is now ``[ e, f, g ]``. Dequeue ``e`` which enqueue the single neighbor node ``h``.
+The queue is now ``[ e, f, g ]``. Dequeue ``e`` and enqueue the single neighbor node ``h``.
 ```swift
 queue.dequeue(e)
 queue.enqueue(h)
@@ -101,6 +101,14 @@ breadthFirstSearch(graph, root: nodeA) // This will output: Performing breadth-f
 
 ```
 
+## Applications
+
+**TODO**: list a few common Applications
+
+# Finding the shortest path
+
+**TODO**: step through example
+
 ## See also
 
 [Graphs](../Graph/), [Queues](../Queue/), [Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search).

From 1a96dc028b3c88226f504a5a58a9c7f41980993b Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 16 Feb 2016 21:08:28 +1300
Subject: [PATCH 0022/1679] BFS Making breadthFirstSearch function in the
 readme match the playground

---
 Breadth-First Search/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 878605fdf..e49ced0a1 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -61,12 +61,12 @@ Simple implementation of breadth-first search using a queue:
 func breadthFirstSearch(graph: Graph, root: Node) {
   print("Performing breadth-first search on '\(root.label)'")
 
-  let q = Queue<Node>()
+  var q = Queue<Node>()
   q.enqueue(root)
 
   while !q.isEmpty {
     let current = q.dequeue()
-    for edge in current!.item!.neighbors {
+    for edge in current!.neighbors {
       let neighborNode = edge.neighbor
       q.enqueue(neighborNode)
 

From 19e0fc7cf6be4444ee8793b0b6dca6924922c191 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 16 Feb 2016 22:30:01 +1300
Subject: [PATCH 0023/1679] BFS. Fixing infinite loop when graph contains
 cycles (by recording seen nodes). Added draft shortest path algorithm.

---
 .../Contents.swift                            | 49 +++++++++++++++--
 Breadth-First Search/README.markdown          | 52 +++++++++++++++----
 2 files changed, 87 insertions(+), 14 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
index a9fabb1c9..545a78fd1 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -14,14 +14,30 @@ class Graph {
   }
 }
 
-class Node {
+class Node : CustomStringConvertible, Equatable {
   private var label: String
   private var neighbors: [Edge]
+  private var distance: Int?
 
   init(label: String) {
     self.label = label
     neighbors = []
   }
+
+  var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infnity)"
+  }
+
+  var hasDistance: Bool {
+    return distance != nil
+  }
+}
+
+func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label
 }
 
 class Edge {
@@ -63,6 +79,25 @@ struct Queue<T> {
 func breadthFirstSearch(graph: Graph, root: Node) {
   print("Performing breadth-first search on '\(root.label)'")
 
+  var seenNodes = [root]
+  var queue = Queue<Node>()
+  queue.enqueue(root)
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()
+    for edge in current!.neighbors {
+      let neighborNode = edge.neighbor
+      if !seenNodes.contains(neighborNode) {
+        queue.enqueue(neighborNode)
+        seenNodes.append(neighborNode)
+        print(neighborNode.label)
+      }
+    }
+  }
+}
+
+func breadthFirstSearchShortestPath(graph: Graph, root: Node) {
+  root.distance = 0
   var q = Queue<Node>()
   q.enqueue(root)
 
@@ -70,13 +105,17 @@ func breadthFirstSearch(graph: Graph, root: Node) {
     let current = q.dequeue()
     for edge in current!.neighbors {
       let neighborNode = edge.neighbor
-      q.enqueue(neighborNode)
-
-      print(neighborNode.label)
+      if !neighborNode.hasDistance {
+        q.enqueue(neighborNode)
+        neighborNode.distance = current!.distance! + 1
+      }
     }
   }
+
+  print(graph.nodes)
 }
 
+
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
@@ -96,4 +135,6 @@ graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
+
 breadthFirstSearch(graph, root: nodeA)
+breadthFirstSearchShortestPath(graph, root: nodeA)
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index e49ced0a1..dc7918ff5 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -61,16 +61,19 @@ Simple implementation of breadth-first search using a queue:
 func breadthFirstSearch(graph: Graph, root: Node) {
   print("Performing breadth-first search on '\(root.label)'")
 
-  var q = Queue<Node>()
-  q.enqueue(root)
+  var seenNodes = [root]
+  var queue = Queue<Node>()
+  queue.enqueue(root)
 
-  while !q.isEmpty {
-    let current = q.dequeue()
+  while !queue.isEmpty {
+    let current = queue.dequeue()
     for edge in current!.neighbors {
       let neighborNode = edge.neighbor
-      q.enqueue(neighborNode)
-
-      print(neighborNode.label)
+      if !seenNodes.contains(neighborNode) {
+        queue.enqueue(neighborNode)
+        seenNodes.append(neighborNode)
+        print(neighborNode.label)
+      }
     }
   }
 }
@@ -103,11 +106,40 @@ breadthFirstSearch(graph, root: nodeA) // This will output: Performing breadth-f
 
 ## Applications
 
-**TODO**: list a few common Applications
+Breadth-first search can be used to solve many problems, for example:
+
+* Computing the shortest path between a source node and each of the other nodes
+  * Only for unweighted graphs
+* Calculating the minimum spanning tree on an unweighted graph
+
+## Shortest path example
+
+TODO: walkthrough + explanation
+
+```swift
+func breadthFirstSearchShortestPath(graph: Graph, root: Node) {
+  root.distance = 0
+  var q = Queue<Node>()
+  q.enqueue(root)
+
+  while !q.isEmpty {
+    let current = q.dequeue()
+    for edge in current!.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.hasDistance {
+        q.enqueue(neighborNode)
+        neighborNode.distance = current!.distance! + 1
+      }
+    }
+  }
+
+  print(graph.nodes)
+}
+```
 
-# Finding the shortest path
+## Minimum spanning tree example
 
-**TODO**: step through example
+TODO
 
 ## See also
 

From eb648b1fcd090abc811de217fbf005f2debec5c5 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 16 Feb 2016 22:31:22 +1300
Subject: [PATCH 0024/1679] BFS fixing typo

---
 .../BreadthFirstSearch.playground/Contents.swift                | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
index 545a78fd1..64134a85c 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -28,7 +28,7 @@ class Node : CustomStringConvertible, Equatable {
     if let distance = distance {
       return "Node(label: \(label), distance: \(distance))"
     }
-    return "Node(label: \(label), distance: infnity)"
+    return "Node(label: \(label), distance: infinity)"
   }
 
   var hasDistance: Bool {

From 0a2649278aa8888f36feece509e9eb4b9b3a75f2 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 16 Feb 2016 19:20:13 +0100
Subject: [PATCH 0025/1679] Additional explanation on Monty Hall

---
 Monty Hall Problem/README.markdown | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/Monty Hall Problem/README.markdown b/Monty Hall Problem/README.markdown
index f227a9b29..81004410e 100644
--- a/Monty Hall Problem/README.markdown	
+++ b/Monty Hall Problem/README.markdown	
@@ -69,6 +69,20 @@ Since probabilities always need to add up to 100%, the chance that the prize is
 
 This is hard to wrap your head around, but easily shown using a simulation that runs a significant number of times. Probability is weird.
 
+By the way, you can simplify the code to this:
+
+```swift
+  let prizeDoor = random(3)
+  let chooseDoor = random(3)
+  if chooseDoor == prizeDoor {
+    winOriginalChoice += 1
+  } else {
+    winChangedMind += 1
+  }
+```
+
+Now it's no longer a simulation but the logic is equivalent. You can clearly see that the `chooseDoor` only wins 1/3rd of the time -- because it's a random number between 1 and 3 -- so changing your mind must win the other 2/3rds of the time.
+
 [Monty Hall Problem on Wikipedia](https://en.wikipedia.org/wiki/Monty_Hall_problem)
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 771163764b33d1b0b757b71fdfa1d67147805371 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Wed, 17 Feb 2016 20:25:57 +0100
Subject: [PATCH 0026/1679] Put brute-force string search in its own folder

---
 .../BoyerMoore.playground/Contents.swift      |  3 +-
 Boyer-Moore/README.markdown                   | 39 ++-----------
 .../Contents.swift                            | 32 +++++++++++
 .../contents.xcplayground                     |  4 ++
 .../timeline.xctimeline                       |  6 ++
 .../BruteForceStringSearch.swift              | 23 ++++++++
 Brute-Force String Search/README.markdown     | 56 +++++++++++++++++++
 README.markdown                               |  1 +
 8 files changed, 130 insertions(+), 34 deletions(-)
 create mode 100644 Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
 create mode 100644 Brute-Force String Search/BruteForceStringSearch.playground/contents.xcplayground
 create mode 100644 Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline
 create mode 100644 Brute-Force String Search/BruteForceStringSearch.swift
 create mode 100644 Brute-Force String Search/README.markdown

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index bba6e0fb6..926a76f93 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -39,11 +39,12 @@ extension String {
   }
 }
 
+
+
 // A few simple tests
 
 let s = "Hello, World"
 s.indexOf("World")  // 7
 
-// Input:
 let animals = "🐶🐔🐷🐮🐱"
 animals.indexOf("🐮")  // 6
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 7050442e2..dce0430f2 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -1,8 +1,8 @@
 # Boyer-Moore String Search
 
-How would you go about writing a string search algorithm in pure Swift if you were not allowed to import Foundation and could not use `NSString`'s `rangeOfString()` method?
-
-The goal is to implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
+Goal: Write a string search algorithm in pure Swift without importing Foundation or using `NSString`'s `rangeOfString()` method. 
+ 
+In other words, implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
  
 For example:
 
@@ -22,36 +22,9 @@ animals.indexOf("🐮")
 <String.Index?> 6
 ```
 
-Note: The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
-
-First, a brute-force solution:
-
-```swift
-extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    for i in self.startIndex ..< self.endIndex {
-      var j = i
-      var found = true
-      for p in pattern.startIndex ..< pattern.endIndex {
-        if j == self.endIndex || self[j] != pattern[p] {
-          found = false
-          break
-        } else {
-          j = j.successor()
-        }
-      }
-      if found {
-        return i
-      }
-    }
-    return nil
-  }
-}
-```
-
-This looks at each character in the source string in turn. If the character equals the first character of the search pattern, then the inner loop checks whether the rest of the pattern matches. If no match is found, the outer loop continues where it left off. This repeats until a complete match is found or the end of the source string is reached.
+> **Note:** The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
 
-The brute-force approach works OK, but it's not very efficient (or pretty). As it turns out, you don't need to look at *every* character from the source string -- you can often skip ahead multiple characters.
+The [brute-force approach](../Brute-Force Search Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at *every* character from the source string -- you can often skip ahead multiple characters.
 
 That skip-ahead algorithm is called [Boyer-Moore](https://en.wikipedia.org/wiki/Boyer–Moore_string_search_algorithm) and it has been around for a long time. It is considered the benchmark for all string search algorithms.
 
@@ -164,4 +137,4 @@ A caveat: If the search pattern consists of only a few characters, it's faster t
 
 Credits: This code is based on the article ["Faster String Searches" by Costas Menico](http://www.drdobbs.com/database/faster-string-searches/184408171) from Dr Dobb's magazine, July 1989 -- Yes, 1989! Sometimes it's useful to keep those old magazines around.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
new file mode 100644
index 000000000..57f2b2090
--- /dev/null
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -0,0 +1,32 @@
+//: Playground - noun: a place where people can play
+
+extension String {
+  func indexOf(pattern: String) -> String.Index? {
+    for i in self.startIndex ..< self.endIndex {
+      var j = i
+      var found = true
+      for p in pattern.startIndex ..< pattern.endIndex {
+        if j == self.endIndex || self[j] != pattern[p] {
+          found = false
+          break
+        } else {
+          j = j.successor()
+        }
+      }
+      if found {
+        return i
+      }
+    }
+    return nil
+  }
+}
+
+
+
+// A few simple tests
+
+let s = "Hello, World"
+s.indexOf("World")  // 7
+
+let animals = "🐶🐔🐷🐮🐱"
+animals.indexOf("🐮")  // 6
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/contents.xcplayground b/Brute-Force String Search/BruteForceStringSearch.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline b/Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Brute-Force String Search/BruteForceStringSearch.swift b/Brute-Force String Search/BruteForceStringSearch.swift
new file mode 100644
index 000000000..431677a4a
--- /dev/null
+++ b/Brute-Force String Search/BruteForceStringSearch.swift	
@@ -0,0 +1,23 @@
+/*
+  Brute-force string search
+*/
+extension String {
+  func indexOf(pattern: String) -> String.Index? {
+    for i in self.startIndex ..< self.endIndex {
+      var j = i
+      var found = true
+      for p in pattern.startIndex ..< pattern.endIndex {
+        if j == self.endIndex || self[j] != pattern[p] {
+          found = false
+          break
+        } else {
+          j = j.successor()
+        }
+      }
+      if found {
+        return i
+      }
+    }
+    return nil
+  }
+}
diff --git a/Brute-Force String Search/README.markdown b/Brute-Force String Search/README.markdown
new file mode 100644
index 000000000..748be872f
--- /dev/null
+++ b/Brute-Force String Search/README.markdown	
@@ -0,0 +1,56 @@
+# Brute-Force String Search
+
+How would you go about writing a string search algorithm in pure Swift if you were not allowed to import Foundation and could not use `NSString`'s `rangeOfString()` method?
+
+The goal is to implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
+ 
+For example:
+
+```swift
+// Input: 
+let s = "Hello, World"
+s.indexOf("World")
+
+// Output:
+<String.Index?> 7
+
+// Input:
+let animals = "🐶🐔🐷🐮🐱"
+animals.indexOf("🐮")
+
+// Output:
+<String.Index?> 6
+```
+
+> **Note:** The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
+
+Here is a brute-force solution:
+
+```swift
+extension String {
+  func indexOf(pattern: String) -> String.Index? {
+    for i in self.startIndex ..< self.endIndex {
+      var j = i
+      var found = true
+      for p in pattern.startIndex ..< pattern.endIndex {
+        if j == self.endIndex || self[j] != pattern[p] {
+          found = false
+          break
+        } else {
+          j = j.successor()
+        }
+      }
+      if found {
+        return i
+      }
+    }
+    return nil
+  }
+}
+```
+
+This looks at each character in the source string in turn. If the character equals the first character of the search pattern, then the inner loop checks whether the rest of the pattern matches. If no match is found, the outer loop continues where it left off. This repeats until a complete match is found or the end of the source string is reached.
+
+The brute-force approach works OK, but it's not very efficient (or pretty). It should work fine on small strings, though. For a smarter algorithm that works better with large chunks of text, check out [Boyer-Moore](../Boyer-Moore/) string search.
+
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/README.markdown b/README.markdown
index a81f8a7ce..db22ae68f 100644
--- a/README.markdown
+++ b/README.markdown
@@ -47,6 +47,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 
 ### String Search
 
+- [Brute-Force String Search](Brute-Force String Search/). A naive method.
 - [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
 - Rabin-Karp
 

From b8cc255cd22886ddfa686bc8cc9c375da8493395 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Thu, 18 Feb 2016 17:44:37 +0100
Subject: [PATCH 0027/1679] Adding project and test target for Array2D data
 structure

---
 .../array2Dtest.xcodeproj/project.pbxproj     | 409 ++++++++++++++++++
 .../array2Dtest/array2Dtest/AppDelegate.swift |  46 ++
 .../AppIcon.appiconset/Contents.json          |  68 +++
 .../Base.lproj/LaunchScreen.storyboard        |  27 ++
 .../array2Dtest/Base.lproj/Main.storyboard    |  25 ++
 Array2D/array2Dtest/array2Dtest/Info.plist    |  47 ++
 .../array2Dtest/ViewController.swift          |  25 ++
 .../array2Dtest/array2DtestTests/Info.plist   |  24 +
 .../array2DtestTests/array2DtestTests.swift   |  88 ++++
 9 files changed, 759 insertions(+)
 create mode 100644 Array2D/array2Dtest/array2Dtest.xcodeproj/project.pbxproj
 create mode 100644 Array2D/array2Dtest/array2Dtest/AppDelegate.swift
 create mode 100644 Array2D/array2Dtest/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Array2D/array2Dtest/array2Dtest/Base.lproj/LaunchScreen.storyboard
 create mode 100644 Array2D/array2Dtest/array2Dtest/Base.lproj/Main.storyboard
 create mode 100644 Array2D/array2Dtest/array2Dtest/Info.plist
 create mode 100644 Array2D/array2Dtest/array2Dtest/ViewController.swift
 create mode 100644 Array2D/array2Dtest/array2DtestTests/Info.plist
 create mode 100644 Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift

diff --git a/Array2D/array2Dtest/array2Dtest.xcodeproj/project.pbxproj b/Array2D/array2Dtest/array2Dtest.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..b1dae1cd7
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest.xcodeproj/project.pbxproj
@@ -0,0 +1,409 @@
+// !$*UTF8*$!
+{
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+	classes = {
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+				PRODUCT_BUNDLE_IDENTIFIER = com.sac.array2DtestTests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/array2Dtest.app/array2Dtest";
+			};
+			name = Debug;
+		};
+		766116301C7625C700358E02 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				INFOPLIST_FILE = array2DtestTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.sac.array2DtestTests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/array2Dtest.app/array2Dtest";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		766116091C7625C600358E02 /* Build configuration list for PBXProject "array2Dtest" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				766116291C7625C700358E02 /* Debug */,
+				7661162A1C7625C700358E02 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7661162B1C7625C700358E02 /* Build configuration list for PBXNativeTarget "array2Dtest" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7661162C1C7625C700358E02 /* Debug */,
+				7661162D1C7625C700358E02 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+		7661162E1C7625C700358E02 /* Build configuration list for PBXNativeTarget "array2DtestTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7661162F1C7625C700358E02 /* Debug */,
+				766116301C7625C700358E02 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 766116061C7625C600358E02 /* Project object */;
+}
diff --git a/Array2D/array2Dtest/array2Dtest/AppDelegate.swift b/Array2D/array2Dtest/array2Dtest/AppDelegate.swift
new file mode 100644
index 000000000..7d1c32f11
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest/AppDelegate.swift
@@ -0,0 +1,46 @@
+//
+//  AppDelegate.swift
+//  array2Dtest
+//
+//  Created by Barbara Rodeker on 2/18/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import UIKit
+
+@UIApplicationMain
+class AppDelegate: UIResponder, UIApplicationDelegate {
+
+    var window: UIWindow?
+
+
+    func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
+        // Override point for customization after application launch.
+        return true
+    }
+
+    func applicationWillResignActive(application: UIApplication) {
+        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
+        // Use this method to pause ongoing tasks, disable timers, and throttle down OpenGL ES frame rates. Games should use this method to pause the game.
+    }
+
+    func applicationDidEnterBackground(application: UIApplication) {
+        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
+        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
+    }
+
+    func applicationWillEnterForeground(application: UIApplication) {
+        // Called as part of the transition from the background to the inactive state; here you can undo many of the changes made on entering the background.
+    }
+
+    func applicationDidBecomeActive(application: UIApplication) {
+        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
+    }
+
+    func applicationWillTerminate(application: UIApplication) {
+        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
+    }
+
+
+}
+
diff --git a/Array2D/array2Dtest/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json b/Array2D/array2Dtest/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..36d2c80d8
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
@@ -0,0 +1,68 @@
+{
+  "images" : [
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Array2D/array2Dtest/array2Dtest/Base.lproj/LaunchScreen.storyboard b/Array2D/array2Dtest/array2Dtest/Base.lproj/LaunchScreen.storyboard
new file mode 100644
index 000000000..2e721e183
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest/Base.lproj/LaunchScreen.storyboard
@@ -0,0 +1,27 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="8150" systemVersion="15A204g" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" initialViewController="01J-lp-oVM">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="8122"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="EHf-IW-A2E">
+            <objects>
+                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
+                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
+                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <animations/>
+                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="53" y="375"/>
+        </scene>
+    </scenes>
+</document>
diff --git a/Array2D/array2Dtest/array2Dtest/Base.lproj/Main.storyboard b/Array2D/array2Dtest/array2Dtest/Base.lproj/Main.storyboard
new file mode 100644
index 000000000..3a2a49bad
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest/Base.lproj/Main.storyboard
@@ -0,0 +1,25 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="6211" systemVersion="14A298i" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" initialViewController="BYZ-38-t0r">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="6204"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="tne-QT-ifu">
+            <objects>
+                <viewController id="BYZ-38-t0r" customClass="ViewController" customModuleProvider="target" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="y3c-jy-aDJ"/>
+                        <viewControllerLayoutGuide type="bottom" id="wfy-db-euE"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="8bC-Xf-vdC">
+                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="dkx-z0-nzr" sceneMemberID="firstResponder"/>
+            </objects>
+        </scene>
+    </scenes>
+</document>
diff --git a/Array2D/array2Dtest/array2Dtest/Info.plist b/Array2D/array2Dtest/array2Dtest/Info.plist
new file mode 100644
index 000000000..40c6215d9
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest/Info.plist
@@ -0,0 +1,47 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSRequiresIPhoneOS</key>
+	<true/>
+	<key>UILaunchStoryboardName</key>
+	<string>LaunchScreen</string>
+	<key>UIMainStoryboardFile</key>
+	<string>Main</string>
+	<key>UIRequiredDeviceCapabilities</key>
+	<array>
+		<string>armv7</string>
+	</array>
+	<key>UISupportedInterfaceOrientations</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>UISupportedInterfaceOrientations~ipad</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationPortraitUpsideDown</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+</dict>
+</plist>
diff --git a/Array2D/array2Dtest/array2Dtest/ViewController.swift b/Array2D/array2Dtest/array2Dtest/ViewController.swift
new file mode 100644
index 000000000..669b79b89
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest/ViewController.swift
@@ -0,0 +1,25 @@
+//
+//  ViewController.swift
+//  array2Dtest
+//
+//  Created by Barbara Rodeker on 2/18/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import UIKit
+
+class ViewController: UIViewController {
+
+    override func viewDidLoad() {
+        super.viewDidLoad()
+        // Do any additional setup after loading the view, typically from a nib.
+    }
+
+    override func didReceiveMemoryWarning() {
+        super.didReceiveMemoryWarning()
+        // Dispose of any resources that can be recreated.
+    }
+
+
+}
+
diff --git a/Array2D/array2Dtest/array2DtestTests/Info.plist b/Array2D/array2Dtest/array2DtestTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Array2D/array2Dtest/array2DtestTests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift b/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
new file mode 100644
index 000000000..0292449b4
--- /dev/null
+++ b/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
@@ -0,0 +1,88 @@
+//
+//  Array2DTest.swift
+//  algorithmclub
+//
+//  Created by Barbara Rodeker on 2/16/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+@testable import array2Dtest
+
+class Array2DTest: XCTestCase {
+    
+    override func setUp() {
+        super.setUp()
+    }
+    
+    override func tearDown() {
+        super.tearDown()
+    }
+    
+    func testIntegerArrayWithPositiveRowsAndColumns() {
+        let array = Array2D<Int>(columns: 3, rows: 2, initialValue: 0)
+        XCTAssert(array.columns == 3, "Column count setup worked")
+        XCTAssert(array.rows == 2, "Rows count setup worked")
+        XCTAssert(array[2,2] == 0, "Integer array: Initialization value properly read")
+    }
+    
+    func testStringArrayWithPositiveRowsAndColumns() {
+        let array = Array2D<String>(columns: 3, rows: 2, initialValue: "empty")
+        XCTAssert(array.columns == 3, "Column count setup worked")
+        XCTAssert(array.rows == 2, "Rows count setup worked")
+        XCTAssert(array[2,2] == "empty", "String array: Initialization value properly read")
+    }
+    
+    func testCustomClassArrayWithPositiveRowsAndColumns() {
+        let array = Array2D<TestElement>(columns: 3, rows: 2, initialValue: TestElement(identifier: "pepe"))
+        XCTAssert(array.columns == 3, "Column count setup worked")
+        XCTAssert(array.rows == 2, "Rows count setup worked")
+        XCTAssert(array[2,2] == TestElement(identifier: "pepe"), "Custom Class array: Initialization value properly read")
+    }
+    
+    func testArrayWithNegativeColumns() {
+        let array = Array2D(columns: -1,rows: 2,initialValue: 0)
+        XCTAssertNil(array)
+    }
+    
+    func testAccessingWrongIndex() {
+        let array = Array2D(columns: 2, rows: 4, initialValue: 5)
+        XCTAssertNil(array[20,20], "Array in 20,20 is not a valid index")
+    }
+    
+    func testPerformanceOnSmallArray() {
+        self.measureBlock {
+            self.printArrayWith(columns: 2, rows: 2, inititalValue: 1)
+        }
+    }
+
+    func testPerformanceOnLargeArray() {
+        self.measureBlock {
+            self.printArrayWith(columns: 2000000, rows: 2000000, inititalValue: 1)
+        }
+    }
+
+    private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int){
+        let array = Array2D(columns: columns, rows: rows, initialValue: 4)
+        for r in 0..<array.rows {
+            for c in 0..<array.columns {
+                print("Array in [\(r), \(c)] value is: \(array[c,r])")
+            }
+        }
+    }
+    
+}
+
+class TestElement : Equatable {
+    let identifier : String
+    
+    init(identifier: String) {
+        self.identifier = identifier
+    }
+    
+}
+
+func == (lhs: TestElement, rhs: TestElement) -> Bool {
+    return lhs.identifier == rhs.identifier
+}
+

From 905dd1a6cf93724336ba26d3d3e8a6e36f446a25 Mon Sep 17 00:00:00 2001
From: Donald Pinckney <donald_pinckney@icloud.com>
Date: Thu, 18 Feb 2016 11:41:24 -0800
Subject: [PATCH 0028/1679] Fix formatting, implement methods to lookup edges.

---
 .../Contents.swift                            | 59 -----------
 .../contents.xcplayground                     |  4 -
 .../timeline.xctimeline                       |  6 --
 .../Contents.swift                            | 51 +++++++---
 .../Contents.swift                            | 97 +++++++++++--------
 5 files changed, 97 insertions(+), 120 deletions(-)
 delete mode 100644 Graph/Graph Adjacency Matrix.playground/Contents.swift
 delete mode 100644 Graph/Graph Adjacency Matrix.playground/contents.xcplayground
 delete mode 100644 Graph/Graph Adjacency Matrix.playground/timeline.xctimeline

diff --git a/Graph/Graph Adjacency Matrix.playground/Contents.swift b/Graph/Graph Adjacency Matrix.playground/Contents.swift
deleted file mode 100644
index 2d634e0c0..000000000
--- a/Graph/Graph Adjacency Matrix.playground/Contents.swift	
+++ /dev/null
@@ -1,59 +0,0 @@
-
-
-public struct GraphVertex<T> {
-  public var data: T
-  let uniqueID: Int
-}
-
-public struct Graph<T> {
-  
-  private var adjacencyMatrix: [[Int?]] = [] // row-major
-  
-  public init() { } // Silence default constructor
-  
-  public mutating func createVertex(data: T) -> GraphVertex<T> {
-    let vertex = GraphVertex(data: data, uniqueID: adjacencyMatrix.count)
-    
-    // Expand each existing row to the right one column
-    for i in 0..<adjacencyMatrix.count {
-      adjacencyMatrix[i].append(nil)
-    }
-    
-    // Add one new row at the bottom
-    let newRow = [Int?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
-    adjacencyMatrix.append(newRow)
-    
-    return vertex
-  }
-  
-  // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
-  public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Int = 0) {
-    adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID] = weight
-  }
-  
-  // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
-  public mutating func connect(someVertex: GraphVertex<T>, withVertex: GraphVertex<T>, withWeight weight: Int = 0) {
-    adjacencyMatrix[someVertex.uniqueID][withVertex.uniqueID] = weight
-    adjacencyMatrix[withVertex.uniqueID][someVertex.uniqueID] = weight
-
-  }
-}
-
-
-
-
-var graph = Graph<Int>()
-let v1 = graph.createVertex(1)
-let v2 = graph.createVertex(2)
-let v3 = graph.createVertex(3)
-let v4 = graph.createVertex(4)
-
-// v1 ---> v2 ---> v3 ---> v4
-// ^                       |
-// |                       V
-// -----------<------------|
-
-graph.connect(v1, toDestinationVertex: v2)
-graph.connect(v2, toDestinationVertex: v3)
-graph.connect(v3, toDestinationVertex: v4)
-graph.connect(v4, toDestinationVertex: v1)
diff --git a/Graph/Graph Adjacency Matrix.playground/contents.xcplayground b/Graph/Graph Adjacency Matrix.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Graph/Graph Adjacency Matrix.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Graph/Graph Adjacency Matrix.playground/timeline.xctimeline b/Graph/Graph Adjacency Matrix.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Graph/Graph Adjacency Matrix.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
index 17c0514ea..3f7ea7e9a 100644
--- a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
@@ -4,34 +4,51 @@ A graph implementation, using an adjacency list.
 
 In an adjacency list implementation, each vertex stores an array of edges, indicating to which vertices it has an edge (note the directionality).  The edge stores the source and destination vertices, as well as a weight.
 
-Connected vertices in this implementation is O(1).
+Connecting vertices in this implementation is O(1).
 
 */
 
+var uniqueIDCounter: Int = 0
+
 public struct GraphEdge<T> {
   public let from: GraphVertex<T>
   public let to: GraphVertex<T>
   public let weight: Double
 }
 
+
 public struct GraphVertex<T> {
   public var data: T
-  public private(set) var edges: [GraphEdge<T>] = [] // This is a simple adjacency list, rather than matrix
+  public private(set) var edges: [GraphEdge<T>] = [] // This is an adjacency list, rather than matrix
+  
+  private let uniqueID: Int
   
   public init(data: T) {
     self.data = data
+    uniqueID = uniqueIDCounter
+    uniqueIDCounter += 1
   }
   
   // Creates a directed edge self -----> dest
-  public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+  public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
     edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
   }
   
   // Creates an undirected edge by making 2 directed edges: self ----> other, and other ----> self
-  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
     edges.append(GraphEdge(from: self, to: otherVertex, weight: weight))
     otherVertex.edges.append(GraphEdge(from: otherVertex, to: self, weight: weight))
   }
+  
+  public func edgeTo(otherVertex: GraphVertex<T>) -> GraphEdge<T>? {
+    for e in edges {
+      if e.to.uniqueID == otherVertex.uniqueID {
+        return e
+      }
+    }
+    
+    return nil
+  }
 }
 
 
@@ -43,15 +60,25 @@ var v3 = GraphVertex(data: 3)
 var v4 = GraphVertex(data: 4)
 
 // Setup a cycle like so:
-// v1 ---> v2 ---> v3 ---> v4
-// ^                       |
-// |                       V
-// -----------<------------|
+// v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
+// ^                                            |
+// |                                            V
+// ---------<-----------<---------(2.8)----<----|
+
+v1.connectTo(v2, withWeight: 1.0)
+v2.connectTo(v3, withWeight: 1.0)
+v3.connectTo(v4, withWeight: 4.5)
+v4.connectTo(v1, withWeight: 2.8)
+
+// Returns the weight of the edge from v1 to v2 (1.0)
+v1.edgeTo(v2)?.weight
 
-v1.connectTo(v2)
-v2.connectTo(v3)
-v3.connectTo(v4)
-v4.connectTo(v1)
+// Returns the weight of the edge from v1 to v3 (nil, since there is not an edge)
+v1.edgeTo(v3)?.weight
 
+// Returns the weight of the edge from v3 to v4 (4.5)
+v3.edgeTo(v4)?.weight
 
+// Returns the weight of the edge from v4 to v1 (2.8)
+v4.edgeTo(v1)?.weight
 //: [Next](@next)
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
index 4fffc4d40..5cff241fb 100644
--- a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
@@ -11,43 +11,49 @@ Connecting vertices os O(1).
 */
 
 public struct GraphVertex<T> {
-    public var data: T
-    private let uniqueID: Int
+  public var data: T
+  private let uniqueID: Int
 }
 
 public struct Graph<T> {
+  
+  // nil entries are used to mark that two vertices are NOT connected.
+  // If adjacencyMatrix[i][j] is not nil, then there is an edge from vertex i to vertex j.
+  private var adjacencyMatrix: [[Double?]] = []
+  
+  public init() { }
+  
+  public mutating func createVertex(data: T) -> GraphVertex<T> {
+    let vertex = GraphVertex(data: data, uniqueID: adjacencyMatrix.count)
     
-    // nil entries are used to mark that two vertices are NOT connected.
-    private var adjacencyMatrix: [[Double?]] = []
-    
-    public init() { }
-    
-    public mutating func createVertex(data: T) -> GraphVertex<T> {
-        let vertex = GraphVertex(data: data, uniqueID: adjacencyMatrix.count)
-        
-        // Expand each existing row to the right one column
-        for i in 0..<adjacencyMatrix.count {
-            adjacencyMatrix[i].append(nil)
-        }
-        
-        // Add one new row at the bottom
-        let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
-        adjacencyMatrix.append(newRow)
-        
-        return vertex
+    // Expand each existing row to the right one column
+    for i in 0..<adjacencyMatrix.count {
+      adjacencyMatrix[i].append(nil)
     }
     
-    // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
-    public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
-        adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID] = weight
-    }
+    // Add one new row at the bottom
+    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+    adjacencyMatrix.append(newRow)
     
-    // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
-    public mutating func connect(someVertex: GraphVertex<T>, withVertex: GraphVertex<T>, withWeight weight: Double = 0) {
-        adjacencyMatrix[someVertex.uniqueID][withVertex.uniqueID] = weight
-        adjacencyMatrix[withVertex.uniqueID][someVertex.uniqueID] = weight
-        
-    }
+    return vertex
+  }
+  
+  // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
+  public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+    adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID] = weight
+  }
+  
+  // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
+  public mutating func connect(someVertex: GraphVertex<T>, symmetricallyWithVertex withVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+    adjacencyMatrix[someVertex.uniqueID][withVertex.uniqueID] = weight
+    adjacencyMatrix[withVertex.uniqueID][someVertex.uniqueID] = weight
+    
+  }
+  
+  public func weightFrom(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>) -> Double? {
+    return adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID]
+  }
+  
 }
 
 
@@ -60,12 +66,25 @@ let v3 = graph.createVertex(3)
 let v4 = graph.createVertex(4)
 
 // Setup a cycle like so:
-// v1 ---> v2 ---> v3 ---> v4
-// ^                       |
-// |                       V
-// -----------<------------|
-
-graph.connect(v1, toDestinationVertex: v2)
-graph.connect(v2, toDestinationVertex: v3)
-graph.connect(v3, toDestinationVertex: v4)
-graph.connect(v4, toDestinationVertex: v1)
+// v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
+// ^                                            |
+// |                                            V
+// ---------<-----------<---------(2.8)----<----|
+
+graph.connect(v1, toDestinationVertex: v2, withWeight: 1.0)
+graph.connect(v2, toDestinationVertex: v3, withWeight: 1.0)
+graph.connect(v3, toDestinationVertex: v4, withWeight: 4.5)
+graph.connect(v4, toDestinationVertex: v1, withWeight: 2.8)
+
+// Returns the weight of the edge from v1 to v2 (1.0)
+graph.weightFrom(v1, toDestinationVertex: v2)
+
+// Returns the weight of the edge from v1 to v3 (nil, since there is not an edge)
+graph.weightFrom(v1, toDestinationVertex: v3)
+
+// Returns the weight of the edge from v3 to v4 (4.5)
+graph.weightFrom(v3, toDestinationVertex: v4)
+
+// Returns the weight of the edge from v4 to v1 (2.8)
+graph.weightFrom(v4, toDestinationVertex: v1)
+

From 8008a24c7a6a631191dcc57191456a9084658867 Mon Sep 17 00:00:00 2001
From: Robert Thompson <robert.thompson@willowtreeapps.com>
Date: Thu, 18 Feb 2016 17:46:11 -0500
Subject: [PATCH 0029/1679] Initial commit

---
 Treap/Treap.swift                             | 160 ++++
 Treap/Treap/Treap.xcodeproj/project.pbxproj   | 400 ++++++++++
 Treap/Treap/Treap/AppDelegate.swift           |  27 +
 .../AppIcon.appiconset/Contents.json          |  58 ++
 Treap/Treap/Treap/Base.lproj/MainMenu.xib     | 681 ++++++++++++++++++
 Treap/Treap/Treap/Info.plist                  |  34 +
 Treap/Treap/TreapTests/Info.plist             |  24 +
 Treap/Treap/TreapTests/TreapTests.swift       |  57 ++
 Treap/TreapCollectionType.swift               |  81 +++
 Treap/TreapMergeSplit.swift                   | 113 +++
 10 files changed, 1635 insertions(+)
 create mode 100644 Treap/Treap.swift
 create mode 100644 Treap/Treap/Treap.xcodeproj/project.pbxproj
 create mode 100644 Treap/Treap/Treap/AppDelegate.swift
 create mode 100644 Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Treap/Treap/Treap/Base.lproj/MainMenu.xib
 create mode 100644 Treap/Treap/Treap/Info.plist
 create mode 100644 Treap/Treap/TreapTests/Info.plist
 create mode 100644 Treap/Treap/TreapTests/TreapTests.swift
 create mode 100644 Treap/TreapCollectionType.swift
 create mode 100644 Treap/TreapMergeSplit.swift

diff --git a/Treap/Treap.swift b/Treap/Treap.swift
new file mode 100644
index 000000000..108eec913
--- /dev/null
+++ b/Treap/Treap.swift
@@ -0,0 +1,160 @@
+//
+//  Treap.swift
+//  TreapExample
+//
+//  Created by Robert Thompson on 7/27/15.
+//  Copyright © 2015 Robert Thompson. All rights reserved.
+//
+
+import Foundation
+
+public indirect enum Treap<Key: Comparable, Element> {
+    case Empty
+    case Node(key: Key, val: Element, p: Int, left: Treap, right: Treap)
+
+    public init() {
+        self = .Empty
+    }
+
+    internal func get(key: Key) -> Element? {
+        switch self {
+        case .Empty:
+            return nil
+        case let .Node(treeKey, val, _, _, _) where treeKey == key:
+            return val
+        case let .Node(treeKey, _, _, left, _) where key < treeKey:
+            return left.get(key)
+        case let .Node(treeKey, _, _, _, right) where key > treeKey:
+            return right.get(key)
+        default:
+            return nil
+        }
+    }
+    
+    public func contains(key: Key) -> Bool {
+        switch self {
+        case .Empty:
+            return false
+        case let .Node(treeKey, _, _, _, _) where treeKey == key:
+            return true
+        case let .Node(treeKey, _, _, left, _) where key < treeKey:
+            return left.contains(key)
+        case let .Node(treeKey, _, _, _, right) where key > treeKey:
+            return right.contains(key)
+        default:
+            return false
+        }
+    }
+    
+    public var depth: Int {
+        get {
+            switch self {
+            case .Empty:
+                return 0
+            case let .Node(_, _, _, left, .Empty):
+                return 1 + left.depth
+            case let .Node(_, _, _, .Empty, right):
+                return 1 + right.depth
+            case let .Node(_, _, _, left, right):
+                let leftDepth = left.depth
+                let rightDepth = right.depth
+                return 1 + max(leftDepth, rightDepth)
+            }
+            
+        }
+    }
+    
+    public var count: Int {
+        get {
+            return Treap.countHelper(self)
+        }
+    }
+    
+    private static func countHelper(treap: Treap<Key, Element>) -> Int
+    {
+        if case let .Node(_, _, _, left, right) = treap
+        {
+            return countHelper(left) + 1 + countHelper(right)
+        }
+        
+        return 0
+    }
+}
+
+internal func leftRotate<Key: Comparable, Element>(tree: Treap<Key, Element>) -> Treap<Key, Element> {
+    if case let .Node(key, val, p, .Node(leftKey, leftVal, leftP, leftLeft, leftRight), right) = tree {
+        return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: Treap.Node(key: key, val: val, p: p, left: leftRight, right: right))
+    }
+    else
+    {
+        return .Empty
+    }
+}
+
+internal func rightRotate<Key: Comparable, Element>(tree: Treap<Key, Element>) -> Treap<Key, Element> {
+    if case let .Node(key, val, p, left, .Node(rightKey, rightVal, rightP, rightLeft, rightRight)) = tree {
+        return .Node(key: rightKey, val: rightVal, p: rightP, left: Treap.Node(key: key, val: val, p: p, left: left, right: rightLeft), right: rightRight)
+    }
+    else
+    {
+        return .Empty
+    }
+}
+
+public extension Treap {
+    internal func set(key: Key, val: Element, p: Int = Int(arc4random())) -> Treap {
+        switch self {
+        case .Empty:
+            return .Node(key: key, val: val, p: p, left: .Empty, right: .Empty)
+        case let .Node(nodeKey, nodeVal, nodeP, left, right) where key != nodeKey:
+            return insertAndBalance(nodeKey, nodeVal, nodeP, left, right, key, val, p)
+        case let .Node(nodeKey, _, nodeP, left, right) where key == nodeKey:
+            return .Node(key: key, val: val, p: nodeP, left: left, right: right)
+        default: // should never happen
+            return .Empty
+        }
+        
+    }
+    
+    private func insertAndBalance(nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap, _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
+        let newChild: Treap<Key, Element>
+        let newNode: Treap<Key, Element>
+        let rotate: (Treap) -> Treap
+        if key < nodeKey {
+            newChild = left.set(key, val: val, p: p)
+            newNode = .Node(key: nodeKey, val: nodeVal, p: nodeP, left: newChild, right: right)
+            rotate = leftRotate
+        }
+        else if key > nodeKey {
+            newChild = right.set(key, val: val, p: p)
+            newNode = .Node(key: nodeKey, val: nodeVal, p: nodeP, left: left, right: newChild)
+            rotate = rightRotate
+        }
+        else {
+            // It should be impossible to reach here
+            newChild = .Empty
+            newNode = .Empty
+            return newNode
+        }
+        
+        if case let .Node(_, _, newChildP, _, _) = newChild where newChildP < nodeP {
+            return rotate(newNode)
+        }
+        else {
+            return newNode
+        }
+    }
+    
+    internal func delete(key: Key) throws -> Treap {
+        switch self {
+        case .Empty:
+            throw NSError(domain: "com.wta.treap.errorDomain", code: -1, userInfo: nil)
+        case let .Node(nodeKey, val, p, left, right) where key < nodeKey:
+                return try Treap.Node(key: nodeKey, val: val, p: p, left: left.delete(key), right: right)
+        case let .Node(nodeKey, val, p, left, right) where key > nodeKey:
+                return try Treap.Node(key: nodeKey, val: val, p: p, left: left, right: right.delete(key))
+        case let .Node(_, _, _, left, right):
+                return merge(left, right: right)
+        }
+    }
+}
diff --git a/Treap/Treap/Treap.xcodeproj/project.pbxproj b/Treap/Treap/Treap.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..319a22f37
--- /dev/null
+++ b/Treap/Treap/Treap.xcodeproj/project.pbxproj
@@ -0,0 +1,400 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		E1E34DC71C7670240023AF4D /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DC61C7670240023AF4D /* AppDelegate.swift */; };
+		E1E34DC91C7670240023AF4D /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = E1E34DC81C7670240023AF4D /* Assets.xcassets */; };
+		E1E34DCC1C7670240023AF4D /* MainMenu.xib in Resources */ = {isa = PBXBuildFile; fileRef = E1E34DCA1C7670240023AF4D /* MainMenu.xib */; };
+		E1E34DD71C7670250023AF4D /* TreapTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DD61C7670250023AF4D /* TreapTests.swift */; };
+		E1E34DE31C7670350023AF4D /* Treap.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE11C7670350023AF4D /* Treap.swift */; };
+		E1E34DE41C7670350023AF4D /* TreapMergeSplit.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE21C7670350023AF4D /* TreapMergeSplit.swift */; };
+		E1E34DEA1C7671200023AF4D /* TreapCollectionType.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE91C7671200023AF4D /* TreapCollectionType.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
+		E1E34DD31C7670250023AF4D /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = E1E34DBB1C7670240023AF4D /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = E1E34DC21C7670240023AF4D;
+			remoteInfo = Treap;
+		};
+/* End PBXContainerItemProxy section */
+
+/* Begin PBXFileReference section */
+		E1E34DC31C7670240023AF4D /* Treap.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = Treap.app; sourceTree = BUILT_PRODUCTS_DIR; };
+		E1E34DC61C7670240023AF4D /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
+		E1E34DC81C7670240023AF4D /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
+		E1E34DCB1C7670240023AF4D /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.xib; name = Base; path = Base.lproj/MainMenu.xib; sourceTree = "<group>"; };
+		E1E34DCD1C7670240023AF4D /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		E1E34DD21C7670250023AF4D /* TreapTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = TreapTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		E1E34DD61C7670250023AF4D /* TreapTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = TreapTests.swift; sourceTree = "<group>"; };
+		E1E34DD81C7670250023AF4D /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		E1E34DE11C7670350023AF4D /* Treap.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Treap.swift; path = ../../Treap.swift; sourceTree = "<group>"; };
+		E1E34DE21C7670350023AF4D /* TreapMergeSplit.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TreapMergeSplit.swift; path = ../../TreapMergeSplit.swift; sourceTree = "<group>"; };
+		E1E34DE91C7671200023AF4D /* TreapCollectionType.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TreapCollectionType.swift; path = ../../TreapCollectionType.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		E1E34DC01C7670240023AF4D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		E1E34DCF1C7670250023AF4D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		E1E34DBA1C7670240023AF4D = {
+			isa = PBXGroup;
+			children = (
+				E1E34DC51C7670240023AF4D /* Treap */,
+				E1E34DD51C7670250023AF4D /* TreapTests */,
+				E1E34DC41C7670240023AF4D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		E1E34DC41C7670240023AF4D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				E1E34DC31C7670240023AF4D /* Treap.app */,
+				E1E34DD21C7670250023AF4D /* TreapTests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		E1E34DC51C7670240023AF4D /* Treap */ = {
+			isa = PBXGroup;
+			children = (
+				E1E34DC61C7670240023AF4D /* AppDelegate.swift */,
+				E1E34DC81C7670240023AF4D /* Assets.xcassets */,
+				E1E34DCA1C7670240023AF4D /* MainMenu.xib */,
+				E1E34DE11C7670350023AF4D /* Treap.swift */,
+				E1E34DE21C7670350023AF4D /* TreapMergeSplit.swift */,
+				E1E34DE91C7671200023AF4D /* TreapCollectionType.swift */,
+				E1E34DCD1C7670240023AF4D /* Info.plist */,
+			);
+			path = Treap;
+			sourceTree = "<group>";
+		};
+		E1E34DD51C7670250023AF4D /* TreapTests */ = {
+			isa = PBXGroup;
+			children = (
+				E1E34DD61C7670250023AF4D /* TreapTests.swift */,
+				E1E34DD81C7670250023AF4D /* Info.plist */,
+			);
+			path = TreapTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		E1E34DC21C7670240023AF4D /* Treap */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = E1E34DDB1C7670250023AF4D /* Build configuration list for PBXNativeTarget "Treap" */;
+			buildPhases = (
+				E1E34DBF1C7670240023AF4D /* Sources */,
+				E1E34DC01C7670240023AF4D /* Frameworks */,
+				E1E34DC11C7670240023AF4D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Treap;
+			productName = Treap;
+			productReference = E1E34DC31C7670240023AF4D /* Treap.app */;
+			productType = "com.apple.product-type.application";
+		};
+		E1E34DD11C7670250023AF4D /* TreapTests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = E1E34DDE1C7670250023AF4D /* Build configuration list for PBXNativeTarget "TreapTests" */;
+			buildPhases = (
+				E1E34DCE1C7670250023AF4D /* Sources */,
+				E1E34DCF1C7670250023AF4D /* Frameworks */,
+				E1E34DD01C7670250023AF4D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				E1E34DD41C7670250023AF4D /* PBXTargetDependency */,
+			);
+			name = TreapTests;
+			productName = TreapTests;
+			productReference = E1E34DD21C7670250023AF4D /* TreapTests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		E1E34DBB1C7670240023AF4D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "WillowTree, Inc.";
+				TargetAttributes = {
+					E1E34DC21C7670240023AF4D = {
+						CreatedOnToolsVersion = 7.2.1;
+					};
+					E1E34DD11C7670250023AF4D = {
+						CreatedOnToolsVersion = 7.2.1;
+						TestTargetID = E1E34DC21C7670240023AF4D;
+					};
+				};
+			};
+			buildConfigurationList = E1E34DBE1C7670240023AF4D /* Build configuration list for PBXProject "Treap" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = E1E34DBA1C7670240023AF4D;
+			productRefGroup = E1E34DC41C7670240023AF4D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				E1E34DC21C7670240023AF4D /* Treap */,
+				E1E34DD11C7670250023AF4D /* TreapTests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		E1E34DC11C7670240023AF4D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				E1E34DC91C7670240023AF4D /* Assets.xcassets in Resources */,
+				E1E34DCC1C7670240023AF4D /* MainMenu.xib in Resources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		E1E34DD01C7670250023AF4D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		E1E34DBF1C7670240023AF4D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				E1E34DEA1C7671200023AF4D /* TreapCollectionType.swift in Sources */,
+				E1E34DE31C7670350023AF4D /* Treap.swift in Sources */,
+				E1E34DC71C7670240023AF4D /* AppDelegate.swift in Sources */,
+				E1E34DE41C7670350023AF4D /* TreapMergeSplit.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		E1E34DCE1C7670250023AF4D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				E1E34DD71C7670250023AF4D /* TreapTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin PBXTargetDependency section */
+		E1E34DD41C7670250023AF4D /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			target = E1E34DC21C7670240023AF4D /* Treap */;
+			targetProxy = E1E34DD31C7670250023AF4D /* PBXContainerItemProxy */;
+		};
+/* End PBXTargetDependency section */
+
+/* Begin PBXVariantGroup section */
+		E1E34DCA1C7670240023AF4D /* MainMenu.xib */ = {
+			isa = PBXVariantGroup;
+			children = (
+				E1E34DCB1C7670240023AF4D /* Base */,
+			);
+			name = MainMenu.xib;
+			sourceTree = "<group>";
+		};
+/* End PBXVariantGroup section */
+
+/* Begin XCBuildConfiguration section */
+		E1E34DD91C7670250023AF4D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		E1E34DDA1C7670250023AF4D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		E1E34DDC1C7670250023AF4D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Treap/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.Treap;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		E1E34DDD1C7670250023AF4D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Treap/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.Treap;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+		E1E34DDF1C7670250023AF4D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = TreapTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Treap.app/Contents/MacOS/Treap";
+			};
+			name = Debug;
+		};
+		E1E34DE01C7670250023AF4D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = TreapTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Treap.app/Contents/MacOS/Treap";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		E1E34DBE1C7670240023AF4D /* Build configuration list for PBXProject "Treap" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				E1E34DD91C7670250023AF4D /* Debug */,
+				E1E34DDA1C7670250023AF4D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		E1E34DDB1C7670250023AF4D /* Build configuration list for PBXNativeTarget "Treap" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				E1E34DDC1C7670250023AF4D /* Debug */,
+				E1E34DDD1C7670250023AF4D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+		E1E34DDE1C7670250023AF4D /* Build configuration list for PBXNativeTarget "TreapTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				E1E34DDF1C7670250023AF4D /* Debug */,
+				E1E34DE01C7670250023AF4D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = E1E34DBB1C7670240023AF4D /* Project object */;
+}
diff --git a/Treap/Treap/Treap/AppDelegate.swift b/Treap/Treap/Treap/AppDelegate.swift
new file mode 100644
index 000000000..a156c1cb4
--- /dev/null
+++ b/Treap/Treap/Treap/AppDelegate.swift
@@ -0,0 +1,27 @@
+//
+//  AppDelegate.swift
+//  Treap
+//
+//  Created by Robert Thompson on 2/18/16.
+//  Copyright © 2016 WillowTree, Inc. All rights reserved.
+//
+
+import Cocoa
+
+@NSApplicationMain
+class AppDelegate: NSObject, NSApplicationDelegate {
+
+    @IBOutlet weak var window: NSWindow!
+
+
+    func applicationDidFinishLaunching(aNotification: NSNotification) {
+        // Insert code here to initialize your application
+    }
+
+    func applicationWillTerminate(aNotification: NSNotification) {
+        // Insert code here to tear down your application
+    }
+
+
+}
+
diff --git a/Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json b/Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..2db2b1c7c
--- /dev/null
+++ b/Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json
@@ -0,0 +1,58 @@
+{
+  "images" : [
+    {
+      "idiom" : "mac",
+      "size" : "16x16",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "16x16",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "32x32",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "32x32",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "128x128",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "128x128",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "256x256",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "256x256",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "512x512",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "512x512",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Treap/Treap/Treap/Base.lproj/MainMenu.xib b/Treap/Treap/Treap/Base.lproj/MainMenu.xib
new file mode 100644
index 000000000..8955ad822
--- /dev/null
+++ b/Treap/Treap/Treap/Base.lproj/MainMenu.xib
@@ -0,0 +1,681 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="9532" systemVersion="15E39c" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
+    <dependencies>
+        <deployment identifier="macosx"/>
+        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="9532"/>
+    </dependencies>
+    <objects>
+        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
+            <connections>
+                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
+            </connections>
+        </customObject>
+        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
+        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
+        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModule="Treap" customModuleProvider="target">
+            <connections>
+                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
+            </connections>
+        </customObject>
+        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
+        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
+            <items>
+                <menuItem title="Treap" id="1Xt-HY-uBw">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Treap" systemMenu="apple" id="uQy-DD-JDr">
+                        <items>
+                            <menuItem title="About Treap" id="5kV-Vb-QxS">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
+                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
+                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
+                            <menuItem title="Services" id="NMo-om-nkz">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
+                            <menuItem title="Hide Treap" keyEquivalent="h" id="Olw-nP-bQN">
+                                <connections>
+                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
+                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                <connections>
+                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Show All" id="Kd2-mp-pUS">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
+                            <menuItem title="Quit Treap" keyEquivalent="q" id="4sb-4s-VLi">
+                                <connections>
+                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="File" id="dMs-cI-mzQ">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="File" id="bib-Uj-vzu">
+                        <items>
+                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
+                                <connections>
+                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
+                                <connections>
+                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Open Recent" id="tXI-mr-wws">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
+                                    <items>
+                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
+                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
+                                <connections>
+                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
+                                <connections>
+                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
+                                <connections>
+                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
+                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
+                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
+                                <connections>
+                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
+                                <connections>
+                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Edit" id="5QF-Oa-p0T">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
+                        <items>
+                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
+                                <connections>
+                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
+                                <connections>
+                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
+                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
+                                <connections>
+                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
+                                <connections>
+                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
+                                <connections>
+                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
+                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                <connections>
+                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Delete" id="pa3-QI-u2k">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
+                                <connections>
+                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
+                            <menuItem title="Find" id="4EN-yA-p0u">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
+                                    <items>
+                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
+                                            <connections>
+                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
+                                            <connections>
+                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
+                                    <items>
+                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
+                                            <connections>
+                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
+                                            <connections>
+                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
+                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Substitutions" id="9ic-FL-obx">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
+                                    <items>
+                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
+                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smart Links" id="cwL-P1-jid">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
+                                    <items>
+                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Speech" id="xrE-MZ-jX0">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
+                                    <items>
+                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Format" id="jxT-CU-nIS">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
+                        <items>
+                            <menuItem title="Font" id="Gi5-1S-RQB">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
+                                    <items>
+                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
+                                            <connections>
+                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
+                                            <connections>
+                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
+                                            <connections>
+                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
+                                            <connections>
+                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
+                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
+                                            <connections>
+                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
+                                            <connections>
+                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
+                                        <menuItem title="Kern" id="jBQ-r6-VK2">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
+                                                <items>
+                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use None" id="cDB-IK-hbR">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Tighten" id="46P-cB-AYj">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
+                                                <items>
+                                                    <menuItem title="Use Default" id="agt-UL-0e3">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use None" id="J7y-lM-qPV">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use All" id="xQD-1f-W4t">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
+                                                <items>
+                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Subscript" id="I0S-gh-46l">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Raise" id="2h7-ER-AoG">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Lower" id="1tx-W0-xDw">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
+                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
+                                            <connections>
+                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
+                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="pasteFont:" target="-1" id="JfD-CL-leO"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Text" id="Fal-I4-PZk">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Text" id="d9c-me-L2H">
+                                    <items>
+                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
+                                            <connections>
+                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
+                                            <connections>
+                                                <action selector="alignCenter:" target="-1" id="spX-mk-kcS"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Justify" id="J5U-5w-g23">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="alignJustified:" target="-1" id="ljL-7U-jND"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
+                                            <connections>
+                                                <action selector="alignRight:" target="-1" id="r48-bG-YeY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
+                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
+                                                <items>
+                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                    </menuItem>
+                                                    <menuItem id="YGs-j5-SAR">
+                                                        <string key="title">	Default</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="Lbh-J2-qVU">
+                                                        <string key="title">	Left to Right</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="jFq-tB-4Kx">
+                                                        <string key="title">	Right to Left</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
+                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                    </menuItem>
+                                                    <menuItem id="Nop-cj-93Q">
+                                                        <string key="title">	Default</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeTextWritingDirectionNatural:" target="-1" id="lPI-Se-ZHp"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="BgM-ve-c93">
+                                                        <string key="title">	Left to Right</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeTextWritingDirectionLeftToRight:" target="-1" id="caW-Bv-w94"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem id="RB4-Sm-HuC">
+                                                        <string key="title">	Right to Left</string>
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="makeTextWritingDirectionRightToLeft:" target="-1" id="EXD-6r-ZUu"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="fKy-g9-1gm"/>
+                                        <menuItem title="Show Ruler" id="vLm-3I-IUL">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="toggleRuler:" target="-1" id="FOx-HJ-KwY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Copy Ruler" keyEquivalent="c" id="MkV-Pr-PK5">
+                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="copyRuler:" target="-1" id="71i-fW-3W2"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Paste Ruler" keyEquivalent="v" id="LVM-kO-fVI">
+                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="pasteRuler:" target="-1" id="cSh-wd-qM2"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="View" id="H8h-7b-M4v">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="View" id="HyV-fh-RgO">
+                        <items>
+                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
+                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                <connections>
+                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="runToolbarCustomizationPalette:" target="-1" id="pQI-g3-MTW"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Window" id="aUF-d1-5bR">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
+                        <items>
+                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
+                                <connections>
+                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem title="Zoom" id="R4o-n2-Eq4">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
+                                </connections>
+                            </menuItem>
+                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
+                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <connections>
+                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+                <menuItem title="Help" id="wpr-3q-Mcd">
+                    <modifierMask key="keyEquivalentModifierMask"/>
+                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
+                        <items>
+                            <menuItem title="Treap Help" keyEquivalent="?" id="FKE-Sm-Kum">
+                                <connections>
+                                    <action selector="showHelp:" target="-1" id="y7X-2Q-9no"/>
+                                </connections>
+                            </menuItem>
+                        </items>
+                    </menu>
+                </menuItem>
+            </items>
+        </menu>
+        <window title="Treap" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" releasedWhenClosed="NO" animationBehavior="default" id="QvC-M9-y7g">
+            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
+            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
+            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
+            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1057"/>
+            <view key="contentView" id="EiT-Mj-1SZ">
+                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
+                <autoresizingMask key="autoresizingMask"/>
+            </view>
+        </window>
+    </objects>
+</document>
diff --git a/Treap/Treap/Treap/Info.plist b/Treap/Treap/Treap/Info.plist
new file mode 100644
index 000000000..63294f2da
--- /dev/null
+++ b/Treap/Treap/Treap/Info.plist
@@ -0,0 +1,34 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIconFile</key>
+	<string></string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSMinimumSystemVersion</key>
+	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
+	<key>NSHumanReadableCopyright</key>
+	<string>Copyright © 2016 WillowTree, Inc. All rights reserved.</string>
+	<key>NSMainNibFile</key>
+	<string>MainMenu</string>
+	<key>NSPrincipalClass</key>
+	<string>NSApplication</string>
+</dict>
+</plist>
diff --git a/Treap/Treap/TreapTests/Info.plist b/Treap/Treap/TreapTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Treap/Treap/TreapTests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
new file mode 100644
index 000000000..06421ad78
--- /dev/null
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -0,0 +1,57 @@
+//
+//  TreapTests.swift
+//  TreapTests
+//
+//  Created by Robert Thompson on 2/18/16.
+//  Copyright © 2016 WillowTree, Inc. All rights reserved.
+//
+
+import XCTest
+@testable import Treap
+
+class TreapTests: XCTestCase {
+    
+    override func setUp() {
+        super.setUp()
+        // Put setup code here. This method is called before the invocation of each test method in the class.
+    }
+    
+    override func tearDown() {
+        // Put teardown code here. This method is called after the invocation of each test method in the class.
+        super.tearDown()
+    }
+    
+    func testSanity() {
+        var treap = Treap<Int, String>.Empty
+        treap = treap.set(5, val: "a").set(7, val: "b")
+        XCTAssert(treap.get(5) == "a")
+        XCTAssert(treap.get(7) == "b")
+        treap = treap.set(2, val: "c")
+        XCTAssert(treap.get(2) == "c")
+        treap = treap.set(2, val: "d")
+        XCTAssert(treap.get(2) == "d")
+        treap = try! treap.delete(5)
+        XCTAssert(!treap.contains(5))
+        XCTAssert(treap.contains(7))
+    }
+
+    func testFairlyBalanced() {
+        var treap = Treap<Int, Int?>.Empty
+        for i in 0..<1000 {
+            treap = treap.set(i, val: nil)
+        }
+        let depth = treap.depth
+        XCTAssert(depth < 30, "treap.depth was \(depth)")
+    }
+
+    func testFairlyBalancedCollection() {
+        var treap = Treap<Int, Int?>()
+        for i in 0..<1000
+        {
+            treap[i] = Optional<Int>.None
+        }
+        let depth = treap.depth
+        XCTAssert(depth > 0 && depth < 30)
+    }
+    
+}
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
new file mode 100644
index 000000000..9753b6207
--- /dev/null
+++ b/Treap/TreapCollectionType.swift
@@ -0,0 +1,81 @@
+//
+//  TreapCollectionType.swift
+//  Treap
+//
+//  Created by Robert Thompson on 2/18/16.
+//  Copyright © 2016 WillowTree, Inc. All rights reserved.
+//
+
+import Foundation
+
+extension Treap: CollectionType {
+    public typealias Index = TreapIndex<Key>
+
+    public subscript(index: TreapIndex<Key>) -> Element {
+        get {
+            guard let result = self.get(index.keys[index.keyIndex]) else {
+                fatalError("Invalid index!")
+            }
+
+            return result
+        }
+
+        mutating set {
+            let key = index.keys[index.keyIndex]
+            self = self.set(key, val: newValue)
+        }
+    }
+
+    public subscript(key: Key) -> Element? {
+        get {
+            return self.get(key)
+        }
+
+        mutating set {
+            guard let value = newValue else {
+                let _ = try? self.delete(key)
+                return
+            }
+
+            self = self.set(key, val: value)
+        }
+    }
+
+    public var startIndex: TreapIndex<Key> {
+        return TreapIndex<Key>(keys: keys, keyIndex: 0)
+    }
+
+    public var endIndex: TreapIndex<Key> {
+        let keys = self.keys
+        return TreapIndex<Key>(keys: keys, keyIndex: keys.count)
+    }
+
+    private var keys: [Key] {
+        var results: [Key] = []
+        if case let .Node(key, _, _, left, right) = self {
+            results.appendContentsOf(left.keys)
+            results.append(key)
+            results.appendContentsOf(right.keys)
+        }
+
+        return results
+    }
+}
+
+public struct TreapIndex<Key: Comparable>: ForwardIndexType {
+    private let keys: [Key]
+    private let keyIndex: Int
+
+    public func successor() -> TreapIndex {
+        return TreapIndex(keys: keys, keyIndex: keyIndex + 1)
+    }
+
+    private init(keys: [Key] = [], keyIndex: Int = 0) {
+        self.keys = keys
+        self.keyIndex = keyIndex
+    }
+}
+
+public func ==<Key: Comparable>(lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
+    return lhs.keys == rhs.keys && lhs.keyIndex == rhs.keyIndex
+}
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
new file mode 100644
index 000000000..eed6d3d94
--- /dev/null
+++ b/Treap/TreapMergeSplit.swift
@@ -0,0 +1,113 @@
+//
+//  TreapMergeSplit.swift
+//  TreapExample
+//
+//  Created by Robert Thompson on 7/27/15.
+//  Copyright © 2015 Robert Thompson. All rights reserved.
+//
+
+import Foundation
+public extension Treap {
+    internal func split(key: Key) -> (left: Treap, right: Treap)
+    {
+        var current = self
+        let val: Element
+        if let newVal = self.get(key)
+        {
+            current = try! current.delete(key)
+            val = newVal
+        }
+        else if case let .Node(_, newVal, _, _, _) = self
+        {
+            val = newVal
+        }
+        else
+        {
+            fatalError("No values in treap")
+        }
+        
+        switch self {
+        case .Node:
+            if case let .Node(_, _, _, left, right) = current.set(key, val: val, p: -1)
+            {
+                return (left: left, right: right)
+            }
+            else
+            {
+                return (left: .Empty, right: .Empty)
+            }
+        default:
+            return (left: .Empty, right: .Empty)
+        }
+    }
+    
+    internal var leastKey: Key? {
+        switch self {
+        case .Empty:
+            return nil
+        case let .Node(key, _, _, .Empty, _):
+            return key
+        case let .Node(_, _, _, left, _):
+            return left.leastKey
+        }
+    }
+    
+    internal var mostKey: Key? {
+        switch self {
+        case .Empty:
+            return nil
+        case let .Node(key, _, _, _, .Empty):
+            return key
+        case let .Node(_, _, _, _, right):
+            return right.mostKey
+        }
+    }
+}
+
+internal func merge<Key: Comparable, Element>(left: Treap<Key, Element>, right: Treap<Key, Element>) -> Treap<Key, Element> {
+    switch (left, right) {
+    case (.Empty, _):
+        return right
+    case (_, .Empty):
+        return left
+        
+    case let (.Node(leftKey, leftVal, leftP, leftLeft, leftRight), .Node(rightKey, rightVal, rightP, rightLeft, rightRight)):
+        if leftP < rightP {
+            return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: merge(leftRight, right: right))
+        }
+        else
+        {
+            return .Node(key: rightKey, val: rightVal, p: rightP, left: merge(rightLeft, right: left), right: rightRight)
+        }
+    default:
+        break
+    }
+    return .Empty
+}
+
+extension Treap: CustomStringConvertible
+{
+    public var description: String {
+        get {
+            return Treap.descHelper(self, indent: 0)
+        }
+    }
+    
+    private static func descHelper(treap: Treap<Key, Element>, indent: Int) -> String
+    {
+        if case let .Node(key, value, priority, left, right) = treap {
+            var result = ""
+            let tabs = String(count: indent, repeatedValue: Character("\t"))
+            
+            result += descHelper(left, indent: indent + 1)
+            result += "\n" + tabs + "\(key), \(value), \(priority)\n"
+            result += descHelper(right, indent: indent + 1)
+            
+            return result
+        }
+        else
+        {
+            return ""
+        }
+    }
+}
\ No newline at end of file

From 0598dc1d9105322489522d79d67a64574e8538fc Mon Sep 17 00:00:00 2001
From: Robert Thompson <robert.thompson@willowtreeapps.com>
Date: Thu, 18 Feb 2016 17:59:35 -0500
Subject: [PATCH 0030/1679] May as well be BidirectionalIndexType

---
 Treap/TreapCollectionType.swift | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index 9753b6207..a4f37c0b7 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -62,7 +62,7 @@ extension Treap: CollectionType {
     }
 }
 
-public struct TreapIndex<Key: Comparable>: ForwardIndexType {
+public struct TreapIndex<Key: Comparable>: BidirectionalIndexType {
     private let keys: [Key]
     private let keyIndex: Int
 
@@ -70,6 +70,10 @@ public struct TreapIndex<Key: Comparable>: ForwardIndexType {
         return TreapIndex(keys: keys, keyIndex: keyIndex + 1)
     }
 
+    public func predecessor() -> TreapIndex {
+        return TreapIndex(keys: keys, keyIndex: keyIndex - 1)
+    }
+
     private init(keys: [Key] = [], keyIndex: Int = 0) {
         self.keys = keys
         self.keyIndex = keyIndex

From d88f10e94866e1cd6088d6236fcadbf379b51603 Mon Sep 17 00:00:00 2001
From: Robert Thompson <robert.thompson@willowtreeapps.com>
Date: Thu, 18 Feb 2016 18:01:22 -0500
Subject: [PATCH 0031/1679] Honestly it's MutableCollectionType

---
 Treap/TreapCollectionType.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index a4f37c0b7..f624bf265 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -8,7 +8,7 @@
 
 import Foundation
 
-extension Treap: CollectionType {
+extension Treap: MutableCollectionType {
     public typealias Index = TreapIndex<Key>
 
     public subscript(index: TreapIndex<Key>) -> Element {

From f907963c4ec7eb795a550ec0d35aeecccf66edb0 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Fri, 19 Feb 2016 11:09:03 +0100
Subject: [PATCH 0032/1679] Reducing the number of columns and rows for testing
 big arrays 2D

---
 .../array2DtestTests/array2DtestTests.swift   | 34 +++++++------------
 1 file changed, 13 insertions(+), 21 deletions(-)

diff --git a/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift b/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
index 0292449b4..926819e45 100644
--- a/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
+++ b/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
@@ -21,33 +21,26 @@ class Array2DTest: XCTestCase {
     
     func testIntegerArrayWithPositiveRowsAndColumns() {
         let array = Array2D<Int>(columns: 3, rows: 2, initialValue: 0)
-        XCTAssert(array.columns == 3, "Column count setup worked")
-        XCTAssert(array.rows == 2, "Rows count setup worked")
-        XCTAssert(array[2,2] == 0, "Integer array: Initialization value properly read")
+        
+        XCTAssertEqual(array.columns, 3, "Column count setup failed")
+        XCTAssertEqual(array.rows, 2, "Rows count setup failed")
+        XCTAssertEqual(array[2,1], 0, "Integer array: Initialization value is wrong")
     }
     
     func testStringArrayWithPositiveRowsAndColumns() {
         let array = Array2D<String>(columns: 3, rows: 2, initialValue: "empty")
-        XCTAssert(array.columns == 3, "Column count setup worked")
-        XCTAssert(array.rows == 2, "Rows count setup worked")
-        XCTAssert(array[2,2] == "empty", "String array: Initialization value properly read")
+        
+        XCTAssertEqual(array.columns, 3, "Column count setup failed")
+        XCTAssertEqual(array.rows, 2, "Rows count setup failed")
+        XCTAssertEqual(array[2,1], "empty", "String array: Initialization value is wrong")
     }
     
     func testCustomClassArrayWithPositiveRowsAndColumns() {
         let array = Array2D<TestElement>(columns: 3, rows: 2, initialValue: TestElement(identifier: "pepe"))
-        XCTAssert(array.columns == 3, "Column count setup worked")
-        XCTAssert(array.rows == 2, "Rows count setup worked")
-        XCTAssert(array[2,2] == TestElement(identifier: "pepe"), "Custom Class array: Initialization value properly read")
-    }
-    
-    func testArrayWithNegativeColumns() {
-        let array = Array2D(columns: -1,rows: 2,initialValue: 0)
-        XCTAssertNil(array)
-    }
-    
-    func testAccessingWrongIndex() {
-        let array = Array2D(columns: 2, rows: 4, initialValue: 5)
-        XCTAssertNil(array[20,20], "Array in 20,20 is not a valid index")
+        
+        XCTAssertEqual(array.columns, 3, "Column count setup failed")
+        XCTAssertEqual(array.rows, 2, "Rows count setup failed")
+        XCTAssertEqual(array[2,1], TestElement(identifier: "pepe"), "Custom Class array: Initialization value is wrong")
     }
     
     func testPerformanceOnSmallArray() {
@@ -58,7 +51,7 @@ class Array2DTest: XCTestCase {
 
     func testPerformanceOnLargeArray() {
         self.measureBlock {
-            self.printArrayWith(columns: 2000000, rows: 2000000, inititalValue: 1)
+            self.printArrayWith(columns: 2000, rows: 2000, inititalValue: 1)
         }
     }
 
@@ -79,7 +72,6 @@ class TestElement : Equatable {
     init(identifier: String) {
         self.identifier = identifier
     }
-    
 }
 
 func == (lhs: TestElement, rhs: TestElement) -> Bool {

From 77152547da2314c0a03937eaf41cc8d16963c1ef Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Fri, 19 Feb 2016 14:00:58 +0100
Subject: [PATCH 0033/1679] Tests for AVLTree

---
 .../AVLTreeTests.xcodeproj/project.pbxproj    | 415 ++++++++++++++++++
 .../AVLTreeTests/AppDelegate.swift            |  46 ++
 .../AppIcon.appiconset/Contents.json          |  68 +++
 .../Base.lproj/LaunchScreen.storyboard        |  27 ++
 .../AVLTreeTests/Base.lproj/Main.storyboard   |  25 ++
 .../AVLTreeTests/AVLTreeTests/Info.plist      |  47 ++
 .../AVLTreeTests/ViewController.swift         |  25 ++
 .../AVLTreeTestsTests/AVLTreeTestsTests.swift |  82 ++++
 .../AVLTreeTests/AVLTreeTestsTests/Info.plist |  24 +
 .../AVLTreeTestsTests/TreeNodeTest.swift      |  86 ++++
 10 files changed, 845 insertions(+)
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests/AppDelegate.swift
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests/Info.plist
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTests/ViewController.swift
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/Info.plist
 create mode 100644 AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift

diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj b/AVLtreeTest/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..45e5ceb17
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
@@ -0,0 +1,415 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		763F28681C77228700AABA94 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F28671C77228700AABA94 /* AppDelegate.swift */; };
+		763F286A1C77228700AABA94 /* ViewController.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F28691C77228700AABA94 /* ViewController.swift */; };
+		763F286D1C77228700AABA94 /* Main.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 763F286B1C77228700AABA94 /* Main.storyboard */; };
+		763F286F1C77228700AABA94 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 763F286E1C77228700AABA94 /* Assets.xcassets */; };
+		763F28721C77228700AABA94 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 763F28701C77228700AABA94 /* LaunchScreen.storyboard */; };
+		763F287D1C77228700AABA94 /* AVLTreeTestsTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F287C1C77228700AABA94 /* AVLTreeTestsTests.swift */; };
+		763F28881C77229D00AABA94 /* AVLTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F28871C77229D00AABA94 /* AVLTree.swift */; };
+		763F288B1C77254000AABA94 /* TreeNodeTest.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F288A1C77254000AABA94 /* TreeNodeTest.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
+		763F28791C77228700AABA94 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 763F285C1C77228600AABA94 /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = 763F28631C77228600AABA94;
+			remoteInfo = AVLTreeTests;
+		};
+/* End PBXContainerItemProxy section */
+
+/* Begin PBXFileReference section */
+		763F28641C77228700AABA94 /* AVLTreeTests.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = AVLTreeTests.app; sourceTree = BUILT_PRODUCTS_DIR; };
+		763F28671C77228700AABA94 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
+		763F28691C77228700AABA94 /* ViewController.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = ViewController.swift; sourceTree = "<group>"; };
+		763F286C1C77228700AABA94 /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.storyboard; name = Base; path = Base.lproj/Main.storyboard; sourceTree = "<group>"; };
+		763F286E1C77228700AABA94 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
+		763F28711C77228700AABA94 /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.storyboard; name = Base; path = Base.lproj/LaunchScreen.storyboard; sourceTree = "<group>"; };
+		763F28731C77228700AABA94 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		763F28781C77228700AABA94 /* AVLTreeTestsTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = AVLTreeTestsTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		763F287C1C77228700AABA94 /* AVLTreeTestsTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AVLTreeTestsTests.swift; sourceTree = "<group>"; };
+		763F287E1C77228700AABA94 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		763F28871C77229D00AABA94 /* AVLTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = AVLTree.swift; path = "../../../AVL Tree/AVLTree.swift"; sourceTree = "<group>"; };
+		763F28891C7722B700AABA94 /* AVLTree.playground */ = {isa = PBXFileReference; lastKnownFileType = file.playground; name = AVLTree.playground; path = "../../../AVL Tree/AVLTree.playground"; sourceTree = "<group>"; };
+		763F288A1C77254000AABA94 /* TreeNodeTest.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = TreeNodeTest.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
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+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		763F28751C77228700AABA94 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		763F285B1C77228600AABA94 = {
+			isa = PBXGroup;
+			children = (
+				763F28661C77228700AABA94 /* AVLTreeTests */,
+				763F287B1C77228700AABA94 /* AVLTreeTestsTests */,
+				763F28651C77228700AABA94 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
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+		};
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+}
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/AppDelegate.swift b/AVLtreeTest/AVLTreeTests/AVLTreeTests/AppDelegate.swift
new file mode 100644
index 000000000..ac29ab4db
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests/AppDelegate.swift
@@ -0,0 +1,46 @@
+//
+//  AppDelegate.swift
+//  AVLTreeTests
+//
+//  Created by Barbara Rodeker on 2/19/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import UIKit
+
+@UIApplicationMain
+class AppDelegate: UIResponder, UIApplicationDelegate {
+
+    var window: UIWindow?
+
+
+    func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
+        // Override point for customization after application launch.
+        return true
+    }
+
+    func applicationWillResignActive(application: UIApplication) {
+        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
+        // Use this method to pause ongoing tasks, disable timers, and throttle down OpenGL ES frame rates. Games should use this method to pause the game.
+    }
+
+    func applicationDidEnterBackground(application: UIApplication) {
+        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
+        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
+    }
+
+    func applicationWillEnterForeground(application: UIApplication) {
+        // Called as part of the transition from the background to the inactive state; here you can undo many of the changes made on entering the background.
+    }
+
+    func applicationDidBecomeActive(application: UIApplication) {
+        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
+    }
+
+    func applicationWillTerminate(application: UIApplication) {
+        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
+    }
+
+
+}
+
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..36d2c80d8
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
@@ -0,0 +1,68 @@
+{
+  "images" : [
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
new file mode 100644
index 000000000..2e721e183
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
@@ -0,0 +1,27 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="8150" systemVersion="15A204g" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" initialViewController="01J-lp-oVM">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="8122"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="EHf-IW-A2E">
+            <objects>
+                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
+                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
+                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <animations/>
+                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="53" y="375"/>
+        </scene>
+    </scenes>
+</document>
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
new file mode 100644
index 000000000..3a2a49bad
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
@@ -0,0 +1,25 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="6211" systemVersion="14A298i" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" initialViewController="BYZ-38-t0r">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="6204"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="tne-QT-ifu">
+            <objects>
+                <viewController id="BYZ-38-t0r" customClass="ViewController" customModuleProvider="target" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="y3c-jy-aDJ"/>
+                        <viewControllerLayoutGuide type="bottom" id="wfy-db-euE"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="8bC-Xf-vdC">
+                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="dkx-z0-nzr" sceneMemberID="firstResponder"/>
+            </objects>
+        </scene>
+    </scenes>
+</document>
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Info.plist b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Info.plist
new file mode 100644
index 000000000..40c6215d9
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests/Info.plist
@@ -0,0 +1,47 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSRequiresIPhoneOS</key>
+	<true/>
+	<key>UILaunchStoryboardName</key>
+	<string>LaunchScreen</string>
+	<key>UIMainStoryboardFile</key>
+	<string>Main</string>
+	<key>UIRequiredDeviceCapabilities</key>
+	<array>
+		<string>armv7</string>
+	</array>
+	<key>UISupportedInterfaceOrientations</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>UISupportedInterfaceOrientations~ipad</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationPortraitUpsideDown</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+</dict>
+</plist>
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/ViewController.swift b/AVLtreeTest/AVLTreeTests/AVLTreeTests/ViewController.swift
new file mode 100644
index 000000000..88030d517
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTests/ViewController.swift
@@ -0,0 +1,25 @@
+//
+//  ViewController.swift
+//  AVLTreeTests
+//
+//  Created by Barbara Rodeker on 2/19/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import UIKit
+
+class ViewController: UIViewController {
+
+    override func viewDidLoad() {
+        super.viewDidLoad()
+        // Do any additional setup after loading the view, typically from a nib.
+    }
+
+    override func didReceiveMemoryWarning() {
+        super.didReceiveMemoryWarning()
+        // Dispose of any resources that can be recreated.
+    }
+
+
+}
+
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift b/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
new file mode 100644
index 000000000..01ac0b5e5
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
@@ -0,0 +1,82 @@
+//
+//  AVLTreeTestsTests.swift
+//  AVLTreeTestsTests
+//
+//  Created by Barbara Rodeker on 2/19/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+@testable import AVLTreeTests
+
+class AVLTreeTestsTests: XCTestCase {
+    
+    var tree : AVLTree<Int, String>?
+    
+    override func setUp() {
+        super.setUp()
+
+        tree = AVLTree()
+        tree?.insert(1, "A")
+        tree?.insert(2, "B")
+        tree?.insert(3, "C")
+        tree?.insert(4, "D")
+    }
+    
+    override func tearDown() {
+        // Put teardown code here. This method is called after the invocation of each test method in the class.
+        super.tearDown()
+    }
+    
+    func testEmptyInitialization() {
+        let tree = AVLTree<Int,String>()
+        
+        XCTAssertEqual(tree.size, 0)
+        XCTAssertNil(tree.root)
+    }
+
+    func testNotEmptyInitialization() {
+        XCTAssertNotNil(self.tree?.root)
+        XCTAssertNotEqual(self.tree!.size, 0)
+    }
+    
+    func testInsertDuplicated() {
+        self.tree?.insert(1, "A")
+        XCTAssertEqual(self.tree?.size, 5, "Duplicated elements should be allowed")
+    }
+    
+    func testSingleInsertionPerformance() {
+        self.measureBlock {
+            self.tree?.insert(5, "E")
+        }
+    }
+    
+    func testMultipleInsertionsPerformance() {
+        self.measureBlock {
+            self.tree?.autopopulateWithNodes(50)
+        }
+    }
+    
+    func testSearchExistentOnSmallTreePerformance() {
+        self.measureBlock {
+            self.tree?.search(2)
+        }
+    }
+    
+    func testSearchExistentElementOnLargeTreePerformance() {
+        self.measureBlock {
+            self.tree?.autopopulateWithNodes(500)
+            self.tree?.search(400)
+        }
+    }
+    
+}
+
+extension AVLTree where Key : SignedIntegerType {
+    func autopopulateWithNodes(count : Int) {
+        var k : Key = 1
+        for _ in 0...count {
+            self.insert(k++)
+        }
+    }
+}
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/Info.plist b/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift b/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift
new file mode 100644
index 000000000..802277ea9
--- /dev/null
+++ b/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift
@@ -0,0 +1,86 @@
+//
+//  TreeNodeTest.swift
+//  AVLTreeTests
+//
+//  Created by Barbara Rodeker on 2/19/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+@testable import AVLTreeTests
+
+
+class TreeNodeTest: XCTestCase {
+    
+    var root : TreeNode<String,String>?
+    var left : TreeNode<String,String>?
+    var right : TreeNode<String,String>?
+    
+    override func setUp() {
+        super.setUp()
+
+        left = TreeNode<String,String>(key: "Name", payload: "Left")
+        right = TreeNode<String,String>(key: "Name", payload: "Right")
+        root = TreeNode<String,String>(key: "Name", payload: "Root", leftChild: left, rightChild: right, parent: nil)
+    }
+    
+    override func tearDown() {
+        // Put teardown code here. This method is called after the invocation of each test method in the class.
+        super.tearDown()
+    }
+    
+    
+    func testSingleNodeCreationNOPayload() {
+        let treeNode = TreeNode<String,String>(key: "Building")
+        XCTAssertNil(treeNode.payload, "Payload for this case should be nil")
+    }
+    
+    func testSingleNodeCreationWithPayload() {
+        XCTAssertNotNil(self.root!, "Payload for this case should not be nil")
+    }
+    
+    func testIsRoot() {
+        XCTAssertTrue(self.root!.isRoot)
+    }
+    
+    func testNotIsLeaf() {
+        XCTAssertFalse(self.root!.isLeaf, "root node is not leaf")
+    }
+    
+    func testNotIsLeftChild() {
+        XCTAssertFalse(self.root!.isLeftChild, "root node is not left child")
+    }
+    
+    func testNotIsRightChild() {
+        XCTAssertFalse(self.root!.isRightChild, "root node is not right child")
+    }
+    
+    func testIsLeftChild() {
+        XCTAssertTrue(self.left!.isLeftChild)
+    }
+
+    func testIsRightChild() {
+        XCTAssertTrue(self.right!.isRightChild)
+    }
+
+    func isLeaf() {
+        XCTAssertTrue(self.left!.isLeaf)
+    }
+    
+    func testHasAnyChild() {
+        XCTAssertTrue(self.root!.hasAnyChild)
+    }
+    
+    func testNotHasAnyChild() {
+        XCTAssertFalse(self.left!.hasAnyChild)
+    }
+    
+    func testHasBothChildren() {
+        XCTAssertTrue(self.root!.hasBothChildren)
+    }
+    
+    func testNotHasBothChildren() {
+        XCTAssertFalse(self.left!.hasBothChildren)
+    }
+    
+}

From 3f7090e4f251349f500b800f3390edab43b2069f Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Fri, 19 Feb 2016 14:15:23 +0100
Subject: [PATCH 0034/1679] Setting a parent reference when a child is added to
 a node. Making parent reference weak

---
 AVL Tree/AVLTree.swift | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 12befbe92..d05cd94bf 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -28,14 +28,16 @@ public class TreeNode<Key: Comparable, Payload> {
   private var key: Key
   private var leftChild: Node?
   private var rightChild: Node?
-  private var parent: Node?
+  weak private var parent: Node?
   private var balance = 0
   
   public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?) {
     self.key = key
     self.payload = payload
     self.leftChild = leftChild
+    self.leftChild?.parent = self
     self.rightChild = rightChild
+    self.rightChild?.parent = self
     self.parent = parent
   }
 

From 3aee5c4bb82acd7cdf123af523ff0eaef4516446 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Fri, 19 Feb 2016 14:21:27 +0100
Subject: [PATCH 0035/1679] Moving AVL test inside its main algortihms folder,
 commiting shared project data

---
 .../AVLTreeTests.xcodeproj/project.pbxproj    |  0
 .../AVLTreeTests/AppDelegate.swift            |  0
 .../AppIcon.appiconset/Contents.json          |  0
 .../Base.lproj/LaunchScreen.storyboard        |  0
 .../AVLTreeTests/Base.lproj/Main.storyboard   |  0
 .../AVLTreeTests/AVLTreeTests/Info.plist      |  0
 .../AVLTreeTests/ViewController.swift         |  0
 .../AVLTreeTestsTests/AVLTreeTestsTests.swift |  0
 .../AVLTreeTests/AVLTreeTestsTests/Info.plist |  0
 .../AVLTreeTestsTests/TreeNodeTest.swift      |  0
 ...B9780967-0BD8-4A91-8657-A96EFB81859F.plist | 22 ++++++++++
 .../Info.plist                                | 40 +++++++++++++++++++
 12 files changed, 62 insertions(+)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests/AppDelegate.swift (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests/Info.plist (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTests/ViewController.swift (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTestsTests/Info.plist (100%)
 rename {AVLtreeTest => AVL Tree}/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift (100%)
 create mode 100644 Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
 create mode 100644 Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist

diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj b/AVL Tree/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
rename to AVL Tree/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/AppDelegate.swift b/AVL Tree/AVLTreeTests/AVLTreeTests/AppDelegate.swift
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests/AppDelegate.swift
rename to AVL Tree/AVLTreeTests/AVLTreeTests/AppDelegate.swift
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json b/AVL Tree/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
rename to AVL Tree/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard b/AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
rename to AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard b/AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
rename to AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/Info.plist b/AVL Tree/AVLTreeTests/AVLTreeTests/Info.plist
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests/Info.plist
rename to AVL Tree/AVLTreeTests/AVLTreeTests/Info.plist
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTests/ViewController.swift b/AVL Tree/AVLTreeTests/AVLTreeTests/ViewController.swift
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTests/ViewController.swift
rename to AVL Tree/AVLTreeTests/AVLTreeTests/ViewController.swift
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift b/AVL Tree/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
rename to AVL Tree/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/Info.plist b/AVL Tree/AVLTreeTests/AVLTreeTestsTests/Info.plist
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/Info.plist
rename to AVL Tree/AVLTreeTests/AVLTreeTestsTests/Info.plist
diff --git a/AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift b/AVL Tree/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift
similarity index 100%
rename from AVLtreeTest/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift
rename to AVL Tree/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift
diff --git a/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist b/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
new file mode 100644
index 000000000..124dc73bc
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>classNames</key>
+	<dict>
+		<key>Array2DTest</key>
+		<dict>
+			<key>testPerformanceOnSmallArray()</key>
+			<dict>
+				<key>com.apple.XCTPerformanceMetric_WallClockTime</key>
+				<dict>
+					<key>baselineAverage</key>
+					<real>0.377</real>
+					<key>baselineIntegrationDisplayName</key>
+					<string>Local Baseline</string>
+				</dict>
+			</dict>
+		</dict>
+	</dict>
+</dict>
+</plist>
diff --git a/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist b/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
new file mode 100644
index 000000000..a0e45b60a
--- /dev/null
+++ b/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>runDestinationsByUUID</key>
+	<dict>
+		<key>B9780967-0BD8-4A91-8657-A96EFB81859F</key>
+		<dict>
+			<key>localComputer</key>
+			<dict>
+				<key>busSpeedInMHz</key>
+				<integer>100</integer>
+				<key>cpuCount</key>
+				<integer>1</integer>
+				<key>cpuKind</key>
+				<string>Intel Core i5</string>
+				<key>cpuSpeedInMHz</key>
+				<integer>2500</integer>
+				<key>logicalCPUCoresPerPackage</key>
+				<integer>4</integer>
+				<key>modelCode</key>
+				<string>Macmini6,1</string>
+				<key>physicalCPUCoresPerPackage</key>
+				<integer>2</integer>
+				<key>platformIdentifier</key>
+				<string>com.apple.platform.macosx</string>
+			</dict>
+			<key>targetArchitecture</key>
+			<string>x86_64</string>
+			<key>targetDevice</key>
+			<dict>
+				<key>modelCode</key>
+				<string>iPhone8,2</string>
+				<key>platformIdentifier</key>
+				<string>com.apple.platform.iphonesimulator</string>
+			</dict>
+		</dict>
+	</dict>
+</dict>
+</plist>

From f75c9e814624d24d6b792f695101e9dd02e58250 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 19 Feb 2016 16:29:46 +0100
Subject: [PATCH 0036/1679] Add link to rosettacode.org

---
 Big-O Notation.markdown | 2 +-
 README.markdown         | 3 ++-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 20c0d9dea..8cb988168 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -14,7 +14,7 @@ Big-O | Name | Description
 **O(n log n)** | "linearithmic" | **Decent performance.** This is slightly worse than linear but not too bad. Example: the fastest general-purpose sorting algorithms.
 **O(n^2)** | quadratic | **Kinda slow.** If you have 100 items, this does 100^2 = 10,000 units of work. Doubling the number of items makes it four times slower (because 2 squared equals 4). Example: algorithms using nested loops, such as insertion sort.
 **O(n^3)** | cubic | **Poor performance.** If you have 100 items, this does 100^3 = 1,000,000 units of work. Doubling the input size makes it eight times slower. Example: matrix multiplication.
-**O(2^n)** | exponential | **Very poor performance.** You want to avoid these kinds of algorithms, but sometimes you have no choice. Example: traveling salesperson problem.
+**O(2^n)** | exponential | **Very poor performance.** You want to avoid these kinds of algorithms, but sometimes you have no choice. Adding just one bit to the input doubles the running time. Example: traveling salesperson problem.
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.
 
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
diff --git a/README.markdown b/README.markdown
index db22ae68f..8a08a7575 100644
--- a/README.markdown
+++ b/README.markdown
@@ -188,9 +188,10 @@ The following books are available for free online:
 - [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
 - Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
 
-Friends of the club:
+Other algorithm repositories:
 
 - [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
+- [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
 
 ## License
 

From 56a7ec75ea1cf313ffa365e344a4d76749d52256 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 19 Feb 2016 16:51:49 +0100
Subject: [PATCH 0037/1679] Small tweaks to folder names for tests

---
 .../AVLTreeTests.xcodeproj/project.pbxproj             |  0
 .../AVLTreeTests/AppDelegate.swift                     |  0
 .../Assets.xcassets/AppIcon.appiconset/Contents.json   |  0
 .../AVLTreeTests/Base.lproj/LaunchScreen.storyboard    |  0
 .../AVLTreeTests/Base.lproj/Main.storyboard            |  0
 .../AVLTreeTests/Info.plist                            |  0
 .../AVLTreeTests/ViewController.swift                  |  0
 .../AVLTreeTestsTests/AVLTreeTestsTests.swift          |  0
 .../AVLTreeTestsTests/Info.plist                       |  0
 .../AVLTreeTestsTests/TreeNodeTest.swift               |  0
 .../array2Dtest.xcodeproj/project.pbxproj              |  0
 .../B9780967-0BD8-4A91-8657-A96EFB81859F.plist         |  0
 .../766116211C7625C700358E02.xcbaseline/Info.plist     |  0
 .../array2Dtest/AppDelegate.swift                      |  0
 .../Assets.xcassets/AppIcon.appiconset/Contents.json   |  0
 .../array2Dtest/Base.lproj/LaunchScreen.storyboard     |  0
 .../array2Dtest/Base.lproj/Main.storyboard             |  0
 .../array2Dtest/Info.plist                             |  0
 .../array2Dtest/ViewController.swift                   |  0
 .../array2DtestTests/Info.plist                        |  0
 .../array2DtestTests/array2DtestTests.swift            | 10 +++++-----
 21 files changed, 5 insertions(+), 5 deletions(-)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests.xcodeproj/project.pbxproj (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests/AppDelegate.swift (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests/Base.lproj/LaunchScreen.storyboard (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests/Base.lproj/Main.storyboard (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests/Info.plist (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTests/ViewController.swift (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTestsTests/AVLTreeTestsTests.swift (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTestsTests/Info.plist (100%)
 rename AVL Tree/{AVLTreeTests => AVLTree Tests}/AVLTreeTestsTests/TreeNodeTest.swift (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest.xcodeproj/project.pbxproj (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest/AppDelegate.swift (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest/Base.lproj/LaunchScreen.storyboard (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest/Base.lproj/Main.storyboard (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest/Info.plist (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2Dtest/ViewController.swift (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2DtestTests/Info.plist (100%)
 rename Array2D/{array2Dtest => Array2D Tests}/array2DtestTests/array2DtestTests.swift (93%)

diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj b/AVL Tree/AVLTree Tests/AVLTreeTests.xcodeproj/project.pbxproj
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests.xcodeproj/project.pbxproj
rename to AVL Tree/AVLTree Tests/AVLTreeTests.xcodeproj/project.pbxproj
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests/AppDelegate.swift b/AVL Tree/AVLTree Tests/AVLTreeTests/AppDelegate.swift
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests/AppDelegate.swift
rename to AVL Tree/AVLTree Tests/AVLTreeTests/AppDelegate.swift
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json b/AVL Tree/AVLTree Tests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
rename to AVL Tree/AVLTree Tests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard b/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
rename to AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard b/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/Main.storyboard
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests/Base.lproj/Main.storyboard
rename to AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/Main.storyboard
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests/Info.plist b/AVL Tree/AVLTree Tests/AVLTreeTests/Info.plist
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests/Info.plist
rename to AVL Tree/AVLTree Tests/AVLTreeTests/Info.plist
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTests/ViewController.swift b/AVL Tree/AVLTree Tests/AVLTreeTests/ViewController.swift
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTests/ViewController.swift
rename to AVL Tree/AVLTree Tests/AVLTreeTests/ViewController.swift
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift b/AVL Tree/AVLTree Tests/AVLTreeTestsTests/AVLTreeTestsTests.swift
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTestsTests/AVLTreeTestsTests.swift
rename to AVL Tree/AVLTree Tests/AVLTreeTestsTests/AVLTreeTestsTests.swift
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTestsTests/Info.plist b/AVL Tree/AVLTree Tests/AVLTreeTestsTests/Info.plist
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTestsTests/Info.plist
rename to AVL Tree/AVLTree Tests/AVLTreeTestsTests/Info.plist
diff --git a/AVL Tree/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift b/AVL Tree/AVLTree Tests/AVLTreeTestsTests/TreeNodeTest.swift
similarity index 100%
rename from AVL Tree/AVLTreeTests/AVLTreeTestsTests/TreeNodeTest.swift
rename to AVL Tree/AVLTree Tests/AVLTreeTestsTests/TreeNodeTest.swift
diff --git a/Array2D/array2Dtest/array2Dtest.xcodeproj/project.pbxproj b/Array2D/Array2D Tests/array2Dtest.xcodeproj/project.pbxproj
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest.xcodeproj/project.pbxproj
rename to Array2D/Array2D Tests/array2Dtest.xcodeproj/project.pbxproj
diff --git a/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist b/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
rename to Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
diff --git a/Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist b/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
rename to Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
diff --git a/Array2D/array2Dtest/array2Dtest/AppDelegate.swift b/Array2D/Array2D Tests/array2Dtest/AppDelegate.swift
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest/AppDelegate.swift
rename to Array2D/Array2D Tests/array2Dtest/AppDelegate.swift
diff --git a/Array2D/array2Dtest/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json b/Array2D/Array2D Tests/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
rename to Array2D/Array2D Tests/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
diff --git a/Array2D/array2Dtest/array2Dtest/Base.lproj/LaunchScreen.storyboard b/Array2D/Array2D Tests/array2Dtest/Base.lproj/LaunchScreen.storyboard
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest/Base.lproj/LaunchScreen.storyboard
rename to Array2D/Array2D Tests/array2Dtest/Base.lproj/LaunchScreen.storyboard
diff --git a/Array2D/array2Dtest/array2Dtest/Base.lproj/Main.storyboard b/Array2D/Array2D Tests/array2Dtest/Base.lproj/Main.storyboard
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest/Base.lproj/Main.storyboard
rename to Array2D/Array2D Tests/array2Dtest/Base.lproj/Main.storyboard
diff --git a/Array2D/array2Dtest/array2Dtest/Info.plist b/Array2D/Array2D Tests/array2Dtest/Info.plist
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest/Info.plist
rename to Array2D/Array2D Tests/array2Dtest/Info.plist
diff --git a/Array2D/array2Dtest/array2Dtest/ViewController.swift b/Array2D/Array2D Tests/array2Dtest/ViewController.swift
similarity index 100%
rename from Array2D/array2Dtest/array2Dtest/ViewController.swift
rename to Array2D/Array2D Tests/array2Dtest/ViewController.swift
diff --git a/Array2D/array2Dtest/array2DtestTests/Info.plist b/Array2D/Array2D Tests/array2DtestTests/Info.plist
similarity index 100%
rename from Array2D/array2Dtest/array2DtestTests/Info.plist
rename to Array2D/Array2D Tests/array2DtestTests/Info.plist
diff --git a/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift b/Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift
similarity index 93%
rename from Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
rename to Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift
index 926819e45..234d0f9b4 100644
--- a/Array2D/array2Dtest/array2DtestTests/array2DtestTests.swift
+++ b/Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift	
@@ -49,11 +49,11 @@ class Array2DTest: XCTestCase {
         }
     }
 
-    func testPerformanceOnLargeArray() {
-        self.measureBlock {
-            self.printArrayWith(columns: 2000, rows: 2000, inititalValue: 1)
-        }
-    }
+//    func testPerformanceOnLargeArray() {
+//        self.measureBlock {
+//            self.printArrayWith(columns: 2000, rows: 2000, inititalValue: 1)
+//        }
+//    }
 
     private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int){
         let array = Array2D(columns: columns, rows: rows, initialValue: 4)

From 3ed00a3d2dd102b0e68cef456920c7f83416d5b1 Mon Sep 17 00:00:00 2001
From: Robert Thompson <robert.thompson@willowtreeapps.com>
Date: Fri, 19 Feb 2016 11:02:24 -0500
Subject: [PATCH 0038/1679] Fix license

---
 Treap/Treap.swift                       | 20 ++++++++++++++++++--
 Treap/Treap/Treap/AppDelegate.swift     | 19 ++++++++++++++++++-
 Treap/Treap/TreapTests/TreapTests.swift | 20 ++++++++++++++++++--
 Treap/TreapCollectionType.swift         | 20 ++++++++++++++++++--
 Treap/TreapMergeSplit.swift             | 20 ++++++++++++++++++--
 5 files changed, 90 insertions(+), 9 deletions(-)

diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 108eec913..5413a17c2 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -3,8 +3,24 @@
 //  TreapExample
 //
 //  Created by Robert Thompson on 7/27/15.
-//  Copyright © 2015 Robert Thompson. All rights reserved.
-//
+//  Copyright © 2016 Robert Thompson
+/* Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.*/
 
 import Foundation
 
diff --git a/Treap/Treap/Treap/AppDelegate.swift b/Treap/Treap/Treap/AppDelegate.swift
index a156c1cb4..1813d840b 100644
--- a/Treap/Treap/Treap/AppDelegate.swift
+++ b/Treap/Treap/Treap/AppDelegate.swift
@@ -3,7 +3,24 @@
 //  Treap
 //
 //  Created by Robert Thompson on 2/18/16.
-//  Copyright © 2016 WillowTree, Inc. All rights reserved.
+//  Copyright © 2016 Robert Thompson
+/* Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.*/
 //
 
 import Cocoa
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index 06421ad78..496e2f940 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -3,8 +3,24 @@
 //  TreapTests
 //
 //  Created by Robert Thompson on 2/18/16.
-//  Copyright © 2016 WillowTree, Inc. All rights reserved.
-//
+//  Copyright © 2016 Robert Thompson
+/* Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.*/
 
 import XCTest
 @testable import Treap
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index f624bf265..36d02eaac 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -3,8 +3,24 @@
 //  Treap
 //
 //  Created by Robert Thompson on 2/18/16.
-//  Copyright © 2016 WillowTree, Inc. All rights reserved.
-//
+//  Copyright © 2016 Robert Thompson
+/* Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.*/
 
 import Foundation
 
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index eed6d3d94..51929893b 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -3,8 +3,24 @@
 //  TreapExample
 //
 //  Created by Robert Thompson on 7/27/15.
-//  Copyright © 2015 Robert Thompson. All rights reserved.
-//
+//  Copyright © 2016 Robert Thompson
+/* Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.*/
 
 import Foundation
 public extension Treap {

From 063f3fe99b93fd76f243e0fb1cff982ea1ccf47e Mon Sep 17 00:00:00 2001
From: Robert Thompson <robert.thompson@willowtreeapps.com>
Date: Fri, 19 Feb 2016 11:05:56 -0500
Subject: [PATCH 0039/1679] Add SequenceType conformance to Stack

As per issue #10
---
 Stack/Stack.swift | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 8186a70de..96c1ff284 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -30,3 +30,13 @@ public struct Stack<T> {
     return array.last
   }
 }
+
+extension Stack: SequenceType {
+    public func generate() -> AnyGenerator<T> {
+        var curr = self
+        return anyGenerator {
+            _ -> T? in
+            return curr.pop()
+        }
+    }
+}

From 464077afd297dbc8f57bb0779fb466a8d99a2086 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 19 Feb 2016 20:49:46 +0100
Subject: [PATCH 0040/1679] Unit tests no longer use host application

---
 .../AVLTreeTests.xcodeproj/project.pbxproj    | 415 -----------
 .../AVLTreeTests/AppDelegate.swift            |  46 --
 .../AppIcon.appiconset/Contents.json          |  68 --
 .../Base.lproj/LaunchScreen.storyboard        |  27 -
 .../AVLTreeTests/Base.lproj/Main.storyboard   |  25 -
 .../AVLTree Tests/AVLTreeTests/Info.plist     |  47 --
 .../AVLTreeTests/ViewController.swift         |  25 -
 .../AVLTreeTestsTests/AVLTreeTestsTests.swift |  82 ---
 AVL Tree/Tests/AVLTreeTests.swift             |  80 +++
 .../AVLTreeTestsTests => Tests}/Info.plist    |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 265 +++++++
 .../TreeNodeTests.swift}                      |   4 +-
 .../array2Dtest.xcodeproj/project.pbxproj     | 409 -----------
 ...B9780967-0BD8-4A91-8657-A96EFB81859F.plist |  22 -
 .../Info.plist                                |  40 --
 .../array2Dtest/AppDelegate.swift             |  46 --
 .../AppIcon.appiconset/Contents.json          |  68 --
 .../Base.lproj/LaunchScreen.storyboard        |  27 -
 .../array2Dtest/Base.lproj/Main.storyboard    |  25 -
 Array2D/Array2D Tests/array2Dtest/Info.plist  |  47 --
 .../array2Dtest/ViewController.swift          |  25 -
 .../array2DtestTests/array2DtestTests.swift   |  80 ---
 Array2D/Tests/Array2DTests.swift              |  78 ++
 .../array2DtestTests => Tests}/Info.plist     |   0
 Array2D/Tests/Tests.xcodeproj/project.pbxproj | 261 +++++++
 .../project.pbxproj                           | 394 ----------
 .../BinarySearchTree/AppDelegate.swift        |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../BinarySearchTree/Base.lproj/MainMenu.xib  | 680 ------------------
 .../BinarySearchTree/Info.plist               |  34 -
 .../BinarySearchTreeTests.swift               |   1 -
 .../Info.plist                                |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 261 +++++++
 .../BinarySearch.xcodeproj/project.pbxproj    | 394 ----------
 .../BinarySearch/AppDelegate.swift            |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../BinarySearch/Base.lproj/MainMenu.xib      | 680 ------------------
 .../BinarySearch/Info.plist                   |  34 -
 .../BinarySearchTests.swift                   |   1 -
 .../BinarySearchTests => Tests}/Info.plist    |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 261 +++++++
 .../HeapSort.xcodeproj/project.pbxproj        | 398 ----------
 .../HeapSort Tests/HeapSort/AppDelegate.swift |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../HeapSort/Base.lproj/MainMenu.xib          | 680 ------------------
 Heap Sort/HeapSort Tests/HeapSort/Info.plist  |  34 -
 .../HeapSortTests.swift                       |   9 -
 .../HeapSortTests => Tests}/Info.plist        |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 265 +++++++
 .../Heap Tests/Heap.xcodeproj/project.pbxproj | 394 ----------
 Heap/Heap Tests/Heap/AppDelegate.swift        |  15 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 Heap/Heap Tests/Heap/Base.lproj/MainMenu.xib  | 680 ------------------
 Heap/Heap Tests/Heap/Info.plist               |  34 -
 .../HeapTests => Tests}/HeapTests.swift       |   1 -
 .../HeapTests => Tests}/Info.plist            |   0
 Heap/Tests/Tests.xcodeproj/project.pbxproj    | 261 +++++++
 .../InsertionSort.xcodeproj/project.pbxproj   | 398 ----------
 .../InsertionSort/AppDelegate.swift           |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../InsertionSort/Base.lproj/MainMenu.xib     | 680 ------------------
 .../InsertionSort/Info.plist                  |  34 -
 .../InsertionSortTests => Tests}/Info.plist   |   0
 .../InsertionSortTests.swift                  |   1 -
 .../Tests/Tests.xcodeproj/project.pbxproj     | 265 +++++++
 .../LinkedList.xcodeproj/project.pbxproj      | 394 ----------
 .../LinkedList/AppDelegate.swift              |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../LinkedList/Base.lproj/MainMenu.xib        | 680 ------------------
 .../LinkedList Tests/LinkedList/Info.plist    |  34 -
 .../LinkedListTests => Tests}/Info.plist      |   0
 .../LinkedListTests.swift                     |   1 -
 .../Tests/Tests.xcodeproj/project.pbxproj     | 261 +++++++
 .../PriorityQueue.xcodeproj/project.pbxproj   | 398 ----------
 .../PriorityQueue/AppDelegate.swift           |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../PriorityQueue/Base.lproj/MainMenu.xib     | 680 ------------------
 .../PriorityQueue/Info.plist                  |  34 -
 .../PriorityQueueTests => Tests}/Info.plist   |   0
 .../PriorityQueueTests.swift                  |   1 -
 .../Tests/Tests.xcodeproj/project.pbxproj     | 265 +++++++
 .../Queue.xcodeproj/project.pbxproj           | 394 ----------
 Queue/Queue Tests/Queue/AppDelegate.swift     |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../Queue Tests/Queue/Base.lproj/MainMenu.xib | 680 ------------------
 Queue/Queue Tests/Queue/Info.plist            |  34 -
 .../QueueTests => Tests}/Info.plist           |   0
 .../QueueTests => Tests}/QueueTests.swift     |   1 -
 Queue/Tests/Tests.xcodeproj/project.pbxproj   | 261 +++++++
 .../Quicksort.xcodeproj/project.pbxproj       | 398 ----------
 .../Quicksort/AppDelegate.swift               |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../Quicksort/Base.lproj/MainMenu.xib         | 680 ------------------
 .../Quicksort Tests/Quicksort/Info.plist      |  34 -
 .../QuicksortTests => Tests}/Info.plist       |   0
 .../QuicksortTests.swift                      |   1 -
 .../SortingTestHelpers.swift                  |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 265 +++++++
 .../RLE Tests/RLE.xcodeproj/project.pbxproj   | 394 ----------
 .../RLE Tests/RLE/AppDelegate.swift           |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../RLE Tests/RLE/Base.lproj/MainMenu.xib     | 680 ------------------
 Run-Length Encoding/RLE Tests/RLE/Info.plist  |  34 -
 Run-Length Encoding/RLE Tests/RLE/RLE.swift   |  70 --
 Run-Length Encoding/RLE.swift                 |  76 +-
 .../{RLE Tests/RLETests => Tests}/Info.plist  |   0
 .../RLETests => Tests}/RLETests.swift         |   1 -
 .../Tests/Tests.xcodeproj/project.pbxproj     | 261 +++++++
 .../MinimumMaximumPairs.swift                 |   3 +-
 .../project.pbxproj                           | 393 ----------
 .../SelectMinimumMaximum/AppDelegate.swift    |  16 -
 .../SelectMinimumMaximum/Info.plist           |  32 -
 .../Info.plist                                |   0
 .../MaximumTests.swift                        |   1 -
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 .../TestHelper.swift                          |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 281 ++++++++
 .../SelectionSort.xcodeproj/project.pbxproj   | 398 ----------
 .../SelectionSort/AppDelegate.swift           |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../SelectionSort/Base.lproj/MainMenu.xib     | 680 ------------------
 .../SelectionSort/Info.plist                  |  34 -
 .../SelectionSortTests => Tests}/Info.plist   |   0
 .../SelectionSortTests.swift                  |   1 -
 .../Tests/Tests.xcodeproj/project.pbxproj     | 265 +++++++
 .../ShellSort.xcodeproj/project.pbxproj       | 398 ----------
 .../ShellSort/AppDelegate.swift               |  27 -
 .../AppIcon.appiconset/Contents.json          |  58 --
 .../ShellSort/Base.lproj/MainMenu.xib         | 680 ------------------
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 .../Stack.xcodeproj/project.pbxproj           | 394 ----------
 Stack/Stack Tests/Stack/AppDelegate.swift     |  27 -
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 .../Stack Tests/Stack/Base.lproj/MainMenu.xib | 680 ------------------
 Stack/Stack Tests/Stack/Info.plist            |  34 -
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 .../StackTests => Tests}/StackTests.swift     |   1 -
 Stack/Tests/Tests.xcodeproj/project.pbxproj   | 261 +++++++
 142 files changed, 4428 insertions(+), 17619 deletions(-)
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests.xcodeproj/project.pbxproj
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests/AppDelegate.swift
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/Main.storyboard
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests/Info.plist
 delete mode 100644 AVL Tree/AVLTree Tests/AVLTreeTests/ViewController.swift
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 create mode 100644 AVL Tree/Tests/AVLTreeTests.swift
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 delete mode 100644 Array2D/Array2D Tests/array2Dtest.xcodeproj/project.pbxproj
 delete mode 100644 Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
 delete mode 100644 Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
 delete mode 100644 Array2D/Array2D Tests/array2Dtest/AppDelegate.swift
 delete mode 100644 Array2D/Array2D Tests/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 Array2D/Array2D Tests/array2Dtest/Base.lproj/LaunchScreen.storyboard
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 delete mode 100644 Array2D/Array2D Tests/array2Dtest/Info.plist
 delete mode 100644 Array2D/Array2D Tests/array2Dtest/ViewController.swift
 delete mode 100644 Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift
 create mode 100644 Array2D/Tests/Array2DTests.swift
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 create mode 100644 Array2D/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree.xcodeproj/project.pbxproj
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/AppDelegate.swift
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Base.lproj/MainMenu.xib
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 rename Binary Search Tree/Solution 1/{BinarySearchTree Tests/BinarySearchTreeTests => Tests}/BinarySearchTreeTests.swift (99%)
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 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Binary Search/BinarySearch Tests/BinarySearch.xcodeproj/project.pbxproj
 delete mode 100644 Binary Search/BinarySearch Tests/BinarySearch/AppDelegate.swift
 delete mode 100644 Binary Search/BinarySearch Tests/BinarySearch/Assets.xcassets/AppIcon.appiconset/Contents.json
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 rename Binary Search/{BinarySearch Tests/BinarySearchTests => Tests}/BinarySearchTests.swift (97%)
 rename Binary Search/{BinarySearch Tests/BinarySearchTests => Tests}/Info.plist (100%)
 create mode 100644 Binary Search/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Heap Sort/HeapSort Tests/HeapSort.xcodeproj/project.pbxproj
 delete mode 100644 Heap Sort/HeapSort Tests/HeapSort/AppDelegate.swift
 delete mode 100644 Heap Sort/HeapSort Tests/HeapSort/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 Heap Sort/HeapSort Tests/HeapSort/Base.lproj/MainMenu.xib
 delete mode 100644 Heap Sort/HeapSort Tests/HeapSort/Info.plist
 rename Heap Sort/{HeapSort Tests/HeapSortTests => Tests}/HeapSortTests.swift (81%)
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 create mode 100644 Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Heap/Heap Tests/Heap.xcodeproj/project.pbxproj
 delete mode 100644 Heap/Heap Tests/Heap/AppDelegate.swift
 delete mode 100644 Heap/Heap Tests/Heap/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 Heap/Heap Tests/Heap/Base.lproj/MainMenu.xib
 delete mode 100644 Heap/Heap Tests/Heap/Info.plist
 rename Heap/{Heap Tests/HeapTests => Tests}/HeapTests.swift (99%)
 rename Heap/{Heap Tests/HeapTests => Tests}/Info.plist (100%)
 create mode 100644 Heap/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Insertion Sort/InsertionSort Tests/InsertionSort.xcodeproj/project.pbxproj
 delete mode 100644 Insertion Sort/InsertionSort Tests/InsertionSort/AppDelegate.swift
 delete mode 100644 Insertion Sort/InsertionSort Tests/InsertionSort/Assets.xcassets/AppIcon.appiconset/Contents.json
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 delete mode 100644 Insertion Sort/InsertionSort Tests/InsertionSort/Info.plist
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 rename Insertion Sort/{InsertionSort Tests/InsertionSortTests => Tests}/InsertionSortTests.swift (80%)
 create mode 100644 Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Linked List/LinkedList Tests/LinkedList.xcodeproj/project.pbxproj
 delete mode 100644 Linked List/LinkedList Tests/LinkedList/AppDelegate.swift
 delete mode 100644 Linked List/LinkedList Tests/LinkedList/Assets.xcassets/AppIcon.appiconset/Contents.json
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 rename Linked List/{LinkedList Tests/LinkedListTests => Tests}/LinkedListTests.swift (99%)
 create mode 100644 Linked List/Tests/Tests.xcodeproj/project.pbxproj
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 delete mode 100644 Priority Queue/PriorityQueue Tests/PriorityQueue/AppDelegate.swift
 delete mode 100644 Priority Queue/PriorityQueue Tests/PriorityQueue/Assets.xcassets/AppIcon.appiconset/Contents.json
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 delete mode 100644 Queue/Queue Tests/Queue/AppDelegate.swift
 delete mode 100644 Queue/Queue Tests/Queue/Assets.xcassets/AppIcon.appiconset/Contents.json
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 delete mode 100644 Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift
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 delete mode 100644 Run-Length Encoding/RLE Tests/RLE/RLE.swift
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 rename Run-Length Encoding/{RLE Tests/RLETests => Tests}/RLETests.swift (99%)
 create mode 100644 Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj
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 delete mode 100644 Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/AppDelegate.swift
 delete mode 100644 Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/Info.plist
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 rename Select Minimum Maximum/{SelectMinimumMaximum Tests/SelectMinimumMaximumTests => Tests}/MaximumTests.swift (96%)
 rename Select Minimum Maximum/{SelectMinimumMaximum Tests/SelectMinimumMaximumTests/SelectMinimumMaximumTests.swift => Tests/MinimumMaximumPairsTests.swift} (95%)
 rename Select Minimum Maximum/{SelectMinimumMaximum Tests/SelectMinimumMaximumTests => Tests}/MinimumTests.swift (96%)
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 create mode 100644 Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Selection Sort/SelectionSort Tests/SelectionSort.xcodeproj/project.pbxproj
 delete mode 100644 Selection Sort/SelectionSort Tests/SelectionSort/AppDelegate.swift
 delete mode 100644 Selection Sort/SelectionSort Tests/SelectionSort/Assets.xcassets/AppIcon.appiconset/Contents.json
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 rename Selection Sort/{SelectionSort Tests/SelectionSortTests => Tests}/SelectionSortTests.swift (80%)
 create mode 100644 Selection Sort/Tests/Tests.xcodeproj/project.pbxproj
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 rename Stack/{Stack Tests/StackTests => Tests}/Info.plist (100%)
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deleted file mode 100644
index 45e5ceb17..000000000
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diff --git a/AVL Tree/AVLTree Tests/AVLTreeTests/AppDelegate.swift b/AVL Tree/AVLTree Tests/AVLTreeTests/AppDelegate.swift
deleted file mode 100644
index ac29ab4db..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTests/AppDelegate.swift	
+++ /dev/null
@@ -1,46 +0,0 @@
-//
-//  AppDelegate.swift
-//  AVLTreeTests
-//
-//  Created by Barbara Rodeker on 2/19/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import UIKit
-
-@UIApplicationMain
-class AppDelegate: UIResponder, UIApplicationDelegate {
-
-    var window: UIWindow?
-
-
-    func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
-        // Override point for customization after application launch.
-        return true
-    }
-
-    func applicationWillResignActive(application: UIApplication) {
-        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
-        // Use this method to pause ongoing tasks, disable timers, and throttle down OpenGL ES frame rates. Games should use this method to pause the game.
-    }
-
-    func applicationDidEnterBackground(application: UIApplication) {
-        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
-        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
-    }
-
-    func applicationWillEnterForeground(application: UIApplication) {
-        // Called as part of the transition from the background to the inactive state; here you can undo many of the changes made on entering the background.
-    }
-
-    func applicationDidBecomeActive(application: UIApplication) {
-        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
-    }
-
-    func applicationWillTerminate(application: UIApplication) {
-        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
-    }
-
-
-}
-
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json b/AVL Tree/AVLTree Tests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 36d2c80d8..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTests/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,68 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "iphone",
-      "size" : "29x29",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "29x29",
-      "scale" : "3x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "40x40",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "40x40",
-      "scale" : "3x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "60x60",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "60x60",
-      "scale" : "3x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "29x29",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "29x29",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "40x40",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "40x40",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "76x76",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "76x76",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard b/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard
deleted file mode 100644
index 2e721e183..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/LaunchScreen.storyboard	
+++ /dev/null
@@ -1,27 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="8150" systemVersion="15A204g" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" initialViewController="01J-lp-oVM">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="8122"/>
-    </dependencies>
-    <scenes>
-        <!--View Controller-->
-        <scene sceneID="EHf-IW-A2E">
-            <objects>
-                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
-                    <layoutGuides>
-                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
-                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
-                    </layoutGuides>
-                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
-                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
-                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
-                        <animations/>
-                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
-                    </view>
-                </viewController>
-                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
-            </objects>
-            <point key="canvasLocation" x="53" y="375"/>
-        </scene>
-    </scenes>
-</document>
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/Main.storyboard b/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/Main.storyboard
deleted file mode 100644
index 3a2a49bad..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTests/Base.lproj/Main.storyboard	
+++ /dev/null
@@ -1,25 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="6211" systemVersion="14A298i" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" initialViewController="BYZ-38-t0r">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="6204"/>
-    </dependencies>
-    <scenes>
-        <!--View Controller-->
-        <scene sceneID="tne-QT-ifu">
-            <objects>
-                <viewController id="BYZ-38-t0r" customClass="ViewController" customModuleProvider="target" sceneMemberID="viewController">
-                    <layoutGuides>
-                        <viewControllerLayoutGuide type="top" id="y3c-jy-aDJ"/>
-                        <viewControllerLayoutGuide type="bottom" id="wfy-db-euE"/>
-                    </layoutGuides>
-                    <view key="view" contentMode="scaleToFill" id="8bC-Xf-vdC">
-                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
-                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
-                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
-                    </view>
-                </viewController>
-                <placeholder placeholderIdentifier="IBFirstResponder" id="dkx-z0-nzr" sceneMemberID="firstResponder"/>
-            </objects>
-        </scene>
-    </scenes>
-</document>
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTests/Info.plist b/AVL Tree/AVLTree Tests/AVLTreeTests/Info.plist
deleted file mode 100644
index 40c6215d9..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTests/Info.plist	
+++ /dev/null
@@ -1,47 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSRequiresIPhoneOS</key>
-	<true/>
-	<key>UILaunchStoryboardName</key>
-	<string>LaunchScreen</string>
-	<key>UIMainStoryboardFile</key>
-	<string>Main</string>
-	<key>UIRequiredDeviceCapabilities</key>
-	<array>
-		<string>armv7</string>
-	</array>
-	<key>UISupportedInterfaceOrientations</key>
-	<array>
-		<string>UIInterfaceOrientationPortrait</string>
-		<string>UIInterfaceOrientationLandscapeLeft</string>
-		<string>UIInterfaceOrientationLandscapeRight</string>
-	</array>
-	<key>UISupportedInterfaceOrientations~ipad</key>
-	<array>
-		<string>UIInterfaceOrientationPortrait</string>
-		<string>UIInterfaceOrientationPortraitUpsideDown</string>
-		<string>UIInterfaceOrientationLandscapeLeft</string>
-		<string>UIInterfaceOrientationLandscapeRight</string>
-	</array>
-</dict>
-</plist>
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTests/ViewController.swift b/AVL Tree/AVLTree Tests/AVLTreeTests/ViewController.swift
deleted file mode 100644
index 88030d517..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTests/ViewController.swift	
+++ /dev/null
@@ -1,25 +0,0 @@
-//
-//  ViewController.swift
-//  AVLTreeTests
-//
-//  Created by Barbara Rodeker on 2/19/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import UIKit
-
-class ViewController: UIViewController {
-
-    override func viewDidLoad() {
-        super.viewDidLoad()
-        // Do any additional setup after loading the view, typically from a nib.
-    }
-
-    override func didReceiveMemoryWarning() {
-        super.didReceiveMemoryWarning()
-        // Dispose of any resources that can be recreated.
-    }
-
-
-}
-
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTestsTests/AVLTreeTestsTests.swift b/AVL Tree/AVLTree Tests/AVLTreeTestsTests/AVLTreeTestsTests.swift
deleted file mode 100644
index 01ac0b5e5..000000000
--- a/AVL Tree/AVLTree Tests/AVLTreeTestsTests/AVLTreeTestsTests.swift	
+++ /dev/null
@@ -1,82 +0,0 @@
-//
-//  AVLTreeTestsTests.swift
-//  AVLTreeTestsTests
-//
-//  Created by Barbara Rodeker on 2/19/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import XCTest
-@testable import AVLTreeTests
-
-class AVLTreeTestsTests: XCTestCase {
-    
-    var tree : AVLTree<Int, String>?
-    
-    override func setUp() {
-        super.setUp()
-
-        tree = AVLTree()
-        tree?.insert(1, "A")
-        tree?.insert(2, "B")
-        tree?.insert(3, "C")
-        tree?.insert(4, "D")
-    }
-    
-    override func tearDown() {
-        // Put teardown code here. This method is called after the invocation of each test method in the class.
-        super.tearDown()
-    }
-    
-    func testEmptyInitialization() {
-        let tree = AVLTree<Int,String>()
-        
-        XCTAssertEqual(tree.size, 0)
-        XCTAssertNil(tree.root)
-    }
-
-    func testNotEmptyInitialization() {
-        XCTAssertNotNil(self.tree?.root)
-        XCTAssertNotEqual(self.tree!.size, 0)
-    }
-    
-    func testInsertDuplicated() {
-        self.tree?.insert(1, "A")
-        XCTAssertEqual(self.tree?.size, 5, "Duplicated elements should be allowed")
-    }
-    
-    func testSingleInsertionPerformance() {
-        self.measureBlock {
-            self.tree?.insert(5, "E")
-        }
-    }
-    
-    func testMultipleInsertionsPerformance() {
-        self.measureBlock {
-            self.tree?.autopopulateWithNodes(50)
-        }
-    }
-    
-    func testSearchExistentOnSmallTreePerformance() {
-        self.measureBlock {
-            self.tree?.search(2)
-        }
-    }
-    
-    func testSearchExistentElementOnLargeTreePerformance() {
-        self.measureBlock {
-            self.tree?.autopopulateWithNodes(500)
-            self.tree?.search(400)
-        }
-    }
-    
-}
-
-extension AVLTree where Key : SignedIntegerType {
-    func autopopulateWithNodes(count : Int) {
-        var k : Key = 1
-        for _ in 0...count {
-            self.insert(k++)
-        }
-    }
-}
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
new file mode 100644
index 000000000..f079603cf
--- /dev/null
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -0,0 +1,80 @@
+//
+//  AVLTreeTestsTests.swift
+//  AVLTreeTestsTests
+//
+//  Created by Barbara Rodeker on 2/19/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+
+class AVLTreeTests: XCTestCase {
+  
+  var tree : AVLTree<Int, String>?
+  
+  override func setUp() {
+    super.setUp()
+    
+    tree = AVLTree()
+    tree?.insert(1, "A")
+    tree?.insert(2, "B")
+    tree?.insert(3, "C")
+    tree?.insert(4, "D")
+  }
+  
+  override func tearDown() {
+    // Put teardown code here. This method is called after the invocation of each test method in the class.
+    super.tearDown()
+  }
+  
+  func testEmptyInitialization() {
+    let tree = AVLTree<Int,String>()
+    
+    XCTAssertEqual(tree.size, 0)
+    XCTAssertNil(tree.root)
+  }
+  
+  func testNotEmptyInitialization() {
+    XCTAssertNotNil(self.tree?.root)
+    XCTAssertNotEqual(self.tree!.size, 0)
+  }
+  
+  func testInsertDuplicated() {
+    self.tree?.insert(1, "A")
+    XCTAssertEqual(self.tree?.size, 5, "Duplicated elements should be allowed")
+  }
+  
+  func testSingleInsertionPerformance() {
+    self.measureBlock {
+      self.tree?.insert(5, "E")
+    }
+  }
+  
+  func testMultipleInsertionsPerformance() {
+    self.measureBlock {
+      self.tree?.autopopulateWithNodes(50)
+    }
+  }
+  
+  func testSearchExistentOnSmallTreePerformance() {
+    self.measureBlock {
+      self.tree?.search(2)
+    }
+  }
+  
+  func testSearchExistentElementOnLargeTreePerformance() {
+    self.measureBlock {
+      self.tree?.autopopulateWithNodes(500)
+      self.tree?.search(400)
+    }
+  }
+}
+
+extension AVLTree where Key : SignedIntegerType {
+  func autopopulateWithNodes(count : Int) {
+    var k : Key = 1
+    for _ in 0...count {
+      self.insert(k++)
+    }
+  }
+}
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTestsTests/Info.plist b/AVL Tree/Tests/Info.plist
similarity index 100%
rename from AVL Tree/AVLTree Tests/AVLTreeTestsTests/Info.plist
rename to AVL Tree/Tests/Info.plist
diff --git a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..dfaf44e8d
--- /dev/null
+++ b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,265 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3C91C77A112003CECC7 /* TreeNodeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3C71C77A112003CECC7 /* TreeNodeTests.swift */; };
+		7B80C3CA1C77A112003CECC7 /* AVLTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3C81C77A112003CECC7 /* AVLTreeTests.swift */; };
+		7B80C3CC1C77A120003CECC7 /* AVLTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3CB1C77A120003CECC7 /* AVLTree.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C3C71C77A112003CECC7 /* TreeNodeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = TreeNodeTests.swift; sourceTree = SOURCE_ROOT; };
+		7B80C3C81C77A112003CECC7 /* AVLTreeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = AVLTreeTests.swift; sourceTree = SOURCE_ROOT; };
+		7B80C3CB1C77A120003CECC7 /* AVLTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = AVLTree.swift; path = ../AVLTree.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B80C3CB1C77A120003CECC7 /* AVLTree.swift */,
+				7B80C3C81C77A112003CECC7 /* AVLTreeTests.swift */,
+				7B80C3C71C77A112003CECC7 /* TreeNodeTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
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+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
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+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
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+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
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+			developmentRegion = English;
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+			knownRegions = (
+				en,
+				Base,
+			);
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+			projectDirPath = "";
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+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C3CC1C77A120003CECC7 /* AVLTree.swift in Sources */,
+				7B80C3C91C77A112003CECC7 /* TreeNodeTests.swift in Sources */,
+				7B80C3CA1C77A112003CECC7 /* AVLTreeTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
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+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
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+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/AVL Tree/AVLTree Tests/AVLTreeTestsTests/TreeNodeTest.swift b/AVL Tree/Tests/TreeNodeTests.swift
similarity index 97%
rename from AVL Tree/AVLTree Tests/AVLTreeTestsTests/TreeNodeTest.swift
rename to AVL Tree/Tests/TreeNodeTests.swift
index 802277ea9..d55c4e5e2 100644
--- a/AVL Tree/AVLTree Tests/AVLTreeTestsTests/TreeNodeTest.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -7,10 +7,8 @@
 //
 
 import XCTest
-@testable import AVLTreeTests
 
-
-class TreeNodeTest: XCTestCase {
+class TreeNodeTests: XCTestCase {
     
     var root : TreeNode<String,String>?
     var left : TreeNode<String,String>?
diff --git a/Array2D/Array2D Tests/array2Dtest.xcodeproj/project.pbxproj b/Array2D/Array2D Tests/array2Dtest.xcodeproj/project.pbxproj
deleted file mode 100644
index b1dae1cd7..000000000
--- a/Array2D/Array2D Tests/array2Dtest.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,409 +0,0 @@
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-{
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-	};
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diff --git a/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist b/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/B9780967-0BD8-4A91-8657-A96EFB81859F.plist
deleted file mode 100644
index 124dc73bc..000000000
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@@ -1,22 +0,0 @@
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-	<dict>
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-			<dict>
-				<key>com.apple.XCTPerformanceMetric_WallClockTime</key>
-				<dict>
-					<key>baselineAverage</key>
-					<real>0.377</real>
-					<key>baselineIntegrationDisplayName</key>
-					<string>Local Baseline</string>
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diff --git a/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist b/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist
deleted file mode 100644
index a0e45b60a..000000000
--- a/Array2D/Array2D Tests/array2Dtest.xcodeproj/xcshareddata/xcbaselines/766116211C7625C700358E02.xcbaseline/Info.plist	
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diff --git a/Array2D/Array2D Tests/array2Dtest/AppDelegate.swift b/Array2D/Array2D Tests/array2Dtest/AppDelegate.swift
deleted file mode 100644
index 7d1c32f11..000000000
--- a/Array2D/Array2D Tests/array2Dtest/AppDelegate.swift	
+++ /dev/null
@@ -1,46 +0,0 @@
-//
-//  AppDelegate.swift
-//  array2Dtest
-//
-//  Created by Barbara Rodeker on 2/18/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import UIKit
-
-@UIApplicationMain
-class AppDelegate: UIResponder, UIApplicationDelegate {
-
-    var window: UIWindow?
-
-
-    func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
-        // Override point for customization after application launch.
-        return true
-    }
-
-    func applicationWillResignActive(application: UIApplication) {
-        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
-        // Use this method to pause ongoing tasks, disable timers, and throttle down OpenGL ES frame rates. Games should use this method to pause the game.
-    }
-
-    func applicationDidEnterBackground(application: UIApplication) {
-        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
-        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
-    }
-
-    func applicationWillEnterForeground(application: UIApplication) {
-        // Called as part of the transition from the background to the inactive state; here you can undo many of the changes made on entering the background.
-    }
-
-    func applicationDidBecomeActive(application: UIApplication) {
-        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
-    }
-
-    func applicationWillTerminate(application: UIApplication) {
-        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
-    }
-
-
-}
-
diff --git a/Array2D/Array2D Tests/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json b/Array2D/Array2D Tests/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 36d2c80d8..000000000
--- a/Array2D/Array2D Tests/array2Dtest/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,68 +0,0 @@
-{
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-      "idiom" : "iphone",
-      "size" : "29x29",
-      "scale" : "2x"
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-      "scale" : "3x"
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-      "size" : "60x60",
-      "scale" : "3x"
-    },
-    {
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-      "size" : "29x29",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "29x29",
-      "scale" : "2x"
-    },
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-      "idiom" : "ipad",
-      "size" : "40x40",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "40x40",
-      "scale" : "2x"
-    },
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-      "size" : "76x76",
-      "scale" : "1x"
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-    {
-      "idiom" : "ipad",
-      "size" : "76x76",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Array2D/Array2D Tests/array2Dtest/Base.lproj/LaunchScreen.storyboard b/Array2D/Array2D Tests/array2Dtest/Base.lproj/LaunchScreen.storyboard
deleted file mode 100644
index 2e721e183..000000000
--- a/Array2D/Array2D Tests/array2Dtest/Base.lproj/LaunchScreen.storyboard	
+++ /dev/null
@@ -1,27 +0,0 @@
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-    <dependencies>
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-        <!--View Controller-->
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-            <objects>
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-                    <layoutGuides>
-                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
-                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
-                    </layoutGuides>
-                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
-                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
-                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
-                        <animations/>
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-                    </view>
-                </viewController>
-                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
-            </objects>
-            <point key="canvasLocation" x="53" y="375"/>
-        </scene>
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deleted file mode 100644
index 3a2a49bad..000000000
--- a/Array2D/Array2D Tests/array2Dtest/Base.lproj/Main.storyboard	
+++ /dev/null
@@ -1,25 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="6211" systemVersion="14A298i" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" initialViewController="BYZ-38-t0r">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="6204"/>
-    </dependencies>
-    <scenes>
-        <!--View Controller-->
-        <scene sceneID="tne-QT-ifu">
-            <objects>
-                <viewController id="BYZ-38-t0r" customClass="ViewController" customModuleProvider="target" sceneMemberID="viewController">
-                    <layoutGuides>
-                        <viewControllerLayoutGuide type="top" id="y3c-jy-aDJ"/>
-                        <viewControllerLayoutGuide type="bottom" id="wfy-db-euE"/>
-                    </layoutGuides>
-                    <view key="view" contentMode="scaleToFill" id="8bC-Xf-vdC">
-                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
-                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
-                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
-                    </view>
-                </viewController>
-                <placeholder placeholderIdentifier="IBFirstResponder" id="dkx-z0-nzr" sceneMemberID="firstResponder"/>
-            </objects>
-        </scene>
-    </scenes>
-</document>
diff --git a/Array2D/Array2D Tests/array2Dtest/Info.plist b/Array2D/Array2D Tests/array2Dtest/Info.plist
deleted file mode 100644
index 40c6215d9..000000000
--- a/Array2D/Array2D Tests/array2Dtest/Info.plist	
+++ /dev/null
@@ -1,47 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSRequiresIPhoneOS</key>
-	<true/>
-	<key>UILaunchStoryboardName</key>
-	<string>LaunchScreen</string>
-	<key>UIMainStoryboardFile</key>
-	<string>Main</string>
-	<key>UIRequiredDeviceCapabilities</key>
-	<array>
-		<string>armv7</string>
-	</array>
-	<key>UISupportedInterfaceOrientations</key>
-	<array>
-		<string>UIInterfaceOrientationPortrait</string>
-		<string>UIInterfaceOrientationLandscapeLeft</string>
-		<string>UIInterfaceOrientationLandscapeRight</string>
-	</array>
-	<key>UISupportedInterfaceOrientations~ipad</key>
-	<array>
-		<string>UIInterfaceOrientationPortrait</string>
-		<string>UIInterfaceOrientationPortraitUpsideDown</string>
-		<string>UIInterfaceOrientationLandscapeLeft</string>
-		<string>UIInterfaceOrientationLandscapeRight</string>
-	</array>
-</dict>
-</plist>
diff --git a/Array2D/Array2D Tests/array2Dtest/ViewController.swift b/Array2D/Array2D Tests/array2Dtest/ViewController.swift
deleted file mode 100644
index 669b79b89..000000000
--- a/Array2D/Array2D Tests/array2Dtest/ViewController.swift	
+++ /dev/null
@@ -1,25 +0,0 @@
-//
-//  ViewController.swift
-//  array2Dtest
-//
-//  Created by Barbara Rodeker on 2/18/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import UIKit
-
-class ViewController: UIViewController {
-
-    override func viewDidLoad() {
-        super.viewDidLoad()
-        // Do any additional setup after loading the view, typically from a nib.
-    }
-
-    override func didReceiveMemoryWarning() {
-        super.didReceiveMemoryWarning()
-        // Dispose of any resources that can be recreated.
-    }
-
-
-}
-
diff --git a/Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift b/Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift
deleted file mode 100644
index 234d0f9b4..000000000
--- a/Array2D/Array2D Tests/array2DtestTests/array2DtestTests.swift	
+++ /dev/null
@@ -1,80 +0,0 @@
-//
-//  Array2DTest.swift
-//  algorithmclub
-//
-//  Created by Barbara Rodeker on 2/16/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import XCTest
-@testable import array2Dtest
-
-class Array2DTest: XCTestCase {
-    
-    override func setUp() {
-        super.setUp()
-    }
-    
-    override func tearDown() {
-        super.tearDown()
-    }
-    
-    func testIntegerArrayWithPositiveRowsAndColumns() {
-        let array = Array2D<Int>(columns: 3, rows: 2, initialValue: 0)
-        
-        XCTAssertEqual(array.columns, 3, "Column count setup failed")
-        XCTAssertEqual(array.rows, 2, "Rows count setup failed")
-        XCTAssertEqual(array[2,1], 0, "Integer array: Initialization value is wrong")
-    }
-    
-    func testStringArrayWithPositiveRowsAndColumns() {
-        let array = Array2D<String>(columns: 3, rows: 2, initialValue: "empty")
-        
-        XCTAssertEqual(array.columns, 3, "Column count setup failed")
-        XCTAssertEqual(array.rows, 2, "Rows count setup failed")
-        XCTAssertEqual(array[2,1], "empty", "String array: Initialization value is wrong")
-    }
-    
-    func testCustomClassArrayWithPositiveRowsAndColumns() {
-        let array = Array2D<TestElement>(columns: 3, rows: 2, initialValue: TestElement(identifier: "pepe"))
-        
-        XCTAssertEqual(array.columns, 3, "Column count setup failed")
-        XCTAssertEqual(array.rows, 2, "Rows count setup failed")
-        XCTAssertEqual(array[2,1], TestElement(identifier: "pepe"), "Custom Class array: Initialization value is wrong")
-    }
-    
-    func testPerformanceOnSmallArray() {
-        self.measureBlock {
-            self.printArrayWith(columns: 2, rows: 2, inititalValue: 1)
-        }
-    }
-
-//    func testPerformanceOnLargeArray() {
-//        self.measureBlock {
-//            self.printArrayWith(columns: 2000, rows: 2000, inititalValue: 1)
-//        }
-//    }
-
-    private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int){
-        let array = Array2D(columns: columns, rows: rows, initialValue: 4)
-        for r in 0..<array.rows {
-            for c in 0..<array.columns {
-                print("Array in [\(r), \(c)] value is: \(array[c,r])")
-            }
-        }
-    }
-    
-}
-
-class TestElement : Equatable {
-    let identifier : String
-    
-    init(identifier: String) {
-        self.identifier = identifier
-    }
-}
-
-func == (lhs: TestElement, rhs: TestElement) -> Bool {
-    return lhs.identifier == rhs.identifier
-}
-
diff --git a/Array2D/Tests/Array2DTests.swift b/Array2D/Tests/Array2DTests.swift
new file mode 100644
index 000000000..3383b5eb3
--- /dev/null
+++ b/Array2D/Tests/Array2DTests.swift
@@ -0,0 +1,78 @@
+//
+//  Array2DTest.swift
+//  algorithmclub
+//
+//  Created by Barbara Rodeker on 2/16/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+
+class Array2DTest: XCTestCase {
+  
+  override func setUp() {
+    super.setUp()
+  }
+  
+  override func tearDown() {
+    super.tearDown()
+  }
+  
+  func testIntegerArrayWithPositiveRowsAndColumns() {
+    let array = Array2D<Int>(columns: 3, rows: 2, initialValue: 0)
+    
+    XCTAssertEqual(array.columns, 3, "Column count setup failed")
+    XCTAssertEqual(array.rows, 2, "Rows count setup failed")
+    XCTAssertEqual(array[2,1], 0, "Integer array: Initialization value is wrong")
+  }
+  
+  func testStringArrayWithPositiveRowsAndColumns() {
+    let array = Array2D<String>(columns: 3, rows: 2, initialValue: "empty")
+    
+    XCTAssertEqual(array.columns, 3, "Column count setup failed")
+    XCTAssertEqual(array.rows, 2, "Rows count setup failed")
+    XCTAssertEqual(array[2,1], "empty", "String array: Initialization value is wrong")
+  }
+  
+  func testCustomClassArrayWithPositiveRowsAndColumns() {
+    let array = Array2D<TestElement>(columns: 3, rows: 2, initialValue: TestElement(identifier: "pepe"))
+    
+    XCTAssertEqual(array.columns, 3, "Column count setup failed")
+    XCTAssertEqual(array.rows, 2, "Rows count setup failed")
+    XCTAssertEqual(array[2,1], TestElement(identifier: "pepe"), "Custom Class array: Initialization value is wrong")
+  }
+  
+  func testPerformanceOnSmallArray() {
+    self.measureBlock {
+      self.printArrayWith(columns: 2, rows: 2, inititalValue: 1)
+    }
+  }
+  
+  //    func testPerformanceOnLargeArray() {
+  //        self.measureBlock {
+  //            self.printArrayWith(columns: 2000, rows: 2000, inititalValue: 1)
+  //        }
+  //    }
+  
+  private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int){
+    let array = Array2D(columns: columns, rows: rows, initialValue: 4)
+    for r in 0..<array.rows {
+      for c in 0..<array.columns {
+        print("Array in [\(r), \(c)] value is: \(array[c,r])")
+      }
+    }
+  }
+  
+}
+
+class TestElement : Equatable {
+  let identifier : String
+  
+  init(identifier: String) {
+    self.identifier = identifier
+  }
+}
+
+func == (lhs: TestElement, rhs: TestElement) -> Bool {
+  return lhs.identifier == rhs.identifier
+}
diff --git a/Array2D/Array2D Tests/array2DtestTests/Info.plist b/Array2D/Tests/Info.plist
similarity index 100%
rename from Array2D/Array2D Tests/array2DtestTests/Info.plist
rename to Array2D/Tests/Info.plist
diff --git a/Array2D/Tests/Tests.xcodeproj/project.pbxproj b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..8618e7530
--- /dev/null
+++ b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B2BBC901C779DAC0067B71D /* Array2DTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B2BBC8F1C779DAC0067B71D /* Array2DTests.swift */; };
+		7B2BBC991C77A04F0067B71D /* Array2D.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B2BBC981C77A04F0067B71D /* Array2D.swift */; };
+/* End PBXBuildFile section */
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+		7B2BBC981C77A04F0067B71D /* Array2D.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Array2D.swift; path = ../Array2D.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
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+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC981C77A04F0067B71D /* Array2D.swift */,
+				7B2BBC8F1C779DAC0067B71D /* Array2DTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
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+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B2BBC901C779DAC0067B71D /* Array2DTests.swift in Sources */,
+				7B2BBC991C77A04F0067B71D /* Array2D.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree.xcodeproj/project.pbxproj
deleted file mode 100644
index d4ed37459..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,394 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
-	classes = {
-	};
-	objectVersion = 46;
-	objects = {
-
-/* Begin PBXBuildFile section */
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diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/AppDelegate.swift b/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/AppDelegate.swift
deleted file mode 100644
index d80dd0269..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  BinarySearchTree
-//
-//  Created by Matthijs Hollemans on 07-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Assets.xcassets/AppIcon.appiconset/Contents.json b/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
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-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Base.lproj/MainMenu.xib b/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Base.lproj/MainMenu.xib
deleted file mode 100644
index f7be413dc..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="BinarySearchTree" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="BinarySearchTree" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About BinarySearchTree" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide BinarySearchTree" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit BinarySearchTree" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
-                                                    <menuItem title="Use Default" id="agt-UL-0e3">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="J7y-lM-qPV">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use All" id="xQD-1f-W4t">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
-                                                <items>
-                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Subscript" id="I0S-gh-46l">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
-                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
-                                            </connections>
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-                </menuItem>
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-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
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-                </menuItem>
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-                    <modifierMask key="keyEquivalentModifierMask"/>
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-                        <items>
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-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
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-                            </menuItem>
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-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                                </connections>
-                            </menuItem>
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-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Info.plist b/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTree/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
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-	<string></string>
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-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
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diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTreeTests/BinarySearchTreeTests.swift b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift
similarity index 99%
rename from Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTreeTests/BinarySearchTreeTests.swift
rename to Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift
index a23c3de5f..bafcd8003 100755
--- a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTreeTests/BinarySearchTreeTests.swift	
+++ b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
@@ -1,6 +1,5 @@
 import Foundation
 import XCTest
-@testable import BinarySearchTree
 
 class BinarySearchTreeTest: XCTestCase {
   func testRootNode() {
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTreeTests/Info.plist b/Binary Search Tree/Solution 1/Tests/Info.plist
similarity index 100%
rename from Binary Search Tree/Solution 1/BinarySearchTree Tests/BinarySearchTreeTests/Info.plist
rename to Binary Search Tree/Solution 1/Tests/Info.plist
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..c1d6c8029
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,261 @@
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+	};
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+}
diff --git a/Binary Search/BinarySearch Tests/BinarySearch.xcodeproj/project.pbxproj b/Binary Search/BinarySearch Tests/BinarySearch.xcodeproj/project.pbxproj
deleted file mode 100644
index b5493845f..000000000
--- a/Binary Search/BinarySearch Tests/BinarySearch.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,394 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
-	classes = {
-	};
-	objectVersion = 46;
-	objects = {
-
-/* Begin PBXBuildFile section */
-		7B18DFF11C5BF66F005A2B8E /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B18DFF01C5BF66F005A2B8E /* AppDelegate.swift */; };
-		7B18DFF31C5BF66F005A2B8E /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 7B18DFF21C5BF66F005A2B8E /* Assets.xcassets */; };
-		7B18DFF61C5BF66F005A2B8E /* MainMenu.xib in Resources */ = {isa = PBXBuildFile; fileRef = 7B18DFF41C5BF66F005A2B8E /* MainMenu.xib */; };
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-/* End PBXBuildFile section */
-
-/* Begin PBXContainerItemProxy section */
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-			proxyType = 1;
-			remoteGlobalIDString = 7B18DFEC1C5BF66F005A2B8E;
-			remoteInfo = BinarySearch;
-		};
-/* End PBXContainerItemProxy section */
-
-/* Begin PBXFileReference section */
-		7B18DFED1C5BF66F005A2B8E /* BinarySearch.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = BinarySearch.app; sourceTree = BUILT_PRODUCTS_DIR; };
-		7B18DFF01C5BF66F005A2B8E /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
-		7B18DFF21C5BF66F005A2B8E /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
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-		7B18DFF71C5BF66F005A2B8E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
-		7B18DFFC1C5BF66F005A2B8E /* BinarySearchTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = BinarySearchTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
-		7B18E0001C5BF66F005A2B8E /* BinarySearchTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = BinarySearchTests.swift; sourceTree = "<group>"; };
-		7B18E0021C5BF66F005A2B8E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
-		7B18E00B1C5BF6B2005A2B8E /* BinarySearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearch.swift; path = ../../BinarySearch.swift; sourceTree = "<group>"; };
-/* End PBXFileReference section */
-
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-			buildActionMask = 2147483647;
-			files = (
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-			runOnlyForDeploymentPostprocessing = 0;
-		};
-		7B18DFF91C5BF66F005A2B8E /* Frameworks */ = {
-			isa = PBXFrameworksBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
-/* End PBXFrameworksBuildPhase section */
-
-/* Begin PBXGroup section */
-		7B18DFE41C5BF66F005A2B8E = {
-			isa = PBXGroup;
-			children = (
-				7B18DFEF1C5BF66F005A2B8E /* BinarySearch */,
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-				7B18DFEE1C5BF66F005A2B8E /* Products */,
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-			sourceTree = "<group>";
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-		7B18DFEE1C5BF66F005A2B8E /* Products */ = {
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-			children = (
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-		7B18DFEF1C5BF66F005A2B8E /* BinarySearch */ = {
-			isa = PBXGroup;
-			children = (
-				7B18DFF01C5BF66F005A2B8E /* AppDelegate.swift */,
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-				7B18DFF71C5BF66F005A2B8E /* Info.plist */,
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-			path = BinarySearch;
-			sourceTree = "<group>";
-		};
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-			isa = PBXGroup;
-			children = (
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-			);
-			path = BinarySearchTests;
-			sourceTree = "<group>";
-		};
-/* End PBXGroup section */
-
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-			dependencies = (
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-			productName = BinarySearchTests;
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-			productType = "com.apple.product-type.bundle.unit-test";
-		};
-/* End PBXNativeTarget section */
-
-/* Begin PBXProject section */
-		7B18DFE51C5BF66F005A2B8E /* Project object */ = {
-			isa = PBXProject;
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-				LastUpgradeCheck = 0720;
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-					7B18DFEC1C5BF66F005A2B8E = {
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-			buildConfigurationList = 7B18DFE81C5BF66F005A2B8E /* Build configuration list for PBXProject "BinarySearch" */;
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-			projectDirPath = "";
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-			targets = (
-				7B18DFEC1C5BF66F005A2B8E /* BinarySearch */,
-				7B18DFFB1C5BF66F005A2B8E /* BinarySearchTests */,
-			);
-		};
-/* End PBXProject section */
-
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-		};
-/* End PBXResourcesBuildPhase section */
-
-/* Begin PBXSourcesBuildPhase section */
-		7B18DFE91C5BF66F005A2B8E /* Sources */ = {
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-			files = (
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-		};
-/* End PBXSourcesBuildPhase section */
-
-/* Begin PBXTargetDependency section */
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-
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-			);
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-		};
-/* End PBXVariantGroup section */
-
-/* Begin XCBuildConfiguration section */
-		7B18E0031C5BF66F005A2B8E /* Debug */ = {
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-				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
-				CLANG_WARN_EMPTY_BODY = YES;
-				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_UNREACHABLE_CODE = YES;
-				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				CODE_SIGN_IDENTITY = "-";
-				COPY_PHASE_STRIP = NO;
-				DEBUG_INFORMATION_FORMAT = dwarf;
-				ENABLE_STRICT_OBJC_MSGSEND = YES;
-				ENABLE_TESTABILITY = YES;
-				GCC_C_LANGUAGE_STANDARD = gnu99;
-				GCC_DYNAMIC_NO_PIC = NO;
-				GCC_NO_COMMON_BLOCKS = YES;
-				GCC_OPTIMIZATION_LEVEL = 0;
-				GCC_PREPROCESSOR_DEFINITIONS = (
-					"DEBUG=1",
-					"$(inherited)",
-				);
-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = YES;
-				ONLY_ACTIVE_ARCH = YES;
-				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-			};
-			name = Debug;
-		};
-		7B18E0041C5BF66F005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
-				CLANG_CXX_LIBRARY = "libc++";
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-				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_UNREACHABLE_CODE = YES;
-				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				CODE_SIGN_IDENTITY = "-";
-				COPY_PHASE_STRIP = NO;
-				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
-				ENABLE_NS_ASSERTIONS = NO;
-				ENABLE_STRICT_OBJC_MSGSEND = YES;
-				GCC_C_LANGUAGE_STANDARD = gnu99;
-				GCC_NO_COMMON_BLOCKS = YES;
-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = NO;
-				SDKROOT = macosx;
-			};
-			name = Release;
-		};
-		7B18E0061C5BF66F005A2B8E /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = BinarySearch/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.BinarySearch;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Debug;
-		};
-		7B18E0071C5BF66F005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = BinarySearch/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.BinarySearch;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Release;
-		};
-		7B18E0091C5BF66F005A2B8E /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = BinarySearchTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.BinarySearchTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/BinarySearch.app/Contents/MacOS/BinarySearch";
-			};
-			name = Debug;
-		};
-		7B18E00A1C5BF66F005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = BinarySearchTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.BinarySearchTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/BinarySearch.app/Contents/MacOS/BinarySearch";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B18DFE81C5BF66F005A2B8E /* Build configuration list for PBXProject "BinarySearch" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0031C5BF66F005A2B8E /* Debug */,
-				7B18E0041C5BF66F005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0051C5BF66F005A2B8E /* Build configuration list for PBXNativeTarget "BinarySearch" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0061C5BF66F005A2B8E /* Debug */,
-				7B18E0071C5BF66F005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0081C5BF66F005A2B8E /* Build configuration list for PBXNativeTarget "BinarySearchTests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0091C5BF66F005A2B8E /* Debug */,
-				7B18E00A1C5BF66F005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B18DFE51C5BF66F005A2B8E /* Project object */;
-}
diff --git a/Binary Search/BinarySearch Tests/BinarySearch/AppDelegate.swift b/Binary Search/BinarySearch Tests/BinarySearch/AppDelegate.swift
deleted file mode 100644
index f3db7bc62..000000000
--- a/Binary Search/BinarySearch Tests/BinarySearch/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  BinarySearch
-//
-//  Created by Matthijs Hollemans on 29-01-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Binary Search/BinarySearch Tests/BinarySearch/Assets.xcassets/AppIcon.appiconset/Contents.json b/Binary Search/BinarySearch Tests/BinarySearch/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Binary Search/BinarySearch Tests/BinarySearch/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Binary Search/BinarySearch Tests/BinarySearch/Base.lproj/MainMenu.xib b/Binary Search/BinarySearch Tests/BinarySearch/Base.lproj/MainMenu.xib
deleted file mode 100644
index ee7982efd..000000000
--- a/Binary Search/BinarySearch Tests/BinarySearch/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="BinarySearch" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="BinarySearch" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About BinarySearch" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide BinarySearch" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit BinarySearch" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
-                                                    <menuItem title="Use Default" id="agt-UL-0e3">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="J7y-lM-qPV">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use All" id="xQD-1f-W4t">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
-                                                <items>
-                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Subscript" id="I0S-gh-46l">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
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-                </menuItem>
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-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
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-                    </menu>
-                </menuItem>
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-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
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-                                </connections>
-                            </menuItem>
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-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                </menuItem>
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-        </menu>
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-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
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-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Binary Search/BinarySearch Tests/BinarySearch/Info.plist b/Binary Search/BinarySearch Tests/BinarySearch/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Binary Search/BinarySearch Tests/BinarySearch/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
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-	<string>en</string>
-	<key>CFBundleExecutable</key>
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-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
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diff --git a/Binary Search/BinarySearch Tests/BinarySearchTests/BinarySearchTests.swift b/Binary Search/Tests/BinarySearchTests.swift
similarity index 97%
rename from Binary Search/BinarySearch Tests/BinarySearchTests/BinarySearchTests.swift
rename to Binary Search/Tests/BinarySearchTests.swift
index d626e475d..35ad9559b 100755
--- a/Binary Search/BinarySearch Tests/BinarySearchTests/BinarySearchTests.swift	
+++ b/Binary Search/Tests/BinarySearchTests.swift	
@@ -1,6 +1,5 @@
 import Foundation
 import XCTest
-@testable import BinarySearch
 
 class BinarySearchTest: XCTestCase {
   var searchList = [Int]()
diff --git a/Binary Search/BinarySearch Tests/BinarySearchTests/Info.plist b/Binary Search/Tests/Info.plist
similarity index 100%
rename from Binary Search/BinarySearch Tests/BinarySearchTests/Info.plist
rename to Binary Search/Tests/Info.plist
diff --git a/Binary Search/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..9ed1ab1a8
--- /dev/null
+++ b/Binary Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,261 @@
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+{
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deleted file mode 100644
index f6da3b7db..000000000
--- a/Heap Sort/HeapSort Tests/HeapSort.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,398 +0,0 @@
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diff --git a/Heap Sort/HeapSort Tests/HeapSort/AppDelegate.swift b/Heap Sort/HeapSort Tests/HeapSort/AppDelegate.swift
deleted file mode 100644
index 08b4b6f47..000000000
--- a/Heap Sort/HeapSort Tests/HeapSort/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  HeapSort
-//
-//  Created by Matthijs Hollemans on 08-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Heap Sort/HeapSort Tests/HeapSort/Assets.xcassets/AppIcon.appiconset/Contents.json b/Heap Sort/HeapSort Tests/HeapSort/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Heap Sort/HeapSort Tests/HeapSort/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
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-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
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-    {
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-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
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-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Heap Sort/HeapSort Tests/HeapSort/Base.lproj/MainMenu.xib b/Heap Sort/HeapSort Tests/HeapSort/Base.lproj/MainMenu.xib
deleted file mode 100644
index cb25f88b2..000000000
--- a/Heap Sort/HeapSort Tests/HeapSort/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="HeapSort" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="HeapSort" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About HeapSort" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide HeapSort" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit HeapSort" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
-                                                    <menuItem title="Use Default" id="agt-UL-0e3">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="J7y-lM-qPV">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use All" id="xQD-1f-W4t">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
-                                                <items>
-                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Subscript" id="I0S-gh-46l">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-        </window>
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-</document>
diff --git a/Heap Sort/HeapSort Tests/HeapSort/Info.plist b/Heap Sort/HeapSort Tests/HeapSort/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Heap Sort/HeapSort Tests/HeapSort/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
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diff --git a/Heap Sort/HeapSort Tests/HeapSortTests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
similarity index 81%
rename from Heap Sort/HeapSort Tests/HeapSortTests/HeapSortTests.swift
rename to Heap Sort/Tests/HeapSortTests.swift
index 70304fea7..e5e847a74 100644
--- a/Heap Sort/HeapSort Tests/HeapSortTests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,13 +1,4 @@
-//
-//  HeapSortTests.swift
-//  HeapSortTests
-//
-//  Created by Matthijs Hollemans on 08-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
 import XCTest
-@testable import HeapSort
 
 class HeapSortTests: XCTestCase {
   func testSort() {
diff --git a/Heap Sort/HeapSort Tests/HeapSortTests/Info.plist b/Heap Sort/Tests/Info.plist
similarity index 100%
rename from Heap Sort/HeapSort Tests/HeapSortTests/Info.plist
rename to Heap Sort/Tests/Info.plist
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..454222c49
--- /dev/null
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,265 @@
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diff --git a/Heap/Heap Tests/Heap.xcodeproj/project.pbxproj b/Heap/Heap Tests/Heap.xcodeproj/project.pbxproj
deleted file mode 100644
index c0fd77f65..000000000
--- a/Heap/Heap Tests/Heap.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,394 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
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-	objectVersion = 46;
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diff --git a/Heap/Heap Tests/Heap/AppDelegate.swift b/Heap/Heap Tests/Heap/AppDelegate.swift
deleted file mode 100644
index 954fc0c35..000000000
--- a/Heap/Heap Tests/Heap/AppDelegate.swift	
+++ /dev/null
@@ -1,15 +0,0 @@
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-  
-  @IBOutlet weak var window: NSWindow!
-  
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-  
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-}
diff --git a/Heap/Heap Tests/Heap/Assets.xcassets/AppIcon.appiconset/Contents.json b/Heap/Heap Tests/Heap/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Heap/Heap Tests/Heap/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Heap/Heap Tests/Heap/Base.lproj/MainMenu.xib b/Heap/Heap Tests/Heap/Base.lproj/MainMenu.xib
deleted file mode 100644
index e6d67c02a..000000000
--- a/Heap/Heap Tests/Heap/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="Heap" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Heap" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About Heap" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide Heap" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit Heap" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
-                                                    <menuItem title="Use Default" id="agt-UL-0e3">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="J7y-lM-qPV">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use All" id="xQD-1f-W4t">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
-                                                <items>
-                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
-                                                        </connections>
-                                                    </menuItem>
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-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
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-                    </menu>
-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="runToolbarCustomizationPalette:" target="-1" id="pQI-g3-MTW"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Window" id="aUF-d1-5bR">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
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-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Help" id="wpr-3q-Mcd">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
-                        <items>
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-                </menuItem>
-            </items>
-        </menu>
-        <window title="Heap" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" releasedWhenClosed="NO" animationBehavior="default" id="QvC-M9-y7g">
-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Heap/Heap Tests/Heap/Info.plist b/Heap/Heap Tests/Heap/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Heap/Heap Tests/Heap/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
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diff --git a/Heap/Heap Tests/HeapTests/HeapTests.swift b/Heap/Tests/HeapTests.swift
similarity index 99%
rename from Heap/Heap Tests/HeapTests/HeapTests.swift
rename to Heap/Tests/HeapTests.swift
index 653cf6af9..b038687ad 100644
--- a/Heap/Heap Tests/HeapTests/HeapTests.swift	
+++ b/Heap/Tests/HeapTests.swift
@@ -4,7 +4,6 @@
 //
 
 import XCTest
-@testable import Heap
 
 class HeapTests: XCTestCase {
   
diff --git a/Heap/Heap Tests/HeapTests/Info.plist b/Heap/Tests/Info.plist
similarity index 100%
rename from Heap/Heap Tests/HeapTests/Info.plist
rename to Heap/Tests/Info.plist
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..a2302e38b
--- /dev/null
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
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+	objects = {
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+				CLANG_WARN_BOOL_CONVERSION = YES;
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+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
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+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
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+				GCC_WARN_UNDECLARED_SELECTOR = YES;
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+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
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+			buildSettings = {
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deleted file mode 100644
index 1eed2d04e..000000000
--- a/Insertion Sort/InsertionSort Tests/InsertionSort.xcodeproj/project.pbxproj	
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@@ -1,398 +0,0 @@
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diff --git a/Insertion Sort/InsertionSort Tests/InsertionSort/AppDelegate.swift b/Insertion Sort/InsertionSort Tests/InsertionSort/AppDelegate.swift
deleted file mode 100644
index 7e8ee6125..000000000
--- a/Insertion Sort/InsertionSort Tests/InsertionSort/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  InsertionSort
-//
-//  Created by Matthijs Hollemans on 29-01-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Insertion Sort/InsertionSort Tests/InsertionSort/Assets.xcassets/AppIcon.appiconset/Contents.json b/Insertion Sort/InsertionSort Tests/InsertionSort/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Insertion Sort/InsertionSort Tests/InsertionSort/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Insertion Sort/InsertionSort Tests/InsertionSort/Base.lproj/MainMenu.xib b/Insertion Sort/InsertionSort Tests/InsertionSort/Base.lproj/MainMenu.xib
deleted file mode 100644
index c08abf93b..000000000
--- a/Insertion Sort/InsertionSort Tests/InsertionSort/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="InsertionSort" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="InsertionSort" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About InsertionSort" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide InsertionSort" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit InsertionSort" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
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-                    </menu>
-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                    </menu>
-                </menuItem>
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-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
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-                            </menuItem>
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-                            </menuItem>
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-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Insertion Sort/InsertionSort Tests/InsertionSort/Info.plist b/Insertion Sort/InsertionSort Tests/InsertionSort/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Insertion Sort/InsertionSort Tests/InsertionSort/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Insertion Sort/InsertionSort Tests/InsertionSortTests/Info.plist b/Insertion Sort/Tests/Info.plist
similarity index 100%
rename from Insertion Sort/InsertionSort Tests/InsertionSortTests/Info.plist
rename to Insertion Sort/Tests/Info.plist
diff --git a/Insertion Sort/InsertionSort Tests/InsertionSortTests/InsertionSortTests.swift b/Insertion Sort/Tests/InsertionSortTests.swift
similarity index 80%
rename from Insertion Sort/InsertionSort Tests/InsertionSortTests/InsertionSortTests.swift
rename to Insertion Sort/Tests/InsertionSortTests.swift
index 351ee6157..49f5eda9a 100644
--- a/Insertion Sort/InsertionSort Tests/InsertionSortTests/InsertionSortTests.swift	
+++ b/Insertion Sort/Tests/InsertionSortTests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import InsertionSort
 
 class InsertionSortTests: XCTestCase {
   func testInsertionSort() {
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..f8c23899c
--- /dev/null
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,265 @@
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-				7B1BF9E01C6288D40051C9A4 /* Debug */,
-				7B1BF9E11C6288D40051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B1BF9BC1C6288D40051C9A4 /* Project object */;
-}
diff --git a/Linked List/LinkedList Tests/LinkedList/AppDelegate.swift b/Linked List/LinkedList Tests/LinkedList/AppDelegate.swift
deleted file mode 100644
index f83b01f35..000000000
--- a/Linked List/LinkedList Tests/LinkedList/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  LinkedList
-//
-//  Created by Matthijs Hollemans on 03-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Linked List/LinkedList Tests/LinkedList/Assets.xcassets/AppIcon.appiconset/Contents.json b/Linked List/LinkedList Tests/LinkedList/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Linked List/LinkedList Tests/LinkedList/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Linked List/LinkedList Tests/LinkedList/Base.lproj/MainMenu.xib b/Linked List/LinkedList Tests/LinkedList/Base.lproj/MainMenu.xib
deleted file mode 100644
index 32e8f7bae..000000000
--- a/Linked List/LinkedList Tests/LinkedList/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="LinkedList" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="LinkedList" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About LinkedList" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide LinkedList" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit LinkedList" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
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-</document>
diff --git a/Linked List/LinkedList Tests/LinkedList/Info.plist b/Linked List/LinkedList Tests/LinkedList/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Linked List/LinkedList Tests/LinkedList/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
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diff --git a/Linked List/LinkedList Tests/LinkedListTests/Info.plist b/Linked List/Tests/Info.plist
similarity index 100%
rename from Linked List/LinkedList Tests/LinkedListTests/Info.plist
rename to Linked List/Tests/Info.plist
diff --git a/Linked List/LinkedList Tests/LinkedListTests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
similarity index 99%
rename from Linked List/LinkedList Tests/LinkedListTests/LinkedListTests.swift
rename to Linked List/Tests/LinkedListTests.swift
index 80241114c..4bdc0adae 100755
--- a/Linked List/LinkedList Tests/LinkedListTests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import LinkedList
 
 class LinkedListTest: XCTestCase {
   let numbers = [8, 2, 10, 9, 7, 5]
diff --git a/Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Linked List/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..7c6a2020a
--- /dev/null
+++ b/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
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index d855143a1..000000000
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-			defaultConfigurationName = Release;
-		};
-		7B1BFA2E1C6914970051C9A4 /* Build configuration list for PBXNativeTarget "PriorityQueue" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B1BFA2F1C6914970051C9A4 /* Debug */,
-				7B1BFA301C6914970051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B1BFA311C6914970051C9A4 /* Build configuration list for PBXNativeTarget "PriorityQueueTests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B1BFA321C6914970051C9A4 /* Debug */,
-				7B1BFA331C6914970051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B1BFA0E1C6914970051C9A4 /* Project object */;
-}
diff --git a/Priority Queue/PriorityQueue Tests/PriorityQueue/AppDelegate.swift b/Priority Queue/PriorityQueue Tests/PriorityQueue/AppDelegate.swift
deleted file mode 100644
index 0154bd5eb..000000000
--- a/Priority Queue/PriorityQueue Tests/PriorityQueue/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  PriorityQueue
-//
-//  Created by Matthijs Hollemans on 08-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Priority Queue/PriorityQueue Tests/PriorityQueue/Assets.xcassets/AppIcon.appiconset/Contents.json b/Priority Queue/PriorityQueue Tests/PriorityQueue/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Priority Queue/PriorityQueue Tests/PriorityQueue/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Priority Queue/PriorityQueue Tests/PriorityQueue/Base.lproj/MainMenu.xib b/Priority Queue/PriorityQueue Tests/PriorityQueue/Base.lproj/MainMenu.xib
deleted file mode 100644
index b36de4331..000000000
--- a/Priority Queue/PriorityQueue Tests/PriorityQueue/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="PriorityQueue" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="PriorityQueue" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About PriorityQueue" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide PriorityQueue" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit PriorityQueue" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
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-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
-                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteFont:" target="-1" id="JfD-CL-leO"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Text" id="Fal-I4-PZk">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
-                                            <connections>
-                                                <action selector="alignCenter:" target="-1" id="spX-mk-kcS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Justify" id="J5U-5w-g23">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="alignJustified:" target="-1" id="ljL-7U-jND"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
-                                            <connections>
-                                                <action selector="alignRight:" target="-1" id="r48-bG-YeY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
-                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
-                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="Nop-cj-93Q">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionNatural:" target="-1" id="lPI-Se-ZHp"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="BgM-ve-c93">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionLeftToRight:" target="-1" id="caW-Bv-w94"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="RB4-Sm-HuC">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionRightToLeft:" target="-1" id="EXD-6r-ZUu"/>
-                                                        </connections>
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-                                        <menuItem title="Show Ruler" id="vLm-3I-IUL">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleRuler:" target="-1" id="FOx-HJ-KwY"/>
-                                            </connections>
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-                                        <menuItem title="Copy Ruler" keyEquivalent="c" id="MkV-Pr-PK5">
-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyRuler:" target="-1" id="71i-fW-3W2"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Ruler" keyEquivalent="v" id="LVM-kO-fVI">
-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteRuler:" target="-1" id="cSh-wd-qM2"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="runToolbarCustomizationPalette:" target="-1" id="pQI-g3-MTW"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Window" id="aUF-d1-5bR">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
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-                <menuItem title="Help" id="wpr-3q-Mcd">
-                    <modifierMask key="keyEquivalentModifierMask"/>
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-                        <items>
-                            <menuItem title="PriorityQueue Help" keyEquivalent="?" id="FKE-Sm-Kum">
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-            </items>
-        </menu>
-        <window title="PriorityQueue" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" releasedWhenClosed="NO" animationBehavior="default" id="QvC-M9-y7g">
-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Priority Queue/PriorityQueue Tests/PriorityQueue/Info.plist b/Priority Queue/PriorityQueue Tests/PriorityQueue/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Priority Queue/PriorityQueue Tests/PriorityQueue/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Priority Queue/PriorityQueue Tests/PriorityQueueTests/Info.plist b/Priority Queue/Tests/Info.plist
similarity index 100%
rename from Priority Queue/PriorityQueue Tests/PriorityQueueTests/Info.plist
rename to Priority Queue/Tests/Info.plist
diff --git a/Priority Queue/PriorityQueue Tests/PriorityQueueTests/PriorityQueueTests.swift b/Priority Queue/Tests/PriorityQueueTests.swift
similarity index 98%
rename from Priority Queue/PriorityQueue Tests/PriorityQueueTests/PriorityQueueTests.swift
rename to Priority Queue/Tests/PriorityQueueTests.swift
index e0fc1bd28..56536310d 100755
--- a/Priority Queue/PriorityQueue Tests/PriorityQueueTests/PriorityQueueTests.swift	
+++ b/Priority Queue/Tests/PriorityQueueTests.swift	
@@ -1,6 +1,5 @@
 import Foundation
 import XCTest
-@testable import PriorityQueue
 
 private struct Message {
   let text: String
diff --git a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..5c6a20355
--- /dev/null
+++ b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,265 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3FC1C77A658003CECC7 /* PriorityQueue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FB1C77A658003CECC7 /* PriorityQueue.swift */; };
+		7B80C3FE1C77A65E003CECC7 /* PriorityQueueTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FD1C77A65E003CECC7 /* PriorityQueueTests.swift */; };
+		7B80C4001C77A67B003CECC7 /* Heap.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FF1C77A67B003CECC7 /* Heap.swift */; };
+/* End PBXBuildFile section */
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+
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+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
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+				7B2BBC721C779D710067B71D /* Products */,
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+			children = (
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+			isa = PBXGroup;
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+			);
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+			path = TestsTests;
+			sourceTree = "<group>";
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+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
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+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
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+				LastUpgradeCheck = 0720;
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+				TargetAttributes = {
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+			);
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+/* End PBXProject section */
+
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+		7B2BBC7E1C779D720067B71D /* Resources */ = {
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+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
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+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C4001C77A67B003CECC7 /* Heap.swift in Sources */,
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+				7B80C3FC1C77A658003CECC7 /* PriorityQueue.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
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deleted file mode 100644
index 5e2275234..000000000
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-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.QueueTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Queue.app/Contents/MacOS/Queue";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B18E0111C5BF7A1005A2B8E /* Build configuration list for PBXProject "Queue" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E02C1C5BF7A1005A2B8E /* Debug */,
-				7B18E02D1C5BF7A1005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E02E1C5BF7A1005A2B8E /* Build configuration list for PBXNativeTarget "Queue" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E02F1C5BF7A1005A2B8E /* Debug */,
-				7B18E0301C5BF7A1005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0311C5BF7A1005A2B8E /* Build configuration list for PBXNativeTarget "QueueTests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0321C5BF7A1005A2B8E /* Debug */,
-				7B18E0331C5BF7A1005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B18E00E1C5BF7A1005A2B8E /* Project object */;
-}
diff --git a/Queue/Queue Tests/Queue/AppDelegate.swift b/Queue/Queue Tests/Queue/AppDelegate.swift
deleted file mode 100644
index 307e0984f..000000000
--- a/Queue/Queue Tests/Queue/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  Queue
-//
-//  Created by Matthijs Hollemans on 29-01-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Queue/Queue Tests/Queue/Assets.xcassets/AppIcon.appiconset/Contents.json b/Queue/Queue Tests/Queue/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Queue/Queue Tests/Queue/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Queue/Queue Tests/Queue/Base.lproj/MainMenu.xib b/Queue/Queue Tests/Queue/Base.lproj/MainMenu.xib
deleted file mode 100644
index fbacc16b3..000000000
--- a/Queue/Queue Tests/Queue/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="Queue" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Queue" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About Queue" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide Queue" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit Queue" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
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-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
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-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
-                                            <connections>
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-                                            </connections>
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-                                        <menuItem title="Justify" id="J5U-5w-g23">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
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-                                            </connections>
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-                                            </connections>
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-                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
-                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
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-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
-                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                        <string key="title">	Default</string>
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-                                                        </connections>
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-                                                    <menuItem id="BgM-ve-c93">
-                                                        <string key="title">	Left to Right</string>
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-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
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-                        <items>
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-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
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-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
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-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Queue/Queue Tests/Queue/Info.plist b/Queue/Queue Tests/Queue/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Queue/Queue Tests/Queue/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Queue/Queue Tests/QueueTests/Info.plist b/Queue/Tests/Info.plist
similarity index 100%
rename from Queue/Queue Tests/QueueTests/Info.plist
rename to Queue/Tests/Info.plist
diff --git a/Queue/Queue Tests/QueueTests/QueueTests.swift b/Queue/Tests/QueueTests.swift
similarity index 98%
rename from Queue/Queue Tests/QueueTests/QueueTests.swift
rename to Queue/Tests/QueueTests.swift
index 1ffea7468..7406f8d35 100755
--- a/Queue/Queue Tests/QueueTests/QueueTests.swift	
+++ b/Queue/Tests/QueueTests.swift
@@ -1,6 +1,5 @@
 import Foundation
 import XCTest
-@testable import Queue
 
 class QueueTest: XCTestCase {
   func testEmpty() {
diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..83e3fc523
--- /dev/null
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C4021C77A6BF003CECC7 /* Queue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4011C77A6BF003CECC7 /* Queue.swift */; };
+		7B80C4041C77A6C5003CECC7 /* QueueTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4031C77A6C5003CECC7 /* QueueTests.swift */; };
+/* End PBXBuildFile section */
+
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+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C4011C77A6BF003CECC7 /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Queue.swift; path = ../Queue.swift; sourceTree = SOURCE_ROOT; };
+		7B80C4031C77A6C5003CECC7 /* QueueTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = QueueTests.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
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+/* End PBXFrameworksBuildPhase section */
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+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
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+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
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+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B80C4011C77A6BF003CECC7 /* Queue.swift */,
+				7B80C4031C77A6C5003CECC7 /* QueueTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
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+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
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+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C4021C77A6BF003CECC7 /* Queue.swift in Sources */,
+				7B80C4041C77A6C5003CECC7 /* QueueTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
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-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.QuicksortTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Quicksort.app/Contents/MacOS/Quicksort";
-			};
-			name = Debug;
-		};
-		7B18E0851C5BF86E005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = QuicksortTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.QuicksortTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Quicksort.app/Contents/MacOS/Quicksort";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B18E0631C5BF86E005A2B8E /* Build configuration list for PBXProject "Quicksort" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E07E1C5BF86E005A2B8E /* Debug */,
-				7B18E07F1C5BF86E005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0801C5BF86E005A2B8E /* Build configuration list for PBXNativeTarget "Quicksort" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0811C5BF86E005A2B8E /* Debug */,
-				7B18E0821C5BF86E005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0831C5BF86E005A2B8E /* Build configuration list for PBXNativeTarget "QuicksortTests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0841C5BF86E005A2B8E /* Debug */,
-				7B18E0851C5BF86E005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B18E0601C5BF86E005A2B8E /* Project object */;
-}
diff --git a/Quicksort/Quicksort Tests/Quicksort/AppDelegate.swift b/Quicksort/Quicksort Tests/Quicksort/AppDelegate.swift
deleted file mode 100644
index 633208e7b..000000000
--- a/Quicksort/Quicksort Tests/Quicksort/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  Quicksort
-//
-//  Created by Matthijs Hollemans on 29-01-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Quicksort/Quicksort Tests/Quicksort/Assets.xcassets/AppIcon.appiconset/Contents.json b/Quicksort/Quicksort Tests/Quicksort/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Quicksort/Quicksort Tests/Quicksort/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Quicksort/Quicksort Tests/Quicksort/Base.lproj/MainMenu.xib b/Quicksort/Quicksort Tests/Quicksort/Base.lproj/MainMenu.xib
deleted file mode 100644
index 41a33b27a..000000000
--- a/Quicksort/Quicksort Tests/Quicksort/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="Quicksort" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Quicksort" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About Quicksort" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide Quicksort" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit Quicksort" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
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-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                    </menu>
-                </menuItem>
-                <menuItem title="Window" id="aUF-d1-5bR">
-                    <modifierMask key="keyEquivalentModifierMask"/>
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-                        <items>
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-                                </connections>
-                            </menuItem>
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-                            </menuItem>
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-                                </connections>
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-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Quicksort/Quicksort Tests/Quicksort/Info.plist b/Quicksort/Quicksort Tests/Quicksort/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Quicksort/Quicksort Tests/Quicksort/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Quicksort/Quicksort Tests/QuicksortTests/Info.plist b/Quicksort/Tests/Info.plist
similarity index 100%
rename from Quicksort/Quicksort Tests/QuicksortTests/Info.plist
rename to Quicksort/Tests/Info.plist
diff --git a/Quicksort/Quicksort Tests/QuicksortTests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
similarity index 96%
rename from Quicksort/Quicksort Tests/QuicksortTests/QuicksortTests.swift
rename to Quicksort/Tests/QuicksortTests.swift
index 215991e98..ef95f1095 100644
--- a/Quicksort/Quicksort Tests/QuicksortTests/QuicksortTests.swift	
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -1,5 +1,4 @@
 import XCTest
-@testable import Quicksort
 
 class QuicksortTests: XCTestCase {
   func testQuicksort() {
diff --git a/Quicksort/Quicksort Tests/QuicksortTests/SortingTestHelpers.swift b/Quicksort/Tests/SortingTestHelpers.swift
similarity index 100%
rename from Quicksort/Quicksort Tests/QuicksortTests/SortingTestHelpers.swift
rename to Quicksort/Tests/SortingTestHelpers.swift
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj b/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..8aecb59f8
--- /dev/null
+++ b/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,265 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
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+/* End PBXBuildFile section */
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+
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+/* End PBXFrameworksBuildPhase section */
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+				7B2BBC721C779D710067B71D /* Products */,
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+		7B2BBC721C779D710067B71D /* Products */ = {
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+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B80C3E51C77A4CA003CECC7 /* Quicksort.swift */,
+				7B80C3E71C77A4D0003CECC7 /* QuicksortTests.swift */,
+				7B80C3E81C77A4D0003CECC7 /* SortingTestHelpers.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
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index 394f2c196..000000000
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-		};
-		7B1BFAB01C6E5CD70051C9A4 /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = RLE/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLE;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Debug;
-		};
-		7B1BFAB11C6E5CD70051C9A4 /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = RLE/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLE;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Release;
-		};
-		7B1BFAB31C6E5CD70051C9A4 /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = RLETests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLETests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/RLE.app/Contents/MacOS/RLE";
-			};
-			name = Debug;
-		};
-		7B1BFAB41C6E5CD70051C9A4 /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = RLETests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.RLETests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/RLE.app/Contents/MacOS/RLE";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B1BFA921C6E5CD70051C9A4 /* Build configuration list for PBXProject "RLE" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B1BFAAD1C6E5CD70051C9A4 /* Debug */,
-				7B1BFAAE1C6E5CD70051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B1BFAAF1C6E5CD70051C9A4 /* Build configuration list for PBXNativeTarget "RLE" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B1BFAB01C6E5CD70051C9A4 /* Debug */,
-				7B1BFAB11C6E5CD70051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B1BFAB21C6E5CD70051C9A4 /* Build configuration list for PBXNativeTarget "RLETests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B1BFAB31C6E5CD70051C9A4 /* Debug */,
-				7B1BFAB41C6E5CD70051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B1BFA8F1C6E5CD70051C9A4 /* Project object */;
-}
diff --git a/Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift b/Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift
deleted file mode 100644
index 4ae9f8243..000000000
--- a/Run-Length Encoding/RLE Tests/RLE/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  RLE
-//
-//  Created by Matthijs Hollemans on 12-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json b/Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Run-Length Encoding/RLE Tests/RLE/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib b/Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib
deleted file mode 100644
index 6f60cc595..000000000
--- a/Run-Length Encoding/RLE Tests/RLE/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="RLE" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="RLE" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About RLE" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide RLE" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit RLE" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
-                                                    <menuItem title="Use Default" id="agt-UL-0e3">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="J7y-lM-qPV">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use All" id="xQD-1f-W4t">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
-                                                <items>
-                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Subscript" id="I0S-gh-46l">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
-                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteFont:" target="-1" id="JfD-CL-leO"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Text" id="Fal-I4-PZk">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
-                                            <connections>
-                                                <action selector="alignCenter:" target="-1" id="spX-mk-kcS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Justify" id="J5U-5w-g23">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="alignJustified:" target="-1" id="ljL-7U-jND"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
-                                            <connections>
-                                                <action selector="alignRight:" target="-1" id="r48-bG-YeY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
-                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
-                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="Nop-cj-93Q">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionNatural:" target="-1" id="lPI-Se-ZHp"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="BgM-ve-c93">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionLeftToRight:" target="-1" id="caW-Bv-w94"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="RB4-Sm-HuC">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionRightToLeft:" target="-1" id="EXD-6r-ZUu"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="fKy-g9-1gm"/>
-                                        <menuItem title="Show Ruler" id="vLm-3I-IUL">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleRuler:" target="-1" id="FOx-HJ-KwY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Copy Ruler" keyEquivalent="c" id="MkV-Pr-PK5">
-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyRuler:" target="-1" id="71i-fW-3W2"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Ruler" keyEquivalent="v" id="LVM-kO-fVI">
-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteRuler:" target="-1" id="cSh-wd-qM2"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="runToolbarCustomizationPalette:" target="-1" id="pQI-g3-MTW"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Window" id="aUF-d1-5bR">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Help" id="wpr-3q-Mcd">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
-                        <items>
-                            <menuItem title="RLE Help" keyEquivalent="?" id="FKE-Sm-Kum">
-                                <connections>
-                                    <action selector="showHelp:" target="-1" id="y7X-2Q-9no"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-            </items>
-        </menu>
-        <window title="RLE" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" releasedWhenClosed="NO" animationBehavior="default" id="QvC-M9-y7g">
-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Run-Length Encoding/RLE Tests/RLE/Info.plist b/Run-Length Encoding/RLE Tests/RLE/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Run-Length Encoding/RLE Tests/RLE/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Run-Length Encoding/RLE Tests/RLE/RLE.swift b/Run-Length Encoding/RLE Tests/RLE/RLE.swift
deleted file mode 100644
index f26299cf1..000000000
--- a/Run-Length Encoding/RLE Tests/RLE/RLE.swift	
+++ /dev/null
@@ -1,70 +0,0 @@
-import Foundation
-
-extension NSData {
-  /*
-    Compresses the NSData using run-length encoding.
-  */
-  public func compressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
-      
-      while ptr < end {
-        var count = 0
-        var byte = ptr.memory
-        var next = byte
-        
-        // Is the next byte the same? Keep reading until we find a different
-        // value, or we reach the end of the data, or the run is 64 bytes.
-        while next == byte && ptr < end && count < 64 {
-          ptr = ptr.advancedBy(1)
-          next = ptr.memory
-          count += 1
-        }
-
-        if count > 1 || byte >= 192 {         // byte run of up to 64 repeats
-          var size = 191 + UInt8(count)
-          data.appendBytes(&size, length: 1)
-          data.appendBytes(&byte, length: 1)
-        } else {                              // single byte between 0 and 192
-          data.appendBytes(&byte, length: 1)
-        }
-      }
-    }
-    return data
-  }
-  
-  /*
-    Converts a run-length encoded NSData back to the original.
-  */
-  public func decompressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
-
-      while ptr < end {
-        // Read the next byte. This is either a single value less than 192, 
-        // or the start of a byte run.
-        var byte = ptr.memory
-        ptr = ptr.advancedBy(1)
-        
-        if byte < 192 {                       // single value
-          data.appendBytes(&byte, length: 1)
-
-        } else if ptr < end {                 // byte run
-          // Read the actual data value.
-          var value = ptr.memory
-          ptr = ptr.advancedBy(1)
-
-          // And write it out repeatedly.
-          for _ in 0 ..< byte - 191 {
-            data.appendBytes(&value, length: 1)
-          }
-        }
-      }
-    }
-    return data
-  }
-}
diff --git a/Run-Length Encoding/RLE.swift b/Run-Length Encoding/RLE.swift
index ee25af997..f26299cf1 100644
--- a/Run-Length Encoding/RLE.swift	
+++ b/Run-Length Encoding/RLE.swift	
@@ -1,29 +1,6 @@
 import Foundation
 
 extension NSData {
-  /*
-    Helper method that reads the next run of bytes. Returns the size of the
-    run (between 1 and 64), the byte value, and the updated read pointer.
-  */
-  private func readRun(start start: UnsafePointer<UInt8>, end: UnsafePointer<UInt8>) -> (Int, UInt8, UnsafePointer<UInt8>) {
-    var ptr = start
-    var count = 0
-
-    // Read the current byte.
-    let previous = ptr.memory
-    var current = previous
-
-    // Is the next byte the same? Then keep reading until we find another
-    // byte, or we reach the end of the data, or the run is 64 bytes.
-    while current == previous && ptr < end && count < 64 {
-      ptr = ptr.advancedBy(1)
-      current = ptr.memory
-      count += 1
-    }
-    
-    return (count, previous, ptr)
-  }
-
   /*
     Compresses the NSData using run-length encoding.
   */
@@ -34,27 +11,60 @@ extension NSData {
       let end = ptr + length
       
       while ptr < end {
-        var (count, byte, out) = readRun(start: ptr, end: end)
+        var count = 0
+        var byte = ptr.memory
+        var next = byte
+        
+        // Is the next byte the same? Keep reading until we find a different
+        // value, or we reach the end of the data, or the run is 64 bytes.
+        while next == byte && ptr < end && count < 64 {
+          ptr = ptr.advancedBy(1)
+          next = ptr.memory
+          count += 1
+        }
 
-        if count == 0 {                        // end-of-file
-          out = end
-        } else if count > 1 || byte >= 192 {   // byte run, up to 64 repeats
-          var pair: [UInt8] = [191 + UInt8(count), byte]
-          data.appendBytes(&pair, length: 2)
-        } else {                               // single byte between 0 and 192
+        if count > 1 || byte >= 192 {         // byte run of up to 64 repeats
+          var size = 191 + UInt8(count)
+          data.appendBytes(&size, length: 1)
+          data.appendBytes(&byte, length: 1)
+        } else {                              // single byte between 0 and 192
           data.appendBytes(&byte, length: 1)
         }
-        ptr = out
       }
     }
     return data
   }
   
-
   /*
     Converts a run-length encoded NSData back to the original.
   */
   public func decompressRLE() -> NSData {
-    return NSData()
+    let data = NSMutableData()
+    if length > 0 {
+      var ptr = UnsafePointer<UInt8>(bytes)
+      let end = ptr + length
+
+      while ptr < end {
+        // Read the next byte. This is either a single value less than 192, 
+        // or the start of a byte run.
+        var byte = ptr.memory
+        ptr = ptr.advancedBy(1)
+        
+        if byte < 192 {                       // single value
+          data.appendBytes(&byte, length: 1)
+
+        } else if ptr < end {                 // byte run
+          // Read the actual data value.
+          var value = ptr.memory
+          ptr = ptr.advancedBy(1)
+
+          // And write it out repeatedly.
+          for _ in 0 ..< byte - 191 {
+            data.appendBytes(&value, length: 1)
+          }
+        }
+      }
+    }
+    return data
   }
 }
diff --git a/Run-Length Encoding/RLE Tests/RLETests/Info.plist b/Run-Length Encoding/Tests/Info.plist
similarity index 100%
rename from Run-Length Encoding/RLE Tests/RLETests/Info.plist
rename to Run-Length Encoding/Tests/Info.plist
diff --git a/Run-Length Encoding/RLE Tests/RLETests/RLETests.swift b/Run-Length Encoding/Tests/RLETests.swift
similarity index 99%
rename from Run-Length Encoding/RLE Tests/RLETests/RLETests.swift
rename to Run-Length Encoding/Tests/RLETests.swift
index 99616a8c2..a55f74fdc 100644
--- a/Run-Length Encoding/RLE Tests/RLETests/RLETests.swift	
+++ b/Run-Length Encoding/Tests/RLETests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import RLE
 
 class RLETests: XCTestCase {
   private var showExtraOutput = false
diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj b/Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..aae67b064
--- /dev/null
+++ b/Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C4181C77A7F3003CECC7 /* RLE.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4171C77A7F3003CECC7 /* RLE.swift */; };
+		7B80C41A1C77A7FA003CECC7 /* RLETests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4191C77A7FA003CECC7 /* RLETests.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C4171C77A7F3003CECC7 /* RLE.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = RLE.swift; path = ../RLE.swift; sourceTree = SOURCE_ROOT; };
+		7B80C4191C77A7FA003CECC7 /* RLETests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = RLETests.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B80C4171C77A7F3003CECC7 /* RLE.swift */,
+				7B80C4191C77A7FA003CECC7 /* RLETests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C4181C77A7F3003CECC7 /* RLE.swift in Sources */,
+				7B80C41A1C77A7FA003CECC7 /* RLETests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index 537210058..5798e1f32 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -2,8 +2,7 @@
   Finds the maximum and minimum value in an array in O(n) time.
 */
 
-func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)?
-{
+func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)? {
   guard !array.isEmpty else {
     return nil
   }
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum.xcodeproj/project.pbxproj b/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum.xcodeproj/project.pbxproj
deleted file mode 100644
index dc319937a..000000000
--- a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,393 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
-	classes = {
-	};
-	objectVersion = 46;
-	objects = {
-
-/* Begin PBXBuildFile section */
-		7B18E0971C5BFA2E005A2B8E /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B18E0961C5BFA2E005A2B8E /* AppDelegate.swift */; };
-		7B18E0A71C5BFA2E005A2B8E /* SelectMinimumMaximumTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B18E0A61C5BFA2E005A2B8E /* SelectMinimumMaximumTests.swift */; };
-		838A4FB41C64AED00092AA8F /* TestHelper.swift in Sources */ = {isa = PBXBuildFile; fileRef = 838A4FB31C64AED00092AA8F /* TestHelper.swift */; };
-		83F3255D1C64A0E700EB0421 /* Maximum.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F3255A1C64A0E700EB0421 /* Maximum.swift */; };
-		83F3255E1C64A0E700EB0421 /* Minimum.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F3255B1C64A0E700EB0421 /* Minimum.swift */; };
-		83F3255F1C64A0E700EB0421 /* MinimumMaximumPairs.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F3255C1C64A0E700EB0421 /* MinimumMaximumPairs.swift */; };
-		83F325611C64A3E000EB0421 /* MinimumTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F325601C64A3E000EB0421 /* MinimumTests.swift */; };
-		83F325631C64A4D400EB0421 /* MaximumTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F325621C64A4D400EB0421 /* MaximumTests.swift */; };
-/* End PBXBuildFile section */
-
-/* Begin PBXContainerItemProxy section */
-		7B18E0A31C5BFA2E005A2B8E /* PBXContainerItemProxy */ = {
-			isa = PBXContainerItemProxy;
-			containerPortal = 7B18E08B1C5BFA2E005A2B8E /* Project object */;
-			proxyType = 1;
-			remoteGlobalIDString = 7B18E0921C5BFA2E005A2B8E;
-			remoteInfo = SelectMinimumMaximum;
-		};
-/* End PBXContainerItemProxy section */
-
-/* Begin PBXFileReference section */
-		7B18E0931C5BFA2E005A2B8E /* SelectMinimumMaximum.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = SelectMinimumMaximum.app; sourceTree = BUILT_PRODUCTS_DIR; };
-		7B18E0961C5BFA2E005A2B8E /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
-		7B18E09D1C5BFA2E005A2B8E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
-		7B18E0A21C5BFA2E005A2B8E /* SelectMinimumMaximumTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = SelectMinimumMaximumTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
-		7B18E0A61C5BFA2E005A2B8E /* SelectMinimumMaximumTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = SelectMinimumMaximumTests.swift; sourceTree = "<group>"; };
-		7B18E0A81C5BFA2E005A2B8E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
-		838A4FB31C64AED00092AA8F /* TestHelper.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = TestHelper.swift; sourceTree = "<group>"; };
-		83F3255A1C64A0E700EB0421 /* Maximum.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Maximum.swift; path = ../../Maximum.swift; sourceTree = "<group>"; };
-		83F3255B1C64A0E700EB0421 /* Minimum.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Minimum.swift; path = ../../Minimum.swift; sourceTree = "<group>"; };
-		83F3255C1C64A0E700EB0421 /* MinimumMaximumPairs.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = MinimumMaximumPairs.swift; path = ../../MinimumMaximumPairs.swift; sourceTree = "<group>"; };
-		83F325601C64A3E000EB0421 /* MinimumTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = MinimumTests.swift; sourceTree = "<group>"; };
-		83F325621C64A4D400EB0421 /* MaximumTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = MaximumTests.swift; sourceTree = "<group>"; };
-/* End PBXFileReference section */
-
-/* Begin PBXFrameworksBuildPhase section */
-		7B18E0901C5BFA2E005A2B8E /* Frameworks */ = {
-			isa = PBXFrameworksBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
-		7B18E09F1C5BFA2E005A2B8E /* Frameworks */ = {
-			isa = PBXFrameworksBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
-/* End PBXFrameworksBuildPhase section */
-
-/* Begin PBXGroup section */
-		7B18E08A1C5BFA2E005A2B8E = {
-			isa = PBXGroup;
-			children = (
-				7B18E0951C5BFA2E005A2B8E /* SelectMinimumMaximum */,
-				7B18E0A51C5BFA2E005A2B8E /* SelectMinimumMaximumTests */,
-				7B18E0941C5BFA2E005A2B8E /* Products */,
-			);
-			sourceTree = "<group>";
-		};
-		7B18E0941C5BFA2E005A2B8E /* Products */ = {
-			isa = PBXGroup;
-			children = (
-				7B18E0931C5BFA2E005A2B8E /* SelectMinimumMaximum.app */,
-				7B18E0A21C5BFA2E005A2B8E /* SelectMinimumMaximumTests.xctest */,
-			);
-			name = Products;
-			sourceTree = "<group>";
-		};
-		7B18E0951C5BFA2E005A2B8E /* SelectMinimumMaximum */ = {
-			isa = PBXGroup;
-			children = (
-				7B18E0961C5BFA2E005A2B8E /* AppDelegate.swift */,
-				83F3255A1C64A0E700EB0421 /* Maximum.swift */,
-				83F3255B1C64A0E700EB0421 /* Minimum.swift */,
-				83F3255C1C64A0E700EB0421 /* MinimumMaximumPairs.swift */,
-				7B18E09D1C5BFA2E005A2B8E /* Info.plist */,
-			);
-			path = SelectMinimumMaximum;
-			sourceTree = "<group>";
-		};
-		7B18E0A51C5BFA2E005A2B8E /* SelectMinimumMaximumTests */ = {
-			isa = PBXGroup;
-			children = (
-				7B18E0A81C5BFA2E005A2B8E /* Info.plist */,
-				7B18E0A61C5BFA2E005A2B8E /* SelectMinimumMaximumTests.swift */,
-				83F325601C64A3E000EB0421 /* MinimumTests.swift */,
-				83F325621C64A4D400EB0421 /* MaximumTests.swift */,
-				838A4FB31C64AED00092AA8F /* TestHelper.swift */,
-			);
-			path = SelectMinimumMaximumTests;
-			sourceTree = "<group>";
-		};
-/* End PBXGroup section */
-
-/* Begin PBXNativeTarget section */
-		7B18E0921C5BFA2E005A2B8E /* SelectMinimumMaximum */ = {
-			isa = PBXNativeTarget;
-			buildConfigurationList = 7B18E0AB1C5BFA2E005A2B8E /* Build configuration list for PBXNativeTarget "SelectMinimumMaximum" */;
-			buildPhases = (
-				7B18E08F1C5BFA2E005A2B8E /* Sources */,
-				7B18E0901C5BFA2E005A2B8E /* Frameworks */,
-				7B18E0911C5BFA2E005A2B8E /* Resources */,
-			);
-			buildRules = (
-			);
-			dependencies = (
-			);
-			name = SelectMinimumMaximum;
-			productName = SelectMinimumMaximum;
-			productReference = 7B18E0931C5BFA2E005A2B8E /* SelectMinimumMaximum.app */;
-			productType = "com.apple.product-type.application";
-		};
-		7B18E0A11C5BFA2E005A2B8E /* SelectMinimumMaximumTests */ = {
-			isa = PBXNativeTarget;
-			buildConfigurationList = 7B18E0AE1C5BFA2E005A2B8E /* Build configuration list for PBXNativeTarget "SelectMinimumMaximumTests" */;
-			buildPhases = (
-				7B18E09E1C5BFA2E005A2B8E /* Sources */,
-				7B18E09F1C5BFA2E005A2B8E /* Frameworks */,
-				7B18E0A01C5BFA2E005A2B8E /* Resources */,
-			);
-			buildRules = (
-			);
-			dependencies = (
-				7B18E0A41C5BFA2E005A2B8E /* PBXTargetDependency */,
-			);
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diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/AppDelegate.swift b/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/AppDelegate.swift
deleted file mode 100644
index 9c4f92293..000000000
--- a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/AppDelegate.swift	
+++ /dev/null
@@ -1,16 +0,0 @@
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-}
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/Info.plist b/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/Info.plist
deleted file mode 100644
index ec6d36e96..000000000
--- a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximum/Info.plist	
+++ /dev/null
@@ -1,32 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/Info.plist b/Select Minimum Maximum/Tests/Info.plist
similarity index 100%
rename from Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/Info.plist
rename to Select Minimum Maximum/Tests/Info.plist
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/MaximumTests.swift b/Select Minimum Maximum/Tests/MaximumTests.swift
similarity index 96%
rename from Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/MaximumTests.swift
rename to Select Minimum Maximum/Tests/MaximumTests.swift
index bd58187fc..38bcf483b 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/MaximumTests.swift	
+++ b/Select Minimum Maximum/Tests/MaximumTests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import SelectMinimumMaximum
 
 class MaximumTests: XCTestCase {
 
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/SelectMinimumMaximumTests.swift b/Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift
similarity index 95%
rename from Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/SelectMinimumMaximumTests.swift
rename to Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift
index 330f0e902..6cde21021 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/SelectMinimumMaximumTests.swift	
+++ b/Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift	
@@ -1,7 +1,6 @@
 import XCTest
-@testable import SelectMinimumMaximum
 
-class SelectMinimumMaximumTests: XCTestCase {
+class MinimumMaximumPairsTests: XCTestCase {
 
   func testMinimumAndMaximumGivenAListContainingOneElement() {
     let array = [ 8 ]
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/MinimumTests.swift b/Select Minimum Maximum/Tests/MinimumTests.swift
similarity index 96%
rename from Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/MinimumTests.swift
rename to Select Minimum Maximum/Tests/MinimumTests.swift
index 235673320..ed4fbe1f0 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/MinimumTests.swift	
+++ b/Select Minimum Maximum/Tests/MinimumTests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import SelectMinimumMaximum
 
 class MinimumTests: XCTestCase {
 
diff --git a/Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/TestHelper.swift b/Select Minimum Maximum/Tests/TestHelper.swift
similarity index 100%
rename from Select Minimum Maximum/SelectMinimumMaximum Tests/SelectMinimumMaximumTests/TestHelper.swift
rename to Select Minimum Maximum/Tests/TestHelper.swift
diff --git a/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj b/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..e2857d2b7
--- /dev/null
+++ b/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,281 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C40C1C77A768003CECC7 /* Maximum.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4091C77A768003CECC7 /* Maximum.swift */; };
+		7B80C40D1C77A768003CECC7 /* Minimum.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C40A1C77A768003CECC7 /* Minimum.swift */; };
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+		7B80C4141C77A770003CECC7 /* MinimumTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4101C77A770003CECC7 /* MinimumTests.swift */; };
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+		7B80C4161C77A770003CECC7 /* TestHelper.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4121C77A770003CECC7 /* TestHelper.swift */; };
+/* End PBXBuildFile section */
+
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+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C4091C77A768003CECC7 /* Maximum.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Maximum.swift; path = ../Maximum.swift; sourceTree = SOURCE_ROOT; };
+		7B80C40A1C77A768003CECC7 /* Minimum.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Minimum.swift; path = ../Minimum.swift; sourceTree = SOURCE_ROOT; };
+		7B80C40B1C77A768003CECC7 /* MinimumMaximumPairs.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = MinimumMaximumPairs.swift; path = ../MinimumMaximumPairs.swift; sourceTree = SOURCE_ROOT; };
+		7B80C40F1C77A770003CECC7 /* MaximumTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = MaximumTests.swift; sourceTree = SOURCE_ROOT; };
+		7B80C4101C77A770003CECC7 /* MinimumTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = MinimumTests.swift; sourceTree = SOURCE_ROOT; };
+		7B80C4111C77A770003CECC7 /* MinimumMaximumPairsTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = MinimumMaximumPairsTests.swift; sourceTree = SOURCE_ROOT; };
+		7B80C4121C77A770003CECC7 /* TestHelper.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = TestHelper.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+				7B80C4091C77A768003CECC7 /* Maximum.swift */,
+				7B80C40F1C77A770003CECC7 /* MaximumTests.swift */,
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+				7B80C40B1C77A768003CECC7 /* MinimumMaximumPairs.swift */,
+				7B80C4111C77A770003CECC7 /* MinimumMaximumPairsTests.swift */,
+				7B80C4121C77A770003CECC7 /* TestHelper.swift */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
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+/* End PBXGroup section */
+
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+				7B2BBC7E1C779D720067B71D /* Resources */,
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+			);
+			dependencies = (
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+			name = Tests;
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+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
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+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
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+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
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+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
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-				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
-				ENABLE_NS_ASSERTIONS = NO;
-				ENABLE_STRICT_OBJC_MSGSEND = YES;
-				GCC_C_LANGUAGE_STANDARD = gnu99;
-				GCC_NO_COMMON_BLOCKS = YES;
-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = NO;
-				SDKROOT = macosx;
-			};
-			name = Release;
-		};
-		7B18E0D71C5BFB2D005A2B8E /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = SelectionSort/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.SelectionSort;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Debug;
-		};
-		7B18E0D81C5BFB2D005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = SelectionSort/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.SelectionSort;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Release;
-		};
-		7B18E0DA1C5BFB2D005A2B8E /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = SelectionSortTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.SelectionSortTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/SelectionSort.app/Contents/MacOS/SelectionSort";
-			};
-			name = Debug;
-		};
-		7B18E0DB1C5BFB2D005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = SelectionSortTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.SelectionSortTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/SelectionSort.app/Contents/MacOS/SelectionSort";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B18E0B91C5BFB2D005A2B8E /* Build configuration list for PBXProject "SelectionSort" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0D41C5BFB2D005A2B8E /* Debug */,
-				7B18E0D51C5BFB2D005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0D61C5BFB2D005A2B8E /* Build configuration list for PBXNativeTarget "SelectionSort" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0D71C5BFB2D005A2B8E /* Debug */,
-				7B18E0D81C5BFB2D005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0D91C5BFB2D005A2B8E /* Build configuration list for PBXNativeTarget "SelectionSortTests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0DA1C5BFB2D005A2B8E /* Debug */,
-				7B18E0DB1C5BFB2D005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B18E0B61C5BFB2D005A2B8E /* Project object */;
-}
diff --git a/Selection Sort/SelectionSort Tests/SelectionSort/AppDelegate.swift b/Selection Sort/SelectionSort Tests/SelectionSort/AppDelegate.swift
deleted file mode 100644
index 79cd1a92a..000000000
--- a/Selection Sort/SelectionSort Tests/SelectionSort/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  SelectionSort
-//
-//  Created by Matthijs Hollemans on 29-01-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Selection Sort/SelectionSort Tests/SelectionSort/Assets.xcassets/AppIcon.appiconset/Contents.json b/Selection Sort/SelectionSort Tests/SelectionSort/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Selection Sort/SelectionSort Tests/SelectionSort/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Selection Sort/SelectionSort Tests/SelectionSort/Base.lproj/MainMenu.xib b/Selection Sort/SelectionSort Tests/SelectionSort/Base.lproj/MainMenu.xib
deleted file mode 100644
index 47b389b06..000000000
--- a/Selection Sort/SelectionSort Tests/SelectionSort/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="SelectionSort" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="SelectionSort" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About SelectionSort" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide SelectionSort" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit SelectionSort" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
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-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
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-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
-                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
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-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
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-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
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-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
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-                                                    </menuItem>
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-                                                        </connections>
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-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                        </connections>
-                                                    </menuItem>
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-                                                        <string key="title">	Right to Left</string>
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-                                            </connections>
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-                    </menu>
-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                <menuItem title="Window" id="aUF-d1-5bR">
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-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
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-                                </connections>
-                            </menuItem>
-                        </items>
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-        </menu>
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-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Selection Sort/SelectionSort Tests/SelectionSort/Info.plist b/Selection Sort/SelectionSort Tests/SelectionSort/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Selection Sort/SelectionSort Tests/SelectionSort/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Selection Sort/SelectionSort Tests/SelectionSortTests/Info.plist b/Selection Sort/Tests/Info.plist
similarity index 100%
rename from Selection Sort/SelectionSort Tests/SelectionSortTests/Info.plist
rename to Selection Sort/Tests/Info.plist
diff --git a/Selection Sort/SelectionSort Tests/SelectionSortTests/SelectionSortTests.swift b/Selection Sort/Tests/SelectionSortTests.swift
similarity index 80%
rename from Selection Sort/SelectionSort Tests/SelectionSortTests/SelectionSortTests.swift
rename to Selection Sort/Tests/SelectionSortTests.swift
index 917332cae..3e26122b0 100644
--- a/Selection Sort/SelectionSort Tests/SelectionSortTests/SelectionSortTests.swift	
+++ b/Selection Sort/Tests/SelectionSortTests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import SelectionSort
 
 class SelectionSortTests: XCTestCase {
   func testSelectionSort() {
diff --git a/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj b/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..11aefac3c
--- /dev/null
+++ b/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,265 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
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+		7B80C3F11C77A598003CECC7 /* SelectionSort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = SelectionSort.swift; path = ../SelectionSort.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
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+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
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+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
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+			);
+			name = Products;
+			sourceTree = "<group>";
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-					"$(inherited)",
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-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = YES;
-				ONLY_ACTIVE_ARCH = YES;
-				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-			};
-			name = Debug;
-		};
-		7B1BFA831C6A40380051C9A4 /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
-				CLANG_CXX_LIBRARY = "libc++";
-				CLANG_ENABLE_MODULES = YES;
-				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
-				CLANG_WARN_EMPTY_BODY = YES;
-				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_UNREACHABLE_CODE = YES;
-				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				CODE_SIGN_IDENTITY = "-";
-				COPY_PHASE_STRIP = NO;
-				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
-				ENABLE_NS_ASSERTIONS = NO;
-				ENABLE_STRICT_OBJC_MSGSEND = YES;
-				GCC_C_LANGUAGE_STANDARD = gnu99;
-				GCC_NO_COMMON_BLOCKS = YES;
-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = NO;
-				SDKROOT = macosx;
-			};
-			name = Release;
-		};
-		7B1BFA851C6A40380051C9A4 /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = ShellSort/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.ShellSort;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Debug;
-		};
-		7B1BFA861C6A40380051C9A4 /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = ShellSort/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.ShellSort;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Release;
-		};
-		7B1BFA881C6A40380051C9A4 /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = ShellSortTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.ShellSortTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/ShellSort.app/Contents/MacOS/ShellSort";
-			};
-			name = Debug;
-		};
-		7B1BFA891C6A40380051C9A4 /* Release */ = {
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-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
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-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.ShellSortTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/ShellSort.app/Contents/MacOS/ShellSort";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B1BFA671C6A40370051C9A4 /* Build configuration list for PBXProject "ShellSort" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B1BFA821C6A40380051C9A4 /* Debug */,
-				7B1BFA831C6A40380051C9A4 /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B1BFA841C6A40380051C9A4 /* Build configuration list for PBXNativeTarget "ShellSort" */ = {
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-			buildConfigurations = (
-				7B1BFA851C6A40380051C9A4 /* Debug */,
-				7B1BFA861C6A40380051C9A4 /* Release */,
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-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B1BFA871C6A40380051C9A4 /* Build configuration list for PBXNativeTarget "ShellSortTests" */ = {
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-			buildConfigurations = (
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-				7B1BFA891C6A40380051C9A4 /* Release */,
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-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B1BFA641C6A40370051C9A4 /* Project object */;
-}
diff --git a/Shell Sort/ShellSort Tests/ShellSort/AppDelegate.swift b/Shell Sort/ShellSort Tests/ShellSort/AppDelegate.swift
deleted file mode 100644
index 8e8d28d24..000000000
--- a/Shell Sort/ShellSort Tests/ShellSort/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  ShellSort
-//
-//  Created by Matthijs Hollemans on 09-02-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Shell Sort/ShellSort Tests/ShellSort/Assets.xcassets/AppIcon.appiconset/Contents.json b/Shell Sort/ShellSort Tests/ShellSort/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Shell Sort/ShellSort Tests/ShellSort/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Shell Sort/ShellSort Tests/ShellSort/Base.lproj/MainMenu.xib b/Shell Sort/ShellSort Tests/ShellSort/Base.lproj/MainMenu.xib
deleted file mode 100644
index 22614e1d7..000000000
--- a/Shell Sort/ShellSort Tests/ShellSort/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="ShellSort" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="ShellSort" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About ShellSort" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide ShellSort" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit ShellSort" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
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-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
-                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteFont:" target="-1" id="JfD-CL-leO"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Text" id="Fal-I4-PZk">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
-                                            <connections>
-                                                <action selector="alignCenter:" target="-1" id="spX-mk-kcS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Justify" id="J5U-5w-g23">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="alignJustified:" target="-1" id="ljL-7U-jND"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
-                                            <connections>
-                                                <action selector="alignRight:" target="-1" id="r48-bG-YeY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
-                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
-                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="Nop-cj-93Q">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
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-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="BgM-ve-c93">
-                                                        <string key="title">	Left to Right</string>
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-                                                        </connections>
-                                                    </menuItem>
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-                                            </connections>
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-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                <menuItem title="Window" id="aUF-d1-5bR">
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-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Help" id="wpr-3q-Mcd">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
-                        <items>
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-        </menu>
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-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Shell Sort/ShellSort Tests/ShellSort/Info.plist b/Shell Sort/ShellSort Tests/ShellSort/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Shell Sort/ShellSort Tests/ShellSort/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Shell Sort/ShellSort Tests/ShellSortTests/Info.plist b/Shell Sort/Tests/Info.plist
similarity index 100%
rename from Shell Sort/ShellSort Tests/ShellSortTests/Info.plist
rename to Shell Sort/Tests/Info.plist
diff --git a/Shell Sort/ShellSort Tests/ShellSortTests/ShellSortTests.swift b/Shell Sort/Tests/ShellSortTests.swift
similarity index 87%
rename from Shell Sort/ShellSort Tests/ShellSortTests/ShellSortTests.swift
rename to Shell Sort/Tests/ShellSortTests.swift
index 780ce1d3b..f9404b781 100644
--- a/Shell Sort/ShellSort Tests/ShellSortTests/ShellSortTests.swift	
+++ b/Shell Sort/Tests/ShellSortTests.swift	
@@ -1,5 +1,4 @@
 import XCTest
-@testable import ShellSort
 
 class ShellSortTests: XCTestCase {
   func testShellSort() {
diff --git a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..9f7f4391e
--- /dev/null
+++ b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,265 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3EA1C77A4D0003CECC7 /* SortingTestHelpers.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3E81C77A4D0003CECC7 /* SortingTestHelpers.swift */; };
+		7B80C3F41C77A5D3003CECC7 /* ShellSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3F31C77A5D3003CECC7 /* ShellSort.swift */; };
+		7B80C3F61C77A5D9003CECC7 /* ShellSortTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3F51C77A5D9003CECC7 /* ShellSortTests.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
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-				CLANG_ENABLE_MODULES = YES;
-				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
-				CLANG_WARN_EMPTY_BODY = YES;
-				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_UNREACHABLE_CODE = YES;
-				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				CODE_SIGN_IDENTITY = "-";
-				COPY_PHASE_STRIP = NO;
-				DEBUG_INFORMATION_FORMAT = dwarf;
-				ENABLE_STRICT_OBJC_MSGSEND = YES;
-				ENABLE_TESTABILITY = YES;
-				GCC_C_LANGUAGE_STANDARD = gnu99;
-				GCC_DYNAMIC_NO_PIC = NO;
-				GCC_NO_COMMON_BLOCKS = YES;
-				GCC_OPTIMIZATION_LEVEL = 0;
-				GCC_PREPROCESSOR_DEFINITIONS = (
-					"DEBUG=1",
-					"$(inherited)",
-				);
-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = YES;
-				ONLY_ACTIVE_ARCH = YES;
-				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-			};
-			name = Debug;
-		};
-		7B18E0561C5BF7F1005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
-				CLANG_CXX_LIBRARY = "libc++";
-				CLANG_ENABLE_MODULES = YES;
-				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
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-				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_UNREACHABLE_CODE = YES;
-				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				CODE_SIGN_IDENTITY = "-";
-				COPY_PHASE_STRIP = NO;
-				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
-				ENABLE_NS_ASSERTIONS = NO;
-				ENABLE_STRICT_OBJC_MSGSEND = YES;
-				GCC_C_LANGUAGE_STANDARD = gnu99;
-				GCC_NO_COMMON_BLOCKS = YES;
-				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
-				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
-				GCC_WARN_UNDECLARED_SELECTOR = YES;
-				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
-				GCC_WARN_UNUSED_FUNCTION = YES;
-				GCC_WARN_UNUSED_VARIABLE = YES;
-				MACOSX_DEPLOYMENT_TARGET = 10.11;
-				MTL_ENABLE_DEBUG_INFO = NO;
-				SDKROOT = macosx;
-			};
-			name = Release;
-		};
-		7B18E0581C5BF7F1005A2B8E /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = Stack/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Stack;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Debug;
-		};
-		7B18E0591C5BF7F1005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = Stack/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Stack;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Release;
-		};
-		7B18E05B1C5BF7F1005A2B8E /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = StackTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.StackTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Stack.app/Contents/MacOS/Stack";
-			};
-			name = Debug;
-		};
-		7B18E05C1C5BF7F1005A2B8E /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = StackTests/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.StackTests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Stack.app/Contents/MacOS/Stack";
-			};
-			name = Release;
-		};
-/* End XCBuildConfiguration section */
-
-/* Begin XCConfigurationList section */
-		7B18E03A1C5BF7F1005A2B8E /* Build configuration list for PBXProject "Stack" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0551C5BF7F1005A2B8E /* Debug */,
-				7B18E0561C5BF7F1005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E0571C5BF7F1005A2B8E /* Build configuration list for PBXNativeTarget "Stack" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E0581C5BF7F1005A2B8E /* Debug */,
-				7B18E0591C5BF7F1005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-		7B18E05A1C5BF7F1005A2B8E /* Build configuration list for PBXNativeTarget "StackTests" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				7B18E05B1C5BF7F1005A2B8E /* Debug */,
-				7B18E05C1C5BF7F1005A2B8E /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-			defaultConfigurationName = Release;
-		};
-/* End XCConfigurationList section */
-	};
-	rootObject = 7B18E0371C5BF7F1005A2B8E /* Project object */;
-}
diff --git a/Stack/Stack Tests/Stack/AppDelegate.swift b/Stack/Stack Tests/Stack/AppDelegate.swift
deleted file mode 100644
index 5daa0ee2d..000000000
--- a/Stack/Stack Tests/Stack/AppDelegate.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-//
-//  AppDelegate.swift
-//  Stack
-//
-//  Created by Matthijs Hollemans on 29-01-16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-  @IBOutlet weak var window: NSWindow!
-
-
-  func applicationDidFinishLaunching(aNotification: NSNotification) {
-    // Insert code here to initialize your application
-  }
-
-  func applicationWillTerminate(aNotification: NSNotification) {
-    // Insert code here to tear down your application
-  }
-
-
-}
-
diff --git a/Stack/Stack Tests/Stack/Assets.xcassets/AppIcon.appiconset/Contents.json b/Stack/Stack Tests/Stack/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Stack/Stack Tests/Stack/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Stack/Stack Tests/Stack/Base.lproj/MainMenu.xib b/Stack/Stack Tests/Stack/Base.lproj/MainMenu.xib
deleted file mode 100644
index d2e0528b5..000000000
--- a/Stack/Stack Tests/Stack/Base.lproj/MainMenu.xib	
+++ /dev/null
@@ -1,680 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="6233" systemVersion="14A329f" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="6233"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="Stack" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Stack" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About Stack" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide Stack" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit Stack" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
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-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
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-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
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-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
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-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
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-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
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-                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
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-                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
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-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
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-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
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-                                            </connections>
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-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
-                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
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-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
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-                                                        <string key="title">	Default</string>
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-                                                        </connections>
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-                                                        <string key="title">	Left to Right</string>
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-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
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-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
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-                    </menu>
-                </menuItem>
-                <menuItem title="Window" id="aUF-d1-5bR">
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-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
-                                </connections>
-                            </menuItem>
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-                <menuItem title="Help" id="wpr-3q-Mcd">
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-                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
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-                            <menuItem title="Stack Help" keyEquivalent="?" id="FKE-Sm-Kum">
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-        </menu>
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-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1177"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Stack/Stack Tests/Stack/Info.plist b/Stack/Stack Tests/Stack/Info.plist
deleted file mode 100644
index 0dca3caa8..000000000
--- a/Stack/Stack Tests/Stack/Info.plist	
+++ /dev/null
@@ -1,34 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIconFile</key>
-	<string></string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSMinimumSystemVersion</key>
-	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Swift Algorithm Club. All rights reserved.</string>
-	<key>NSMainNibFile</key>
-	<string>MainMenu</string>
-	<key>NSPrincipalClass</key>
-	<string>NSApplication</string>
-</dict>
-</plist>
diff --git a/Stack/Stack Tests/StackTests/Info.plist b/Stack/Tests/Info.plist
similarity index 100%
rename from Stack/Stack Tests/StackTests/Info.plist
rename to Stack/Tests/Info.plist
diff --git a/Stack/Stack Tests/StackTests/StackTests.swift b/Stack/Tests/StackTests.swift
similarity index 98%
rename from Stack/Stack Tests/StackTests/StackTests.swift
rename to Stack/Tests/StackTests.swift
index 13aa77479..62e26b0fa 100755
--- a/Stack/Stack Tests/StackTests/StackTests.swift	
+++ b/Stack/Tests/StackTests.swift
@@ -1,6 +1,5 @@
 import Foundation
 import XCTest
-@testable import Stack
 
 class StackTest: XCTestCase {
   func testEmpty() {
diff --git a/Stack/Tests/Tests.xcodeproj/project.pbxproj b/Stack/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..a36d7c51d
--- /dev/null
+++ b/Stack/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
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+}

From c5b3ac93c05d3684d6e1e467ba5b5bdb5f7689c3 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 23 Feb 2016 22:22:24 +0100
Subject: [PATCH 0041/1679] Add Huffman coding

---
 .../Huffman.playground/Contents.swift         |  23 +
 .../Huffman.playground/Sources/Heap.swift     | 223 ++++++++++
 .../Huffman.playground/Sources/Huffman.swift  | 191 ++++++++
 .../Sources/NSData+Bits.swift                 |  50 +++
 .../Sources/PriorityQueue.swift               |  58 +++
 .../Huffman.playground/contents.xcplayground  |   4 +
 .../Huffman.playground/timeline.xctimeline    |   6 +
 Huffman Coding/Huffman.swift                  | 191 ++++++++
 Huffman Coding/Images/BuildTree.gif           | Bin 0 -> 24647 bytes
 Huffman Coding/Images/BuildTree.graffle       | Bin 0 -> 13580 bytes
 Huffman Coding/Images/BuildTree.psd           | Bin 0 -> 2619878 bytes
 Huffman Coding/Images/Compression.graffle     | Bin 0 -> 4299 bytes
 Huffman Coding/Images/Compression.png         | Bin 0 -> 54972 bytes
 Huffman Coding/Images/Decompression.graffle   | Bin 0 -> 3944 bytes
 Huffman Coding/Images/Decompression.png       | Bin 0 -> 47499 bytes
 Huffman Coding/Images/Tree.graffle            | Bin 0 -> 3963 bytes
 Huffman Coding/Images/Tree.png                | Bin 0 -> 38273 bytes
 Huffman Coding/NSData+Bits.swift              |  50 +++
 Huffman Coding/README.markdown                | 417 ++++++++++++++++++
 Priority Queue/README.markdown                |   2 +-
 README.markdown                               |   7 +-
 21 files changed, 1219 insertions(+), 3 deletions(-)
 create mode 100644 Huffman Coding/Huffman.playground/Contents.swift
 create mode 100644 Huffman Coding/Huffman.playground/Sources/Heap.swift
 create mode 100644 Huffman Coding/Huffman.playground/Sources/Huffman.swift
 create mode 100644 Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift
 create mode 100644 Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift
 create mode 100644 Huffman Coding/Huffman.playground/contents.xcplayground
 create mode 100644 Huffman Coding/Huffman.playground/timeline.xctimeline
 create mode 100644 Huffman Coding/Huffman.swift
 create mode 100644 Huffman Coding/Images/BuildTree.gif
 create mode 100644 Huffman Coding/Images/BuildTree.graffle
 create mode 100644 Huffman Coding/Images/BuildTree.psd
 create mode 100644 Huffman Coding/Images/Compression.graffle
 create mode 100644 Huffman Coding/Images/Compression.png
 create mode 100644 Huffman Coding/Images/Decompression.graffle
 create mode 100644 Huffman Coding/Images/Decompression.png
 create mode 100644 Huffman Coding/Images/Tree.graffle
 create mode 100644 Huffman Coding/Images/Tree.png
 create mode 100644 Huffman Coding/NSData+Bits.swift
 create mode 100644 Huffman Coding/README.markdown

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
new file mode 100644
index 000000000..99170fa91
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -0,0 +1,23 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+let s1 = "so much words wow many compression"
+if let originalData = s1.dataUsingEncoding(NSUTF8StringEncoding) {
+  print(originalData.length)
+  
+  let huffman1 = Huffman()
+  let compressedData = huffman1.compressData(originalData)
+  print(compressedData.length)
+  
+  let frequencyTable = huffman1.frequencyTable()
+  //print(frequencyTable)
+  
+  let huffman2 = Huffman()
+  let decompressedData = huffman2.decompressData(compressedData, frequencyTable: frequencyTable)
+  print(decompressedData.length)
+  
+  let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
+  print(s2)
+  assert(s1 == s2)
+}
diff --git a/Huffman Coding/Huffman.playground/Sources/Heap.swift b/Huffman Coding/Huffman.playground/Sources/Heap.swift
new file mode 100644
index 000000000..3293f75bb
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/Sources/Heap.swift	
@@ -0,0 +1,223 @@
+//
+//  Heap.swift
+//  Written for the Swift Algorithm Club by Kevin Randrup and Matthijs Hollemans
+//
+
+public struct Heap<T> {
+  /** The array that stores the heap's nodes. */
+  var elements = [T]()
+  
+  /** Determines whether this is a max-heap (>) or min-heap (<). */
+  private var isOrderedBefore: (T, T) -> Bool
+ 
+  /**
+   * Creates an empty heap.
+   * The sort function determines whether this is a min-heap or max-heap.
+   * For integers, > makes a max-heap, < makes a min-heap.
+   */
+  public init(sort: (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+  }
+
+  /**
+   * Creates a heap from an array. The order of the array does not matter;
+   * the elements are inserted into the heap in the order determined by the
+   * sort function.
+   */
+  public init(array: [T], sort: (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+    buildHeap(array)
+  }
+
+  /*
+  // This version has O(n log n) performance.
+  private mutating func buildHeap(array: [T]) {
+    elements.reserveCapacity(array.count)
+    for value in array {
+      insert(value)
+    }
+  }
+  */
+  
+  /**
+   * Converts an array to a max-heap or min-heap in a bottom-up manner.
+   * Performance: This runs pretty much in O(n).
+   */
+  private mutating func buildHeap(array: [T]) {
+    elements = array
+    for i in (elements.count/2 - 1).stride(through: 0, by: -1) {
+      shiftDown(index: i, heapSize: elements.count)
+    }
+  }
+
+  public var isEmpty: Bool {
+    return elements.isEmpty
+  }
+  
+  public var count: Int {
+    return elements.count
+  }
+  
+  /**
+   * Returns the index of the parent of the element at index i.
+   * The element at index 0 is the root of the tree and has no parent.
+   */
+  @inline(__always) func indexOfParent(i: Int) -> Int {
+    return (i - 1) / 2
+  }
+
+  /**
+   * Returns the index of the left child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no left child.
+   */
+  @inline(__always) func indexOfLeftChild(i: Int) -> Int {
+    return 2*i + 1
+  }
+
+  /**
+   * Returns the index of the right child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no right child.
+   */
+  @inline(__always) func indexOfRightChild(i: Int) -> Int {
+    return 2*i + 2
+  }
+  
+  /**
+   * Returns the maximum value in the heap (for a max-heap) or the minimum
+   * value (for a min-heap).
+   */
+  public func peek() -> T? {
+    return elements.first
+  }
+
+  /**
+   * Adds a new value to the heap. This reorders the heap so that the max-heap
+   * or min-heap property still holds. Performance: O(log n).
+   */
+  public mutating func insert(value: T) {
+    elements.append(value)
+    shiftUp(index: elements.count - 1)
+  }
+  
+  public mutating func insert<S : SequenceType where S.Generator.Element == T>(sequence: S) {
+    for value in sequence {
+      insert(value)
+    }
+  }
+  
+  /**
+   * Allows you to change an element. In a max-heap, the new element should be
+   * larger than the old one; in a min-heap it should be smaller.
+   */
+  public mutating func replace(index i: Int, value: T) {
+    assert(isOrderedBefore(value, elements[i]))
+    elements[i] = value
+    shiftUp(index: i)
+  }
+
+  /**
+   * Removes the root node from the heap. For a max-heap, this is the maximum
+   * value; for a min-heap it is the minimum value. Performance: O(log n).
+   */
+  public mutating func remove() -> T? {
+    if elements.isEmpty {
+      return nil
+    } else if elements.count == 1 {
+      return elements.removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = elements[0]
+      elements[0] = elements.removeLast()
+      shiftDown()
+      return value
+    }
+  }
+  
+  /**
+   * Removes an arbitrary node from the heap. Performance: O(log n). You need
+   * to know the node's index, which may actually take O(n) steps to find.
+   */
+  public mutating func removeAtIndex(i: Int) -> T? {
+    let size = elements.count - 1
+    if i != size {
+      swap(&elements[i], &elements[size])
+      shiftDown(index: i, heapSize: size)
+      shiftUp(index: i)
+    }
+    return elements.removeLast()
+  }
+  
+  /**
+   * Takes a child node and looks at its parents; if a parent is not larger 
+   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+   */
+  mutating func shiftUp(index index: Int) {
+    var childIndex = index
+    let child = elements[childIndex]
+    var parentIndex = indexOfParent(childIndex)
+
+    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+      elements[childIndex] = elements[parentIndex]
+      childIndex = parentIndex
+      parentIndex = indexOfParent(childIndex)
+    }
+
+    elements[childIndex] = child
+  }
+  
+  mutating func shiftDown() {
+    shiftDown(index: 0, heapSize: elements.count)
+  }
+
+  /**
+   * Looks at a parent node and makes sure it is still larger (max-heap) or
+   * smaller (min-heap) than its childeren.
+   */
+  mutating func shiftDown(index index: Int, heapSize: Int) {
+    var parentIndex = index
+
+    while true {
+      let leftChildIndex = indexOfLeftChild(parentIndex)
+      let rightChildIndex = leftChildIndex + 1
+
+      // Figure out which comes first if we order them by the sort function:
+      // the parent, the left child, or the right child. If the parent comes
+      // first, we're done. If not, that element is out-of-place and we make
+      // it "float down" the tree until the heap property is restored.
+      var first = parentIndex
+      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+        first = leftChildIndex
+      }
+      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+        first = rightChildIndex
+      }
+      if first == parentIndex { return }
+
+      swap(&elements[parentIndex], &elements[first])
+      parentIndex = first
+    }
+  }
+}
+
+// MARK: - Searching
+
+extension Heap where T: Equatable {
+  /**
+   * Searches the heap for the given element. Performance: O(n).
+   */
+  public func indexOf(element: T) -> Int? {
+    return indexOf(element, 0)
+  }
+
+  private func indexOf(element: T, _ i: Int) -> Int? {
+    if i >= count { return nil }
+    if isOrderedBefore(element, elements[i]) { return nil }
+    if element == elements[i] { return i }
+    if let j = indexOf(element, indexOfLeftChild(i)) { return j }
+    if let j = indexOf(element, indexOfRightChild(i)) { return j }
+    return nil
+  }
+}
diff --git a/Huffman Coding/Huffman.playground/Sources/Huffman.swift b/Huffman Coding/Huffman.playground/Sources/Huffman.swift
new file mode 100644
index 000000000..0b6da03af
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/Sources/Huffman.swift	
@@ -0,0 +1,191 @@
+import Foundation
+
+/*
+  Basic implementation of Huffman encoding. It encodes bytes that occur often 
+  with a smaller number of bits than bytes that occur less frequently.
+
+  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 
+  1991 and October 1992. 
+
+  Note: This code is not optimized for speed but explanation.
+*/
+public class Huffman {
+  /* Tree nodes don't use pointers to refer to each other, but simple integer 
+     indices. That allows us to use structs for the nodes. */
+  typealias NodeIndex = Int
+  
+  /* A node in the compression tree. Leaf nodes represent the actual bytes that
+     are present in the input data. The count of an intermediary node is the sum
+     of the counts of all nodes below it. The root node's count is the number of
+     bytes in the original, uncompressed input data. */
+  struct Node {
+    var count = 0
+    var index: NodeIndex = -1
+    var parent: NodeIndex = -1
+    var left: NodeIndex = -1
+    var right: NodeIndex = -1
+  }
+  
+  /* The tree structure. The first 256 entries are for the leaf nodes (not all 
+     of those may be used, depending on the input). We add additional nodes as 
+     we build the tree. */
+  var tree = [Node](count: 256, repeatedValue: Node())
+
+  /* This is the last node we add to the tree. */
+  var root: NodeIndex = -1
+
+  /* The frequency table describes how often a byte occurs in the input data. 
+     You need it to decompress the Huffman-encoded data. The frequency table
+     should be serialized along with the compressed data. */
+  public struct Freq {
+    var byte: UInt8 = 0
+    var count = 0
+  }
+  
+  public init() { }
+}
+
+extension Huffman {
+  /* To compress a block of data, first we need to count how often each byte 
+     occurs. These counts are stored in the first 256 nodes in the tree, i.e. 
+     the leaf nodes. The frequency table used by decompression is derived from
+     this. */
+  private func countByteFrequency(data: NSData) {
+    var ptr = UnsafePointer<UInt8>(data.bytes)
+    for _ in 0..<data.length {
+      let i = Int(ptr.memory)
+      tree[i].count += 1
+      tree[i].index = i
+      ptr = ptr.successor()
+    }
+  }
+  
+  /* Takes a frequency table and rebuilds the tree. This is the first step of
+     decompression. */
+  private func restoreTree(frequencyTable: [Freq]) {
+    for freq in frequencyTable {
+      let i = Int(freq.byte)
+      tree[i].count = freq.count
+      tree[i].index = i
+    }
+    buildTree()
+  }
+  
+  /* Returns the frequency table. This is the first 256 nodes from the tree but 
+     only those that are actually used, without the parent/left/right pointers. 
+     You would serialize this along with the compressed file. */
+  public func frequencyTable() -> [Freq] {
+    var a = [Freq]()
+    for i in 0..<256 where tree[i].count > 0 {
+      a.append(Freq(byte: UInt8(i), count: tree[i].count))
+    }
+    return a
+  }
+}
+
+extension Huffman {
+  /* Builds a Huffman tree from a frequency table. */
+  private func buildTree() {
+    // Create a min-priority queue and enqueue all used nodes.
+    var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
+    for node in tree where node.count > 0 {
+      queue.enqueue(node)
+    }
+
+    while queue.count > 1 {
+      // Find the two nodes with the smallest frequencies that do not have
+      // a parent node yet.
+      let node1 = queue.dequeue()!
+      let node2 = queue.dequeue()!
+
+      // Create a new intermediate node.
+      var parentNode = Node()
+      parentNode.count = node1.count + node2.count
+      parentNode.left = node1.index
+      parentNode.right = node2.index
+      parentNode.index = tree.count
+      tree.append(parentNode)
+
+      // Link the two nodes into their new parent node.
+      tree[node1.index].parent = parentNode.index
+      tree[node2.index].parent = parentNode.index
+      
+      // Put the intermediate node back into the queue.
+      queue.enqueue(parentNode)
+    }
+
+    // The final remaining node in the queue becomes the root of the tree.
+    let rootNode = queue.dequeue()!
+    root = rootNode.index
+  }
+}
+
+extension Huffman {
+  /* Compresses the contents of an NSData object. */
+  public func compressData(data: NSData) -> NSData {
+    countByteFrequency(data)
+    buildTree()
+    
+    let writer = BitWriter()
+    var ptr = UnsafePointer<UInt8>(data.bytes)
+    for _ in 0..<data.length {
+      let c = ptr.memory
+      let i = Int(c)
+      traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
+      ptr = ptr.successor()
+    }
+    writer.flush()
+    return writer.data
+  }
+  
+  /* Recursively walks the tree from a leaf node up to the root, and then back 
+     again. If a child is the right node, we emit a 0 bit; if it's the left node,
+     we emit a 1 bit. */
+  private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
+    if tree[h].parent != -1 {
+      traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
+    }
+    if child != -1 {
+      if child == tree[h].left {
+        writer.writeBit(true)
+      } else if child == tree[h].right {
+        writer.writeBit(false)
+      }
+    }
+  }
+}
+
+extension Huffman {
+  /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
+  public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
+    restoreTree(frequencyTable)
+
+    let reader = BitReader(data: data)
+    let outData = NSMutableData()
+    let byteCount = tree[root].count
+
+    var i = 0
+    while i < byteCount {
+      var b = findLeafNode(reader: reader, nodeIndex: root)
+      outData.appendBytes(&b, length: 1)
+      i += 1
+    }
+    return outData
+  }
+  
+  /* Walks the tree from the root down to the leaf node. At every node, read the 
+     next bit and use that to determine whether to step to the left or right.
+     When we get to the leaf node, we simply return its index, which is equal to
+     the original byte value. */
+  private func findLeafNode(reader reader: BitReader, nodeIndex: Int) -> UInt8 {
+    var h = nodeIndex
+    while tree[h].right != -1 {
+      if reader.readBit() {
+        h = tree[h].left
+      } else {
+        h = tree[h].right
+      }
+    }
+    return UInt8(h)
+  }
+}
diff --git a/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift b/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift
new file mode 100644
index 000000000..beb669dd1
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift	
@@ -0,0 +1,50 @@
+import Foundation
+
+/* Helper class for writing bits to an NSData object. */
+public class BitWriter {
+  public var data = NSMutableData()
+  var outByte: UInt8 = 0
+  var outCount = 0
+  
+  public func writeBit(bit: Bool) {
+    if outCount == 8 {
+      data.appendBytes(&outByte, length: 1)
+      outCount = 0
+    }
+    outByte = (outByte << 1) | (bit ? 1 : 0)
+    outCount += 1
+  }
+
+  public func flush() {
+    if outCount > 0 {
+      if outCount < 8 {
+        let diff = UInt8(8 - outCount)
+        outByte <<= diff
+      }
+      data.appendBytes(&outByte, length: 1)
+    }
+  }
+}
+
+/* Helper class for reading bits from an NSData object. */
+public class BitReader {
+  var ptr: UnsafePointer<UInt8>
+  var inByte: UInt8 = 0
+  var inCount = 8
+  
+  public init(data: NSData) {
+    ptr = UnsafePointer<UInt8>(data.bytes)
+  }
+  
+  public func readBit() -> Bool {
+    if inCount == 8 {
+      inByte = ptr.memory    // load the next byte
+      inCount = 0
+      ptr = ptr.successor()
+    }
+    let bit = inByte & 0x80  // read the next bit
+    inByte <<= 1
+    inCount += 1
+    return bit == 0 ? false : true
+  }
+}
diff --git a/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift b/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift
new file mode 100644
index 000000000..7a7cee34b
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift	
@@ -0,0 +1,58 @@
+/*
+  Priority Queue, a queue where the most "important" items are at the front of
+  the queue.
+
+  The heap is a natural data structure for a priority queue, so this object
+  simply wraps the Heap struct. 
+
+  All operations are O(lg n).
+
+  Just like a heap can be a max-heap or min-heap, the queue can be a max-priority
+  queue (largest element first) or a min-priority queue (smallest element first).
+*/
+public struct PriorityQueue<T> {
+  private var heap: Heap<T>
+
+  /*
+    To create a max-priority queue, supply a > sort function. For a min-priority
+    queue, use <.
+  */
+  public init(sort: (T, T) -> Bool) {
+    heap = Heap(sort: sort)
+  }
+
+  public var isEmpty: Bool {
+    return heap.isEmpty
+  }
+
+  public var count: Int {
+    return heap.count
+  }
+
+  public func peek() -> T? {
+    return heap.peek()
+  }
+
+  public mutating func enqueue(element: T) {
+    heap.insert(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    return heap.remove()
+  }
+
+  /*
+    Allows you to change the priority of an element. In a max-priority queue,
+    the new priority should be larger than the old one; in a min-priority queue
+    it should be smaller.
+  */
+  public mutating func changePriority(index i: Int, value: T) {
+    return heap.replace(index: i, value: value)
+  }
+}
+
+extension PriorityQueue where T: Equatable {
+  public func indexOf(element: T) -> Int? {
+    return heap.indexOf(element)
+  }
+}
diff --git a/Huffman Coding/Huffman.playground/contents.xcplayground b/Huffman Coding/Huffman.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Huffman Coding/Huffman.playground/timeline.xctimeline b/Huffman Coding/Huffman.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Huffman Coding/Huffman.swift b/Huffman Coding/Huffman.swift
new file mode 100644
index 000000000..0b6da03af
--- /dev/null
+++ b/Huffman Coding/Huffman.swift	
@@ -0,0 +1,191 @@
+import Foundation
+
+/*
+  Basic implementation of Huffman encoding. It encodes bytes that occur often 
+  with a smaller number of bits than bytes that occur less frequently.
+
+  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 
+  1991 and October 1992. 
+
+  Note: This code is not optimized for speed but explanation.
+*/
+public class Huffman {
+  /* Tree nodes don't use pointers to refer to each other, but simple integer 
+     indices. That allows us to use structs for the nodes. */
+  typealias NodeIndex = Int
+  
+  /* A node in the compression tree. Leaf nodes represent the actual bytes that
+     are present in the input data. The count of an intermediary node is the sum
+     of the counts of all nodes below it. The root node's count is the number of
+     bytes in the original, uncompressed input data. */
+  struct Node {
+    var count = 0
+    var index: NodeIndex = -1
+    var parent: NodeIndex = -1
+    var left: NodeIndex = -1
+    var right: NodeIndex = -1
+  }
+  
+  /* The tree structure. The first 256 entries are for the leaf nodes (not all 
+     of those may be used, depending on the input). We add additional nodes as 
+     we build the tree. */
+  var tree = [Node](count: 256, repeatedValue: Node())
+
+  /* This is the last node we add to the tree. */
+  var root: NodeIndex = -1
+
+  /* The frequency table describes how often a byte occurs in the input data. 
+     You need it to decompress the Huffman-encoded data. The frequency table
+     should be serialized along with the compressed data. */
+  public struct Freq {
+    var byte: UInt8 = 0
+    var count = 0
+  }
+  
+  public init() { }
+}
+
+extension Huffman {
+  /* To compress a block of data, first we need to count how often each byte 
+     occurs. These counts are stored in the first 256 nodes in the tree, i.e. 
+     the leaf nodes. The frequency table used by decompression is derived from
+     this. */
+  private func countByteFrequency(data: NSData) {
+    var ptr = UnsafePointer<UInt8>(data.bytes)
+    for _ in 0..<data.length {
+      let i = Int(ptr.memory)
+      tree[i].count += 1
+      tree[i].index = i
+      ptr = ptr.successor()
+    }
+  }
+  
+  /* Takes a frequency table and rebuilds the tree. This is the first step of
+     decompression. */
+  private func restoreTree(frequencyTable: [Freq]) {
+    for freq in frequencyTable {
+      let i = Int(freq.byte)
+      tree[i].count = freq.count
+      tree[i].index = i
+    }
+    buildTree()
+  }
+  
+  /* Returns the frequency table. This is the first 256 nodes from the tree but 
+     only those that are actually used, without the parent/left/right pointers. 
+     You would serialize this along with the compressed file. */
+  public func frequencyTable() -> [Freq] {
+    var a = [Freq]()
+    for i in 0..<256 where tree[i].count > 0 {
+      a.append(Freq(byte: UInt8(i), count: tree[i].count))
+    }
+    return a
+  }
+}
+
+extension Huffman {
+  /* Builds a Huffman tree from a frequency table. */
+  private func buildTree() {
+    // Create a min-priority queue and enqueue all used nodes.
+    var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
+    for node in tree where node.count > 0 {
+      queue.enqueue(node)
+    }
+
+    while queue.count > 1 {
+      // Find the two nodes with the smallest frequencies that do not have
+      // a parent node yet.
+      let node1 = queue.dequeue()!
+      let node2 = queue.dequeue()!
+
+      // Create a new intermediate node.
+      var parentNode = Node()
+      parentNode.count = node1.count + node2.count
+      parentNode.left = node1.index
+      parentNode.right = node2.index
+      parentNode.index = tree.count
+      tree.append(parentNode)
+
+      // Link the two nodes into their new parent node.
+      tree[node1.index].parent = parentNode.index
+      tree[node2.index].parent = parentNode.index
+      
+      // Put the intermediate node back into the queue.
+      queue.enqueue(parentNode)
+    }
+
+    // The final remaining node in the queue becomes the root of the tree.
+    let rootNode = queue.dequeue()!
+    root = rootNode.index
+  }
+}
+
+extension Huffman {
+  /* Compresses the contents of an NSData object. */
+  public func compressData(data: NSData) -> NSData {
+    countByteFrequency(data)
+    buildTree()
+    
+    let writer = BitWriter()
+    var ptr = UnsafePointer<UInt8>(data.bytes)
+    for _ in 0..<data.length {
+      let c = ptr.memory
+      let i = Int(c)
+      traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
+      ptr = ptr.successor()
+    }
+    writer.flush()
+    return writer.data
+  }
+  
+  /* Recursively walks the tree from a leaf node up to the root, and then back 
+     again. If a child is the right node, we emit a 0 bit; if it's the left node,
+     we emit a 1 bit. */
+  private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
+    if tree[h].parent != -1 {
+      traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
+    }
+    if child != -1 {
+      if child == tree[h].left {
+        writer.writeBit(true)
+      } else if child == tree[h].right {
+        writer.writeBit(false)
+      }
+    }
+  }
+}
+
+extension Huffman {
+  /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
+  public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
+    restoreTree(frequencyTable)
+
+    let reader = BitReader(data: data)
+    let outData = NSMutableData()
+    let byteCount = tree[root].count
+
+    var i = 0
+    while i < byteCount {
+      var b = findLeafNode(reader: reader, nodeIndex: root)
+      outData.appendBytes(&b, length: 1)
+      i += 1
+    }
+    return outData
+  }
+  
+  /* Walks the tree from the root down to the leaf node. At every node, read the 
+     next bit and use that to determine whether to step to the left or right.
+     When we get to the leaf node, we simply return its index, which is equal to
+     the original byte value. */
+  private func findLeafNode(reader reader: BitReader, nodeIndex: Int) -> UInt8 {
+    var h = nodeIndex
+    while tree[h].right != -1 {
+      if reader.readBit() {
+        h = tree[h].left
+      } else {
+        h = tree[h].right
+      }
+    }
+    return UInt8(h)
+  }
+}
diff --git a/Huffman Coding/Images/BuildTree.gif b/Huffman Coding/Images/BuildTree.gif
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diff --git a/Huffman Coding/NSData+Bits.swift b/Huffman Coding/NSData+Bits.swift
new file mode 100644
index 000000000..beb669dd1
--- /dev/null
+++ b/Huffman Coding/NSData+Bits.swift	
@@ -0,0 +1,50 @@
+import Foundation
+
+/* Helper class for writing bits to an NSData object. */
+public class BitWriter {
+  public var data = NSMutableData()
+  var outByte: UInt8 = 0
+  var outCount = 0
+  
+  public func writeBit(bit: Bool) {
+    if outCount == 8 {
+      data.appendBytes(&outByte, length: 1)
+      outCount = 0
+    }
+    outByte = (outByte << 1) | (bit ? 1 : 0)
+    outCount += 1
+  }
+
+  public func flush() {
+    if outCount > 0 {
+      if outCount < 8 {
+        let diff = UInt8(8 - outCount)
+        outByte <<= diff
+      }
+      data.appendBytes(&outByte, length: 1)
+    }
+  }
+}
+
+/* Helper class for reading bits from an NSData object. */
+public class BitReader {
+  var ptr: UnsafePointer<UInt8>
+  var inByte: UInt8 = 0
+  var inCount = 8
+  
+  public init(data: NSData) {
+    ptr = UnsafePointer<UInt8>(data.bytes)
+  }
+  
+  public func readBit() -> Bool {
+    if inCount == 8 {
+      inByte = ptr.memory    // load the next byte
+      inCount = 0
+      ptr = ptr.successor()
+    }
+    let bit = inByte & 0x80  // read the next bit
+    inByte <<= 1
+    inCount += 1
+    return bit == 0 ? false : true
+  }
+}
diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
new file mode 100644
index 000000000..56623d60f
--- /dev/null
+++ b/Huffman Coding/README.markdown	
@@ -0,0 +1,417 @@
+# Huffman Coding
+
+The idea: Encode objects that occur often with a smaller number of bits than objects that occur less frequently.
+
+Although you can encode any type of objects with this scheme, it's most common to compress a stream of bytes. Let's say you have the following text, where each character is one byte:
+
+	so much words wow many compression
+
+If you count how often each byte appears, you can clearly see that some bytes occur more than others:
+
+	space: 5                  u: 1
+	    o: 5	              h: 1
+	    s: 4	              d: 1
+	    m: 3	              a: 1
+	    w: 3	              y: 1
+	    c: 2	              p: 1
+	    r: 2	              e: 1
+	    n: 2	              i: 1
+	
+We can assign bit strings to each of these bytes. The more common a byte is, the fewer bits we assign to it. We might get something like this:
+
+	space: 5    010           u: 1    11001
+	    o: 5    000	          h: 1    10001
+	    s: 4    101	          d: 1    11010
+	    m: 3    111	          a: 1    11011
+	    w: 3    0010	      y: 1    01111
+	    c: 2    0011	      p: 1    11000
+	    r: 2    1001	      e: 1    01110
+	    n: 2    0110	      i: 1    10000
+
+Now if we replace the original bytes with these bit strings, the compressed output becomes:
+
+	101 000 010 111 11001 0011 10001 010 0010 000 1001 11010 101 
+	s   o   _   m   u     c    h     _   w    o   r    d     s
+	
+	010 0010 000 0010 010 111 11011 0110 01111 010 0011 000 111
+	_   w    o   w    _   m   a     n    y     _   c    o   m
+	
+	11000 1001 01110 101 101 10000 000 0110 0
+	p     r    e     s   s   i     o   n
+
+The extra 0-bit at the end is there to make a full number of bytes. We were able to compress the original 34 bytes into merely 16 bytes, a space savings of over 50%!
+
+But hold on... to be able to decode these bits we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data, otherwise the decoder doesn't know how to interpret the bits. Because of the overhead of this frequency table, it doesn't really pay to use Huffman encoding on very small inputs.
+
+## How it works
+
+When compressing a stream of bytes, the algorithm first creates a frequency table that counts how often each byte occurs. Based on this table it creates a binary tree that describes the bit strings for each of the input bytes.
+
+For our example, the tree looks like this:
+
+![The compression tree](Images/Tree.png)
+
+Note that the tree has 16 leaf nodes (the grey ones), one for each byte value from the input. Each leaf node also shows the count of how often it occurs. The other nodes are "intermediate" nodes. The number shown in these nodes is the sum of the counts of their child nodes. The count of the root node is therefore the total number of bytes in the input.
+
+The edges between the nodes either say "1" or "0". These correspond to the bit-encodings of the leaf nodes. Notice how each left branch is always 1 and each right branch is always 0.
+
+Compression is then a matter of looping through the input bytes, and for each byte traverse the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
+
+For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`. 
+
+Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until we get to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
+
+## The code
+
+Before we get to the actual Huffman coding scheme, it's useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte. But we're dealing in bits, so we need to translate between the two.
+
+```swift
+public class BitWriter {
+  public var data = NSMutableData()
+  var outByte: UInt8 = 0
+  var outCount = 0
+  
+  public func writeBit(bit: Bool) {
+    if outCount == 8 {
+      data.appendBytes(&outByte, length: 1)
+      outCount = 0
+    }
+    outByte = (outByte << 1) | (bit ? 1 : 0)
+    outCount += 1
+  }
+
+  public func flush() {
+    if outCount > 0 {
+      if outCount < 8 {
+        let diff = UInt8(8 - outCount)
+        outByte <<= diff
+      }
+      data.appendBytes(&outByte, length: 1)
+    }
+  }
+}
+```
+
+To add a bit to the `NSData` you call `writeBit()`. This simply stuffs each new bit into the `outByte` variable. Once you've written 8 bits, `outByte` gets added to the `NSData` object for real.
+
+The `flush()` method is used for outputting the very last byte. There is no guarantee that the number of compressed bits is a nice round multiple of 8, in which case there may be some spare bits at the end. If so, `flush()` adds a few 0-bits to make sure that we write a full byte.
+
+We'll use a similar helper object for reading individual bits from `NSData`:
+
+```swift
+public class BitReader {
+  var ptr: UnsafePointer<UInt8>
+  var inByte: UInt8 = 0
+  var inCount = 8
+  
+  public init(data: NSData) {
+    ptr = UnsafePointer<UInt8>(data.bytes)
+  }
+  
+  public func readBit() -> Bool {
+    if inCount == 8 {
+      inByte = ptr.memory    // load the next byte
+      inCount = 0
+      ptr = ptr.successor()
+    }
+    let bit = inByte & 0x80  // read the next bit
+    inByte <<= 1
+    inCount += 1
+    return bit == 0 ? false : true
+  }
+}
+```
+
+This works in a similar fashion. We read one whole byte from the `NSData` object and put it in `inByte`. Then `readBit()` returns the individual bits from that byte. Once `readBit()` has been called 8 times, we read the next byte from the `NSData`.
+
+> **Note:** It's no big deal if you're unfamiliar with this sort of bit manipulation. Just know that these two helper objects make it simple for us to write and read bits and not worry about all the messy stuff of making sure they end up in the right place.
+
+## The frequency table
+
+The first step in Huffman compression is to read the entire input stream and build a frequency table. This table contains a list of all 256 possible byte values and how often each of these bytes occurs in the input data.
+
+We could store this frequency information in a dictionary or an array, but since we're going to need to build a tree anyway, we might as well store the frequency table as the leaves of the tree.
+
+Here are the definitions we need:
+
+```swift
+class Huffman {
+  typealias NodeIndex = Int
+ 
+  struct Node {
+    var count = 0
+    var index: NodeIndex = -1
+    var parent: NodeIndex = -1
+    var left: NodeIndex = -1
+    var right: NodeIndex = -1
+  }
+  
+  var tree = [Node](count: 256, repeatedValue: Node())
+
+  var root: NodeIndex = -1
+}
+```
+
+The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
+
+Note that `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we'll add more nodes as we build up the actual tree. For the moment there isn't a tree yet, just 256 separate leaf nodes with no connections between them. All the node counts are 0.
+
+We use the following method to count how often each byte occurs in the input data:
+
+```swift
+  private func countByteFrequency(data: NSData) {
+    var ptr = UnsafePointer<UInt8>(data.bytes)
+    for _ in 0..<data.length {
+      let i = Int(ptr.memory)
+      tree[i].count += 1
+      tree[i].index = i
+      ptr = ptr.successor()
+    }
+  }
+```
+
+This steps through the `NSData` object from beginning to end and for each byte increments the `count` of the corresponding leaf node. That's all there is to it. After `countByteFrequency()` completes, the first 256 `Node` objects in the `tree` array represent the frequency table.
+
+Now, I mentioned that in order to decompress a Huffman-encoded block of data, you also need to have the original frequency table. If you were writing the compressed data to a file, then somewhere in the file you'd include the frequency table.
+
+You could simply dump the first 256 elements from the `tree` array but that's not very efficient. It's likely that not all of these 256 elements will be used, plus you don't need to serialize the `parent`, `right`, and `left` pointers. All we need is the frequency information, not the entire tree.
+
+Instead, we'll add a method to export the frequency table without all the pieces we don't need:
+
+```swift
+  struct Freq {
+    var byte: UInt8 = 0
+    var count = 0
+  }
+  
+  func frequencyTable() -> [Freq] {
+    var a = [Freq]()
+    for i in 0..<256 where tree[i].count > 0 {
+      a.append(Freq(byte: UInt8(i), count: tree[i].count))
+    }
+    return a
+  }
+```
+
+The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are actually used, without the `parent`, `left`, and `right` pointers. You would serialize the array it returns along with the compressed file so that it can be properly decompressed later.
+
+## The tree
+
+As a reminder, there is the compression tree for the example:
+
+![The compression tree](Images/Tree.png)
+
+The leaf nodes represent the actual bytes that are present in the input data. The intermediary nodes connect the leaves in such a way that the path from the root to a frequently-used byte value is shorter than the path to a less common byte value. As you can see, `m`, `s`, space, and `o` are the most common letters in our input data and therefore they are highest up in the tree.
+
+To build the tree, we do the following:
+
+1. Find the two nodes with the smallest counts that do not have a parent node yet.
+2. Add a new parent node that links these two nodes together.
+3. This repeats over and over until only one node with no parent remains. This becomes the root node of the tree.
+
+This is an ideal place to use a [priority queue](../Priority Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
+
+The function `buildTree()` then becomes:
+
+```swift
+  private func buildTree() {
+    var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
+    for node in tree where node.count > 0 {
+      queue.enqueue(node)                            // 1
+    }
+
+    while queue.count > 1 {
+      let node1 = queue.dequeue()!                   // 2
+      let node2 = queue.dequeue()!
+
+      var parentNode = Node()                        // 3
+      parentNode.count = node1.count + node2.count
+      parentNode.left = node1.index
+      parentNode.right = node2.index
+      parentNode.index = tree.count
+      tree.append(parentNode)
+
+      tree[node1.index].parent = parentNode.index    // 4
+      tree[node2.index].parent = parentNode.index
+      
+      queue.enqueue(parentNode)                      // 5
+    }
+
+    let rootNode = queue.dequeue()!                  // 6
+    root = rootNode.index
+  }
+```
+
+Here is how it works step-by-step:
+
+1. Create a priority queue and enqueue all the leaf nodes that have at least a count of 1. (If the count is 0, then this byte value did not appear in the input data.) The `PriorityQueue` object sorts the nodes by their count, so that the node with the lowest count is always the first one that gets dequeued.
+
+2. While there are at least two nodes left in the queue, remove the two nodes that are at the front of the queue. Since this is a min-priority queue, this gives us the two nodes with the smallest counts that do not have a parent node yet.
+
+3. Create a new intermediate node that connects `node1` and `node2`. The count of this new node is the sum of the counts of `node1` and `node2`. Because the nodes are connected using array indices instead of real pointers, we use `node1.index` and `node2.index` to find these nodes in the `tree` array. (This is why a `Node` needs to know its own index.)
+
+4. Link the two nodes into their new parent node. Now this new intermediate node has become part of the tree.
+
+5. Put the new intermediate node back into the queue. At this point we're done with `node1` and `node2`, but the `parentNode` stills need to be connected to other nodes in the tree.
+
+6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we're done.
+
+This is what the process looks like:
+
+![Building the tree](Images/BuildTree.gif)
+
+> **Note:** Instead of using a priority queue, you can iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor quite slow, **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
+
+> **Note:** Due to the nature of binary trees, if we have *x* leaf nodes we can at most add *x - 1* additional nodes to the tree. Given that at most there will be 256 leaf nodes, the tree will never contain more than 511 nodes total.
+
+## Compression
+
+Now that we know how to build the compression tree from the frequency table, we can use it to compress the contents of an `NSData` object. Here is the code:
+
+```
+  func compressData(data: NSData) -> NSData {
+    countByteFrequency(data)
+    buildTree()
+    
+    let writer = BitWriter()
+    var ptr = UnsafePointer<UInt8>(data.bytes)
+
+    for _ in 0..<data.length {
+      let c = ptr.memory
+      let i = Int(c)
+      traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
+      ptr = ptr.successor()
+    }
+
+    writer.flush()
+    return writer.data
+  }
+```
+
+This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits. 
+
+Then it loops through the entire input and for each byte calls `traverseTree()`. That method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
+
+> **Note:** Compression always requires two passes through the entire input data: first to build the frequency table, second to convert the bytes to their compressed bit sequences.
+
+The interesting stuff happens in `traverseTree()`. This is a recursive method:
+
+```
+  private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
+    if tree[h].parent != -1 {
+      traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
+    }
+    if child != -1 {
+      if child == tree[h].left {
+        writer.writeBit(true)
+      } else if child == tree[h].right {
+        writer.writeBit(false)
+      }
+    }
+  }
+```
+
+When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again. 
+
+As we're going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it's the right node, we emit a 0.
+
+In a picture:
+
+![How compression works](Images/Compression.png)
+
+Note that, even through the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 aren't actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we're going in is enough to determine what bit value to write.
+
+You use the `compressData()` method as follows:
+
+```swift
+let s1 = "so much words wow many compression"
+if let originalData = s1.dataUsingEncoding(NSUTF8StringEncoding) {
+  let huffman1 = Huffman()
+  let compressedData = huffman1.compressData(originalData)
+  print(compressedData.length)
+}
+```
+
+## Decompression
+
+Decompression is pretty much compression in reverse. However, the compressed bits are useless to us without the frequency table. Earlier you saw the `frequencyTable()` method that returns an array of `Freq` objects. The idea is that if you were saving the compressed data into a file or sending it across the network, you'd also save that `[Freq]` array along with it.
+
+We first need some way to turn the `[Freq]` array back into a compression tree. Fortunately, this is pretty easy:
+
+```swift
+  private func restoreTree(frequencyTable: [Freq]) {
+    for freq in frequencyTable {
+      let i = Int(freq.byte)
+      tree[i].count = freq.count
+      tree[i].index = i
+    }
+    buildTree()
+  }
+```
+
+We convert the `Freq` objects into leaf nodes and then call `buildTree()` to do the rest.
+
+Here is the code for `decompressData()`, which takes an `NSData` object with Huffman-encoded bits and a frequency table, and returns the original data:
+
+```swift
+  func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
+    restoreTree(frequencyTable)
+
+    let reader = BitReader(data: data)
+    let outData = NSMutableData()
+    let byteCount = tree[root].count
+
+    var i = 0
+    while i < byteCount {
+      var b = findLeafNode(reader: reader, nodeIndex: root)
+      outData.appendBytes(&b, length: 1)
+      i += 1
+    }
+    return outData
+  }
+```
+
+This also uses a helper method to traverse the tree:
+
+```swift
+  private func findLeafNode(reader reader: BitReader, nodeIndex: Int) -> UInt8 {
+    var h = nodeIndex
+    while tree[h].right != -1 {
+      if reader.readBit() {
+        h = tree[h].left
+      } else {
+        h = tree[h].right
+      }
+    }
+    return UInt8(h)
+  }
+```
+
+`findLeafNode()` walks the tree from the root down to the leaf node given by `nodeIndex`. At each intermediate node we read a new bit and then step to the left (bit is 1) or the right (bit is 0). When we get to the leaf node, we simply return its index, which is equal to the original byte value.
+
+In a picture:
+
+![How decompression works](Images/Decompression.png)
+
+Here's how you would use the decompression method:
+
+```swift
+  let frequencyTable = huffman1.frequencyTable()
+  
+  let huffman2 = Huffman()
+  let decompressedData = huffman2.decompressData(compressedData, frequencyTable: frequencyTable)
+  
+  let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
+```
+
+First you get the frequency table from somewhere (in this case the `Huffman` object we used to encode the data) and then call `decompressData()`. The string that results should be equal to the one you compressed in the first place.
+
+You can see how this works in more detail in the Playground.
+
+## See also
+
+[Huffman coding at Wikipedia](https://en.wikipedia.org/wiki/Huffman_coding)
+
+The code is based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 1991 and October 1992.
+
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Priority Queue/README.markdown b/Priority Queue/README.markdown
index c5e088520..0c04e7445 100644
--- a/Priority Queue/README.markdown	
+++ b/Priority Queue/README.markdown	
@@ -12,7 +12,7 @@ Examples of algorithms that can benefit from a priority queue:
 
 - Event-driven simulations. Each event is given a timestamp and you want events to be performed in order of their timestamps. The priority queue makes it easy to find the next event that needs to be simulated.
 - Dijkstra's algorithm for graph searching uses a priority queue to calculate the minimum cost.
-- [Huffman encoding](../Huffman Encoding/) for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.
+- [Huffman coding](../Huffman Coding/) for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.
 - A* pathfinding for artificial intelligence.
 - Lots of other places!
 
diff --git a/README.markdown b/README.markdown
index 8a08a7575..b924f88f1 100644
--- a/README.markdown
+++ b/README.markdown
@@ -80,8 +80,8 @@ Bad sorting algorithms (don't use these!):
 
 ### Compression
 
-- [Run-Length Encoding (RLE)](Run-Length Encoding)
-- Huffman Encoding
+- [Run-Length Encoding (RLE)](Run-Length Encoding/). Store repeated values as a single byte and a count.
+- [Huffman Coding](Huffman Coding/). Store more common elements using a smaller number of bits.
 
 ### Miscellaneous
 
@@ -96,6 +96,9 @@ Bad sorting algorithms (don't use these!):
 ### Machine learning
 
 - k-Nearest Neighbors
+- Linear Regression
+- Logistic Regression
+- Neural Networks
 - PageRank
 
 ## Data structures

From b791185c165f2f6a12f0b44f744e316fe6d35b8f Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 23 Feb 2016 22:24:36 +0100
Subject: [PATCH 0042/1679] Missing syntax highlighting

---
 Huffman Coding/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 56623d60f..3f78aa203 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -268,7 +268,7 @@ This is what the process looks like:
 
 Now that we know how to build the compression tree from the frequency table, we can use it to compress the contents of an `NSData` object. Here is the code:
 
-```
+```swift
   func compressData(data: NSData) -> NSData {
     countByteFrequency(data)
     buildTree()
@@ -296,7 +296,7 @@ Then it loops through the entire input and for each byte calls `traverseTree()`.
 
 The interesting stuff happens in `traverseTree()`. This is a recursive method:
 
-```
+```swift
   private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
     if tree[h].parent != -1 {
       traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)

From f5cc3cf5c055885ce2eb80fceffdf3f0f0cc833a Mon Sep 17 00:00:00 2001
From: Donald Pinckney <donald_pinckney@icloud.com>
Date: Tue, 23 Feb 2016 20:02:11 -0800
Subject: [PATCH 0043/1679] Write content for README

---
 .../Contents.swift                            |  11 +-
 .../Contents.swift                            |  19 +--
 Graph/README.markdown                         | 142 +++++++++++++++++-
 3 files changed, 152 insertions(+), 20 deletions(-)

diff --git a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
index 3f7ea7e9a..6c239f75d 100644
--- a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
@@ -4,8 +4,6 @@ A graph implementation, using an adjacency list.
 
 In an adjacency list implementation, each vertex stores an array of edges, indicating to which vertices it has an edge (note the directionality).  The edge stores the source and destination vertices, as well as a weight.
 
-Connecting vertices in this implementation is O(1).
-
 */
 
 var uniqueIDCounter: Int = 0
@@ -19,7 +17,7 @@ public struct GraphEdge<T> {
 
 public struct GraphVertex<T> {
   public var data: T
-  public private(set) var edges: [GraphEdge<T>] = [] // This is an adjacency list, rather than matrix
+  private var edges: [GraphEdge<T>] = [] // This is an adjacency list, rather than matrix
   
   private let uniqueID: Int
   
@@ -35,11 +33,12 @@ public struct GraphVertex<T> {
   }
   
   // Creates an undirected edge by making 2 directed edges: self ----> other, and other ----> self
-  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
-    edges.append(GraphEdge(from: self, to: otherVertex, weight: weight))
-    otherVertex.edges.append(GraphEdge(from: otherVertex, to: self, weight: weight))
+  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {  
+    connectTo(otherVertex, withWeight: weight)
+    otherVertex.connectTo(self, withWeight: weight)
   }
   
+  // Queries for an edge from self -----> otherVertex
   public func edgeTo(otherVertex: GraphVertex<T>) -> GraphEdge<T>? {
     for e in edges {
       if e.to.uniqueID == otherVertex.uniqueID {
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
index 5cff241fb..c8c5fdf8c 100644
--- a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
@@ -5,14 +5,11 @@ A graph implementation, using an adjacency matrix.
 
 In an adjacency matrix implementation, each vertex is associated with an index from 0..<V (V being the number of vertices). Then a matrix (a 2D array) is stored for the entire graph, with each entry indicating if the corresponding vertices are connected, and the weight.  For example, if matrix[3][5] = 4.6, then vertex #3 is connected to vertex #5, with a weight of 4.6.  Note that vertex #5 is not necessarily connected to vertex #3.
 
-Creating a new vertex must expand the adjacency matrix in this implementation, so creating a new vertex is O(V).  
-Connecting vertices os O(1).
-
 */
 
 public struct GraphVertex<T> {
   public var data: T
-  private let uniqueID: Int
+  private let index: Int
 }
 
 public struct Graph<T> {
@@ -21,10 +18,9 @@ public struct Graph<T> {
   // If adjacencyMatrix[i][j] is not nil, then there is an edge from vertex i to vertex j.
   private var adjacencyMatrix: [[Double?]] = []
   
-  public init() { }
-  
+  // Possibly O(n^2) because of the resizing of the matrix
   public mutating func createVertex(data: T) -> GraphVertex<T> {
-    let vertex = GraphVertex(data: data, uniqueID: adjacencyMatrix.count)
+    let vertex = GraphVertex(data: data, index: adjacencyMatrix.count)
     
     // Expand each existing row to the right one column
     for i in 0..<adjacencyMatrix.count {
@@ -40,18 +36,17 @@ public struct Graph<T> {
   
   // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
   public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID] = weight
+    adjacencyMatrix[sourceVertex.index][toDestinationVertex.index] = weight
   }
   
   // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
   public mutating func connect(someVertex: GraphVertex<T>, symmetricallyWithVertex withVertex: GraphVertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[someVertex.uniqueID][withVertex.uniqueID] = weight
-    adjacencyMatrix[withVertex.uniqueID][someVertex.uniqueID] = weight
-    
+    adjacencyMatrix[someVertex.index][withVertex.index] = weight
+    adjacencyMatrix[withVertex.index][someVertex.index] = weight
   }
   
   public func weightFrom(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>) -> Double? {
-    return adjacencyMatrix[sourceVertex.uniqueID][toDestinationVertex.uniqueID]
+    return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
   }
   
 }
diff --git a/Graph/README.markdown b/Graph/README.markdown
index 30327f474..42b71b6b2 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,6 +1,144 @@
 # Graph
 
-YAY Graphs!
-TODO: Write stuff here.
+A graph is a set of *vertices* paired with a set of *edges*.  Each vertex has a set of associated edges, which connect to other vertices.
 
+For example, a graph can represent a social network.  Each person is a vertex, and people that know each other are connected with edges.
+
+// TODO: Insert image here
+
+## Weighted and Directed Edges
+Edges can optionally be *weighted*, where an arbitrary weight is assigned to each edge.  Consider an example of a graph representing airplane flights.  Cities can be represented as vertices, and flights as edges.  Then an edge weight could represent flight time.
+
+In addition, edges can optionally be *directed*.  A directed edge from vertex A to vertex B connects *A to B*, but **not** *B to A*. Continuing from the flight path example, a directed edge from San Francisco, CA to Juneau, AK would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco.
+
+// TODO: Insert image here
+
+## Representing Graphs in Code
+There are two main strategies for representing graphs:
+
+1. Adjacency List
+2. Adjacency Matrix
+
+### Adjacency List
+In an adjacency list implementation, each vertex stores a list of edges that originate from the vertex.  For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list of 3 edges.
+
+### Adjacency Matrix
+In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for  vertex A, column for vertex B would have value 5.6:
+```
+	matrix[index(A)][index(B)] == 5.6
+```
+
+### Comparing Graph Representations
+Let *V* be the number of vertices in the graph, and *E* the number of edges.  Then we have:
+
+| Operation       | Adjacency List | Adjacency Matrix |
+|-----------------|----------------|------------------|
+| Storage Space   | O(V + E)       | O(V^2)           |
+| Add Vertex      | O(1)           | O(V^2)           |
+| Add Edge        | O(1)           | O(1)             |
+| Check Adjacency | O(V)           | O(1)             |
+
+Note that the time to check adjacency for an adjacency list is **O(V)**, because at worst a vertex is connected to *every* other vertex.  So, in the case of a *sparse* graph, in which each vertex is connected to a handfull of other vertices, an Adjacency List is preferred.  If the graph is *dense*, that is, vertices are connected to most of the other vertices, then an Adjacency Matrix is preferred.
+
+## The Code
+Below we have implementations of both Adjacency List and Adjacency Matrix graph representations.
+
+In both cases, we also let the vertex store arbitrary data with a generic parameter.
+### Adjacency List
+First, we have the data structures for edges and vertices:
+
+```swift
+var uniqueIDCounter: Int = 0
+
+public struct GraphEdge<T> {
+  public let from: GraphVertex<T>
+  public let to: GraphVertex<T>
+  public let weight: Double
+}
+
+public struct GraphVertex<T> {
+  public var data: T
+  private var edges: [GraphEdge<T>] = []
+  
+  private let uniqueID: Int
+  
+  public init(data: T) {
+    self.data = data
+    uniqueID = uniqueIDCounter
+    uniqueIDCounter += 1
+  }
+}
+```
+Note that each vertex has a unique identifier, which we use to compare equality later.
+
+Now, lets see how to connect vertices:
+
+```swift
+// Creates a directed edge self -----> dest
+public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
+    edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
+}
+```
+And then we can check for an edge between vertices:
+
+```swift
+// Queries for an edge from self -----> otherVertex
+public func edgeTo(otherVertex: GraphVertex<T>) -> GraphEdge<T>? {
+  for e in edges {
+    if e.to.uniqueID == otherVertex.uniqueID {
+      return e
+    }
+  } 
+  return nil
+}
+```
+
+### Adjacency Matrix
+Fundamentally, we will store a `[[Double?]]` which is the adjacency matrix.  An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight.  To index into the matrix using vertices, we give each `GraphVertex` a unique integer index:
+
+```swift
+public struct GraphVertex<T> {
+  public var data: T
+  private let index: Int
+}
+```
+
+Then the `Graph` struct keeps track of the matrix.  To create a new vertex, the graph must resize the matrix:
+
+```swift
+public struct Graph<T> {
+  
+  // nil entries are used to mark that two vertices are NOT connected.
+  // If adjacencyMatrix[i][j] is not nil, then there is an edge from vertex i to vertex j.
+  private var adjacencyMatrix: [[Double?]] = []
+    
+  // O(n^2) because of the resizing of the matrix
+  public mutating func createVertex(data: T) -> GraphVertex<T> {
+    let vertex = GraphVertex(data: data, index: adjacencyMatrix.count)
+    
+    // Expand each existing row to the right one column
+    for i in 0..<adjacencyMatrix.count {
+      adjacencyMatrix[i].append(nil)
+    }
+    
+    // Add one new row at the bottom
+    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+    adjacencyMatrix.append(newRow)
+    
+    return vertex
+  }
+```
+
+Once we have the matrix properly configured, adding edges and querying for edges are simple indexing operations into the matrix:
+
+```swift
+// Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
+public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+  adjacencyMatrix[sourceVertex.index][toDestinationVertex.index] = weight
+}
+
+public func weightFrom(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>) -> Double? {
+  return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
+}
+```
 *Written by Donald Pinckney*

From d29704db2c2bc82628220641fef23f0c168c764b Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 24 Feb 2016 21:12:50 +1300
Subject: [PATCH 0044/1679] BFS Shortest path example in readme. Unwrapping in
 a single place.

---
 .../Contents.swift                            | 30 ++++-----
 Breadth-First Search/README.markdown          | 67 ++++++++++++++-----
 2 files changed, 66 insertions(+), 31 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
index 64134a85c..328bccaa9 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -76,12 +76,12 @@ struct Queue<T> {
   }
 }
 
-func breadthFirstSearch(graph: Graph, root: Node) {
-  print("Performing breadth-first search on '\(root.label)'")
+func breadthFirstSearch(graph: Graph, source: Node) {
+  print("Performing breadth-first search on '\(source.label)'")
 
-  var seenNodes = [root]
+  var seenNodes = [source]
   var queue = Queue<Node>()
-  queue.enqueue(root)
+  queue.enqueue(source)
 
   while !queue.isEmpty {
     let current = queue.dequeue()
@@ -96,18 +96,18 @@ func breadthFirstSearch(graph: Graph, root: Node) {
   }
 }
 
-func breadthFirstSearchShortestPath(graph: Graph, root: Node) {
-  root.distance = 0
-  var q = Queue<Node>()
-  q.enqueue(root)
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+  var queue = Queue<Node>()
+  queue.enqueue(source)
+  source.distance = 0
 
-  while !q.isEmpty {
-    let current = q.dequeue()
-    for edge in current!.neighbors {
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
-        q.enqueue(neighborNode)
-        neighborNode.distance = current!.distance! + 1
+        queue.enqueue(neighborNode)
+        neighborNode.distance = current.distance! + 1
       }
     }
   }
@@ -136,5 +136,5 @@ graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
 
-breadthFirstSearch(graph, root: nodeA)
-breadthFirstSearchShortestPath(graph, root: nodeA)
+breadthFirstSearch(graph, source: nodeA)
+breadthFirstSearchShortestPath(graph, source: nodeA)
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index dc7918ff5..bf2236dd5 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -8,7 +8,7 @@ Breadth-first search (BFS) is an algorithm for traversing or searching tree or g
 
 Let's follow the animated example by using a [queue](../Queue/).
 
-Start with the root node ``a`` and add it to a queue.
+Start with the source node ``a`` and add it to a queue.
 ```swift
 queue.enqueue(a)
 ```
@@ -58,12 +58,12 @@ The queue is now empty which means all nodes have been explored.
 Simple implementation of breadth-first search using a queue:
 
 ```swift
-func breadthFirstSearch(graph: Graph, root: Node) {
-  print("Performing breadth-first search on '\(root.label)'")
+func breadthFirstSearch(graph: Graph, source: Node) {
+  print("Performing breadth-first search on '\(source.label)'")
 
-  var seenNodes = [root]
+  var seenNodes = [source]
   var queue = Queue<Node>()
-  queue.enqueue(root)
+  queue.enqueue(source)
 
   while !queue.isEmpty {
     let current = queue.dequeue()
@@ -100,7 +100,7 @@ graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
-breadthFirstSearch(graph, root: nodeA) // This will output: Performing breadth-first search on 'a', b, c, d, e, f, g, h
+breadthFirstSearch(graph, source: nodeA) // This will output: Performing breadth-first search on 'a', b, c, d, e, f, g, h
 
 ```
 
@@ -114,21 +114,46 @@ Breadth-first search can be used to solve many problems, for example:
 
 ## Shortest path example
 
-TODO: walkthrough + explanation
+Bread breadth-first can be used to compute the shortest path between a source node and each of the other nodes because it explores all of the neighbor nodes before moving to the next level neighbors. Let's follow the animated example and calculate the shortest path to all the other nodes:
 
+Start with the source node ``a`` and add it to a queue with a distance of ``0``.
 ```swift
-func breadthFirstSearchShortestPath(graph: Graph, root: Node) {
-  root.distance = 0
-  var q = Queue<Node>()
-  q.enqueue(root)
+queue.enqueue(a)
+a.distance = 0
+```
+The queue is now ``[ a ]``. Dequeue ``a`` and enqueue the neighbor nodes ``b`` and ``c`` with a distance of ``1``.
+```swift
+queue.dequeue(a)
+queue.enqueue(b)
+b.distance = a.distance + 1 // result: 1
+queue.enqueue(c)
+c.distance = a.distance + 1 // result: 1
+```
+The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue the neighbor nodes ``d`` and ``e`` with a distance of ``2``.
+```swift
+queue.dequeue(b)
+queue.enqueue(d)
+d.distance = b.distance + 1 // result: 2
+queue.enqueue(e)
+e.distance = b.distance + 1 // result: 2
+```
 
-  while !q.isEmpty {
-    let current = q.dequeue()
-    for edge in current!.neighbors {
+Continue until the queue is empty to calculate the shortest path to all other nodes.
+
+Here's the code:
+```swift
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+  var queue = Queue<Node>()
+  queue.enqueue(source)
+  source.distance = 0
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
-        q.enqueue(neighborNode)
-        neighborNode.distance = current!.distance! + 1
+        queue.enqueue(neighborNode)
+        neighborNode.distance = current.distance! + 1
       }
     }
   }
@@ -137,6 +162,16 @@ func breadthFirstSearchShortestPath(graph: Graph, root: Node) {
 }
 ```
 
+Put this code in a playground and test it like so:
+```swift
+breadthFirstSearchShortestPath(graph, source: nodeA)
+
+// This will output:
+// Node(label: a, distance: 0), Node(label: b, distance: 1), Node(label: c, distance: 1),
+// Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
+// Node(label: g, distance: 2), Node(label: h, distance: 3)
+```
+
 ## Minimum spanning tree example
 
 TODO

From 81ba37568fadf5c1a40de9bb27fd9b6fdb035027 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 24 Feb 2016 23:09:50 +1300
Subject: [PATCH 0045/1679] BFS adding image for minimum spanning tree

---
 .../Images/MinimumSpanningTree.sketch           | Bin 0 -> 81920 bytes
 .../Images/Minimum_Spanning_Tree.png            | Bin 0 -> 24095 bytes
 Breadth-First Search/README.markdown            |  15 ++++++++++-----
 3 files changed, 10 insertions(+), 5 deletions(-)
 create mode 100644 Breadth-First Search/Images/MinimumSpanningTree.sketch
 create mode 100644 Breadth-First Search/Images/Minimum_Spanning_Tree.png

diff --git a/Breadth-First Search/Images/MinimumSpanningTree.sketch b/Breadth-First Search/Images/MinimumSpanningTree.sketch
new file mode 100644
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diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index bf2236dd5..e4b1db44d 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,6 +1,6 @@
 # Breadth-First Search
 
-Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root and explores the neighbor nodes first, before moving to the next level neighbors.
+Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores the neighbor nodes first, before moving to the next level neighbors.
 
 ## Animated example
 
@@ -101,7 +101,6 @@ graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
 breadthFirstSearch(graph, source: nodeA) // This will output: Performing breadth-first search on 'a', b, c, d, e, f, g, h
-
 ```
 
 ## Applications
@@ -114,7 +113,7 @@ Breadth-first search can be used to solve many problems, for example:
 
 ## Shortest path example
 
-Bread breadth-first can be used to compute the shortest path between a source node and each of the other nodes because it explores all of the neighbor nodes before moving to the next level neighbors. Let's follow the animated example and calculate the shortest path to all the other nodes:
+Breadth-first search can be used to compute the [shortest path](../Shortest Path/) between a source node and each of the other nodes because it explores all of the neighbor nodes before moving to the next level neighbors. Let's follow the animated example and calculate the shortest path to all the other nodes:
 
 Start with the source node ``a`` and add it to a queue with a distance of ``0``.
 ```swift
@@ -174,10 +173,16 @@ breadthFirstSearchShortestPath(graph, source: nodeA)
 
 ## Minimum spanning tree example
 
-TODO
+Breadth-first search can be used to calculate the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph.
+
+![Minimum spanning tree](Images/Minimum_Spanning_Tree.png)
+
+The minimum spanning tree is represented by the bold edges.
+
+TODO: explain steps to generate minimum spanning tree
 
 ## See also
 
-[Graphs](../Graph/), [Queues](../Queue/), [Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search).
+[Graph](../Graph/), [Tree](../Tree/), [Queues](../Queue/), [Shortest Path](../Shortest Path/), [Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search), [Minimum spanning tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree).
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher)*

From ba8326641ad8a3abb548e5beb081fe35252fb139 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 24 Feb 2016 23:14:45 +1300
Subject: [PATCH 0046/1679] BFS unwrapping in a single place

---
 .../BreadthFirstSearch.playground/Contents.swift              | 4 ++--
 Breadth-First Search/README.markdown                          | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
index 328bccaa9..640a0e045 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
@@ -84,8 +84,8 @@ func breadthFirstSearch(graph: Graph, source: Node) {
   queue.enqueue(source)
 
   while !queue.isEmpty {
-    let current = queue.dequeue()
-    for edge in current!.neighbors {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !seenNodes.contains(neighborNode) {
         queue.enqueue(neighborNode)
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index e4b1db44d..96be1d4b4 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -66,8 +66,8 @@ func breadthFirstSearch(graph: Graph, source: Node) {
   queue.enqueue(source)
 
   while !queue.isEmpty {
-    let current = queue.dequeue()
-    for edge in current!.neighbors {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !seenNodes.contains(neighborNode) {
         queue.enqueue(neighborNode)

From 7b420565d6e9595c78c980426ffadaec80fb61f0 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 24 Feb 2016 23:21:05 +1300
Subject: [PATCH 0047/1679] BFS updating minimum spanning tree

---
 .../Images/MinimumSpanningTree.sketch         | Bin 81920 -> 81920 bytes
 .../Images/Minimum_Spanning_Tree.png          | Bin 24095 -> 23928 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)

diff --git a/Breadth-First Search/Images/MinimumSpanningTree.sketch b/Breadth-First Search/Images/MinimumSpanningTree.sketch
index 882fbc9d67149f0cb77baf6570f0b77e5c91304b..93a5b808cdca5702194429d6334f9f58eda147dd 100644
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From b91edfddfb9ff565c0f6bd725a7388d66accc568 Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Thu, 25 Feb 2016 19:16:18 +0530
Subject: [PATCH 0048/1679] Shunting yard algorithm

---
 .../Shunting Yard.playground/Contents.swift   | 229 +++++++++++++++++
 .../Sources/Stack.swift                       |  43 ++++
 .../contents.xcplayground                     |   4 +
 .../timeline.xctimeline                       |   6 +
 Shunting Yard/ShuntingYardAlgorithm.swift     | 233 ++++++++++++++++++
 Shunting Yard/Stack.swift                     |  43 ++++
 6 files changed, 558 insertions(+)
 create mode 100644 Shunting Yard/Shunting Yard.playground/Contents.swift
 create mode 100644 Shunting Yard/Shunting Yard.playground/Sources/Stack.swift
 create mode 100644 Shunting Yard/Shunting Yard.playground/contents.xcplayground
 create mode 100644 Shunting Yard/Shunting Yard.playground/timeline.xctimeline
 create mode 100644 Shunting Yard/ShuntingYardAlgorithm.swift
 create mode 100644 Shunting Yard/Stack.swift

diff --git a/Shunting Yard/Shunting Yard.playground/Contents.swift b/Shunting Yard/Shunting Yard.playground/Contents.swift
new file mode 100644
index 000000000..e0bf80bcf
--- /dev/null
+++ b/Shunting Yard/Shunting Yard.playground/Contents.swift	
@@ -0,0 +1,229 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+internal enum OperatorAssociativity {
+    case LeftAssociative
+    case RightAssociative
+}
+
+internal enum OperatorType: CustomStringConvertible {
+    case Add
+    case Subtract
+    case Divide
+    case Multiply
+    case Percent
+    case Exponent
+    
+    var description: String {
+        switch self {
+        case Add:
+            return "+"
+        case Subtract:
+            return "-"
+        case Divide:
+            return "/"
+        case Multiply:
+            return "*"
+        case Percent:
+            return "%"
+        case Exponent:
+            return "^"
+        }
+    }
+}
+
+internal struct OperatorToken: CustomStringConvertible {
+    
+    var operatorType: OperatorType
+    
+    init(operatorType: OperatorType) {
+        self.operatorType = operatorType
+    }
+    
+    var precedance: Int {
+        switch operatorType {
+        case .Add, .Subtract:
+            return 0
+        case .Divide, .Multiply, .Percent:
+            return 5;
+        case .Exponent:
+            return 10
+        }
+    }
+    
+    var associativity: OperatorAssociativity {
+        switch operatorType {
+        case .Add, .Subtract, .Divide, .Multiply, .Percent:
+            return .LeftAssociative;
+        case .Exponent:
+            return .RightAssociative
+        }
+    }
+    
+    var description: String {
+        return operatorType.description
+    }
+}
+
+func <=(left: OperatorToken, right: OperatorToken) -> Bool {
+    if left.precedance <= right.precedance {
+        return true
+    }
+    return false
+}
+
+func <(left: OperatorToken, right: OperatorToken) -> Bool {
+    if left.precedance < right.precedance {
+        return true
+    }
+    return false
+}
+
+internal enum TokenType: CustomStringConvertible {
+    case OpenBracket
+    case CloseBracket
+    case Operator(OperatorToken)
+    case Operand(Double)
+    
+    var description: String {
+        switch self {
+        case OpenBracket:
+            return "("
+        case CloseBracket:
+            return ")"
+        case Operator(let operatorToken):
+            return operatorToken.description
+        case Operand(let value):
+            return "\(value)"
+        }
+    }
+}
+
+internal struct Token: CustomStringConvertible {
+    
+    var tokenType: TokenType
+    
+    init(tokenType: TokenType) {
+        self.tokenType = tokenType
+    }
+    
+    init(operand: Double) {
+        tokenType = .Operand(operand)
+    }
+    
+    init(operatorType: OperatorType) {
+        tokenType = .Operator(OperatorToken(operatorType: operatorType))
+    }
+    
+    var isOpenBracket: Bool {
+        switch tokenType {
+        case .OpenBracket:
+            return true
+        default:
+            return false
+        }
+    }
+    
+    var isOperator: Bool {
+        switch tokenType {
+        case .Operator(_):
+            return true
+        default:
+            return false
+        }
+    }
+    
+    var operatorToken: OperatorToken? {
+        switch tokenType {
+        case .Operator(let operatorToken):
+            return operatorToken
+        default:
+            return nil
+        }
+    }
+    
+    var description: String {
+        return tokenType.description
+    }
+}
+
+public struct Expression {
+    var expression = Array<Token>()
+    
+    init() {
+        expression.append(Token(operand: 3))
+        expression.append(Token(operatorType: OperatorType.Add))
+        expression.append(Token(operand: 4))
+        expression.append(Token(operatorType: OperatorType.Multiply))
+        expression.append(Token(operand: 2))
+        expression.append(Token(operatorType: OperatorType.Divide))
+        expression.append(Token(tokenType: TokenType.OpenBracket))
+        expression.append(Token(operand: 1))
+        expression.append(Token(operatorType: OperatorType.Subtract))
+        expression.append(Token(operand: 5))
+        expression.append(Token(tokenType: TokenType.CloseBracket))
+        expression.append(Token(operatorType: OperatorType.Exponent))
+        expression.append(Token(operand: 2))
+        expression.append(Token(operatorType: OperatorType.Exponent))
+        expression.append(Token(operand: 3))
+    }
+    
+    public func reversePolishNotation() -> String {
+        
+        var tokenStack = Stack<Token>()
+        var reversePolishNotation = [Token]()
+        
+        for token in expression {
+            switch token.tokenType {
+            case .Operand(_):
+                reversePolishNotation.append(token)
+                break
+            case .OpenBracket:
+                tokenStack.push(token)
+                break
+            case .CloseBracket:
+                while tokenStack.count > 0 {
+                    if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+                        reversePolishNotation.append(tempToken)
+                    } else {
+                        break
+                    }
+                }
+                break
+            case .Operator(let operatorToken):
+                
+                for tempToken in tokenStack.generate() {
+                    if !tempToken.isOperator {
+                        break
+                    }
+                    
+                    if let tempOperatorToken = tempToken.operatorToken {
+                        
+                        if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
+                            || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
+                                
+                                reversePolishNotation.append(tokenStack.pop()!)
+                        } else {
+                            break
+                        }
+                    }
+                }
+                
+                tokenStack.push(token)
+                break
+                
+            }
+        }
+        
+        while tokenStack.count > 0 {
+            reversePolishNotation.append(tokenStack.pop()!)
+        }
+        
+        return reversePolishNotation.map({token in
+            return token.description
+        }).joinWithSeparator(", ")
+    }
+}
+
+print(Expression().reversePolishNotation())
diff --git a/Shunting Yard/Shunting Yard.playground/Sources/Stack.swift b/Shunting Yard/Shunting Yard.playground/Sources/Stack.swift
new file mode 100644
index 000000000..93feb2ca1
--- /dev/null
+++ b/Shunting Yard/Shunting Yard.playground/Sources/Stack.swift	
@@ -0,0 +1,43 @@
+import Foundation
+
+public struct Stack<T> {
+    private var array = [T]()
+    
+    public init() {
+        array = []
+    }
+    
+    public var isEmpty: Bool {
+        return array.isEmpty
+    }
+    
+    public var count: Int {
+        return array.count
+    }
+    
+    public mutating func push(element: T) {
+        array.append(element)
+    }
+    
+    public mutating func pop() -> T? {
+        if isEmpty {
+            return nil
+        } else {
+            return array.removeLast()
+        }
+    }
+    
+    public func peek() -> T? {
+        return array.last
+    }
+}
+
+extension Stack: SequenceType {
+    public func generate() -> AnyGenerator<T> {
+        var curr = self
+        return anyGenerator {
+            _ -> T? in
+            return curr.pop()
+        }
+    }
+}
\ No newline at end of file
diff --git a/Shunting Yard/Shunting Yard.playground/contents.xcplayground b/Shunting Yard/Shunting Yard.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Shunting Yard/Shunting Yard.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Shunting Yard/Shunting Yard.playground/timeline.xctimeline b/Shunting Yard/Shunting Yard.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Shunting Yard/Shunting Yard.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Shunting Yard/ShuntingYardAlgorithm.swift b/Shunting Yard/ShuntingYardAlgorithm.swift
new file mode 100644
index 000000000..980fc88ef
--- /dev/null
+++ b/Shunting Yard/ShuntingYardAlgorithm.swift	
@@ -0,0 +1,233 @@
+//
+//  ShuntingYardAlgorithm.swift
+//
+//
+//  Created by Ali Hafizji on 2016-02-25.
+//
+//
+
+import Foundation
+
+internal enum OperatorAssociativity {
+    case LeftAssociative
+    case RightAssociative
+}
+
+internal enum OperatorType: CustomStringConvertible {
+    case Add
+    case Subtract
+    case Divide
+    case Multiply
+    case Percent
+    case Exponent
+    
+    var description: String {
+        switch self {
+        case Add:
+            return "+"
+        case Subtract:
+            return "-"
+        case Divide:
+            return "/"
+        case Multiply:
+            return "*"
+        case Percent:
+            return "%"
+        case Exponent:
+            return "^"
+        }
+    }
+}
+
+internal struct OperatorToken: CustomStringConvertible {
+    
+    var operatorType: OperatorType
+    
+    init(operatorType: OperatorType) {
+        self.operatorType = operatorType
+    }
+    
+    var precedance: Int {
+        switch operatorType {
+        case .Add, .Subtract:
+            return 0
+        case .Divide, .Multiply, .Percent:
+            return 5;
+        case .Exponent:
+            return 10
+        }
+    }
+    
+    var associativity: OperatorAssociativity {
+        switch operatorType {
+        case .Add, .Subtract, .Divide, .Multiply, .Percent:
+            return .LeftAssociative;
+        case .Exponent:
+            return .RightAssociative
+        }
+    }
+    
+    var description: String {
+        return operatorType.description
+    }
+}
+
+func <=(left: OperatorToken, right: OperatorToken) -> Bool {
+    if left.precedance <= right.precedance {
+        return true
+    }
+    return false
+}
+
+func <(left: OperatorToken, right: OperatorToken) -> Bool {
+    if left.precedance < right.precedance {
+        return true
+    }
+    return false
+}
+
+internal enum TokenType: CustomStringConvertible {
+    case OpenBracket
+    case CloseBracket
+    case Operator(OperatorToken)
+    case Operand(Double)
+    
+    var description: String {
+        switch self {
+        case OpenBracket:
+            return "("
+        case CloseBracket:
+            return ")"
+        case Operator(let operatorToken):
+            return operatorToken.description
+        case Operand(let value):
+            return "\(value)"
+        }
+    }
+}
+
+internal struct Token: CustomStringConvertible {
+    
+    var tokenType: TokenType
+    
+    init(tokenType: TokenType) {
+        self.tokenType = tokenType
+    }
+    
+    init(operand: Double) {
+        tokenType = .Operand(operand)
+    }
+    
+    init(operatorType: OperatorType) {
+        tokenType = .Operator(OperatorToken(operatorType: operatorType))
+    }
+    
+    var isOpenBracket: Bool {
+        switch tokenType {
+        case .OpenBracket:
+            return true
+        default:
+            return false
+        }
+    }
+    
+    var isOperator: Bool {
+        switch tokenType {
+        case .Operator(_):
+            return true
+        default:
+            return false
+        }
+    }
+    
+    var operatorToken: OperatorToken? {
+        switch tokenType {
+        case .Operator(let operatorToken):
+            return operatorToken
+        default:
+            return nil
+        }
+    }
+    
+    var description: String {
+        return tokenType.description
+    }
+}
+
+public struct Expression {
+    var expression = Array<Token>()
+    
+    init() {
+        expression.append(Token(operand: 3))
+        expression.append(Token(operatorType: OperatorType.Add))
+        expression.append(Token(operand: 4))
+        expression.append(Token(operatorType: OperatorType.Multiply))
+        expression.append(Token(operand: 2))
+        expression.append(Token(operatorType: OperatorType.Divide))
+        expression.append(Token(tokenType: TokenType.OpenBracket))
+        expression.append(Token(operand: 1))
+        expression.append(Token(operatorType: OperatorType.Subtract))
+        expression.append(Token(operand: 5))
+        expression.append(Token(tokenType: TokenType.CloseBracket))
+        expression.append(Token(operatorType: OperatorType.Exponent))
+        expression.append(Token(operand: 2))
+        expression.append(Token(operatorType: OperatorType.Exponent))
+        expression.append(Token(operand: 3))
+    }
+    
+    public func reversePolishNotation() -> String {
+        
+        var tokenStack = Stack<Token>()
+        var reversePolishNotation = [Token]()
+        
+        for token in expression {
+            switch token.tokenType {
+            case .Operand(_):
+                reversePolishNotation.append(token)
+                break
+            case .OpenBracket:
+                tokenStack.push(token)
+                break
+            case .CloseBracket:
+                while tokenStack.count > 0 {
+                    if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+                        reversePolishNotation.append(tempToken)
+                    } else {
+                        break
+                    }
+                }
+                break
+            case .Operator(let operatorToken):
+                
+                for tempToken in tokenStack.generate() {
+                    if !tempToken.isOperator {
+                        break
+                    }
+                    
+                    if let tempOperatorToken = tempToken.operatorToken {
+                        
+                        if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
+                            || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
+                                
+                                reversePolishNotation.append(tokenStack.pop()!)
+                        } else {
+                            break
+                        }
+                    }
+                }
+                
+                tokenStack.push(token)
+                break
+                
+            }
+        }
+        
+        while tokenStack.count > 0 {
+            reversePolishNotation.append(tokenStack.pop()!)
+        }
+        
+        return reversePolishNotation.map({token in
+            return token.description
+        }).joinWithSeparator(", ")
+    }
+}
\ No newline at end of file
diff --git a/Shunting Yard/Stack.swift b/Shunting Yard/Stack.swift
new file mode 100644
index 000000000..93feb2ca1
--- /dev/null
+++ b/Shunting Yard/Stack.swift	
@@ -0,0 +1,43 @@
+import Foundation
+
+public struct Stack<T> {
+    private var array = [T]()
+    
+    public init() {
+        array = []
+    }
+    
+    public var isEmpty: Bool {
+        return array.isEmpty
+    }
+    
+    public var count: Int {
+        return array.count
+    }
+    
+    public mutating func push(element: T) {
+        array.append(element)
+    }
+    
+    public mutating func pop() -> T? {
+        if isEmpty {
+            return nil
+        } else {
+            return array.removeLast()
+        }
+    }
+    
+    public func peek() -> T? {
+        return array.last
+    }
+}
+
+extension Stack: SequenceType {
+    public func generate() -> AnyGenerator<T> {
+        var curr = self
+        return anyGenerator {
+            _ -> T? in
+            return curr.pop()
+        }
+    }
+}
\ No newline at end of file

From 23d433573dfa6272cc05b8b631ec6417ff720a1a Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 13:46:48 -0800
Subject: [PATCH 0049/1679] Initial fileset

---
 K-Means/K-Means.playground/Contents.swift     | 116 ++++++++++++++++++
 .../K-Means.playground/contents.xcplayground  |   4 +
 .../K-Means.playground/timeline.xctimeline    |   6 +
 K-Means/README.md                             |   0
 4 files changed, 126 insertions(+)
 create mode 100644 K-Means/K-Means.playground/Contents.swift
 create mode 100644 K-Means/K-Means.playground/contents.xcplayground
 create mode 100644 K-Means/K-Means.playground/timeline.xctimeline
 create mode 100644 K-Means/README.md

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
new file mode 100644
index 000000000..a3071733e
--- /dev/null
+++ b/K-Means/K-Means.playground/Contents.swift
@@ -0,0 +1,116 @@
+//
+//  K-Means.swift
+//
+//  Created by John Gill on 2/25/16.
+
+import Foundation
+
+// Need a container to easily hold 2 Dimensional Vector2Ds
+class Vector2D: CustomStringConvertible {
+    var x:Float = 0.0 // x-Coordinate of Vector2D
+    var y:Float = 0.0 // y-Coordinate of Vector2D
+    
+    init(x: Float, y: Float) {
+        self.x = x
+        self.y = y
+    }
+    
+    var description: String {
+        return "Vector2D (\(self.x), \(self.y))"
+    }
+}
+
+// Ability to use std operators on Vector2D object
+func +(left: Vector2D, right: Vector2D) -> Vector2D {
+    return Vector2D(x: left.x + right.x, y: left.y + right.y)
+}
+func +=(inout left: Vector2D, right: Vector2D) {
+    left = left + right
+}
+func /(left:Vector2D, right: Float) -> Vector2D {
+    return Vector2D(x: left.x / right, y: left.y / right)
+}
+func /=(inout left: Vector2D, right: Float) {
+    left = left / right
+}
+
+// TODO: Explain/Replace/Cleanup
+extension Array {
+    var shuffle: [Element] {
+        var elements = self
+        for index in indices {
+            let anotherIndex = Int(arc4random_uniform(UInt32(elements.count - index))) + index
+            anotherIndex != index ? swap(&elements[index], &elements[anotherIndex]) : ()
+        }
+        return elements
+    }
+    func choose(n: Int) -> [Element] {
+        return Array(shuffle.prefix(n))
+    }
+}
+
+// Calculates the Euclidean distance between two Vector2Ds
+func euclidean(v1:Vector2D, v2:Vector2D) -> Float {
+    return sqrt(pow((v1.x - v2.x), 2.0) + pow((v1.y - v2.y), 2.0))
+}
+
+// Get the INDEX of nearest Center to X
+func nearestCenter(x: Vector2D, Centers: [Vector2D]) -> Int {
+    var nearestDist = FLT_MAX
+    var minIndex:Int = 0;
+    // Calculate the distance from Vector2D X to all the centers
+    for (idx, c) in Centers.enumerate() {
+        let dist = euclidean(x, v2: c)
+        if dist < nearestDist {
+            minIndex = idx
+            nearestDist = dist
+        }
+    }
+    return minIndex
+}
+
+func kNN(numCenters: Int, convergeDist: Float, points: [Vector2D]) -> [Vector2D] {
+    var centerMoveDist:Float = 0.0
+    
+    // 1. Choose k Random Vector2Ds as the initial centers
+    var kCenters:[Vector2D] = points.choose(numCenters)
+    
+    // do following steps until convergence
+    repeat {
+        var cnts = [Float](count: numCenters, repeatedValue: 0.0)
+        var nCenters = [Vector2D](count:numCenters, repeatedValue: Vector2D(x:0, y:0))
+        // 2. Assign Vector2Ds to centers
+        //    a. Determine which center each Vector2D is closest to
+        //    b. Record how many Vector2Ds are assigned to each center
+        for p in points {
+            let c = nearestCenter(p, Centers: kCenters)
+            cnts[c]++
+            nCenters[c] += p
+        }
+        // 3. Calculate a new centers
+        for idx in 0..<numCenters {
+            nCenters[idx] /= cnts[idx]
+        }
+        // 4. Determine how far centers moved
+        centerMoveDist = 0.0
+        for idx in 0..<numCenters {
+            centerMoveDist += euclidean(kCenters[idx], v2: nCenters[idx])
+        }
+        // 5. Update centers to the newly calculated ones
+        kCenters = nCenters
+        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
+    } while(centerMoveDist > convergeDist)
+    return kCenters
+}
+var points = [Vector2D]()
+let lim = 50
+for _ in 0..<lim {
+    let x = Float(arc4random_uniform(UInt32(lim)))
+    let y = Float(arc4random_uniform(UInt32(lim)))
+    points.append(Vector2D(x: Float(x), y: y))
+}
+
+print("\nCenters")
+for c in kNN(10, convergeDist: 0.1, points: points) {
+    print(c)
+}
diff --git a/K-Means/K-Means.playground/contents.xcplayground b/K-Means/K-Means.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/K-Means/K-Means.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/K-Means/K-Means.playground/timeline.xctimeline b/K-Means/K-Means.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/K-Means/K-Means.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/K-Means/README.md b/K-Means/README.md
new file mode 100644
index 000000000..e69de29bb

From 973db8d50f2f1840a17d1a7fd52d879563a90dc9 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 15:16:57 -0800
Subject: [PATCH 0050/1679] Change 2D vector to ND vector

---
 K-Means/K-Means.playground/Contents.swift     | 82 +++++++++++--------
 .../K-Means.playground/contents.xcplayground  |  2 +-
 2 files changed, 49 insertions(+), 35 deletions(-)

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
index a3071733e..d1d6a05fd 100644
--- a/K-Means/K-Means.playground/Contents.swift
+++ b/K-Means/K-Means.playground/Contents.swift
@@ -5,32 +5,40 @@
 
 import Foundation
 
-// Need a container to easily hold 2 Dimensional Vector2Ds
-class Vector2D: CustomStringConvertible {
-    var x:Float = 0.0 // x-Coordinate of Vector2D
-    var y:Float = 0.0 // y-Coordinate of Vector2D
+// Need a container to easily hold N Dimensional Vectors
+class VectorND: CustomStringConvertible {
+    private var length:Int = 0
+    private var data:[Float] = [Float]()
     
-    init(x: Float, y: Float) {
-        self.x = x
-        self.y = y
+    init(d:[Float]) {
+        self.data = d
+        self.length = d.count
     }
     
-    var description: String {
-        return "Vector2D (\(self.x), \(self.y))"
-    }
+    var description: String { return "VectorND (\(self.data)" }
+    func getData() -> [Float] { return data }
+    func getLength() -> Int { return length }
 }
 
-// Ability to use std operators on Vector2D object
-func +(left: Vector2D, right: Vector2D) -> Vector2D {
-    return Vector2D(x: left.x + right.x, y: left.y + right.y)
+// Ability to use std operators on VectorND object
+func +(left: VectorND, right: VectorND) -> VectorND {
+    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+    for idx in 0..<left.getLength() {
+        results[idx] = left.getData()[idx] + right.getData()[idx]
+    }
+    return VectorND(d: results)
 }
-func +=(inout left: Vector2D, right: Vector2D) {
+func +=(inout left: VectorND, right: VectorND) {
     left = left + right
 }
-func /(left:Vector2D, right: Float) -> Vector2D {
-    return Vector2D(x: left.x / right, y: left.y / right)
+func /(left:VectorND, right: Float) -> VectorND  {
+    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+    for (idx, value) in left.getData().enumerate() {
+        results[idx] = value / right
+    }
+    return VectorND(d: results)
 }
-func /=(inout left: Vector2D, right: Float) {
+func /=(inout left: VectorND, right: Float) {
     left = left / right
 }
 
@@ -49,16 +57,20 @@ extension Array {
     }
 }
 
-// Calculates the Euclidean distance between two Vector2Ds
-func euclidean(v1:Vector2D, v2:Vector2D) -> Float {
-    return sqrt(pow((v1.x - v2.x), 2.0) + pow((v1.y - v2.y), 2.0))
+// Calculates the Euclidean distance between two VectorNDs
+func euclidean(v1:VectorND, v2:VectorND) -> Float {
+    var result:Float = 0.0
+    for idx in 0..<v1.getLength() {
+        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
+    }
+    return sqrt(result)
 }
 
 // Get the INDEX of nearest Center to X
-func nearestCenter(x: Vector2D, Centers: [Vector2D]) -> Int {
+func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
     var nearestDist = FLT_MAX
     var minIndex:Int = 0;
-    // Calculate the distance from Vector2D X to all the centers
+    // Calculate the distance from VectorND X to all the centers
     for (idx, c) in Centers.enumerate() {
         let dist = euclidean(x, v2: c)
         if dist < nearestDist {
@@ -69,19 +81,20 @@ func nearestCenter(x: Vector2D, Centers: [Vector2D]) -> Int {
     return minIndex
 }
 
-func kNN(numCenters: Int, convergeDist: Float, points: [Vector2D]) -> [Vector2D] {
+func kNN(numCenters: Int, convergeDist: Float, points: [VectorND]) -> [VectorND] {
     var centerMoveDist:Float = 0.0
+    let zeros = [Float](count: points[0].getLength(), repeatedValue: 0.0)
     
-    // 1. Choose k Random Vector2Ds as the initial centers
-    var kCenters:[Vector2D] = points.choose(numCenters)
+    // 1. Choose k Random VectorNDs as the initial centers
+    var kCenters:[VectorND] = points.choose(numCenters)
     
     // do following steps until convergence
     repeat {
         var cnts = [Float](count: numCenters, repeatedValue: 0.0)
-        var nCenters = [Vector2D](count:numCenters, repeatedValue: Vector2D(x:0, y:0))
-        // 2. Assign Vector2Ds to centers
-        //    a. Determine which center each Vector2D is closest to
-        //    b. Record how many Vector2Ds are assigned to each center
+        var nCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        // 2. Assign VectorNDs to centers
+        //    a. Determine which center each VectorND is closest to
+        //    b. Record how many VectorNDs are assigned to each center
         for p in points {
             let c = nearestCenter(p, Centers: kCenters)
             cnts[c]++
@@ -102,15 +115,16 @@ func kNN(numCenters: Int, convergeDist: Float, points: [Vector2D]) -> [Vector2D]
     } while(centerMoveDist > convergeDist)
     return kCenters
 }
-var points = [Vector2D]()
-let lim = 50
+
+var points = [VectorND]()
+let lim = 10
 for _ in 0..<lim {
     let x = Float(arc4random_uniform(UInt32(lim)))
     let y = Float(arc4random_uniform(UInt32(lim)))
-    points.append(Vector2D(x: Float(x), y: y))
+    points.append(VectorND(d: [x, y]))
 }
 
 print("\nCenters")
-for c in kNN(10, convergeDist: 0.1, points: points) {
+for c in kNN(3, convergeDist: 0.1, points: points) {
     print(c)
-}
+}
\ No newline at end of file
diff --git a/K-Means/K-Means.playground/contents.xcplayground b/K-Means/K-Means.playground/contents.xcplayground
index 06828af92..9f9eecc96 100644
--- a/K-Means/K-Means.playground/contents.xcplayground
+++ b/K-Means/K-Means.playground/contents.xcplayground
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 07f47e2f2acb62cdeeaeee8816a0d2e4b365b103 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 20:45:12 -0800
Subject: [PATCH 0051/1679] Update to follow Swift Style Guide

---
 K-Means/K-Means.playground/Contents.swift     | 100 ++++++++++--------
 .../K-Means.playground/timeline.xctimeline    |  35 ++++++
 2 files changed, 90 insertions(+), 45 deletions(-)

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
index d1d6a05fd..9f35e5863 100644
--- a/K-Means/K-Means.playground/Contents.swift
+++ b/K-Means/K-Means.playground/Contents.swift
@@ -7,22 +7,22 @@ import Foundation
 
 // Need a container to easily hold N Dimensional Vectors
 class VectorND: CustomStringConvertible {
-    private var length:Int = 0
-    private var data:[Float] = [Float]()
+    private var length = 0
+    private var data = [Double]()
     
-    init(d:[Float]) {
-        self.data = d
-        self.length = d.count
+    init(d:[Double]) {
+        data = d
+        length = d.count
     }
     
-    var description: String { return "VectorND (\(self.data)" }
-    func getData() -> [Float] { return data }
+    var description: String { return "VectorND (\(data)" }
+    func getData() -> [Double] { return data }
     func getLength() -> Int { return length }
 }
 
-// Ability to use std operators on VectorND object
+// MARK: VectorND Operators
 func +(left: VectorND, right: VectorND) -> VectorND {
-    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
     for idx in 0..<left.getLength() {
         results[idx] = left.getData()[idx] + right.getData()[idx]
     }
@@ -31,35 +31,39 @@ func +(left: VectorND, right: VectorND) -> VectorND {
 func +=(inout left: VectorND, right: VectorND) {
     left = left + right
 }
-func /(left:VectorND, right: Float) -> VectorND  {
-    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+func /(left:VectorND, right: Double) -> VectorND  {
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
     for (idx, value) in left.getData().enumerate() {
         results[idx] = value / right
     }
     return VectorND(d: results)
 }
-func /=(inout left: VectorND, right: Float) {
+func /=(inout left: VectorND, right: Double) {
     left = left / right
 }
 
-// TODO: Explain/Replace/Cleanup
-extension Array {
-    var shuffle: [Element] {
-        var elements = self
-        for index in indices {
-            let anotherIndex = Int(arc4random_uniform(UInt32(elements.count - index))) + index
-            anotherIndex != index ? swap(&elements[index], &elements[anotherIndex]) : ()
-        }
-        return elements
+// MARK: Assist Functions
+// Pick a k random elements from samples
+func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
+    var result = [VectorND]()
+    
+    // Fill the result array with first k elements
+    for i in 0..<k {
+        result.append(samples[i])
     }
-    func choose(n: Int) -> [Element] {
-        return Array(shuffle.prefix(n))
+    // randomly replace elements from remaining ones 
+    for i in (k+1)..<samples.count {
+        let j = Int(arc4random_uniform(UInt32(i+1)))
+        if j < k {
+            result[j] = samples[i]
+        }
     }
+    return result
 }
 
 // Calculates the Euclidean distance between two VectorNDs
-func euclidean(v1:VectorND, v2:VectorND) -> Float {
-    var result:Float = 0.0
+func euclidean(v1:VectorND, v2:VectorND) -> Double {
+    var result = 0.0
     for idx in 0..<v1.getLength() {
         result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
     }
@@ -68,9 +72,9 @@ func euclidean(v1:VectorND, v2:VectorND) -> Float {
 
 // Get the INDEX of nearest Center to X
 func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
-    var nearestDist = FLT_MAX
-    var minIndex:Int = 0;
-    // Calculate the distance from VectorND X to all the centers
+    var nearestDist = DBL_MAX
+    var minIndex = 0;
+    
     for (idx, c) in Centers.enumerate() {
         let dist = euclidean(x, v2: c)
         if dist < nearestDist {
@@ -81,50 +85,56 @@ func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
     return minIndex
 }
 
-func kNN(numCenters: Int, convergeDist: Float, points: [VectorND]) -> [VectorND] {
-    var centerMoveDist:Float = 0.0
-    let zeros = [Float](count: points[0].getLength(), repeatedValue: 0.0)
+// MARK: Main Function
+func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
     
     // 1. Choose k Random VectorNDs as the initial centers
-    var kCenters:[VectorND] = points.choose(numCenters)
+    var kCenters = reservoirSample(points, k: numCenters)
     
     // do following steps until convergence
     repeat {
-        var cnts = [Float](count: numCenters, repeatedValue: 0.0)
-        var nCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
         // 2. Assign VectorNDs to centers
         //    a. Determine which center each VectorND is closest to
         //    b. Record how many VectorNDs are assigned to each center
         for p in points {
             let c = nearestCenter(p, Centers: kCenters)
             cnts[c]++
-            nCenters[c] += p
+            newCenters[c] += p
         }
         // 3. Calculate a new centers
         for idx in 0..<numCenters {
-            nCenters[idx] /= cnts[idx]
+            newCenters[idx] /= cnts[idx]
         }
         // 4. Determine how far centers moved
         centerMoveDist = 0.0
         for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: nCenters[idx])
+            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
         }
         // 5. Update centers to the newly calculated ones
-        kCenters = nCenters
+        kCenters = newCenters
         print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
     } while(centerMoveDist > convergeDist)
     return kCenters
 }
 
+// MARK: Sample Data
 var points = [VectorND]()
-let lim = 10
-for _ in 0..<lim {
-    let x = Float(arc4random_uniform(UInt32(lim)))
-    let y = Float(arc4random_uniform(UInt32(lim)))
-    points.append(VectorND(d: [x, y]))
+let numPoints = 10
+let numDimmensions = 5
+for _ in 0..<numPoints {
+    var data = [Double]()
+    for x in 0..<numDimmensions {
+        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
+    }
+    points.append(VectorND(d: data))
 }
 
 print("\nCenters")
-for c in kNN(3, convergeDist: 0.1, points: points) {
+for c in kMeans(3, convergeDist: 0.01, points: points) {
     print(c)
-}
\ No newline at end of file
+}
+
diff --git a/K-Means/K-Means.playground/timeline.xctimeline b/K-Means/K-Means.playground/timeline.xctimeline
index bf468afec..850856b0b 100644
--- a/K-Means/K-Means.playground/timeline.xctimeline
+++ b/K-Means/K-Means.playground/timeline.xctimeline
@@ -2,5 +2,40 @@
 <Timeline
    version = "3.0">
    <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=37&amp;EndingLineNumber=138&amp;StartingColumnNumber=1&amp;StartingLineNumber=138&amp;Timestamp=478154433.694733"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/johngill/git/swift-algorithm-club/K-Means/K-Means.playground#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingLineNumber=138&amp;StartingLineNumber=138&amp;Timestamp=478154433.694858"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=18&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.69495"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=19&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.695038"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695117"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695195"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695273"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
    </TimelineItems>
 </Timeline>

From 49687da9e865fed62d190409e1ed1c44fb42af58 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 22:22:37 -0800
Subject: [PATCH 0052/1679] add k-Means algorithm

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index b924f88f1..1af54642d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -95,6 +95,7 @@ Bad sorting algorithms (don't use these!):
 
 ### Machine learning
 
+- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression

From 5dd6948bf82d1bc2442d90e38a4ea277b45cc3f5 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 22:29:14 -0800
Subject: [PATCH 0053/1679] Move Contents into own source file

---
 K-Means/KMeans.swift | 139 +++++++++++++++++++++++++++++++++++++++++++
 K-Means/README.md    |   3 +
 2 files changed, 142 insertions(+)
 create mode 100644 K-Means/KMeans.swift

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
new file mode 100644
index 000000000..05e973ba0
--- /dev/null
+++ b/K-Means/KMeans.swift
@@ -0,0 +1,139 @@
+//
+//  KMeans.swift
+//
+//  Created by John Gill on 2/25/16.
+
+import Foundation
+
+// Need a container to easily hold N Dimensional Vectors
+class VectorND: CustomStringConvertible {
+    private var length = 0
+    private var data = [Double]()
+
+    init(d:[Double]) {
+        data = d
+        length = d.count
+    }
+
+    var description: String { return "VectorND (\(data)" }
+    func getData() -> [Double] { return data }
+    func getLength() -> Int { return length }
+}
+
+// MARK: VectorND Operators
+func +(left: VectorND, right: VectorND) -> VectorND {
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
+    for idx in 0..<left.getLength() {
+        results[idx] = left.getData()[idx] + right.getData()[idx]
+    }
+    return VectorND(d: results)
+}
+func +=(inout left: VectorND, right: VectorND) {
+    left = left + right
+}
+func /(left:VectorND, right: Double) -> VectorND  {
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
+    for (idx, value) in left.getData().enumerate() {
+        results[idx] = value / right
+    }
+    return VectorND(d: results)
+}
+func /=(inout left: VectorND, right: Double) {
+    left = left / right
+}
+
+// MARK: Assist Functions
+// Pick a k random elements from samples
+func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
+    var result = [VectorND]()
+
+    // Fill the result array with first k elements
+    for i in 0..<k {
+        result.append(samples[i])
+    }
+    // randomly replace elements from remaining ones
+    for i in (k+1)..<samples.count {
+        let j = Int(arc4random_uniform(UInt32(i+1)))
+        if j < k {
+            result[j] = samples[i]
+        }
+    }
+    return result
+}
+
+// Calculates the Euclidean distance between two VectorNDs
+func euclidean(v1:VectorND, v2:VectorND) -> Double {
+    var result = 0.0
+    for idx in 0..<v1.getLength() {
+        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
+    }
+    return sqrt(result)
+}
+
+// Get the INDEX of nearest Center to X
+func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
+    var nearestDist = DBL_MAX
+    var minIndex = 0;
+
+    for (idx, c) in Centers.enumerate() {
+        let dist = euclidean(x, v2: c)
+        if dist < nearestDist {
+            minIndex = idx
+            nearestDist = dist
+        }
+    }
+    return minIndex
+}
+
+// MARK: Main Function
+func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
+
+    // 1. Choose k Random VectorNDs as the initial centers
+    var kCenters = reservoirSample(points, k: numCenters)
+
+    // do following steps until convergence
+    repeat {
+        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        // 2. Assign VectorNDs to centers
+        //    a. Determine which center each VectorND is closest to
+        //    b. Record how many VectorNDs are assigned to each center
+        for p in points {
+            let c = nearestCenter(p, Centers: kCenters)
+            cnts[c]++
+            newCenters[c] += p
+        }
+        // 3. Calculate a new centers
+        for idx in 0..<numCenters {
+            newCenters[idx] /= cnts[idx]
+        }
+        // 4. Determine how far centers moved
+        centerMoveDist = 0.0
+        for idx in 0..<numCenters {
+            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
+        }
+        // 5. Update centers to the newly calculated ones
+        kCenters = newCenters
+        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
+    } while(centerMoveDist > convergeDist)
+    return kCenters
+}
+
+// MARK: Sample Data
+var points = [VectorND]()
+let numPoints = 10
+let numDimmensions = 5
+for _ in 0..<numPoints {
+    var data = [Double]()
+    for x in 0..<numDimmensions {
+        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
+    }
+    points.append(VectorND(d: data))
+}
+
+print("\nCenters")
+for c in kMeans(3, convergeDist: 0.01, points: points) {
+    print(c)
+}
diff --git a/K-Means/README.md b/K-Means/README.md
index e69de29bb..a801fea7a 100644
--- a/K-Means/README.md
+++ b/K-Means/README.md
@@ -0,0 +1,3 @@
+# K-Means
+
+Goal:  Partition data into k clusters based on nearest mean

From 0d82baf6233a5a434295717baecd9f72c1bb8dce Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Fri, 26 Feb 2016 19:03:18 +0530
Subject: [PATCH 0054/1679] Updated code style

---
 .../Shunting Yard.playground/Contents.swift   | 412 +++++++++---------
 Shunting Yard/ShuntingYardAlgorithm.swift     | 412 +++++++++---------
 2 files changed, 420 insertions(+), 404 deletions(-)

diff --git a/Shunting Yard/Shunting Yard.playground/Contents.swift b/Shunting Yard/Shunting Yard.playground/Contents.swift
index e0bf80bcf..f70f36c5a 100644
--- a/Shunting Yard/Shunting Yard.playground/Contents.swift	
+++ b/Shunting Yard/Shunting Yard.playground/Contents.swift	
@@ -3,227 +3,235 @@
 import Foundation
 
 internal enum OperatorAssociativity {
-    case LeftAssociative
-    case RightAssociative
+  case LeftAssociative
+  case RightAssociative
 }
 
-internal enum OperatorType: CustomStringConvertible {
-    case Add
-    case Subtract
-    case Divide
-    case Multiply
-    case Percent
-    case Exponent
-    
-    var description: String {
-        switch self {
-        case Add:
-            return "+"
-        case Subtract:
-            return "-"
-        case Divide:
-            return "/"
-        case Multiply:
-            return "*"
-        case Percent:
-            return "%"
-        case Exponent:
-            return "^"
-        }
-    }
+public enum OperatorType: CustomStringConvertible {
+  case Add
+  case Subtract
+  case Divide
+  case Multiply
+  case Percent
+  case Exponent
+  
+  public var description: String {
+    switch self {
+      case Add:
+        return "+"
+      case Subtract:
+        return "-"
+      case Divide:
+        return "/"
+      case Multiply:
+        return "*"
+      case Percent:
+        return "%"
+      case Exponent:
+        return "^"
+    }
+  }
 }
 
-internal struct OperatorToken: CustomStringConvertible {
-    
-    var operatorType: OperatorType
-    
-    init(operatorType: OperatorType) {
-        self.operatorType = operatorType
-    }
-    
-    var precedance: Int {
-        switch operatorType {
-        case .Add, .Subtract:
-            return 0
-        case .Divide, .Multiply, .Percent:
-            return 5;
-        case .Exponent:
-            return 10
-        }
-    }
-    
-    var associativity: OperatorAssociativity {
-        switch operatorType {
-        case .Add, .Subtract, .Divide, .Multiply, .Percent:
-            return .LeftAssociative;
-        case .Exponent:
-            return .RightAssociative
-        }
-    }
-    
-    var description: String {
-        return operatorType.description
-    }
+public enum TokenType: CustomStringConvertible {
+  case OpenBracket
+  case CloseBracket
+  case Operator(OperatorToken)
+  case Operand(Double)
+  
+  public var description: String {
+    switch self {
+      case OpenBracket:
+        return "("
+      case CloseBracket:
+        return ")"
+      case Operator(let operatorToken):
+        return operatorToken.description
+      case Operand(let value):
+        return "\(value)"
+    }
+  }
+}
+
+public struct OperatorToken: CustomStringConvertible {
+  
+  var operatorType: OperatorType
+  
+  init(operatorType: OperatorType) {
+    self.operatorType = operatorType
+  }
+  
+  var precedance: Int {
+    switch operatorType {
+      case .Add, .Subtract:
+        return 0
+      case .Divide, .Multiply, .Percent:
+        return 5;
+      case .Exponent:
+        return 10
+    }
+  }
+  
+  var associativity: OperatorAssociativity {
+    switch operatorType {
+      case .Add, .Subtract, .Divide, .Multiply, .Percent:
+        return .LeftAssociative;
+      case .Exponent:
+        return .RightAssociative
+    }
+  }
+  
+  public var description: String {
+    return operatorType.description
+  }
 }
 
 func <=(left: OperatorToken, right: OperatorToken) -> Bool {
-    if left.precedance <= right.precedance {
-        return true
-    }
-    return false
+  if left.precedance <= right.precedance {
+    return true
+  }
+  return false
 }
 
 func <(left: OperatorToken, right: OperatorToken) -> Bool {
-    if left.precedance < right.precedance {
-        return true
-    }
-    return false
+  if left.precedance < right.precedance {
+    return true
+  }
+  return false
 }
 
-internal enum TokenType: CustomStringConvertible {
-    case OpenBracket
-    case CloseBracket
-    case Operator(OperatorToken)
-    case Operand(Double)
-    
-    var description: String {
-        switch self {
-        case OpenBracket:
-            return "("
-        case CloseBracket:
-            return ")"
-        case Operator(let operatorToken):
-            return operatorToken.description
-        case Operand(let value):
-            return "\(value)"
-        }
-    }
+public struct Token: CustomStringConvertible {
+  
+  var tokenType: TokenType
+  
+  init(tokenType: TokenType) {
+    self.tokenType = tokenType
+  }
+  
+  init(operand: Double) {
+    tokenType = .Operand(operand)
+  }
+  
+  init(operatorType: OperatorType) {
+    tokenType = .Operator(OperatorToken(operatorType: operatorType))
+  }
+  
+  var isOpenBracket: Bool {
+    switch tokenType {
+      case .OpenBracket:
+        return true
+      default:
+        return false
+    }
+  }
+  
+  var isOperator: Bool {
+    switch tokenType {
+      case .Operator(_):
+        return true
+      default:
+        return false
+    }
+  }
+  
+  var operatorToken: OperatorToken? {
+    switch tokenType {
+    case .Operator(let operatorToken):
+        return operatorToken
+    default:
+        return nil
+    }
+  }
+  
+  public var description: String {
+    return tokenType.description
+  }
 }
 
-internal struct Token: CustomStringConvertible {
-    
-    var tokenType: TokenType
-    
-    init(tokenType: TokenType) {
-        self.tokenType = tokenType
-    }
-    
-    init(operand: Double) {
-        tokenType = .Operand(operand)
-    }
-    
-    init(operatorType: OperatorType) {
-        tokenType = .Operator(OperatorToken(operatorType: operatorType))
-    }
-    
-    var isOpenBracket: Bool {
-        switch tokenType {
-        case .OpenBracket:
-            return true
-        default:
-            return false
-        }
-    }
-    
-    var isOperator: Bool {
-        switch tokenType {
-        case .Operator(_):
-            return true
-        default:
-            return false
-        }
-    }
-    
-    var operatorToken: OperatorToken? {
-        switch tokenType {
-        case .Operator(let operatorToken):
-            return operatorToken
-        default:
-            return nil
-        }
-    }
-    
-    var description: String {
-        return tokenType.description
-    }
+public class InfixExpressionBuilder {
+  
+  private var expression = Array<Token>()
+  
+  public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
+    expression.append(Token(operatorType: operatorType))
+    return self
+  }
+  
+  public func addOperand(operand: Double) -> InfixExpressionBuilder {
+    expression.append(Token(operand: operand))
+    return self
+  }
+  
+  public func addOpenBracket() -> InfixExpressionBuilder {
+    expression.append(Token(tokenType: .OpenBracket))
+    return self
+  }
+  
+  public func addCloseBracket() -> InfixExpressionBuilder {
+    expression.append(Token(tokenType: .CloseBracket))
+    return self
+  }
+  
+  public func build() -> Array<Token> {
+    // Maybe do some validation here
+    return expression
+  }
 }
 
-public struct Expression {
-    var expression = Array<Token>()
-    
-    init() {
-        expression.append(Token(operand: 3))
-        expression.append(Token(operatorType: OperatorType.Add))
-        expression.append(Token(operand: 4))
-        expression.append(Token(operatorType: OperatorType.Multiply))
-        expression.append(Token(operand: 2))
-        expression.append(Token(operatorType: OperatorType.Divide))
-        expression.append(Token(tokenType: TokenType.OpenBracket))
-        expression.append(Token(operand: 1))
-        expression.append(Token(operatorType: OperatorType.Subtract))
-        expression.append(Token(operand: 5))
-        expression.append(Token(tokenType: TokenType.CloseBracket))
-        expression.append(Token(operatorType: OperatorType.Exponent))
-        expression.append(Token(operand: 2))
-        expression.append(Token(operatorType: OperatorType.Exponent))
-        expression.append(Token(operand: 3))
-    }
-    
-    public func reversePolishNotation() -> String {
-        
-        var tokenStack = Stack<Token>()
-        var reversePolishNotation = [Token]()
-        
-        for token in expression {
-            switch token.tokenType {
-            case .Operand(_):
-                reversePolishNotation.append(token)
-                break
-            case .OpenBracket:
-                tokenStack.push(token)
-                break
-            case .CloseBracket:
-                while tokenStack.count > 0 {
-                    if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
-                        reversePolishNotation.append(tempToken)
-                    } else {
-                        break
-                    }
-                }
-                break
-            case .Operator(let operatorToken):
-                
-                for tempToken in tokenStack.generate() {
-                    if !tempToken.isOperator {
-                        break
-                    }
+// This returns the result of the shunting yard algorithm
+public func reversePolishNotation(expression: Array<Token>) -> String {
+  
+  var tokenStack = Stack<Token>()
+  var reversePolishNotation = [Token]()
+  
+  for token in expression {
+    switch token.tokenType {
+      case .Operand(_):
+        reversePolishNotation.append(token)
+        break
+      case .OpenBracket:
+        tokenStack.push(token)
+        break
+      case .CloseBracket:
+        while tokenStack.count > 0 {
+          if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+            reversePolishNotation.append(tempToken)
+          } else {
+            break
+          }
+        }
+        break
+      case .Operator(let operatorToken):
+          
+        for tempToken in tokenStack.generate() {
+          if !tempToken.isOperator {
+            break
+          }
+          
+          if let tempOperatorToken = tempToken.operatorToken {
+              
+            if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
+                || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
                     
-                    if let tempOperatorToken = tempToken.operatorToken {
-                        
-                        if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
-                            || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
-                                
-                                reversePolishNotation.append(tokenStack.pop()!)
-                        } else {
-                            break
-                        }
-                    }
-                }
-                
-                tokenStack.push(token)
-                break
-                
+              reversePolishNotation.append(tokenStack.pop()!)
+            } else {
+              break
             }
+          }
         }
         
-        while tokenStack.count > 0 {
-            reversePolishNotation.append(tokenStack.pop()!)
-        }
-        
-        return reversePolishNotation.map({token in
-            return token.description
-        }).joinWithSeparator(", ")
-    }
+        tokenStack.push(token)
+        break
+    }
+  }
+  
+  while tokenStack.count > 0 {
+    reversePolishNotation.append(tokenStack.pop()!)
+  }
+  
+  return reversePolishNotation.map({token in
+    return token.description
+  }).joinWithSeparator(" ")
 }
 
-print(Expression().reversePolishNotation())
+print(reversePolishNotation(InfixExpressionBuilder().addOperand(3).addOperator(.Add).addOperand(4).addOperator(.Multiply).addOperand(2).addOperator(.Divide).addOpenBracket().addOperand(1).addOperator(.Subtract).addOperand(5).addCloseBracket().addOperator(.Exponent).addOperand(2).addOperator(.Exponent).addOperand(3).build()))
diff --git a/Shunting Yard/ShuntingYardAlgorithm.swift b/Shunting Yard/ShuntingYardAlgorithm.swift
index 980fc88ef..dbaba475c 100644
--- a/Shunting Yard/ShuntingYardAlgorithm.swift	
+++ b/Shunting Yard/ShuntingYardAlgorithm.swift	
@@ -9,225 +9,233 @@
 import Foundation
 
 internal enum OperatorAssociativity {
-    case LeftAssociative
-    case RightAssociative
+  case LeftAssociative
+  case RightAssociative
 }
 
-internal enum OperatorType: CustomStringConvertible {
-    case Add
-    case Subtract
-    case Divide
-    case Multiply
-    case Percent
-    case Exponent
-    
-    var description: String {
-        switch self {
-        case Add:
-            return "+"
-        case Subtract:
-            return "-"
-        case Divide:
-            return "/"
-        case Multiply:
-            return "*"
-        case Percent:
-            return "%"
-        case Exponent:
-            return "^"
-        }
-    }
+public enum OperatorType: CustomStringConvertible {
+  case Add
+  case Subtract
+  case Divide
+  case Multiply
+  case Percent
+  case Exponent
+  
+  public var description: String {
+    switch self {
+    case Add:
+      return "+"
+    case Subtract:
+      return "-"
+    case Divide:
+      return "/"
+    case Multiply:
+      return "*"
+    case Percent:
+      return "%"
+    case Exponent:
+      return "^"
+    }
+  }
 }
 
-internal struct OperatorToken: CustomStringConvertible {
-    
-    var operatorType: OperatorType
-    
-    init(operatorType: OperatorType) {
-        self.operatorType = operatorType
-    }
-    
-    var precedance: Int {
-        switch operatorType {
-        case .Add, .Subtract:
-            return 0
-        case .Divide, .Multiply, .Percent:
-            return 5;
-        case .Exponent:
-            return 10
-        }
-    }
-    
-    var associativity: OperatorAssociativity {
-        switch operatorType {
-        case .Add, .Subtract, .Divide, .Multiply, .Percent:
-            return .LeftAssociative;
-        case .Exponent:
-            return .RightAssociative
-        }
-    }
-    
-    var description: String {
-        return operatorType.description
-    }
+public enum TokenType: CustomStringConvertible {
+  case OpenBracket
+  case CloseBracket
+  case Operator(OperatorToken)
+  case Operand(Double)
+  
+  public var description: String {
+    switch self {
+    case OpenBracket:
+      return "("
+    case CloseBracket:
+      return ")"
+    case Operator(let operatorToken):
+      return operatorToken.description
+    case Operand(let value):
+      return "\(value)"
+    }
+  }
+}
+
+public struct OperatorToken: CustomStringConvertible {
+  
+  var operatorType: OperatorType
+  
+  init(operatorType: OperatorType) {
+    self.operatorType = operatorType
+  }
+  
+  var precedance: Int {
+    switch operatorType {
+    case .Add, .Subtract:
+      return 0
+    case .Divide, .Multiply, .Percent:
+      return 5;
+    case .Exponent:
+      return 10
+    }
+  }
+  
+  var associativity: OperatorAssociativity {
+    switch operatorType {
+    case .Add, .Subtract, .Divide, .Multiply, .Percent:
+      return .LeftAssociative;
+    case .Exponent:
+      return .RightAssociative
+    }
+  }
+  
+  public var description: String {
+    return operatorType.description
+  }
 }
 
 func <=(left: OperatorToken, right: OperatorToken) -> Bool {
-    if left.precedance <= right.precedance {
-        return true
-    }
-    return false
+  if left.precedance <= right.precedance {
+    return true
+  }
+  return false
 }
 
 func <(left: OperatorToken, right: OperatorToken) -> Bool {
-    if left.precedance < right.precedance {
-        return true
-    }
-    return false
+  if left.precedance < right.precedance {
+    return true
+  }
+  return false
 }
 
-internal enum TokenType: CustomStringConvertible {
-    case OpenBracket
-    case CloseBracket
-    case Operator(OperatorToken)
-    case Operand(Double)
-    
-    var description: String {
-        switch self {
-        case OpenBracket:
-            return "("
-        case CloseBracket:
-            return ")"
-        case Operator(let operatorToken):
-            return operatorToken.description
-        case Operand(let value):
-            return "\(value)"
-        }
-    }
+public struct Token: CustomStringConvertible {
+  
+  var tokenType: TokenType
+  
+  init(tokenType: TokenType) {
+    self.tokenType = tokenType
+  }
+  
+  init(operand: Double) {
+    tokenType = .Operand(operand)
+  }
+  
+  init(operatorType: OperatorType) {
+    tokenType = .Operator(OperatorToken(operatorType: operatorType))
+  }
+  
+  var isOpenBracket: Bool {
+    switch tokenType {
+    case .OpenBracket:
+      return true
+    default:
+      return false
+    }
+  }
+  
+  var isOperator: Bool {
+    switch tokenType {
+    case .Operator(_):
+      return true
+    default:
+      return false
+    }
+  }
+  
+  var operatorToken: OperatorToken? {
+    switch tokenType {
+    case .Operator(let operatorToken):
+      return operatorToken
+    default:
+      return nil
+    }
+  }
+  
+  public var description: String {
+    return tokenType.description
+  }
 }
 
-internal struct Token: CustomStringConvertible {
-    
-    var tokenType: TokenType
-    
-    init(tokenType: TokenType) {
-        self.tokenType = tokenType
-    }
-    
-    init(operand: Double) {
-        tokenType = .Operand(operand)
-    }
-    
-    init(operatorType: OperatorType) {
-        tokenType = .Operator(OperatorToken(operatorType: operatorType))
-    }
-    
-    var isOpenBracket: Bool {
-        switch tokenType {
-        case .OpenBracket:
-            return true
-        default:
-            return false
-        }
-    }
-    
-    var isOperator: Bool {
-        switch tokenType {
-        case .Operator(_):
-            return true
-        default:
-            return false
-        }
-    }
-    
-    var operatorToken: OperatorToken? {
-        switch tokenType {
-        case .Operator(let operatorToken):
-            return operatorToken
-        default:
-            return nil
-        }
-    }
-    
-    var description: String {
-        return tokenType.description
-    }
+public class InfixExpressionBuilder {
+  
+  private var expression = Array<Token>()
+  
+  public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
+    expression.append(Token(operatorType: operatorType))
+    return self
+  }
+  
+  public func addOperand(operand: Double) -> InfixExpressionBuilder {
+    expression.append(Token(operand: operand))
+    return self
+  }
+  
+  public func addOpenBracket() -> InfixExpressionBuilder {
+    expression.append(Token(tokenType: .OpenBracket))
+    return self
+  }
+  
+  public func addCloseBracket() -> InfixExpressionBuilder {
+    expression.append(Token(tokenType: .CloseBracket))
+    return self
+  }
+  
+  public func build() -> Array<Token> {
+    // Maybe do some validation here
+    return expression
+  }
 }
 
-public struct Expression {
-    var expression = Array<Token>()
-    
-    init() {
-        expression.append(Token(operand: 3))
-        expression.append(Token(operatorType: OperatorType.Add))
-        expression.append(Token(operand: 4))
-        expression.append(Token(operatorType: OperatorType.Multiply))
-        expression.append(Token(operand: 2))
-        expression.append(Token(operatorType: OperatorType.Divide))
-        expression.append(Token(tokenType: TokenType.OpenBracket))
-        expression.append(Token(operand: 1))
-        expression.append(Token(operatorType: OperatorType.Subtract))
-        expression.append(Token(operand: 5))
-        expression.append(Token(tokenType: TokenType.CloseBracket))
-        expression.append(Token(operatorType: OperatorType.Exponent))
-        expression.append(Token(operand: 2))
-        expression.append(Token(operatorType: OperatorType.Exponent))
-        expression.append(Token(operand: 3))
-    }
-    
-    public func reversePolishNotation() -> String {
-        
-        var tokenStack = Stack<Token>()
-        var reversePolishNotation = [Token]()
-        
-        for token in expression {
-            switch token.tokenType {
-            case .Operand(_):
-                reversePolishNotation.append(token)
-                break
-            case .OpenBracket:
-                tokenStack.push(token)
-                break
-            case .CloseBracket:
-                while tokenStack.count > 0 {
-                    if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
-                        reversePolishNotation.append(tempToken)
-                    } else {
-                        break
-                    }
-                }
-                break
-            case .Operator(let operatorToken):
-                
-                for tempToken in tokenStack.generate() {
-                    if !tempToken.isOperator {
-                        break
-                    }
-                    
-                    if let tempOperatorToken = tempToken.operatorToken {
-                        
-                        if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
-                            || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
-                                
-                                reversePolishNotation.append(tokenStack.pop()!)
-                        } else {
-                            break
-                        }
-                    }
-                }
-                
-                tokenStack.push(token)
-                break
-                
-            }
+// This returns the result of the shunting yard algorithm
+public func reversePolishNotation(expression: Array<Token>) -> String {
+  
+  var tokenStack = Stack<Token>()
+  var reversePolishNotation = [Token]()
+  
+  for token in expression {
+    switch token.tokenType {
+    case .Operand(_):
+      reversePolishNotation.append(token)
+      break
+    case .OpenBracket:
+      tokenStack.push(token)
+      break
+    case .CloseBracket:
+      while tokenStack.count > 0 {
+        if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+          reversePolishNotation.append(tempToken)
+        } else {
+          break
         }
-        
-        while tokenStack.count > 0 {
-            reversePolishNotation.append(tokenStack.pop()!)
+      }
+      break
+    case .Operator(let operatorToken):
+      
+      for tempToken in tokenStack.generate() {
+        if !tempToken.isOperator {
+          break
         }
         
-        return reversePolishNotation.map({token in
-            return token.description
-        }).joinWithSeparator(", ")
-    }
+        if let tempOperatorToken = tempToken.operatorToken {
+          
+          if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
+            || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
+              
+              reversePolishNotation.append(tokenStack.pop()!)
+          } else {
+            break
+          }
+        }
+      }
+      
+      tokenStack.push(token)
+      break
+    }
+  }
+  
+  while tokenStack.count > 0 {
+    reversePolishNotation.append(tokenStack.pop()!)
+  }
+  
+  return reversePolishNotation.map({token in
+    return token.description
+  }).joinWithSeparator(" ")
 }
\ No newline at end of file

From 6943444ba42894d3dec642acda215a3256da6ef9 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 27 Feb 2016 17:12:46 +0100
Subject: [PATCH 0055/1679] Add recursive implementation of GCD

---
 GCD/GCD.playground/Contents.swift | 19 +++++++++++---
 GCD/GCD.swift                     | 12 +++++++++
 GCD/README.markdown               | 43 +++++++++++++++++++------------
 3 files changed, 54 insertions(+), 20 deletions(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index ab18c9a05..387d5de94 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,5 +1,17 @@
 //: Playground - noun: a place where people can play
 
+// Recursive version
+func gcd(a: Int, _ b: Int) -> Int {
+  let r = a % b
+  if r != 0 {
+    return gcd(b, r)
+  } else {
+    return b
+  }
+}
+
+/*
+// Iterative version
 func gcd(m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
@@ -12,14 +24,15 @@ func gcd(m: Int, _ n: Int) -> Int {
   }
   return b
 }
+*/
 
 func lcm(m: Int, _ n: Int) -> Int {
   return m*n / gcd(m, n)
 }
 
-gcd(39, 52)       // 13
-gcd(36, 228)      // 12
-gcd(3819, 51357)  // 57
+gcd(52, 39)       // 13
+gcd(228, 36)      // 12
+gcd(51357, 3819)  // 57
 gcd(841, 299)     // 1
 
 lcm(2, 3)   // 6
diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index 222f8284e..dc473ccd4 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -14,6 +14,18 @@ func gcd(m: Int, _ n: Int) -> Int {
   return b
 }
 
+/*
+// Recursive version
+func gcd(a: Int, _ b: Int) -> Int {
+  let r = a % b
+  if r != 0 {
+    return gcd(b, r)
+  } else {
+    return b
+  }
+}
+*/
+
 /*
   Returns the least common multiple of two numbers.
 */
diff --git a/GCD/README.markdown b/GCD/README.markdown
index 63cd9afa4..a7fe799d9 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -17,34 +17,26 @@ where `a % b` calculates the remainder of `a` divided by `b`.
 Here is an implementation of this idea in Swift:
 
 ```swift
-func gcd(m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
-
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
+func gcd(a: Int, _ b: Int) -> Int {
+  let r = a % b
+  if r != 0 {
+    return gcd(b, r)
+  } else {
+    return b
   }
-  return b
 }
 ```
 
 Put it in a playground and try it out with these examples:
 
 ```swift
-gcd(39, 52)       // 13
-gcd(36, 228)      // 12
-gcd(3819, 51357)  // 57
+gcd(52, 39)       // 13
+gcd(228, 36)      // 12
+gcd(51357, 3819)  // 57
 ```
 
 Let's step through the third example:
 
-	gcd(3819, 51357)
-
-It's convenient to have the larger number first, so we swap them. That's what the `max()` and `min()` are for at the top of the function. We now have:
-
 	gcd(51357, 3819)
 
 According to Euclid's rule, this is equivalent to:
@@ -73,6 +65,23 @@ By the way, it's also possible that two numbers have a GCD of 1. They are said t
 gcd(841, 299)     // 1
 ```
 
+Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop. The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+
+```swift
+func gcd(m: Int, _ n: Int) -> Int {
+  var a = 0
+  var b = max(m, n)
+  var r = min(m, n)
+
+  while r != 0 {
+    a = b
+    b = r
+    r = a % b
+  }
+  return b
+}
+```
+
 ## Least Common Multiple
 
 An idea related to the GCD is the *least common multiple* or LCM.

From ae60a894e2b3d8438043672819b04f0e912f56d3 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 28 Feb 2016 21:59:39 +1300
Subject: [PATCH 0056/1679] BFS adding readme documentation for calculating
 minimum spanning tree

---
 Breadth-First Search/README.markdown | 148 ++++++++++++++++++++++++++-
 1 file changed, 145 insertions(+), 3 deletions(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 96be1d4b4..41ef739b8 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -175,14 +175,156 @@ breadthFirstSearchShortestPath(graph, source: nodeA)
 
 Breadth-first search can be used to calculate the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph.
 
+Let's calculate the minimum spanning tree for the following graph:
+
 ![Minimum spanning tree](Images/Minimum_Spanning_Tree.png)
 
-The minimum spanning tree is represented by the bold edges.
+*Note: the minimum spanning tree is represented by the bold edges.*
+
+Start with the source node ``a`` and add it to a queue and mark it as visited.
+```swift
+queue.enqueue(a)
+a.visited = true
+```
+The queue is now ``[ a ]``. Dequeue ``a`` and enqueue the neighbor nodes ``b`` and ``h`` and mark them as visited.
+```swift
+queue.dequeue(a)
+queue.enqueue(b)
+b.visited = true
+queue.enqueue(h)
+h.visited = true
+```
+The queue is now ``[ b, h ]``. Dequeue ``b`` and enqueue the neighbor node ``c`` mark it as visited. Remove the edge between ``b`` to ``h`` because ``h`` has already been visited.
+```swift
+queue.dequeue(b)
+queue.enqueue(c)
+c.visited = true
+b.removeEdgeTo(h)
+```
+The queue is now ``[ h, c ]``. Dequeue ``h`` and enqueue the neighbor nodes ``g`` and ``i`` and mark them as visited.
+```swift
+queue.dequeue(h)
+queue.enqueue(g)
+g.visited = true
+queue.enqueue(i)
+i.visited = true
+```
+The queue is now ``[ c, g, i ]``. Dequeue ``c`` and enqueue the neighbor nodes ``d`` and ``f`` and mark them as visited. Remove the edge between ``c`` to ``i`` because ``i`` has already been visited.
+```swift
+queue.dequeue(c)
+queue.enqueue(d)
+d.visited = true
+queue.enqueue(f)
+f.visited = true
+c.removeEdgeTo(i)
+```
+The queue is now ``[ g, i, d, f ]``. Dequeue ``g`` and remove the edges between ``g`` to ``f`` and ``g`` to ``i`` because ``f`` and ``i`` have already been visited.
+```swift
+queue.dequeue(g)
+g.removeEdgeTo(f)
+g.removeEdgeTo(i)
+```
+The queue is now ``[ i, d, f ]``. Dequeue ``i``.
+```swift
+queue.dequeue(i)
+```
+The queue is now ``[ d, f ]``. Dequeue ``d`` and enqueue the neighbor node ``e`` mark it as visited. Remove the edge between ``d`` to ``f`` because ``f`` has already been visited.
+```swift
+queue.dequeue(d)
+queue.enqueue(e)
+e.visited = true
+d.removeEdgeTo(f)
+```
+The queue is now ``[ f, e ]``. Dequeue ``f``. Remove the edge between ``f`` to ``e`` because ``e`` has already been visited.
+```swift
+queue.dequeue(f)
+f.removeEdgeTo(e)
+```
+The queue is now ``[ e ]``. Dequeue ``e``.
+```swift
+queue.dequeue(e)
+```
+The queue is now empty which means the minimum spanning tree has been computed.
+
+Here's the code:
+```swift
+func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
+  let minimumSpanningTree = graph.duplicate()
+
+  var queue = Queue<Node>()
+  let sourceInMinimumSpanningTree = minimumSpanningTree.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInMinimumSpanningTree)
+  sourceInMinimumSpanningTree.visited = true
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.visited {
+        neighborNode.visited = true
+        queue.enqueue(neighborNode)
+      } else {
+        current.remove(edge)
+      }
+    }
+  }
+
+  return minimumSpanningTree
+}
+```
+Put this code in a playground and test it like so:
+```swift
+let graph = Graph()
 
-TODO: explain steps to generate minimum spanning tree
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+let nodeI = graph.addNode("i")
 
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeH)
+graph.addEdge(nodeB, neighbor: nodeA)
+graph.addEdge(nodeB, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeH)
+graph.addEdge(nodeC, neighbor: nodeB)
+graph.addEdge(nodeC, neighbor: nodeD)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeI)
+graph.addEdge(nodeD, neighbor: nodeC)
+graph.addEdge(nodeD, neighbor: nodeE)
+graph.addEdge(nodeD, neighbor: nodeF)
+graph.addEdge(nodeE, neighbor: nodeD)
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeC)
+graph.addEdge(nodeF, neighbor: nodeD)
+graph.addEdge(nodeF, neighbor: nodeE)
+graph.addEdge(nodeF, neighbor: nodeG)
+graph.addEdge(nodeG, neighbor: nodeF)
+graph.addEdge(nodeG, neighbor: nodeH)
+graph.addEdge(nodeG, neighbor: nodeI)
+graph.addEdge(nodeH, neighbor: nodeA)
+graph.addEdge(nodeH, neighbor: nodeB)
+graph.addEdge(nodeH, neighbor: nodeG)
+graph.addEdge(nodeH, neighbor: nodeI)
+graph.addEdge(nodeI, neighbor: nodeC)
+graph.addEdge(nodeI, neighbor: nodeG)
+graph.addEdge(nodeI, neighbor: nodeH)
+
+let minimumSpanningTree = breadthFirstSearchMinimumSpanningTree(graph, source: nodeA)
+
+print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
+                           // [node: b edges: ["c"]]
+                           // [node: c edges: ["d", "f"]]
+                           // [node: d edges: ["e"]]
+                           // [node: h edges: ["g", "i"]]
+```
 ## See also
 
-[Graph](../Graph/), [Tree](../Tree/), [Queues](../Queue/), [Shortest Path](../Shortest Path/), [Breadth-first search on Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search), [Minimum spanning tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree).
+[Graph](../Graph/), [Tree](../Tree/), [Queues](../Queue/), [Shortest Path](../Shortest Path/), [Minimum Spanning Tree](../Minimum Spanning Tree/).
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher)*

From a1f6cac6d83372d44bb49e68a9cb68460dc55694 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 28 Feb 2016 22:50:28 +1300
Subject: [PATCH 0057/1679] BFS adding pages to playground. Including minimum
 spanning tree example.

---
 .../Contents.swift                            | 140 ------------------
 .../Contents.swift                            |  71 +++++++++
 .../timeline.xctimeline                       |   0
 .../Contents.swift                            |  43 ++++++
 .../timeline.xctimeline                       |   6 +
 .../Contents.swift                            |  45 ++++++
 .../timeline.xctimeline                       |   6 +
 .../Resources/Animated_BFS.gif                | Bin 0 -> 33276 bytes
 .../Resources/Minimum_Spanning_Tree.png       | Bin 0 -> 23928 bytes
 .../Sources/Edge.swift                        |   7 +
 .../Sources/Graph.swift                       |  52 +++++++
 .../Sources/Node.swift                        |  32 ++++
 .../Sources/Queue.swift                       |  31 ++++
 .../contents.xcplayground                     |   8 +-
 Breadth-First Search/README.markdown          |   6 +-
 15 files changed, 302 insertions(+), 145 deletions(-)
 delete mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
 rename Breadth-First Search/BreadthFirstSearch.playground/{ => Pages/Minimum spanning tree example.xcplaygroundpage}/timeline.xctimeline (100%)
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Resources/Animated_BFS.gif
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Resources/Minimum_Spanning_Tree.png
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift
deleted file mode 100644
index 640a0e045..000000000
--- a/Breadth-First Search/BreadthFirstSearch.playground/Contents.swift	
+++ /dev/null
@@ -1,140 +0,0 @@
-class Graph {
-  private var nodes = [Node]()
-
-  func addNode(label: String) -> Node {
-    let node = Node(label: label)
-    nodes.append(node)
-    return node
-  }
-
-  func addEdge(source: Node, neighbor: Node) {
-    let edge = Edge(neighbor: neighbor)
-    edge.neighbor = neighbor
-    source.neighbors.append(edge)
-  }
-}
-
-class Node : CustomStringConvertible, Equatable {
-  private var label: String
-  private var neighbors: [Edge]
-  private var distance: Int?
-
-  init(label: String) {
-    self.label = label
-    neighbors = []
-  }
-
-  var description: String {
-    if let distance = distance {
-      return "Node(label: \(label), distance: \(distance))"
-    }
-    return "Node(label: \(label), distance: infinity)"
-  }
-
-  var hasDistance: Bool {
-    return distance != nil
-  }
-}
-
-func ==(lhs: Node, rhs: Node) -> Bool {
-  return lhs.label == rhs.label
-}
-
-class Edge {
-  private var neighbor: Node
-
-  init(neighbor: Node) {
-    self.neighbor = neighbor
-  }
-}
-
-struct Queue<T> {
-  var array = [T]()
-
-  var isEmpty: Bool {
-    return array.isEmpty
-  }
-
-  var count: Int {
-    return array.count
-  }
-
-  mutating func enqueue(element: T) {
-    array.append(element)
-  }
-
-  mutating func dequeue() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array.removeFirst()
-    }
-  }
-
-  func peek() -> T? {
-    return array.first
-  }
-}
-
-func breadthFirstSearch(graph: Graph, source: Node) {
-  print("Performing breadth-first search on '\(source.label)'")
-
-  var seenNodes = [source]
-  var queue = Queue<Node>()
-  queue.enqueue(source)
-
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
-    for edge in current.neighbors {
-      let neighborNode = edge.neighbor
-      if !seenNodes.contains(neighborNode) {
-        queue.enqueue(neighborNode)
-        seenNodes.append(neighborNode)
-        print(neighborNode.label)
-      }
-    }
-  }
-}
-
-func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
-  var queue = Queue<Node>()
-  queue.enqueue(source)
-  source.distance = 0
-
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
-    for edge in current.neighbors {
-      let neighborNode = edge.neighbor
-      if !neighborNode.hasDistance {
-        queue.enqueue(neighborNode)
-        neighborNode.distance = current.distance! + 1
-      }
-    }
-  }
-
-  print(graph.nodes)
-}
-
-
-let graph = Graph()
-
-let nodeA = graph.addNode("a")
-let nodeB = graph.addNode("b")
-let nodeC = graph.addNode("c")
-let nodeD = graph.addNode("d")
-let nodeE = graph.addNode("e")
-let nodeF = graph.addNode("f")
-let nodeG = graph.addNode("g")
-let nodeH = graph.addNode("h")
-
-graph.addEdge(nodeA, neighbor: nodeB)
-graph.addEdge(nodeA, neighbor: nodeC)
-graph.addEdge(nodeB, neighbor: nodeD)
-graph.addEdge(nodeB, neighbor: nodeE)
-graph.addEdge(nodeC, neighbor: nodeF)
-graph.addEdge(nodeC, neighbor: nodeG)
-graph.addEdge(nodeE, neighbor: nodeH)
-
-
-breadthFirstSearch(graph, source: nodeA)
-breadthFirstSearchShortestPath(graph, source: nodeA)
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..181d566d4
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,71 @@
+func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
+  let minimumSpanningTree = graph.duplicate()
+
+  var queue = Queue<Node>()
+  let sourceInMinimumSpanningTree = minimumSpanningTree.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInMinimumSpanningTree)
+  sourceInMinimumSpanningTree.visited = true
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.visited {
+        neighborNode.visited = true
+        queue.enqueue(neighborNode)
+      } else {
+        current.remove(edge)
+      }
+    }
+  }
+
+  return minimumSpanningTree
+}
+
+/*:
+![Animated example of a breadth-first search](Minimum_Spanning_Tree.png)
+*/
+
+let graph = Graph()
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+let nodeI = graph.addNode("i")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeH)
+graph.addEdge(nodeB, neighbor: nodeA)
+graph.addEdge(nodeB, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeH)
+graph.addEdge(nodeC, neighbor: nodeB)
+graph.addEdge(nodeC, neighbor: nodeD)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeI)
+graph.addEdge(nodeD, neighbor: nodeC)
+graph.addEdge(nodeD, neighbor: nodeE)
+graph.addEdge(nodeD, neighbor: nodeF)
+graph.addEdge(nodeE, neighbor: nodeD)
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeC)
+graph.addEdge(nodeF, neighbor: nodeD)
+graph.addEdge(nodeF, neighbor: nodeE)
+graph.addEdge(nodeF, neighbor: nodeG)
+graph.addEdge(nodeG, neighbor: nodeF)
+graph.addEdge(nodeG, neighbor: nodeH)
+graph.addEdge(nodeG, neighbor: nodeI)
+graph.addEdge(nodeH, neighbor: nodeA)
+graph.addEdge(nodeH, neighbor: nodeB)
+graph.addEdge(nodeH, neighbor: nodeG)
+graph.addEdge(nodeH, neighbor: nodeI)
+graph.addEdge(nodeI, neighbor: nodeC)
+graph.addEdge(nodeI, neighbor: nodeG)
+graph.addEdge(nodeI, neighbor: nodeH)
+
+let minimumSpanningTree = breadthFirstSearchMinimumSpanningTree(graph, source: nodeA)
+print(minimumSpanningTree)
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/timeline.xctimeline b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
similarity index 100%
rename from Breadth-First Search/BreadthFirstSearch.playground/timeline.xctimeline
rename to Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..175821efc
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,43 @@
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+  var queue = Queue<Node>()
+  queue.enqueue(source)
+  source.distance = 0
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.hasDistance {
+        queue.enqueue(neighborNode)
+        neighborNode.distance = current.distance! + 1
+      }
+    }
+  }
+
+  print(graph.nodes)
+}
+
+/*:
+![Animated example of a breadth-first search](Animated_BFS.gif)
+*/
+
+let graph = Graph()
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeD)
+graph.addEdge(nodeB, neighbor: nodeE)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeG)
+graph.addEdge(nodeE, neighbor: nodeH)
+
+breadthFirstSearchShortestPath(graph, source: nodeA)
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..b2ac225ab
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,45 @@
+func breadthFirstSearch(graph: Graph, source: Node) {
+  var seenNodes = [source]
+  var queue = Queue<Node>()
+  queue.enqueue(source)
+
+  print(source.label)
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !seenNodes.contains(neighborNode) {
+        queue.enqueue(neighborNode)
+        seenNodes.append(neighborNode)
+        print(neighborNode.label)
+      }
+    }
+  }
+}
+
+/*:
+![Animated example of a breadth-first search](Animated_BFS.gif)
+*/
+
+let graph = Graph()
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeD)
+graph.addEdge(nodeB, neighbor: nodeE)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeG)
+graph.addEdge(nodeE, neighbor: nodeH)
+
+
+breadthFirstSearch(graph, source: nodeA)
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Resources/Animated_BFS.gif b/Breadth-First Search/BreadthFirstSearch.playground/Resources/Animated_BFS.gif
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HcmV?d00001

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift
new file mode 100644
index 000000000..8f2128ac5
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
@@ -0,0 +1,7 @@
+public class Edge {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
new file mode 100644
index 000000000..6792ebf7b
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -0,0 +1,52 @@
+public class Graph : CustomStringConvertible {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    edge.neighbor = neighbor
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift
new file mode 100644
index 000000000..4c261ffca
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
@@ -0,0 +1,32 @@
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label
+}
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift
new file mode 100644
index 000000000..bf462bbdd
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift	
@@ -0,0 +1,31 @@
+public struct Queue<T> {
+  private var array: [T]
+
+  public init() {
+    array = []
+  }
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeFirst()
+    }
+  }
+
+  public func peek() -> T? {
+    return array.first
+  }
+}
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground
index 5da2641c9..fc13b7766 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
@@ -1,4 +1,8 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
+<playground version='6.0' target-platform='ios' display-mode='rendered'>
+    <pages>
+        <page name='Simple example'/>
+        <page name='Shortest path example'/>
+        <page name='Minimum spanning tree example'/>
+    </pages>
 </playground>
\ No newline at end of file
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 41ef739b8..d71cca15c 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -59,12 +59,12 @@ Simple implementation of breadth-first search using a queue:
 
 ```swift
 func breadthFirstSearch(graph: Graph, source: Node) {
-  print("Performing breadth-first search on '\(source.label)'")
-
   var seenNodes = [source]
   var queue = Queue<Node>()
   queue.enqueue(source)
 
+  print(source.label)
+
   while !queue.isEmpty {
     let current = queue.dequeue()!
     for edge in current.neighbors {
@@ -100,7 +100,7 @@ graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
-breadthFirstSearch(graph, source: nodeA) // This will output: Performing breadth-first search on 'a', b, c, d, e, f, g, h
+breadthFirstSearch(graph, source: nodeA) // This will output: a, b, c, d, e, f, g, h
 ```
 
 ## Applications

From 0ad6cca09442b693d39b62f3e309a95e14e7c8fd Mon Sep 17 00:00:00 2001
From: Jeroen Houtzager <houtzager@gmail.com>
Date: Sun, 28 Feb 2016 11:39:49 +0100
Subject: [PATCH 0058/1679] Add B-tree paragraph placeholder,

---
 B Tree/README.markdown | 8 ++++++++
 1 file changed, 8 insertions(+)
 create mode 100644 B Tree/README.markdown

diff --git a/B Tree/README.markdown b/B Tree/README.markdown
new file mode 100644
index 000000000..a96d59be2
--- /dev/null
+++ b/B Tree/README.markdown	
@@ -0,0 +1,8 @@
+# B Tree
+
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/B-tree).
+
+*Written by Jeroen Houtzager*
+

From ab15e38562c8607382bddcaa16a41460ad69054a Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 28 Feb 2016 12:38:05 +0100
Subject: [PATCH 0059/1679] Add optimized version of Queue

---
 Queue/Queue-Optimized.swift               |  47 ++++++
 Queue/{Queue.swift => Queue-Simple.swift} |  10 +-
 Queue/Queue.playground/Contents.swift     |  21 +--
 Queue/README.markdown                     | 187 +++++++++++++++++++++-
 4 files changed, 245 insertions(+), 20 deletions(-)
 create mode 100644 Queue/Queue-Optimized.swift
 rename Queue/{Queue.swift => Queue-Simple.swift} (96%)

diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
new file mode 100644
index 000000000..efc573442
--- /dev/null
+++ b/Queue/Queue-Optimized.swift
@@ -0,0 +1,47 @@
+/*
+  First-in first-out queue (FIFO)
+
+  New elements are added to the end of the queue. Dequeuing pulls elements from
+  the front of the queue.
+
+  Enqueuing and dequeuing are O(1) operations.
+*/
+public struct Queue<T> {
+  private var array = [T?]()
+  private var head = 0
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
+
+    let percentage = Double(head)/Double(array.count)
+    if array.count > 50 && percentage > 0.25 {
+      array.removeFirst(head)
+      head = 0
+    }
+    
+    return element
+  }
+  
+  public func peek() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
+  }
+}
diff --git a/Queue/Queue.swift b/Queue/Queue-Simple.swift
similarity index 96%
rename from Queue/Queue.swift
rename to Queue/Queue-Simple.swift
index 70830df7a..6d3c197ee 100644
--- a/Queue/Queue.swift
+++ b/Queue/Queue-Simple.swift
@@ -8,16 +8,16 @@
   implemented with a linked list, then both would be O(1).
 */
 public struct Queue<T> {
-  var array = [T]()
-
-  public var isEmpty: Bool {
-    return array.isEmpty
-  }
+  private var array = [T]()
 
   public var count: Int {
     return array.count
   }
 
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 8289c46ac..da556d156 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -13,32 +13,35 @@
 
 public struct Queue<T> {
   private var array = [T]()
-  
-  public var count: Int {
-    return array.count
-  }
-  
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
+  public var count: Int {
+    return array.count
+  }
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
-  
+
   public mutating func dequeue() -> T? {
-    if count == 0 {
+    if isEmpty {
       return nil
     } else {
       return array.removeFirst()
     }
   }
-  
+
   public func peek() -> T? {
     return array.first
   }
 }
 
+
+
+
 // Create a queue and put some elements on it already.
 var queueOfNames = Queue(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
diff --git a/Queue/README.markdown b/Queue/README.markdown
index 7b90daa9a..70a6a76eb 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -40,12 +40,14 @@ This returns `3`, the next dequeue returns `57`, and so on. If the queue is empt
 
 > **Note:** A queue is not always the best choice. If the order in which the items are added and removed from the list isn't important, you might as well use a [stack](../Stack/) instead of a queue. Stacks are simpler and faster.
 
+## The code
+
 Here is a very simplistic implementation of a queue in Swift. It's just a wrapper around an array that lets you enqueue, dequeue, and peek at the front-most item:
 
 ```swift
 public struct Queue<T> {
-  var array = [T]()
-  
+  private var array = [T]()
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
@@ -53,7 +55,7 @@ public struct Queue<T> {
   public var count: Int {
     return array.count
   }
-  
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
@@ -76,10 +78,183 @@ This queue works just fine but it is not optimal.
 
 Enqueuing is an **O(1)** operation because adding to the end of an array always takes the same amount of time, regardless of the size of the array. So that's great.
 
-However, to dequeue we remove the element from the beginning of the array. This is an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
+You might be wondering why appending items to an array is **O(1)**, or a constant-time operation. That is so because an array in Swift always has some empty space at the end. If we do the following:
+
+```swift
+var queue = Queue<String>()
+queue.enqueue("Ada")
+queue.enqueue("Steve")
+queue.enqueue("Tim")
+```
+
+then the array might actually look like this:
+
+	[ "Ada", "Steve", "Tim", xxx, xxx, xxx ]
+
+where `xxx` is memory that is reserved but not filled in yet. Adding a new element to the array overwrites the next unused spot:
+
+	[ "Ada", "Steve", "Tim", "Grace", xxx, xxx ]
+
+This is simply matter of copying memory from one place to another, a constant-time operation.
+
+Of course, there are only a limited number of such unused spots at the end of the array. When the last `xxx` gets used and you want to add another item, the array needs to resize to make more room. Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process, so relatively slow. But since it happens only every so often, the time for appending a new element to the end of the array is still **O(1)** on average, or **O(1)** "amortized".
+
+The story for dequeueing is slightly different. To dequeue we remove the element from the *beginning* of the array, not the end. This is always an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
+
+In our example, dequeuing the first element `"Ada"` copies `"Steve"` in the place of `"Ada"`, `"Tim"` in the place of `"Steve"`, and `"Grace"` in the place of `"Tim"`:
+
+	before   [ "Ada", "Steve", "Tim", "Grace", xxx, xxx ]
+	                   /       /      /
+	                  /       /      /
+	                 /       /      /
+	                /       /      /
+	 after   [ "Steve", "Tim", "Grace", xxx, xxx, xxx ]
+ 
+Moving all these elements in memory is always an **O(n)** operation. So with our simple implementation of a queue, enqueuing is efficient but dequeueing leaves something to be desired...
+
+## A more efficient queue
+
+To make dequeuing more efficient, we can use the same trick of reserving some extra free space, but this time do it at the front of the array. We're going to have to write this code ourselves as the built-in Swift array doesn't support this out of the box.
+
+The idea is this: whenever we dequeue an item, we don't shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
+
+	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
+
+After dequeuing `"Steve"`, the array is:
+
+	[ xxx, xxx, "Tim", "Grace", xxx, xxx ]
+
+These empty spots at the front never get reused for anything, so they're wasting space. Every so often you can trim the array by moving the remaining elements to the front again:
+
+	[ "Tim", "Grace", xxx, xxx, xxx, xxx ]
+
+This trimming procedure involves shifting memory so it's an **O(n)** operation. But because it only happens once in a while, dequeuing is now **O(1)** on average.
+
+Here is how you could implement this version of `Queue`:
+
+```swift
+public struct Queue<T> {
+  private var array = [T?]()
+  private var head = 0
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
+
+    let percentage = Double(head)/Double(array.count)
+    if head > 20 && percentage > 0.25 {
+      array.removeFirst(head)
+      head = 0
+    }
+    
+    return element
+  }
+  
+  public func peek() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
+  }
+}
+```
+
+The array now stores objects of type `T?` instead of just `T` because we need some way to mark array elements as being empty. The `head` variable is the index in the array of the front-most object.
+
+Most of the new functionality sits in `dequeue()`. When we dequeue an item, we first set `array[head]` to `nil` to remove the object from the array. Then we increment `head` because now the next item has become the front one.
+
+We go from this:
+
+	[ "Ada", "Steve", "Tim", "Grace", xxx, xxx ]
+	  head
+
+to this:
+
+	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
+	        head
+
+It's like some weird supermarket where the people in the checkout lane don't shuffle forward towards the cash register, but the cash register moves up the queue.
+
+Of course, if we never remove those empty spots at the front then the array will keep growing as we enqueue and dequeue elements. To periodically trim down the array, we do the following:
+
+```swift
+    let percentage = Double(head)/Double(array.count)
+    if array.count > 50 && percentage > 0.25 {
+      array.removeFirst(head)
+      head = 0
+    }
+```
+
+This calculates the percentage of empty spots at the beginning as a ratio of the total array size. If more than 25% of the array is unused, we chop off that wasted space. However, if the array is small we don't want to resize it all the time, so there must be at least 50 elements in the array before we try to trim it. 
+
+> **Note:** I just pulled these numbers out of thin air -- you may need to tweak them based on the behavior of your app in a production environment.
+
+To test this in a playground, do:
+
+```swift
+var q = Queue<String>()
+q.array                   // [] empty array
+
+q.enqueue("Ada")
+q.enqueue("Steve")
+q.enqueue("Tim")
+q.array             // [{Some "Ada"}, {Some "Steve"}, {Some "Tim"}]
+q.count             // 3
+
+q.dequeue()         // "Ada"
+q.array             // [nil, {Some "Steve"}, {Some "Tim"}]
+q.count             // 2
+
+q.dequeue()         // "Steve"
+q.array             // [nil, nil, {Some "Tim"}]
+q.count             // 1
+
+q.enqueue("Grace")
+q.array             // [nil, nil, {Some "Tim"}, {Some "Grace"}]
+q.count             // 2
+```
+
+To test the trimming behavior, replace the line
+
+```swift
+    if array.count > 50 && percentage > 0.25 {
+```
+
+with:
+
+```swift
+    if head > 2 {
+```
+
+Now if you dequeue another object, the array will look as follows:
+
+```swift
+q.dequeue()         // "Tim"
+q.array             // [{Some "Grace"}]
+q.count             // 1
+```
+
+The `nil` objects at the front have been removed and the array is no longer wasting space. This new version of `Queue` isn't much more complicated than the first one but dequeuing is now also an **O(1)** operation, just because we were a bit smarter about how we used the array.
+
+## See also
 
-More efficient implementations would use a linked list, a [circular buffer](../Ring Buffer/), or a [heap](../Heap/). (I might add an example of this later.)
+There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or a [heap](../Heap/). 
 
 Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority Queue/), a sorted queue where the "most important" item is always at the front.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*

From 16e4285f85663d27bf2b786f89d799d10a3299ac Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 28 Feb 2016 15:28:44 +0100
Subject: [PATCH 0060/1679] Add optimized version of Deque

---
 Deque/Deque-Optimized.swift               |  77 ++++++++
 Deque/{Deque.swift => Deque-Simple.swift} |   0
 Deque/README.markdown                     | 229 +++++++++++++++++++++-
 3 files changed, 304 insertions(+), 2 deletions(-)
 create mode 100644 Deque/Deque-Optimized.swift
 rename Deque/{Deque.swift => Deque-Simple.swift} (100%)

diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
new file mode 100644
index 000000000..e78942543
--- /dev/null
+++ b/Deque/Deque-Optimized.swift
@@ -0,0 +1,77 @@
+/*
+  Deque (pronounced "deck"), a double-ended queue
+
+  All enqueuing and dequeuing operations are O(1).
+*/
+public struct Deque<T> {
+  private var array: [T?]
+  private var head: Int
+  private var capacity: Int
+  
+  public init(capacity: Int = 10) {
+    self.capacity = max(capacity, 1)
+    array = .init(count: capacity, repeatedValue: nil)
+    head = capacity
+  }
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+  
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func enqueueFront(element: T) {
+    if head == 0 {
+      capacity *= 2
+      let emptySpace = [T?](count: capacity, repeatedValue: nil)
+      array.insertContentsOf(emptySpace, at: 0)
+      head = capacity
+    }
+
+    head -= 1
+    array[head] = element
+  }
+
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
+
+    if capacity > 10 && head >= capacity*2 {
+      array.removeFirst(capacity)
+      head -= capacity
+    }
+    return element
+  }
+  
+  public mutating func dequeueBack() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeLast()
+    }
+  }
+  
+  public func peekFront() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
+  }
+  
+  public func peekBack() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.last!
+    }
+  }
+}
diff --git a/Deque/Deque.swift b/Deque/Deque-Simple.swift
similarity index 100%
rename from Deque/Deque.swift
rename to Deque/Deque-Simple.swift
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 8ccaf8361..a4889f546 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -2,7 +2,7 @@
 
 A double-ended queue. For some reason this is pronounced as "deck".
 
-A regular [queue](../Queue/) adds new elements to the back and dequeues from the front. The deque also allows enqueuing at the front and dequeuing from the back, and peeking at both ends.
+A regular [queue](../Queue/) adds new elements to the back and removes from the front. The deque also allows enqueuing at the front and dequeuing from the back, and peeking at both ends.
 
 Here is a very basic implementation of a deque in Swift:
 
@@ -71,7 +71,232 @@ deque.dequeue()       // 5
 ```
 
 This particular implementation of `Deque` is simple but not very efficient. Several operations are **O(n)**, notably `enqueueFront()` and `dequeue()`. I've included it only to show the principle of what a deque does.
+
+## A more efficient version
+  
+The reason that `dequeue()` and `enqueueFront()` are **O(n)** is that they work on the front of the array. If you remove an element at the front of an array, what happens is that all the remaining elements need to be shifted in memory.
+
+Let's say the deque's array contains the following items:
+
+	[ 1, 2, 3, 4 ]
+
+Then `dequeue()` will remove `1` from the array and the elements `2`, `3`, and `4`, are shifted one position to the front:
+
+	[ 2, 3, 4 ]
+
+This is an **O(n)** operation because all array elements need to be moved by one position in the computer's memory.
+
+Likewise, inserting an element at the front of the array is expensive because it requires that all other elements must be shifted one position to the back. So `enqueueFront(5)` will change the array to be:
+
+	[ 5, 2, 3, 4 ]
+
+First, the elements `2`, `3`, and `4`, are move up by one position in the computer's memory, and then the new element `5` is inserted at the position where `2` used to be.
+
+Why is this not an issue at for `enqueue()` and `dequeueBack()`? Well, these operations are performed at the end of the array. The way resizable arrays are implemented in Swift is by reserving a certain amount of free space at the back. 
+
+Our initial array `[ 1, 2, 3, 4]` actually looks like this in memory:
+
+	[ 1, 2, 3, 4, x, x, x ]
+
+where the `x`s denote additional positions in the array that are not being used yet. Calling `enqueue(6)` simply copies the new item into the next unused spot:
+
+	[ 1, 2, 3, 4, 6, x, x ]
+
+And `dequeueBack()` uses `array.removeLast()` to read that item and decrement `array.count` by one. There is no shifting of memory involved here. So operations at the back of the array are fast, **O(1)**.
+
+It is possible the array runs out of free spots at the back. In that case, Swift will allocate a new, larger array and copy over all the data. This is an **O(n)** operation but because it only happens once in a while, adding new elements at the end of an array is still **O(1)** on average.
+
+Of course, we can use this same trick at the *beginning* of the array. That will make our deque efficient too for operations at the front of the queue. Our array will look like this:
+
+	[ x, x, x, 1, 2, 3, 4, x, x, x ]
+
+There is now a chunk of free space at the start of the array, which allows adding or removing elements at the front of the queue to be **O(1)** as well.
+
+Here is the new version of `Deque`:
+
+```swift
+public struct Deque<T> {
+  private var array: [T?]
+  private var head: Int
+  private var capacity: Int
+  
+  public init(capacity: Int = 10) {
+    self.capacity = max(capacity, 1)
+    array = .init(count: capacity, repeatedValue: nil)
+    head = capacity
+  }
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+  
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
   
-A more efficient implementation would use a [doubly linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or two [stacks](../Stack/) facing opposite directions.
+  public mutating func enqueueFront(element: T) {
+    // this is explained below
+  }
+
+  public mutating func dequeue() -> T? {
+    // this is explained below
+  }
+
+  public mutating func dequeueBack() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeLast()
+    }
+  }
+  
+  public func peekFront() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
+  }
+  
+  public func peekBack() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.last!
+    }
+  }  
+}
+```
+
+It still largely looks the same -- `enqueue()` and `dequeueBack()` haven't changed -- but there are also a few important differences. The array now stores objects of type `T?` instead of just `T` because we need some way to mark array elements as being empty.
+
+The `init` method allocates a new array that contains a certain number of `nil` values. This is the free room we have to work with at the beginning of the array. By default this creates 10 empty spots. 
+
+The `head` variable is the index in the array of the front-most object. Since the queue is currently empty, `head` points at an index beyond the end of the array.
+
+	[ x, x, x, x, x, x, x, x, x, x ]
+	                                 |
+	                                 head
+
+To enqueue an object at the front, we move `head` one position to the left and then copy the new object into the array at index `head`. For example, `enqueueFront(5)` gives:
+
+	[ x, x, x, x, x, x, x, x, x, 5 ]
+	                             |
+	                             head
+
+Followed by `enqueueFront(7)`:
+
+	[ x, x, x, x, x, x, x, x, 7, 5 ]
+	                          |
+	                          head
+
+And so on... the `head` keeps moving to the left and always points at the first item in the queue. `enqueueFront()` is now **O(1)** because it only involves copying a value into the array, a constant-time operation.
+
+Here is the code:
+
+```swift
+  public mutating func enqueueFront(element: T) {
+    head -= 1
+    array[head] = element
+  }
+```
+
+Appending to the back of the queue has not changed (it's the exact same code as before). For example, `enqueue(1)` gives:
+
+	[ x, x, x, x, x, x, x, x, 7, 5, 1, x, x, x, x, x, x, x, x, x ]
+	                          |
+	                          head
+
+Notice how the array has resized itself. There was no room to add the `1`, so Swift decided to make the array larger and add a number of empty spots to the end. If you enqueue another object, it gets added to the next empty spot in the back. For example, `enqueue(2)`:
+
+	[ x, x, x, x, x, x, x, x, 7, 5, 1, 2, x, x, x, x, x, x, x, x ]
+	                          |
+	                          head
+
+> **Note:** You won't see those empty spots at the back when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up. 
+
+The `dequeue()` method does the opposite of `enqueueFront()`, it reads the value at `head`, sets the array element back to `nil`, and then moves `head` one position to the right:
+
+```swift
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
+
+    return element
+  }
+```
+
+There is one tiny problem... If you enqueue a lot of objects at the front, you're going to run out of empty spots at the front at some point. When this happens at the back of the array, Swift automatically resizes it. But at the front of the array we have to handle this ourselves with some extra logic in `enqueueFront()`:
+
+```swift
+  public mutating func enqueueFront(element: T) {
+    if head == 0 {
+      capacity *= 2
+      let emptySpace = [T?](count: capacity, repeatedValue: nil)
+      array.insertContentsOf(emptySpace, at: 0)
+      head = capacity
+    }
+
+    head -= 1
+    array[head] = element
+  }
+```
+
+If `head` equals 0, there is no room left at the front. When that happens, we add a whole bunch of new `nil` elements to the array. This is an **O(n)** operation but since this cost gets divided over all the `enqueueFront()`s, each individual call to `enqueueFront()` is still **O(1)** on average. 
+
+> **Note:** We also multiply the capacity by 2 each time this happens, so if your queue grows bigger and bigger, the resizing happens less often. This is also what Swift arrays automatically do at the back.
+
+We have to do something similar for `dequeue()`. If you mostly enqueue a lot of elements at the back and mostly dequeue from the front, then you may end up with an array that looks like this:
+
+	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
+	                                                           |
+	                                                           head
+
+Those empty spots at the front only get used when you use `enqueueFront()`. But if enqueuing objects at the front happens only rarely, this leaves a lot of wasted space. So let's add some code to `dequeue()` to clean this up:
+
+```swift
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
+
+    if capacity > 10 && head >= capacity*2 {
+      array.removeFirst(capacity)
+      head -= capacity
+    }
+    return element
+  }
+```
+
+Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off half of these empty spots.
+
+For example, this:
+
+	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
+	                             |                             |
+	                             capacity                      head
+
+becomes this after trimming:
+
+	[ x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
+	                             |
+	                             head
+
+This way we can strike a balance between fast enqueuing and dequeuing at the front and keeping the memory requirements reasonable.
+
+> **Note:** We don't perform this trimming on very small arrays. It's not worth it for saving just a few bytes of memory.
+
+## See also
+
+Other ways to implement deque are by using a [doubly linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or two [stacks](../Stack/) facing opposite directions.
+
+[A fully-featured deque implementation in Swift](https://github.com/lorentey/Deque)
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From fcedd45411e7e5c7ee0a68ec9c25103b2a8a994c Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 28 Feb 2016 16:55:03 +0100
Subject: [PATCH 0061/1679] Also reduce capacity on dequeue

---
 Deque/Deque-Optimized.swift |  6 ++++--
 Deque/README.markdown       | 25 ++++++++++++++-----------
 2 files changed, 18 insertions(+), 13 deletions(-)

diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index e78942543..3b0d724dd 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -45,8 +45,10 @@ public struct Deque<T> {
     head += 1
 
     if capacity > 10 && head >= capacity*2 {
-      array.removeFirst(capacity)
-      head -= capacity
+      let amountToRemove = capacity + capacity/2
+      array.removeFirst(amountToRemove)
+      head -= amountToRemove
+      capacity /= 2
     }
     return element
   }
diff --git a/Deque/README.markdown b/Deque/README.markdown
index a4889f546..87b5d2791 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -254,11 +254,11 @@ If `head` equals 0, there is no room left at the front. When that happens, we ad
 
 We have to do something similar for `dequeue()`. If you mostly enqueue a lot of elements at the back and mostly dequeue from the front, then you may end up with an array that looks like this:
 
-	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
+	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
 	                                                           |
 	                                                           head
 
-Those empty spots at the front only get used when you use `enqueueFront()`. But if enqueuing objects at the front happens only rarely, this leaves a lot of wasted space. So let's add some code to `dequeue()` to clean this up:
+Those empty spots at the front only get used when you call `enqueueFront()`. But if enqueuing objects at the front happens only rarely, this leaves a lot of wasted space. So let's add some code to `dequeue()` to clean this up:
 
 ```swift
   public mutating func dequeue() -> T? {
@@ -268,26 +268,29 @@ Those empty spots at the front only get used when you use `enqueueFront()`. But
     head += 1
 
     if capacity > 10 && head >= capacity*2 {
-      array.removeFirst(capacity)
-      head -= capacity
+      let amountToRemove = capacity + capacity/2
+      array.removeFirst(amountToRemove)
+      head -= amountToRemove
+      capacity /= 2
     }
     return element
   }
 ```
 
-Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off half of these empty spots.
+Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off a bunch of these empty spots. We reduce it to about 25%.
 
 For example, this:
 
-	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
-	                             |                             |
-	                             capacity                      head
+	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
+	                                |                             |
+	                                capacity                      head
 
 becomes this after trimming:
 
-	[ x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
-	                             |
-	                             head
+	[ x, x, x, x, x, 1, 2, 3 ]
+	              |
+	              head
+	              capacity
 
 This way we can strike a balance between fast enqueuing and dequeuing at the front and keeping the memory requirements reasonable.
 

From 111469cd4f6ba87793fe4bf444d92db3b1ac946c Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 28 Feb 2016 17:58:36 +0100
Subject: [PATCH 0062/1679] Fix path to file in test project

---
 Queue/Tests/Tests.xcodeproj/project.pbxproj | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
index 83e3fc523..ac23063a5 100644
--- a/Queue/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -7,14 +7,14 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		7B80C4021C77A6BF003CECC7 /* Queue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4011C77A6BF003CECC7 /* Queue.swift */; };
+		7B80C4021C77A6BF003CECC7 /* Queue-Optimized.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4011C77A6BF003CECC7 /* Queue-Optimized.swift */; };
 		7B80C4041C77A6C5003CECC7 /* QueueTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4031C77A6C5003CECC7 /* QueueTests.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
-		7B80C4011C77A6BF003CECC7 /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Queue.swift; path = ../Queue.swift; sourceTree = SOURCE_ROOT; };
+		7B80C4011C77A6BF003CECC7 /* Queue-Optimized.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = "Queue-Optimized.swift"; path = "../Queue-Optimized.swift"; sourceTree = SOURCE_ROOT; };
 		7B80C4031C77A6C5003CECC7 /* QueueTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = QueueTests.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -48,7 +48,7 @@
 		7B2BBC831C779D720067B71D /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				7B80C4011C77A6BF003CECC7 /* Queue.swift */,
+				7B80C4011C77A6BF003CECC7 /* Queue-Optimized.swift */,
 				7B80C4031C77A6C5003CECC7 /* QueueTests.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
@@ -124,7 +124,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				7B80C4021C77A6BF003CECC7 /* Queue.swift in Sources */,
+				7B80C4021C77A6BF003CECC7 /* Queue-Optimized.swift in Sources */,
 				7B80C4041C77A6C5003CECC7 /* QueueTests.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;

From 084b7566db311dfe111bb1590a6364c1c5808505 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Sun, 28 Feb 2016 14:41:43 -0800
Subject: [PATCH 0063/1679] Write README for K-Means Algorithm

---
 K-Means/Images/k_means_bad1.png | Bin 0 -> 16294 bytes
 K-Means/Images/k_means_bad2.png | Bin 0 -> 15826 bytes
 K-Means/Images/k_means_good.png | Bin 0 -> 15983 bytes
 K-Means/README.md               |  82 +++++++++++++++++++++++++++++++-
 README.markdown                 |   5 +-
 5 files changed, 85 insertions(+), 2 deletions(-)
 create mode 100644 K-Means/Images/k_means_bad1.png
 create mode 100644 K-Means/Images/k_means_bad2.png
 create mode 100644 K-Means/Images/k_means_good.png

diff --git a/K-Means/Images/k_means_bad1.png b/K-Means/Images/k_means_bad1.png
new file mode 100644
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diff --git a/K-Means/README.md b/K-Means/README.md
index a801fea7a..05240ebe2 100644
--- a/K-Means/README.md
+++ b/K-Means/README.md
@@ -1,3 +1,83 @@
 # K-Means
 
-Goal:  Partition data into k clusters based on nearest mean
+Goal:  Partition data into k clusters based on nearest means
+
+The idea behind K-Means is to try and take data that has no formal classification to it and determine if there are any natural clusters within the data.
+
+K-Means assumes that there are **k-centers** within the data. The data that is then closest to these *centroids* become classified or grouped together. K-Means doesn't tell you what the classifier is for that particular data group, but it assists in trying to find what clusters potentially exist.
+
+## Algorithm
+The k-means algorithm is really quite simple at it's core:
+1. Choose k random points to be the initial centers
+2. Repeat the following two steps until the *centroid* reach convergence
+    1. Assign each point to it's nearest *centroid*
+    2. Update the *centroid* to the mean of it's nearest points
+
+Convergence is said to be reached when all of the *centroids* have not changed.
+
+This brings about a few of the parameters that are required for k-means:
+- **k** -  This is the number of *centroids* to attempt to locate
+- **convergence distance** - This is minimum distance that the centers are allowed to moved after a particular update step.
+- **distance function** - There are a number of distance functions that can be used, but mostly commonly the euclidean distance function is adequate. But often can lead to convergence not being reached in higher dimensionally.
+
+This is what the algorithm would look like in swift
+```swift
+func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
+
+    var kCenters = reservoirSample(points, k: numCenters)
+
+    repeat {
+        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        for p in points {
+            let c = nearestCenter(p, Centers: kCenters)
+            cnts[c]++
+            newCenters[c] += p
+        }
+        for idx in 0..<numCenters {
+            newCenters[idx] /= cnts[idx]
+        }
+        centerMoveDist = 0.0
+        for idx in 0..<numCenters {
+            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
+        }
+        kCenters = newCenters
+    } while(centerMoveDist > convergeDist)
+    return kCenters
+}
+```
+
+## Example
+These examples are contrived to show the exact nature of K-Means and finding clusters. These clusters are very easily identified by human eyes, we see there is one in the lower left corner, one in the upper right corner and maybe one in the middle.
+
+In all these examples the stars represent the *centroids* and the squares are the points.
+
+##### Good clusters
+This first example shows K-Means finding all three clusters:
+![Good Clustering](Images/k_means_good.png)
+
+The selection of initial centroids found that lower left (indicated by red) and did pretty good on the center and upper left clusters.
+
+#### Bad Clustering
+The next two examples highlight the unpredictability of k-Means and how not always does it find the best clustering.
+![Bad Clustering 1](Images/k_means_bad1.png)
+As you can see in this one the initial *centroids* were all a little two close and the 'blue' didn't quite get to a good place. By adjusting the convergence distance should be able to get it better.
+
+![Bad Clustering 1](Images/k_means_bad2.png)
+This one the blue cluster never really could separate from the red cluster and as such sort of got stuck down there.
+
+## Performance
+The first thing to recognize is that k-Means is classified as an NP-Hard type of problem. The selection of the initial *centroids* has a big effect on how the resulting clusters may end up. This means that trying to find an exact solution is not likely - even in 2 dimensional space.
+
+As seem from the steps above the complexity really isn't that bad - it is often considered to be on the order of O(kndi), where **k** is the number of *centroids*, **n** is the number of **d** dimensional vectors and **i** is the number of iterations for convergence.
+
+The amount of data has a big linear effect on the running time of k-means, but tuning how far you want the *centroids* to converge can have a big impact how many iterations will be done - **k** should be relatively small compared to the number of vectors.
+
+Often times as more data is added certain points may lie in the boundary between two *centroids* and as such those centroids would continue to bounce back and forth and the **convergence** distance would need to be tuned to prevent that.
+
+## See Also
+See also [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
+
+*Written by John Gill*
diff --git a/README.markdown b/README.markdown
index 1af54642d..ebff0be73 100644
--- a/README.markdown
+++ b/README.markdown
@@ -95,13 +95,16 @@ Bad sorting algorithms (don't use these!):
 
 ### Machine learning
 
-- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
+##### Supervised learning
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression
 - Neural Networks
 - PageRank
 
+##### Clustering
+- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
+
 ## Data structures
 
 The choice of data structure for a particular task depends on a few things.

From ebcf1f4155afe2d57fd1967f60456bbbfeb70232 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Sun, 28 Feb 2016 14:44:04 -0800
Subject: [PATCH 0064/1679] Modify main README to add k-Means

---
 README.markdown | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/README.markdown b/README.markdown
index ebff0be73..1f77f12a7 100644
--- a/README.markdown
+++ b/README.markdown
@@ -94,17 +94,13 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 
 ### Machine learning
-
-##### Supervised learning
+- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression
 - Neural Networks
 - PageRank
 
-##### Clustering
-- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
-
 ## Data structures
 
 The choice of data structure for a particular task depends on a few things.

From 87d798d949d2807bdb4d2a679d1155cb455bcc9f Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 29 Feb 2016 22:02:39 +1300
Subject: [PATCH 0065/1679] Changed simple example to used node.visited flag
 instead of storing separate "seenNodes" list

---
 .../Pages/Simple example.xcplaygroundpage/Contents.swift     | 5 ++---
 Breadth-First Search/README.markdown                         | 5 ++---
 2 files changed, 4 insertions(+), 6 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index b2ac225ab..7cb9122e3 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,5 +1,4 @@
 func breadthFirstSearch(graph: Graph, source: Node) {
-  var seenNodes = [source]
   var queue = Queue<Node>()
   queue.enqueue(source)
 
@@ -9,9 +8,9 @@ func breadthFirstSearch(graph: Graph, source: Node) {
     let current = queue.dequeue()!
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
-      if !seenNodes.contains(neighborNode) {
+      if !neighborNode.visited {
         queue.enqueue(neighborNode)
-        seenNodes.append(neighborNode)
+        neighborNode.visited = true
         print(neighborNode.label)
       }
     }
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index d71cca15c..eea81bfd0 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -59,7 +59,6 @@ Simple implementation of breadth-first search using a queue:
 
 ```swift
 func breadthFirstSearch(graph: Graph, source: Node) {
-  var seenNodes = [source]
   var queue = Queue<Node>()
   queue.enqueue(source)
 
@@ -69,9 +68,9 @@ func breadthFirstSearch(graph: Graph, source: Node) {
     let current = queue.dequeue()!
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
-      if !seenNodes.contains(neighborNode) {
+      if !neighborNode.visited {
         queue.enqueue(neighborNode)
-        seenNodes.append(neighborNode)
+        neighborNode.visited = true
         print(neighborNode.label)
       }
     }

From 32ac84bcaf4d444d70c2a06562aaef1acec83f21 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 29 Feb 2016 22:28:07 +1300
Subject: [PATCH 0066/1679] BFS Added test project with implementation files.

---
 Breadth-First Search/BreadthFirstSearch.swift |  18 ++
 ...readthFirstSearchMinimumSpanningTree.swift |  23 ++
 .../BreadthFirstSearchShortestPath.swift      |  18 ++
 Breadth-First Search/Edge.swift               |   7 +
 Breadth-First Search/Graph.swift              |  52 ++++
 Breadth-First Search/Node.swift               |  32 ++
 Breadth-First Search/Queue.swift              |  31 ++
 .../Tests/BreadthFirstSearchTests.swift       |   8 +
 Breadth-First Search/Tests/Info.plist         |  24 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 288 ++++++++++++++++++
 10 files changed, 501 insertions(+)
 create mode 100644 Breadth-First Search/BreadthFirstSearch.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift
 create mode 100644 Breadth-First Search/BreadthFirstSearchShortestPath.swift
 create mode 100644 Breadth-First Search/Edge.swift
 create mode 100644 Breadth-First Search/Graph.swift
 create mode 100644 Breadth-First Search/Node.swift
 create mode 100644 Breadth-First Search/Queue.swift
 create mode 100755 Breadth-First Search/Tests/BreadthFirstSearchTests.swift
 create mode 100644 Breadth-First Search/Tests/Info.plist
 create mode 100644 Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj

diff --git a/Breadth-First Search/BreadthFirstSearch.swift b/Breadth-First Search/BreadthFirstSearch.swift
new file mode 100644
index 000000000..d58c2367c
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.swift	
@@ -0,0 +1,18 @@
+func breadthFirstSearch(graph: Graph, source: Node) {
+  var queue = Queue<Node>()
+  queue.enqueue(source)
+
+  print(source.label)
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.visited {
+        queue.enqueue(neighborNode)
+        neighborNode.visited = true
+        print(neighborNode.label)
+      }
+    }
+  }
+}
diff --git a/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift b/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift
new file mode 100644
index 000000000..9329a0d3c
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift	
@@ -0,0 +1,23 @@
+func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
+  let minimumSpanningTree = graph.duplicate()
+
+  var queue = Queue<Node>()
+  let sourceInMinimumSpanningTree = minimumSpanningTree.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInMinimumSpanningTree)
+  sourceInMinimumSpanningTree.visited = true
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.visited {
+        neighborNode.visited = true
+        queue.enqueue(neighborNode)
+      } else {
+        current.remove(edge)
+      }
+    }
+  }
+
+  return minimumSpanningTree
+}
diff --git a/Breadth-First Search/BreadthFirstSearchShortestPath.swift b/Breadth-First Search/BreadthFirstSearchShortestPath.swift
new file mode 100644
index 000000000..cb251cf0e
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearchShortestPath.swift	
@@ -0,0 +1,18 @@
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+  var queue = Queue<Node>()
+  queue.enqueue(source)
+  source.distance = 0
+
+  while !queue.isEmpty {
+    let current = queue.dequeue()!
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.hasDistance {
+        queue.enqueue(neighborNode)
+        neighborNode.distance = current.distance! + 1
+      }
+    }
+  }
+
+  print(graph.nodes)
+}
diff --git a/Breadth-First Search/Edge.swift b/Breadth-First Search/Edge.swift
new file mode 100644
index 000000000..8f2128ac5
--- /dev/null
+++ b/Breadth-First Search/Edge.swift	
@@ -0,0 +1,7 @@
+public class Edge {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
diff --git a/Breadth-First Search/Graph.swift b/Breadth-First Search/Graph.swift
new file mode 100644
index 000000000..6792ebf7b
--- /dev/null
+++ b/Breadth-First Search/Graph.swift	
@@ -0,0 +1,52 @@
+public class Graph : CustomStringConvertible {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    edge.neighbor = neighbor
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
diff --git a/Breadth-First Search/Node.swift b/Breadth-First Search/Node.swift
new file mode 100644
index 000000000..4c261ffca
--- /dev/null
+++ b/Breadth-First Search/Node.swift	
@@ -0,0 +1,32 @@
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label
+}
diff --git a/Breadth-First Search/Queue.swift b/Breadth-First Search/Queue.swift
new file mode 100644
index 000000000..bf462bbdd
--- /dev/null
+++ b/Breadth-First Search/Queue.swift	
@@ -0,0 +1,31 @@
+public struct Queue<T> {
+  private var array: [T]
+
+  public init() {
+    array = []
+  }
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeFirst()
+    }
+  }
+
+  public func peek() -> T? {
+    return array.first
+  }
+}
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift
new file mode 100755
index 000000000..c68d369dc
--- /dev/null
+++ b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
@@ -0,0 +1,8 @@
+import Foundation
+import XCTest
+
+class QueueTest: XCTestCase {
+  func testFail() {
+    XCTAssertFalse(true)
+  }
+}
diff --git a/Breadth-First Search/Tests/Info.plist b/Breadth-First Search/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Breadth-First Search/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..9d32cfdaa
--- /dev/null
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,288 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		83F9C9681C84437C00B3A87F /* BreadthFirstSearch.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */; };
+		83F9C9691C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */; };
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From aa8e35292dd7b1bd10694cfb54adbb0a74c94cc8 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 29 Feb 2016 22:53:59 +1300
Subject: [PATCH 0067/1679] BFS Changed simple example to return array instead
 of printing explored nodes to allow for testing. Added tests for simple
 example.

---
 .../Contents.swift                            | 13 ++-
 Breadth-First Search/BreadthFirstSearch.swift | 12 ++-
 Breadth-First Search/README.markdown          | 13 ++-
 .../Tests/BreadthFirstSearchTests.swift       | 81 ++++++++++++++++++-
 4 files changed, 105 insertions(+), 14 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 7cb9122e3..44a6a284e 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,8 +1,9 @@
-func breadthFirstSearch(graph: Graph, source: Node) {
+func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
 
-  print(source.label)
+  var nodesExplored = [source.label]
+  source.visited = true
 
   while !queue.isEmpty {
     let current = queue.dequeue()!
@@ -11,10 +12,13 @@ func breadthFirstSearch(graph: Graph, source: Node) {
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
         neighborNode.visited = true
-        print(neighborNode.label)
+
+        nodesExplored.append(neighborNode.label)
       }
     }
   }
+
+  return nodesExplored
 }
 
 /*:
@@ -41,4 +45,5 @@ graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
 
-breadthFirstSearch(graph, source: nodeA)
+let nodesExplored = breadthFirstSearch(graph, source: nodeA)
+print(nodesExplored)
diff --git a/Breadth-First Search/BreadthFirstSearch.swift b/Breadth-First Search/BreadthFirstSearch.swift
index d58c2367c..eb9fe30a6 100644
--- a/Breadth-First Search/BreadthFirstSearch.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.swift	
@@ -1,9 +1,10 @@
-func breadthFirstSearch(graph: Graph, source: Node) {
+func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
 
-  print(source.label)
-
+  var nodesExplored = [source.label]
+  source.visited = true
+  
   while !queue.isEmpty {
     let current = queue.dequeue()!
     for edge in current.neighbors {
@@ -11,8 +12,11 @@ func breadthFirstSearch(graph: Graph, source: Node) {
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
         neighborNode.visited = true
-        print(neighborNode.label)
+
+        nodesExplored.append(neighborNode.label)
       }
     }
   }
+
+  return nodesExplored
 }
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index eea81bfd0..9971cd081 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -58,11 +58,12 @@ The queue is now empty which means all nodes have been explored.
 Simple implementation of breadth-first search using a queue:
 
 ```swift
-func breadthFirstSearch(graph: Graph, source: Node) {
+func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
 
-  print(source.label)
+  var nodesExplored = [source.label]
+  source.visited = true
 
   while !queue.isEmpty {
     let current = queue.dequeue()!
@@ -71,10 +72,13 @@ func breadthFirstSearch(graph: Graph, source: Node) {
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
         neighborNode.visited = true
-        print(neighborNode.label)
+
+        nodesExplored.append(neighborNode.label)
       }
     }
   }
+
+  return nodesExplored
 }
 ```
 
@@ -99,7 +103,8 @@ graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
-breadthFirstSearch(graph, source: nodeA) // This will output: a, b, c, d, e, f, g, h
+let nodesExplored = breadthFirstSearch(graph, source: nodeA)
+print(nodesExplored) // This will output: ["a", "b", "c", "d", "e", "f", "g", "h"]
 ```
 
 ## Applications
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift
index c68d369dc..86487d8b7 100755
--- a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
+++ b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
@@ -2,7 +2,84 @@ import Foundation
 import XCTest
 
 class QueueTest: XCTestCase {
-  func testFail() {
-    XCTAssertFalse(true)
+
+  func testExploringTree() {
+    let tree = Graph()
+    let nodeA = tree.addNode("a")
+    let nodeB = tree.addNode("b")
+    let nodeC = tree.addNode("c")
+    let nodeD = tree.addNode("d")
+    let nodeE = tree.addNode("e")
+    let nodeF = tree.addNode("f")
+    let nodeG = tree.addNode("g")
+    let nodeH = tree.addNode("h")
+    tree.addEdge(nodeA, neighbor: nodeB)
+    tree.addEdge(nodeA, neighbor: nodeC)
+    tree.addEdge(nodeB, neighbor: nodeD)
+    tree.addEdge(nodeB, neighbor: nodeE)
+    tree.addEdge(nodeC, neighbor: nodeF)
+    tree.addEdge(nodeC, neighbor: nodeG)
+    tree.addEdge(nodeE, neighbor: nodeH)
+
+    let nodesExplored = breadthFirstSearch(tree, source: nodeA)
+
+    XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h"])
+  }
+
+  func testExploringGraph() {
+    let graph = Graph()
+
+    let nodeA = graph.addNode("a")
+    let nodeB = graph.addNode("b")
+    let nodeC = graph.addNode("c")
+    let nodeD = graph.addNode("d")
+    let nodeE = graph.addNode("e")
+    let nodeF = graph.addNode("f")
+    let nodeG = graph.addNode("g")
+    let nodeH = graph.addNode("h")
+    let nodeI = graph.addNode("i")
+
+    graph.addEdge(nodeA, neighbor: nodeB)
+    graph.addEdge(nodeA, neighbor: nodeH)
+    graph.addEdge(nodeB, neighbor: nodeA)
+    graph.addEdge(nodeB, neighbor: nodeC)
+    graph.addEdge(nodeB, neighbor: nodeH)
+    graph.addEdge(nodeC, neighbor: nodeB)
+    graph.addEdge(nodeC, neighbor: nodeD)
+    graph.addEdge(nodeC, neighbor: nodeF)
+    graph.addEdge(nodeC, neighbor: nodeI)
+    graph.addEdge(nodeD, neighbor: nodeC)
+    graph.addEdge(nodeD, neighbor: nodeE)
+    graph.addEdge(nodeD, neighbor: nodeF)
+    graph.addEdge(nodeE, neighbor: nodeD)
+    graph.addEdge(nodeE, neighbor: nodeF)
+    graph.addEdge(nodeF, neighbor: nodeC)
+    graph.addEdge(nodeF, neighbor: nodeD)
+    graph.addEdge(nodeF, neighbor: nodeE)
+    graph.addEdge(nodeF, neighbor: nodeG)
+    graph.addEdge(nodeG, neighbor: nodeF)
+    graph.addEdge(nodeG, neighbor: nodeH)
+    graph.addEdge(nodeG, neighbor: nodeI)
+    graph.addEdge(nodeH, neighbor: nodeA)
+    graph.addEdge(nodeH, neighbor: nodeB)
+    graph.addEdge(nodeH, neighbor: nodeG)
+    graph.addEdge(nodeH, neighbor: nodeI)
+    graph.addEdge(nodeI, neighbor: nodeC)
+    graph.addEdge(nodeI, neighbor: nodeG)
+    graph.addEdge(nodeI, neighbor: nodeH)
+
+    let nodesExplored = breadthFirstSearch(graph, source: nodeA)
+
+    XCTAssertEqual(nodesExplored, ["a", "b", "h", "c", "g", "i", "d", "f", "e"])
+
+  }
+
+  func testExploringGraphWithASingleNode() {
+    let graph = Graph()
+    let node = graph.addNode("a")
+
+    let nodesExplored = breadthFirstSearch(graph, source: node)
+
+    XCTAssertEqual(nodesExplored, ["a"])
   }
 }

From edf5673f3b3a528b1d3005bd67c959acf674343e Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 29 Feb 2016 15:58:01 +0530
Subject: [PATCH 0068/1679] Algorithm explanation

---
 Shunting Yard/README.markdown | 108 ++++++++++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)
 create mode 100644 Shunting Yard/README.markdown

diff --git a/Shunting Yard/README.markdown b/Shunting Yard/README.markdown
new file mode 100644
index 000000000..92555de9a
--- /dev/null
+++ b/Shunting Yard/README.markdown	
@@ -0,0 +1,108 @@
+# Shunting Yard Algorithm
+
+Any mathematical expression that we write is expressed in a notation known as Infix Notation.
+
+For example:
+
+A + B * C
+
+In the above expression the operator is placed between operands hence the expression is said to be in Infix form.
+If you think about it any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
+
+Now, think about the way the above expression is evaluated, you would first multiply B and C then add the result to A. This is because multiplication has
+higher precedence than addition. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. If you were to 
+write an algorithm than parsed and evaluated the infix notation you'll soon realize that it's a tedious process. You'd have to parse the expression
+multiple times to know what operation to perform first. As the number of operators increase so does the complexity.
+
+##  Postfix notations / Reverse Polish Notation 
+
+An expression when represented in postfix form will not have any brackets and neither will you have to worry about scanning for operator precedence. This makes it easy for the computer to evaluate
+expressions since the order in which the operator need to be applied is fixed.
+
+For example:
+
+**A B C * +**
+
+The above is the postfix representation of the example in the previous section. The operators come after the corresponding operands.
+
+### Evaluating a postfix expression
+
+A stack is used to evaluate a postfix expression. Here is the pseudocode:
+
+1. read postfix expression token by token
+2.   if the token is an operand, push it
+     into the stack
+3.   if the token is a binary operator,
+3.1    pop the two top most operands
+       from the stack
+3.2    apply the binary operator with the
+       two operands
+3.3    push the result into the stack
+4. finally, the value of the whole postfix
+   expression remains in the stack
+
+Using the above psuedocode the evaluation on the stack would be as follows:
+
+| Expression    | Stack   |
+| ------------- | --------|
+| A B C * +     |         |
+| B C * +       | A       |
+| C * +         | A, B    |
+| * +           | A, B, C |
+| +             | A, D    |
+|               | E       |
+
+Where **D = B * C** and **E = A + D.**
+
+As seen above a postfix operation is relatively easy to evaluate as the order in which the operators need to be applied is predecided.
+
+## Shunting yard algorithm
+
+The Shunting yard algorithm was invented by Edsger Dijkstra to convert an infix expression to postfix. Many calculators use this algorithm to convert the expression being entered to postfix form.
+
+Here is the psedocode of the algorithm:
+
+1. For all the input tokens
+    1. Read the next token
+    2. If token is an operator (x)
+        1. While there is an operator (y) at the top of the operators stack and either (x) is left-associative and its precedence is less or equal to that of (y), or (x) is right-associative and its precedence is less than (y)
+            1. Pop (y) from the stack
+            2. Add (y) output buffer
+        2. Push (x) on the stack
+    3. Else If token is left parenthesis, then push it on the stack
+    4. Else If token is a right parenthesis
+        1. Until the top token (from the stack) is left parenthesis, pop from the stack to the output buffer
+        2. Also pop the left parenthesis but don’t include it in the output buffer
+    7. Else add token to output buffer
+2. While there are still operator tokens in the stack, pop them to output
+
+### How does it work
+
+Let's take a small example and see how the psuedocode works. 
+
+**4 + 4 * 2 / ( 1 - 5 )**
+
+| Operator | Precedence   | Associativity   |
+| ---------| -------------| ----------------|
+| ^        | 10           | Right           |
+| *        | 5            | Left            |
+| /        | 5            | Left            |
+| +        | 0            | Left            |
+| -        | 0            | Left            |
+
+The above table describes the precedence and the associativity for each operator. The same values are used in the algorithm.
+
+| Token | Action                                      | Output            | Operator stack |
+|-------|---------------------------------------------|-------------------|----------------|
+| 3     | Add token to output                         | 4                 |                |
+| +     | Push token to stack                         | 4                 | +              |
+| 4     | Add token to output                         | 4 4               | +              |
+| *     | Push token to stack                         | 4 4               | * +            |
+| 2     | Add token to output                         | 4 4 2             | * +            |
+| /     | * Pop stack to output * Push token to stack | 4 4 2 *           | / +            |
+| (     | Push token to stack                         | 4 4 2 *           | ( / +          |
+| 1     | Add token to output                         | 4 4 2 * 1         | ( / +          |
+| -     | Push token to stack                         | 4 4 2 * 1         | - ( / +        |
+| 5     | Add token to output                         | 4 4 2 * 1 5       | - ( / +        |
+| )     | * Pop stack to output * Pop stack           | 4 4 2 * 1 5 -     | /  +           |
+| end   | Pop entire stack to output                  | 4 4 2 * 1 5 - / + |                |
\ No newline at end of file

From abba1fa41d862d7e759a4d2865df97d0c6e5f880 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 29 Feb 2016 23:28:50 +1300
Subject: [PATCH 0069/1679] BFS Added tests for minimum spanning tree.

---
 .../Sources/Edge.swift                        |   6 +-
 .../Sources/Graph.swift                       |   6 +-
 .../Sources/Node.swift                        |   4 +-
 Breadth-First Search/Edge.swift               |   6 +-
 Breadth-First Search/Graph.swift              |   6 +-
 Breadth-First Search/Node.swift               |   2 +-
 ...hFirstSearchMinimumSpanningTreeTests.swift | 107 ++++++++++++++++++
 .../Tests/BreadthFirstSearchTests.swift       |   4 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     |   4 +
 9 files changed, 136 insertions(+), 9 deletions(-)
 create mode 100644 Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift
index 8f2128ac5..3937a2cc7 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
@@ -1,7 +1,11 @@
-public class Edge {
+public class Edge : Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
     self.neighbor = neighbor
   }
 }
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
index 6792ebf7b..181af9e85 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -1,4 +1,4 @@
-public class Graph : CustomStringConvertible {
+public class Graph : CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -50,3 +50,7 @@ public class Graph : CustomStringConvertible {
     return duplicated
   }
 }
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift
index 4c261ffca..9d8435ffa 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
@@ -1,6 +1,6 @@
 public class Node : CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-  
+
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
@@ -28,5 +28,5 @@ public class Node : CustomStringConvertible, Equatable {
 }
 
 public func ==(lhs: Node, rhs: Node) -> Bool {
-  return lhs.label == rhs.label
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Breadth-First Search/Edge.swift b/Breadth-First Search/Edge.swift
index 8f2128ac5..3937a2cc7 100644
--- a/Breadth-First Search/Edge.swift	
+++ b/Breadth-First Search/Edge.swift	
@@ -1,7 +1,11 @@
-public class Edge {
+public class Edge : Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
     self.neighbor = neighbor
   }
 }
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
diff --git a/Breadth-First Search/Graph.swift b/Breadth-First Search/Graph.swift
index 6792ebf7b..181af9e85 100644
--- a/Breadth-First Search/Graph.swift	
+++ b/Breadth-First Search/Graph.swift	
@@ -1,4 +1,4 @@
-public class Graph : CustomStringConvertible {
+public class Graph : CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -50,3 +50,7 @@ public class Graph : CustomStringConvertible {
     return duplicated
   }
 }
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Breadth-First Search/Node.swift b/Breadth-First Search/Node.swift
index 4c261ffca..000fd78f6 100644
--- a/Breadth-First Search/Node.swift	
+++ b/Breadth-First Search/Node.swift	
@@ -28,5 +28,5 @@ public class Node : CustomStringConvertible, Equatable {
 }
 
 public func ==(lhs: Node, rhs: Node) -> Bool {
-  return lhs.label == rhs.label
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift b/Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift
new file mode 100644
index 000000000..527387062
--- /dev/null
+++ b/Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift	
@@ -0,0 +1,107 @@
+import XCTest
+
+class BreadthFirstSearchMinimumSpanningTreeTests: XCTestCase {
+
+  func testMinimumSpanningTreeReturnsSameTreeWhenGivenTree() {
+    let tree = Graph()
+    let nodeA = tree.addNode("a")
+    let nodeB = tree.addNode("b")
+    let nodeC = tree.addNode("c")
+    let nodeD = tree.addNode("d")
+    let nodeE = tree.addNode("e")
+    let nodeF = tree.addNode("f")
+    let nodeG = tree.addNode("g")
+    let nodeH = tree.addNode("h")
+    tree.addEdge(nodeA, neighbor: nodeB)
+    tree.addEdge(nodeA, neighbor: nodeC)
+    tree.addEdge(nodeB, neighbor: nodeD)
+    tree.addEdge(nodeB, neighbor: nodeE)
+    tree.addEdge(nodeC, neighbor: nodeF)
+    tree.addEdge(nodeC, neighbor: nodeG)
+    tree.addEdge(nodeE, neighbor: nodeH)
+
+    let minimumSpanningTree = breadthFirstSearchMinimumSpanningTree(tree, source: nodeA)
+
+    XCTAssertEqual(minimumSpanningTree, tree)
+  }
+
+  func testMinimumSpanningTreeReturnsMinimumSpanningTreeWhenGivenGraph() {
+    let graphAndSourceNode = createGraph()
+    let expectedMinimumSpanningTree = createMinimumSpanningTree()
+
+    let actualMinimumSpanningTree = breadthFirstSearchMinimumSpanningTree(graphAndSourceNode.graph,
+                                                                  source: graphAndSourceNode.source)
+
+    XCTAssertEqual(actualMinimumSpanningTree, expectedMinimumSpanningTree)
+  }
+
+  func createGraph() -> (graph: Graph, source: Node) {
+    let graph = Graph()
+
+    let nodeA = graph.addNode("a")
+    let nodeB = graph.addNode("b")
+    let nodeC = graph.addNode("c")
+    let nodeD = graph.addNode("d")
+    let nodeE = graph.addNode("e")
+    let nodeF = graph.addNode("f")
+    let nodeG = graph.addNode("g")
+    let nodeH = graph.addNode("h")
+    let nodeI = graph.addNode("i")
+
+    graph.addEdge(nodeA, neighbor: nodeB)
+    graph.addEdge(nodeA, neighbor: nodeH)
+    graph.addEdge(nodeB, neighbor: nodeA)
+    graph.addEdge(nodeB, neighbor: nodeC)
+    graph.addEdge(nodeB, neighbor: nodeH)
+    graph.addEdge(nodeC, neighbor: nodeB)
+    graph.addEdge(nodeC, neighbor: nodeD)
+    graph.addEdge(nodeC, neighbor: nodeF)
+    graph.addEdge(nodeC, neighbor: nodeI)
+    graph.addEdge(nodeD, neighbor: nodeC)
+    graph.addEdge(nodeD, neighbor: nodeE)
+    graph.addEdge(nodeD, neighbor: nodeF)
+    graph.addEdge(nodeE, neighbor: nodeD)
+    graph.addEdge(nodeE, neighbor: nodeF)
+    graph.addEdge(nodeF, neighbor: nodeC)
+    graph.addEdge(nodeF, neighbor: nodeD)
+    graph.addEdge(nodeF, neighbor: nodeE)
+    graph.addEdge(nodeF, neighbor: nodeG)
+    graph.addEdge(nodeG, neighbor: nodeF)
+    graph.addEdge(nodeG, neighbor: nodeH)
+    graph.addEdge(nodeG, neighbor: nodeI)
+    graph.addEdge(nodeH, neighbor: nodeA)
+    graph.addEdge(nodeH, neighbor: nodeB)
+    graph.addEdge(nodeH, neighbor: nodeG)
+    graph.addEdge(nodeH, neighbor: nodeI)
+    graph.addEdge(nodeI, neighbor: nodeC)
+    graph.addEdge(nodeI, neighbor: nodeG)
+    graph.addEdge(nodeI, neighbor: nodeH)
+
+    return (graph, nodeA)
+  }
+
+  func createMinimumSpanningTree() -> Graph {
+    let minimumSpanningTree = Graph()
+
+    let nodeA = minimumSpanningTree.addNode("a")
+    let nodeB = minimumSpanningTree.addNode("b")
+    let nodeC = minimumSpanningTree.addNode("c")
+    let nodeD = minimumSpanningTree.addNode("d")
+    let nodeE = minimumSpanningTree.addNode("e")
+    let nodeF = minimumSpanningTree.addNode("f")
+    let nodeG = minimumSpanningTree.addNode("g")
+    let nodeH = minimumSpanningTree.addNode("h")
+    let nodeI = minimumSpanningTree.addNode("i")
+
+    minimumSpanningTree.addEdge(nodeA, neighbor: nodeB)
+    minimumSpanningTree.addEdge(nodeA, neighbor: nodeH)
+    minimumSpanningTree.addEdge(nodeB, neighbor: nodeC)
+    minimumSpanningTree.addEdge(nodeH, neighbor: nodeG)
+    minimumSpanningTree.addEdge(nodeH, neighbor: nodeI)
+    minimumSpanningTree.addEdge(nodeC, neighbor: nodeD)
+    minimumSpanningTree.addEdge(nodeC, neighbor: nodeF)
+    minimumSpanningTree.addEdge(nodeD, neighbor: nodeE)
+
+    return minimumSpanningTree
+  }
+}
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift
index 86487d8b7..6c0d382d9 100755
--- a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
+++ b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
@@ -1,7 +1,6 @@
-import Foundation
 import XCTest
 
-class QueueTest: XCTestCase {
+class BreadthFirstSearchTests: XCTestCase {
 
   func testExploringTree() {
     let tree = Graph()
@@ -83,3 +82,4 @@ class QueueTest: XCTestCase {
     XCTAssertEqual(nodesExplored, ["a"])
   }
 }
+
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 9d32cfdaa..b0e34b310 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -7,6 +7,7 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
+		83AACB421C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */; };
 		83F9C9681C84437C00B3A87F /* BreadthFirstSearch.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */; };
 		83F9C9691C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */; };
 		83F9C96A1C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */; };
@@ -20,6 +21,7 @@
 /* Begin PBXFileReference section */
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BreadthFirstSearchMinimumSpanningTreeTests.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearch.swift; path = ../BreadthFirstSearch.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearchMinimumSpanningTree.swift; path = ../BreadthFirstSearchMinimumSpanningTree.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearchShortestPath.swift; path = ../BreadthFirstSearchShortestPath.swift; sourceTree = SOURCE_ROOT; };
@@ -69,6 +71,7 @@
 				83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */,
 				83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
+				83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */,
 			);
 			name = Tests;
 			path = TestsTests;
@@ -142,6 +145,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				83AACB421C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift in Sources */,
 				83F9C9721C84449D00B3A87F /* Graph.swift in Sources */,
 				83F9C9691C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift in Sources */,
 				83F9C9681C84437C00B3A87F /* BreadthFirstSearch.swift in Sources */,

From ea0df5b52394bd63d8d4b1440a4f39816a12ae4a Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 29 Feb 2016 16:07:54 +0530
Subject: [PATCH 0070/1679] Fixed some typos

---
 Shunting Yard/README.markdown | 30 +++++++++++++++++-------------
 1 file changed, 17 insertions(+), 13 deletions(-)

diff --git a/Shunting Yard/README.markdown b/Shunting Yard/README.markdown
index 92555de9a..3668888b2 100644
--- a/Shunting Yard/README.markdown	
+++ b/Shunting Yard/README.markdown	
@@ -4,14 +4,14 @@ Any mathematical expression that we write is expressed in a notation known as In
 
 For example:
 
-A + B * C
+**A + B * C**
 
 In the above expression the operator is placed between operands hence the expression is said to be in Infix form.
 If you think about it any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
 
 Now, think about the way the above expression is evaluated, you would first multiply B and C then add the result to A. This is because multiplication has
 higher precedence than addition. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. If you were to 
-write an algorithm than parsed and evaluated the infix notation you'll soon realize that it's a tedious process. You'd have to parse the expression
+write an algorithm that parsed and evaluated the infix notation you will realize that it's a tedious process. You'd have to parse the expression
 multiple times to know what operation to perform first. As the number of operators increase so does the complexity.
 
 ##  Postfix notations / Reverse Polish Notation 
@@ -29,16 +29,13 @@ The above is the postfix representation of the example in the previous section.
 
 A stack is used to evaluate a postfix expression. Here is the pseudocode:
 
-1. read postfix expression token by token
-2.   if the token is an operand, push it
-     into the stack
-3.   if the token is a binary operator,
-3.1    pop the two top most operands
-       from the stack
-3.2    apply the binary operator with the
-       two operands
-3.3    push the result into the stack
-4. finally, the value of the whole postfix
+1. Read postfix expression token by token
+2. If the token is an operand, push it into the stack
+3. If the token is a binary operator,
+    1. Pop the two top most operands from the stack
+    2. Apply the binary operator with thetwo operands
+    3. Push the result into the stack
+4. Finally, the value of the whole postfix
    expression remains in the stack
 
 Using the above psuedocode the evaluation on the stack would be as follows:
@@ -105,4 +102,11 @@ The above table describes the precedence and the associativity for each operator
 | -     | Push token to stack                         | 4 4 2 * 1         | - ( / +        |
 | 5     | Add token to output                         | 4 4 2 * 1 5       | - ( / +        |
 | )     | * Pop stack to output * Pop stack           | 4 4 2 * 1 5 -     | /  +           |
-| end   | Pop entire stack to output                  | 4 4 2 * 1 5 - / + |                |
\ No newline at end of file
+| end   | Pop entire stack to output                  | 4 4 2 * 1 5 - / + |                |
+
+
+# See Also
+
+[Shunting yard algorithm on Wikipedia](https://en.wikipedia.org/wiki/Shunting-yard_algorithm)
+
+*Written for the Swift Algorithm Club by [Ali Hafizji](http://www.github.com/aliHafizji)*
\ No newline at end of file

From b6ab5205d84ed700e6fcd191cb71f1d0f005468a Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Mon, 29 Feb 2016 23:46:07 +1300
Subject: [PATCH 0071/1679] BFS Added tests for shortest path

---
 .../Contents.swift                            | 15 ++--
 .../BreadthFirstSearchShortestPath.swift      | 11 ++-
 Breadth-First Search/README.markdown          | 14 +--
 .../BreadthFirstSearchShortestPathTests.swift | 89 +++++++++++++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++-
 5 files changed, 121 insertions(+), 18 deletions(-)
 create mode 100644 Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index 175821efc..28cdc6093 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,10 @@
-func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
+  let shortestPathGraph = graph.duplicate()
+
   var queue = Queue<Node>()
-  queue.enqueue(source)
-  source.distance = 0
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInShortestPathsGraph)
+  sourceInShortestPathsGraph.distance = 0
 
   while !queue.isEmpty {
     let current = queue.dequeue()!
@@ -14,9 +17,8 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
     }
   }
 
-  print(graph.nodes)
+  return shortestPathGraph
 }
-
 /*:
 ![Animated example of a breadth-first search](Animated_BFS.gif)
 */
@@ -40,4 +42,5 @@ graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
-breadthFirstSearchShortestPath(graph, source: nodeA)
+let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
+print(shortestPathGraph.nodes)
diff --git a/Breadth-First Search/BreadthFirstSearchShortestPath.swift b/Breadth-First Search/BreadthFirstSearchShortestPath.swift
index cb251cf0e..2e5a9c1d0 100644
--- a/Breadth-First Search/BreadthFirstSearchShortestPath.swift	
+++ b/Breadth-First Search/BreadthFirstSearchShortestPath.swift	
@@ -1,7 +1,10 @@
-func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
+  let shortestPathGraph = graph.duplicate()
+
   var queue = Queue<Node>()
-  queue.enqueue(source)
-  source.distance = 0
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInShortestPathsGraph)
+  sourceInShortestPathsGraph.distance = 0
 
   while !queue.isEmpty {
     let current = queue.dequeue()!
@@ -14,5 +17,5 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
     }
   }
 
-  print(graph.nodes)
+  return shortestPathGraph
 }
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 9971cd081..8d3266d39 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -145,10 +145,13 @@ Continue until the queue is empty to calculate the shortest path to all other no
 
 Here's the code:
 ```swift
-func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
+  let shortestPathGraph = graph.duplicate()
+
   var queue = Queue<Node>()
-  queue.enqueue(source)
-  source.distance = 0
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInShortestPathsGraph)
+  sourceInShortestPathsGraph.distance = 0
 
   while !queue.isEmpty {
     let current = queue.dequeue()!
@@ -161,13 +164,14 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) {
     }
   }
 
-  print(graph.nodes)
+  return shortestPathGraph
 }
 ```
 
 Put this code in a playground and test it like so:
 ```swift
-breadthFirstSearchShortestPath(graph, source: nodeA)
+let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
+print(shortestPathGraph.nodes)
 
 // This will output:
 // Node(label: a, distance: 0), Node(label: b, distance: 1), Node(label: c, distance: 1),
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift b/Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift
new file mode 100644
index 000000000..b13fac2d1
--- /dev/null
+++ b/Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift	
@@ -0,0 +1,89 @@
+import XCTest
+
+class BreadthFirstSearchShortestPathTests: XCTestCase {
+
+  func testShortestPathWhenGivenTree() {
+    let tree = Graph()
+    let nodeA = tree.addNode("a")
+    let nodeB = tree.addNode("b")
+    let nodeC = tree.addNode("c")
+    let nodeD = tree.addNode("d")
+    let nodeE = tree.addNode("e")
+    let nodeF = tree.addNode("f")
+    let nodeG = tree.addNode("g")
+    let nodeH = tree.addNode("h")
+    tree.addEdge(nodeA, neighbor: nodeB)
+    tree.addEdge(nodeA, neighbor: nodeC)
+    tree.addEdge(nodeB, neighbor: nodeD)
+    tree.addEdge(nodeB, neighbor: nodeE)
+    tree.addEdge(nodeC, neighbor: nodeF)
+    tree.addEdge(nodeC, neighbor: nodeG)
+    tree.addEdge(nodeE, neighbor: nodeH)
+
+    let shortestPaths = breadthFirstSearchShortestPath(tree, source: nodeA)
+
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeA.label).distance, 0)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeB.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeC.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeD.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeE.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeF.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeG.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeH.label).distance, 3)
+  }
+
+  func testShortestPathWhenGivenGraph() {
+    let graph = Graph()
+
+    let nodeA = graph.addNode("a")
+    let nodeB = graph.addNode("b")
+    let nodeC = graph.addNode("c")
+    let nodeD = graph.addNode("d")
+    let nodeE = graph.addNode("e")
+    let nodeF = graph.addNode("f")
+    let nodeG = graph.addNode("g")
+    let nodeH = graph.addNode("h")
+    let nodeI = graph.addNode("i")
+
+    graph.addEdge(nodeA, neighbor: nodeB)
+    graph.addEdge(nodeA, neighbor: nodeH)
+    graph.addEdge(nodeB, neighbor: nodeA)
+    graph.addEdge(nodeB, neighbor: nodeC)
+    graph.addEdge(nodeB, neighbor: nodeH)
+    graph.addEdge(nodeC, neighbor: nodeB)
+    graph.addEdge(nodeC, neighbor: nodeD)
+    graph.addEdge(nodeC, neighbor: nodeF)
+    graph.addEdge(nodeC, neighbor: nodeI)
+    graph.addEdge(nodeD, neighbor: nodeC)
+    graph.addEdge(nodeD, neighbor: nodeE)
+    graph.addEdge(nodeD, neighbor: nodeF)
+    graph.addEdge(nodeE, neighbor: nodeD)
+    graph.addEdge(nodeE, neighbor: nodeF)
+    graph.addEdge(nodeF, neighbor: nodeC)
+    graph.addEdge(nodeF, neighbor: nodeD)
+    graph.addEdge(nodeF, neighbor: nodeE)
+    graph.addEdge(nodeF, neighbor: nodeG)
+    graph.addEdge(nodeG, neighbor: nodeF)
+    graph.addEdge(nodeG, neighbor: nodeH)
+    graph.addEdge(nodeG, neighbor: nodeI)
+    graph.addEdge(nodeH, neighbor: nodeA)
+    graph.addEdge(nodeH, neighbor: nodeB)
+    graph.addEdge(nodeH, neighbor: nodeG)
+    graph.addEdge(nodeH, neighbor: nodeI)
+    graph.addEdge(nodeI, neighbor: nodeC)
+    graph.addEdge(nodeI, neighbor: nodeG)
+    graph.addEdge(nodeI, neighbor: nodeH)
+
+    let shortestPaths = breadthFirstSearchShortestPath(graph, source: nodeA)
+
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeA.label).distance, 0)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeB.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeC.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeD.label).distance, 3)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeE.label).distance, 4)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeF.label).distance, 3)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeG.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeH.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeI.label).distance, 2)
+  }
+}
\ No newline at end of file
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index b0e34b310..8946ba1a6 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -8,6 +8,7 @@
 
 /* Begin PBXBuildFile section */
 		83AACB421C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */; };
+		83AACB441C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83AACB431C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift */; };
 		83F9C9681C84437C00B3A87F /* BreadthFirstSearch.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */; };
 		83F9C9691C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */; };
 		83F9C96A1C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */; };
@@ -22,6 +23,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BreadthFirstSearchMinimumSpanningTreeTests.swift; sourceTree = SOURCE_ROOT; };
+		83AACB431C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BreadthFirstSearchShortestPathTests.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearch.swift; path = ../BreadthFirstSearch.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearchMinimumSpanningTree.swift; path = ../BreadthFirstSearchMinimumSpanningTree.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearchShortestPath.swift; path = ../BreadthFirstSearchShortestPath.swift; sourceTree = SOURCE_ROOT; };
@@ -66,12 +68,13 @@
 				83F9C96E1C84449D00B3A87F /* Graph.swift */,
 				83F9C96F1C84449D00B3A87F /* Node.swift */,
 				83F9C9701C84449D00B3A87F /* Queue.swift */,
-				83F9C96B1C8443E800B3A87F /* BreadthFirstSearchTests.swift */,
 				83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */,
-				83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */,
 				83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */,
-				7B2BBC941C779E7B0067B71D /* Info.plist */,
+				83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */,
+				83F9C96B1C8443E800B3A87F /* BreadthFirstSearchTests.swift */,
+				83AACB431C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift */,
 				83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
 			name = Tests;
 			path = TestsTests;
@@ -145,6 +148,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				83AACB441C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift in Sources */,
 				83AACB421C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift in Sources */,
 				83F9C9721C84449D00B3A87F /* Graph.swift in Sources */,
 				83F9C9691C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift in Sources */,

From fa073ec9da6ec25430e99759d98af316f7aea7d1 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Mon, 29 Feb 2016 19:08:04 +0100
Subject: [PATCH 0072/1679] Small tweaks to text

---
 .../Contents.swift                            |   1 -
 Breadth-First Search/BreadthFirstSearch.swift |   1 -
 Breadth-First Search/README.markdown          | 145 ++++++++++++------
 3 files changed, 99 insertions(+), 48 deletions(-)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 44a6a284e..ed655b591 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -12,7 +12,6 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
         neighborNode.visited = true
-
         nodesExplored.append(neighborNode.label)
       }
     }
diff --git a/Breadth-First Search/BreadthFirstSearch.swift b/Breadth-First Search/BreadthFirstSearch.swift
index eb9fe30a6..31bb1c594 100644
--- a/Breadth-First Search/BreadthFirstSearch.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.swift	
@@ -12,7 +12,6 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
         neighborNode.visited = true
-
         nodesExplored.append(neighborNode.label)
       }
     }
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 8d3266d39..584b37c1d 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,6 +1,6 @@
 # Breadth-First Search
 
-Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores the neighbor nodes first, before moving to the next level neighbors.
+Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores the immediate neighbor nodes first, before moving to the next level neighbors.
 
 ## Animated example
 
@@ -9,49 +9,67 @@ Breadth-first search (BFS) is an algorithm for traversing or searching [tree](..
 Let's follow the animated example by using a [queue](../Queue/).
 
 Start with the source node ``a`` and add it to a queue.
+
 ```swift
 queue.enqueue(a)
 ```
-The queue is now ``[ a ]``. Dequeue ``a`` and enqueue the neighbor nodes ``b`` and ``c``.
+
+The queue is now ``[ a ]``. Dequeue ``a`` and enqueue its two neighbor nodes ``b`` and ``c``.
+
 ```swift
-queue.dequeue(a)
+queue.dequeue()   // a
 queue.enqueue(b)
 queue.enqueue(c)
 ```
-The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue the neighbor nodes ``d`` and ``e``.
+
+The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue `b`'s neighbor nodes ``d`` and ``e``.
+
 ```swift
-queue.dequeue(b)
+queue.dequeue()   // b
 queue.enqueue(d)
 queue.enqueue(e)
 ```
-The queue is now ``[ c, d, e ]``. Dequeue ``c`` and enqueue the neighbor nodes ``f`` and ``g``.
+
+The queue is now ``[ c, d, e ]``. Dequeue ``c`` and enqueue `c`'s neighbor nodes ``f`` and ``g``.
+
 ```swift
-queue.dequeue(c)
+queue.dequeue()   // c
 queue.enqueue(f)
 queue.enqueue(g)
 ```
+
 The queue is now ``[ d, e, f, g ]``. Dequeue ``d`` which has no neighbor nodes.
+
 ```swift
-queue.dequeue(d)
+queue.dequeue()   // d
 ```
-The queue is now ``[ e, f, g ]``. Dequeue ``e`` and enqueue the single neighbor node ``h``.
+
+The queue is now ``[ e, f, g ]``. Dequeue ``e`` and enqueue its single neighbor node ``h``.
+
 ```swift
-queue.dequeue(e)
+queue.dequeue()   // e
 queue.enqueue(h)
 ```
+
 The queue is now ``[ f, g, h ]``. Dequeue ``f`` which has no neighbor nodes.
+
 ```swift
-queue.dequeue(f)
+queue.dequeue()   // f
 ```
+
 The queue is now ``[ g, h ]``. Dequeue ``g`` which has no neighbor nodes.
+
 ```swift
-queue.dequeue(g)
+queue.dequeue()   // g
 ```
+
 The queue is now ``[ h ]``. Dequeue ``h`` which has no neighbor nodes.
+
 ```swift
-queue.dequeue(h)
+queue.dequeue()   // h
 ```
-The queue is now empty which means all nodes have been explored.
+
+The queue is now empty, meaning that all nodes have been explored. The order in which the nodes were explored is `a`, `b`, `c`, `d`, `e`, `f`, `g`, `h`.
 
 ## The code
 
@@ -72,7 +90,6 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
         neighborNode.visited = true
-
         nodesExplored.append(neighborNode.label)
       }
     }
@@ -83,8 +100,9 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
 ```
 
 Put this code in a playground and test it like so:
+
 ```swift
-let graph = Graph() // Representing the graph from the animated example
+let graph = Graph()   // Representing the graph from the animated example
 
 let nodeA = graph.addNode("a")
 let nodeB = graph.addNode("b")
@@ -104,46 +122,53 @@ graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
-print(nodesExplored) // This will output: ["a", "b", "c", "d", "e", "f", "g", "h"]
+print(nodesExplored)
 ```
 
+This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
+   
 ## Applications
 
 Breadth-first search can be used to solve many problems, for example:
 
-* Computing the shortest path between a source node and each of the other nodes
-  * Only for unweighted graphs
+* Computing the shortest path between a source node and each of the other nodes (only for unweighted graphs)
 * Calculating the minimum spanning tree on an unweighted graph
 
 ## Shortest path example
 
-Breadth-first search can be used to compute the [shortest path](../Shortest Path/) between a source node and each of the other nodes because it explores all of the neighbor nodes before moving to the next level neighbors. Let's follow the animated example and calculate the shortest path to all the other nodes:
+Breadth-first search can be used to compute the [shortest path](../Shortest Path/) between a source node and each of the other nodes in the tree or graph, because it explores all of the immediate neighbor nodes first before moving to the next level neighbors.
+
+Let's follow the animated example and calculate the shortest path to all the other nodes. Start with the source node ``a`` and add it to a queue with a distance of ``0``.
 
-Start with the source node ``a`` and add it to a queue with a distance of ``0``.
 ```swift
 queue.enqueue(a)
 a.distance = 0
 ```
-The queue is now ``[ a ]``. Dequeue ``a`` and enqueue the neighbor nodes ``b`` and ``c`` with a distance of ``1``.
+
+The queue is now ``[ a ]``. Dequeue ``a`` and enqueue its two neighbor nodes ``b`` and ``c`` with a distance of ``1``.
+
 ```swift
-queue.dequeue(a)
+queue.dequeue()   // a
 queue.enqueue(b)
-b.distance = a.distance + 1 // result: 1
+b.distance = a.distance + 1   // result: 1
 queue.enqueue(c)
-c.distance = a.distance + 1 // result: 1
+c.distance = a.distance + 1   // result: 1
 ```
-The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue the neighbor nodes ``d`` and ``e`` with a distance of ``2``.
+
+The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue `b`'s neighbor nodes ``d`` and ``e`` with a distance of ``2``.
+
 ```swift
-queue.dequeue(b)
+queue.dequeue()   // b
 queue.enqueue(d)
-d.distance = b.distance + 1 // result: 2
+d.distance = b.distance + 1   // result: 2
 queue.enqueue(e)
-e.distance = b.distance + 1 // result: 2
+e.distance = b.distance + 1   // result: 2
 ```
 
 Continue until the queue is empty to calculate the shortest path to all other nodes.
 
 Here's the code:
+
 ```swift
 func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
@@ -169,19 +194,21 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
 ```
 
 Put this code in a playground and test it like so:
+
 ```swift
 let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
 print(shortestPathGraph.nodes)
-
-// This will output:
-// Node(label: a, distance: 0), Node(label: b, distance: 1), Node(label: c, distance: 1),
-// Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
-// Node(label: g, distance: 2), Node(label: h, distance: 3)
 ```
 
+This will output:
+
+	Node(label: a, distance: 0), Node(label: b, distance: 1), Node(label: c, distance: 1),
+	Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
+	Node(label: g, distance: 2), Node(label: h, distance: 3)
+
 ## Minimum spanning tree example
 
-Breadth-first search can be used to calculate the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph.
+Breadth-first search can be used to calculate the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph. A minimum spanning tree describes a path that contains the smallest number of edges that are needed to visit every node in the graph.
 
 Let's calculate the minimum spanning tree for the following graph:
 
@@ -190,71 +217,92 @@ Let's calculate the minimum spanning tree for the following graph:
 *Note: the minimum spanning tree is represented by the bold edges.*
 
 Start with the source node ``a`` and add it to a queue and mark it as visited.
+
 ```swift
 queue.enqueue(a)
 a.visited = true
 ```
-The queue is now ``[ a ]``. Dequeue ``a`` and enqueue the neighbor nodes ``b`` and ``h`` and mark them as visited.
+
+The queue is now ``[ a ]``. Dequeue ``a`` and enqueue its immediate neighbor nodes ``b`` and ``h`` and mark them as visited.
+
 ```swift
-queue.dequeue(a)
+queue.dequeue()   // a
 queue.enqueue(b)
 b.visited = true
 queue.enqueue(h)
 h.visited = true
 ```
+
 The queue is now ``[ b, h ]``. Dequeue ``b`` and enqueue the neighbor node ``c`` mark it as visited. Remove the edge between ``b`` to ``h`` because ``h`` has already been visited.
+
 ```swift
-queue.dequeue(b)
+queue.dequeue()   // b
 queue.enqueue(c)
 c.visited = true
 b.removeEdgeTo(h)
 ```
+
 The queue is now ``[ h, c ]``. Dequeue ``h`` and enqueue the neighbor nodes ``g`` and ``i`` and mark them as visited.
+
 ```swift
-queue.dequeue(h)
+queue.dequeue()   // h
 queue.enqueue(g)
 g.visited = true
 queue.enqueue(i)
 i.visited = true
 ```
+
 The queue is now ``[ c, g, i ]``. Dequeue ``c`` and enqueue the neighbor nodes ``d`` and ``f`` and mark them as visited. Remove the edge between ``c`` to ``i`` because ``i`` has already been visited.
+
 ```swift
-queue.dequeue(c)
+queue.dequeue()   // c
 queue.enqueue(d)
 d.visited = true
 queue.enqueue(f)
 f.visited = true
 c.removeEdgeTo(i)
 ```
+
 The queue is now ``[ g, i, d, f ]``. Dequeue ``g`` and remove the edges between ``g`` to ``f`` and ``g`` to ``i`` because ``f`` and ``i`` have already been visited.
+
 ```swift
-queue.dequeue(g)
+queue.dequeue()   // g
 g.removeEdgeTo(f)
 g.removeEdgeTo(i)
 ```
+
 The queue is now ``[ i, d, f ]``. Dequeue ``i``.
+
 ```swift
-queue.dequeue(i)
+queue.dequeue()   // i
 ```
+
 The queue is now ``[ d, f ]``. Dequeue ``d`` and enqueue the neighbor node ``e`` mark it as visited. Remove the edge between ``d`` to ``f`` because ``f`` has already been visited.
+
 ```swift
-queue.dequeue(d)
+queue.dequeue()   // d
 queue.enqueue(e)
 e.visited = true
 d.removeEdgeTo(f)
 ```
+
 The queue is now ``[ f, e ]``. Dequeue ``f``. Remove the edge between ``f`` to ``e`` because ``e`` has already been visited.
+
 ```swift
-queue.dequeue(f)
+queue.dequeue()   // f
 f.removeEdgeTo(e)
 ```
+
 The queue is now ``[ e ]``. Dequeue ``e``.
+
 ```swift
-queue.dequeue(e)
+queue.dequeue()   // e
 ```
-The queue is now empty which means the minimum spanning tree has been computed.
+
+The queue is now empty, which means the minimum spanning tree has been computed.
 
 Here's the code:
+
 ```swift
 func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
@@ -280,7 +328,11 @@ func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph
   return minimumSpanningTree
 }
 ```
+
+This function returns a new `Graph` object that describes just the minimum spanning tree. In the figure, that would be the graph containing just the bold edges.
+
 Put this code in a playground and test it like so:
+
 ```swift
 let graph = Graph()
 
@@ -331,6 +383,7 @@ print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
                            // [node: d edges: ["e"]]
                            // [node: h edges: ["g", "i"]]
 ```
+
 ## See also
 
 [Graph](../Graph/), [Tree](../Tree/), [Queues](../Queue/), [Shortest Path](../Shortest Path/), [Minimum Spanning Tree](../Minimum Spanning Tree/).

From d81b544453c8221d77300cddaf00325975958258 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Mon, 29 Feb 2016 19:34:11 +0100
Subject: [PATCH 0073/1679] Small tweaks to the text and code

Don't need to have a duplicate copy of Stack in this folder
---
 README.markdown                               |   1 +
 Shunting Yard/README.markdown                 |  55 +++---
 .../Contents.swift                            |  67 +++----
 .../Sources/Stack.swift                       |   0
 .../contents.xcplayground                     |   0
 .../timeline.xctimeline                       |   0
 ...YardAlgorithm.swift => ShuntingYard.swift} | 170 ++++++++----------
 Shunting Yard/Stack.swift                     |  43 -----
 8 files changed, 128 insertions(+), 208 deletions(-)
 rename Shunting Yard/{Shunting Yard.playground => ShuntingYard.playground}/Contents.swift (77%)
 rename Shunting Yard/{Shunting Yard.playground => ShuntingYard.playground}/Sources/Stack.swift (100%)
 rename Shunting Yard/{Shunting Yard.playground => ShuntingYard.playground}/contents.xcplayground (100%)
 rename Shunting Yard/{Shunting Yard.playground => ShuntingYard.playground}/timeline.xctimeline (100%)
 rename Shunting Yard/{ShuntingYardAlgorithm.swift => ShuntingYard.swift} (54%)
 delete mode 100644 Shunting Yard/Stack.swift

diff --git a/README.markdown b/README.markdown
index 650ad2f57..579e7c182 100644
--- a/README.markdown
+++ b/README.markdown
@@ -91,6 +91,7 @@ Bad sorting algorithms (don't use these!):
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
 - [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
+- [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
 - Statistics
 
 ### Machine learning
diff --git a/Shunting Yard/README.markdown b/Shunting Yard/README.markdown
index 3668888b2..6d9332629 100644
--- a/Shunting Yard/README.markdown	
+++ b/Shunting Yard/README.markdown	
@@ -1,29 +1,24 @@
 # Shunting Yard Algorithm
 
-Any mathematical expression that we write is expressed in a notation known as Infix Notation.
+Any mathematical expression that we write is expressed in a notation known as *infix notation*.
 
 For example:
 
 **A + B * C**
 
-In the above expression the operator is placed between operands hence the expression is said to be in Infix form.
-If you think about it any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
+In the above expression the operator is placed between operands, hence the expression is said to be in *infix* form. If you think about it, any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
 
-Now, think about the way the above expression is evaluated, you would first multiply B and C then add the result to A. This is because multiplication has
-higher precedence than addition. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. If you were to 
-write an algorithm that parsed and evaluated the infix notation you will realize that it's a tedious process. You'd have to parse the expression
-multiple times to know what operation to perform first. As the number of operators increase so does the complexity.
+When the above expression is evaluated, you would first multiply **B** and **C**, and then add the result to **A**. This is because multiplication has higher precedence than addition. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. 
 
-##  Postfix notations / Reverse Polish Notation 
+If you were to write an algorithm that parsed and evaluated the infix notation you will realize that it's a tedious process. You'd have to parse the expression multiple times to know what operation to perform first. As the number of operators increase so does the complexity.
 
-An expression when represented in postfix form will not have any brackets and neither will you have to worry about scanning for operator precedence. This makes it easy for the computer to evaluate
-expressions since the order in which the operator need to be applied is fixed.
+## Postfix notations / Reverse Polish Notation 
 
-For example:
+In postfix notation, also known as Reverse Polish Notation or RPN, the operators come after the corresponding operands. Here is the postfix representation of the example from the previous section:
 
 **A B C * +**
 
-The above is the postfix representation of the example in the previous section. The operators come after the corresponding operands.
+An expression when represented in postfix form will not have any brackets and neither will you have to worry about scanning for operator precedence. This makes it easy for the computer to evaluate expressions, since the order in which the operators need to be applied is fixed.
 
 ### Evaluating a postfix expression
 
@@ -33,12 +28,11 @@ A stack is used to evaluate a postfix expression. Here is the pseudocode:
 2. If the token is an operand, push it into the stack
 3. If the token is a binary operator,
     1. Pop the two top most operands from the stack
-    2. Apply the binary operator with thetwo operands
+    2. Apply the binary operator to the two operands
     3. Push the result into the stack
-4. Finally, the value of the whole postfix
-   expression remains in the stack
+4. Finally, the value of the whole postfix expression remains in the stack
 
-Using the above psuedocode the evaluation on the stack would be as follows:
+Using the above pseudocode, the evaluation on the stack would be as follows:
 
 | Expression    | Stack   |
 | ------------- | --------|
@@ -51,23 +45,23 @@ Using the above psuedocode the evaluation on the stack would be as follows:
 
 Where **D = B * C** and **E = A + D.**
 
-As seen above a postfix operation is relatively easy to evaluate as the order in which the operators need to be applied is predecided.
+As seen above, a postfix operation is relatively easy to evaluate as the order in which the operators need to be applied is pre-decided.
 
-## Shunting yard algorithm
+## Dijkstra's shunting yard algorithm
 
-The Shunting yard algorithm was invented by Edsger Dijkstra to convert an infix expression to postfix. Many calculators use this algorithm to convert the expression being entered to postfix form.
+The shunting yard algorithm was invented by Edsger Dijkstra to convert an infix expression to postfix. Many calculators use this algorithm to convert the expression being entered to postfix form.
 
 Here is the psedocode of the algorithm:
 
-1. For all the input tokens
+1. For all the input tokens:
     1. Read the next token
     2. If token is an operator (x)
         1. While there is an operator (y) at the top of the operators stack and either (x) is left-associative and its precedence is less or equal to that of (y), or (x) is right-associative and its precedence is less than (y)
             1. Pop (y) from the stack
             2. Add (y) output buffer
         2. Push (x) on the stack
-    3. Else If token is left parenthesis, then push it on the stack
-    4. Else If token is a right parenthesis
+    3. Else if token is left parenthesis, then push it on the stack
+    4. Else if token is a right parenthesis
         1. Until the top token (from the stack) is left parenthesis, pop from the stack to the output buffer
         2. Also pop the left parenthesis but don’t include it in the output buffer
     7. Else add token to output buffer
@@ -75,10 +69,12 @@ Here is the psedocode of the algorithm:
 
 ### How does it work
 
-Let's take a small example and see how the psuedocode works. 
+Let's take a small example and see how the pseudocode works. 
 
 **4 + 4 * 2 / ( 1 - 5 )**
 
+The following table describes the precedence and the associativity for each operator. The same values are used in the algorithm.
+
 | Operator | Precedence   | Associativity   |
 | ---------| -------------| ----------------|
 | ^        | 10           | Right           |
@@ -87,25 +83,28 @@ Let's take a small example and see how the psuedocode works.
 | +        | 0            | Left            |
 | -        | 0            | Left            |
 
-The above table describes the precedence and the associativity for each operator. The same values are used in the algorithm.
+Here we go:
 
 | Token | Action                                      | Output            | Operator stack |
 |-------|---------------------------------------------|-------------------|----------------|
-| 3     | Add token to output                         | 4                 |                |
+| 4     | Add token to output                         | 4                 |                |
 | +     | Push token to stack                         | 4                 | +              |
 | 4     | Add token to output                         | 4 4               | +              |
 | *     | Push token to stack                         | 4 4               | * +            |
 | 2     | Add token to output                         | 4 4 2             | * +            |
-| /     | * Pop stack to output * Push token to stack | 4 4 2 *           | / +            |
+| /     | Pop stack to output, Push token to stack | 4 4 2 *           | / +            |
 | (     | Push token to stack                         | 4 4 2 *           | ( / +          |
 | 1     | Add token to output                         | 4 4 2 * 1         | ( / +          |
 | -     | Push token to stack                         | 4 4 2 * 1         | - ( / +        |
 | 5     | Add token to output                         | 4 4 2 * 1 5       | - ( / +        |
-| )     | * Pop stack to output * Pop stack           | 4 4 2 * 1 5 -     | /  +           |
+| )     | Pop stack to output, Pop stack           | 4 4 2 * 1 5 -     | /  +           |
 | end   | Pop entire stack to output                  | 4 4 2 * 1 5 - / + |                |
 
+We end up with the postfix expression:
+
+** 4 4 2 * 1 5 - / + **
 
-# See Also
+# See also
 
 [Shunting yard algorithm on Wikipedia](https://en.wikipedia.org/wiki/Shunting-yard_algorithm)
 
diff --git a/Shunting Yard/Shunting Yard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
similarity index 77%
rename from Shunting Yard/Shunting Yard.playground/Contents.swift
rename to Shunting Yard/ShuntingYard.playground/Contents.swift
index f70f36c5a..52b952d1f 100644
--- a/Shunting Yard/Shunting Yard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -1,7 +1,5 @@
 //: Playground - noun: a place where people can play
 
-import Foundation
-
 internal enum OperatorAssociativity {
   case LeftAssociative
   case RightAssociative
@@ -54,19 +52,18 @@ public enum TokenType: CustomStringConvertible {
 }
 
 public struct OperatorToken: CustomStringConvertible {
-  
-  var operatorType: OperatorType
+  let operatorType: OperatorType
   
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
   
-  var precedance: Int {
+  var precedence: Int {
     switch operatorType {
       case .Add, .Subtract:
         return 0
       case .Divide, .Multiply, .Percent:
-        return 5;
+        return 5
       case .Exponent:
         return 10
     }
@@ -87,22 +84,15 @@ public struct OperatorToken: CustomStringConvertible {
 }
 
 func <=(left: OperatorToken, right: OperatorToken) -> Bool {
-  if left.precedance <= right.precedance {
-    return true
-  }
-  return false
+  return left.precedence <= right.precedence
 }
 
 func <(left: OperatorToken, right: OperatorToken) -> Bool {
-  if left.precedance < right.precedance {
-    return true
-  }
-  return false
+  return left.precedence < right.precedence
 }
 
 public struct Token: CustomStringConvertible {
-  
-  var tokenType: TokenType
+  let tokenType: TokenType
   
   init(tokenType: TokenType) {
     self.tokenType = tokenType
@@ -136,9 +126,9 @@ public struct Token: CustomStringConvertible {
   
   var operatorToken: OperatorToken? {
     switch tokenType {
-    case .Operator(let operatorToken):
+      case .Operator(let operatorToken):
         return operatorToken
-    default:
+      default:
         return nil
     }
   }
@@ -149,8 +139,7 @@ public struct Token: CustomStringConvertible {
 }
 
 public class InfixExpressionBuilder {
-  
-  private var expression = Array<Token>()
+  private var expression = [Token]()
   
   public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
@@ -172,15 +161,15 @@ public class InfixExpressionBuilder {
     return self
   }
   
-  public func build() -> Array<Token> {
+  public func build() -> [Token] {
     // Maybe do some validation here
     return expression
   }
 }
 
 // This returns the result of the shunting yard algorithm
-public func reversePolishNotation(expression: Array<Token>) -> String {
-  
+public func reversePolishNotation(expression: [Token]) -> String {
+
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
   
@@ -188,40 +177,31 @@ public func reversePolishNotation(expression: Array<Token>) -> String {
     switch token.tokenType {
       case .Operand(_):
         reversePolishNotation.append(token)
-        break
+
       case .OpenBracket:
         tokenStack.push(token)
-        break
+
       case .CloseBracket:
-        while tokenStack.count > 0 {
-          if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
-            reversePolishNotation.append(tempToken)
-          } else {
-            break
-          }
+        while tokenStack.count > 0, let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+          reversePolishNotation.append(tempToken)
         }
-        break
+
       case .Operator(let operatorToken):
-          
         for tempToken in tokenStack.generate() {
           if !tempToken.isOperator {
             break
           }
           
           if let tempOperatorToken = tempToken.operatorToken {
-              
             if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
                 || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
-                    
               reversePolishNotation.append(tokenStack.pop()!)
             } else {
               break
             }
           }
         }
-        
         tokenStack.push(token)
-        break
     }
   }
   
@@ -229,9 +209,14 @@ public func reversePolishNotation(expression: Array<Token>) -> String {
     reversePolishNotation.append(tokenStack.pop()!)
   }
   
-  return reversePolishNotation.map({token in
-    return token.description
-  }).joinWithSeparator(" ")
+  return reversePolishNotation.map({token in token.description}).joinWithSeparator(" ")
 }
 
-print(reversePolishNotation(InfixExpressionBuilder().addOperand(3).addOperator(.Add).addOperand(4).addOperator(.Multiply).addOperand(2).addOperator(.Divide).addOpenBracket().addOperand(1).addOperator(.Subtract).addOperand(5).addCloseBracket().addOperator(.Exponent).addOperand(2).addOperator(.Exponent).addOperand(3).build()))
+
+// Simple demo
+
+let expr = InfixExpressionBuilder().addOperand(3).addOperator(.Add).addOperand(4).addOperator(.Multiply).addOperand(2).addOperator(.Divide).addOpenBracket().addOperand(1).addOperator(.Subtract).addOperand(5).addCloseBracket().addOperator(.Exponent).addOperand(2).addOperator(.Exponent).addOperand(3).build()
+
+print(expr.description)
+print(reversePolishNotation(expr))
+
diff --git a/Shunting Yard/Shunting Yard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
similarity index 100%
rename from Shunting Yard/Shunting Yard.playground/Sources/Stack.swift
rename to Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
diff --git a/Shunting Yard/Shunting Yard.playground/contents.xcplayground b/Shunting Yard/ShuntingYard.playground/contents.xcplayground
similarity index 100%
rename from Shunting Yard/Shunting Yard.playground/contents.xcplayground
rename to Shunting Yard/ShuntingYard.playground/contents.xcplayground
diff --git a/Shunting Yard/Shunting Yard.playground/timeline.xctimeline b/Shunting Yard/ShuntingYard.playground/timeline.xctimeline
similarity index 100%
rename from Shunting Yard/Shunting Yard.playground/timeline.xctimeline
rename to Shunting Yard/ShuntingYard.playground/timeline.xctimeline
diff --git a/Shunting Yard/ShuntingYardAlgorithm.swift b/Shunting Yard/ShuntingYard.swift
similarity index 54%
rename from Shunting Yard/ShuntingYardAlgorithm.swift
rename to Shunting Yard/ShuntingYard.swift
index dbaba475c..1da67990d 100644
--- a/Shunting Yard/ShuntingYardAlgorithm.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -6,8 +6,6 @@
 //
 //
 
-import Foundation
-
 internal enum OperatorAssociativity {
   case LeftAssociative
   case RightAssociative
@@ -23,18 +21,18 @@ public enum OperatorType: CustomStringConvertible {
   
   public var description: String {
     switch self {
-    case Add:
-      return "+"
-    case Subtract:
-      return "-"
-    case Divide:
-      return "/"
-    case Multiply:
-      return "*"
-    case Percent:
-      return "%"
-    case Exponent:
-      return "^"
+      case Add:
+        return "+"
+      case Subtract:
+        return "-"
+      case Divide:
+        return "/"
+      case Multiply:
+        return "*"
+      case Percent:
+        return "%"
+      case Exponent:
+        return "^"
     }
   }
 }
@@ -47,43 +45,42 @@ public enum TokenType: CustomStringConvertible {
   
   public var description: String {
     switch self {
-    case OpenBracket:
-      return "("
-    case CloseBracket:
-      return ")"
-    case Operator(let operatorToken):
-      return operatorToken.description
-    case Operand(let value):
-      return "\(value)"
+      case OpenBracket:
+        return "("
+      case CloseBracket:
+        return ")"
+      case Operator(let operatorToken):
+        return operatorToken.description
+      case Operand(let value):
+        return "\(value)"
     }
   }
 }
 
 public struct OperatorToken: CustomStringConvertible {
-  
-  var operatorType: OperatorType
+  let operatorType: OperatorType
   
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
   
-  var precedance: Int {
+  var precedence: Int {
     switch operatorType {
-    case .Add, .Subtract:
-      return 0
-    case .Divide, .Multiply, .Percent:
-      return 5;
-    case .Exponent:
-      return 10
+      case .Add, .Subtract:
+        return 0
+      case .Divide, .Multiply, .Percent:
+        return 5
+      case .Exponent:
+        return 10
     }
   }
   
   var associativity: OperatorAssociativity {
     switch operatorType {
-    case .Add, .Subtract, .Divide, .Multiply, .Percent:
-      return .LeftAssociative;
-    case .Exponent:
-      return .RightAssociative
+      case .Add, .Subtract, .Divide, .Multiply, .Percent:
+        return .LeftAssociative;
+      case .Exponent:
+        return .RightAssociative
     }
   }
   
@@ -93,22 +90,15 @@ public struct OperatorToken: CustomStringConvertible {
 }
 
 func <=(left: OperatorToken, right: OperatorToken) -> Bool {
-  if left.precedance <= right.precedance {
-    return true
-  }
-  return false
+  return left.precedence <= right.precedence
 }
 
 func <(left: OperatorToken, right: OperatorToken) -> Bool {
-  if left.precedance < right.precedance {
-    return true
-  }
-  return false
+  return left.precedence < right.precedence
 }
 
 public struct Token: CustomStringConvertible {
-  
-  var tokenType: TokenType
+  let tokenType: TokenType
   
   init(tokenType: TokenType) {
     self.tokenType = tokenType
@@ -124,28 +114,28 @@ public struct Token: CustomStringConvertible {
   
   var isOpenBracket: Bool {
     switch tokenType {
-    case .OpenBracket:
-      return true
-    default:
-      return false
+      case .OpenBracket:
+        return true
+      default:
+        return false
     }
   }
   
   var isOperator: Bool {
     switch tokenType {
-    case .Operator(_):
-      return true
-    default:
-      return false
+      case .Operator(_):
+        return true
+      default:
+        return false
     }
   }
   
   var operatorToken: OperatorToken? {
     switch tokenType {
-    case .Operator(let operatorToken):
-      return operatorToken
-    default:
-      return nil
+      case .Operator(let operatorToken):
+        return operatorToken
+      default:
+        return nil
     }
   }
   
@@ -155,8 +145,7 @@ public struct Token: CustomStringConvertible {
 }
 
 public class InfixExpressionBuilder {
-  
-  private var expression = Array<Token>()
+  private var expression = [Token]()
   
   public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
@@ -178,56 +167,47 @@ public class InfixExpressionBuilder {
     return self
   }
   
-  public func build() -> Array<Token> {
+  public func build() -> [Token] {
     // Maybe do some validation here
     return expression
   }
 }
 
 // This returns the result of the shunting yard algorithm
-public func reversePolishNotation(expression: Array<Token>) -> String {
-  
+public func reversePolishNotation(expression: [Token]) -> String {
+
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
   
   for token in expression {
     switch token.tokenType {
-    case .Operand(_):
-      reversePolishNotation.append(token)
-      break
-    case .OpenBracket:
-      tokenStack.push(token)
-      break
-    case .CloseBracket:
-      while tokenStack.count > 0 {
-        if let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+      case .Operand(_):
+        reversePolishNotation.append(token)
+
+      case .OpenBracket:
+        tokenStack.push(token)
+
+      case .CloseBracket:
+        while tokenStack.count > 0, let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
           reversePolishNotation.append(tempToken)
-        } else {
-          break
         }
-      }
-      break
-    case .Operator(let operatorToken):
-      
-      for tempToken in tokenStack.generate() {
-        if !tempToken.isOperator {
-          break
-        }
-        
-        if let tempOperatorToken = tempToken.operatorToken {
+
+      case .Operator(let operatorToken):
+        for tempToken in tokenStack.generate() {
+          if !tempToken.isOperator {
+            break
+          }
           
-          if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
-            || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
-              
+          if let tempOperatorToken = tempToken.operatorToken {
+            if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
+                || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
               reversePolishNotation.append(tokenStack.pop()!)
-          } else {
-            break
+            } else {
+              break
+            }
           }
         }
-      }
-      
-      tokenStack.push(token)
-      break
+        tokenStack.push(token)
     }
   }
   
@@ -235,7 +215,5 @@ public func reversePolishNotation(expression: Array<Token>) -> String {
     reversePolishNotation.append(tokenStack.pop()!)
   }
   
-  return reversePolishNotation.map({token in
-    return token.description
-  }).joinWithSeparator(" ")
-}
\ No newline at end of file
+  return reversePolishNotation.map({token in token.description}).joinWithSeparator(" ")
+}
diff --git a/Shunting Yard/Stack.swift b/Shunting Yard/Stack.swift
deleted file mode 100644
index 93feb2ca1..000000000
--- a/Shunting Yard/Stack.swift	
+++ /dev/null
@@ -1,43 +0,0 @@
-import Foundation
-
-public struct Stack<T> {
-    private var array = [T]()
-    
-    public init() {
-        array = []
-    }
-    
-    public var isEmpty: Bool {
-        return array.isEmpty
-    }
-    
-    public var count: Int {
-        return array.count
-    }
-    
-    public mutating func push(element: T) {
-        array.append(element)
-    }
-    
-    public mutating func pop() -> T? {
-        if isEmpty {
-            return nil
-        } else {
-            return array.removeLast()
-        }
-    }
-    
-    public func peek() -> T? {
-        return array.last
-    }
-}
-
-extension Stack: SequenceType {
-    public func generate() -> AnyGenerator<T> {
-        var curr = self
-        return anyGenerator {
-            _ -> T? in
-            return curr.pop()
-        }
-    }
-}
\ No newline at end of file

From 5721ee725ddf5aede392b844e4ad8bc8168a448c Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Mon, 29 Feb 2016 19:35:53 +0100
Subject: [PATCH 0074/1679] Fix bold text

---
 Shunting Yard/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Shunting Yard/README.markdown b/Shunting Yard/README.markdown
index 6d9332629..d4d7c3e22 100644
--- a/Shunting Yard/README.markdown	
+++ b/Shunting Yard/README.markdown	
@@ -102,7 +102,7 @@ Here we go:
 
 We end up with the postfix expression:
 
-** 4 4 2 * 1 5 - / + **
+**4 4 2 * 1 5 - / +**
 
 # See also
 

From 35a8ed4c18a6978063306596d8443350a424becf Mon Sep 17 00:00:00 2001
From: jamil <jamil.dhanani@gmail.com>
Date: Mon, 29 Feb 2016 22:00:48 -0500
Subject: [PATCH 0075/1679] Add code for Bloom Filter, tests

---
 Bloom Filter/BloomFilter.swift                | 58 ++++++++++++++
 .../BloomFilterTests/BloomFilterTests.swift   | 78 +++++++++++++++++++
 Bloom Filter/BloomFilterTests/Info.plist      | 24 ++++++
 3 files changed, 160 insertions(+)
 create mode 100644 Bloom Filter/BloomFilter.swift
 create mode 100644 Bloom Filter/BloomFilterTests/BloomFilterTests.swift
 create mode 100644 Bloom Filter/BloomFilterTests/Info.plist

diff --git a/Bloom Filter/BloomFilter.swift b/Bloom Filter/BloomFilter.swift
new file mode 100644
index 000000000..6f5232b0d
--- /dev/null
+++ b/Bloom Filter/BloomFilter.swift	
@@ -0,0 +1,58 @@
+import Foundation
+
+public class BloomFilter<T> {
+    private(set) private var arr: [Bool]
+    private(set) private var hashFunctions: [T -> Int]
+    
+    public init(size: Int = 1024, hashFunctions: [T -> Int]) {
+        self.arr = Array<Bool>(count: size, repeatedValue: false)
+        self.hashFunctions = hashFunctions
+    }
+    
+    private func computeHashes(value: T) -> [Int] {
+        return hashFunctions.map() { hashFunc in
+            abs(hashFunc(value) % self.arr.count)
+        }
+    }
+    
+    public func insert(toInsert: T) {
+        let hashValues: [Int] = self.computeHashes(toInsert)
+        
+        for hashValue in hashValues {
+            self.arr[hashValue] = true
+        }
+    }
+    
+    public func insert(values: [T]) {
+        for value in values {
+            self.insert(value)
+        }
+    }
+    
+    public func query(value: T) -> Bool {
+        let hashValues = self.computeHashes(value)
+        
+        // Map hashes to indices in the Bloom filter
+        let results = hashValues.map() { hashValue in
+            self.arr[hashValue]
+        }
+        
+        // All values must be 'true' for the query to return true
+
+        // This does NOT imply that the value is in the Bloom filter,
+        // only that it may be. If the query returns false, however,
+        // you can be certain that the value was not added.
+
+        let exists = results.reduce(true, combine: { $0 && $1 })
+        
+        return exists
+    }
+    
+    public func isEmpty() -> Bool {
+        // Reduce list; as soon as the reduction hits a 'true' value, the && condition will fail
+        return arr.reduce(true) { prev, next in
+            prev && !next
+        }
+    }
+    
+}
\ No newline at end of file
diff --git a/Bloom Filter/BloomFilterTests/BloomFilterTests.swift b/Bloom Filter/BloomFilterTests/BloomFilterTests.swift
new file mode 100644
index 000000000..bb11f80aa
--- /dev/null
+++ b/Bloom Filter/BloomFilterTests/BloomFilterTests.swift	
@@ -0,0 +1,78 @@
+import XCTest
+import BloomFilter
+
+/* Two hash functions, adapted from
+    http://www.cse.yorku.ca/~oz/hash.html */
+
+
+func djb2(x: String) -> Int {
+    var hash = 5381
+    
+    for char in x.characters {
+        hash = ((hash << 5) &+ hash) &+ char.hashValue
+    }
+    
+    return Int(hash)
+}
+
+func sdbm(x: String) -> Int {
+    var hash = 0
+    
+    for char in x.characters {
+        hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash;
+    }
+    
+    return Int(hash)
+}
+
+
+class BloomFilterTests: XCTestCase {
+    
+    func testSingleHashFunction() {
+        let bloom = BloomFilter<String>(hashFunctions: [djb2])
+        
+        bloom.insert("Hello world!")
+        
+        let result_good = bloom.query("Hello world!")
+        let result_bad = bloom.query("Hello world")
+        
+        XCTAssertTrue(result_good)
+        XCTAssertFalse(result_bad)
+    }
+    
+    func testEmptyFilter() {
+        let bloom = BloomFilter<String>(hashFunctions: [djb2])
+        
+        let empty = bloom.isEmpty()
+        
+        XCTAssertTrue(empty)
+    }
+    
+    func testMultipleHashFunctions() {
+        let bloom = BloomFilter<String>(hashFunctions: [djb2, sdbm])
+        
+        bloom.insert("Hello world!")
+        
+        let result_good = bloom.query("Hello world!")
+        let result_bad = bloom.query("Hello world")
+        
+        XCTAssertTrue(result_good)
+        XCTAssertFalse(result_bad)
+    }
+    
+    func testFalsePositive() {
+        let bloom = BloomFilter<String>(size: 5, hashFunctions: [djb2, sdbm])
+        
+        bloom.insert(["hello", "elloh", "llohe", "lohel", "ohell"])
+        
+        print("Inserted")
+        
+        let query = bloom.query("This wasn't inserted!")
+        
+        // This is true even though we did not insert the value in the Bloom filter;
+        // the Bloom filter is capable of producing false positives but NOT 
+        // false negatives.
+        
+        XCTAssertTrue(query)
+    }
+}
diff --git a/Bloom Filter/BloomFilterTests/Info.plist b/Bloom Filter/BloomFilterTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Bloom Filter/BloomFilterTests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>

From 20d3c0e45ce932116fdef8241e4c7bc04e02e161 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Mon, 29 Feb 2016 18:34:09 -0800
Subject: [PATCH 0076/1679] Move kMeans from playground to project

---
 K-Means/K-Means.playground/Contents.swift     | 140 ----------
 .../K-Means.playground/contents.xcplayground  |   4 -
 .../K-Means.playground/timeline.xctimeline    |  41 ---
 K-Means/KMeans.swift                          | 168 ++++-------
 K-Means/README.md                             |   4 +-
 K-Means/Tests/Info.plist                      |  24 ++
 K-Means/Tests/KMeansTests.swift               |  65 +++++
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 261 ++++++++++++++++++
 K-Means/Tests/Vector.swift                    |  76 +++++
 9 files changed, 482 insertions(+), 301 deletions(-)
 delete mode 100644 K-Means/K-Means.playground/Contents.swift
 delete mode 100644 K-Means/K-Means.playground/contents.xcplayground
 delete mode 100644 K-Means/K-Means.playground/timeline.xctimeline
 create mode 100644 K-Means/Tests/Info.plist
 create mode 100644 K-Means/Tests/KMeansTests.swift
 create mode 100644 K-Means/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 K-Means/Tests/Vector.swift

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
deleted file mode 100644
index 9f35e5863..000000000
--- a/K-Means/K-Means.playground/Contents.swift
+++ /dev/null
@@ -1,140 +0,0 @@
-//
-//  K-Means.swift
-//
-//  Created by John Gill on 2/25/16.
-
-import Foundation
-
-// Need a container to easily hold N Dimensional Vectors
-class VectorND: CustomStringConvertible {
-    private var length = 0
-    private var data = [Double]()
-    
-    init(d:[Double]) {
-        data = d
-        length = d.count
-    }
-    
-    var description: String { return "VectorND (\(data)" }
-    func getData() -> [Double] { return data }
-    func getLength() -> Int { return length }
-}
-
-// MARK: VectorND Operators
-func +(left: VectorND, right: VectorND) -> VectorND {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for idx in 0..<left.getLength() {
-        results[idx] = left.getData()[idx] + right.getData()[idx]
-    }
-    return VectorND(d: results)
-}
-func +=(inout left: VectorND, right: VectorND) {
-    left = left + right
-}
-func /(left:VectorND, right: Double) -> VectorND  {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for (idx, value) in left.getData().enumerate() {
-        results[idx] = value / right
-    }
-    return VectorND(d: results)
-}
-func /=(inout left: VectorND, right: Double) {
-    left = left / right
-}
-
-// MARK: Assist Functions
-// Pick a k random elements from samples
-func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
-    var result = [VectorND]()
-    
-    // Fill the result array with first k elements
-    for i in 0..<k {
-        result.append(samples[i])
-    }
-    // randomly replace elements from remaining ones 
-    for i in (k+1)..<samples.count {
-        let j = Int(arc4random_uniform(UInt32(i+1)))
-        if j < k {
-            result[j] = samples[i]
-        }
-    }
-    return result
-}
-
-// Calculates the Euclidean distance between two VectorNDs
-func euclidean(v1:VectorND, v2:VectorND) -> Double {
-    var result = 0.0
-    for idx in 0..<v1.getLength() {
-        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
-    }
-    return sqrt(result)
-}
-
-// Get the INDEX of nearest Center to X
-func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
-    var nearestDist = DBL_MAX
-    var minIndex = 0;
-    
-    for (idx, c) in Centers.enumerate() {
-        let dist = euclidean(x, v2: c)
-        if dist < nearestDist {
-            minIndex = idx
-            nearestDist = dist
-        }
-    }
-    return minIndex
-}
-
-// MARK: Main Function
-func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
-    var centerMoveDist = 0.0
-    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
-    
-    // 1. Choose k Random VectorNDs as the initial centers
-    var kCenters = reservoirSample(points, k: numCenters)
-    
-    // do following steps until convergence
-    repeat {
-        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
-        // 2. Assign VectorNDs to centers
-        //    a. Determine which center each VectorND is closest to
-        //    b. Record how many VectorNDs are assigned to each center
-        for p in points {
-            let c = nearestCenter(p, Centers: kCenters)
-            cnts[c]++
-            newCenters[c] += p
-        }
-        // 3. Calculate a new centers
-        for idx in 0..<numCenters {
-            newCenters[idx] /= cnts[idx]
-        }
-        // 4. Determine how far centers moved
-        centerMoveDist = 0.0
-        for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
-        }
-        // 5. Update centers to the newly calculated ones
-        kCenters = newCenters
-        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
-    } while(centerMoveDist > convergeDist)
-    return kCenters
-}
-
-// MARK: Sample Data
-var points = [VectorND]()
-let numPoints = 10
-let numDimmensions = 5
-for _ in 0..<numPoints {
-    var data = [Double]()
-    for x in 0..<numDimmensions {
-        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
-    }
-    points.append(VectorND(d: data))
-}
-
-print("\nCenters")
-for c in kMeans(3, convergeDist: 0.01, points: points) {
-    print(c)
-}
-
diff --git a/K-Means/K-Means.playground/contents.xcplayground b/K-Means/K-Means.playground/contents.xcplayground
deleted file mode 100644
index 9f9eecc96..000000000
--- a/K-Means/K-Means.playground/contents.xcplayground
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/K-Means/K-Means.playground/timeline.xctimeline b/K-Means/K-Means.playground/timeline.xctimeline
deleted file mode 100644
index 850856b0b..000000000
--- a/K-Means/K-Means.playground/timeline.xctimeline
+++ /dev/null
@@ -1,41 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=37&amp;EndingLineNumber=138&amp;StartingColumnNumber=1&amp;StartingLineNumber=138&amp;Timestamp=478154433.694733"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/johngill/git/swift-algorithm-club/K-Means/K-Means.playground#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingLineNumber=138&amp;StartingLineNumber=138&amp;Timestamp=478154433.694858"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=18&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.69495"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=19&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.695038"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695117"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695195"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695273"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-   </TimelineItems>
-</Timeline>
diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 05e973ba0..9a3193bfe 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -5,55 +5,71 @@
 
 import Foundation
 
-// Need a container to easily hold N Dimensional Vectors
-class VectorND: CustomStringConvertible {
-    private var length = 0
-    private var data = [Double]()
-
-    init(d:[Double]) {
-        data = d
-        length = d.count
+class KMeans {
+    var numCenters:Int
+    var convergeDist:Double
+    
+    init(numCenters:Int, convergeDist:Double) {
+        self.numCenters = numCenters
+        self.convergeDist = convergeDist
     }
-
-    var description: String { return "VectorND (\(data)" }
-    func getData() -> [Double] { return data }
-    func getLength() -> Int { return length }
-}
-
-// MARK: VectorND Operators
-func +(left: VectorND, right: VectorND) -> VectorND {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for idx in 0..<left.getLength() {
-        results[idx] = left.getData()[idx] + right.getData()[idx]
+    
+    private func nearestCenter(x: Vector, Centers: [Vector]) -> Int {
+        var nearestDist = DBL_MAX
+        var minIndex = 0;
+        
+        for (idx, c) in Centers.enumerate() {
+            let dist = x.distTo(c)
+            if dist < nearestDist {
+                minIndex = idx
+                nearestDist = dist
+            }
+        }
+        return minIndex
     }
-    return VectorND(d: results)
-}
-func +=(inout left: VectorND, right: VectorND) {
-    left = left + right
-}
-func /(left:VectorND, right: Double) -> VectorND  {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for (idx, value) in left.getData().enumerate() {
-        results[idx] = value / right
+    
+    func findCenters(points: [Vector]) -> [Vector] {
+        var centerMoveDist = 0.0
+        let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
+        
+        var kCenters = reservoirSample(points, k: numCenters)
+        
+        repeat {
+            var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+            var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
+        
+            for p in points {
+                let c = nearestCenter(p, Centers: kCenters)
+                cnts[c]++
+                newCenters[c] += p
+            }
+            
+            for idx in 0..<numCenters {
+                newCenters[idx] /= cnts[idx]
+            }
+            
+            centerMoveDist = 0.0
+            for idx in 0..<numCenters {
+                centerMoveDist += kCenters[idx].distTo(newCenters[idx])
+            }
+            
+            kCenters = newCenters
+        } while(centerMoveDist > convergeDist)
+        return kCenters
     }
-    return VectorND(d: results)
-}
-func /=(inout left: VectorND, right: Double) {
-    left = left / right
 }
 
-// MARK: Assist Functions
-// Pick a k random elements from samples
-func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
-    var result = [VectorND]()
+// Pick k random elements from samples
+func reservoirSample<T>(samples:[T], k:Int) -> [T] {
+    var result = [T]()
 
     // Fill the result array with first k elements
     for i in 0..<k {
         result.append(samples[i])
     }
-    // randomly replace elements from remaining ones
+    // randomly replace elements from remaining pool
     for i in (k+1)..<samples.count {
-        let j = Int(arc4random_uniform(UInt32(i+1)))
+        let j = random()%(i+1)
         if j < k {
             result[j] = samples[i]
         }
@@ -61,79 +77,3 @@ func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
     return result
 }
 
-// Calculates the Euclidean distance between two VectorNDs
-func euclidean(v1:VectorND, v2:VectorND) -> Double {
-    var result = 0.0
-    for idx in 0..<v1.getLength() {
-        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
-    }
-    return sqrt(result)
-}
-
-// Get the INDEX of nearest Center to X
-func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
-    var nearestDist = DBL_MAX
-    var minIndex = 0;
-
-    for (idx, c) in Centers.enumerate() {
-        let dist = euclidean(x, v2: c)
-        if dist < nearestDist {
-            minIndex = idx
-            nearestDist = dist
-        }
-    }
-    return minIndex
-}
-
-// MARK: Main Function
-func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
-    var centerMoveDist = 0.0
-    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
-
-    // 1. Choose k Random VectorNDs as the initial centers
-    var kCenters = reservoirSample(points, k: numCenters)
-
-    // do following steps until convergence
-    repeat {
-        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
-        // 2. Assign VectorNDs to centers
-        //    a. Determine which center each VectorND is closest to
-        //    b. Record how many VectorNDs are assigned to each center
-        for p in points {
-            let c = nearestCenter(p, Centers: kCenters)
-            cnts[c]++
-            newCenters[c] += p
-        }
-        // 3. Calculate a new centers
-        for idx in 0..<numCenters {
-            newCenters[idx] /= cnts[idx]
-        }
-        // 4. Determine how far centers moved
-        centerMoveDist = 0.0
-        for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
-        }
-        // 5. Update centers to the newly calculated ones
-        kCenters = newCenters
-        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
-    } while(centerMoveDist > convergeDist)
-    return kCenters
-}
-
-// MARK: Sample Data
-var points = [VectorND]()
-let numPoints = 10
-let numDimmensions = 5
-for _ in 0..<numPoints {
-    var data = [Double]()
-    for x in 0..<numDimmensions {
-        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
-    }
-    points.append(VectorND(d: data))
-}
-
-print("\nCenters")
-for c in kMeans(3, convergeDist: 0.01, points: points) {
-    print(c)
-}
diff --git a/K-Means/README.md b/K-Means/README.md
index 05240ebe2..e1314a825 100644
--- a/K-Means/README.md
+++ b/K-Means/README.md
@@ -22,7 +22,7 @@ This brings about a few of the parameters that are required for k-means:
 
 This is what the algorithm would look like in swift
 ```swift
-func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+func kMeans(numCenters: Int, convergeDist: Double, points: [Vector]) -> [Vector] {
     var centerMoveDist = 0.0
     let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
 
@@ -30,7 +30,7 @@ func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [Vecto
 
     repeat {
         var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
         for p in points {
             let c = nearestCenter(p, Centers: kCenters)
             cnts[c]++
diff --git a/K-Means/Tests/Info.plist b/K-Means/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/K-Means/Tests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
new file mode 100644
index 000000000..436cab4fe
--- /dev/null
+++ b/K-Means/Tests/KMeansTests.swift
@@ -0,0 +1,65 @@
+//
+//  Tests.swift
+//  Tests
+//
+//  Created by John Gill on 2/29/16.
+//
+//
+
+import Foundation
+import XCTest
+
+class KMeansTests: XCTestCase {
+    var points = [Vector]()
+    
+    func genPoints(numPoints:Int, numDimmensions:Int) {
+        for _ in 0..<numPoints {
+            var data = [Double]()
+            for _ in 0..<numDimmensions {
+                data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
+            }
+            points.append(Vector(d: data))
+        }
+
+    }
+    
+    func testSmall_2D() {
+        genPoints(10, numDimmensions: 2)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 3, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+    
+    func testSmall_10D() {
+        genPoints(10, numDimmensions: 10)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 3, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+    
+    func testLarge_2D() {
+        genPoints(10000, numDimmensions: 2)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 5, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+    
+    func testLarge_10D() {
+        genPoints(10000, numDimmensions: 10)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 5, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+}
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..55f861d02
--- /dev/null
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		B80894E41C852D100018730E /* KMeansTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = B80894E31C852D100018730E /* KMeansTests.swift */; };
+		B80894EA1C852DA00018730E /* Vector.swift in Sources */ = {isa = PBXBuildFile; fileRef = B80894E91C852DA00018730E /* Vector.swift */; };
+		B80894EB1C8530830018730E /* KMeans.swift in Sources */ = {isa = PBXBuildFile; fileRef = B80894DB1C852CFA0018730E /* KMeans.swift */; };
+/* End PBXBuildFile section */
+
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+		B80894DB1C852CFA0018730E /* KMeans.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = KMeans.swift; path = ../KMeans.swift; sourceTree = SOURCE_ROOT; };
+		B80894E01C852D100018730E /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		B80894E31C852D100018730E /* KMeansTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = KMeansTests.swift; sourceTree = SOURCE_ROOT; };
+		B80894E51C852D100018730E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; name = Info.plist; path = ../Info.plist; sourceTree = "<group>"; };
+		B80894E91C852DA00018730E /* Vector.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Vector.swift; path = ../Vector.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		B80894DD1C852D100018730E /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		B80894D41C852CDC0018730E = {
+			isa = PBXGroup;
+			children = (
+				B80894E21C852D100018730E /* Tests */,
+				B80894E11C852D100018730E /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		B80894E11C852D100018730E /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				B80894E01C852D100018730E /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		B80894E21C852D100018730E /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				B80894E91C852DA00018730E /* Vector.swift */,
+				B80894DB1C852CFA0018730E /* KMeans.swift */,
+				B80894E31C852D100018730E /* KMeansTests.swift */,
+				B80894E51C852D100018730E /* Info.plist */,
+			);
+			path = Tests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
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+		B80894DF1C852D100018730E /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = B80894E61C852D100018730E /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				B80894DC1C852D100018730E /* Sources */,
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+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = Tests;
+			productReference = B80894E01C852D100018730E /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		B80894D51C852CDC0018730E /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				TargetAttributes = {
+					B80894DF1C852D100018730E = {
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+			};
+			buildConfigurationList = B80894D81C852CDC0018730E /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
+			mainGroup = B80894D41C852CDC0018730E;
+			productRefGroup = B80894E11C852D100018730E /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				B80894DF1C852D100018730E /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		B80894DE1C852D100018730E /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		B80894DC1C852D100018730E /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				B80894EA1C852DA00018730E /* Vector.swift in Sources */,
+				B80894E41C852D100018730E /* KMeansTests.swift in Sources */,
+				B80894EB1C8530830018730E /* KMeans.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		B80894D91C852CDC0018730E /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Debug;
+		};
+		B80894DA1C852CDC0018730E /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Release;
+		};
+		B80894E71C852D100018730E /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		B80894E81C852D100018730E /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		B80894D81C852CDC0018730E /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				B80894D91C852CDC0018730E /* Debug */,
+				B80894DA1C852CDC0018730E /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		B80894E61C852D100018730E /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				B80894E71C852D100018730E /* Debug */,
+				B80894E81C852D100018730E /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = B80894D51C852CDC0018730E /* Project object */;
+}
diff --git a/K-Means/Tests/Vector.swift b/K-Means/Tests/Vector.swift
new file mode 100644
index 000000000..a920de7de
--- /dev/null
+++ b/K-Means/Tests/Vector.swift
@@ -0,0 +1,76 @@
+//
+//  Vector.swift
+//  Tests
+//
+//  Created by John Gill on 2/29/16.
+//
+//
+
+import Foundation
+
+// Container to easily hold N Dimensional Vectors
+class Vector: CustomStringConvertible, Equatable {
+    private(set) var length = 0
+    private(set) var data = [Double]()
+    
+    init(d:[Double]) {
+        data = d
+        length = d.count
+    }
+    
+    var description: String { return "Vector (\(data)" }
+    
+    func distTo(v2:Vector) -> Double {
+        var result = 0.0
+        for idx in 0..<self.length {
+            result += pow(self.data[idx] - v2.data[idx], 2.0)
+        }
+        return sqrt(result)
+    }
+}
+
+// MARK: Vector Operators
+func ==(left: Vector, right: Vector) -> Bool {
+    for idx in 0..<left.length {
+        if left.data[idx] != right.data[idx] {
+            return false
+        }
+    }
+    return true
+}
+
+func +(left: Vector, right: Vector) -> Vector {
+    var results = [Double]()
+    for idx in 0..<left.length {
+        results.append(left.data[idx] + right.data[idx])
+    }
+    return Vector(d: results)
+}
+
+func +=(inout left: Vector, right: Vector) {
+    left = left + right
+}
+
+func -(left: Vector, right: Vector) -> Vector {
+    var results = [Double]()
+    for idx in 0..<left.length {
+        results.append(left.data[idx] - right.data[idx])
+    }
+    return Vector(d: results)
+}
+
+func -=(inout left: Vector, right: Vector) {
+    left = left - right
+}
+
+func /(left:Vector, right: Double) -> Vector  {
+    var results = [Double](count: left.length, repeatedValue: 0.0)
+    for (idx, value) in left.data.enumerate() {
+        results[idx] = value / right
+    }
+    return Vector(d: results)
+}
+
+func /=(inout left: Vector, right: Double) {
+    left = left / right
+}
\ No newline at end of file

From 79810762a3186def99297986bedeb14b61e1d009 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 13:46:48 -0800
Subject: [PATCH 0077/1679] Initial fileset

---
 K-Means/K-Means.playground/Contents.swift     | 116 ++++++++++++++++++
 .../K-Means.playground/contents.xcplayground  |   4 +
 .../K-Means.playground/timeline.xctimeline    |   6 +
 K-Means/README.md                             |   0
 4 files changed, 126 insertions(+)
 create mode 100644 K-Means/K-Means.playground/Contents.swift
 create mode 100644 K-Means/K-Means.playground/contents.xcplayground
 create mode 100644 K-Means/K-Means.playground/timeline.xctimeline
 create mode 100644 K-Means/README.md

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
new file mode 100644
index 000000000..a3071733e
--- /dev/null
+++ b/K-Means/K-Means.playground/Contents.swift
@@ -0,0 +1,116 @@
+//
+//  K-Means.swift
+//
+//  Created by John Gill on 2/25/16.
+
+import Foundation
+
+// Need a container to easily hold 2 Dimensional Vector2Ds
+class Vector2D: CustomStringConvertible {
+    var x:Float = 0.0 // x-Coordinate of Vector2D
+    var y:Float = 0.0 // y-Coordinate of Vector2D
+    
+    init(x: Float, y: Float) {
+        self.x = x
+        self.y = y
+    }
+    
+    var description: String {
+        return "Vector2D (\(self.x), \(self.y))"
+    }
+}
+
+// Ability to use std operators on Vector2D object
+func +(left: Vector2D, right: Vector2D) -> Vector2D {
+    return Vector2D(x: left.x + right.x, y: left.y + right.y)
+}
+func +=(inout left: Vector2D, right: Vector2D) {
+    left = left + right
+}
+func /(left:Vector2D, right: Float) -> Vector2D {
+    return Vector2D(x: left.x / right, y: left.y / right)
+}
+func /=(inout left: Vector2D, right: Float) {
+    left = left / right
+}
+
+// TODO: Explain/Replace/Cleanup
+extension Array {
+    var shuffle: [Element] {
+        var elements = self
+        for index in indices {
+            let anotherIndex = Int(arc4random_uniform(UInt32(elements.count - index))) + index
+            anotherIndex != index ? swap(&elements[index], &elements[anotherIndex]) : ()
+        }
+        return elements
+    }
+    func choose(n: Int) -> [Element] {
+        return Array(shuffle.prefix(n))
+    }
+}
+
+// Calculates the Euclidean distance between two Vector2Ds
+func euclidean(v1:Vector2D, v2:Vector2D) -> Float {
+    return sqrt(pow((v1.x - v2.x), 2.0) + pow((v1.y - v2.y), 2.0))
+}
+
+// Get the INDEX of nearest Center to X
+func nearestCenter(x: Vector2D, Centers: [Vector2D]) -> Int {
+    var nearestDist = FLT_MAX
+    var minIndex:Int = 0;
+    // Calculate the distance from Vector2D X to all the centers
+    for (idx, c) in Centers.enumerate() {
+        let dist = euclidean(x, v2: c)
+        if dist < nearestDist {
+            minIndex = idx
+            nearestDist = dist
+        }
+    }
+    return minIndex
+}
+
+func kNN(numCenters: Int, convergeDist: Float, points: [Vector2D]) -> [Vector2D] {
+    var centerMoveDist:Float = 0.0
+    
+    // 1. Choose k Random Vector2Ds as the initial centers
+    var kCenters:[Vector2D] = points.choose(numCenters)
+    
+    // do following steps until convergence
+    repeat {
+        var cnts = [Float](count: numCenters, repeatedValue: 0.0)
+        var nCenters = [Vector2D](count:numCenters, repeatedValue: Vector2D(x:0, y:0))
+        // 2. Assign Vector2Ds to centers
+        //    a. Determine which center each Vector2D is closest to
+        //    b. Record how many Vector2Ds are assigned to each center
+        for p in points {
+            let c = nearestCenter(p, Centers: kCenters)
+            cnts[c]++
+            nCenters[c] += p
+        }
+        // 3. Calculate a new centers
+        for idx in 0..<numCenters {
+            nCenters[idx] /= cnts[idx]
+        }
+        // 4. Determine how far centers moved
+        centerMoveDist = 0.0
+        for idx in 0..<numCenters {
+            centerMoveDist += euclidean(kCenters[idx], v2: nCenters[idx])
+        }
+        // 5. Update centers to the newly calculated ones
+        kCenters = nCenters
+        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
+    } while(centerMoveDist > convergeDist)
+    return kCenters
+}
+var points = [Vector2D]()
+let lim = 50
+for _ in 0..<lim {
+    let x = Float(arc4random_uniform(UInt32(lim)))
+    let y = Float(arc4random_uniform(UInt32(lim)))
+    points.append(Vector2D(x: Float(x), y: y))
+}
+
+print("\nCenters")
+for c in kNN(10, convergeDist: 0.1, points: points) {
+    print(c)
+}
diff --git a/K-Means/K-Means.playground/contents.xcplayground b/K-Means/K-Means.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/K-Means/K-Means.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/K-Means/K-Means.playground/timeline.xctimeline b/K-Means/K-Means.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/K-Means/K-Means.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/K-Means/README.md b/K-Means/README.md
new file mode 100644
index 000000000..e69de29bb

From 62d152001463ee53a5987441f078d66c2ff0f564 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 15:16:57 -0800
Subject: [PATCH 0078/1679] Change 2D vector to ND vector

---
 K-Means/K-Means.playground/Contents.swift     | 82 +++++++++++--------
 .../K-Means.playground/contents.xcplayground  |  2 +-
 2 files changed, 49 insertions(+), 35 deletions(-)

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
index a3071733e..d1d6a05fd 100644
--- a/K-Means/K-Means.playground/Contents.swift
+++ b/K-Means/K-Means.playground/Contents.swift
@@ -5,32 +5,40 @@
 
 import Foundation
 
-// Need a container to easily hold 2 Dimensional Vector2Ds
-class Vector2D: CustomStringConvertible {
-    var x:Float = 0.0 // x-Coordinate of Vector2D
-    var y:Float = 0.0 // y-Coordinate of Vector2D
+// Need a container to easily hold N Dimensional Vectors
+class VectorND: CustomStringConvertible {
+    private var length:Int = 0
+    private var data:[Float] = [Float]()
     
-    init(x: Float, y: Float) {
-        self.x = x
-        self.y = y
+    init(d:[Float]) {
+        self.data = d
+        self.length = d.count
     }
     
-    var description: String {
-        return "Vector2D (\(self.x), \(self.y))"
-    }
+    var description: String { return "VectorND (\(self.data)" }
+    func getData() -> [Float] { return data }
+    func getLength() -> Int { return length }
 }
 
-// Ability to use std operators on Vector2D object
-func +(left: Vector2D, right: Vector2D) -> Vector2D {
-    return Vector2D(x: left.x + right.x, y: left.y + right.y)
+// Ability to use std operators on VectorND object
+func +(left: VectorND, right: VectorND) -> VectorND {
+    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+    for idx in 0..<left.getLength() {
+        results[idx] = left.getData()[idx] + right.getData()[idx]
+    }
+    return VectorND(d: results)
 }
-func +=(inout left: Vector2D, right: Vector2D) {
+func +=(inout left: VectorND, right: VectorND) {
     left = left + right
 }
-func /(left:Vector2D, right: Float) -> Vector2D {
-    return Vector2D(x: left.x / right, y: left.y / right)
+func /(left:VectorND, right: Float) -> VectorND  {
+    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+    for (idx, value) in left.getData().enumerate() {
+        results[idx] = value / right
+    }
+    return VectorND(d: results)
 }
-func /=(inout left: Vector2D, right: Float) {
+func /=(inout left: VectorND, right: Float) {
     left = left / right
 }
 
@@ -49,16 +57,20 @@ extension Array {
     }
 }
 
-// Calculates the Euclidean distance between two Vector2Ds
-func euclidean(v1:Vector2D, v2:Vector2D) -> Float {
-    return sqrt(pow((v1.x - v2.x), 2.0) + pow((v1.y - v2.y), 2.0))
+// Calculates the Euclidean distance between two VectorNDs
+func euclidean(v1:VectorND, v2:VectorND) -> Float {
+    var result:Float = 0.0
+    for idx in 0..<v1.getLength() {
+        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
+    }
+    return sqrt(result)
 }
 
 // Get the INDEX of nearest Center to X
-func nearestCenter(x: Vector2D, Centers: [Vector2D]) -> Int {
+func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
     var nearestDist = FLT_MAX
     var minIndex:Int = 0;
-    // Calculate the distance from Vector2D X to all the centers
+    // Calculate the distance from VectorND X to all the centers
     for (idx, c) in Centers.enumerate() {
         let dist = euclidean(x, v2: c)
         if dist < nearestDist {
@@ -69,19 +81,20 @@ func nearestCenter(x: Vector2D, Centers: [Vector2D]) -> Int {
     return minIndex
 }
 
-func kNN(numCenters: Int, convergeDist: Float, points: [Vector2D]) -> [Vector2D] {
+func kNN(numCenters: Int, convergeDist: Float, points: [VectorND]) -> [VectorND] {
     var centerMoveDist:Float = 0.0
+    let zeros = [Float](count: points[0].getLength(), repeatedValue: 0.0)
     
-    // 1. Choose k Random Vector2Ds as the initial centers
-    var kCenters:[Vector2D] = points.choose(numCenters)
+    // 1. Choose k Random VectorNDs as the initial centers
+    var kCenters:[VectorND] = points.choose(numCenters)
     
     // do following steps until convergence
     repeat {
         var cnts = [Float](count: numCenters, repeatedValue: 0.0)
-        var nCenters = [Vector2D](count:numCenters, repeatedValue: Vector2D(x:0, y:0))
-        // 2. Assign Vector2Ds to centers
-        //    a. Determine which center each Vector2D is closest to
-        //    b. Record how many Vector2Ds are assigned to each center
+        var nCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        // 2. Assign VectorNDs to centers
+        //    a. Determine which center each VectorND is closest to
+        //    b. Record how many VectorNDs are assigned to each center
         for p in points {
             let c = nearestCenter(p, Centers: kCenters)
             cnts[c]++
@@ -102,15 +115,16 @@ func kNN(numCenters: Int, convergeDist: Float, points: [Vector2D]) -> [Vector2D]
     } while(centerMoveDist > convergeDist)
     return kCenters
 }
-var points = [Vector2D]()
-let lim = 50
+
+var points = [VectorND]()
+let lim = 10
 for _ in 0..<lim {
     let x = Float(arc4random_uniform(UInt32(lim)))
     let y = Float(arc4random_uniform(UInt32(lim)))
-    points.append(Vector2D(x: Float(x), y: y))
+    points.append(VectorND(d: [x, y]))
 }
 
 print("\nCenters")
-for c in kNN(10, convergeDist: 0.1, points: points) {
+for c in kNN(3, convergeDist: 0.1, points: points) {
     print(c)
-}
+}
\ No newline at end of file
diff --git a/K-Means/K-Means.playground/contents.xcplayground b/K-Means/K-Means.playground/contents.xcplayground
index 06828af92..9f9eecc96 100644
--- a/K-Means/K-Means.playground/contents.xcplayground
+++ b/K-Means/K-Means.playground/contents.xcplayground
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 12f5a241b69190d47f8697cbb1d4bfaca7390605 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 20:45:12 -0800
Subject: [PATCH 0079/1679] Update to follow Swift Style Guide

---
 K-Means/K-Means.playground/Contents.swift     | 100 ++++++++++--------
 .../K-Means.playground/timeline.xctimeline    |  35 ++++++
 2 files changed, 90 insertions(+), 45 deletions(-)

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
index d1d6a05fd..9f35e5863 100644
--- a/K-Means/K-Means.playground/Contents.swift
+++ b/K-Means/K-Means.playground/Contents.swift
@@ -7,22 +7,22 @@ import Foundation
 
 // Need a container to easily hold N Dimensional Vectors
 class VectorND: CustomStringConvertible {
-    private var length:Int = 0
-    private var data:[Float] = [Float]()
+    private var length = 0
+    private var data = [Double]()
     
-    init(d:[Float]) {
-        self.data = d
-        self.length = d.count
+    init(d:[Double]) {
+        data = d
+        length = d.count
     }
     
-    var description: String { return "VectorND (\(self.data)" }
-    func getData() -> [Float] { return data }
+    var description: String { return "VectorND (\(data)" }
+    func getData() -> [Double] { return data }
     func getLength() -> Int { return length }
 }
 
-// Ability to use std operators on VectorND object
+// MARK: VectorND Operators
 func +(left: VectorND, right: VectorND) -> VectorND {
-    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
     for idx in 0..<left.getLength() {
         results[idx] = left.getData()[idx] + right.getData()[idx]
     }
@@ -31,35 +31,39 @@ func +(left: VectorND, right: VectorND) -> VectorND {
 func +=(inout left: VectorND, right: VectorND) {
     left = left + right
 }
-func /(left:VectorND, right: Float) -> VectorND  {
-    var results = [Float](count: left.getLength(), repeatedValue: 0.0)
+func /(left:VectorND, right: Double) -> VectorND  {
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
     for (idx, value) in left.getData().enumerate() {
         results[idx] = value / right
     }
     return VectorND(d: results)
 }
-func /=(inout left: VectorND, right: Float) {
+func /=(inout left: VectorND, right: Double) {
     left = left / right
 }
 
-// TODO: Explain/Replace/Cleanup
-extension Array {
-    var shuffle: [Element] {
-        var elements = self
-        for index in indices {
-            let anotherIndex = Int(arc4random_uniform(UInt32(elements.count - index))) + index
-            anotherIndex != index ? swap(&elements[index], &elements[anotherIndex]) : ()
-        }
-        return elements
+// MARK: Assist Functions
+// Pick a k random elements from samples
+func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
+    var result = [VectorND]()
+    
+    // Fill the result array with first k elements
+    for i in 0..<k {
+        result.append(samples[i])
     }
-    func choose(n: Int) -> [Element] {
-        return Array(shuffle.prefix(n))
+    // randomly replace elements from remaining ones 
+    for i in (k+1)..<samples.count {
+        let j = Int(arc4random_uniform(UInt32(i+1)))
+        if j < k {
+            result[j] = samples[i]
+        }
     }
+    return result
 }
 
 // Calculates the Euclidean distance between two VectorNDs
-func euclidean(v1:VectorND, v2:VectorND) -> Float {
-    var result:Float = 0.0
+func euclidean(v1:VectorND, v2:VectorND) -> Double {
+    var result = 0.0
     for idx in 0..<v1.getLength() {
         result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
     }
@@ -68,9 +72,9 @@ func euclidean(v1:VectorND, v2:VectorND) -> Float {
 
 // Get the INDEX of nearest Center to X
 func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
-    var nearestDist = FLT_MAX
-    var minIndex:Int = 0;
-    // Calculate the distance from VectorND X to all the centers
+    var nearestDist = DBL_MAX
+    var minIndex = 0;
+    
     for (idx, c) in Centers.enumerate() {
         let dist = euclidean(x, v2: c)
         if dist < nearestDist {
@@ -81,50 +85,56 @@ func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
     return minIndex
 }
 
-func kNN(numCenters: Int, convergeDist: Float, points: [VectorND]) -> [VectorND] {
-    var centerMoveDist:Float = 0.0
-    let zeros = [Float](count: points[0].getLength(), repeatedValue: 0.0)
+// MARK: Main Function
+func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
     
     // 1. Choose k Random VectorNDs as the initial centers
-    var kCenters:[VectorND] = points.choose(numCenters)
+    var kCenters = reservoirSample(points, k: numCenters)
     
     // do following steps until convergence
     repeat {
-        var cnts = [Float](count: numCenters, repeatedValue: 0.0)
-        var nCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
         // 2. Assign VectorNDs to centers
         //    a. Determine which center each VectorND is closest to
         //    b. Record how many VectorNDs are assigned to each center
         for p in points {
             let c = nearestCenter(p, Centers: kCenters)
             cnts[c]++
-            nCenters[c] += p
+            newCenters[c] += p
         }
         // 3. Calculate a new centers
         for idx in 0..<numCenters {
-            nCenters[idx] /= cnts[idx]
+            newCenters[idx] /= cnts[idx]
         }
         // 4. Determine how far centers moved
         centerMoveDist = 0.0
         for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: nCenters[idx])
+            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
         }
         // 5. Update centers to the newly calculated ones
-        kCenters = nCenters
+        kCenters = newCenters
         print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
     } while(centerMoveDist > convergeDist)
     return kCenters
 }
 
+// MARK: Sample Data
 var points = [VectorND]()
-let lim = 10
-for _ in 0..<lim {
-    let x = Float(arc4random_uniform(UInt32(lim)))
-    let y = Float(arc4random_uniform(UInt32(lim)))
-    points.append(VectorND(d: [x, y]))
+let numPoints = 10
+let numDimmensions = 5
+for _ in 0..<numPoints {
+    var data = [Double]()
+    for x in 0..<numDimmensions {
+        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
+    }
+    points.append(VectorND(d: data))
 }
 
 print("\nCenters")
-for c in kNN(3, convergeDist: 0.1, points: points) {
+for c in kMeans(3, convergeDist: 0.01, points: points) {
     print(c)
-}
\ No newline at end of file
+}
+
diff --git a/K-Means/K-Means.playground/timeline.xctimeline b/K-Means/K-Means.playground/timeline.xctimeline
index bf468afec..850856b0b 100644
--- a/K-Means/K-Means.playground/timeline.xctimeline
+++ b/K-Means/K-Means.playground/timeline.xctimeline
@@ -2,5 +2,40 @@
 <Timeline
    version = "3.0">
    <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=37&amp;EndingLineNumber=138&amp;StartingColumnNumber=1&amp;StartingLineNumber=138&amp;Timestamp=478154433.694733"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/johngill/git/swift-algorithm-club/K-Means/K-Means.playground#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingLineNumber=138&amp;StartingLineNumber=138&amp;Timestamp=478154433.694858"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=18&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.69495"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=19&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.695038"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695117"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695195"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695273"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
    </TimelineItems>
 </Timeline>

From 1e25e02e96ba5cd26feda8f655f3854c69b820b7 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 22:29:14 -0800
Subject: [PATCH 0080/1679] Move Contents into own source file

---
 K-Means/KMeans.swift | 139 +++++++++++++++++++++++++++++++++++++++++++
 K-Means/README.md    |   3 +
 2 files changed, 142 insertions(+)
 create mode 100644 K-Means/KMeans.swift

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
new file mode 100644
index 000000000..05e973ba0
--- /dev/null
+++ b/K-Means/KMeans.swift
@@ -0,0 +1,139 @@
+//
+//  KMeans.swift
+//
+//  Created by John Gill on 2/25/16.
+
+import Foundation
+
+// Need a container to easily hold N Dimensional Vectors
+class VectorND: CustomStringConvertible {
+    private var length = 0
+    private var data = [Double]()
+
+    init(d:[Double]) {
+        data = d
+        length = d.count
+    }
+
+    var description: String { return "VectorND (\(data)" }
+    func getData() -> [Double] { return data }
+    func getLength() -> Int { return length }
+}
+
+// MARK: VectorND Operators
+func +(left: VectorND, right: VectorND) -> VectorND {
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
+    for idx in 0..<left.getLength() {
+        results[idx] = left.getData()[idx] + right.getData()[idx]
+    }
+    return VectorND(d: results)
+}
+func +=(inout left: VectorND, right: VectorND) {
+    left = left + right
+}
+func /(left:VectorND, right: Double) -> VectorND  {
+    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
+    for (idx, value) in left.getData().enumerate() {
+        results[idx] = value / right
+    }
+    return VectorND(d: results)
+}
+func /=(inout left: VectorND, right: Double) {
+    left = left / right
+}
+
+// MARK: Assist Functions
+// Pick a k random elements from samples
+func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
+    var result = [VectorND]()
+
+    // Fill the result array with first k elements
+    for i in 0..<k {
+        result.append(samples[i])
+    }
+    // randomly replace elements from remaining ones
+    for i in (k+1)..<samples.count {
+        let j = Int(arc4random_uniform(UInt32(i+1)))
+        if j < k {
+            result[j] = samples[i]
+        }
+    }
+    return result
+}
+
+// Calculates the Euclidean distance between two VectorNDs
+func euclidean(v1:VectorND, v2:VectorND) -> Double {
+    var result = 0.0
+    for idx in 0..<v1.getLength() {
+        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
+    }
+    return sqrt(result)
+}
+
+// Get the INDEX of nearest Center to X
+func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
+    var nearestDist = DBL_MAX
+    var minIndex = 0;
+
+    for (idx, c) in Centers.enumerate() {
+        let dist = euclidean(x, v2: c)
+        if dist < nearestDist {
+            minIndex = idx
+            nearestDist = dist
+        }
+    }
+    return minIndex
+}
+
+// MARK: Main Function
+func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
+
+    // 1. Choose k Random VectorNDs as the initial centers
+    var kCenters = reservoirSample(points, k: numCenters)
+
+    // do following steps until convergence
+    repeat {
+        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        // 2. Assign VectorNDs to centers
+        //    a. Determine which center each VectorND is closest to
+        //    b. Record how many VectorNDs are assigned to each center
+        for p in points {
+            let c = nearestCenter(p, Centers: kCenters)
+            cnts[c]++
+            newCenters[c] += p
+        }
+        // 3. Calculate a new centers
+        for idx in 0..<numCenters {
+            newCenters[idx] /= cnts[idx]
+        }
+        // 4. Determine how far centers moved
+        centerMoveDist = 0.0
+        for idx in 0..<numCenters {
+            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
+        }
+        // 5. Update centers to the newly calculated ones
+        kCenters = newCenters
+        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
+    } while(centerMoveDist > convergeDist)
+    return kCenters
+}
+
+// MARK: Sample Data
+var points = [VectorND]()
+let numPoints = 10
+let numDimmensions = 5
+for _ in 0..<numPoints {
+    var data = [Double]()
+    for x in 0..<numDimmensions {
+        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
+    }
+    points.append(VectorND(d: data))
+}
+
+print("\nCenters")
+for c in kMeans(3, convergeDist: 0.01, points: points) {
+    print(c)
+}
diff --git a/K-Means/README.md b/K-Means/README.md
index e69de29bb..a801fea7a 100644
--- a/K-Means/README.md
+++ b/K-Means/README.md
@@ -0,0 +1,3 @@
+# K-Means
+
+Goal:  Partition data into k clusters based on nearest mean

From 71c4241101b8f50b886dbde220db28e9022b7219 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Thu, 25 Feb 2016 22:22:37 -0800
Subject: [PATCH 0081/1679] add k-Means algorithm

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 579e7c182..f19944aa3 100644
--- a/README.markdown
+++ b/README.markdown
@@ -96,6 +96,7 @@ Bad sorting algorithms (don't use these!):
 
 ### Machine learning
 
+- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression

From a52aa68cdc8ea9d21d35dee3cad5768ef4322fd9 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Sun, 28 Feb 2016 14:41:43 -0800
Subject: [PATCH 0082/1679] Write README for K-Means Algorithm

---
 K-Means/Images/k_means_bad1.png | Bin 0 -> 16294 bytes
 K-Means/Images/k_means_bad2.png | Bin 0 -> 15826 bytes
 K-Means/Images/k_means_good.png | Bin 0 -> 15983 bytes
 K-Means/README.md               |  82 +++++++++++++++++++++++++++++++-
 README.markdown                 |   5 +-
 5 files changed, 85 insertions(+), 2 deletions(-)
 create mode 100644 K-Means/Images/k_means_bad1.png
 create mode 100644 K-Means/Images/k_means_bad2.png
 create mode 100644 K-Means/Images/k_means_good.png

diff --git a/K-Means/Images/k_means_bad1.png b/K-Means/Images/k_means_bad1.png
new file mode 100644
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diff --git a/K-Means/README.md b/K-Means/README.md
index a801fea7a..05240ebe2 100644
--- a/K-Means/README.md
+++ b/K-Means/README.md
@@ -1,3 +1,83 @@
 # K-Means
 
-Goal:  Partition data into k clusters based on nearest mean
+Goal:  Partition data into k clusters based on nearest means
+
+The idea behind K-Means is to try and take data that has no formal classification to it and determine if there are any natural clusters within the data.
+
+K-Means assumes that there are **k-centers** within the data. The data that is then closest to these *centroids* become classified or grouped together. K-Means doesn't tell you what the classifier is for that particular data group, but it assists in trying to find what clusters potentially exist.
+
+## Algorithm
+The k-means algorithm is really quite simple at it's core:
+1. Choose k random points to be the initial centers
+2. Repeat the following two steps until the *centroid* reach convergence
+    1. Assign each point to it's nearest *centroid*
+    2. Update the *centroid* to the mean of it's nearest points
+
+Convergence is said to be reached when all of the *centroids* have not changed.
+
+This brings about a few of the parameters that are required for k-means:
+- **k** -  This is the number of *centroids* to attempt to locate
+- **convergence distance** - This is minimum distance that the centers are allowed to moved after a particular update step.
+- **distance function** - There are a number of distance functions that can be used, but mostly commonly the euclidean distance function is adequate. But often can lead to convergence not being reached in higher dimensionally.
+
+This is what the algorithm would look like in swift
+```swift
+func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
+
+    var kCenters = reservoirSample(points, k: numCenters)
+
+    repeat {
+        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        for p in points {
+            let c = nearestCenter(p, Centers: kCenters)
+            cnts[c]++
+            newCenters[c] += p
+        }
+        for idx in 0..<numCenters {
+            newCenters[idx] /= cnts[idx]
+        }
+        centerMoveDist = 0.0
+        for idx in 0..<numCenters {
+            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
+        }
+        kCenters = newCenters
+    } while(centerMoveDist > convergeDist)
+    return kCenters
+}
+```
+
+## Example
+These examples are contrived to show the exact nature of K-Means and finding clusters. These clusters are very easily identified by human eyes, we see there is one in the lower left corner, one in the upper right corner and maybe one in the middle.
+
+In all these examples the stars represent the *centroids* and the squares are the points.
+
+##### Good clusters
+This first example shows K-Means finding all three clusters:
+![Good Clustering](Images/k_means_good.png)
+
+The selection of initial centroids found that lower left (indicated by red) and did pretty good on the center and upper left clusters.
+
+#### Bad Clustering
+The next two examples highlight the unpredictability of k-Means and how not always does it find the best clustering.
+![Bad Clustering 1](Images/k_means_bad1.png)
+As you can see in this one the initial *centroids* were all a little two close and the 'blue' didn't quite get to a good place. By adjusting the convergence distance should be able to get it better.
+
+![Bad Clustering 1](Images/k_means_bad2.png)
+This one the blue cluster never really could separate from the red cluster and as such sort of got stuck down there.
+
+## Performance
+The first thing to recognize is that k-Means is classified as an NP-Hard type of problem. The selection of the initial *centroids* has a big effect on how the resulting clusters may end up. This means that trying to find an exact solution is not likely - even in 2 dimensional space.
+
+As seem from the steps above the complexity really isn't that bad - it is often considered to be on the order of O(kndi), where **k** is the number of *centroids*, **n** is the number of **d** dimensional vectors and **i** is the number of iterations for convergence.
+
+The amount of data has a big linear effect on the running time of k-means, but tuning how far you want the *centroids* to converge can have a big impact how many iterations will be done - **k** should be relatively small compared to the number of vectors.
+
+Often times as more data is added certain points may lie in the boundary between two *centroids* and as such those centroids would continue to bounce back and forth and the **convergence** distance would need to be tuned to prevent that.
+
+## See Also
+See also [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
+
+*Written by John Gill*
diff --git a/README.markdown b/README.markdown
index f19944aa3..241099e98 100644
--- a/README.markdown
+++ b/README.markdown
@@ -96,13 +96,16 @@ Bad sorting algorithms (don't use these!):
 
 ### Machine learning
 
-- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
+##### Supervised learning
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression
 - Neural Networks
 - PageRank
 
+##### Clustering
+- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
+
 ## Data structures
 
 The choice of data structure for a particular task depends on a few things.

From 3c228e980e363119ad5e7ed472f0cff5576c947d Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Sun, 28 Feb 2016 14:44:04 -0800
Subject: [PATCH 0083/1679] Modify main README to add k-Means

---
 README.markdown | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/README.markdown b/README.markdown
index 241099e98..984bb1bfd 100644
--- a/README.markdown
+++ b/README.markdown
@@ -95,17 +95,13 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 
 ### Machine learning
-
-##### Supervised learning
+- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression
 - Neural Networks
 - PageRank
 
-##### Clustering
-- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
-
 ## Data structures
 
 The choice of data structure for a particular task depends on a few things.

From 824e88fd7ff2d0308f022702688a8f6f4383b4f5 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Mon, 29 Feb 2016 18:34:09 -0800
Subject: [PATCH 0084/1679] Move kMeans from playground to project

---
 K-Means/K-Means.playground/Contents.swift     | 140 ----------
 .../K-Means.playground/contents.xcplayground  |   4 -
 .../K-Means.playground/timeline.xctimeline    |  41 ---
 K-Means/KMeans.swift                          | 168 ++++-------
 K-Means/README.md                             |   4 +-
 K-Means/Tests/Info.plist                      |  24 ++
 K-Means/Tests/KMeansTests.swift               |  65 +++++
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 261 ++++++++++++++++++
 K-Means/Tests/Vector.swift                    |  76 +++++
 9 files changed, 482 insertions(+), 301 deletions(-)
 delete mode 100644 K-Means/K-Means.playground/Contents.swift
 delete mode 100644 K-Means/K-Means.playground/contents.xcplayground
 delete mode 100644 K-Means/K-Means.playground/timeline.xctimeline
 create mode 100644 K-Means/Tests/Info.plist
 create mode 100644 K-Means/Tests/KMeansTests.swift
 create mode 100644 K-Means/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 K-Means/Tests/Vector.swift

diff --git a/K-Means/K-Means.playground/Contents.swift b/K-Means/K-Means.playground/Contents.swift
deleted file mode 100644
index 9f35e5863..000000000
--- a/K-Means/K-Means.playground/Contents.swift
+++ /dev/null
@@ -1,140 +0,0 @@
-//
-//  K-Means.swift
-//
-//  Created by John Gill on 2/25/16.
-
-import Foundation
-
-// Need a container to easily hold N Dimensional Vectors
-class VectorND: CustomStringConvertible {
-    private var length = 0
-    private var data = [Double]()
-    
-    init(d:[Double]) {
-        data = d
-        length = d.count
-    }
-    
-    var description: String { return "VectorND (\(data)" }
-    func getData() -> [Double] { return data }
-    func getLength() -> Int { return length }
-}
-
-// MARK: VectorND Operators
-func +(left: VectorND, right: VectorND) -> VectorND {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for idx in 0..<left.getLength() {
-        results[idx] = left.getData()[idx] + right.getData()[idx]
-    }
-    return VectorND(d: results)
-}
-func +=(inout left: VectorND, right: VectorND) {
-    left = left + right
-}
-func /(left:VectorND, right: Double) -> VectorND  {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for (idx, value) in left.getData().enumerate() {
-        results[idx] = value / right
-    }
-    return VectorND(d: results)
-}
-func /=(inout left: VectorND, right: Double) {
-    left = left / right
-}
-
-// MARK: Assist Functions
-// Pick a k random elements from samples
-func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
-    var result = [VectorND]()
-    
-    // Fill the result array with first k elements
-    for i in 0..<k {
-        result.append(samples[i])
-    }
-    // randomly replace elements from remaining ones 
-    for i in (k+1)..<samples.count {
-        let j = Int(arc4random_uniform(UInt32(i+1)))
-        if j < k {
-            result[j] = samples[i]
-        }
-    }
-    return result
-}
-
-// Calculates the Euclidean distance between two VectorNDs
-func euclidean(v1:VectorND, v2:VectorND) -> Double {
-    var result = 0.0
-    for idx in 0..<v1.getLength() {
-        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
-    }
-    return sqrt(result)
-}
-
-// Get the INDEX of nearest Center to X
-func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
-    var nearestDist = DBL_MAX
-    var minIndex = 0;
-    
-    for (idx, c) in Centers.enumerate() {
-        let dist = euclidean(x, v2: c)
-        if dist < nearestDist {
-            minIndex = idx
-            nearestDist = dist
-        }
-    }
-    return minIndex
-}
-
-// MARK: Main Function
-func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
-    var centerMoveDist = 0.0
-    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
-    
-    // 1. Choose k Random VectorNDs as the initial centers
-    var kCenters = reservoirSample(points, k: numCenters)
-    
-    // do following steps until convergence
-    repeat {
-        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
-        // 2. Assign VectorNDs to centers
-        //    a. Determine which center each VectorND is closest to
-        //    b. Record how many VectorNDs are assigned to each center
-        for p in points {
-            let c = nearestCenter(p, Centers: kCenters)
-            cnts[c]++
-            newCenters[c] += p
-        }
-        // 3. Calculate a new centers
-        for idx in 0..<numCenters {
-            newCenters[idx] /= cnts[idx]
-        }
-        // 4. Determine how far centers moved
-        centerMoveDist = 0.0
-        for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
-        }
-        // 5. Update centers to the newly calculated ones
-        kCenters = newCenters
-        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
-    } while(centerMoveDist > convergeDist)
-    return kCenters
-}
-
-// MARK: Sample Data
-var points = [VectorND]()
-let numPoints = 10
-let numDimmensions = 5
-for _ in 0..<numPoints {
-    var data = [Double]()
-    for x in 0..<numDimmensions {
-        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
-    }
-    points.append(VectorND(d: data))
-}
-
-print("\nCenters")
-for c in kMeans(3, convergeDist: 0.01, points: points) {
-    print(c)
-}
-
diff --git a/K-Means/K-Means.playground/contents.xcplayground b/K-Means/K-Means.playground/contents.xcplayground
deleted file mode 100644
index 9f9eecc96..000000000
--- a/K-Means/K-Means.playground/contents.xcplayground
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/K-Means/K-Means.playground/timeline.xctimeline b/K-Means/K-Means.playground/timeline.xctimeline
deleted file mode 100644
index 850856b0b..000000000
--- a/K-Means/K-Means.playground/timeline.xctimeline
+++ /dev/null
@@ -1,41 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=37&amp;EndingLineNumber=138&amp;StartingColumnNumber=1&amp;StartingLineNumber=138&amp;Timestamp=478154433.694733"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/johngill/git/swift-algorithm-club/K-Means/K-Means.playground#CharacterRangeLen=1&amp;CharacterRangeLoc=4157&amp;EndingLineNumber=138&amp;StartingLineNumber=138&amp;Timestamp=478154433.694858"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=18&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.69495"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=19&amp;EndingLineNumber=138&amp;StartingColumnNumber=5&amp;StartingLineNumber=138&amp;Timestamp=478154433.695038"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695117"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695195"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=4157&amp;EndingColumnNumber=17&amp;EndingLineNumber=138&amp;StartingColumnNumber=9&amp;StartingLineNumber=138&amp;Timestamp=478154433.695273"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-   </TimelineItems>
-</Timeline>
diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 05e973ba0..9a3193bfe 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -5,55 +5,71 @@
 
 import Foundation
 
-// Need a container to easily hold N Dimensional Vectors
-class VectorND: CustomStringConvertible {
-    private var length = 0
-    private var data = [Double]()
-
-    init(d:[Double]) {
-        data = d
-        length = d.count
+class KMeans {
+    var numCenters:Int
+    var convergeDist:Double
+    
+    init(numCenters:Int, convergeDist:Double) {
+        self.numCenters = numCenters
+        self.convergeDist = convergeDist
     }
-
-    var description: String { return "VectorND (\(data)" }
-    func getData() -> [Double] { return data }
-    func getLength() -> Int { return length }
-}
-
-// MARK: VectorND Operators
-func +(left: VectorND, right: VectorND) -> VectorND {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for idx in 0..<left.getLength() {
-        results[idx] = left.getData()[idx] + right.getData()[idx]
+    
+    private func nearestCenter(x: Vector, Centers: [Vector]) -> Int {
+        var nearestDist = DBL_MAX
+        var minIndex = 0;
+        
+        for (idx, c) in Centers.enumerate() {
+            let dist = x.distTo(c)
+            if dist < nearestDist {
+                minIndex = idx
+                nearestDist = dist
+            }
+        }
+        return minIndex
     }
-    return VectorND(d: results)
-}
-func +=(inout left: VectorND, right: VectorND) {
-    left = left + right
-}
-func /(left:VectorND, right: Double) -> VectorND  {
-    var results = [Double](count: left.getLength(), repeatedValue: 0.0)
-    for (idx, value) in left.getData().enumerate() {
-        results[idx] = value / right
+    
+    func findCenters(points: [Vector]) -> [Vector] {
+        var centerMoveDist = 0.0
+        let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
+        
+        var kCenters = reservoirSample(points, k: numCenters)
+        
+        repeat {
+            var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+            var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
+        
+            for p in points {
+                let c = nearestCenter(p, Centers: kCenters)
+                cnts[c]++
+                newCenters[c] += p
+            }
+            
+            for idx in 0..<numCenters {
+                newCenters[idx] /= cnts[idx]
+            }
+            
+            centerMoveDist = 0.0
+            for idx in 0..<numCenters {
+                centerMoveDist += kCenters[idx].distTo(newCenters[idx])
+            }
+            
+            kCenters = newCenters
+        } while(centerMoveDist > convergeDist)
+        return kCenters
     }
-    return VectorND(d: results)
-}
-func /=(inout left: VectorND, right: Double) {
-    left = left / right
 }
 
-// MARK: Assist Functions
-// Pick a k random elements from samples
-func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
-    var result = [VectorND]()
+// Pick k random elements from samples
+func reservoirSample<T>(samples:[T], k:Int) -> [T] {
+    var result = [T]()
 
     // Fill the result array with first k elements
     for i in 0..<k {
         result.append(samples[i])
     }
-    // randomly replace elements from remaining ones
+    // randomly replace elements from remaining pool
     for i in (k+1)..<samples.count {
-        let j = Int(arc4random_uniform(UInt32(i+1)))
+        let j = random()%(i+1)
         if j < k {
             result[j] = samples[i]
         }
@@ -61,79 +77,3 @@ func reservoirSample(samples:[VectorND], k:Int) -> [VectorND] {
     return result
 }
 
-// Calculates the Euclidean distance between two VectorNDs
-func euclidean(v1:VectorND, v2:VectorND) -> Double {
-    var result = 0.0
-    for idx in 0..<v1.getLength() {
-        result += pow(v1.getData()[idx] - v2.getData()[idx], 2.0)
-    }
-    return sqrt(result)
-}
-
-// Get the INDEX of nearest Center to X
-func nearestCenter(x: VectorND, Centers: [VectorND]) -> Int {
-    var nearestDist = DBL_MAX
-    var minIndex = 0;
-
-    for (idx, c) in Centers.enumerate() {
-        let dist = euclidean(x, v2: c)
-        if dist < nearestDist {
-            minIndex = idx
-            nearestDist = dist
-        }
-    }
-    return minIndex
-}
-
-// MARK: Main Function
-func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
-    var centerMoveDist = 0.0
-    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
-
-    // 1. Choose k Random VectorNDs as the initial centers
-    var kCenters = reservoirSample(points, k: numCenters)
-
-    // do following steps until convergence
-    repeat {
-        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
-        // 2. Assign VectorNDs to centers
-        //    a. Determine which center each VectorND is closest to
-        //    b. Record how many VectorNDs are assigned to each center
-        for p in points {
-            let c = nearestCenter(p, Centers: kCenters)
-            cnts[c]++
-            newCenters[c] += p
-        }
-        // 3. Calculate a new centers
-        for idx in 0..<numCenters {
-            newCenters[idx] /= cnts[idx]
-        }
-        // 4. Determine how far centers moved
-        centerMoveDist = 0.0
-        for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
-        }
-        // 5. Update centers to the newly calculated ones
-        kCenters = newCenters
-        print("Complete iteration coverge(\(centerMoveDist) <? \(convergeDist))")
-    } while(centerMoveDist > convergeDist)
-    return kCenters
-}
-
-// MARK: Sample Data
-var points = [VectorND]()
-let numPoints = 10
-let numDimmensions = 5
-for _ in 0..<numPoints {
-    var data = [Double]()
-    for x in 0..<numDimmensions {
-        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
-    }
-    points.append(VectorND(d: data))
-}
-
-print("\nCenters")
-for c in kMeans(3, convergeDist: 0.01, points: points) {
-    print(c)
-}
diff --git a/K-Means/README.md b/K-Means/README.md
index 05240ebe2..e1314a825 100644
--- a/K-Means/README.md
+++ b/K-Means/README.md
@@ -22,7 +22,7 @@ This brings about a few of the parameters that are required for k-means:
 
 This is what the algorithm would look like in swift
 ```swift
-func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [VectorND] {
+func kMeans(numCenters: Int, convergeDist: Double, points: [Vector]) -> [Vector] {
     var centerMoveDist = 0.0
     let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
 
@@ -30,7 +30,7 @@ func kMeans(numCenters: Int, convergeDist: Double, points: [VectorND]) -> [Vecto
 
     repeat {
         var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [VectorND](count:numCenters, repeatedValue: VectorND(d:zeros))
+        var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
         for p in points {
             let c = nearestCenter(p, Centers: kCenters)
             cnts[c]++
diff --git a/K-Means/Tests/Info.plist b/K-Means/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/K-Means/Tests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
new file mode 100644
index 000000000..436cab4fe
--- /dev/null
+++ b/K-Means/Tests/KMeansTests.swift
@@ -0,0 +1,65 @@
+//
+//  Tests.swift
+//  Tests
+//
+//  Created by John Gill on 2/29/16.
+//
+//
+
+import Foundation
+import XCTest
+
+class KMeansTests: XCTestCase {
+    var points = [Vector]()
+    
+    func genPoints(numPoints:Int, numDimmensions:Int) {
+        for _ in 0..<numPoints {
+            var data = [Double]()
+            for _ in 0..<numDimmensions {
+                data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
+            }
+            points.append(Vector(d: data))
+        }
+
+    }
+    
+    func testSmall_2D() {
+        genPoints(10, numDimmensions: 2)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 3, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+    
+    func testSmall_10D() {
+        genPoints(10, numDimmensions: 10)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 3, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+    
+    func testLarge_2D() {
+        genPoints(10000, numDimmensions: 2)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 5, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+    
+    func testLarge_10D() {
+        genPoints(10000, numDimmensions: 10)
+        
+        print("\nCenters")
+        let kmm = KMeans(numCenters: 5, convergeDist: 0.01)
+        for c in kmm.findCenters(points) {
+            print(c)
+        }
+    }
+}
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..55f861d02
--- /dev/null
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,261 @@
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+
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+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
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+				B80894EA1C852DA00018730E /* Vector.swift in Sources */,
+				B80894E41C852D100018730E /* KMeansTests.swift in Sources */,
+				B80894EB1C8530830018730E /* KMeans.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		B80894D91C852CDC0018730E /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Debug;
+		};
+		B80894DA1C852CDC0018730E /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Release;
+		};
+		B80894E71C852D100018730E /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
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+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		B80894E81C852D100018730E /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
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+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		B80894D81C852CDC0018730E /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				B80894D91C852CDC0018730E /* Debug */,
+				B80894DA1C852CDC0018730E /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		B80894E61C852D100018730E /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				B80894E71C852D100018730E /* Debug */,
+				B80894E81C852D100018730E /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = B80894D51C852CDC0018730E /* Project object */;
+}
diff --git a/K-Means/Tests/Vector.swift b/K-Means/Tests/Vector.swift
new file mode 100644
index 000000000..a920de7de
--- /dev/null
+++ b/K-Means/Tests/Vector.swift
@@ -0,0 +1,76 @@
+//
+//  Vector.swift
+//  Tests
+//
+//  Created by John Gill on 2/29/16.
+//
+//
+
+import Foundation
+
+// Container to easily hold N Dimensional Vectors
+class Vector: CustomStringConvertible, Equatable {
+    private(set) var length = 0
+    private(set) var data = [Double]()
+    
+    init(d:[Double]) {
+        data = d
+        length = d.count
+    }
+    
+    var description: String { return "Vector (\(data)" }
+    
+    func distTo(v2:Vector) -> Double {
+        var result = 0.0
+        for idx in 0..<self.length {
+            result += pow(self.data[idx] - v2.data[idx], 2.0)
+        }
+        return sqrt(result)
+    }
+}
+
+// MARK: Vector Operators
+func ==(left: Vector, right: Vector) -> Bool {
+    for idx in 0..<left.length {
+        if left.data[idx] != right.data[idx] {
+            return false
+        }
+    }
+    return true
+}
+
+func +(left: Vector, right: Vector) -> Vector {
+    var results = [Double]()
+    for idx in 0..<left.length {
+        results.append(left.data[idx] + right.data[idx])
+    }
+    return Vector(d: results)
+}
+
+func +=(inout left: Vector, right: Vector) {
+    left = left + right
+}
+
+func -(left: Vector, right: Vector) -> Vector {
+    var results = [Double]()
+    for idx in 0..<left.length {
+        results.append(left.data[idx] - right.data[idx])
+    }
+    return Vector(d: results)
+}
+
+func -=(inout left: Vector, right: Vector) {
+    left = left - right
+}
+
+func /(left:Vector, right: Double) -> Vector  {
+    var results = [Double](count: left.length, repeatedValue: 0.0)
+    for (idx, value) in left.data.enumerate() {
+        results[idx] = value / right
+    }
+    return Vector(d: results)
+}
+
+func /=(inout left: Vector, right: Double) {
+    left = left / right
+}
\ No newline at end of file

From 6cc2f29f6b2c30cc6f59e70e2ea1d59e1a9749ae Mon Sep 17 00:00:00 2001
From: jamil <jamil.dhanani@gmail.com>
Date: Mon, 29 Feb 2016 22:21:10 -0500
Subject: [PATCH 0085/1679] Add README

---
 Bloom Filter/README.markdown | 58 ++++++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 Bloom Filter/README.markdown

diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
new file mode 100644
index 000000000..f50877138
--- /dev/null
+++ b/Bloom Filter/README.markdown	
@@ -0,0 +1,58 @@
+# Binary Tree
+
+## Introduction
+
+A Bloom Filter is a space-efficient data structure to check for an element in a set, that guarantees that there are no false negatives on queries. In other words, a query to a Bloom filter either returns "false", meaning the element is definitely not in the set, or "true", meaning that the element could be in the set. At first, this may not seem too useful. However, it's important in applications like cache filtering and data synchronization.
+
+An advantage of the Bloom Filter over a hash table is that the former maintains constant memory usage and constant-time insert and search. For a large number of elements in a set, the performance difference between a hash table and a Bloom Filter is significant, and it is a viable option if you do not need the guarantee of no false positives.
+
+## Implementation
+
+A Bloom Filter is essentially a fixed-length bit vector. To insert an element in the filter, it is hashed with *m* different hash functions, which map to indices in the array. The bits at these indices are set to `1`, or `true`, when an element is inserted.
+
+Querying, similarly, is accomplished by hashing the expected value, and checking to see if all of the bits at the indices are `true`. If even one of the bits is not `true`, the element could not have been inserted - and the query returns `false`. If all the bits are `true`, the query returns likewise. If there are "collisions", the query may erroneously return `true` even though the element was not inserted - bringing about the issue with false positives mentioned earlier.
+
+Deletion is not possible with a Bloom Filter, since any one bit might have been set by multiple elements inserted. Once you add an element, it's in there for good.
+
+## The Code
+
+The code is extremely straightforward, as you can imagine. The internal bit array is set to a fixed length on initialization, which cannot be mutated once it is initialized. Several hash functions should be specified at initialization, which will depend on the types you're using. You can see some examples in the tests - the djb2 and sdbm hash functions for strings.
+
+```swift
+public init(size: Int = 1024, hashFunctions: [T -> Int]) {
+    self.arr = Array<Bool>(count: size, repeatedValue: false)
+    self.hashFunctions = hashFunctions
+}
+```
+
+Insertion just flips the required bits to `true`:
+
+```swift
+public func insert(toInsert: T) {
+    let hashValues: [Int] = self.computeHashes(toInsert)
+
+    for hashValue in hashValues {
+        self.arr[hashValue] = true
+    }
+}
+```
+
+And querying checks to make sure the bits at the hashed values are `true`:
+
+```swift
+public func query(value: T) -> Bool {
+    let hashValues = self.computeHashes(value)
+
+    let results = hashValues.map() { hashValue in
+        self.arr[hashValue]
+    }
+
+    let exists = results.reduce(true, combine: { $0 && $1 })
+
+    return exists
+}
+```
+
+If you're coming from another imperative language, you might notice the unusual syntax in the `exists` constant assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case, `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop. 
+
+*Written for Swift Algorithm Club by Jamil Dhanani*

From 7faca17d67592f8c072ac5615d040e8807a9e9d5 Mon Sep 17 00:00:00 2001
From: jamil <jamil.dhanani@gmail.com>
Date: Mon, 29 Feb 2016 22:21:40 -0500
Subject: [PATCH 0086/1679] Remove Info.plist in Test directory

---
 Bloom Filter/BloomFilterTests/Info.plist | 24 ------------------------
 1 file changed, 24 deletions(-)
 delete mode 100644 Bloom Filter/BloomFilterTests/Info.plist

diff --git a/Bloom Filter/BloomFilterTests/Info.plist b/Bloom Filter/BloomFilterTests/Info.plist
deleted file mode 100644
index ba72822e8..000000000
--- a/Bloom Filter/BloomFilterTests/Info.plist	
+++ /dev/null
@@ -1,24 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>BNDL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-</dict>
-</plist>

From cf97f25bfb3a615671e12d0fdbab82d8d2d5fd19 Mon Sep 17 00:00:00 2001
From: Jamil Dhanani <jamil.dhanani@gmail.com>
Date: Mon, 29 Feb 2016 22:31:31 -0500
Subject: [PATCH 0087/1679] Fix typos in README

---
 Bloom Filter/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index f50877138..f06bef5bd 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -1,4 +1,4 @@
-# Binary Tree
+# Bloom Filter
 
 ## Introduction
 

From 11e3d64c90fa5369a1898d9dee9ef73f7b73871f Mon Sep 17 00:00:00 2001
From: jamil <jamil.dhanani@gmail.com>
Date: Mon, 29 Feb 2016 22:39:20 -0500
Subject: [PATCH 0088/1679] Add Bloom Filter to README

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 579e7c182..c53232982 100644
--- a/README.markdown
+++ b/README.markdown
@@ -154,7 +154,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 ### Sets
 
-- Bloom Filter
+- [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash Set/). A set implemented using a hash table.
 - Multiset
 - Ordered Set

From a070fb29613b36acf50e14795f348af93d457f7b Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Sun, 28 Feb 2016 18:01:20 -0800
Subject: [PATCH 0089/1679] Initital implementation of Bounded Priority Queue

---
 .../BoundedPriorityQueue.swift                | 105 +++++++
 .../Tests/BoundedPriorityQueueTests.swift     | 115 ++++++++
 Bounded Priority Queue/Tests/Info.plist       |  24 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 260 ++++++++++++++++++
 .../Contents.swift                            |  47 ++++
 .../contents.xcplayground                     |   4 +
 .../timeline.xctimeline                       |  31 +++
 K-Nearest Neighbors/README.md                 |   7 +
 8 files changed, 593 insertions(+)
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.swift
 create mode 100644 Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift
 create mode 100644 Bounded Priority Queue/Tests/Info.plist
 create mode 100644 Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift
 create mode 100644 K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground
 create mode 100644 K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline
 create mode 100644 K-Nearest Neighbors/README.md

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.swift
new file mode 100644
index 000000000..f5f3a2221
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.swift	
@@ -0,0 +1,105 @@
+//
+//  BoundedPriorityQueue.swift
+//  Tests
+//
+//  Created by John Gill on 2/28/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import Foundation
+
+public class LinkedListNode<T> {
+    var value: T
+    var next: LinkedListNode?
+    var previous: LinkedListNode?
+    
+    public init(value: T) {
+        self.value = value
+        self.next = nil
+        self.previous = nil
+    }
+}
+
+public class BoundedPriorityQueue<T> {
+    public typealias Node = LinkedListNode<T>
+    private var head: Node?
+    private var isLessThan:(T, T) -> Bool
+    private var curNumElements:Int
+    private var maxNumElements: Int
+    
+    public init(sort: (T, T) -> Bool, maxElements:Int) {
+        isLessThan = sort
+        head = nil
+        maxNumElements = maxElements
+        curNumElements = 0
+    }
+    
+    public var isEmpty: Bool {
+        return curNumElements == 0
+    }
+    
+    public var count: Int {
+        return curNumElements
+    }
+    
+    public func peek() -> T? {
+        if curNumElements > 0 {
+            return head!.value
+        }
+        return nil
+    }
+    
+    public func enqueue(value: T) {
+        let newNode = Node(value: value)
+        
+        if head == nil  {
+            head = newNode
+        } else {
+            var node = head
+            if curNumElements == maxNumElements && !isLessThan(newNode.value, node!.value) {
+                return
+            }
+
+            while node!.next != nil && isLessThan(newNode.value, node!.value) { node = node!.next }
+            
+            if isLessThan(newNode.value, node!.value) {
+                newNode.next = node!.next
+                newNode.previous = node
+                
+                if(newNode.next != nil) { /* TAIL */
+                    newNode.next!.previous = newNode
+                }
+                node!.next = newNode
+            } else {
+                newNode.previous = node!.previous
+                newNode.next = node
+                if(node!.previous == nil) { /* HEAD */
+                    head = newNode
+                } else {
+                    node!.previous!.next = newNode
+                }
+                node!.previous = newNode
+            }
+            if(curNumElements == maxNumElements) { dequeue() }
+        }
+        curNumElements++
+    }
+    
+    public func dequeue() -> T? {
+        if curNumElements > 0 {
+            let retVal = head!.value
+            
+            if curNumElements == 1 {
+                head = nil
+            }
+            else {
+                head = head!.next
+                head!.previous = nil
+            }
+
+            curNumElements--
+            return retVal
+        }
+        return nil
+    }
+}
\ No newline at end of file
diff --git a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift
new file mode 100644
index 000000000..4b68b0bab
--- /dev/null
+++ b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
@@ -0,0 +1,115 @@
+//
+//  BoundedPriorityQueueTests.swift
+//  Tests
+//
+//  Created by John Gill on 2/28/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+import Foundation
+import XCTest
+
+private struct Message {
+    let name: String
+    let priority: Int
+}
+
+private func < (m1: Message, m2: Message) -> Bool {
+    return m1.priority < m2.priority
+}
+
+class BoundedPriorityQueueTest: XCTestCase {
+    func testEmpty() {
+        let queue = BoundedPriorityQueue<Message>(sort: <, maxElements: 5)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.dequeue())
+    }
+    
+    func testOneElement() {
+        let queue = BoundedPriorityQueue<Message>(sort: <, maxElements: 5)
+        
+        queue.enqueue(Message(name: "hello", priority: 100))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        
+        let result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 100)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+    }
+    
+    func testMaxElements() {
+        let queue = BoundedPriorityQueue<Message>(sort: <, maxElements: 5)
+        XCTAssertTrue(queue.isEmpty)
+        
+        queue.enqueue(Message(name: "john", priority: 100))
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()?.priority, 100)
+        
+        queue.enqueue(Message(name: "james", priority: 200))
+        XCTAssertEqual(queue.count, 2)
+        XCTAssertEqual(queue.peek()?.priority, 200)
+        
+        queue.enqueue(Message(name: "mark", priority: 300))
+        XCTAssertEqual(queue.count, 3)
+        XCTAssertEqual(queue.peek()?.priority, 300)
+        
+        queue.enqueue(Message(name: "ken", priority: 400))
+        XCTAssertEqual(queue.count, 4)
+        XCTAssertEqual(queue.peek()?.priority, 400)
+
+        queue.enqueue(Message(name: "thomas", priority: 500))
+        XCTAssertEqual(queue.count, 5)
+        XCTAssertEqual(queue.peek()?.priority, 500)
+        
+        queue.enqueue(Message(name: "melanie", priority: 550))
+        XCTAssertEqual(queue.count, 5)
+        XCTAssertEqual(queue.peek()?.priority, 500)
+        
+        queue.enqueue(Message(name: "lily", priority: 450))
+        XCTAssertEqual(queue.count, 5)
+        XCTAssertEqual(queue.peek()?.priority, 450)
+        
+        queue.enqueue(Message(name: "fred", priority: 350))
+        XCTAssertEqual(queue.count, 5)
+        XCTAssertEqual(queue.peek()?.priority, 400)
+        
+        queue.enqueue(Message(name: "rachel", priority: 50))
+        XCTAssertEqual(queue.count, 5)
+        XCTAssertEqual(queue.peek()?.priority, 350)
+        
+        var result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 350)
+        XCTAssertEqual(queue.count, 4)
+        
+        result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 300)
+        XCTAssertEqual(queue.count, 3)
+        
+        result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 200)
+        XCTAssertEqual(queue.count, 2)
+        
+        queue.enqueue(Message(name: "ryan", priority: 150))
+        XCTAssertEqual(queue.count, 3)
+        XCTAssertEqual(queue.peek()?.priority, 150)
+        
+        result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 150)
+        XCTAssertEqual(queue.count, 2)
+        
+        result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 100)
+        XCTAssertEqual(queue.count, 1)
+        
+        result = queue.dequeue()
+        XCTAssertEqual(result!.priority, 50)
+        XCTAssertEqual(queue.count, 0)
+        
+        result = queue.dequeue()
+        XCTAssertNil(result)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertTrue(queue.isEmpty)
+    }
+}
\ No newline at end of file
diff --git a/Bounded Priority Queue/Tests/Info.plist b/Bounded Priority Queue/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..2920474ae
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,260 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		B810B5B11C83E3B200450324 /* BoundedPriorityQueueTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = B810B5B01C83E3B200450324 /* BoundedPriorityQueueTests.swift */; };
+		B8F635A81C83E4270060805E /* BoundedPriorityQueue.swift in Sources */ = {isa = PBXBuildFile; fileRef = B8F635A71C83E4270060805E /* BoundedPriorityQueue.swift */; };
+/* End PBXBuildFile section */
+
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+		B80004B31C83E342001FE2D7 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		B80004B81C83E342001FE2D7 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		B810B5B01C83E3B200450324 /* BoundedPriorityQueueTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoundedPriorityQueueTests.swift; path = ../BoundedPriorityQueueTests.swift; sourceTree = "<group>"; };
+		B8F635A71C83E4270060805E /* BoundedPriorityQueue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoundedPriorityQueue.swift; path = ../../BoundedPriorityQueue.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		B80004B01C83E342001FE2D7 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		B80004A81C83E324001FE2D7 = {
+			isa = PBXGroup;
+			children = (
+				B80004B51C83E342001FE2D7 /* Tests */,
+				B80004B41C83E342001FE2D7 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		B80004B41C83E342001FE2D7 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				B80004B31C83E342001FE2D7 /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		B80004B51C83E342001FE2D7 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				B8F635A71C83E4270060805E /* BoundedPriorityQueue.swift */,
+				B810B5B01C83E3B200450324 /* BoundedPriorityQueueTests.swift */,
+				B80004B81C83E342001FE2D7 /* Info.plist */,
+			);
+			path = Tests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
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+			buildPhases = (
+				B80004AF1C83E342001FE2D7 /* Sources */,
+				B80004B11C83E342001FE2D7 /* Resources */,
+				B80004B01C83E342001FE2D7 /* Frameworks */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = Tests;
+			productReference = B80004B31C83E342001FE2D7 /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		B80004A91C83E324001FE2D7 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				TargetAttributes = {
+					B80004B21C83E342001FE2D7 = {
+						CreatedOnToolsVersion = 7.2.1;
+					};
+				};
+			};
+			buildConfigurationList = B80004AC1C83E324001FE2D7 /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
+			mainGroup = B80004A81C83E324001FE2D7;
+			productRefGroup = B80004B41C83E342001FE2D7 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				B80004B21C83E342001FE2D7 /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		B80004B11C83E342001FE2D7 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		B80004AF1C83E342001FE2D7 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				B810B5B11C83E3B200450324 /* BoundedPriorityQueueTests.swift in Sources */,
+				B8F635A81C83E4270060805E /* BoundedPriorityQueue.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		B80004AD1C83E324001FE2D7 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Debug;
+		};
+		B80004AE1C83E324001FE2D7 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Release;
+		};
+		B80004BA1C83E342001FE2D7 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OBJC_BRIDGING_HEADER = "";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		B80004BB1C83E342001FE2D7 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OBJC_BRIDGING_HEADER = "";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		B80004AC1C83E324001FE2D7 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				B80004AD1C83E324001FE2D7 /* Debug */,
+				B80004AE1C83E324001FE2D7 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		B80004B91C83E342001FE2D7 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				B80004BA1C83E342001FE2D7 /* Debug */,
+				B80004BB1C83E342001FE2D7 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = B80004A91C83E324001FE2D7 /* Project object */;
+}
diff --git a/K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift b/K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift
new file mode 100644
index 000000000..a4dd21dd0
--- /dev/null
+++ b/K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift	
@@ -0,0 +1,47 @@
+//
+//  K-NearestNeighbors.swift
+//
+//  Created by John Gill on 2/23/16.
+import Foundation
+
+// Container to easily hold N Dimensional Vectors
+class VectorND: CustomStringConvertible {
+    private var length = 0
+    private var data = [Double]()
+    
+    init(d:[Double]) {
+        data = d
+        length = d.count
+    }
+    
+    var description: String { return "VectorND (\(data)" }
+    func getData() -> [Double] { return data }
+    func getLength() -> Int { return length }
+    
+    // Calculates the Euclidean distance from 
+    // this point to another VectorND
+    func getDist(v:VectorND) -> Double {
+        var result = 0.0
+        for idx in 0..<length {
+            result += pow(data[idx] - v.getData()[idx], 2.0)
+        }
+        return sqrt(result)
+    }
+}
+
+class kNearestNeighbrs {
+    var k:Int // Number of Neighbors
+    
+    init(k:Int) {
+        self.k = k
+    }
+    
+    func train (data:[VectorND], labels:[Int]) {
+        
+    }
+    
+    func predict (data: [VectorND]) -> [Int] {
+        
+        return []
+    }
+}
\ No newline at end of file
diff --git a/K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground b/K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground
new file mode 100644
index 000000000..9f9eecc96
--- /dev/null
+++ b/K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline b/K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline
new file mode 100644
index 000000000..4dca8e784
--- /dev/null
+++ b/K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline	
@@ -0,0 +1,31 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=3&amp;EndingLineNumber=46&amp;StartingColumnNumber=1&amp;StartingLineNumber=46&amp;Timestamp=478157983.180935"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=19&amp;EndingLineNumber=46&amp;StartingColumnNumber=5&amp;StartingLineNumber=46&amp;Timestamp=478157983.181127"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=16&amp;EndingLineNumber=46&amp;StartingColumnNumber=5&amp;StartingLineNumber=46&amp;Timestamp=478157983.181274"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=7&amp;EndingLineNumber=46&amp;StartingColumnNumber=1&amp;StartingLineNumber=46&amp;Timestamp=478157983.181423"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=37&amp;EndingLineNumber=46&amp;StartingColumnNumber=1&amp;StartingLineNumber=46&amp;Timestamp=478157983.181558"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>
diff --git a/K-Nearest Neighbors/README.md b/K-Nearest Neighbors/README.md
new file mode 100644
index 000000000..9e22c4a02
--- /dev/null
+++ b/K-Nearest Neighbors/README.md	
@@ -0,0 +1,7 @@
+# k-Nearest Neighbors
+
+Goal: Label Data into Clusters by k Nearest other points
+
+Machine Learning algorithms are two pass:
+    1. Train the algorithm on a set of Data
+    2. Predict new labels for data based on training

From f0d833a5a718ea23b381ce22cc658ae63dec19c8 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 1 Mar 2016 19:59:35 +0100
Subject: [PATCH 0090/1679] Tweak text and code style

Add examples to description
Add playground
Add test project
---
 .../BloomFilter.playground/Contents.swift     |  86 ++++++
 .../contents.xcplayground                     |   4 +
 .../timeline.xctimeline                       |   6 +
 Bloom Filter/BloomFilter.swift                |  90 +++---
 Bloom Filter/README.markdown                  |  93 +++++--
 .../BloomFilterTests.swift                    |   2 -
 Bloom Filter/Tests/Info.plist                 |  24 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 261 ++++++++++++++++++
 8 files changed, 488 insertions(+), 78 deletions(-)
 create mode 100644 Bloom Filter/BloomFilter.playground/Contents.swift
 create mode 100644 Bloom Filter/BloomFilter.playground/contents.xcplayground
 create mode 100644 Bloom Filter/BloomFilter.playground/timeline.xctimeline
 rename Bloom Filter/{BloomFilterTests => Tests}/BloomFilterTests.swift (98%)
 create mode 100644 Bloom Filter/Tests/Info.plist
 create mode 100644 Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
new file mode 100644
index 000000000..0727ea439
--- /dev/null
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -0,0 +1,86 @@
+//: Playground - noun: a place where people can play
+
+public class BloomFilter<T> {
+  private var array: [Bool]
+  private var hashFunctions: [T -> Int]
+  
+  public init(size: Int = 1024, hashFunctions: [T -> Int]) {
+    self.array = .init(count: size, repeatedValue: false)
+    self.hashFunctions = hashFunctions
+  }
+  
+  private func computeHashes(value: T) -> [Int] {
+    return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
+  }
+  
+  public func insert(element: T) {
+    for hashValue in computeHashes(element) {
+      array[hashValue] = true
+    }
+  }
+  
+  public func insert(values: [T]) {
+    for value in values {
+      insert(value)
+    }
+  }
+  
+  public func query(value: T) -> Bool {
+    let hashValues = computeHashes(value)
+    
+    // Map hashes to indices in the Bloom Filter
+    let results = hashValues.map() { hashValue in array[hashValue] }
+    
+    // All values must be 'true' for the query to return true
+    
+    // This does NOT imply that the value is in the Bloom filter,
+    // only that it may be. If the query returns false, however,
+    // you can be certain that the value was not added.
+    
+    let exists = results.reduce(true, combine: { $0 && $1 })
+    return exists
+  }
+  
+  public func isEmpty() -> Bool {
+    // As soon as the reduction hits a 'true' value, the && condition will fail.
+    return array.reduce(true) { prev, next in prev && !next }
+  }
+}
+
+
+
+/* Two hash functions, adapted from http://www.cse.yorku.ca/~oz/hash.html */
+
+func djb2(x: String) -> Int {
+  var hash = 5381
+  for char in x.characters {
+    hash = ((hash << 5) &+ hash) &+ char.hashValue
+  }
+  return Int(hash)
+}
+
+func sdbm(x: String) -> Int {
+  var hash = 0
+  for char in x.characters {
+    hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
+  }
+  return Int(hash)
+}
+
+
+
+/* A simple test */
+
+let bloom = BloomFilter<String>(size: 17, hashFunctions: [djb2, sdbm])
+
+bloom.insert("Hello world!")
+print(bloom.array)
+
+bloom.query("Hello world!")    // true
+bloom.query("Hello WORLD")     // false
+
+bloom.insert("Bloom Filterz")
+print(bloom.array)
+
+bloom.query("Bloom Filterz")   // true
+bloom.query("Hello WORLD")     // true
diff --git a/Bloom Filter/BloomFilter.playground/contents.xcplayground b/Bloom Filter/BloomFilter.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Bloom Filter/BloomFilter.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Bloom Filter/BloomFilter.playground/timeline.xctimeline b/Bloom Filter/BloomFilter.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Bloom Filter/BloomFilter.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Bloom Filter/BloomFilter.swift b/Bloom Filter/BloomFilter.swift
index 6f5232b0d..83787ee7b 100644
--- a/Bloom Filter/BloomFilter.swift	
+++ b/Bloom Filter/BloomFilter.swift	
@@ -1,58 +1,46 @@
-import Foundation
-
 public class BloomFilter<T> {
-    private(set) private var arr: [Bool]
-    private(set) private var hashFunctions: [T -> Int]
-    
-    public init(size: Int = 1024, hashFunctions: [T -> Int]) {
-        self.arr = Array<Bool>(count: size, repeatedValue: false)
-        self.hashFunctions = hashFunctions
+  private var array: [Bool]
+  private var hashFunctions: [T -> Int]
+  
+  public init(size: Int = 1024, hashFunctions: [T -> Int]) {
+    self.array = .init(count: size, repeatedValue: false)
+    self.hashFunctions = hashFunctions
+  }
+  
+  private func computeHashes(value: T) -> [Int] {
+    return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
+  }
+  
+  public func insert(element: T) {
+    for hashValue in computeHashes(element) {
+      array[hashValue] = true
     }
-    
-    private func computeHashes(value: T) -> [Int] {
-        return hashFunctions.map() { hashFunc in
-            abs(hashFunc(value) % self.arr.count)
-        }
+  }
+  
+  public func insert(values: [T]) {
+    for value in values {
+      insert(value)
     }
+  }
+  
+  public func query(value: T) -> Bool {
+    let hashValues = computeHashes(value)
     
-    public func insert(toInsert: T) {
-        let hashValues: [Int] = self.computeHashes(toInsert)
-        
-        for hashValue in hashValues {
-            self.arr[hashValue] = true
-        }
-    }
+    // Map hashes to indices in the Bloom Filter
+    let results = hashValues.map() { hashValue in array[hashValue] }
     
-    public func insert(values: [T]) {
-        for value in values {
-            self.insert(value)
-        }
-    }
+    // All values must be 'true' for the query to return true
     
-    public func query(value: T) -> Bool {
-        let hashValues = self.computeHashes(value)
-        
-        // Map hashes to indices in the Bloom filter
-        let results = hashValues.map() { hashValue in
-            self.arr[hashValue]
-        }
-        
-        // All values must be 'true' for the query to return true
-
-        // This does NOT imply that the value is in the Bloom filter,
-        // only that it may be. If the query returns false, however,
-        // you can be certain that the value was not added.
-
-        let exists = results.reduce(true, combine: { $0 && $1 })
-        
-        return exists
-    }
-    
-    public func isEmpty() -> Bool {
-        // Reduce list; as soon as the reduction hits a 'true' value, the && condition will fail
-        return arr.reduce(true) { prev, next in
-            prev && !next
-        }
-    }
+    // This does NOT imply that the value is in the Bloom filter,
+    // only that it may be. If the query returns false, however,
+    // you can be certain that the value was not added.
     
-}
\ No newline at end of file
+    let exists = results.reduce(true, combine: { $0 && $1 })
+    return exists
+  }
+  
+  public func isEmpty() -> Bool {
+    // As soon as the reduction hits a 'true' value, the && condition will fail.
+    return array.reduce(true) { prev, next in prev && !next }
+  }
+}
diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index f06bef5bd..c0c06400b 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -2,38 +2,86 @@
 
 ## Introduction
 
-A Bloom Filter is a space-efficient data structure to check for an element in a set, that guarantees that there are no false negatives on queries. In other words, a query to a Bloom filter either returns "false", meaning the element is definitely not in the set, or "true", meaning that the element could be in the set. At first, this may not seem too useful. However, it's important in applications like cache filtering and data synchronization.
+A Bloom Filter is a space-efficient data structure that tells you whether or not an element is present in a set.
 
-An advantage of the Bloom Filter over a hash table is that the former maintains constant memory usage and constant-time insert and search. For a large number of elements in a set, the performance difference between a hash table and a Bloom Filter is significant, and it is a viable option if you do not need the guarantee of no false positives.
+This is a probabilistic data structure: a query to a Bloom filter either returns `false`, meaning the element is definitely not in the set, or `true`, meaning that the element *might* be in the set.
 
-## Implementation
+There is a small probability of false positives, where the element isn't actually in the set even though the query returned `true`. But there will never any false negatives: you're guaranteed that if the query returns `false`, then the element really isn't in the set.
 
-A Bloom Filter is essentially a fixed-length bit vector. To insert an element in the filter, it is hashed with *m* different hash functions, which map to indices in the array. The bits at these indices are set to `1`, or `true`, when an element is inserted.
+So a Bloom Filter tells you, "definitely not" or "probably yes".
 
-Querying, similarly, is accomplished by hashing the expected value, and checking to see if all of the bits at the indices are `true`. If even one of the bits is not `true`, the element could not have been inserted - and the query returns `false`. If all the bits are `true`, the query returns likewise. If there are "collisions", the query may erroneously return `true` even though the element was not inserted - bringing about the issue with false positives mentioned earlier.
+At first, this may not seem too useful. However, it's important in applications like cache filtering and data synchronization.
+
+An advantage of the Bloom Filter over a hash table is that the former maintains constant memory usage and constant-time insert and search. For sets with a large number of elements, the performance difference between a hash table and a Bloom Filter is significant, and it is a viable option if you do not need the guarantee of no false positives.
+
+> **Note:** Unlike a hash table, the Bloom Filter does not store the actual objects. It just remembers what objects you’ve seen (with a degree of uncertainty) and which ones you haven’t.
+
+## How it works
+
+A Bloom Filter is essentially a fixed-length [bit vector](../Bit Set/), an array of bits. When we insert objects, we set some of these bits to `1`, and when we query for objects we check if certain bits are `0` or `1`. Both operations use hash functions.
+
+To insert an element in the filter, the element is hashed with several different hash functions. Each hash function returns a value that we map to an index in the array. We set the bits at these indices to `1` or true.
+
+For example, let's say this is our array of bits. We have 17 bits and initially they are all `0` or false:
+
+	[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
+
+Now we want to insert the string `"Hello world!"` into the Bloom Filter. We apply two hash functions to this string. The first one gives the value 1999532104120917762. We map this hash value to an index into our array by taking the modulo of the array length: `1999532104120917762 % 17 = 4`. This means we set the bit at index 4 to `1` or true:
+
+	[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
+
+Then we hash the original string again but this time with a different hash function. It gives the hash value 9211818684948223801. Modulo 17 that is 12, and we set the bit at index 12 to `1` as well:
+
+	[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
+
+These two bits are enough to tell the Bloom Filter that it now contains the string `"Hello world!"`.
+
+Querying, similarly, is accomplished by first hashing the expected value, which gives several array indices, and then checking to see if all of the bits at those indices are `true`. If even one of the bits is not `true`, the element could not have been inserted and the query returns `false`. If all the bits are `true`, the query returns likewise.
+
+For example, if we query for the string `"Hello WORLD"`, then the first hash function returns 5383892684077141175, which modulo 17 is 12. That bit is `1`. But the second hash function gives 5625257205398334446, which maps to array index 9. That bit is `0`. This means the string `"Hello WORLD"` is not in the filter and the query returns `false`.
+
+The fact that the first hash function mapped to a `1` bit is a coincidence (it has nothing to do with the fact that both strings start with `"Hello "`). Too many such coincidences can lead to "collisions". If there are collisions, the query may erroneously return `true` even though the element was not inserted -- bringing about the issue with false positives mentioned earlier.
+
+Let's say we insert some other element, `"Bloom Filterz"`, which sets bits 7 and 9. Now the array looks like this:
+
+	[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0 ]
+
+If you query for `"Hello WORLD"` again, the filter sees that bit 12 is true and bit 9 is now true as well. It reports that `"Hello WORLD"` is indeed present in the set, even though it isn't... because we never inserted that particular string. It's a false positive. This example shows why a Bloom Filter will never say, "definitely yes", only "probably yes".
+
+You can fix such issues by using an array with more bits and using additional hash functions. Of course, the more hash functions you use the slower the Bloom Filter will be. So you have to strike a balance.
 
 Deletion is not possible with a Bloom Filter, since any one bit might have been set by multiple elements inserted. Once you add an element, it's in there for good.
 
-## The Code
+Performance of a Bloom Filter is **O(k)** where **k** is the number of hashing functions.
+
+## The code
 
-The code is extremely straightforward, as you can imagine. The internal bit array is set to a fixed length on initialization, which cannot be mutated once it is initialized. Several hash functions should be specified at initialization, which will depend on the types you're using. You can see some examples in the tests - the djb2 and sdbm hash functions for strings.
+The code is quite straightforward. The internal bit array is set to a fixed length on initialization, which cannot be mutated once it is initialized. 
 
 ```swift
 public init(size: Int = 1024, hashFunctions: [T -> Int]) {
-    self.arr = Array<Bool>(count: size, repeatedValue: false)
-    self.hashFunctions = hashFunctions
+  self.array = .init(count: size, repeatedValue: false)
+  self.hashFunctions = hashFunctions
 }
 ```
 
+Several hash functions should be specified at initialization. Which hash functions you use will depend on the datatypes of the elements you'll be adding to the set. You can see some examples in the playground and the tests -- the `djb2` and `sdbm` hash functions for strings.
+
 Insertion just flips the required bits to `true`:
 
 ```swift
-public func insert(toInsert: T) {
-    let hashValues: [Int] = self.computeHashes(toInsert)
+public func insert(element: T) {
+  for hashValue in computeHashes(element) {
+    array[hashValue] = true
+  }
+}
+```
 
-    for hashValue in hashValues {
-        self.arr[hashValue] = true
-    }
+This uses the `computeHashes()` function, which loops through the specified `hashFunctions` and returns an array of indices:
+
+```swift
+private func computeHashes(value: T) -> [Int] {
+  return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
 }
 ```
 
@@ -41,18 +89,13 @@ And querying checks to make sure the bits at the hashed values are `true`:
 
 ```swift
 public func query(value: T) -> Bool {
-    let hashValues = self.computeHashes(value)
-
-    let results = hashValues.map() { hashValue in
-        self.arr[hashValue]
-    }
-
-    let exists = results.reduce(true, combine: { $0 && $1 })
-
-    return exists
+  let hashValues = computeHashes(value)
+  let results = hashValues.map() { hashValue in array[hashValue] }
+  let exists = results.reduce(true, combine: { $0 && $1 })
+  return exists
 }
 ```
 
-If you're coming from another imperative language, you might notice the unusual syntax in the `exists` constant assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case, `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop. 
+If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case, `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop. 
 
-*Written for Swift Algorithm Club by Jamil Dhanani*
+*Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans.*
diff --git a/Bloom Filter/BloomFilterTests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
similarity index 98%
rename from Bloom Filter/BloomFilterTests/BloomFilterTests.swift
rename to Bloom Filter/Tests/BloomFilterTests.swift
index bb11f80aa..1248e0150 100644
--- a/Bloom Filter/BloomFilterTests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -1,10 +1,8 @@
 import XCTest
-import BloomFilter
 
 /* Two hash functions, adapted from
     http://www.cse.yorku.ca/~oz/hash.html */
 
-
 func djb2(x: String) -> Int {
     var hash = 5381
     
diff --git a/Bloom Filter/Tests/Info.plist b/Bloom Filter/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Bloom Filter/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..d413110c9
--- /dev/null
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,261 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3D01C77A263003CECC7 /* BloomFilter.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3CF1C77A263003CECC7 /* BloomFilter.swift */; };
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+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}

From c2fe941be578faaefdb3e83de2b68ff51599a7ea Mon Sep 17 00:00:00 2001
From: Paulo Tanaka <ptanaka@linkedin.com>
Date: Tue, 1 Mar 2016 15:16:56 -0800
Subject: [PATCH 0091/1679] Adding simple depth first search example

---
 .../Contents.swift                            |  38 +++
 .../timeline.xctimeline                       |   6 +
 .../Resources/Animated_BFS.gif                | Bin 0 -> 33276 bytes
 .../Resources/Minimum_Spanning_Tree.png       | Bin 0 -> 23928 bytes
 .../Sources/Edge.swift                        |  11 +
 .../Sources/Graph.swift                       |  56 ++++
 .../Sources/Node.swift                        |  32 ++
 .../contents.xcplayground                     |   2 +
 Depth-First Search/DepthFirstSearch.swift     |  15 +
 Depth-First Search/Edge.swift                 |  11 +
 Depth-First Search/Graph.swift                |  56 ++++
 Depth-First Search/Images/Animated_BFS.gif    | Bin 0 -> 33276 bytes
 .../Images/MinimumSpanningTree.sketch         | Bin 0 -> 81920 bytes
 .../Images/Minimum_Spanning_Tree.png          | Bin 0 -> 23928 bytes
 Depth-First Search/Node.swift                 |  32 ++
 Depth-First Search/README.markdown            |  61 ++++
 .../Tests/DepthFirstSearchTests.swift         |  84 ++++++
 Depth-First Search/Tests/Info.plist           |  24 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 276 ++++++++++++++++++
 19 files changed, 704 insertions(+)
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Resources/Animated_BFS.gif
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Resources/Minimum_Spanning_Tree.png
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/contents.xcplayground
 create mode 100644 Depth-First Search/DepthFirstSearch.swift
 create mode 100644 Depth-First Search/Edge.swift
 create mode 100644 Depth-First Search/Graph.swift
 create mode 100644 Depth-First Search/Images/Animated_BFS.gif
 create mode 100644 Depth-First Search/Images/MinimumSpanningTree.sketch
 create mode 100644 Depth-First Search/Images/Minimum_Spanning_Tree.png
 create mode 100644 Depth-First Search/Node.swift
 create mode 100644 Depth-First Search/README.markdown
 create mode 100755 Depth-First Search/Tests/DepthFirstSearchTests.swift
 create mode 100644 Depth-First Search/Tests/Info.plist
 create mode 100644 Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..e18e7cc58
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,38 @@
+func depthFirstSearch(graph: Graph, source: Node) -> [String] {
+  var nodesExplored: [String] = [source.label]
+  source.visited = true
+
+  // Iterate through all neighbors, and for each one visit all of its neighbors
+  for edge in source.neighbors {
+    let neighbor: Node = edge.neighbor
+
+    if (!neighbor.visited) {
+      nodesExplored += depthFirstSearch(graph, source: neighbor)
+    }
+  }
+  return nodesExplored
+}
+
+
+let graph = Graph()
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeD)
+graph.addEdge(nodeB, neighbor: nodeE)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeG)
+graph.addEdge(nodeE, neighbor: nodeH)
+
+
+let nodesExplored = depthFirstSearch(graph, source: nodeA)
+print(nodesExplored)
\ No newline at end of file
diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Depth-First Search/DepthFirstSearch.playground/Resources/Animated_BFS.gif b/Depth-First Search/DepthFirstSearch.playground/Resources/Animated_BFS.gif
new file mode 100644
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diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift
new file mode 100644
index 000000000..3937a2cc7
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
@@ -0,0 +1,11 @@
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
new file mode 100644
index 000000000..181af9e85
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -0,0 +1,56 @@
+public class Graph : CustomStringConvertible, Equatable {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    edge.neighbor = neighbor
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift
new file mode 100644
index 000000000..9d8435ffa
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
@@ -0,0 +1,32 @@
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
diff --git a/Depth-First Search/DepthFirstSearch.playground/contents.xcplayground b/Depth-First Search/DepthFirstSearch.playground/contents.xcplayground
new file mode 100644
index 000000000..5ed29117b
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/contents.xcplayground	
@@ -0,0 +1,2 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='6.0' target-platform='ios' display-mode='rendered'/>
\ No newline at end of file
diff --git a/Depth-First Search/DepthFirstSearch.swift b/Depth-First Search/DepthFirstSearch.swift
new file mode 100644
index 000000000..79e835f3e
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.swift	
@@ -0,0 +1,15 @@
+func depthFirstSearch(graph: Graph, source: Node) -> [String] {
+  var nodesExplored: [String] = [source.label]
+  source.visited = true
+
+  // Iterate through all neighbors, and for each one visit all of its neighbors
+  for edge in source.neighbors {
+    let neighbor: Node = edge.neighbor
+
+    if (!neighbor.visited) {
+      nodesExplored += depthFirstSearch(graph, source: neighbor)
+    }
+  }
+
+  return nodesExplored
+}
diff --git a/Depth-First Search/Edge.swift b/Depth-First Search/Edge.swift
new file mode 100644
index 000000000..3937a2cc7
--- /dev/null
+++ b/Depth-First Search/Edge.swift	
@@ -0,0 +1,11 @@
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
diff --git a/Depth-First Search/Graph.swift b/Depth-First Search/Graph.swift
new file mode 100644
index 000000000..181af9e85
--- /dev/null
+++ b/Depth-First Search/Graph.swift	
@@ -0,0 +1,56 @@
+public class Graph : CustomStringConvertible, Equatable {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    edge.neighbor = neighbor
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Depth-First Search/Images/Animated_BFS.gif b/Depth-First Search/Images/Animated_BFS.gif
new file mode 100644
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diff --git a/Depth-First Search/Node.swift b/Depth-First Search/Node.swift
new file mode 100644
index 000000000..000fd78f6
--- /dev/null
+++ b/Depth-First Search/Node.swift	
@@ -0,0 +1,32 @@
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
new file mode 100644
index 000000000..da5fd1b0b
--- /dev/null
+++ b/Depth-First Search/README.markdown	
@@ -0,0 +1,61 @@
+# Depth-First Search
+
+Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores as far as possible along each branch before backtracking.
+
+## The code
+
+Simple implementation of breadth-first search using a queue:
+
+```swift
+func depthFirstSearch(graph: Graph, source: Node) -> [String] {
+  var nodesExplored: [String] = [source.label]
+  source.visited = true
+
+  // Iterate through all neighbors, and for each one visit all of its neighbors
+  for edge in source.neighbors {
+    let neighbor: Node = edge.neighbor
+
+    if (!neighbor.visited) {
+      nodesExplored += depthFirstSearch(graph, source: neighbor)
+    }
+  }
+  return nodesExplored
+}
+```
+
+Put this code in a playground and test it like so:
+
+```swift
+let graph = Graph()   // Representing the graph from the animated example
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeD)
+graph.addEdge(nodeB, neighbor: nodeE)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeG)
+graph.addEdge(nodeE, neighbor: nodeH)
+
+let nodesExplored = depthFirstSearch(graph, source: nodeA)
+print(nodesExplored)
+```
+
+This will output: `["a", "b", "d", "e", "h", "c", "f", "g"]`
+   
+## Applications
+
+Depth-first search can be used to solve many problems, for example:
+
+* Finding connected components of a sparse graph
+* Topological sorting of nodes in a graph
+* Finding bridges of a graph (see: [Bridges](https://en.wikipedia.org/wiki/Bridge_(graph_theory)#Bridge-finding_algorithm))
+* Among others
diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
new file mode 100755
index 000000000..aacc8efcf
--- /dev/null
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -0,0 +1,84 @@
+import XCTest
+
+class DepthFirstSearchTests: XCTestCase {
+
+  func testExploringTree() {
+    let tree = Graph()
+    let nodeA = tree.addNode("a")
+    let nodeB = tree.addNode("b")
+    let nodeC = tree.addNode("c")
+    let nodeD = tree.addNode("d")
+    let nodeE = tree.addNode("e")
+    let nodeF = tree.addNode("f")
+    let nodeG = tree.addNode("g")
+    let nodeH = tree.addNode("h")
+    tree.addEdge(nodeA, neighbor: nodeB)
+    tree.addEdge(nodeA, neighbor: nodeC)
+    tree.addEdge(nodeB, neighbor: nodeD)
+    tree.addEdge(nodeB, neighbor: nodeE)
+    tree.addEdge(nodeC, neighbor: nodeF)
+    tree.addEdge(nodeC, neighbor: nodeG)
+    tree.addEdge(nodeE, neighbor: nodeH)
+
+    let nodesExplored = depthFirstSearch(tree, source: nodeA)
+
+    XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
+  }
+
+  func testExploringGraph() {
+    let graph = Graph()
+
+    let nodeA = graph.addNode("a")
+    let nodeB = graph.addNode("b")
+    let nodeC = graph.addNode("c")
+    let nodeD = graph.addNode("d")
+    let nodeE = graph.addNode("e")
+    let nodeF = graph.addNode("f")
+    let nodeG = graph.addNode("g")
+    let nodeH = graph.addNode("h")
+    let nodeI = graph.addNode("i")
+
+    graph.addEdge(nodeA, neighbor: nodeB)
+    graph.addEdge(nodeA, neighbor: nodeH)
+    graph.addEdge(nodeB, neighbor: nodeA)
+    graph.addEdge(nodeB, neighbor: nodeC)
+    graph.addEdge(nodeB, neighbor: nodeH)
+    graph.addEdge(nodeC, neighbor: nodeB)
+    graph.addEdge(nodeC, neighbor: nodeD)
+    graph.addEdge(nodeC, neighbor: nodeF)
+    graph.addEdge(nodeC, neighbor: nodeI)
+    graph.addEdge(nodeD, neighbor: nodeC)
+    graph.addEdge(nodeD, neighbor: nodeE)
+    graph.addEdge(nodeD, neighbor: nodeF)
+    graph.addEdge(nodeE, neighbor: nodeD)
+    graph.addEdge(nodeE, neighbor: nodeF)
+    graph.addEdge(nodeF, neighbor: nodeC)
+    graph.addEdge(nodeF, neighbor: nodeD)
+    graph.addEdge(nodeF, neighbor: nodeE)
+    graph.addEdge(nodeF, neighbor: nodeG)
+    graph.addEdge(nodeG, neighbor: nodeF)
+    graph.addEdge(nodeG, neighbor: nodeH)
+    graph.addEdge(nodeG, neighbor: nodeI)
+    graph.addEdge(nodeH, neighbor: nodeA)
+    graph.addEdge(nodeH, neighbor: nodeB)
+    graph.addEdge(nodeH, neighbor: nodeG)
+    graph.addEdge(nodeH, neighbor: nodeI)
+    graph.addEdge(nodeI, neighbor: nodeC)
+    graph.addEdge(nodeI, neighbor: nodeG)
+    graph.addEdge(nodeI, neighbor: nodeH)
+
+    let nodesExplored = depthFirstSearch(graph, source: nodeA)
+
+    XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
+
+  }
+
+  func testExploringGraphWithASingleNode() {
+    let graph = Graph()
+    let node = graph.addNode("a")
+
+    let nodesExplored = depthFirstSearch(graph, source: node)
+
+    XCTAssertEqual(nodesExplored, ["a"])
+  }
+}
\ No newline at end of file
diff --git a/Depth-First Search/Tests/Info.plist b/Depth-First Search/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Depth-First Search/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..e3c46e3cc
--- /dev/null
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,276 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
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+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		83F9C96B1C8443E800B3A87F /* DepthFirstSearchTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = DepthFirstSearchTests.swift; sourceTree = SOURCE_ROOT; };
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+		83F9C96E1C84449D00B3A87F /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Graph.swift; path = ../Graph.swift; sourceTree = SOURCE_ROOT; };
+		83F9C96F1C84449D00B3A87F /* Node.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Node.swift; path = ../Node.swift; sourceTree = SOURCE_ROOT; };
+		FFC6E11D1C8656D10046BA79 /* DepthFirstSearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = DepthFirstSearch.swift; path = ../DepthFirstSearch.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
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+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				83F9C96D1C84449D00B3A87F /* Edge.swift */,
+				83F9C96E1C84449D00B3A87F /* Graph.swift */,
+				83F9C96F1C84449D00B3A87F /* Node.swift */,
+				83F9C96B1C8443E800B3A87F /* DepthFirstSearchTests.swift */,
+				FFC6E11D1C8656D10046BA79 /* DepthFirstSearch.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
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+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
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+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
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+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
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+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				83F9C9721C84449D00B3A87F /* Graph.swift in Sources */,
+				83F9C9711C84449D00B3A87F /* Edge.swift in Sources */,
+				FFC6E11E1C8656D10046BA79 /* DepthFirstSearch.swift in Sources */,
+				83F9C96C1C8443E800B3A87F /* DepthFirstSearchTests.swift in Sources */,
+				83F9C9731C84449D00B3A87F /* Node.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
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+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
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+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
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+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
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+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
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+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
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+			buildConfigurations = (
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+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
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+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
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+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}

From 17aa1a043d7a634424a9d9a48a8ebe744ae9e0e1 Mon Sep 17 00:00:00 2001
From: Paulo Tanaka <ptanaka@linkedin.com>
Date: Tue, 1 Mar 2016 15:18:38 -0800
Subject: [PATCH 0092/1679] Removing dfs images

---
 .../Resources/Animated_BFS.gif                  | Bin 33276 -> 0 bytes
 .../Resources/Minimum_Spanning_Tree.png         | Bin 23928 -> 0 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Depth-First Search/DepthFirstSearch.playground/Resources/Animated_BFS.gif
 delete mode 100644 Depth-First Search/DepthFirstSearch.playground/Resources/Minimum_Spanning_Tree.png

diff --git a/Depth-First Search/DepthFirstSearch.playground/Resources/Animated_BFS.gif b/Depth-First Search/DepthFirstSearch.playground/Resources/Animated_BFS.gif
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From e98fe5c64dcd5b6d58340a360a3dec8805d22599 Mon Sep 17 00:00:00 2001
From: Paulo Tanaka <ptanaka@linkedin.com>
Date: Tue, 1 Mar 2016 15:22:47 -0800
Subject: [PATCH 0093/1679] Removing README images

---
 Depth-First Search/Images/Animated_BFS.gif      | Bin 33276 -> 0 bytes
 .../Images/MinimumSpanningTree.sketch           | Bin 81920 -> 0 bytes
 .../Images/Minimum_Spanning_Tree.png            | Bin 23928 -> 0 bytes
 3 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Depth-First Search/Images/Animated_BFS.gif
 delete mode 100644 Depth-First Search/Images/MinimumSpanningTree.sketch
 delete mode 100644 Depth-First Search/Images/Minimum_Spanning_Tree.png

diff --git a/Depth-First Search/Images/Animated_BFS.gif b/Depth-First Search/Images/Animated_BFS.gif
deleted file mode 100644
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From 4c25b90064d28033c3ced696cd6445ede8524a78 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Tue, 1 Mar 2016 22:14:35 -0800
Subject: [PATCH 0094/1679] Write BPQ README.md

---
 Bounded Priority Queue/README.md | 80 ++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 Bounded Priority Queue/README.md

diff --git a/Bounded Priority Queue/README.md b/Bounded Priority Queue/README.md
new file mode 100644
index 000000000..2d19ecba9
--- /dev/null
+++ b/Bounded Priority Queue/README.md	
@@ -0,0 +1,80 @@
+# Bounded Priority queue
+
+A bounded priority queue is similar to a regular [priority queue](../Priority Queue), except that there is a fixed upper bound on the number of elements that can be stored. Whenever a new element is added to the queue, if the queue is at capacity, the element with the highest priority value is ejected from the queue.
+
+## Example
+Supposed we have a bounded-priority-queue with maximum size 5 that has the following values and priorities:
+```
+Value:    [A,   B,    C,    D,   E]
+Priority: [0.1, 0.25, 1.33, 3.2, 4.6]
+```
+Suppose that we want to insert the element `F` with priority `0.4` into this bounded priority queue. Because this bounded-priority-queue has maximum size five, this will insert the element `F`, but then evict the lowest-priority element (`E`), yielding the updated queue:
+```
+Value:    [A,   B,    F,   C,    D]
+Priority: [0.1, 0.25, 0.4, 1.33, 3.2]
+```
+Now suppose that we wish to insert the element G with priority 4.0 into this BPQ. Because G's priority value is greater than the maximum-priority element in the BPQ, upon inserting G it will immediately be evicted. In other words, inserting an element into a BPQ with priority greater than the maximum-priority element of the BPQ has no effect.
+
+## Implementation
+While a [heap](../Heap) may be a really simple implementation for a priority queue, an sorted [linked list](../Linked List) allows for `O(k)` insertion and `O(1)` deletion. Where `k` is the bounding number of elements.
+```swift
+public func enqueue(value: T) {
+    let newNode = Node(value: value)
+
+    if head == nil  {
+        head = newNode
+    } else {
+        var node = head
+        if curNumElements == maxNumElements && !(newNode.value < node!.value) {
+            return
+        }
+
+        while (node!.next != nil) && (newNode.value < node!.value) { node = node!.next }
+
+        if newNode.value < node!.value {
+            newNode.next = node!.next
+            newNode.previous = node
+
+            if(newNode.next != nil) { /* TAIL */
+                newNode.next!.previous = newNode
+            }
+            node!.next = newNode
+        } else {
+            newNode.previous = node!.previous
+            newNode.next = node
+            if(node!.previous == nil) { /* HEAD */
+                head = newNode
+            } else {
+                node!.previous!.next = newNode
+            }
+            node!.previous = newNode
+        }
+        if(curNumElements == maxNumElements) { dequeue() }
+    }
+    curNumElements += 1
+}
+```
+The `enqueue(_:)` method checks if the queue already has the maximum number of elements. If the new value is greater than the `head` value then don't insert it. If the new value is less than `head` search through the list to find the proper insertion location and update the pointers.
+
+Lastly if the queue has reached the maximum number of elements `dequeue()` the highest priority one.
+
+By keeping the element with the highest priority as the head it allows for a simple update of the `head` variable in a `dequeue()`:
+```swift
+public func dequeue() -> T? {
+    if curNumElements > 0 {
+        let retVal = head!.value
+
+        if curNumElements == 1 {
+            head = nil
+        }
+        else {
+            head = head!.next
+            head!.previous = nil
+        }
+
+        curNumElements -= 1
+        return retVal
+    }
+    return nil
+}
+```

From 3467142bca114217f8393bcf19c5d99b80d81b62 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Tue, 1 Mar 2016 22:17:51 -0800
Subject: [PATCH 0095/1679] Apply type constraint Comparable

---
 .../BoundedPriorityQueue.swift                | 44 ++++++-------
 .../Tests/BoundedPriorityQueueTests.swift     | 62 ++++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  4 +-
 3 files changed, 56 insertions(+), 54 deletions(-)

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.swift
index f5f3a2221..91b6d30b6 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.swift	
@@ -1,18 +1,16 @@
 //
 //  BoundedPriorityQueue.swift
-//  Tests
 //
 //  Created by John Gill on 2/28/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
 //
 
 import Foundation
 
-public class LinkedListNode<T> {
+public class LinkedListNode<T: Comparable> {
     var value: T
     var next: LinkedListNode?
     var previous: LinkedListNode?
-    
+
     public init(value: T) {
         self.value = value
         self.next = nil
@@ -20,52 +18,50 @@ public class LinkedListNode<T> {
     }
 }
 
-public class BoundedPriorityQueue<T> {
+public class BoundedPriorityQueue<T: Comparable> {
     public typealias Node = LinkedListNode<T>
     private var head: Node?
-    private var isLessThan:(T, T) -> Bool
     private var curNumElements:Int
     private var maxNumElements: Int
-    
-    public init(sort: (T, T) -> Bool, maxElements:Int) {
-        isLessThan = sort
+
+    public init(maxElements:Int) {
         head = nil
         maxNumElements = maxElements
         curNumElements = 0
     }
-    
+
     public var isEmpty: Bool {
         return curNumElements == 0
     }
-    
+
     public var count: Int {
         return curNumElements
     }
-    
+
     public func peek() -> T? {
         if curNumElements > 0 {
             return head!.value
         }
         return nil
     }
-    
+
     public func enqueue(value: T) {
         let newNode = Node(value: value)
-        
+
         if head == nil  {
             head = newNode
         } else {
             var node = head
-            if curNumElements == maxNumElements && !isLessThan(newNode.value, node!.value) {
+            if curNumElements == maxNumElements && newNode.value > node!.value {
                 return
             }
 
-            while node!.next != nil && isLessThan(newNode.value, node!.value) { node = node!.next }
-            
-            if isLessThan(newNode.value, node!.value) {
+            while (node!.next != nil) && (newNode.value < node!.value) { node = node!.next }
+
+            if newNode.value < node!.value {
                 newNode.next = node!.next
                 newNode.previous = node
-                
+
                 if(newNode.next != nil) { /* TAIL */
                     newNode.next!.previous = newNode
                 }
@@ -82,13 +78,13 @@ public class BoundedPriorityQueue<T> {
             }
             if(curNumElements == maxNumElements) { dequeue() }
         }
-        curNumElements++
+        curNumElements += 1
     }
-    
+
     public func dequeue() -> T? {
         if curNumElements > 0 {
             let retVal = head!.value
-            
+
             if curNumElements == 1 {
                 head = nil
             }
@@ -97,9 +93,9 @@ public class BoundedPriorityQueue<T> {
                 head!.previous = nil
             }
 
-            curNumElements--
+            curNumElements -= 1
             return retVal
         }
         return nil
     }
-}
\ No newline at end of file
+}
diff --git a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift
index 4b68b0bab..772999e84 100644
--- a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
+++ b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
@@ -1,60 +1,66 @@
 //
 //  BoundedPriorityQueueTests.swift
-//  Tests
 //
 //  Created by John Gill on 2/28/16.
-//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
 //
 
 import Foundation
 import XCTest
 
-private struct Message {
+private struct Message: Comparable {
     let name: String
     let priority: Int
 }
 
-private func < (m1: Message, m2: Message) -> Bool {
+private func ==(m1: Message, m2: Message) -> Bool {
+    return m1.priority == m2.priority
+}
+
+private func <(m1: Message, m2: Message) -> Bool {
     return m1.priority < m2.priority
 }
 
+private func >(m1: Message, m2: Message) -> Bool {
+    return m1.priority > m2.priority
+}
+
 class BoundedPriorityQueueTest: XCTestCase {
     func testEmpty() {
-        let queue = BoundedPriorityQueue<Message>(sort: <, maxElements: 5)
+        let queue = BoundedPriorityQueue<Message>(maxElements: 5)
         XCTAssertTrue(queue.isEmpty)
         XCTAssertEqual(queue.count, 0)
         XCTAssertNil(queue.dequeue())
     }
-    
+
     func testOneElement() {
-        let queue = BoundedPriorityQueue<Message>(sort: <, maxElements: 5)
-        
+        let queue = BoundedPriorityQueue<Message>(maxElements: 5)
+
         queue.enqueue(Message(name: "hello", priority: 100))
         XCTAssertFalse(queue.isEmpty)
         XCTAssertEqual(queue.count, 1)
-        
+
         let result = queue.dequeue()
         XCTAssertEqual(result!.priority, 100)
         XCTAssertTrue(queue.isEmpty)
         XCTAssertEqual(queue.count, 0)
     }
-    
+
     func testMaxElements() {
-        let queue = BoundedPriorityQueue<Message>(sort: <, maxElements: 5)
+        let queue = BoundedPriorityQueue<Message>(maxElements: 5)
         XCTAssertTrue(queue.isEmpty)
-        
+
         queue.enqueue(Message(name: "john", priority: 100))
         XCTAssertEqual(queue.count, 1)
         XCTAssertEqual(queue.peek()?.priority, 100)
-        
+
         queue.enqueue(Message(name: "james", priority: 200))
         XCTAssertEqual(queue.count, 2)
         XCTAssertEqual(queue.peek()?.priority, 200)
-        
+
         queue.enqueue(Message(name: "mark", priority: 300))
         XCTAssertEqual(queue.count, 3)
         XCTAssertEqual(queue.peek()?.priority, 300)
-        
+
         queue.enqueue(Message(name: "ken", priority: 400))
         XCTAssertEqual(queue.count, 4)
         XCTAssertEqual(queue.peek()?.priority, 400)
@@ -62,54 +68,54 @@ class BoundedPriorityQueueTest: XCTestCase {
         queue.enqueue(Message(name: "thomas", priority: 500))
         XCTAssertEqual(queue.count, 5)
         XCTAssertEqual(queue.peek()?.priority, 500)
-        
+
         queue.enqueue(Message(name: "melanie", priority: 550))
         XCTAssertEqual(queue.count, 5)
         XCTAssertEqual(queue.peek()?.priority, 500)
-        
+
         queue.enqueue(Message(name: "lily", priority: 450))
         XCTAssertEqual(queue.count, 5)
         XCTAssertEqual(queue.peek()?.priority, 450)
-        
+
         queue.enqueue(Message(name: "fred", priority: 350))
         XCTAssertEqual(queue.count, 5)
         XCTAssertEqual(queue.peek()?.priority, 400)
-        
+
         queue.enqueue(Message(name: "rachel", priority: 50))
         XCTAssertEqual(queue.count, 5)
         XCTAssertEqual(queue.peek()?.priority, 350)
-        
+
         var result = queue.dequeue()
         XCTAssertEqual(result!.priority, 350)
         XCTAssertEqual(queue.count, 4)
-        
+
         result = queue.dequeue()
         XCTAssertEqual(result!.priority, 300)
         XCTAssertEqual(queue.count, 3)
-        
+
         result = queue.dequeue()
         XCTAssertEqual(result!.priority, 200)
         XCTAssertEqual(queue.count, 2)
-        
+
         queue.enqueue(Message(name: "ryan", priority: 150))
         XCTAssertEqual(queue.count, 3)
         XCTAssertEqual(queue.peek()?.priority, 150)
-        
+
         result = queue.dequeue()
         XCTAssertEqual(result!.priority, 150)
         XCTAssertEqual(queue.count, 2)
-        
+
         result = queue.dequeue()
         XCTAssertEqual(result!.priority, 100)
         XCTAssertEqual(queue.count, 1)
-        
+
         result = queue.dequeue()
         XCTAssertEqual(result!.priority, 50)
         XCTAssertEqual(queue.count, 0)
-        
+
         result = queue.dequeue()
         XCTAssertNil(result)
         XCTAssertEqual(queue.count, 0)
         XCTAssertTrue(queue.isEmpty)
     }
-}
\ No newline at end of file
+}
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 2920474ae..6fd5c0b46 100644
--- a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -14,8 +14,8 @@
 /* Begin PBXFileReference section */
 		B80004B31C83E342001FE2D7 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		B80004B81C83E342001FE2D7 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
-		B810B5B01C83E3B200450324 /* BoundedPriorityQueueTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoundedPriorityQueueTests.swift; path = ../BoundedPriorityQueueTests.swift; sourceTree = "<group>"; };
-		B8F635A71C83E4270060805E /* BoundedPriorityQueue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoundedPriorityQueue.swift; path = ../../BoundedPriorityQueue.swift; sourceTree = "<group>"; };
+		B810B5B01C83E3B200450324 /* BoundedPriorityQueueTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoundedPriorityQueueTests.swift; sourceTree = SOURCE_ROOT; };
+		B8F635A71C83E4270060805E /* BoundedPriorityQueue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoundedPriorityQueue.swift; path = ../BoundedPriorityQueue.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */

From 591f711dc832cd1d8b091a2c6830d4cb5ffb6e84 Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Tue, 1 Mar 2016 22:42:47 -0800
Subject: [PATCH 0096/1679] BPQ Update main README.markdown

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 03bd2601b..e3f85f910 100644
--- a/README.markdown
+++ b/README.markdown
@@ -125,6 +125,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Queue](Queue/). First-in, first-out!
 - [Deque](Deque/). A double-ended queue.
 - [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
+- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements.
 - [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
 
 ### Lists

From 671926fe755d3b727a25be505d67c156c1aa993e Mon Sep 17 00:00:00 2001
From: John Gill <king2bgill@gmail.com>
Date: Tue, 1 Mar 2016 22:51:20 -0800
Subject: [PATCH 0097/1679] BPQ Remove kNN code from branch

---
 .../Contents.swift                            | 47 -------------------
 .../contents.xcplayground                     |  4 --
 .../timeline.xctimeline                       | 31 ------------
 K-Nearest Neighbors/README.md                 |  7 ---
 4 files changed, 89 deletions(-)
 delete mode 100644 K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift
 delete mode 100644 K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground
 delete mode 100644 K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline
 delete mode 100644 K-Nearest Neighbors/README.md

diff --git a/K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift b/K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift
deleted file mode 100644
index a4dd21dd0..000000000
--- a/K-Nearest Neighbors/K-Nearest Neighbors.playground/Contents.swift	
+++ /dev/null
@@ -1,47 +0,0 @@
-//
-//  K-NearestNeighbors.swift
-//
-//  Created by John Gill on 2/23/16.
-import Foundation
-
-// Container to easily hold N Dimensional Vectors
-class VectorND: CustomStringConvertible {
-    private var length = 0
-    private var data = [Double]()
-    
-    init(d:[Double]) {
-        data = d
-        length = d.count
-    }
-    
-    var description: String { return "VectorND (\(data)" }
-    func getData() -> [Double] { return data }
-    func getLength() -> Int { return length }
-    
-    // Calculates the Euclidean distance from 
-    // this point to another VectorND
-    func getDist(v:VectorND) -> Double {
-        var result = 0.0
-        for idx in 0..<length {
-            result += pow(data[idx] - v.getData()[idx], 2.0)
-        }
-        return sqrt(result)
-    }
-}
-
-class kNearestNeighbrs {
-    var k:Int // Number of Neighbors
-    
-    init(k:Int) {
-        self.k = k
-    }
-    
-    func train (data:[VectorND], labels:[Int]) {
-        
-    }
-    
-    func predict (data: [VectorND]) -> [Int] {
-        
-        return []
-    }
-}
\ No newline at end of file
diff --git a/K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground b/K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground
deleted file mode 100644
index 9f9eecc96..000000000
--- a/K-Nearest Neighbors/K-Nearest Neighbors.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline b/K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline
deleted file mode 100644
index 4dca8e784..000000000
--- a/K-Nearest Neighbors/K-Nearest Neighbors.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,31 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=3&amp;EndingLineNumber=46&amp;StartingColumnNumber=1&amp;StartingLineNumber=46&amp;Timestamp=478157983.180935"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=19&amp;EndingLineNumber=46&amp;StartingColumnNumber=5&amp;StartingLineNumber=46&amp;Timestamp=478157983.181127"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=16&amp;EndingLineNumber=46&amp;StartingColumnNumber=5&amp;StartingLineNumber=46&amp;Timestamp=478157983.181274"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=7&amp;EndingLineNumber=46&amp;StartingColumnNumber=1&amp;StartingLineNumber=46&amp;Timestamp=478157983.181423"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=1038&amp;EndingColumnNumber=37&amp;EndingLineNumber=46&amp;StartingColumnNumber=1&amp;StartingLineNumber=46&amp;Timestamp=478157983.181558"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-   </TimelineItems>
-</Timeline>
diff --git a/K-Nearest Neighbors/README.md b/K-Nearest Neighbors/README.md
deleted file mode 100644
index 9e22c4a02..000000000
--- a/K-Nearest Neighbors/README.md	
+++ /dev/null
@@ -1,7 +0,0 @@
-# k-Nearest Neighbors
-
-Goal: Label Data into Clusters by k Nearest other points
-
-Machine Learning algorithms are two pass:
-    1. Train the algorithm on a set of Data
-    2. Predict new labels for data based on training

From bf6680591a58b3cb5bdd9b30db815091d33e1d78 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 22:21:06 +1300
Subject: [PATCH 0098/1679] Travis-CI - Adding several test projects

---
 travis.yml | 6 ++++++
 1 file changed, 6 insertions(+)
 create mode 100644 travis.yml

diff --git a/travis.yml b/travis.yml
new file mode 100644
index 000000000..7882690d3
--- /dev/null
+++ b/travis.yml
@@ -0,0 +1,6 @@
+osx_image: xcode7.2
+
+script:
+- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests

From 914ca49c2f81c91049b197abb45cba910965040e Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 22:25:33 +1300
Subject: [PATCH 0099/1679] Travis: Renaming travis file

---
 travis.yml => .travis.yml | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename travis.yml => .travis.yml (100%)

diff --git a/travis.yml b/.travis.yml
similarity index 100%
rename from travis.yml
rename to .travis.yml

From 59dee733d4c3d54776b0394be396fba30b97f4e3 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 22:28:32 +1300
Subject: [PATCH 0100/1679] Travis: adding language

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 7882690d3..87fcc6438 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,3 +1,4 @@
+language: objective-c
 osx_image: xcode7.2
 
 script:

From a2ec9dda5c1112083df30a7f327d2b546548e004 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 22:32:18 +1300
Subject: [PATCH 0101/1679] Building before running tests

---
 .travis.yml | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 87fcc6438..591f2cbdc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,6 +2,7 @@ language: objective-c
 osx_image: xcode7.2
 
 script:
+- xcodebuild build -project ./AVL\ Tree/Tests/Tests.xcodeproj
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+#- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+#- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests

From ce6e7b4f4f3ebbe266ee68e3df1b4c36a45058b0 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 22:50:29 +1300
Subject: [PATCH 0102/1679] Travis: making test scheme shared

---
 .travis.yml                                   | 23 ++++++--
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 2 files changed, 75 insertions(+), 4 deletions(-)
 create mode 100644 Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/.travis.yml b/.travis.yml
index 591f2cbdc..d1a498cd6 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,22 @@ language: objective-c
 osx_image: xcode7.2
 
 script:
-- xcodebuild build -project ./AVL\ Tree/Tests/Tests.xcodeproj
-- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-#- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-#- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+
+- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild build -project ./AVL\ Tree/Tests/Tests.xcodeproj
+# - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+
+# - xcodebuild build -project ./Array2D/Tests/Tests.xcodeproj
+# - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+
+# - xcodebuild build -project ./Binary\ Search/Tests/Tests.xcodeproj
+# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+
+# - xcodebuild build -project ./Binary\ Search/Tests/Tests.xcodeproj
+# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+
+
+
+
+# - xcodebuild build -project ./Heap/Tests/Tests.xcodeproj
+# - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 2e7e1e8a87c30db59d3a2c2a937e67a2b5aa2ee2 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 23:12:53 +1300
Subject: [PATCH 0103/1679] Including all files. Changing all schemes to
 "shared"

---
 .travis.yml                                   | 35 ++++++------
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 19 files changed, 1026 insertions(+), 17 deletions(-)
 create mode 100644 AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/.travis.yml b/.travis.yml
index d1a498cd6..9a4806998 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -3,21 +3,22 @@ osx_image: xcode7.2
 
 script:
 
+- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild build -project ./AVL\ Tree/Tests/Tests.xcodeproj
-# - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-
-# - xcodebuild build -project ./Array2D/Tests/Tests.xcodeproj
-# - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-
-# - xcodebuild build -project ./Binary\ Search/Tests/Tests.xcodeproj
-# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-
-# - xcodebuild build -project ./Binary\ Search/Tests/Tests.xcodeproj
-# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-
-
-
-
-# - xcodebuild build -project ./Heap/Tests/Tests.xcodeproj
-# - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
diff --git a/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
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+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
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+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
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+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
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new file mode 100644
index 000000000..54b00dc9a
--- /dev/null
+++ b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "B80894DF1C852D100018730E"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
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+   <ArchiveAction
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+      revealArchiveInOrganizer = "YES">
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new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
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+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
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+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
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+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
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diff --git a/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
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+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
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+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
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+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
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diff --git a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
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+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
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diff --git a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
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+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
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diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
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+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
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+   <LaunchAction
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+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
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+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
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+      revealArchiveInOrganizer = "YES">
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diff --git a/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
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diff --git a/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 6f8badd5247fdcb248e4d0e6a65b9fb9d18d8403 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 2 Mar 2016 23:43:41 +1300
Subject: [PATCH 0104/1679] Travis: adding contribution guidelines for
 Travis-CI test projects

---
 How to Contribute.markdown            |  11 +++++++++--
 Images/scheme-settings-for-travis.png | Bin 0 -> 70387 bytes
 README.markdown                       |   2 ++
 3 files changed, 11 insertions(+), 2 deletions(-)
 create mode 100644 Images/scheme-settings-for-travis.png

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 0069c57ba..215539ae2 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -6,9 +6,9 @@ Want to help out with the Swift Algorithm Club? Great!
 
 Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
 
-New algorithms and data structures are always welcome (even if they aren't on the list). 
+New algorithms and data structures are always welcome (even if they aren't on the list).
 
-We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library. 
+We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library.
 
 Unit tests. Fixes for typos. No contribution is too small. :-)
 
@@ -21,6 +21,13 @@ To keep this a high quality repo, please follow this process when submitting you
 3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
 4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. If you wrote it, you deserve the credit and fame.
 5. Add a playground and/or unit tests.
+  - Add unit test projects to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/hollance/swift-algorithm-club)
+    - `- xcodebuild test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests`
+  - Configure scheme to run on Travis-CI
+    - Open `Product` -> `Scheme` -> `Manage Schemes ...`
+      - Uncheck `Autocreate schemes`
+      - Check `Shared`
+    - [Screenshot of scheme settings](/images/scheme-settings-for-travis.png)
 
 Just so you know, I will probably edit your text and code for grammar etc, just to ensure a certain level of polish.
 
diff --git a/Images/scheme-settings-for-travis.png b/Images/scheme-settings-for-travis.png
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diff --git a/README.markdown b/README.markdown
index 03bd2601b..7ffb56271 100644
--- a/README.markdown
+++ b/README.markdown
@@ -200,3 +200,5 @@ Other algorithm repositories:
 ## License
 
 All content is licensed under the terms of the MIT open source license.
+
+[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg)](https://travis-ci.org/hollance/swift-algorithm-club)

From 87dc391796e95f2d400353f933e29b341f070399 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Wed, 2 Mar 2016 15:07:35 +0100
Subject: [PATCH 0105/1679] More test cases for AVLTree

---
 AVL Tree/Tests/AVLTreeTests.swift | 48 +++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)

diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index f079603cf..5fd0b9a2a 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -7,6 +7,7 @@
 //
 
 import XCTest
+@testable import testAVL
 
 class AVLTreeTests: XCTestCase {
   
@@ -68,6 +69,53 @@ class AVLTreeTests: XCTestCase {
       self.tree?.search(400)
     }
   }
+    
+    func testMinimumOnPopulatedTree() {
+        self.tree?.autopopulateWithNodes(500)
+        let min = self.tree?.root?.minimum()
+        XCTAssertNotNil(min, "Minimum function not working")
+    }
+    
+    func testMinimumOnSingleTreeNode() {
+        let treeNode = TreeNode(key: 1, payload: "A")
+        let min = treeNode.minimum()
+        
+        XCTAssertNotNil(min, "Minimum on single node should be returned")
+        XCTAssertEqual(min?.payload,treeNode.payload)
+    }
+    
+    func testSuccessorOfRoot() {
+        self.tree?.autopopulateWithNodes(10)
+        let successor = self.tree?.root?.successor()
+        XCTAssertNotNil(successor, "Succesor of root, non-empty tree, not found")
+    }
+    
+    func testSuccessorOfMinimum() {
+        self.tree?.autopopulateWithNodes(10)
+        
+        let minimum = self.tree?.root?.minimum()
+        XCTAssertNotNil(minimum, "Minimum should exist here")
+        
+        let successor = minimum!.successor()
+        XCTAssertNotNil(successor, "Succesor of minimum, non-empty tree, not found")
+    }
+    
+    func testSuccessorSingleNode() {
+        let singleNode = TreeNode(key: 1, payload: "A")
+        let successor = singleNode.successor()
+        XCTAssertNil(successor, "Empty node should not have succesor")
+    }
+    
+    func testDeleteExistentKey() {
+        self.tree?.delete(1)
+        XCTAssertNil(self.tree?.search(1), "Key should not exist anymore")
+    }
+
+    func testDeleteNOTExistentKey() {
+        self.tree?.delete(1056)
+        XCTAssertNil(self.tree?.search(1056), "Key should not exist")
+    }
+
 }
 
 extension AVLTree where Key : SignedIntegerType {

From 73ca46e31c7aa964edb3e952847310debf712c3c Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Wed, 2 Mar 2016 15:09:36 +0100
Subject: [PATCH 0106/1679] Removing testable from local app

---
 AVL Tree/Tests/AVLTreeTests.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 5fd0b9a2a..d631c7688 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -7,7 +7,6 @@
 //
 
 import XCTest
-@testable import testAVL
 
 class AVLTreeTests: XCTestCase {
   

From 7868b032f7d89f33a8bf7310dc96698b232b355a Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 17:51:19 +0100
Subject: [PATCH 0107/1679] Tons of tiny text tweaks

---
 AVL Tree/README.markdown                      |  10 +--
 Algorithm Design.markdown                     |   6 +-
 Array2D/README.markdown                       |  12 +++-
 Binary Search Tree/README.markdown            |  46 +++++++-------
 .../Sources/BinarySearchTree.swift            |   2 +-
 .../Solution 1/BinarySearchTree.swift         |   2 +-
 Binary Search/README.markdown                 |  22 +++----
 Binary Tree/README.markdown                   |   8 +--
 Bit Set/README.markdown                       |  24 +++----
 Bloom Filter/README.markdown                  |  14 +++--
 Boyer-Moore/README.markdown                   |   8 +--
 Breadth-First Search/README.markdown          |   8 +--
 Combinatorics/README.markdown                 |  38 +++++------
 Count Occurrences/README.markdown             |  12 ++--
 Deque/README.markdown                         |  24 +++----
 Fixed Size Array/README.markdown              |  12 ++--
 Fizz Buzz/README.markdown                     |  41 +++++++-----
 GCD/README.markdown                           |  12 ++--
 Hash Set/README.markdown                      |   6 +-
 Hash Table/README.markdown                    |  32 +++++-----
 Heap Sort/README.markdown                     |   8 +--
 Heap/README.markdown                          |  44 ++++++-------
 Huffman Coding/Images/BuildTree.gif           | Bin 24647 -> 18044 bytes
 Huffman Coding/Images/BuildTree.psd           | Bin 2619878 -> 2611102 bytes
 Huffman Coding/Images/Compression.graffle     | Bin 4299 -> 4300 bytes
 Huffman Coding/Images/Compression.png         | Bin 54972 -> 54850 bytes
 Huffman Coding/Images/Decompression.graffle   | Bin 3944 -> 3946 bytes
 Huffman Coding/Images/Decompression.png       | Bin 47499 -> 47379 bytes
 Huffman Coding/README.markdown                |  20 +++---
 Insertion Sort/README.markdown                |  26 ++++----
 Kth Largest Element/README.markdown           |  30 ++++-----
 .../kthLargest.playground/Contents.swift      |  11 ++--
 Kth Largest Element/kthLargest.swift          |  17 ++---
 Linear Search/README.markdown                 |  20 +++---
 Linked List/README.markdown                   |  22 ++++---
 Merge Sort/README.markdown                    |  28 ++++-----
 Monty Hall Problem/README.markdown            |   4 +-
 Ordered Array/README.markdown                 |   6 +-
 Queue/README.markdown                         |   8 ++-
 Quicksort/README.markdown                     |  14 ++---
 README.markdown                               |  12 ++--
 Ring Buffer/README.markdown                   |  10 +--
 Run-Length Encoding/README.markdown           |   2 +-
 Segment Tree/README.markdown                  |  26 +++++---
 Select Minimum Maximum/README.markdown        |  59 +++++++++---------
 Selection Sampling/README.markdown            |   6 +-
 Selection Sort/README.markdown                |  32 +++++-----
 Shell Sort/README.markdown                    |  40 ++++++------
 Shuffle/README.markdown                       |   2 +-
 Shunting Yard/README.markdown                 |  42 ++++++-------
 Stack/README.markdown                         |   4 +-
 Tree/README.markdown                          |  10 +--
 Tree/Tree.playground/Contents.swift           |   5 +-
 Tree/Tree.swift                               |   2 +-
 Two-Sum Problem/README.markdown               |   6 +-
 Union-Find/README.markdown                    |   6 +-
 56 files changed, 454 insertions(+), 407 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 9e3a2cdc6..744d9a272 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -8,7 +8,7 @@ This is an example of an unbalanced tree:
 
 ![Unbalanced tree](Images/Unbalanced.png)
 
-All the children are in the left branch and none are in the right. This is essentially the same as a [linked list](../Linked List/) and as a result, searching takes **O(n)** time instead of the much faster **O(log n)** that you'd expect from a binary search tree.
+All the children are in the left branch and none are in the right. This is essentially the same as a [linked list](../Linked List/). As a result, searching takes **O(n)** time instead of the much faster **O(log n)** that you'd expect from a binary search tree.
 
 A balanced version of that tree would look like this:
 
@@ -16,7 +16,7 @@ A balanced version of that tree would look like this:
 
 One way to make the binary search tree balanced is to insert the nodes in a totally random order. But that doesn't guarantee success, nor is it always practical.
 
-The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. The height of such a tree is guaranteed to be *log(n)* where *n* is the number nodes. On a balanced tree all insert, remove, and search operations take **O(log n)** time. That means fast. ;-)
+The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. The height of such a tree is guaranteed to be *log(n)* where *n* is the number nodes. On a balanced tree all insert, remove, and search operations take only **O(log n)** time. That means fast. ;-)
 
 ## Introducing the AVL tree
 
@@ -32,7 +32,7 @@ As mentioned, in an AVL tree a node is balanced if its left and right subtree ha
 
 ![Balanced trees](Images/BalanceOK.png)
 
-But these are trees that are unbalanced, because the height of the left subtree is too large compared to the right subtree:
+But the following are trees that are unbalanced, because the height of the left subtree is too large compared to the right subtree:
 
 ![Unbalanced trees](Images/BalanceNotOK.png)
 
@@ -52,7 +52,7 @@ Insertion never needs more than 2 rotations. Removal might require up to *log(n)
 
 ## The code
 
-Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently is inserting and deleting the nodes.
+Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
 
 > **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary Search Tree/). It will make the rest of the AVL tree easier to understand.
 
@@ -66,6 +66,6 @@ The interesting bits are in the following methods:
 
 [AVL tree on Wikipedia](https://en.wikipedia.org/wiki/AVL_tree)
 
-AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black Tree/) seems to be more common.
+AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black Tree/) seems to be more popular.
 
 *Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*
diff --git a/Algorithm Design.markdown b/Algorithm Design.markdown
index d9376f82e..23f8ad70e 100644
--- a/Algorithm Design.markdown	
+++ b/Algorithm Design.markdown	
@@ -4,9 +4,9 @@ What to do when you're faced with a new problem and you need to find an algorith
 
 ### Is it similar to another problem?
 
-One thing I like about [The Algorithm Design Manual](http://www.algorist.com) by Steven Skiena is that it includes a catalog of problems and solutions you can try. 
+If you can frame your problem in terms of another, more general problem, then you might be able to use an existing algorithm. Why reinvent the wheel?
 
-If you can frame your problem in terms of another, more general problem, then you might be able to use an existing algorithm.
+One thing I like about [The Algorithm Design Manual](http://www.algorist.com) by Steven Skiena is that it includes a catalog of problems and solutions you can try. (See also his [algorithm repository](http://www3.cs.stonybrook.edu/~algorith/).)
 
 ### It's OK to start with brute force
 
@@ -14,7 +14,7 @@ Naive, brute force solutions are often too slow for practical use but they're a
 
 Once you have a brute force implementation you can use that to verify that any improvements you come up with are correct. 
 
-And if you only work with small datasets, then a brute force approach may actually be good enough on its own.
+And if you only work with small datasets, then a brute force approach may actually be good enough on its own. Don't fall into the trap of premature optimization!
 
 ### Divide and conquer
 
diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 32cde4d67..e73d453a6 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -1,6 +1,6 @@
 # Array2D
 
-In C and Objective-C you can write this,
+In C and Objective-C you can write the following line,
 
 	int cookies[9][7];
 	
@@ -61,7 +61,7 @@ var threeDimensions = dim(2, dim(3, dim(4, 0)))
 
 The downside of using multi-dimensional arrays in this fashion -- actually, multiple nested arrays -- is that it's easy to lose track of what dimension represents what.
 
-So instead let's create our own type that acts like a 2-D array and that is more convenient to use. Here it is:
+So instead let's create our own type that acts like a 2-D array and that is more convenient to use. Here it is, short and sweet:
 
 ```swift
 public struct Array2D<T> {
@@ -100,8 +100,14 @@ Thanks to the `subscript` function, you can do the following to retrieve an obje
 let myCookie = cookies[column, row]
 ```
 
+Or change it:
+
+```swift
+cookies[column, row] = newCookie
+```
+
 Internally, `Array2D` uses a single one-dimensional array to store the data. The index of an object in that array is given by `(row x numberOfColumns) + column`. But as a user of `Array2D` you don't have to worry about that; you only have to think in terms of "column" and "row", and let `Array2D` figure out the details for you. That's the advantage of wrapping primitive types into a wrapper class or struct.
 
 And that's all there is to it.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index f08cc0ad1..25d56803b 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -1,12 +1,12 @@
 # Binary Search Tree (BST)
 
-A binary search tree is a special kind of [binary tree](../Binary Tree/) (a tree in which a node only has two children) that performs insertions and deletions such that the tree is always sorted.
+A binary search tree is a special kind of [binary tree](../Binary Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
 
 If you don't know what a tree is or what it is for, then [read this first](../Tree/).
 
 ## "Always sorted" property
 
-This is an example of a valid binary search tree:
+Here is an example of a valid binary search tree:
 
 ![A binary search tree](Images/Tree1.png)
 
@@ -33,7 +33,7 @@ There is always only one possible place where the new element can be inserted in
 
 > **Note:** The *height* of a node is the number of steps it takes to go from that node to its lowest leaf. The height of the entire tree is the distance from the root to the lowest leaf. Many of the operations on a binary search tree are expressed in terms of the tree's height.
 
-By following this simple rule -- smaller values on the left, larger values on the right -- we keep the tree sorted in a way that whenever we query it, we can quickly check if a value is in the tree.
+By following this simple rule -- smaller values on the left, larger values on the right -- we keep the tree sorted in a way such that whenever we query it, we can quickly check if a value is in the tree.
 
 ## Searching the tree
 
@@ -49,7 +49,7 @@ If we were looking for the value `5` in the example, it would go as follows:
 
 ![Searching the tree](Images/Searching.png)
 
-Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary Search) in an array.)
+Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary Search) in an array.)
 
 ## Traversing the tree
 
@@ -57,7 +57,7 @@ Sometimes you don't want to look at just a single node, but at all of them.
 
 There are three ways to traverse a binary tree:
 
-1. *In-order* (or *depth-first*): first look at the left child node, then at the node itself, and finally at the right child.
+1. *In-order* (or *depth-first*): first look at the left child of a node, then at the node itself, and finally at its right child.
 2. *Pre-order*: first look at a node, then its left and right children. 
 3. *Post-order*: first look at the left and right children and process the node itself last.
 
@@ -148,9 +148,9 @@ Here's how you'd use it:
 let tree = BinarySearchTree<Int>(value: 7)
 ```
 
-The `count` property determines how many nodes are in the subtree described by this node. This doesn't just count the node's immediate children but also their children and their children's children, and so on. If this is the root node, then it counts how many nodes are in the entire tree. Initially, `count = 0`.
+The `count` property determines how many nodes are in the subtree described by this node. This doesn't just count the node's immediate children but also their children and their children's children, and so on. If this particular object is the root node, then it counts how many nodes are in the entire tree. Initially, `count = 0`.
 
-> **Note:** Because `left`, `right`, and `parent` are optionals, we can make good use of Swift's optional chaining (`?`) and nil-coalescing operators (`??`). You could also write this sort of thing with `if let` but that takes up more space.
+> **Note:** Because `left`, `right`, and `parent` are optionals, we can make good use of Swift's optional chaining (`?`) and nil-coalescing operators (`??`). You could also write this sort of thing with `if let` but that is less concise.
 
 ### Inserting nodes
 
@@ -182,7 +182,7 @@ A tree node by itself is pretty useless, so here is how you would add new nodes
 
 Like so many other tree operations, insertion is easiest to implement with recursion. We compare the new value to the values of the existing nodes and decide whether to add it to the left branch or the right branch.
 
-If there is no more left or right child to look at, we create a new `BinarySearchTree` object for the new node and connect it to the tree by setting its `parent` property.
+If there is no more left or right child to look at, we create a `BinarySearchTree` object for the new node and connect it to the tree by setting its `parent` property.
 
 > **Note:** Because the whole point of a binary search tree is to have smaller nodes on the left and larger ones on the right, you should always insert elements at the root, to make to sure this remains a valid binary tree!
 
@@ -197,7 +197,7 @@ tree.insert(9)
 tree.insert(1)
 ```
 
-> **Note:** For reasons that will become clear later, you should insert the numbers in a somewhat random order. If you insert them in sorted order, then the tree won't have the right shape.
+> **Note:** For reasons that will become clear later, you should insert the numbers in a somewhat random order. If you insert them in sorted order, the tree won't have the right shape.
 
 For convenience, let's add an init method that calls `insert()` for all the elements in an array:
 
@@ -243,11 +243,11 @@ When you do a `print(tree)`, you should get something like this:
 
 	((1) <- 2 -> (5)) <- 7 -> ((9) <- 10)
 
-With some imagination, you should see now that this indeed corresponds to the following tree:
+The root node is in the middle. With some imagination, you should see that this indeed corresponds to the following tree:
 
 ![The tree](Images/Tree2.png)
 
-By the way, you may be wondering what happens when you insert duplicate items? We always insert those kinds of items in the right branch. Try it out!
+By the way, you may be wondering what happens when you insert duplicate items? We always insert those in the right branch. Try it out!
 
 ### Searching
 
@@ -269,7 +269,7 @@ Here is the implementation of `search()`:
 
 I hope the logic is clear: this starts at the current node (usually the root) and compares the values. If the search value is less than the node's value, we continue searching in the left branch; if the search value is greater, we dive into the right branch.
 
-Of course, if there are no more nodes to look at -- when `left` or `right` is nil -- then we return nil to indicate the search value is not in the tree. 
+Of course, if there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree. 
 
 > **Note:** In Swift that's very conveniently done with optional chaining; when you write `left?.search(value)` it automatically returns nil if `left` is nil. There's no need to explicitly check for this with an `if` statement.
 
@@ -299,7 +299,7 @@ Here's how to test searching:
 tree.search(5)
 tree.search(2)
 tree.search(7)
-tree.search(6)  // nil
+tree.search(6)   // nil
 ```
 
 The first three lines all return the corresponding `BinaryTreeNode` object. The last line returns `nil` because there is no node with value `6`.
@@ -426,7 +426,7 @@ We won't need it for deleting, but for completeness' sake, here is the opposite
   }
 ```
 
-It returns the rightmost descendent of this node. We find it by following `right` pointers until we get to the end. In the above example, the rightmost descendent of node `2` is `5`. The maximum value in the entire tree is `11`, because that is the rightmost descendent of the root node `7`.
+It returns the rightmost descendent of the node. We find it by following `right` pointers until we get to the end. In the above example, the rightmost descendent of node `2` is `5`. The maximum value in the entire tree is `11`, because that is the rightmost descendent of the root node `7`.
 
 Finally, we can write the code the remove a node from the tree:
 
@@ -460,8 +460,6 @@ It doesn't look so scary after all. ;-) Here is what it does:
 
 The only tricky situation here is `// 1`. Rather than deleting the current node, we give it the successor's value and remove the successor node instead.
 
-> **Note:** What would happen if you deleted the root node? Specifically, how would you know which node becomes the new root node? It turns out you don't have to worry about that because the root never actually gets deleted. We simply give it a new value.
-
 Try it out:
 
 ```swift
@@ -482,6 +480,8 @@ But after `remove()` you get:
 
 As you can see, node `5` has taken the place of `2`. In fact, if you do `print(node2)` you'll see that it now has the value `5`. We didn't actually remove the `node2` object, we just gave it a new value.
 
+> **Note:** What would happen if you deleted the root node? Specifically, how would you know which node becomes the new root node? It turns out you don't have to worry about that because the root never actually gets deleted. We simply give it a new value.
+
 Like most binary search tree operations, removing a node runs in **O(h)** time, where **h** is the height of the tree.
 
 ### Depth and height
@@ -516,7 +516,7 @@ You can also calculate the *depth* of a node, which is the distance to the root.
     var edges = 0
     while case let parent? = node.parent {
       node = parent
-      ++edges
+      edges += 1
     }
     return edges
   }
@@ -624,6 +624,8 @@ We've implemented the binary tree node as a class but you can also use an enum.
 
 The difference is reference semantics versus value semantics. Making a change to the class-based tree will update that same instance in memory. But the enum-based tree is immutable -- any insertions or deletions will give you an entirely new copy of the tree. Which one is best totally depends on what you want to use it for.
 
+Here's how you'd make a binary search tree using an enum:
+
 ```swift
 public enum BinarySearchTree<T: Comparable> {
   case Empty
@@ -638,9 +640,9 @@ The enum has three cases:
 - `Leaf` for a leaf node that has no children.
 - `Node` for a node that has one or two children. This is marked `indirect` so that it can hold `BinarySearchTree` values. Without `indirect` you can't make recursive enums.
 
-> **Note:** The nodes in this binary tree don't have a reference to their parent node. That will make certain operations slightly more cumbersome to implement.
+> **Note:** The nodes in this binary tree don't have a reference to their parent node. It's not a major impediment but it will make certain operations slightly more cumbersome to implement.
 
-A usual, we'll implement most functionality recursively. We'll treat each case slightly differently. For example, this is how you could calculate the number of nodes in the tree and the height of the tree:
+A usual, we'll implement most functionality recursively. We'll treat each case of the enum slightly differently. For example, this is how you could calculate the number of nodes in the tree and the height of the tree:
 
 ```swift
   public var count: Int {
@@ -696,7 +698,7 @@ tree = tree.insert(9)
 tree = tree.insert(1)
 ```
 
-Notice that each time you insert something, you get back a completely new tree. That's why you need to assign the result back to the `tree` variable.
+Notice that each time you insert something, you get back a completely new tree object. That's why you need to assign the result back to the `tree` variable.
 
 Here is the all-important search function:
 
@@ -748,13 +750,13 @@ When you do `print(tree)` it will look something like this:
 
 	((1 <- 2 -> 5) <- 7 -> (9 <- 10 -> .))
 
-The root node is in the middle. A dot means there is no child at that position.
+The root node is in the middle; a dot means there is no child at that position.
 
 ## When the tree becomes unbalanced...
 
 A binary search tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That's the ideal situation.
 
-However, if one branch is significantly longer than the other, searching becomes very slow. We need to check way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
+However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
 
 One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree quite nicely. But it doesn't guarantee success, nor is it always practical.
 
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index f509195f9..7ef0280cf 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -212,7 +212,7 @@ extension BinarySearchTree {
     var edges = 0
     while case let parent? = node.parent {
       node = parent
-      ++edges
+      edges += 1
     }
     return edges
   }
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.swift
index f509195f9..7ef0280cf 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.swift	
@@ -212,7 +212,7 @@ extension BinarySearchTree {
     var edges = 0
     while case let parent? = node.parent {
       node = parent
-      ++edges
+      edges += 1
     }
     return edges
   }
diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 792b15c4a..8c5d8f0f1 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -31,7 +31,7 @@ And you'd use it like this:
 linearSearch(numbers, 43)  // returns 15
 ```
 
-So what's the problem? `linearSearch()` loops through the entire array from the beginning until it finds the element you're looking for. In the worst case, the value isn't in the array and all that work is done for nothing.
+So what's the problem? `linearSearch()` loops through the entire array from the beginning, until it finds the element you're looking for. In the worst case, the value isn't even in the array and all that work is done for nothing.
 
 On average, the linear search algorithm needs to look at half the values in the array. If your array is large enough, this starts to become very slow!
 
@@ -41,12 +41,12 @@ The classic way to speed this up is to use a *binary search*. The trick is to ke
 
 For an array of size `n`, the performance is not **O(n)** as with linear search but only **O(log n)**. To put that in perspective, binary search on an array with 1,000,000 elements only takes about 20 steps to find what you're looking for, because `log_2(1,000,000) = 19.9`. And for an array with a billion elements it only takes 30 steps. (Then again, when was the last time you used an array with a billion items?)
 
-Sounds great, but there is one downside to using binary search: the array must be sorted. In practice, this usually isn't a problem.
+Sounds great, but there is a downside to using binary search: the array must be sorted. In practice, this usually isn't a problem.
 
 Here's how binary search works:
 
 - Split the array in half and determine whether the thing you're looking for, known as the *search key*, is in the left half or in the right half. 
-- How do you determine in which half the search key is? This is why you sorted the array first, so you can do a simple less-than or greater-than comparison.
+- How do you determine in which half the search key is? This is why you sorted the array first, so you can do a simple `<` or `>` comparison.
 - If the search key is in the left half, you repeat the process there: split the left half into two even smaller pieces and look in which piece the search key must lie. (Likewise for when it's the right half.)
 - This repeats until the search key is found. If the array cannot be split up any further, you must regrettably conclude that the search key is not present in the array.
 
@@ -92,11 +92,9 @@ binarySearch(numbers, key: 43, range: 0 ..< numbers.count)  // gives 13
 
 Note that the `numbers` array is sorted. The binary search algorithm does not work otherwise!
 
-I said that binary search works by splitting the array in half, but we don't actually create two new arrays. Instead, we keep track of these splits using a Swift `Range` object. 
+I said that binary search works by splitting the array in half, but we don't actually create two new arrays. Instead, we keep track of these splits using a Swift `Range` object. Initially, this range covers the entire array, `0 ..< numbers.count`.  As we split the array, the range becomes smaller and smaller.
 
-Initially, this range covers the entire array, `0 ..< numbers.count`.  As we split the array, the range becomes smaller and smaller.
-
-> **Note:** One thing to be aware of is that `range.endIndex` always points one beyond the last element. In the example, the range is `0..<19` because there are 19 numbers in the array, and so `range.startIndex = 0` and `range.endIndex = 19`. But in our array the last element is at index 18, since we start counting from 0. Just keep this in mind when working with ranges: the `endIndex` is always one more than the index of the last element.
+> **Note:** One thing to be aware of is that `range.endIndex` always points one beyond the last element. In the example, the range is `0..<19` because there are 19 numbers in the array, and so `range.startIndex = 0` and `range.endIndex = 19`. But in our array the last element is at index 18, not 19, since we start counting from 0. Just keep this in mind when working with ranges: the `endIndex` is always one more than the index of the last element.
 
 ## Stepping through the example
 
@@ -133,7 +131,7 @@ Now binary search will determine which half to use. The relevant section from th
     }
 ```
 
-In this case, `a[midIndex] = 29`. That's less than the search key, so we can safely conclude that the search key will never be in the left half of the array, since that only contains numbers smaller than `29`. Hence, the search key must be in the right half somewhere (or not in the array at all).
+In this case, `a[midIndex] = 29`. That's less than the search key, so we can safely conclude that the search key will never be in the left half of the array. After all, the left half only contains numbers smaller than `29`. Hence, the search key must be in the right half somewhere (or not in the array at all).
 
 Now we can simply repeat the binary search, but on the array interval from `midIndex + 1` to `range.endIndex`:
 
@@ -167,13 +165,13 @@ Again, the search key is greater, so split once more and take the right side:
 	[ x, x, x, x, x, x, x, x, x, x | x, x | x | 43 | x, x, x, x, x ]
 	                                            *
 
-And now we're done. The search key equals the array element we're looking at, so we've finally found what we were looking for. Number `43` is at array index `13`. w00t!
+And now we're done. The search key equals the array element we're looking at, so we've finally found what we were searching for: number `43` is at array index `13`. w00t!
 
 It may have seemed like a lot of work, but in reality it only took four steps to find the search key in the array, which sounds about right because `log_2(19) = 4.23`. With a linear search, it would have taken 14 steps.
 
-What would happen if we were to look for `42` instead of `43`? In that case, we can't split up the array any further.The `range.endIndex` becomes smaller than `range.startIndex` and that tells the algorithm the search key is not in the array and it returns `nil`.
+What would happen if we were to search for `42` instead of `43`? In that case, we can't split up the array any further. The `range.endIndex` becomes smaller than `range.startIndex`. That tells the algorithm the search key is not in the array and it returns `nil`.
 
-> **Note:** Many implementations of binary search calculate `midIndex = (start + end) / 2`. This contains a subtle bug that only appears with very large arrays, because `start + end` may overflow the maximum number an integer can hold. This situation is unlikely to happen on a 64-bit CPU, but it definitely can on 32-bit machines.
+> **Note:** Many implementations of binary search calculate `midIndex = (startIndex + endIndex) / 2`. This contains a subtle bug that only appears with very large arrays, because `startIndex + endIndex` may overflow the maximum number an integer can hold. This situation is unlikely to happen on a 64-bit CPU, but it definitely can on 32-bit machines.
 
 ## Iterative vs recursive
 
@@ -214,4 +212,4 @@ Is it a problem that the array must be sorted first? It depends. Keep in mind th
 
 See also [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm).
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index ed829ec0c..24498b035 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -4,7 +4,7 @@ A binary tree is a [tree](../Tree/) where each node has 0, 1, or 2 children. Thi
 
 ![A binary tree](Images/BinaryTree.png)
 
-The child nodes are usually called the "left" child and the "right" child. If a node doesn't have any children, it's called a *leaf* node. The *root* is the node at the very top of the tree (programmers like their trees upside down).
+The child nodes are usually called the *left* child and the *right* child. If a node doesn't have any children, it's called a *leaf* node. The *root* is the node at the very top of the tree (programmers like their trees upside down).
 
 Often nodes will have a link back to their parent but this is not strictly necessary.
 
@@ -104,9 +104,9 @@ On the tree from the example, `tree.count` should be 12.
 
 Something you often need to do with trees is traverse them, i.e. look at all the nodes in some order. There are three ways to traverse a binary tree:
 
-1. *In-order* (or *depth-first*): first look at the left child node, then at the node itself, and finally at the right child.
-2. *Pre-order*: first look at a node, then its left and right children. 
-3. *Post-order*: first look at the left and right children and process the node last.
+1. *In-order* (or *depth-first*): first look at the left child of a node, then at the node itself, and finally at its right child.
+2. *Pre-order*: first look at a node, then at its left and right children. 
+3. *Post-order*: first look at the left and right children and process the node itself last.
 
 Here is how you'd implement that:
 
diff --git a/Bit Set/README.markdown b/Bit Set/README.markdown
index 380463d33..85d55e06e 100644
--- a/Bit Set/README.markdown	
+++ b/Bit Set/README.markdown	
@@ -10,7 +10,7 @@ Since manipulating individual bits is a little tricky, you can use `BitSet` to h
 
 ## The code
 
-A bit set is simply a wrapper around an array. The array doesn't store individual bits but larger integers that we call the "words". The `BitSet` maps the bits to the right word.
+A bit set is simply a wrapper around an array. The array doesn't store individual bits but larger integers called the "words". The main job of `BitSet` is to map the bits to the right word.
 
 ```swift
 public struct BitSet {
@@ -38,9 +38,9 @@ If you write,
 var bits = BitSet(size: 140)
 ```
 
-then the `BitSet` allocates an array of three words. Each word holds 64 bits and therefore three words can hold 192 bits. We only use 140 of those bits so we're wasting a bit of space (but of course we can never use less than a whole word.)
+then the `BitSet` allocates an array of three words. Each word has 64 bits and therefore three words can hold 192 bits. We only use 140 of those bits so we're wasting a bit of space (but of course we can never use less than a whole word).
 
-> **Note:** The first entry in the `words` array is the least-significant word, so these words are stored in little endian order.
+> **Note:** The first entry in the `words` array is the least-significant word, so these words are stored in little endian order in the array.
 
 ## Looking up the bits
 
@@ -56,9 +56,9 @@ Most of the operations on `BitSet` take the index of the bit as a parameter, so
   }
 ```
 
-The `indexOf()` function returns the array index of the word, as well as a "mask" that shows where the bit sits inside that word.
+The `indexOf()` function returns the array index of the word, as well as a "mask" that shows exactly where the bit sits inside that word.
 
-For example, `indexOf(2)` returns the tuple `(0, 4)` because bit 2 is in the first word (index 0). The mask is 4. In binary that looks like:
+For example, `indexOf(2)` returns the tuple `(0, 4)` because bit 2 is in the first word (index 0). The mask is 4. In binary the mask looks like the following:
 
 	0010000000000000000000000000000000000000000000000000000000000000
 
@@ -94,7 +94,7 @@ Clearing the bit -- i.e. changing it to 0 -- is just as easy:
   }
 ```
 
-Instead of a bitwise OR we now do a bitwise AND with the inverse of the mask. So if the mask was `00100000...0`, then the inverse is `11011111...1`. All the bits are 1, except for the bit we want to set to 0. Due to the way `&` works, this leaves all other bits alone and only changes that one to 0.
+Instead of a bitwise OR we now do a bitwise AND with the inverse of the mask. So if the mask was `00100000...0`, then the inverse is `11011111...1`. All the bits are 1, except for the bit we want to set to 0. Due to the way `&` works, this leaves all other bits alone and only changes that single bit to 0.
 
 To see if a bit is set we also use the bitwise AND but without inverting:
 
@@ -185,7 +185,7 @@ But this is incorrect... Since we don't use most of the last word, we should lea
 
 Instead of 192 one-bits we now have only 140 one-bits. The fact that the last word may not be completely filled up means that we always have to treat this last word specially.
 
-Setting those "leftover" bits to 0 is what the `clearUnusedBits()` helper function does. If the size is not a multiple of `N` (i.e. 64), then we have to clear out the bits that we're not using. If we don't do this, bitwise operations between two differently sized `BitSet`s will go wrong (an example follows).
+Setting those "leftover" bits to 0 is what the `clearUnusedBits()` helper function does. If the `BitSet`'s size is not a multiple of `N` (i.e. 64), then we have to clear out the bits that we're not using. If we don't do this, bitwise operations between two differently sized `BitSet`s will go wrong (an example follows).
 
 This uses some advanced bit manipulation, so pay close attention:
 
@@ -209,7 +209,7 @@ Here's what it does, step-by-step:
 
 1) `diff` is the number of "leftover" bits. In the above example that is 52 because `3*64 - 140 = 52`.
 
-2) Create a mask that is all 0's. Except the highest bit that's still valid is a 1. In our example, that would be:
+2) Create a mask that is all 0's, except the highest bit that's still valid is a 1. In our example, that would be:
 
 	0000000000010000000000000000000000000000000000000000000000000000 
 
@@ -230,7 +230,7 @@ An example of where this is important is when you combine two `BitSet`s of diffe
 	10001111  size=4
 	00100011  size=8
 
-The first one only uses the first 4 bits; the second one uses 8 bits. The first one should really be `10000000` but let's pretend we forgot to clear out those 1's. Then a bitwise or between the two results in:
+The first one only uses the first 4 bits; the second one uses 8 bits. The first one should really be `10000000` but let's pretend we forgot to clear out those 1's at the end. Then a bitwise OR between the two results in:
 
 	10001111  
 	00100011  
@@ -299,7 +299,7 @@ To count the number of bits that are set to 1 we could scan through the entire a
   }
 ```
 
-When you write `x & ~(x - 1)`, it gives you a new value with a single bit set. This is the lowest bit that is one. For example take this 8-bit value (again, I'm showing this with the least significant bit on the left):
+When you write `x & ~(x - 1)`, it gives you a new value with only a single bit set. This is the lowest bit that is one. For example take this 8-bit value (again, I'm showing this with the least significant bit on the left):
 
 	00101101
 
@@ -325,7 +325,9 @@ The only value they have in common is the lowest (or least significant) 1-bit. T
 	-------- XOR
 	00001101
 
-We keep repeating this until the value consists of all zeros. The time complexity is **O(s)** where **s** is the number of 1-bits.
+This is the original value but with the lowest 1-bit removed.
+
+We keep repeating this process until the value consists of all zeros. The time complexity is **O(s)** where **s** is the number of 1-bits.
 
 ## See also
 
diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index c0c06400b..3e37ee50b 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -16,11 +16,11 @@ An advantage of the Bloom Filter over a hash table is that the former maintains
 
 > **Note:** Unlike a hash table, the Bloom Filter does not store the actual objects. It just remembers what objects you’ve seen (with a degree of uncertainty) and which ones you haven’t.
 
-## How it works
+## Inserting objects into the set
 
 A Bloom Filter is essentially a fixed-length [bit vector](../Bit Set/), an array of bits. When we insert objects, we set some of these bits to `1`, and when we query for objects we check if certain bits are `0` or `1`. Both operations use hash functions.
 
-To insert an element in the filter, the element is hashed with several different hash functions. Each hash function returns a value that we map to an index in the array. We set the bits at these indices to `1` or true.
+To insert an element in the filter, the element is hashed with several different hash functions. Each hash function returns a value that we map to an index in the array. We then set the bits at these indices to `1` or true.
 
 For example, let's say this is our array of bits. We have 17 bits and initially they are all `0` or false:
 
@@ -34,9 +34,11 @@ Then we hash the original string again but this time with a different hash funct
 
 	[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
 
-These two bits are enough to tell the Bloom Filter that it now contains the string `"Hello world!"`.
+These two 1-bits are enough to tell the Bloom Filter that it now contains the string `"Hello world!"`. Of course, it doesn't contain the actual string, so you can't ask the Bloom Filter, "give me a list of all the objects you contain". All it has is a bunch of ones and zeros.
 
-Querying, similarly, is accomplished by first hashing the expected value, which gives several array indices, and then checking to see if all of the bits at those indices are `true`. If even one of the bits is not `true`, the element could not have been inserted and the query returns `false`. If all the bits are `true`, the query returns likewise.
+## Querying the set
+
+Querying, similarly to inserting, is accomplished by first hashing the expected value, which gives several array indices, and then checking to see if all of the bits at those indices are `1`. If even one of the bits is not `1`, the element could not have been inserted and the query returns `false`. If all the bits are `1`, the query returns `true`.
 
 For example, if we query for the string `"Hello WORLD"`, then the first hash function returns 5383892684077141175, which modulo 17 is 12. That bit is `1`. But the second hash function gives 5625257205398334446, which maps to array index 9. That bit is `0`. This means the string `"Hello WORLD"` is not in the filter and the query returns `false`.
 
@@ -50,7 +52,7 @@ If you query for `"Hello WORLD"` again, the filter sees that bit 12 is true and
 
 You can fix such issues by using an array with more bits and using additional hash functions. Of course, the more hash functions you use the slower the Bloom Filter will be. So you have to strike a balance.
 
-Deletion is not possible with a Bloom Filter, since any one bit might have been set by multiple elements inserted. Once you add an element, it's in there for good.
+Deletion is not possible with a Bloom Filter, since any one bit might belong to multiple elements. Once you add an element, it's in there for good.
 
 Performance of a Bloom Filter is **O(k)** where **k** is the number of hashing functions.
 
@@ -96,6 +98,6 @@ public func query(value: T) -> Bool {
 }
 ```
 
-If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case, `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop. 
+If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop. 
 
 *Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans.*
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index dce0430f2..73a7943a2 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -2,7 +2,7 @@
 
 Goal: Write a string search algorithm in pure Swift without importing Foundation or using `NSString`'s `rangeOfString()` method. 
  
-In other words, implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
+In other words, we want to implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
  
 For example:
 
@@ -24,9 +24,9 @@ animals.indexOf("🐮")
 
 > **Note:** The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
 
-The [brute-force approach](../Brute-Force Search Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at *every* character from the source string -- you can often skip ahead multiple characters.
+The [brute-force approach](../Brute-Force String Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at *every* character from the source string -- you can often skip ahead multiple characters.
 
-That skip-ahead algorithm is called [Boyer-Moore](https://en.wikipedia.org/wiki/Boyer–Moore_string_search_algorithm) and it has been around for a long time. It is considered the benchmark for all string search algorithms.
+The skip-ahead algorithm is called [Boyer-Moore](https://en.wikipedia.org/wiki/Boyer–Moore_string_search_algorithm) and it has been around for a long time. It is considered the benchmark for all string search algorithms.
 
 Here's how you could write it in Swift:
 
@@ -133,7 +133,7 @@ The amount to skip ahead at any given time is determined by the "skip table", wh
 
 The closer a character is to the end of the pattern, the smaller the skip amount. If a character appears more than once in the pattern, the one nearest to the end of the pattern determines the skip value for that character.
 
-A caveat: If the search pattern consists of only a few characters, it's faster to do a brute-force search. There's a trade-off between the time it takes to build the skip table and doing brute-force for short patterns.
+> **Note:** If the search pattern consists of only a few characters, it's faster to do a brute-force search. There's a trade-off between the time it takes to build the skip table and doing brute-force for short patterns.
 
 Credits: This code is based on the article ["Faster String Searches" by Costas Menico](http://www.drdobbs.com/database/faster-string-searches/184408171) from Dr Dobb's magazine, July 1989 -- Yes, 1989! Sometimes it's useful to keep those old magazines around.
 
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 584b37c1d..e75d2b913 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,6 +1,6 @@
 # Breadth-First Search
 
-Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores the immediate neighbor nodes first, before moving to the next level neighbors.
+Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors.
 
 ## Animated example
 
@@ -129,10 +129,10 @@ This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
    
 ## Applications
 
-Breadth-first search can be used to solve many problems, for example:
+Breadth-first search can be used to solve many problems. A small selection:
 
-* Computing the shortest path between a source node and each of the other nodes (only for unweighted graphs)
-* Calculating the minimum spanning tree on an unweighted graph
+* Computing the shortest path between a source node and each of the other nodes (only for unweighted graphs).
+* Calculating the minimum spanning tree on an unweighted graph.
 
 ## Shortest path example
 
diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index d491aab28..2d7a6ac83 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -10,20 +10,20 @@ This is another permutation:
 
 For a collection of `n` objects, there are `n!` possible permutations, where `!` is the "factorial" function. So for our collection of five letters, the total number of permutations you can make is:
 
-	5! = 5 x 4 x 3 x 2 x 1 = 120
+	5! = 5 * 4 * 3 * 2 * 1 = 120
 
-A collection of six items has `6! = 720` permutations. For ten items, it is `10! = 3.628.800`. That adds up quick!
+A collection of six items has `6! = 720` permutations. For ten items, it is `10! = 3,628,800`. That adds up quick!
 
 Where does this `n!` come from? The logic is as follows: we have a collection of five letters that we want to put in some order. To do this, you need to pick up these letters one-by-one. Initially, you have the choice of five letters: `a, b, c, d, e`. That gives 5 possibilities.
 
-After picking the first letter, you only have four letters left to choose from. That gives `5 x 4 = 20` possibilities:
+After picking the first letter, you only have four letters left to choose from. That gives `5 * 4 = 20` possibilities:
 
 	a+b    b+a    c+a    d+a    e+a
 	a+c    b+c    c+b    d+b    e+b
 	a+d    b+d    c+d    d+c    e+c
 	a+e    b+e    c+e    d+e    e+d
 
-After picking the second letter, there are only three letters left to choose from. And so on... When you get to the last letter, you don't have any choice because there is only one letter left. That's why the total number of possibilities is `5 x 4 x 3 x 2 x 1`.
+After picking the second letter, there are only three letters left to choose from. And so on... When you get to the last letter, you don't have any choice because there is only one letter left. That's why the total number of possibilities is `5 * 4 * 3 * 2 * 1`.
 
 To calculate the factorial in Swift:
 
@@ -47,7 +47,7 @@ factorial(5)   // returns 120
 
 Note that `factorial(20)` is the largest number you can calculate with this function, or you'll get integer overflow.
 
-Let's say that from that collection of five letters you want to choose only 3 elements. How many possible ways can you do this? Well, that works the same way as before, except that you stop after the third letter. So now the number of possibilities is `5 x 4 x 3 = 60`.
+Let's say that from that collection of five letters you want to choose only 3 elements. How many possible ways can you do this? Well, that works the same way as before, except that you stop after the third letter. So now the number of possibilities is `5 * 4 * 3 = 60`.
 
 The formula for this is:
 
@@ -83,11 +83,13 @@ permutations(9, 4)   // returns 3024
 
 This function takes advantage of the following algebra fact:
 
-	          9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
-	P(9, 4) = --------------------------------- = 9 x 8 x 7 x 6 = 3024
-	                          5 x 4 x 3 x 2 x 1
+	          9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
+	P(9, 4) = --------------------------------- = 9 * 8 * 7 * 6 = 3024
+	                          5 * 4 * 3 * 2 * 1
 
-The denominator cancels out part of the numerator, so there's no need to perform a division and you're not dealing with intermediate results that are potentially too large. However, there are still limits to what you can calculate; for example the number of groups of size 15 that you can make from a collection of 30 objects -- i.e. `P(30, 15)` -- is ginormous and breaks Swift. Huh, you wouldn't think it would be so large but combinatorics is funny that way.
+The denominator cancels out part of the numerator, so there's no need to perform a division and you're not dealing with intermediate results that are potentially too large.
+
+However, there are still limits to what you can calculate; for example the number of groups of size 15 that you can make from a collection of 30 objects -- i.e. `P(30, 15)` -- is ginormous and breaks Swift. Huh, you wouldn't think it would be so large but combinatorics is funny that way.
 
 ## Generating the permutations
 
@@ -211,7 +213,7 @@ Of course, the larger your array is, the more swaps it performs and the deeper t
 
 If the above is still not entirely clear, then I suggest you give it a go in the playground. That's what playgrounds are great for. :-)
 
-For fun, here is an alternative algorithm, by Sedgewick:
+For fun, here is an alternative algorithm, by Robert Sedgewick:
 
 ```swift
 func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
@@ -259,7 +261,7 @@ Try to figure out for yourself how this algorithm works!
 
 ## Combinations
 
-A combination is like a permutation where the order does not matter. So the following are six different permutations of the letters `k` `l` `m` but they all count as the same combination:
+A combination is like a permutation where the order does not matter. The following are six different permutations of the letters `k` `l` `m` but they all count as the same combination:
 
 	k, l, m      k, m, l      m, l, k
 	l, m, k      l, k, m      m, k, l
@@ -276,15 +278,15 @@ The formula for `C(n, k)` is:
 
 	               n!         P(n, k)
 	C(n, k) = ------------- = --------
-	          (n - k)! x k!      k!
+	          (n - k)! * k!      k!
 
 As you can see, you can derive it from the formula for `P(n, k)`. There are always more permutations than combinations. You divide the number of permutations by `k!` because a total of `k!` of these permutations give the same combination.
 
-Above I showed that the number of permutations of `k` `l` `m` is 6 but, if you pick only two of those letters, the number of combinations is 3. If we use the formula we should get the same answer. We want to calculate `C(3, 2)` because we choose 2 letters out of a collection of 3. 
+Above I showed that the number of permutations of `k` `l` `m` is 6, but if you pick only two of those letters the number of combinations is 3. If we use the formula we should get the same answer. We want to calculate `C(3, 2)` because we choose 2 letters out of a collection of 3. 
 
-	          3 x 2 x 1    6
+	          3 * 2 * 1    6
 	C(3, 2) = --------- = --- = 3
-	           1! x 2!     2
+	           1! * 2!     2
 
 Here's a simple function to calculate `C(n, k)`:
 
@@ -300,7 +302,7 @@ Use it like this:
 combinations(28, 5)    // prints 98280
 ```
 
-Because this uses the `permutations()` and `factorial()` functions under the hood, you're still limited by how large these numbers can get. For example, `combinations(30, 15)` is "only" `155.117.520` but because the intermediate results don't fit into a 64-bit integer, you can't calculate it with the given function.
+Because this uses the `permutations()` and `factorial()` functions under the hood, you're still limited by how large these numbers can get. For example, `combinations(30, 15)` is "only" `155,117,520` but because the intermediate results don't fit into a 64-bit integer, you can't calculate it with the given function.
 
 Here is an algorithm that uses dynamic programming to overcome the need for calculating factorials. It is based on Pascal's triangle:
 
@@ -312,7 +314,7 @@ Here is an algorithm that uses dynamic programming to overcome the need for calc
 	5:     1   5  10   10  5   1 
 	6:   1   6  15  20   15  6   1 
 
-Each number in the next row is made up by adding two numbers from the previous row. For example, in row 6, the number 15 is made by adding the 5 and 10 from row 5. These numbers are called the binomial coefficients and as it happens they are the same as `C(n, k)`.
+Each number in the next row is made up by adding two numbers from the previous row. For example in row 6, the number 15 is made by adding the 5 and 10 from row 5. These numbers are called the binomial coefficients and as it happens they are the same as `C(n, k)`.
 
 For example, for row 6:
 
@@ -360,6 +362,6 @@ You may wonder what the point is in calculating these permutations and combinati
 
 ## References
 
-Wirth's and Sedgewick's permutation algorithms and the code for counting permutations and combinations is based on the Algorithm Alley column from Dr.Dobb's Magazine, June 1993. The dynamic programming binomial coefficient algorithm is from The Algorithm Design Manual by Skiena.
+Wirth's and Sedgewick's permutation algorithms and the code for counting permutations and combinations are based on the Algorithm Alley column from Dr.Dobb's Magazine, June 1993. The dynamic programming binomial coefficient algorithm is from The Algorithm Design Manual by Skiena.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index d22609025..be8c2061e 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -2,7 +2,7 @@
 
 Goal: Count how often a certain value appears in an array.
 
-The obvious way to do this is with a [linear search](../Linear Search/) from the beginning of the array until the end, keeping count of how often you come across the value. This is an **O(n)** algorithm.
+The obvious way to do this is with a [linear search](../Linear Search/) from the beginning of the array until the end, keeping count of how often you come across the value. That is an **O(n)** algorithm.
 
 However, if the array is sorted you can do it much faster, in **O(log n)** time, by using a modification of [binary search](../Binary Search/).
 
@@ -10,7 +10,7 @@ Let's say we have the following array:
 
 	[ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 
-If we want to know how often the value `3` occurs, we can do a binary search for `3`. That could give us any of these four indices:
+If we want to know how often the value `3` occurs, we can do a regular binary search for `3`. That could give us any of these four indices:
 
 	[ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 	           *  *  *  *
@@ -55,7 +55,7 @@ func countOccurrencesOfKey(key: Int, inArray a: [Int]) -> Int {
 }
 ```
 
-Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the binary search algorithm. The big difference is that they don't stop when they find the search key, but keep going.
+Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the [binary search](../Binary Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.
 
 To test this algorithm, copy the code to a playground and then do:
 
@@ -65,7 +65,7 @@ let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 countOccurrencesOfKey(3, inArray: a)  // returns 4
 ```
 
-Remember: If you use your own array, make sure it is sorted first!
+> **Remember:** If you use your own array, make sure it is sorted first!
 
 Let's walk through the example. The array is:
 
@@ -111,10 +111,10 @@ Now let's start over and try to find the right boundary. This is very similar, s
 
 The right boundary is at index 7. The difference between the two boundaries is 7 - 3 = 4, so the number `3` occurs four times in this array.
 
-Each binary search took 4 steps, so in total this algorithm took 8 steps. Not a big gain on an array of only 12 items, but the bigger the array, the more efficient this algorithm becomes. For a sorted array with 1,000,000 items, it only takes 2x20 = 40 steps to count the number of occurrences for any particular value.
+Each binary search took 4 steps, so in total this algorithm took 8 steps. Not a big gain on an array of only 12 items, but the bigger the array, the more efficient this algorithm becomes. For a sorted array with 1,000,000 items, it only takes 2 x 20 = 40 steps to count the number of occurrences for any particular value.
 
 By the way, if the value you're looking for is not in the array, then `rightBoundary()` and `leftBoundary()` return the same value and so the difference between them is 0.
 
 This is an example of how you can modify the basic binary search to solve other algorithmic problems as well. Of course, it does require that the array is sorted.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 87b5d2791..3329adca0 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -2,7 +2,7 @@
 
 A double-ended queue. For some reason this is pronounced as "deck".
 
-A regular [queue](../Queue/) adds new elements to the back and removes from the front. The deque also allows enqueuing at the front and dequeuing from the back, and peeking at both ends.
+A regular [queue](../Queue/) adds elements to the back and removes from the front. The deque also allows enqueuing at the front and dequeuing from the back, and peeking at both ends.
 
 Here is a very basic implementation of a deque in Swift:
 
@@ -52,7 +52,7 @@ public struct Deque<T> {
 }
 ```
 
-This uses an array internally. Enqueuing and dequeuing is simply a matter of adding and removing items from the front or back of the array.
+This uses an array internally. Enqueuing and dequeuing are simply a matter of adding and removing items from the front or back of the array.
 
 An example of how to use it in a playground:
 
@@ -90,7 +90,7 @@ Likewise, inserting an element at the front of the array is expensive because it
 
 	[ 5, 2, 3, 4 ]
 
-First, the elements `2`, `3`, and `4`, are move up by one position in the computer's memory, and then the new element `5` is inserted at the position where `2` used to be.
+First, the elements `2`, `3`, and `4` are moved up by one position in the computer's memory, and then the new element `5` is inserted at the position where `2` used to be.
 
 Why is this not an issue at for `enqueue()` and `dequeueBack()`? Well, these operations are performed at the end of the array. The way resizable arrays are implemented in Swift is by reserving a certain amount of free space at the back. 
 
@@ -102,7 +102,7 @@ where the `x`s denote additional positions in the array that are not being used
 
 	[ 1, 2, 3, 4, 6, x, x ]
 
-And `dequeueBack()` uses `array.removeLast()` to read that item and decrement `array.count` by one. There is no shifting of memory involved here. So operations at the back of the array are fast, **O(1)**.
+The `dequeueBack()` function uses `array.removeLast()` to delete that item. This does not shrink the array's memory but only decrements `array.count` by one. There are no expensive memory copies involved here. So operations at the back of the array are fast, **O(1)**.
 
 It is possible the array runs out of free spots at the back. In that case, Swift will allocate a new, larger array and copy over all the data. This is an **O(n)** operation but because it only happens once in a while, adding new elements at the end of an array is still **O(1)** on average.
 
@@ -110,7 +110,7 @@ Of course, we can use this same trick at the *beginning* of the array. That will
 
 	[ x, x, x, 1, 2, 3, 4, x, x, x ]
 
-There is now a chunk of free space at the start of the array, which allows adding or removing elements at the front of the queue to be **O(1)** as well.
+There is now also a chunk of free space at the start of the array, which allows adding or removing elements at the front of the queue to be **O(1)** as well.
 
 Here is the new version of `Deque`:
 
@@ -217,7 +217,7 @@ Notice how the array has resized itself. There was no room to add the `1`, so Sw
 	                          |
 	                          head
 
-> **Note:** You won't see those empty spots at the back when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up. 
+> **Note:** You won't see those empty spots at the back of the array when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up. 
 
 The `dequeue()` method does the opposite of `enqueueFront()`, it reads the value at `head`, sets the array element back to `nil`, and then moves `head` one position to the right:
 
@@ -232,7 +232,7 @@ The `dequeue()` method does the opposite of `enqueueFront()`, it reads the value
   }
 ```
 
-There is one tiny problem... If you enqueue a lot of objects at the front, you're going to run out of empty spots at the front at some point. When this happens at the back of the array, Swift automatically resizes it. But at the front of the array we have to handle this ourselves with some extra logic in `enqueueFront()`:
+There is one tiny problem... If you enqueue a lot of objects at the front, you're going to run out of empty spots at the front at some point. When this happens at the back of the array, Swift automatically resizes it. But at the front of the array we have to handle this situation ourselves, with some extra logic in `enqueueFront()`:
 
 ```swift
   public mutating func enqueueFront(element: T) {
@@ -252,11 +252,11 @@ If `head` equals 0, there is no room left at the front. When that happens, we ad
 
 > **Note:** We also multiply the capacity by 2 each time this happens, so if your queue grows bigger and bigger, the resizing happens less often. This is also what Swift arrays automatically do at the back.
 
-We have to do something similar for `dequeue()`. If you mostly enqueue a lot of elements at the back and mostly dequeue from the front, then you may end up with an array that looks like this:
+We have to do something similar for `dequeue()`. If you mostly enqueue a lot of elements at the back and mostly dequeue from the front, then you may end up with an array that looks as follows:
 
 	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
-	                                                           |
-	                                                           head
+	                                                              |
+	                                                              head
 
 Those empty spots at the front only get used when you call `enqueueFront()`. But if enqueuing objects at the front happens only rarely, this leaves a lot of wasted space. So let's add some code to `dequeue()` to clean this up:
 
@@ -285,7 +285,7 @@ For example, this:
 	                                |                             |
 	                                capacity                      head
 
-becomes this after trimming:
+becomes after trimming:
 
 	[ x, x, x, x, x, 1, 2, 3 ]
 	              |
@@ -294,7 +294,7 @@ becomes this after trimming:
 
 This way we can strike a balance between fast enqueuing and dequeuing at the front and keeping the memory requirements reasonable.
 
-> **Note:** We don't perform this trimming on very small arrays. It's not worth it for saving just a few bytes of memory.
+> **Note:** We don't perform trimming on very small arrays. It's not worth it for saving just a few bytes of memory.
 
 ## See also
 
diff --git a/Fixed Size Array/README.markdown b/Fixed Size Array/README.markdown
index ec72852a8..8a87f077c 100644
--- a/Fixed Size Array/README.markdown	
+++ b/Fixed Size Array/README.markdown	
@@ -2,7 +2,7 @@
 
 Early programming languages didn't have very fancy arrays. You'd create the array with a specific size and from that moment on it would never grow or shrink. Even the standard arrays in C and Objective-C are still of this type. 
 
-When you define an array like this,
+When you define an array like so,
 
 	int myArray[10];
 	
@@ -14,7 +14,7 @@ That's your array. It will always be this size. If you need to fit more than 10
 
 To get an array that grows when it gets full you need to use a [dynamic array](https://en.wikipedia.org/wiki/Dynamic_array) object such as `NSMutableArray` in Objective-C or `std::vector` in C++, or a language like Swift whose arrays increase their capacity as needed.
 
-A big downside of the old-style arrays is that they need to be big enough or you run out of space. But if they are too big you're wasting memory. And you need to be careful about security flaws and crashes due to buffer overflows. In summary, fixed-size arrays are not flexible and they leave no room for error.
+A major downside of the old-style arrays is that they need to be big enough or you run out of space. But if they are too big you're wasting memory. And you need to be careful about security flaws and crashes due to buffer overflows. In summary, fixed-size arrays are not flexible and they leave no room for error.
 
 That said, **I like fixed-size arrays** because they are simple, fast, and predictable.
 
@@ -38,7 +38,7 @@ These two operations have complexity **O(1)**, meaning the time it takes to perf
 
 For an array that can grow, appending is more involved: if the array is full, new memory must be allocated and the old contents copied over to the new memory buffer. On average, appending is still an **O(1)** operation, but what goes on under the hood is less predictable.
 
-The expensive operations are inserting and deleting. When you insert an element somewhere that's not at the end, it requires moving up the remainder of the array by one position. That involves a relatively costly memory copy operation:
+The expensive operations are inserting and deleting. When you insert an element somewhere that's not at the end, it requires moving up the remainder of the array by one position. That involves a relatively costly memory copy operation. For example, inserting the value `7` in the middle of the array:
 
 ![Insert requires a memory copy](Images/insert.png)
 
@@ -48,7 +48,7 @@ Deleting requires a copy the other way around:
 
 ![Delete also requires a memory copy](Images/delete.png)
 
-This, by the way, is also true for `NSMutableArray` or Swift arrays. Inserting and deleting are **O(n)** operations -- the larger the array is the more time it takes.
+This, by the way, is also true for `NSMutableArray` or Swift arrays. Inserting and deleting are **O(n)** operations -- the larger the array the more time it takes.
 
 Fixed-size arrays are a good solution when:
 
@@ -87,7 +87,7 @@ This copies the last element on top of the element you want to remove, and then
 
 This is why the array is not sorted. To avoid an expensive copy of a potentially large portion of the array we copy just one element, but that does change the order of the elements.
 
-There are now two copies of element "6" in the array, but what was previously the last element is no longer part of the active array. It's just junk data -- the next time you append an new element, this old version of "6" will be overwritten.
+There are now two copies of element `6` in the array, but what was previously the last element is no longer part of the active array. It's just junk data -- the next time you append an new element, this old version of `6` will be overwritten.
 
 Under these two constraints -- a limit on the number of elements and an unsorted array -- fixed-size arrays are still perfectly suitable for use in modern software.
 
@@ -138,4 +138,4 @@ var a = FixedSizeArray(maxSize: 10, defaultValue: 0)
 
 Note that `removeAtIndex()` overwrites the last element with this `defaultValue` to clean up the "junk" object that gets left behind. Normally it wouldn't matter to leave that duplicate object in the array, but if it's a class or a struct it may have strong references to other objects and it's good boyscout practice to zero those out.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Fizz Buzz/README.markdown b/Fizz Buzz/README.markdown
index 066cbe2de..0ce1e2c42 100644
--- a/Fizz Buzz/README.markdown	
+++ b/Fizz Buzz/README.markdown	
@@ -18,38 +18,40 @@ The modulus operator returns the remainder after an integer division. Here is an
 
 | Division      | Division Result            | Modulus         | Modulus Result  |
 | ------------- | -------------------------- | --------------- | ---------------:|
-| 1 `/` 3       | `0` with a remainder of 3  | 1 `%` 3         | `3`             |
-| 5 `/` 3       | `1` with a remainder of 2  | 5 `%` 3         | `2`             |
-| 16 `/` 3      | `5` with a remainder of 1  | 16 `%` 3        | `1`             |
+| 1 / 3       | 0 with a remainder of 3  | 1 % 3         | 3             |
+| 5 / 3       | 1 with a remainder of 2  | 5 % 3         | 2             |
+| 16 / 3      | 5 with a remainder of 1  | 16 % 3        | 1             |
 
 A common approach to determine if a number is even or odd is to use the modulus operator:
 
 | Modulus       | Result          | Swift Code                      | Swift Code Result | Comment                                       |
 | ------------- | ---------------:| ------------------------------- | -----------------:| --------------------------------------------- |
-| 6 `%` 2       | 0               | `let isEven = number % 2 == 0`  | `true`            | If a number is divisible by 2 it is `even`    |
-| 5 `%` 2       | 1               | `let isOdd = number % 2 != 0`   | `true`            | If a number is not divisible by 2 it is `odd` |
+| 6 % 2       | 0               | `let isEven = (number % 2 == 0)`  | `true`            | If a number is divisible by 2 it is *even*    |
+| 5 % 2       | 1               | `let isOdd = (number % 2 != 0)`   | `true`            | If a number is not divisible by 2 it is *odd* |
 
-Now we can use the modulus operator `%`  to solve fizz buzz.
+## Solving fizz buzz
+
+Now we can use the modulus operator `%` to solve fizz buzz.
 
 Finding numbers divisible by three:
 
 | Modulus | Modulus Result | Swift Code    | Swift Code Result |
 | ------- | --------------:| ------------- |------------------:|
-| 1 `%` 3 | `1`            | `1 % 3 == 0`  | `false`           |
-| 2 `%` 3 | `2`            | `2 % 3 == 0`  | `false`           |
-| 3 `%` 3 | `0`            | `3 % 3 == 0`  | `true`            |
-| 4 `%` 3 | `1`            | `4 % 3 == 0`  | `false`           |
+| 1 % 3 | 1            | `1 % 3 == 0`  | `false`           |
+| 2 % 3 | 2            | `2 % 3 == 0`  | `false`           |
+| 3 % 3 | 0            | `3 % 3 == 0`  | `true`            |
+| 4 % 3 | 1            | `4 % 3 == 0`  | `false`           |
 
 Finding numbers divisible by five:
 
 | Modulus | Modulus Result | Swift Code    | Swift Code Result |
 | ------- | --------------:| ------------- |------------------:|
-| 1 `%` 5 | `1`            | `1 % 5 == 0`  | `false`           |
-| 2 `%` 5 | `2`            | `2 % 5 == 0`  | `false`           |
-| 3 `%` 5 | `3`            | `3 % 5 == 0`  | `false`           |
-| 4 `%` 5 | `4`            | `4 % 5 == 0`  | `false`           |
-| 5 `%` 5 | `0`            | `5 % 5 == 0`  | `true`            |
-| 6 `%` 5 | `1`            | `6 % 5 == 0`  | `false`           |
+| 1 % 5 | 1            | `1 % 5 == 0`  | `false`           |
+| 2 % 5 | 2            | `2 % 5 == 0`  | `false`           |
+| 3 % 5 | 3            | `3 % 5 == 0`  | `false`           |
+| 4 % 5 | 4            | `4 % 5 == 0`  | `false`           |
+| 5 % 5 | 0            | `5 % 5 == 0`  | `true`            |
+| 6 % 5 | 1            | `6 % 5 == 0`  | `false`           |
 
 ## The code
 
@@ -80,8 +82,13 @@ func fizzBuzz(numberOfTurns: Int) {
 Put this code in a playground and test it like so:
 
 ```swift
-fizzBuzz(15) // This will output 1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, Fizz Buzz
+fizzBuzz(15)
 ```
+
+This will output:
+
+	1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, Fizz Buzz
+
 ## See also
 
 [Fizz buzz on Wikipedia](https://en.wikipedia.org/wiki/Fizz_buzz)
diff --git a/GCD/README.markdown b/GCD/README.markdown
index a7fe799d9..1d20fb9cb 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -30,16 +30,16 @@ func gcd(a: Int, _ b: Int) -> Int {
 Put it in a playground and try it out with these examples:
 
 ```swift
-gcd(52, 39)       // 13
-gcd(228, 36)      // 12
-gcd(51357, 3819)  // 57
+gcd(52, 39)        // 13
+gcd(228, 36)       // 12
+gcd(51357, 3819)   // 57
 ```
 
 Let's step through the third example:
 
 	gcd(51357, 3819)
 
-According to Euclid's rule, this is equivalent to:
+According to Euclid's rule, this is equivalent to,
 
 	gcd(3819, 51357 % 3819) = gcd(3819, 1710)
 
@@ -65,7 +65,7 @@ By the way, it's also possible that two numbers have a GCD of 1. They are said t
 gcd(841, 299)     // 1
 ```
 
-Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop. The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop.
 
 ```swift
 func gcd(m: Int, _ n: Int) -> Int {
@@ -82,6 +82,8 @@ func gcd(m: Int, _ n: Int) -> Int {
 }
 ```
 
+The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+
 ## Least Common Multiple
 
 An idea related to the GCD is the *least common multiple* or LCM.
diff --git a/Hash Set/README.markdown b/Hash Set/README.markdown
index 8dcc891d3..c6616fb42 100644
--- a/Hash Set/README.markdown	
+++ b/Hash Set/README.markdown	
@@ -11,7 +11,7 @@ If the following were arrays, they'd all be different. However, they all represe
 [1, 2, 2, 3, 1]
 ```
 
-(Because each element can appear only once, it doesn't matter how often you write it down -- only one of them counts.) 
+Because each element can appear only once, it doesn't matter how often you write the element down -- only one of them counts.
 
 > **Note:** I often prefer to use sets over arrays when I have a collection of objects but don't care what order they are in. Using a set communicates to the programmer that the order of the elements is unimportant. If you're using an array, then you can't assume the same thing.
 
@@ -135,7 +135,7 @@ let union = setA.union(setB)
 union.allElements()           // [5, 6, 2, 3, 1, 4]
 ```
 
-As you can see, the union of the two sets contains all of the elements now. The values `3` and `4` appear only once, even though they were in both sets.
+As you can see, the union of the two sets contains all of the elements now. The values `3` and `4` still appear only once, even though they were in both sets.
 
 The *intersection* of two sets contains only the elements that they have in common. Here is the code:
 
@@ -192,7 +192,7 @@ difference2.allElements()                // [5, 6]
 
 If you look at the [documentation](http://swiftdoc.org/v2.1/type/Set/) for Swift's own `Set`, you'll notice it has tons more functionality. An obvious extension would be to make `HashSet` conform to `SequenceType` so that you can iterate it with a `for`...`in` loop.
 
-Another thing you could do is replace the `Dictionary` with an actual [hash table](../Hash Table), but one that just stores the keys and doesn't associate them with anything.
+Another thing you could do is replace the `Dictionary` with an actual [hash table](../Hash Table), but one that just stores the keys and doesn't associate them with anything. So you wouldn't need the `Bool` values anymore.
 
 If you often need to look up whether an element belongs to a set and perform unions, then the [union-find](../Union-Find/) data structure may be more suitable. It uses a tree structure instead of a dictionary to make the find and union operations very efficient.
 
diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 5afecabba..02a2c9578 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -4,11 +4,11 @@ A hash table allows you to store and retrieve objects by a "key".
 
 Also called dictionary, map, associative array. There are other ways to implement these, such as with a tree or even a plain array, but hash table is the most common.
 
-This should explain why Swift's built-in `Dictionary` type requires that keys conform to the `Hashable` protocol: internally it uses a hash table.
+This should explain why Swift's built-in `Dictionary` type requires that keys conform to the `Hashable` protocol: internally it uses a hash table, just like the one you'll learn about here.
 
-## How a hash table works
+## How it works
 
-At its most basic, a hash table is nothing more than an array. Initially, this array is empty. When you put a value into the hash table, it uses the key to calculate an index in the array, like so:
+At its most basic, a hash table is nothing more than an array. Initially, this array is empty. When you put a value into the hash table under a certain key, it uses that key to calculate an index in the array, like so:
 
 ```swift
 hashTable["firstName"] = "Steve"
@@ -68,11 +68,11 @@ Using hashes in this manner is what makes the dictionary so efficient: to find a
 
 ## Avoiding collisions
 
-There is one problem: because we take the modulo of the hash value with the size of the array, it can happen than two or more keys get assigned the same array index. This is called a collision.
+There is one problem: because we take the modulo of the hash value with the size of the array, it can happen that two or more keys get assigned the same array index. This is called a collision.
 
 One way to avoid collisions is to have a very large array. That reduces the likelihood of two keys mapping to the same index. Another trick is to use a prime number for the array size. However, collisions are bound to occur so you need some way to handle them.
 
-Because our table is so small it's easy to show a collision. For example, the array index for the key `"lastName"` is also 3.
+Because our table is so small it's easy to show a collision. For example, the array index for the key `"lastName"` is also 3. That's a problem, as we don't want to overwrite the value that's already at this array index.
 
 There are a few ways to handle collisions. A common one is to use chaining. The array now looks as follows:
 
@@ -91,7 +91,7 @@ There are a few ways to handle collisions. A common one is to use chaining. The
 	+-----+
 ```
 
-Keys are not stored directly in the array. Instead, each element in the array is really a list of key/value pairs. The array elements are usually called the *buckets* and the lists are called the *chains*. So here we have 5 buckets and two of these buckets have chains. The other three buckets are empty.
+With chaining, keys and their values are not stored directly in the array. Instead, each array element is really a list of zero or more key/value pairs. The array elements are usually called the *buckets* and the lists are called the *chains*. So here we have 5 buckets and two of these buckets have chains. The other three buckets are empty.
 
 If we now write the following to retrieve an item from the hash table,
 
@@ -99,13 +99,13 @@ If we now write the following to retrieve an item from the hash table,
 let x = hashTable["lastName"]
 ```
 
-then this first hashes the key `"lastName"` to calculate the array index, which is 3. Bucket 3 has a chain, so we step through that list to find the item with the key `"lastName"`. That is done by comparing the keys, so here that involves a string comparison. The hash table sees that this key belongs to the last item in the chain and returns the corresponding value, `"Jobs"`.
+then this first hashes the key `"lastName"` to calculate the array index, which is 3. Bucket 3 has a chain, so we step through that list to find the value with the key `"lastName"`. That is done by comparing the keys, so here that involves a string comparison. The hash table sees that this key belongs to the last item in the chain and returns the corresponding value, `"Jobs"`.
 
-Common ways to implement this chaining mechanism are to use a linked list or another array. Technically speaking the order of the items in the chain doesn't matter, so you also can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from.)
+Common ways to implement this chaining mechanism are to use a linked list or another array. Technically speaking the order of the items in the chain doesn't matter, so you also can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-It's important that chains do not become too long or looking up items in the hash table becomes really slow. Ideally, we would have no chains at all but in practice it is impossible to avoid collisions. But you can improve the odds by giving the hash table enough buckets and by using high-quality hash functions.
+It's important that chains do not become too long or looking up items in the hash table becomes really slow. Ideally, we would have no chains at all but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets and by using high-quality hash functions.
 
-> **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in an unused bucket. Of course, this approach has its own upsides and downsides.
+> **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. Of course, this approach has its own upsides and downsides.
 
 ## The code
 
@@ -129,9 +129,9 @@ public struct HashTable<Key: Hashable, Value> {
   }
 ```
 
-The `HashTable` is a generic container and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for use in a chain and `Bucket` is an array of such `Element`s.
+The `HashTable` is a generic container and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for use in a chain and `Bucket` is an array of such `Elements`.
 
-The main array is named `buckets`. It has a fixed size, the so-called capacity, provided bythe `init(capacity)` method. We're also keeping track of how many items have been added to the hash table using the `count` variable.
+The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We're also keeping track of how many items have been added to the hash table using the `count` variable.
 
 An example of how to create a new hash table object:
 
@@ -197,9 +197,9 @@ This calls three helper functions to do the actual work. Let's take a look at `v
   }
 ```
 
-First it calls `indexForKey()` to convert the key into an array index. That gives us the bucket, but if there were collisions this bucket may be used by more than one key. So `valueForKey()` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
+First it calls `indexForKey()` to convert the key into an array index. That gives us the bucket number, but if there were collisions this bucket may be used by more than one key. So `valueForKey()` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
 
-The code to insert or update an existing element lives in `updateValue(forKey)`. It's a little bit more complicated:
+The code to insert a new element or update an existing element lives in `updateValue(forKey)`. It's a little bit more complicated:
 
 ```swift
   public mutating func updateValue(value: Value, forKey key: Key) -> Value? {
@@ -243,7 +243,7 @@ Removing is similar in that again it loops through the chain:
   }
 ```
 
-And these are the basic functions of the hash table. They all work the same way: convert the key into an array index using its hash value, then loop through the chain for that bucket and perform the desired operation.
+These are the basic functions of the hash table. They all work the same way: convert the key into an array index using its hash value, find the bucket, then loop through that bucket's chain and perform the desired operation.
 
 Try this stuff out in a playground. It should work just like a standard Swift `Dictionary`.
 
@@ -255,7 +255,7 @@ The *load factor* of a hash table is the percentage of the capacity that is curr
 
 If the hash table is too small and the chains are long, the load factor can become greater than 1. That's not a good idea.
 
-If the load factor becomes too high, say > 75%, you can resize the hash table. Adding the code for this is left as an exercise for the reader. Keep in mind that making the buckets array larger will change the array indices that the keys map to!
+If the load factor becomes too high, say > 75%, you can resize the hash table. Adding the code for this is left as an exercise for the reader. Keep in mind that making the buckets array larger will change the array indices that the keys map to! To account for this, you'll have to insert all the elements again after resizing the array.
 
 ## Where to go from here?
 
diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index 84f978931..3d8b0f394 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -18,16 +18,16 @@ The heap's internal array is then:
 
 	[ 25, 13, 20, 8, 7, 17, 2, 5, 4 ]
 
-That's hardly what you'd call sorted! But now the sorting process starts: we swap the first element (index *0*) with the last one (index *n-1*) to get:
+That's hardly what you'd call sorted! But now the sorting process starts: we swap the first element (index *0*) with the last one at index *n-1*, to get:
 
 	[ 4, 13, 20, 8, 7, 17, 2, 5, 25 ]
 	  *                          *
 
-Now the new root node, `4`, will be smaller than its children, so we fix up the max-heap up to element to *n-2* using the *shift down* or "heapify" procedure. After repairing the heap, the new root is now the second-largest item in the array:
+Now the new root node, `4`, will be smaller than its children, so we fix up the max-heap up to element *n-2* using the *shift down* or "heapify" procedure. After repairing the heap, the new root is now the second-largest item in the array:
 
 	[20, 13, 17, 8, 7, 4, 2, 5 | 25]
 
-Important: When we fix the heap, we ignore the last item. That now contains the array's maximum value, so it is in its final sorted place already. The `|` bar indicates where the sorted portion of the array begins. We'll leave that part of the array alone from now on.
+Important: When we fix the heap, we ignore the last item at index *n-1*. That now contains the array's maximum value, so it is in its final sorted place already. The `|` bar indicates where the sorted portion of the array begins. We'll leave that part of the array alone from now on.
 
 Again, we swap the first element with the last one (this time at index *n-2*):
 
@@ -67,7 +67,7 @@ let a1 = h1.sort()
 
 Because we need a max-heap to sort from low-to-high, you need to give `Heap` the reverse of the sort function. To sort `<`, the `Heap` object must be created with `>` as the sort function. In other words, sorting from low-to-high creates a max-heap and turns it into a min-heap.
 
-We can write a helper function for that:
+We can write a handy helper function for that:
 
 ```swift
 public func heapsort<T>(a: [T], _ sort: (T, T) -> Bool) -> [T] {
diff --git a/Heap/README.markdown b/Heap/README.markdown
index a51f97636..fb5092fe3 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -13,7 +13,7 @@ Common uses for heap:
 
 There are two kinds of heaps: a *max-heap* and a *min-heap*. They are identical, except that the order in which they store the tree nodes is opposite.
 
-In a max-heap, parent nodes must always have a greater value than each one of their children. For a min-heap it's the other way around: every parent node has a smaller value than its child nodes. This is called the "heap property" and it is true for every single node in the tree.
+In a max-heap, parent nodes must always have a greater value than each of their children. For a min-heap it's the other way around: every parent node has a smaller value than its child nodes. This is called the "heap property" and it is true for every single node in the tree.
 
 An example:
 
@@ -21,19 +21,19 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority Queue/) where you want to quickly access the most important element.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority Queue/) where you want to quickly access the "most important" element.
 
-Note that you can't really say anything else about the sort order of the heap. For example, in a max-heap the maximum element is always at index 0 but the minimum element isn’t necessarily the last one -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
+> **Note:** You can't really say anything else about the sort order of the heap. For example, in a max-heap the maximum element is always at index 0 but the minimum element isn’t necessarily the last one -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
 ## How does heap compare to regular trees?
 
-A heap isn't really intended to be a replacement for a binary search tree. But there are many similarities between the two and also some differences. Here are some of the bigger differences:
+A heap isn't intended to be a replacement for a binary search tree. But there are many similarities between the two and also some differences. Here are some of the bigger differences:
 
 **Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**Balancing.** A binary search tree must be balanced so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL Tree/) or [red-black tree](../Red-Black Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
+**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL Tree/) or [red-black tree](../Red-Black Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
 **Searching.** Searching a binary tree is really fast -- that's its whole purpose. In a heap, searching is slow. The purpose of a heap is to always put the largest (or smallest) node at the front, and to allow relatively fast inserts and deletes. Searching isn't a top priority.
 
@@ -77,17 +77,15 @@ Recall that in a max-heap, the parent's value is always greater than (or equal t
 array[parent(i)] >= array[i]
 ```
 	
-Verify that this heap property holds for the array for the example heap.
+Verify that this heap property holds for the array from the example heap.
 
 As you can see, these equations let us find the parent or child index for any node without the need for pointers. True, it's slightly more complicated than just dereferencing a pointer but that's the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
 
-It's important to understand this relationship between array index and position in the tree. Here's a slightly larger heap:
+It's important to understand this relationship between array index and position in the tree. Here's a slightly larger heap, this tree has 15 nodes divided over four levels:
 
 ![Large heap](Images/LargeHeap.png)
 
-This tree has 15 nodes divided over four levels. Note that the numbers in this picture aren't the values of the nodes but the array indices that store the nodes!
-
-Those array indices correspond to the different levels of the tree like this:
+The numbers in this picture aren't the values of the nodes but the array indices that store the nodes! Those array indices correspond to the different levels of the tree like this:
 
 ![The heap array](Images/Array.png)
 
@@ -119,7 +117,7 @@ The heap property holds for each node because a parent is always smaller than it
 
 In case you are curious, here are a few more formulas that describe certain properties of a heap. You don't need to know these by heart but they come in handy sometimes. Feel free to skip this section!
 
-The *height* of a tree is defined as the number of steps it takes to go from the root node to the lowest leaf node (or more formally: the maximum number of edges between the nodes). A heap of height *h* has *h + 1* levels.
+The *height* of a tree is defined as the number of steps it takes to go from the root node to the lowest leaf node. Or more formally: the height is the maximum number of edges between the nodes. A heap of height *h* has *h + 1* levels.
 
 This heap has height 3 and therefore has 4 levels:
 
@@ -143,9 +141,9 @@ There are two primitive operations necessary to make sure the heap is a valid ma
 
 - `shiftUp()`: If the element is greater (max-heap) or smaller (min-heap) than its parent, it needs to be swapped with the parent. This makes it move up the tree.
 
-- `shiftDown()`. If the element is smaller (max-heap) or greater (min-heap) than its children, it needs to move down the tree. This is also called "heapify". 
+- `shiftDown()`. If the element is smaller (max-heap) or greater (min-heap) than its children, it needs to move down the tree. This operation is also called "heapify". 
 
-Shifting is a recursive procedure that takes **O(log n)** time.
+Shifting up or down is a recursive procedure that takes **O(log n)** time.
 
 The other operations are built on these primitives. They are:
 
@@ -155,7 +153,7 @@ The other operations are built on these primitives. They are:
 
 - `removeAtIndex(index)`: Just like `remove()` except it lets you remove any item from the heap, not just the root. This calls both `shiftDown()`, in case the new element is out-of-order with its children, and `shiftUp()`, in case the element is out-of-order with its parents.
 
-- `replace(index, value)`: Assigns a smaller (min-heap) or larger (max-heap)  value to a node. Because this invalidates the heap property, this uses `shiftUp()` to patch things up. (Also called "decrease key" and "increase key".)
+- `replace(index, value)`: Assigns a smaller (min-heap) or larger (max-heap)  value to a node. Because this invalidates the heap property, it uses `shiftUp()` to patch things up. (Also called "decrease key" and "increase key".)
 
 All of the above take time **O(log n)** because shifting up or down is the most expensive thing they do. There are also a few operations that take more time:
 
@@ -205,7 +203,7 @@ The time required for shifting up is proportional to the height of the tree so i
 
 ## Removing the root
 
-Let's remove 10 from this tree:
+Let's remove `(10)` from this tree:
 
 ![The heap before removal](Images/Heap1.png)
 
@@ -217,7 +215,7 @@ When inserting, we put the new value at the end of the array. Here, we'll do the
 
 ![The last node goes to the root](Images/Remove2.png)
 
-Let's look at how to **shift-down** `(1)`. To maintain the heap property for this max-heap, we want to the highest number of top. We have 2 candidates for swapping places with: `(7)` and `(2)`. We choose the highest number between these three nodes to be on top. This is `(7)`, so swapping `(1)` and `(7)` gives us the following tree.
+Let's look at how to **shift-down** `(1)`. To maintain the heap property for this max-heap, we want to the highest number of top. We have two candidates for swapping places with: `(7)` and `(2)`. We choose the highest number between these three nodes to be on top. That is `(7)`, so swapping `(1)` and `(7)` gives us the following tree.
 
 ![The last node goes to the root](Images/Remove3.png)
 
@@ -249,7 +247,7 @@ As you know, removing an element could potentially invalidate the max-heap or mi
 
 The last element is the one that we'll return; we'll call `removeLast()` to remove it from the heap. The `(1)` is now out-of-order because it's smaller than its child, `(5)`, but sits higher in the tree. We call `shiftDown()` to repair this.
 
-However, it may also happen that the new element must be shifted up. Consider what happens if you remove `(5)` from the following heap:
+However, shifting down is not the only situation we need to handle -- it may also happen that the new element must be shifted up. Consider what happens if you remove `(5)` from the following heap:
 
 ![We need to shift up](Images/Remove5.png)
 
@@ -271,7 +269,7 @@ In code it would look like this:
 
 We simply call `insert()` for each of the values in the array. Simple enough, but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
 
-If you didn't skip the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order. 
+If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order. 
 
 In code:
 
@@ -288,7 +286,7 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 ## Searching the heap
 
-Heaps aren't made for fast searches, but if you want to remove an arbitrary item using `removeAtIndex()` or change the value of an item with `replace()`, then you need to obtain the index of that item somehow. Searching is one way to do this but it's kind of slow.
+Heaps aren't made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element somehow. Searching is one way to do this but it's kind of slow.
 
 In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
 
@@ -298,15 +296,13 @@ Let's take our example heap again:
 
 If we want to search for the index of node `(1)`, we could just step through the array `[ 10, 7, 2, 5, 1 ]` with a linear search.
 
-But even though the heap property wasn't conceived with searching in mind, we can still take advantage of it. Because we know that in a max-heap a parent node is always larger than its children.
-
-Let's say we want to see if the heap contains the value `8` (it doesn't). We start at the root `(10)`. This is obviously not what we're looking for, so we recursively look at its left and right child.
+But even though the heap property wasn't conceived with searching in mind, we can still take advantage of it. We know that in a max-heap a parent node is always larger than its children, so we can ignore those children (and their children, and so on...) if the parent is already smaller than the value we're looking for.
 
-The left child is `(7)`. That is also not what we want, but since this is a max-heap, we know there's no point in looking at the children of `(7)`. They will always be smaller than `7` and are therefore never equal to `8`. Likewise for the right child, `(2)`.
+Let's say we want to see if the heap contains the value `8` (it doesn't). We start at the root `(10)`. This is obviously not what we're looking for, so we recursively look at its left and right child. The left child is `(7)`. That is also not what we want, but since this is a max-heap, we know there's no point in looking at the children of `(7)`. They will always be smaller than `7` and are therefore never equal to `8`. Likewise for the right child, `(2)`.
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
-> **Note:** There is away to turn this into **O(1)** by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority Queue/) that's built on a heap.
+> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority Queue/) that's built on a heap.
 
 ## The code
 
diff --git a/Huffman Coding/Images/BuildTree.gif b/Huffman Coding/Images/BuildTree.gif
index ddfce5c9bd630123123e7ed8dfd2f01c24c237d3..6f5e51523b4a112fcd0bd0a09376034a6374bcb0 100644
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diff --git a/Huffman Coding/Images/Compression.graffle b/Huffman Coding/Images/Compression.graffle
index 81920ac70587bc3bac22df5ec0451d6afe321f02..e69912012836df1e0a32835cd86f8845ede3e7dd 100644
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diff --git a/Huffman Coding/Images/Decompression.graffle b/Huffman Coding/Images/Decompression.graffle
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diff --git a/Huffman Coding/Images/Decompression.png b/Huffman Coding/Images/Decompression.png
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diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 3f78aa203..528ba3a1d 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -41,7 +41,7 @@ Now if we replace the original bytes with these bit strings, the compressed outp
 
 The extra 0-bit at the end is there to make a full number of bytes. We were able to compress the original 34 bytes into merely 16 bytes, a space savings of over 50%!
 
-But hold on... to be able to decode these bits we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data, otherwise the decoder doesn't know how to interpret the bits. Because of the overhead of this frequency table, it doesn't really pay to use Huffman encoding on very small inputs.
+But hold on... to be able to decode these bits we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data, otherwise the decoder doesn't know how to interpret the bits. Because of the overhead of this frequency table (about 1 kilobyte), it doesn't really pay to use Huffman encoding on very small inputs.
 
 ## How it works
 
@@ -63,7 +63,7 @@ Decompression works in exactly the opposite way. It reads the compressed bits on
 
 ## The code
 
-Before we get to the actual Huffman coding scheme, it's useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte. But we're dealing in bits, so we need to translate between the two.
+Before we get to the actual Huffman coding scheme, it's useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte, but we're dealing in bits, so we need to translate between the two.
 
 ```swift
 public class BitWriter {
@@ -92,7 +92,7 @@ public class BitWriter {
 }
 ```
 
-To add a bit to the `NSData` you call `writeBit()`. This simply stuffs each new bit into the `outByte` variable. Once you've written 8 bits, `outByte` gets added to the `NSData` object for real.
+To add a bit to the `NSData` you call `writeBit()`. This stuffs each new bit into the `outByte` variable. Once you've written 8 bits, `outByte` gets added to the `NSData` object for real.
 
 The `flush()` method is used for outputting the very last byte. There is no guarantee that the number of compressed bits is a nice round multiple of 8, in which case there may be some spare bits at the end. If so, `flush()` adds a few 0-bits to make sure that we write a full byte.
 
@@ -193,7 +193,7 @@ Instead, we'll add a method to export the frequency table without all the pieces
   }
 ```
 
-The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are actually used, without the `parent`, `left`, and `right` pointers. You would serialize the array it returns along with the compressed file so that it can be properly decompressed later.
+The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are actually used, without the `parent`, `left`, and `right` pointers. It returns an array of `Freq` objects. You have to serialize this array along with the compressed data so that it can be properly decompressed later.
 
 ## The tree
 
@@ -206,7 +206,7 @@ The leaf nodes represent the actual bytes that are present in the input data. Th
 To build the tree, we do the following:
 
 1. Find the two nodes with the smallest counts that do not have a parent node yet.
-2. Add a new parent node that links these two nodes together.
+2. Create a new parent node that links these two nodes together.
 3. This repeats over and over until only one node with no parent remains. This becomes the root node of the tree.
 
 This is an ideal place to use a [priority queue](../Priority Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
@@ -256,13 +256,13 @@ Here is how it works step-by-step:
 
 6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we're done.
 
-This is what the process looks like:
+The animation shows what the process looks like:
 
 ![Building the tree](Images/BuildTree.gif)
 
-> **Note:** Instead of using a priority queue, you can iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor quite slow, **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
+> **Note:** Instead of using a priority queue, you can repeatedly iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor quite slow, **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
 
-> **Note:** Due to the nature of binary trees, if we have *x* leaf nodes we can at most add *x - 1* additional nodes to the tree. Given that at most there will be 256 leaf nodes, the tree will never contain more than 511 nodes total.
+> **Fun fact:** Due to the nature of binary trees, if we have *x* leaf nodes we can at most add *x - 1* additional nodes to the tree. Given that at most there will be 256 leaf nodes, the tree will never contain more than 511 nodes total.
 
 ## Compression
 
@@ -319,7 +319,7 @@ In a picture:
 
 ![How compression works](Images/Compression.png)
 
-Note that, even through the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 aren't actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we're going in is enough to determine what bit value to write.
+Even though the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 aren't actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we're going in is enough to determine what bit value to write.
 
 You use the `compressData()` method as follows:
 
@@ -412,6 +412,6 @@ You can see how this works in more detail in the Playground.
 
 [Huffman coding at Wikipedia](https://en.wikipedia.org/wiki/Huffman_coding)
 
-The code is based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 1991 and October 1992.
+The code is loosely based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 1991 and October 1992.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index ea39f5dad..b67541669 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -13,7 +13,7 @@ You are given an array of numbers and need to put them in the right order. The i
 
 That's why this is called an "insertion" sort, because you take a number from the pile and insert it in the array in its proper sorted position. 
 
-### An example
+## An example
 
 Let's say the numbers to sort are `[ 8, 3, 5, 4, 6 ]`. This is our unsorted pile.
 
@@ -25,7 +25,7 @@ Pick the next number from the pile, `5`, and insert it into the sorted array. It
 
 Repeat this process until the pile is empty.
 
-### In-place sort
+## In-place sort
 
 The above explanation makes it seem like you need two arrays: one for the unsorted pile and one that contains the numbers in sorted order.
 
@@ -54,7 +54,7 @@ This is how the content of the array changes during the sort:
 
 In each step, the `|` bar moves up one position. As you can see, the beginning of the array up to the `|` is always sorted. The pile shrinks by one and the sorted portion grows by one, until the pile is empty and there are no more unsorted numbers left.
 
-### How to insert
+## How to insert
 
 At each step you pick the top-most number from the unsorted pile and insert it into the sorted portion of the array. You must put that number in the proper place so that the beginning of the array remains sorted. How does that work?
 
@@ -85,9 +85,9 @@ Again, look at the previous element. Is `3` greater than `4`? No, it is not. Tha
 
 This was a description of the inner loop of the insertion sort algorithm, which you'll see in the next section. It inserts the number from the top of the pile into the sorted portion by swapping numbers.
 
-### The code
+## The code
 
-Here is a simple implementation of insertion sort in Swift:
+Here is an implementation of insertion sort in Swift:
 
 ```swift
 func insertionSort(array: [Int]) -> [Int] {
@@ -118,9 +118,9 @@ Here is how the code works.
 
 3. The inner loop looks at the element at position `x`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
 
-Note: The outer loop starts at index 1, not 0. Moving the very first element from the pile to the sorted portion doesn't actually change anything, so we might as well skip it. 
+> **Note:** The outer loop starts at index 1, not 0. Moving the very first element from the pile to the sorted portion doesn't actually change anything, so we might as well skip it. 
 
-### No more swaps
+## No more swaps
 
 The above version of insertion sort works fine, but it can be made a tiny bit faster by removing the call to `swap()`. 
 
@@ -168,7 +168,7 @@ func insertionSort(array: [Int]) -> [Int] {
 
 The line at `//1` is what shifts up the previous elements by one position. At the end of the inner loop, `y` is the destination index for the new number in the sorted portion, and the line at `//2` copies this number into place.
 
-### Making it generic
+## Making it generic
 
 It would be nice to sort other things than just numbers. We can make the datatype of the array generic and use a user-supplied function (or closure) to perform the less-than comparison. This only requires two changes to the code.
 
@@ -188,7 +188,7 @@ The only other change is in the inner loop, which now becomes:
       while y > 0 && isOrderedBefore(temp, a[y - 1]) {
 ```
 
-Instead of writing `temp < a[y - 1]`, we now call the `isOrderedBefore()` function. It does the exact same thing, except we can now compare any kind of object, not just numbers.
+Instead of writing `temp < a[y - 1]`, we call the `isOrderedBefore()` function. It does the exact same thing, except we can now compare any kind of object, not just numbers.
 
 To test this in a playground, do:
 
@@ -218,7 +218,7 @@ The closure tells `insertionSort()` to sort on the `priority` property of the ob
 
 Insertion sort is a *stable* sort. A sort is stable when elements that have identical sort keys remain in the same relative order after sorting. This is not important for simple values such as numbers or strings, but it is important when sorting more complex objects. In the example above, if two objects have the same `priority`, regardless of the values of their other properties, those two objects don't get swapped around.
 
-### Performance
+## Performance
 
 Insertion sort is really fast if the array is already sorted. That sounds obvious, but this is not true for all search algorithms. In practice, a lot of data will already be largely -- if not entirely -- sorted and insertion sort works quite well in that case.
 
@@ -228,8 +228,8 @@ Insertion sort is actually very fast for sorting small arrays. Some standard lib
 
 I did a quick test comparing our `insertionSort()` with Swift's built-in `sort()`. On arrays of about 100 items or so, the difference in speed is tiny. However, as your input becomes larger, **O(n^2)** quickly starts to perform a lot worse than **O(n log n)** and insertion sort just can't keep up.
 
-### See also
+## See also
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Insertion_sort).
+[Insertion sort on Wikipedia](https://en.wikipedia.org/wiki/Insertion_sort)
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index 04d10ad99..d50d691a1 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -6,21 +6,21 @@ For example, the 1-st largest element is the maximum value that occurs in the ar
 
 ## The naive solution
 
-The following solution is semi-naive. Its time complexity is **O(n log n)** since it first sorts the array, and uses an additional **O(n)** space. Better solutions using heaps exist that run in **O(n)** time.
+The following solution is semi-naive. Its time complexity is **O(n log n)** since it first sorts the array, and therefore also uses additional **O(n)** space.
 
 ```swift
 func kthLargest(a: [Int], k: Int) -> Int? {
   let len = a.count
-
-  if k <= 0 || k > len || len < 1 { return nil }
-
-  let sorted = a.sort()
-
-  return sorted[len - k]
+  if k > 0 && k <= len {
+    let sorted = a.sort()
+    return sorted[len - k]
+  } else {
+    return nil
+  }
 }
 ```
 
-The `kthLargest()` function takes two parameters: the array `a` consisting of integers, and `k`. It returns the k-th largest element.
+The `kthLargest()` function takes two parameters: the array `a` consisting of integers, and `k`. It returns the *k*-th largest element.
 
 Let's take a look at an example and run through the algorithm to see how it works. Given `k = 4` and the array:
 
@@ -48,9 +48,9 @@ There is a clever algorithm that combines the ideas of [binary search](../Binary
 
 Recall that binary search splits the array in half over and over again, to quickly narrow in on the value you're searching for. That's what we'll do here too.
 
-Quicksort also splits up arrays. It uses partitioning to move all smaller values to the left of the pivot and all greater values to the right. After partitioning around a certain pivot, that pivot will already be in its final, sorted position. We can use that to our advantage here.
+Quicksort also splits up arrays. It uses partitioning to move all smaller values to the left of the pivot and all greater values to the right. After partitioning around a certain pivot, that pivot value will already be in its final, sorted position. We can use that to our advantage here.
 
-We choose a random pivot, partition the array around that pivot, and then act like a binary search and only continue in the left or right partition. This repeats until we've found a pivot that happens to end up in the *k*-th position.
+Here's how it works: We choose a random pivot, partition the array around that pivot, then act like a binary search and only continue in the left or right partition. This repeats until we've found a pivot that happens to end up in the *k*-th position.
 
 Let's look at the original example again. We're looking for the 4-th largest element in this array:
 
@@ -58,12 +58,12 @@ Let's look at the original example again. We're looking for the 4-th largest ele
 
 The algorithm is a bit easier to follow if we look for the k-th *smallest* item instead, so let's take `k = 4` and look for the 4-th smallest element.
 
-Note that we don't have to sort the array first. We pick a random pivot, let's say `11` and partition the array around that. We might end up with something like this:
+Note that we don't have to sort the array first. We pick one of the elements at random to be the pivot, let's say `11`, and partition the array around that. We might end up with something like this:
 
 	[ 7, 9, -1, 0, 6, 11, 92, 23 ]
 	 <------ smaller    larger -->
 
-As you can see, all values smaller than `11` are on the left; all values larger are on the right. The pivot value is now in its final place. The index of the pivot is 5, so the 4-th smallest element must be in the left partition somewhere. We can ignore the rest of the array from now on:
+As you can see, all values smaller than `11` are on the left; all values larger are on the right. The pivot value `11` is now in its final place. The index of the pivot is 5, so the 4-th smallest element must be in the left partition somewhere. We can ignore the rest of the array from now on:
 
 	[ 7, 9, -1, 0, 6, x, x, x ]
 
@@ -126,15 +126,15 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
 }
 ```
 
-To keep things readable, it splits up the functionality into three inner functions:
+To keep things readable, the functionality is split into three inner functions:
 
 - `randomPivot()` picks a random number and puts it at the end of the current partition (this is a requirement of the Lomuto partitioning scheme, see the discussion on [quicksort](../Quicksort/) for more details).
 
 - `randomizedPartition()` is Lomuto's partitioning scheme from quicksort. When this completes, the randomly chosen pivot is in its final sorted position in the array. It returns the array index of the pivot.
 
-- `randomizedSelect()` does all the hard work. It first calls the partitioning function and then decides what to do next. If the index of the pivot is equal to the k-th number we're looking for, we're done. If `k` is less than the pivot index, it must be in the left partition and we'll recursively try again there. Likewise for when the k-th number must be in the right partition.
+- `randomizedSelect()` does all the hard work. It first calls the partitioning function and then decides what to do next. If the index of the pivot is equal to the *k*-th number we're looking for, we're done. If `k` is less than the pivot index, it must be in the left partition and we'll recursively try again there. Likewise for when the *k*-th number must be in the right partition.
 
-Pretty cool, huh?
+Pretty cool, huh? Normally quicksort is an **O(n log n)** algorithm, but because we only partition smaller and smaller slices of the array, the running time of `randomizedSelect()` works out to **O(n)**.
 
 > **Note:** This function calculates the *k*-th smallest item in the array, where *k* starts at 0. If you want the *k*-th largest item, call it with `a.count - k`.
 
diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 9cac62f4e..7f97bb271 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -2,13 +2,14 @@
 
 func kthLargest(a: [Int], k: Int) -> Int? {
   let len = a.count
-  if k <= 0 || k > len || len < 1 { return nil }
-  
-  let sorted = a.sort()
-  return sorted[len - k]
+  if k > 0 && k <= len {
+    let sorted = a.sort()
+    return sorted[len - k]
+  } else {
+    return nil
+  }
 }
 
-
 let a = [5, 1, 3, 2, 7, 6, 4]
 
 kthLargest(a, k: 0)
diff --git a/Kth Largest Element/kthLargest.swift b/Kth Largest Element/kthLargest.swift
index 69c03b76f..5bf781932 100644
--- a/Kth Largest Element/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.swift	
@@ -1,17 +1,20 @@
 import Foundation
 
 /*
- * Returns the k-th largest value inside of an array a.
- * This is an O(n log n) solution since we sort the array.
- */
+  Returns the k-th largest value inside of an array a.
+  This is an O(n log n) solution since we sort the array.
+*/
 func kthLargest(a: [Int], k: Int) -> Int? {
   let len = a.count
-  if k <= 0 || k > len || len < 1 { return nil }
-  
-  let sorted = a.sort()
-  return sorted[len - k]
+  if k > 0 && k <= len {
+    let sorted = a.sort()
+    return sorted[len - k]
+  } else {
+    return nil
+  }
 }
 
+
 // MARK: - Randomized selection
 
 /* Returns a random integer in the range min...max, inclusive. */
diff --git a/Linear Search/README.markdown b/Linear Search/README.markdown
index 178a1dd09..115dd7ee2 100644
--- a/Linear Search/README.markdown	
+++ b/Linear Search/README.markdown	
@@ -2,15 +2,17 @@
 
 Goal: Find a particular value in an array.
 
-We have an array of generic objects and we iterate over all the objects by comparing each one to the object we're looking for. If the two objects are equal, we stop and we return the index of the object in the array. If not, we continue to look for the next object as long as we have objects in the array.
+We have an array of generic objects. With linear search, we iterate over all the objects in the array and compare each one to the object we're looking for. If the two objects are equal, we stop and return the current array index. If not, we continue to look for the next object as long as we have objects in the array.
 
-### An example
+## An example
 
 Let's say we have an array of numbers `[5, 2, 4, 7]` and we want to check if the array contains the number `2`.
 
-We start by comparing the first number in the array, `5` with the number we're looking for, `2`. They are obviously not the same number and so we continue by taking the second element in the array. We compare the number `2` to our number `2` and we notice that they are the same. We stop our iteration and we return `1`, which is the index of the number `2` in the array.
+We start by comparing the first number in the array, `5`, to the number we're looking for, `2`. They are obviously not the same, and so we continue to the next array element.
 
-### The code
+We compare the number `2` from the array to our number `2` and notice they are equal. Now we can stop our iteration and return 1, which is the index of the number `2` in the array.
+
+## The code
 
 Here is a simple implementation of linear search in Swift:
 
@@ -30,14 +32,14 @@ let array = [5, 2, 4, 7]
 linearSearch(array, 2) 	// This will return 1
 ```
 
-### Performance
+## Performance
 
-Linear search runs at **O(n)**. It compares the object we are looking for with each object in the array and so the time it takes is proportional to the array length.
+Linear search runs at **O(n)**. It compares the object we are looking for with each object in the array and so the time it takes is proportional to the array length. In the worst case, we need to look at all the elements in the array.
 
-The best-case performance is **O(1)** but this case is rare because the object we're looking for has to be positioned at the start of the array to be immediately found.
+The best-case performance is **O(1)** but this case is rare because the object we're looking for has to be positioned at the start of the array to be immediately found. You might get lucky, but most of the time you won't. On average, linear search needs to look at half the objects in the array.
 
-### See also
+## See also
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Linear_search).
+[Linear search on Wikipedia](https://en.wikipedia.org/wiki/Linear_search)
 
 *Written by [Patrick Balestra](http://www.github.com/BalestraPatrick)*
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0ce6c57fa..d37749acd 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -1,6 +1,6 @@
 # Linked List
 
-A linked list is a sequence of data items, just like an array. But where an array allocates a big block of memory and then divides this into different parts to store the objects, the elements in a linked list are totally separate objects in memory and are connected through links:
+A linked list is a sequence of data items, just like an array. But where an array allocates a big block of memory to store the objects, the elements in a linked list are totally separate objects in memory and are connected through links:
 
 	+--------+    +--------+    +--------+    +--------+
 	|        |    |        |    |        |    |        |
@@ -38,15 +38,17 @@ This means that when you're dealing with a linked list, you should insert new it
 
 ## Singly vs doubly linked lists
 
-A singly linked list uses less memory than a doubly linked list because it doesn't need to store all those `previous` pointers.
+A singly linked list uses a little less memory than a doubly linked list because it doesn't need to store all those `previous` pointers.
 
-But if you have a node and you need to find its previous node, you're screwed. You have to start back at the head of the list and iterate through the entire list until you get to the right node.
+But if you have a node and you need to find its previous node, you're screwed. You have to start at the head of the list and iterate through the entire list until you get to the right node.
 
 For many tasks, a doubly linked list makes things easier.
 
 ## Why use a linked list?
 
-An example of where to use a linked list is when you need a [queue](../Queue/). With an array, removing elements from the front of the queue is slow because it needs to shift down all the other elements in memory. But with a linked list it's just a matter of changing `head` to point to the second element. Much faster.
+A typical example of where to use a linked list is when you need a [queue](../Queue/). With an array, removing elements from the front of the queue is slow because it needs to shift down all the other elements in memory. But with a linked list it's just a matter of changing `head` to point to the second element. Much faster.
+
+But to be honest, you hardly ever need to write your own linked list these days. Still, it's useful to understand how they work; the principle of linking objects together is also used with [trees](../Tree/) and [graphs](../Graph/).
 
 ## The code
 
@@ -86,7 +88,7 @@ public class LinkedList<T> {
 }
 ```
 
-Ideally, I'd like to put the `LinkedListNode` class inside `LinkedList` but Swift 2 doesn't allow generic types to have nested types. Instead we're using a typealias so inside `LinkedList` we can write the shorter `Node` instead of `LinkedListNode<T>`.
+Ideally, I'd like to put the `LinkedListNode` class inside `LinkedList` but Swift currently doesn't allow generic types to have nested types. Instead we're using a typealias so inside `LinkedList` we can write the shorter `Node` instead of `LinkedListNode<T>`.
 
 This linked list only has a `head` pointer, not a tail. Adding a tail pointer is left as an exercise for the reader. (I'll point out which functions would be different if we also had a tail pointer.)
 
@@ -329,13 +331,13 @@ Now that we have this helper function, we can write the method for inserting nod
   }
 ```
 
-Some notes about this method:
+Some remarks about this method:
 
 1. First, we need to find where to insert this node. After calling the helper method, `prev` points to the previous node and `next` is the node currently at the given index. We'll insert the new node in between these two. Note that `prev` can be nil (index is 0), `next` can be nil (index equals size of the list), or both can be nil if the list is empty.
 
 2. Create the new node and connect the `previous` and `next` pointers. Because the local `prev` and `next` variables are optionals and may be nil, so we use optional chaining here.
 
-3. If the new node is being inserted at the front of the list, we need to update the `head` pointer. Note: If the list had a tail pointer, you'd also need to update that pointer here if `next == nil`, because that means the last element has changed.
+3. If the new node is being inserted at the front of the list, we need to update the `head` pointer. (Note: If the list had a tail pointer, you'd also need to update that pointer here if `next == nil`, because that means the last element has changed.)
 
 Try it out:
 
@@ -419,7 +421,7 @@ list.removeAtIndex(0)          // "Swift"
 list.count                     // 0
 ```
 
-> **Note:** For a singly linked list, it's slightly more complicated. You can't just use `last` to find the end of the list because you also need a reference to the second-to-last node. You'd need to use the `nodesBeforeAndAfter()` helper method instead. If you're using a tail pointer, then `removeLast()` is really quick, but you do need to remember to make `tail` point to the previous node.
+> **Note:** For a singly linked list, removing the last node is slightly more complicated. You can't just use `last` to find the end of the list because you also need a reference to the second-to-last node. Instead, use the `nodesBeforeAndAfter()` helper method. If the list has a tail pointer, then `removeLast()` is really quick, but you do need to remember to make `tail` point to the previous node.
 
 There's a few other fun things we can do with our `LinkedList` class. It's handy to have some sort of readable debug output:
 
@@ -520,7 +522,7 @@ Exercise for the reader: These implementations of `map()` and `filter()` aren't
 
 ## An alternative approach
 
-The version of `LinkedList` you've seen so far uses nodes that are classes and therefore use reference semantics. Nothing wrong with that, but that does make them a bit more heavyweight than Swift's other collections such as `Array` and `Dictionary`.
+The version of `LinkedList` you've seen so far uses nodes that are classes and therefore have reference semantics. Nothing wrong with that, but that does make them a bit more heavyweight than Swift's other collections such as `Array` and `Dictionary`.
 
 It is possible to implement a linked list with value semantics using an enum. That would look somewhat like this:
 
@@ -541,6 +543,6 @@ Linked lists are flexible but many operations are **O(n)**.
 
 When performing operations on a linked list, you always need to be careful to update the relevant `next` and `previous` pointers, and possibly also the `head` and `tail` pointers. If you mess this up, your list will no longer be correct and your program will likely crash at some point. Be careful!
 
-When processing lists, you can often use recursion: process the first element and then recursively call the operation on the rest of the list. You’re done when there is no next element. This is why linked lists are the foundation of functional programming languages such as LISP.
+When processing lists, you can often use recursion: process the first element and then recursively call the function again on the rest of the list. You’re done when there is no next element. This is why linked lists are the foundation of functional programming languages such as LISP.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 190f76a34..023e18b32 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -4,28 +4,28 @@ Goal: Sort an array from low to high (or high to low)
 
 Invented in 1945 by John von Neumann, merge sort is a fairly efficient sorting algorithm with a best, worst, and average time complexity of **O(n log n)**.
 
-The idea behind merge sort is to **divide and conquer**. To divide a big problem into smaller problems and solving many small problems instead of solving a big one. I think of merge sort as **split first** and **merge after**. 
+The idea behind merge sort is to **divide and conquer**: to divide a big problem into smaller problems and solving many small problems instead of solving a big one. I think of merge sort as **split first** and **merge after**. 
 
 Assume you're given an array of *n* numbers and you need to put them in the right order. The merge sort algorithm works as follows:
 
 - Put the numbers in a pile. The pile is unsorted.
 - Split the pile into 2. Now you have **two unsorted piles** of numbers.
-- Keep splitting the resulting piles until you can't anymore. In the end, you will have *n* piles with 1 number in each pile.
-- Begin to **merge** the piles together by sequentially pairing a pile with another pile. During each merge, you want to sort the contents in order.
+- Keep splitting the resulting piles until you can't split anymore. In the end, you will have *n* piles with 1 number in each pile.
+- Begin to **merge** the piles together by sequentially pairing a pile with another pile. During each merge, you put the contents in sorted order. This is fairly easy because each individual pile is already sorted.
 
 ## An example
 
 ### Splitting
 
-Let's say the numbers to sort are `[2, 1, 5, 4, 9]`. This is your unsorted pile. Our goal is to keep splitting the pile until you can't anymore. 
+Let's say the numbers to sort are `[2, 1, 5, 4, 9]`. This is your unsorted pile. The goal is to keep splitting the pile until you can't split anymore. 
 
-Split the array into two halves: `[2, 1,]` and `[5, 4, 9]`. Can you keep splitting them? Yes you can!
+First, split the array into two halves: `[2, 1,]` and `[5, 4, 9]`. Can you keep splitting them? Yes you can!
 
 Focus on the left pile. `[2, 1]` will split into `[2]` and `[1]`. Can you keep splitting them? No. Time to check the other pile.
 
-`[5, 4, 9]` splits to `[5]` and `[4, 9]`. Unsurprisingly, `[5]` can't split into anymore, but `[4, 9]` splits into `[4]` and `[9]`. 
+`[5, 4, 9]` splits to `[5]` and `[4, 9]`. Unsurprisingly, `[5]` can't be split anymore, but `[4, 9]` splits into `[4]` and `[9]`. 
 
-The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9]`
+The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9]`. Notice that each pile consists of just one element.
 
 ### Merging
 
@@ -35,7 +35,7 @@ Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1
 
 The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again since it's the odd one out. 
 
-Since you're left with only two piles, `[9]` finally gets its chance to merge, resulting in the sorted array `[1, 2, 4, 5, 9]`. 
+You're left with only two piles and `[9]` finally gets its chance to merge, resulting in the sorted array `[1, 2, 4, 5, 9]`. 
 
 ## Top-down implementation
 
@@ -61,9 +61,9 @@ A step-by-step explanation of how the code works:
 
 2. Find the middle index. 
 
-3. Using the middle index from the previous step, recursively split the left side of the resulting arrays.
+3. Using the middle index from the previous step, recursively split the left side of the array.
 
-4. Using the middle index, recursively split the right side of the resulting arrays.
+4. Also recursively split the right side of the array.
 
 5. Finally, merge all the values together, making sure that it's always sorted.
 
@@ -119,7 +119,7 @@ This method may look scary but it is quite straightforward:
 
 4. If control exits from the previous while loop, it means that either `leftPile` or `rightPile` has its contents completely merged into the `orderedPile`. At this point, you no longer need to do comparisons. Just append the rest of the contents of the other array until there's no more to append.
 
-As an example of how `merge()` works, suppose that we have the following piles: `leftPile = [1, 7, 8]` and `rightPile = [3, 6, 9]`. Note that each of these piles is individually sorted already. These are merged into one larger sorted pile in the following steps:
+As an example of how `merge()` works, suppose that we have the following piles: `leftPile = [1, 7, 8]` and `rightPile = [3, 6, 9]`. Note that each of these piles is individually sorted already -- that is always true with merge sort. These are merged into one larger sorted pile in the following steps:
 
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ ]
@@ -218,7 +218,7 @@ Notable points:
 
 1. Merge sort needs a temporary working array because you can't merge the left and right piles and at the same time overwrite their contents. But allocating a new array for each merge is wasteful. Therefore, we're using two working arrays and we'll switch between them using the value of `d`, which is either 0 or 1. The array `z[d]` is used for reading, `z[1 - d]` is used for writing. This is called *double-buffering*.
 
-2. Conceptually, the bottom-up version works the same way as the top-down version. First, it merges small piles of 1 element each, then it merges piles of 2 elements each, then piles of 4 elements each, and so on. The size of the pile is given by `width`. Initially, this is `1` but at the end of each loop iteration we multiply it by 2. So this outer loop determines the size of the piles being merged. And in each step, the subarrays to merge become larger.
+2. Conceptually, the bottom-up version works the same way as the top-down version. First, it merges small piles of 1 element each, then it merges piles of 2 elements each, then piles of 4 elements each, and so on. The size of the pile is given by `width`. Initially, `width` is `1` but at the end of each loop iteration we multiply it by 2. So this outer loop determines the size of the piles being merged. And in each step, the subarrays to merge become larger.
 
 3. The inner loop steps through the piles and merges each pair of piles into a larger one. The result is written in the array given by `z[1 - d]`.
 
@@ -237,7 +237,7 @@ mergeSortBottomUp(array, <)   // [1, 2, 4, 5, 9]
 
 ## Performance
 
-The speed of merge sort is dependent on the size of the array it needs to sort. 
+The speed of merge sort is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do. 
 
 Whether or not the initial array is sorted already doesn't affect the speed of merge sort since you'll be doing the same amount splits and comparisons regardless of the initial order of the elements.
 
@@ -249,6 +249,6 @@ Most implementations of merge sort produce a **stable** sort. This means that ar
 
 ## See also
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Merge_sort)
+[Merge sort on Wikipedia](https://en.wikipedia.org/wiki/Merge_sort)
 
 *Written by Kelvin Lau. Additions by Matthijs Hollemans.*
diff --git a/Monty Hall Problem/README.markdown b/Monty Hall Problem/README.markdown
index 81004410e..f096a3a7a 100644
--- a/Monty Hall Problem/README.markdown	
+++ b/Monty Hall Problem/README.markdown	
@@ -8,7 +8,7 @@ Now Monty gives you the opportunity to change your mind. Should you stick with y
 
 You'd think that changing your answer wouldn't improve your chances... but it does!
 
-This is a very nonintuitive result. Maybe you have trouble believing this is true. Don't worry, when this problem was first proposed many mathematicians didn't believe it either, so you're in good company.
+This is a very nonintuitive result. Maybe you have trouble believing this is true. Don't worry, when this problem was first proposed many professional mathematicians didn't believe it either, so you're in good company.
 
 There's a simple way to verify this claim: we can write a program to test it out! We should be able to show who wins more often by playing the game a large number of times.
 
@@ -65,7 +65,7 @@ Here's why: When you first make a choice, your chances of picking the prize are
 
 After Monty opens one of the doors, this gives you new information. However, it doesn't change the probability of your original choice being the winner. That chance remains 33% because you made that choice when you didn't know yet what was behind this open door.
 
-Since probabilities always need to add up to 100%, the chance that the prize is behind the other door is now 100 - 33 = 67%. So, as strange as it may sound, you're better of switching doors!
+Since probabilities always need to add up to 100%, the chance that the prize is behind the other door is now 100 - 33 = 67%. So, as strange as it may sound, you're better off switching doors!
 
 This is hard to wrap your head around, but easily shown using a simulation that runs a significant number of times. Probability is weird.
 
diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index d258024d3..f64e55057 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -63,7 +63,7 @@ What remains is the `insert()` function. Here is an initial stab at it:
   }
 ```
 
-The helper function `findInsertionPoint()` simply loops through the entire array, looking for the right place to insert the new element. 
+The helper function `findInsertionPoint()` simply iterates through the entire array, looking for the right place to insert the new element. 
 
 > **Note:** Quite conveniently, `array.insert(... atIndex: array.count)` adds the new object to the end of the array, so if no suitable insertion point was found we can simply return `array.count` as the index.
 
@@ -83,7 +83,7 @@ a              // [-2, -1, 1, 3, 4, 5, 7, 9, 10]
 
 The array's contents will always be sorted from low to high, now matter what. 
 
-Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array in order to insert the new element. We can speed this up by using a [binary search](../Binary Search) to find the insertion point.
+Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array. We can speed this up by using a [binary search](../Binary Search) to find the insertion point.
 
 Here is the new version:
 
@@ -106,6 +106,6 @@ Here is the new version:
 
 The big difference with a regular binary search is that this doesn't return `nil` when the value can't be found, but the array index where the element would have been. That's where we insert the new object.
 
-Note that using binary search doesn't change the worst-case running time complexity of `insert()`. The binary search itself takes only **O(log n)** time, but inserting a new object in the middle of an array still involves shifting all remaining elements to the right in memory. So overall, the time complexity is still **O(n)**. But in practice this new version definitely is a lot faster, especially on large arrays.
+Note that using binary search doesn't change the worst-case running time complexity of `insert()`. The binary search itself takes only **O(log n)** time, but inserting a new object in the middle of an array still involves shifting all remaining elements in memory. So overall, the time complexity is still **O(n)**. But in practice this new version definitely is a lot faster, especially on large arrays.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Queue/README.markdown b/Queue/README.markdown
index 70a6a76eb..7cf4bd484 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -97,7 +97,9 @@ where `xxx` is memory that is reserved but not filled in yet. Adding a new eleme
 
 This is simply matter of copying memory from one place to another, a constant-time operation.
 
-Of course, there are only a limited number of such unused spots at the end of the array. When the last `xxx` gets used and you want to add another item, the array needs to resize to make more room. Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process, so relatively slow. But since it happens only every so often, the time for appending a new element to the end of the array is still **O(1)** on average, or **O(1)** "amortized".
+Of course, there are only a limited number of such unused spots at the end of the array. When the last `xxx` gets used and you want to add another item, the array needs to resize to make more room.
+
+Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process, so it's relatively slow. But since it happens only every so often, the time for appending a new element to the end of the array is still **O(1)** on average, or **O(1)** "amortized".
 
 The story for dequeueing is slightly different. To dequeue we remove the element from the *beginning* of the array, not the end. This is always an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
 
@@ -116,7 +118,7 @@ Moving all these elements in memory is always an **O(n)** operation. So with our
 
 To make dequeuing more efficient, we can use the same trick of reserving some extra free space, but this time do it at the front of the array. We're going to have to write this code ourselves as the built-in Swift array doesn't support this out of the box.
 
-The idea is this: whenever we dequeue an item, we don't shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
+The idea is as follows: whenever we dequeue an item, we don't shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
 
 	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
 
@@ -229,7 +231,7 @@ q.array             // [nil, nil, {Some "Tim"}, {Some "Grace"}]
 q.count             // 2
 ```
 
-To test the trimming behavior, replace the line
+To test the trimming behavior, replace the line,
 
 ```swift
     if array.count > 50 && percentage > 0.25 {
diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index eda50aff5..b8a908985 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -31,7 +31,7 @@ Here's how it works. When given an array, `quicksort()` splits it up into three
 
 All the elements less than the pivot go into a new array called `less`. All the elements equal to the pivot go into the `equal` array. And you guessed it, all elements greater than the pivot go into the third array, `greater`. This is why the generic type `T` must be `Comparable`, so we can compare the elements with `<`, `==`, and `>`.
 
-Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `right` array, then glues those sorted subarrays back together to get the final result. 
+Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `right` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
 
 ## An example
 
@@ -160,16 +160,16 @@ Note that `list` needs to be a `var` because `partitionLomuto()` directly change
 
 The `low` and `high` parameters are necessary because when this is used inside quicksort, you don't always want to (re)partition the entire array, only a limited range that becomes smaller and smaller.
 
-Previously we used the middle array element as the pivot but it's important to realize that the Lomuto algorithm always uses the *last* element, `a[high]`. Because we've been pivoting around `8` all this time, I swapped the positions of `8` and `26` in the example so that `8` is at the end of the array and is used as the pivot value here too.
+Previously we used the middle array element as the pivot but it's important to realize that the Lomuto algorithm always uses the *last* element, `a[high]`, for the pivot. Because we've been pivoting around `8` all this time, I swapped the positions of `8` and `26` in the example so that `8` is at the end of the array and is used as the pivot value here too.
 
 After partitioning, the array looks like this:
 
 	[ 0, 3, 2, 1, 5, 8, -1, 8, 9, 10, 14, 26, 27 ]
 	                        *
 
-The variable `p` contains the return value of the call to `partitionLomuto()` and is 7. This is the index of the pivot element in the new array (marked with a star). 
+The variable `p` contains the return value of the call to `partitionLomuto()` and is 7. This is the index of the pivot element in the new array (marked with a star).
 
-The left partition goes from 0 to `p-1` and is `[ 0, 3, 2, 1, 5, 8, -1 ]`. The right partition goes from `p+1` to the end, and is `[ 9, 10, 14, 26, 27 ]` (the fact that this is already sorted is a coincidence). 
+The left partition goes from 0 to `p-1` and is `[ 0, 3, 2, 1, 5, 8, -1 ]`. The right partition goes from `p+1` to the end, and is `[ 9, 10, 14, 26, 27 ]` (the fact that the right partition is already sorted is a coincidence). 
 
 You may notice something interesting... The value `8` occurs more than once in the array. One of those `8`s did not end up neatly in the middle but somewhere in the left partition. That's a small downside of the Lomuto algorithm as it makes quicksort slower if there are a lot of duplicate elements.
 
@@ -372,7 +372,7 @@ You might think this means we should always choose the middle element rather tha
 
 Now the middle element is `1` and that gives the same lousy results as in the previous example.
 
-Ideally, the pivot is the *median* element of the array that you're partitioning. Of course, you won't know what the median is until after you've sorted the array, so this is a bit of a chicken-and-egg problem. However, there are some tricks to choose good, if not ideal, pivots.
+Ideally, the pivot is the *median* element of the array that you're partitioning, i.e. the element that sits in the middle of the sorted array. Of course, you won't know what the median is until after you've sorted the array, so this is a bit of a chicken-and-egg problem. However, there are some tricks to choose good, if not ideal, pivots.
 
 One trick is "median-of-three", where you find the median of the first, middle, and last element in this subarray. In theory that often gives a good approximation of the true median.
 
@@ -478,6 +478,6 @@ Using Dutch flag partitioning makes for a more efficient quicksort if the array
 
 ## See also
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Quicksort).
+[Quicksort on Wikipedia](https://en.wikipedia.org/wiki/Quicksort)
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/README.markdown b/README.markdown
index 03bd2601b..c389f219b 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,9 @@ The goal of this project is to **explain how algorithms work**. The focus is on
 
 All code is compatible with **Xcode 7.2** and **Swift 2.1**. We'll keep this updated with the latest version of Swift.
 
-This is a work in progress. More algorithms will be added soon. :-)
+This is a work in progress. More algorithms will be added soon. :-) 
+
+:heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 
 ## Important links
 
@@ -20,7 +22,7 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 [Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
 
-[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request. **Suggestions and contributions are welcome!**
+[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
 
 ## Where to start?
 
@@ -41,7 +43,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Binary Search](Binary Search/). Quickly find elements in a sorted array.
 - [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
 - [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
-- [k-th Largest Element](Kth Largest Element/). Find the *k*th largest element in an array, such as the median.
+- [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
 - [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
 - [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
 
@@ -108,7 +110,7 @@ The choice of data structure for a particular task depends on a few things.
 
 First, there is the shape of your data and the kinds of operations that you'll need to perform on it. If you want to look up objects by a key you need some kind of dictionary; if your data is hierarchical in nature you want a tree structure of some sort; if your data is sequential you want a stack or queue.
 
-Second, it matters what particular operations you'll be performing most, as certain data structures are optimized for certain actions. For example, if you often need to find the most important object in a queue, then a heap or priority queue is more optimal than a plain array.
+Second, it matters what particular operations you'll be performing most, as certain data structures are optimized for certain actions. For example, if you often need to find the most important object in a collection, then a heap or priority queue is more optimal than a plain array.
 
 Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types is sufficient, but sometimes you may want something more fancy...
 
@@ -136,7 +138,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Tree](Tree/). A general-purpose tree structure.
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
-- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree with the special requirement that elements are inserted in a specific way, allowing for faster queries, like when using a [binary search](Binary Search/) algorithm.
+- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
 - Red-Black Tree
 - Splay Tree
diff --git a/Ring Buffer/README.markdown b/Ring Buffer/README.markdown
index 72fb08ebd..70e0ad108 100644
--- a/Ring Buffer/README.markdown	
+++ b/Ring Buffer/README.markdown	
@@ -41,7 +41,7 @@ Now the app decides it's time to write again and enqueues two more data items, `
 	[ 123, 456, 789, 666, 333 ]
 	                 r    ---> w
 
-Whoops, the write pointer has reached the end of the array, so there is no more room. What now? Well, this is why it's a circular buffer: we wrap the write pointer back to the beginning and write the remaining data:
+Whoops, the write pointer has reached the end of the array, so there is no more room for object `555`. What now? Well, this is why it's a circular buffer: we wrap the write pointer back to the beginning and write the remaining data:
 
 	[ 555, 456, 789, 666, 333 ]
 	  ---> w         r        
@@ -113,7 +113,7 @@ public struct RingBuffer<T> {
 
 The `RingBuffer` object has an array for the actual storage of the data, and `readIndex` and `writeIndex` variables for the "pointers" into the array. The `write()` function puts the new element into the array at the `writeIndex`, and the `read()` function returns the element at the `readIndex`.
 
-But hold up, you say, how does this wrapping around work? There are several ways to accomplish this and I chose a slightly controversial one. In this implementation, the `writeIndex` and `readIndex` always increment and never actually wrap around. Instead, we do this to find the actual index into the array:
+But hold up, you say, how does this wrapping around work? There are several ways to accomplish this and I chose a slightly controversial one. In this implementation, the `writeIndex` and `readIndex` always increment and never actually wrap around. Instead, we do the following to find the actual index into the array:
 
 ```swift
 array[writeIndex % array.count]
@@ -125,7 +125,7 @@ and:
 array[readIndex % array.count]
 ```
 
-In other words, we take the modulo (or the remainder) of the read and write index divided by the size of the underlying array.
+In other words, we take the modulo (or the remainder) of the read index and write index divided by the size of the underlying array.
 
 The reason this is a bit controversial is that `writeIndex` and `readIndex` always increment, so in theory these values could become too large to fit into an integer and the app will crash. However, a quick back-of-the-napkin calculation should take away those fears.
 
@@ -158,8 +158,8 @@ You've seen that a ring buffer can make a more optimal queue but it also has a d
 
 A ring buffer is also very useful for when a producer of data writes into the array at a different rate than the consumer of the data reads it. This happens often with file or network I/O. Ring buffers are also the preferred way of communicating between high priority threads (such as an audio rendering callback) and other, slower, parts of the system.
 
-The implementation given here is not thread safe. It only serves as an example of how a ring buffer works. That said, it should be fairly straightforward to make it thread-safe for a single reader and single writer by using `OSAtomicIncrement64()` to change the read and write pointers.
+The implementation given here is not thread-safe. It only serves as an example of how a ring buffer works. That said, it should be fairly straightforward to make it thread-safe for a single reader and single writer by using `OSAtomicIncrement64()` to change the read and write pointers.
 
 A cool trick to make a really fast ring buffer is to use the operating system's virtual memory system to map the same buffer onto different memory pages. Crazy stuff but worth looking into if you need to use a ring buffer in a high performance environment.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Run-Length Encoding/README.markdown b/Run-Length Encoding/README.markdown
index 0f6041885..8371b1227 100644
--- a/Run-Length Encoding/README.markdown	
+++ b/Run-Length Encoding/README.markdown	
@@ -8,7 +8,7 @@ then RLE encodes it as follows:
 
 	5a3b1c1d7e1f...
 
-Instead of repeating bytes, you first write how often that byte occurs and then the byte's actual value. If the data has a lot of "byte runs", that is lots of repeating bytes, then RLE can save quite a bit of space. It works quite well on images.
+Instead of repeating bytes, you first write how often that byte occurs and then the byte's actual value. So `5a` means `aaaaa`. If the data has a lot of "byte runs", that is lots of repeating bytes, then RLE can save quite a bit of space. It works quite well on images.
 
 There are many different ways you can implement RLE. Here's an extension of `NSData` that does a version of RLE inspired by the old [PCX image file format](https://en.wikipedia.org/wiki/PCX).
 
diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index fb9b6aaa1..0bb6d8da5 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -4,11 +4,23 @@ I'm pleased to present to you Segment Tree. It's actually one of my favorite dat
 
 Let's suppose that you have an array **a** of some type and some associative function **f**. For example, the function can be sum, multiplication, min, max, [gcd](../GCD/), and so on.
 
-Your task is:
+Your task is to:
 
 - answer a query for an interval given by **l** and **r**, i.e. perform `f(a[l], a[l+1], ..., a[r-1], a[r])`
 - support replacing an item at some index `a[index] = newItem`
 
+For example, if we have an array of numbers:
+
+```swift
+var a = [ 20, 3, -1, 101, 14, 29, 5, 61, 99 ]
+```
+
+We want to query this array on the interval from 3 to 7 for the function "sum". That means we do the following:
+
+	101 + 14 + 29 + 5 + 61 = 210
+	
+because `101` is at index 3 in the array and `61` is at index 7. So we pass all the numbers between `101` and `61` to the sum function, which adds them all up. If we had used the "min" function, the result would have been `5` because that's the smallest number in the interval from 3 to 7.
+
 Here's naive approach if our array's type is `Int` and **f** is just the sum of two integers:
 
 ```swift
@@ -21,7 +33,7 @@ func query(array: [Int], l: Int, r: Int) -> Int {
 }
 ```
 
-The running time of this algorithm is **O(n)** in the worst case, that is when **l = 0, r = n-1**. And if we have **m** queries to answer we get **O(m*n)** complexity.
+The running time of this algorithm is **O(n)** in the worst case, that is when **l = 0, r = n-1** (where **n** is the number of elements in the array). And if we have **m** queries to answer we get **O(m*n)** complexity.
 
 If we have an array with 100,000 items (**n = 10^5**) and we have to do 100 queries (**m = 100**), then our algorithm will do **10^7** units of work. Ouch, that doesn't sound very good. Let's look at how we can improve it.
 
@@ -48,7 +60,7 @@ Each node has the following data:
 
 - `leftBound` and `rightBound` describe an interval
 - `leftChild` and `rightChild` are pointers to child nodes
-- `value` is actually the application of the function `f(a[leftBound], a[leftBound+1], ..., a[rightBound-1], a[rightBound])`
+- `value` is the result of applying the function `f(a[leftBound], a[leftBound+1], ..., a[rightBound-1], a[rightBound])`
 
 If our array is `[1, 2, 3, 4]` and the function `f = a + b`, the segment tree looks like this:
 
@@ -80,11 +92,11 @@ public init(array: [T], leftBound: Int, rightBound: Int, function: (T, T) -> T)
   }
 ```
 
-Notice that this is a recursive method! You give it an array, such as `[1, 2, 3, 4]` and it creates the root node of the tree and all the child nodes as well.
+Notice that this is a recursive method. You give it an array such as `[1, 2, 3, 4]` and it builds up the entire tree, from the root node to all the child nodes.
 
-1. The recursion terminates if `leftBound` and `rightBound` are equal. That means this `SegmentTree` instance will represent a leaf node. For the input array `[1, 2, 3, 4]`, it will create four such leaf nodes: `1`, `2`, `3`, and `4`. We just fill in the `value` property with the number from the array.
+1. The recursion terminates if `leftBound` and `rightBound` are equal. Such a `SegmentTree` instance represents a leaf node. For the input array `[1, 2, 3, 4]`, this process will create four such leaf nodes: `1`, `2`, `3`, and `4`. We just fill in the `value` property with the number from the array.
 
-2. However, if `rightBound` is still greater than `leftBound`, we create two child nodes. We divide the current segment into two equal (if length is even) segments.
+2. However, if `rightBound` is still greater than `leftBound`, we create two child nodes. We divide the current segment into two equal segments (at least, if the length is even; if it's odd, one segment will be slightly larger).
 
 3. Recursively build child nodes for those two segments. The left child node covers the interval **[leftBound, middle]** and the right child node covers **[middle+1, rightBound]**.
 
@@ -143,7 +155,7 @@ Again, this is a recursive method. It checks four different possibilities.
 
 ![mixedSegment](Images/MixedSegment.png)
 
-For example, this is how you could test it out in a playground:
+This is how you can test it out in a playground:
 
 ```swift
 let array = [1, 2, 3, 4]
diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index 5d7c11731..5e006f50e 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -2,23 +2,23 @@
 
 Goal: Find the minimum/maximum object in an unsorted array.
 
-### Maximum or minimum
+## Maximum or minimum
 
 We have an array of generic objects and we iterate over all the objects keeping track of the minimum/maximum element so far.
 
-#### An example
+### An example
 
 Let's say the we want to find the maximum value in the unsorted list `[ 8, 3, 9, 4, 6 ]`.
 
 Pick the first number, `8`, and store it as the maximum element so far. 
 
-Pick the next number from the list, `3`, and compare it to the current maximum `8`. `3` is less than `8` so the maximum `8` does not change.
+Pick the next number from the list, `3`, and compare it to the current maximum. `3` is less than `8` so the maximum `8` does not change.
 
-Pick the next number from the list, `9`, and compare it to the current maximum `8`. `9` is greater than `8` so we store `9` as the maximum.
+Pick the next number from the list, `9`, and compare it to the current maximum. `9` is greater than `8` so we store `9` as the maximum.
 
 Repeat this process until the all elements in the list have been processed.
 
-#### The code
+### The code
 
 Here is a simple implementation in Swift:
 
@@ -52,35 +52,44 @@ Put this code in a playground and test it like so:
 
 ```swift
 let array = [ 8, 3, 9, 4, 6 ]
-minimum(array) // This will return 3
-maximum(array) // This will return 9
+minimum(array)   // This will return 3
+maximum(array)   // This will return 9
 ```
 
-### Maximum and minimum
+### In the Swift standard library
+
+The Swift library already contains an extension to `SequenceType` that returns the minimum/maximum element in a sequence.
+
+```swift
+let array = [ 8, 3, 9, 4, 6 ]
+array.minElement()   // This will return 3
+array.maxElement()   // This will return 9
+```
+
+## Maximum and minimum
 
 To find both the maximum and minimum values contained in array while minimizing the number of comparisons we can compare the items in pairs. 
 
-#### An example
+### An example
 
-Let's say the we want to find the minimum and maximum value in the unsorted list `[ 8, 3, 9, 4, 6 ]`.
+Let's say the we want to find the minimum and maximum value in the unsorted list `[ 8, 3, 9, 6, 4 ]`.
 
 Pick the first number, `8`, and store it as the minimum and maximum element so far. 
 
-Because we have an odd number of items we remove `8` from the list which leaves the pairs `[ 3, 9 ]` and `[ 4, 6 ]`.
+Because we have an odd number of items we remove `8` from the list which leaves the pairs `[ 3, 9 ]` and `[ 6, 4 ]`.
 
-Pick the next pair of numbers from the list, `[ 3, 9 ]`, `3` is less than `9` so we compare `3` to the current minimum `8` and `9` to the current maximum `8`. `3` is less than `8` so the new minimum is `3`. `9` is greater than `8` so the new maximum is `9`.
+Pick the next pair of numbers from the list, `[ 3, 9 ]`. Of these two numbers, `3` is the smaller one, so we compare `3` to the current minimum `8`, and we compare `9` to the current maximum `8`. `3` is less than `8` so the new minimum is `3`. `9` is greater than `8` so the new maximum is `9`.
 
-Pick the next pair of numbers from the list, `[ 4, 6 ]`, `4` is less than `6` so we compare `4` to the current minimum `3` and `6` to the current maximum `9`. `4` is greater than `3` so the minimum does not change. `6` is less than `9` so the maximum does not change.
+Pick the next pair of numbers from the list, `[ 6, 4 ]`. Here, `4` is the smaller one, so we compare `4` to the current minimum `3`, and we compare `6` to the current maximum `9`. `4` is greater than `3` so the minimum does not change. `6` is less than `9` so the maximum does not change.
 
 The result is a minimum of `3` and a maximum of `9`.
 
-#### The code
+### The code
 
 Here is a simple implementation in Swift:
 
 ```swift
-func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)?
-{
+func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)? {
   guard !array.isEmpty else {
     return nil
   }
@@ -95,7 +104,6 @@ func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)?
 
   while !array.isEmpty {
     let pair = (array.removeFirst(), array.removeFirst())
-
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0
@@ -120,26 +128,15 @@ func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)?
 Put this code in a playground and test it like so:
 
 ```swift
-
 let result = minimumMaximum(array)!
-result.minimum // This will return 3
-result.maximum // This will return 9
+result.minimum   // This will return 3
+result.maximum   // This will return 9
 ```
 
 By picking elements in pairs and comparing their maximum and minimum with the running minimum and maximum we reduce the number of comparisons to 3 for every 2 elements.
 
-### Performance
+## Performance
 
 These algorithms run at **O(n)**. Each object in the array is compared with the running minimum/maximum so the time it takes is proportional to the array length.
 
-### Swift library
-
-The Swift library already contains an extension to `SequenceType` that returns the minimum/maximum element in a sequence.
-
-```swift
-let array = [ 8, 3, 9, 4, 6 ]
-array.minElement() // This will return 3
-array.maxElement() // This will return 9
-```
-
 *Written by [Chris Pilcher](https://github.com/chris-pilcher)*
diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index 174b3a3da..a02c17b79 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -19,7 +19,7 @@ func select<T>(from a: [T], count k: Int) -> [T] {
 }
 ```
 
-As often happens with these [kinds of algorithms](../Shuffle/), it divides the array into two regions. The first region is the selected items; the second region is all the remaining items.
+As often happens with these [kinds of algorithms](../Shuffle/), it divides the array into two regions. The first region contains the selected items; the second region is all the remaining items.
 
 Here's an example. Let's say the array is:
 
@@ -115,7 +115,7 @@ Only one item left to select but there are still 4 candidates to look at. Suppos
 
 	4 * 0.718 = 2.872
 
-For this element to be selected the number has to be less than 1, since there is only 1 element left to be picked. It isn't, so we skip `"d"`. Only three possibilities left -- will we make it?
+For this element to be selected the number has to be less than 1, as there is only 1 element left to be picked. It isn't, so we skip `"d"`. Only three possibilities left -- will we make it before we run out of elements?
 
 The random number is 0.346. The formula gives:
 
@@ -135,7 +135,7 @@ Let's say our final random number is 0.999 (remember, it can never be 1.0 or hig
 
 And so the last element will always be chosen if we didn't have a big enough selection yet. The final selection is `[ "b", "c", "g" ]`. Notice that the elements are still in their original order, because we examined the array from left to right.
 
-Maybe you're not convinced yet... What if we always got 0.999 as the random value, would that still select 3 items? Well, let's do the math:
+Maybe you're not convinced yet... What if we always got 0.999 as the random value (the maximum possible), would that still select 3 items? Well, let's do the math:
 
 	7 * 0.999 = 6.993     is this less than 3? no
 	6 * 0.999 = 5.994     is this less than 3? no
diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index 57b1d09f5..6eb019ab1 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -2,7 +2,7 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still need to be sorted. 
+You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted. 
 
 	[ ...sorted numbers... | ...unsorted numbers... ]
 
@@ -17,11 +17,11 @@ It works as follows:
 - Swap it with the number at index 1. Now the sorted portion contains two numbers and extends from index 0 to index 1.
 - Go to index 2.
 - Find the lowest number in the rest of the array, starting from index 2, and swap it with the one at index 2. Now the array is sorted from index 0 to 2; this range contains the three lowest numbers in the array.
-- And so on, until no numbers remain to be sorted.
+- And so on... until no numbers remain to be sorted.
 
 It's called a "selection" sort, because at every step you search through the rest of the array to select the next lowest number.
 
-### An example
+## An example
 
 Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol. 
 
@@ -48,11 +48,13 @@ With every step, the `|` bar moves one position to the right. We again look thro
 	[ 3, 4, 5 | 8, 6 ]
 	        *
 
-This process repeats until the array is sorted. Note that everything to the left of the `|` bar is always in sorted order and always contains the lowest numbers in the array.
+This process repeats until the array is sorted. Note that everything to the left of the `|` bar is always in sorted order and always contains the lowest numbers in the array. Finally, we end up with:
 
-As you can see, selection sort is an *in-place* sort because everything happens in the same array; no additional memory is necessary. You can also implement this as a *stable* sort so that identical elements do not get swapped around relative to each other (note that the version below isn't stable).
+	[ 3, 4, 5, 6, 8 |]
 
-### The code
+As you can see, selection sort is an *in-place* sort because everything happens in the same array; no additional memory is necessary. You can also implement this as a *stable* sort so that identical elements do not get swapped around relative to each other (note that the version given below isn't stable).
+
+## The code
 
 Here is an implementation of selection sort in Swift:
 
@@ -90,7 +92,7 @@ A step-by-step explanation of how the code works:
 
 1. If the array is empty or only contains a single element, then there's not much point to sorting it.
 
-2. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sort()`, the `selectionSort()` function will return a sorted *copy* of the original array.
+2. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly in Swift. Like Swift's own `sort()`, the `selectionSort()` function will return a sorted *copy* of the original array.
 
 3. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what moves the `|` bar forward.
 
@@ -98,18 +100,20 @@ A step-by-step explanation of how the code works:
 
 5. Swap the lowest number with the current array index. The `if` check is necessary because you can't `swap()` an element with itself in Swift.
 
-In summary: For each element of the array, it swaps positions with the lowest value from the rest of the array. As a result, the array gets sorted from the left to the right. (You can also do it right-to-left, in which case you always look for the largest number in the array. Give that a try!)
+In summary: For each element of the array, selection sort swaps positions with the lowest value from the rest of the array. As a result, the array gets sorted from the left to the right. (You can also do it right-to-left, in which case you always look for the largest number in the array. Give that a try!)
 
-Note: The outer loop ends at index `a.count - 2`. The very last element will automatically always be in the correct position because at that point there are no other smaller elements left.
+> **Note:** The outer loop ends at index `a.count - 2`. The very last element will automatically always be in the correct position because at that point there are no other smaller elements left.
 
 The source file [SelectionSort.swift](SelectionSort.swift) has a version of this function that uses generics, so you can also use it to sort strings and other types.
 
-### Performance
+## Performance
+
+Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than insertion sort but better than bubble sort. The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+[Heap sort](../Heap Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
 
-### See also
+## See also
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Selection_sort).
+[Selection sort on Wikipedia](https://en.wikipedia.org/wiki/Selection_sort)
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index 8870ffea6..6cb682035 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Shell Sort
 
-Shell sort is based on [insertion sort](../Insertion%20Sort/) as a general way to improve its performance, by breaking the original list into smaller sublists which can then be individually sorted using insertion sort.
+Shell sort is based on [insertion sort](../Insertion%20Sort/) as a general way to improve its performance, by breaking the original list into smaller sublists which are then individually sorted using insertion sort.
 
 [There is a nice video created at Sapientia University](https://www.youtube.com/watch?v=CmPA7zE8mx0) which shows the process as a Hungarian folk dance.
 
@@ -12,7 +12,7 @@ The distance between elements is known as the *gap*. If the elements being compa
 
 The idea is that by moving the elements over large gaps, the array becomes partially sorted quite quickly. This makes later passes faster because they don't have to swap so many items anymore.
 
-Once a pass has been completed, the gap is made smaller and a new pass starts.  This repeats until the gap is 1, at which point the algorithm functions just like  insertion sort. But since the data is already fairly well sorted by then, the final pass can be very quick.
+Once a pass has been completed, the gap is made smaller and a new pass starts.  This repeats until the gap has size 1, at which point the algorithm functions just like  insertion sort. But since the data is already fairly well sorted by then, the final pass can be very quick.
 
 ## An example
 
@@ -26,36 +26,36 @@ This is the gap size.
 
 We create `n` sublists. In each sublist, the items are spaced apart by a gap of size `n`. In our example, we need to make four of these sublists. The sublists are sorted by the `insertionSort()` function.
 
-That probably didn't make a whole lot of sense, so let's look at what happens.
+That may not have made a whole lot of sense, so let's take a closer look at what happens.
 
 The first pass is as follows. We have `n = 4`, so we make four sublists:
 
-	list 0:  [ 64, xx, xx, xx, 72, xx, xx, xx, 4  ]
-	list 1:  [ xx, 20, xx, xx, xx, 10, xx, xx, xx ]
-	list 2:  [ xx, xx, 50, xx, xx, xx, 23, xx, xx ]
-	list 3:  [ xx, xx, xx, 33, xx, xx, xx, -1, xx ]
+	sublist 0:  [ 64, xx, xx, xx, 72, xx, xx, xx, 4  ]
+	sublist 1:  [ xx, 20, xx, xx, xx, 10, xx, xx, xx ]
+	sublist 2:  [ xx, xx, 50, xx, xx, xx, 23, xx, xx ]
+	sublist 3:  [ xx, xx, xx, 33, xx, xx, xx, -1, xx ]
 
-As you can see, each list contains only every 4th item from the original array. The items that are not in a sublist are marked with `xx`. So the first list is `[ 64, 72, 4]` and the second is `[ 20, 10 ]`, and so on. The reason we use this "gap" is so that we don't have to actually make new arrays. Instead, we interleave them in the original array.
+As you can see, each sublist contains only every 4th item from the original array. The items that are not in a sublist are marked with `xx`. So the first sublist is `[ 64, 72, 4 ]` and the second is `[ 20, 10 ]`, and so on. The reason we use this "gap" is so that we don't have to actually make new arrays. Instead, we interleave them in the original array.
 
 We now call `insertionSort()` once on each sublist.
 
-This particular version of [insertion sort](../Insertion Sort/) sorts from the back to the front. Each item in the sublist is compared against the others. If they're in the wrong order, the value is swapped and travels all the way down until we reach the start of the list.
+This particular version of [insertion sort](../Insertion Sort/) sorts from the back to the front. Each item in the sublist is compared against the others. If they're in the wrong order, the value is swapped and travels all the way down until we reach the start of the sublist.
 
-So for list 0, we swap `4` with `72`, then swap `4` with `64`. After sorting, this sublist looks like:
+So for sublist 0, we swap `4` with `72`, then swap `4` with `64`. After sorting, this sublist looks like:
 
-    list 0:  [ 4, xx, xx, xx, 64, xx, xx, xx, 72 ]
+    sublist 0:  [ 4, xx, xx, xx, 64, xx, xx, xx, 72 ]
 
 The other three sublists after sorting:
 
-	list 1:  [ xx, 10, xx, xx, xx, 20, xx, xx, xx ]
-	list 2:  [ xx, xx, 23, xx, xx, xx, 50, xx, xx ]
-	list 3:  [ xx, xx, xx, -1, xx, xx, xx, 33, xx ]
+	sublist 1:  [ xx, 10, xx, xx, xx, 20, xx, xx, xx ]
+	sublist 2:  [ xx, xx, 23, xx, xx, xx, 50, xx, xx ]
+	sublist 3:  [ xx, xx, xx, -1, xx, xx, xx, 33, xx ]
     
 The total array looks like this now:
 
 	[ 4, 10, 23, -1, 64, 20, 50, 33, 72 ]
 
-It's not sorted yet but it's more sorted than before. This completes the first pass.
+It's not entirely sorted yet but it's more sorted than before. This completes the first pass.
 
 In the second pass, we divide the gap size by two:
 
@@ -63,13 +63,13 @@ In the second pass, we divide the gap size by two:
 
 That means we now create only two sublists:
 
-	list 0:  [  4, xx, 23, xx, 64, xx, 50, xx, 72 ]
-	list 1:  [ xx, 10, xx, -1, xx, 20, xx, 33, xx ]
+	sublist 0:  [  4, xx, 23, xx, 64, xx, 50, xx, 72 ]
+	sublist 1:  [ xx, 10, xx, -1, xx, 20, xx, 33, xx ]
 
 Each sublist contains every 2nd item. Again, we call `insertionSort()` to sort these sublists. The result is:
 
-	list 0:  [  4, xx, 23, xx, 50, xx, 64, xx, 72 ]
-	list 1:  [ xx, -1, xx, 10, xx, 20, xx, 33, xx ]
+	sublist 0:  [  4, xx, 23, xx, 50, xx, 64, xx, 72 ]
+	sublist 1:  [ xx, -1, xx, 10, xx, 20, xx, 33, xx ]
 
 Note that in each list only two elements were out of place. So the insertion sort is really fast. That's because we already sorted the array a little in the first pass.
 
@@ -85,7 +85,7 @@ A gap size of 1 means we only have a single sublist, the array itself, and once
 
 	[ -1, 4, 10, 20, 23, 33, 50, 64, 72 ]
 
-The performance of shell sort is **O(n^2)** or **O(n log n)** if you get lucky. This algorithm produces an unstable sort; it may change the relative order of elements with equal values.
+The performance of shell sort is **O(n^2)** in most cases or **O(n log n)** if you get lucky. This algorithm produces an unstable sort; it may change the relative order of elements with equal values.
   
 ## The gap sequence
 
diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index 6cbb23016..e0be6c1e4 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -29,7 +29,7 @@ list.shuffle()
 list.shuffle()
 ```
 
-You should see three different arrangements -- or permutations to use math-speak -- of the objects in the array.
+You should see three different arrangements -- or [permutations](../Combinatorics/) to use math-speak -- of the objects in the array.
 
 This shuffle works *in place*, it modifies the contents of the original array. The algorithm works by creating a new array, `temp`, that is initially empty. Then we randomly choose an element from the original array and append it to `temp`, until the original array is empty. Finally, the temporary array is copied back into the original one.
 
diff --git a/Shunting Yard/README.markdown b/Shunting Yard/README.markdown
index d4d7c3e22..d2e568d39 100644
--- a/Shunting Yard/README.markdown	
+++ b/Shunting Yard/README.markdown	
@@ -1,38 +1,40 @@
 # Shunting Yard Algorithm
 
-Any mathematical expression that we write is expressed in a notation known as *infix notation*.
-
-For example:
+Any mathematics we write is expressed in a notation known as *infix notation*. For example:
 
 **A + B * C**
 
-In the above expression the operator is placed between operands, hence the expression is said to be in *infix* form. If you think about it, any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
+The operator is placed in between the operands, hence the expression is said to be in *infix* form. If you think about it, any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
+
+Multiplication has higher precedence than addition, so when the above expression is evaluated you would first multiply **B** and **C**, and then add the result to **A**. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. 
+
+To change the order of evaluation, we can use parentheses:
 
-When the above expression is evaluated, you would first multiply **B** and **C**, and then add the result to **A**. This is because multiplication has higher precedence than addition. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. 
+**(A + B) * C**
 
-If you were to write an algorithm that parsed and evaluated the infix notation you will realize that it's a tedious process. You'd have to parse the expression multiple times to know what operation to perform first. As the number of operators increase so does the complexity.
+Now **A** is first added to **B** and then the sum is multiplied by **C**.
 
-## Postfix notations / Reverse Polish Notation 
+If you were to write an algorithm that parsed and evaluated expressions in infix notation you will realize that it's a tedious process. You'd have to parse the expression multiple times to know what operation to perform first. As the number of operators increase so does the complexity.
+
+## Postfix notation
 
 In postfix notation, also known as Reverse Polish Notation or RPN, the operators come after the corresponding operands. Here is the postfix representation of the example from the previous section:
 
 **A B C * +**
 
-An expression when represented in postfix form will not have any brackets and neither will you have to worry about scanning for operator precedence. This makes it easy for the computer to evaluate expressions, since the order in which the operators need to be applied is fixed.
-
-### Evaluating a postfix expression
+An expression in postfix form will not have any parentheses and neither will you have to worry about scanning for operator precedence. This makes it easy for the computer to evaluate expressions, since the order in which the operators need to be applied is fixed.
 
-A stack is used to evaluate a postfix expression. Here is the pseudocode:
+Evaluating a postfix expression is easily done using a stack. Here is the pseudocode:
 
-1. Read postfix expression token by token
-2. If the token is an operand, push it into the stack
+1. Read the postfix expression token by token
+2. If the token is an operand, push it onto the stack
 3. If the token is a binary operator,
-    1. Pop the two top most operands from the stack
+    1. Pop the two topmost operands from the stack
     2. Apply the binary operator to the two operands
-    3. Push the result into the stack
+    3. Push the result back onto the stack
 4. Finally, the value of the whole postfix expression remains in the stack
 
-Using the above pseudocode, the evaluation on the stack would be as follows:
+Using the above pseudocode, the evaluation of **A B C * +** would be as follows:
 
 | Expression    | Stack   |
 | ------------- | --------|
@@ -47,7 +49,7 @@ Where **D = B * C** and **E = A + D.**
 
 As seen above, a postfix operation is relatively easy to evaluate as the order in which the operators need to be applied is pre-decided.
 
-## Dijkstra's shunting yard algorithm
+## Converting infix to postfix
 
 The shunting yard algorithm was invented by Edsger Dijkstra to convert an infix expression to postfix. Many calculators use this algorithm to convert the expression being entered to postfix form.
 
@@ -65,11 +67,9 @@ Here is the psedocode of the algorithm:
         1. Until the top token (from the stack) is left parenthesis, pop from the stack to the output buffer
         2. Also pop the left parenthesis but don’t include it in the output buffer
     7. Else add token to output buffer
-2. While there are still operator tokens in the stack, pop them to output
-
-### How does it work
+2. Pop any remaining operator tokens from the stack to the output
 
-Let's take a small example and see how the pseudocode works. 
+Let's take a small example and see how the pseudocode works. Here is the infix expression to convert:
 
 **4 + 4 * 2 / ( 1 - 5 )**
 
diff --git a/Stack/README.markdown b/Stack/README.markdown
index fbc2512e4..6e832b69b 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -72,6 +72,6 @@ public struct Stack<T> {
 
 Notice that a push puts the new element at the end of the array, not the beginning. Inserting at the beginning of an array is expensive, an **O(n)** operation, because it requires all existing array elements to be shifted in memory. Adding at the end is **O(1)**; it always takes the same amount of time, regardless of the size of the array.
 
-Fun fact about stacks: each time you call a function or a method, the return address is placed on a stack by the CPU. When the function ends, the CPU uses that return address to jump back to the caller. That's why if you call too many functions -- for example in a recursive function that never ends -- you get a so-called "stack overflow" as the CPU stack is out of space.
+Fun fact about stacks: Each time you call a function or a method, the CPU places the return address on a stack. When the function ends, the CPU uses that return address to jump back to the caller. That's why if you call too many functions -- for example in a recursive function that never ends -- you get a so-called "stack overflow" as the CPU stack has run out of space.
 
-*Written by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Tree/README.markdown b/Tree/README.markdown
index 98d1bec12..52a46c597 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -1,10 +1,10 @@
-# Tree
+# Trees
 
 A tree represents hierarchical relationships between objects. This is a tree:
 
 ![A tree](Images/Tree.png)
 
-A tree consists of nodes. 
+A tree consists of nodes, and these nodes are linked to one another.
 
 Nodes have links to their children and usually to their parent as well. The children are the nodes below a given node; the parent is the node above. A node always has just one parent but can have multiple children.
 
@@ -16,7 +16,7 @@ The pointers in a tree do not form cycles. This is not a tree:
 
 ![Not a tree](Images/Cycles.png)
 
-Such a structure is called a [graph](../Graph/). A tree is really a very simple form of a graph. (In a similar vein, a [linked list](../Linked List) is a simple version of a tree. Think about it!)
+Such a structure is called a [graph](../Graph/). A tree is really a very simple form of a graph. (In a similar vein, a [linked list](../Linked List/) is a simple version of a tree. Think about it!)
 
 This article talks about a general-purpose tree. That's a tree without any kind of restrictions on how many children each node may have, or on the order of the nodes in the tree.
 
@@ -33,7 +33,7 @@ public class TreeNode<T> {
     self.value = value
   }
   
-  func addChild(node: TreeNode<T>) {
+  public func addChild(node: TreeNode<T>) {
     children.append(node)
     node.parent = self
   }
@@ -165,4 +165,6 @@ Then we can describe the tree with the following array:
 
 Each entry in the array is a pointer to its parent node. The item at index 3, `tea`, has the value 1 because its parent is `hot`. The root node points to `-1` because it has no parent. You can only traverse such trees from a node back to the root but not the other way around.
 
+By the way, sometimes you see algorithms using the term *forest*. Unsurprisingly, that is the name given to a collection of separate tree objects. For an example of this, see [union-find](../Union-Find/).
+
 *Written for Swift Algorithm Club by Matthijs Hollemans*
diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index c4e8959f5..966870bdf 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -10,7 +10,7 @@ public class TreeNode<T> {
     self.value = value
   }
   
-  func addChild(node: TreeNode<T>) {
+  public func addChild(node: TreeNode<T>) {
     children.append(node)
     node.parent = self
   }
@@ -26,6 +26,9 @@ extension TreeNode: CustomStringConvertible {
   }
 }
 
+
+
+
 let tree = TreeNode<String>(value: "beverages")
 
 let hotNode = TreeNode<String>(value: "hot")
diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index e77045339..5c027141c 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -8,7 +8,7 @@ public class TreeNode<T> {
     self.value = value
   }
   
-  func addChild(node: TreeNode<T>) {
+  public func addChild(node: TreeNode<T>) {
     children.append(node)
     node.parent = self
   }
diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 0c010954a..e2e15d4c0 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -8,7 +8,7 @@ There are a variety of solutions to this problem (some better than others). The
 
 This solution uses a dictionary to store differences between each element in the array and the sum `k` that we're looking for. The dictionary also stores the indices of each element.
 
-With this approach, each key in the dictionary corresponds to a new target value. If one of the following numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum to `k`. 
+With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum to `k`. 
 
 ```swift
 func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
@@ -38,7 +38,7 @@ Let's find out if there exist two entries whose sum is equal to 10.
 
 Initially, our dictionary is empty. We begin looping through each element:
 
-- **i = 0**: Is `0` in the dictionary? No. We add the difference between the target `k` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
+- **i = 0**: Is `7` in the dictionary? No. We add the difference between the target `k` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
 
 ```swift
 [ 3: 0 ]
@@ -148,4 +148,4 @@ It's possible, of course, that there are no values for `a[i] + a[j]` that sum to
 
 I'm quite enamored by this little algorithm. It shows that with some basic preprocessing on the input data -- sorting it from low to high -- you can turn a tricky problem into a very simple and beautiful algorithm.
 
-*Written by Matthijs Hollemans and Daniel Speiser*
+*Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser*
diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 66937cf69..1d674e965 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -54,10 +54,10 @@ There are two trees in this forest, each of which corresponds to one set of elem
 
 We give each subset a unique number to identify it. That number is the index of  the root node of that subset's tree. In the example, node `1` is the root of the first tree and `6` is the root of the second tree.
 
-Note that the `parent[]` of a root node points to itself. So `parent[1] = 1` and `parent[6] = 6`. That's how we can tell something is a root node.
-
 So in this example we have two subsets, the first with the label `1` and the second with the label `6`. The **Find** operation actually returns the set's label, not its contents.
 
+Note that the `parent[]` of a root node points to itself. So `parent[1] = 1` and `parent[6] = 6`. That's how we can tell something is a root node.
+
 ## Add set
 
 Let's look at the implementation of these basic operations, starting with adding a new set.
@@ -181,7 +181,7 @@ Now we call `unionSetsContaining(4, and: 3)`. The smaller tree is attached to th
 
 ![AfterUnion](Images/AfterUnion.png)
 
-Note that, because we call `setOf()` in the beginning of the method, the larger tree was also optimized in the process -- node `3` now hangs directly off the root.
+Note that, because we call `setOf()` at the start of the method, the larger tree was also optimized in the process -- node `3` now hangs directly off the root.
 
 Union with optimizations also takes almost **O(1)** time.
 

From 04966b1ef55ef4dc573f939553ae08eaf54bf823 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 19:08:49 +0100
Subject: [PATCH 0108/1679] Clean up Travis-CI instructions

---
 How to Contribute.markdown | 22 +++++++++++++++-------
 1 file changed, 15 insertions(+), 7 deletions(-)

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 215539ae2..aa2cf3dea 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -21,16 +21,24 @@ To keep this a high quality repo, please follow this process when submitting you
 3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
 4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. If you wrote it, you deserve the credit and fame.
 5. Add a playground and/or unit tests.
-  - Add unit test projects to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/hollance/swift-algorithm-club)
-    - `- xcodebuild test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests`
-  - Configure scheme to run on Travis-CI
-    - Open `Product` -> `Scheme` -> `Manage Schemes ...`
-      - Uncheck `Autocreate schemes`
-      - Check `Shared`
-    - [Screenshot of scheme settings](/images/scheme-settings-for-travis.png)
 
 Just so you know, I will probably edit your text and code for grammar etc, just to ensure a certain level of polish.
 
+For the unit tests:
+
+- Add the unit test project to `.travis.yml` so they it be run on [Travis-CI](https://travis-ci.org/hollance/swift-algorithm-club). Add a line to `.travis.yml` like this:
+
+```
+- xcodebuild test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
+```
+
+- Configure the Test project's scheme to run on Travis-CI:
+    - Open **Product -> Scheme -> Manage Schemes...**
+    - Uncheck **Autocreate schemes**
+    - Check **Shared**
+
+![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
+
 ## Want to chat?
 
 This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/hollance/swift-algorithm-club/issues) and we'll talk!

From dda4729089a1666a0cea756a5221152c46d513fe Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 19:38:25 +0100
Subject: [PATCH 0109/1679] Add Travis-CI build status badge

---
 README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.markdown b/README.markdown
index d17b87072..7cb2fbca4 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,5 +1,7 @@
 # Welcome to the Swift Algorithm Club!
 
+[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)
+
 Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.
 
 If you're a computer science student who needs to learn this stuff for exams -- or if you're a self-taught programmer who wants to brush up on the theory behind your craft -- you've come to the right place!

From 2e27f222b1e327859753dc3363319bc95ffa97a6 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 19:46:58 +0100
Subject: [PATCH 0110/1679] Clean up of Bounded Priority Queue

---
 .../BoundedPriorityQueue.swift                | 155 +++++++++---------
 Bounded Priority Queue/README.markdown        | 131 +++++++++++++++
 Bounded Priority Queue/README.md              |  80 ---------
 3 files changed, 207 insertions(+), 159 deletions(-)
 create mode 100644 Bounded Priority Queue/README.markdown
 delete mode 100644 Bounded Priority Queue/README.md

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.swift
index 91b6d30b6..abee9e526 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.swift	
@@ -4,98 +4,95 @@
 //  Created by John Gill on 2/28/16.
 //
 
-import Foundation
-
 public class LinkedListNode<T: Comparable> {
-    var value: T
-    var next: LinkedListNode?
-    var previous: LinkedListNode?
-
-    public init(value: T) {
-        self.value = value
-        self.next = nil
-        self.previous = nil
-    }
+  var value: T
+  var next: LinkedListNode?
+  var previous: LinkedListNode?
+  
+  public init(value: T) {
+    self.value = value
+    self.next = nil
+    self.previous = nil
+  }
 }
 
 public class BoundedPriorityQueue<T: Comparable> {
-    public typealias Node = LinkedListNode<T>
-    private var head: Node?
-    private var curNumElements:Int
-    private var maxNumElements: Int
-
-    public init(maxElements:Int) {
-        head = nil
-        maxNumElements = maxElements
-        curNumElements = 0
-    }
-
-    public var isEmpty: Bool {
-        return curNumElements == 0
-    }
-
-    public var count: Int {
-        return curNumElements
-    }
+  private typealias Node = LinkedListNode<T>
 
-    public func peek() -> T? {
-        if curNumElements > 0 {
-            return head!.value
-        }
-        return nil
-    }
+  private(set) public var count = 0
+  private var head: Node?
+  private var maxElements: Int
 
-    public func enqueue(value: T) {
-        let newNode = Node(value: value)
+  public init(maxElements: Int) {
+    self.maxElements = maxElements
+  }
 
-        if head == nil  {
-            head = newNode
-        } else {
-            var node = head
-            if curNumElements == maxNumElements && newNode.value > node!.value {
-                return
-            }
+  public var isEmpty: Bool {
+    return count == 0
+  }
 
-            while (node!.next != nil) && (newNode.value < node!.value) { node = node!.next }
+  public func peek() -> T? {
+    return head?.value
+  }
 
-            if newNode.value < node!.value {
-                newNode.next = node!.next
-                newNode.previous = node
+  public func enqueue(value: T) {
+    let newNode = Node(value: value)
 
-                if(newNode.next != nil) { /* TAIL */
-                    newNode.next!.previous = newNode
-                }
-                node!.next = newNode
-            } else {
-                newNode.previous = node!.previous
-                newNode.next = node
-                if(node!.previous == nil) { /* HEAD */
-                    head = newNode
-                } else {
-                    node!.previous!.next = newNode
-                }
-                node!.previous = newNode
-            }
-            if(curNumElements == maxNumElements) { dequeue() }
-        }
-        curNumElements += 1
+    if head == nil  {
+      head = newNode
+      count = 1
+      return
     }
 
-    public func dequeue() -> T? {
-        if curNumElements > 0 {
-            let retVal = head!.value
+    var node = head
+    if count == maxElements && newNode.value > node!.value {
+      return
+    }
+    
+    while (node!.next != nil) && (newNode.value < node!.value) {
+      node = node!.next
+    }
+    
+    if newNode.value < node!.value {
+      newNode.next = node!.next
+      newNode.previous = node
+      
+      if newNode.next != nil {     /* TAIL */
+        newNode.next!.previous = newNode
+      }
+      node!.next = newNode
+    } else {
+      newNode.previous = node!.previous
+      newNode.next = node
+      if node!.previous == nil {   /* HEAD */
+        head = newNode
+      } else {
+        node!.previous!.next = newNode
+      }
+      node!.previous = newNode
+    }
 
-            if curNumElements == 1 {
-                head = nil
-            }
-            else {
-                head = head!.next
-                head!.previous = nil
-            }
+    if count == maxElements {
+      dequeue()
+    }
+    count += 1
+  }
+  
+  public func dequeue() -> T? {
+    if count == 0 {
+      return nil
+    }
 
-            curNumElements -= 1
-            return retVal
-        }
-        return nil
+    let retVal = head!.value
+    
+    if count == 1 {
+      head = nil
+    } else {
+      head = head!.next
+      head!.previous = nil
     }
+
+    count -= 1
+    return retVal
+  }
 }
diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
new file mode 100644
index 000000000..b62d87678
--- /dev/null
+++ b/Bounded Priority Queue/README.markdown	
@@ -0,0 +1,131 @@
+# Bounded Priority queue
+
+A bounded priority queue is similar to a regular [priority queue](../Priority Queue/), except that there is a fixed upper bound on the number of elements that can be stored. When a new element is added to the queue while the queue is at capacity, the element with the highest priority value is ejected from the queue.
+
+## Example
+
+Suppose we have a bounded-priority-queue with maximum size 5 that has the following values and priorities:
+
+```
+Value:    [ A,   B,    C,    D,   E   ]
+Priority: [ 0.1, 0.25, 1.33, 3.2, 4.6 ]
+```
+
+Here, we consider the object with the lowest priority value to be the most important (so this is a *min-priority* queue). The larger the priority value, the less we care about the object. So `A` is more important than `B`, `B` is more important than `C`, and so on.
+
+Now we want to insert the element `F` with priority `0.4` into this bounded priority queue. Because the queue has maximum size 5, this will insert the element `F` but then evict the lowest-priority element (`E`), yielding the updated queue:
+
+```
+Value:    [ A,   B,    F,   C,    D   ]
+Priority: [ 0.1, 0.25, 0.4, 1.33, 3.2 ]
+```
+
+`F` is inserted between `B` and `C` because of its priority value. It's less important than `B` but more important than `C`.
+
+Suppose that we wish to insert the element `G` with priority 4.0 into this BPQ. Because `G`'s priority value is greater than the maximum-priority element in the queue, upon inserting `G` it will immediately be evicted. In other words, inserting an element into a BPQ with priority greater than the maximum-priority element of the BPQ has no effect.
+
+## Implementation
+
+While a [heap](../Heap/) may be a really simple implementation for a priority queue, a sorted [linked list](../Linked List/) allows for **O(k)** insertion and **O(1)** deletion, where **k** is the bounding number of elements.
+
+Here's how you could implement it in Swift:
+
+```swift
+public class BoundedPriorityQueue<T: Comparable> {
+  private typealias Node = LinkedListNode<T>
+
+  private(set) public var count = 0
+  private var head: Node?
+  private var maxElements: Int
+
+  public init(maxElements: Int) {
+    self.maxElements = maxElements
+  }
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+
+  public func peek() -> T? {
+    return head?.value
+  } 
+```
+
+The `BoundedPriorityQueue` class contains a doubly linked list of `LinkedListNode` objects. Nothing special here yet. The fun stuff happens in the `enqueue()` method:
+
+```swift
+  public func enqueue(value: T) {
+    let newNode = Node(value: value)
+
+    if head == nil  {
+      head = newNode
+      count = 1
+      return
+    }
+
+    var node = head
+    if count == maxElements && newNode.value > node!.value {
+      return
+    }
+    
+    while (node!.next != nil) && (newNode.value < node!.value) {
+      node = node!.next
+    }
+    
+    if newNode.value < node!.value {
+      newNode.next = node!.next
+      newNode.previous = node
+      
+      if newNode.next != nil {     /* TAIL */
+        newNode.next!.previous = newNode
+      }
+      node!.next = newNode
+    } else {
+      newNode.previous = node!.previous
+      newNode.next = node
+      if node!.previous == nil {   /* HEAD */
+        head = newNode
+      } else {
+        node!.previous!.next = newNode
+      }
+      node!.previous = newNode
+    }
+
+    if count == maxElements {
+      dequeue()
+    }
+    count += 1
+  }
+```
+
+We first check if the queue already has the maximum number of elements. If so, and the new priority value is greater than the `head` element's priority value, then there is no room for this new element and we return without inserting it.
+
+If the new value is acceptable, then we search through the list to find the proper insertion location and update the `next` and `previous` pointers.
+
+Lastly, if the queue has now reached the maximum number of elements, then we `dequeue()` the one with the largest priority value.
+
+By keeping the most important element at the front of the list, it makes dequeueing very easy:
+
+```swift
+  public func dequeue() -> T? {
+    if count == 0 {
+      return nil
+    }
+
+    let retVal = head!.value
+    
+    if count == 1 {
+      head = nil
+    } else {
+      head = head!.next
+      head!.previous = nil
+    }
+
+    count -= 1
+    return retVal
+  }
+```
+
+This simply removes the `head` element from the list and returns it.
+
+*Written for Swift Algorithm Club by John Gill and Matthijs Hollemans*
diff --git a/Bounded Priority Queue/README.md b/Bounded Priority Queue/README.md
deleted file mode 100644
index 2d19ecba9..000000000
--- a/Bounded Priority Queue/README.md	
+++ /dev/null
@@ -1,80 +0,0 @@
-# Bounded Priority queue
-
-A bounded priority queue is similar to a regular [priority queue](../Priority Queue), except that there is a fixed upper bound on the number of elements that can be stored. Whenever a new element is added to the queue, if the queue is at capacity, the element with the highest priority value is ejected from the queue.
-
-## Example
-Supposed we have a bounded-priority-queue with maximum size 5 that has the following values and priorities:
-```
-Value:    [A,   B,    C,    D,   E]
-Priority: [0.1, 0.25, 1.33, 3.2, 4.6]
-```
-Suppose that we want to insert the element `F` with priority `0.4` into this bounded priority queue. Because this bounded-priority-queue has maximum size five, this will insert the element `F`, but then evict the lowest-priority element (`E`), yielding the updated queue:
-```
-Value:    [A,   B,    F,   C,    D]
-Priority: [0.1, 0.25, 0.4, 1.33, 3.2]
-```
-Now suppose that we wish to insert the element G with priority 4.0 into this BPQ. Because G's priority value is greater than the maximum-priority element in the BPQ, upon inserting G it will immediately be evicted. In other words, inserting an element into a BPQ with priority greater than the maximum-priority element of the BPQ has no effect.
-
-## Implementation
-While a [heap](../Heap) may be a really simple implementation for a priority queue, an sorted [linked list](../Linked List) allows for `O(k)` insertion and `O(1)` deletion. Where `k` is the bounding number of elements.
-```swift
-public func enqueue(value: T) {
-    let newNode = Node(value: value)
-
-    if head == nil  {
-        head = newNode
-    } else {
-        var node = head
-        if curNumElements == maxNumElements && !(newNode.value < node!.value) {
-            return
-        }
-
-        while (node!.next != nil) && (newNode.value < node!.value) { node = node!.next }
-
-        if newNode.value < node!.value {
-            newNode.next = node!.next
-            newNode.previous = node
-
-            if(newNode.next != nil) { /* TAIL */
-                newNode.next!.previous = newNode
-            }
-            node!.next = newNode
-        } else {
-            newNode.previous = node!.previous
-            newNode.next = node
-            if(node!.previous == nil) { /* HEAD */
-                head = newNode
-            } else {
-                node!.previous!.next = newNode
-            }
-            node!.previous = newNode
-        }
-        if(curNumElements == maxNumElements) { dequeue() }
-    }
-    curNumElements += 1
-}
-```
-The `enqueue(_:)` method checks if the queue already has the maximum number of elements. If the new value is greater than the `head` value then don't insert it. If the new value is less than `head` search through the list to find the proper insertion location and update the pointers.
-
-Lastly if the queue has reached the maximum number of elements `dequeue()` the highest priority one.
-
-By keeping the element with the highest priority as the head it allows for a simple update of the `head` variable in a `dequeue()`:
-```swift
-public func dequeue() -> T? {
-    if curNumElements > 0 {
-        let retVal = head!.value
-
-        if curNumElements == 1 {
-            head = nil
-        }
-        else {
-            head = head!.next
-            head!.previous = nil
-        }
-
-        curNumElements -= 1
-        return retVal
-    }
-    return nil
-}
-```

From a72a812e41df0b0294116fb0d1dacee88b8fc4b2 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 19:57:11 +0100
Subject: [PATCH 0111/1679] Quickie cleanup of depth-first search. Needs more
 work.

---
 .../Contents.swift                            | 12 ++++------
 Depth-First Search/DepthFirstSearch.swift     | 10 +++-----
 Depth-First Search/README.markdown            | 23 +++++++++++--------
 README.markdown                               |  2 +-
 4 files changed, 22 insertions(+), 25 deletions(-)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index e18e7cc58..cc4bd7dd3 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,19 +1,17 @@
 func depthFirstSearch(graph: Graph, source: Node) -> [String] {
-  var nodesExplored: [String] = [source.label]
+  var nodesExplored = [source.label]
   source.visited = true
 
-  // Iterate through all neighbors, and for each one visit all of its neighbors
   for edge in source.neighbors {
-    let neighbor: Node = edge.neighbor
-
-    if (!neighbor.visited) {
-      nodesExplored += depthFirstSearch(graph, source: neighbor)
+    if !edge.neighbor.visited {
+      nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
     }
   }
   return nodesExplored
 }
 
 
+
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
@@ -35,4 +33,4 @@ graph.addEdge(nodeE, neighbor: nodeH)
 
 
 let nodesExplored = depthFirstSearch(graph, source: nodeA)
-print(nodesExplored)
\ No newline at end of file
+print(nodesExplored)
diff --git a/Depth-First Search/DepthFirstSearch.swift b/Depth-First Search/DepthFirstSearch.swift
index 79e835f3e..4393ac864 100644
--- a/Depth-First Search/DepthFirstSearch.swift	
+++ b/Depth-First Search/DepthFirstSearch.swift	
@@ -1,15 +1,11 @@
 func depthFirstSearch(graph: Graph, source: Node) -> [String] {
-  var nodesExplored: [String] = [source.label]
+  var nodesExplored = [source.label]
   source.visited = true
 
-  // Iterate through all neighbors, and for each one visit all of its neighbors
   for edge in source.neighbors {
-    let neighbor: Node = edge.neighbor
-
-    if (!neighbor.visited) {
-      nodesExplored += depthFirstSearch(graph, source: neighbor)
+    if !edge.neighbor.visited {
+      nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
     }
   }
-
   return nodesExplored
 }
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index da5fd1b0b..322635d7a 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -1,32 +1,33 @@
 # Depth-First Search
 
-Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores as far as possible along each branch before backtracking.
+Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores as far as possible along each branch before backtracking.
+
+[TODO: this is a work-in-progress]
 
 ## The code
 
-Simple implementation of breadth-first search using a queue:
+Simple recursive implementation of depth-first search:
 
 ```swift
 func depthFirstSearch(graph: Graph, source: Node) -> [String] {
-  var nodesExplored: [String] = [source.label]
+  var nodesExplored = [source.label]
   source.visited = true
 
-  // Iterate through all neighbors, and for each one visit all of its neighbors
   for edge in source.neighbors {
-    let neighbor: Node = edge.neighbor
-
-    if (!neighbor.visited) {
-      nodesExplored += depthFirstSearch(graph, source: neighbor)
+    if !edge.neighbor.visited {
+      nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
     }
   }
   return nodesExplored
 }
 ```
 
+Where a [breadth-first search](../Breadth-First Search/) visits all immediate neighbors first, a depth-first search tries to go as deep down the tree or graph as it can.
+
 Put this code in a playground and test it like so:
 
 ```swift
-let graph = Graph()   // Representing the graph from the animated example
+let graph = Graph()
 
 let nodeA = graph.addNode("a")
 let nodeB = graph.addNode("b")
@@ -58,4 +59,6 @@ Depth-first search can be used to solve many problems, for example:
 * Finding connected components of a sparse graph
 * Topological sorting of nodes in a graph
 * Finding bridges of a graph (see: [Bridges](https://en.wikipedia.org/wiki/Bridge_(graph_theory)#Bridge-finding_algorithm))
-* Among others
+* And lots of others!
+
+*Written for Swift Algorithm Club by Paulo Tanaka*
diff --git a/README.markdown b/README.markdown
index 7cb2fbca4..b7d878e7e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -168,7 +168,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - Graph
 - [Breadth-First Search (BFS)](Breadth-First Search/)
-- Depth-First Search (DFS)
+- [Depth-First Search (DFS)](Depth-First Search/)
 - Shortest Path
 - Minimum Spanning Tree
 - All Paths

From b311d34025a7779a31cee29f040bde24bb0bbcc5 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 20:16:02 +0100
Subject: [PATCH 0112/1679] Clean up of k-Means Clustering.

---
 K-Means/KMeans.swift                          | 123 +++++++++---------
 K-Means/README.markdown                       | 101 ++++++++++++++
 K-Means/README.md                             |  83 ------------
 K-Means/Tests/Tests.xcodeproj/project.pbxproj |   5 +-
 README.markdown                               |   3 +-
 5 files changed, 168 insertions(+), 147 deletions(-)
 create mode 100644 K-Means/README.markdown
 delete mode 100644 K-Means/README.md

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 9a3193bfe..9073b7b46 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -6,74 +6,75 @@
 import Foundation
 
 class KMeans {
-    var numCenters:Int
-    var convergeDist:Double
-    
-    init(numCenters:Int, convergeDist:Double) {
-        self.numCenters = numCenters
-        self.convergeDist = convergeDist
+  let numCenters: Int
+  let convergeDist: Double
+
+  init(numCenters: Int, convergeDist: Double) {
+    self.numCenters = numCenters
+    self.convergeDist = convergeDist
+  }
+
+  private func nearestCenter(x: Vector, centers: [Vector]) -> Int {
+    var nearestDist = DBL_MAX
+    var minIndex = 0
+
+    for (idx, c) in centers.enumerate() {
+      let dist = x.distTo(c)
+      if dist < nearestDist {
+        minIndex = idx
+        nearestDist = dist
+      }
     }
+    return minIndex
+  }
+  
+  func findCenters(points: [Vector]) -> [Vector] {
+    var centerMoveDist = 0.0
+    let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
     
-    private func nearestCenter(x: Vector, Centers: [Vector]) -> Int {
-        var nearestDist = DBL_MAX
-        var minIndex = 0;
-        
-        for (idx, c) in Centers.enumerate() {
-            let dist = x.distTo(c)
-            if dist < nearestDist {
-                minIndex = idx
-                nearestDist = dist
-            }
-        }
-        return minIndex
-    }
+    var kCenters = reservoirSample(points, k: numCenters)
     
-    func findCenters(points: [Vector]) -> [Vector] {
-        var centerMoveDist = 0.0
-        let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
-        
-        var kCenters = reservoirSample(points, k: numCenters)
-        
-        repeat {
-            var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-            var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
-        
-            for p in points {
-                let c = nearestCenter(p, Centers: kCenters)
-                cnts[c]++
-                newCenters[c] += p
-            }
-            
-            for idx in 0..<numCenters {
-                newCenters[idx] /= cnts[idx]
-            }
-            
-            centerMoveDist = 0.0
-            for idx in 0..<numCenters {
-                centerMoveDist += kCenters[idx].distTo(newCenters[idx])
-            }
-            
-            kCenters = newCenters
-        } while(centerMoveDist > convergeDist)
-        return kCenters
-    }
+    repeat {
+      var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+      var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
+
+      for p in points {
+        let c = nearestCenter(p, centers: kCenters)
+        cnts[c] += 1
+        newCenters[c] += p
+      }
+      
+      for idx in 0..<numCenters {
+        newCenters[idx] /= cnts[idx]
+      }
+      
+      centerMoveDist = 0.0
+      for idx in 0..<numCenters {
+        centerMoveDist += kCenters[idx].distTo(newCenters[idx])
+      }
+      
+      kCenters = newCenters
+    } while centerMoveDist > convergeDist
+
+    return kCenters
+  }
 }
 
 // Pick k random elements from samples
 func reservoirSample<T>(samples:[T], k:Int) -> [T] {
-    var result = [T]()
-
-    // Fill the result array with first k elements
-    for i in 0..<k {
-        result.append(samples[i])
-    }
-    // randomly replace elements from remaining pool
-    for i in (k+1)..<samples.count {
-        let j = random()%(i+1)
-        if j < k {
-            result[j] = samples[i]
-        }
+  var result = [T]()
+  
+  // Fill the result array with first k elements
+  for i in 0..<k {
+    result.append(samples[i])
+  }
+  // randomly replace elements from remaining pool
+  for i in (k+1)..<samples.count {
+    let j = random() % (i+1)
+    if j < k {
+      result[j] = samples[i]
     }
-    return result
+  }
+  return result
 }
 
diff --git a/K-Means/README.markdown b/K-Means/README.markdown
new file mode 100644
index 000000000..de828299f
--- /dev/null
+++ b/K-Means/README.markdown
@@ -0,0 +1,101 @@
+# k-Means Clustering
+
+Goal: Partition data into **k** clusters based on nearest means.
+
+The idea behind k-Means is to take data that has no formal classification to it and determine if there are any natural clusters (groups of related objects) within the data.
+
+k-Means assumes that there are **k-centers** within the data. The data that is closest to these *centroids* become classified or grouped together. k-Means doesn't tell you what the classifier is for that particular data group, but it assists in trying to find what clusters potentially exist.
+
+## The algorithm
+
+The k-Means algorithm is really quite simple at its core:
+
+1. Choose **k** random points to be the initial centers
+2. Repeat the following two steps until the *centroids* reach convergence:
+	1. Assign each point to its nearest *centroid*
+	2. Update the *centroid* to the mean of its nearest points
+
+Convergence is said to be reached when all of the *centroids* have not changed.
+
+This brings about a few of the parameters that are required for k-Means:
+
+- **k**: This is the number of *centroids* to attempt to locate.
+- **convergence distance**: The minimum distance that the centers are allowed to move after a particular update step.
+- **distance function**: There are a number of distance functions that can be used, but mostly commonly the Euclidean distance function is adequate. But often that can lead to convergence not being reached in higher dimensionally.
+
+This is what the algorithm would look like in Swift:
+
+```swift
+func kMeans(numCenters: Int, convergeDist: Double, points: [Vector]) -> [Vector] {
+  var centerMoveDist = 0.0
+  let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
+  
+  var kCenters = reservoirSample(points, k: numCenters)
+  
+  repeat {
+    var cnts = [Double](count: numCenters, repeatedValue: 0.0)
+    var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
+
+    for p in points {
+      let c = nearestCenter(p, centers: kCenters)
+      cnts[c] += 1
+      newCenters[c] += p
+    }
+    
+    for idx in 0..<numCenters {
+      newCenters[idx] /= cnts[idx]
+    }
+    
+    centerMoveDist = 0.0
+    for idx in 0..<numCenters {
+      centerMoveDist += euclidean(kCenters[idx], newCenters[idx])
+    }
+    
+    kCenters = newCenters
+  } while centerMoveDist > convergeDist
+
+  return kCenters
+}
+```
+
+## Example
+
+These examples are contrived to show the exact nature of k-Means and finding clusters. These clusters are very easily identified by human eyes: we see there is one in the lower left corner, one in the upper right corner, and maybe one in the middle.
+
+In all these examples the squares represent the data points and the stars represent the *centroids*.
+
+##### Good clusters
+
+This first example shows k-Means finding all three clusters:
+
+![Good Clustering](Images/k_means_good.png)
+
+The selection of initial centroids found the lower left cluster (indicated by red) and did pretty good on the center and upper left clusters.
+
+#### Bad Clustering
+
+The next two examples highlight the unpredictability of k-Means and how it not always finds the best clustering.
+
+![Bad Clustering 1](Images/k_means_bad1.png)
+
+As you can see in this one, the initial *centroids* were all a little too close and the 'blue' didn't quite get to a good place. By adjusting the convergence distance we should be able to get it better.
+
+![Bad Clustering 1](Images/k_means_bad2.png)
+
+In this example, the blue cluster never really could separate from the red cluster and as such sort of got stuck down there.
+
+## Performance
+
+The first thing to recognize is that k-Means is classified as an NP-Hard type of problem. The selection of the initial *centroids* has a big effect on how the resulting clusters may end up. This means that trying to find an exact solution is not likely -- even in 2 dimensional space.
+
+As seen from the steps above the complexity really isn't that bad -- it is often considered to be on the order of **O(kndi)**, where **k** is the number of *centroids*, **n** is the number of **d**-dimensional vectors, and **i** is the number of iterations for convergence.
+
+The amount of data has a big linear effect on the running time of k-Means, but tuning how far you want the *centroids* to converge can have a big impact how many iterations will be done. As a general rule, **k** should be relatively small compared to the number of vectors.
+
+Often times as more data is added certain points may lie in the boundary between two *centroids* and as such those centroids would continue to bounce back and forth and the **convergence** distance would need to be tuned to prevent that.
+
+## See Also
+
+[K-Means Clustering on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
+
+*Written by John Gill*
diff --git a/K-Means/README.md b/K-Means/README.md
deleted file mode 100644
index e1314a825..000000000
--- a/K-Means/README.md
+++ /dev/null
@@ -1,83 +0,0 @@
-# K-Means
-
-Goal:  Partition data into k clusters based on nearest means
-
-The idea behind K-Means is to try and take data that has no formal classification to it and determine if there are any natural clusters within the data.
-
-K-Means assumes that there are **k-centers** within the data. The data that is then closest to these *centroids* become classified or grouped together. K-Means doesn't tell you what the classifier is for that particular data group, but it assists in trying to find what clusters potentially exist.
-
-## Algorithm
-The k-means algorithm is really quite simple at it's core:
-1. Choose k random points to be the initial centers
-2. Repeat the following two steps until the *centroid* reach convergence
-    1. Assign each point to it's nearest *centroid*
-    2. Update the *centroid* to the mean of it's nearest points
-
-Convergence is said to be reached when all of the *centroids* have not changed.
-
-This brings about a few of the parameters that are required for k-means:
-- **k** -  This is the number of *centroids* to attempt to locate
-- **convergence distance** - This is minimum distance that the centers are allowed to moved after a particular update step.
-- **distance function** - There are a number of distance functions that can be used, but mostly commonly the euclidean distance function is adequate. But often can lead to convergence not being reached in higher dimensionally.
-
-This is what the algorithm would look like in swift
-```swift
-func kMeans(numCenters: Int, convergeDist: Double, points: [Vector]) -> [Vector] {
-    var centerMoveDist = 0.0
-    let zeros = [Double](count: points[0].getLength(), repeatedValue: 0.0)
-
-    var kCenters = reservoirSample(points, k: numCenters)
-
-    repeat {
-        var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-        var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
-        for p in points {
-            let c = nearestCenter(p, Centers: kCenters)
-            cnts[c]++
-            newCenters[c] += p
-        }
-        for idx in 0..<numCenters {
-            newCenters[idx] /= cnts[idx]
-        }
-        centerMoveDist = 0.0
-        for idx in 0..<numCenters {
-            centerMoveDist += euclidean(kCenters[idx], v2: newCenters[idx])
-        }
-        kCenters = newCenters
-    } while(centerMoveDist > convergeDist)
-    return kCenters
-}
-```
-
-## Example
-These examples are contrived to show the exact nature of K-Means and finding clusters. These clusters are very easily identified by human eyes, we see there is one in the lower left corner, one in the upper right corner and maybe one in the middle.
-
-In all these examples the stars represent the *centroids* and the squares are the points.
-
-##### Good clusters
-This first example shows K-Means finding all three clusters:
-![Good Clustering](Images/k_means_good.png)
-
-The selection of initial centroids found that lower left (indicated by red) and did pretty good on the center and upper left clusters.
-
-#### Bad Clustering
-The next two examples highlight the unpredictability of k-Means and how not always does it find the best clustering.
-![Bad Clustering 1](Images/k_means_bad1.png)
-As you can see in this one the initial *centroids* were all a little two close and the 'blue' didn't quite get to a good place. By adjusting the convergence distance should be able to get it better.
-
-![Bad Clustering 1](Images/k_means_bad2.png)
-This one the blue cluster never really could separate from the red cluster and as such sort of got stuck down there.
-
-## Performance
-The first thing to recognize is that k-Means is classified as an NP-Hard type of problem. The selection of the initial *centroids* has a big effect on how the resulting clusters may end up. This means that trying to find an exact solution is not likely - even in 2 dimensional space.
-
-As seem from the steps above the complexity really isn't that bad - it is often considered to be on the order of O(kndi), where **k** is the number of *centroids*, **n** is the number of **d** dimensional vectors and **i** is the number of iterations for convergence.
-
-The amount of data has a big linear effect on the running time of k-means, but tuning how far you want the *centroids* to converge can have a big impact how many iterations will be done - **k** should be relatively small compared to the number of vectors.
-
-Often times as more data is added certain points may lie in the boundary between two *centroids* and as such those centroids would continue to bounce back and forth and the **convergence** distance would need to be tuned to prevent that.
-
-## See Also
-See also [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
-
-*Written by John Gill*
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 55f861d02..c70acba0d 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -16,8 +16,8 @@
 		B80894DB1C852CFA0018730E /* KMeans.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = KMeans.swift; path = ../KMeans.swift; sourceTree = SOURCE_ROOT; };
 		B80894E01C852D100018730E /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		B80894E31C852D100018730E /* KMeansTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = KMeansTests.swift; sourceTree = SOURCE_ROOT; };
-		B80894E51C852D100018730E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; name = Info.plist; path = ../Info.plist; sourceTree = "<group>"; };
-		B80894E91C852DA00018730E /* Vector.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Vector.swift; path = ../Vector.swift; sourceTree = "<group>"; };
+		B80894E51C852D100018730E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist; path = Info.plist; sourceTree = "<group>"; };
+		B80894E91C852DA00018730E /* Vector.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Vector.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -254,6 +254,7 @@
 				B80894E81C852D100018730E /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/README.markdown b/README.markdown
index b7d878e7e..49f93c562 100644
--- a/README.markdown
+++ b/README.markdown
@@ -99,7 +99,8 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 
 ### Machine learning
-- [k-Means](K-Means/). Unsupervised classifier that partitions data into k clusters.
+
+- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression

From ef35bf044802f963c85a038e94ac26b7a806ff12 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 20:27:38 +0100
Subject: [PATCH 0113/1679] Small edits to graph explanation

---
 Graph/README.markdown | 40 ++++++++++++++++++++++++----------------
 README.markdown       |  2 +-
 2 files changed, 25 insertions(+), 17 deletions(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index 42b71b6b2..75ac34abd 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,34 +1,37 @@
 # Graph
 
-A graph is a set of *vertices* paired with a set of *edges*.  Each vertex has a set of associated edges, which connect to other vertices.
+[TODO: this is a work-in-progress]
 
-For example, a graph can represent a social network.  Each person is a vertex, and people that know each other are connected with edges.
+A graph is a set of *vertices* paired with a set of *edges*. Each vertex has a number of associated edges, which connect the vertex to other vertices.
+
+For example, a graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges.
 
 // TODO: Insert image here
 
+> **Note:** Vertices are sometimes also called "nodes" and edges are also called "links".
+
 ## Weighted and Directed Edges
-Edges can optionally be *weighted*, where an arbitrary weight is assigned to each edge.  Consider an example of a graph representing airplane flights.  Cities can be represented as vertices, and flights as edges.  Then an edge weight could represent flight time.
+
+Edges can optionally be *weighted*, where an arbitrary weight -- a positive or negative numeric value -- is assigned to each edge.  Consider an example of a graph representing airplane flights. Cities can be represented as vertices, and flights as edges. Then an edge weight could represent flight time or the cost of the trip.
 
 In addition, edges can optionally be *directed*.  A directed edge from vertex A to vertex B connects *A to B*, but **not** *B to A*. Continuing from the flight path example, a directed edge from San Francisco, CA to Juneau, AK would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco.
 
 // TODO: Insert image here
 
 ## Representing Graphs in Code
+
 There are two main strategies for representing graphs:
 
-1. Adjacency List
-2. Adjacency Matrix
+**Adjacency List.** In an adjacency list implementation, each vertex stores a list of edges that originate from the vertex. For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list of 3 edges.
 
-### Adjacency List
-In an adjacency list implementation, each vertex stores a list of edges that originate from the vertex.  For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list of 3 edges.
+**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for  vertex A, column for vertex B would have value 5.6:
 
-### Adjacency Matrix
-In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for  vertex A, column for vertex B would have value 5.6:
 ```
-	matrix[index(A)][index(B)] == 5.6
+matrix[index(A)][index(B)] == 5.6
 ```
 
 ### Comparing Graph Representations
+
 Let *V* be the number of vertices in the graph, and *E* the number of edges.  Then we have:
 
 | Operation       | Adjacency List | Adjacency Matrix |
@@ -38,17 +41,20 @@ Let *V* be the number of vertices in the graph, and *E* the number of edges.  Th
 | Add Edge        | O(1)           | O(1)             |
 | Check Adjacency | O(V)           | O(1)             |
 
-Note that the time to check adjacency for an adjacency list is **O(V)**, because at worst a vertex is connected to *every* other vertex.  So, in the case of a *sparse* graph, in which each vertex is connected to a handfull of other vertices, an Adjacency List is preferred.  If the graph is *dense*, that is, vertices are connected to most of the other vertices, then an Adjacency Matrix is preferred.
+Note that the time to check adjacency for an adjacency list is **O(V)**, because at worst a vertex is connected to *every* other vertex.
+
+In the case of a *sparse* graph, where each vertex is connected to only a handful of other vertices, an Adjacency List is preferred. If the graph is *dense*, where each vertex is connected to most of the other vertices, then an Adjacency Matrix is preferred.
 
 ## The Code
-Below we have implementations of both Adjacency List and Adjacency Matrix graph representations.
 
-In both cases, we also let the vertex store arbitrary data with a generic parameter.
+Below we have implementations of both Adjacency List and Adjacency Matrix graph representations. In both cases, we also let the vertex store arbitrary data with a generic parameter.
+
 ### Adjacency List
+
 First, we have the data structures for edges and vertices:
 
 ```swift
-var uniqueIDCounter: Int = 0
+var uniqueIDCounter = 0
 
 public struct GraphEdge<T> {
   public let from: GraphVertex<T>
@@ -69,6 +75,7 @@ public struct GraphVertex<T> {
   }
 }
 ```
+
 Note that each vertex has a unique identifier, which we use to compare equality later.
 
 Now, lets see how to connect vertices:
@@ -76,7 +83,7 @@ Now, lets see how to connect vertices:
 ```swift
 // Creates a directed edge self -----> dest
 public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
-    edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
+  edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
 }
 ```
 And then we can check for an edge between vertices:
@@ -94,7 +101,8 @@ public func edgeTo(otherVertex: GraphVertex<T>) -> GraphEdge<T>? {
 ```
 
 ### Adjacency Matrix
-Fundamentally, we will store a `[[Double?]]` which is the adjacency matrix.  An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight.  To index into the matrix using vertices, we give each `GraphVertex` a unique integer index:
+
+Fundamentally, we will store a `[[Double?]]` array, which is the adjacency matrix. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight.  To index into the matrix using vertices, we give each `GraphVertex` a unique integer index:
 
 ```swift
 public struct GraphVertex<T> {
diff --git a/README.markdown b/README.markdown
index 49f93c562..85173ab6e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -167,7 +167,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 ### Graphs
 
-- Graph
+- [Graph](Graph/)
 - [Breadth-First Search (BFS)](Breadth-First Search/)
 - [Depth-First Search (DFS)](Depth-First Search/)
 - Shortest Path

From 6a00819508c354c92ec334ed563aedd54049dba4 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 20:30:11 +0100
Subject: [PATCH 0114/1679] Add :construction: emoji to articles that need work

---
 README.markdown | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/README.markdown b/README.markdown
index 85173ab6e..2cab9e1b4 100644
--- a/README.markdown
+++ b/README.markdown
@@ -100,7 +100,7 @@ Bad sorting algorithms (don't use these!):
 
 ### Machine learning
 
-- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
+- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters. :construction:
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression
@@ -130,7 +130,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Queue](Queue/). First-in, first-out!
 - [Deque](Deque/). A double-ended queue.
 - [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
-- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements.
+- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements. :construction:
 - [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
 
 ### Lists
@@ -143,7 +143,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Tree](Tree/). A general-purpose tree structure.
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
-- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
+- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
 - Red-Black Tree
 - Splay Tree
 - Threaded Binary Tree
@@ -152,6 +152,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - Trie
+- [B-Tree](B Tree/) :construction:
 
 ### Hashing
 
@@ -167,9 +168,9 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 ### Graphs
 
-- [Graph](Graph/)
+- [Graph](Graph/) :construction:
 - [Breadth-First Search (BFS)](Breadth-First Search/)
-- [Depth-First Search (DFS)](Depth-First Search/)
+- [Depth-First Search (DFS)](Depth-First Search/) :construction:
 - Shortest Path
 - Minimum Spanning Tree
 - All Paths

From 8f6e5b66d7f677587104a095c70c60f77775d0f3 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 20:32:28 +0100
Subject: [PATCH 0115/1679] Didn't realize we already had a Travis build badge
 on the main page

---
 README.markdown | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/README.markdown b/README.markdown
index 2cab9e1b4..ff2902bc7 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,7 +1,5 @@
 # Welcome to the Swift Algorithm Club!
 
-[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)
-
 Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.
 
 If you're a computer science student who needs to learn this stuff for exams -- or if you're a self-taught programmer who wants to brush up on the theory behind your craft -- you've come to the right place!
@@ -208,4 +206,4 @@ Other algorithm repositories:
 
 All content is licensed under the terms of the MIT open source license.
 
-[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg)](https://travis-ci.org/hollance/swift-algorithm-club)
+[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)

From f15eb772912658394dffcd39827e778b60028002 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 3 Mar 2016 20:33:18 +0100
Subject: [PATCH 0116/1679] Add note about construction badge

---
 How to Contribute.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index aa2cf3dea..385d712e0 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -6,6 +6,8 @@ Want to help out with the Swift Algorithm Club? Great!
 
 Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
 
+Things marked with :construction: need work.
+
 New algorithms and data structures are always welcome (even if they aren't on the list).
 
 We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library.

From 0903d54de48c6c803f72d434ccf09016a246d207 Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Fri, 4 Mar 2016 02:15:53 +0530
Subject: [PATCH 0117/1679] Initial playground

---
 Topological Sort/Topological Sort.playground/Contents.swift  | 5 +++++
 .../Topological Sort.playground/contents.xcplayground        | 4 ++++
 2 files changed, 9 insertions(+)
 create mode 100644 Topological Sort/Topological Sort.playground/Contents.swift
 create mode 100644 Topological Sort/Topological Sort.playground/contents.xcplayground

diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
new file mode 100644
index 000000000..c9a67424b
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -0,0 +1,5 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+
+var str = "Hello, playground"
diff --git a/Topological Sort/Topological Sort.playground/contents.xcplayground b/Topological Sort/Topological Sort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From ecd1ee3a4ba71d2c5baf2c93c9c6f13a5822a734 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 4 Mar 2016 19:24:11 +0100
Subject: [PATCH 0118/1679] Improve graph

---
 Graph/AdjacencyList.swift                     |  39 +++
 Graph/AdjacencyMatrix.swift                   |  43 +++
 .../Contents.swift                            |  74 ++---
 .../Contents.swift                            |  76 +++---
 Graph/Images/AdjacencyList.graffle            | Bin 0 -> 2581 bytes
 Graph/Images/AdjacencyList.png                | Bin 0 -> 18147 bytes
 Graph/Images/AdjacencyMatrix.graffle          | Bin 0 -> 3223 bytes
 Graph/Images/AdjacencyMatrix.png              | Bin 0 -> 21209 bytes
 Graph/Images/ChordMap.graffle                 | Bin 0 -> 2244 bytes
 Graph/Images/ChordMap.png                     | Bin 0 -> 17202 bytes
 Graph/Images/CoreData.graffle                 | Bin 0 -> 2092 bytes
 Graph/Images/CoreData.png                     | Bin 0 -> 5632 bytes
 Graph/Images/DAG.graffle                      | Bin 0 -> 2018 bytes
 Graph/Images/DAG.png                          | Bin 0 -> 9119 bytes
 Graph/Images/Demo1.graffle                    | Bin 0 -> 2172 bytes
 Graph/Images/Demo1.png                        | Bin 0 -> 9314 bytes
 Graph/Images/Flights.graffle                  | Bin 0 -> 2566 bytes
 Graph/Images/Flights.png                      | Bin 0 -> 34735 bytes
 Graph/Images/FlightsDirected.graffle          | Bin 0 -> 2268 bytes
 Graph/Images/FlightsDirected.png              | Bin 0 -> 32004 bytes
 Graph/Images/Graph.graffle                    | Bin 0 -> 2160 bytes
 Graph/Images/Graph.png                        | Bin 0 -> 14516 bytes
 Graph/Images/SocialNetwork.graffle            | Bin 0 -> 2416 bytes
 Graph/Images/SocialNetwork.png                | Bin 0 -> 31918 bytes
 Graph/Images/StateMachine.graffle             | Bin 0 -> 2517 bytes
 Graph/Images/StateMachine.png                 | Bin 0 -> 24128 bytes
 Graph/Images/Tasks.graffle                    | Bin 0 -> 2361 bytes
 Graph/Images/Tasks.png                        | Bin 0 -> 14987 bytes
 Graph/Images/TreeAndList.graffle              | Bin 0 -> 2648 bytes
 Graph/Images/TreeAndList.png                  | Bin 0 -> 19198 bytes
 Graph/README.markdown                         | 254 +++++++++++++-----
 README.markdown                               |   2 +-
 32 files changed, 355 insertions(+), 133 deletions(-)
 create mode 100644 Graph/AdjacencyList.swift
 create mode 100644 Graph/AdjacencyMatrix.swift
 create mode 100644 Graph/Images/AdjacencyList.graffle
 create mode 100644 Graph/Images/AdjacencyList.png
 create mode 100644 Graph/Images/AdjacencyMatrix.graffle
 create mode 100644 Graph/Images/AdjacencyMatrix.png
 create mode 100644 Graph/Images/ChordMap.graffle
 create mode 100644 Graph/Images/ChordMap.png
 create mode 100644 Graph/Images/CoreData.graffle
 create mode 100644 Graph/Images/CoreData.png
 create mode 100644 Graph/Images/DAG.graffle
 create mode 100644 Graph/Images/DAG.png
 create mode 100644 Graph/Images/Demo1.graffle
 create mode 100644 Graph/Images/Demo1.png
 create mode 100644 Graph/Images/Flights.graffle
 create mode 100644 Graph/Images/Flights.png
 create mode 100644 Graph/Images/FlightsDirected.graffle
 create mode 100644 Graph/Images/FlightsDirected.png
 create mode 100644 Graph/Images/Graph.graffle
 create mode 100644 Graph/Images/Graph.png
 create mode 100644 Graph/Images/SocialNetwork.graffle
 create mode 100644 Graph/Images/SocialNetwork.png
 create mode 100644 Graph/Images/StateMachine.graffle
 create mode 100644 Graph/Images/StateMachine.png
 create mode 100644 Graph/Images/Tasks.graffle
 create mode 100644 Graph/Images/Tasks.png
 create mode 100644 Graph/Images/TreeAndList.graffle
 create mode 100644 Graph/Images/TreeAndList.png

diff --git a/Graph/AdjacencyList.swift b/Graph/AdjacencyList.swift
new file mode 100644
index 000000000..3a8bc3006
--- /dev/null
+++ b/Graph/AdjacencyList.swift
@@ -0,0 +1,39 @@
+private var uniqueIDCounter = 0
+
+public struct Edge<T> {
+  public let from: Vertex<T>
+  public let to: Vertex<T>
+  public let weight: Double
+}
+
+public struct Vertex<T> {
+  public var data: T
+  public let uniqueID: Int
+  
+  private(set) public var edges: [Edge<T>] = []   // the adjacency list
+  
+  public init(data: T) {
+    self.data = data
+    uniqueID = uniqueIDCounter
+    uniqueIDCounter += 1
+  }
+
+  // Creates the directed edge: self -----> dest
+  public mutating func connectTo(destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
+    edges.append(Edge(from: self, to: destinationVertex, weight: weight))
+  }
+  
+  // Creates an undirected edge by making two directed edges: self ----> other, and other ----> self
+  public mutating func connectBetween(inout otherVertex: Vertex<T>, withWeight weight: Double = 0) {
+    connectTo(otherVertex, withWeight: weight)
+    otherVertex.connectTo(self, withWeight: weight)
+  }
+  
+  // Does this vertex have an edge -----> otherVertex?
+  public func edgeTo(otherVertex: Vertex<T>) -> Edge<T>? {
+    for e in edges where e.to.uniqueID == otherVertex.uniqueID {
+      return e
+    }
+    return nil
+  }
+}
diff --git a/Graph/AdjacencyMatrix.swift b/Graph/AdjacencyMatrix.swift
new file mode 100644
index 000000000..85a16d94f
--- /dev/null
+++ b/Graph/AdjacencyMatrix.swift
@@ -0,0 +1,43 @@
+public struct Vertex<T> {
+  public var data: T
+  private let index: Int
+}
+
+public struct Graph<T> {
+  // If adjacencyMatrix[i][j] is not nil, then there is an edge from
+  // vertex i to vertex j.
+  private var adjacencyMatrix: [[Double?]] = []
+  
+  // Adds a new vertex to the matrix.
+  // Performance: possibly O(n^2) because of the resizing of the matrix.
+  public mutating func createVertex(data: T) -> Vertex<T> {
+    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
+    
+    // Expand each existing row to the right one column.
+    for i in 0..<adjacencyMatrix.count {
+      adjacencyMatrix[i].append(nil)
+    }
+    
+    // Add one new row at the bottom.
+    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+    adjacencyMatrix.append(newRow)
+
+    return vertex
+  }
+  
+  // Creates a directed edge source -----> dest.
+  public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
+    adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
+  }
+  
+  // Creates an undirected edge by making 2 directed edges:
+  // some ----> other, and other ----> some.
+  public mutating func connect(someVertex: Vertex<T>, symmetricallyWithVertex withVertex: Vertex<T>, withWeight weight: Double = 0) {
+    adjacencyMatrix[someVertex.index][withVertex.index] = weight
+    adjacencyMatrix[withVertex.index][someVertex.index] = weight
+  }
+
+  public func weightFrom(sourceVertex: Vertex<T>, toDestinationVertex: Vertex<T>) -> Double? {
+    return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
+  }
+}
diff --git a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
index 6c239f75d..f3c89b112 100644
--- a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
@@ -1,64 +1,65 @@
-/*
+//: # Graph using an adjacency list
+//:
+//: In an adjacency list implementation of a graph, each vertex stores an
+//: array of edges, indicating to which other vertices it has an edge.
+//: (Note the directionality: we only record "to" edges, not "from" edges.)
 
-A graph implementation, using an adjacency list.
+private var uniqueIDCounter = 0
 
-In an adjacency list implementation, each vertex stores an array of edges, indicating to which vertices it has an edge (note the directionality).  The edge stores the source and destination vertices, as well as a weight.
-
-*/
-
-var uniqueIDCounter: Int = 0
-
-public struct GraphEdge<T> {
-  public let from: GraphVertex<T>
-  public let to: GraphVertex<T>
+public struct Edge<T> {
+  public let from: Vertex<T>
+  public let to: Vertex<T>
   public let weight: Double
 }
 
-
-public struct GraphVertex<T> {
+public struct Vertex<T> {
   public var data: T
-  private var edges: [GraphEdge<T>] = [] // This is an adjacency list, rather than matrix
+  public let uniqueID: Int
   
-  private let uniqueID: Int
+  private(set) public var edges: [Edge<T>] = []   // the adjacency list
   
   public init(data: T) {
     self.data = data
     uniqueID = uniqueIDCounter
     uniqueIDCounter += 1
   }
-  
-  // Creates a directed edge self -----> dest
-  public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
-    edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
+
+  // Creates the directed edge: self -----> dest
+  public mutating func connectTo(destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
+    edges.append(Edge(from: self, to: destinationVertex, weight: weight))
   }
   
-  // Creates an undirected edge by making 2 directed edges: self ----> other, and other ----> self
-  public mutating func connectBetween(inout otherVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {  
+  // Creates an undirected edge by making two directed edges: self ----> other, and other ----> self
+  public mutating func connectBetween(inout otherVertex: Vertex<T>, withWeight weight: Double = 0) {
     connectTo(otherVertex, withWeight: weight)
     otherVertex.connectTo(self, withWeight: weight)
   }
   
-  // Queries for an edge from self -----> otherVertex
-  public func edgeTo(otherVertex: GraphVertex<T>) -> GraphEdge<T>? {
-    for e in edges {
-      if e.to.uniqueID == otherVertex.uniqueID {
-        return e
-      }
+  // Does this vertex have an edge -----> otherVertex?
+  public func edgeTo(otherVertex: Vertex<T>) -> Edge<T>? {
+    for e in edges where e.to.uniqueID == otherVertex.uniqueID {
+      return e
     }
-    
     return nil
   }
 }
 
 
 
-// Create 4 separate vertices
-var v1 = GraphVertex(data: 1)
-var v2 = GraphVertex(data: 2)
-var v3 = GraphVertex(data: 3)
-var v4 = GraphVertex(data: 4)
+//: ### Demo
+
+// Create the vertices
+var v1 = Vertex(data: 1)
+var v2 = Vertex(data: 2)
+var v3 = Vertex(data: 3)
+var v4 = Vertex(data: 4)
+var v5 = Vertex(data: 5)
 
-// Setup a cycle like so:
+// Set up a cycle like so:
+//               v5
+//                ^
+//                | (3.2)
+//                |
 // v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
 // ^                                            |
 // |                                            V
@@ -68,6 +69,8 @@ v1.connectTo(v2, withWeight: 1.0)
 v2.connectTo(v3, withWeight: 1.0)
 v3.connectTo(v4, withWeight: 4.5)
 v4.connectTo(v1, withWeight: 2.8)
+v2.connectTo(v5, withWeight: 3.2)
+
 
 // Returns the weight of the edge from v1 to v2 (1.0)
 v1.edgeTo(v2)?.weight
@@ -80,4 +83,5 @@ v3.edgeTo(v4)?.weight
 
 // Returns the weight of the edge from v4 to v1 (2.8)
 v4.edgeTo(v1)?.weight
-//: [Next](@next)
+
+//: [Next: Adjacency Matrix](@next)
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
index c8c5fdf8c..8d9fb5080 100644
--- a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
+++ b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
@@ -1,75 +1,87 @@
-//: [Previous](@previous)
-/*
+//: [Previous: Adjacency List](@previous)
 
-A graph implementation, using an adjacency matrix.
+//: # Graph using an adjacency matrix
+//:
+//: In an adjacency matrix implementation, each vertex is given an index 
+//: from `0..<V`, where `V` is the total number of vertices. The matrix is 
+//: a 2D array, with each entry indicating if the corresponding two vertices
+//: are connected, and the weight of that edge.
+//:
+//: For example, if `matrix[3][5] = 4.6`, then vertex #3 is connected to
+//: vertex #5, with a weight of 4.6. Note that vertex #5 is not necessarily
+//: connected back to vertex #3 (that would be recorded in `matrix[5][3]`).
 
-In an adjacency matrix implementation, each vertex is associated with an index from 0..<V (V being the number of vertices). Then a matrix (a 2D array) is stored for the entire graph, with each entry indicating if the corresponding vertices are connected, and the weight.  For example, if matrix[3][5] = 4.6, then vertex #3 is connected to vertex #5, with a weight of 4.6.  Note that vertex #5 is not necessarily connected to vertex #3.
-
-*/
-
-public struct GraphVertex<T> {
+public struct Vertex<T> {
   public var data: T
   private let index: Int
 }
 
 public struct Graph<T> {
-  
-  // nil entries are used to mark that two vertices are NOT connected.
-  // If adjacencyMatrix[i][j] is not nil, then there is an edge from vertex i to vertex j.
+  // If adjacencyMatrix[i][j] is not nil, then there is an edge from
+  // vertex i to vertex j.
   private var adjacencyMatrix: [[Double?]] = []
   
-  // Possibly O(n^2) because of the resizing of the matrix
-  public mutating func createVertex(data: T) -> GraphVertex<T> {
-    let vertex = GraphVertex(data: data, index: adjacencyMatrix.count)
+  // Adds a new vertex to the matrix.
+  // Performance: possibly O(n^2) because of the resizing of the matrix.
+  public mutating func createVertex(data: T) -> Vertex<T> {
+    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
     
-    // Expand each existing row to the right one column
+    // Expand each existing row to the right one column.
     for i in 0..<adjacencyMatrix.count {
       adjacencyMatrix[i].append(nil)
     }
     
-    // Add one new row at the bottom
+    // Add one new row at the bottom.
     let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
     adjacencyMatrix.append(newRow)
-    
+
     return vertex
   }
   
-  // Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
-  public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[sourceVertex.index][toDestinationVertex.index] = weight
+  // Creates a directed edge source -----> dest.
+  public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
+    adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
   }
   
-  // Creates an undirected edge by making 2 directed edges: some ----> other, and other ----> some
-  public mutating func connect(someVertex: GraphVertex<T>, symmetricallyWithVertex withVertex: GraphVertex<T>, withWeight weight: Double = 0) {
+  // Creates an undirected edge by making 2 directed edges:
+  // some ----> other, and other ----> some.
+  public mutating func connect(someVertex: Vertex<T>, symmetricallyWithVertex withVertex: Vertex<T>, withWeight weight: Double = 0) {
     adjacencyMatrix[someVertex.index][withVertex.index] = weight
     adjacencyMatrix[withVertex.index][someVertex.index] = weight
   }
-  
-  public func weightFrom(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>) -> Double? {
+
+  public func weightFrom(sourceVertex: Vertex<T>, toDestinationVertex: Vertex<T>) -> Double? {
     return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
   }
-  
 }
 
 
 
-// Create 4 separate vertices
+//: ### Demo
+
+// Create the vertices
 var graph = Graph<Int>()
 let v1 = graph.createVertex(1)
 let v2 = graph.createVertex(2)
 let v3 = graph.createVertex(3)
 let v4 = graph.createVertex(4)
+let v5 = graph.createVertex(5)
 
-// Setup a cycle like so:
+// Set up a cycle like so:
+//               v5
+//                ^
+//                | (3.2)
+//                |
 // v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
 // ^                                            |
 // |                                            V
 // ---------<-----------<---------(2.8)----<----|
 
-graph.connect(v1, toDestinationVertex: v2, withWeight: 1.0)
-graph.connect(v2, toDestinationVertex: v3, withWeight: 1.0)
-graph.connect(v3, toDestinationVertex: v4, withWeight: 4.5)
-graph.connect(v4, toDestinationVertex: v1, withWeight: 2.8)
+graph.connect(v1, to: v2, withWeight: 1.0)
+graph.connect(v2, to: v3, withWeight: 1.0)
+graph.connect(v3, to: v4, withWeight: 4.5)
+graph.connect(v4, to: v1, withWeight: 2.8)
+graph.connect(v2, to: v5, withWeight: 3.2)
 
 // Returns the weight of the edge from v1 to v2 (1.0)
 graph.weightFrom(v1, toDestinationVertex: v2)
@@ -83,3 +95,5 @@ graph.weightFrom(v3, toDestinationVertex: v4)
 // Returns the weight of the edge from v4 to v1 (2.8)
 graph.weightFrom(v4, toDestinationVertex: v1)
 
+print(graph.adjacencyMatrix)
+
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diff --git a/Graph/README.markdown b/Graph/README.markdown
index 75ac34abd..546d4c599 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,36 +1,92 @@
 # Graph
 
-[TODO: this is a work-in-progress]
+A graph is something that looks like this:
 
-A graph is a set of *vertices* paired with a set of *edges*. Each vertex has a number of associated edges, which connect the vertex to other vertices.
+![A graph](Images/Graph.png)
 
-For example, a graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges.
-
-// TODO: Insert image here
+In computer-science lingo, a graph is a set of *vertices* paired with a set of *edges*. The vertices are the round things and the edges are the lines between them. Edges connect a vertex to other vertices.
 
 > **Note:** Vertices are sometimes also called "nodes" and edges are also called "links".
 
-## Weighted and Directed Edges
+For example, a graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges. A somewhat historically inaccurate example:
 
-Edges can optionally be *weighted*, where an arbitrary weight -- a positive or negative numeric value -- is assigned to each edge.  Consider an example of a graph representing airplane flights. Cities can be represented as vertices, and flights as edges. Then an edge weight could represent flight time or the cost of the trip.
+![Social network](Images/SocialNetwork.png)
 
-In addition, edges can optionally be *directed*.  A directed edge from vertex A to vertex B connects *A to B*, but **not** *B to A*. Continuing from the flight path example, a directed edge from San Francisco, CA to Juneau, AK would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco.
+Graphs come in all kinds of shapes and sizes. The edges can have a *weight*, where a positive or negative numeric value is assigned to each edge. Consider an example of a graph representing airplane flights. Cities can be vertices, and flights can be edges. Then an edge weight could describe flight time or the price of a ticket.
 
-// TODO: Insert image here
+![Airplane flights](Images/Flights.png)
 
-## Representing Graphs in Code
+With this hypothetical airline, flying from San Francisco to Moscow is cheapest by going through New York.
 
-There are two main strategies for representing graphs:
+Edges can also be *directed*. So far the edges you've seen have been undirected, so if Ada knows Charles, then Charles also knows Ada. A directed edge, on the other hand, implies a one-way relationship. A directed edge from vertex X to vertex Y connects X to Y, but *not* Y to X.
 
-**Adjacency List.** In an adjacency list implementation, each vertex stores a list of edges that originate from the vertex. For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list of 3 edges.
+Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back!).
 
-**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for  vertex A, column for vertex B would have value 5.6:
+![One-way flights](Images/FlightsDirected.png)
 
-```
-matrix[index(A)][index(B)] == 5.6
-```
+The following are also graphs:
+
+![Tree and linked list](Images/TreeAndList.png)
+
+On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
+
+The very first graph I showed you contained *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
+
+Another very common type of graph is the *directed acyclic graph* or DAG:
+
+![DAG](Images/DAG.png)
+
+Like a tree this does not have any cycles in it (no matter where you start, there is no path back to the starting vertex), but unlike a tree the edges are directional and the shape doesn't necessarily form a hierarchy.
+
+## Why use graphs?
+
+Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that graphs are an extremely useful data structure.
+
+If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First Search/) or [depth-first search](../Depth-First Search) to find a solution. 
+
+For example, let's say you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
+
+![Tasks as a graph](Images/Tasks.png)
+
+Each vertex represents a task. Here, an edge between two vertices means that the source task must be completed before the destination task can start. So task C cannot start before B and D are finished, and B nor D can start before A is finished.
+
+Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
+
+Whenever you're faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationship".
+
+If you're a musician you might appreciate this graph:
+
+![Chord map](Images/ChordMap.png)
+
+The vertices are chords from the C major scale. The edges -- the relationships between the chords -- represent how [likely one chord is to follow another](http://mugglinworks.com/chordmaps/genmap.htm). This is a directed graph, so the direction of the arrows shows how you can go from one chord to the next. It's also a weighted graph, where the weight of the edges -- portrayed here by line thickness -- shows a strong relationship between two chords. As you can see, a G7-chord is very likely to be followed by a C chord, and much less likely by a Am chord.
 
-### Comparing Graph Representations
+You're probably already using graphs without even knowing it. Your data model is also a graph (from Apple's Core Data documentation):
+
+![Core Data model](https://developer.apple.com/library/ios/documentation/Cocoa/Conceptual/CoreDataVersioning/Art/recipe_version2.0.jpg)
+
+Another common graph that's used by programmers is the state machine, where edges depict the conditions for transitioning between states. Here is a state machine that models my cat:
+
+![State machine](Images/StateMachine.png)
+
+Graphs are awesome. Facebook made a fortune from them. If you're going to learn any data structure, it should be the graph, and the vast collection of standard graph algorithms.
+
+## Vertices and edges, oh my!
+
+In theory, a graph is just a bunch of vertex objects and a bunch of edge objects. But how do you describe these in code?
+
+There are two main strategies:
+
+**Adjacency List.** In an adjacency list implementation, each vertex stores a list of edges that originate from the vertex. For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list containing 3 edges.
+
+![Adjacency list](Images/AdjacencyList.png)
+
+The adjacency list describes outgoing edges. A has an edge to B but B does not have an edge back to A, so A does not appear in B's adjacency list.
+
+**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for vertex A, column for vertex B would have value 5.6:
+
+![Adjacency matrix](Images/AdjacencyMatrix.png)
+
+So which one should you use? Most of the time, the adjacency list is the right approach. What follows is a more detailed comparison between the two.
 
 Let *V* be the number of vertices in the graph, and *E* the number of edges.  Then we have:
 
@@ -41,98 +97,132 @@ Let *V* be the number of vertices in the graph, and *E* the number of edges.  Th
 | Add Edge        | O(1)           | O(1)             |
 | Check Adjacency | O(V)           | O(1)             |
 
-Note that the time to check adjacency for an adjacency list is **O(V)**, because at worst a vertex is connected to *every* other vertex.
+"Checking adjacency" means that we try to determine that a given vertex is an immediate neighbor of another vertex. The time to check adjacency for an adjacency list is **O(V)**, because at worst a vertex is connected to *every* other vertex.
 
-In the case of a *sparse* graph, where each vertex is connected to only a handful of other vertices, an Adjacency List is preferred. If the graph is *dense*, where each vertex is connected to most of the other vertices, then an Adjacency Matrix is preferred.
+In the case of a *sparse* graph, where each vertex is connected to only a handful of other vertices, an adjacency list is the best way to store the edges. If the graph is *dense*, where each vertex is connected to most of the other vertices, then a matrix is preferred.
 
-## The Code
+We'll show you sample implementations of both adjacency list and adjacency matrix.
 
-Below we have implementations of both Adjacency List and Adjacency Matrix graph representations. In both cases, we also let the vertex store arbitrary data with a generic parameter.
+## The code: adjacency list
 
-### Adjacency List
-
-First, we have the data structures for edges and vertices:
+The adjacency list for each vertex consists of `Edge` objects:
 
 ```swift
-var uniqueIDCounter = 0
-
-public struct GraphEdge<T> {
-  public let from: GraphVertex<T>
-  public let to: GraphVertex<T>
+public struct Edge<T> {
+  public let from: Vertex<T>
+  public let to: Vertex<T>
   public let weight: Double
 }
+```
+
+This struct describes the "from" and "to" vertices and a weight value. Note that an `Edge` object is always directed, a one-way connection (shown as arrows in the illustrations above). If you want the connection to go both ways, you also need to add an `Edge` object to the adjacency list of the destination vertex.
+
+The `Vertex` looks like this:
+
+```swift
+private var uniqueIDCounter = 0
 
-public struct GraphVertex<T> {
+public struct Vertex<T> {
   public var data: T
-  private var edges: [GraphEdge<T>] = []
+  public let uniqueID: Int
   
-  private let uniqueID: Int
+  private(set) public var edges: [Edge<T>] = []
   
   public init(data: T) {
     self.data = data
     uniqueID = uniqueIDCounter
     uniqueIDCounter += 1
   }
-}
 ```
 
-Note that each vertex has a unique identifier, which we use to compare equality later.
+It stores arbitrary data with a generic type `T`. The vertex also has a unique identifier, which we use to compare equality later. The `edges` array is the adjacency list.
 
-Now, lets see how to connect vertices:
+To connect two vertices using a directed edge:
 
 ```swift
-// Creates a directed edge self -----> dest
-public mutating func connectTo(destinationVertex: GraphVertex<T>, withWeight weight: Double = 1.0) {
-  edges.append(GraphEdge(from: self, to: destinationVertex, weight: weight))
-}
+  public mutating func connectTo(destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
+    edges.append(Edge(from: self, to: destinationVertex, weight: weight))
+  }
+```
+
+As mentioned, to create an undirected edge you need to make two directed edges:
+
+```
+  public mutating func connectBetween(inout otherVertex: Vertex<T>, withWeight weight: Double = 0) {
+    connectTo(otherVertex, withWeight: weight)
+    otherVertex.connectTo(self, withWeight: weight)
+  }
 ```
-And then we can check for an edge between vertices:
+
+There is also a method for checking adjacency, i.e. to determine if there is an edge between two vertices:
 
 ```swift
-// Queries for an edge from self -----> otherVertex
-public func edgeTo(otherVertex: GraphVertex<T>) -> GraphEdge<T>? {
-  for e in edges {
-    if e.to.uniqueID == otherVertex.uniqueID {
+  public func edgeTo(otherVertex: Vertex<T>) -> Edge<T>? {
+    for e in edges where e.to.uniqueID == otherVertex.uniqueID {
       return e
     }
-  } 
-  return nil
+    return nil
+  }
+```
+
+Here's an example of a very simple graph:
+
+![Demo](Images/Demo1.png)
+
+This is how you'd create it using `Vertex` objects:
+
+```swift
+var v1 = Vertex(data: 1)
+var v2 = Vertex(data: 2)
+var v3 = Vertex(data: 3)
+var v4 = Vertex(data: 4)
+var v5 = Vertex(data: 5)
+
+v1.connectTo(v2, withWeight: 1.0)
+v2.connectTo(v3, withWeight: 1.0)
+v3.connectTo(v4, withWeight: 4.5)
+v4.connectTo(v1, withWeight: 2.8)
+v2.connectTo(v5, withWeight: 3.2)
+```
+
+> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code for each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
+
+## The code: adjacency matrix
+
+We'll keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight.
+
+```swift
+public struct Graph<T> {
+  private var adjacencyMatrix: [[Double?]] = []
 }
 ```
 
-### Adjacency Matrix
+If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
 
-Fundamentally, we will store a `[[Double?]]` array, which is the adjacency matrix. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight.  To index into the matrix using vertices, we give each `GraphVertex` a unique integer index:
+To index into the matrix using vertices, we give each `Vertex` a unique integer index:
 
 ```swift
-public struct GraphVertex<T> {
+public struct Vertex<T> {
   public var data: T
   private let index: Int
 }
 ```
 
-Then the `Graph` struct keeps track of the matrix.  To create a new vertex, the graph must resize the matrix:
+To create a new vertex, the graph must resize the matrix:
 
 ```swift
-public struct Graph<T> {
-  
-  // nil entries are used to mark that two vertices are NOT connected.
-  // If adjacencyMatrix[i][j] is not nil, then there is an edge from vertex i to vertex j.
-  private var adjacencyMatrix: [[Double?]] = []
-    
-  // O(n^2) because of the resizing of the matrix
-  public mutating func createVertex(data: T) -> GraphVertex<T> {
-    let vertex = GraphVertex(data: data, index: adjacencyMatrix.count)
+  public mutating func createVertex(data: T) -> Vertex<T> {
+    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
     
-    // Expand each existing row to the right one column
+    // Expand each existing row to the right one column.
     for i in 0..<adjacencyMatrix.count {
       adjacencyMatrix[i].append(nil)
     }
     
-    // Add one new row at the bottom
+    // Add one new row at the bottom.
     let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
     adjacencyMatrix.append(newRow)
-    
+
     return vertex
   }
 ```
@@ -140,13 +230,45 @@ public struct Graph<T> {
 Once we have the matrix properly configured, adding edges and querying for edges are simple indexing operations into the matrix:
 
 ```swift
-// Creates a directed edge source -----> dest.  Represented by M[source][dest] = weight
-public mutating func connect(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>, withWeight weight: Double = 0) {
-  adjacencyMatrix[sourceVertex.index][toDestinationVertex.index] = weight
+public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
+  adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
 }
 
 public func weightFrom(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>) -> Double? {
   return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
 }
 ```
-*Written by Donald Pinckney*
+
+You use these objects as follows:
+
+```swift
+var graph = Graph<Int>()
+let v1 = graph.createVertex(1)
+let v2 = graph.createVertex(2)
+let v3 = graph.createVertex(3)
+let v4 = graph.createVertex(4)
+let v5 = graph.createVertex(5)
+
+graph.connect(v1, to: v2, withWeight: 1.0)
+graph.connect(v2, to: v3, withWeight: 1.0)
+graph.connect(v3, to: v4, withWeight: 4.5)
+graph.connect(v4, to: v1, withWeight: 2.8)
+graph.connect(v2, to: v5, withWeight: 3.2)
+```
+
+Then the adjacency matrix looks like this:
+
+	[[nil, 1.0, nil, nil, nil]    v1
+	 [nil, nil, 1.0, nil, 3.2]    v2
+	 [nil, nil, nil, 4.5, nil]    v3
+	 [2.8, nil, nil, nil, nil]    v4
+	 [nil, nil, nil, nil, nil]]   v5
+	 
+	  v1   v2   v3   v4   v5
+
+
+## See also
+
+This article described what a graph is and how you can implement the basic data structure. But we have many more articles on practical uses for graphs, so check those out too!
+
+*Written by Donald Pinckney and Matthijs Hollemans*
diff --git a/README.markdown b/README.markdown
index ff2902bc7..ac2dbf9a9 100644
--- a/README.markdown
+++ b/README.markdown
@@ -166,7 +166,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 ### Graphs
 
-- [Graph](Graph/) :construction:
+- [Graph](Graph/)
 - [Breadth-First Search (BFS)](Breadth-First Search/)
 - [Depth-First Search (DFS)](Depth-First Search/) :construction:
 - Shortest Path

From 05b9ef2725f27298fe3a07ab4ebe30a571fce57a Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Sat, 5 Mar 2016 02:18:25 +0530
Subject: [PATCH 0119/1679] Adding DFS

---
 .../Contents.swift                            | 25 ++++++++-
 .../Sources/Graph.swift                       | 56 +++++++++++++++++++
 .../Sources/Stack.swift                       | 39 +++++++++++++
 .../timeline.xctimeline                       |  6 ++
 4 files changed, 125 insertions(+), 1 deletion(-)
 create mode 100644 Topological Sort/Topological Sort.playground/Sources/Graph.swift
 create mode 100644 Topological Sort/Topological Sort.playground/Sources/Stack.swift
 create mode 100644 Topological Sort/Topological Sort.playground/timeline.xctimeline

diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index c9a67424b..4b9680f38 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -2,4 +2,27 @@
 
 import UIKit
 
-var str = "Hello, playground"
+let graph = Graph()
+
+let node5 = graph.addNode("5")
+let node7 = graph.addNode("7")
+let node3 = graph.addNode("3")
+let node11 = graph.addNode("11")
+let node8 = graph.addNode("8")
+let node2 = graph.addNode("2")
+let node9 = graph.addNode("9")
+let node10 = graph.addNode("10")
+
+graph.addEdge(fromNode: node5, toNode: node11)
+graph.addEdge(fromNode: node7, toNode: node11)
+graph.addEdge(fromNode: node7, toNode: node8)
+graph.addEdge(fromNode: node3, toNode: node8)
+graph.addEdge(fromNode: node3, toNode: node10)
+graph.addEdge(fromNode: node11, toNode: node2)
+graph.addEdge(fromNode: node11, toNode: node9)
+graph.addEdge(fromNode: node11, toNode: node10)
+graph.addEdge(fromNode: node8, toNode: node9)
+
+print(graph.description, terminator: "")
+
+graph.depthFirstSearch("5")
\ No newline at end of file
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
new file mode 100644
index 000000000..748591d28
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -0,0 +1,56 @@
+
+public class Graph: CustomStringConvertible {
+  
+  private var adjacencyLists: [String : [String]]
+
+  public init() {
+    adjacencyLists = [String : [String]]()
+  }
+  
+  public func addNode(value: String) -> String {
+    adjacencyLists[value] = []
+    return value
+  }
+  
+  public func addEdge(fromNode from: String, toNode to: String) -> Bool {
+    adjacencyLists[from]?.append(to)
+    return adjacencyLists[from] != nil ? true : false
+  }
+  
+  public var description: String {
+    return adjacencyLists.description
+  }
+  
+  private func adjacencyList(forValue: String) -> [String]? {
+    for (key, adjacencyList) in adjacencyLists {
+      if key == forValue {
+        return adjacencyList
+      }
+    }
+    return nil
+  }
+}
+
+extension Graph {
+
+  public func depthFirstSearch(source: String) -> [String] {
+    var result = [String]()
+    var stack = Stack<String>()
+    
+    result.append(source)
+    stack.push(source)
+    
+    while !stack.isEmpty {
+      if let element = stack.pop(), temp = adjacencyList(element) {
+        for node in temp {
+          stack.push(node)
+          result.append(node)
+        }
+      }
+    }
+    
+    return result
+  }
+}
+
+
diff --git a/Topological Sort/Topological Sort.playground/Sources/Stack.swift b/Topological Sort/Topological Sort.playground/Sources/Stack.swift
new file mode 100644
index 000000000..7099e5f55
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/Sources/Stack.swift	
@@ -0,0 +1,39 @@
+import Foundation
+
+public struct Stack<T> {
+  private var array = [T]()
+  
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+  
+  public var count: Int {
+    return array.count
+  }
+  
+  public mutating func push(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func pop() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeLast()
+    }
+  }
+  
+  public func peek() -> T? {
+    return array.last
+  }
+}
+
+extension Stack: SequenceType {
+  public func generate() -> AnyGenerator<T> {
+    var curr = self
+    return anyGenerator {
+      _ -> T? in
+      return curr.pop()
+    }
+  }
+}
\ No newline at end of file
diff --git a/Topological Sort/Topological Sort.playground/timeline.xctimeline b/Topological Sort/Topological Sort.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>

From 8ec5ab149791003b76de95670c05d5c8db9b7f3a Mon Sep 17 00:00:00 2001
From: TheCmar7 <runner.cram@gmail.com>
Date: Fri, 4 Mar 2016 13:04:16 -0800
Subject: [PATCH 0120/1679] I added a playground for the 2D array

---
 Array2D/Array2D.playground/Contents.swift     | 73 +++++++++++++++++++
 .../Array2D.playground/contents.xcplayground  |  4 +
 .../Array2D.playground/timeline.xctimeline    |  6 ++
 3 files changed, 83 insertions(+)
 create mode 100644 Array2D/Array2D.playground/Contents.swift
 create mode 100644 Array2D/Array2D.playground/contents.xcplayground
 create mode 100644 Array2D/Array2D.playground/timeline.xctimeline

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
new file mode 100644
index 000000000..995804ab0
--- /dev/null
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -0,0 +1,73 @@
+/*
+Two-dimensional array with a fixed number of rows and columns.
+This is mostly handy for games that are played on a grid, such as chess.
+Performance is always O(1).
+*/
+public struct Array2D<T> {
+    public let columns: Int
+    public let rows: Int
+    private var array: [T]
+    
+    public init(columns: Int, rows: Int, initialValue: T) {
+        self.columns = columns
+        self.rows = rows
+        array = .init(count: rows*columns, repeatedValue: initialValue)
+    }
+    
+    public subscript(column: Int, row: Int)  -> T {
+        get {
+            return array[row*columns + column]
+        }
+        set {
+            array[row*columns + column] = newValue
+        }
+    }
+
+}
+
+// initialization
+var Array2DNumbers = Array2D(columns: 3, rows: 5, initialValue: 0)
+
+// makes an array of rows * columns elements all filled with zero
+print(Array2DNumbers.array)
+
+//setting numbers
+Array2DNumbers[0, 0] = 1
+Array2DNumbers[1, 0] = 2
+
+Array2DNumbers[0, 1] = 3
+Array2DNumbers[1, 1] = 4
+
+Array2DNumbers[0, 2] = 5
+Array2DNumbers[1, 2] = 6
+
+Array2DNumbers[0, 3] = 7
+Array2DNumbers[1, 3] = 8
+Array2DNumbers[2, 3] = 9
+
+// now the numbers are set in the array
+print(Array2DNumbers.array)
+
+// printint out the 2D array with a reference around the grid [x, y]
+print("  ", terminator: "")
+for k in 0..<Array2DNumbers.columns {
+    print(" \(k)", terminator:"")
+    if (k == Array2DNumbers.columns - 1){
+        print(" x")
+    }
+}
+
+for i in 0..<Array2DNumbers.rows {
+    print("\(i) [", terminator: "");
+    for j in 0..<Array2DNumbers.columns {
+        if (j == Array2DNumbers.columns - 1) {
+            print("\(Array2DNumbers[j, i])", terminator: "");
+        } else {
+            print("\(Array2DNumbers[j, i]) ", terminator: "");
+        }
+    }
+    print("]");
+}
+print("y")
+
+
diff --git a/Array2D/Array2D.playground/contents.xcplayground b/Array2D/Array2D.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Array2D/Array2D.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Array2D/Array2D.playground/timeline.xctimeline b/Array2D/Array2D.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Array2D/Array2D.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>

From b65ac551776deb704cadb051c0d9d0dae45d0fa8 Mon Sep 17 00:00:00 2001
From: TheCmar7 <runner.cram@gmail.com>
Date: Fri, 4 Mar 2016 13:07:37 -0800
Subject: [PATCH 0121/1679] I took off the grid around the printing out of the
 2dArray I thought it might confuse people more than it helps

---
 Array2D/Array2D.playground/Contents.swift | 16 ++++------------
 1 file changed, 4 insertions(+), 12 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 995804ab0..3f72db3bd 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -31,7 +31,7 @@ var Array2DNumbers = Array2D(columns: 3, rows: 5, initialValue: 0)
 // makes an array of rows * columns elements all filled with zero
 print(Array2DNumbers.array)
 
-//setting numbers
+// setting numbers using subscript [x, y]
 Array2DNumbers[0, 0] = 1
 Array2DNumbers[1, 0] = 2
 
@@ -48,17 +48,9 @@ Array2DNumbers[2, 3] = 9
 // now the numbers are set in the array
 print(Array2DNumbers.array)
 
-// printint out the 2D array with a reference around the grid [x, y]
-print("  ", terminator: "")
-for k in 0..<Array2DNumbers.columns {
-    print(" \(k)", terminator:"")
-    if (k == Array2DNumbers.columns - 1){
-        print(" x")
-    }
-}
-
+// print out the 2D array with a reference around the grid
 for i in 0..<Array2DNumbers.rows {
-    print("\(i) [", terminator: "");
+    print("[", terminator: "");
     for j in 0..<Array2DNumbers.columns {
         if (j == Array2DNumbers.columns - 1) {
             print("\(Array2DNumbers[j, i])", terminator: "");
@@ -68,6 +60,6 @@ for i in 0..<Array2DNumbers.rows {
     }
     print("]");
 }
-print("y")
+
 
 

From 78af3a3ab7e70c1347d5044bca45d9794e5d38d0 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 5 Mar 2016 10:10:56 +0100
Subject: [PATCH 0122/1679] Rename variable to matrix

---
 Array2D/Array2D.playground/Contents.swift | 85 +++++++++++------------
 1 file changed, 42 insertions(+), 43 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 3f72db3bd..f73ba8b13 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,65 +1,64 @@
 /*
-Two-dimensional array with a fixed number of rows and columns.
-This is mostly handy for games that are played on a grid, such as chess.
-Performance is always O(1).
+  Two-dimensional array with a fixed number of rows and columns.
+  This is mostly handy for games that are played on a grid, such as chess.
+  Performance is always O(1).
 */
 public struct Array2D<T> {
-    public let columns: Int
-    public let rows: Int
-    private var array: [T]
-    
-    public init(columns: Int, rows: Int, initialValue: T) {
-        self.columns = columns
-        self.rows = rows
-        array = .init(count: rows*columns, repeatedValue: initialValue)
+  public let columns: Int
+  public let rows: Int
+  private var array: [T]
+  
+  public init(columns: Int, rows: Int, initialValue: T) {
+    self.columns = columns
+    self.rows = rows
+    array = .init(count: rows*columns, repeatedValue: initialValue)
+  }
+  
+  public subscript(column: Int, row: Int)  -> T {
+    get {
+      return array[row*columns + column]
     }
-    
-    public subscript(column: Int, row: Int)  -> T {
-        get {
-            return array[row*columns + column]
-        }
-        set {
-            array[row*columns + column] = newValue
-        }
+    set {
+      array[row*columns + column] = newValue
     }
-
+  }
 }
 
+
+
 // initialization
-var Array2DNumbers = Array2D(columns: 3, rows: 5, initialValue: 0)
+var matrix = Array2D(columns: 3, rows: 5, initialValue: 0)
 
 // makes an array of rows * columns elements all filled with zero
-print(Array2DNumbers.array)
+print(matrix.array)
 
 // setting numbers using subscript [x, y]
-Array2DNumbers[0, 0] = 1
-Array2DNumbers[1, 0] = 2
+matrix[0, 0] = 1
+matrix[1, 0] = 2
 
-Array2DNumbers[0, 1] = 3
-Array2DNumbers[1, 1] = 4
+matrix[0, 1] = 3
+matrix[1, 1] = 4
 
-Array2DNumbers[0, 2] = 5
-Array2DNumbers[1, 2] = 6
+matrix[0, 2] = 5
+matrix[1, 2] = 6
 
-Array2DNumbers[0, 3] = 7
-Array2DNumbers[1, 3] = 8
-Array2DNumbers[2, 3] = 9
+matrix[0, 3] = 7
+matrix[1, 3] = 8
+matrix[2, 3] = 9
 
 // now the numbers are set in the array
-print(Array2DNumbers.array)
+print(matrix.array)
 
 // print out the 2D array with a reference around the grid
-for i in 0..<Array2DNumbers.rows {
-    print("[", terminator: "");
-    for j in 0..<Array2DNumbers.columns {
-        if (j == Array2DNumbers.columns - 1) {
-            print("\(Array2DNumbers[j, i])", terminator: "");
-        } else {
-            print("\(Array2DNumbers[j, i]) ", terminator: "");
-        }
+for i in 0..<matrix.rows {
+  print("[", terminator: "");
+  for j in 0..<matrix.columns {
+    if (j == matrix.columns - 1) {
+      print("\(matrix[j, i])", terminator: "");
+    } else {
+      print("\(matrix[j, i]) ", terminator: "");
     }
-    print("]");
+  }
+  print("]");
 }
 
-
-

From 4a6bd11597bdfd097367b69603fcdb22d3d46f2a Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 7 Mar 2016 14:32:50 +0530
Subject: [PATCH 0123/1679] Adding tests and completed topological sort

---
 .../Contents.swift                            |   3 +-
 .../Sources/Graph.swift                       |  83 ++++--
 .../TopologicalSort.xcodeproj/project.pbxproj | 260 ++++++++++++++++++
 .../TopologicalSort/Graph.swift               |  93 +++++++
 .../TopologicalSort/Info.plist                |  24 ++
 .../TopologicalSort/Stack.swift               |  39 +++
 .../TopologicalSort/TopologicalSort.swift     |  42 +++
 7 files changed, 518 insertions(+), 26 deletions(-)
 create mode 100644 Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj
 create mode 100644 Topological Sort/TopologicalSort/TopologicalSort/Graph.swift
 create mode 100644 Topological Sort/TopologicalSort/TopologicalSort/Info.plist
 create mode 100644 Topological Sort/TopologicalSort/TopologicalSort/Stack.swift
 create mode 100644 Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift

diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index 4b9680f38..2d6af7e4f 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -23,6 +23,5 @@ graph.addEdge(fromNode: node11, toNode: node9)
 graph.addEdge(fromNode: node11, toNode: node10)
 graph.addEdge(fromNode: node8, toNode: node9)
 
-print(graph.description, terminator: "")
 
-graph.depthFirstSearch("5")
\ No newline at end of file
+graph.topologicalSort()
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index 748591d28..5cf228d65 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -1,18 +1,19 @@
-
 public class Graph: CustomStringConvertible {
   
-  private var adjacencyLists: [String : [String]]
-
+  public typealias Node = String
+  
+  private var adjacencyLists: [Node : [Node]]
+  
   public init() {
-    adjacencyLists = [String : [String]]()
+    adjacencyLists = [Node : [Node]]()
   }
   
-  public func addNode(value: String) -> String {
+  public func addNode(value: Node) -> Node {
     adjacencyLists[value] = []
     return value
   }
   
-  public func addEdge(fromNode from: String, toNode to: String) -> Bool {
+  public func addEdge(fromNode from: Node, toNode to: Node) -> Bool {
     adjacencyLists[from]?.append(to)
     return adjacencyLists[from] != nil ? true : false
   }
@@ -21,9 +22,9 @@ public class Graph: CustomStringConvertible {
     return adjacencyLists.description
   }
   
-  private func adjacencyList(forValue: String) -> [String]? {
+  private func adjacencyList(forNode node: Node) -> [Node]? {
     for (key, adjacencyList) in adjacencyLists {
-      if key == forValue {
+      if key == node {
         return adjacencyList
       }
     }
@@ -32,25 +33,59 @@ public class Graph: CustomStringConvertible {
 }
 
 extension Graph {
-
-  public func depthFirstSearch(source: String) -> [String] {
-    var result = [String]()
-    var stack = Stack<String>()
-    
-    result.append(source)
-    stack.push(source)
-    
-    while !stack.isEmpty {
-      if let element = stack.pop(), temp = adjacencyList(element) {
-        for node in temp {
-          stack.push(node)
-          result.append(node)
+  
+  typealias InDegree = Int
+  private func calculateInDegreeOfNodes() -> [Node : InDegree] {
+    
+    var inDegrees = [Node : InDegree]()
+    
+    for (node, _) in adjacencyLists {
+      inDegrees[node] = 0
+    }
+    
+    for (_, adjacencyList) in adjacencyLists {
+      for nodeInList in adjacencyList {
+        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
+      }
+    }
+    return inDegrees
+  }
+  
+  private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
+    var result = [source]
+    visited[source] = true
+    
+    if let adjacencyList = adjacencyList(forNode: source) {
+      for nodeInAdjacencyList in adjacencyList {
+        if !(visited[nodeInAdjacencyList] ?? false) {
+          result += (depthFirstSearch(nodeInAdjacencyList, visited: &visited))
         }
       }
     }
     
     return result
   }
-}
-
-
+  
+  public func topologicalSort() -> [Node] {
+    
+    let startNodes = calculateInDegreeOfNodes().filter({(_, indegree) in
+      return indegree == 0
+    }).map({(node, indegree) in
+      return node
+    })
+    
+    var visited = [Node : Bool]()
+    
+    for (node, _) in adjacencyLists {
+      visited[node] = false
+    }
+    
+    var result = [Node]()
+    
+    for startNode in startNodes {
+      result += depthFirstSearch(startNode, visited: &visited)
+    }
+    
+    return result
+  }
+}
\ No newline at end of file
diff --git a/Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj b/Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..2d0ec1b6b
--- /dev/null
+++ b/Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj	
@@ -0,0 +1,260 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		61FB15B41C8D70B7000CEA54 /* TopologicalSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 61FB15B31C8D70B7000CEA54 /* TopologicalSort.swift */; };
+		61FB15BB1C8D70D7000CEA54 /* Graph.swift in Sources */ = {isa = PBXBuildFile; fileRef = 61FB15B91C8D70D7000CEA54 /* Graph.swift */; };
+		61FB15BC1C8D70D7000CEA54 /* Stack.swift in Sources */ = {isa = PBXBuildFile; fileRef = 61FB15BA1C8D70D7000CEA54 /* Stack.swift */; };
+/* End PBXBuildFile section */
+
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+		61FB15B31C8D70B7000CEA54 /* TopologicalSort.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = TopologicalSort.swift; sourceTree = "<group>"; };
+		61FB15B51C8D70B7000CEA54 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		61FB15B91C8D70D7000CEA54 /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Graph.swift; sourceTree = "<group>"; };
+		61FB15BA1C8D70D7000CEA54 /* Stack.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Stack.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		61FB15AD1C8D70B7000CEA54 /* Frameworks */ = {
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+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
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+		61FB15A51C8D709E000CEA54 = {
+			isa = PBXGroup;
+			children = (
+				61FB15B21C8D70B7000CEA54 /* TopologicalSort */,
+				61FB15B11C8D70B7000CEA54 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		61FB15B11C8D70B7000CEA54 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				61FB15B01C8D70B7000CEA54 /* TopologicalSort.xctest */,
+			);
+			name = Products;
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+		};
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+			isa = PBXGroup;
+			children = (
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+				61FB15B51C8D70B7000CEA54 /* Info.plist */,
+			);
+			path = TopologicalSort;
+			sourceTree = "<group>";
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+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
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+			buildPhases = (
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+				61FB15AD1C8D70B7000CEA54 /* Frameworks */,
+				61FB15AE1C8D70B7000CEA54 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = TopologicalSort;
+			productName = TopologicalSort;
+			productReference = 61FB15B01C8D70B7000CEA54 /* TopologicalSort.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		61FB15A61C8D709E000CEA54 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				TargetAttributes = {
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+			buildConfigurationList = 61FB15A91C8D709E000CEA54 /* Build configuration list for PBXProject "TopologicalSort" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
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+			targets = (
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+
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+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		61FB15AC1C8D70B7000CEA54 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				61FB15BB1C8D70D7000CEA54 /* Graph.swift in Sources */,
+				61FB15BC1C8D70D7000CEA54 /* Stack.swift in Sources */,
+				61FB15B41C8D70B7000CEA54 /* TopologicalSort.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		61FB15AA1C8D709E000CEA54 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Debug;
+		};
+		61FB15AB1C8D709E000CEA54 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Release;
+		};
+		61FB15B71C8D70B7000CEA54 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = TopologicalSort/Info.plist;
+				IPHONEOS_DEPLOYMENT_TARGET = 9.2;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alihafizji.TopologicalSort;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = iphoneos;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		61FB15B81C8D70B7000CEA54 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = TopologicalSort/Info.plist;
+				IPHONEOS_DEPLOYMENT_TARGET = 9.2;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alihafizji.TopologicalSort;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = iphoneos;
+				VALIDATE_PRODUCT = YES;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		61FB15A91C8D709E000CEA54 /* Build configuration list for PBXProject "TopologicalSort" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				61FB15AA1C8D709E000CEA54 /* Debug */,
+				61FB15AB1C8D709E000CEA54 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		61FB15B61C8D70B7000CEA54 /* Build configuration list for PBXNativeTarget "TopologicalSort" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				61FB15B71C8D70B7000CEA54 /* Debug */,
+				61FB15B81C8D70B7000CEA54 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 61FB15A61C8D709E000CEA54 /* Project object */;
+}
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/Graph.swift b/Topological Sort/TopologicalSort/TopologicalSort/Graph.swift
new file mode 100644
index 000000000..f30f30241
--- /dev/null
+++ b/Topological Sort/TopologicalSort/TopologicalSort/Graph.swift	
@@ -0,0 +1,93 @@
+
+public class Graph: CustomStringConvertible {
+  
+  public typealias Node = String
+  
+  private var adjacencyLists: [Node : [Node]]
+
+  public init() {
+    adjacencyLists = [Node : [Node]]()
+  }
+  
+  public func addNode(value: Node) -> Node {
+    adjacencyLists[value] = []
+    return value
+  }
+  
+  public func addEdge(fromNode from: Node, toNode to: Node) -> Bool {
+    adjacencyLists[from]?.append(to)
+    return adjacencyLists[from] != nil ? true : false
+  }
+  
+  public var description: String {
+    return adjacencyLists.description
+  }
+  
+  private func adjacencyList(forNode node: Node) -> [Node]? {
+    for (key, adjacencyList) in adjacencyLists {
+      if key == node {
+        return adjacencyList
+      }
+    }
+    return nil
+  }
+}
+
+extension Graph {
+  
+  typealias InDegree = Int
+  private func calculateInDegreeOfNodes() -> [Node : InDegree] {
+    
+    var inDegrees = [Node : InDegree]()
+    
+    for (node, _) in adjacencyLists {
+      inDegrees[node] = 0
+    }
+    
+    for (_, adjacencyList) in adjacencyLists {
+      for nodeInList in adjacencyList {
+        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
+      }
+    }
+    return inDegrees
+  }
+  
+  private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
+    var result = [source]
+    visited[source] = true
+    
+    if let adjacencyList = adjacencyList(forNode: source) {
+      for nodeInAdjacencyList in adjacencyList {
+        if !(visited[nodeInAdjacencyList] ?? false) {
+          result += (depthFirstSearch(nodeInAdjacencyList, visited: &visited))
+        }
+      }
+    }
+    
+    return result
+  }
+  
+  public func topologicalSort() -> [Node] {
+    
+    let startNodes = calculateInDegreeOfNodes().filter({(_, indegree) in
+      return indegree == 0
+    }).map({(node, indegree) in
+      return node
+    })
+
+    var visited = [Node : Bool]()
+    
+    for (node, _) in adjacencyLists {
+      visited[node] = false
+    }
+    
+    var result = [Node]()
+    
+    for startNode in startNodes {
+      result += depthFirstSearch(startNode, visited: &visited)
+    }
+    
+    return result
+  }
+}
+
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/Info.plist b/Topological Sort/TopologicalSort/TopologicalSort/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Topological Sort/TopologicalSort/TopologicalSort/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/Stack.swift b/Topological Sort/TopologicalSort/TopologicalSort/Stack.swift
new file mode 100644
index 000000000..7099e5f55
--- /dev/null
+++ b/Topological Sort/TopologicalSort/TopologicalSort/Stack.swift	
@@ -0,0 +1,39 @@
+import Foundation
+
+public struct Stack<T> {
+  private var array = [T]()
+  
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+  
+  public var count: Int {
+    return array.count
+  }
+  
+  public mutating func push(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func pop() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeLast()
+    }
+  }
+  
+  public func peek() -> T? {
+    return array.last
+  }
+}
+
+extension Stack: SequenceType {
+  public func generate() -> AnyGenerator<T> {
+    var curr = self
+    return anyGenerator {
+      _ -> T? in
+      return curr.pop()
+    }
+  }
+}
\ No newline at end of file
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift b/Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift
new file mode 100644
index 000000000..97436c5d0
--- /dev/null
+++ b/Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift	
@@ -0,0 +1,42 @@
+//
+//  TopologicalSort.swift
+//  TopologicalSort
+//
+//  Created by Kauserali on 07/03/16.
+//
+//
+
+import XCTest
+
+class TopologicalSort: XCTestCase {
+  
+  var graph: Graph!
+  
+  override func setUp() {
+    super.setUp()
+    graph = Graph()
+    
+    let node5 = graph.addNode("5")
+    let node7 = graph.addNode("7")
+    let node3 = graph.addNode("3")
+    let node11 = graph.addNode("11")
+    let node8 = graph.addNode("8")
+    let node2 = graph.addNode("2")
+    let node9 = graph.addNode("9")
+    let node10 = graph.addNode("10")
+    
+    graph.addEdge(fromNode: node5, toNode: node11)
+    graph.addEdge(fromNode: node7, toNode: node11)
+    graph.addEdge(fromNode: node7, toNode: node8)
+    graph.addEdge(fromNode: node3, toNode: node8)
+    graph.addEdge(fromNode: node3, toNode: node10)
+    graph.addEdge(fromNode: node11, toNode: node2)
+    graph.addEdge(fromNode: node11, toNode: node9)
+    graph.addEdge(fromNode: node11, toNode: node10)
+    graph.addEdge(fromNode: node8, toNode: node9)
+  }
+  
+  func testTopologicalSort() {
+    XCTAssertEqual(graph.topologicalSort(), ["3", "8", "9", "10", "7", "11", "2", "5"])
+  }
+}

From 4a512ea97a12d598a56a7b5badce6c7dfa8e59b7 Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 7 Mar 2016 15:49:37 +0530
Subject: [PATCH 0124/1679] Adding readme

---
 Topological Sort/Images/algorithm_example.png | Bin 0 -> 187544 bytes
 Topological Sort/Images/graph_example.png     | Bin 0 -> 114041 bytes
 Topological Sort/README.markdown              |  50 ++++++++++++++++++
 3 files changed, 50 insertions(+)
 create mode 100644 Topological Sort/Images/algorithm_example.png
 create mode 100644 Topological Sort/Images/graph_example.png
 create mode 100644 Topological Sort/README.markdown

diff --git a/Topological Sort/Images/algorithm_example.png b/Topological Sort/Images/algorithm_example.png
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diff --git a/Topological Sort/Images/graph_example.png b/Topological Sort/Images/graph_example.png
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diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
new file mode 100644
index 000000000..12fcd5fc1
--- /dev/null
+++ b/Topological Sort/README.markdown	
@@ -0,0 +1,50 @@
+# Topological Sort
+
+Topological sort is an algorithm aimed at ordering a directed graph such that for each directed edge *uv* from vertex *u* to vertex *v*, *u* comes before *v*.
+
+## Where is this used?
+
+Let's consider that you want to learn all the algorithms present in the swift-algorithm-club, this might seem daunting at first but  we can use topological sort to get things organized.
+
+For e.g. To learn the depth first search algorithm you need to know how a graph is represented. Similarly, to understand how to calculate the length of a binary tree you need to know details of how a tree is traversed. If we were to represent these in the form of a graph it would be as follows:
+
+//add image
+
+If we consider each algorithm to be a node in the graph you'll see dependancies among them i.e. to learn something you might have to know something else first. This is exactly what topological sort is used for, it will sort things out such that you know what to learn first.
+
+## How does it work?
+
+### Step 1: Find all nodes that have in-degree of 0
+
+The in-degree of a node is the number of incoming edges to that node. All nodes that have no incoming edges have an in-degree of 0. These nodes are the starting points for the sort.
+
+If you think about it in the context of the previous example these nodes represent algorithms that don't need anything else to be learnt, hence the sort starts with them.
+
+### Step 2: Use depth first search for traversal
+
+Depth first search is an algorithm that is used to traverse a graph. This algorithm traverses all the child nodes recursively and uses backtracking to find other edges.
+
+To know more about this algorithm please take a look at the explanation here.
+
+### Step 3: Remember all visited nodes
+
+The last step of the sort is to maintain a list of all the nodes that have already been visited.
+
+## Example
+
+Consider the following graph:
+
+*Step 1* Nodes with 0 in-degree: **5, 7, 3**
+*Step 2* Depth first search for each without remembering nodes that have already been visited:
+
+Node 3: 3, 8, 9, 10
+Node 7: 7, 11, 2, 8, 9
+Node 5: 5, 11, 2, 9, 10
+
+*Step 3* Remember nodes already visited in each DFS.
+
+Node 3: 3, 8, 9, 10
+Node 7: 7, 11, 2
+Node 5: 5
+
+The final sorted order is a concatenation of the above three traversals: **3, 8, 9, 10, 7, 11, 2, 5**

From d868a05e319479210a474d01fc434301118b7d21 Mon Sep 17 00:00:00 2001
From: Kauserali <aliHafizji@users.noreply.github.com>
Date: Mon, 7 Mar 2016 15:52:42 +0530
Subject: [PATCH 0125/1679] Update README.markdown

---
 Topological Sort/README.markdown | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index 12fcd5fc1..fb0b2360c 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -8,7 +8,7 @@ Let's consider that you want to learn all the algorithms present in the swift-al
 
 For e.g. To learn the depth first search algorithm you need to know how a graph is represented. Similarly, to understand how to calculate the length of a binary tree you need to know details of how a tree is traversed. If we were to represent these in the form of a graph it would be as follows:
 
-//add image
+![Example](Images/algorithm_example.png)
 
 If we consider each algorithm to be a node in the graph you'll see dependancies among them i.e. to learn something you might have to know something else first. This is exactly what topological sort is used for, it will sort things out such that you know what to learn first.
 
@@ -34,17 +34,23 @@ The last step of the sort is to maintain a list of all the nodes that have alrea
 
 Consider the following graph:
 
+![Graph Example](Images/graph_example.png)
+
 *Step 1* Nodes with 0 in-degree: **5, 7, 3**
 *Step 2* Depth first search for each without remembering nodes that have already been visited:
 
+```
 Node 3: 3, 8, 9, 10
 Node 7: 7, 11, 2, 8, 9
 Node 5: 5, 11, 2, 9, 10
+```
 
 *Step 3* Remember nodes already visited in each DFS.
 
+```
 Node 3: 3, 8, 9, 10
 Node 7: 7, 11, 2
 Node 5: 5
+```
 
 The final sorted order is a concatenation of the above three traversals: **3, 8, 9, 10, 7, 11, 2, 5**

From 5e228b437577a0a92ee0797ff0091f666ee84a1f Mon Sep 17 00:00:00 2001
From: Kauserali <aliHafizji@users.noreply.github.com>
Date: Mon, 7 Mar 2016 15:57:34 +0530
Subject: [PATCH 0126/1679] Update README.markdown

---
 Topological Sort/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index fb0b2360c..4bc7508c8 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -20,15 +20,15 @@ The in-degree of a node is the number of incoming edges to that node. All nodes
 
 If you think about it in the context of the previous example these nodes represent algorithms that don't need anything else to be learnt, hence the sort starts with them.
 
-### Step 2: Use depth first search for traversal
+### Step 2: Depth first search for traversal
 
-Depth first search is an algorithm that is used to traverse a graph. This algorithm traverses all the child nodes recursively and uses backtracking to find other edges.
+Depth first search is an algorithm that is used to traverse a graph. This algorithm traverses all the child nodes recursively and uses backtracking.
 
-To know more about this algorithm please take a look at the explanation here.
+To know more about this algorithm please take a look at the explanation [here](https://github.com/hollance/swift-algorithm-club/tree/master/Depth-First%20Search).
 
 ### Step 3: Remember all visited nodes
 
-The last step of the sort is to maintain a list of all the nodes that have already been visited.
+The last step of the sort is to maintain a list of all the nodes that have been visited. This is to avoid visiting the same node twice.
 
 ## Example
 

From 99907cfc303dde2f4fbd8602b34be7a042be62db Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 8 Mar 2016 20:02:25 +0100
Subject: [PATCH 0127/1679] Additions to topological sort

---
 README.markdown                               |   2 +-
 Topological Sort/Graph.swift                  |  32 ++
 Topological Sort/Images/GraphResult.graffle   | Bin 0 -> 2251 bytes
 Topological Sort/Images/GraphResult.png       | Bin 0 -> 8911 bytes
 .../Images/TopologicalSort.graffle            | Bin 0 -> 2833 bytes
 Topological Sort/Images/TopologicalSort.png   | Bin 0 -> 24083 bytes
 Topological Sort/README.markdown              |  44 ++-
 .../TopologicalSort => }/Stack.swift          |  12 -
 .../TopologicalSort => Tests}/Info.plist      |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 273 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++++
 .../TopologicalSortTests.swift}               |   2 +
 .../Contents.swift                            |   5 +
 .../Sources/Graph.swift                       |  63 +---
 .../Sources/Stack.swift                       |  12 -
 .../Sources/TopologicalSort1.swift}           |  44 +--
 .../Sources/TopologicalSort2.swift            |  41 +++
 .../TopologicalSort.xcodeproj/project.pbxproj | 260 -----------------
 Topological Sort/TopologicalSort1.swift       |  55 ++++
 Topological Sort/TopologicalSort2.swift       |  41 +++
 20 files changed, 542 insertions(+), 400 deletions(-)
 create mode 100644 Topological Sort/Graph.swift
 create mode 100644 Topological Sort/Images/GraphResult.graffle
 create mode 100644 Topological Sort/Images/GraphResult.png
 create mode 100644 Topological Sort/Images/TopologicalSort.graffle
 create mode 100644 Topological Sort/Images/TopologicalSort.png
 rename Topological Sort/{TopologicalSort/TopologicalSort => }/Stack.swift (68%)
 rename Topological Sort/{TopologicalSort/TopologicalSort => Tests}/Info.plist (100%)
 create mode 100644 Topological Sort/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 rename Topological Sort/{TopologicalSort/TopologicalSort/TopologicalSort.swift => Tests/TopologicalSortTests.swift} (92%)
 rename Topological Sort/{TopologicalSort/TopologicalSort/Graph.swift => Topological Sort.playground/Sources/TopologicalSort1.swift} (61%)
 create mode 100644 Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift
 delete mode 100644 Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj
 create mode 100644 Topological Sort/TopologicalSort1.swift
 create mode 100644 Topological Sort/TopologicalSort2.swift

diff --git a/README.markdown b/README.markdown
index ac2dbf9a9..1465626f5 100644
--- a/README.markdown
+++ b/README.markdown
@@ -74,7 +74,7 @@ Special-purpose sorts:
 - Bucket Sort
 - Counting Sort
 - Radix Sort
-- Topological Sort
+- [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
 
diff --git a/Topological Sort/Graph.swift b/Topological Sort/Graph.swift
new file mode 100644
index 000000000..49f4db96a
--- /dev/null
+++ b/Topological Sort/Graph.swift	
@@ -0,0 +1,32 @@
+public class Graph: CustomStringConvertible {
+  public typealias Node = String
+  
+  private(set) public var adjacencyLists: [Node : [Node]]
+
+  public init() {
+    adjacencyLists = [Node : [Node]]()
+  }
+  
+  public func addNode(value: Node) -> Node {
+    adjacencyLists[value] = []
+    return value
+  }
+  
+  public func addEdge(fromNode from: Node, toNode to: Node) -> Bool {
+    adjacencyLists[from]?.append(to)
+    return adjacencyLists[from] != nil ? true : false
+  }
+  
+  public var description: String {
+    return adjacencyLists.description
+  }
+  
+  public func adjacencyList(forNode node: Node) -> [Node]? {
+    for (key, adjacencyList) in adjacencyLists {
+      if key == node {
+        return adjacencyList
+      }
+    }
+    return nil
+  }
+}
diff --git a/Topological Sort/Images/GraphResult.graffle b/Topological Sort/Images/GraphResult.graffle
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diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index 4bc7508c8..045f910b6 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -2,31 +2,39 @@
 
 Topological sort is an algorithm aimed at ordering a directed graph such that for each directed edge *uv* from vertex *u* to vertex *v*, *u* comes before *v*.
 
+In other words, a topological sort places the vertices of a directed acyclic graph on a line so that all directed edges go from left to right. 
+
+The graph in the following example has two possible topological sorts:
+
+![Example](Images/TopologicalSort.png)
+
 ## Where is this used?
 
-Let's consider that you want to learn all the algorithms present in the swift-algorithm-club, this might seem daunting at first but  we can use topological sort to get things organized.
+Let's consider that you want to learn all the algorithms present in the Swift Algorithm Club. This might seem daunting at first but  we can use topological sort to get things organized.
 
-For e.g. To learn the depth first search algorithm you need to know how a graph is represented. Similarly, to understand how to calculate the length of a binary tree you need to know details of how a tree is traversed. If we were to represent these in the form of a graph it would be as follows:
+For example, to learn the [depth-first search](../Depth-First Search/) algorithm you need to know how a [graph](../Graph/) is represented. Similarly, to understand how to calculate the length of a [binary tree](../Binary Tree/) you need to know details of how a [tree is traversed](../Tree/).
+
+If we were to represent these objectives in the form of a graph it would be as follows:
 
 ![Example](Images/algorithm_example.png)
 
-If we consider each algorithm to be a node in the graph you'll see dependancies among them i.e. to learn something you might have to know something else first. This is exactly what topological sort is used for, it will sort things out such that you know what to learn first.
+If we consider each algorithm to be a node in the graph you'll see dependancies among them, i.e. to learn something you might have to know something else first. This is exactly what topological sort is used for -- it will sort things out such that you know what to learn first.
 
 ## How does it work?
 
-### Step 1: Find all nodes that have in-degree of 0
+**Step 1: Find all nodes that have in-degree of 0**
 
-The in-degree of a node is the number of incoming edges to that node. All nodes that have no incoming edges have an in-degree of 0. These nodes are the starting points for the sort.
+The *in-degree* of a node is the number of incoming edges to that node. Nodes that have no incoming edges have an in-degree of 0. These nodes are the starting points for the sort.
 
-If you think about it in the context of the previous example these nodes represent algorithms that don't need anything else to be learnt, hence the sort starts with them.
+If you think about it in the context of the previous example, these nodes represent algorithms that don't have any prerequisites; you don't need to learn anything else first, hence the sort starts with them.
 
-### Step 2: Depth first search for traversal
+**Step 2: Depth-first search for traversal**
 
-Depth first search is an algorithm that is used to traverse a graph. This algorithm traverses all the child nodes recursively and uses backtracking.
+Depth-first search is an algorithm that is used to traverse a graph. This algorithm traverses all the child nodes recursively and uses backtracking.
 
-To know more about this algorithm please take a look at the explanation [here](https://github.com/hollance/swift-algorithm-club/tree/master/Depth-First%20Search).
+To find out more about depth-first search, please take a look at the [detailed explanation](../Depth-First%20Search/).
 
-### Step 3: Remember all visited nodes
+**Step 3: Remember all visited nodes**
 
 The last step of the sort is to maintain a list of all the nodes that have been visited. This is to avoid visiting the same node twice.
 
@@ -36,8 +44,9 @@ Consider the following graph:
 
 ![Graph Example](Images/graph_example.png)
 
-*Step 1* Nodes with 0 in-degree: **5, 7, 3**
-*Step 2* Depth first search for each without remembering nodes that have already been visited:
+**Step 1:** The nodes with 0 in-degree are: **5, 7, 3**
+
+**Step 2:** Depth-first search for each starting node, without remembering nodes that have already been visited:
 
 ```
 Node 3: 3, 8, 9, 10
@@ -45,7 +54,7 @@ Node 7: 7, 11, 2, 8, 9
 Node 5: 5, 11, 2, 9, 10
 ```
 
-*Step 3* Remember nodes already visited in each DFS.
+**Step 3:** Remember nodes already visited in each DFS:
 
 ```
 Node 3: 3, 8, 9, 10
@@ -54,3 +63,12 @@ Node 5: 5
 ```
 
 The final sorted order is a concatenation of the above three traversals: **3, 8, 9, 10, 7, 11, 2, 5**
+
+The result of the topological sort looks like this:
+
+![Result of the sort](Images/GraphResult.png)
+
+TODO: I don't think this is correct! There should be no arrows going from right to left! (A valid topological order would be 3, 7, 5, 10, 8, 11, 9, 2 -- or 3, 7, 5, 8, 11, 2, 9, 10.)
+
+
+*Written for Swift Algorithm Club by Ali Hafizji*
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/Stack.swift b/Topological Sort/Stack.swift
similarity index 68%
rename from Topological Sort/TopologicalSort/TopologicalSort/Stack.swift
rename to Topological Sort/Stack.swift
index 7099e5f55..7f4aadc8b 100644
--- a/Topological Sort/TopologicalSort/TopologicalSort/Stack.swift	
+++ b/Topological Sort/Stack.swift	
@@ -1,5 +1,3 @@
-import Foundation
-
 public struct Stack<T> {
   private var array = [T]()
   
@@ -27,13 +25,3 @@ public struct Stack<T> {
     return array.last
   }
 }
-
-extension Stack: SequenceType {
-  public func generate() -> AnyGenerator<T> {
-    var curr = self
-    return anyGenerator {
-      _ -> T? in
-      return curr.pop()
-    }
-  }
-}
\ No newline at end of file
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/Info.plist b/Topological Sort/Tests/Info.plist
similarity index 100%
rename from Topological Sort/TopologicalSort/TopologicalSort/Info.plist
rename to Topological Sort/Tests/Info.plist
diff --git a/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj b/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..cb32961df
--- /dev/null
+++ b/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,273 @@
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diff --git a/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
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+   version = "1.3">
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+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
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+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
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+      shouldUseLaunchSchemeArgsEnv = "YES"
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diff --git a/Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift b/Topological Sort/Tests/TopologicalSortTests.swift
similarity index 92%
rename from Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift
rename to Topological Sort/Tests/TopologicalSortTests.swift
index 97436c5d0..41e7a854f 100644
--- a/Topological Sort/TopologicalSort/TopologicalSort/TopologicalSort.swift	
+++ b/Topological Sort/Tests/TopologicalSortTests.swift	
@@ -38,5 +38,7 @@ class TopologicalSort: XCTestCase {
   
   func testTopologicalSort() {
     XCTAssertEqual(graph.topologicalSort(), ["3", "8", "9", "10", "7", "11", "2", "5"])
+
+    XCTAssertEqual(graph.topologicalSort2(), ["3", "7", "5", "8", "11", "2", "9", "10"])
   }
 }
diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index 2d6af7e4f..d1a92abbc 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -24,4 +24,9 @@ graph.addEdge(fromNode: node11, toNode: node10)
 graph.addEdge(fromNode: node8, toNode: node9)
 
 
+
+// using depth-first search
 graph.topologicalSort()
+
+// alternative method
+graph.topologicalSort2()
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index 5cf228d65..fca7485e8 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -1,8 +1,7 @@
 public class Graph: CustomStringConvertible {
-  
   public typealias Node = String
   
-  private var adjacencyLists: [Node : [Node]]
+  private(set) public var adjacencyLists: [Node : [Node]]
   
   public init() {
     adjacencyLists = [Node : [Node]]()
@@ -22,7 +21,7 @@ public class Graph: CustomStringConvertible {
     return adjacencyLists.description
   }
   
-  private func adjacencyList(forNode node: Node) -> [Node]? {
+  public func adjacencyList(forNode node: Node) -> [Node]? {
     for (key, adjacencyList) in adjacencyLists {
       if key == node {
         return adjacencyList
@@ -31,61 +30,3 @@ public class Graph: CustomStringConvertible {
     return nil
   }
 }
-
-extension Graph {
-  
-  typealias InDegree = Int
-  private func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    
-    var inDegrees = [Node : InDegree]()
-    
-    for (node, _) in adjacencyLists {
-      inDegrees[node] = 0
-    }
-    
-    for (_, adjacencyList) in adjacencyLists {
-      for nodeInList in adjacencyList {
-        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
-      }
-    }
-    return inDegrees
-  }
-  
-  private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
-    var result = [source]
-    visited[source] = true
-    
-    if let adjacencyList = adjacencyList(forNode: source) {
-      for nodeInAdjacencyList in adjacencyList {
-        if !(visited[nodeInAdjacencyList] ?? false) {
-          result += (depthFirstSearch(nodeInAdjacencyList, visited: &visited))
-        }
-      }
-    }
-    
-    return result
-  }
-  
-  public func topologicalSort() -> [Node] {
-    
-    let startNodes = calculateInDegreeOfNodes().filter({(_, indegree) in
-      return indegree == 0
-    }).map({(node, indegree) in
-      return node
-    })
-    
-    var visited = [Node : Bool]()
-    
-    for (node, _) in adjacencyLists {
-      visited[node] = false
-    }
-    
-    var result = [Node]()
-    
-    for startNode in startNodes {
-      result += depthFirstSearch(startNode, visited: &visited)
-    }
-    
-    return result
-  }
-}
\ No newline at end of file
diff --git a/Topological Sort/Topological Sort.playground/Sources/Stack.swift b/Topological Sort/Topological Sort.playground/Sources/Stack.swift
index 7099e5f55..7f4aadc8b 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Stack.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Stack.swift	
@@ -1,5 +1,3 @@
-import Foundation
-
 public struct Stack<T> {
   private var array = [T]()
   
@@ -27,13 +25,3 @@ public struct Stack<T> {
     return array.last
   }
 }
-
-extension Stack: SequenceType {
-  public func generate() -> AnyGenerator<T> {
-    var curr = self
-    return anyGenerator {
-      _ -> T? in
-      return curr.pop()
-    }
-  }
-}
\ No newline at end of file
diff --git a/Topological Sort/TopologicalSort/TopologicalSort/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
similarity index 61%
rename from Topological Sort/TopologicalSort/TopologicalSort/Graph.swift
rename to Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index f30f30241..011c4164b 100644
--- a/Topological Sort/TopologicalSort/TopologicalSort/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -1,43 +1,7 @@
-
-public class Graph: CustomStringConvertible {
-  
-  public typealias Node = String
-  
-  private var adjacencyLists: [Node : [Node]]
-
-  public init() {
-    adjacencyLists = [Node : [Node]]()
-  }
-  
-  public func addNode(value: Node) -> Node {
-    adjacencyLists[value] = []
-    return value
-  }
-  
-  public func addEdge(fromNode from: Node, toNode to: Node) -> Bool {
-    adjacencyLists[from]?.append(to)
-    return adjacencyLists[from] != nil ? true : false
-  }
-  
-  public var description: String {
-    return adjacencyLists.description
-  }
-  
-  private func adjacencyList(forNode node: Node) -> [Node]? {
-    for (key, adjacencyList) in adjacencyLists {
-      if key == node {
-        return adjacencyList
-      }
-    }
-    return nil
-  }
-}
-
 extension Graph {
-  
   typealias InDegree = Int
-  private func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    
+
+  func calculateInDegreeOfNodes() -> [Node : InDegree] {
     var inDegrees = [Node : InDegree]()
     
     for (node, _) in adjacencyLists {
@@ -63,7 +27,6 @@ extension Graph {
         }
       }
     }
-    
     return result
   }
   
@@ -74,7 +37,7 @@ extension Graph {
     }).map({(node, indegree) in
       return node
     })
-
+    
     var visited = [Node : Bool]()
     
     for (node, _) in adjacencyLists {
@@ -90,4 +53,3 @@ extension Graph {
     return result
   }
 }
-
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift
new file mode 100644
index 000000000..468e098df
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
@@ -0,0 +1,41 @@
+extension Graph {
+  /* Topological sort that does not use a depth-first search. */
+  public func topologicalSort2() -> [Node] {
+    var nodes = calculateInDegreeOfNodes()
+
+    // Find vertices with no predecessors and puts them into a new list.
+    // These are the "leaders". The leaders array eventually becomes the
+    // topologically sorted list.
+    var leaders = nodes.filter({ _, indegree in
+      return indegree == 0
+    }).map({ node, indegree in
+      return node
+    })
+
+    // "Remove" each of the leaders. We do this by decrementing the in-degree
+    // of the nodes they point to. As soon as such a node has itself no more
+    // predecessors, it is added to the leaders array. This repeats until there
+    // are no more vertices left.
+    var l = 0
+    while l < leaders.count {
+      if let edges = adjacencyList(forNode: leaders[l]) {
+        for neighbor in edges {
+          if let count = nodes[neighbor] {
+            nodes[neighbor] = count - 1
+            if count == 1 {             // this leader was the last predecessor
+              leaders.append(neighbor)  // so neighbor is now a leader itself
+            }
+          }
+        }
+      }
+      l += 1
+    }
+
+    // Was there a cycle in the graph?
+    if leaders.count != nodes.count {
+      print("Error: graphs with cycles are not allowed")
+    }
+
+    return leaders
+  }
+}
diff --git a/Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj b/Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj
deleted file mode 100644
index 2d0ec1b6b..000000000
--- a/Topological Sort/TopologicalSort/TopologicalSort.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,260 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
-	classes = {
-	};
-	objectVersion = 46;
-	objects = {
-
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-/* End PBXBuildFile section */
-
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-/* End PBXFileReference section */
-
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-/* End PBXFrameworksBuildPhase section */
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diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
new file mode 100644
index 000000000..500b8ca11
--- /dev/null
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -0,0 +1,55 @@
+extension Graph {
+  typealias InDegree = Int
+
+  func calculateInDegreeOfNodes() -> [Node : InDegree] {
+    var inDegrees = [Node : InDegree]()
+    
+    for (node, _) in adjacencyLists {
+      inDegrees[node] = 0
+    }
+    
+    for (_, adjacencyList) in adjacencyLists {
+      for nodeInList in adjacencyList {
+        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
+      }
+    }
+    return inDegrees
+  }
+  
+  private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
+    var result = [source]
+    visited[source] = true
+    
+    if let adjacencyList = adjacencyList(forNode: source) {
+      for nodeInAdjacencyList in adjacencyList {
+        if !(visited[nodeInAdjacencyList] ?? false) {
+          result += (depthFirstSearch(nodeInAdjacencyList, visited: &visited))
+        }
+      }
+    }
+    return result
+  }
+  
+  public func topologicalSort() -> [Node] {
+    
+    let startNodes = calculateInDegreeOfNodes().filter({(_, indegree) in
+      return indegree == 0
+    }).map({(node, indegree) in
+      return node
+    })
+    
+    var visited = [Node : Bool]()
+    
+    for (node, _) in adjacencyLists {
+      visited[node] = false
+    }
+    
+    var result = [Node]()
+    
+    for startNode in startNodes {
+      result += depthFirstSearch(startNode, visited: &visited)
+    }
+
+    return result
+  }
+}
diff --git a/Topological Sort/TopologicalSort2.swift b/Topological Sort/TopologicalSort2.swift
new file mode 100644
index 000000000..468e098df
--- /dev/null
+++ b/Topological Sort/TopologicalSort2.swift	
@@ -0,0 +1,41 @@
+extension Graph {
+  /* Topological sort that does not use a depth-first search. */
+  public func topologicalSort2() -> [Node] {
+    var nodes = calculateInDegreeOfNodes()
+
+    // Find vertices with no predecessors and puts them into a new list.
+    // These are the "leaders". The leaders array eventually becomes the
+    // topologically sorted list.
+    var leaders = nodes.filter({ _, indegree in
+      return indegree == 0
+    }).map({ node, indegree in
+      return node
+    })
+
+    // "Remove" each of the leaders. We do this by decrementing the in-degree
+    // of the nodes they point to. As soon as such a node has itself no more
+    // predecessors, it is added to the leaders array. This repeats until there
+    // are no more vertices left.
+    var l = 0
+    while l < leaders.count {
+      if let edges = adjacencyList(forNode: leaders[l]) {
+        for neighbor in edges {
+          if let count = nodes[neighbor] {
+            nodes[neighbor] = count - 1
+            if count == 1 {             // this leader was the last predecessor
+              leaders.append(neighbor)  // so neighbor is now a leader itself
+            }
+          }
+        }
+      }
+      l += 1
+    }
+
+    // Was there a cycle in the graph?
+    if leaders.count != nodes.count {
+      print("Error: graphs with cycles are not allowed")
+    }
+
+    return leaders
+  }
+}

From 87802ee1f878ef854ac52059fac97289e16a163f Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Wed, 9 Mar 2016 14:28:41 +0100
Subject: [PATCH 0128/1679] Put Edge and Node into Graph.swift

It's only supporting code so it shouldn't draw too much attention to itself.
---
 .../Contents.swift                            |  4 ++
 .../Contents.swift                            |  7 +++
 .../Contents.swift                            |  5 ++
 .../Sources/Graph.swift                       |  1 -
 Breadth-First Search/Edge.swift               | 11 ----
 Breadth-First Search/Graph.swift              | 52 ++++++++++++++++++-
 Breadth-First Search/Node.swift               | 32 ------------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 18 ++-----
 .../Sources/Graph.swift                       |  1 -
 Depth-First Search/Edge.swift                 | 11 ----
 Depth-First Search/Graph.swift                | 52 ++++++++++++++++++-
 Depth-First Search/Node.swift                 | 32 ------------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  8 ---
 13 files changed, 123 insertions(+), 111 deletions(-)
 delete mode 100644 Breadth-First Search/Edge.swift
 delete mode 100644 Breadth-First Search/Node.swift
 delete mode 100644 Depth-First Search/Edge.swift
 delete mode 100644 Depth-First Search/Node.swift

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 181d566d4..c0868c653 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,7 @@
+//: [Previous](@previous)
+
+//: # Minimum Spanning Tree Example
+
 func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index 28cdc6093..be35cc684 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,7 @@
+//: [Previous](@previous)
+
+//: # Shortest Path Example
+
 func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
@@ -44,3 +48,6 @@ graph.addEdge(nodeE, neighbor: nodeH)
 
 let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
 print(shortestPathGraph.nodes)
+
+//: [Next: Minimum Spanning Tree Example](@next)
+
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index ed655b591..8cd7df2f5 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,5 @@
+//: # Breadth-First Search
+
 func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
@@ -46,3 +48,6 @@ graph.addEdge(nodeE, neighbor: nodeH)
 
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
+
+//: [Next: Shortest Path Example](@next)
+
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
index 181af9e85..e89d4ac97 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -13,7 +13,6 @@ public class Graph : CustomStringConvertible, Equatable {
 
   public func addEdge(source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
-    edge.neighbor = neighbor
     source.neighbors.append(edge)
   }
 
diff --git a/Breadth-First Search/Edge.swift b/Breadth-First Search/Edge.swift
deleted file mode 100644
index 3937a2cc7..000000000
--- a/Breadth-First Search/Edge.swift	
+++ /dev/null
@@ -1,11 +0,0 @@
-public class Edge : Equatable {
-  public var neighbor: Node
-
-  public init(neighbor: Node) {
-    self.neighbor = neighbor
-  }
-}
-
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
-  return lhs.neighbor == rhs.neighbor
-}
diff --git a/Breadth-First Search/Graph.swift b/Breadth-First Search/Graph.swift
index 181af9e85..6f69ee800 100644
--- a/Breadth-First Search/Graph.swift	
+++ b/Breadth-First Search/Graph.swift	
@@ -1,3 +1,54 @@
+// MARK: - Edge
+
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
+
+// MARK: - Node
+
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
+
+// MARK: - Graph
+
 public class Graph : CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
@@ -13,7 +64,6 @@ public class Graph : CustomStringConvertible, Equatable {
 
   public func addEdge(source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
-    edge.neighbor = neighbor
     source.neighbors.append(edge)
   }
 
diff --git a/Breadth-First Search/Node.swift b/Breadth-First Search/Node.swift
deleted file mode 100644
index 000fd78f6..000000000
--- a/Breadth-First Search/Node.swift	
+++ /dev/null
@@ -1,32 +0,0 @@
-public class Node : CustomStringConvertible, Equatable {
-  public var neighbors: [Edge]
-  
-  public private(set) var label: String
-  public var distance: Int?
-  public var visited: Bool
-
-  public init(label: String) {
-    self.label = label
-    neighbors = []
-    visited = false
-  }
-
-  public var description: String {
-    if let distance = distance {
-      return "Node(label: \(label), distance: \(distance))"
-    }
-    return "Node(label: \(label), distance: infinity)"
-  }
-
-  public var hasDistance: Bool {
-    return distance != nil
-  }
-
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
-  }
-}
-
-public func ==(lhs: Node, rhs: Node) -> Bool {
-  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
-}
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 8946ba1a6..061e1be44 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -13,9 +13,7 @@
 		83F9C9691C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */; };
 		83F9C96A1C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */; };
 		83F9C96C1C8443E800B3A87F /* BreadthFirstSearchTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96B1C8443E800B3A87F /* BreadthFirstSearchTests.swift */; };
-		83F9C9711C84449D00B3A87F /* Edge.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96D1C84449D00B3A87F /* Edge.swift */; };
 		83F9C9721C84449D00B3A87F /* Graph.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96E1C84449D00B3A87F /* Graph.swift */; };
-		83F9C9731C84449D00B3A87F /* Node.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96F1C84449D00B3A87F /* Node.swift */; };
 		83F9C9741C84449D00B3A87F /* Queue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9701C84449D00B3A87F /* Queue.swift */; };
 /* End PBXBuildFile section */
 
@@ -28,9 +26,7 @@
 		83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearchMinimumSpanningTree.swift; path = ../BreadthFirstSearchMinimumSpanningTree.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BreadthFirstSearchShortestPath.swift; path = ../BreadthFirstSearchShortestPath.swift; sourceTree = SOURCE_ROOT; };
 		83F9C96B1C8443E800B3A87F /* BreadthFirstSearchTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BreadthFirstSearchTests.swift; sourceTree = SOURCE_ROOT; };
-		83F9C96D1C84449D00B3A87F /* Edge.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Edge.swift; path = ../Edge.swift; sourceTree = SOURCE_ROOT; };
 		83F9C96E1C84449D00B3A87F /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Graph.swift; path = ../Graph.swift; sourceTree = SOURCE_ROOT; };
-		83F9C96F1C84449D00B3A87F /* Node.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Node.swift; path = ../Node.swift; sourceTree = SOURCE_ROOT; };
 		83F9C9701C84449D00B3A87F /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Queue.swift; path = ../Queue.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -64,16 +60,14 @@
 		7B2BBC831C779D720067B71D /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				83F9C96D1C84449D00B3A87F /* Edge.swift */,
-				83F9C96E1C84449D00B3A87F /* Graph.swift */,
-				83F9C96F1C84449D00B3A87F /* Node.swift */,
-				83F9C9701C84449D00B3A87F /* Queue.swift */,
 				83F9C9651C84437C00B3A87F /* BreadthFirstSearch.swift */,
-				83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */,
-				83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */,
 				83F9C96B1C8443E800B3A87F /* BreadthFirstSearchTests.swift */,
-				83AACB431C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift */,
+				83F9C9661C84437C00B3A87F /* BreadthFirstSearchMinimumSpanningTree.swift */,
 				83AACB411C844CED00DDAFC7 /* BreadthFirstSearchMinimumSpanningTreeTests.swift */,
+				83F9C9671C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift */,
+				83AACB431C8456D200DDAFC7 /* BreadthFirstSearchShortestPathTests.swift */,
+				83F9C96E1C84449D00B3A87F /* Graph.swift */,
+				83F9C9701C84449D00B3A87F /* Queue.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
 			name = Tests;
@@ -155,9 +149,7 @@
 				83F9C9681C84437C00B3A87F /* BreadthFirstSearch.swift in Sources */,
 				83F9C9741C84449D00B3A87F /* Queue.swift in Sources */,
 				83F9C96A1C84437C00B3A87F /* BreadthFirstSearchShortestPath.swift in Sources */,
-				83F9C9711C84449D00B3A87F /* Edge.swift in Sources */,
 				83F9C96C1C8443E800B3A87F /* BreadthFirstSearchTests.swift in Sources */,
-				83F9C9731C84449D00B3A87F /* Node.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index 181af9e85..e89d4ac97 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -13,7 +13,6 @@ public class Graph : CustomStringConvertible, Equatable {
 
   public func addEdge(source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
-    edge.neighbor = neighbor
     source.neighbors.append(edge)
   }
 
diff --git a/Depth-First Search/Edge.swift b/Depth-First Search/Edge.swift
deleted file mode 100644
index 3937a2cc7..000000000
--- a/Depth-First Search/Edge.swift	
+++ /dev/null
@@ -1,11 +0,0 @@
-public class Edge : Equatable {
-  public var neighbor: Node
-
-  public init(neighbor: Node) {
-    self.neighbor = neighbor
-  }
-}
-
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
-  return lhs.neighbor == rhs.neighbor
-}
diff --git a/Depth-First Search/Graph.swift b/Depth-First Search/Graph.swift
index 181af9e85..6f69ee800 100644
--- a/Depth-First Search/Graph.swift	
+++ b/Depth-First Search/Graph.swift	
@@ -1,3 +1,54 @@
+// MARK: - Edge
+
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
+
+// MARK: - Node
+
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
+
+// MARK: - Graph
+
 public class Graph : CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
@@ -13,7 +64,6 @@ public class Graph : CustomStringConvertible, Equatable {
 
   public func addEdge(source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
-    edge.neighbor = neighbor
     source.neighbors.append(edge)
   }
 
diff --git a/Depth-First Search/Node.swift b/Depth-First Search/Node.swift
deleted file mode 100644
index 000fd78f6..000000000
--- a/Depth-First Search/Node.swift	
+++ /dev/null
@@ -1,32 +0,0 @@
-public class Node : CustomStringConvertible, Equatable {
-  public var neighbors: [Edge]
-  
-  public private(set) var label: String
-  public var distance: Int?
-  public var visited: Bool
-
-  public init(label: String) {
-    self.label = label
-    neighbors = []
-    visited = false
-  }
-
-  public var description: String {
-    if let distance = distance {
-      return "Node(label: \(label), distance: \(distance))"
-    }
-    return "Node(label: \(label), distance: infinity)"
-  }
-
-  public var hasDistance: Bool {
-    return distance != nil
-  }
-
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
-  }
-}
-
-public func ==(lhs: Node, rhs: Node) -> Bool {
-  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
-}
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index e3c46e3cc..39c15ce79 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -8,9 +8,7 @@
 
 /* Begin PBXBuildFile section */
 		83F9C96C1C8443E800B3A87F /* DepthFirstSearchTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96B1C8443E800B3A87F /* DepthFirstSearchTests.swift */; };
-		83F9C9711C84449D00B3A87F /* Edge.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96D1C84449D00B3A87F /* Edge.swift */; };
 		83F9C9721C84449D00B3A87F /* Graph.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96E1C84449D00B3A87F /* Graph.swift */; };
-		83F9C9731C84449D00B3A87F /* Node.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96F1C84449D00B3A87F /* Node.swift */; };
 		FFC6E11E1C8656D10046BA79 /* DepthFirstSearch.swift in Sources */ = {isa = PBXBuildFile; fileRef = FFC6E11D1C8656D10046BA79 /* DepthFirstSearch.swift */; };
 /* End PBXBuildFile section */
 
@@ -18,9 +16,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		83F9C96B1C8443E800B3A87F /* DepthFirstSearchTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = DepthFirstSearchTests.swift; sourceTree = SOURCE_ROOT; };
-		83F9C96D1C84449D00B3A87F /* Edge.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Edge.swift; path = ../Edge.swift; sourceTree = SOURCE_ROOT; };
 		83F9C96E1C84449D00B3A87F /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Graph.swift; path = ../Graph.swift; sourceTree = SOURCE_ROOT; };
-		83F9C96F1C84449D00B3A87F /* Node.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Node.swift; path = ../Node.swift; sourceTree = SOURCE_ROOT; };
 		FFC6E11D1C8656D10046BA79 /* DepthFirstSearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = DepthFirstSearch.swift; path = ../DepthFirstSearch.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -54,9 +50,7 @@
 		7B2BBC831C779D720067B71D /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				83F9C96D1C84449D00B3A87F /* Edge.swift */,
 				83F9C96E1C84449D00B3A87F /* Graph.swift */,
-				83F9C96F1C84449D00B3A87F /* Node.swift */,
 				83F9C96B1C8443E800B3A87F /* DepthFirstSearchTests.swift */,
 				FFC6E11D1C8656D10046BA79 /* DepthFirstSearch.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
@@ -134,10 +128,8 @@
 			buildActionMask = 2147483647;
 			files = (
 				83F9C9721C84449D00B3A87F /* Graph.swift in Sources */,
-				83F9C9711C84449D00B3A87F /* Edge.swift in Sources */,
 				FFC6E11E1C8656D10046BA79 /* DepthFirstSearch.swift in Sources */,
 				83F9C96C1C8443E800B3A87F /* DepthFirstSearchTests.swift in Sources */,
-				83F9C9731C84449D00B3A87F /* Node.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};

From 619e604e0086cdc4a4752eb7bdac163c776f3b74 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Wed, 9 Mar 2016 14:32:20 +0100
Subject: [PATCH 0129/1679] Add link to @lorentey's repos

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 1465626f5..833d12a54 100644
--- a/README.markdown
+++ b/README.markdown
@@ -200,6 +200,7 @@ The following books are available for free online:
 Other algorithm repositories:
 
 - [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
+- [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
 - [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
 
 ## License

From a6ddf98faa0d68865b6edf0d70308a16055efa4e Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 12 Mar 2016 14:25:21 +0100
Subject: [PATCH 0130/1679] Add explanation of alternative algorithm + more
 tests

---
 README.markdown                               |  2 +-
 Topological Sort/README.markdown              | 15 +++-
 .../Tests/TopologicalSortTests.swift          | 73 ++++++++++++++-----
 3 files changed, 71 insertions(+), 19 deletions(-)

diff --git a/README.markdown b/README.markdown
index 833d12a54..92dfa013f 100644
--- a/README.markdown
+++ b/README.markdown
@@ -74,7 +74,7 @@ Special-purpose sorts:
 - Bucket Sort
 - Counting Sort
 - Radix Sort
-- [Topological Sort](Topological Sort/)
+- [Topological Sort](Topological Sort/) :construction:
 
 Bad sorting algorithms (don't use these!):
 
diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index 045f910b6..58985c908 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -70,5 +70,18 @@ The result of the topological sort looks like this:
 
 TODO: I don't think this is correct! There should be no arrows going from right to left! (A valid topological order would be 3, 7, 5, 10, 8, 11, 9, 2 -- or 3, 7, 5, 8, 11, 2, 9, 10.)
 
+## Alternative algorithm
 
-*Written for Swift Algorithm Club by Ali Hafizji*
+Even though depth-first search is the typical way to perform a topological sort, there is another algorithm that also does the job. 
+
+1. Find out what the in-degree is of every vertex.
+2. Put all the vertices that have no predecessors in a new array called `leaders`. These vertices have in-degree 0 and therefore do not depend on any other vertices.
+3. Go through this list of leaders and remove them one-by-one from the graph. We don't actually modify the graph, we just decrement the in-degree of the vertices they point to. That has the same effect.
+4. Look at the (former) immediate neighbor vertices of each leader. If any of them now have an in-degree of 0, then they no longer have any predecessors themselves. We'll add those vertices to the `leaders` array too.
+5. This repeats until there are no more vertices left to look at. At this point, the `leaders` array contains all the vertices in sorted order.
+
+This is an **O(n + m)** algorithm where **n** is the number of vertices and **m** is the number of edges. You can see the implementation in [TopologicalSort2.swift](TopologicalSort2.swift).
+
+I first read about this algorithm in the Algorithm Alley column in Dr. Dobb's Magazine from May 1993.
+
+*Written for Swift Algorithm Club by Ali Hafizji and Matthijs Hollemans*
diff --git a/Topological Sort/Tests/TopologicalSortTests.swift b/Topological Sort/Tests/TopologicalSortTests.swift
index 41e7a854f..4d4178cfb 100644
--- a/Topological Sort/Tests/TopologicalSortTests.swift	
+++ b/Topological Sort/Tests/TopologicalSortTests.swift	
@@ -1,20 +1,25 @@
-//
-//  TopologicalSort.swift
-//  TopologicalSort
-//
-//  Created by Kauserali on 07/03/16.
-//
-//
-
+import Foundation
 import XCTest
 
+extension Graph {
+  public func loadEdgeList(lines: [String]) {
+    for line in lines {
+      let items = line.componentsSeparatedByString(" ").filter { s in !s.isEmpty }
+      if adjacencyList(forNode: items[0]) == nil {
+        addNode(items[0])
+      }
+      if adjacencyList(forNode: items[1]) == nil {
+        addNode(items[1])
+      }
+      addEdge(fromNode: items[0], toNode: items[1])
+    }
+  }
+}
+
 class TopologicalSort: XCTestCase {
   
-  var graph: Graph!
-  
-  override func setUp() {
-    super.setUp()
-    graph = Graph()
+  func testTopologicalSort() {
+    let graph = Graph()
     
     let node5 = graph.addNode("5")
     let node7 = graph.addNode("7")
@@ -34,11 +39,45 @@ class TopologicalSort: XCTestCase {
     graph.addEdge(fromNode: node11, toNode: node9)
     graph.addEdge(fromNode: node11, toNode: node10)
     graph.addEdge(fromNode: node8, toNode: node9)
-  }
-  
-  func testTopologicalSort() {
-    XCTAssertEqual(graph.topologicalSort(), ["3", "8", "9", "10", "7", "11", "2", "5"])
 
+    XCTAssertEqual(graph.topologicalSort(), ["3", "8", "9", "10", "7", "11", "2", "5"])
     XCTAssertEqual(graph.topologicalSort2(), ["3", "7", "5", "8", "11", "2", "9", "10"])
   }
+
+  func testTopologicalSortEdgeLists() {
+    let p1 = ["A B", "A C", "B C", "B D", "C E", "C F", "E D", "F E", "G A", "G F"]
+    let a1 = ["G", "A", "B", "C", "F", "E", "D"]  // TODO
+    let s1 = ["G", "A", "B", "C", "F", "E", "D"]
+
+    let p2 = ["B C", "C D", "C G", "B F", "D G", "G E", "F G", "F G"]
+    let a2 = ["B", "C", "F", "D", "G", "E"]  // TODO
+    let s2 = ["B", "C", "F", "D", "G", "E"]
+
+    let p3 = ["S V", "S W", "V T", "W T"]
+    let a3 = ["S", "V", "W", "T"]  // TODO
+    let s3 = ["S", "V", "W", "T"]
+
+    let p4 = ["5 11", "7 11", "7 8", "3 8", "3 10", "11 2", "11 9", "11 10", "8 9"]
+    let a4 = ["3", "8", "9", "10", "7", "11", "2", "5"]
+    let s4 = ["3", "7", "5", "8", "11", "2", "9", "10"]
+
+    let data = [
+      (p1, a1, s1),
+      (p2, a2, s2),
+      (p3, a3, s3),
+      (p4, a4, s4),
+    ]
+
+    for d in data {
+      let graph = Graph()
+      graph.loadEdgeList(d.0)
+
+      // TODO: this fails the tests
+      //let sorted1 = graph.topologicalSort()
+      //XCTAssertEqual(sorted1, d.1)
+
+      let sorted2 = graph.topologicalSort2()
+      XCTAssertEqual(sorted2, d.2)
+    }
+  }
 }

From 6a7d25873f9adde1e844e3ad95ae412dd408683a Mon Sep 17 00:00:00 2001
From: Pedro Vereza <pdrvereza@gmail.com>
Date: Wed, 9 Mar 2016 09:45:32 -0300
Subject: [PATCH 0131/1679] Adds playground for Longest Common Subsequence

---
 .../Contents.swift                            | 62 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 .../timeline.xctimeline                       |  6 ++
 3 files changed, 72 insertions(+)
 create mode 100644 Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
 create mode 100644 Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground
 create mode 100644 Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
new file mode 100644
index 000000000..8f49b45fb
--- /dev/null
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -0,0 +1,62 @@
+extension String {
+    func longestCommonSubsequence(other:String) -> String {
+        
+        func lcsLength(other: String) -> [[Int]] {
+            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
+            
+            for (i, selfChar) in self.characters.enumerate() {
+                for (j, otherChar) in other.characters.enumerate() {
+                    if (otherChar == selfChar) {
+                        matrix[i+1][j+1] = (matrix[i][j]) + 1
+                    }
+                    else {
+                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+                    }
+                }
+            }
+            
+            return matrix;
+        }
+        
+        func backtrack(matrix: [[Int]]) -> String {
+            var i = self.characters.count
+            var j = other.characters.count
+            var charInSequence = self.endIndex
+            
+            var lcs = String()
+            
+            while (i >= 1 && j >= 1) {
+                if (matrix[i][j] == matrix[i][j - 1]) {
+                    j = j - 1
+                }
+                else if (matrix[i][j] == matrix[i - 1][j]) {
+                    i = i - 1
+                    charInSequence = charInSequence.predecessor()
+                }
+                else {
+                    i = i - 1
+                    j = j - 1
+                    charInSequence = charInSequence.predecessor()
+                    
+                    lcs.append(self[charInSequence])
+                }
+            }
+            
+            return String(lcs.characters.reverse());
+        }
+        
+        return backtrack(lcsLength(other))
+    }
+}
+
+// Examples
+
+let a = "ABCBX"
+let b = "ABDCAB"
+let c = "KLMK"
+
+a.longestCommonSubsequence(c) //""
+a.longestCommonSubsequence("") //""
+a.longestCommonSubsequence(b) //"ABCB"
+b.longestCommonSubsequence(a) //"ABCB"
+a.longestCommonSubsequence(a) // "ABCBX"
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline b/Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>

From 308d8e040a41817929509d9b73d593742a901c55 Mon Sep 17 00:00:00 2001
From: Pedro Vereza <pdrvereza@gmail.com>
Date: Wed, 9 Mar 2016 21:20:16 -0300
Subject: [PATCH 0132/1679] Adds code with comments

---
 .../LongestCommonSubsequence.swift            | 68 +++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 Longest Common Subsequence/LongestCommonSubsequence.swift

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.swift b/Longest Common Subsequence/LongestCommonSubsequence.swift
new file mode 100644
index 000000000..a6225bb74
--- /dev/null
+++ b/Longest Common Subsequence/LongestCommonSubsequence.swift	
@@ -0,0 +1,68 @@
+extension String {
+    func longestCommonSubsequence(other:String) -> String {
+        
+        // Computes the length of the lcs using dynamic programming
+        // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] indicates the length
+        // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
+        func lcsLength(other: String) -> [[Int]] {
+            
+            //Matrix of size (n+1)x(m+1), algorithm needs first row and first column to be filled with 0
+            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
+            
+            for (i, selfChar) in self.characters.enumerate() {
+                for (j, otherChar) in other.characters.enumerate() {
+                    if (otherChar == selfChar) {
+                        //Common char found, add 1 to highest lcs found so far
+                        matrix[i+1][j+1] = (matrix[i][j]) + 1
+                    }
+                    else {
+                        //Not a match, propagates highest lcs length found so far
+                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+                    }
+                }
+            }
+            
+            //Due to propagation, lcs length is at matrix[n][m]
+            return matrix;
+        }
+        
+        //Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are common to both strings
+        func backtrack(matrix: [[Int]]) -> String {
+            var i = self.characters.count
+            var j = other.characters.count
+            
+            //charInSequence is in sync with i so we can get self[i]
+            var charInSequence = self.endIndex
+            
+            var lcs = String()
+            
+            while (i >= 1 && j >= 1) {
+                //Indicates propagation without change, i.e. no new char was added to lcs
+                if (matrix[i][j] == matrix[i][j - 1]) {
+                    j = j - 1
+                }
+                //Indicates propagation without change, i.e. no new char was added to lcs
+                else if (matrix[i][j] == matrix[i - 1][j]) {
+                    i = i - 1
+                    //As i was subtracted, move back charInSequence
+                    charInSequence = charInSequence.predecessor()
+                }
+                //Value on the left and above are different than current cell. This means 1 was added to lcs length (line 16)
+                else {
+                    i = i - 1
+                    j = j - 1
+                    charInSequence = charInSequence.predecessor()
+                    
+                    lcs.append(self[charInSequence])
+                }
+            }
+            
+            //Due to backtrack, chars were added in reverse order: reverse it back.
+            //Append and reverse is faster than inserting at index 0
+            return String(lcs.characters.reverse());
+        }
+        
+        //Combine dynamic programming approach with backtrack to find the lcs
+        return backtrack(lcsLength(other))
+    }
+}
\ No newline at end of file

From 1a075f3a636d96977c7719d4ec7d5a918cbb3782 Mon Sep 17 00:00:00 2001
From: Pedro Vereza <pdrvereza@gmail.com>
Date: Sat, 12 Mar 2016 17:27:14 -0300
Subject: [PATCH 0133/1679] Adds tests for LCS

---
 .../Tests/LongestCommonSubsquenceTests.swift  |  32 +++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 257 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  90 ++++++
 .../Tests/Tests/Info.plist                    |  24 ++
 4 files changed, 403 insertions(+)
 create mode 100644 Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift
 create mode 100644 Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Longest Common Subsequence/Tests/Tests/Info.plist

diff --git a/Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift b/Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift
new file mode 100644
index 000000000..75859ca1a
--- /dev/null
+++ b/Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift	
@@ -0,0 +1,32 @@
+import Foundation
+import XCTest
+
+class LongestCommonSubsquenceTests: XCTestCase {
+    
+    func testLCSwithSelfIsSelf() {
+        let a = "ABCDE"
+
+        XCTAssertEqual(a, a.longestCommonSubsequence(a))
+    }
+    
+    func testLCSWithEmptyStringIsEmptyString() {
+        let a = "ABCDE"
+
+        XCTAssertEqual("", a.longestCommonSubsequence(""))
+    }
+    
+    func testLCSIsEmptyWhenNoCharMatches() {
+        let a = "ABCDE"
+        let b = "WXYZ"
+
+        XCTAssertEqual("", a.longestCommonSubsequence(b))
+    }
+    
+    func testLCSIsNotCommutative() {
+        let a = "ABCDEF"
+        let b = "XAWDMVBEKD"
+
+        XCTAssertEqual("ADE", a.longestCommonSubsequence(b))
+        XCTAssertEqual("ABD", b.longestCommonSubsequence(a))
+    }
+}
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..39422654f
--- /dev/null
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,257 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		4716C7AF1C93751E00F6C1C0 /* LongestCommonSubsquenceTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 4716C7891C936E0E00F6C1C0 /* LongestCommonSubsquenceTests.swift */; };
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+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		4716C7881C936DDD00F6C1C0 /* LongestCommonSubsequence.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = LongestCommonSubsequence.swift; path = ../../LongestCommonSubsequence.swift; sourceTree = "<group>"; };
+		4716C7891C936E0E00F6C1C0 /* LongestCommonSubsquenceTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = LongestCommonSubsquenceTests.swift; path = ../LongestCommonSubsquenceTests.swift; sourceTree = "<group>"; };
+		4716C7A71C93750500F6C1C0 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		4716C7AB1C93750500F6C1C0 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		4716C7A41C93750500F6C1C0 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		4716C7811C936DCB00F6C1C0 = {
+			isa = PBXGroup;
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+				4716C7A81C93750500F6C1C0 /* Tests */,
+				4716C78F1C93746D00F6C1C0 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		4716C78F1C93746D00F6C1C0 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				4716C7A71C93750500F6C1C0 /* Tests.xctest */,
+			);
+			name = Products;
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+		};
+		4716C7A81C93750500F6C1C0 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				4716C7891C936E0E00F6C1C0 /* LongestCommonSubsquenceTests.swift */,
+				4716C7881C936DDD00F6C1C0 /* LongestCommonSubsequence.swift */,
+				4716C7AB1C93750500F6C1C0 /* Info.plist */,
+			);
+			path = Tests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
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+				4716C7A41C93750500F6C1C0 /* Frameworks */,
+				4716C7A51C93750500F6C1C0 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = Tests;
+			productReference = 4716C7A71C93750500F6C1C0 /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		4716C7821C936DCB00F6C1C0 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				TargetAttributes = {
+					4716C7A61C93750500F6C1C0 = {
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+					};
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+			);
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+
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+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
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+			buildActionMask = 2147483647;
+			files = (
+				4716C7AF1C93751E00F6C1C0 /* LongestCommonSubsquenceTests.swift in Sources */,
+				4716C7B01C93751E00F6C1C0 /* LongestCommonSubsequence.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		4716C7861C936DCB00F6C1C0 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Debug;
+		};
+		4716C7871C936DCB00F6C1C0 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Release;
+		};
+		4716C7AD1C93750500F6C1C0 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.10;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = me.pedrovereza.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		4716C7AE1C93750500F6C1C0 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.10;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = me.pedrovereza.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		4716C7851C936DCB00F6C1C0 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				4716C7861C936DCB00F6C1C0 /* Debug */,
+				4716C7871C936DCB00F6C1C0 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		4716C7AC1C93750500F6C1C0 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				4716C7AD1C93750500F6C1C0 /* Debug */,
+				4716C7AE1C93750500F6C1C0 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 4716C7821C936DCB00F6C1C0 /* Project object */;
+}
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..19caeb2ad
--- /dev/null
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "4716C7A61C93750500F6C1C0"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "4716C7A61C93750500F6C1C0"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "4716C7A61C93750500F6C1C0"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "4716C7A61C93750500F6C1C0"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Longest Common Subsequence/Tests/Tests/Info.plist b/Longest Common Subsequence/Tests/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Longest Common Subsequence/Tests/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>

From 6832500b62dba4676c2beffd3451f00827acd033 Mon Sep 17 00:00:00 2001
From: Pedro Vereza <pdrvereza@gmail.com>
Date: Sat, 12 Mar 2016 17:47:51 -0300
Subject: [PATCH 0134/1679] Adds README for LCS

---
 Longest Common Subsequence/README.markdown | 211 +++++++++++++++++++++
 1 file changed, 211 insertions(+)
 create mode 100644 Longest Common Subsequence/README.markdown

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
new file mode 100644
index 000000000..719135a54
--- /dev/null
+++ b/Longest Common Subsequence/README.markdown	
@@ -0,0 +1,211 @@
+# Longest Common Subsequence
+
+
+The Longest Common Subsequence (LCS) of two strings is the longest sequence of characters that appear in the same order in both strings. Should not be confused with the Longest Common Substring problem, where characters **must** be a substring of both strings (i.e they have to be immediate neighbours).
+
+One way to find what's the LCS of two strings `a` and `b` is using Dynamic Programming and a backtracking strategy. During the explanation, remember that `n` is the length of `a` and `m` the length of `b`.
+
+## Length of LCS - Dynamic Programming 
+
+Dynamic programming is used to determine the length of LCS between all combinations of substrings of `a` and `b`. 
+
+
+```swift
+        // Computes the length of the lcs using dynamic programming
+        // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] indicates the length
+        // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
+        func lcsLength(other: String) -> [[Int]] {
+            
+            //Matrix of size (n+1)x(m+1), algorithm needs first row and first line to be filled with 0
+            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
+            
+            for (i, selfChar) in self.characters.enumerate() {
+                for (j, otherChar) in other.characters.enumerate() {
+                    if (otherChar == selfChar) {
+                        //Common char found, add 1 to highest lcs found so far
+                        matrix[i+1][j+1] = (matrix[i][j]) + 1
+                    }
+                    else {
+                        //Not a match, propagates highest lcs length found so far
+                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+                    }
+                }
+            }
+            
+            //Due to propagation, lcs length is at matrix[n][m]
+            return matrix;
+        }
+```
+
+Given strings `"ABCBX"` and `"ABDCAB"` the output matrix of `lcsLength` is the following:
+
+*First row and column added for easier understanding, actual matrix starts on zeros*
+
+```
+|   | Ø | A | B | D | C | A | B |
+| Ø | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+| A | 0 | 1 | 1 | 1 | 1 | 1 | 1 |  
+| B | 0 | 1 | 2 | 2 | 2 | 2 | 2 |
+| C | 0 | 1 | 2 | 2 | 3 | 3 | 3 |
+| B | 0 | 1 | 2 | 2 | 3 | 3 | 4 |
+| X | 0 | 1 | 2 | 2 | 3 | 3 | 4 |
+```
+
+The content of the matrix indicates that position `(i, j)` contains the length of the LCS between substring `(0, i - 1)` of `a` and substring `(0, j - 1)` of `b`.
+
+Example: `(2, 3)` says that the LCS for `"AB"` and `"ABD"` is 2
+
+
+## Actual LCS - Backtrack
+
+Having the length of every combination makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
+
+Backtrack starts at matrix[n + 1][m + 1] and *walks* up and left (in this priority) looking for changes that do not indicate a simple propagation. If the number on the left and above are different than the number in the current cell, no propagation happened, it means that `(i, j)` indicates a common char between `a` and `b`, so char at `a[i - 1]` and `b[j - 1]` are part of the LCS and should be stored in the returned value (`self[i - 1]` was used in the code but could be `other[j - 1]`).
+
+```
+|   |  Ø|  A|  B|  D|  C|  A|  B|
+| Ø |  0|  0|  0|  0|  0|  0|  0|
+| A |  0|↖ 1|  1|  1|  1|  1|  1|  
+| B |  0|  1|↖ 2|← 2|  2|  2|  2|
+| C |  0|  1|  2|  2|↖ 3|← 3|  3|
+| B |  0|  1|  2|  2|  3|  3|↖ 4|
+| X |  0|  1|  2|  2|  3|  3|↑ 4|
+```
+Each `↖` move indicates a character (in row/column header) that is part of the LCS.
+
+One thing to notice is, as it's running backwards, the LCS is built in reverse order. Before returning, the result is reversed to reflect the actual LCS.
+
+
+
+```swift
+        //Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are common to both strings
+        func backtrack(matrix: [[Int]]) -> String {
+            var i = self.characters.count
+            var j = other.characters.count
+            
+            //charInSequence is in sync with i so we can get self[i]
+            var charInSequence = self.endIndex
+            
+            var lcs = String()
+            
+            while (i >= 1 && j >= 1) {
+                //Indicates propagation without change, i.e. no new char was added to lcs
+                if (matrix[i][j] == matrix[i][j - 1]) {
+                    j = j - 1
+                }
+                //Indicates propagation without change, i.e. no new char was added to lcs
+                else if (matrix[i][j] == matrix[i - 1][j]) {
+                    i = i - 1
+                    //As i was subtracted, move back charInSequence
+                    charInSequence = charInSequence.predecessor()
+                }
+                //Value on the left and above are different than current cell. This means 1 was added to lcs length (line 16)
+                else {
+                    i = i - 1
+                    j = j - 1
+                    charInSequence = charInSequence.predecessor()
+                    
+                    lcs.append(self[charInSequence])
+                }
+            }
+            
+            //Due to backtrack, chars were added in reverse order: reverse it back.
+            //Append and reverse is faster than inserting at index 0
+            return String(lcs.characters.reverse());
+        }
+
+```  
+
+
+
+
+## Putting it all together
+
+
+```swift
+extension String {
+    func longestCommonSubsequence(other:String) -> String {
+        
+        // Computes the same of the lcs using dynamic programming
+        // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] indicates the length
+        // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
+        func lcsLength(other: String) -> [[Int]] {
+            
+            //Matrix of size (n+1)x(m+1), algorithm needs first row and first line to be filled with 0
+            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
+            
+            for (i, selfChar) in self.characters.enumerate() {
+                for (j, otherChar) in other.characters.enumerate() {
+                    if (otherChar == selfChar) {
+                        //Common char found, add 1 to highest lcs found so far
+                        matrix[i+1][j+1] = (matrix[i][j]) + 1
+                    }
+                    else {
+                        //Not a match, propagates highest lcs length found so far
+                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+                    }
+                }
+            }
+            
+            //Due to propagation, lcs length is at matrix[n][m]
+            return matrix;
+        }
+        
+        //Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are common to both strings
+        func backtrack(matrix: [[Int]]) -> String {
+            var i = self.characters.count
+            var j = other.characters.count
+            
+            //charInSequence is in sync with i so we can get self[i]
+            var charInSequence = self.endIndex
+            
+            var lcs = String()
+            
+            while (i >= 1 && j >= 1) {
+                //Indicates propagation without change, i.e. no new char was added to lcs
+                if (matrix[i][j] == matrix[i][j - 1]) {
+                    j = j - 1
+                }
+                //Indicates propagation without change, i.e. no new char was added to lcs
+                else if (matrix[i][j] == matrix[i - 1][j]) {
+                    i = i - 1
+                    //As i was subtracted, move back charInSequence
+                    charInSequence = charInSequence.predecessor()
+                }
+                //Value on the left and above are different than current cell. This means 1 was added to lcs length (line 16)
+                else {
+                    i = i - 1
+                    j = j - 1
+                    charInSequence = charInSequence.predecessor()
+                    
+                    lcs.append(self[charInSequence])
+                }
+            }
+            
+            //Due to backtrack, chars were added in reverse order: reverse it back.
+            //Append and reverse is faster than inserting at index 0
+            return String(lcs.characters.reverse());
+        }
+        
+        //Combine dynamic programming approach with backtrack to find the lcs
+        return backtrack(lcsLength(other))
+    }
+}
+```
+
+**Examples:**
+
+```swift
+let a = "ABCBX"
+let b = "ABDCAB"
+let c = "KLMK"
+
+a.longestCommonSubsequence(c) //""
+a.longestCommonSubsequence("") //""
+a.longestCommonSubsequence(b) //"ABCB"
+b.longestCommonSubsequence(a) //"ABCB"
+a.longestCommonSubsequence(a) // "ABCBX"
+```
+
+
+*Written for Swift Algorithm Club by Pedro Vereza*
\ No newline at end of file

From a5440104ba5008b3105f0f0208bad28b84e95c8e Mon Sep 17 00:00:00 2001
From: Pedro Vereza <pdrvereza@gmail.com>
Date: Sat, 12 Mar 2016 17:49:32 -0300
Subject: [PATCH 0135/1679] Adds LCS tests on travis

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 9a4806998..3a2bcb7b2 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -22,3 +22,4 @@ script:
 - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests

From d344becbfbfb054269148cc23261306c337c246a Mon Sep 17 00:00:00 2001
From: Matteo Piombo <matteo.piombo@fedro.org>
Date: Sun, 13 Mar 2016 10:15:58 +0100
Subject: [PATCH 0136/1679] Introduce Associated Labels to centroids.

This could help showing how to use KMeans as a classifier.

Some changes to KMeans properties and function.
Updated Tests accordingly.
Demo the usage of labels in one small test.
---
 K-Means/KMeans.swift                          | 58 ++++++++++++-------
 K-Means/Tests/KMeansTests.swift               | 45 ++++++++------
 K-Means/Tests/Tests.xcodeproj/project.pbxproj |  2 +-
 3 files changed, 67 insertions(+), 38 deletions(-)

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 9073b7b46..245a93b4a 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -5,21 +5,24 @@
 
 import Foundation
 
-class KMeans {
+class KMeans<Label: Hashable> {
   let numCenters: Int
-  let convergeDist: Double
+  let labels: Array<Label>
+  private(set) var centroids: Array<Vector>
 
-  init(numCenters: Int, convergeDist: Double) {
-    self.numCenters = numCenters
-    self.convergeDist = convergeDist
+  init(labels: Array<Label>) {
+    assert(labels.count > 1, "Exception: KMeans with less than 2 centers.")
+    self.labels = labels
+    self.numCenters = labels.count
+    centroids = []
   }
 
-  private func nearestCenter(x: Vector, centers: [Vector]) -> Int {
+  private func nearestCenterIndex(x: Vector, centers: [Vector]) -> Int {
     var nearestDist = DBL_MAX
     var minIndex = 0
-
-    for (idx, c) in centers.enumerate() {
-      let dist = x.distTo(c)
+    
+    for (idx, center) in centers.enumerate() {
+      let dist = x.distTo(center)
       if dist < nearestDist {
         minIndex = idx
         nearestDist = dist
@@ -28,24 +31,26 @@ class KMeans {
     return minIndex
   }
   
-  func findCenters(points: [Vector]) -> [Vector] {
+  
+  
+  func trainCenters(points: [Vector], convergeDist: Double) {
+    
     var centerMoveDist = 0.0
-    let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
+    let zeroVector = Vector(d: [Double](count: points[0].length, repeatedValue: 0.0))
     
     var kCenters = reservoirSample(points, k: numCenters)
     
     repeat {
-      var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-      var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
-
+      
+      var classification: Array<[Vector]> = Array(count: numCenters, repeatedValue: [])
+      
       for p in points {
-        let c = nearestCenter(p, centers: kCenters)
-        cnts[c] += 1
-        newCenters[c] += p
+        let classIndex = nearestCenterIndex(p, centers: kCenters)
+        classification[classIndex].append(p)
       }
       
-      for idx in 0..<numCenters {
-        newCenters[idx] /= cnts[idx]
+      let newCenters = classification.map { assignedPoints in
+        assignedPoints.reduce(zeroVector, combine: +) / Double(assignedPoints.count)
       }
       
       centerMoveDist = 0.0
@@ -56,7 +61,20 @@ class KMeans {
       kCenters = newCenters
     } while centerMoveDist > convergeDist
 
-    return kCenters
+    centroids = kCenters
+  }
+  
+  func fit(point: Vector) -> Label {
+    assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
+    
+    let centroidIndex = nearestCenterIndex(point, centers: centroids)
+    return labels[centroidIndex]
+  }
+  
+  func fit(points: [Vector]) -> [Label] {
+    assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
+    
+    return points.map(fit)
   }
 }
 
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index 436cab4fe..4f1c18b1a 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,9 +10,10 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
-    var points = [Vector]()
     
-    func genPoints(numPoints:Int, numDimmensions:Int) {
+    func genPoints(numPoints:Int, numDimmensions:Int) -> [Vector] {
+        var points = [Vector]()
+        
         for _ in 0..<numPoints {
             var data = [Double]()
             for _ in 0..<numDimmensions {
@@ -20,45 +21,55 @@ class KMeansTests: XCTestCase {
             }
             points.append(Vector(d: data))
         }
-
+        return points
     }
     
     func testSmall_2D() {
-        genPoints(10, numDimmensions: 2)
-        
+        let points = genPoints(10, numDimmensions: 2)
+
         print("\nCenters")
-        let kmm = KMeans(numCenters: 3, convergeDist: 0.01)
-        for c in kmm.findCenters(points) {
-            print(c)
+        let kmm = KMeans<Character>(labels: ["A", "B", "C"])
+        kmm.trainCenters(points, convergeDist: 0.01)
+        
+        for (label, centroid) in zip(kmm.labels, kmm.centroids) {
+            print("\(label): \(centroid)")
+        }
+        
+        print("\nClassifications")
+        for (label, point) in zip(kmm.fit(points), points) {
+            print("\(label): \(point)")
         }
     }
     
     func testSmall_10D() {
-        genPoints(10, numDimmensions: 10)
+        let points = genPoints(10, numDimmensions: 10)
         
         print("\nCenters")
-        let kmm = KMeans(numCenters: 3, convergeDist: 0.01)
-        for c in kmm.findCenters(points) {
+        let kmm = KMeans<Int>(labels: [1, 2, 3])
+        kmm.trainCenters(points, convergeDist: 0.01)
+        for c in kmm.centroids {
             print(c)
         }
     }
     
     func testLarge_2D() {
-        genPoints(10000, numDimmensions: 2)
+        let points = genPoints(10000, numDimmensions: 2)
         
         print("\nCenters")
-        let kmm = KMeans(numCenters: 5, convergeDist: 0.01)
-        for c in kmm.findCenters(points) {
+        let kmm = KMeans<Character>(labels: ["A","B","C","D","E"])
+        kmm.trainCenters(points, convergeDist: 0.01)
+        for c in kmm.centroids {
             print(c)
         }
     }
     
     func testLarge_10D() {
-        genPoints(10000, numDimmensions: 10)
+        let points = genPoints(10000, numDimmensions: 10)
         
         print("\nCenters")
-        let kmm = KMeans(numCenters: 5, convergeDist: 0.01)
-        for c in kmm.findCenters(points) {
+        let kmm = KMeans<Int>(labels: [1,2,3,4,5])
+        kmm.trainCenters(points, convergeDist: 0.01)
+        for c in kmm.centroids {
             print(c)
         }
     }
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index c70acba0d..084152c1c 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -13,7 +13,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		B80894DB1C852CFA0018730E /* KMeans.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = KMeans.swift; path = ../KMeans.swift; sourceTree = SOURCE_ROOT; };
+		B80894DB1C852CFA0018730E /* KMeans.swift */ = {isa = PBXFileReference; indentWidth = 2; lastKnownFileType = sourcecode.swift; name = KMeans.swift; path = ../KMeans.swift; sourceTree = SOURCE_ROOT; tabWidth = 2; };
 		B80894E01C852D100018730E /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		B80894E31C852D100018730E /* KMeansTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = KMeansTests.swift; sourceTree = SOURCE_ROOT; };
 		B80894E51C852D100018730E /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist; path = Info.plist; sourceTree = "<group>"; };

From 5d207729ddaf26485b53bed37d2655f871053af5 Mon Sep 17 00:00:00 2001
From: Ahmed Onawale <ahmed.onawale@andela.com>
Date: Sun, 13 Mar 2016 17:14:32 +0100
Subject: [PATCH 0137/1679] refactor reverse method of LinedList class to make
 the code more Swift-like, without the forced unwrapping

---
 Linked List/LinkedList.swift | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 9c6382c94..165b54737 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -158,10 +158,10 @@ extension LinkedList: CustomStringConvertible {
 extension LinkedList {
   public func reverse() {
     var node = head
-    while node != nil {
-      swap(&node!.next, &node!.previous)
-      head = node
-      node = node!.previous
+    while let currentNode = node {
+        swap(&currentNode.next, &currentNode.previous)
+        head = currentNode
+        node = currentNode.previous
     }
   }
 }

From cc17adcdc3df89034164ac9066cb78e19bf47379 Mon Sep 17 00:00:00 2001
From: Ahmed Onawale <ahmed.onawale@andela.com>
Date: Sun, 13 Mar 2016 17:15:17 +0100
Subject: [PATCH 0138/1679] refactor README.md file to remove the help
 statement

---
 Linked List/README.markdown | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index d37749acd..53bb7118f 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -465,9 +465,7 @@ This loops through the entire list and simply swaps the `next` and `previous` po
 	 nil <---|        |--->|        |--->|        |--->|        |<--- head
 	         +--------+    +--------+    +--------+    +--------+
 
-You may be wondering why the last statement says `node = node!.previous` to go to the next node instead of `node!.next` like you'd expect, but remember that we just swapped those pointers!
-
-> **Note:** I couldn't find a way to make this code more Swift-like, without the forced unwrapping. Suggestions for improvements are welcome!
+You may be wondering why the last statement says `node = currentNode.previous` to go to the next node instead of `currentNode.next` like you'd expect, but remember that we just swapped those pointers!
 
 Arrays have `map()` and `filter()` functions, and there's no reason why linked lists shouldn't either.
 

From 0723f381e9249c2d58e99e5a180480a1fc824b39 Mon Sep 17 00:00:00 2001
From: Ahmed Onawale <ahmed.onawale@andela.com>
Date: Mon, 14 Mar 2016 01:33:06 +0100
Subject: [PATCH 0139/1679] update readme to include refactored code

---
 Linked List/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 53bb7118f..2ccbe3784 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -449,10 +449,10 @@ How about reversing a list, so that the head becomes the tail and vice versa? Th
 ```swift
   public func reverse() {
     var node = head
-    while node != nil {
-      swap(&node!.next, &node!.previous)
-      head = node
-      node = node!.previous
+    while let currentNode = node {
+      swap(&currentNode.next, &currentNode.previous)
+      head = currentNode
+      node = currentNode.previous
     }
   }
 ```

From da7c065fa62a17bfb97bec9a19de259aa647d12f Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Tue, 15 Mar 2016 14:47:10 -0700
Subject: [PATCH 0140/1679] Created TST and TSTNode class declarations.

---
 TernarySearchTree/TSTNode.swift           | 13 +++++++++++++
 TernarySearchTree/TernarySearchTree.swift | 13 +++++++++++++
 2 files changed, 26 insertions(+)
 create mode 100644 TernarySearchTree/TSTNode.swift
 create mode 100644 TernarySearchTree/TernarySearchTree.swift

diff --git a/TernarySearchTree/TSTNode.swift b/TernarySearchTree/TSTNode.swift
new file mode 100644
index 000000000..b3308ccd6
--- /dev/null
+++ b/TernarySearchTree/TSTNode.swift
@@ -0,0 +1,13 @@
+//
+//  TSTNode.swift
+//  
+//
+//  Created by Siddharth Atre on 3/15/16.
+//
+//
+
+import Foundation
+
+class TSTNode {
+    
+}
\ No newline at end of file
diff --git a/TernarySearchTree/TernarySearchTree.swift b/TernarySearchTree/TernarySearchTree.swift
new file mode 100644
index 000000000..24c0c6844
--- /dev/null
+++ b/TernarySearchTree/TernarySearchTree.swift
@@ -0,0 +1,13 @@
+//
+//  TernarySearchTree.swift
+//  
+//
+//  Created by Siddharth Atre on 3/15/16.
+//
+//
+
+import Foundation
+
+class TernarySearchTree {
+    
+}
\ No newline at end of file

From 6811ab6205c8f359ddc2fa977862991be1cf60b0 Mon Sep 17 00:00:00 2001
From: Matthew Wo <9029537@gmail.com>
Date: Tue, 15 Mar 2016 23:31:36 -0700
Subject: [PATCH 0141/1679] Fixed AVL Tree bug

- Tree rotation was replaced by updating links of the tree structure
- Removed irrelevant test cases

On March 16:
* Fixed indentation to match repo's coding style
---
 AVL Tree/AVLTree.playground/Contents.swift    |  11 +-
 .../AVLTree.playground/Sources/AVLTree.swift  | 380 +++++++++---------
 AVL Tree/AVLTree.swift                        | 380 +++++++++---------
 AVL Tree/Tests/AVLTreeTests.swift             |  22 -
 AVL Tree/Tests/TreeNodeTests.swift            |   2 +-
 5 files changed, 380 insertions(+), 415 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 140ec1292..4b4e1f3e2 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -20,11 +20,8 @@ print(tree.debugDescription)
 
 let node = tree.search(2)   // "two"
 
-let minim = tree.root?.minimum()!  // node 1
-var succ = minim!.successor()!     // node 2
-succ = succ.successor()!           // node 3
-succ = succ.successor()!           // node 4
-succ = succ.successor()!           // node 5
-succ.successor()                   // nil
-
+tree.delete(5)
 tree.delete(2)
+tree.delete(1)
+tree.delete(4)
+tree.delete(3)
\ No newline at end of file
diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index 12befbe92..82ad93a96 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -28,45 +28,49 @@ public class TreeNode<Key: Comparable, Payload> {
   private var key: Key
   private var leftChild: Node?
   private var rightChild: Node?
-  private var parent: Node?
-  private var balance = 0
-  
-  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?) {
+  private var height: Int
+  weak private var parent: Node?
+
+  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
     self.key = key
     self.payload = payload
     self.leftChild = leftChild
     self.rightChild = rightChild
     self.parent = parent
+    self.height = height
+
+    self.leftChild?.parent = self
+    self.rightChild?.parent = self
   }
 
   public convenience init(key: Key, payload: Payload?) {
-    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil)
+    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
   }
 
   public convenience init(key: Key) {
     self.init(key: key, payload: nil)
   }
-  
+
   public var isRoot: Bool {
     return parent == nil
   }
-  
+
   public var isLeaf: Bool {
     return rightChild == nil && leftChild == nil
   }
-  
+
   public var isLeftChild: Bool {
     return parent?.leftChild === self
   }
-  
+
   public var isRightChild: Bool {
     return parent?.rightChild === self
   }
-  
+
   public var hasLeftChild: Bool {
     return leftChild != nil
   }
-  
+
   public var hasRightChild: Bool {
     return rightChild != nil
   }
@@ -74,7 +78,7 @@ public class TreeNode<Key: Comparable, Payload> {
   public var hasAnyChild: Bool {
     return leftChild != nil || rightChild != nil
   }
-  
+
   public var hasBothChildren: Bool {
     return leftChild != nil && rightChild != nil
   }
@@ -87,7 +91,7 @@ public class AVLTree<Key: Comparable, Payload> {
 
   private(set) public var root: Node?
   private(set) public var size = 0
-  
+
   public init() { }
 }
 
@@ -95,27 +99,17 @@ public class AVLTree<Key: Comparable, Payload> {
 
 extension TreeNode {
   public func minimum() -> TreeNode? {
-    var curr: TreeNode? = self
-    while curr != nil && curr!.hasLeftChild {
-      curr = curr!.leftChild
+    if let leftChild = self.leftChild {
+      return leftChild.minimum()
     }
-    return curr
+    return self
   }
-  
-  public func successor() -> Node? {
-    if let right = rightChild {
-      return right.minimum()
-    } else if let parent = parent {
-      if isLeftChild {
-        return parent
-      } else {
-        parent.rightChild = nil
-        let result = parent.successor()
-        parent.rightChild = self
-        return result
-      }
+
+  public func maximum() -> TreeNode? {
+    if let rightChild = self.rightChild {
+      return rightChild.maximum()
     }
-    return nil
+    return self
   }
 }
 
@@ -164,64 +158,168 @@ extension AVLTree {
       if let child = node.leftChild {
         insert(input, payload, child)
       } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node)
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.leftChild = child
-        updateBalance(child)
+        balance(child)
       }
     } else {
       if let child = node.rightChild {
         insert(input, payload, child)
       } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node)
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.rightChild = child
-        updateBalance(child)
+        balance(child)
       }
     }
   }
 }
 
-// MARK: - Deleting items
+// MARK: - Balancing tree
 
-extension TreeNode {
-  private func spliceout(){
-    if isLeaf {
-      if isLeftChild {
-        parent!.leftChild = nil
-      } else if isRightChild {
-        parent!.rightChild = nil
-      }
-    } else if hasAnyChild {
-      if hasLeftChild {
-        parent!.leftChild = leftChild!
+extension AVLTree {
+  private func updateHeightUpwards(node: Node?) {
+    if let node = node {
+      let lHeight = node.leftChild?.height ?? 0
+      let rHeight = node.rightChild?.height ?? 0
+      node.height = max(lHeight, rHeight) + 1
+      updateHeightUpwards(node.parent)
+    }
+  }
+
+  private func lrDifference(node: Node?) -> Int {
+    let lHeight = node?.leftChild?.height ?? 0
+    let rHeight = node?.rightChild?.height ?? 0
+    return lHeight - rHeight
+  }
+
+  private func balance(node: Node?) {
+    guard let node = node else {
+      return
+    }
+
+    updateHeightUpwards(node.leftChild)
+    updateHeightUpwards(node.rightChild)
+
+    var nodes = [Node?](count: 3, repeatedValue: nil)
+    var subtrees = [Node?](count: 4, repeatedValue: nil)
+    let nodeParent = node.parent
+
+    let lrFactor = lrDifference(node)
+    if lrFactor > 1 {
+      // left-left or left-right
+      if (lrDifference(node.leftChild) > 0) {
+        // left-left
+        nodes[0] = node
+        nodes[2] = node.leftChild
+        nodes[1] = nodes[2]?.leftChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[1]?.rightChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
       } else {
-        parent!.rightChild = rightChild!
+        // left-right
+        nodes[0] = node
+        nodes[1] = node.leftChild
+        nodes[2] = nodes[1]?.rightChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
       }
-      leftChild!.parent = parent!
-    } else {
-      if isLeftChild {
-        parent!.leftChild = rightChild!
+    } else if lrFactor < -1 {
+      // right-left or right-right
+      if lrDifference(node.rightChild) < 0 {
+        // right-right
+        nodes[1] = node
+        nodes[2] = node.rightChild
+        nodes[0] = nodes[2]?.rightChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[0]?.leftChild
+        subtrees[3] = nodes[0]?.rightChild
       } else {
-        parent!.rightChild = rightChild!
+        // right-left
+        nodes[1] = node
+        nodes[0] = node.rightChild
+        nodes[2] = nodes[0]?.leftChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
       }
-      rightChild!.parent = parent!
+    } else {
+      // Don't need to balance 'node', go for parent
+      balance(node.parent)
+      return
     }
-  }
 
-  private func replace(key: Key, _ payload: Payload?, _ leftChild: Node?, _ rightChild: Node?) {
-    self.key = key
-    self.payload = payload
-    self.leftChild = leftChild
-    self.rightChild = rightChild
-    
-    if hasLeftChild {
-      self.leftChild!.parent! = self
+    // nodes[2] is always the head
+
+    if node.isRoot {
+      root = nodes[2]
+      root?.parent = nil
+    } else if node.isLeftChild {
+      nodeParent?.leftChild = nodes[2]
+      nodes[2]?.parent = nodeParent
+    } else if node.isRightChild {
+      nodeParent?.rightChild = nodes[2]
+      nodes[2]?.parent = nodeParent
     }
-    if hasRightChild {
-      self.rightChild!.parent! = self
+
+
+    nodes[2]?.leftChild = nodes[1]
+    nodes[1]?.parent = nodes[2]
+    nodes[2]?.rightChild = nodes[0]
+    nodes[0]?.parent = nodes[2]
+
+    nodes[1]?.leftChild = subtrees[0]
+    subtrees[0]?.parent = nodes[1]
+    nodes[1]?.rightChild = subtrees[1]
+    subtrees[1]?.parent = nodes[1]
+
+    nodes[0]?.leftChild = subtrees[2]
+    subtrees[2]?.parent = nodes[0]
+    nodes[0]?.rightChild = subtrees[3]
+    subtrees[3]?.parent = nodes[0]
+
+    updateHeightUpwards(nodes[1])    // Update height from left
+    updateHeightUpwards(nodes[0])    // Update height from right
+
+
+    balance(nodes[2]?.parent)
+  }
+}
+
+// MARK: - Displaying tree
+
+extension AVLTree {
+  private func display(node: Node?, level: Int) {
+    if let node = node {
+      display(node.rightChild, level: level + 1)
+      print("")
+      if node.isRoot {
+        print("Root -> ", terminator: "")
+      }
+      for _ in 0..<level {
+        print("        ", terminator:  "")
+      }
+      print("(\(node.key):\(node.height))", terminator: "")
+      display(node.leftChild, level: level + 1)
     }
   }
+
+  public func display(node: Node) {
+    display(node, level: 0)
+    print("")
+  }
 }
 
+// MARK: - Delete node
+
 extension AVLTree {
   public func delete(key: Key) {
     if size == 1 {
@@ -235,145 +333,43 @@ extension AVLTree {
 
   private func delete(node: Node) {
     if node.isLeaf {
-      if node.isLeftChild {
-        node.parent!.leftChild = nil
-      } else if node.isRightChild {
-        node.parent!.rightChild = nil
-      }
-    } else if node.hasBothChildren {
-      let successor = node.successor()!
-      successor.spliceout()
-      node.key = successor.key
-      node.payload = successor.payload
-
-      if node.hasAnyChild {
-        if node.hasBothChildren {
-          node.balance = max(node.leftChild!.balance, node.rightChild!.balance) + 1
-        } else if node.hasRightChild {
-          node.balance = node.rightChild!.balance + 1
-        } else if node.hasLeftChild {
-          node.balance = node.leftChild!.balance + 1
+      // Just remove and balance up
+      if let parent = node.parent {
+        guard node.isLeftChild || node.isRightChild else {
+          // just in case
+          fatalError("Error: tree is invalid.")
         }
-      }
-    } else if node.hasLeftChild {
-      if node.isLeftChild {
-        node.leftChild!.parent = node.parent
-        node.parent!.leftChild = node.leftChild
-        node.balance = node.leftChild!.balance + 1
-      } else if node.isRightChild {
-        node.leftChild!.parent = node.parent
-        node.parent!.rightChild = node.rightChild
-        node.balance = node.rightChild!.balance + 1
-      } else {
-        node.replace(node.leftChild!.key, node.leftChild!.payload, node.leftChild!.leftChild, node.leftChild!.rightChild)
-      }
-    } else if node.hasRightChild{
-      if node.isRightChild{
-        node.rightChild!.parent = node.parent
-        node.parent!.rightChild = node.rightChild
-        node.balance = node.rightChild!.balance + 1
-      } else if node.isLeftChild{
-        node.rightChild!.parent = node.parent
-        node.parent!.leftChild = node.leftChild
-        node.balance = node.leftChild!.balance + 1
-      } else {
-        node.replace(node.rightChild!.key, node.rightChild!.payload, node.rightChild!.leftChild, node.rightChild!.rightChild)
-      }
-    }
-  }
-}
 
-// MARK: - Balancing the tree
-
-extension AVLTree {
-  private func updateBalance(node: Node) {
-    if node.balance > 1 || node.balance < -1 {
-      rebalance(node)
-
-    } else if let parent = node.parent {
-      if node.isLeftChild {
-        parent.balance += 1
-      } else if node.isRightChild {
-        parent.balance -= 1
-      }
-      if parent.balance != 0 {
-        updateBalance(parent)
-      }
-    }
-  }
- 
-  private func rebalance(node: Node) {
-    if node.balance < 0 {
-      if let child = node.rightChild where child.balance > 0 {
-        rotateRight(child)
-        rotateLeft(node)
+        if node.isLeftChild {
+          parent.leftChild = nil
+        } else if node.isRightChild {
+          parent.rightChild = nil
+        }
       } else {
-        rotateLeft(node)
+        // at root
+        root = nil
       }
-    } else if node.balance > 0 {
-      if let child = node.leftChild where child.balance < 0 {
-        rotateLeft(child)
-        rotateRight(node)
-      } else {
-        rotateRight(node)
+    } else {
+      // Handle stem cases
+      if let replacement = node.leftChild?.maximum() where replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(replacement)
+      } else if let replacement = node.rightChild?.minimum() where replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(replacement)
       }
     }
   }
-
-  private func rotateRight(node: Node) {
-    let newRoot = node.leftChild!
-    node.leftChild = newRoot.rightChild
- 
-    if let child = newRoot.rightChild {
-      child.parent = node
-    }
-
-    newRoot.parent = node.parent
-    
-    if node.isRoot {
-      root = newRoot
-    } else if node.isRightChild {
-      node.parent!.rightChild = newRoot
-    } else if node.isLeftChild {
-      node.parent!.leftChild = newRoot
-    }
-
-    newRoot.rightChild = node
-    node.parent = newRoot
-    node.balance = node.balance + 1 - min(newRoot.balance, 0)
-    newRoot.balance = newRoot.balance + 1 - max(node.balance, 0)
-  }
-  
-  private func rotateLeft(node: Node) {
-    let newRoot = node.rightChild!
-    node.rightChild = newRoot.leftChild
-    
-    if let child = newRoot.leftChild {
-      child.parent = node
-    }
-    
-    newRoot.parent = node.parent
-    
-    if node.isRoot {
-      root = newRoot
-    } else if node.isLeftChild {
-      node.parent!.leftChild = newRoot
-    } else if node.isRightChild {
-      node.parent!.rightChild = newRoot
-    }
-
-    newRoot.leftChild = node
-    node.parent = newRoot
-    node.balance = node.balance + 1 - min(newRoot.balance, 0)
-    newRoot.balance = newRoot.balance + 1 - max(node.balance, 0)
-  }
 }
 
+
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
   public var debugDescription: String {
-    var s = "key: \(key), payload: \(payload), balance: \(balance)"
+    var s = "key: \(key), payload: \(payload), height: \(height)"
     if let parent = parent {
       s += ", parent: \(parent.key)"
     }
@@ -419,4 +415,4 @@ extension AVLTree: CustomStringConvertible {
       return "[]"
     }
   }
-}
+}
\ No newline at end of file
diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index d05cd94bf..82ad93a96 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -28,47 +28,49 @@ public class TreeNode<Key: Comparable, Payload> {
   private var key: Key
   private var leftChild: Node?
   private var rightChild: Node?
+  private var height: Int
   weak private var parent: Node?
-  private var balance = 0
-  
-  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?) {
+
+  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
     self.key = key
     self.payload = payload
     self.leftChild = leftChild
-    self.leftChild?.parent = self
     self.rightChild = rightChild
-    self.rightChild?.parent = self
     self.parent = parent
+    self.height = height
+
+    self.leftChild?.parent = self
+    self.rightChild?.parent = self
   }
 
   public convenience init(key: Key, payload: Payload?) {
-    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil)
+    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
   }
 
   public convenience init(key: Key) {
     self.init(key: key, payload: nil)
   }
-  
+
   public var isRoot: Bool {
     return parent == nil
   }
-  
+
   public var isLeaf: Bool {
     return rightChild == nil && leftChild == nil
   }
-  
+
   public var isLeftChild: Bool {
     return parent?.leftChild === self
   }
-  
+
   public var isRightChild: Bool {
     return parent?.rightChild === self
   }
-  
+
   public var hasLeftChild: Bool {
     return leftChild != nil
   }
-  
+
   public var hasRightChild: Bool {
     return rightChild != nil
   }
@@ -76,7 +78,7 @@ public class TreeNode<Key: Comparable, Payload> {
   public var hasAnyChild: Bool {
     return leftChild != nil || rightChild != nil
   }
-  
+
   public var hasBothChildren: Bool {
     return leftChild != nil && rightChild != nil
   }
@@ -89,7 +91,7 @@ public class AVLTree<Key: Comparable, Payload> {
 
   private(set) public var root: Node?
   private(set) public var size = 0
-  
+
   public init() { }
 }
 
@@ -97,27 +99,17 @@ public class AVLTree<Key: Comparable, Payload> {
 
 extension TreeNode {
   public func minimum() -> TreeNode? {
-    var curr: TreeNode? = self
-    while curr != nil && curr!.hasLeftChild {
-      curr = curr!.leftChild
+    if let leftChild = self.leftChild {
+      return leftChild.minimum()
     }
-    return curr
+    return self
   }
-  
-  public func successor() -> Node? {
-    if let right = rightChild {
-      return right.minimum()
-    } else if let parent = parent {
-      if isLeftChild {
-        return parent
-      } else {
-        parent.rightChild = nil
-        let result = parent.successor()
-        parent.rightChild = self
-        return result
-      }
+
+  public func maximum() -> TreeNode? {
+    if let rightChild = self.rightChild {
+      return rightChild.maximum()
     }
-    return nil
+    return self
   }
 }
 
@@ -166,64 +158,168 @@ extension AVLTree {
       if let child = node.leftChild {
         insert(input, payload, child)
       } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node)
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.leftChild = child
-        updateBalance(child)
+        balance(child)
       }
     } else {
       if let child = node.rightChild {
         insert(input, payload, child)
       } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node)
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.rightChild = child
-        updateBalance(child)
+        balance(child)
       }
     }
   }
 }
 
-// MARK: - Deleting items
+// MARK: - Balancing tree
 
-extension TreeNode {
-  private func spliceout(){
-    if isLeaf {
-      if isLeftChild {
-        parent!.leftChild = nil
-      } else if isRightChild {
-        parent!.rightChild = nil
-      }
-    } else if hasAnyChild {
-      if hasLeftChild {
-        parent!.leftChild = leftChild!
+extension AVLTree {
+  private func updateHeightUpwards(node: Node?) {
+    if let node = node {
+      let lHeight = node.leftChild?.height ?? 0
+      let rHeight = node.rightChild?.height ?? 0
+      node.height = max(lHeight, rHeight) + 1
+      updateHeightUpwards(node.parent)
+    }
+  }
+
+  private func lrDifference(node: Node?) -> Int {
+    let lHeight = node?.leftChild?.height ?? 0
+    let rHeight = node?.rightChild?.height ?? 0
+    return lHeight - rHeight
+  }
+
+  private func balance(node: Node?) {
+    guard let node = node else {
+      return
+    }
+
+    updateHeightUpwards(node.leftChild)
+    updateHeightUpwards(node.rightChild)
+
+    var nodes = [Node?](count: 3, repeatedValue: nil)
+    var subtrees = [Node?](count: 4, repeatedValue: nil)
+    let nodeParent = node.parent
+
+    let lrFactor = lrDifference(node)
+    if lrFactor > 1 {
+      // left-left or left-right
+      if (lrDifference(node.leftChild) > 0) {
+        // left-left
+        nodes[0] = node
+        nodes[2] = node.leftChild
+        nodes[1] = nodes[2]?.leftChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[1]?.rightChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
       } else {
-        parent!.rightChild = rightChild!
+        // left-right
+        nodes[0] = node
+        nodes[1] = node.leftChild
+        nodes[2] = nodes[1]?.rightChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
       }
-      leftChild!.parent = parent!
-    } else {
-      if isLeftChild {
-        parent!.leftChild = rightChild!
+    } else if lrFactor < -1 {
+      // right-left or right-right
+      if lrDifference(node.rightChild) < 0 {
+        // right-right
+        nodes[1] = node
+        nodes[2] = node.rightChild
+        nodes[0] = nodes[2]?.rightChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[0]?.leftChild
+        subtrees[3] = nodes[0]?.rightChild
       } else {
-        parent!.rightChild = rightChild!
+        // right-left
+        nodes[1] = node
+        nodes[0] = node.rightChild
+        nodes[2] = nodes[0]?.leftChild
+
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
       }
-      rightChild!.parent = parent!
+    } else {
+      // Don't need to balance 'node', go for parent
+      balance(node.parent)
+      return
     }
-  }
 
-  private func replace(key: Key, _ payload: Payload?, _ leftChild: Node?, _ rightChild: Node?) {
-    self.key = key
-    self.payload = payload
-    self.leftChild = leftChild
-    self.rightChild = rightChild
-    
-    if hasLeftChild {
-      self.leftChild!.parent! = self
+    // nodes[2] is always the head
+
+    if node.isRoot {
+      root = nodes[2]
+      root?.parent = nil
+    } else if node.isLeftChild {
+      nodeParent?.leftChild = nodes[2]
+      nodes[2]?.parent = nodeParent
+    } else if node.isRightChild {
+      nodeParent?.rightChild = nodes[2]
+      nodes[2]?.parent = nodeParent
     }
-    if hasRightChild {
-      self.rightChild!.parent! = self
+
+
+    nodes[2]?.leftChild = nodes[1]
+    nodes[1]?.parent = nodes[2]
+    nodes[2]?.rightChild = nodes[0]
+    nodes[0]?.parent = nodes[2]
+
+    nodes[1]?.leftChild = subtrees[0]
+    subtrees[0]?.parent = nodes[1]
+    nodes[1]?.rightChild = subtrees[1]
+    subtrees[1]?.parent = nodes[1]
+
+    nodes[0]?.leftChild = subtrees[2]
+    subtrees[2]?.parent = nodes[0]
+    nodes[0]?.rightChild = subtrees[3]
+    subtrees[3]?.parent = nodes[0]
+
+    updateHeightUpwards(nodes[1])    // Update height from left
+    updateHeightUpwards(nodes[0])    // Update height from right
+
+
+    balance(nodes[2]?.parent)
+  }
+}
+
+// MARK: - Displaying tree
+
+extension AVLTree {
+  private func display(node: Node?, level: Int) {
+    if let node = node {
+      display(node.rightChild, level: level + 1)
+      print("")
+      if node.isRoot {
+        print("Root -> ", terminator: "")
+      }
+      for _ in 0..<level {
+        print("        ", terminator:  "")
+      }
+      print("(\(node.key):\(node.height))", terminator: "")
+      display(node.leftChild, level: level + 1)
     }
   }
+
+  public func display(node: Node) {
+    display(node, level: 0)
+    print("")
+  }
 }
 
+// MARK: - Delete node
+
 extension AVLTree {
   public func delete(key: Key) {
     if size == 1 {
@@ -237,145 +333,43 @@ extension AVLTree {
 
   private func delete(node: Node) {
     if node.isLeaf {
-      if node.isLeftChild {
-        node.parent!.leftChild = nil
-      } else if node.isRightChild {
-        node.parent!.rightChild = nil
-      }
-    } else if node.hasBothChildren {
-      let successor = node.successor()!
-      successor.spliceout()
-      node.key = successor.key
-      node.payload = successor.payload
-
-      if node.hasAnyChild {
-        if node.hasBothChildren {
-          node.balance = max(node.leftChild!.balance, node.rightChild!.balance) + 1
-        } else if node.hasRightChild {
-          node.balance = node.rightChild!.balance + 1
-        } else if node.hasLeftChild {
-          node.balance = node.leftChild!.balance + 1
+      // Just remove and balance up
+      if let parent = node.parent {
+        guard node.isLeftChild || node.isRightChild else {
+          // just in case
+          fatalError("Error: tree is invalid.")
         }
-      }
-    } else if node.hasLeftChild {
-      if node.isLeftChild {
-        node.leftChild!.parent = node.parent
-        node.parent!.leftChild = node.leftChild
-        node.balance = node.leftChild!.balance + 1
-      } else if node.isRightChild {
-        node.leftChild!.parent = node.parent
-        node.parent!.rightChild = node.rightChild
-        node.balance = node.rightChild!.balance + 1
-      } else {
-        node.replace(node.leftChild!.key, node.leftChild!.payload, node.leftChild!.leftChild, node.leftChild!.rightChild)
-      }
-    } else if node.hasRightChild{
-      if node.isRightChild{
-        node.rightChild!.parent = node.parent
-        node.parent!.rightChild = node.rightChild
-        node.balance = node.rightChild!.balance + 1
-      } else if node.isLeftChild{
-        node.rightChild!.parent = node.parent
-        node.parent!.leftChild = node.leftChild
-        node.balance = node.leftChild!.balance + 1
-      } else {
-        node.replace(node.rightChild!.key, node.rightChild!.payload, node.rightChild!.leftChild, node.rightChild!.rightChild)
-      }
-    }
-  }
-}
-
-// MARK: - Balancing the tree
 
-extension AVLTree {
-  private func updateBalance(node: Node) {
-    if node.balance > 1 || node.balance < -1 {
-      rebalance(node)
-
-    } else if let parent = node.parent {
-      if node.isLeftChild {
-        parent.balance += 1
-      } else if node.isRightChild {
-        parent.balance -= 1
-      }
-      if parent.balance != 0 {
-        updateBalance(parent)
-      }
-    }
-  }
- 
-  private func rebalance(node: Node) {
-    if node.balance < 0 {
-      if let child = node.rightChild where child.balance > 0 {
-        rotateRight(child)
-        rotateLeft(node)
+        if node.isLeftChild {
+          parent.leftChild = nil
+        } else if node.isRightChild {
+          parent.rightChild = nil
+        }
       } else {
-        rotateLeft(node)
+        // at root
+        root = nil
       }
-    } else if node.balance > 0 {
-      if let child = node.leftChild where child.balance < 0 {
-        rotateLeft(child)
-        rotateRight(node)
-      } else {
-        rotateRight(node)
+    } else {
+      // Handle stem cases
+      if let replacement = node.leftChild?.maximum() where replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(replacement)
+      } else if let replacement = node.rightChild?.minimum() where replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(replacement)
       }
     }
   }
-
-  private func rotateRight(node: Node) {
-    let newRoot = node.leftChild!
-    node.leftChild = newRoot.rightChild
- 
-    if let child = newRoot.rightChild {
-      child.parent = node
-    }
-
-    newRoot.parent = node.parent
-    
-    if node.isRoot {
-      root = newRoot
-    } else if node.isRightChild {
-      node.parent!.rightChild = newRoot
-    } else if node.isLeftChild {
-      node.parent!.leftChild = newRoot
-    }
-
-    newRoot.rightChild = node
-    node.parent = newRoot
-    node.balance = node.balance + 1 - min(newRoot.balance, 0)
-    newRoot.balance = newRoot.balance + 1 - max(node.balance, 0)
-  }
-  
-  private func rotateLeft(node: Node) {
-    let newRoot = node.rightChild!
-    node.rightChild = newRoot.leftChild
-    
-    if let child = newRoot.leftChild {
-      child.parent = node
-    }
-    
-    newRoot.parent = node.parent
-    
-    if node.isRoot {
-      root = newRoot
-    } else if node.isLeftChild {
-      node.parent!.leftChild = newRoot
-    } else if node.isRightChild {
-      node.parent!.rightChild = newRoot
-    }
-
-    newRoot.leftChild = node
-    node.parent = newRoot
-    node.balance = node.balance + 1 - min(newRoot.balance, 0)
-    newRoot.balance = newRoot.balance + 1 - max(node.balance, 0)
-  }
 }
 
+
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
   public var debugDescription: String {
-    var s = "key: \(key), payload: \(payload), balance: \(balance)"
+    var s = "key: \(key), payload: \(payload), height: \(height)"
     if let parent = parent {
       s += ", parent: \(parent.key)"
     }
@@ -421,4 +415,4 @@ extension AVLTree: CustomStringConvertible {
       return "[]"
     }
   }
-}
+}
\ No newline at end of file
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index d631c7688..a981726b8 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -83,28 +83,6 @@ class AVLTreeTests: XCTestCase {
         XCTAssertEqual(min?.payload,treeNode.payload)
     }
     
-    func testSuccessorOfRoot() {
-        self.tree?.autopopulateWithNodes(10)
-        let successor = self.tree?.root?.successor()
-        XCTAssertNotNil(successor, "Succesor of root, non-empty tree, not found")
-    }
-    
-    func testSuccessorOfMinimum() {
-        self.tree?.autopopulateWithNodes(10)
-        
-        let minimum = self.tree?.root?.minimum()
-        XCTAssertNotNil(minimum, "Minimum should exist here")
-        
-        let successor = minimum!.successor()
-        XCTAssertNotNil(successor, "Succesor of minimum, non-empty tree, not found")
-    }
-    
-    func testSuccessorSingleNode() {
-        let singleNode = TreeNode(key: 1, payload: "A")
-        let successor = singleNode.successor()
-        XCTAssertNil(successor, "Empty node should not have succesor")
-    }
-    
     func testDeleteExistentKey() {
         self.tree?.delete(1)
         XCTAssertNil(self.tree?.search(1), "Key should not exist anymore")
diff --git a/AVL Tree/Tests/TreeNodeTests.swift b/AVL Tree/Tests/TreeNodeTests.swift
index d55c4e5e2..c15721655 100644
--- a/AVL Tree/Tests/TreeNodeTests.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -19,7 +19,7 @@ class TreeNodeTests: XCTestCase {
 
         left = TreeNode<String,String>(key: "Name", payload: "Left")
         right = TreeNode<String,String>(key: "Name", payload: "Right")
-        root = TreeNode<String,String>(key: "Name", payload: "Root", leftChild: left, rightChild: right, parent: nil)
+        root = TreeNode<String,String>(key: "Name", payload: "Root", leftChild: left, rightChild: right, parent: nil, height: 0)
     }
     
     override func tearDown() {

From 33a4df1c6c9ebb82fbf63a68910f8e3eb2abb7c0 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 11:42:30 -0700
Subject: [PATCH 0142/1679] Created class template for Ternary Search Tree.

---
 TernarySearchTree/TernarySearchTree.swift | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/TernarySearchTree/TernarySearchTree.swift b/TernarySearchTree/TernarySearchTree.swift
index 24c0c6844..79a5e7ac3 100644
--- a/TernarySearchTree/TernarySearchTree.swift
+++ b/TernarySearchTree/TernarySearchTree.swift
@@ -10,4 +10,18 @@ import Foundation
 
 class TernarySearchTree {
     
+    init() {}
+    
+    //MARK: - Insertion
+    func insert(data:String) -> Bool{
+        
+    }
+    
+    private func insertNode(aNode: TSTNode, data: String, charIndex: Int) -> Bool {
+        
+    }
+    
+    //MARK: - Finding
+    
+    
 }
\ No newline at end of file

From 58fd2b1721f0e3c9eee5fa807fe77c1c4886f6ef Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 11:43:58 -0700
Subject: [PATCH 0143/1679] Created README file for TST.

---
 TernarySearchTree/README.markdown | 3 +++
 1 file changed, 3 insertions(+)
 create mode 100644 TernarySearchTree/README.markdown

diff --git a/TernarySearchTree/README.markdown b/TernarySearchTree/README.markdown
new file mode 100644
index 000000000..a6d571d7c
--- /dev/null
+++ b/TernarySearchTree/README.markdown
@@ -0,0 +1,3 @@
+# Ternary Search Tree
+
+Work in progress. Coming soon.
\ No newline at end of file

From 64fcfcd0769276104ccc2cfa471f132886ac13f6 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 11:45:36 -0700
Subject: [PATCH 0144/1679] Renamed folder to include spaces.

---
 {TernarySearchTree => Ternary Search Tree}/README.markdown        | 0
 {TernarySearchTree => Ternary Search Tree}/TSTNode.swift          | 0
 .../TernarySearchTree.swift                                       | 0
 3 files changed, 0 insertions(+), 0 deletions(-)
 rename {TernarySearchTree => Ternary Search Tree}/README.markdown (100%)
 rename {TernarySearchTree => Ternary Search Tree}/TSTNode.swift (100%)
 rename {TernarySearchTree => Ternary Search Tree}/TernarySearchTree.swift (100%)

diff --git a/TernarySearchTree/README.markdown b/Ternary Search Tree/README.markdown
similarity index 100%
rename from TernarySearchTree/README.markdown
rename to Ternary Search Tree/README.markdown
diff --git a/TernarySearchTree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
similarity index 100%
rename from TernarySearchTree/TSTNode.swift
rename to Ternary Search Tree/TSTNode.swift
diff --git a/TernarySearchTree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
similarity index 100%
rename from TernarySearchTree/TernarySearchTree.swift
rename to Ternary Search Tree/TernarySearchTree.swift

From ef914bee2bd3b6d25888afb73604332f6c2a91b7 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 11:58:14 -0700
Subject: [PATCH 0145/1679] Made initializers for TSTNode

---
 Ternary Search Tree/TSTNode.swift | 17 ++++++++++++++++-
 1 file changed, 16 insertions(+), 1 deletion(-)

diff --git a/Ternary Search Tree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
index b3308ccd6..c5e3ca9fc 100644
--- a/Ternary Search Tree/TSTNode.swift	
+++ b/Ternary Search Tree/TSTNode.swift	
@@ -8,6 +8,21 @@
 
 import Foundation
 
-class TSTNode {
+class TSTNode<Element> {
+    var key: String
+    var data: Element?
+    var isKey: Bool
+    
+    init(key: String, data: Element?) {
+        self.key = key
+        self.data = data
+        self.isKey = (data != nil)
+    }
+    
+    init(key:String) {
+        self.key = key
+        self.data = nil
+        self.isKey = false
+    }
     
 }
\ No newline at end of file

From 8045d8da2b31c4b5bf438de58d5661ccf5cac8da Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 11:59:40 -0700
Subject: [PATCH 0146/1679] Added variables for children

---
 Ternary Search Tree/TSTNode.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Ternary Search Tree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
index c5e3ca9fc..f4a6974a5 100644
--- a/Ternary Search Tree/TSTNode.swift	
+++ b/Ternary Search Tree/TSTNode.swift	
@@ -9,10 +9,15 @@
 import Foundation
 
 class TSTNode<Element> {
+    //Member properties of a particular node.
     var key: String
     var data: Element?
     var isKey: Bool
     
+    //Children
+    var left: TSTNode?, right: TSTNode?, middle: TSTNode?
+    
+    
     init(key: String, data: Element?) {
         self.key = key
         self.data = data

From c4e1b1a64cd7dc2ba2645aca76e89e4f25427007 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:03:08 -0700
Subject: [PATCH 0147/1679] Updated tree to use generics

---
 Ternary Search Tree/TernarySearchTree.swift | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 79a5e7ac3..3c8374a2e 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -8,16 +8,19 @@
 
 import Foundation
 
-class TernarySearchTree {
+class TernarySearchTree<Element> {
+    
+    var root: TSTNode?
     
     init() {}
     
     //MARK: - Insertion
-    func insert(data:String) -> Bool{
+    func insert(data:Element, withKey key: String) -> Bool{
+        
         
     }
     
-    private func insertNode(aNode: TSTNode, data: String, charIndex: Int) -> Bool {
+    private func insertNode(aNode: TSTNode<Element>, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
         
     }
     

From 79113d99e4187641c9715d3b91911fa4fccb7b5a Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:08:26 -0700
Subject: [PATCH 0148/1679] Changed key variable to be of type Character

---
 Ternary Search Tree/TSTNode.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Ternary Search Tree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
index f4a6974a5..520f18946 100644
--- a/Ternary Search Tree/TSTNode.swift	
+++ b/Ternary Search Tree/TSTNode.swift	
@@ -10,7 +10,7 @@ import Foundation
 
 class TSTNode<Element> {
     //Member properties of a particular node.
-    var key: String
+    var key: Character
     var data: Element?
     var isKey: Bool
     
@@ -18,13 +18,13 @@ class TSTNode<Element> {
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
     
     
-    init(key: String, data: Element?) {
+    init(key: Character, data: Element?) {
         self.key = key
         self.data = data
         self.isKey = (data != nil)
     }
     
-    init(key:String) {
+    init(key:Character) {
         self.key = key
         self.data = nil
         self.isKey = false

From c3cde70bbf170bac8eac4369b63e494d165ffc1b Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:25:06 -0700
Subject: [PATCH 0149/1679] Renamed isKey variable to hasData

---
 Ternary Search Tree/TSTNode.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Ternary Search Tree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
index 520f18946..b6030400f 100644
--- a/Ternary Search Tree/TSTNode.swift	
+++ b/Ternary Search Tree/TSTNode.swift	
@@ -12,7 +12,7 @@ class TSTNode<Element> {
     //Member properties of a particular node.
     var key: Character
     var data: Element?
-    var isKey: Bool
+    var hasData: Bool
     
     //Children
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
@@ -21,13 +21,13 @@ class TSTNode<Element> {
     init(key: Character, data: Element?) {
         self.key = key
         self.data = data
-        self.isKey = (data != nil)
+        self.hasData = (data != nil)
     }
     
     init(key:Character) {
         self.key = key
         self.data = nil
-        self.isKey = false
+        self.hasData = false
     }
     
 }
\ No newline at end of file

From bf86737ac5d8f97b63ef5415c0f47c7cfb831a48 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:41:50 -0700
Subject: [PATCH 0150/1679] Fixed recursive insert to use inout parameter

---
 Ternary Search Tree/TernarySearchTree.swift | 44 ++++++++++++++++++---
 1 file changed, 39 insertions(+), 5 deletions(-)

diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 3c8374a2e..dcb96552d 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -8,23 +8,57 @@
 
 import Foundation
 
+
 class TernarySearchTree<Element> {
     
-    var root: TSTNode?
+    var root: TSTNode<Element>?
     
     init() {}
     
     //MARK: - Insertion
+    
     func insert(data:Element, withKey key: String) -> Bool{
-        
+        return insertNode(&root, withData: data, andKey: key, atIndex: 0)
         
     }
     
-    private func insertNode(aNode: TSTNode<Element>, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
+    private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
+        
+        //sanity check.
+        if(key.characters.count == 0) {
+            return false
+        }
         
+        //create a new node if necessary.
+        if(aNode == nil) {
+            let index = key.startIndex.advancedBy(charIndex)
+            aNode = TSTNode<Element>(key: key[index])
+        }
+        
+        //if current char is less than the current node's char, go left
+        let index = key.startIndex.advancedBy(charIndex)
+        if(key[index] < aNode!.key) {
+            return insertNode(&aNode!.left, withData: data, andKey: key, atIndex: charIndex)
+        }
+            //if it's greater, go right.
+        else if(key[index] > aNode!.key) {
+            return insertNode(&aNode!.right, withData: data, andKey: key, atIndex: charIndex)
+        }
+            //current char is equal to the current nodes, go middle
+        else {
+            //continue down the middle.
+            if(charIndex + 1 < key.characters.count) {
+                return insertNode(&aNode!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
+            }
+                //otherwise, all done.
+            else {
+                aNode!.data = data
+                aNode?.hasData = true
+                return true
+            }
+        }
     }
     
-    //MARK: - Finding
-    
     
+    //MARK: - Finding
 }
\ No newline at end of file

From 834aeb0449def43b4ebab6b22d483c7964c62ddd Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:43:45 -0700
Subject: [PATCH 0151/1679] implemented recursive find.

---
 Ternary Search Tree/TernarySearchTree.swift | 33 +++++++++++++++++++++
 1 file changed, 33 insertions(+)

diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index dcb96552d..ab5c0faba 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -61,4 +61,37 @@ class TernarySearchTree<Element> {
     
     
     //MARK: - Finding
+    
+    
+    func find(key:String) -> Element? {
+        return findNode(root, withKey: key, atIndex: 0)
+    }
+    
+    
+    private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
+        
+        //Given key does not exist in tree.
+        if aNode == nil {
+            return nil
+        }
+        
+        let index = key.startIndex.advancedBy(charIndex)
+        //go left
+        if key[index] < aNode!.key {
+            return findNode(aNode!.left, withKey: key, atIndex: charIndex)
+        }
+            //go right
+        else if key[index] > aNode!.key {
+            return findNode(aNode!.right, withKey: key, atIndex: charIndex)
+        }
+            //go middle
+        else {
+            if charIndex + 1 < key.characters.count {
+                return findNode(aNode!.middle, withKey: key, atIndex: charIndex + 1)
+            } else {
+                return aNode!.data
+            }
+        }
+    }
+}
 }
\ No newline at end of file

From c810711bbb3bbc8cf96ba292a56ba90ff2d829a9 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:46:57 -0700
Subject: [PATCH 0152/1679] Created playground for testing

---
 .../TST.playground/Contents.swift             |  4 +
 .../TST.playground/Sources/TSTNode.swift      | 33 +++++++
 .../Sources/TernarySearchTree.swift           | 97 +++++++++++++++++++
 .../TST.playground/contents.xcplayground      |  4 +
 .../TST.playground/timeline.xctimeline        |  6 ++
 5 files changed, 144 insertions(+)
 create mode 100644 Ternary Search Tree/TST.playground/Contents.swift
 create mode 100644 Ternary Search Tree/TST.playground/Sources/TSTNode.swift
 create mode 100644 Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
 create mode 100644 Ternary Search Tree/TST.playground/contents.xcplayground
 create mode 100644 Ternary Search Tree/TST.playground/timeline.xctimeline

diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
new file mode 100644
index 000000000..e14b4581e
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -0,0 +1,4 @@
+//: Playground - noun: a place where people can play
+
+import Cocoa
+
diff --git a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift
new file mode 100644
index 000000000..b6030400f
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
@@ -0,0 +1,33 @@
+//
+//  TSTNode.swift
+//  
+//
+//  Created by Siddharth Atre on 3/15/16.
+//
+//
+
+import Foundation
+
+class TSTNode<Element> {
+    //Member properties of a particular node.
+    var key: Character
+    var data: Element?
+    var hasData: Bool
+    
+    //Children
+    var left: TSTNode?, right: TSTNode?, middle: TSTNode?
+    
+    
+    init(key: Character, data: Element?) {
+        self.key = key
+        self.data = data
+        self.hasData = (data != nil)
+    }
+    
+    init(key:Character) {
+        self.key = key
+        self.data = nil
+        self.hasData = false
+    }
+    
+}
\ No newline at end of file
diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
new file mode 100644
index 000000000..ab5c0faba
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -0,0 +1,97 @@
+//
+//  TernarySearchTree.swift
+//  
+//
+//  Created by Siddharth Atre on 3/15/16.
+//
+//
+
+import Foundation
+
+
+class TernarySearchTree<Element> {
+    
+    var root: TSTNode<Element>?
+    
+    init() {}
+    
+    //MARK: - Insertion
+    
+    func insert(data:Element, withKey key: String) -> Bool{
+        return insertNode(&root, withData: data, andKey: key, atIndex: 0)
+        
+    }
+    
+    private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
+        
+        //sanity check.
+        if(key.characters.count == 0) {
+            return false
+        }
+        
+        //create a new node if necessary.
+        if(aNode == nil) {
+            let index = key.startIndex.advancedBy(charIndex)
+            aNode = TSTNode<Element>(key: key[index])
+        }
+        
+        //if current char is less than the current node's char, go left
+        let index = key.startIndex.advancedBy(charIndex)
+        if(key[index] < aNode!.key) {
+            return insertNode(&aNode!.left, withData: data, andKey: key, atIndex: charIndex)
+        }
+            //if it's greater, go right.
+        else if(key[index] > aNode!.key) {
+            return insertNode(&aNode!.right, withData: data, andKey: key, atIndex: charIndex)
+        }
+            //current char is equal to the current nodes, go middle
+        else {
+            //continue down the middle.
+            if(charIndex + 1 < key.characters.count) {
+                return insertNode(&aNode!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
+            }
+                //otherwise, all done.
+            else {
+                aNode!.data = data
+                aNode?.hasData = true
+                return true
+            }
+        }
+    }
+    
+    
+    //MARK: - Finding
+    
+    
+    func find(key:String) -> Element? {
+        return findNode(root, withKey: key, atIndex: 0)
+    }
+    
+    
+    private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
+        
+        //Given key does not exist in tree.
+        if aNode == nil {
+            return nil
+        }
+        
+        let index = key.startIndex.advancedBy(charIndex)
+        //go left
+        if key[index] < aNode!.key {
+            return findNode(aNode!.left, withKey: key, atIndex: charIndex)
+        }
+            //go right
+        else if key[index] > aNode!.key {
+            return findNode(aNode!.right, withKey: key, atIndex: charIndex)
+        }
+            //go middle
+        else {
+            if charIndex + 1 < key.characters.count {
+                return findNode(aNode!.middle, withKey: key, atIndex: charIndex + 1)
+            } else {
+                return aNode!.data
+            }
+        }
+    }
+}
+}
\ No newline at end of file
diff --git a/Ternary Search Tree/TST.playground/contents.xcplayground b/Ternary Search Tree/TST.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Ternary Search Tree/TST.playground/timeline.xctimeline b/Ternary Search Tree/TST.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>

From 4f1b2bf39e89de62097c9802886cbeda5757f081 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:48:37 -0700
Subject: [PATCH 0153/1679] Removed extraneous }

---
 .../TST.playground/Sources/TernarySearchTree.swift               | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index ab5c0faba..9cd761f1e 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -93,5 +93,4 @@ class TernarySearchTree<Element> {
             }
         }
     }
-}
 }
\ No newline at end of file

From 41b60c5da6b7b9ffca87b20ae920b46acbe63139 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:51:56 -0700
Subject: [PATCH 0154/1679] Made class public to be accessible by playground

---
 .../TST.playground/Sources/TernarySearchTree.swift            | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index 9cd761f1e..d0e515da9 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -9,11 +9,11 @@
 import Foundation
 
 
-class TernarySearchTree<Element> {
+public class TernarySearchTree<Element> {
     
     var root: TSTNode<Element>?
     
-    init() {}
+    public init() {}
     
     //MARK: - Insertion
     

From de505ef38dd6506dc40f52b4612a1ea6eb48e073 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:53:24 -0700
Subject: [PATCH 0155/1679] made insert and find methods publicly accessible.

---
 .../TST.playground/Sources/TernarySearchTree.swift            | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index d0e515da9..1bbc1c390 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -17,7 +17,7 @@ public class TernarySearchTree<Element> {
     
     //MARK: - Insertion
     
-    func insert(data:Element, withKey key: String) -> Bool{
+    public func insert(data:Element, withKey key: String) -> Bool{
         return insertNode(&root, withData: data, andKey: key, atIndex: 0)
         
     }
@@ -63,7 +63,7 @@ public class TernarySearchTree<Element> {
     //MARK: - Finding
     
     
-    func find(key:String) -> Element? {
+    public func find(key:String) -> Element? {
         return findNode(root, withKey: key, atIndex: 0)
     }
     

From 4c96d0338e822afce7429c7da5072551c833c8ac Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 12:54:27 -0700
Subject: [PATCH 0156/1679] updated external class file with changes.

---
 Ternary Search Tree/TernarySearchTree.swift | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index ab5c0faba..1bbc1c390 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -9,15 +9,15 @@
 import Foundation
 
 
-class TernarySearchTree<Element> {
+public class TernarySearchTree<Element> {
     
     var root: TSTNode<Element>?
     
-    init() {}
+    public init() {}
     
     //MARK: - Insertion
     
-    func insert(data:Element, withKey key: String) -> Bool{
+    public func insert(data:Element, withKey key: String) -> Bool{
         return insertNode(&root, withData: data, andKey: key, atIndex: 0)
         
     }
@@ -63,7 +63,7 @@ class TernarySearchTree<Element> {
     //MARK: - Finding
     
     
-    func find(key:String) -> Element? {
+    public func find(key:String) -> Element? {
         return findNode(root, withKey: key, atIndex: 0)
     }
     
@@ -93,5 +93,4 @@ class TernarySearchTree<Element> {
             }
         }
     }
-}
 }
\ No newline at end of file

From 07c4da4f928506e9e965f8db3c6f4cb1ecaf22b5 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 13:16:56 -0700
Subject: [PATCH 0157/1679] Created testing program in playground.

All tests passing.
---
 .../TST.playground/Contents.swift             | 69 +++++++++++++++++++
 1 file changed, 69 insertions(+)

diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index e14b4581e..e9606c653 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -1,4 +1,73 @@
 //: Playground - noun: a place where people can play
 
 import Cocoa
+import Foundation
+
+let treeOfStrings = TernarySearchTree<String>()
+
+//Random string generator from: 
+//http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
+func randomAlphaNumericString(length: Int) -> String {
+    
+    let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
+    let allowedCharsCount = UInt32(allowedChars.characters.count)
+    var randomString = ""
+    
+    for _ in (0..<length) {
+        let randomNum = Int(arc4random_uniform(allowedCharsCount))
+        let newCharacter = allowedChars[allowedChars.startIndex.advancedBy(randomNum)]
+        randomString += String(newCharacter)
+    }
+    
+    return randomString
+}
+
+var testStrings: [(key:String, data:String)] = []
+let testCount = 30
+for _ in (1...testCount) {
+    let randomLength = Int(arc4random_uniform(10))
+    let key = randomAlphaNumericString(randomLength)
+    let data = randomAlphaNumericString(randomLength)
+//    print("Key: \(key) Data: \(data)")
+    
+    if key != "" && data != "" {
+        testStrings.append((key, data))
+        treeOfStrings.insert(data, withKey: key)
+    }
+}
+
+for aTest in testStrings {
+    let data = treeOfStrings.find(aTest.key)
+    
+    if data == nil {
+        print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
+    }
+    if data != aTest.data {
+        print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
+    }
+}
+
+var testNums: [(key: String, data: Int)] = []
+let treeOfInts = TernarySearchTree<Int>()
+for _ in (1...testCount) {
+    let randomNum = Int(arc4random_uniform(UInt32.max))
+    let randomLength = Int(arc4random_uniform(10))
+    let key = randomAlphaNumericString(randomLength)
+    
+    if key != "" {
+        testNums.append((key, randomNum))
+        treeOfInts.insert(randomNum, withKey: key)
+    }
+}
+
+for aTest in testNums {
+    let data = treeOfInts.find(aTest.key)
+    
+    if data == nil {
+        print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
+    }
+    if data != aTest.data {
+        print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
+    }
+}
 

From 5521d011fcca56647707576123643c6b5e0546e7 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Thu, 17 Mar 2016 13:21:20 -0700
Subject: [PATCH 0158/1679] Updated status

---
 Ternary Search Tree/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Ternary Search Tree/README.markdown b/Ternary Search Tree/README.markdown
index a6d571d7c..fee2874cf 100644
--- a/Ternary Search Tree/README.markdown	
+++ b/Ternary Search Tree/README.markdown	
@@ -1,3 +1,4 @@
 # Ternary Search Tree
 
-Work in progress. Coming soon.
\ No newline at end of file
+Data structure and simple test in playground has been implemented. 
+Documentation and examples coming soon!! :)

From 0634627397315ceb9bd0177d7ad9fd24223a1516 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 11:02:00 +0100
Subject: [PATCH 0159/1679] Add test case for old AVL Tree crash

---
 .../AVLTree.playground/Sources/AVLTree.swift  |  6 +-
 AVL Tree/AVLTree.swift                        |  6 +-
 AVL Tree/Tests/AVLTreeTests.swift             | 67 +++++++++++++------
 3 files changed, 49 insertions(+), 30 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index 82ad93a96..91df1ed9e 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -207,7 +207,7 @@ extension AVLTree {
     let lrFactor = lrDifference(node)
     if lrFactor > 1 {
       // left-left or left-right
-      if (lrDifference(node.leftChild) > 0) {
+      if lrDifference(node.leftChild) > 0 {
         // left-left
         nodes[0] = node
         nodes[2] = node.leftChild
@@ -270,7 +270,6 @@ extension AVLTree {
       nodes[2]?.parent = nodeParent
     }
 
-
     nodes[2]?.leftChild = nodes[1]
     nodes[1]?.parent = nodes[2]
     nodes[2]?.rightChild = nodes[0]
@@ -289,7 +288,6 @@ extension AVLTree {
     updateHeightUpwards(nodes[1])    // Update height from left
     updateHeightUpwards(nodes[0])    // Update height from right
 
-
     balance(nodes[2]?.parent)
   }
 }
@@ -415,4 +413,4 @@ extension AVLTree: CustomStringConvertible {
       return "[]"
     }
   }
-}
\ No newline at end of file
+}
diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 82ad93a96..91df1ed9e 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -207,7 +207,7 @@ extension AVLTree {
     let lrFactor = lrDifference(node)
     if lrFactor > 1 {
       // left-left or left-right
-      if (lrDifference(node.leftChild) > 0) {
+      if lrDifference(node.leftChild) > 0 {
         // left-left
         nodes[0] = node
         nodes[2] = node.leftChild
@@ -270,7 +270,6 @@ extension AVLTree {
       nodes[2]?.parent = nodeParent
     }
 
-
     nodes[2]?.leftChild = nodes[1]
     nodes[1]?.parent = nodes[2]
     nodes[2]?.rightChild = nodes[0]
@@ -289,7 +288,6 @@ extension AVLTree {
     updateHeightUpwards(nodes[1])    // Update height from left
     updateHeightUpwards(nodes[0])    // Update height from right
 
-
     balance(nodes[2]?.parent)
   }
 }
@@ -415,4 +413,4 @@ extension AVLTree: CustomStringConvertible {
       return "[]"
     }
   }
-}
\ No newline at end of file
+}
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index a981726b8..6ec9b5f65 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -68,38 +68,61 @@ class AVLTreeTests: XCTestCase {
       self.tree?.search(400)
     }
   }
+  
+  func testMinimumOnPopulatedTree() {
+    self.tree?.autopopulateWithNodes(500)
+    let min = self.tree?.root?.minimum()
+    XCTAssertNotNil(min, "Minimum function not working")
+  }
+  
+  func testMinimumOnSingleTreeNode() {
+    let treeNode = TreeNode(key: 1, payload: "A")
+    let min = treeNode.minimum()
     
-    func testMinimumOnPopulatedTree() {
-        self.tree?.autopopulateWithNodes(500)
-        let min = self.tree?.root?.minimum()
-        XCTAssertNotNil(min, "Minimum function not working")
-    }
-    
-    func testMinimumOnSingleTreeNode() {
-        let treeNode = TreeNode(key: 1, payload: "A")
-        let min = treeNode.minimum()
-        
-        XCTAssertNotNil(min, "Minimum on single node should be returned")
-        XCTAssertEqual(min?.payload,treeNode.payload)
-    }
+    XCTAssertNotNil(min, "Minimum on single node should be returned")
+    XCTAssertEqual(min?.payload,treeNode.payload)
+  }
+  
+  func testDeleteExistentKey() {
+    self.tree?.delete(1)
+    XCTAssertNil(self.tree?.search(1), "Key should not exist anymore")
+  }
+  
+  func testDeleteNotExistentKey() {
+    self.tree?.delete(1056)
+    XCTAssertNil(self.tree?.search(1056), "Key should not exist")
+  }
+  
+  func testDelete() {
+    let permutations = [
+      [5, 1, 4, 2, 3],
+      [2, 3, 1, 5, 4],
+      [4, 5, 3, 2, 1],
+      [3, 2, 5, 4, 1],
+    ]
     
-    func testDeleteExistentKey() {
-        self.tree?.delete(1)
-        XCTAssertNil(self.tree?.search(1), "Key should not exist anymore")
-    }
+    for p in permutations {
+      let tree = AVLTree<Int, String>()
 
-    func testDeleteNOTExistentKey() {
-        self.tree?.delete(1056)
-        XCTAssertNil(self.tree?.search(1056), "Key should not exist")
+      tree.insert(1, "five")
+      tree.insert(2, "four")
+      tree.insert(3, "three")
+      tree.insert(4, "two")
+      tree.insert(5, "one")
+      
+      for i in p {
+        tree.delete(i)
+      }
     }
-
+  }
 }
 
 extension AVLTree where Key : SignedIntegerType {
   func autopopulateWithNodes(count : Int) {
     var k : Key = 1
     for _ in 0...count {
-      self.insert(k++)
+      self.insert(k)
+      k = k + 1
     }
   }
 }

From 05ef99b25582d6397194512f8a70f0c4bb9d5966 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 14:56:09 +0100
Subject: [PATCH 0160/1679] Small tweaks to text and code

---
 .../Contents.swift                            |  96 +++---
 .../timeline.xctimeline                       |   6 -
 .../LongestCommonSubsequence.swift            | 129 ++++----
 Longest Common Subsequence/README.markdown    | 285 +++++++++---------
 ...ft => LongestCommonSubsequenceTests.swift} |   2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     |   9 +-
 README.markdown                               |   1 +
 7 files changed, 256 insertions(+), 272 deletions(-)
 delete mode 100644 Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline
 rename Longest Common Subsequence/Tests/{LongestCommonSubsquenceTests.swift => LongestCommonSubsequenceTests.swift} (93%)

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index 8f49b45fb..0fa00d48b 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,52 +1,46 @@
 extension String {
-    func longestCommonSubsequence(other:String) -> String {
-        
-        func lcsLength(other: String) -> [[Int]] {
-            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
-            
-            for (i, selfChar) in self.characters.enumerate() {
-                for (j, otherChar) in other.characters.enumerate() {
-                    if (otherChar == selfChar) {
-                        matrix[i+1][j+1] = (matrix[i][j]) + 1
-                    }
-                    else {
-                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
-                    }
-                }
-            }
-            
-            return matrix;
+  public func longestCommonSubsequence(other: String) -> String {
+    
+    func lcsLength(other: String) -> [[Int]] {
+      var matrix = [[Int]](count: self.characters.count+1, repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
+      
+      for (i, selfChar) in self.characters.enumerate() {
+        for (j, otherChar) in other.characters.enumerate() {
+          if otherChar == selfChar {
+            matrix[i+1][j+1] = matrix[i][j] + 1
+          } else {
+            matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+          }
         }
-        
-        func backtrack(matrix: [[Int]]) -> String {
-            var i = self.characters.count
-            var j = other.characters.count
-            var charInSequence = self.endIndex
-            
-            var lcs = String()
-            
-            while (i >= 1 && j >= 1) {
-                if (matrix[i][j] == matrix[i][j - 1]) {
-                    j = j - 1
-                }
-                else if (matrix[i][j] == matrix[i - 1][j]) {
-                    i = i - 1
-                    charInSequence = charInSequence.predecessor()
-                }
-                else {
-                    i = i - 1
-                    j = j - 1
-                    charInSequence = charInSequence.predecessor()
-                    
-                    lcs.append(self[charInSequence])
-                }
-            }
-            
-            return String(lcs.characters.reverse());
+      }
+      return matrix
+    }
+    
+    func backtrack(matrix: [[Int]]) -> String {
+      var i = self.characters.count
+      var j = other.characters.count
+      var charInSequence = self.endIndex
+      
+      var lcs = String()
+      
+      while i >= 1 && j >= 1 {
+        if matrix[i][j] == matrix[i][j - 1] {
+          j -= 1
+        } else if matrix[i][j] == matrix[i - 1][j] {
+          i -= 1
+          charInSequence = charInSequence.predecessor()
+        } else {
+          i -= 1
+          j -= 1
+          charInSequence = charInSequence.predecessor()
+          lcs.append(self[charInSequence])
         }
-        
-        return backtrack(lcsLength(other))
+      }
+      return String(lcs.characters.reverse())
     }
+    
+    return backtrack(lcsLength(other))
+  }
 }
 
 // Examples
@@ -55,8 +49,10 @@ let a = "ABCBX"
 let b = "ABDCAB"
 let c = "KLMK"
 
-a.longestCommonSubsequence(c) //""
-a.longestCommonSubsequence("") //""
-a.longestCommonSubsequence(b) //"ABCB"
-b.longestCommonSubsequence(a) //"ABCB"
-a.longestCommonSubsequence(a) // "ABCBX"
+a.longestCommonSubsequence(c)   // ""
+a.longestCommonSubsequence("")  // ""
+a.longestCommonSubsequence(b)   // "ABCB"
+b.longestCommonSubsequence(a)   // "ABCB"
+a.longestCommonSubsequence(a)   // "ABCBX"
+
+"Hello World".longestCommonSubsequence("Bonjour le monde")
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline b/Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.swift b/Longest Common Subsequence/LongestCommonSubsequence.swift
index a6225bb74..d9dda1364 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.swift	
@@ -1,68 +1,69 @@
 extension String {
-    func longestCommonSubsequence(other:String) -> String {
-        
-        // Computes the length of the lcs using dynamic programming
-        // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] indicates the length
-        // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
-        func lcsLength(other: String) -> [[Int]] {
-            
-            //Matrix of size (n+1)x(m+1), algorithm needs first row and first column to be filled with 0
-            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
-            
-            for (i, selfChar) in self.characters.enumerate() {
-                for (j, otherChar) in other.characters.enumerate() {
-                    if (otherChar == selfChar) {
-                        //Common char found, add 1 to highest lcs found so far
-                        matrix[i+1][j+1] = (matrix[i][j]) + 1
-                    }
-                    else {
-                        //Not a match, propagates highest lcs length found so far
-                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
-                    }
-                }
-            }
-            
-            //Due to propagation, lcs length is at matrix[n][m]
-            return matrix;
+  public func longestCommonSubsequence(other: String) -> String {
+    
+    // Computes the length of the lcs using dynamic programming.
+    // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] is the length
+    // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
+    func lcsLength(other: String) -> [[Int]] {
+
+      // Create matrix of size (n+1)x(m+1). The algorithm needs first row and
+      // first column to be filled with 0.
+      var matrix = [[Int]](count: self.characters.count+1, repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
+
+      for (i, selfChar) in self.characters.enumerate() {
+        for (j, otherChar) in other.characters.enumerate() {
+          if otherChar == selfChar {
+            // Common char found, add 1 to highest lcs found so far.
+            matrix[i+1][j+1] = matrix[i][j] + 1
+          } else {
+            // Not a match, propagates highest lcs length found so far.
+            matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+          }
         }
-        
-        //Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are common to both strings
-        func backtrack(matrix: [[Int]]) -> String {
-            var i = self.characters.count
-            var j = other.characters.count
-            
-            //charInSequence is in sync with i so we can get self[i]
-            var charInSequence = self.endIndex
-            
-            var lcs = String()
-            
-            while (i >= 1 && j >= 1) {
-                //Indicates propagation without change, i.e. no new char was added to lcs
-                if (matrix[i][j] == matrix[i][j - 1]) {
-                    j = j - 1
-                }
-                //Indicates propagation without change, i.e. no new char was added to lcs
-                else if (matrix[i][j] == matrix[i - 1][j]) {
-                    i = i - 1
-                    //As i was subtracted, move back charInSequence
-                    charInSequence = charInSequence.predecessor()
-                }
-                //Value on the left and above are different than current cell. This means 1 was added to lcs length (line 16)
-                else {
-                    i = i - 1
-                    j = j - 1
-                    charInSequence = charInSequence.predecessor()
-                    
-                    lcs.append(self[charInSequence])
-                }
-            }
-            
-            //Due to backtrack, chars were added in reverse order: reverse it back.
-            //Append and reverse is faster than inserting at index 0
-            return String(lcs.characters.reverse());
+      }
+
+      // Due to propagation, lcs length is at matrix[n][m].
+      return matrix
+    }
+
+    // Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are
+    // common to both strings.
+    func backtrack(matrix: [[Int]]) -> String {
+      var i = self.characters.count
+      var j = other.characters.count
+      
+      // charInSequence is in sync with i so we can get self[i]
+      var charInSequence = self.endIndex
+      
+      var lcs = String()
+      
+      while i >= 1 && j >= 1 {
+        // Indicates propagation without change: no new char was added to lcs.
+        if matrix[i][j] == matrix[i][j - 1] {
+          j -= 1
+        }
+        // Indicates propagation without change: no new char was added to lcs.
+        else if matrix[i][j] == matrix[i - 1][j] {
+          i -= 1
+          // As i was decremented, move back charInSequence.
+          charInSequence = charInSequence.predecessor()
+        }
+        // Value on the left and above are different than current cell.
+        // This means 1 was added to lcs length (line 17).
+        else {
+          i -= 1
+          j -= 1
+          charInSequence = charInSequence.predecessor()
+          lcs.append(self[charInSequence])
         }
-        
-        //Combine dynamic programming approach with backtrack to find the lcs
-        return backtrack(lcsLength(other))
+      }
+      
+      // Due to backtrack, chars were added in reverse order: reverse it back.
+      // Append and reverse is faster than inserting at index 0.
+      return String(lcs.characters.reverse())
     }
-}
\ No newline at end of file
+    
+    // Combine dynamic programming approach with backtrack to find the lcs.
+    return backtrack(lcsLength(other))
+  }
+}
diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index 719135a54..64d3988c6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -1,45 +1,26 @@
 # Longest Common Subsequence
 
+The Longest Common Subsequence (LCS) of two strings is the longest sequence of characters that appear in the same order in both strings.
 
-The Longest Common Subsequence (LCS) of two strings is the longest sequence of characters that appear in the same order in both strings. Should not be confused with the Longest Common Substring problem, where characters **must** be a substring of both strings (i.e they have to be immediate neighbours).
+For example the LCS of `"Hello World"` and `"Bonjour le monde"` is `"oorld"`. If you go through both strings from left-to-right, you'll find that the characters `o`, `o`, `r`, `l`, `d` appear in both strings in that order.
 
-One way to find what's the LCS of two strings `a` and `b` is using Dynamic Programming and a backtracking strategy. During the explanation, remember that `n` is the length of `a` and `m` the length of `b`.
+Other possible subsequences are `"ed"` and `"old"`, but these are all shorter than `"oorld"`. 
 
-## Length of LCS - Dynamic Programming 
+> **Note:** This should not be confused with the Longest Common Substring problem, where the characters must form a substring of both strings, i.e they have to be immediate neighbors. With a subsequence, it's OK if the characters are not right next to each other, but they must be in the same order.
 
-Dynamic programming is used to determine the length of LCS between all combinations of substrings of `a` and `b`. 
+One way to find the LCS of two strings `a` and `b` is using dynamic programming and a backtracking strategy.
 
+## Finding the length of the LCS with dynamic programming
 
-```swift
-        // Computes the length of the lcs using dynamic programming
-        // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] indicates the length
-        // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
-        func lcsLength(other: String) -> [[Int]] {
-            
-            //Matrix of size (n+1)x(m+1), algorithm needs first row and first line to be filled with 0
-            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
-            
-            for (i, selfChar) in self.characters.enumerate() {
-                for (j, otherChar) in other.characters.enumerate() {
-                    if (otherChar == selfChar) {
-                        //Common char found, add 1 to highest lcs found so far
-                        matrix[i+1][j+1] = (matrix[i][j]) + 1
-                    }
-                    else {
-                        //Not a match, propagates highest lcs length found so far
-                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
-                    }
-                }
-            }
-            
-            //Due to propagation, lcs length is at matrix[n][m]
-            return matrix;
-        }
-```
+First, we want to find the length of the longest common subsequence between strings `a` and `b`. We're not looking for the actual subsequence yet, only how long it is.
+
+To determine the length of the LCS between all combinations of substrings of `a` and `b`, we can use a *dynamic programming* technique. Dynamic programming basically means that you compute all possibilities and store them inside a look-up table.
 
-Given strings `"ABCBX"` and `"ABDCAB"` the output matrix of `lcsLength` is the following:
+> **Note:** During the following explanation, `n` is the length of string `a`, and `m` is the length of string `b`.
 
-*First row and column added for easier understanding, actual matrix starts on zeros*
+To find the lengths of all possible subsequences, we use a helper function, `lcsLength()`. This creates a matrix of size `(n+1)` by `(m+1)`, where `matrix[x][y]` is the length of the LCS between the substrings `a[0...x-1]` and `b[0...y-1]`.
+
+Given strings `"ABCBX"` and `"ABDCAB"`, the output matrix of `lcsLength()` is the following:
 
 ```
 |   | Ø | A | B | D | C | A | B |
@@ -51,16 +32,79 @@ Given strings `"ABCBX"` and `"ABDCAB"` the output matrix of `lcsLength` is the f
 | X | 0 | 1 | 2 | 2 | 3 | 3 | 4 |
 ```
 
-The content of the matrix indicates that position `(i, j)` contains the length of the LCS between substring `(0, i - 1)` of `a` and substring `(0, j - 1)` of `b`.
+In this example, if we look at `matrix[3][4]` we find the value `3`. This means the length of the LCS between `a[0...2]` and `b[0...3]`, or between `"ABC"` and `"ABDC"`, is 3. That is correct, because these two substrings have the subsequence `ABC` in common. (Note: the first row and column of the matrix are always filled with zeros.)
 
-Example: `(2, 3)` says that the LCS for `"AB"` and `"ABD"` is 2
+Here is the source code for `lcsLength()`; this lives in an extension on `String`:
 
+```swift
+func lcsLength(other: String) -> [[Int]] {
+
+  var matrix = [[Int]](count: self.characters.count+1, 
+                       repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
+
+  for (i, selfChar) in self.characters.enumerate() {
+	for (j, otherChar) in other.characters.enumerate() {
+	  if otherChar == selfChar {
+		// Common char found, add 1 to highest lcs found so far.
+		matrix[i+1][j+1] = matrix[i][j] + 1
+	  } else {
+		// Not a match, propagates highest lcs length found so far.
+		matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+	  }
+	}
+  }
+
+  return matrix
+}
+```
 
-## Actual LCS - Backtrack
+First, this creates a new matrix -- really a 2-dimensional array -- and fills it with zeros. Then it loops through both strings, `self` and `other`, and compares their characters in order to fill in the matrix. If two characters match, we increment the length of the subsequence. However, if two characters are different, then we "propagate" the highest LCS length found so far.
 
-Having the length of every combination makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
+Let's say the following is the current situation:
 
-Backtrack starts at matrix[n + 1][m + 1] and *walks* up and left (in this priority) looking for changes that do not indicate a simple propagation. If the number on the left and above are different than the number in the current cell, no propagation happened, it means that `(i, j)` indicates a common char between `a` and `b`, so char at `a[i - 1]` and `b[j - 1]` are part of the LCS and should be stored in the returned value (`self[i - 1]` was used in the code but could be `other[j - 1]`).
+```
+|   | Ø | A | B | D | C | A | B |
+| Ø | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+| A | 0 | 1 | 1 | 1 | 1 | 1 | 1 |  
+| B | 0 | 1 | 2 | 2 | 2 | 2 | 2 |
+| C | 0 | 1 | 2 | * |   |   |   |
+| B | 0 |   |   |   |   |   |   |
+| X | 0 |   |   |   |   |   |   |
+```
+
+The `*` marks the two characters we're currently comparing, `C` versus `D`. These characters are not the same, so we propagate the highest length we've seen so far, which is `2`:
+
+```
+|   | Ø | A | B | D | C | A | B |
+| Ø | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+| A | 0 | 1 | 1 | 1 | 1 | 1 | 1 |  
+| B | 0 | 1 | 2 | 2 | 2 | 2 | 2 |
+| C | 0 | 1 | 2 | 2 | * |   |   |
+| B | 0 |   |   |   |   |   |   |
+| X | 0 |   |   |   |   |   |   |
+```
+
+Now we compare `C` with `C`. These are equal, and we increment the length to `3`:
+
+```
+|   | Ø | A | B | D | C | A | B |
+| Ø | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+| A | 0 | 1 | 1 | 1 | 1 | 1 | 1 |  
+| B | 0 | 1 | 2 | 2 | 2 | 2 | 2 |
+| C | 0 | 1 | 2 | 2 | 3 | * |   |
+| B | 0 |   |   |   |   |   |   |
+| X | 0 |   |   |   |   |   |   |
+```
+
+And so on... this is how `lcsLength()` fills in the entire matrix.
+
+## Backtracking to find the actual subsequence
+
+So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-left corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
+
+Having the length of every combination of substrings makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
+
+Backtracking starts at `matrix[n+1][m+1]` and walks up and left (in this priority) looking for changes that do not indicate a simple propagation.
 
 ```
 |   |  Ø|  A|  B|  D|  C|  A|  B|
@@ -71,141 +115,88 @@ Backtrack starts at matrix[n + 1][m + 1] and *walks* up and left (in this priori
 | B |  0|  1|  2|  2|  3|  3|↖ 4|
 | X |  0|  1|  2|  2|  3|  3|↑ 4|
 ```
+
 Each `↖` move indicates a character (in row/column header) that is part of the LCS.
 
-One thing to notice is, as it's running backwards, the LCS is built in reverse order. Before returning, the result is reversed to reflect the actual LCS.
+If the number on the left and above are different than the number in the current cell, no propagation happened. In that case `matrix[i][j]` indicates a common char between the strings `a` and `b`, so the characters at `a[i - 1]` and `b[j - 1]` are part of the LCS that we're looking for.
 
+One thing to notice is, as it's running backwards, the LCS is built in reverse order. Before returning, the result is reversed to reflect the actual LCS.
 
+Here is the backtracking code:
 
 ```swift
-        //Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are common to both strings
-        func backtrack(matrix: [[Int]]) -> String {
-            var i = self.characters.count
-            var j = other.characters.count
-            
-            //charInSequence is in sync with i so we can get self[i]
-            var charInSequence = self.endIndex
-            
-            var lcs = String()
-            
-            while (i >= 1 && j >= 1) {
-                //Indicates propagation without change, i.e. no new char was added to lcs
-                if (matrix[i][j] == matrix[i][j - 1]) {
-                    j = j - 1
-                }
-                //Indicates propagation without change, i.e. no new char was added to lcs
-                else if (matrix[i][j] == matrix[i - 1][j]) {
-                    i = i - 1
-                    //As i was subtracted, move back charInSequence
-                    charInSequence = charInSequence.predecessor()
-                }
-                //Value on the left and above are different than current cell. This means 1 was added to lcs length (line 16)
-                else {
-                    i = i - 1
-                    j = j - 1
-                    charInSequence = charInSequence.predecessor()
-                    
-                    lcs.append(self[charInSequence])
-                }
-            }
-            
-            //Due to backtrack, chars were added in reverse order: reverse it back.
-            //Append and reverse is faster than inserting at index 0
-            return String(lcs.characters.reverse());
-        }
-
+func backtrack(matrix: [[Int]]) -> String {
+  var i = self.characters.count
+  var j = other.characters.count
+  
+  var charInSequence = self.endIndex
+  
+  var lcs = String()
+  
+  while i >= 1 && j >= 1 {
+	// Indicates propagation without change: no new char was added to lcs.
+	if matrix[i][j] == matrix[i][j - 1] {
+	  j -= 1
+	}
+	// Indicates propagation without change: no new char was added to lcs.
+	else if matrix[i][j] == matrix[i - 1][j] {
+	  i -= 1
+	  charInSequence = charInSequence.predecessor()
+	}
+	// Value on the left and above are different than current cell.
+	// This means 1 was added to lcs length.
+	else {
+	  i -= 1
+	  j -= 1
+	  charInSequence = charInSequence.predecessor()
+	  lcs.append(self[charInSequence])
+	}
+  }
+  
+  return String(lcs.characters.reverse())
+}
 ```  
 
+This backtracks from `matrix[n+1][m+1]` (bottom-right corner) to `matrix[1][1]` (top-right corner), looking for characters that are common to both strings. It adds those characters to a new string, `lcs`.
 
+The `charInSequence` variable is an index into the string given by `self`. Initially this points to the last character of the string. Each time we decrement `i`, we also move back `charInSequence`. When the two characters are found to be equal, we add the character at `self[charInSequence]` to the new `lcs` string. (We can't just write `self[i]` because `i` may not map to the current position inside the Swift string.)
 
+Due to backtracking, characters are added in reverse order, so at the end of the function we call `reverse()` to put the string in the right order. (Appending new characters to the end of the string and then reversing it once is faster than always inserting the characters at the front of the string.)
 
 ## Putting it all together
 
+To find the LCS between two strings, we first call `lcsLength()` and then `backtrack()`:
 
 ```swift
 extension String {
-    func longestCommonSubsequence(other:String) -> String {
-        
-        // Computes the same of the lcs using dynamic programming
-        // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] indicates the length
-        // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
-        func lcsLength(other: String) -> [[Int]] {
-            
-            //Matrix of size (n+1)x(m+1), algorithm needs first row and first line to be filled with 0
-            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
-            
-            for (i, selfChar) in self.characters.enumerate() {
-                for (j, otherChar) in other.characters.enumerate() {
-                    if (otherChar == selfChar) {
-                        //Common char found, add 1 to highest lcs found so far
-                        matrix[i+1][j+1] = (matrix[i][j]) + 1
-                    }
-                    else {
-                        //Not a match, propagates highest lcs length found so far
-                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
-                    }
-                }
-            }
-            
-            //Due to propagation, lcs length is at matrix[n][m]
-            return matrix;
-        }
-        
-        //Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are common to both strings
-        func backtrack(matrix: [[Int]]) -> String {
-            var i = self.characters.count
-            var j = other.characters.count
-            
-            //charInSequence is in sync with i so we can get self[i]
-            var charInSequence = self.endIndex
-            
-            var lcs = String()
-            
-            while (i >= 1 && j >= 1) {
-                //Indicates propagation without change, i.e. no new char was added to lcs
-                if (matrix[i][j] == matrix[i][j - 1]) {
-                    j = j - 1
-                }
-                //Indicates propagation without change, i.e. no new char was added to lcs
-                else if (matrix[i][j] == matrix[i - 1][j]) {
-                    i = i - 1
-                    //As i was subtracted, move back charInSequence
-                    charInSequence = charInSequence.predecessor()
-                }
-                //Value on the left and above are different than current cell. This means 1 was added to lcs length (line 16)
-                else {
-                    i = i - 1
-                    j = j - 1
-                    charInSequence = charInSequence.predecessor()
-                    
-                    lcs.append(self[charInSequence])
-                }
-            }
-            
-            //Due to backtrack, chars were added in reverse order: reverse it back.
-            //Append and reverse is faster than inserting at index 0
-            return String(lcs.characters.reverse());
-        }
-        
-        //Combine dynamic programming approach with backtrack to find the lcs
-        return backtrack(lcsLength(other))
+  public func longestCommonSubsequence(other: String) -> String {
+
+    func lcsLength(other: String) -> [[Int]] {
+      ...
     }
+    
+    func backtrack(matrix: [[Int]]) -> String {
+      ...
+    }
+
+    return backtrack(lcsLength(other))
+  }
 }
 ```
 
-**Examples:**
+To keep everything tidy, the two helper functions are nested inside the main `longestCommonSubsequence()` function.
+
+Here's how you could try it out in a Playground:
 
 ```swift
 let a = "ABCBX"
 let b = "ABDCAB"
+a.longestCommonSubsequence(b)   // "ABCB"
+
 let c = "KLMK"
+a.longestCommonSubsequence(c)   // "" (no common subsequence)
 
-a.longestCommonSubsequence(c) //""
-a.longestCommonSubsequence("") //""
-a.longestCommonSubsequence(b) //"ABCB"
-b.longestCommonSubsequence(a) //"ABCB"
-a.longestCommonSubsequence(a) // "ABCBX"
+"Hello World".longestCommonSubsequence("Bonjour le monde")   // "oorld"
 ```
 
-
-*Written for Swift Algorithm Club by Pedro Vereza*
\ No newline at end of file
+*Written for Swift Algorithm Club by Pedro Vereza*
diff --git a/Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift b/Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift
similarity index 93%
rename from Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift
rename to Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift
index 75859ca1a..db388a65f 100644
--- a/Longest Common Subsequence/Tests/LongestCommonSubsquenceTests.swift	
+++ b/Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift	
@@ -1,7 +1,7 @@
 import Foundation
 import XCTest
 
-class LongestCommonSubsquenceTests: XCTestCase {
+class LongestCommonSubsequenceTests: XCTestCase {
     
     func testLCSwithSelfIsSelf() {
         let a = "ABCDE"
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj
index 39422654f..abf3084dd 100644
--- a/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj	
@@ -7,13 +7,13 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		4716C7AF1C93751E00F6C1C0 /* LongestCommonSubsquenceTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 4716C7891C936E0E00F6C1C0 /* LongestCommonSubsquenceTests.swift */; };
+		4716C7AF1C93751E00F6C1C0 /* LongestCommonSubsequenceTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 4716C7891C936E0E00F6C1C0 /* LongestCommonSubsequenceTests.swift */; };
 		4716C7B01C93751E00F6C1C0 /* LongestCommonSubsequence.swift in Sources */ = {isa = PBXBuildFile; fileRef = 4716C7881C936DDD00F6C1C0 /* LongestCommonSubsequence.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
 		4716C7881C936DDD00F6C1C0 /* LongestCommonSubsequence.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = LongestCommonSubsequence.swift; path = ../../LongestCommonSubsequence.swift; sourceTree = "<group>"; };
-		4716C7891C936E0E00F6C1C0 /* LongestCommonSubsquenceTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = LongestCommonSubsquenceTests.swift; path = ../LongestCommonSubsquenceTests.swift; sourceTree = "<group>"; };
+		4716C7891C936E0E00F6C1C0 /* LongestCommonSubsequenceTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = LongestCommonSubsequenceTests.swift; path = ../LongestCommonSubsequenceTests.swift; sourceTree = "<group>"; };
 		4716C7A71C93750500F6C1C0 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		4716C7AB1C93750500F6C1C0 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 /* End PBXFileReference section */
@@ -48,8 +48,8 @@
 		4716C7A81C93750500F6C1C0 /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				4716C7891C936E0E00F6C1C0 /* LongestCommonSubsquenceTests.swift */,
 				4716C7881C936DDD00F6C1C0 /* LongestCommonSubsequence.swift */,
+				4716C7891C936E0E00F6C1C0 /* LongestCommonSubsequenceTests.swift */,
 				4716C7AB1C93750500F6C1C0 /* Info.plist */,
 			);
 			path = Tests;
@@ -121,7 +121,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				4716C7AF1C93751E00F6C1C0 /* LongestCommonSubsquenceTests.swift in Sources */,
+				4716C7AF1C93751E00F6C1C0 /* LongestCommonSubsequenceTests.swift in Sources */,
 				4716C7B01C93751E00F6C1C0 /* LongestCommonSubsequence.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
@@ -250,6 +250,7 @@
 				4716C7AE1C93750500F6C1C0 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/README.markdown b/README.markdown
index 92dfa013f..75285d1e0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -52,6 +52,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Brute-Force String Search](Brute-Force String Search/). A naive method.
 - [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
 - Rabin-Karp
+- [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
 
 ### Sorting
 

From cf27c005be8eb5336b59d2a0638f89e7c2ab5019 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 18:01:26 +0100
Subject: [PATCH 0161/1679] Fix topological sort bug, improve explanation

When concatenating the results from the individual depth-first searches, the subsequent results need to be prepended, not appended, to the final list.
---
 README.markdown                               |   2 +-
 Topological Sort/Graph.swift                  |  19 +++
 Topological Sort/Images/Algorithms.graffle    | Bin 0 -> 2125 bytes
 Topological Sort/Images/Algorithms.png        | Bin 0 -> 25598 bytes
 Topological Sort/Images/Example.graffle       | Bin 0 -> 2150 bytes
 Topological Sort/Images/Example.png           | Bin 0 -> 9312 bytes
 Topological Sort/Images/Graph.graffle         | Bin 0 -> 2219 bytes
 Topological Sort/Images/Graph.png             | Bin 0 -> 8132 bytes
 Topological Sort/Images/GraphResult.graffle   | Bin 2251 -> 2253 bytes
 Topological Sort/Images/GraphResult.png       | Bin 8911 -> 10286 bytes
 Topological Sort/Images/InvalidSort.graffle   | Bin 0 -> 2290 bytes
 Topological Sort/Images/InvalidSort.png       | Bin 0 -> 7330 bytes
 .../Images/TopologicalSort.graffle            | Bin 2833 -> 2585 bytes
 Topological Sort/Images/TopologicalSort.png   | Bin 24083 -> 13199 bytes
 Topological Sort/Images/algorithm_example.png | Bin 187544 -> 0 bytes
 Topological Sort/Images/graph_example.png     | Bin 114041 -> 0 bytes
 Topological Sort/README.markdown              | 116 +++++++++++++-----
 Topological Sort/Stack.swift                  |  27 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     |   8 +-
 .../Tests/TopologicalSortTests.swift          |  41 ++++---
 .../Contents.swift                            |   7 +-
 .../Sources/Graph.swift                       |  19 +++
 .../Sources/Stack.swift                       |  27 ----
 .../Sources/TopologicalSort1.swift            |  30 +----
 .../Sources/TopologicalSort2.swift            |   4 +-
 .../Sources/TopologicalSort3.swift            |  35 ++++++
 Topological Sort/TopologicalSort1.swift       |  32 ++---
 Topological Sort/TopologicalSort2.swift       |   4 +-
 Topological Sort/TopologicalSort3.swift       |  35 ++++++
 29 files changed, 245 insertions(+), 161 deletions(-)
 create mode 100644 Topological Sort/Images/Algorithms.graffle
 create mode 100644 Topological Sort/Images/Algorithms.png
 create mode 100644 Topological Sort/Images/Example.graffle
 create mode 100644 Topological Sort/Images/Example.png
 create mode 100644 Topological Sort/Images/Graph.graffle
 create mode 100644 Topological Sort/Images/Graph.png
 create mode 100644 Topological Sort/Images/InvalidSort.graffle
 create mode 100644 Topological Sort/Images/InvalidSort.png
 delete mode 100644 Topological Sort/Images/algorithm_example.png
 delete mode 100644 Topological Sort/Images/graph_example.png
 delete mode 100644 Topological Sort/Stack.swift
 delete mode 100644 Topological Sort/Topological Sort.playground/Sources/Stack.swift
 create mode 100644 Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift
 create mode 100644 Topological Sort/TopologicalSort3.swift

diff --git a/README.markdown b/README.markdown
index 75285d1e0..d086ca298 100644
--- a/README.markdown
+++ b/README.markdown
@@ -75,7 +75,7 @@ Special-purpose sorts:
 - Bucket Sort
 - Counting Sort
 - Radix Sort
-- [Topological Sort](Topological Sort/) :construction:
+- [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
 
diff --git a/Topological Sort/Graph.swift b/Topological Sort/Graph.swift
index 49f4db96a..5db37ad45 100644
--- a/Topological Sort/Graph.swift	
+++ b/Topological Sort/Graph.swift	
@@ -30,3 +30,22 @@ public class Graph: CustomStringConvertible {
     return nil
   }
 }
+
+extension Graph {
+  typealias InDegree = Int
+
+  func calculateInDegreeOfNodes() -> [Node : InDegree] {
+    var inDegrees = [Node : InDegree]()
+    
+    for (node, _) in adjacencyLists {
+      inDegrees[node] = 0
+    }
+    
+    for (_, adjacencyList) in adjacencyLists {
+      for nodeInList in adjacencyList {
+        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
+      }
+    }
+    return inDegrees
+  }
+}
diff --git a/Topological Sort/Images/Algorithms.graffle b/Topological Sort/Images/Algorithms.graffle
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diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index 58985c908..c92072539 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -1,76 +1,132 @@
 # Topological Sort
 
-Topological sort is an algorithm aimed at ordering a directed graph such that for each directed edge *uv* from vertex *u* to vertex *v*, *u* comes before *v*.
+Topological sort is an algorithm that orders a directed graph such that for each directed edge *u→v*, vertex *u* comes before vertex *v*.
 
-In other words, a topological sort places the vertices of a directed acyclic graph on a line so that all directed edges go from left to right. 
+In other words, a topological sort places the vertices of a [directed acyclic graph](../Graph/) on a line so that all directed edges go from left to right. 
 
-The graph in the following example has two possible topological sorts:
+Consider the graph in the following example:
+
+![Example](Images/Graph.png)
+
+This graph has two possible topological sorts:
 
 ![Example](Images/TopologicalSort.png)
 
+The topological orderings are **S, V, W, T, X** and **S, W, V, T, X**. Notice how the arrows all go from left to right.
+
+The following is not a valid topological sort for this graph, since **X** and **T** cannot happen before **V**:
+
+![Example](Images/InvalidSort.png)
+
 ## Where is this used?
 
-Let's consider that you want to learn all the algorithms present in the Swift Algorithm Club. This might seem daunting at first but  we can use topological sort to get things organized.
+Let's consider that you want to learn all the algorithms and data structures from the Swift Algorithm Club. This might seem daunting at first but we can use topological sort to get things organized.
 
-For example, to learn the [depth-first search](../Depth-First Search/) algorithm you need to know how a [graph](../Graph/) is represented. Similarly, to understand how to calculate the length of a [binary tree](../Binary Tree/) you need to know details of how a [tree is traversed](../Tree/).
+Since you're learning about topological sort, let's take this topic as an example. What else do you need to learn first before you can fully understand topological sort? Well, topological sort uses [depth-first search](../Depth-First Search/) as well as a [stack](../Stack/). But before you can learn about the depth-first search algorithm, you need to know what a [graph](../Graph/) is, and it helps to know what a [tree](../Tree/) is. In turn, graphs and trees use the idea of linking objects together, so you may need to read up on that first. And so on...
 
-If we were to represent these objectives in the form of a graph it would be as follows:
+If we were to represent these objectives in the form of a graph it would look as follows:
 
-![Example](Images/algorithm_example.png)
+![Example](Images/Algorithms.png)
 
-If we consider each algorithm to be a node in the graph you'll see dependancies among them, i.e. to learn something you might have to know something else first. This is exactly what topological sort is used for -- it will sort things out such that you know what to learn first.
+If we consider each algorithm to be a vertex in the graph you can clearly see the dependencies between them. To learn something you might have to know something else first. This is exactly what topological sort is used for -- it will sort things out such that you know what to do first.
 
 ## How does it work?
 
-**Step 1: Find all nodes that have in-degree of 0**
+**Step 1: Find all vertices that have in-degree of 0**
+
+The *in-degree* of a vertex is the number of edges pointing at that vertex. Vertices with no incoming edges have an in-degree of 0. These vertices are the starting points for the topological sort.
+
+In the context of the previous example, these vertices represent algorithms that don't have any prerequisites; you don't need to learn anything else first, hence the sort starts with them.
 
-The *in-degree* of a node is the number of incoming edges to that node. Nodes that have no incoming edges have an in-degree of 0. These nodes are the starting points for the sort.
+**Step 2: Traverse the graph with depth-first search**
 
-If you think about it in the context of the previous example, these nodes represent algorithms that don't have any prerequisites; you don't need to learn anything else first, hence the sort starts with them.
+Depth-first search is an algorithm that starts traversing the graph from a certain vertex and explores as far as possible along each branch before backtracking. To find out more about depth-first search, please take a look at the [detailed explanation](../Depth-First%20Search/).
 
-**Step 2: Depth-first search for traversal**
+We perform a depth-first search on each vertex with in-degree 0. This tells us which vertices are connected to each of these starting vertices.
 
-Depth-first search is an algorithm that is used to traverse a graph. This algorithm traverses all the child nodes recursively and uses backtracking.
+**Step 3: Remember all visited vertices**
 
-To find out more about depth-first search, please take a look at the [detailed explanation](../Depth-First%20Search/).
+As we perform the depth-first search, we maintain a list of all the vertices that have been visited. This is to avoid visiting the same vertex twice.
 
-**Step 3: Remember all visited nodes**
+**Step 4: Put it all together**
 
-The last step of the sort is to maintain a list of all the nodes that have been visited. This is to avoid visiting the same node twice.
+The last step of the sort is to combine the results of the different depth-first searches and put the vertices in a sorted list.
 
 ## Example
 
 Consider the following graph:
 
-![Graph Example](Images/graph_example.png)
+![Graph Example](Images/Example.png)
 
-**Step 1:** The nodes with 0 in-degree are: **5, 7, 3**
+**Step 1:** The vertices with 0 in-degree are: **3, 7, 5**. These are our starting vertices.
 
-**Step 2:** Depth-first search for each starting node, without remembering nodes that have already been visited:
+**Step 2:** Perform depth-first search for each starting vertex, without remembering vertices that have already been visited:
 
 ```
-Node 3: 3, 8, 9, 10
-Node 7: 7, 11, 2, 8, 9
-Node 5: 5, 11, 2, 9, 10
+Vertex 3: 3, 8, 9, 10
+Vertex 7: 7, 11, 2, 8, 9
+Vertex 5: 5, 11, 2, 9, 10
 ```
 
-**Step 3:** Remember nodes already visited in each DFS:
+**Step 3:** Filter out the vertices already visited in each previous search:
 
 ```
-Node 3: 3, 8, 9, 10
-Node 7: 7, 11, 2
-Node 5: 5
+Vertex 3: 3, 8, 9, 10
+Vertex 7: 7, 11, 2
+Vertex 5: 5
 ```
 
-The final sorted order is a concatenation of the above three traversals: **3, 8, 9, 10, 7, 11, 2, 5**
+**Step 4:** Combine the results of these three depth-first searches. The final sorted order is **5, 7, 11, 2, 3, 8, 9, 10**. (Important: we need to add the results of each subsequent search to the *front* of the list.)
 
 The result of the topological sort looks like this:
 
 ![Result of the sort](Images/GraphResult.png)
 
-TODO: I don't think this is correct! There should be no arrows going from right to left! (A valid topological order would be 3, 7, 5, 10, 8, 11, 9, 2 -- or 3, 7, 5, 8, 11, 2, 9, 10.)
+> **Note:** This is not the only possible topological sort for this graph. For example, other valid solutions are **3, 7, 5, 10, 8, 11, 9, 2** and **3, 7, 5, 8, 11, 2, 9, 10**. Any order where all the arrows are going from left to right will do. 
+
+## The code
+
+Here is how you could implement topological sort in Swift (see also [TopologicalSort1.swift](TopologicalSort1.swift)):
+
+```swift
+extension Graph {
+  public func topologicalSort() -> [Node] {
+    // 1
+    let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
+      return indegree == 0
+    }).map({ node, indegree in
+      return node
+    })
+    
+    // 2
+    var visited = [Node : Bool]()
+    for (node, _) in adjacencyLists {
+      visited[node] = false
+    }
+    
+    // 3
+    var result = [Node]()
+    for startNode in startNodes {
+      result = depthFirstSearch(startNode, visited: &visited) + result
+    }
+
+    // 4    
+    return result
+  }
+}
+```
+
+Some remarks:
+
+1. Find the in-degree of each vertex and put all the vertices with in-degree 0 in the `startNodes` array. In this graph implementation, vertices are called "nodes". Both terms are used interchangeably by people who write graph code.
+
+2. The `visited` array keeps track of whether we've already seen a vertex during the depth-first search. Initially, we set all elements to `false`.
+
+3. For each of the vertices in the `startNodes` array, perform a depth-first search. This returns an array of `Node` objects. We prepend that array to our own `result` array.
+
+4. The `result` array contains all the vertices in topologically sorted order.
 
-## Alternative algorithm
+## Alternative method (Kahn's algorithm)
 
 Even though depth-first search is the typical way to perform a topological sort, there is another algorithm that also does the job. 
 
@@ -82,6 +138,6 @@ Even though depth-first search is the typical way to perform a topological sort,
 
 This is an **O(n + m)** algorithm where **n** is the number of vertices and **m** is the number of edges. You can see the implementation in [TopologicalSort2.swift](TopologicalSort2.swift).
 
-I first read about this algorithm in the Algorithm Alley column in Dr. Dobb's Magazine from May 1993.
+Source: I first read about this alternative algorithm in the Algorithm Alley column in Dr. Dobb's Magazine from May 1993.
 
 *Written for Swift Algorithm Club by Ali Hafizji and Matthijs Hollemans*
diff --git a/Topological Sort/Stack.swift b/Topological Sort/Stack.swift
deleted file mode 100644
index 7f4aadc8b..000000000
--- a/Topological Sort/Stack.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-public struct Stack<T> {
-  private var array = [T]()
-  
-  public var isEmpty: Bool {
-    return array.isEmpty
-  }
-  
-  public var count: Int {
-    return array.count
-  }
-  
-  public mutating func push(element: T) {
-    array.append(element)
-  }
-  
-  public mutating func pop() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array.removeLast()
-    }
-  }
-  
-  public func peek() -> T? {
-    return array.last
-  }
-}
diff --git a/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj b/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj
index cb32961df..83c59dbab 100644
--- a/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -9,9 +9,9 @@
 /* Begin PBXBuildFile section */
 		7B3471BB1C8F50CF008381CD /* TopologicalSortTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B3471BA1C8F50CF008381CD /* TopologicalSortTests.swift */; };
 		7B3471BF1C8F50DD008381CD /* Graph.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B3471BC1C8F50DD008381CD /* Graph.swift */; };
-		7B3471C01C8F50DD008381CD /* Stack.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B3471BD1C8F50DD008381CD /* Stack.swift */; };
 		7B3471C11C8F50DD008381CD /* TopologicalSort1.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B3471BE1C8F50DD008381CD /* TopologicalSort1.swift */; };
 		7B3471C31C8F5348008381CD /* TopologicalSort2.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B3471C21C8F5348008381CD /* TopologicalSort2.swift */; };
+		7BE143491C9C6A93001BC747 /* TopologicalSort3.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7BE143481C9C6A93001BC747 /* TopologicalSort3.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
@@ -19,9 +19,9 @@
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B3471BA1C8F50CF008381CD /* TopologicalSortTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = TopologicalSortTests.swift; sourceTree = SOURCE_ROOT; };
 		7B3471BC1C8F50DD008381CD /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Graph.swift; path = ../Graph.swift; sourceTree = SOURCE_ROOT; };
-		7B3471BD1C8F50DD008381CD /* Stack.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Stack.swift; path = ../Stack.swift; sourceTree = SOURCE_ROOT; };
 		7B3471BE1C8F50DD008381CD /* TopologicalSort1.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TopologicalSort1.swift; path = ../TopologicalSort1.swift; sourceTree = SOURCE_ROOT; };
 		7B3471C21C8F5348008381CD /* TopologicalSort2.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TopologicalSort2.swift; path = ../TopologicalSort2.swift; sourceTree = SOURCE_ROOT; };
+		7BE143481C9C6A93001BC747 /* TopologicalSort3.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TopologicalSort3.swift; path = ../TopologicalSort3.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -55,9 +55,9 @@
 			isa = PBXGroup;
 			children = (
 				7B3471BC1C8F50DD008381CD /* Graph.swift */,
-				7B3471BD1C8F50DD008381CD /* Stack.swift */,
 				7B3471BE1C8F50DD008381CD /* TopologicalSort1.swift */,
 				7B3471C21C8F5348008381CD /* TopologicalSort2.swift */,
+				7BE143481C9C6A93001BC747 /* TopologicalSort3.swift */,
 				7B3471BA1C8F50CF008381CD /* TopologicalSortTests.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
@@ -135,9 +135,9 @@
 			files = (
 				7B3471C31C8F5348008381CD /* TopologicalSort2.swift in Sources */,
 				7B3471BF1C8F50DD008381CD /* Graph.swift in Sources */,
-				7B3471C01C8F50DD008381CD /* Stack.swift in Sources */,
 				7B3471BB1C8F50CF008381CD /* TopologicalSortTests.swift in Sources */,
 				7B3471C11C8F50DD008381CD /* TopologicalSort1.swift in Sources */,
+				7BE143491C9C6A93001BC747 /* TopologicalSort3.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
diff --git a/Topological Sort/Tests/TopologicalSortTests.swift b/Topological Sort/Tests/TopologicalSortTests.swift
index 4d4178cfb..bc4dd7f60 100644
--- a/Topological Sort/Tests/TopologicalSortTests.swift	
+++ b/Topological Sort/Tests/TopologicalSortTests.swift	
@@ -40,44 +40,51 @@ class TopologicalSort: XCTestCase {
     graph.addEdge(fromNode: node11, toNode: node10)
     graph.addEdge(fromNode: node8, toNode: node9)
 
-    XCTAssertEqual(graph.topologicalSort(), ["3", "8", "9", "10", "7", "11", "2", "5"])
-    XCTAssertEqual(graph.topologicalSort2(), ["3", "7", "5", "8", "11", "2", "9", "10"])
+    XCTAssertEqual(graph.topologicalSort(), ["5", "7", "11", "2", "3", "8", "9", "10"])
+    XCTAssertEqual(graph.topologicalSortKahn(), ["3", "7", "5", "8", "11", "2", "9", "10"])
+    XCTAssertEqual(graph.topologicalSortAlternative(), ["5", "7", "3", "8", "11", "10", "9", "2"])
   }
 
   func testTopologicalSortEdgeLists() {
     let p1 = ["A B", "A C", "B C", "B D", "C E", "C F", "E D", "F E", "G A", "G F"]
-    let a1 = ["G", "A", "B", "C", "F", "E", "D"]  // TODO
-    let s1 = ["G", "A", "B", "C", "F", "E", "D"]
+    let s1 = ["G", "A", "B", "C", "E", "D", "F"]
+    let a1 = ["G", "A", "B", "C", "F", "E", "D"]
+    let k1 = ["G", "A", "B", "C", "F", "E", "D"]
 
     let p2 = ["B C", "C D", "C G", "B F", "D G", "G E", "F G", "F G"]
-    let a2 = ["B", "C", "F", "D", "G", "E"]  // TODO
-    let s2 = ["B", "C", "F", "D", "G", "E"]
+    let s2 = ["B", "C", "D", "G", "E", "F"]
+    let a2 = ["B", "C", "F", "D", "G", "E"]
+    let k2 = ["B", "F", "C", "D", "G", "E"]
 
     let p3 = ["S V", "S W", "V T", "W T"]
-    let a3 = ["S", "V", "W", "T"]  // TODO
     let s3 = ["S", "V", "W", "T"]
+    let a3 = ["S", "V", "W", "T"]
+    let k3 = ["S", "V", "W", "T"]
 
     let p4 = ["5 11", "7 11", "7 8", "3 8", "3 10", "11 2", "11 9", "11 10", "8 9"]
-    let a4 = ["3", "8", "9", "10", "7", "11", "2", "5"]
-    let s4 = ["3", "7", "5", "8", "11", "2", "9", "10"]
+    let s4 = ["5", "7", "11", "2", "3", "8", "9", "10"]
+    let a4 = ["3", "7", "5", "8", "11", "2", "9", "10"]
+    let k4 = ["5", "7", "3", "8", "11", "10", "9", "2"]
 
     let data = [
-      (p1, a1, s1),
-      (p2, a2, s2),
-      (p3, a3, s3),
-      (p4, a4, s4),
+      (p1, s1, a1, k1),
+      (p2, s2, a2, k2),
+      (p3, s3, a3, k3),
+      (p4, s4, a4, k4),
     ]
 
     for d in data {
       let graph = Graph()
       graph.loadEdgeList(d.0)
 
-      // TODO: this fails the tests
-      //let sorted1 = graph.topologicalSort()
-      //XCTAssertEqual(sorted1, d.1)
+      let sorted1 = graph.topologicalSort()
+      XCTAssertEqual(sorted1, d.1)
 
-      let sorted2 = graph.topologicalSort2()
+      let sorted2 = graph.topologicalSortKahn()
       XCTAssertEqual(sorted2, d.2)
+
+      let sorted3 = graph.topologicalSortAlternative()
+      XCTAssertEqual(sorted3, d.3)
     }
   }
 }
diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index d1a92abbc..d0ebe550d 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -28,5 +28,8 @@ graph.addEdge(fromNode: node8, toNode: node9)
 // using depth-first search
 graph.topologicalSort()
 
-// alternative method
-graph.topologicalSort2()
+// also using depth-first search
+graph.topologicalSortAlternative()
+
+// Kahn's algorithm
+graph.topologicalSortKahn()
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index fca7485e8..7fbadb6ce 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -30,3 +30,22 @@ public class Graph: CustomStringConvertible {
     return nil
   }
 }
+
+extension Graph {
+  typealias InDegree = Int
+
+  func calculateInDegreeOfNodes() -> [Node : InDegree] {
+    var inDegrees = [Node : InDegree]()
+    
+    for (node, _) in adjacencyLists {
+      inDegrees[node] = 0
+    }
+    
+    for (_, adjacencyList) in adjacencyLists {
+      for nodeInList in adjacencyList {
+        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
+      }
+    }
+    return inDegrees
+  }
+}
diff --git a/Topological Sort/Topological Sort.playground/Sources/Stack.swift b/Topological Sort/Topological Sort.playground/Sources/Stack.swift
deleted file mode 100644
index 7f4aadc8b..000000000
--- a/Topological Sort/Topological Sort.playground/Sources/Stack.swift	
+++ /dev/null
@@ -1,27 +0,0 @@
-public struct Stack<T> {
-  private var array = [T]()
-  
-  public var isEmpty: Bool {
-    return array.isEmpty
-  }
-  
-  public var count: Int {
-    return array.count
-  }
-  
-  public mutating func push(element: T) {
-    array.append(element)
-  }
-  
-  public mutating func pop() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array.removeLast()
-    }
-  }
-  
-  public func peek() -> T? {
-    return array.last
-  }
-}
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index 011c4164b..a6051a4bf 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -1,53 +1,35 @@
 extension Graph {
-  typealias InDegree = Int
-
-  func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    var inDegrees = [Node : InDegree]()
-    
-    for (node, _) in adjacencyLists {
-      inDegrees[node] = 0
-    }
-    
-    for (_, adjacencyList) in adjacencyLists {
-      for nodeInList in adjacencyList {
-        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
-      }
-    }
-    return inDegrees
-  }
-  
   private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
     var result = [source]
     visited[source] = true
     
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
-        if !(visited[nodeInAdjacencyList] ?? false) {
-          result += (depthFirstSearch(nodeInAdjacencyList, visited: &visited))
+        if let seen = visited[nodeInAdjacencyList] where !seen {
+          result += depthFirstSearch(nodeInAdjacencyList, visited: &visited)
         }
       }
     }
     return result
   }
   
+  /* Topological sort using depth-first search. */
   public func topologicalSort() -> [Node] {
     
-    let startNodes = calculateInDegreeOfNodes().filter({(_, indegree) in
+    let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
-    }).map({(node, indegree) in
+    }).map({ node, indegree in
       return node
     })
     
     var visited = [Node : Bool]()
-    
     for (node, _) in adjacencyLists {
       visited[node] = false
     }
     
     var result = [Node]()
-    
     for startNode in startNodes {
-      result += depthFirstSearch(startNode, visited: &visited)
+      result = depthFirstSearch(startNode, visited: &visited) + result
     }
     
     return result
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift
index 468e098df..f4c1cdd6f 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
@@ -1,6 +1,6 @@
 extension Graph {
-  /* Topological sort that does not use a depth-first search. */
-  public func topologicalSort2() -> [Node] {
+  /* Topological sort using Kahn's algorithm. */
+  public func topologicalSortKahn() -> [Node] {
     var nodes = calculateInDegreeOfNodes()
 
     // Find vertices with no predecessors and puts them into a new list.
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift
new file mode 100644
index 000000000..24a6189fa
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift	
@@ -0,0 +1,35 @@
+/*
+  An alternative implementation of topological sort using depth-first search.
+  This does not start at vertices with in-degree 0 but simply at the first one
+  it finds. It uses a stack to build up the sorted list, but in reverse order.
+*/
+extension Graph {
+  public func topologicalSortAlternative() -> [Node] {
+    var stack = [Node]()
+    
+    var visited = [Node: Bool]()
+    for (node, _) in adjacencyLists {
+      visited[node] = false
+    }
+
+    func depthFirstSearch(source: Node) {
+      if let adjacencyList = adjacencyList(forNode: source) {
+        for neighbor in adjacencyList {
+          if let seen = visited[neighbor] where !seen {
+            depthFirstSearch(neighbor)
+          }
+        }
+      }
+      stack.append(source)
+      visited[source] = true
+    }
+
+    for (node, _) in visited {
+      if let seen = visited[node] where !seen {
+        depthFirstSearch(node)
+      }
+    }
+
+    return stack.reverse()
+  }
+}
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 500b8ca11..a6051a4bf 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -1,55 +1,37 @@
 extension Graph {
-  typealias InDegree = Int
-
-  func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    var inDegrees = [Node : InDegree]()
-    
-    for (node, _) in adjacencyLists {
-      inDegrees[node] = 0
-    }
-    
-    for (_, adjacencyList) in adjacencyLists {
-      for nodeInList in adjacencyList {
-        inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
-      }
-    }
-    return inDegrees
-  }
-  
   private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
     var result = [source]
     visited[source] = true
     
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
-        if !(visited[nodeInAdjacencyList] ?? false) {
-          result += (depthFirstSearch(nodeInAdjacencyList, visited: &visited))
+        if let seen = visited[nodeInAdjacencyList] where !seen {
+          result += depthFirstSearch(nodeInAdjacencyList, visited: &visited)
         }
       }
     }
     return result
   }
   
+  /* Topological sort using depth-first search. */
   public func topologicalSort() -> [Node] {
     
-    let startNodes = calculateInDegreeOfNodes().filter({(_, indegree) in
+    let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
-    }).map({(node, indegree) in
+    }).map({ node, indegree in
       return node
     })
     
     var visited = [Node : Bool]()
-    
     for (node, _) in adjacencyLists {
       visited[node] = false
     }
     
     var result = [Node]()
-    
     for startNode in startNodes {
-      result += depthFirstSearch(startNode, visited: &visited)
+      result = depthFirstSearch(startNode, visited: &visited) + result
     }
-
+    
     return result
   }
 }
diff --git a/Topological Sort/TopologicalSort2.swift b/Topological Sort/TopologicalSort2.swift
index 468e098df..f4c1cdd6f 100644
--- a/Topological Sort/TopologicalSort2.swift	
+++ b/Topological Sort/TopologicalSort2.swift	
@@ -1,6 +1,6 @@
 extension Graph {
-  /* Topological sort that does not use a depth-first search. */
-  public func topologicalSort2() -> [Node] {
+  /* Topological sort using Kahn's algorithm. */
+  public func topologicalSortKahn() -> [Node] {
     var nodes = calculateInDegreeOfNodes()
 
     // Find vertices with no predecessors and puts them into a new list.
diff --git a/Topological Sort/TopologicalSort3.swift b/Topological Sort/TopologicalSort3.swift
new file mode 100644
index 000000000..24a6189fa
--- /dev/null
+++ b/Topological Sort/TopologicalSort3.swift	
@@ -0,0 +1,35 @@
+/*
+  An alternative implementation of topological sort using depth-first search.
+  This does not start at vertices with in-degree 0 but simply at the first one
+  it finds. It uses a stack to build up the sorted list, but in reverse order.
+*/
+extension Graph {
+  public func topologicalSortAlternative() -> [Node] {
+    var stack = [Node]()
+    
+    var visited = [Node: Bool]()
+    for (node, _) in adjacencyLists {
+      visited[node] = false
+    }
+
+    func depthFirstSearch(source: Node) {
+      if let adjacencyList = adjacencyList(forNode: source) {
+        for neighbor in adjacencyList {
+          if let seen = visited[neighbor] where !seen {
+            depthFirstSearch(neighbor)
+          }
+        }
+      }
+      stack.append(source)
+      visited[source] = true
+    }
+
+    for (node, _) in visited {
+      if let seen = visited[node] where !seen {
+        depthFirstSearch(node)
+      }
+    }
+
+    return stack.reverse()
+  }
+}

From 160522b4528cd4a536ed1e593f0c862903f17377 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 19:35:11 +0100
Subject: [PATCH 0162/1679] Fix error in depth-first search

Results were added in the wrong order inside the DFS too.
Unit tests now use a function to check whether the result is a valid topological sort.
---
 Topological Sort/README.markdown              | 16 ++++---
 .../Tests/TopologicalSortTests.swift          | 44 ++++++++-----------
 .../Sources/TopologicalSort1.swift            | 11 ++---
 Topological Sort/TopologicalSort1.swift       |  9 ++--
 4 files changed, 38 insertions(+), 42 deletions(-)

diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index c92072539..4429a0754 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -28,7 +28,7 @@ If we were to represent these objectives in the form of a graph it would look as
 
 ![Example](Images/Algorithms.png)
 
-If we consider each algorithm to be a vertex in the graph you can clearly see the dependencies between them. To learn something you might have to know something else first. This is exactly what topological sort is used for -- it will sort things out such that you know what to do first.
+If we consider each algorithm to be a vertex in the graph you can clearly see the dependencies between them. To learn something you might have to know something else first. This is exactly what topological sort is used for -- it will sort things out so that you know what to do first.
 
 ## How does it work?
 
@@ -36,7 +36,7 @@ If we consider each algorithm to be a vertex in the graph you can clearly see th
 
 The *in-degree* of a vertex is the number of edges pointing at that vertex. Vertices with no incoming edges have an in-degree of 0. These vertices are the starting points for the topological sort.
 
-In the context of the previous example, these vertices represent algorithms that don't have any prerequisites; you don't need to learn anything else first, hence the sort starts with them.
+In the context of the previous example, these starting vertices represent algorithms and data structures that don't have any prerequisites; you don't need to learn anything else first, hence the sort starts with them.
 
 **Step 2: Traverse the graph with depth-first search**
 
@@ -63,7 +63,7 @@ Consider the following graph:
 **Step 2:** Perform depth-first search for each starting vertex, without remembering vertices that have already been visited:
 
 ```
-Vertex 3: 3, 8, 9, 10
+Vertex 3: 3, 10, 8, 9
 Vertex 7: 7, 11, 2, 8, 9
 Vertex 5: 5, 11, 2, 9, 10
 ```
@@ -71,12 +71,12 @@ Vertex 5: 5, 11, 2, 9, 10
 **Step 3:** Filter out the vertices already visited in each previous search:
 
 ```
-Vertex 3: 3, 8, 9, 10
+Vertex 3: 3, 10, 8, 9
 Vertex 7: 7, 11, 2
 Vertex 5: 5
 ```
 
-**Step 4:** Combine the results of these three depth-first searches. The final sorted order is **5, 7, 11, 2, 3, 8, 9, 10**. (Important: we need to add the results of each subsequent search to the *front* of the list.)
+**Step 4:** Combine the results of these three depth-first searches. The final sorted order is **5, 7, 11, 2, 3, 10, 8, 9**. (Important: we need to add the results of each subsequent search to the *front* of the sorted list.)
 
 The result of the topological sort looks like this:
 
@@ -122,11 +122,13 @@ Some remarks:
 
 2. The `visited` array keeps track of whether we've already seen a vertex during the depth-first search. Initially, we set all elements to `false`.
 
-3. For each of the vertices in the `startNodes` array, perform a depth-first search. This returns an array of `Node` objects. We prepend that array to our own `result` array.
+3. For each of the vertices in the `startNodes` array, perform a depth-first search. This returns an array of sorted `Node` objects. We prepend that array to our own `result` array.
 
 4. The `result` array contains all the vertices in topologically sorted order.
 
-## Alternative method (Kahn's algorithm)
+> **Note:** For a slightly different implementation of topological sort using depth-first search, see [TopologicalSort3.swift](TopologicalSort3.swift). This uses a stack and does not require you to find all vertices with in-degree 0 first.
+
+## Kahn's algorithm
 
 Even though depth-first search is the typical way to perform a topological sort, there is another algorithm that also does the job. 
 
diff --git a/Topological Sort/Tests/TopologicalSortTests.swift b/Topological Sort/Tests/TopologicalSortTests.swift
index bc4dd7f60..441422703 100644
--- a/Topological Sort/Tests/TopologicalSortTests.swift	
+++ b/Topological Sort/Tests/TopologicalSortTests.swift	
@@ -18,6 +18,18 @@ extension Graph {
 
 class TopologicalSort: XCTestCase {
   
+  // The topological sort is valid if a node does not have any of its
+  // predecessors in its adjacency list.
+  func checkIsValidTopologicalSort(graph: Graph, _ a: [Graph.Node]) {
+    for i in (a.count - 1).stride(to: 0, by: -1) {
+      if let neighbors = graph.adjacencyList(forNode: a[i]) {
+        for j in (i - 1).stride(through: 0, by: -1) {
+          XCTAssertFalse(neighbors.contains(a[j]), "\(a) is not a valid topological sort")
+        }
+      }
+    }
+  }
+  
   func testTopologicalSort() {
     let graph = Graph()
     
@@ -40,51 +52,31 @@ class TopologicalSort: XCTestCase {
     graph.addEdge(fromNode: node11, toNode: node10)
     graph.addEdge(fromNode: node8, toNode: node9)
 
-    XCTAssertEqual(graph.topologicalSort(), ["5", "7", "11", "2", "3", "8", "9", "10"])
+    XCTAssertEqual(graph.topologicalSort(), ["5", "7", "11", "2", "3", "10", "8", "9"])
     XCTAssertEqual(graph.topologicalSortKahn(), ["3", "7", "5", "8", "11", "2", "9", "10"])
     XCTAssertEqual(graph.topologicalSortAlternative(), ["5", "7", "3", "8", "11", "10", "9", "2"])
   }
 
   func testTopologicalSortEdgeLists() {
     let p1 = ["A B", "A C", "B C", "B D", "C E", "C F", "E D", "F E", "G A", "G F"]
-    let s1 = ["G", "A", "B", "C", "E", "D", "F"]
-    let a1 = ["G", "A", "B", "C", "F", "E", "D"]
-    let k1 = ["G", "A", "B", "C", "F", "E", "D"]
-
     let p2 = ["B C", "C D", "C G", "B F", "D G", "G E", "F G", "F G"]
-    let s2 = ["B", "C", "D", "G", "E", "F"]
-    let a2 = ["B", "C", "F", "D", "G", "E"]
-    let k2 = ["B", "F", "C", "D", "G", "E"]
-
     let p3 = ["S V", "S W", "V T", "W T"]
-    let s3 = ["S", "V", "W", "T"]
-    let a3 = ["S", "V", "W", "T"]
-    let k3 = ["S", "V", "W", "T"]
-
     let p4 = ["5 11", "7 11", "7 8", "3 8", "3 10", "11 2", "11 9", "11 10", "8 9"]
-    let s4 = ["5", "7", "11", "2", "3", "8", "9", "10"]
-    let a4 = ["3", "7", "5", "8", "11", "2", "9", "10"]
-    let k4 = ["5", "7", "3", "8", "11", "10", "9", "2"]
 
-    let data = [
-      (p1, s1, a1, k1),
-      (p2, s2, a2, k2),
-      (p3, s3, a3, k3),
-      (p4, s4, a4, k4),
-    ]
+    let data = [ p1, p2, p3, p4 ]
 
     for d in data {
       let graph = Graph()
-      graph.loadEdgeList(d.0)
+      graph.loadEdgeList(d)
 
       let sorted1 = graph.topologicalSort()
-      XCTAssertEqual(sorted1, d.1)
+      checkIsValidTopologicalSort(graph, sorted1)
 
       let sorted2 = graph.topologicalSortKahn()
-      XCTAssertEqual(sorted2, d.2)
+      checkIsValidTopologicalSort(graph, sorted2)
 
       let sorted3 = graph.topologicalSortAlternative()
-      XCTAssertEqual(sorted3, d.3)
+      checkIsValidTopologicalSort(graph, sorted3)
     }
   }
 }
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index a6051a4bf..a7be2803c 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -1,18 +1,19 @@
 extension Graph {
   private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
-    var result = [source]
-    visited[source] = true
+    var result = [Node]()
     
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
         if let seen = visited[nodeInAdjacencyList] where !seen {
-          result += depthFirstSearch(nodeInAdjacencyList, visited: &visited)
+          result = depthFirstSearch(nodeInAdjacencyList, visited: &visited) + result
         }
       }
     }
-    return result
+    
+    visited[source] = true
+    return [source] + result
   }
-  
+
   /* Topological sort using depth-first search. */
   public func topologicalSort() -> [Node] {
     
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index a6051a4bf..e134bf9ce 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -1,16 +1,17 @@
 extension Graph {
   private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
-    var result = [source]
-    visited[source] = true
+    var result = [Node]()
     
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
         if let seen = visited[nodeInAdjacencyList] where !seen {
-          result += depthFirstSearch(nodeInAdjacencyList, visited: &visited)
+          result = depthFirstSearch(nodeInAdjacencyList, visited: &visited) + result
         }
       }
     }
-    return result
+    
+    visited[source] = true
+    return [source] + result
   }
   
   /* Topological sort using depth-first search. */

From 784023d3269b2a4e88bb994a6badd89b4ed46c4f Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 19:49:07 +0100
Subject: [PATCH 0163/1679] Tweak graph images and text

---
 Graph/Images/DAG.graffle           | Bin 2018 -> 2033 bytes
 Graph/Images/DAG.png               | Bin 9119 -> 17463 bytes
 Graph/Images/Flights.png           | Bin 34735 -> 42005 bytes
 Graph/Images/FlightsDirected.png   | Bin 32004 -> 38653 bytes
 Graph/Images/SocialNetwork.graffle | Bin 2416 -> 2419 bytes
 Graph/Images/SocialNetwork.png     | Bin 31918 -> 36342 bytes
 Graph/README.markdown              |  12 ++++++------
 7 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Graph/Images/DAG.graffle b/Graph/Images/DAG.graffle
index af6a84ab09879a7a314d339b827746f6393968f0..68cb09554fc31c95169b268ff3b3688848e585e4 100644
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diff --git a/Graph/README.markdown b/Graph/README.markdown
index 546d4c599..b76fae732 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -20,7 +20,7 @@ With this hypothetical airline, flying from San Francisco to Moscow is cheapest
 
 Edges can also be *directed*. So far the edges you've seen have been undirected, so if Ada knows Charles, then Charles also knows Ada. A directed edge, on the other hand, implies a one-way relationship. A directed edge from vertex X to vertex Y connects X to Y, but *not* Y to X.
 
-Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back!).
+Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back).
 
 ![One-way flights](Images/FlightsDirected.png)
 
@@ -68,15 +68,15 @@ Another common graph that's used by programmers is the state machine, where edge
 
 ![State machine](Images/StateMachine.png)
 
-Graphs are awesome. Facebook made a fortune from them. If you're going to learn any data structure, it should be the graph, and the vast collection of standard graph algorithms.
+Graphs are awesome. Facebook made a fortune from their social graph. If you're going to learn any data structure, it should be the graph and the vast collection of standard graph algorithms.
 
 ## Vertices and edges, oh my!
 
 In theory, a graph is just a bunch of vertex objects and a bunch of edge objects. But how do you describe these in code?
 
-There are two main strategies:
+There are two main strategies: adjacency list and adjacency matrix.
 
-**Adjacency List.** In an adjacency list implementation, each vertex stores a list of edges that originate from the vertex. For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list containing 3 edges.
+**Adjacency List.** In an adjacency list implementation, each vertex stores a list of edges that originate from that vertex. For example, if vertex A has an edge to vertices B, C, and D, then vertex A would have a list containing 3 edges.
 
 ![Adjacency list](Images/AdjacencyList.png)
 
@@ -97,7 +97,7 @@ Let *V* be the number of vertices in the graph, and *E* the number of edges.  Th
 | Add Edge        | O(1)           | O(1)             |
 | Check Adjacency | O(V)           | O(1)             |
 
-"Checking adjacency" means that we try to determine that a given vertex is an immediate neighbor of another vertex. The time to check adjacency for an adjacency list is **O(V)**, because at worst a vertex is connected to *every* other vertex.
+"Checking adjacency" means that we try to determine that a given vertex is an immediate neighbor of another vertex. The time to check adjacency for an adjacency list is **O(V)**, because in the worst case a vertex is connected to *every* other vertex.
 
 In the case of a *sparse* graph, where each vertex is connected to only a handful of other vertices, an adjacency list is the best way to store the edges. If the graph is *dense*, where each vertex is connected to most of the other vertices, then a matrix is preferred.
 
@@ -185,7 +185,7 @@ v4.connectTo(v1, withWeight: 2.8)
 v2.connectTo(v5, withWeight: 3.2)
 ```
 
-> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code for each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
+> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
 
 ## The code: adjacency matrix
 

From efe956a55dc7e3dfa84d3cf4586fd250b0f98933 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 21:01:54 +0100
Subject: [PATCH 0164/1679] Replace animation with my own

The original was apparently taken from Wikipedia and I don't know if we had the rights to it. Besides, it was ugly.
---
 .../Contents.swift                            |   5 +-
 .../Contents.swift                            |   8 +-
 .../Contents.swift                            |  12 +--
 .../Resources/Animated_BFS.gif                | Bin 33276 -> 0 bytes
 Breadth-First Search/BreadthFirstSearch.swift |   3 +-
 ...readthFirstSearchMinimumSpanningTree.swift |   3 +-
 .../BreadthFirstSearchShortestPath.swift      |   3 +-
 .../Images/AnimatedExample.gif                | Bin 0 -> 9713 bytes
 .../Images/AnimatedExample.graffle            | Bin 0 -> 4912 bytes
 .../Images/AnimatedExample.psd                | Bin 0 -> 582072 bytes
 Breadth-First Search/Images/Animated_BFS.gif  | Bin 33276 -> 0 bytes
 .../Images/TraversalTree.graffle              | Bin 0 -> 2088 bytes
 Breadth-First Search/Images/TraversalTree.png | Bin 0 -> 9817 bytes
 Breadth-First Search/README.markdown          |  91 ++++++++++--------
 .../Tests/BreadthFirstSearchTests.swift       |   4 +-
 15 files changed, 69 insertions(+), 60 deletions(-)
 delete mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Resources/Animated_BFS.gif
 create mode 100644 Breadth-First Search/Images/AnimatedExample.gif
 create mode 100644 Breadth-First Search/Images/AnimatedExample.graffle
 create mode 100644 Breadth-First Search/Images/AnimatedExample.psd
 delete mode 100644 Breadth-First Search/Images/Animated_BFS.gif
 create mode 100644 Breadth-First Search/Images/TraversalTree.graffle
 create mode 100644 Breadth-First Search/Images/TraversalTree.png

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index c0868c653..006ce1873 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -10,8 +10,7 @@ func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph
   queue.enqueue(sourceInMinimumSpanningTree)
   sourceInMinimumSpanningTree.visited = true
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.visited {
@@ -26,10 +25,12 @@ func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph
   return minimumSpanningTree
 }
 
+
 /*:
 ![Animated example of a breadth-first search](Minimum_Spanning_Tree.png)
 */
 
+
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index be35cc684..2a9c1676f 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -10,8 +10,7 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   queue.enqueue(sourceInShortestPathsGraph)
   sourceInShortestPathsGraph.distance = 0
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
@@ -23,9 +22,8 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
 
   return shortestPathGraph
 }
-/*:
-![Animated example of a breadth-first search](Animated_BFS.gif)
-*/
+
+
 
 let graph = Graph()
 
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 8cd7df2f5..c761d9e99 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -7,9 +7,8 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
-    for edge in current.neighbors {
+  while let node = queue.dequeue() {
+    for edge in node.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
@@ -22,9 +21,7 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   return nodesExplored
 }
 
-/*:
-![Animated example of a breadth-first search](Animated_BFS.gif)
-*/
+
 
 let graph = Graph()
 
@@ -44,10 +41,11 @@ graph.addEdge(nodeB, neighbor: nodeE)
 graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeG)
 
 
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
 
 //: [Next: Shortest Path Example](@next)
-
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Resources/Animated_BFS.gif b/Breadth-First Search/BreadthFirstSearch.playground/Resources/Animated_BFS.gif
deleted file mode 100644
index d8fe07cbc40a0a19534b597e123bf803de42f205..0000000000000000000000000000000000000000
GIT binary patch
literal 0
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diff --git a/Breadth-First Search/BreadthFirstSearch.swift b/Breadth-First Search/BreadthFirstSearch.swift
index 31bb1c594..296bf42ed 100644
--- a/Breadth-First Search/BreadthFirstSearch.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.swift	
@@ -5,8 +5,7 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
   
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.visited {
diff --git a/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift b/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift
index 9329a0d3c..92d370878 100644
--- a/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift	
+++ b/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift	
@@ -6,8 +6,7 @@ func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph
   queue.enqueue(sourceInMinimumSpanningTree)
   sourceInMinimumSpanningTree.visited = true
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.visited {
diff --git a/Breadth-First Search/BreadthFirstSearchShortestPath.swift b/Breadth-First Search/BreadthFirstSearchShortestPath.swift
index 2e5a9c1d0..13ed0c080 100644
--- a/Breadth-First Search/BreadthFirstSearchShortestPath.swift	
+++ b/Breadth-First Search/BreadthFirstSearchShortestPath.swift	
@@ -6,8 +6,7 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   queue.enqueue(sourceInShortestPathsGraph)
   sourceInShortestPathsGraph.distance = 0
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
diff --git a/Breadth-First Search/Images/AnimatedExample.gif b/Breadth-First Search/Images/AnimatedExample.gif
new file mode 100644
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diff --git a/Breadth-First Search/Images/TraversalTree.png b/Breadth-First Search/Images/TraversalTree.png
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diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index e75d2b913..70127db5a 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -4,72 +4,86 @@ Breadth-first search (BFS) is an algorithm for traversing or searching [tree](..
 
 ## Animated example
 
-![Animated example of a breadth-first search](Images/Animated_BFS.gif)
+Here's how breadth-first search works on a graph:
 
-Let's follow the animated example by using a [queue](../Queue/).
+![Animated example of a breadth-first search](Images/AnimatedExample.gif)
 
-Start with the source node ``a`` and add it to a queue.
+When we visit a node, we color it black. We also put its neighbor nodes into a [queue](../Queue/). In the animation the nodes that are enqueued but not visited yet are shown in gray.
+
+Let's follow the animated example. We start with the source node `A` and add it to a queue. In the animation this is shown as node `A` becoming gray.
 
 ```swift
-queue.enqueue(a)
+queue.enqueue(A)
 ```
 
-The queue is now ``[ a ]``. Dequeue ``a`` and enqueue its two neighbor nodes ``b`` and ``c``.
+The queue is now `[ A ]`. The idea is that, as long as there are nodes in the queue, we visit the node that's at the front of the queue, and enqueue its immediate neighbor nodes if they have not been visited yet.
+
+To start traversing the graph, we pull the first node off the queue, `A`, and color it black. Then we enqueue its two neighbor nodes `B` and `C`. This colors them gray.
 
 ```swift
-queue.dequeue()   // a
-queue.enqueue(b)
-queue.enqueue(c)
+queue.dequeue()   // A
+queue.enqueue(B)
+queue.enqueue(C)
 ```
 
-The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue `b`'s neighbor nodes ``d`` and ``e``.
+The queue is now `[ B, C ]`. We dequeue `B`, and enqueue `B`'s neighbor nodes `D` and `E`.
 
 ```swift
-queue.dequeue()   // b
-queue.enqueue(d)
-queue.enqueue(e)
+queue.dequeue()   // B
+queue.enqueue(D)
+queue.enqueue(E)
 ```
 
-The queue is now ``[ c, d, e ]``. Dequeue ``c`` and enqueue `c`'s neighbor nodes ``f`` and ``g``.
+The queue is now `[ C, D, E ]`. Dequeue `C`, and enqueue `C`'s neighbor nodes `F` and `G`.
 
 ```swift
-queue.dequeue()   // c
-queue.enqueue(f)
-queue.enqueue(g)
+queue.dequeue()   // C
+queue.enqueue(F)
+queue.enqueue(G)
 ```
 
-The queue is now ``[ d, e, f, g ]``. Dequeue ``d`` which has no neighbor nodes.
+The queue is now `[ D, E, F, G ]`. Dequeue `D`, which has no neighbor nodes.
 
 ```swift
-queue.dequeue()   // d
+queue.dequeue()   // D
 ```
 
-The queue is now ``[ e, f, g ]``. Dequeue ``e`` and enqueue its single neighbor node ``h``.
+The queue is now `[ E, F, G ]`. Dequeue `E` and enqueue its single neighbor node `H`. Note that `B` is also a neighbor for `E` but we've already visited `B`, so we're not adding it to the queue again.
 
 ```swift
-queue.dequeue()   // e
-queue.enqueue(h)
+queue.dequeue()   // E
+queue.enqueue(H)
 ```
 
-The queue is now ``[ f, g, h ]``. Dequeue ``f`` which has no neighbor nodes.
+The queue is now `[ F, G, H ]`. Dequeue `F`, which has no unvisited neighbor nodes.
 
 ```swift
-queue.dequeue()   // f
+queue.dequeue()   // F
 ```
 
-The queue is now ``[ g, h ]``. Dequeue ``g`` which has no neighbor nodes.
+The queue is now `[ G, H ]`. Dequeue `G`, which has no unvisited neighbor nodes.
 
 ```swift
-queue.dequeue()   // g
+queue.dequeue()   // G
 ```
 
-The queue is now ``[ h ]``. Dequeue ``h`` which has no neighbor nodes.
+The queue is now `[ H ]`. Dequeue `H`, which has no unvisited neighbor nodes.
 
 ```swift
-queue.dequeue()   // h
+queue.dequeue()   // H
 ```
 
-The queue is now empty, meaning that all nodes have been explored. The order in which the nodes were explored is `a`, `b`, `c`, `d`, `e`, `f`, `g`, `h`.
+The queue is now empty, meaning that all nodes have been explored. The order in which the nodes were explored is `A`, `B`, `C`, `D`, `E`, `F`, `G`, `H`.
+
+We can show this as a tree:
+
+![The BFS tree](Images/TraversalTree.png)
+
+The parent of a node is the one that "discovered" that node. The root of the tree is the node you started the breadth-first search from.
+
+For an unweighted graph, this tree defines a shortest path from the starting node to every other node in the tree. So breadth-first search is one way to find the shortest path between two nodes in a graph.
+
+Breadth-first search can be used on directed and undirected graphs.
 
 ## The code
 
@@ -83,9 +97,8 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
-    for edge in current.neighbors {
+  while let node = queue.dequeue() {
+    for edge in node.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.visited {
         queue.enqueue(neighborNode)
@@ -99,10 +112,12 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
 }
 ```
 
+While there are nodes in the queue, we visit the first one and then enqueue its immediate neighbors if they haven't been visited yet.
+
 Put this code in a playground and test it like so:
 
 ```swift
-let graph = Graph()   // Representing the graph from the animated example
+let graph = Graph()
 
 let nodeA = graph.addNode("a")
 let nodeB = graph.addNode("b")
@@ -120,6 +135,8 @@ graph.addEdge(nodeB, neighbor: nodeE)
 graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeG)
 
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
@@ -178,8 +195,7 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   queue.enqueue(sourceInShortestPathsGraph)
   sourceInShortestPathsGraph.distance = 0
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
@@ -312,8 +328,7 @@ func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph
   queue.enqueue(sourceInMinimumSpanningTree)
   sourceInMinimumSpanningTree.visited = true
 
-  while !queue.isEmpty {
-    let current = queue.dequeue()!
+  while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.visited {
@@ -386,6 +401,6 @@ print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
 
 ## See also
 
-[Graph](../Graph/), [Tree](../Tree/), [Queues](../Queue/), [Shortest Path](../Shortest Path/), [Minimum Spanning Tree](../Minimum Spanning Tree/).
+[Graph](../Graph/), [Tree](../Tree/), [Queue](../Queue/), [Shortest Path](../Shortest Path/), [Minimum Spanning Tree](../Minimum Spanning Tree/).
 
-*Written by [Chris Pilcher](https://github.com/chris-pilcher)*
+*Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift
index 6c0d382d9..b5e3adac6 100755
--- a/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
+++ b/Breadth-First Search/Tests/BreadthFirstSearchTests.swift	
@@ -4,6 +4,7 @@ class BreadthFirstSearchTests: XCTestCase {
 
   func testExploringTree() {
     let tree = Graph()
+
     let nodeA = tree.addNode("a")
     let nodeB = tree.addNode("b")
     let nodeC = tree.addNode("c")
@@ -12,6 +13,7 @@ class BreadthFirstSearchTests: XCTestCase {
     let nodeF = tree.addNode("f")
     let nodeG = tree.addNode("g")
     let nodeH = tree.addNode("h")
+
     tree.addEdge(nodeA, neighbor: nodeB)
     tree.addEdge(nodeA, neighbor: nodeC)
     tree.addEdge(nodeB, neighbor: nodeD)
@@ -70,7 +72,6 @@ class BreadthFirstSearchTests: XCTestCase {
     let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 
     XCTAssertEqual(nodesExplored, ["a", "b", "h", "c", "g", "i", "d", "f", "e"])
-
   }
 
   func testExploringGraphWithASingleNode() {
@@ -82,4 +83,3 @@ class BreadthFirstSearchTests: XCTestCase {
     XCTAssertEqual(nodesExplored, ["a"])
   }
 }
-

From 1f5c20ed74d614b3e5a4afab01a4df4b831081f4 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 18 Mar 2016 22:30:58 +0100
Subject: [PATCH 0165/1679] Extract shortest path and minimum spanning tree
 from breadth-first search

---
 .../Contents.swift                            |   4 -
 .../contents.xcplayground                     |   8 +-
 Breadth-First Search/README.markdown          | 258 +----------------
 Breadth-First Search/{ => Tests}/Graph.swift  |   0
 Breadth-First Search/{ => Tests}/Queue.swift  |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     |  20 +-
 Minimum Spanning Tree/Images/Graph.png        | Bin 0 -> 20362 bytes
 Minimum Spanning Tree/Images/Graph.sketch     | Bin 0 -> 81920 bytes
 .../Images/MinimumSpanningTree.png            | Bin
 .../Images/MinimumSpanningTree.sketch         | Bin
 Minimum Spanning Tree/Images/Tree.graffle     | Bin 0 -> 2146 bytes
 Minimum Spanning Tree/Images/Tree.png         | Bin 0 -> 11733 bytes
 .../Contents.swift                            |   6 +-
 .../timeline.xctimeline                       |   0
 .../Resources}/Minimum_Spanning_Tree.png      | Bin
 .../Sources/Edge.swift                        |  11 +
 .../Sources/Graph.swift                       |  55 ++++
 .../Sources/Node.swift                        |  32 +++
 .../Sources/Queue.swift                       |  31 ++
 .../contents.xcplayground                     |   2 +
 .../MinimumSpanningTree.swift                 |   0
 Minimum Spanning Tree/README.markdown         | 190 ++++++++++++
 Minimum Spanning Tree/Tests/Graph.swift       | 106 +++++++
 Minimum Spanning Tree/Tests/Info.plist        |  24 ++
 .../Tests/MinimumSpanningTreeTests.swift      |   2 +-
 Minimum Spanning Tree/Tests/Queue.swift       |  31 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 272 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++++
 README.markdown                               |   4 +-
 Shortest Path/Images/Graph.graffle            | Bin 0 -> 2127 bytes
 Shortest Path/Images/Graph.png                | Bin 0 -> 12819 bytes
 Shortest Path/README.markdown                 | 106 +++++++
 .../Contents.swift                            |   7 -
 .../timeline.xctimeline                       |   0
 .../Sources/Edge.swift                        |  11 +
 .../Sources/Graph.swift                       |  55 ++++
 .../Sources/Node.swift                        |  32 +++
 .../Sources/Queue.swift                       |  31 ++
 .../contents.xcplayground                     |   2 +
 .../ShortestPath.swift                        |   0
 Shortest Path/Tests/Graph.swift               | 106 +++++++
 Shortest Path/Tests/Info.plist                |  24 ++
 Shortest Path/Tests/Queue.swift               |  31 ++
 .../Tests/ShortestPathTests.swift             |   2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     | 272 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++++
 46 files changed, 1547 insertions(+), 300 deletions(-)
 rename Breadth-First Search/{ => Tests}/Graph.swift (100%)
 rename Breadth-First Search/{ => Tests}/Queue.swift (100%)
 create mode 100644 Minimum Spanning Tree/Images/Graph.png
 create mode 100644 Minimum Spanning Tree/Images/Graph.sketch
 rename Breadth-First Search/BreadthFirstSearch.playground/Resources/Minimum_Spanning_Tree.png => Minimum Spanning Tree/Images/MinimumSpanningTree.png (100%)
 rename {Breadth-First Search => Minimum Spanning Tree}/Images/MinimumSpanningTree.sketch (100%)
 create mode 100644 Minimum Spanning Tree/Images/Tree.graffle
 create mode 100644 Minimum Spanning Tree/Images/Tree.png
 rename {Breadth-First Search/BreadthFirstSearch.playground => Minimum Spanning Tree/MinimumSpanningTree.playground}/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift (93%)
 rename {Breadth-First Search/BreadthFirstSearch.playground => Minimum Spanning Tree/MinimumSpanningTree.playground}/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline (100%)
 rename {Breadth-First Search/Images => Minimum Spanning Tree/MinimumSpanningTree.playground/Resources}/Minimum_Spanning_Tree.png (100%)
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Edge.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Node.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Queue.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
 rename Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift => Minimum Spanning Tree/MinimumSpanningTree.swift (100%)
 create mode 100644 Minimum Spanning Tree/README.markdown
 create mode 100644 Minimum Spanning Tree/Tests/Graph.swift
 create mode 100644 Minimum Spanning Tree/Tests/Info.plist
 rename Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift => Minimum Spanning Tree/Tests/MinimumSpanningTreeTests.swift (98%)
 create mode 100644 Minimum Spanning Tree/Tests/Queue.swift
 create mode 100644 Minimum Spanning Tree/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Minimum Spanning Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Shortest Path/Images/Graph.graffle
 create mode 100644 Shortest Path/Images/Graph.png
 create mode 100644 Shortest Path/README.markdown
 rename {Breadth-First Search/BreadthFirstSearch.playground => Shortest Path/ShortestPath.playground}/Pages/Shortest path example.xcplaygroundpage/Contents.swift (92%)
 rename {Breadth-First Search/BreadthFirstSearch.playground => Shortest Path/ShortestPath.playground}/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline (100%)
 create mode 100644 Shortest Path/ShortestPath.playground/Sources/Edge.swift
 create mode 100644 Shortest Path/ShortestPath.playground/Sources/Graph.swift
 create mode 100644 Shortest Path/ShortestPath.playground/Sources/Node.swift
 create mode 100644 Shortest Path/ShortestPath.playground/Sources/Queue.swift
 create mode 100644 Shortest Path/ShortestPath.playground/contents.xcplayground
 rename Breadth-First Search/BreadthFirstSearchShortestPath.swift => Shortest Path/ShortestPath.swift (100%)
 create mode 100644 Shortest Path/Tests/Graph.swift
 create mode 100644 Shortest Path/Tests/Info.plist
 create mode 100644 Shortest Path/Tests/Queue.swift
 rename Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift => Shortest Path/Tests/ShortestPathTests.swift (98%)
 create mode 100644 Shortest Path/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Shortest Path/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index c761d9e99..93aa6b337 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,5 +1,3 @@
-//: # Breadth-First Search
-
 func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
@@ -47,5 +45,3 @@ graph.addEdge(nodeF, neighbor: nodeG)
 
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
-
-//: [Next: Shortest Path Example](@next)
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground
index fc13b7766..513c2e7e9 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
@@ -1,8 +1,2 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='6.0' target-platform='ios' display-mode='rendered'>
-    <pages>
-        <page name='Simple example'/>
-        <page name='Shortest path example'/>
-        <page name='Minimum spanning tree example'/>
-    </pages>
-</playground>
\ No newline at end of file
+<playground version='6.0' target-platform='ios' display-mode='raw'/>
\ No newline at end of file
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 70127db5a..4eb77b0ac 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -144,263 +144,11 @@ print(nodesExplored)
 
 This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
    
-## Applications
+## What is BFS good for?
 
 Breadth-first search can be used to solve many problems. A small selection:
 
-* Computing the shortest path between a source node and each of the other nodes (only for unweighted graphs).
-* Calculating the minimum spanning tree on an unweighted graph.
-
-## Shortest path example
-
-Breadth-first search can be used to compute the [shortest path](../Shortest Path/) between a source node and each of the other nodes in the tree or graph, because it explores all of the immediate neighbor nodes first before moving to the next level neighbors.
-
-Let's follow the animated example and calculate the shortest path to all the other nodes. Start with the source node ``a`` and add it to a queue with a distance of ``0``.
-
-```swift
-queue.enqueue(a)
-a.distance = 0
-```
-
-The queue is now ``[ a ]``. Dequeue ``a`` and enqueue its two neighbor nodes ``b`` and ``c`` with a distance of ``1``.
-
-```swift
-queue.dequeue()   // a
-queue.enqueue(b)
-b.distance = a.distance + 1   // result: 1
-queue.enqueue(c)
-c.distance = a.distance + 1   // result: 1
-```
-
-The queue is now ``[ b, c ]``. Dequeue ``b`` and enqueue `b`'s neighbor nodes ``d`` and ``e`` with a distance of ``2``.
-
-```swift
-queue.dequeue()   // b
-queue.enqueue(d)
-d.distance = b.distance + 1   // result: 2
-queue.enqueue(e)
-e.distance = b.distance + 1   // result: 2
-```
-
-Continue until the queue is empty to calculate the shortest path to all other nodes.
-
-Here's the code:
-
-```swift
-func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
-  let shortestPathGraph = graph.duplicate()
-
-  var queue = Queue<Node>()
-  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
-  queue.enqueue(sourceInShortestPathsGraph)
-  sourceInShortestPathsGraph.distance = 0
-
-  while let current = queue.dequeue() {
-    for edge in current.neighbors {
-      let neighborNode = edge.neighbor
-      if !neighborNode.hasDistance {
-        queue.enqueue(neighborNode)
-        neighborNode.distance = current.distance! + 1
-      }
-    }
-  }
-
-  return shortestPathGraph
-}
-```
-
-Put this code in a playground and test it like so:
-
-```swift
-let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
-print(shortestPathGraph.nodes)
-```
-
-This will output:
-
-	Node(label: a, distance: 0), Node(label: b, distance: 1), Node(label: c, distance: 1),
-	Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
-	Node(label: g, distance: 2), Node(label: h, distance: 3)
-
-## Minimum spanning tree example
-
-Breadth-first search can be used to calculate the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph. A minimum spanning tree describes a path that contains the smallest number of edges that are needed to visit every node in the graph.
-
-Let's calculate the minimum spanning tree for the following graph:
-
-![Minimum spanning tree](Images/Minimum_Spanning_Tree.png)
-
-*Note: the minimum spanning tree is represented by the bold edges.*
-
-Start with the source node ``a`` and add it to a queue and mark it as visited.
-
-```swift
-queue.enqueue(a)
-a.visited = true
-```
-
-The queue is now ``[ a ]``. Dequeue ``a`` and enqueue its immediate neighbor nodes ``b`` and ``h`` and mark them as visited.
-
-```swift
-queue.dequeue()   // a
-queue.enqueue(b)
-b.visited = true
-queue.enqueue(h)
-h.visited = true
-```
-
-The queue is now ``[ b, h ]``. Dequeue ``b`` and enqueue the neighbor node ``c`` mark it as visited. Remove the edge between ``b`` to ``h`` because ``h`` has already been visited.
-
-```swift
-queue.dequeue()   // b
-queue.enqueue(c)
-c.visited = true
-b.removeEdgeTo(h)
-```
-
-The queue is now ``[ h, c ]``. Dequeue ``h`` and enqueue the neighbor nodes ``g`` and ``i`` and mark them as visited.
-
-```swift
-queue.dequeue()   // h
-queue.enqueue(g)
-g.visited = true
-queue.enqueue(i)
-i.visited = true
-```
-
-The queue is now ``[ c, g, i ]``. Dequeue ``c`` and enqueue the neighbor nodes ``d`` and ``f`` and mark them as visited. Remove the edge between ``c`` to ``i`` because ``i`` has already been visited.
-
-```swift
-queue.dequeue()   // c
-queue.enqueue(d)
-d.visited = true
-queue.enqueue(f)
-f.visited = true
-c.removeEdgeTo(i)
-```
-
-The queue is now ``[ g, i, d, f ]``. Dequeue ``g`` and remove the edges between ``g`` to ``f`` and ``g`` to ``i`` because ``f`` and ``i`` have already been visited.
-
-```swift
-queue.dequeue()   // g
-g.removeEdgeTo(f)
-g.removeEdgeTo(i)
-```
-
-The queue is now ``[ i, d, f ]``. Dequeue ``i``.
-
-```swift
-queue.dequeue()   // i
-```
-
-The queue is now ``[ d, f ]``. Dequeue ``d`` and enqueue the neighbor node ``e`` mark it as visited. Remove the edge between ``d`` to ``f`` because ``f`` has already been visited.
-
-```swift
-queue.dequeue()   // d
-queue.enqueue(e)
-e.visited = true
-d.removeEdgeTo(f)
-```
-
-The queue is now ``[ f, e ]``. Dequeue ``f``. Remove the edge between ``f`` to ``e`` because ``e`` has already been visited.
-
-```swift
-queue.dequeue()   // f
-f.removeEdgeTo(e)
-```
-
-The queue is now ``[ e ]``. Dequeue ``e``.
-
-```swift
-queue.dequeue()   // e
-```
-
-The queue is now empty, which means the minimum spanning tree has been computed.
-
-Here's the code:
-
-```swift
-func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
-  let minimumSpanningTree = graph.duplicate()
-
-  var queue = Queue<Node>()
-  let sourceInMinimumSpanningTree = minimumSpanningTree.findNodeWithLabel(source.label)
-  queue.enqueue(sourceInMinimumSpanningTree)
-  sourceInMinimumSpanningTree.visited = true
-
-  while let current = queue.dequeue() {
-    for edge in current.neighbors {
-      let neighborNode = edge.neighbor
-      if !neighborNode.visited {
-        neighborNode.visited = true
-        queue.enqueue(neighborNode)
-      } else {
-        current.remove(edge)
-      }
-    }
-  }
-
-  return minimumSpanningTree
-}
-```
-
-This function returns a new `Graph` object that describes just the minimum spanning tree. In the figure, that would be the graph containing just the bold edges.
-
-Put this code in a playground and test it like so:
-
-```swift
-let graph = Graph()
-
-let nodeA = graph.addNode("a")
-let nodeB = graph.addNode("b")
-let nodeC = graph.addNode("c")
-let nodeD = graph.addNode("d")
-let nodeE = graph.addNode("e")
-let nodeF = graph.addNode("f")
-let nodeG = graph.addNode("g")
-let nodeH = graph.addNode("h")
-let nodeI = graph.addNode("i")
-
-graph.addEdge(nodeA, neighbor: nodeB)
-graph.addEdge(nodeA, neighbor: nodeH)
-graph.addEdge(nodeB, neighbor: nodeA)
-graph.addEdge(nodeB, neighbor: nodeC)
-graph.addEdge(nodeB, neighbor: nodeH)
-graph.addEdge(nodeC, neighbor: nodeB)
-graph.addEdge(nodeC, neighbor: nodeD)
-graph.addEdge(nodeC, neighbor: nodeF)
-graph.addEdge(nodeC, neighbor: nodeI)
-graph.addEdge(nodeD, neighbor: nodeC)
-graph.addEdge(nodeD, neighbor: nodeE)
-graph.addEdge(nodeD, neighbor: nodeF)
-graph.addEdge(nodeE, neighbor: nodeD)
-graph.addEdge(nodeE, neighbor: nodeF)
-graph.addEdge(nodeF, neighbor: nodeC)
-graph.addEdge(nodeF, neighbor: nodeD)
-graph.addEdge(nodeF, neighbor: nodeE)
-graph.addEdge(nodeF, neighbor: nodeG)
-graph.addEdge(nodeG, neighbor: nodeF)
-graph.addEdge(nodeG, neighbor: nodeH)
-graph.addEdge(nodeG, neighbor: nodeI)
-graph.addEdge(nodeH, neighbor: nodeA)
-graph.addEdge(nodeH, neighbor: nodeB)
-graph.addEdge(nodeH, neighbor: nodeG)
-graph.addEdge(nodeH, neighbor: nodeI)
-graph.addEdge(nodeI, neighbor: nodeC)
-graph.addEdge(nodeI, neighbor: nodeG)
-graph.addEdge(nodeI, neighbor: nodeH)
-
-let minimumSpanningTree = breadthFirstSearchMinimumSpanningTree(graph, source: nodeA)
-
-print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
-                           // [node: b edges: ["c"]]
-                           // [node: c edges: ["d", "f"]]
-                           // [node: d edges: ["e"]]
-                           // [node: h edges: ["g", "i"]]
-```
-
-## See also
-
-[Graph](../Graph/), [Tree](../Tree/), [Queue](../Queue/), [Shortest Path](../Shortest Path/), [Minimum Spanning Tree](../Minimum Spanning Tree/).
+* Computing the [shortest path](../Shortest Path/) between a source node and each of the other nodes (only for unweighted graphs).
+* Calculating the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Breadth-First Search/Graph.swift b/Breadth-First Search/Tests/Graph.swift
similarity index 100%
rename from Breadth-First Search/Graph.swift
rename to Breadth-First Search/Tests/Graph.swift
diff --git a/Breadth-First Search/Queue.swift b/Breadth-First Search/Tests/Queue.swift
similarity index 100%
rename from Breadth-First Search/Queue.swift
rename to Breadth-First Search/Tests/Queue.swift
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 061e1be44..33be43391 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
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diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
similarity index 93%
rename from Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
rename to Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 006ce1873..088da1d11 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,3 @@
-//: [Previous](@previous)
-
-//: # Minimum Spanning Tree Example
-
 func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 
@@ -27,7 +23,7 @@ func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph
 
 
 /*:
-![Animated example of a breadth-first search](Minimum_Spanning_Tree.png)
+![Graph](Minimum_Spanning_Tree.png)
 */
 
 
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline b/Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
similarity index 100%
rename from Breadth-First Search/BreadthFirstSearch.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
rename to Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
diff --git a/Breadth-First Search/Images/Minimum_Spanning_Tree.png b/Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png
similarity index 100%
rename from Breadth-First Search/Images/Minimum_Spanning_Tree.png
rename to Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Edge.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Edge.swift
new file mode 100644
index 000000000..3937a2cc7
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Edge.swift	
@@ -0,0 +1,11 @@
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
new file mode 100644
index 000000000..e89d4ac97
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -0,0 +1,55 @@
+public class Graph : CustomStringConvertible, Equatable {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Node.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Node.swift
new file mode 100644
index 000000000..9d8435ffa
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Node.swift	
@@ -0,0 +1,32 @@
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Queue.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Queue.swift
new file mode 100644
index 000000000..bf462bbdd
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Queue.swift	
@@ -0,0 +1,31 @@
+public struct Queue<T> {
+  private var array: [T]
+
+  public init() {
+    array = []
+  }
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeFirst()
+    }
+  }
+
+  public func peek() -> T? {
+    return array.first
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground b/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5ed29117b
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground	
@@ -0,0 +1,2 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='6.0' target-platform='ios' display-mode='rendered'/>
\ No newline at end of file
diff --git a/Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift b/Minimum Spanning Tree/MinimumSpanningTree.swift
similarity index 100%
rename from Breadth-First Search/BreadthFirstSearchMinimumSpanningTree.swift
rename to Minimum Spanning Tree/MinimumSpanningTree.swift
diff --git a/Minimum Spanning Tree/README.markdown b/Minimum Spanning Tree/README.markdown
new file mode 100644
index 000000000..5d988eee6
--- /dev/null
+++ b/Minimum Spanning Tree/README.markdown	
@@ -0,0 +1,190 @@
+# Minimum Spanning Tree
+
+A minimum spanning tree describes a path that contains the smallest number of edges that are needed to visit every node in the graph.
+
+Take a look at the following graph:
+
+![Graph](Images/Graph.png)
+
+If we start from node `a` and want to visit every other node, then what is the most efficient path to do that? We can calculate this with the minimum spanning tree algorithm.
+
+Here is the minimum spanning tree for the graph. It is represented by the bold edges:
+
+![Minimum spanning tree](Images/MinimumSpanningTree.png)
+
+Drawn as a more conventional tree it looks like this:
+
+![An actual tree](Images/Tree.png)
+
+To calculate the minimum spanning tree on an unweighted graph, we can use the [breadth-first search](../Breadth-First Search/) algorithm. Breadth-first search starts at a source node and traverses the graph by exploring the immediate neighbor nodes first, before moving to the next level neighbors. If we tweak this algorithm by selectively removing edges, then it can convert the graph into the minimum spanning tree.
+
+Let's step through the example. We start with the source node `a`, add it to a queue and mark it as visited.
+
+```swift
+queue.enqueue(a)
+a.visited = true
+```
+
+The queue is now `[ a ]`. As is usual with breadth-first search, we dequeue the node at the front of the queue, `a`, and enqueue its immediate neighbor nodes `b` and `h`. We mark them as visited too.
+
+```swift
+queue.dequeue()   // a
+queue.enqueue(b)
+b.visited = true
+queue.enqueue(h)
+h.visited = true
+```
+
+The queue is now `[ b, h ]`. Dequeue `b` and enqueue the neighbor node `c`. Mark it as visited. Remove the edge from `b` to `h` because `h` has already been visited.
+
+```swift
+queue.dequeue()   // b
+queue.enqueue(c)
+c.visited = true
+b.removeEdgeTo(h)
+```
+
+The queue is now `[ h, c ]`. Dequeue `h` and enqueue the neighbor nodes `g` and `i`, and mark them as visited.
+
+```swift
+queue.dequeue()   // h
+queue.enqueue(g)
+g.visited = true
+queue.enqueue(i)
+i.visited = true
+```
+
+The queue is now `[ c, g, i ]`. Dequeue `c` and enqueue the neighbor nodes `d` and `f`, and mark them as visited. Remove the edge between `c` and `i` because `i` has already been visited.
+
+```swift
+queue.dequeue()   // c
+queue.enqueue(d)
+d.visited = true
+queue.enqueue(f)
+f.visited = true
+c.removeEdgeTo(i)
+```
+
+The queue is now `[ g, i, d, f ]`. Dequeue `g`. All of its neighbors have been discovered already, so there is nothing to enqueue. Remove the edges from `g` to `f`, as well as `g` to `i`, because `f` and `i` have already been discovered.
+
+```swift
+queue.dequeue()   // g
+g.removeEdgeTo(f)
+g.removeEdgeTo(i)
+```
+
+The queue is now `[ i, d, f ]`. Dequeue `i`. Nothing else to do for this node.
+
+```swift
+queue.dequeue()   // i
+```
+
+The queue is now `[ d, f ]`. Dequeue `d` and enqueue the neighbor node `e`. Mark it as visited. Remove the edge from `d` to `f` because `f` has already been visited.
+
+```swift
+queue.dequeue()   // d
+queue.enqueue(e)
+e.visited = true
+d.removeEdgeTo(f)
+```
+
+The queue is now `[ f, e ]`. Dequeue `f`. Remove the edge between `f` and `e` because `e` has already been visited.
+
+```swift
+queue.dequeue()   // f
+f.removeEdgeTo(e)
+```
+
+The queue is now `[ e ]`. Dequeue `e`.
+
+```swift
+queue.dequeue()   // e
+```
+
+The queue is empty, which means the minimum spanning tree has been computed.
+
+Here's the code:
+
+```swift
+func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
+  let minimumSpanningTree = graph.duplicate()
+
+  var queue = Queue<Node>()
+  let sourceInMinimumSpanningTree = minimumSpanningTree.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInMinimumSpanningTree)
+  sourceInMinimumSpanningTree.visited = true
+
+  while let current = queue.dequeue() {
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.visited {
+        neighborNode.visited = true
+        queue.enqueue(neighborNode)
+      } else {
+        current.remove(edge)
+      }
+    }
+  }
+
+  return minimumSpanningTree
+}
+```
+
+This function returns a new `Graph` object that describes just the minimum spanning tree. In the figure, that would be the graph containing just the bold edges.
+
+Put this code in a playground and test it like so:
+
+```swift
+let graph = Graph()
+
+let nodeA = graph.addNode("a")
+let nodeB = graph.addNode("b")
+let nodeC = graph.addNode("c")
+let nodeD = graph.addNode("d")
+let nodeE = graph.addNode("e")
+let nodeF = graph.addNode("f")
+let nodeG = graph.addNode("g")
+let nodeH = graph.addNode("h")
+let nodeI = graph.addNode("i")
+
+graph.addEdge(nodeA, neighbor: nodeB)
+graph.addEdge(nodeA, neighbor: nodeH)
+graph.addEdge(nodeB, neighbor: nodeA)
+graph.addEdge(nodeB, neighbor: nodeC)
+graph.addEdge(nodeB, neighbor: nodeH)
+graph.addEdge(nodeC, neighbor: nodeB)
+graph.addEdge(nodeC, neighbor: nodeD)
+graph.addEdge(nodeC, neighbor: nodeF)
+graph.addEdge(nodeC, neighbor: nodeI)
+graph.addEdge(nodeD, neighbor: nodeC)
+graph.addEdge(nodeD, neighbor: nodeE)
+graph.addEdge(nodeD, neighbor: nodeF)
+graph.addEdge(nodeE, neighbor: nodeD)
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeC)
+graph.addEdge(nodeF, neighbor: nodeD)
+graph.addEdge(nodeF, neighbor: nodeE)
+graph.addEdge(nodeF, neighbor: nodeG)
+graph.addEdge(nodeG, neighbor: nodeF)
+graph.addEdge(nodeG, neighbor: nodeH)
+graph.addEdge(nodeG, neighbor: nodeI)
+graph.addEdge(nodeH, neighbor: nodeA)
+graph.addEdge(nodeH, neighbor: nodeB)
+graph.addEdge(nodeH, neighbor: nodeG)
+graph.addEdge(nodeH, neighbor: nodeI)
+graph.addEdge(nodeI, neighbor: nodeC)
+graph.addEdge(nodeI, neighbor: nodeG)
+graph.addEdge(nodeI, neighbor: nodeH)
+
+let minimumSpanningTree = breadthFirstSearchMinimumSpanningTree(graph, source: nodeA)
+
+print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
+                           // [node: b edges: ["c"]]
+                           // [node: c edges: ["d", "f"]]
+                           // [node: d edges: ["e"]]
+                           // [node: h edges: ["g", "i"]]
+```
+
+> **Note:** On an unweighed graph, any spanning tree is always a minimal spanning tree. This means you can also use a [depth-first search](../Depth-First Search) to find the minimum spanning tree.
+
+*Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Minimum Spanning Tree/Tests/Graph.swift b/Minimum Spanning Tree/Tests/Graph.swift
new file mode 100644
index 000000000..6f69ee800
--- /dev/null
+++ b/Minimum Spanning Tree/Tests/Graph.swift	
@@ -0,0 +1,106 @@
+// MARK: - Edge
+
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
+
+// MARK: - Node
+
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
+
+// MARK: - Graph
+
+public class Graph : CustomStringConvertible, Equatable {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Minimum Spanning Tree/Tests/Info.plist b/Minimum Spanning Tree/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Minimum Spanning Tree/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift b/Minimum Spanning Tree/Tests/MinimumSpanningTreeTests.swift
similarity index 98%
rename from Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift
rename to Minimum Spanning Tree/Tests/MinimumSpanningTreeTests.swift
index 527387062..af8da4e5a 100644
--- a/Breadth-First Search/Tests/BreadthFirstSearchMinimumSpanningTreeTests.swift	
+++ b/Minimum Spanning Tree/Tests/MinimumSpanningTreeTests.swift	
@@ -1,6 +1,6 @@
 import XCTest
 
-class BreadthFirstSearchMinimumSpanningTreeTests: XCTestCase {
+class MinimumSpanningTreeTests: XCTestCase {
 
   func testMinimumSpanningTreeReturnsSameTreeWhenGivenTree() {
     let tree = Graph()
diff --git a/Minimum Spanning Tree/Tests/Queue.swift b/Minimum Spanning Tree/Tests/Queue.swift
new file mode 100644
index 000000000..bf462bbdd
--- /dev/null
+++ b/Minimum Spanning Tree/Tests/Queue.swift	
@@ -0,0 +1,31 @@
+public struct Queue<T> {
+  private var array: [T]
+
+  public init() {
+    array = []
+  }
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeFirst()
+    }
+  }
+
+  public func peek() -> T? {
+    return array.first
+  }
+}
diff --git a/Minimum Spanning Tree/Tests/Tests.xcodeproj/project.pbxproj b/Minimum Spanning Tree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..659c7e9f2
--- /dev/null
+++ b/Minimum Spanning Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,272 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		83AACB421C844CED00DDAFC7 /* MinimumSpanningTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83AACB411C844CED00DDAFC7 /* MinimumSpanningTreeTests.swift */; };
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+		83F9C9701C84449D00B3A87F /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Queue.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
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+			files = (
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+/* End PBXFrameworksBuildPhase section */
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+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
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+			name = Products;
+			sourceTree = "<group>";
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+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				83F9C9661C84437C00B3A87F /* MinimumSpanningTree.swift */,
+				83AACB411C844CED00DDAFC7 /* MinimumSpanningTreeTests.swift */,
+				83F9C96E1C84449D00B3A87F /* Graph.swift */,
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+			);
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+			sourceTree = "<group>";
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new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Minimum Spanning Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
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diff --git a/README.markdown b/README.markdown
index d086ca298..c3e3e43ea 100644
--- a/README.markdown
+++ b/README.markdown
@@ -170,8 +170,8 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Graph](Graph/)
 - [Breadth-First Search (BFS)](Breadth-First Search/)
 - [Depth-First Search (DFS)](Depth-First Search/) :construction:
-- Shortest Path
-- Minimum Spanning Tree
+- [Shortest Path](Shortest Path/)
+- [Minimum Spanning Tree](Minimum Spanning Tree/)
 - All Paths
 
 ## Puzzles
diff --git a/Shortest Path/Images/Graph.graffle b/Shortest Path/Images/Graph.graffle
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diff --git a/Shortest Path/README.markdown b/Shortest Path/README.markdown
new file mode 100644
index 000000000..b3fb1692d
--- /dev/null
+++ b/Shortest Path/README.markdown	
@@ -0,0 +1,106 @@
+# Shortest Path
+
+Goal: find the shortest route to go from one node to another in a graph.
+
+Suppose we have to following graph:
+
+![Example graph](Images/Graph.png)
+
+We may want to find out what the shortest way is to get from node `A` to node `F`.
+
+If the [graph is unweighed](../Graph/), then finding the shortest path is easy: we can use the breadth-first search algorithm. For a weighted graph, we can use Dijkstra's algorithm.
+
+## Unweighted graph: breadth-first search
+
+[Breadth-first search](../Breadth-First Search/) is a method for traversing a tree or graph data structure. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors. As a convenient side effect, it automatically computes the shortest path between a source node and each of the other nodes in the tree or graph.
+
+The result of the breadth-first search can be represented with a tree:
+
+![The BFS tree](../Breadth-First Search/Images/TraversalTree.png)
+
+The root of the tree is the node you started the breadth-first search from. To find the distance from node `A` to any other node, we simply count the number of edges in the tree. And so we find that the shortest path between `A` and `F` is 2. The tree not only tells you how long that path is, but also how to actually get from `A` to `F` (or any of the other nodes).
+
+Let's put breadth-first search into practice and calculate the shortest path from `A` to all the other nodes. We start with the source node `A` and add it to a queue with a distance of `0`.
+
+```swift
+queue.enqueue(A)
+A.distance = 0
+```
+
+The queue is now `[ A ]`. We dequeue `A` and enqueue its two immediate neighbor nodes `B` and `C` with a distance of `1`.
+
+```swift
+queue.dequeue()   // A
+queue.enqueue(B)
+B.distance = A.distance + 1   // result: 1
+queue.enqueue(C)
+C.distance = A.distance + 1   // result: 1
+```
+
+The queue is now `[ B, C ]`. Dequeue `B` and enqueue `B`'s neighbor nodes `D` and `E` with a distance of `2`.
+
+```swift
+queue.dequeue()   // B
+queue.enqueue(D)
+D.distance = B.distance + 1   // result: 2
+queue.enqueue(E)
+E.distance = B.distance + 1   // result: 2
+```
+
+The queue is now `[ C, D, E ]`. Dequeue `C` and enqueue `C`'s neighbor nodes `F` and `G`, also with a distance of `2`.
+
+```swift
+queue.dequeue()   // C
+queue.enqueue(F)
+F.distance = C.distance + 1   // result: 2
+queue.enqueue(G)
+G.distance = C.distance + 1   // result: 2
+```
+
+This continues until the queue is empty and we've visited all the nodes. Each time we discover a new node, it gets the `distance` of its parent plus 1. As you can see, this is exactly what the [breadth-first search](../Breadth-First Search/) algorithm does, except that we now also keep track of the distance travelled.
+
+Here's the code:
+
+```swift
+func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
+  let shortestPathGraph = graph.duplicate()
+
+  var queue = Queue<Node>()
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
+  queue.enqueue(sourceInShortestPathsGraph)
+  sourceInShortestPathsGraph.distance = 0
+
+  while let current = queue.dequeue() {
+    for edge in current.neighbors {
+      let neighborNode = edge.neighbor
+      if !neighborNode.hasDistance {
+        queue.enqueue(neighborNode)
+        neighborNode.distance = current.distance! + 1
+      }
+    }
+  }
+
+  return shortestPathGraph
+}
+```
+
+Put this code in a playground and test it like so:
+
+```swift
+let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
+print(shortestPathGraph.nodes)
+```
+
+This will output:
+
+	Node(label: a, distance: 0), Node(label: b, distance: 1), Node(label: c, distance: 1),
+	Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
+	Node(label: g, distance: 2), Node(label: h, distance: 3)
+
+> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum Spanning Tree/) on how you can convert the graph into a tree by removing edges.
+
+## Weighted graph: Dijkstra's algorithm
+
+[Coming soon]
+
+*Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
similarity index 92%
rename from Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
rename to Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index 2a9c1676f..cfc582c49 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,3 @@
-//: [Previous](@previous)
-
-//: # Shortest Path Example
-
 func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
@@ -46,6 +42,3 @@ graph.addEdge(nodeE, neighbor: nodeH)
 
 let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
 print(shortestPathGraph.nodes)
-
-//: [Next: Minimum Spanning Tree Example](@next)
-
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline b/Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
similarity index 100%
rename from Breadth-First Search/BreadthFirstSearch.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
rename to Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
diff --git a/Shortest Path/ShortestPath.playground/Sources/Edge.swift b/Shortest Path/ShortestPath.playground/Sources/Edge.swift
new file mode 100644
index 000000000..3937a2cc7
--- /dev/null
+++ b/Shortest Path/ShortestPath.playground/Sources/Edge.swift	
@@ -0,0 +1,11 @@
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
diff --git a/Shortest Path/ShortestPath.playground/Sources/Graph.swift b/Shortest Path/ShortestPath.playground/Sources/Graph.swift
new file mode 100644
index 000000000..e89d4ac97
--- /dev/null
+++ b/Shortest Path/ShortestPath.playground/Sources/Graph.swift	
@@ -0,0 +1,55 @@
+public class Graph : CustomStringConvertible, Equatable {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Shortest Path/ShortestPath.playground/Sources/Node.swift b/Shortest Path/ShortestPath.playground/Sources/Node.swift
new file mode 100644
index 000000000..9d8435ffa
--- /dev/null
+++ b/Shortest Path/ShortestPath.playground/Sources/Node.swift	
@@ -0,0 +1,32 @@
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
diff --git a/Shortest Path/ShortestPath.playground/Sources/Queue.swift b/Shortest Path/ShortestPath.playground/Sources/Queue.swift
new file mode 100644
index 000000000..bf462bbdd
--- /dev/null
+++ b/Shortest Path/ShortestPath.playground/Sources/Queue.swift	
@@ -0,0 +1,31 @@
+public struct Queue<T> {
+  private var array: [T]
+
+  public init() {
+    array = []
+  }
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeFirst()
+    }
+  }
+
+  public func peek() -> T? {
+    return array.first
+  }
+}
diff --git a/Shortest Path/ShortestPath.playground/contents.xcplayground b/Shortest Path/ShortestPath.playground/contents.xcplayground
new file mode 100644
index 000000000..513c2e7e9
--- /dev/null
+++ b/Shortest Path/ShortestPath.playground/contents.xcplayground	
@@ -0,0 +1,2 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='6.0' target-platform='ios' display-mode='raw'/>
\ No newline at end of file
diff --git a/Breadth-First Search/BreadthFirstSearchShortestPath.swift b/Shortest Path/ShortestPath.swift
similarity index 100%
rename from Breadth-First Search/BreadthFirstSearchShortestPath.swift
rename to Shortest Path/ShortestPath.swift
diff --git a/Shortest Path/Tests/Graph.swift b/Shortest Path/Tests/Graph.swift
new file mode 100644
index 000000000..6f69ee800
--- /dev/null
+++ b/Shortest Path/Tests/Graph.swift	
@@ -0,0 +1,106 @@
+// MARK: - Edge
+
+public class Edge : Equatable {
+  public var neighbor: Node
+
+  public init(neighbor: Node) {
+    self.neighbor = neighbor
+  }
+}
+
+public func ==(lhs: Edge, rhs: Edge) -> Bool {
+  return lhs.neighbor == rhs.neighbor
+}
+
+// MARK: - Node
+
+public class Node : CustomStringConvertible, Equatable {
+  public var neighbors: [Edge]
+  
+  public private(set) var label: String
+  public var distance: Int?
+  public var visited: Bool
+
+  public init(label: String) {
+    self.label = label
+    neighbors = []
+    visited = false
+  }
+
+  public var description: String {
+    if let distance = distance {
+      return "Node(label: \(label), distance: \(distance))"
+    }
+    return "Node(label: \(label), distance: infinity)"
+  }
+
+  public var hasDistance: Bool {
+    return distance != nil
+  }
+
+  public func remove(edge: Edge) {
+    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+  }
+}
+
+public func ==(lhs: Node, rhs: Node) -> Bool {
+  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+}
+
+// MARK: - Graph
+
+public class Graph : CustomStringConvertible, Equatable {
+  public private(set) var nodes: [Node]
+
+  public init() {
+    self.nodes = []
+  }
+
+  public func addNode(label: String) -> Node {
+    let node = Node(label: label)
+    nodes.append(node)
+    return node
+  }
+
+  public func addEdge(source: Node, neighbor: Node) {
+    let edge = Edge(neighbor: neighbor)
+    source.neighbors.append(edge)
+  }
+
+  public var description: String {
+    var description = ""
+
+    for node in nodes {
+      if !node.neighbors.isEmpty {
+        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+      }
+    }
+    return description
+  }
+
+  public func findNodeWithLabel(label: String) -> Node {
+    return nodes.filter{ $0.label == label }.first!
+  }
+
+  public func duplicate() -> Graph {
+    let duplicated = Graph()
+
+    for node in nodes {
+      duplicated.addNode(node.label)
+    }
+
+    for node in nodes {
+      for edge in node.neighbors {
+        let source = duplicated.findNodeWithLabel(node.label)
+        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        duplicated.addEdge(source, neighbor: neighbour)
+      }
+    }
+
+    return duplicated
+  }
+}
+
+public func ==(lhs: Graph, rhs: Graph) -> Bool {
+  return lhs.nodes == rhs.nodes
+}
diff --git a/Shortest Path/Tests/Info.plist b/Shortest Path/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Shortest Path/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Shortest Path/Tests/Queue.swift b/Shortest Path/Tests/Queue.swift
new file mode 100644
index 000000000..bf462bbdd
--- /dev/null
+++ b/Shortest Path/Tests/Queue.swift	
@@ -0,0 +1,31 @@
+public struct Queue<T> {
+  private var array: [T]
+
+  public init() {
+    array = []
+  }
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array.removeFirst()
+    }
+  }
+
+  public func peek() -> T? {
+    return array.first
+  }
+}
diff --git a/Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift b/Shortest Path/Tests/ShortestPathTests.swift
similarity index 98%
rename from Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift
rename to Shortest Path/Tests/ShortestPathTests.swift
index b13fac2d1..17c9264a1 100644
--- a/Breadth-First Search/Tests/BreadthFirstSearchShortestPathTests.swift	
+++ b/Shortest Path/Tests/ShortestPathTests.swift	
@@ -1,6 +1,6 @@
 import XCTest
 
-class BreadthFirstSearchShortestPathTests: XCTestCase {
+class ShortestPathTests: XCTestCase {
 
   func testShortestPathWhenGivenTree() {
     let tree = Graph()
diff --git a/Shortest Path/Tests/Tests.xcodeproj/project.pbxproj b/Shortest Path/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..35aeffa54
--- /dev/null
+++ b/Shortest Path/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,272 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		83AACB441C8456D200DDAFC7 /* ShortestPathTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83AACB431C8456D200DDAFC7 /* ShortestPathTests.swift */; };
+		83F9C96A1C84437C00B3A87F /* ShortestPath.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9671C84437C00B3A87F /* ShortestPath.swift */; };
+		83F9C9721C84449D00B3A87F /* Graph.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C96E1C84449D00B3A87F /* Graph.swift */; };
+		83F9C9741C84449D00B3A87F /* Queue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 83F9C9701C84449D00B3A87F /* Queue.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		83AACB431C8456D200DDAFC7 /* ShortestPathTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = ShortestPathTests.swift; sourceTree = SOURCE_ROOT; };
+		83F9C9671C84437C00B3A87F /* ShortestPath.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = ShortestPath.swift; path = ../ShortestPath.swift; sourceTree = SOURCE_ROOT; };
+		83F9C96E1C84449D00B3A87F /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Graph.swift; sourceTree = SOURCE_ROOT; };
+		83F9C9701C84449D00B3A87F /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Queue.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				83F9C9671C84437C00B3A87F /* ShortestPath.swift */,
+				83AACB431C8456D200DDAFC7 /* ShortestPathTests.swift */,
+				83F9C96E1C84449D00B3A87F /* Graph.swift */,
+				83F9C9701C84449D00B3A87F /* Queue.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				83AACB441C8456D200DDAFC7 /* ShortestPathTests.swift in Sources */,
+				83F9C9721C84449D00B3A87F /* Graph.swift in Sources */,
+				83F9C9741C84449D00B3A87F /* Queue.swift in Sources */,
+				83F9C96A1C84437C00B3A87F /* ShortestPath.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Shortest Path/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Shortest Path/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Shortest Path/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 21ce7ad2fe0943bad1e7eb91b8b72c8d4c876ca7 Mon Sep 17 00:00:00 2001
From: Matthew Wo <9029537@gmail.com>
Date: Fri, 18 Mar 2016 19:12:34 -0700
Subject: [PATCH 0166/1679] added more test cases to test the validity of the
 AVL Tree

---
 .../AVLTree.playground/Sources/AVLTree.swift  |  6 +-
 AVL Tree/AVLTree.swift                        |  6 +-
 AVL Tree/Tests/AVLTreeTests.swift             | 97 +++++++++++++++----
 3 files changed, 87 insertions(+), 22 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index 91df1ed9e..580a51e8e 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -26,8 +26,8 @@ public class TreeNode<Key: Comparable, Payload> {
   public var payload: Payload?
 
   private var key: Key
-  private var leftChild: Node?
-  private var rightChild: Node?
+  internal var leftChild: Node?
+  internal var rightChild: Node?
   private var height: Int
   weak private var parent: Node?
 
@@ -343,6 +343,8 @@ extension AVLTree {
         } else if node.isRightChild {
           parent.rightChild = nil
         }
+
+        balance(parent)
       } else {
         // at root
         root = nil
diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 91df1ed9e..580a51e8e 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -26,8 +26,8 @@ public class TreeNode<Key: Comparable, Payload> {
   public var payload: Payload?
 
   private var key: Key
-  private var leftChild: Node?
-  private var rightChild: Node?
+  internal var leftChild: Node?
+  internal var rightChild: Node?
   private var height: Int
   weak private var parent: Node?
 
@@ -343,6 +343,8 @@ extension AVLTree {
         } else if node.isRightChild {
           parent.rightChild = nil
         }
+
+        balance(parent)
       } else {
         // at root
         root = nil
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 6ec9b5f65..51e1211c3 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -11,39 +11,61 @@ import XCTest
 class AVLTreeTests: XCTestCase {
   
   var tree : AVLTree<Int, String>?
-  
+
   override func setUp() {
     super.setUp()
     
     tree = AVLTree()
-    tree?.insert(1, "A")
-    tree?.insert(2, "B")
-    tree?.insert(3, "C")
-    tree?.insert(4, "D")
   }
   
   override func tearDown() {
     // Put teardown code here. This method is called after the invocation of each test method in the class.
     super.tearDown()
   }
-  
+
+  func testAVLTreeBalancedAutoPopulate() {
+    self.tree?.autopopulateWithNodes(10)
+
+    do {
+      try self.tree?.inOrderCheckBalanced(self.tree?.root)
+    } catch _ {
+      XCTFail("Tree is not balanced after autopopulate")
+    }
+  }
+
+  func testAVLTreeBalancedInsert() {
+    self.tree?.autopopulateWithNodes(5)
+
+    for i in 6...10 {
+      self.tree?.insert(i)
+      do {
+        try self.tree?.inOrderCheckBalanced(self.tree?.root)
+      } catch _ {
+        XCTFail("Tree is not balanced after inserting " + String(i))
+      }
+    }
+  }
+
+  func testAVLTreeBalancedDelete() {
+    self.tree?.autopopulateWithNodes(5)
+
+    for i in 1...6 {
+      self.tree?.delete(i)
+      do {
+        try self.tree?.inOrderCheckBalanced(self.tree?.root)
+      } catch _ {
+        XCTFail("Tree is not balanced after deleting " + String(i))
+      }
+    }
+  }
+
   func testEmptyInitialization() {
     let tree = AVLTree<Int,String>()
     
     XCTAssertEqual(tree.size, 0)
     XCTAssertNil(tree.root)
   }
-  
-  func testNotEmptyInitialization() {
-    XCTAssertNotNil(self.tree?.root)
-    XCTAssertNotEqual(self.tree!.size, 0)
-  }
-  
-  func testInsertDuplicated() {
-    self.tree?.insert(1, "A")
-    XCTAssertEqual(self.tree?.size, 5, "Duplicated elements should be allowed")
-  }
-  
+
   func testSingleInsertionPerformance() {
     self.measureBlock {
       self.tree?.insert(5, "E")
@@ -92,6 +114,14 @@ class AVLTreeTests: XCTestCase {
     self.tree?.delete(1056)
     XCTAssertNil(self.tree?.search(1056), "Key should not exist")
   }
+
+  func testInsertSize() {
+    let tree = AVLTree<Int, String>()
+    for i in 0...5 {
+      tree.insert(i, "")
+      XCTAssertEqual(tree.size, i + 1, "Insert didn't update size correctly!")
+    }
+  }
   
   func testDelete() {
     let permutations = [
@@ -109,9 +139,12 @@ class AVLTreeTests: XCTestCase {
       tree.insert(3, "three")
       tree.insert(4, "two")
       tree.insert(5, "one")
-      
+
+      var count = tree.size
       for i in p {
         tree.delete(i)
+        count -= 1
+        XCTAssertEqual(tree.size, count, "Delete didn't update size correctly!")
       }
     }
   }
@@ -126,3 +159,31 @@ extension AVLTree where Key : SignedIntegerType {
     }
   }
 }
+
+enum AVLTreeError: ErrorType {
+  case NotBalanced
+}
+
+extension AVLTree where Key : SignedIntegerType {
+  func height(node: Node?) -> Int {
+    if let node = node {
+      let lHeight = height(node.leftChild)
+      let rHeight = height(node.rightChild)
+
+      return max(lHeight, rHeight) + 1
+    }
+    return 0
+  }
+
+  func inOrderCheckBalanced(node: Node?) throws {
+    if let node = node {
+      guard abs(height(node.leftChild) - height(node.rightChild)) <= 1 else {
+        throw AVLTreeError.NotBalanced
+      }
+      try inOrderCheckBalanced(node.leftChild)
+      try inOrderCheckBalanced(node.rightChild)
+    }
+  }
+}
+
+

From 243f9257410f85debc7a1d15699a02c4b89e755f Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 19 Mar 2016 12:04:40 +0100
Subject: [PATCH 0167/1679] Improve explanation of DFS

---
 Breadth-First Search/README.markdown          |   4 +--
 .../Contents.swift                            |   3 +-
 Depth-First Search/Images/AnimatedExample.gif | Bin 0 -> 17042 bytes
 .../Images/AnimatedExample.graffle            | Bin 0 -> 6537 bytes
 Depth-First Search/Images/AnimatedExample.psd | Bin 0 -> 1059655 bytes
 .../Images/TraversalTree.graffle              | Bin 0 -> 2118 bytes
 Depth-First Search/Images/TraversalTree.png   | Bin 0 -> 11619 bytes
 Depth-First Search/README.markdown            |  30 +++++++++++++++---
 .../Tests/DepthFirstSearchTests.swift         |   5 +--
 Depth-First Search/{ => Tests}/Graph.swift    |   0
 .../Tests/Tests.xcodeproj/project.pbxproj     |   2 +-
 11 files changed, 33 insertions(+), 11 deletions(-)
 create mode 100644 Depth-First Search/Images/AnimatedExample.gif
 create mode 100644 Depth-First Search/Images/AnimatedExample.graffle
 create mode 100644 Depth-First Search/Images/AnimatedExample.psd
 create mode 100644 Depth-First Search/Images/TraversalTree.graffle
 create mode 100644 Depth-First Search/Images/TraversalTree.png
 rename Depth-First Search/{ => Tests}/Graph.swift (100%)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 4eb77b0ac..12e906532 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -2,6 +2,8 @@
 
 Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors.
 
+Breadth-first search can be used on both directed and undirected graphs.
+
 ## Animated example
 
 Here's how breadth-first search works on a graph:
@@ -83,8 +85,6 @@ The parent of a node is the one that "discovered" that node. The root of the tre
 
 For an unweighted graph, this tree defines a shortest path from the starting node to every other node in the tree. So breadth-first search is one way to find the shortest path between two nodes in a graph.
 
-Breadth-first search can be used on directed and undirected graphs.
-
 ## The code
 
 Simple implementation of breadth-first search using a queue:
diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index cc4bd7dd3..770712bfb 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -30,7 +30,8 @@ graph.addEdge(nodeB, neighbor: nodeE)
 graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
-
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeG)
 
 let nodesExplored = depthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
diff --git a/Depth-First Search/Images/AnimatedExample.gif b/Depth-First Search/Images/AnimatedExample.gif
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diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index 322635d7a..a44ae8163 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -2,7 +2,25 @@
 
 Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores as far as possible along each branch before backtracking.
 
-[TODO: this is a work-in-progress]
+Depth-first search can be used on both directed and undirected graphs.
+
+## Animated example
+
+Here's how depth-first search works on a graph:
+
+![Animated example](Images/AnimatedExample.gif)
+
+Let's say we start the search from node `A`. In depth-first search we look at the starting node's first neighbor and visit that. In the example that is node `B`. Then we look at node `B`'s first neighbor and visit it. This is node `D`. Since `D` doesn't have any unvisited neighbors of its own, we backtrack to node `B` and go to its other neighbor `E`. And so on, until we've visited all the nodes in the graph.
+
+Each time we visit the first neighbor and keep going until there's nowhere left to go, and then we backtrack to a point where there are again nodes to visit. When we've backtracked all the way to node `A`, the search is complete.
+
+For the example, the nodes were visited in the order `A`, `B`, `D`, `E`, `H`, `F`, `G`, `C`.
+
+The depth-first search process can also be visualized as a tree:
+
+![Traversal tree](Images/TraversalTree.png)
+
+The parent of a node is the one that "discovered" that node. The root of the tree is the node you started the depth-first search from. Whenever there's a branch, that's where we backtracked.
 
 ## The code
 
@@ -45,20 +63,22 @@ graph.addEdge(nodeB, neighbor: nodeE)
 graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
+graph.addEdge(nodeE, neighbor: nodeF)
+graph.addEdge(nodeF, neighbor: nodeG)
 
 let nodesExplored = depthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
 ```
 
-This will output: `["a", "b", "d", "e", "h", "c", "f", "g"]`
+This will output: `["a", "b", "d", "e", "h", "f", "g", "c"]`
    
-## Applications
+## What is DFS good for?
 
 Depth-first search can be used to solve many problems, for example:
 
 * Finding connected components of a sparse graph
-* Topological sorting of nodes in a graph
+* [Topological sorting](../Topological Sort/) of nodes in a graph
 * Finding bridges of a graph (see: [Bridges](https://en.wikipedia.org/wiki/Bridge_(graph_theory)#Bridge-finding_algorithm))
 * And lots of others!
 
-*Written for Swift Algorithm Club by Paulo Tanaka*
+*Written for Swift Algorithm Club by Paulo Tanaka and Matthijs Hollemans*
diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index aacc8efcf..2cb2556ce 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -4,6 +4,7 @@ class DepthFirstSearchTests: XCTestCase {
 
   func testExploringTree() {
     let tree = Graph()
+
     let nodeA = tree.addNode("a")
     let nodeB = tree.addNode("b")
     let nodeC = tree.addNode("c")
@@ -12,6 +13,7 @@ class DepthFirstSearchTests: XCTestCase {
     let nodeF = tree.addNode("f")
     let nodeG = tree.addNode("g")
     let nodeH = tree.addNode("h")
+
     tree.addEdge(nodeA, neighbor: nodeB)
     tree.addEdge(nodeA, neighbor: nodeC)
     tree.addEdge(nodeB, neighbor: nodeD)
@@ -70,7 +72,6 @@ class DepthFirstSearchTests: XCTestCase {
     let nodesExplored = depthFirstSearch(graph, source: nodeA)
 
     XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
-
   }
 
   func testExploringGraphWithASingleNode() {
@@ -81,4 +82,4 @@ class DepthFirstSearchTests: XCTestCase {
 
     XCTAssertEqual(nodesExplored, ["a"])
   }
-}
\ No newline at end of file
+}
diff --git a/Depth-First Search/Graph.swift b/Depth-First Search/Tests/Graph.swift
similarity index 100%
rename from Depth-First Search/Graph.swift
rename to Depth-First Search/Tests/Graph.swift
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 39c15ce79..9e2872f88 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -16,7 +16,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		83F9C96B1C8443E800B3A87F /* DepthFirstSearchTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = DepthFirstSearchTests.swift; sourceTree = SOURCE_ROOT; };
-		83F9C96E1C84449D00B3A87F /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Graph.swift; path = ../Graph.swift; sourceTree = SOURCE_ROOT; };
+		83F9C96E1C84449D00B3A87F /* Graph.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Graph.swift; sourceTree = SOURCE_ROOT; };
 		FFC6E11D1C8656D10046BA79 /* DepthFirstSearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = DepthFirstSearch.swift; path = ../DepthFirstSearch.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 

From 13e69562bac29edd716871254ec0816407ddc344 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 19 Mar 2016 12:11:33 +0100
Subject: [PATCH 0168/1679] Shortest path and minimum spanning tree are for
 unweighted graphs only

---
 .../Images/Graph.png                                | Bin
 .../Images/Graph.sketch                             | Bin
 .../Images/MinimumSpanningTree.png                  | Bin
 .../Images/MinimumSpanningTree.sketch               | Bin
 .../Images/Tree.graffle                             | Bin
 .../Images/Tree.png                                 | Bin
 .../Contents.swift                                  |   0
 .../timeline.xctimeline                             |   0
 .../Resources/Minimum_Spanning_Tree.png             | Bin
 .../Sources/Edge.swift                              |   0
 .../Sources/Graph.swift                             |   0
 .../Sources/Node.swift                              |   0
 .../Sources/Queue.swift                             |   0
 .../contents.xcplayground                           |   0
 .../MinimumSpanningTree.swift                       |   0
 .../README.markdown                                 |   2 +-
 .../Tests/Graph.swift                               |   0
 .../Tests/Info.plist                                |   0
 .../Tests/MinimumSpanningTreeTests.swift            |   0
 .../Tests/Queue.swift                               |   0
 .../Tests/Tests.xcodeproj/project.pbxproj           |   0
 .../xcshareddata/xcschemes/Tests.xcscheme           |   0
 README.markdown                                     |   6 +++---
 .../Images/Graph.graffle                            | Bin
 .../Images/Graph.png                                | Bin
 .../README.markdown                                 |   6 +-----
 .../Contents.swift                                  |   0
 .../timeline.xctimeline                             |   0
 .../ShortestPath.playground/Sources/Edge.swift      |   0
 .../ShortestPath.playground/Sources/Graph.swift     |   0
 .../ShortestPath.playground/Sources/Node.swift      |   0
 .../ShortestPath.playground/Sources/Queue.swift     |   0
 .../ShortestPath.playground/contents.xcplayground   |   0
 .../ShortestPath.swift                              |   0
 .../Tests/Graph.swift                               |   0
 .../Tests/Info.plist                                |   0
 .../Tests/Queue.swift                               |   0
 .../Tests/ShortestPathTests.swift                   |   0
 .../Tests/Tests.xcodeproj/project.pbxproj           |   0
 .../xcshareddata/xcschemes/Tests.xcscheme           |   0
 40 files changed, 5 insertions(+), 9 deletions(-)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Images/Graph.png (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Images/Graph.sketch (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Images/MinimumSpanningTree.png (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Images/MinimumSpanningTree.sketch (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Images/Tree.graffle (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Images/Tree.png (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Sources/Edge.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Sources/Graph.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Sources/Node.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/Sources/Queue.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.playground/contents.xcplayground (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/MinimumSpanningTree.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/README.markdown (99%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Tests/Graph.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Tests/Info.plist (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Tests/MinimumSpanningTreeTests.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Tests/Queue.swift (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Tests/Tests.xcodeproj/project.pbxproj (100%)
 rename {Minimum Spanning Tree => Minimum Spanning Tree (Unweighted)}/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Images/Graph.graffle (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Images/Graph.png (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/README.markdown (98%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/Sources/Edge.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/Sources/Graph.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/Sources/Node.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/Sources/Queue.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.playground/contents.xcplayground (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/ShortestPath.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Tests/Graph.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Tests/Info.plist (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Tests/Queue.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Tests/ShortestPathTests.swift (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Tests/Tests.xcodeproj/project.pbxproj (100%)
 rename {Shortest Path => Shortest Path (Unweighted)}/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme (100%)

diff --git a/Minimum Spanning Tree/Images/Graph.png b/Minimum Spanning Tree (Unweighted)/Images/Graph.png
similarity index 100%
rename from Minimum Spanning Tree/Images/Graph.png
rename to Minimum Spanning Tree (Unweighted)/Images/Graph.png
diff --git a/Minimum Spanning Tree/Images/Graph.sketch b/Minimum Spanning Tree (Unweighted)/Images/Graph.sketch
similarity index 100%
rename from Minimum Spanning Tree/Images/Graph.sketch
rename to Minimum Spanning Tree (Unweighted)/Images/Graph.sketch
diff --git a/Minimum Spanning Tree/Images/MinimumSpanningTree.png b/Minimum Spanning Tree (Unweighted)/Images/MinimumSpanningTree.png
similarity index 100%
rename from Minimum Spanning Tree/Images/MinimumSpanningTree.png
rename to Minimum Spanning Tree (Unweighted)/Images/MinimumSpanningTree.png
diff --git a/Minimum Spanning Tree/Images/MinimumSpanningTree.sketch b/Minimum Spanning Tree (Unweighted)/Images/MinimumSpanningTree.sketch
similarity index 100%
rename from Minimum Spanning Tree/Images/MinimumSpanningTree.sketch
rename to Minimum Spanning Tree (Unweighted)/Images/MinimumSpanningTree.sketch
diff --git a/Minimum Spanning Tree/Images/Tree.graffle b/Minimum Spanning Tree (Unweighted)/Images/Tree.graffle
similarity index 100%
rename from Minimum Spanning Tree/Images/Tree.graffle
rename to Minimum Spanning Tree (Unweighted)/Images/Tree.graffle
diff --git a/Minimum Spanning Tree/Images/Tree.png b/Minimum Spanning Tree (Unweighted)/Images/Tree.png
similarity index 100%
rename from Minimum Spanning Tree/Images/Tree.png
rename to Minimum Spanning Tree (Unweighted)/Images/Tree.png
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Resources/Minimum_Spanning_Tree.png
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Edge.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Edge.swift
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Edge.swift
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Edge.swift
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Node.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Node.swift
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Queue.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Queue.swift
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Queue.swift
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Queue.swift
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/contents.xcplayground
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/contents.xcplayground
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.swift
similarity index 100%
rename from Minimum Spanning Tree/MinimumSpanningTree.swift
rename to Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.swift
diff --git a/Minimum Spanning Tree/README.markdown b/Minimum Spanning Tree (Unweighted)/README.markdown
similarity index 99%
rename from Minimum Spanning Tree/README.markdown
rename to Minimum Spanning Tree (Unweighted)/README.markdown
index 5d988eee6..cfd29c987 100644
--- a/Minimum Spanning Tree/README.markdown	
+++ b/Minimum Spanning Tree (Unweighted)/README.markdown	
@@ -1,4 +1,4 @@
-# Minimum Spanning Tree
+# Minimum Spanning Tree (Unweighted Graph)
 
 A minimum spanning tree describes a path that contains the smallest number of edges that are needed to visit every node in the graph.
 
diff --git a/Minimum Spanning Tree/Tests/Graph.swift b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift
similarity index 100%
rename from Minimum Spanning Tree/Tests/Graph.swift
rename to Minimum Spanning Tree (Unweighted)/Tests/Graph.swift
diff --git a/Minimum Spanning Tree/Tests/Info.plist b/Minimum Spanning Tree (Unweighted)/Tests/Info.plist
similarity index 100%
rename from Minimum Spanning Tree/Tests/Info.plist
rename to Minimum Spanning Tree (Unweighted)/Tests/Info.plist
diff --git a/Minimum Spanning Tree/Tests/MinimumSpanningTreeTests.swift b/Minimum Spanning Tree (Unweighted)/Tests/MinimumSpanningTreeTests.swift
similarity index 100%
rename from Minimum Spanning Tree/Tests/MinimumSpanningTreeTests.swift
rename to Minimum Spanning Tree (Unweighted)/Tests/MinimumSpanningTreeTests.swift
diff --git a/Minimum Spanning Tree/Tests/Queue.swift b/Minimum Spanning Tree (Unweighted)/Tests/Queue.swift
similarity index 100%
rename from Minimum Spanning Tree/Tests/Queue.swift
rename to Minimum Spanning Tree (Unweighted)/Tests/Queue.swift
diff --git a/Minimum Spanning Tree/Tests/Tests.xcodeproj/project.pbxproj b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
similarity index 100%
rename from Minimum Spanning Tree/Tests/Tests.xcodeproj/project.pbxproj
rename to Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
diff --git a/Minimum Spanning Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 100%
rename from Minimum Spanning Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
diff --git a/README.markdown b/README.markdown
index c3e3e43ea..7c776225c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -169,9 +169,9 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Graph](Graph/)
 - [Breadth-First Search (BFS)](Breadth-First Search/)
-- [Depth-First Search (DFS)](Depth-First Search/) :construction:
-- [Shortest Path](Shortest Path/)
-- [Minimum Spanning Tree](Minimum Spanning Tree/)
+- [Depth-First Search (DFS)](Depth-First Search/)
+- [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
+- [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
 - All Paths
 
 ## Puzzles
diff --git a/Shortest Path/Images/Graph.graffle b/Shortest Path (Unweighted)/Images/Graph.graffle
similarity index 100%
rename from Shortest Path/Images/Graph.graffle
rename to Shortest Path (Unweighted)/Images/Graph.graffle
diff --git a/Shortest Path/Images/Graph.png b/Shortest Path (Unweighted)/Images/Graph.png
similarity index 100%
rename from Shortest Path/Images/Graph.png
rename to Shortest Path (Unweighted)/Images/Graph.png
diff --git a/Shortest Path/README.markdown b/Shortest Path (Unweighted)/README.markdown
similarity index 98%
rename from Shortest Path/README.markdown
rename to Shortest Path (Unweighted)/README.markdown
index b3fb1692d..64ae52a80 100644
--- a/Shortest Path/README.markdown	
+++ b/Shortest Path (Unweighted)/README.markdown	
@@ -1,4 +1,4 @@
-# Shortest Path
+# Shortest Path (Unweighted Graph)
 
 Goal: find the shortest route to go from one node to another in a graph.
 
@@ -99,8 +99,4 @@ This will output:
 
 > **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum Spanning Tree/) on how you can convert the graph into a tree by removing edges.
 
-## Weighted graph: Dijkstra's algorithm
-
-[Coming soon]
-
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
similarity index 100%
rename from Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
rename to Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
diff --git a/Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
similarity index 100%
rename from Shortest Path/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
rename to Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
diff --git a/Shortest Path/ShortestPath.playground/Sources/Edge.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Edge.swift
similarity index 100%
rename from Shortest Path/ShortestPath.playground/Sources/Edge.swift
rename to Shortest Path (Unweighted)/ShortestPath.playground/Sources/Edge.swift
diff --git a/Shortest Path/ShortestPath.playground/Sources/Graph.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift
similarity index 100%
rename from Shortest Path/ShortestPath.playground/Sources/Graph.swift
rename to Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift
diff --git a/Shortest Path/ShortestPath.playground/Sources/Node.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift
similarity index 100%
rename from Shortest Path/ShortestPath.playground/Sources/Node.swift
rename to Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift
diff --git a/Shortest Path/ShortestPath.playground/Sources/Queue.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Queue.swift
similarity index 100%
rename from Shortest Path/ShortestPath.playground/Sources/Queue.swift
rename to Shortest Path (Unweighted)/ShortestPath.playground/Sources/Queue.swift
diff --git a/Shortest Path/ShortestPath.playground/contents.xcplayground b/Shortest Path (Unweighted)/ShortestPath.playground/contents.xcplayground
similarity index 100%
rename from Shortest Path/ShortestPath.playground/contents.xcplayground
rename to Shortest Path (Unweighted)/ShortestPath.playground/contents.xcplayground
diff --git a/Shortest Path/ShortestPath.swift b/Shortest Path (Unweighted)/ShortestPath.swift
similarity index 100%
rename from Shortest Path/ShortestPath.swift
rename to Shortest Path (Unweighted)/ShortestPath.swift
diff --git a/Shortest Path/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
similarity index 100%
rename from Shortest Path/Tests/Graph.swift
rename to Shortest Path (Unweighted)/Tests/Graph.swift
diff --git a/Shortest Path/Tests/Info.plist b/Shortest Path (Unweighted)/Tests/Info.plist
similarity index 100%
rename from Shortest Path/Tests/Info.plist
rename to Shortest Path (Unweighted)/Tests/Info.plist
diff --git a/Shortest Path/Tests/Queue.swift b/Shortest Path (Unweighted)/Tests/Queue.swift
similarity index 100%
rename from Shortest Path/Tests/Queue.swift
rename to Shortest Path (Unweighted)/Tests/Queue.swift
diff --git a/Shortest Path/Tests/ShortestPathTests.swift b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift
similarity index 100%
rename from Shortest Path/Tests/ShortestPathTests.swift
rename to Shortest Path (Unweighted)/Tests/ShortestPathTests.swift
diff --git a/Shortest Path/Tests/Tests.xcodeproj/project.pbxproj b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
similarity index 100%
rename from Shortest Path/Tests/Tests.xcodeproj/project.pbxproj
rename to Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
diff --git a/Shortest Path/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 100%
rename from Shortest Path/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Shortest Path (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

From e3c921b85589aa524c244b576cca4f44d0564f8a Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sat, 19 Mar 2016 14:57:12 +0100
Subject: [PATCH 0169/1679] Tweaks to K-Means code, text, and images

Vector is a struct instead of a class.
---
 K-Means/Images/k_means_bad1.png               | Bin 16294 -> 11976 bytes
 K-Means/Images/k_means_bad2.png               | Bin 15826 -> 11127 bytes
 K-Means/Images/k_means_good.png               | Bin 15983 -> 11887 bytes
 K-Means/KMeans.swift                          |  65 ++++----
 K-Means/README.markdown                       | 149 +++++++++++-------
 K-Means/Tests/KMeansTests.swift               | 104 ++++++------
 K-Means/Tests/Tests.xcodeproj/project.pbxproj |   2 +-
 K-Means/Tests/Vector.swift                    |  94 +++++------
 README.markdown                               |   2 +-
 9 files changed, 217 insertions(+), 199 deletions(-)

diff --git a/K-Means/Images/k_means_bad1.png b/K-Means/Images/k_means_bad1.png
index 55df0e7eedb8e60921a9c84c2ea0718fc77e3e99..07cb656b6e38ad76bb0d7b7a78cc12694c4f7373 100644
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diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 245a93b4a..e9d48cb04 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -1,28 +1,22 @@
-//
-//  KMeans.swift
-//
-//  Created by John Gill on 2/25/16.
-
 import Foundation
 
 class KMeans<Label: Hashable> {
   let numCenters: Int
-  let labels: Array<Label>
-  private(set) var centroids: Array<Vector>
-
-  init(labels: Array<Label>) {
+  let labels: [Label]
+  private(set) var centroids = [Vector]()
+  
+  init(labels: [Label]) {
     assert(labels.count > 1, "Exception: KMeans with less than 2 centers.")
     self.labels = labels
     self.numCenters = labels.count
-    centroids = []
   }
-
-  private func nearestCenterIndex(x: Vector, centers: [Vector]) -> Int {
+  
+  private func indexOfNearestCenter(x: Vector, centers: [Vector]) -> Int {
     var nearestDist = DBL_MAX
     var minIndex = 0
     
     for (idx, center) in centers.enumerate() {
-      let dist = x.distTo(center)
+      let dist = x.distanceTo(center)
       if dist < nearestDist {
         minIndex = idx
         nearestDist = dist
@@ -31,43 +25,46 @@ class KMeans<Label: Hashable> {
     return minIndex
   }
   
-  
-  
-  func trainCenters(points: [Vector], convergeDist: Double) {
-    
-    var centerMoveDist = 0.0
-    let zeroVector = Vector(d: [Double](count: points[0].length, repeatedValue: 0.0))
+  func trainCenters(points: [Vector], convergeDistance: Double) {
+    let zeroVector = Vector([Double](count: points[0].length, repeatedValue: 0))
     
-    var kCenters = reservoirSample(points, k: numCenters)
+    // Randomly take k objects from the input data to make the initial centroids.
+    var centers = reservoirSample(points, k: numCenters)
     
+    var centerMoveDist = 0.0
     repeat {
+      // This array keeps track of which data points belong to which centroids.
+      var classification: [[Vector]] = .init(count: numCenters, repeatedValue: [])
       
-      var classification: Array<[Vector]> = Array(count: numCenters, repeatedValue: [])
-      
+      // For each data point, find the centroid that it is closest to.
       for p in points {
-        let classIndex = nearestCenterIndex(p, centers: kCenters)
+        let classIndex = indexOfNearestCenter(p, centers: centers)
         classification[classIndex].append(p)
       }
-      
+
+      // Take the average of all the data points that belong to each centroid.
+      // This moves the centroid to a new position.
       let newCenters = classification.map { assignedPoints in
         assignedPoints.reduce(zeroVector, combine: +) / Double(assignedPoints.count)
       }
       
+      // Find out how far each centroid moved since the last iteration. If it's
+      // only a small distance, then we're done.
       centerMoveDist = 0.0
       for idx in 0..<numCenters {
-        centerMoveDist += kCenters[idx].distTo(newCenters[idx])
+        centerMoveDist += centers[idx].distanceTo(newCenters[idx])
       }
       
-      kCenters = newCenters
-    } while centerMoveDist > convergeDist
-
-    centroids = kCenters
+      centers = newCenters
+    } while centerMoveDist > convergeDistance
+    
+    centroids = centers
   }
   
   func fit(point: Vector) -> Label {
     assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
     
-    let centroidIndex = nearestCenterIndex(point, centers: centroids)
+    let centroidIndex = indexOfNearestCenter(point, centers: centroids)
     return labels[centroidIndex]
   }
   
@@ -79,20 +76,20 @@ class KMeans<Label: Hashable> {
 }
 
 // Pick k random elements from samples
-func reservoirSample<T>(samples:[T], k:Int) -> [T] {
+func reservoirSample<T>(samples: [T], k: Int) -> [T] {
   var result = [T]()
   
   // Fill the result array with first k elements
   for i in 0..<k {
     result.append(samples[i])
   }
-  // randomly replace elements from remaining pool
+
+  // Randomly replace elements from remaining pool
   for i in (k+1)..<samples.count {
-    let j = random() % (i+1)
+    let j = Int(arc4random_uniform(UInt32(i + 1)))
     if j < k {
       result[j] = samples[i]
     }
   }
   return result
 }
-
diff --git a/K-Means/README.markdown b/K-Means/README.markdown
index de828299f..bebcf225b 100644
--- a/K-Means/README.markdown
+++ b/K-Means/README.markdown
@@ -1,101 +1,132 @@
 # k-Means Clustering
 
-Goal: Partition data into **k** clusters based on nearest means.
+Goal: Partition data into two or more clusters.
 
-The idea behind k-Means is to take data that has no formal classification to it and determine if there are any natural clusters (groups of related objects) within the data.
+The idea behind k-Means Clustering is to take a bunch of data and determine if there are any natural clusters (groups of related objects) within the data.
 
-k-Means assumes that there are **k-centers** within the data. The data that is closest to these *centroids* become classified or grouped together. k-Means doesn't tell you what the classifier is for that particular data group, but it assists in trying to find what clusters potentially exist.
+The k-Means algorithm is a so-called *unsupervised* learning algorithm. We don't know in advance what patterns exist in the data -- it has no formal classification to it -- but we would like to see if we can divide the data into groups somehow.
 
-## The algorithm
+For example, you can use k-Means to find what are the 3 most prominent colors in an image by telling it to group pixels into 3 clusters based on their color value. Or you can use it to group related news articles together, without deciding beforehand what categories to use. The algorithm will automatically figure out what the best groups are.
 
-The k-Means algorithm is really quite simple at its core:
+The "k" in k-Means is a number. The algorithm assumes that there are **k** centers within the data that the various data elements are scattered around. The data that is closest to these so-called **centroids** become classified or grouped together.
 
-1. Choose **k** random points to be the initial centers
-2. Repeat the following two steps until the *centroids* reach convergence:
-	1. Assign each point to its nearest *centroid*
-	2. Update the *centroid* to the mean of its nearest points
+k-Means doesn't tell you what the classifier is for each particular data group. After dividing news articles into groups, it doesn't say that group 1 is about science, group 2 is about celebrities, group 3 is about the upcoming election, etc. You only know that related news stories are now together, but not necessarily what that relationship signifies. k-Means only assists in trying to find what clusters potentially exist.
 
-Convergence is said to be reached when all of the *centroids* have not changed.
+## The algorithm
 
-This brings about a few of the parameters that are required for k-Means:
+The k-Means algorithm is really quite simple at its core.
 
-- **k**: This is the number of *centroids* to attempt to locate.
-- **convergence distance**: The minimum distance that the centers are allowed to move after a particular update step.
-- **distance function**: There are a number of distance functions that can be used, but mostly commonly the Euclidean distance function is adequate. But often that can lead to convergence not being reached in higher dimensionally.
+First, we choose **k** random data points to be the initial centroids. Then, we repeat the following two steps until we've found our clusters:
 
-This is what the algorithm would look like in Swift:
+1. For each data point, find which centroid it is closest to. We assign each point to its nearest centroid.
+2. Update the centroid to the mean (i.e. the average) of its nearest data points. We move the centroid so that it really sits in the center of the cluster.
 
-```swift
-func kMeans(numCenters: Int, convergeDist: Double, points: [Vector]) -> [Vector] {
-  var centerMoveDist = 0.0
-  let zeros = [Double](count: points[0].length, repeatedValue: 0.0)
-  
-  var kCenters = reservoirSample(points, k: numCenters)
-  
-  repeat {
-    var cnts = [Double](count: numCenters, repeatedValue: 0.0)
-    var newCenters = [Vector](count:numCenters, repeatedValue: Vector(d:zeros))
+We need to repeat this multiple times because moving the centroid changes which data points belong to it. This goes back and forth for a bit until everything stabilizes. That's when we reach "convergence", i.e. when the centroids no longer move around.
 
-    for p in points {
-      let c = nearestCenter(p, centers: kCenters)
-      cnts[c] += 1
-      newCenters[c] += p
-    }
-    
-    for idx in 0..<numCenters {
-      newCenters[idx] /= cnts[idx]
-    }
-    
-    centerMoveDist = 0.0
-    for idx in 0..<numCenters {
-      centerMoveDist += euclidean(kCenters[idx], newCenters[idx])
-    }
-    
-    kCenters = newCenters
-  } while centerMoveDist > convergeDist
+A few of the parameters that are required for k-Means:
 
-  return kCenters
-}
-```
+- **k**: This is the number of centroids to attempt to locate. If you want to group news articles, this is the number of groups to look for.
+- **convergence distance**: If all the centroids move less than this distance after a particular update step, we're done.
+- **distance function**: This calculates how far data points are from the centroids, to find which centroid they are closest to. There are a number of distance functions that can be used, but most commonly the Euclidean distance function is adequate (you know, Pythagoras). But often that can lead to convergence not being reached in higher dimensionally.
 
-## Example
+Let's look at an example.
 
-These examples are contrived to show the exact nature of k-Means and finding clusters. These clusters are very easily identified by human eyes: we see there is one in the lower left corner, one in the upper right corner, and maybe one in the middle.
+#### Good clusters
 
-In all these examples the squares represent the data points and the stars represent the *centroids*.
+This first example shows k-Means finding all three clusters. In all these examples the circles represent the data points and the stars represent the centroids.
 
-##### Good clusters
-
-This first example shows k-Means finding all three clusters:
+In the first iteration, we choose three data points at random and put our centroids on top of them. Then in each subsequent iteration, we figure out which data points are closest to these centroids, and move the centroids to the average position of those data points. This repeats until we reach equilibrium and the centroids stop moving.
 
 ![Good Clustering](Images/k_means_good.png)
 
-The selection of initial centroids found the lower left cluster (indicated by red) and did pretty good on the center and upper left clusters.
+The selection of initial centroids was fortuitous! We found the lower left cluster (indicated by red) and did pretty good on the center and upper left clusters.
+
+> **Note:** These examples are contrived to show the exact nature of k-Means and finding clusters. The clusters in these examples are very easily identified by human eyes: we see there is one in the lower left corner, one in the upper right corner, and maybe one in the middle. In practice, however, data may have many dimensions and may be impossible to visualize. In such cases, k-Means is much better at this job than  human eyes!
 
-#### Bad Clustering
+#### Bad clustering
 
 The next two examples highlight the unpredictability of k-Means and how it not always finds the best clustering.
 
 ![Bad Clustering 1](Images/k_means_bad1.png)
 
-As you can see in this one, the initial *centroids* were all a little too close and the 'blue' didn't quite get to a good place. By adjusting the convergence distance we should be able to get it better.
+As you can see in this one, the initial centroids were all a little too close to one another, and the blue one didn't quite get to a good place. By adjusting the convergence distance we should be able to get it better.
 
 ![Bad Clustering 1](Images/k_means_bad2.png)
 
 In this example, the blue cluster never really could separate from the red cluster and as such sort of got stuck down there.
 
+#### Improving bad clustering 
+
+In these examples of "bad" clustering, the algorithm got stuck in a local optimum. It does find clusters but they're not the best way to divide up the data. To increase your chances of success, you can run the algorithm several times, each time with different points as the initial centroids. You choose the clustering that gives the best results.
+
+To calculate how "good" the clustering is, you find the distance of each data point to its cluster, and add up all these distances. The lower this number, the better! That means each cluster is really in the center of a group of data points, and all clusters are roughly the same size and are spaced evenly apart.
+
+## The code
+
+This is what the algorithm could look like in Swift. The `points` array contains the input data as `Vector` objects. The output is an array of `Vector` objects representing the clusters that were found.
+
+```swift
+func kMeans(numCenters: Int, convergeDistance: Double, points: [Vector]) -> [Vector] {
+ 
+  // Randomly take k objects from the input data to make the initial centroids.
+  var centers = reservoirSample(points, k: numCenters)
+
+  // This loop repeats until we've reached convergence, i.e. when the centroids
+  // have moved less than convergeDistance since the last iteration.
+  var centerMoveDist = 0.0
+  repeat {
+    // In each iteration of the loop, we move the centroids to a new position.
+    // The newCenters array contains those new positions.
+    let zeros = [Double](count: points[0].length, repeatedValue: 0)
+    var newCenters = [Vector](count: numCenters, repeatedValue: Vector(zeros))
+
+    // We keep track of how many data points belong to each centroid, so we
+    // can calculate the average later.
+    var counts = [Double](count: numCenters, repeatedValue: 0)
+
+    // For each data point, find the centroid that it is closest to. We also 
+    // add up the data points that belong to that centroid, in order to compute
+    // that average.
+    for p in points {
+      let c = indexOfNearestCenter(p, centers: centers)
+      newCenters[c] += p
+      counts[c] += 1
+    }
+    
+    // Take the average of all the data points that belong to each centroid.
+    // This moves the centroid to a new position.
+    for idx in 0..<numCenters {
+      newCenters[idx] /= counts[idx]
+    }
+
+    // Find out how far each centroid moved since the last iteration. If it's
+    // only a small distance, then we're done.
+    centerMoveDist = 0.0
+    for idx in 0..<numCenters {
+      centerMoveDist += centers[idx].distanceTo(newCenters[idx])
+    }
+    
+    centers = newCenters
+  } while centerMoveDist > convergeDistance
+
+  return centers
+}
+```
+
+> **Note:** The code in [KMeans.swift](KMeans.swift) is slightly more advanced than the above listing. It also assigns labels to the clusters and has a few other tricks up its sleeve. Check it out!
+
 ## Performance
 
-The first thing to recognize is that k-Means is classified as an NP-Hard type of problem. The selection of the initial *centroids* has a big effect on how the resulting clusters may end up. This means that trying to find an exact solution is not likely -- even in 2 dimensional space.
+k-Means is classified as an NP-Hard type of problem. That means it's almost impossible to find the optimal solution. The selection of the initial centroids has a big effect on how the resulting clusters may end up. Finding an exact solution is not likely -- even in 2 dimensional space.
 
-As seen from the steps above the complexity really isn't that bad -- it is often considered to be on the order of **O(kndi)**, where **k** is the number of *centroids*, **n** is the number of **d**-dimensional vectors, and **i** is the number of iterations for convergence.
+As seen from the steps above the complexity really isn't that bad -- it is often considered to be on the order of **O(kndi)**, where **k** is the number of centroids, **n** is the number of **d**-dimensional vectors, and **i** is the number of iterations for convergence.
 
-The amount of data has a big linear effect on the running time of k-Means, but tuning how far you want the *centroids* to converge can have a big impact how many iterations will be done. As a general rule, **k** should be relatively small compared to the number of vectors.
+The amount of data has a linear effect on the running time of k-Means, but tuning how far you want the centroids to converge can have a big impact how many iterations will be done. As a general rule, **k** should be relatively small compared to the number of vectors.
 
-Often times as more data is added certain points may lie in the boundary between two *centroids* and as such those centroids would continue to bounce back and forth and the **convergence** distance would need to be tuned to prevent that.
+Often times as more data is added certain points may lie in the boundary between two centroids and as such those centroids would continue to bounce back and forth and the convergence distance would need to be tuned to prevent that.
 
 ## See Also
 
 [K-Means Clustering on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
 
-*Written by John Gill*
+*Written by John Gill and Matthijs Hollemans*
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index 4f1c18b1a..7a6803f63 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,67 +10,65 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
+  func genPoints(numPoints: Int, numDimensions: Int) -> [Vector] {
+    var points = [Vector]()
+    for _ in 0..<numPoints {
+      var data = [Double]()
+      for _ in 0..<numDimensions {
+        data.append(Double(arc4random_uniform(UInt32(numPoints*numDimensions))))
+      }
+      points.append(Vector(data))
+    }
+    return points
+  }
+  
+  func testSmall_2D() {
+    let points = genPoints(10, numDimensions: 2)
+    
+    print("\nCenters")
+    let kmm = KMeans<Character>(labels: ["A", "B", "C"])
+    kmm.trainCenters(points, convergeDistance: 0.01)
     
-    func genPoints(numPoints:Int, numDimmensions:Int) -> [Vector] {
-        var points = [Vector]()
-        
-        for _ in 0..<numPoints {
-            var data = [Double]()
-            for _ in 0..<numDimmensions {
-                data.append(Double(arc4random_uniform(UInt32(numPoints*numDimmensions))))
-            }
-            points.append(Vector(d: data))
-        }
-        return points
+    for (label, centroid) in zip(kmm.labels, kmm.centroids) {
+      print("\(label): \(centroid)")
     }
     
-    func testSmall_2D() {
-        let points = genPoints(10, numDimmensions: 2)
-
-        print("\nCenters")
-        let kmm = KMeans<Character>(labels: ["A", "B", "C"])
-        kmm.trainCenters(points, convergeDist: 0.01)
-        
-        for (label, centroid) in zip(kmm.labels, kmm.centroids) {
-            print("\(label): \(centroid)")
-        }
-        
-        print("\nClassifications")
-        for (label, point) in zip(kmm.fit(points), points) {
-            print("\(label): \(point)")
-        }
+    print("\nClassifications")
+    for (label, point) in zip(kmm.fit(points), points) {
+      print("\(label): \(point)")
     }
+  }
+  
+  func testSmall_10D() {
+    let points = genPoints(10, numDimensions: 10)
     
-    func testSmall_10D() {
-        let points = genPoints(10, numDimmensions: 10)
-        
-        print("\nCenters")
-        let kmm = KMeans<Int>(labels: [1, 2, 3])
-        kmm.trainCenters(points, convergeDist: 0.01)
-        for c in kmm.centroids {
-            print(c)
-        }
+    print("\nCenters")
+    let kmm = KMeans<Int>(labels: [1, 2, 3])
+    kmm.trainCenters(points, convergeDistance: 0.01)
+    for c in kmm.centroids {
+      print(c)
     }
+  }
+  
+  func testLarge_2D() {
+    let points = genPoints(10000, numDimensions: 2)
     
-    func testLarge_2D() {
-        let points = genPoints(10000, numDimmensions: 2)
-        
-        print("\nCenters")
-        let kmm = KMeans<Character>(labels: ["A","B","C","D","E"])
-        kmm.trainCenters(points, convergeDist: 0.01)
-        for c in kmm.centroids {
-            print(c)
-        }
+    print("\nCenters")
+    let kmm = KMeans<Character>(labels: ["A","B","C","D","E"])
+    kmm.trainCenters(points, convergeDistance: 0.01)
+    for c in kmm.centroids {
+      print(c)
     }
+  }
+  
+  func testLarge_10D() {
+    let points = genPoints(10000, numDimensions: 10)
     
-    func testLarge_10D() {
-        let points = genPoints(10000, numDimmensions: 10)
-        
-        print("\nCenters")
-        let kmm = KMeans<Int>(labels: [1,2,3,4,5])
-        kmm.trainCenters(points, convergeDist: 0.01)
-        for c in kmm.centroids {
-            print(c)
-        }
+    print("\nCenters")
+    let kmm = KMeans<Int>(labels: [1,2,3,4,5])
+    kmm.trainCenters(points, convergeDistance: 0.01)
+    for c in kmm.centroids {
+      print(c)
     }
+  }
 }
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 084152c1c..c43576ac3 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -50,9 +50,9 @@
 		B80894E21C852D100018730E /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				B80894E91C852DA00018730E /* Vector.swift */,
 				B80894DB1C852CFA0018730E /* KMeans.swift */,
 				B80894E31C852D100018730E /* KMeansTests.swift */,
+				B80894E91C852DA00018730E /* Vector.swift */,
 				B80894E51C852D100018730E /* Info.plist */,
 			);
 			path = Tests;
diff --git a/K-Means/Tests/Vector.swift b/K-Means/Tests/Vector.swift
index a920de7de..659bd914f 100644
--- a/K-Means/Tests/Vector.swift
+++ b/K-Means/Tests/Vector.swift
@@ -1,76 +1,68 @@
-//
-//  Vector.swift
-//  Tests
-//
-//  Created by John Gill on 2/29/16.
-//
-//
-
 import Foundation
 
-// Container to easily hold N Dimensional Vectors
-class Vector: CustomStringConvertible, Equatable {
-    private(set) var length = 0
-    private(set) var data = [Double]()
-    
-    init(d:[Double]) {
-        data = d
-        length = d.count
-    }
-    
-    var description: String { return "Vector (\(data)" }
-    
-    func distTo(v2:Vector) -> Double {
-        var result = 0.0
-        for idx in 0..<self.length {
-            result += pow(self.data[idx] - v2.data[idx], 2.0)
-        }
-        return sqrt(result)
+struct Vector: CustomStringConvertible, Equatable {
+  private(set) var length = 0
+  private(set) var data: [Double]
+
+  init(_ data: [Double]) {
+    self.data = data
+    self.length = data.count
+  }
+  
+  var description: String {
+    return "Vector (\(data)"
+  }
+  
+  func distanceTo(other: Vector) -> Double {
+    var result = 0.0
+    for idx in 0..<length {
+      result += pow(data[idx] - other.data[idx], 2.0)
     }
+    return sqrt(result)
+  }
 }
 
-// MARK: Vector Operators
 func ==(left: Vector, right: Vector) -> Bool {
-    for idx in 0..<left.length {
-        if left.data[idx] != right.data[idx] {
-            return false
-        }
+  for idx in 0..<left.length {
+    if left.data[idx] != right.data[idx] {
+      return false
     }
-    return true
+  }
+  return true
 }
 
 func +(left: Vector, right: Vector) -> Vector {
-    var results = [Double]()
-    for idx in 0..<left.length {
-        results.append(left.data[idx] + right.data[idx])
-    }
-    return Vector(d: results)
+  var results = [Double]()
+  for idx in 0..<left.length {
+    results.append(left.data[idx] + right.data[idx])
+  }
+  return Vector(results)
 }
 
 func +=(inout left: Vector, right: Vector) {
-    left = left + right
+  left = left + right
 }
 
 func -(left: Vector, right: Vector) -> Vector {
-    var results = [Double]()
-    for idx in 0..<left.length {
-        results.append(left.data[idx] - right.data[idx])
-    }
-    return Vector(d: results)
+  var results = [Double]()
+  for idx in 0..<left.length {
+    results.append(left.data[idx] - right.data[idx])
+  }
+  return Vector(results)
 }
 
 func -=(inout left: Vector, right: Vector) {
-    left = left - right
+  left = left - right
 }
 
 func /(left:Vector, right: Double) -> Vector  {
-    var results = [Double](count: left.length, repeatedValue: 0.0)
-    for (idx, value) in left.data.enumerate() {
-        results[idx] = value / right
-    }
-    return Vector(d: results)
+  var results = [Double](count: left.length, repeatedValue: 0)
+  for (idx, value) in left.data.enumerate() {
+    results[idx] = value / right
+  }
+  return Vector(results)
 }
 
 func /=(inout left: Vector, right: Double) {
-    left = left / right
-}
\ No newline at end of file
+  left = left / right
+}
diff --git a/README.markdown b/README.markdown
index 7c776225c..9eaac70ed 100644
--- a/README.markdown
+++ b/README.markdown
@@ -99,7 +99,7 @@ Bad sorting algorithms (don't use these!):
 
 ### Machine learning
 
-- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters. :construction:
+- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
 - Linear Regression
 - Logistic Regression

From 14667d40852e6ae37ed3c06550689bfe489c57e7 Mon Sep 17 00:00:00 2001
From: Hamdullah shah <hamdullahshah@users.noreply.github.com>
Date: Sun, 20 Mar 2016 14:49:49 +0800
Subject: [PATCH 0170/1679] modified percentage

Make it same as explanation, i.e at least 50 elements and 0.25 percent.
---
 Queue/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Queue/README.markdown b/Queue/README.markdown
index 7cf4bd484..92118d37b 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -158,7 +158,7 @@ public struct Queue<T> {
     head += 1
 
     let percentage = Double(head)/Double(array.count)
-    if head > 20 && percentage > 0.25 {
+    if array.count > 50 && percentage > 0.25 {
       array.removeFirst(head)
       head = 0
     }

From 6449a785bbf8005a5682934cb19bac7f8d3baff3 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 20 Mar 2016 11:34:16 +0100
Subject: [PATCH 0171/1679] Improve removing node with two children

Previously, if the node had two children we'd remove one of the children and copy its value into the node you called remove() on. The advantage of that approach is that calling remove() on the root of the tree doesn't invalidate the root node. However, this wasn't true for when you tried to delete a root node that has only one child. That was confusing.

Now we always truly remove the node you called remove() on, and tell you what its replacement is. As a consequence, if you remove the root node you must make sure to use its replacement node as the new root from then on.
---
 Binary Search Tree/README.markdown            | 60 +++++++++++----
 .../Contents.swift                            |  2 +-
 .../Sources/BinarySearchTree.swift            | 65 ++++++++++++----
 .../Solution 1/BinarySearchTree.swift         | 65 ++++++++++++----
 .../Tests/BinarySearchTreeTests.swift         | 76 ++++++++++++-------
 5 files changed, 191 insertions(+), 77 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 25d56803b..54468070b 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -431,34 +431,62 @@ It returns the rightmost descendent of the node. We find it by following `right`
 Finally, we can write the code the remove a node from the tree:
 
 ```swift
-  public func remove() {
+  public func remove() -> BinarySearchTree? {
+    let replacement: BinarySearchTree?
+
     if let left = left {
       if let right = right {
-        let successor = right.minimum()  // 1
-        value = successor.value
-        successor.remove()
+        replacement = removeNodeWithTwoChildren(left, right)  // 1
       } else {
-        reconnectParentToNode(left)      // 2
+        replacement = left           // 2
       }
-    } else if let right = right {        // 3
-      reconnectParentToNode(right)
+    } else if let right = right {    // 3
+      replacement = right
     } else {
-      reconnectParentToNode(nil)         // 4 
+      replacement = nil              // 4
     }
+    
+    reconnectParentToNode(replacement)
+
+    parent = nil
+    left = nil
+    right = nil
+
+    return replacement
   }
 ```
 
-It doesn't look so scary after all. ;-) Here is what it does:
-
-1. This node has two children. It must be replaced by the smallest child that is larger than this node's value, which is the leftmost descendent of the right child, i.e. `right.minimum()`. 
+It doesn't look so scary after all. ;-) There are four situations to handle:
 
+1. This node has two children. 
 2. This node only has a left child. The left child replaces the node.
-
 3. This node only has a right child. The right child replaces the node.
-
 4. This node has no children. We just disconnect it from its parent.
 
-The only tricky situation here is `// 1`. Rather than deleting the current node, we give it the successor's value and remove the successor node instead.
+First, we determine which node will replace the one we're removing and then we call `reconnectParentToNode()` to change the `left`, `right`, and `parent` pointers to make that happen. Since the current node is no longer part of the tree, we clean it up by setting its pointers to `nil`. Finally, we return the node that has replaced the removed one (or `nil` if this was a leaf node).
+
+The only tricky situation here is `// 1` and that logic has its own helper method:
+
+```swift
+  private func removeNodeWithTwoChildren(left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
+    let successor = right.minimum()
+    successor.remove()
+    
+    successor.left = left
+    left.parent = successor
+    
+    if right !== successor {
+      successor.right = right
+      right.parent = successor
+    } else {
+      successor.right = nil
+    }
+    
+    return successor
+  }
+```
+
+If the node to remove has two children, it must be replaced by the smallest child that is larger than this node's value. That always happens to be the leftmost descendent of the right child, i.e. `right.minimum()`. We take that node out of its original position in the tree and put it into the place of the node we're removing.
 
 Try it out:
 
@@ -478,9 +506,9 @@ But after `remove()` you get:
 
 	((1) <- 5) <- 7 -> ((9) <- 10)
 
-As you can see, node `5` has taken the place of `2`. In fact, if you do `print(node2)` you'll see that it now has the value `5`. We didn't actually remove the `node2` object, we just gave it a new value.
+As you can see, node `5` has taken the place of `2`.
 
-> **Note:** What would happen if you deleted the root node? Specifically, how would you know which node becomes the new root node? It turns out you don't have to worry about that because the root never actually gets deleted. We simply give it a new value.
+> **Note:** What would happen if you deleted the root node? In that case, `remove()` tells you which node has become the new root. Try it out: call `tree.remove()` and see what happens.
 
 Like most binary search tree operations, removing a node runs in **O(h)** time, where **h** is the height of the tree.
 
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 7f982464a..1b9b070a1 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -26,7 +26,7 @@ tree.maximum()
 
 if let node2 = tree.search(2) {
   node2.remove()
-  node2.value          // this is now node "5"
+  node2
   print(tree)
 }
 
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 7ef0280cf..55683b639 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -101,34 +101,67 @@ extension BinarySearchTree {
 extension BinarySearchTree {
   /*
     Deletes a node from the tree.
+
+    Returns the node that has replaced this removed one (or nil if this was a
+    leaf node). That is primarily useful for when you delete the root node, in
+    which case the tree gets a new root.
+
     Performance: runs in O(h) time, where h is the height of the tree.
   */
-  public func remove() {
+  public func remove() -> BinarySearchTree? {
+    let replacement: BinarySearchTree?
+
     if let left = left {
       if let right = right {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
-        
-        // Rather than deleting the current node (which is problematic for the
-        // root node) we give it the successor's value and remove the successor.
-        value = successor.value
-        
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
+        replacement = removeNodeWithTwoChildren(left, right)
       } else {
         // This node only has a left child. The left child replaces the node.
-        reconnectParentToNode(left)
+        replacement = left
       }
     } else if let right = right {
       // This node only has a right child. The right child replaces the node.
-      reconnectParentToNode(right)
+      replacement = right
     } else {
       // This node has no children. We just disconnect it from its parent.
-      reconnectParentToNode(nil)
+      replacement = nil
+    }
+
+    reconnectParentToNode(replacement)
+
+    // The current node is no longer part of the tree, so clean it up.
+    parent = nil
+    left = nil
+    right = nil
+
+    return replacement
+  }
+
+  private func removeNodeWithTwoChildren(left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
+    // This node has two children. It must be replaced by the smallest
+    // child that is larger than this node's value, which is the leftmost
+    // descendent of the right child.
+    let successor = right.minimum()
+
+    // If this in-order successor has a right child of its own (it cannot
+    // have a left child by definition), then that must take its place.
+    successor.remove()
+
+    // Connect our left child with the new node.
+    successor.left = left
+    left.parent = successor
+
+    // Connect our right child with the new node. If the right child does
+    // not have any left children of its own, then the in-order successor
+    // *is* the right child.
+    if right !== successor {
+      successor.right = right
+      right.parent = successor
+    } else {
+      successor.right = nil
     }
+
+    // And finally, connect the successor node to our parent.
+    return successor
   }
 
   private func reconnectParentToNode(node: BinarySearchTree?) {
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.swift
index 7ef0280cf..55683b639 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.swift	
@@ -101,34 +101,67 @@ extension BinarySearchTree {
 extension BinarySearchTree {
   /*
     Deletes a node from the tree.
+
+    Returns the node that has replaced this removed one (or nil if this was a
+    leaf node). That is primarily useful for when you delete the root node, in
+    which case the tree gets a new root.
+
     Performance: runs in O(h) time, where h is the height of the tree.
   */
-  public func remove() {
+  public func remove() -> BinarySearchTree? {
+    let replacement: BinarySearchTree?
+
     if let left = left {
       if let right = right {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
-        
-        // Rather than deleting the current node (which is problematic for the
-        // root node) we give it the successor's value and remove the successor.
-        value = successor.value
-        
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
+        replacement = removeNodeWithTwoChildren(left, right)
       } else {
         // This node only has a left child. The left child replaces the node.
-        reconnectParentToNode(left)
+        replacement = left
       }
     } else if let right = right {
       // This node only has a right child. The right child replaces the node.
-      reconnectParentToNode(right)
+      replacement = right
     } else {
       // This node has no children. We just disconnect it from its parent.
-      reconnectParentToNode(nil)
+      replacement = nil
+    }
+
+    reconnectParentToNode(replacement)
+
+    // The current node is no longer part of the tree, so clean it up.
+    parent = nil
+    left = nil
+    right = nil
+
+    return replacement
+  }
+
+  private func removeNodeWithTwoChildren(left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
+    // This node has two children. It must be replaced by the smallest
+    // child that is larger than this node's value, which is the leftmost
+    // descendent of the right child.
+    let successor = right.minimum()
+
+    // If this in-order successor has a right child of its own (it cannot
+    // have a left child by definition), then that must take its place.
+    successor.remove()
+
+    // Connect our left child with the new node.
+    successor.left = left
+    left.parent = successor
+
+    // Connect our right child with the new node. If the right child does
+    // not have any left children of its own, then the in-order successor
+    // *is* the right child.
+    if right !== successor {
+      successor.right = right
+      right.parent = successor
+    } else {
+      successor.right = nil
     }
+
+    // And finally, connect the successor node to our parent.
+    return successor
   }
 
   private func reconnectParentToNode(node: BinarySearchTree?) {
diff --git a/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift
index bafcd8003..46fdd7c8a 100755
--- a/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
+++ b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
@@ -139,14 +139,17 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertTrue(node5.left === node4)
     XCTAssertNil(node5.right)
 
-    node4.remove()
+    let replacement1 = node4.remove()
     XCTAssertNil(node5.left)
+    XCTAssertNil(replacement1)
 
-    node5.remove()
+    let replacement2 = node5.remove()
     XCTAssertNil(tree.left)
+    XCTAssertNil(replacement2)
 
-    node10.remove()
+    let replacement3 = node10.remove()
     XCTAssertNil(tree.right)
+    XCTAssertNil(replacement3)
 
     XCTAssertEqual(tree.count, 1)
     XCTAssertEqual(tree.toArray(), [8])
@@ -223,15 +226,18 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertTrue(node5 === node4.parent)
     XCTAssertTrue(node5 === node6.parent)
 
-    node5.remove()
-    XCTAssertTrue(tree.left === node5)
-    XCTAssertTrue(tree === node5.parent)
-    XCTAssertTrue(node5.left === node4)
-    XCTAssertTrue(node5 === node4.parent)
+    let replacement1 = node5.remove()
+    XCTAssertTrue(replacement1 === node6)
+    XCTAssertTrue(tree.left === node6)
+    XCTAssertTrue(tree === node6.parent)
+    XCTAssertTrue(node6.left === node4)
+    XCTAssertTrue(node6 === node4.parent)
+    XCTAssertNil(node5.left)
     XCTAssertNil(node5.right)
+    XCTAssertNil(node5.parent)
     XCTAssertNil(node4.left)
     XCTAssertNil(node4.right)
-    XCTAssertEqual(node5.value, 6)
+    XCTAssertNotNil(node4.parent)
     XCTAssertEqual(tree.count, 6)
     XCTAssertEqual(tree.toArray(), [4, 6, 8, 9, 10, 11])
 
@@ -243,15 +249,18 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertTrue(node10 === node9.parent)
     XCTAssertTrue(node10 === node11.parent)
 
-    node10.remove()
-    XCTAssertTrue(tree.right === node10)
-    XCTAssertTrue(tree === node10.parent)
-    XCTAssertTrue(node10.left === node9)
-    XCTAssertTrue(node10 === node9.parent)
+    let replacement2 = node10.remove()
+    XCTAssertTrue(replacement2 === node11)
+    XCTAssertTrue(tree.right === node11)
+    XCTAssertTrue(tree === node11.parent)
+    XCTAssertTrue(node11.left === node9)
+    XCTAssertTrue(node11 === node9.parent)
+    XCTAssertNil(node10.left)
     XCTAssertNil(node10.right)
+    XCTAssertNil(node10.parent)
     XCTAssertNil(node9.left)
     XCTAssertNil(node9.right)
-    XCTAssertEqual(node10.value, 11)
+    XCTAssertNotNil(node9.parent)
     XCTAssertEqual(tree.count, 5)
     XCTAssertEqual(tree.toArray(), [4, 6, 8, 9, 11])
   }
@@ -273,28 +282,39 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertTrue(node11.right === node15)
     XCTAssertTrue(node11 === node15.parent)
 
-    node10.remove()
-    XCTAssertTrue(tree.right === node10)
-    XCTAssertTrue(tree === node10.parent)
-    XCTAssertTrue(node10.left === node9)
-    XCTAssertTrue(node10 === node9.parent)
-    XCTAssertTrue(node10.right === node20)
-    XCTAssertTrue(node10 === node20.parent)
+    let replacement = node10.remove()
+    XCTAssertTrue(replacement === node11)
+    XCTAssertTrue(tree.right === node11)
+    XCTAssertTrue(tree === node11.parent)
+    XCTAssertTrue(node11.left === node9)
+    XCTAssertTrue(node11 === node9.parent)
+    XCTAssertTrue(node11.right === node20)
+    XCTAssertTrue(node11 === node20.parent)
     XCTAssertTrue(node20.left === node15)
     XCTAssertTrue(node20 === node15.parent)
     XCTAssertNil(node20.right)
-    XCTAssertEqual(node10.value, 11)
+    XCTAssertNil(node10.left)
+    XCTAssertNil(node10.right)
+    XCTAssertNil(node10.parent)
     XCTAssertEqual(tree.count, 8)
     XCTAssertEqual(tree.toArray(), [4, 5, 8, 9, 11, 13, 15, 20])
   }
 
   func testRemoveRoot() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4, 9, 20, 11, 15, 13])
-    tree.remove()
-
-    XCTAssertEqual(tree.value, 9)
-    XCTAssertEqual(tree.count, 8)
-    XCTAssertEqual(tree.toArray(), [4, 5, 9, 10, 11, 13, 15, 20])
+    
+    let node9 = tree.search(9)!
+    
+    let newRoot = tree.remove()
+    XCTAssertTrue(newRoot === node9)
+    XCTAssertEqual(newRoot!.value, 9)
+    XCTAssertEqual(newRoot!.count, 8)
+    XCTAssertEqual(newRoot!.toArray(), [4, 5, 9, 10, 11, 13, 15, 20])
+
+    // The old root is a subtree of a single element.
+    XCTAssertEqual(tree.value, 8)
+    XCTAssertEqual(tree.count, 1)
+    XCTAssertEqual(tree.toArray(), [8])
   }
 
   func testPredecessor() {

From 4965c9cd1b2edebb6e8a92406188e0c3e832070f Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Mon, 21 Mar 2016 16:29:24 -0700
Subject: [PATCH 0172/1679] Added documentation

---
 Ternary Search Tree/TSTNode.swift | 24 ++++++++++++++++++++++--
 1 file changed, 22 insertions(+), 2 deletions(-)

diff --git a/Ternary Search Tree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
index b6030400f..95376591f 100644
--- a/Ternary Search Tree/TSTNode.swift	
+++ b/Ternary Search Tree/TSTNode.swift	
@@ -8,22 +8,42 @@
 
 import Foundation
 
+/**
+ This class represents a node in the Ternary Search Tree. 
+ A node has two main data members, the key and the data. 
+ All nodes in a TST must have keys, but only some will have data.
+ This can be seen in the way the data variable is of Optional type.
+*/
 class TSTNode<Element> {
     //Member properties of a particular node.
+    
+    /// The key that identifies this node.
     var key: Character
+    /// The data stored in this node. May be `nil`
     var data: Element?
+    /// Boolean flag to depict whether this node holds data or not.
     var hasData: Bool
     
-    //Children
+    /// The children of this node
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
     
-    
+    /**
+     Initializer for key and/or data
+     
+     - parameter key:  The key to set for this node.
+     - parameter data: The optional data to set in this node.
+     */
     init(key: Character, data: Element?) {
         self.key = key
         self.data = data
         self.hasData = (data != nil)
     }
     
+    /**
+     Make a node that only has a key
+    
+     - parameter key: The key to ascribe to this node.
+     */
     init(key:Character) {
         self.key = key
         self.data = nil

From 993812b6d83f8a528017f11168d047908878da28 Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Mon, 21 Mar 2016 16:36:55 -0700
Subject: [PATCH 0173/1679] Added Documentation.

---
 .../TST.playground/Contents.swift             |  1 -
 Ternary Search Tree/TernarySearchTree.swift   | 43 ++++++++++++++++++-
 2 files changed, 41 insertions(+), 3 deletions(-)

diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index e9606c653..5048895ac 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -62,7 +62,6 @@ for _ in (1...testCount) {
 
 for aTest in testNums {
     let data = treeOfInts.find(aTest.key)
-    
     if data == nil {
         print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
     }
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 1bbc1c390..5187e1e78 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -8,20 +8,45 @@
 
 import Foundation
 
-
+/**
+The Ternary Search Tree (TST) Data structure.
+Data structure uses key-value mappings. Keys are strings used to map to any data element.
+See README for more information.
+*/
 public class TernarySearchTree<Element> {
     
+    /// A reference to the root node of this TST
     var root: TSTNode<Element>?
     
+    /**
+     Standard initializer
+     */
     public init() {}
     
     //MARK: - Insertion
     
+    /**
+    Public insertion method.
+    
+    - parameter data: The value to store in this TST.
+    - parameter key:  The key to associate with this value.
+    
+    - returns: Value indicating insertion success/failure.
+    */
     public func insert(data:Element, withKey key: String) -> Bool{
         return insertNode(&root, withData: data, andKey: key, atIndex: 0)
-        
     }
     
+    /**
+     Helper method for insertion that does the actual legwork. Insertion is performed recursively.
+     
+     - parameter aNode:     The current node to insert below.
+     - parameter data:      The data being inserted.
+     - parameter key:       The key being used to find an insertion location for the given data
+     - parameter charIndex: The index of the character in the key string to use to for the next node.
+     
+     - returns: Value indicating insertion success/failure.
+     */
     private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
         
         //sanity check.
@@ -62,12 +87,26 @@ public class TernarySearchTree<Element> {
     
     //MARK: - Finding
     
+    /**
+    Public find method.
+    
+    - parameter key: Search for an object associated with this key.
     
+    - returns: The element, if found. Otherwise, nil.
+    */
     public func find(key:String) -> Element? {
         return findNode(root, withKey: key, atIndex: 0)
     }
     
+    /**
+     Helper method that performs actual legwork of find operation. Implemented recursively.
     
+     - parameter aNode:     The current node being evaluated.
+     - parameter key:       The key being used for the search.
+     - parameter charIndex: The index of the current char in the search key
+     
+     - returns: The element, if found. Nil otherwise.
+     */
     private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
         
         //Given key does not exist in tree.

From 636fd45097727ff9ff14f4e12626e85dd5879b2b Mon Sep 17 00:00:00 2001
From: Siddharth Atre <sidatre@gmail.com>
Date: Mon, 21 Mar 2016 16:42:39 -0700
Subject: [PATCH 0174/1679] Moved variable outside function.

Unnecessary to recreate var each time.
---
 Ternary Search Tree/TST.playground/Contents.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index 5048895ac..cc2225057 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -4,12 +4,11 @@ import Cocoa
 import Foundation
 
 let treeOfStrings = TernarySearchTree<String>()
+let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
 
-//Random string generator from: 
+//Random string generator from:
 //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
 func randomAlphaNumericString(length: Int) -> String {
-    
-    let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     let allowedCharsCount = UInt32(allowedChars.characters.count)
     var randomString = ""
     

From f021897a456d8f4b6b1c447be21e696f2afcacf2 Mon Sep 17 00:00:00 2001
From: 318236213 <zain.muhammad@rbc.com>
Date: Mon, 21 Mar 2016 20:45:10 -0400
Subject: [PATCH 0175/1679] added Ordered Set Folder

---
 Ordered Set/README.md | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Ordered Set/README.md

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
new file mode 100644
index 000000000..e69de29bb

From 94660567652fc30cc45d601ca812f6769e08cbb0 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Mon, 21 Mar 2016 20:52:05 -0400
Subject: [PATCH 0176/1679] Updated README

---
 Ordered Set/README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index e69de29bb..e19df8fee 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -0,0 +1,5 @@
+# Ordered Set
+
+Under Construction
+
+*Written By Zain Humayun*

From 75049e1884589e6afb238c75e4276e1b99ffb1e9 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Mon, 21 Mar 2016 21:04:29 -0400
Subject: [PATCH 0177/1679] Added link to Ordered Set Folder.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 9eaac70ed..d4ce78753 100644
--- a/README.markdown
+++ b/README.markdown
@@ -163,7 +163,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash Set/). A set implemented using a hash table.
 - Multiset
-- Ordered Set
+- [Ordered Set](Ordered Set/) :construction:
 
 ### Graphs
 

From 90eb49b414ca3a1d99f9b254c407f7965d6a1966 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 22 Mar 2016 13:00:38 +0100
Subject: [PATCH 0178/1679] Update to Xcode 7.3

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 9eaac70ed..5746d8960 100644
--- a/README.markdown
+++ b/README.markdown
@@ -6,7 +6,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-All code is compatible with **Xcode 7.2** and **Swift 2.1**. We'll keep this updated with the latest version of Swift.
+All code is compatible with **Xcode 7.3** and **Swift 2.2**. We'll keep this updated with the latest version of Swift.
 
 This is a work in progress. More algorithms will be added soon. :-) 
 

From 172532c1b0387caece0494ecc725b7da787811a0 Mon Sep 17 00:00:00 2001
From: 318236213 <zain.muhammad@rbc.com>
Date: Tue, 22 Mar 2016 21:51:16 -0400
Subject: [PATCH 0179/1679] added playground and .swift code

---
 .../OrderedSet.playground/Contents.swift      | 214 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../OrderedSet.playground/timeline.xctimeline |   6 +
 Ordered Set/OrderedSet.swift                  | 101 +++++++++
 4 files changed, 325 insertions(+)
 create mode 100644 Ordered Set/OrderedSet.playground/Contents.swift
 create mode 100644 Ordered Set/OrderedSet.playground/contents.xcplayground
 create mode 100644 Ordered Set/OrderedSet.playground/timeline.xctimeline
 create mode 100644 Ordered Set/OrderedSet.swift

diff --git a/Ordered Set/OrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
new file mode 100644
index 000000000..0804ea712
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -0,0 +1,214 @@
+// random function returns a random number between the given range
+func randomNum(min: Int, max: Int) -> Int {
+    return min + Int(arc4random_uniform(UInt32(max - min + 1)))
+}
+
+// extension for String generates a random alphanumeric string of length 8
+extension String {
+    static func random(length: Int = 8) -> String {
+        
+        let base = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
+        var randomString: String = ""
+        
+        for _ in 0..<length {
+            let randomValue = arc4random_uniform(UInt32(base.characters.count))
+            randomString += "\(base[base.startIndex.advancedBy(Int(randomValue))])"
+        }
+        
+        return randomString
+    }
+}
+
+// Player data type stores a random name, and a random number of points from 0 - 5000
+struct Player : Comparable {
+    var name: String! = String.random()
+    var points = randomNum(0, max: 5000)
+}
+
+// == operator for struct Player
+// Player x is equal to Player y if and only if both players have the same name and number of points
+func ==(x: Player, y: Player) -> Bool {
+    return x.name == y.name && x.points == y.points
+}
+
+// < operator for struct Player
+// Player x is less than Player y if and only if x has less points than y
+func <(x: Player, y: Player) -> Bool {
+    return x.points < y.points
+}
+
+// prints a Player formatted with their name and number of points
+func print(player: Player){
+    print("Player: \(player.name) | Points: \(player.points)")
+}
+
+import Foundation
+
+// An Ordered Set is a collection where all items in the set follow an ordering, usually ordered from
+// 'least' to 'most'. The way you value, and compare items can be user defined.
+public struct OrderedSet<T: Comparable> {
+    private var internalSet: [T]! = nil
+    
+    // returns size of Set
+    public var count: Int {
+        return internalSet!.count
+    }
+    
+    public init(){
+        internalSet = [T]() // create the internal array on init
+    }
+    
+    // inserts an item
+    // O(n log n)
+    public mutating func insert(item: T){
+        if exists(item) {
+            return // don't add an item if it already exists
+        }
+        
+        // if the set is initially empty, we need to simply append the item to internalSet
+        if count == 0 {
+            internalSet.append(item)
+            return
+        }
+        
+        for i in 0..<count {
+            if internalSet[i] > item {
+                internalSet.insert(item, atIndex: i)
+                return
+            }
+        }
+        
+        // if an item is larger than any item in the current set, append it to the back.
+        internalSet.append(item)
+    }
+    
+    // removes an item if it exists
+    public mutating func remove(item: T) {
+        if !exists(item) {
+            return
+        }
+        
+        internalSet.removeAtIndex(findIndex(item))
+    }
+    
+    // returns true if and only if the item exists somewhere in the set
+    public func exists(item: T) -> Bool {
+        let index = findIndex(item)
+        return index != -1 && internalSet[index] == item
+    }
+    
+    // returns the index of an item if it exists, otherwise returns -1.
+    public func findIndex(item: T) -> Int {
+        var leftBound = 0
+        var rightBound = count - 1
+        
+        while leftBound <= rightBound {
+            let mid = leftBound + ((rightBound - leftBound) / 2)
+            
+            if internalSet[mid] > item {
+                rightBound = mid - 1
+            } else if internalSet[mid] < item {
+                leftBound = mid + 1
+            } else {
+                return mid
+            }
+        }
+        
+        return -1
+    }
+
+    // returns the item at the given index. assertion fails if the index is out of the range
+    // of [0, count)
+    public subscript(index: Int) -> T {
+        assert(index >= 0 && index < count)
+        return internalSet[index]
+    }
+    
+    // returns the 'maximum' or 'largest' value in the set
+    public func max() -> T! {
+        return count == 0 ? nil : internalSet[count - 1]
+    }
+    
+    // returns the 'minimum' or 'smallest' value in the set
+    public func min() -> T! {
+        return count == 0 ? nil : internalSet[0]
+    }
+    
+    // returns the k largest element in the set, if k is in the range [1, count]
+    // returns nil otherwise
+    public func kLargest(k: Int) -> T! {
+        return k > count || k <= 0 ? nil : internalSet[count - k]
+    }
+    
+    // returns the k smallest element in the set, if k is in the range [1, count]
+    // returns nil otherwise
+    public func kSmallest(k: Int) -> T! {
+        return k > count || k <= 0 ? nil : internalSet[k - 1]
+    }
+}
+
+// Example 1 with type Int
+var mySet = OrderedSet<Int>()
+
+// insert random ints into the set
+
+for _ in 0..<50 {
+    mySet.insert(randomNum(50, max: 500))
+}
+
+print(mySet)
+
+print(mySet.max())
+print(mySet.min())
+
+// print the 5 largest values
+for k in 1..<6 {
+    print(mySet.kLargest(k))
+}
+
+// print the 5 lowest values
+for k in 1..<6 {
+    print(mySet.kSmallest(k))
+}
+
+
+// Example 2 with type Player
+var playerSet = OrderedSet<Player>()
+
+// populate with random players.
+var anotherPlayer = Player()
+for _ in 0..<20 {
+    playerSet.insert(Player())
+}
+
+// we'll look for this player later
+playerSet.insert(anotherPlayer)
+
+// print all players in order
+for i in 0..<playerSet.count {
+    print(playerSet[playerSet.count - i - 1])
+}
+
+
+// highest and lowest players:
+print(playerSet.max())
+print(playerSet.min())
+
+// we'll find our player now
+print("'Another Player (\(anotherPlayer.name))' is ranked at level: \(playerSet.count - playerSet.findIndex(anotherPlayer)) with \(anotherPlayer.points) points")
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/Ordered Set/OrderedSet.playground/contents.xcplayground b/Ordered Set/OrderedSet.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Ordered Set/OrderedSet.playground/timeline.xctimeline b/Ordered Set/OrderedSet.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
new file mode 100644
index 000000000..9f0fe4652
--- /dev/null
+++ b/Ordered Set/OrderedSet.swift	
@@ -0,0 +1,101 @@
+// An Ordered Set is a collection where all items in the set follow an ordering, usually ordered from
+// 'least' to 'most'. The way you value, and compare items can be user defined.
+public struct OrderedSet<T: Comparable> {
+    private var internalSet: [T]! = nil
+    
+    // returns size of Set
+    public var count: Int {
+        return internalSet!.count
+    }
+    
+    public init(){
+        internalSet = [T]() // create the internal array on init
+    }
+    
+    // inserts an item into the set if it doesn't exist
+    public mutating func insert(item: T){
+        if exists(item) {
+            return // don't add an item if it already exists
+        }
+        
+        // if the set is initially empty, we need to simply append the item to internalSet
+        if count == 0 {
+            internalSet.append(item)
+            return
+        }
+        
+        for i in 0..<count {
+            if internalSet[i] > item {
+                internalSet.insert(item, atIndex: i)
+                return
+            }
+        }
+        
+        // if an item is larger than any item in the current set, append it to the back.
+        internalSet.append(item)
+    }
+    
+    // removes an item if it exists
+    public mutating func remove(item: T) {
+        if !exists(item) {
+            return
+        }
+        
+        internalSet.removeAtIndex(findIndex(item))
+    }
+    
+    // returns true if and only if the item exists somewhere in the set
+    public func exists(item: T) -> Bool {
+        let index = findIndex(item)
+        return index != -1 && internalSet[index] == item
+    }
+    
+    // returns the index of an item if it exists, otherwise returns -1.
+    public func findIndex(item: T) -> Int {
+        var leftBound = 0
+        var rightBound = count - 1
+        
+        while leftBound <= rightBound {
+            let mid = leftBound + ((rightBound - leftBound) / 2)
+            
+            if internalSet[mid] > item {
+                rightBound = mid - 1
+            } else if internalSet[mid] < item {
+                leftBound = mid + 1
+            } else {
+                return mid
+            }
+        }
+        
+        return -1
+    }
+    
+    // returns the item at the given index. assertion fails if the index is out of the range
+    // of [0, count)
+    public subscript(index: Int) -> T {
+        assert(index >= 0 && index < count)
+        return internalSet[index]
+    }
+    
+    // returns the 'maximum' or 'largest' value in the set
+    public func max() -> T! {
+        return count == 0 ? nil : internalSet[count - 1]
+    }
+    
+    // returns the 'minimum' or 'smallest' value in the set
+    public func min() -> T! {
+        return count == 0 ? nil : internalSet[0]
+    }
+    
+    // returns the k largest element in the set, if k is in the range [1, count]
+    // returns nil otherwise
+    public func kLargest(k: Int) -> T! {
+        return k > count || k <= 0 ? nil : internalSet[count - k]
+    }
+    
+    // returns the k smallest element in the set, if k is in the range [1, count]
+    // returns nil otherwise
+    public func kSmallest(k: Int) -> T! {
+        return k > count || k <= 0 ? nil : internalSet[k - 1]
+    }
+}

From 46ac8546aa26fd6193410fedb03fa6a3b81ecae7 Mon Sep 17 00:00:00 2001
From: 318236213 <zain.muhammad@rbc.com>
Date: Wed, 23 Mar 2016 20:45:49 -0400
Subject: [PATCH 0180/1679] fixed find function

---
 .../OrderedSet.playground/Contents.swift      | 68 ++++++++++++++++---
 Ordered Set/OrderedSet.swift                  | 34 ++++++++--
 2 files changed, 89 insertions(+), 13 deletions(-)

diff --git a/Ordered Set/OrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
index 0804ea712..36d87df08 100644
--- a/Ordered Set/OrderedSet.playground/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -23,6 +23,13 @@ extension String {
 struct Player : Comparable {
     var name: String! = String.random()
     var points = randomNum(0, max: 5000)
+    
+    init(name: String, points: Int){
+        self.name = name
+        self.points = points
+    }
+    
+    init(){}
 }
 
 // == operator for struct Player
@@ -42,6 +49,12 @@ func print(player: Player){
     print("Player: \(player.name) | Points: \(player.points)")
 }
 
+func print(set: OrderedSet<Player>){
+    for i in 0..<set.count {
+        print(set[set.count - i - 1])
+    }
+}
+
 import Foundation
 
 // An Ordered Set is a collection where all items in the set follow an ordering, usually ordered from
@@ -94,7 +107,7 @@ public struct OrderedSet<T: Comparable> {
     // returns true if and only if the item exists somewhere in the set
     public func exists(item: T) -> Bool {
         let index = findIndex(item)
-        return index != -1 && internalSet[index] == item
+        return index != -1
     }
     
     // returns the index of an item if it exists, otherwise returns -1.
@@ -110,13 +123,38 @@ public struct OrderedSet<T: Comparable> {
             } else if internalSet[mid] < item {
                 leftBound = mid + 1
             } else {
-                return mid
+                // check the mid value to see if it is the item we are looking for
+                if internalSet[mid] == item {
+                    return mid
+                }
+                
+                var j = mid
+                
+                // check right side of mid
+                while j < internalSet.count - 1 && !(internalSet[j] < internalSet[j + 1]) {
+                    if internalSet[j + 1] == item {
+                        return j + 1
+                    }
+                    
+                    j++
+                }
+                
+                
+                // check right side of mid
+                while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
+                    if internalSet[j - 1] == item {
+                        return j - 1
+                    }
+                    
+                    j--
+                }
+                return -1
             }
         }
         
         return -1
     }
-
+    
     // returns the item at the given index. assertion fails if the index is out of the range
     // of [0, count)
     public subscript(index: Int) -> T {
@@ -185,9 +223,7 @@ for _ in 0..<20 {
 playerSet.insert(anotherPlayer)
 
 // print all players in order
-for i in 0..<playerSet.count {
-    print(playerSet[playerSet.count - i - 1])
-}
+print(playerSet)
 
 
 // highest and lowest players:
@@ -199,13 +235,27 @@ print("'Another Player (\(anotherPlayer.name))' is ranked at level: \(playerSet.
 
 
 
+// Example with multiple entries with the same value
 
+var repeatedSet = OrderedSet<Player>()
 
+repeatedSet.insert(Player(name:"Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 2", points: 100))
+repeatedSet.insert(Player(name: "Player 3", points: 100))
+repeatedSet.insert(Player(name: "Player 4", points: 100))
+repeatedSet.insert(Player(name: "Player 5", points: 100))
+repeatedSet.insert(Player(name: "Player 6", points: 50))
+repeatedSet.insert(Player(name: "Player 7", points: 200))
+repeatedSet.insert(Player(name: "Player 8", points: 250))
+repeatedSet.insert(Player(name: "Player 9", points: 25))
 
+print(repeatedSet)
 
-
-
-
+// find player 5
+print(repeatedSet.findIndex(Player(name: "Player 5", points: 100)))
+print(repeatedSet.findIndex(Player(name: "Random Player", points: 100)))
+print(repeatedSet.findIndex(Player(name: "Player 5", points: 1000)))
 
 
 
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 9f0fe4652..a92f45717 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -12,7 +12,8 @@ public struct OrderedSet<T: Comparable> {
         internalSet = [T]() // create the internal array on init
     }
     
-    // inserts an item into the set if it doesn't exist
+    // inserts an item
+    // O(n log n)
     public mutating func insert(item: T){
         if exists(item) {
             return // don't add an item if it already exists
@@ -47,7 +48,7 @@ public struct OrderedSet<T: Comparable> {
     // returns true if and only if the item exists somewhere in the set
     public func exists(item: T) -> Bool {
         let index = findIndex(item)
-        return index != -1 && internalSet[index] == item
+        return index != -1
     }
     
     // returns the index of an item if it exists, otherwise returns -1.
@@ -63,7 +64,32 @@ public struct OrderedSet<T: Comparable> {
             } else if internalSet[mid] < item {
                 leftBound = mid + 1
             } else {
-                return mid
+                // check the mid value to see if it is the item we are looking for
+                if internalSet[mid] == item {
+                    return mid
+                }
+                
+                var j = mid
+                
+                // check right side of mid
+                while j < internalSet.count - 1 && !(internalSet[j] < internalSet[j + 1]) {
+                    if internalSet[j + 1] == item {
+                        return j + 1
+                    }
+                    
+                    j++
+                }
+                
+                
+                // check right side of mid
+                while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
+                    if internalSet[j - 1] == item {
+                        return j - 1
+                    }
+                    
+                    j--
+                }
+                return -1
             }
         }
         
@@ -98,4 +124,4 @@ public struct OrderedSet<T: Comparable> {
     public func kSmallest(k: Int) -> T! {
         return k > count || k <= 0 ? nil : internalSet[k - 1]
     }
-}
+}
\ No newline at end of file

From 58d58237377f95c3c320b3aca50651328ec3689d Mon Sep 17 00:00:00 2001
From: 318236213 <zain.muhammad@rbc.com>
Date: Wed, 23 Mar 2016 21:15:35 -0400
Subject: [PATCH 0181/1679] Updated deprecated code to be Swift 3 compatable

---
 Ordered Set/OrderedSet.playground/Contents.swift      | 4 ++--
 Ordered Set/OrderedSet.playground/timeline.xctimeline | 6 ------
 Ordered Set/OrderedSet.swift                          | 4 ++--
 3 files changed, 4 insertions(+), 10 deletions(-)
 delete mode 100644 Ordered Set/OrderedSet.playground/timeline.xctimeline

diff --git a/Ordered Set/OrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
index 36d87df08..333df31c8 100644
--- a/Ordered Set/OrderedSet.playground/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -136,7 +136,7 @@ public struct OrderedSet<T: Comparable> {
                         return j + 1
                     }
                     
-                    j++
+                    j += 1
                 }
                 
                 
@@ -146,7 +146,7 @@ public struct OrderedSet<T: Comparable> {
                         return j - 1
                     }
                     
-                    j--
+                    j -= 1
                 }
                 return -1
             }
diff --git a/Ordered Set/OrderedSet.playground/timeline.xctimeline b/Ordered Set/OrderedSet.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ordered Set/OrderedSet.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index a92f45717..25b3c114a 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -77,7 +77,7 @@ public struct OrderedSet<T: Comparable> {
                         return j + 1
                     }
                     
-                    j++
+                    j += 1
                 }
                 
                 
@@ -87,7 +87,7 @@ public struct OrderedSet<T: Comparable> {
                         return j - 1
                     }
                     
-                    j--
+                    j -= 1
                 }
                 return -1
             }

From 356cea0458d25b65d44dd760fe5410bf6b73cf5b Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Wed, 23 Mar 2016 21:53:50 -0400
Subject: [PATCH 0182/1679] Updated README with two code examples

---
 Ordered Set/README.md | 83 ++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 82 insertions(+), 1 deletion(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index e19df8fee..f44556bb0 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -1,5 +1,86 @@
 # Ordered Set
+An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. The Ordered Set data type is a representation of a [Set in Mathematics](https://en.wikipedia.org/wiki/Set_(mathematics)). It's important to keep in mind that two items can have the same *value* but still may not be equal. 
+For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
+
+### Examples of Ordered Sets
+```
+{1, 2, 3, 6, 8, 10, 1000}
+Where each item (Integers) has it's normal definition of value and equality
+```
+```
+{"a", "is", "set", "this"}
+Where each item (String) has it's value equal to it's length
+```
+
+### These are not Ordered Sets
+```
+{1, 1, 2, 3, 5, 8}
+This Set violates the property of uniqueness
+```
+```
+{1, 11, 2, 3}
+This Set violates the sorted property
+```
+
+## The Code
+We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep our set sorted, we need to compare the individual elemants. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
+
+``` swift
+public struct OrderedSet<T: Comparable> {
+    private var internalSet: [T]! = nil
+    
+    // returns size of Set
+    public var count: Int {
+        return internalSet!.count
+    }
+    
+    public init(){
+        internalSet = [T]() // create the internal array on init
+    }
+    ...
+```
+
+Lets take a look at the insert function first. The insert function first checks if the item already exists, and if so returns and does not insert the item. Otherwise, it will insert the item through straight forward iteration. It starts from the first item, and checks to see if this item is larger than the item we want to insert. Once we find such an item, we insert the given item into it's place, and shift the array over to the right by 1.
+
+``` swift
+  // inserts an item
+  public mutating func insert(item: T){
+      if exists(item) {
+          return // don't add an item if it already exists
+      }
+      // if the set is initially empty, we need to simply append the item to internalSet
+      if count == 0 {
+          internalSet.append(item)
+          return
+      }
+        
+      for i in 0..<count {
+          if internalSet[i] > item {
+            internalSet.insert(item, atIndex: i)
+            return
+          }
+        }
+        
+      // if an item is larger than any item in the current set, append it to the back.
+      internalSet.append(item)
+  }
+```
+The first part of the function checks if the item is already in the set.As we'll see later on, this has an efficiency of **O(nlog n + k)**. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(nlog(n))**, thus making the insert function for our Ordered Set **O(nlog(n) + k)** where k is the number of items with the same value as the item we are inserting.
+
+
+Next we have the remove function. First check if the item exists. If not, then return and no nothing. If it does exist, remove it.
+
+``` swift
+    // removes an item if it exists
+    public mutating func remove(item: T) {
+        if !exists(item) {
+            return
+        }
+        
+        internalSet.removeAtIndex(findIndex(item))
+    }
+```
+Again, because of the `exists` function, the efficiency for remove is **O(nlog(n) + k)**
 
-Under Construction
 
 *Written By Zain Humayun*

From 53799fda78cdb691fef06e4e909ee8cdbf98ea10 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Wed, 23 Mar 2016 22:01:07 -0400
Subject: [PATCH 0183/1679] Fixed Big-O typo

---
 Ordered Set/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index f44556bb0..68712c9bc 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -65,7 +65,7 @@ Lets take a look at the insert function first. The insert function first checks
       internalSet.append(item)
   }
 ```
-The first part of the function checks if the item is already in the set.As we'll see later on, this has an efficiency of **O(nlog n + k)**. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(nlog(n))**, thus making the insert function for our Ordered Set **O(nlog(n) + k)** where k is the number of items with the same value as the item we are inserting.
+The first part of the function checks if the item is already in the set.As we'll see later on, this has an efficiency of **O(log n + k)** where k is the number of items with the same value as the item we are inserting. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(log(n))**, thus making the insert function for our Ordered Set **O(log(n) + k)**.
 
 
 Next we have the remove function. First check if the item exists. If not, then return and no nothing. If it does exist, remove it.
@@ -80,7 +80,7 @@ Next we have the remove function. First check if the item exists. If not, then r
         internalSet.removeAtIndex(findIndex(item))
     }
 ```
-Again, because of the `exists` function, the efficiency for remove is **O(nlog(n) + k)**
+Again, because of the `exists` function, the efficiency for remove is **O(log(n) + k)**
 
 
 *Written By Zain Humayun*

From f31f7699520173c45d710112d5ec841f582f0d39 Mon Sep 17 00:00:00 2001
From: nuts23 <linouk23@gmail.com>
Date: Fri, 25 Mar 2016 17:50:46 +0300
Subject: [PATCH 0184/1679] Add a fast approach to calculate C(n, k)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Add a faster approach to calculate `C(n, k)’ in 'O(k)' time and 'O(1)'
extra space.
---
 .../Combinatorics.playground/Contents.swift   | 19 ++++++++++
 Combinatorics/README.markdown                 | 37 +++++++++++++++++++
 2 files changed, 56 insertions(+)

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index bd7c174a3..6040ae711 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -165,3 +165,22 @@ func binomialCoefficient(n: Int, _ k: Int) -> Int {
 
 binomialCoefficient(30, 15)
 binomialCoefficient(66, 33)
+
+
+
+/*
+Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+k things out of n possibilities.
+*/
+func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+  var result = 1
+    
+  for i in 0..<k {
+    result *= (n - i)
+    result /=  (i + 1)
+  }
+  return result
+}
+
+quickBinomialCoefficient(30, 15)
+quickBinomialCoefficient(8, 2)
diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 2d7a6ac83..e580add26 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -358,6 +358,43 @@ binomialCoefficient(30, 15)   // prints 155117520
 binomialCoefficient(66, 33)   // prints a very large number
 ```
 
+There's a faster approach to calculate `C(n, k)` in 'O(k)' time and 'O(1)' extra space.
+
+The idea behind it is that the formula for `C(n, k)` is:
+
+                   n!                      n * (n - 1) * ... * 1
+    C(n, k) = ------------- = ------------------------------------------
+              (n - k)! * k!      (n - k) * (n - k - 1) * ... * 1 * k!
+
+After reduction of fractions, we get the following formula:
+
+                   n * (n - 1) * ... * (n - k + 1)         (n - 0) * (n - 1) * ... * (n - k + 1)  
+    C(n, k) = --------------------------------------- = -----------------------------------------
+                               k!                          (k - 0) * (k - 1) * ... * 1
+
+So the following code calculates the `C(n, k)` you're looking for:
+
+```swift
+func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+  var result = 1
+    
+  for i in 0..<k {
+    result *= (n - i)
+    result /=  (i + 1)
+  }
+  return result
+}
+```
+
+As there're the divisors for numbers from '1...k' among 'k' consecutive numbers, what is exactly we've got in the numerator of our fast formula every time we devide 'result' by '(i + 1)' we won't have a real number.
+
+Now you can calculate `C(30, 15)` without any problems:
+
+```swift
+quickbinomialCoefficient(30, 15)   // prints 155117520
+quickbinomialCoefficient(8, 2)   // prints 28
+```
+
 You may wonder what the point is in calculating these permutations and combinations, but many algorithm problems are really combinatorics problems in disguise. Often you may need to look at all possible combinations of your data to see which one gives the right solution. If that means you need to search through `n!` potential solutions, you may want to consider a different approach -- as you've seen, these numbers become huge very quickly!
 
 ## References

From 538b05b92eec6b02e740dfc7d9eb2e0bd845ced5 Mon Sep 17 00:00:00 2001
From: nuts23 <linouk23@gmail.com>
Date: Fri, 25 Mar 2016 17:54:31 +0300
Subject: [PATCH 0185/1679] Fix tiny text tweaks

---
 Combinatorics/README.markdown | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index e580add26..366f23769 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -358,7 +358,7 @@ binomialCoefficient(30, 15)   // prints 155117520
 binomialCoefficient(66, 33)   // prints a very large number
 ```
 
-There's a faster approach to calculate `C(n, k)` in 'O(k)' time and 'O(1)' extra space.
+There's a faster approach to calculate `C(n, k)` in `O(k) time and `O(1)` extra space.
 
 The idea behind it is that the formula for `C(n, k)` is:
 
@@ -366,9 +366,9 @@ The idea behind it is that the formula for `C(n, k)` is:
     C(n, k) = ------------- = ------------------------------------------
               (n - k)! * k!      (n - k) * (n - k - 1) * ... * 1 * k!
 
-After reduction of fractions, we get the following formula:
+After the reduction of fractions, we get the following formula:
 
-                   n * (n - 1) * ... * (n - k + 1)         (n - 0) * (n - 1) * ... * (n - k + 1)  
+                   n * (n - 1) * ... * (n - k + 1)         (n - 0) * (n - 1) * ... * (n - k + 1)
     C(n, k) = --------------------------------------- = -----------------------------------------
                                k!                          (k - 0) * (k - 1) * ... * 1
 
@@ -377,7 +377,7 @@ So the following code calculates the `C(n, k)` you're looking for:
 ```swift
 func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
   var result = 1
-    
+
   for i in 0..<k {
     result *= (n - i)
     result /=  (i + 1)
@@ -388,7 +388,7 @@ func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
 
 As there're the divisors for numbers from '1...k' among 'k' consecutive numbers, what is exactly we've got in the numerator of our fast formula every time we devide 'result' by '(i + 1)' we won't have a real number.
 
-Now you can calculate `C(30, 15)` without any problems:
+Here's how you can use it:
 
 ```swift
 quickbinomialCoefficient(30, 15)   // prints 155117520

From e4b0d61b44e05e64798a6e25cbe2690ce9dbbb63 Mon Sep 17 00:00:00 2001
From: nuts23 <linouk23@gmail.com>
Date: Fri, 25 Mar 2016 17:56:32 +0300
Subject: [PATCH 0186/1679] Fix tiny text tweaks

---
 Combinatorics/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 366f23769..138a22761 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -370,7 +370,7 @@ After the reduction of fractions, we get the following formula:
 
                    n * (n - 1) * ... * (n - k + 1)         (n - 0) * (n - 1) * ... * (n - k + 1)
     C(n, k) = --------------------------------------- = -----------------------------------------
-                               k!                          (k - 0) * (k - 1) * ... * 1
+                               k!                          (0 + 1) * (1 + 1) * ... * (k - 1 + 1)
 
 So the following code calculates the `C(n, k)` you're looking for:
 

From 8575f132472e06145fe8c1842849e2c207493cb2 Mon Sep 17 00:00:00 2001
From: nuts23 <linouk23@gmail.com>
Date: Fri, 25 Mar 2016 17:57:17 +0300
Subject: [PATCH 0187/1679] Fix tiny text tweaks

---
 Combinatorics/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 138a22761..9754b56f3 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -391,8 +391,8 @@ As there're the divisors for numbers from '1...k' among 'k' consecutive numbers,
 Here's how you can use it:
 
 ```swift
-quickbinomialCoefficient(30, 15)   // prints 155117520
-quickbinomialCoefficient(8, 2)   // prints 28
+quickBinomialCoefficient(30, 15)   // prints 155117520
+quickBinomialCoefficient(8, 2)   // prints 28
 ```
 
 You may wonder what the point is in calculating these permutations and combinations, but many algorithm problems are really combinatorics problems in disguise. Often you may need to look at all possible combinations of your data to see which one gives the right solution. If that means you need to search through `n!` potential solutions, you may want to consider a different approach -- as you've seen, these numbers become huge very quickly!

From c32e1efb3888524de994a5eca190414ba38e9ec8 Mon Sep 17 00:00:00 2001
From: nuts23 <linouk23@gmail.com>
Date: Fri, 25 Mar 2016 18:08:20 +0300
Subject: [PATCH 0188/1679] Fix tiny text tweaks

---
 Combinatorics/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 9754b56f3..b148c88db 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -386,7 +386,7 @@ func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
 }
 ```
 
-As there're the divisors for numbers from '1...k' among 'k' consecutive numbers, what is exactly we've got in the numerator of our fast formula every time we devide 'result' by '(i + 1)' we won't have a real number.
+As there're the divisors for numbers from `1...k` among `k` consecutive numbers, what is exactly we've got in the numerator of our fast formula every time we devide `result` by `(i + 1)` we won't have a real number.
 
 Here's how you can use it:
 

From 949310096daf67d60845569e8735a55a615f8e5b Mon Sep 17 00:00:00 2001
From: nuts23 <linouk23@gmail.com>
Date: Fri, 25 Mar 2016 18:09:29 +0300
Subject: [PATCH 0189/1679] Fix tiny text tweaks

---
 Combinatorics/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index b148c88db..48723b065 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -358,7 +358,7 @@ binomialCoefficient(30, 15)   // prints 155117520
 binomialCoefficient(66, 33)   // prints a very large number
 ```
 
-There's a faster approach to calculate `C(n, k)` in `O(k) time and `O(1)` extra space.
+There's a faster approach to calculate `C(n, k)` in `O(k)` time and `O(1)` extra space.
 
 The idea behind it is that the formula for `C(n, k)` is:
 

From c521136dcff60f2b76224800461302c47588823e Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 13:54:08 -0400
Subject: [PATCH 0190/1679] Added more functions

---
 Ordered Set/README.md | 92 ++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 86 insertions(+), 6 deletions(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index 68712c9bc..6986d02c9 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -4,21 +4,21 @@ For example, we could define "a" and "z" to have the same value (their lengths),
 
 ### Examples of Ordered Sets
 ```
-{1, 2, 3, 6, 8, 10, 1000}
+[1, 2, 3, 6, 8, 10, 1000]
 Where each item (Integers) has it's normal definition of value and equality
 ```
 ```
-{"a", "is", "set", "this"}
+["a", "is", "set", "this"]
 Where each item (String) has it's value equal to it's length
 ```
 
 ### These are not Ordered Sets
 ```
-{1, 1, 2, 3, 5, 8}
+[1, 1, 2, 3, 5, 8]
 This Set violates the property of uniqueness
 ```
 ```
-{1, 11, 2, 3}
+[1, 11, 2, 3]
 This Set violates the sorted property
 ```
 
@@ -65,10 +65,10 @@ Lets take a look at the insert function first. The insert function first checks
       internalSet.append(item)
   }
 ```
-The first part of the function checks if the item is already in the set.As we'll see later on, this has an efficiency of **O(log n + k)** where k is the number of items with the same value as the item we are inserting. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(log(n))**, thus making the insert function for our Ordered Set **O(log(n) + k)**.
+The first part of the function checks if the item is already in the set.As we'll see later on, this has an efficiency of **O(log(n) + k)** where k is the number of items with the same value as the item we are inserting. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(log(n))**, thus making the insert function for our Ordered Set **O(log(n) + k)**.
 
 
-Next we have the remove function. First check if the item exists. If not, then return and no nothing. If it does exist, remove it.
+Next we have the `remove` function. First check if the item exists. If not, then return and no nothing. If it does exist, remove it.
 
 ``` swift
     // removes an item if it exists
@@ -82,5 +82,85 @@ Next we have the remove function. First check if the item exists. If not, then r
 ```
 Again, because of the `exists` function, the efficiency for remove is **O(log(n) + k)**
 
+The next function is the `findIndex` function which takes in an item of type `T` and returns the index of the item if it is in the set, otherwise returns -1. 
+
+``` swift
+// returns the index of an item if it exists, otherwise returns -1.
+    public func findIndex(item: T) -> Int {
+        var leftBound = 0
+        var rightBound = count - 1
+        
+        while leftBound <= rightBound {
+            let mid = leftBound + ((rightBound - leftBound) / 2)
+            
+            if internalSet[mid] > item {
+                rightBound = mid - 1
+            } else if internalSet[mid] < item {
+                leftBound = mid + 1
+            } else {
+                // check the mid value to see if it is the item we are looking for
+                if internalSet[mid] == item {
+                    return mid
+                }
+                
+                var j = mid
+                
+                // check right side of mid
+                while j < internalSet.count - 1 && !(internalSet[j] < internalSet[j + 1]) {
+                    if internalSet[j + 1] == item {
+                        return j + 1
+                    }
+                    
+                    j += 1
+                }
+                
+                j = mid
+                
+                // check right side of mid
+                while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
+                    if internalSet[j - 1] == item {
+                        return j - 1
+                    }
+                    
+                    j -= 1
+                }
+                return -1
+            }
+        }
+        
+        return -1
+    }
+```
+Since our set is sorted, we can use a binary search to quickly search for the item. If you are not familiar with the concept of binary search, we have an article all about it [here](../Binary\ Search). 
+
+Since a set can contain multiple items with the same *value*, it is important to check to see if we have the correct item.
+
+For example, consider this Ordered  Set
+```
+["a", "b", "c", "longer string", "even longer string"]
+Where the value of each String is equal to it's length.
+```
+The call `findIndex("a")` with the traditional implementation of Binary Search would give us the value of 2, however we know that "a" is located at index 0. Thus, we need to check the items with the same *value* to the right and left of the mid value.
+
+The code to check the left and right side are similar so we will only look at the code that checks the left side.
+``` swift
+    j = mid
+
+    // check right side of mid
+    while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
+        if internalSet[j - 1] == item {
+            return j - 1
+        }
+                    
+        j -= 1
+    }
+    return -1
+```
+First, `j` starts at the mid value. Above, we've already checked to see that the item at index `j` is not equal to the item we are looking for. Then, we keep looping until we either reach the end of the array, or hit an element which has a lower value than the current item at index `j`. If the item at value `j - 1` is equal to the one we are looking for, we return that index, otherwise we keep decreasing `j`. Once the loop terminates, we were unable to find the item and so we return -1. 
+
+The combined runtime for this function is **O(log(n) + k)** where `n` is the length of the set, and `k` is the number of 
+items with the same *value* as the one that is being searched for. 
+
+
 
 *Written By Zain Humayun*

From 564a7d5e632019a260090436e30e646c9e80a986 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 13:55:05 -0400
Subject: [PATCH 0191/1679] Changed right to left

---
 Ordered Set/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index 6986d02c9..ab8726eda 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -116,7 +116,7 @@ The next function is the `findIndex` function which takes in an item of type `T`
                 
                 j = mid
                 
-                // check right side of mid
+                // check left side of mid
                 while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
                     if internalSet[j - 1] == item {
                         return j - 1
@@ -146,7 +146,7 @@ The code to check the left and right side are similar so we will only look at th
 ``` swift
     j = mid
 
-    // check right side of mid
+    // check left side of mid
     while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
         if internalSet[j - 1] == item {
             return j - 1

From 599fc0acfa8ad8418310e14abbdfc8fb6edc1e7c Mon Sep 17 00:00:00 2001
From: 318236213 <zain.muhammad@rbc.com>
Date: Fri, 25 Mar 2016 18:06:02 -0400
Subject: [PATCH 0192/1679] fixed bug

---
 Ordered Set/OrderedSet.playground/Contents.swift | 3 ++-
 Ordered Set/OrderedSet.swift                     | 1 +
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/Ordered Set/OrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
index 333df31c8..33d7ce0f2 100644
--- a/Ordered Set/OrderedSet.playground/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -139,8 +139,9 @@ public struct OrderedSet<T: Comparable> {
                     j += 1
                 }
                 
+                j = mid
                 
-                // check right side of mid
+                // check left side of mid
                 while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
                     if internalSet[j - 1] == item {
                         return j - 1
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 25b3c114a..2325c0e58 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -80,6 +80,7 @@ public struct OrderedSet<T: Comparable> {
                     j += 1
                 }
                 
+                j = mid
                 
                 // check right side of mid
                 while j > 0 && !(internalSet[j] < internalSet[j - 1]) {

From 48c7f697467b2799ea3009b0aa5e4a41c36e4e64 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 18:56:34 -0400
Subject: [PATCH 0193/1679] Finished README

---
 Ordered Set/README.md | 176 +++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 175 insertions(+), 1 deletion(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index ab8726eda..43fcb6605 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -2,7 +2,10 @@
 An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. The Ordered Set data type is a representation of a [Set in Mathematics](https://en.wikipedia.org/wiki/Set_(mathematics)). It's important to keep in mind that two items can have the same *value* but still may not be equal. 
 For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
 
-### Examples of Ordered Sets
+## Why use an Ordered Set?
+Ordered Sets should be considered for use when you need to require keeping your collection sorted at all times, and do lookups on the collection much more freuqently than inserting or deleting items. A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below). Many of the lookup operations for an Ordered Set are **O(1)**. 
+
+### These are Ordered Sets
 ```
 [1, 2, 3, 6, 8, 10, 1000]
 Where each item (Integers) has it's normal definition of value and equality
@@ -161,6 +164,177 @@ First, `j` starts at the mid value. Above, we've already checked to see that the
 The combined runtime for this function is **O(log(n) + k)** where `n` is the length of the set, and `k` is the number of 
 items with the same *value* as the one that is being searched for. 
 
+Since the set is sorted, the following operations are all **O(1)**:
+
+```swift
+    // returns the 'maximum' or 'largest' value in the set
+    public func max() -> T! {
+        return count == 0 ? nil : internalSet[count - 1]
+    }
+    
+    // returns the 'minimum' or 'smallest' value in the set
+    public func min() -> T! {
+        return count == 0 ? nil : internalSet[0]
+    }
+    
+    // returns the k largest element in the set, if k is in the range [1, count]
+    // returns nil otherwise
+    public func kLargest(k: Int) -> T! {
+        return k > count || k <= 0 ? nil : internalSet[count - k]
+    }
+    
+    // returns the k smallest element in the set, if k is in the range [1, count]
+    // returns nil otherwise
+    public func kSmallest(k: Int) -> T! {
+        return k > count || k <= 0 ? nil : internalSet[k - 1]
+    }
+```
+
+## Examples
+Below are a few examples that can be found in the playground file.
+
+### Example 1
+Here we create a set with random Integers. Pringint the largest/smallest 5 numbers in the set is fairly easy.
+``` swift
+// Example 1 with type Int
+var mySet = OrderedSet<Int>()
+
+// insert random ints into the set
+
+for _ in 0..<50 {
+    mySet.insert(randomNum(50, max: 500))
+}
+
+print(mySet)
+
+print(mySet.max())
+print(mySet.min())
+
+// print the 5 largest values
+for k in 1..<6 {
+    print(mySet.kLargest(k))
+}
+
+// print the 5 lowest values
+for k in 1..<6 {
+    print(mySet.kSmallest(k))
+}
+```
+
+### Exmaple 2
+In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
+``` swift
+struct Player : Comparable {
+    var name: String! = String.random()
+    var points = randomNum(0, max: 5000)
+    
+    init(name: String, points: Int){
+        self.name = name
+        self.points = points
+    }
+    
+    init(){}
+}
+
+// == operator for struct Player
+// Player x is equal to Player y if and only if both players have the same name and number of points
+func ==(x: Player, y: Player) -> Bool {
+    return x.name == y.name && x.points == y.points
+}
+
+// < operator for struct Player
+// Player x is less than Player y if and only if x has less points than y
+func <(x: Player, y: Player) -> Bool {
+    return x.points < y.points
+}
+```
+The set we create will hold players. One thing to note is that two `Player`'s can each have the same value, but are not guaranteed to be equal. 
+
+Inserting 20 random players and one player we will track of.
+``` swift
+// Example 2 with type Player
+var playerSet = OrderedSet<Player>()
+
+// populate with random players.
+var anotherPlayer = Player()
+for _ in 0..<20 {
+    playerSet.insert(Player())
+}
+
+// we'll look for this player later
+playerSet.insert(anotherPlayer)
+```
+
+Next, we can find the players with the most and least amount of points very quickly.
+``` swift
+// highest and lowest players:
+print(playerSet.max())
+print(playerSet.min())
+```
+
+Next we use the findIndex function to find out what rank `anotherPlayer` in comparison to the other `Player`s.
+``` swift
+// we'll find our player now
+print("'Another Player (\(anotherPlayer.name))' is ranked at level: \(playerSet.count - playerSet.findIndex(anotherPlayer)) with \(anotherPlayer.points) points")
+```
+
+### Example 3
+The final example demonstrates the need to look for the right item even after the Binary Search has completed. 9 Players are inserted into the set.
+``` swift
+
+var repeatedSet = OrderedSet<Player>()
+
+repeatedSet.insert(Player(name:"Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 2", points: 100))
+repeatedSet.insert(Player(name: "Player 3", points: 100))
+repeatedSet.insert(Player(name: "Player 4", points: 100))
+repeatedSet.insert(Player(name: "Player 5", points: 100))
+repeatedSet.insert(Player(name: "Player 6", points: 50))
+repeatedSet.insert(Player(name: "Player 7", points: 200))
+repeatedSet.insert(Player(name: "Player 8", points: 250))
+repeatedSet.insert(Player(name: "Player 9", points: 25))
+
+print(repeatedSet)
+```
+
+The set looks something like this:
+```
+[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+```
 
+The next line looks for `Player 2`:
+``` swift
+print(repeatedSet.findIndex(Player(name: "Player 2", points: 100)))
+```
+
+After the Binary Search finishes, the value of `mid` is at index 5
+```
+[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+                                                      mid
+```
+However, we know this may not be where `Player 2` is, so we check both sides of `mid`. The shown Players below are the ones with the same value as `Player 4`, and are the ones we check after the Binary Search.
+
+```
+[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+                                       mid 
+```
+
+The code then checks the right of `mid` (Every `Player` with an * below it)
+```
+[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+                                       mid        *
+```
+
+The right side did not contain the item, so we look at the left side.
+```
+[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+                              *        mid        
+```
+```
+[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+                    *                  mid        
+```
+We've found `Player 2`! Index 3 is then returned. 
 
 *Written By Zain Humayun*

From ac06b1fec0462fcf3cb7bb264873f5cb7660d7c5 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 19:17:35 -0400
Subject: [PATCH 0194/1679] Fixed Typos

---
 Ordered Set/README.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index 43fcb6605..bc7f79e41 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -3,7 +3,7 @@ An Ordered Set is a collection of unique items in sorted order. Items are usuall
 For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
 
 ## Why use an Ordered Set?
-Ordered Sets should be considered for use when you need to require keeping your collection sorted at all times, and do lookups on the collection much more freuqently than inserting or deleting items. A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below). Many of the lookup operations for an Ordered Set are **O(1)**. 
+Ordered Sets should be considered for use when you require keeping your collection sorted at all times, and do lookups on the collection much more freuqently than inserting or deleting items. A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below). Many of the lookup operations for an Ordered Set are **O(1)**. 
 
 ### These are Ordered Sets
 ```
@@ -26,7 +26,7 @@ This Set violates the sorted property
 ```
 
 ## The Code
-We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep our set sorted, we need to compare the individual elemants. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
+We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep our set sorted, we need to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
 
 ``` swift
 public struct OrderedSet<T: Comparable> {
@@ -68,7 +68,7 @@ Lets take a look at the insert function first. The insert function first checks
       internalSet.append(item)
   }
 ```
-The first part of the function checks if the item is already in the set.As we'll see later on, this has an efficiency of **O(log(n) + k)** where k is the number of items with the same value as the item we are inserting. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(log(n))**, thus making the insert function for our Ordered Set **O(log(n) + k)**.
+The first part of the function checks if the item is already in the set. As we'll see later on, this has an efficiency of **O(log(n) + k)** where k is the number of items with the same value as the item we are inserting. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(nlog(n))**, thus making the insert function for our Ordered Set **O(nlog(n))**.
 
 
 Next we have the `remove` function. First check if the item exists. If not, then return and no nothing. If it does exist, remove it.
@@ -83,7 +83,7 @@ Next we have the `remove` function. First check if the item exists. If not, then
         internalSet.removeAtIndex(findIndex(item))
     }
 ```
-Again, because of the `exists` function, the efficiency for remove is **O(log(n) + k)**
+Again, because of the `removeAtIndex` function, the efficiency for remove is **O(nlog(n))**
 
 The next function is the `findIndex` function which takes in an item of type `T` and returns the index of the item if it is in the set, otherwise returns -1. 
 
@@ -194,7 +194,7 @@ Since the set is sorted, the following operations are all **O(1)**:
 Below are a few examples that can be found in the playground file.
 
 ### Example 1
-Here we create a set with random Integers. Pringint the largest/smallest 5 numbers in the set is fairly easy.
+Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
 ``` swift
 // Example 1 with type Int
 var mySet = OrderedSet<Int>()
@@ -248,7 +248,7 @@ func <(x: Player, y: Player) -> Bool {
     return x.points < y.points
 }
 ```
-The set we create will hold players. One thing to note is that two `Player`'s can each have the same value, but are not guaranteed to be equal. 
+The set we create will hold players. One thing to note is that two `Player`s can each have the same value, but are not guaranteed to be equal. 
 
 Inserting 20 random players and one player we will track of.
 ``` swift
@@ -272,7 +272,7 @@ print(playerSet.max())
 print(playerSet.min())
 ```
 
-Next we use the findIndex function to find out what rank `anotherPlayer` in comparison to the other `Player`s.
+Next we use the findIndex function to find out what rank `anotherPlayer` is.
 ``` swift
 // we'll find our player now
 print("'Another Player (\(anotherPlayer.name))' is ranked at level: \(playerSet.count - playerSet.findIndex(anotherPlayer)) with \(anotherPlayer.points) points")

From a9a98343bd82ad148e930e7e7c2bfef46a09acee Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 19:20:33 -0400
Subject: [PATCH 0195/1679] Removed Construction emoticon for Ordered Set

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index d4ce78753..21efc0a0d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -163,7 +163,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash Set/). A set implemented using a hash table.
 - Multiset
-- [Ordered Set](Ordered Set/) :construction:
+- [Ordered Set](Ordered Set/)
 
 ### Graphs
 

From d5d38324d81dd4ac484e8227a6e095727fff636b Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 19:35:16 -0400
Subject: [PATCH 0196/1679] Added clarification

---
 Ordered Set/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index bc7f79e41..d878cd660 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -1,5 +1,5 @@
 # Ordered Set
-An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. The Ordered Set data type is a representation of a [Set in Mathematics](https://en.wikipedia.org/wiki/Set_(mathematics)). It's important to keep in mind that two items can have the same *value* but still may not be equal. 
+An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. The Ordered Set data type is a hybrid of a [Set](https://en.wikipedia.org/wiki/Set_(mathematics)), and a [Sequence](https://en.wikipedia.org/wiki/Sequence). It's important to keep in mind that two items can have the same *value* but still may not be equal. 
 For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
 
 ## Why use an Ordered Set?

From 506dbcf439a14f547cc989e1a29925d030765d13 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Fri, 25 Mar 2016 22:22:38 -0400
Subject: [PATCH 0197/1679] Changed right to left

---
 Ordered Set/OrderedSet.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 2325c0e58..9d4645e19 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -82,7 +82,7 @@ public struct OrderedSet<T: Comparable> {
                 
                 j = mid
                 
-                // check right side of mid
+                // check left side of mid
                 while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
                     if internalSet[j - 1] == item {
                         return j - 1
@@ -125,4 +125,4 @@ public struct OrderedSet<T: Comparable> {
     public func kSmallest(k: Int) -> T! {
         return k > count || k <= 0 ? nil : internalSet[k - 1]
     }
-}
\ No newline at end of file
+}

From 4f8becb03a1362b86546e2e33f8af8af13207c9e Mon Sep 17 00:00:00 2001
From: 318236213 <zain.muhammad@rbc.com>
Date: Sat, 26 Mar 2016 10:53:44 -0400
Subject: [PATCH 0198/1679] removed redundant code

---
 Ordered Set/OrderedSet.playground/Contents.swift | 11 +----------
 Ordered Set/OrderedSet.swift                     |  6 ------
 2 files changed, 1 insertion(+), 16 deletions(-)

diff --git a/Ordered Set/OrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
index 33d7ce0f2..dabc009cf 100644
--- a/Ordered Set/OrderedSet.playground/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -77,13 +77,7 @@ public struct OrderedSet<T: Comparable> {
         if exists(item) {
             return // don't add an item if it already exists
         }
-        
-        // if the set is initially empty, we need to simply append the item to internalSet
-        if count == 0 {
-            internalSet.append(item)
-            return
-        }
-        
+
         for i in 0..<count {
             if internalSet[i] > item {
                 internalSet.insert(item, atIndex: i)
@@ -260,6 +254,3 @@ print(repeatedSet.findIndex(Player(name: "Player 5", points: 1000)))
 
 
 
-
-
-
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 9d4645e19..301ffa529 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -19,12 +19,6 @@ public struct OrderedSet<T: Comparable> {
             return // don't add an item if it already exists
         }
         
-        // if the set is initially empty, we need to simply append the item to internalSet
-        if count == 0 {
-            internalSet.append(item)
-            return
-        }
-        
         for i in 0..<count {
             if internalSet[i] > item {
                 internalSet.insert(item, atIndex: i)

From 7be8994eb148eea03549708122ef330c025ac2c5 Mon Sep 17 00:00:00 2001
From: Zain Humayun <zain1019@hotmail.com>
Date: Sat, 26 Mar 2016 10:54:53 -0400
Subject: [PATCH 0199/1679] removed redundant code

---
 Ordered Set/README.md | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Ordered Set/README.md b/Ordered Set/README.md
index d878cd660..e56ae23d4 100644
--- a/Ordered Set/README.md	
+++ b/Ordered Set/README.md	
@@ -51,11 +51,6 @@ Lets take a look at the insert function first. The insert function first checks
       if exists(item) {
           return // don't add an item if it already exists
       }
-      // if the set is initially empty, we need to simply append the item to internalSet
-      if count == 0 {
-          internalSet.append(item)
-          return
-      }
         
       for i in 0..<count {
           if internalSet[i] > item {

From 0871bc9567118872d4ae71203bd7da6a82801867 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 27 Mar 2016 15:07:44 +0200
Subject: [PATCH 0200/1679] Text tweaks

---
 .../Combinatorics.playground/Contents.swift   | 36 ++++-----
 .../timeline.xctimeline                       |  6 --
 Combinatorics/Combinatorics.swift             | 14 ++++
 Combinatorics/README.markdown                 | 80 +++++++++----------
 4 files changed, 71 insertions(+), 65 deletions(-)
 delete mode 100644 Combinatorics/Combinatorics.playground/timeline.xctimeline

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 6040ae711..2cafaa0c1 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -117,6 +117,24 @@ for i in 1...20 {
 
 
 
+/*
+  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+  k things out of n possibilities.
+*/
+func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+  var result = 1
+    
+  for i in 0..<k {
+    result *= (n - i)
+    result /= (i + 1)
+  }
+  return result
+}
+
+quickBinomialCoefficient(8, 2)
+quickBinomialCoefficient(30, 15)
+
+
 
 /* Supporting code because Swift doesn't have a built-in 2D array. */
 struct Array2D<T> {
@@ -166,21 +184,3 @@ func binomialCoefficient(n: Int, _ k: Int) -> Int {
 binomialCoefficient(30, 15)
 binomialCoefficient(66, 33)
 
-
-
-/*
-Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-k things out of n possibilities.
-*/
-func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
-  var result = 1
-    
-  for i in 0..<k {
-    result *= (n - i)
-    result /=  (i + 1)
-  }
-  return result
-}
-
-quickBinomialCoefficient(30, 15)
-quickBinomialCoefficient(8, 2)
diff --git a/Combinatorics/Combinatorics.playground/timeline.xctimeline b/Combinatorics/Combinatorics.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Combinatorics/Combinatorics.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Combinatorics/Combinatorics.swift b/Combinatorics/Combinatorics.swift
index a204f7252..eb67fb53f 100644
--- a/Combinatorics/Combinatorics.swift
+++ b/Combinatorics/Combinatorics.swift
@@ -78,6 +78,20 @@ func combinations(n: Int, _ k: Int) -> Int {
   return permutations(n, k) / factorial(k)
 }
 
+/*
+  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+  k things out of n possibilities.
+*/
+func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+  var result = 1
+    
+  for i in 0..<k {
+    result *= (n - i)
+    result /= (i + 1)
+  }
+  return result
+}
+
 /*
   Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
   k things out of n possibilities.
diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 48723b065..6e16e93c3 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -304,7 +304,43 @@ combinations(28, 5)    // prints 98280
 
 Because this uses the `permutations()` and `factorial()` functions under the hood, you're still limited by how large these numbers can get. For example, `combinations(30, 15)` is "only" `155,117,520` but because the intermediate results don't fit into a 64-bit integer, you can't calculate it with the given function.
 
-Here is an algorithm that uses dynamic programming to overcome the need for calculating factorials. It is based on Pascal's triangle:
+There's a faster approach to calculate `C(n, k)` in **O(k)** time and **O(1)** extra space. The idea behind it is that the formula for `C(n, k)` is:
+
+                   n!                      n * (n - 1) * ... * 1
+    C(n, k) = ------------- = ------------------------------------------
+              (n - k)! * k!      (n - k) * (n - k - 1) * ... * 1 * k!
+
+After the reduction of fractions, we get the following formula:
+
+                   n * (n - 1) * ... * (n - k + 1)         (n - 0) * (n - 1) * ... * (n - k + 1)
+    C(n, k) = --------------------------------------- = -----------------------------------------
+                               k!                          (0 + 1) * (1 + 1) * ... * (k - 1 + 1)
+
+We can implement this formula as follows:
+
+```swift
+func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+  var result = 1
+  for i in 0..<k {
+    result *= (n - i)
+    result /= (i + 1)
+  }
+  return result
+}
+```
+
+This algorithm can create larger numbers than the previous method. Instead of calculating the entire numerator (a potentially huge number) and then dividing it by the factorial (also a very large number), here we already divide in each step. That causes the temporary results to grow much less quickly.
+
+Here's how you can use this improved algorithm:
+
+```swift
+quickBinomialCoefficient(8, 2)     // prints 28
+quickBinomialCoefficient(30, 15)   // prints 155117520
+```
+
+This new method is quite fast but you're still limited in how large the numbers can get. You can calculate `C(30, 15)` without any problems, but something like `C(66, 33)` will still cause integer overflow in the numerator.
+
+Here is an algorithm that uses dynamic programming to overcome the need for calculating factorials and doing divisions. It is based on Pascal's triangle:
 
 	0:               1
 	1:             1   1
@@ -351,54 +387,16 @@ func binomialCoefficient(n: Int, _ k: Int) -> Int {
 
 This uses [Array2D](../Array2D/) as helper code because Swift doesn't have a built-in two-dimensional array. The algorithm itself is quite simple: the first loop fills in the 1s at the outer edges of the triangle. The other loops calculate each number in the triangle by adding up the two numbers from the previous row.
 
-Now you can calculate `C(30, 15)` without any problems:
+Now you can calculate `C(66, 33)` without any problems:
 
 ```swift
-binomialCoefficient(30, 15)   // prints 155117520
 binomialCoefficient(66, 33)   // prints a very large number
 ```
 
-There's a faster approach to calculate `C(n, k)` in `O(k)` time and `O(1)` extra space.
-
-The idea behind it is that the formula for `C(n, k)` is:
-
-                   n!                      n * (n - 1) * ... * 1
-    C(n, k) = ------------- = ------------------------------------------
-              (n - k)! * k!      (n - k) * (n - k - 1) * ... * 1 * k!
-
-After the reduction of fractions, we get the following formula:
-
-                   n * (n - 1) * ... * (n - k + 1)         (n - 0) * (n - 1) * ... * (n - k + 1)
-    C(n, k) = --------------------------------------- = -----------------------------------------
-                               k!                          (0 + 1) * (1 + 1) * ... * (k - 1 + 1)
-
-So the following code calculates the `C(n, k)` you're looking for:
-
-```swift
-func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
-  var result = 1
-
-  for i in 0..<k {
-    result *= (n - i)
-    result /=  (i + 1)
-  }
-  return result
-}
-```
-
-As there're the divisors for numbers from `1...k` among `k` consecutive numbers, what is exactly we've got in the numerator of our fast formula every time we devide `result` by `(i + 1)` we won't have a real number.
-
-Here's how you can use it:
-
-```swift
-quickBinomialCoefficient(30, 15)   // prints 155117520
-quickBinomialCoefficient(8, 2)   // prints 28
-```
-
 You may wonder what the point is in calculating these permutations and combinations, but many algorithm problems are really combinatorics problems in disguise. Often you may need to look at all possible combinations of your data to see which one gives the right solution. If that means you need to search through `n!` potential solutions, you may want to consider a different approach -- as you've seen, these numbers become huge very quickly!
 
 ## References
 
 Wirth's and Sedgewick's permutation algorithms and the code for counting permutations and combinations are based on the Algorithm Alley column from Dr.Dobb's Magazine, June 1993. The dynamic programming binomial coefficient algorithm is from The Algorithm Design Manual by Skiena.
 
-*Written for Swift Algorithm Club by Matthijs Hollemans*
+*Written for Swift Algorithm Club by Matthijs Hollemans and [Kanstantsin Linou](https://github.com/nuts23)*

From a656e254226b1547e19925ef2f9c375e6333b7a4 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 27 Mar 2016 17:16:24 +0200
Subject: [PATCH 0201/1679] Text and code tweaks

---
 .../OrderedSet.playground/Contents.swift      | 256 -------------
 .../Example 1.xcplaygroundpage/Contents.swift |  30 ++
 .../Example 2.xcplaygroundpage/Contents.swift |  29 ++
 .../Example 3.xcplaygroundpage/Contents.swift |  22 ++
 .../Sources/OrderedSet.swift                  | 117 ++++++
 .../Sources/Player.swift                      |  38 ++
 .../Sources/Random.swift                      |  20 ++
 .../contents.xcplayground                     |   8 +-
 Ordered Set/OrderedSet.swift                  | 223 ++++++------
 Ordered Set/README.markdown                   | 332 +++++++++++++++++
 Ordered Set/README.md                         | 335 ------------------
 README.markdown                               |   2 +-
 12 files changed, 704 insertions(+), 708 deletions(-)
 delete mode 100644 Ordered Set/OrderedSet.playground/Contents.swift
 create mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
 create mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
 create mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
 create mode 100644 Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
 create mode 100644 Ordered Set/OrderedSet.playground/Sources/Player.swift
 create mode 100644 Ordered Set/OrderedSet.playground/Sources/Random.swift
 create mode 100644 Ordered Set/README.markdown
 delete mode 100644 Ordered Set/README.md

diff --git a/Ordered Set/OrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
deleted file mode 100644
index dabc009cf..000000000
--- a/Ordered Set/OrderedSet.playground/Contents.swift	
+++ /dev/null
@@ -1,256 +0,0 @@
-// random function returns a random number between the given range
-func randomNum(min: Int, max: Int) -> Int {
-    return min + Int(arc4random_uniform(UInt32(max - min + 1)))
-}
-
-// extension for String generates a random alphanumeric string of length 8
-extension String {
-    static func random(length: Int = 8) -> String {
-        
-        let base = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
-        var randomString: String = ""
-        
-        for _ in 0..<length {
-            let randomValue = arc4random_uniform(UInt32(base.characters.count))
-            randomString += "\(base[base.startIndex.advancedBy(Int(randomValue))])"
-        }
-        
-        return randomString
-    }
-}
-
-// Player data type stores a random name, and a random number of points from 0 - 5000
-struct Player : Comparable {
-    var name: String! = String.random()
-    var points = randomNum(0, max: 5000)
-    
-    init(name: String, points: Int){
-        self.name = name
-        self.points = points
-    }
-    
-    init(){}
-}
-
-// == operator for struct Player
-// Player x is equal to Player y if and only if both players have the same name and number of points
-func ==(x: Player, y: Player) -> Bool {
-    return x.name == y.name && x.points == y.points
-}
-
-// < operator for struct Player
-// Player x is less than Player y if and only if x has less points than y
-func <(x: Player, y: Player) -> Bool {
-    return x.points < y.points
-}
-
-// prints a Player formatted with their name and number of points
-func print(player: Player){
-    print("Player: \(player.name) | Points: \(player.points)")
-}
-
-func print(set: OrderedSet<Player>){
-    for i in 0..<set.count {
-        print(set[set.count - i - 1])
-    }
-}
-
-import Foundation
-
-// An Ordered Set is a collection where all items in the set follow an ordering, usually ordered from
-// 'least' to 'most'. The way you value, and compare items can be user defined.
-public struct OrderedSet<T: Comparable> {
-    private var internalSet: [T]! = nil
-    
-    // returns size of Set
-    public var count: Int {
-        return internalSet!.count
-    }
-    
-    public init(){
-        internalSet = [T]() // create the internal array on init
-    }
-    
-    // inserts an item
-    // O(n log n)
-    public mutating func insert(item: T){
-        if exists(item) {
-            return // don't add an item if it already exists
-        }
-
-        for i in 0..<count {
-            if internalSet[i] > item {
-                internalSet.insert(item, atIndex: i)
-                return
-            }
-        }
-        
-        // if an item is larger than any item in the current set, append it to the back.
-        internalSet.append(item)
-    }
-    
-    // removes an item if it exists
-    public mutating func remove(item: T) {
-        if !exists(item) {
-            return
-        }
-        
-        internalSet.removeAtIndex(findIndex(item))
-    }
-    
-    // returns true if and only if the item exists somewhere in the set
-    public func exists(item: T) -> Bool {
-        let index = findIndex(item)
-        return index != -1
-    }
-    
-    // returns the index of an item if it exists, otherwise returns -1.
-    public func findIndex(item: T) -> Int {
-        var leftBound = 0
-        var rightBound = count - 1
-        
-        while leftBound <= rightBound {
-            let mid = leftBound + ((rightBound - leftBound) / 2)
-            
-            if internalSet[mid] > item {
-                rightBound = mid - 1
-            } else if internalSet[mid] < item {
-                leftBound = mid + 1
-            } else {
-                // check the mid value to see if it is the item we are looking for
-                if internalSet[mid] == item {
-                    return mid
-                }
-                
-                var j = mid
-                
-                // check right side of mid
-                while j < internalSet.count - 1 && !(internalSet[j] < internalSet[j + 1]) {
-                    if internalSet[j + 1] == item {
-                        return j + 1
-                    }
-                    
-                    j += 1
-                }
-                
-                j = mid
-                
-                // check left side of mid
-                while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
-                    if internalSet[j - 1] == item {
-                        return j - 1
-                    }
-                    
-                    j -= 1
-                }
-                return -1
-            }
-        }
-        
-        return -1
-    }
-    
-    // returns the item at the given index. assertion fails if the index is out of the range
-    // of [0, count)
-    public subscript(index: Int) -> T {
-        assert(index >= 0 && index < count)
-        return internalSet[index]
-    }
-    
-    // returns the 'maximum' or 'largest' value in the set
-    public func max() -> T! {
-        return count == 0 ? nil : internalSet[count - 1]
-    }
-    
-    // returns the 'minimum' or 'smallest' value in the set
-    public func min() -> T! {
-        return count == 0 ? nil : internalSet[0]
-    }
-    
-    // returns the k largest element in the set, if k is in the range [1, count]
-    // returns nil otherwise
-    public func kLargest(k: Int) -> T! {
-        return k > count || k <= 0 ? nil : internalSet[count - k]
-    }
-    
-    // returns the k smallest element in the set, if k is in the range [1, count]
-    // returns nil otherwise
-    public func kSmallest(k: Int) -> T! {
-        return k > count || k <= 0 ? nil : internalSet[k - 1]
-    }
-}
-
-// Example 1 with type Int
-var mySet = OrderedSet<Int>()
-
-// insert random ints into the set
-
-for _ in 0..<50 {
-    mySet.insert(randomNum(50, max: 500))
-}
-
-print(mySet)
-
-print(mySet.max())
-print(mySet.min())
-
-// print the 5 largest values
-for k in 1..<6 {
-    print(mySet.kLargest(k))
-}
-
-// print the 5 lowest values
-for k in 1..<6 {
-    print(mySet.kSmallest(k))
-}
-
-
-// Example 2 with type Player
-var playerSet = OrderedSet<Player>()
-
-// populate with random players.
-var anotherPlayer = Player()
-for _ in 0..<20 {
-    playerSet.insert(Player())
-}
-
-// we'll look for this player later
-playerSet.insert(anotherPlayer)
-
-// print all players in order
-print(playerSet)
-
-
-// highest and lowest players:
-print(playerSet.max())
-print(playerSet.min())
-
-// we'll find our player now
-print("'Another Player (\(anotherPlayer.name))' is ranked at level: \(playerSet.count - playerSet.findIndex(anotherPlayer)) with \(anotherPlayer.points) points")
-
-
-
-// Example with multiple entries with the same value
-
-var repeatedSet = OrderedSet<Player>()
-
-repeatedSet.insert(Player(name:"Player 1", points: 100))
-repeatedSet.insert(Player(name: "Player 1", points: 100))
-repeatedSet.insert(Player(name: "Player 2", points: 100))
-repeatedSet.insert(Player(name: "Player 3", points: 100))
-repeatedSet.insert(Player(name: "Player 4", points: 100))
-repeatedSet.insert(Player(name: "Player 5", points: 100))
-repeatedSet.insert(Player(name: "Player 6", points: 50))
-repeatedSet.insert(Player(name: "Player 7", points: 200))
-repeatedSet.insert(Player(name: "Player 8", points: 250))
-repeatedSet.insert(Player(name: "Player 9", points: 25))
-
-print(repeatedSet)
-
-// find player 5
-print(repeatedSet.findIndex(Player(name: "Player 5", points: 100)))
-print(repeatedSet.findIndex(Player(name: "Random Player", points: 100)))
-print(repeatedSet.findIndex(Player(name: "Player 5", points: 1000)))
-
-
-
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..c1fe6fe11
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,30 @@
+//: # Example 1 with type Int
+
+var mySet = OrderedSet<Int>()
+
+// Insert random numbers into the set
+for _ in 0..<50 {
+  mySet.insert(random(50, max: 500))
+}
+
+print(mySet)
+
+print("\nMaximum:")
+print(mySet.max())
+
+print("\nMinimum:")
+print(mySet.min())
+
+// Print the 5 largest values
+print("\n5 Largest:")
+for k in 1...5 {
+  print(mySet.kLargest(k))
+}
+
+// Print the 5 lowest values
+print("\n5 Smallest:")
+for k in 1...5 {
+  print(mySet.kSmallest(k))
+}
+
+//: [Next](@next)
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..6fc1f66ed
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,29 @@
+//: [Previous](@previous)
+
+//: # Example 2 with Player objects
+
+var playerSet = OrderedSet<Player>()
+
+// Populate the set with random players.
+for _ in 0..<20 {
+  playerSet.insert(Player())
+}
+
+// We'll look for this player later.
+var anotherPlayer = Player()
+playerSet.insert(anotherPlayer)
+
+// Print all players in order from highest points to lowest points.
+// (Note: this is the reverse order of how they are stored in the set!)
+print(playerSet)
+//debugPrint(playerSet)
+
+// Highest and lowest players:
+print(playerSet.max())
+print(playerSet.min())
+
+// We'll find our player now:
+let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
+print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
+
+//: [Next](@next)
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
new file mode 100644
index 000000000..872b5aeb4
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
@@ -0,0 +1,22 @@
+//: [Previous](@previous)
+
+//: # Example 3: multiple entries with the same value
+
+var repeatedSet = OrderedSet<Player>()
+
+repeatedSet.insert(Player(name: "Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 2", points: 100))
+repeatedSet.insert(Player(name: "Player 3", points: 100))
+repeatedSet.insert(Player(name: "Player 4", points: 100))
+repeatedSet.insert(Player(name: "Player 5", points: 100))
+repeatedSet.insert(Player(name: "Player 6", points: 50))
+repeatedSet.insert(Player(name: "Player 7", points: 200))
+repeatedSet.insert(Player(name: "Player 8", points: 250))
+repeatedSet.insert(Player(name: "Player 9", points: 25))
+
+print(repeatedSet)
+//debugPrint(repeatedSet)
+
+print(repeatedSet.indexOf(Player(name: "Player 5", points: 100)))
+print(repeatedSet.indexOf(Player(name: "Random Player", points: 100)))
+print(repeatedSet.indexOf(Player(name: "Player 5", points: 1000)))
diff --git a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
new file mode 100644
index 000000000..8a431a63b
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
@@ -0,0 +1,117 @@
+/* 
+  An Ordered Set is a collection where all items in the set follow an ordering,
+  usually ordered from 'least' to 'most'. The way you value and compare items
+  can be user-defined.
+*/
+public struct OrderedSet<T: Comparable> {
+  private var internalSet = [T]()
+
+  public init() { }
+
+  // Returns the number of elements in the OrderedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+
+  // Inserts an item. Performance: O(n log n)
+  public mutating func insert(item: T){
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, atIndex: i)
+        return
+      }
+    }
+
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+
+  // Removes an item if it exists.
+  public mutating func remove(item: T) {
+    if let index = indexOf(item) {
+      internalSet.removeAtIndex(index)
+    }
+  }
+
+  // Returns true if and only if the item exists somewhere in the set.
+  public func exists(item: T) -> Bool {
+    return indexOf(item) != nil
+  }
+
+  // Returns the index of an item if it exists, or -1 otherwise.
+  public func indexOf(item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+        // When we get here, we've landed on an item whose value is equal to the
+        // value of the item we're looking for, but the items themselves are not
+        // equal. We need to check the items with the same value to the right 
+        // and to the left in order to find an exact match.
+
+        // Check to the right.
+        for j in mid.stride(to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+
+        // Check to the left.
+        for j in mid.stride(to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+        return nil
+      }
+    }
+    return nil
+  }
+
+  // Returns the item at the given index. 
+  // Assertion fails if the index is out of the range of [0, count).
+  public subscript(index: Int) -> T {
+    assert(index >= 0 && index < count)
+    return internalSet[index]
+  }
+
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+
+  // Returns the k-th largest element in the set, if k is in the range 
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+}
diff --git a/Ordered Set/OrderedSet.playground/Sources/Player.swift b/Ordered Set/OrderedSet.playground/Sources/Player.swift
new file mode 100644
index 000000000..7b8175107
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Sources/Player.swift	
@@ -0,0 +1,38 @@
+// The Player data type stores a random name, and a random number of
+// points from 0 - 5000.
+public struct Player: Comparable {
+  public var name: String
+  public var points: Int
+
+  public init() {
+    self.name = String.random()
+    self.points = random(0, max: 5000)
+  }
+
+  public init(name: String, points: Int) {
+    self.name = name
+    self.points = points
+  }
+}
+
+// Player x is equal to Player y if and only if both players have the 
+// same name and number of points.
+public func ==(x: Player, y: Player) -> Bool {
+  return x.name == y.name && x.points == y.points
+}
+
+// Player x is less than Player y if x has less points than y.
+public func <(x: Player, y: Player) -> Bool {
+  return x.points < y.points
+}
+
+// Prints a Player formatted with their name and number of points.
+public func print(player: Player) {
+  print("Player: \(player.name) | Points: \(player.points)")
+}
+
+public func print(set: OrderedSet<Player>) {
+  for i in 0..<set.count {
+    print(set[set.count - i - 1])
+  }
+}
diff --git a/Ordered Set/OrderedSet.playground/Sources/Random.swift b/Ordered Set/OrderedSet.playground/Sources/Random.swift
new file mode 100644
index 000000000..b6e1f7736
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Sources/Random.swift	
@@ -0,0 +1,20 @@
+import Foundation
+
+// Returns a random number between the given range.
+public func random(min: Int, max: Int) -> Int {
+  return min + Int(arc4random_uniform(UInt32(max - min + 1)))
+}
+
+// Generates a random alphanumeric string of a given length.
+extension String {
+  public static func random(length: Int = 8) -> String {
+    let base = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
+    var randomString: String = ""
+
+    for _ in 0..<length {
+      let randomValue = arc4random_uniform(UInt32(base.characters.count))
+      randomString += "\(base[base.startIndex.advancedBy(Int(randomValue))])"
+    }
+    return randomString
+  }
+}
diff --git a/Ordered Set/OrderedSet.playground/contents.xcplayground b/Ordered Set/OrderedSet.playground/contents.xcplayground
index 9f5f2f40c..18c02c912 100644
--- a/Ordered Set/OrderedSet.playground/contents.xcplayground	
+++ b/Ordered Set/OrderedSet.playground/contents.xcplayground	
@@ -1,4 +1,8 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
-    <timeline fileName='timeline.xctimeline'/>
+<playground version='6.0' target-platform='ios' display-mode='raw' executeOnSourceChanges='false'>
+    <pages>
+        <page name='Example 1'/>
+        <page name='Example 2'/>
+        <page name='Example 3'/>
+    </pages>
 </playground>
\ No newline at end of file
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 301ffa529..8a431a63b 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -1,122 +1,117 @@
-// An Ordered Set is a collection where all items in the set follow an ordering, usually ordered from
-// 'least' to 'most'. The way you value, and compare items can be user defined.
+/* 
+  An Ordered Set is a collection where all items in the set follow an ordering,
+  usually ordered from 'least' to 'most'. The way you value and compare items
+  can be user-defined.
+*/
 public struct OrderedSet<T: Comparable> {
-    private var internalSet: [T]! = nil
-    
-    // returns size of Set
-    public var count: Int {
-        return internalSet!.count
+  private var internalSet = [T]()
+
+  public init() { }
+
+  // Returns the number of elements in the OrderedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+
+  // Inserts an item. Performance: O(n log n)
+  public mutating func insert(item: T){
+    if exists(item) {
+      return  // don't add an item if it already exists
     }
-    
-    public init(){
-        internalSet = [T]() // create the internal array on init
+
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, atIndex: i)
+        return
+      }
     }
-    
-    // inserts an item
-    // O(n log n)
-    public mutating func insert(item: T){
-        if exists(item) {
-            return // don't add an item if it already exists
-        }
-        
-        for i in 0..<count {
-            if internalSet[i] > item {
-                internalSet.insert(item, atIndex: i)
-                return
-            }
-        }
-        
-        // if an item is larger than any item in the current set, append it to the back.
-        internalSet.append(item)
+
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+
+  // Removes an item if it exists.
+  public mutating func remove(item: T) {
+    if let index = indexOf(item) {
+      internalSet.removeAtIndex(index)
     }
-    
-    // removes an item if it exists
-    public mutating func remove(item: T) {
-        if !exists(item) {
-            return
+  }
+
+  // Returns true if and only if the item exists somewhere in the set.
+  public func exists(item: T) -> Bool {
+    return indexOf(item) != nil
+  }
+
+  // Returns the index of an item if it exists, or -1 otherwise.
+  public func indexOf(item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+        // When we get here, we've landed on an item whose value is equal to the
+        // value of the item we're looking for, but the items themselves are not
+        // equal. We need to check the items with the same value to the right 
+        // and to the left in order to find an exact match.
+
+        // Check to the right.
+        for j in mid.stride(to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
         }
-        
-        internalSet.removeAtIndex(findIndex(item))
-    }
-    
-    // returns true if and only if the item exists somewhere in the set
-    public func exists(item: T) -> Bool {
-        let index = findIndex(item)
-        return index != -1
-    }
-    
-    // returns the index of an item if it exists, otherwise returns -1.
-    public func findIndex(item: T) -> Int {
-        var leftBound = 0
-        var rightBound = count - 1
-        
-        while leftBound <= rightBound {
-            let mid = leftBound + ((rightBound - leftBound) / 2)
-            
-            if internalSet[mid] > item {
-                rightBound = mid - 1
-            } else if internalSet[mid] < item {
-                leftBound = mid + 1
-            } else {
-                // check the mid value to see if it is the item we are looking for
-                if internalSet[mid] == item {
-                    return mid
-                }
-                
-                var j = mid
-                
-                // check right side of mid
-                while j < internalSet.count - 1 && !(internalSet[j] < internalSet[j + 1]) {
-                    if internalSet[j + 1] == item {
-                        return j + 1
-                    }
-                    
-                    j += 1
-                }
-                
-                j = mid
-                
-                // check left side of mid
-                while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
-                    if internalSet[j - 1] == item {
-                        return j - 1
-                    }
-                    
-                    j -= 1
-                }
-                return -1
-            }
+
+        // Check to the left.
+        for j in mid.stride(to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
         }
-        
-        return -1
-    }
-    
-    // returns the item at the given index. assertion fails if the index is out of the range
-    // of [0, count)
-    public subscript(index: Int) -> T {
-        assert(index >= 0 && index < count)
-        return internalSet[index]
-    }
-    
-    // returns the 'maximum' or 'largest' value in the set
-    public func max() -> T! {
-        return count == 0 ? nil : internalSet[count - 1]
-    }
-    
-    // returns the 'minimum' or 'smallest' value in the set
-    public func min() -> T! {
-        return count == 0 ? nil : internalSet[0]
-    }
-    
-    // returns the k largest element in the set, if k is in the range [1, count]
-    // returns nil otherwise
-    public func kLargest(k: Int) -> T! {
-        return k > count || k <= 0 ? nil : internalSet[count - k]
-    }
-    
-    // returns the k smallest element in the set, if k is in the range [1, count]
-    // returns nil otherwise
-    public func kSmallest(k: Int) -> T! {
-        return k > count || k <= 0 ? nil : internalSet[k - 1]
+        return nil
+      }
     }
+    return nil
+  }
+
+  // Returns the item at the given index. 
+  // Assertion fails if the index is out of the range of [0, count).
+  public subscript(index: Int) -> T {
+    assert(index >= 0 && index < count)
+    return internalSet[index]
+  }
+
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+
+  // Returns the k-th largest element in the set, if k is in the range 
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
 }
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
new file mode 100644
index 000000000..281a7e0d1
--- /dev/null
+++ b/Ordered Set/README.markdown	
@@ -0,0 +1,332 @@
+# Ordered Set
+
+An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. 
+
+The Ordered Set data type is a hybrid of:
+
+- a [Set](https://en.wikipedia.org/wiki/Set_%28mathematics%29), a collection of unique items where the order does not matter, and
+- a [Sequence](https://en.wikipedia.org/wiki/Sequence), an ordered list of items where each item may appear more than once.
+
+It's important to keep in mind that two items can have the same *value* but still may not be equal. For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
+
+## Why use an ordered set?
+
+Ordered Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Ordered Set are **O(1)**. 
+
+A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below).
+
+#### These are ordered sets
+
+A set of integers:
+
+	[1, 2, 3, 6, 8, 10, 1000]
+
+A set of strings:
+
+	["a", "is", "set", "this"]
+
+The "value" of these strings could be their text content, but also for example their length.
+
+#### These are not ordered sets
+
+This set violates the property of uniqueness:
+
+	[1, 1, 2, 3, 5, 8]
+
+This set violates the sorted property:
+
+	[1, 11, 2, 3]
+
+## The code
+
+We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep the set sorted, we need to be able to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
+
+```swift
+public struct OrderedSet<T: Comparable> {
+  private var internalSet = [T]()
+
+  // Returns the number of elements in the OrderedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  ...
+```
+
+Lets take a look at the `insert()` function first. This first checks if the item already exists in the collection. If so, it returns and does not insert the item.  Otherwise, it will insert the item through straightforward iteration.
+
+```swift
+  public mutating func insert(item: T){
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, atIndex: i)
+        return
+      }
+    }
+
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+```
+
+As we'll see later on, checking if the item is already in the set has an efficiency of **O(log(n) + k)** where **k** is the number of items with the same value as the item we are inserting.
+
+To insert the new item, the `for` loop starts from the beginning of the array, and checks to see if each item is larger than the item we want to insert. Once we find such an item, we insert the new one into its place. This shifts the rest of the array over to the right by 1 position. This loop is at worst **O(n)**.
+
+The total performance of the `insert()` function is therefore **O(n log(n))**.
+
+Next up is the `remove()` function:
+
+```swift
+  public mutating func remove(item: T) {
+    if let index = indexOf(item) {
+      internalSet.removeAtIndex(index)
+    }
+  }
+```
+
+First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n log(n))**.
+
+The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item. 
+
+```swift
+  public func indexOf(item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+      	// see below
+      }
+    }
+    return nil
+  }
+```
+
+> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary Search). 
+
+However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item. 
+
+For example, consider this ordered set of `Player` objects. Each `Player` has a name and a number of points:
+
+	[ ("Bill", 50), ("Ada", 50), ("Jony", 50), ("Steve", 200), ("Jean-Louis", 500), ("Woz", 1000) ]
+
+We want the set to be ordered by points, from low to high. Multiple players can have the same number of points. The name of the player is not important for this ordering. However, the name *is* important for retrieving the correct item.
+
+Let's say we do `indexOf(bill)` where `bill` is player object `("Bill", 50)`. If we did a traditional binary search we'd land on index 2, which is the object `("Jony", 50)`. The value 50 matches, but it's not the object we're looking for!
+
+Therefore, we also need to check the items with the same value to the right and left of the midpoint. The code to check the left and right side looks like this:
+
+```swift
+        // Check to the right.
+        for j in mid.stride(to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+
+        // Check to the left.
+        for j in mid.stride(to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+        
+        return nil
+```
+
+These loops start at the current `mid` value and then look at the neighboring values until we've found the correct object.
+
+The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for. 
+
+Since the set is sorted, the following operations are all **O(1)**:
+
+```swift
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+
+  // Returns the k-th largest element in the set, if k is in the range 
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+```
+
+## Examples
+
+Below are a few examples that can be found in the playground file.
+
+### Example 1
+
+Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
+
+```swift
+// Example 1 with type Int
+var mySet = OrderedSet<Int>()
+
+// Insert random numbers into the set
+for _ in 0..<50 {
+  mySet.insert(randomNum(50, max: 500))
+}
+
+print(mySet)
+
+print(mySet.max())
+print(mySet.min())
+
+// Print the 5 largest values
+for k in 1...5 {
+  print(mySet.kLargest(k))
+}
+
+// Print the 5 lowest values
+for k in 1...5 {
+  print(mySet.kSmallest(k))
+}
+```
+
+### Example 2
+
+In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
+
+```swift
+public struct Player: Comparable {
+  public var name: String
+  public var points: Int
+}
+```
+
+The `Player` also gets its own `==` and `<` operators. The `<` operator is used to determine the sort order of the set, while `==` determines whether two objects are really equal.
+
+Note that `==` compares both the name and the points:  
+  
+```swifr
+func ==(x: Player, y: Player) -> Bool {
+  return x.name == y.name && x.points == y.points
+}
+```
+
+But `<` only compares the points:
+
+```swift
+func <(x: Player, y: Player) -> Bool {
+  return x.points < y.points
+}
+```
+
+Therefore, two `Player`s can each have the same value (the number of points), but are not guaranteed to be equal (they can have different names).
+
+We create a new set and insert 20 random players. The `Player()` constructor gives each player a random name and score:
+
+```swift
+var playerSet = OrderedSet<Player>()
+
+// Populate the set with random players.
+for _ in 0..<20 {
+  playerSet.insert(Player())
+}
+```
+
+Insert another player:
+
+```swift
+var anotherPlayer = Player()
+playerSet.insert(anotherPlayer)
+```
+
+Now we use the `indexOf()` function to find out what rank `anotherPlayer` is.
+
+```swift
+let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
+print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
+```
+
+### Example 3
+
+The final example demonstrates the need to look for the right item even after the binary search has completed. 
+
+We insert 9 players into the set:
+
+```swift
+var repeatedSet = OrderedSet<Player>()
+
+repeatedSet.insert(Player(name: "Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 2", points: 100))
+repeatedSet.insert(Player(name: "Player 3", points: 100))
+repeatedSet.insert(Player(name: "Player 4", points: 100))
+repeatedSet.insert(Player(name: "Player 5", points: 100))
+repeatedSet.insert(Player(name: "Player 6", points: 50))
+repeatedSet.insert(Player(name: "Player 7", points: 200))
+repeatedSet.insert(Player(name: "Player 8", points: 250))
+repeatedSet.insert(Player(name: "Player 9", points: 25))
+```
+
+Notice how several of these players have the same value of 100 points.
+
+The set looks something like this:
+
+	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+
+The next line looks for `Player 2`:
+
+```swift
+print(repeatedSet.indexOf(Player(name: "Player 2", points: 100)))
+```
+
+After the binary search finishes, the value of `mid` is at index 5:
+
+	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+	                                                      mid
+
+However, this is not `Player 2`. Both `Player 4` and `Player 2` have the same points, but a different name. The binary search only looked at the points, not the name.
+
+But we do know that `Player 2` must be either to the immediate left or the right of `Player 4`, so we check both sides of `mid`. We only need to look at the objects with the same value as `Player 4`. The others are replaced by `X`:
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                                       mid 
+
+The code then first checks on the right of `mid` (where the `*` is):
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                                       mid        *
+
+The right side did not contain the item, so we look at the left side:
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                              *        mid        
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                    *                  mid        
+
+Finally, we've found `Player 2`, and return index 3.
+
+*Written By Zain Humayun*
diff --git a/Ordered Set/README.md b/Ordered Set/README.md
deleted file mode 100644
index e56ae23d4..000000000
--- a/Ordered Set/README.md	
+++ /dev/null
@@ -1,335 +0,0 @@
-# Ordered Set
-An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. The Ordered Set data type is a hybrid of a [Set](https://en.wikipedia.org/wiki/Set_(mathematics)), and a [Sequence](https://en.wikipedia.org/wiki/Sequence). It's important to keep in mind that two items can have the same *value* but still may not be equal. 
-For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
-
-## Why use an Ordered Set?
-Ordered Sets should be considered for use when you require keeping your collection sorted at all times, and do lookups on the collection much more freuqently than inserting or deleting items. A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below). Many of the lookup operations for an Ordered Set are **O(1)**. 
-
-### These are Ordered Sets
-```
-[1, 2, 3, 6, 8, 10, 1000]
-Where each item (Integers) has it's normal definition of value and equality
-```
-```
-["a", "is", "set", "this"]
-Where each item (String) has it's value equal to it's length
-```
-
-### These are not Ordered Sets
-```
-[1, 1, 2, 3, 5, 8]
-This Set violates the property of uniqueness
-```
-```
-[1, 11, 2, 3]
-This Set violates the sorted property
-```
-
-## The Code
-We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep our set sorted, we need to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
-
-``` swift
-public struct OrderedSet<T: Comparable> {
-    private var internalSet: [T]! = nil
-    
-    // returns size of Set
-    public var count: Int {
-        return internalSet!.count
-    }
-    
-    public init(){
-        internalSet = [T]() // create the internal array on init
-    }
-    ...
-```
-
-Lets take a look at the insert function first. The insert function first checks if the item already exists, and if so returns and does not insert the item. Otherwise, it will insert the item through straight forward iteration. It starts from the first item, and checks to see if this item is larger than the item we want to insert. Once we find such an item, we insert the given item into it's place, and shift the array over to the right by 1.
-
-``` swift
-  // inserts an item
-  public mutating func insert(item: T){
-      if exists(item) {
-          return // don't add an item if it already exists
-      }
-        
-      for i in 0..<count {
-          if internalSet[i] > item {
-            internalSet.insert(item, atIndex: i)
-            return
-          }
-        }
-        
-      // if an item is larger than any item in the current set, append it to the back.
-      internalSet.append(item)
-  }
-```
-The first part of the function checks if the item is already in the set. As we'll see later on, this has an efficiency of **O(log(n) + k)** where k is the number of items with the same value as the item we are inserting. The second part iterates through the interal array so that it can find a spot for our given item. This is at worse **O(n)**. The insert function for arrays has an efficiency of **O(nlog(n))**, thus making the insert function for our Ordered Set **O(nlog(n))**.
-
-
-Next we have the `remove` function. First check if the item exists. If not, then return and no nothing. If it does exist, remove it.
-
-``` swift
-    // removes an item if it exists
-    public mutating func remove(item: T) {
-        if !exists(item) {
-            return
-        }
-        
-        internalSet.removeAtIndex(findIndex(item))
-    }
-```
-Again, because of the `removeAtIndex` function, the efficiency for remove is **O(nlog(n))**
-
-The next function is the `findIndex` function which takes in an item of type `T` and returns the index of the item if it is in the set, otherwise returns -1. 
-
-``` swift
-// returns the index of an item if it exists, otherwise returns -1.
-    public func findIndex(item: T) -> Int {
-        var leftBound = 0
-        var rightBound = count - 1
-        
-        while leftBound <= rightBound {
-            let mid = leftBound + ((rightBound - leftBound) / 2)
-            
-            if internalSet[mid] > item {
-                rightBound = mid - 1
-            } else if internalSet[mid] < item {
-                leftBound = mid + 1
-            } else {
-                // check the mid value to see if it is the item we are looking for
-                if internalSet[mid] == item {
-                    return mid
-                }
-                
-                var j = mid
-                
-                // check right side of mid
-                while j < internalSet.count - 1 && !(internalSet[j] < internalSet[j + 1]) {
-                    if internalSet[j + 1] == item {
-                        return j + 1
-                    }
-                    
-                    j += 1
-                }
-                
-                j = mid
-                
-                // check left side of mid
-                while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
-                    if internalSet[j - 1] == item {
-                        return j - 1
-                    }
-                    
-                    j -= 1
-                }
-                return -1
-            }
-        }
-        
-        return -1
-    }
-```
-Since our set is sorted, we can use a binary search to quickly search for the item. If you are not familiar with the concept of binary search, we have an article all about it [here](../Binary\ Search). 
-
-Since a set can contain multiple items with the same *value*, it is important to check to see if we have the correct item.
-
-For example, consider this Ordered  Set
-```
-["a", "b", "c", "longer string", "even longer string"]
-Where the value of each String is equal to it's length.
-```
-The call `findIndex("a")` with the traditional implementation of Binary Search would give us the value of 2, however we know that "a" is located at index 0. Thus, we need to check the items with the same *value* to the right and left of the mid value.
-
-The code to check the left and right side are similar so we will only look at the code that checks the left side.
-``` swift
-    j = mid
-
-    // check left side of mid
-    while j > 0 && !(internalSet[j] < internalSet[j - 1]) {
-        if internalSet[j - 1] == item {
-            return j - 1
-        }
-                    
-        j -= 1
-    }
-    return -1
-```
-First, `j` starts at the mid value. Above, we've already checked to see that the item at index `j` is not equal to the item we are looking for. Then, we keep looping until we either reach the end of the array, or hit an element which has a lower value than the current item at index `j`. If the item at value `j - 1` is equal to the one we are looking for, we return that index, otherwise we keep decreasing `j`. Once the loop terminates, we were unable to find the item and so we return -1. 
-
-The combined runtime for this function is **O(log(n) + k)** where `n` is the length of the set, and `k` is the number of 
-items with the same *value* as the one that is being searched for. 
-
-Since the set is sorted, the following operations are all **O(1)**:
-
-```swift
-    // returns the 'maximum' or 'largest' value in the set
-    public func max() -> T! {
-        return count == 0 ? nil : internalSet[count - 1]
-    }
-    
-    // returns the 'minimum' or 'smallest' value in the set
-    public func min() -> T! {
-        return count == 0 ? nil : internalSet[0]
-    }
-    
-    // returns the k largest element in the set, if k is in the range [1, count]
-    // returns nil otherwise
-    public func kLargest(k: Int) -> T! {
-        return k > count || k <= 0 ? nil : internalSet[count - k]
-    }
-    
-    // returns the k smallest element in the set, if k is in the range [1, count]
-    // returns nil otherwise
-    public func kSmallest(k: Int) -> T! {
-        return k > count || k <= 0 ? nil : internalSet[k - 1]
-    }
-```
-
-## Examples
-Below are a few examples that can be found in the playground file.
-
-### Example 1
-Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
-``` swift
-// Example 1 with type Int
-var mySet = OrderedSet<Int>()
-
-// insert random ints into the set
-
-for _ in 0..<50 {
-    mySet.insert(randomNum(50, max: 500))
-}
-
-print(mySet)
-
-print(mySet.max())
-print(mySet.min())
-
-// print the 5 largest values
-for k in 1..<6 {
-    print(mySet.kLargest(k))
-}
-
-// print the 5 lowest values
-for k in 1..<6 {
-    print(mySet.kSmallest(k))
-}
-```
-
-### Exmaple 2
-In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
-``` swift
-struct Player : Comparable {
-    var name: String! = String.random()
-    var points = randomNum(0, max: 5000)
-    
-    init(name: String, points: Int){
-        self.name = name
-        self.points = points
-    }
-    
-    init(){}
-}
-
-// == operator for struct Player
-// Player x is equal to Player y if and only if both players have the same name and number of points
-func ==(x: Player, y: Player) -> Bool {
-    return x.name == y.name && x.points == y.points
-}
-
-// < operator for struct Player
-// Player x is less than Player y if and only if x has less points than y
-func <(x: Player, y: Player) -> Bool {
-    return x.points < y.points
-}
-```
-The set we create will hold players. One thing to note is that two `Player`s can each have the same value, but are not guaranteed to be equal. 
-
-Inserting 20 random players and one player we will track of.
-``` swift
-// Example 2 with type Player
-var playerSet = OrderedSet<Player>()
-
-// populate with random players.
-var anotherPlayer = Player()
-for _ in 0..<20 {
-    playerSet.insert(Player())
-}
-
-// we'll look for this player later
-playerSet.insert(anotherPlayer)
-```
-
-Next, we can find the players with the most and least amount of points very quickly.
-``` swift
-// highest and lowest players:
-print(playerSet.max())
-print(playerSet.min())
-```
-
-Next we use the findIndex function to find out what rank `anotherPlayer` is.
-``` swift
-// we'll find our player now
-print("'Another Player (\(anotherPlayer.name))' is ranked at level: \(playerSet.count - playerSet.findIndex(anotherPlayer)) with \(anotherPlayer.points) points")
-```
-
-### Example 3
-The final example demonstrates the need to look for the right item even after the Binary Search has completed. 9 Players are inserted into the set.
-``` swift
-
-var repeatedSet = OrderedSet<Player>()
-
-repeatedSet.insert(Player(name:"Player 1", points: 100))
-repeatedSet.insert(Player(name: "Player 1", points: 100))
-repeatedSet.insert(Player(name: "Player 2", points: 100))
-repeatedSet.insert(Player(name: "Player 3", points: 100))
-repeatedSet.insert(Player(name: "Player 4", points: 100))
-repeatedSet.insert(Player(name: "Player 5", points: 100))
-repeatedSet.insert(Player(name: "Player 6", points: 50))
-repeatedSet.insert(Player(name: "Player 7", points: 200))
-repeatedSet.insert(Player(name: "Player 8", points: 250))
-repeatedSet.insert(Player(name: "Player 9", points: 25))
-
-print(repeatedSet)
-```
-
-The set looks something like this:
-```
-[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
-```
-
-The next line looks for `Player 2`:
-``` swift
-print(repeatedSet.findIndex(Player(name: "Player 2", points: 100)))
-```
-
-After the Binary Search finishes, the value of `mid` is at index 5
-```
-[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
-                                                      mid
-```
-However, we know this may not be where `Player 2` is, so we check both sides of `mid`. The shown Players below are the ones with the same value as `Player 4`, and are the ones we check after the Binary Search.
-
-```
-[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-                                       mid 
-```
-
-The code then checks the right of `mid` (Every `Player` with an * below it)
-```
-[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-                                       mid        *
-```
-
-The right side did not contain the item, so we look at the left side.
-```
-[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-                              *        mid        
-```
-```
-[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-                    *                  mid        
-```
-We've found `Player 2`! Index 3 is then returned. 
-
-*Written By Zain Humayun*
diff --git a/README.markdown b/README.markdown
index 3338fe077..f7ff7833b 100644
--- a/README.markdown
+++ b/README.markdown
@@ -163,7 +163,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash Set/). A set implemented using a hash table.
 - Multiset
-- [Ordered Set](Ordered Set/)
+- [Ordered Set](Ordered Set/). A set where the order of items matters.
 
 ### Graphs
 

From ba69a89c9592a756fd0489eb355c1da3b66e50f8 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 27 Mar 2016 17:19:17 +0200
Subject: [PATCH 0202/1679] Fix big-O performance for insert and remove.

Was O(n log n) but should be O(n).
---
 Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift | 4 ++--
 Ordered Set/OrderedSet.swift                               | 4 ++--
 Ordered Set/README.markdown                                | 4 ++--
 3 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
index 8a431a63b..5f5a73fa2 100644
--- a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
@@ -13,7 +13,7 @@ public struct OrderedSet<T: Comparable> {
     return internalSet.count
   }
 
-  // Inserts an item. Performance: O(n log n)
+  // Inserts an item. Performance: O(n)
   public mutating func insert(item: T){
     if exists(item) {
       return  // don't add an item if it already exists
@@ -31,7 +31,7 @@ public struct OrderedSet<T: Comparable> {
     internalSet.append(item)
   }
 
-  // Removes an item if it exists.
+  // Removes an item if it exists. Performance: O(n)
   public mutating func remove(item: T) {
     if let index = indexOf(item) {
       internalSet.removeAtIndex(index)
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 8a431a63b..5f5a73fa2 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -13,7 +13,7 @@ public struct OrderedSet<T: Comparable> {
     return internalSet.count
   }
 
-  // Inserts an item. Performance: O(n log n)
+  // Inserts an item. Performance: O(n)
   public mutating func insert(item: T){
     if exists(item) {
       return  // don't add an item if it already exists
@@ -31,7 +31,7 @@ public struct OrderedSet<T: Comparable> {
     internalSet.append(item)
   }
 
-  // Removes an item if it exists.
+  // Removes an item if it exists. Performance: O(n)
   public mutating func remove(item: T) {
     if let index = indexOf(item) {
       internalSet.removeAtIndex(index)
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 281a7e0d1..b2e4e737c 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -77,7 +77,7 @@ As we'll see later on, checking if the item is already in the set has an efficie
 
 To insert the new item, the `for` loop starts from the beginning of the array, and checks to see if each item is larger than the item we want to insert. Once we find such an item, we insert the new one into its place. This shifts the rest of the array over to the right by 1 position. This loop is at worst **O(n)**.
 
-The total performance of the `insert()` function is therefore **O(n log(n))**.
+The total performance of the `insert()` function is therefore **O(n)**.
 
 Next up is the `remove()` function:
 
@@ -89,7 +89,7 @@ Next up is the `remove()` function:
   }
 ```
 
-First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n log(n))**.
+First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n)**.
 
 The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item. 
 

From 40a43c8c1454208d3ff0957197bbe0da89f1be87 Mon Sep 17 00:00:00 2001
From: Rinat Gabdullin <lostrinat@gmail.com>
Date: Sun, 27 Mar 2016 23:57:35 +0300
Subject: [PATCH 0203/1679] Fixing memory management of LinkedListNode

---
 Linked List/LinkedList.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 165b54737..c405ec42f 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -6,7 +6,7 @@
 public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
-  var previous: LinkedListNode?
+  weak var previous: LinkedListNode?
   
   public init(value: T) {
     self.value = value
@@ -159,9 +159,9 @@ extension LinkedList {
   public func reverse() {
     var node = head
     while let currentNode = node {
+        node = currentNode.next
         swap(&currentNode.next, &currentNode.previous)
         head = currentNode
-        node = currentNode.previous
     }
   }
 }

From 46ad0534ce951962959065c09b478dfa00672e19 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Thu, 31 Mar 2016 11:49:17 -0400
Subject: [PATCH 0204/1679] Create READMEs for Fibonacci Heap and Threaded
 Binary Tree

---
 Fibonacci Heap/README.md       | 3 +++
 Threaded Binary Tree/README.md | 3 +++
 2 files changed, 6 insertions(+)
 create mode 100644 Fibonacci Heap/README.md
 create mode 100644 Threaded Binary Tree/README.md

diff --git a/Fibonacci Heap/README.md b/Fibonacci Heap/README.md
new file mode 100644
index 000000000..c0516bcb2
--- /dev/null
+++ b/Fibonacci Heap/README.md	
@@ -0,0 +1,3 @@
+# Fibonacci Heaps
+
+*Written for Swift Algorithms Club by Jayson Tung*
diff --git a/Threaded Binary Tree/README.md b/Threaded Binary Tree/README.md
new file mode 100644
index 000000000..7ca7cc8c9
--- /dev/null
+++ b/Threaded Binary Tree/README.md	
@@ -0,0 +1,3 @@
+# Threaded Binary Trees
+
+*Written for Swift Algorithm Club by Jayson Tung*

From b7397f23c4167ff621a951ba22d90f92cb7c9949 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Thu, 31 Mar 2016 11:56:10 -0400
Subject: [PATCH 0205/1679] Add 'under construction' tags to Fib Heap and
 Thread Bin Tree

---
 Fibonacci Heap/README.markdown       | 7 +++++++
 Fibonacci Heap/README.md             | 3 ---
 Threaded Binary Tree/README.markdown | 7 +++++++
 Threaded Binary Tree/README.md       | 3 ---
 4 files changed, 14 insertions(+), 6 deletions(-)
 create mode 100644 Fibonacci Heap/README.markdown
 delete mode 100644 Fibonacci Heap/README.md
 create mode 100644 Threaded Binary Tree/README.markdown
 delete mode 100644 Threaded Binary Tree/README.md

diff --git a/Fibonacci Heap/README.markdown b/Fibonacci Heap/README.markdown
new file mode 100644
index 000000000..f7d7efe71
--- /dev/null
+++ b/Fibonacci Heap/README.markdown	
@@ -0,0 +1,7 @@
+# Fibonacci Heaps
+
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_heap).
+
+*Written for the Swift Algorithm Club by Jayson Tung*
diff --git a/Fibonacci Heap/README.md b/Fibonacci Heap/README.md
deleted file mode 100644
index c0516bcb2..000000000
--- a/Fibonacci Heap/README.md	
+++ /dev/null
@@ -1,3 +0,0 @@
-# Fibonacci Heaps
-
-*Written for Swift Algorithms Club by Jayson Tung*
diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
new file mode 100644
index 000000000..1ca75ad75
--- /dev/null
+++ b/Threaded Binary Tree/README.markdown	
@@ -0,0 +1,7 @@
+# Threaded Binary Trees
+
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree).
+
+*Written for the Swift Algorithm Club by Jayson Tung*
diff --git a/Threaded Binary Tree/README.md b/Threaded Binary Tree/README.md
deleted file mode 100644
index 7ca7cc8c9..000000000
--- a/Threaded Binary Tree/README.md	
+++ /dev/null
@@ -1,3 +0,0 @@
-# Threaded Binary Trees
-
-*Written for Swift Algorithm Club by Jayson Tung*

From f61974bac527ac29c6fd4d084bed8539bc435a4a Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Thu, 31 Mar 2016 20:42:08 +0200
Subject: [PATCH 0206/1679] Add explanation of ownership cycle

---
 Linked List/LinkedList.playground/Contents.swift      | 10 +++++-----
 Linked List/LinkedList.playground/timeline.xctimeline |  6 ------
 Linked List/LinkedList.swift                          |  6 +++---
 Linked List/README.markdown                           |  8 ++++----
 4 files changed, 12 insertions(+), 18 deletions(-)
 delete mode 100644 Linked List/LinkedList.playground/timeline.xctimeline

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 1f3d98bc4..c09bed736 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,7 +3,7 @@
 public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
-  var previous: LinkedListNode?
+  weak var previous: LinkedListNode?
 
   public init(value: T) {
     self.value = value
@@ -155,10 +155,10 @@ extension LinkedList: CustomStringConvertible {
 extension LinkedList {
   public func reverse() {
     var node = head
-    while node != nil {
-      swap(&node!.next, &node!.previous)
-      head = node
-      node = node!.previous
+    while let currentNode = node {
+      node = currentNode.next
+      swap(&currentNode.next, &currentNode.previous)
+      head = currentNode
     }
   }
 }
diff --git a/Linked List/LinkedList.playground/timeline.xctimeline b/Linked List/LinkedList.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Linked List/LinkedList.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index c405ec42f..8d2c27d7e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -159,9 +159,9 @@ extension LinkedList {
   public func reverse() {
     var node = head
     while let currentNode = node {
-        node = currentNode.next
-        swap(&currentNode.next, &currentNode.previous)
-        head = currentNode
+      node = currentNode.next
+      swap(&currentNode.next, &currentNode.previous)
+      head = currentNode
     }
   }
 }
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 2ccbe3784..24360e2b5 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -58,7 +58,7 @@ We'll start by defining a type to describe the nodes:
 public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
-  var previous: LinkedListNode?
+  weak var previous: LinkedListNode?
 
   public init(value: T) {
     self.value = value
@@ -70,6 +70,8 @@ This is a generic type, so `T` can be any kind of data that you'd like to store
 
 Ours is a doubly-linked list and each node has a `next` and `previous` pointer. These can be `nil` if there are no next or previous nodes, so these variables must be optionals. (In what follows, I'll point out which functions would need to change if this was just a singly- instead of a doubly-linked list.)
 
+> **Note:** To avoid ownership cycles, we declare the `previous` pointer to be weak. If you have a node `A` that is followed by node `B` in the list, then `A` points to `B` but also `B` points to `A`. In certain circumstances, this ownership cycle can cause nodes to be kept alive even after you deleted them. We don't want that, so we make one of the pointers `weak` to break the cycle.
+
 Let's start building `LinkedList`. Here's the first bit:
 
 ```swift
@@ -450,9 +452,9 @@ How about reversing a list, so that the head becomes the tail and vice versa? Th
   public func reverse() {
     var node = head
     while let currentNode = node {
+      node = currentNode.next
       swap(&currentNode.next, &currentNode.previous)
       head = currentNode
-      node = currentNode.previous
     }
   }
 ```
@@ -465,8 +467,6 @@ This loops through the entire list and simply swaps the `next` and `previous` po
 	 nil <---|        |--->|        |--->|        |--->|        |<--- head
 	         +--------+    +--------+    +--------+    +--------+
 
-You may be wondering why the last statement says `node = currentNode.previous` to go to the next node instead of `currentNode.next` like you'd expect, but remember that we just swapped those pointers!
-
 Arrays have `map()` and `filter()` functions, and there's no reason why linked lists shouldn't either.
 
 ```swift

From d9fb909e05157f1e621b64091d1b46ddcaa16e7f Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 31 Mar 2016 20:51:29 -0400
Subject: [PATCH 0207/1679] Added Under Construction tags to ReadMe.md Files
 for Radix Sort, Counting Sort, and Trie Data Structure.

---
 Counting-Sort/ReadMe.md | 2 ++
 Radix-Sort/ReadMe.md    | 5 +++++
 Trie/ReadMe.md          | 2 ++
 3 files changed, 9 insertions(+)
 create mode 100644 Counting-Sort/ReadMe.md
 create mode 100644 Radix-Sort/ReadMe.md
 create mode 100644 Trie/ReadMe.md

diff --git a/Counting-Sort/ReadMe.md b/Counting-Sort/ReadMe.md
new file mode 100644
index 000000000..d0398ab4a
--- /dev/null
+++ b/Counting-Sort/ReadMe.md
@@ -0,0 +1,2 @@
+##Counting Sort
+Under Construction
diff --git a/Radix-Sort/ReadMe.md b/Radix-Sort/ReadMe.md
new file mode 100644
index 000000000..72528e5c7
--- /dev/null
+++ b/Radix-Sort/ReadMe.md
@@ -0,0 +1,5 @@
+##Radix Sort
+Under Construction
+See also Wikipedia
+
+Written for the Swift Algorithm Club by Christian Encarnacion
diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
new file mode 100644
index 000000000..b15bc4127
--- /dev/null
+++ b/Trie/ReadMe.md
@@ -0,0 +1,2 @@
+##Trie
+Under Construction

From 16ec08f10793bf694677604ec1d1aa49b7daa364 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 31 Mar 2016 20:52:23 -0400
Subject: [PATCH 0208/1679] Update ReadMe.md

---
 Radix-Sort/ReadMe.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Radix-Sort/ReadMe.md b/Radix-Sort/ReadMe.md
index 72528e5c7..924665a1d 100644
--- a/Radix-Sort/ReadMe.md
+++ b/Radix-Sort/ReadMe.md
@@ -1,5 +1,4 @@
 ##Radix Sort
 Under Construction
-See also Wikipedia
 
 Written for the Swift Algorithm Club by Christian Encarnacion

From 484e8c1c694438ff2143a1ea6df66c34e52310a9 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 31 Mar 2016 20:52:44 -0400
Subject: [PATCH 0209/1679] Update ReadMe.md

---
 Counting-Sort/ReadMe.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Counting-Sort/ReadMe.md b/Counting-Sort/ReadMe.md
index d0398ab4a..f28249e0d 100644
--- a/Counting-Sort/ReadMe.md
+++ b/Counting-Sort/ReadMe.md
@@ -1,2 +1,3 @@
 ##Counting Sort
 Under Construction
+Written for the Swift Algorithm Club by Christian Encarnacion

From f366732a61258246a52105d608038c40ae97a613 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 31 Mar 2016 20:53:04 -0400
Subject: [PATCH 0210/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index b15bc4127..0509b68d4 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,2 +1,4 @@
 ##Trie
 Under Construction
+
+Written for the Swift Algorithm Club by Christian Encarnacion

From 36c3fc3a5a03d11314e201214d1064202b412ec0 Mon Sep 17 00:00:00 2001
From: Yasuhiro Inami <inamiy@gmail.com>
Date: Sat, 2 Apr 2016 01:32:44 +0900
Subject: [PATCH 0211/1679] [Boyer-Moore] Update README, adding
 Boyer-Moore-Horspool algorithm

---
 Boyer-Moore/README.markdown | 42 +++++++++++++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)

diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 73a7943a2..d5c657420 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -138,3 +138,45 @@ The closer a character is to the end of the pattern, the smaller the skip amount
 Credits: This code is based on the article ["Faster String Searches" by Costas Menico](http://www.drdobbs.com/database/faster-string-searches/184408171) from Dr Dobb's magazine, July 1989 -- Yes, 1989! Sometimes it's useful to keep those old magazines around.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
+
+## Boyer-Moore-Horspool Algorithm
+
+In addition to the above algorithm, there is also a revised one called [Boyer-Moore–Horspool algorithm](https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm), which always and only uses "bad-character shift" (`skipTable`) and not "good-suffix shift" (see [here](http://www.inf.fh-flensburg.de/lang/algorithmen/pattern/bmen.htm) for more information).
+
+Boyer–Moore–Horspool algorithm works as follows:
+
+```swift
+extension String {
+  public func indexOf(pattern: String) -> String.Index?
+  {
+    let patternLength = pattern.characters.count
+    assert(patternLength > 0)
+    assert(patternLength <= self.characters.count)
+
+    var skipTable = [Character: Int]()
+    for (i, c) in pattern.characters.dropLast().enumerate() {
+      skipTable[c] = patternLength - i - 1
+    }
+
+    var index = self.startIndex.advancedBy(patternLength - 1)
+
+    while index < self.endIndex {
+      var i = index
+      var p = pattern.endIndex.predecessor()
+
+      while self[i] == pattern[p] {
+        if p == pattern.startIndex { return i }
+        i = i.predecessor()
+        p = p.predecessor()
+      }
+
+      let advance = skipTable[self[index]] ?? patternLength
+      index = index.advancedBy(advance)
+    }
+
+    return nil
+  }
+}
+```
+
+Credits: This code is based on the paper: [R. N. Horspool (1980). "Practical fast searching in strings". Software - Practice & Experience 10 (6): 501–506.](http://www.cin.br/~paguso/courses/if767/bib/Horspool_1980.pdf)

From 836481323cda65ecee6eb4b51916bc63b6d5d3e0 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 3 Apr 2016 11:52:33 +0200
Subject: [PATCH 0212/1679] Tweak text

---
 Boyer-Moore/README.markdown | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index d5c657420..a8f2c9f7a 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -137,18 +137,19 @@ The closer a character is to the end of the pattern, the smaller the skip amount
 
 Credits: This code is based on the article ["Faster String Searches" by Costas Menico](http://www.drdobbs.com/database/faster-string-searches/184408171) from Dr Dobb's magazine, July 1989 -- Yes, 1989! Sometimes it's useful to keep those old magazines around.
 
-*Written for Swift Algorithm Club by Matthijs Hollemans*
+See also: [a detailed analysis](http://www.inf.fh-flensburg.de/lang/algorithmen/pattern/bmen.htm) of the algorithm.
+
+## Boyer-Moore-Horspool algorithm
 
-## Boyer-Moore-Horspool Algorithm
+A variation on the above algorithm is the [Boyer-Moore-Horspool algorithm](https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm).
 
-In addition to the above algorithm, there is also a revised one called [Boyer-Moore–Horspool algorithm](https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm), which always and only uses "bad-character shift" (`skipTable`) and not "good-suffix shift" (see [here](http://www.inf.fh-flensburg.de/lang/algorithmen/pattern/bmen.htm) for more information).
+Like the regular Boyer-Moore algorithm, it uses the `skipTable` to skip ahead a number of characters. The difference is in how we check partial matches. In the above version, it a partial match is found but it's not a complete match, we skip ahead by just one character. In this revised version, we also use the skip table in that situation.
 
-Boyer–Moore–Horspool algorithm works as follows:
+Here's an implementation of the Boyer-Moore-Horspool algorithm:
 
 ```swift
 extension String {
-  public func indexOf(pattern: String) -> String.Index?
-  {
+  public func indexOf(pattern: String) -> String.Index? {
     let patternLength = pattern.characters.count
     assert(patternLength > 0)
     assert(patternLength <= self.characters.count)
@@ -179,4 +180,8 @@ extension String {
 }
 ```
 
+In practice, the Horspool version of the algorithm tends to perform a little better than the original. However, it depends on the tradeoffs you're willing to make.
+
 Credits: This code is based on the paper: [R. N. Horspool (1980). "Practical fast searching in strings". Software - Practice & Experience 10 (6): 501–506.](http://www.cin.br/~paguso/courses/if767/bib/Horspool_1980.pdf)
+
+*Written for Swift Algorithm Club by Matthijs Hollemans*

From 513fbe6f9183c44c1f5506b2fba16ad97327ef17 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Mon, 4 Apr 2016 16:19:49 +0200
Subject: [PATCH 0213/1679] README and TODO: claiming Bucket Sort

---
 Bucket Sort/README.markdown | 4 ++++
 1 file changed, 4 insertions(+)
 create mode 100644 Bucket Sort/README.markdown

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
new file mode 100644
index 000000000..8f5183f0e
--- /dev/null
+++ b/Bucket Sort/README.markdown	
@@ -0,0 +1,4 @@
+# Bucket Sort
+
+TODO: Implementation in progress
+

From 2200f37c2e88aa1934540f68b7997e727732d0f6 Mon Sep 17 00:00:00 2001
From: Keita Ito <keitaitok@gmail.com>
Date: Mon, 4 Apr 2016 18:09:16 -0700
Subject: [PATCH 0214/1679] Fix typo

---
 Binary Search Tree/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 54468070b..483e75a58 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -428,7 +428,7 @@ We won't need it for deleting, but for completeness' sake, here is the opposite
 
 It returns the rightmost descendent of the node. We find it by following `right` pointers until we get to the end. In the above example, the rightmost descendent of node `2` is `5`. The maximum value in the entire tree is `11`, because that is the rightmost descendent of the root node `7`.
 
-Finally, we can write the code the remove a node from the tree:
+Finally, we can write the code that removes a node from the tree:
 
 ```swift
   public func remove() -> BinarySearchTree? {
@@ -670,7 +670,7 @@ The enum has three cases:
 
 > **Note:** The nodes in this binary tree don't have a reference to their parent node. It's not a major impediment but it will make certain operations slightly more cumbersome to implement.
 
-A usual, we'll implement most functionality recursively. We'll treat each case of the enum slightly differently. For example, this is how you could calculate the number of nodes in the tree and the height of the tree:
+As usual, we'll implement most functionality recursively. We'll treat each case of the enum slightly differently. For example, this is how you could calculate the number of nodes in the tree and the height of the tree:
 
 ```swift
   public var count: Int {

From 60f72b02e945939bfa4dfad1f56b6ba1342c2c3a Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Wed, 6 Apr 2016 14:19:06 +0200
Subject: [PATCH 0215/1679] Bucket sort algorith: playground, implementation
 and tests

---
 .../BucketSort.playground/Contents.swift      |  46 ++++
 .../Sources/BucketSort.swift                  | 144 ++++++++++
 .../contents.xcplayground                     |   4 +
 Bucket Sort/BucketSort.swift                  | 170 ++++++++++++
 .../Test/Test.xcodeproj/project.pbxproj       | 260 ++++++++++++++++++
 Bucket Sort/Test/TestTests/Info.plist         |  24 ++
 Bucket Sort/Test/TestTests/Test.swift         |  98 +++++++
 7 files changed, 746 insertions(+)
 create mode 100644 Bucket Sort/BucketSort.playground/Contents.swift
 create mode 100644 Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
 create mode 100644 Bucket Sort/BucketSort.playground/contents.xcplayground
 create mode 100644 Bucket Sort/BucketSort.swift
 create mode 100644 Bucket Sort/Test/Test.xcodeproj/project.pbxproj
 create mode 100644 Bucket Sort/Test/TestTests/Info.plist
 create mode 100644 Bucket Sort/Test/TestTests/Test.swift

diff --git a/Bucket Sort/BucketSort.playground/Contents.swift b/Bucket Sort/BucketSort.playground/Contents.swift
new file mode 100644
index 000000000..32cd6ed29
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/Contents.swift	
@@ -0,0 +1,46 @@
+//
+//  BucketSort.playground
+//
+//  Created by Barbara Rodeker on 4/4/16.
+//
+//  Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
+//  associated documentation files (the "Software"), to deal in the Software without restriction, including
+//  without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//  copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the
+//  following conditions:
+//
+//  The above copyright notice and this permission notice shall be included in all copies or substantial
+//  portions of the Software.
+//
+//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
+//  LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
+//  EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+//  AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
+//  OR OTHER DEALINGS IN THE SOFTWARE.
+//
+//
+
+
+
+
+//////////////////////////////////////
+// MARK: Extensions
+//////////////////////////////////////
+
+extension Int: IntConvertible, Sortable {
+    public func toInt() -> Int {
+        return self
+    }
+}
+
+//////////////////////////////////////
+// MARK: Playing code
+//////////////////////////////////////
+
+let input = [1,2,4,6,10]
+let buckets = [Bucket<Int>(capacity: 15),Bucket<Int>(capacity: 15),Bucket<Int>(capacity: 15)]
+
+let sortedElements = bucketSort(input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
+
+print(sortedElements)
+
diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
new file mode 100644
index 000000000..8dfa80cd4
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -0,0 +1,144 @@
+//
+//  BucketSort.swift
+//
+//  Created by Barbara Rodeker on 4/4/16.
+//
+//  Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
+//  associated documentation files (the "Software"), to deal in the Software without restriction, including
+//  without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//  copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the
+//  following conditions:
+//
+//  The above copyright notice and this permission notice shall be included in all copies or substantial
+//  portions of the Software.
+//
+//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
+//  LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
+//  EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+//  AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
+//  OR OTHER DEALINGS IN THE SOFTWARE.
+//
+//
+
+import Foundation
+
+//////////////////////////////////////
+// MARK: Main algorithm
+//////////////////////////////////////
+
+
+public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+  var bucketsCopy = buckets
+  for elem in elements {
+    distributor.distribute(elem, buckets: &bucketsCopy)
+  }
+  
+  var results = [T]()
+  
+  for bucket in buckets {
+    results += bucket.sort(sorter)
+  }
+  
+  return results
+}
+
+//////////////////////////////////////
+// MARK: Distributor
+//////////////////////////////////////
+
+
+public protocol Distributor {
+  func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
+}
+
+/*
+ * An example of a simple distribution function that send every elements to
+ * the bucket representing the range in which it fits.An
+ *
+ * If the range of values to sort is 0..<49 i.e, there could be 5 buckets of capacity = 10
+ * So every element will be classified by the ranges:
+ *
+ * -  0 ..< 10
+ * - 10 ..< 20
+ * - 20 ..< 30
+ * - 30 ..< 40
+ * - 40 ..< 50
+ *
+ * By following the formula: element / capacity = #ofBucket
+ */
+public struct RangeDistributor: Distributor {
+  
+  public init() {}
+  
+  public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
+    let value = element.toInt()
+    let bucketCapacity = buckets.first!.capacity
+    
+    let bucketIndex = value / bucketCapacity
+    buckets[bucketIndex].add(element)
+  }
+}
+
+//////////////////////////////////////
+// MARK: Sortable
+//////////////////////////////////////
+
+public protocol IntConvertible {
+  func toInt() -> Int
+}
+
+public protocol Sortable: IntConvertible, Comparable {
+}
+
+//////////////////////////////////////
+// MARK: Sorter
+//////////////////////////////////////
+
+public protocol Sorter {
+  func sort<T:Sortable>(items: [T]) -> [T]
+}
+
+public struct InsertionSorter: Sorter {
+  
+  public init() {}
+  
+  public func sort<T:Sortable>(items: [T]) -> [T] {
+    var results = items
+    for i in 0 ..< results.count {
+      var j = i
+      while ( j > 0 && results[j-i] > results[j]) {
+        
+        let auxiliar = results[i]
+        results[i] = results[j]
+        results[j] = auxiliar
+        
+        j -= 1
+      }
+    }
+    return results
+  }
+}
+
+//////////////////////////////////////
+// MARK: Bucket
+//////////////////////////////////////
+
+public struct Bucket<T:Sortable> {
+  var elements: [T]
+  let capacity: Int
+  
+  public init(capacity: Int) {
+    self.capacity = capacity
+    elements = [T]()
+  }
+  
+  public mutating func add(item: T) {
+    if (elements.count < capacity) {
+      elements.append(item)
+    }
+  }
+  
+  public func sort(algorithm: Sorter) -> [T] {
+    return algorithm.sort(elements)
+  }
+}
diff --git a/Bucket Sort/BucketSort.playground/contents.xcplayground b/Bucket Sort/BucketSort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
new file mode 100644
index 000000000..0c75ce40a
--- /dev/null
+++ b/Bucket Sort/BucketSort.swift	
@@ -0,0 +1,170 @@
+//
+//  BucketSort.swift
+//
+//  Created by Barbara Rodeker on 4/4/16.
+//
+//  Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
+//  associated documentation files (the "Software"), to deal in the Software without restriction, including
+//  without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//  copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the
+//  following conditions:
+//
+//  The above copyright notice and this permission notice shall be included in all copies or substantial
+//  portions of the Software.
+//
+//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
+//  LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
+//  EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+//  AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
+//  OR OTHER DEALINGS IN THE SOFTWARE.
+//
+//
+
+import Foundation
+
+//////////////////////////////////////
+// MARK: Main algorithm
+//////////////////////////////////////
+
+
+/**
+    Perform buckets srot algorithm on the given input elements.
+    [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
+ 
+    - Parameter elements:     Array of Sortable elements
+    - Parameter distributor:  Performs the distribution of each element of a bucket
+    - Parameter sorter:       Performs the sorting inside each bucket, after all the elements are distributed
+    - Parameter buckets:      An array of buckets
+ 
+    - Returns: A new array with sorted elements
+ */
+
+public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+    precondition(allPositiveNumbers(elements))
+    precondition(enoughSpaceInBuckets(buckets, elements: elements))
+    
+    var bucketsCopy = buckets
+    for elem in elements {
+        distributor.distribute(elem, buckets: &bucketsCopy)
+    }
+    
+    var results = [T]()
+    
+    for bucket in bucketsCopy {
+        results += bucket.sort(sorter)
+    }
+    
+    return results
+}
+
+private func allPositiveNumbers<T:Sortable>(array: [T]) -> Bool {
+    return array.filter{ $0.toInt() >= 0 }.count > 0
+}
+
+private func enoughSpaceInBuckets<T:Sortable>(buckets: [Bucket<T>], elements: [T]) -> Bool {
+    let maximumValue = elements.maxElement()?.toInt()
+    let totalCapacity = buckets.count * (buckets.first?.capacity)!
+ 
+    return totalCapacity >= maximumValue
+}
+
+//////////////////////////////////////
+// MARK: Distributor
+//////////////////////////////////////
+
+
+public protocol Distributor {
+    func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
+}
+
+/*
+ * An example of a simple distribution function that send every elements to
+ * the bucket representing the range in which it fits.An
+ *
+ * If the range of values to sort is 0..<49 i.e, there could be 5 buckets of capacity = 10
+ * So every element will be classified by the ranges:
+ *
+ * -  0 ..< 10
+ * - 10 ..< 20
+ * - 20 ..< 30
+ * - 30 ..< 40
+ * - 40 ..< 50
+ *
+ * By following the formula: element / capacity = #ofBucket
+ */
+public struct RangeDistributor: Distributor {
+    
+    public init() {}
+    
+    public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
+        let value = element.toInt()
+        let bucketCapacity = buckets.first!.capacity
+        
+        let bucketIndex = value / bucketCapacity
+        buckets[bucketIndex].add(element)
+    }
+}
+
+//////////////////////////////////////
+// MARK: Sortable
+//////////////////////////////////////
+
+public protocol IntConvertible {
+    func toInt() -> Int
+}
+
+public protocol Sortable: IntConvertible, Comparable {
+}
+
+//////////////////////////////////////
+// MARK: Sorter
+//////////////////////////////////////
+
+public protocol Sorter {
+    func sort<T:Sortable>(items: [T]) -> [T]
+}
+
+public struct InsertionSorter: Sorter {
+    
+    public init() {}
+    
+    public func sort<T:Sortable>(items: [T]) -> [T] {
+        var results = items
+        for i in 0 ..< results.count {
+            var j = i
+            while ( j > 0 && results[j-1] > results[j]) {
+                
+                let auxiliar = results[j-1]
+                results[j-1] = results[j]
+                results[j] = auxiliar
+                
+                j -= 1
+            }
+        }
+        return results
+    }
+}
+
+//////////////////////////////////////
+// MARK: Bucket
+//////////////////////////////////////
+
+public struct Bucket<T:Sortable> {
+    var elements: [T]
+    let capacity: Int
+    
+    public init(capacity: Int) {
+        self.capacity = capacity
+        elements = [T]()
+    }
+    
+    public mutating func add(item: T) {
+        if (elements.count < capacity) {
+            elements.append(item)
+        }
+    }
+    
+    public func sort(algorithm: Sorter) -> [T] {
+        return algorithm.sort(elements)
+    }
+}
diff --git a/Bucket Sort/Test/Test.xcodeproj/project.pbxproj b/Bucket Sort/Test/Test.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..f39678cf2
--- /dev/null
+++ b/Bucket Sort/Test/Test.xcodeproj/project.pbxproj	
@@ -0,0 +1,260 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		761476CC1CB51A8400E00457 /* BucketSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 761476CB1CB51A8400E00457 /* BucketSort.swift */; };
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+/* End PBXBuildFile section */
+
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+		768EBC121CB4E97900D5A78A /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
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+		76CC7DBC1CB41D07003398A8 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
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+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		76CC7D991CB41D03003398A8 = {
+			isa = PBXGroup;
+			children = (
+				76CC7DB91CB41D07003398A8 /* Tests */,
+				768EBC121CB4E97900D5A78A /* Tests.xctest */,
+			);
+			sourceTree = "<group>";
+		};
+		76CC7DB91CB41D07003398A8 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				761476CB1CB51A8400E00457 /* BucketSort.swift */,
+				76CC7DBA1CB41D07003398A8 /* Test.swift */,
+				76CC7DBC1CB41D07003398A8 /* Info.plist */,
+			);
+			name = Tests;
+			path = TestTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
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+				76CC7DB31CB41D07003398A8 /* Frameworks */,
+				76CC7DB41CB41D07003398A8 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestTests;
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+			productType = "com.apple.product-type.bundle.unit-test";
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+/* End PBXNativeTarget section */
+
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+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0730;
+				LastUpgradeCheck = 0730;
+				ORGANIZATIONNAME = "Barbara M. Rodeker";
+				TargetAttributes = {
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+						CreatedOnToolsVersion = 7.3;
+						DevelopmentTeam = 6V43LV5QCY;
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+					};
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+			};
+			buildConfigurationList = 76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Test" */;
+			compatibilityVersion = "Xcode 3.2";
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+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 76CC7D991CB41D03003398A8;
+			productRefGroup = 76CC7D991CB41D03003398A8;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				76CC7DB51CB41D07003398A8 /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		76CC7DB41CB41D07003398A8 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		76CC7DB21CB41D07003398A8 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				76CC7DBB1CB41D07003398A8 /* Test.swift in Sources */,
+				761476CC1CB51A8400E00457 /* BucketSort.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		76CC7DBD1CB41D07003398A8 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = iphoneos;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		76CC7DBE1CB41D07003398A8 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = iphoneos;
+				VALIDATE_PRODUCT = YES;
+			};
+			name = Release;
+		};
+		76CC7DC31CB41D07003398A8 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "";
+				INFOPLIST_FILE = TestTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
+			};
+			name = Debug;
+		};
+		76CC7DC41CB41D07003398A8 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "";
+				INFOPLIST_FILE = TestTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Test" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				76CC7DBD1CB41D07003398A8 /* Debug */,
+				76CC7DBE1CB41D07003398A8 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		76CC7DC21CB41D07003398A8 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				76CC7DC31CB41D07003398A8 /* Debug */,
+				76CC7DC41CB41D07003398A8 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 76CC7D9A1CB41D03003398A8 /* Project object */;
+}
diff --git a/Bucket Sort/Test/TestTests/Info.plist b/Bucket Sort/Test/TestTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Bucket Sort/Test/TestTests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Bucket Sort/Test/TestTests/Test.swift b/Bucket Sort/Test/TestTests/Test.swift
new file mode 100644
index 000000000..f3b897b2b
--- /dev/null
+++ b/Bucket Sort/Test/TestTests/Test.swift	
@@ -0,0 +1,98 @@
+//
+//  TestTests.swift
+//  TestTests
+//
+//  Created by Barbara Rodeker on 4/5/16.
+//  Copyright © 2016 Barbara M. Rodeker. All rights reserved.
+//
+
+import XCTest
+
+class TestTests: XCTestCase {
+    
+    var smallArray: [Int]?
+
+    let total = 400
+    let maximum = 1000
+    var largeArray: [Int]?
+    
+    var sparsedArray: [Int]?
+    
+    override func setUp() {
+        super.setUp()
+        
+        smallArray = [8,3,33,0,12,8,2,18]
+        
+        largeArray = [Int]()
+        for _ in 0..<total {
+            largeArray!.append( random() % maximum )
+        }
+        
+        sparsedArray = [Int]()
+        sparsedArray = [10,400,1500,500]
+    }
+    
+    override func tearDown() {
+        // Put teardown code here. This method is called after the invocation of each test method in the class.
+        super.tearDown()
+    }
+    
+    func testSmallArray() {
+        
+        let results = performBucketSort(smallArray!, totalBuckets: 3)
+        XCTAssert(isSorted(results))
+    }
+
+    func testBigArray() {
+        
+        let results = performBucketSort(largeArray!, totalBuckets: 8)
+        XCTAssert(isSorted(results))
+    }
+    
+    func testSparsedArray() {
+        
+        let results = performBucketSort(sparsedArray!, totalBuckets: 3)
+        XCTAssert(isSorted(results))
+    }
+    
+    // MARK: Private functions
+    
+    private func performBucketSort(elements: [Int], totalBuckets: Int) -> [Int] {
+
+        let value = (elements.maxElement()?.toInt())! + 1
+        let capacityRequired = Int( ceil( Double(value) / Double(totalBuckets) ) )
+        
+        var buckets = [Bucket<Int>]()
+        for _ in 0..<totalBuckets {
+            buckets.append(Bucket<Int>(capacity: capacityRequired))
+        }
+        
+        let results = bucketSort(smallArray!, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
+        return results
+    }
+    
+    func isSorted(array: [Int]) -> Bool {
+        
+        var index = 0
+        var sorted = true
+        while index < (array.count - 1) && sorted {
+            if (array[index] > array[index+1]) {
+                sorted = false
+            }
+            index += 1
+        }
+        
+        return sorted
+    }
+}
+
+
+//////////////////////////////////////
+// MARK: Extensions
+//////////////////////////////////////
+
+extension Int: IntConvertible, Sortable {
+    public func toInt() -> Int {
+        return self
+    }
+}

From d63e27bcf117100bbb51544ed5b354d86c08c090 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Wed, 6 Apr 2016 14:22:34 +0200
Subject: [PATCH 0216/1679] Adding Wikibook about Algorithms

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index f7ff7833b..21503d87d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -197,6 +197,7 @@ The following books are available for free online:
 - [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
 - [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
 - Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
+- [Wikibooks: Algorithms and Implementations](https://en.wikibooks.org/wiki/Algorithm_Implementation)
 
 Other algorithm repositories:
 

From 04da8e04ca933304a5d06b2527e09f1ebf69fd0e Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Wed, 6 Apr 2016 14:33:41 +0200
Subject: [PATCH 0217/1679] Renaming Test to Tests. Configuring schemes for
 Travis CI

---
 .../Tests.xcodeproj}/project.pbxproj          | 31 +++++-----
 .../xcshareddata/xcschemes/Tests.xcscheme     | 56 +++++++++++++++++++
 .../TestTests => Tests/Tests}/Info.plist      |  0
 .../Test.swift => Tests/Tests/Tests.swift}    |  0
 4 files changed, 72 insertions(+), 15 deletions(-)
 rename Bucket Sort/{Test/Test.xcodeproj => Tests/Tests.xcodeproj}/project.pbxproj (82%)
 create mode 100644 Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 rename Bucket Sort/{Test/TestTests => Tests/Tests}/Info.plist (100%)
 rename Bucket Sort/{Test/TestTests/Test.swift => Tests/Tests/Tests.swift} (100%)

diff --git a/Bucket Sort/Test/Test.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
similarity index 82%
rename from Bucket Sort/Test/Test.xcodeproj/project.pbxproj
rename to Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index f39678cf2..3457e90ba 100644
--- a/Bucket Sort/Test/Test.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -8,14 +8,15 @@
 
 /* Begin PBXBuildFile section */
 		761476CC1CB51A8400E00457 /* BucketSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 761476CB1CB51A8400E00457 /* BucketSort.swift */; };
-		76CC7DBB1CB41D07003398A8 /* Test.swift in Sources */ = {isa = PBXBuildFile; fileRef = 76CC7DBA1CB41D07003398A8 /* Test.swift */; };
+		762141891CB538BC00CD552E /* Info.plist in Resources */ = {isa = PBXBuildFile; fileRef = 762141871CB538BC00CD552E /* Info.plist */; };
+		7621418A1CB538BC00CD552E /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 762141881CB538BC00CD552E /* Tests.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
 		761476CB1CB51A8400E00457 /* BucketSort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BucketSort.swift; path = ../../BucketSort.swift; sourceTree = "<group>"; };
-		768EBC121CB4E97900D5A78A /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
-		76CC7DBA1CB41D07003398A8 /* Test.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Test.swift; sourceTree = "<group>"; };
-		76CC7DBC1CB41D07003398A8 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		762141871CB538BC00CD552E /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; name = Info.plist; path = Tests/Info.plist; sourceTree = SOURCE_ROOT; };
+		762141881CB538BC00CD552E /* Tests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Tests.swift; path = Tests/Tests.swift; sourceTree = SOURCE_ROOT; };
+		7621418B1CB5390E00CD552E /* Tests.temp_caseinsensitive_rename.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; name = Tests.temp_caseinsensitive_rename.xctest; path = "/Users/barbararodeker/Desktop/Projects/SwiftAlgorithms/swift-algorithm-club/Bucket Sort/Tests/build/Debug-iphoneos/Tests.temp_caseinsensitive_rename.xctest"; sourceTree = "<absolute>"; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -33,7 +34,6 @@
 			isa = PBXGroup;
 			children = (
 				76CC7DB91CB41D07003398A8 /* Tests */,
-				768EBC121CB4E97900D5A78A /* Tests.xctest */,
 			);
 			sourceTree = "<group>";
 		};
@@ -41,8 +41,8 @@
 			isa = PBXGroup;
 			children = (
 				761476CB1CB51A8400E00457 /* BucketSort.swift */,
-				76CC7DBA1CB41D07003398A8 /* Test.swift */,
-				76CC7DBC1CB41D07003398A8 /* Info.plist */,
+				762141881CB538BC00CD552E /* Tests.swift */,
+				762141871CB538BC00CD552E /* Info.plist */,
 			);
 			name = Tests;
 			path = TestTests;
@@ -65,7 +65,7 @@
 			);
 			name = Tests;
 			productName = TestTests;
-			productReference = 768EBC121CB4E97900D5A78A /* Tests.xctest */;
+			productReference = 7621418B1CB5390E00CD552E /* Tests.temp_caseinsensitive_rename.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -85,7 +85,7 @@
 					};
 				};
 			};
-			buildConfigurationList = 76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Test" */;
+			buildConfigurationList = 76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Tests" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -108,6 +108,7 @@
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				762141891CB538BC00CD552E /* Info.plist in Resources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -118,7 +119,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				76CC7DBB1CB41D07003398A8 /* Test.swift in Sources */,
+				7621418A1CB538BC00CD552E /* Tests.swift in Sources */,
 				761476CC1CB51A8400E00457 /* BucketSort.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
@@ -213,10 +214,10 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "";
-				INFOPLIST_FILE = TestTests/Info.plist;
+				INFOPLIST_FILE = Tests/Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
+				PRODUCT_NAME = Tests.temp_caseinsensitive_rename;
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
 			};
 			name = Debug;
@@ -225,10 +226,10 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "";
-				INFOPLIST_FILE = TestTests/Info.plist;
+				INFOPLIST_FILE = Tests/Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
-				PRODUCT_NAME = "$(TARGET_NAME)";
+				PRODUCT_NAME = Tests.temp_caseinsensitive_rename;
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
 			};
 			name = Release;
@@ -236,7 +237,7 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Test" */ = {
+		76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				76CC7DBD1CB41D07003398A8 /* Debug */,
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..574e1d2ea
--- /dev/null
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "76CC7DB51CB41D07003398A8"
+               BuildableName = "Tests.temp_caseinsensitive_rename.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Bucket Sort/Test/TestTests/Info.plist b/Bucket Sort/Tests/Tests/Info.plist
similarity index 100%
rename from Bucket Sort/Test/TestTests/Info.plist
rename to Bucket Sort/Tests/Tests/Info.plist
diff --git a/Bucket Sort/Test/TestTests/Test.swift b/Bucket Sort/Tests/Tests/Tests.swift
similarity index 100%
rename from Bucket Sort/Test/TestTests/Test.swift
rename to Bucket Sort/Tests/Tests/Tests.swift

From 25a99a4b1620064dabc951f9856d6809e52fa06e Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Wed, 6 Apr 2016 14:34:07 +0200
Subject: [PATCH 0218/1679] Configuring scheme for Travis CI

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 3a2bcb7b2..a980968be 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -23,3 +23,4 @@ script:
 - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
\ No newline at end of file

From 9bf7a10b478c128c59c03e1400a8891ff641c418 Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Wed, 6 Apr 2016 18:34:08 -0400
Subject: [PATCH 0219/1679] added constructing

---
 README.markdown            |   2 +-
 README.markdown~           | 211 +++++++++++++++++++++++++++++++++++++
 Red Black Trees/README.md  |   8 ++
 Red Black Trees/README.md~ |   0
 4 files changed, 220 insertions(+), 1 deletion(-)
 create mode 100644 README.markdown~
 create mode 100644 Red Black Trees/README.md
 create mode 100644 Red Black Trees/README.md~

diff --git a/README.markdown b/README.markdown
index 5746d8960..d37a929d5 100644
--- a/README.markdown
+++ b/README.markdown
@@ -143,7 +143,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- Red-Black Tree
+- [Red-Black Tree](Red\ Black\ Tree/) :construction:
 - Splay Tree
 - Threaded Binary Tree
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
diff --git a/README.markdown~ b/README.markdown~
new file mode 100644
index 000000000..5746d8960
--- /dev/null
+++ b/README.markdown~
@@ -0,0 +1,211 @@
+# Welcome to the Swift Algorithm Club!
+
+Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.
+
+If you're a computer science student who needs to learn this stuff for exams -- or if you're a self-taught programmer who wants to brush up on the theory behind your craft -- you've come to the right place!
+
+The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
+
+All code is compatible with **Xcode 7.3** and **Swift 2.2**. We'll keep this updated with the latest version of Swift.
+
+This is a work in progress. More algorithms will be added soon. :-) 
+
+:heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
+
+## Important links
+
+[What are algorithms and data structures?](What are Algorithms.markdown) Pancakes!
+
+[Why learn algorithms?](Why Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
+
+[Big-O notation](Big-O Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
+
+[Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
+
+[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
+
+## Where to start?
+
+If you're new to algorithms and data structures, here are a few good ones to start out with:
+
+- [Stack](Stack/)
+- [Queue](Queue/)
+- [Insertion Sort](Insertion Sort/)
+- [Binary Search](Binary Search/) and [Binary Search Tree](Binary Search Tree/)
+- [Merge Sort](Merge Sort/)
+- [Boyer-Moore string search](Boyer-Moore/)
+
+## The algorithms
+
+### Searching
+
+- [Linear Search](Linear Search/). Find an element in an array.
+- [Binary Search](Binary Search/). Quickly find elements in a sorted array.
+- [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
+- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
+- [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
+- [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
+- [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
+
+### String Search
+
+- [Brute-Force String Search](Brute-Force String Search/). A naive method.
+- [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
+- Rabin-Karp
+- [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
+
+### Sorting
+
+It's fun to see how sorting algorithms work, but in practice you'll almost never have to provide your own sorting routines. Swift's own `sort()` is more than up to the job. But if you're curious, read on...
+
+Basic sorts:
+
+- [Insertion Sort](Insertion Sort/)
+- [Selection Sort](Selection Sort/)
+- [Shell Sort](Shell Sort/)
+
+Fast sorts:
+
+- [Quicksort](Quicksort/)
+- [Merge Sort](Merge Sort/)
+- [Heap Sort](Heap Sort/)
+
+Special-purpose sorts:
+
+- Bucket Sort
+- Counting Sort
+- Radix Sort
+- [Topological Sort](Topological Sort/)
+
+Bad sorting algorithms (don't use these!):
+
+- [Bubble Sort](Bubble Sort/)
+
+### Compression
+
+- [Run-Length Encoding (RLE)](Run-Length Encoding/). Store repeated values as a single byte and a count.
+- [Huffman Coding](Huffman Coding/). Store more common elements using a smaller number of bits.
+
+### Miscellaneous
+
+- [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
+
+### Mathematics
+
+- [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
+- [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
+- [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
+- Statistics
+
+### Machine learning
+
+- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
+- k-Nearest Neighbors
+- Linear Regression
+- Logistic Regression
+- Neural Networks
+- PageRank
+
+## Data structures
+
+The choice of data structure for a particular task depends on a few things.
+
+First, there is the shape of your data and the kinds of operations that you'll need to perform on it. If you want to look up objects by a key you need some kind of dictionary; if your data is hierarchical in nature you want a tree structure of some sort; if your data is sequential you want a stack or queue.
+
+Second, it matters what particular operations you'll be performing most, as certain data structures are optimized for certain actions. For example, if you often need to find the most important object in a collection, then a heap or priority queue is more optimal than a plain array.
+
+Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types is sufficient, but sometimes you may want something more fancy...
+
+### Variations on arrays
+
+- [Array2D](Array2D/). A two-dimensional array with fixed dimensions. Useful for board games.
+- [Bit Set](Bit Set/). A fixed-size sequence of *n* bits.
+- [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
+- [Ordered Array](Ordered Array/). An array that is always sorted.
+
+### Queues
+
+- [Stack](Stack/). Last-in, first-out!
+- [Queue](Queue/). First-in, first-out!
+- [Deque](Deque/). A double-ended queue.
+- [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
+- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements. :construction:
+- [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
+
+### Lists
+
+- [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
+- Skip List
+
+### Trees
+
+- [Tree](Tree/). A general-purpose tree structure.
+- [Binary Tree](Binary Tree/). A tree where each node has at most two children.
+- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
+- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
+- Red-Black Tree
+- Splay Tree
+- Threaded Binary Tree
+- [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
+- kd-Tree
+- [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
+- Fibonacci Heap
+- Trie
+- [B-Tree](B Tree/) :construction:
+
+### Hashing
+
+- [Hash Table](Hash Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
+- Hash Functions
+
+### Sets
+
+- [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
+- [Hash Set](Hash Set/). A set implemented using a hash table.
+- Multiset
+- Ordered Set
+
+### Graphs
+
+- [Graph](Graph/)
+- [Breadth-First Search (BFS)](Breadth-First Search/)
+- [Depth-First Search (DFS)](Depth-First Search/)
+- [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
+- [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
+- All Paths
+
+## Puzzles
+
+A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see [here](http://elementsofprogramminginterviews.com/) and [here](http://www.crackingthecodinginterview.com).
+
+- [Two-Sum Problem](Two-Sum Problem/)
+- [Fizz Buzz](Fizz Buzz/)
+- [Monty Hall Problem](Monty Hall Problem/)
+
+## Learn more!
+
+For more information, check out these great books:
+
+- [Introduction to Algorithms](https://mitpress.mit.edu/books/introduction-algorithms) by Cormen, Leiserson, Rivest, Stein
+- [The Algorithm Design Manual](http://www.algorist.com) by Skiena
+- [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
+- [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
+
+The following books are available for free online:
+
+- [Algorithms](http://www.beust.com/algorithms.pdf) by Dasgupta, Papadimitriou, Vazirani
+- [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
+- [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
+- Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
+
+Other algorithm repositories:
+
+- [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
+- [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
+- [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
+
+## License
+
+All content is licensed under the terms of the MIT open source license.
+
+[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)
diff --git a/Red Black Trees/README.md b/Red Black Trees/README.md
new file mode 100644
index 000000000..6747154b8
--- /dev/null
+++ b/Red Black Trees/README.md	
@@ -0,0 +1,8 @@
+# Red Black Tree
+
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).
+
+*Written for the Swift Algorithm Club by Ashwin Raghuraman*
+
diff --git a/Red Black Trees/README.md~ b/Red Black Trees/README.md~
new file mode 100644
index 000000000..e69de29bb

From 8637316da3d84417c9f889e311ae85c33f7f86a2 Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Wed, 6 Apr 2016 20:52:25 -0400
Subject: [PATCH 0220/1679] Started Red Black Trees

---
 Red Black Trees/RBTree.swift | 86 ++++++++++++++++++++++++++++++++++++
 1 file changed, 86 insertions(+)
 create mode 100644 Red Black Trees/RBTree.swift

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
new file mode 100644
index 000000000..12f97b21f
--- /dev/null
+++ b/Red Black Trees/RBTree.swift	
@@ -0,0 +1,86 @@
+public class RBTNode {
+    var color: Int?
+    var left: RBTNode?
+    var right: RBTNode?
+    var parent: RBTNode?
+    var data: Int
+
+    init(data: Int) {
+        self.data = data
+        self.left = nil
+        self.right = nil
+        self.parent = nil
+        self.color = nil
+    }
+
+    public var isLeaf: Bool {
+    return left == nil && right == nil
+  }
+
+  public var isLeftChild: Bool {
+    return parent?.left === self
+  }
+
+  public var isRightChild: Bool {
+    return parent?.right === self
+  }
+
+  public var hasLeftChild: Bool {
+    return left != nil
+  }
+
+  public var hasRightChild: Bool {
+    return right != nil
+  }
+
+  public var hasAnyChild: Bool {
+    return hasLeftChild || hasRightChild
+  }
+
+  public var hasBothChildren: Bool {
+    return hasLeftChild && hasRightChild
+  }
+}
+
+extension RBTNode {
+  public func insert(value: Int) {
+    insert(value, parent: self)
+  }
+  private func insert(value: Int, parent: RBTNode) {
+    if value < self.data {
+      if let left = left {
+        left.insert(value, parent: left)
+      } else {
+        left = RBTNode(data: value)
+        left?.parent = parent
+      }
+    } else {
+      if let right = right {
+        right.insert(value, parent: right)
+      } else {
+        right = RBTNode(data: value)
+        right?.parent = parent
+      }
+    }
+  }
+}
+extension RBTNode{
+  public func inOrder(root: RBTNode?){
+    if(root == nil){
+      return
+    }
+    inOrder(root!.left)
+    print(root!.data)
+    inOrder(root!.right)
+  }
+}
+
+var me = RBTNode(data: 5)
+var me2 = RBTNode(data: 6)
+
+me.insert(4)
+me.insert(3)
+me.insert(2)
+me.insert(1)
+me.insert(0)
+me.inOrder(me) //stupid way to call this

From 9968b2021d3e1840d7ff9d6270a1b9b8022bd6ca Mon Sep 17 00:00:00 2001
From: Jayson Tung <JFTung@users.noreply.github.com>
Date: Fri, 8 Apr 2016 14:00:49 -0400
Subject: [PATCH 0221/1679] Delete redundant README

---
 README.markdown~ | 211 -----------------------------------------------
 1 file changed, 211 deletions(-)
 delete mode 100644 README.markdown~

diff --git a/README.markdown~ b/README.markdown~
deleted file mode 100644
index 5746d8960..000000000
--- a/README.markdown~
+++ /dev/null
@@ -1,211 +0,0 @@
-# Welcome to the Swift Algorithm Club!
-
-Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.
-
-If you're a computer science student who needs to learn this stuff for exams -- or if you're a self-taught programmer who wants to brush up on the theory behind your craft -- you've come to the right place!
-
-The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
-
-All code is compatible with **Xcode 7.3** and **Swift 2.2**. We'll keep this updated with the latest version of Swift.
-
-This is a work in progress. More algorithms will be added soon. :-) 
-
-:heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
-
-## Important links
-
-[What are algorithms and data structures?](What are Algorithms.markdown) Pancakes!
-
-[Why learn algorithms?](Why Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
-
-[Big-O notation](Big-O Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
-
-[Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
-
-[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
-
-## Where to start?
-
-If you're new to algorithms and data structures, here are a few good ones to start out with:
-
-- [Stack](Stack/)
-- [Queue](Queue/)
-- [Insertion Sort](Insertion Sort/)
-- [Binary Search](Binary Search/) and [Binary Search Tree](Binary Search Tree/)
-- [Merge Sort](Merge Sort/)
-- [Boyer-Moore string search](Boyer-Moore/)
-
-## The algorithms
-
-### Searching
-
-- [Linear Search](Linear Search/). Find an element in an array.
-- [Binary Search](Binary Search/). Quickly find elements in a sorted array.
-- [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
-- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
-- [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
-- [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
-- [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
-
-### String Search
-
-- [Brute-Force String Search](Brute-Force String Search/). A naive method.
-- [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
-- Rabin-Karp
-- [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
-
-### Sorting
-
-It's fun to see how sorting algorithms work, but in practice you'll almost never have to provide your own sorting routines. Swift's own `sort()` is more than up to the job. But if you're curious, read on...
-
-Basic sorts:
-
-- [Insertion Sort](Insertion Sort/)
-- [Selection Sort](Selection Sort/)
-- [Shell Sort](Shell Sort/)
-
-Fast sorts:
-
-- [Quicksort](Quicksort/)
-- [Merge Sort](Merge Sort/)
-- [Heap Sort](Heap Sort/)
-
-Special-purpose sorts:
-
-- Bucket Sort
-- Counting Sort
-- Radix Sort
-- [Topological Sort](Topological Sort/)
-
-Bad sorting algorithms (don't use these!):
-
-- [Bubble Sort](Bubble Sort/)
-
-### Compression
-
-- [Run-Length Encoding (RLE)](Run-Length Encoding/). Store repeated values as a single byte and a count.
-- [Huffman Coding](Huffman Coding/). Store more common elements using a smaller number of bits.
-
-### Miscellaneous
-
-- [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
-
-### Mathematics
-
-- [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
-- [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
-- [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
-- Statistics
-
-### Machine learning
-
-- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
-- k-Nearest Neighbors
-- Linear Regression
-- Logistic Regression
-- Neural Networks
-- PageRank
-
-## Data structures
-
-The choice of data structure for a particular task depends on a few things.
-
-First, there is the shape of your data and the kinds of operations that you'll need to perform on it. If you want to look up objects by a key you need some kind of dictionary; if your data is hierarchical in nature you want a tree structure of some sort; if your data is sequential you want a stack or queue.
-
-Second, it matters what particular operations you'll be performing most, as certain data structures are optimized for certain actions. For example, if you often need to find the most important object in a collection, then a heap or priority queue is more optimal than a plain array.
-
-Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types is sufficient, but sometimes you may want something more fancy...
-
-### Variations on arrays
-
-- [Array2D](Array2D/). A two-dimensional array with fixed dimensions. Useful for board games.
-- [Bit Set](Bit Set/). A fixed-size sequence of *n* bits.
-- [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
-- [Ordered Array](Ordered Array/). An array that is always sorted.
-
-### Queues
-
-- [Stack](Stack/). Last-in, first-out!
-- [Queue](Queue/). First-in, first-out!
-- [Deque](Deque/). A double-ended queue.
-- [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
-- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements. :construction:
-- [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
-
-### Lists
-
-- [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
-- Skip List
-
-### Trees
-
-- [Tree](Tree/). A general-purpose tree structure.
-- [Binary Tree](Binary Tree/). A tree where each node has at most two children.
-- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
-- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- Red-Black Tree
-- Splay Tree
-- Threaded Binary Tree
-- [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
-- kd-Tree
-- [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
-- Fibonacci Heap
-- Trie
-- [B-Tree](B Tree/) :construction:
-
-### Hashing
-
-- [Hash Table](Hash Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
-- Hash Functions
-
-### Sets
-
-- [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
-- [Hash Set](Hash Set/). A set implemented using a hash table.
-- Multiset
-- Ordered Set
-
-### Graphs
-
-- [Graph](Graph/)
-- [Breadth-First Search (BFS)](Breadth-First Search/)
-- [Depth-First Search (DFS)](Depth-First Search/)
-- [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
-- [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
-- All Paths
-
-## Puzzles
-
-A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see [here](http://elementsofprogramminginterviews.com/) and [here](http://www.crackingthecodinginterview.com).
-
-- [Two-Sum Problem](Two-Sum Problem/)
-- [Fizz Buzz](Fizz Buzz/)
-- [Monty Hall Problem](Monty Hall Problem/)
-
-## Learn more!
-
-For more information, check out these great books:
-
-- [Introduction to Algorithms](https://mitpress.mit.edu/books/introduction-algorithms) by Cormen, Leiserson, Rivest, Stein
-- [The Algorithm Design Manual](http://www.algorist.com) by Skiena
-- [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
-- [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
-
-The following books are available for free online:
-
-- [Algorithms](http://www.beust.com/algorithms.pdf) by Dasgupta, Papadimitriou, Vazirani
-- [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
-- [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
-- Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
-
-Other algorithm repositories:
-
-- [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
-- [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
-- [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
-
-## License
-
-All content is licensed under the terms of the MIT open source license.
-
-[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)

From adaf239ef056d34e85378da303f497f0e3b69b23 Mon Sep 17 00:00:00 2001
From: Jayson Tung <JFTung@users.noreply.github.com>
Date: Fri, 8 Apr 2016 14:05:36 -0400
Subject: [PATCH 0222/1679] Link Threaded Binary Tree and Fib. Heap in README

---
 README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.markdown b/README.markdown
index d37a929d5..bfb0d5e10 100644
--- a/README.markdown
+++ b/README.markdown
@@ -145,11 +145,11 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
 - [Red-Black Tree](Red\ Black\ Tree/) :construction:
 - Splay Tree
-- Threaded Binary Tree
+- [Threaded Binary Tree](Threaded\ Binary\ Tree/) :construction:
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
-- Fibonacci Heap
+- [Fibonacci Heap](Fibonacci\ Heap/) :construction:
 - Trie
 - [B-Tree](B Tree/) :construction:
 

From 9e839654dfbf1734cbfb922448c1923288bb0653 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Fri, 8 Apr 2016 14:34:34 -0400
Subject: [PATCH 0223/1679] Update ReadMe.md

updated formatting
---
 Trie/ReadMe.md | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 0509b68d4..edabbb994 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,4 +1,8 @@
-##Trie
-Under Construction
+# Trie
+
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Trie).
+
+*Written for the Swift Algorithm Club by Christian Encarnacion*
 
-Written for the Swift Algorithm Club by Christian Encarnacion

From e5b44de507c4ccab63947c7aff198c2691928948 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Fri, 8 Apr 2016 14:35:21 -0400
Subject: [PATCH 0224/1679] Update ReadMe.md

---
 Radix-Sort/ReadMe.md | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/Radix-Sort/ReadMe.md b/Radix-Sort/ReadMe.md
index 924665a1d..27dcf6eb3 100644
--- a/Radix-Sort/ReadMe.md
+++ b/Radix-Sort/ReadMe.md
@@ -1,4 +1,7 @@
-##Radix Sort
-Under Construction
+# Radix Sort
 
-Written for the Swift Algorithm Club by Christian Encarnacion
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Radix_Sort).
+
+*Written for the Swift Algorithm Club by Christian Encarnacion*

From 8be3106ea8ffbf55524d8052c709f9b9f0b157a3 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Fri, 8 Apr 2016 14:35:53 -0400
Subject: [PATCH 0225/1679] Update ReadMe.md

---
 Counting-Sort/ReadMe.md | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/Counting-Sort/ReadMe.md b/Counting-Sort/ReadMe.md
index f28249e0d..30b7fbb98 100644
--- a/Counting-Sort/ReadMe.md
+++ b/Counting-Sort/ReadMe.md
@@ -1,3 +1,7 @@
-##Counting Sort
-Under Construction
-Written for the Swift Algorithm Club by Christian Encarnacion
+# Counting Sort
+
+Under Construction.
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Counting_Sort).
+
+*Written for the Swift Algorithm Club by Christian Encarnacion*

From 53adbc8bfa20e95e57318f318756016db99fb948 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 10 Apr 2016 09:36:56 +0200
Subject: [PATCH 0226/1679] Add reservoir sampling to selection sampling
 chapter

---
 Selection Sampling/README.markdown         | 30 +++++++++++++++++++++-
 Selection Sampling/SelectionSampling.swift | 23 +++++++++++++++++
 2 files changed, 52 insertions(+), 1 deletion(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index a02c17b79..f8bd1c084 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -50,7 +50,35 @@ One more random number to pick, let's say it is 4 again. We swap `"c"` with `"a"
 
 And that's it. Easy peasy. The performance of this function is **O(k)** because as soon as we've selected *k* elements, we're done.
 
-However, there is one downside: this algorithm does not keep the elements in the original order. In the input array `"a"` came before `"e"` but now it's the other way around. If that is an issue for your app, you can't use this particular method.
+Here is an alternative algorithm, called "reservoir sampling":
+
+```swift
+func reservoirSample<T>(from a: [T], count k: Int) -> [T] {
+  precondition(a.count >= k)
+
+  var result = [T]()      // 1
+  for i in 0..<k {
+    result.append(a[i])
+  }
+
+  for i in k..<a.count {  // 2
+    let j = random(min: 0, max: i)
+    if j < k {
+      result[j] = a[i]
+    }
+  }
+  return result
+}
+```
+
+This works in two steps:
+
+1. Fill the `result` array with the first `k` elements from the original array. This is called the "reservoir".
+2. Randomly replace elements in the reservoir with elements from the remaining pool.
+
+The performance of this algorithm is **O(n)**, so it's a little bit slower than the first algorithm. However, its big advantage is that it can be used for arrays that are too large to fit in memory, even if you don't know what the size of the array is (in Swift this might be something like a lazy generator that reads the elements from a file).
+
+There is one downside to the previous two algorithms: they do not keep the elements in the original order. In the input array `"a"` came before `"e"` but now it's the other way around. If that is an issue for your app, you can't use this particular method.
 
 Here is an alternative approach that does keep the original order intact, but is a little more involved:
 
diff --git a/Selection Sampling/SelectionSampling.swift b/Selection Sampling/SelectionSampling.swift
index 8b9653d45..d562481c6 100644
--- a/Selection Sampling/SelectionSampling.swift	
+++ b/Selection Sampling/SelectionSampling.swift	
@@ -23,6 +23,29 @@ func select<T>(from a: [T], count k: Int) -> [T] {
   return Array(a[0..<k])
 }
 
+/*
+  Pick k random elements from an array. Performance: O(n).
+*/
+func reservoirSample<T>(from a: [T], count k: Int) -> [T] {
+  precondition(a.count >= k)
+
+  var result = [T]()
+  
+  // Fill the result array with first k elements.
+  for i in 0..<k {
+    result.append(a[i])
+  }
+
+  // Randomly replace elements from remaining pool.
+  for i in k..<a.count {
+    let j = random(min: 0, max: i)
+    if j < k {
+      result[j] = a[i]
+    }
+  }
+  return result
+}
+
 /*
   Selects `count` items at random from an array. Respects the original order of
   the elements. Performance: O(n).

From 892c1d490dd4eea6e134674d75d113e6b36366e1 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 10 Apr 2016 09:37:09 +0200
Subject: [PATCH 0227/1679] Fix off-by-one error

---
 K-Means/KMeans.swift                                          | 2 +-
 K-Means/Tests/Tests.xcodeproj/project.pbxproj                 | 4 +++-
 .../Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme     | 2 +-
 3 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index e9d48cb04..743cdc824 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -85,7 +85,7 @@ func reservoirSample<T>(samples: [T], k: Int) -> [T] {
   }
 
   // Randomly replace elements from remaining pool
-  for i in (k+1)..<samples.count {
+  for i in k..<samples.count {
     let j = Int(arc4random_uniform(UInt32(i + 1)))
     if j < k {
       result[j] = samples[i]
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index c43576ac3..34fe7fd21 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,7 +85,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0730;
 				TargetAttributes = {
 					B80894DF1C852D100018730E = {
 						CreatedOnToolsVersion = 7.2.1;
@@ -136,6 +136,8 @@
 		B80894D91C852CDC0018730E /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				ENABLE_TESTABILITY = YES;
+				ONLY_ACTIVE_ARCH = YES;
 			};
 			name = Debug;
 		};
diff --git a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 54b00dc9a..81f549cef 100644
--- a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0730"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 332530aa7574e6620c91bde219dbc06219d420c4 Mon Sep 17 00:00:00 2001
From: Jayson Tung <JFTung@users.noreply.github.com>
Date: Sun, 10 Apr 2016 13:51:27 -0400
Subject: [PATCH 0228/1679] Update README construction tags

---
 README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.markdown b/README.markdown
index bfb0d5e10..0ab973d85 100644
--- a/README.markdown
+++ b/README.markdown
@@ -73,8 +73,8 @@ Fast sorts:
 Special-purpose sorts:
 
 - Bucket Sort
-- Counting Sort
-- Radix Sort
+- [Counting Sort](Counting Sort) :construction:
+- [Radix Sort](Radix Sort/) :construction:
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
@@ -150,7 +150,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - [Fibonacci Heap](Fibonacci\ Heap/) :construction:
-- Trie
+- [Trie](Trie/) :construction:
 - [B-Tree](B Tree/) :construction:
 
 ### Hashing

From ecb56e9cd089cd80fbaa24d26e2ae7c4cb93e077 Mon Sep 17 00:00:00 2001
From: Jayson Tung <JFTung@users.noreply.github.com>
Date: Sun, 10 Apr 2016 13:54:35 -0400
Subject: [PATCH 0229/1679] Fix README links

---
 README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.markdown b/README.markdown
index 0ab973d85..fa6e263bc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -73,8 +73,8 @@ Fast sorts:
 Special-purpose sorts:
 
 - Bucket Sort
-- [Counting Sort](Counting Sort) :construction:
-- [Radix Sort](Radix Sort/) :construction:
+- [Counting Sort](Counting-Sort/) :construction:
+- [Radix Sort](Radix-Sort/) :construction:
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
@@ -143,7 +143,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- [Red-Black Tree](Red\ Black\ Tree/) :construction:
+- [Red-Black Tree](Red Black Trees/) :construction:
 - Splay Tree
 - [Threaded Binary Tree](Threaded\ Binary\ Tree/) :construction:
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.

From d9681be480f6f03b0dbe31f7e7a98009a76935c6 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Sun, 10 Apr 2016 15:32:14 -0400
Subject: [PATCH 0230/1679] Add intro to Threaded Bin Tree README

---
 Fibonacci Heap/README.markdown       |  8 +--
 Threaded Binary Tree/README.markdown | 75 ++++++++++++++++++++++++++--
 2 files changed, 77 insertions(+), 6 deletions(-)

diff --git a/Fibonacci Heap/README.markdown b/Fibonacci Heap/README.markdown
index f7d7efe71..c973701b2 100644
--- a/Fibonacci Heap/README.markdown	
+++ b/Fibonacci Heap/README.markdown	
@@ -1,7 +1,9 @@
-# Fibonacci Heaps
+# Fibonacci Heap
 
-Under Construction.
+Under construction.
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_heap).
+## See also 
+
+[Fibonacci Heap on Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_heap).
 
 *Written for the Swift Algorithm Club by Jayson Tung*
diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 1ca75ad75..beed0687e 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -1,7 +1,76 @@
-# Threaded Binary Trees
+# Threaded Binary Tree
 
-Under Construction.
+A threaded binary tree is a special kind of [binary tree](../Binary Tree/) (a
+tree in which each node has at most two children) that maintains a few extra
+pointers to allow cheap and fast **in-order traversal** of the tree.
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree).
+If you don't know what a tree is or what it is for, then [read this
+first](../Tree/).
+
+
+## In-order traversal
+
+The main motivation behind using a threaded binary tree over a simpler and
+smaller standard binary tree is to increase the speed of **in-order traversal**
+of the tree.  An in-order traversal of a binary tree visits the nodes in the
+order in which they are stored, which matches the underlying ordering of a
+[binary search tree](../Binary Search Tree/).  The idea is to visit all the
+left children of a node first, then visit the node itself, and visit the left
+children last.
+
+In-order traversal of any binary tree generally goes as follows:
+
+```
+traverse(n):
+	if (n == NULL) return
+	else:
+		traverse(n->leftChild)
+		visit n
+		traverse(n->rightChild)
+```
+Where `n` is a pointer to a node in the tree (or `NULL`), each node stores
+pointers to its children as `leftChild` and `rightChild`, and "visiting" a
+node can mean performing any action desired on it.
+
+While simple and understandable, this algorithm uses stack space proportional
+to the height of the tree due to its recursive nature.  If the tree has **n**
+nodes, this usage can range anywhere from **O(log n)** for a fairly balanced
+tree, to **O(n)** to a very unbalanced tree.
+
+A threaded binary tree fixes this problem.
+
+> For more information about in-order traversals [see here](../Binary Tree/).
+
+
+## Predecessors and successors
+
+An in-order traversal of a tree yields a linear ordering of the nodes.  Thus
+each node has both a predecessor and a successor (except for the first and last
+nodes, which only have a successor or a predecessor respectively).  What makes
+a threaded binary tree special is how it keeps track of each node's predecessor
+and/or successor.  Just as how nodes keep track of their left and right
+children, they also keep track of their predecessor and/or successor.
+
+There are two types of threaded binary trees:  single threaded and double
+threaded:
+- A single threaded tree keeps track of **either** the in-order predecessor
+  **or** successor (left **or** right).
+- A double threaded tree keeps track of **both** the in-order predecessor
+  **and** successor (left **and** right).
+
+Using a single or double threaded tree depends on what you want to accomplish.
+If you only need to traverse the tree in one direction (either forward or
+backward), use a single threaded tree.  If you want to traverse in both
+directions, use a double threaded tree.
+
+
+## An example
+
+
+### Still under construction.
+
+## See also 
+
+[Threaded Binary Tree on Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree).
 
 *Written for the Swift Algorithm Club by Jayson Tung*

From 1b48c5f156793a3018762717fa33f00ecd052157 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Sun, 10 Apr 2016 21:05:55 -0400
Subject: [PATCH 0231/1679] Add initial draft of ThreadBinTree traversal

---
 Threaded Binary Tree/README.markdown | 75 ++++++++++++++++++++++++----
 1 file changed, 64 insertions(+), 11 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index beed0687e..d75809d7d 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -24,13 +24,14 @@ In-order traversal of any binary tree generally goes as follows:
 traverse(n):
 	if (n == NULL) return
 	else:
-		traverse(n->leftChild)
+		traverse(n->left)
 		visit n
-		traverse(n->rightChild)
+		traverse(n->right)
 ```
 Where `n` is a pointer to a node in the tree (or `NULL`), each node stores
-pointers to its children as `leftChild` and `rightChild`, and "visiting" a
-node can mean performing any action desired on it.
+pointers to its children as `left` and `right`, and "visiting" a node can mean
+performing any desired action on it.  We would call this function by passing to
+it the root of the tree we wish to traverse.
 
 While simple and understandable, this algorithm uses stack space proportional
 to the height of the tree due to its recursive nature.  If the tree has **n**
@@ -46,10 +47,12 @@ A threaded binary tree fixes this problem.
 
 An in-order traversal of a tree yields a linear ordering of the nodes.  Thus
 each node has both a predecessor and a successor (except for the first and last
-nodes, which only have a successor or a predecessor respectively).  What makes
-a threaded binary tree special is how it keeps track of each node's predecessor
-and/or successor.  Just as how nodes keep track of their left and right
-children, they also keep track of their predecessor and/or successor.
+nodes, which only have a successor or a predecessor respectively).  In a
+threaded binary tree, each left child pointer that would normally be `NULL`
+instead points to the node's predecessor (if it exists), and each right child
+pointer that would normally be `NULL` instead points to the node's successor
+(if it exists).  This is what separates threaded binary trees from standard
+binary trees.
 
 There are two types of threaded binary trees:  single threaded and double
 threaded:
@@ -58,11 +61,61 @@ threaded:
 - A double threaded tree keeps track of **both** the in-order predecessor
   **and** successor (left **and** right).
 
-Using a single or double threaded tree depends on what you want to accomplish.
-If you only need to traverse the tree in one direction (either forward or
-backward), use a single threaded tree.  If you want to traverse in both
+Using a single or double threaded tree depends on what we want to accomplish.
+If we only need to traverse the tree in one direction (either forward or
+backward), use a single threaded tree.  If we want to traverse in both
 directions, use a double threaded tree.
 
+It is important to note that each node stores either its predecessor or its
+left child, and either its successor or its right child.  The nodes do not
+need to keep track of both.  For example, in a double threaded tree, if a node
+has a right child but no left child, it will track its predecessor in place of
+its left child.
+
+
+## Traversal algorithm
+
+Because predecessors and/or successors are tracked, an in-order traversal of a
+threaded binary tree is much more efficient than the recursive algorithm
+outlined above.  We use these predecessor/successor attributes to great effect
+in this new algorithm (note that this is for a forward traversal):
+
+```
+traverse(root):
+	if (root == NULL) return
+ 
+    // Find the leftmost Node
+    Node *n = root
+	while (n->left != NULL):
+		n = n->left
+ 
+    while (n != NULL):
+		visit n
+
+        // If this Node is a thread Node, then go to its in-order successor
+        if (n->rightThread):
+            n = n->right
+ 
+		// Else go to the leftmost Node in its right subtree
+        else:
+            n = n->right
+			while (n->left != NULL):
+				n = n->left
+```
+Where:
+- `root` is a pointer to the root of the tree (or `NULL`).
+- Each node stores pointers to its children or predecessor/successor as `left`
+  and `right`.
+- "Visiting" a node can mean performing any desired action on it.
+- The booleans `leftThread` and `rightThread` keep track of whether `left` and
+  `right` point to a child or a predecessor/successor.
+	- They are `true` for predecessors/successors, and `false` for children.
+	- While `leftThread` is not used here, it would be used in a backwards
+	  traversal in a double threaded tree or a single threaded tree "pointing"
+	  the other direction.
+- The first node in the traversal has `leftThread = true` and `left = NULL`
+- The last node in the traversal has `rightThread = true` and `right = NULL`
+
 
 ## An example
 

From 6b8946ec604fa03e386e77a4f7cb0a2cc825aac1 Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 11 Apr 2016 13:20:43 +0530
Subject: [PATCH 0232/1679] Adding counting sort

---
 Counting Sort/CountingSort.playground/Contents.swift        | 5 +++++
 Counting Sort/CountingSort.playground/contents.xcplayground | 4 ++++
 Counting Sort/README.markdown                               | 0
 3 files changed, 9 insertions(+)
 create mode 100644 Counting Sort/CountingSort.playground/Contents.swift
 create mode 100644 Counting Sort/CountingSort.playground/contents.xcplayground
 create mode 100644 Counting Sort/README.markdown

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
new file mode 100644
index 000000000..c9a67424b
--- /dev/null
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -0,0 +1,5 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+
+var str = "Hello, playground"
diff --git a/Counting Sort/CountingSort.playground/contents.xcplayground b/Counting Sort/CountingSort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Counting Sort/CountingSort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Counting Sort/README.markdown b/Counting Sort/README.markdown
new file mode 100644
index 000000000..e69de29bb

From 6fcd572a1a2d6bfba40927f037ef7de03ae4ac3c Mon Sep 17 00:00:00 2001
From: xspyhack <xspyhack@gmail.com>
Date: Mon, 11 Apr 2016 16:33:09 +0800
Subject: [PATCH 0233/1679] Add invert a binary tree.

---
 Binary Tree/BinaryTree.swift | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index 9f1b80393..edcb3b461 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -53,3 +53,13 @@ extension BinaryTree {
     }
   }
 }
+
+extension BinaryTree {
+  func invert() -> BinaryTree {
+    if case let .Node(left, value, right) = self {
+      return .Node(right.invert(), value, left.invert())
+    } else {
+      return .Empty
+    }
+  }
+}

From a77353f2e7a7dc0ff51bafe5f7b3d9b59ec7c05c Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 11 Apr 2016 16:52:33 +0530
Subject: [PATCH 0234/1679] Completed algorithm

---
 .../CountingSort.playground/Contents.swift    |  41 ++-
 Counting Sort/CountingSort/CountingSort.swift |  47 ++++
 .../CountingSort.xcodeproj/project.pbxproj    | 258 ++++++++++++++++++
 .../CountingSort/CountingSortTest.swift       |  24 ++
 .../CountingSort/CountingSort/Info.plist      |  24 ++
 5 files changed, 393 insertions(+), 1 deletion(-)
 create mode 100644 Counting Sort/CountingSort/CountingSort.swift
 create mode 100644 Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj
 create mode 100644 Counting Sort/CountingSort/CountingSort/CountingSortTest.swift
 create mode 100644 Counting Sort/CountingSort/CountingSort/Info.plist

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index c9a67424b..11743a49e 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,5 +1,44 @@
 //: Playground - noun: a place where people can play
 
 import UIKit
+import Foundation
 
-var str = "Hello, playground"
+enum CountingSortError: ErrorType {
+  case ArrayEmpty
+}
+
+
+func countingSort(array: [Int]) throws-> Array<Int> {
+  
+  guard array.count > 0 else {
+    throw CountingSortError.ArrayEmpty
+  }
+  
+  // Step 1:
+  // Create an array to store the count of each element
+  let maxElement = array.maxElement() ?? 0
+  
+  var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
+  
+  for element in array {
+    countArray[element] += 1
+  }
+  
+  // Step 2
+  // Set each value to be the sum of the previous two values
+  for index in 1 ..< countArray.count {
+    let sum = countArray[index] + countArray[index-1]
+    countArray[index] = sum
+  }
+  
+  // Step 3
+  // Place the element in the final array as per the number of elements before it
+  var sortedArray = [Int](count: array.count, repeatedValue: 0)
+  for element in array {
+    countArray[element] = countArray[element] - 1
+    sortedArray[countArray[element]] = element
+  }
+  return sortedArray
+}
+
+try countingSort([10, 9, 8, 7, 1, 2, 3, 4, 5])
\ No newline at end of file
diff --git a/Counting Sort/CountingSort/CountingSort.swift b/Counting Sort/CountingSort/CountingSort.swift
new file mode 100644
index 000000000..1151d2d11
--- /dev/null
+++ b/Counting Sort/CountingSort/CountingSort.swift	
@@ -0,0 +1,47 @@
+//
+//  Sort.swift
+//  test
+//
+//  Created by Kauserali on 11/04/16.
+//  Copyright © 2016 Ali Hafizji. All rights reserved.
+//
+
+import Foundation
+
+enum CountingSortError: ErrorType {
+  case ArrayEmpty
+}
+
+
+func countingSort(array: [Int]) throws-> Array<Int> {
+  
+  guard array.count > 0 else {
+    throw CountingSortError.ArrayEmpty
+  }
+  
+  // Step 1:
+  // Create an array to store the count of each element
+  let maxElement = array.maxElement() ?? 0
+  
+  var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
+  
+  for element in array {
+    countArray[element] += 1
+  }
+  
+  // Step 2
+  // Set each value to be the sum of the previous two values
+  for index in 1 ..< countArray.count {
+    let sum = countArray[index] + countArray[index-1]
+    countArray[index] = sum
+  }
+  
+  // Step 3
+  // Place the element in the final array as per the number of elements before it
+  var sortedArray = [Int](count: array.count, repeatedValue: 0)
+  for element in array {
+    countArray[element] = countArray[element] - 1
+    sortedArray[countArray[element]] = element
+  }
+  return sortedArray
+}
\ No newline at end of file
diff --git a/Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj b/Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..a87866ec2
--- /dev/null
+++ b/Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj	
@@ -0,0 +1,258 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		617F9B441CBBB9080085A8F4 /* CountingSortTest.swift in Sources */ = {isa = PBXBuildFile; fileRef = 617F9B431CBBB9080085A8F4 /* CountingSortTest.swift */; };
+		617F9B491CBBB9500085A8F4 /* CountingSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 617F9B3B1CBBB8BD0085A8F4 /* CountingSort.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		617F9B3B1CBBB8BD0085A8F4 /* CountingSort.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = CountingSort.swift; sourceTree = "<group>"; };
+		617F9B401CBBB9080085A8F4 /* CountingSort.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = CountingSort.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		617F9B431CBBB9080085A8F4 /* CountingSortTest.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = CountingSortTest.swift; sourceTree = "<group>"; };
+		617F9B451CBBB9080085A8F4 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		617F9B3D1CBBB9080085A8F4 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		617F9B341CBBB8A90085A8F4 = {
+			isa = PBXGroup;
+			children = (
+				617F9B3B1CBBB8BD0085A8F4 /* CountingSort.swift */,
+				617F9B421CBBB9080085A8F4 /* CountingSort */,
+				617F9B411CBBB9080085A8F4 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		617F9B411CBBB9080085A8F4 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				617F9B401CBBB9080085A8F4 /* CountingSort.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		617F9B421CBBB9080085A8F4 /* CountingSort */ = {
+			isa = PBXGroup;
+			children = (
+				617F9B431CBBB9080085A8F4 /* CountingSortTest.swift */,
+				617F9B451CBBB9080085A8F4 /* Info.plist */,
+			);
+			path = CountingSort;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		617F9B3F1CBBB9080085A8F4 /* CountingSort */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 617F9B481CBBB9080085A8F4 /* Build configuration list for PBXNativeTarget "CountingSort" */;
+			buildPhases = (
+				617F9B3C1CBBB9080085A8F4 /* Sources */,
+				617F9B3D1CBBB9080085A8F4 /* Frameworks */,
+				617F9B3E1CBBB9080085A8F4 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = CountingSort;
+			productName = CountingSort;
+			productReference = 617F9B401CBBB9080085A8F4 /* CountingSort.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		617F9B351CBBB8A90085A8F4 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0730;
+				LastUpgradeCheck = 0730;
+				TargetAttributes = {
+					617F9B3F1CBBB9080085A8F4 = {
+						CreatedOnToolsVersion = 7.3;
+					};
+				};
+			};
+			buildConfigurationList = 617F9B381CBBB8A90085A8F4 /* Build configuration list for PBXProject "CountingSort" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
+			mainGroup = 617F9B341CBBB8A90085A8F4;
+			productRefGroup = 617F9B411CBBB9080085A8F4 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				617F9B3F1CBBB9080085A8F4 /* CountingSort */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		617F9B3E1CBBB9080085A8F4 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		617F9B3C1CBBB9080085A8F4 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				617F9B491CBBB9500085A8F4 /* CountingSort.swift in Sources */,
+				617F9B441CBBB9080085A8F4 /* CountingSortTest.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		617F9B391CBBB8A90085A8F4 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Debug;
+		};
+		617F9B3A1CBBB8A90085A8F4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+			};
+			name = Release;
+		};
+		617F9B461CBBB9080085A8F4 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = CountingSort/Info.plist;
+				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alihafizji.CountingSort;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = iphoneos;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		617F9B471CBBB9080085A8F4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = CountingSort/Info.plist;
+				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = com.alihafizji.CountingSort;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = iphoneos;
+				VALIDATE_PRODUCT = YES;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		617F9B381CBBB8A90085A8F4 /* Build configuration list for PBXProject "CountingSort" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				617F9B391CBBB8A90085A8F4 /* Debug */,
+				617F9B3A1CBBB8A90085A8F4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		617F9B481CBBB9080085A8F4 /* Build configuration list for PBXNativeTarget "CountingSort" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				617F9B461CBBB9080085A8F4 /* Debug */,
+				617F9B471CBBB9080085A8F4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 617F9B351CBBB8A90085A8F4 /* Project object */;
+}
diff --git a/Counting Sort/CountingSort/CountingSort/CountingSortTest.swift b/Counting Sort/CountingSort/CountingSort/CountingSortTest.swift
new file mode 100644
index 000000000..fba639ba4
--- /dev/null
+++ b/Counting Sort/CountingSort/CountingSort/CountingSortTest.swift	
@@ -0,0 +1,24 @@
+//
+//  CountingSort.swift
+//  CountingSort
+//
+//  Created by Kauserali on 11/04/16.
+//
+//
+
+import XCTest
+
+class CountingSort: XCTestCase {
+    
+  func testCountingSort() {
+    let sequence = [10, 8, 1, 2, 5, 8]
+    let sortedSequence = [1, 2, 5, 8, 8, 10]
+    
+    do {
+      let afterCountingSort = try countingSort(sequence)
+      XCTAssertEqual(afterCountingSort, sortedSequence)
+    } catch {
+      XCTFail("")
+    }
+  }
+}
diff --git a/Counting Sort/CountingSort/CountingSort/Info.plist b/Counting Sort/CountingSort/CountingSort/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Counting Sort/CountingSort/CountingSort/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>

From 12eb87df5bdff4876e46095c78669a5d6dfeb9aa Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 11 Apr 2016 18:03:24 +0530
Subject: [PATCH 0235/1679] Updated readme

---
 Counting Sort/README.markdown | 43 +++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/Counting Sort/README.markdown b/Counting Sort/README.markdown
index e69de29bb..ccc37bc83 100644
--- a/Counting Sort/README.markdown	
+++ b/Counting Sort/README.markdown	
@@ -0,0 +1,43 @@
+# Counting Sort
+Counting sort is an algorithm for sorting a collection of objects according to keys that are small integers. It operates by counting the number of objects that have each distinct key values, and using arithmetic on those counts to determine the positions of each key value in the output sequence.
+
+## Example
+
+To understand the algorithm let's walk through a small example.
+
+Consider the array: [ 10, 9, 8, 7, 1, 2, 3]
+
+### Step 1:
+The first step is to count the total number of occurrences for each item in the array. The output for the first step would be as follows
+
+```
+Index 0 1 2 3 4 5 6 7 8 9 10
+Count 0 1 1 1 0 0 0 1 1 1 1
+```
+
+### Step 2:
+In this step the algorithm tries to determine the number of elements that are placed before each element. Since, you already know the total occurrences for each element you can use this information to your advantage. The way it works is to sum up the previous counts and store them at each index.
+
+The count array would be as follows:
+
+```
+Index 0 1 2 3 4 5 6 7 8 9 10
+Count 0 1 2 3 3 3 3 4 5 6 7
+```
+
+### Step 3:
+This is the last step in the algorithm. In it each element in the original array is placed at the position defined by the output of step 2. For e.g. the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array.
+
+The final output would be:
+
+```
+Index  0 1 2 3 4 5 6
+Output 1 2 3 7 8 9 10
+```
+
+## Performance
+The algorithm uses simple loops to sort a collection. Hence, the time to run the entire algorithm is `O(n+k)` where `O(n)` represent the loops that are required to initialize the output arrays and `O(k)` is the loop required to create the count array.
+
+The algorithm uses arrays of length `n + 1` and `n`, so the total space required is `O(2n)`. Hence for collections where the keys are scattered in a dense area along the number line it can be space efficient.
+
+*Written for Swift Algorithm Club by Ali Hafizji*

From 72cac4d87e0c311a7dcc62c4747a279a359bcda8 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 12 Apr 2016 08:25:52 +0200
Subject: [PATCH 0236/1679] Small tweaks.

---
 .../CountingSort.playground/Contents.swift    |  23 ++-
 .../{CountingSort => }/CountingSort.swift     |  21 ++-
 Counting Sort/README.markdown                 |  54 +++++--
 .../CountingSortTest.swift                    |   0
 .../CountingSort => Tests}/Info.plist         |   0
 .../Tests.xcodeproj}/project.pbxproj          | 153 +++++++++---------
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 +++++++
 README.markdown                               |   2 +-
 8 files changed, 199 insertions(+), 110 deletions(-)
 rename Counting Sort/{CountingSort => }/CountingSort.swift (81%)
 rename Counting Sort/{CountingSort/CountingSort => Tests}/CountingSortTest.swift (100%)
 rename Counting Sort/{CountingSort/CountingSort => Tests}/Info.plist (100%)
 rename Counting Sort/{CountingSort/CountingSort.xcodeproj => Tests/Tests.xcodeproj}/project.pbxproj (55%)
 create mode 100644 Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 11743a49e..13249aea8 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,44 +1,41 @@
 //: Playground - noun: a place where people can play
 
-import UIKit
-import Foundation
-
 enum CountingSortError: ErrorType {
   case ArrayEmpty
 }
 
-
-func countingSort(array: [Int]) throws-> Array<Int> {
-  
+func countingSort(array: [Int]) throws -> [Int] {
   guard array.count > 0 else {
     throw CountingSortError.ArrayEmpty
   }
   
-  // Step 1:
+  // Step 1
   // Create an array to store the count of each element
   let maxElement = array.maxElement() ?? 0
   
   var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
-  
   for element in array {
     countArray[element] += 1
   }
-  
+
   // Step 2
   // Set each value to be the sum of the previous two values
   for index in 1 ..< countArray.count {
-    let sum = countArray[index] + countArray[index-1]
+    let sum = countArray[index] + countArray[index - 1]
     countArray[index] = sum
   }
-  
+
+  print(countArray)
+
   // Step 3
   // Place the element in the final array as per the number of elements before it
   var sortedArray = [Int](count: array.count, repeatedValue: 0)
   for element in array {
-    countArray[element] = countArray[element] - 1
+    countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }
   return sortedArray
 }
 
-try countingSort([10, 9, 8, 7, 1, 2, 3, 4, 5])
\ No newline at end of file
+
+try countingSort([10, 9, 8, 7, 1, 2, 7, 3])
diff --git a/Counting Sort/CountingSort/CountingSort.swift b/Counting Sort/CountingSort.swift
similarity index 81%
rename from Counting Sort/CountingSort/CountingSort.swift
rename to Counting Sort/CountingSort.swift
index 1151d2d11..156782fef 100644
--- a/Counting Sort/CountingSort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -6,42 +6,39 @@
 //  Copyright © 2016 Ali Hafizji. All rights reserved.
 //
 
-import Foundation
-
 enum CountingSortError: ErrorType {
   case ArrayEmpty
 }
 
-
-func countingSort(array: [Int]) throws-> Array<Int> {
-  
+func countingSort(array: [Int]) throws -> [Int] {
   guard array.count > 0 else {
     throw CountingSortError.ArrayEmpty
   }
   
-  // Step 1:
+  // Step 1
   // Create an array to store the count of each element
   let maxElement = array.maxElement() ?? 0
   
   var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
-  
   for element in array {
     countArray[element] += 1
   }
-  
+
   // Step 2
   // Set each value to be the sum of the previous two values
   for index in 1 ..< countArray.count {
-    let sum = countArray[index] + countArray[index-1]
+    let sum = countArray[index] + countArray[index - 1]
     countArray[index] = sum
   }
-  
+
+  print(countArray)
+
   // Step 3
   // Place the element in the final array as per the number of elements before it
   var sortedArray = [Int](count: array.count, repeatedValue: 0)
   for element in array {
-    countArray[element] = countArray[element] - 1
+    countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }
   return sortedArray
-}
\ No newline at end of file
+}
diff --git a/Counting Sort/README.markdown b/Counting Sort/README.markdown
index ccc37bc83..55b60104f 100644
--- a/Counting Sort/README.markdown	
+++ b/Counting Sort/README.markdown	
@@ -1,43 +1,79 @@
 # Counting Sort
+
 Counting sort is an algorithm for sorting a collection of objects according to keys that are small integers. It operates by counting the number of objects that have each distinct key values, and using arithmetic on those counts to determine the positions of each key value in the output sequence.
 
 ## Example
 
 To understand the algorithm let's walk through a small example.
 
-Consider the array: [ 10, 9, 8, 7, 1, 2, 3]
+Consider the array: `[ 10, 9, 8, 7, 1, 2, 7, 3 ]`
 
 ### Step 1:
-The first step is to count the total number of occurrences for each item in the array. The output for the first step would be as follows
+
+The first step is to count the total number of occurrences for each item in the array. The output for the first step would be a new array that looks as follows:
 
 ```
 Index 0 1 2 3 4 5 6 7 8 9 10
-Count 0 1 1 1 0 0 0 1 1 1 1
+Count 0 1 1 1 0 0 0 2 1 1 1
+```
+
+Here is the code to accomplish this:
+
+```swift
+  let maxElement = array.maxElement() ?? 0
+  
+  var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
+  for element in array {
+    countArray[element] += 1
+  }
 ```
 
 ### Step 2:
+
 In this step the algorithm tries to determine the number of elements that are placed before each element. Since, you already know the total occurrences for each element you can use this information to your advantage. The way it works is to sum up the previous counts and store them at each index.
 
 The count array would be as follows:
 
 ```
 Index 0 1 2 3 4 5 6 7 8 9 10
-Count 0 1 2 3 3 3 3 4 5 6 7
+Count 0 1 2 3 3 3 3 5 6 7 8
+```
+
+The code for step 2 is:
+
+```swift
+  for index in 1 ..< countArray.count {
+    let sum = countArray[index] + countArray[index - 1]
+    countArray[index] = sum
+  }
 ```
 
 ### Step 3:
-This is the last step in the algorithm. In it each element in the original array is placed at the position defined by the output of step 2. For e.g. the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array.
+
+This is the last step in the algorithm. Each element in the original array is placed at the position defined by the output of step 2. For example, the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array.
 
 The final output would be:
 
 ```
-Index  0 1 2 3 4 5 6
-Output 1 2 3 7 8 9 10
+Index  0 1 2 3 4 5 6 7
+Output 1 2 3 7 7 8 9 10
+```
+
+Here is the code for this final step:
+
+```swift
+  var sortedArray = [Int](count: array.count, repeatedValue: 0)
+  for element in array {
+    countArray[element] -= 1
+    sortedArray[countArray[element]] = element
+  }
+  return sortedArray
 ```
 
 ## Performance
-The algorithm uses simple loops to sort a collection. Hence, the time to run the entire algorithm is `O(n+k)` where `O(n)` represent the loops that are required to initialize the output arrays and `O(k)` is the loop required to create the count array.
 
-The algorithm uses arrays of length `n + 1` and `n`, so the total space required is `O(2n)`. Hence for collections where the keys are scattered in a dense area along the number line it can be space efficient.
+The algorithm uses simple loops to sort a collection. Hence, the time to run the entire algorithm is **O(n+k)** where **O(n)** represents the loops that are required to initialize the output arrays and **O(k)** is the loop required to create the count array.
+
+The algorithm uses arrays of length **n + 1** and **n**, so the total space required is **O(2n)**. Hence for collections where the keys are scattered in a dense area along the number line it can be space efficient.
 
 *Written for Swift Algorithm Club by Ali Hafizji*
diff --git a/Counting Sort/CountingSort/CountingSort/CountingSortTest.swift b/Counting Sort/Tests/CountingSortTest.swift
similarity index 100%
rename from Counting Sort/CountingSort/CountingSort/CountingSortTest.swift
rename to Counting Sort/Tests/CountingSortTest.swift
diff --git a/Counting Sort/CountingSort/CountingSort/Info.plist b/Counting Sort/Tests/Info.plist
similarity index 100%
rename from Counting Sort/CountingSort/CountingSort/Info.plist
rename to Counting Sort/Tests/Info.plist
diff --git a/Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj
similarity index 55%
rename from Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj
rename to Counting Sort/Tests/Tests.xcodeproj/project.pbxproj
index a87866ec2..6801bb587 100644
--- a/Counting Sort/CountingSort/CountingSort.xcodeproj/project.pbxproj	
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -7,19 +7,19 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		617F9B441CBBB9080085A8F4 /* CountingSortTest.swift in Sources */ = {isa = PBXBuildFile; fileRef = 617F9B431CBBB9080085A8F4 /* CountingSortTest.swift */; };
-		617F9B491CBBB9500085A8F4 /* CountingSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 617F9B3B1CBBB8BD0085A8F4 /* CountingSort.swift */; };
+		7B74638C1CBCCC3C006DB977 /* CountingSortTest.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B74638B1CBCCC3C006DB977 /* CountingSortTest.swift */; };
+		7B80C3D81C77A313003CECC7 /* CountingSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3D71C77A313003CECC7 /* CountingSort.swift */; };
 /* End PBXBuildFile section */
 
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-		617F9B401CBBB9080085A8F4 /* CountingSort.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = CountingSort.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
-		617F9B431CBBB9080085A8F4 /* CountingSortTest.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = CountingSortTest.swift; sourceTree = "<group>"; };
-		617F9B451CBBB9080085A8F4 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B74638B1CBCCC3C006DB977 /* CountingSortTest.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = CountingSortTest.swift; sourceTree = SOURCE_ROOT; };
+		7B80C3D71C77A313003CECC7 /* CountingSort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = CountingSort.swift; path = ../CountingSort.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
-		617F9B3D1CBBB9080085A8F4 /* Frameworks */ = {
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -29,85 +29,88 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
-		617F9B341CBBB8A90085A8F4 = {
+		7B2BBC681C779D710067B71D = {
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 			children = (
-				617F9B3B1CBBB8BD0085A8F4 /* CountingSort.swift */,
-				617F9B421CBBB9080085A8F4 /* CountingSort */,
-				617F9B411CBBB9080085A8F4 /* Products */,
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
 			);
 			sourceTree = "<group>";
 		};
-		617F9B411CBBB9080085A8F4 /* Products */ = {
+		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				617F9B401CBBB9080085A8F4 /* CountingSort.xctest */,
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
 		};
-		617F9B421CBBB9080085A8F4 /* CountingSort */ = {
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 			isa = PBXGroup;
 			children = (
-				617F9B431CBBB9080085A8F4 /* CountingSortTest.swift */,
-				617F9B451CBBB9080085A8F4 /* Info.plist */,
+				7B80C3D71C77A313003CECC7 /* CountingSort.swift */,
+				7B74638B1CBCCC3C006DB977 /* CountingSortTest.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
-			path = CountingSort;
+			name = Tests;
+			path = TestsTests;
 			sourceTree = "<group>";
 		};
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		617F9B3F1CBBB9080085A8F4 /* CountingSort */ = {
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 			isa = PBXNativeTarget;
-			buildConfigurationList = 617F9B481CBBB9080085A8F4 /* Build configuration list for PBXNativeTarget "CountingSort" */;
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 			buildPhases = (
-				617F9B3C1CBBB9080085A8F4 /* Sources */,
-				617F9B3D1CBBB9080085A8F4 /* Frameworks */,
-				617F9B3E1CBBB9080085A8F4 /* Resources */,
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
 			);
 			buildRules = (
 			);
 			dependencies = (
 			);
-			name = CountingSort;
-			productName = CountingSort;
-			productReference = 617F9B401CBBB9080085A8F4 /* CountingSort.xctest */;
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
 
 /* Begin PBXProject section */
-		617F9B351CBBB8A90085A8F4 /* Project object */ = {
+		7B2BBC691C779D710067B71D /* Project object */ = {
 			isa = PBXProject;
 			attributes = {
-				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0730;
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
-					617F9B3F1CBBB9080085A8F4 = {
-						CreatedOnToolsVersion = 7.3;
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
 					};
 				};
 			};
-			buildConfigurationList = 617F9B381CBBB8A90085A8F4 /* Build configuration list for PBXProject "CountingSort" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
 				en,
+				Base,
 			);
-			mainGroup = 617F9B341CBBB8A90085A8F4;
-			productRefGroup = 617F9B411CBBB9080085A8F4 /* Products */;
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				617F9B3F1CBBB9080085A8F4 /* CountingSort */,
+				7B2BBC7F1C779D720067B71D /* Tests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
-		617F9B3E1CBBB9080085A8F4 /* Resources */ = {
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -117,35 +120,22 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
-		617F9B3C1CBBB9080085A8F4 /* Sources */ = {
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				617F9B491CBBB9500085A8F4 /* CountingSort.swift in Sources */,
-				617F9B441CBBB9080085A8F4 /* CountingSortTest.swift in Sources */,
+				7B74638C1CBCCC3C006DB977 /* CountingSortTest.swift in Sources */,
+				7B80C3D81C77A313003CECC7 /* CountingSort.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
 /* End PBXSourcesBuildPhase section */
 
 /* Begin XCBuildConfiguration section */
-		617F9B391CBBB8A90085A8F4 /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-			};
-			name = Debug;
-		};
-		617F9B3A1CBBB8A90085A8F4 /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-			};
-			name = Release;
-		};
-		617F9B461CBBB9080085A8F4 /* Debug */ = {
+		7B2BBC871C779D720067B71D /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_ANALYZER_NONNULL = YES;
 				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
@@ -159,7 +149,7 @@
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				CODE_SIGN_IDENTITY = "-";
 				COPY_PHASE_STRIP = NO;
 				DEBUG_INFORMATION_FORMAT = dwarf;
 				ENABLE_STRICT_OBJC_MSGSEND = YES;
@@ -178,23 +168,18 @@
 				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
 				GCC_WARN_UNUSED_FUNCTION = YES;
 				GCC_WARN_UNUSED_VARIABLE = YES;
-				INFOPLIST_FILE = CountingSort/Info.plist;
-				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = YES;
 				ONLY_ACTIVE_ARCH = YES;
-				PRODUCT_BUNDLE_IDENTIFIER = com.alihafizji.CountingSort;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-				SDKROOT = iphoneos;
+				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 			};
 			name = Debug;
 		};
-		617F9B471CBBB9080085A8F4 /* Release */ = {
+		7B2BBC881C779D720067B71D /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_ANALYZER_NONNULL = YES;
 				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
@@ -208,7 +193,7 @@
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				CODE_SIGN_IDENTITY = "-";
 				COPY_PHASE_STRIP = NO;
 				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
 				ENABLE_NS_ASSERTIONS = NO;
@@ -221,38 +206,56 @@
 				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
 				GCC_WARN_UNUSED_FUNCTION = YES;
 				GCC_WARN_UNUSED_VARIABLE = YES;
-				INFOPLIST_FILE = CountingSort/Info.plist;
-				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
-				PRODUCT_BUNDLE_IDENTIFIER = com.alihafizji.CountingSort;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SDKROOT = iphoneos;
-				VALIDATE_PRODUCT = YES;
 			};
 			name = Release;
 		};
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		617F9B381CBBB8A90085A8F4 /* Build configuration list for PBXProject "CountingSort" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
-				617F9B391CBBB8A90085A8F4 /* Debug */,
-				617F9B3A1CBBB8A90085A8F4 /* Release */,
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		617F9B481CBBB9080085A8F4 /* Build configuration list for PBXNativeTarget "CountingSort" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
-				617F9B461CBBB9080085A8F4 /* Debug */,
-				617F9B471CBBB9080085A8F4 /* Release */,
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
-	rootObject = 617F9B351CBBB8A90085A8F4 /* Project object */;
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
 }
diff --git a/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..74dd9450b
--- /dev/null
+++ b/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/README.markdown b/README.markdown
index f7ff7833b..f6fe1d429 100644
--- a/README.markdown
+++ b/README.markdown
@@ -73,7 +73,7 @@ Fast sorts:
 Special-purpose sorts:
 
 - Bucket Sort
-- Counting Sort
+- [Counting Sort](Counting Sort/)
 - Radix Sort
 - [Topological Sort](Topological Sort/)
 

From e86b683c6781abca7190f7c472655d5d1554cfa4 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Tue, 12 Apr 2016 11:41:25 +0200
Subject: [PATCH 0237/1679] Changes for tests configuration

---
 Bucket Sort/Tests/{Tests => }/Info.plist      |  0
 Bucket Sort/Tests/{Tests => }/Tests.swift     |  0
 .../Tests/Tests.xcodeproj/project.pbxproj     | 33 ++++++++++---------
 3 files changed, 17 insertions(+), 16 deletions(-)
 rename Bucket Sort/Tests/{Tests => }/Info.plist (100%)
 rename Bucket Sort/Tests/{Tests => }/Tests.swift (100%)

diff --git a/Bucket Sort/Tests/Tests/Info.plist b/Bucket Sort/Tests/Info.plist
similarity index 100%
rename from Bucket Sort/Tests/Tests/Info.plist
rename to Bucket Sort/Tests/Info.plist
diff --git a/Bucket Sort/Tests/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
similarity index 100%
rename from Bucket Sort/Tests/Tests/Tests.swift
rename to Bucket Sort/Tests/Tests.swift
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 3457e90ba..8608af8d2 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -7,16 +7,15 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		761476CC1CB51A8400E00457 /* BucketSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 761476CB1CB51A8400E00457 /* BucketSort.swift */; };
-		762141891CB538BC00CD552E /* Info.plist in Resources */ = {isa = PBXBuildFile; fileRef = 762141871CB538BC00CD552E /* Info.plist */; };
-		7621418A1CB538BC00CD552E /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 762141881CB538BC00CD552E /* Tests.swift */; };
+		768206991CBCEA94008B2B5A /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 768206971CBCEA94008B2B5A /* Tests.swift */; };
+		7682069F1CBCEC82008B2B5A /* BucketSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7682069E1CBCEC82008B2B5A /* BucketSort.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		761476CB1CB51A8400E00457 /* BucketSort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BucketSort.swift; path = ../../BucketSort.swift; sourceTree = "<group>"; };
-		762141871CB538BC00CD552E /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; name = Info.plist; path = Tests/Info.plist; sourceTree = SOURCE_ROOT; };
-		762141881CB538BC00CD552E /* Tests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Tests.swift; path = Tests/Tests.swift; sourceTree = SOURCE_ROOT; };
-		7621418B1CB5390E00CD552E /* Tests.temp_caseinsensitive_rename.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; name = Tests.temp_caseinsensitive_rename.xctest; path = "/Users/barbararodeker/Desktop/Projects/SwiftAlgorithms/swift-algorithm-club/Bucket Sort/Tests/build/Debug-iphoneos/Tests.temp_caseinsensitive_rename.xctest"; sourceTree = "<absolute>"; };
+		768206961CBCEA94008B2B5A /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		768206971CBCEA94008B2B5A /* Tests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Tests.swift; sourceTree = SOURCE_ROOT; };
+		7682069D1CBCEC47008B2B5A /* Tests.temp_caseinsensitive_rename.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; name = Tests.temp_caseinsensitive_rename.xctest; path = "/Users/barbararodeker/Desktop/Projects/SwiftAlgorithms/swift-algorithm-club/Bucket Sort/Tests/build/Debug-iphoneos/Tests.temp_caseinsensitive_rename.xctest"; sourceTree = "<absolute>"; };
+		7682069E1CBCEC82008B2B5A /* BucketSort.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = BucketSort.swift; path = ../BucketSort.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -40,9 +39,9 @@
 		76CC7DB91CB41D07003398A8 /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				761476CB1CB51A8400E00457 /* BucketSort.swift */,
-				762141881CB538BC00CD552E /* Tests.swift */,
-				762141871CB538BC00CD552E /* Info.plist */,
+				768206971CBCEA94008B2B5A /* Tests.swift */,
+				7682069E1CBCEC82008B2B5A /* BucketSort.swift */,
+				768206961CBCEA94008B2B5A /* Info.plist */,
 			);
 			name = Tests;
 			path = TestTests;
@@ -65,7 +64,7 @@
 			);
 			name = Tests;
 			productName = TestTests;
-			productReference = 7621418B1CB5390E00CD552E /* Tests.temp_caseinsensitive_rename.xctest */;
+			productReference = 7682069D1CBCEC47008B2B5A /* Tests.temp_caseinsensitive_rename.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -108,7 +107,6 @@
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				762141891CB538BC00CD552E /* Info.plist in Resources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -119,8 +117,8 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				7621418A1CB538BC00CD552E /* Tests.swift in Sources */,
-				761476CC1CB51A8400E00457 /* BucketSort.swift in Sources */,
+				768206991CBCEA94008B2B5A /* Tests.swift in Sources */,
+				7682069F1CBCEC82008B2B5A /* BucketSort.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -214,10 +212,12 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "";
-				INFOPLIST_FILE = Tests/Info.plist;
+				CLANG_ENABLE_MODULES = YES;
+				INFOPLIST_FILE = Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
 				PRODUCT_NAME = Tests.temp_caseinsensitive_rename;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
 			};
 			name = Debug;
@@ -226,7 +226,8 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "";
-				INFOPLIST_FILE = Tests/Info.plist;
+				CLANG_ENABLE_MODULES = YES;
+				INFOPLIST_FILE = Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
 				PRODUCT_NAME = Tests.temp_caseinsensitive_rename;

From 94099089e745fda831734eda5add5cacefeff223 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Tue, 12 Apr 2016 12:24:24 +0200
Subject: [PATCH 0238/1679] Adding documentation image

---
 Bucket Sort/Docs/BucketSort.png | Bin 0 -> 71092 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Bucket Sort/Docs/BucketSort.png

diff --git a/Bucket Sort/Docs/BucketSort.png b/Bucket Sort/Docs/BucketSort.png
new file mode 100644
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From 236f292bb50600c3ccc2714bea9baf107615adad Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Tue, 12 Apr 2016 12:33:02 +0200
Subject: [PATCH 0239/1679] Initial Documentation  - still in progress

---
 Bucket Sort/README.markdown | 119 +++++++++++++++++++++++++++++++++++-
 1 file changed, 118 insertions(+), 1 deletion(-)

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index 8f5183f0e..5c785993e 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -1,4 +1,121 @@
 # Bucket Sort
 
-TODO: Implementation in progress
+## Definition
+[Bucket Sort or Bin Sort](https://en.wikipedia.org/wiki/Bucket_sort) is a distributed sorting algorithm, which sort elements from an array by performing these steps:  
+
+1) Distribute the elements into buckets or bin.  
+2) Sort each bucket individually.  
+3) Merge the buckets in order to produce a sort array as results.  
+
+A more complete definition could be
+
+>
+Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, and is a cousin of radix sort in the most to least significant digit flavour. Bucket sort is a generalization of pigeonhole sort. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity estimates involve the number of buckets. [1](https://en.wikipedia.org/wiki/Bucket_sort)
+
+
+## Pseudocode
+
+A [pseudocode](https://en.wikipedia.org/wiki/Bucket_sort#Pseudocode) of the algorithm is as follows:  
+
+    function bucketSort(array, n) is
+        buckets ← new array of n empty lists
+        for i = 0 to (length(array)-1) do
+            insert array[i] into buckets[msbits(array[i], k)]
+        for i = 0 to n - 1 do
+            nextSort(buckets[i]);
+        return the concatenation of buckets[0], ...., buckets[n-1]
+
+
+## Graphically explained
+
+###Distribute elements in buckets  
+
+![distribution step](https://upload.wikimedia.org/wikipedia/commons/6/61/Bucket_sort_1.png)
+
+###Sorting inside every bucket and merging  
+
+![sorting each bucket and merge](https://upload.wikimedia.org/wikipedia/commons/3/39/Bucket_sort_2.png)
+
+##Swift implementation
+
+###Classes
+
+![classes](https://github.com/barbaramartina/swift-algorithm-club/blob/BucketSort/Bucket%20Sort/Docs/BucketSort.png)
+
+###Code
+
+Bucket Sort implementation use the following functions, data structures and protocols:
+
+####Main function
+
+`bucketSort` is a generic function that can apply the algorithm to any element of type T, as long as T is Sortable.
+
+    public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+        precondition(allPositiveNumbers(elements))
+        precondition(enoughSpaceInBuckets(buckets, elements: elements))
+    
+        var bucketsCopy = buckets
+        for elem in elements {
+            distributor.distribute(elem, buckets: &bucketsCopy)
+         }
+    
+        var results = [T]()
+    
+       for bucket in bucketsCopy {
+            results += bucket.sort(sorter)
+        }
+    
+        return results
+     }
+
+
+####Bucket
+
+    public struct Bucket<T:Sortable> {
+        var elements: [T]
+        let capacity: Int
+    
+        public init(capacity: Int) {
+            self.capacity = capacity
+            elements = [T]()
+        }
+    
+        public mutating func add(item: T) {
+            if (elements.count < capacity) {
+                elements.append(item)
+            }
+         }
+    
+         public func sort(algorithm: Sorter) -> [T] {
+            return algorithm.sort(elements)
+         }
+    }
+
+####Sortable
+
+    public protocol Sortable: IntConvertible, Comparable {
+    }
+
+####IntConvertible
+
+The algorithm is designed to sort integers, so all the elements to be sorted should be mapped to an integer value.
+
+    public protocol IntConvertible {
+        func toInt() -> Int
+    }
+
+
+####Sorter
+
+    public protocol Sorter {
+        func sort<T:Sortable>(items: [T]) -> [T]
+    }
+
+####Distributor
+
+    public protocol Distributor {
+        func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
+    }
+
+
 

From d0768342a74e0d4650cad3b02f31ad2de0f9e287 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:18:05 -0400
Subject: [PATCH 0240/1679] Create README.markdown

---
 Adjacency-List/README.markdown | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Adjacency-List/README.markdown

diff --git a/Adjacency-List/README.markdown b/Adjacency-List/README.markdown
new file mode 100644
index 000000000..aebd1a631
--- /dev/null
+++ b/Adjacency-List/README.markdown
@@ -0,0 +1 @@
+Adjacency List README

From 9db2b26acdab8ab25ed79bd0289d212d7ebbb9f4 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:19:01 -0400
Subject: [PATCH 0241/1679] Update README.markdown

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index f6fe1d429..ffc28fe9d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -136,6 +136,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
 - Skip List
+- [Adjacency List](Adjacency List/) :construction:
 
 ### Trees
 

From 5146ec236be35500441d5bb90d3672c025b62976 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:21:40 -0400
Subject: [PATCH 0242/1679] Create Adjacency\ List

---
 "Adjacency\\ List" | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 "Adjacency\\ List"

diff --git "a/Adjacency\\ List" "b/Adjacency\\ List"
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ "b/Adjacency\\ List"	
@@ -0,0 +1 @@
+

From a51ae75d47c1c66dcf89f40eeaa525c6df61c3c7 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:22:22 -0400
Subject: [PATCH 0243/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index ffc28fe9d..e9ec2f188 100644
--- a/README.markdown
+++ b/README.markdown
@@ -136,7 +136,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
 - Skip List
-- [Adjacency List](Adjacency List/) :construction:
+- [Adjacency List](Adjacency-List/) :construction:
 
 ### Trees
 

From 841af298e4928539527b7c0bf1d4610ebd525f27 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:25:07 -0400
Subject: [PATCH 0244/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index e9ec2f188..b501a6dc0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -136,7 +136,6 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
 - Skip List
-- [Adjacency List](Adjacency-List/) :construction:
 
 ### Trees
 
@@ -174,6 +173,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
 - [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
 - All Paths
+- [Adjacency List](Adjacency-List/) :construction:
 
 ## Puzzles
 

From 5cc1018d122ccc64f44b4eb70274cf695c8d8cbd Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:26:31 -0400
Subject: [PATCH 0245/1679] Added Adjacency List and Radix Tree links

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index b501a6dc0..9a536bb63 100644
--- a/README.markdown
+++ b/README.markdown
@@ -152,6 +152,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - Fibonacci Heap
 - Trie
 - [B-Tree](B Tree/) :construction:
+- [Radix Tree](Radix-Tree/) :construction:
 
 ### Hashing
 

From 6aecff1194009c0dd8ac9408300085c37bac51b0 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Tue, 12 Apr 2016 16:26:54 -0400
Subject: [PATCH 0246/1679] Create README.markdown

---
 Radix-Tree/README.markdown | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Radix-Tree/README.markdown

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
new file mode 100644
index 000000000..6e4542f6d
--- /dev/null
+++ b/Radix-Tree/README.markdown
@@ -0,0 +1 @@
+Radix Tree README

From a13108a82a4fe0879735cf32d1b2527bd0207f1e Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Tue, 12 Apr 2016 22:01:51 -0400
Subject: [PATCH 0247/1679] Added Node class for Trie data structure

---
 Trie/trie.swift | 49 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 Trie/trie.swift

diff --git a/Trie/trie.swift b/Trie/trie.swift
new file mode 100644
index 000000000..5bcae6745
--- /dev/null
+++ b/Trie/trie.swift
@@ -0,0 +1,49 @@
+public class Node {
+  var character: Character?
+  var parent: Node?
+  var children: [Node?]
+  var isAWord: Bool = false
+
+  init(c: Character){
+    self.character = c
+    self.children = [Node?]()
+    }
+
+  //Easier getter function, probably will make it more swift like
+  func char() -> Character {
+    return self.character!
+  }
+
+  func changeChar(c: Character) -> Void {
+    self.character = c
+  }
+  
+  //For Testing purposes
+  func getParent() -> Node {
+    return parent!
+  }
+
+  //Is this node marked as the end of a word?
+  func isValidWord() -> Bool{
+    return self.isAWord
+  }
+
+  //Setters
+  func isWord() -> Void {
+    self.isAWord = true
+  }
+
+  func isNotWord() -> Void {
+    self.isAWord = false
+  }
+}
+
+
+
+print("tests")
+
+var x: Node = Node(c: "c")
+print(x.char())
+print(x.isValidWord())
+x.isWord()
+print(x.isValidWord())

From 3af9c370f813c9bca051af6b6f8e0241c24038ed Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Wed, 13 Apr 2016 11:28:45 -0400
Subject: [PATCH 0248/1679] Changed Character Typing to String Typing (Made
 more sense)

---
 Trie/trie       | Bin 0 -> 22390 bytes
 Trie/trie.swift |  15 ++++++++++-----
 2 files changed, 10 insertions(+), 5 deletions(-)
 create mode 100755 Trie/trie

diff --git a/Trie/trie b/Trie/trie
new file mode 100755
index 0000000000000000000000000000000000000000..a9f6e269f8158efc047108ddee0b7535ad80ea52
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znS+$2E%<W57b4ZT;PCa>P&G1FMQax|A|2=@{hK|r870-h*t&4suv(!_3=M+LW;l8(
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literal 0
HcmV?d00001

diff --git a/Trie/trie.swift b/Trie/trie.swift
index 5bcae6745..027ee513b 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -1,23 +1,23 @@
 public class Node {
-  var character: Character?
+  var character: String?
   var parent: Node?
   var children: [Node?]
   var isAWord: Bool = false
 
-  init(c: Character){
+  init(c: String){
     self.character = c
     self.children = [Node?]()
     }
 
   //Easier getter function, probably will make it more swift like
-  func char() -> Character {
+  func char() -> String {
     return self.character!
   }
 
-  func changeChar(c: Character) -> Void {
+  func changeChar(c: String) -> Void {
     self.character = c
   }
-  
+
   //For Testing purposes
   func getParent() -> Node {
     return parent!
@@ -38,8 +38,13 @@ public class Node {
   }
 }
 
+public class Trie {
+  var root: Node = Node(c: "")
+
 
 
+}
+
 print("tests")
 
 var x: Node = Node(c: "c")

From eb0d9f222517ccc42b655d01862bd573218811ea Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Wed, 13 Apr 2016 11:53:40 -0400
Subject: [PATCH 0249/1679] Updated Node class to be a bit cleaner and not as
 redundant.  Started on Trie Class.

---
 Trie/trie       | Bin 22390 -> 23362 bytes
 Trie/trie.swift |  21 ++++++++++++++++++---
 2 files changed, 18 insertions(+), 3 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index a9f6e269f8158efc047108ddee0b7535ad80ea52..9459e471d729d947cf78e2e3b199647501c58738 100755
GIT binary patch
literal 23362
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zK)AtCBXG2Al&}0fB_RztRa2VKo}5PZ_ZwGskDCSS2<o_wlAJW;B&pQ|Cr<`9O6*`c
zKdOH2eKV`~p7vpre*gKN(+Ao+^SO8K+_^JzXZF3f^9gTLLvBuvBClNKLki`lO56<T
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 027ee513b..391300739 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -2,11 +2,12 @@ public class Node {
   var character: String?
   var parent: Node?
   var children: [Node?]
-  var isAWord: Bool = false
+  var isAWord: Bool
 
   init(c: String){
     self.character = c
-    self.children = [Node?]()
+    self.children = []
+    self.isAWord = false
     }
 
   //Easier getter function, probably will make it more swift like
@@ -36,13 +37,27 @@ public class Node {
   func isNotWord() -> Void {
     self.isAWord = false
   }
+
+  func isRoot() -> Bool {
+    return self.character == ""
+  }
 }
 
 public class Trie {
-  var root: Node = Node(c: "")
+  var root: Node
+  var nodes: [Node]
 
+  init() {
+    self.root = Node(c: "")
+    self.nodes = []
+    self.nodes.append(self.root)
+  }
 
 
+  func insertWord(w: String) -> Void {
+
+  }
+
 }
 
 print("tests")

From 5e0ca14f8126d0c673f9925491c848e7c58144b1 Mon Sep 17 00:00:00 2001
From: barbaramartina <barbararodeker@gmail.com>
Date: Thu, 14 Apr 2016 13:52:28 +0200
Subject: [PATCH 0250/1679] Fix for: Tests target not found (was failing due to
 renaming operation failure). Adding OSX like target. Using the null identity
 for signing

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 134 +++++++++---------
 .../xcshareddata/xcschemes/Tests.xcscheme     |   6 +-
 2 files changed, 71 insertions(+), 69 deletions(-)

diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 8608af8d2..9a42afa4b 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -7,19 +7,19 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		768206991CBCEA94008B2B5A /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 768206971CBCEA94008B2B5A /* Tests.swift */; };
-		7682069F1CBCEC82008B2B5A /* BucketSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7682069E1CBCEC82008B2B5A /* BucketSort.swift */; };
+		76E90BEB1CBFB317009E04FE /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 76E90BEA1CBFB317009E04FE /* Tests.swift */; };
+		76E90BED1CBFB322009E04FE /* BucketSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 76E90BEC1CBFB322009E04FE /* BucketSort.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		768206961CBCEA94008B2B5A /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
-		768206971CBCEA94008B2B5A /* Tests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Tests.swift; sourceTree = SOURCE_ROOT; };
-		7682069D1CBCEC47008B2B5A /* Tests.temp_caseinsensitive_rename.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; name = Tests.temp_caseinsensitive_rename.xctest; path = "/Users/barbararodeker/Desktop/Projects/SwiftAlgorithms/swift-algorithm-club/Bucket Sort/Tests/build/Debug-iphoneos/Tests.temp_caseinsensitive_rename.xctest"; sourceTree = "<absolute>"; };
-		7682069E1CBCEC82008B2B5A /* BucketSort.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; name = BucketSort.swift; path = ../BucketSort.swift; sourceTree = SOURCE_ROOT; };
+		76E90BEA1CBFB317009E04FE /* Tests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Tests.swift; sourceTree = SOURCE_ROOT; };
+		76E90BEC1CBFB322009E04FE /* BucketSort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BucketSort.swift; path = ../BucketSort.swift; sourceTree = SOURCE_ROOT; };
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
-		76CC7DB31CB41D07003398A8 /* Frameworks */ = {
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -29,62 +29,69 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
-		76CC7D991CB41D03003398A8 = {
+		7B2BBC681C779D710067B71D = {
 			isa = PBXGroup;
 			children = (
-				76CC7DB91CB41D07003398A8 /* Tests */,
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
 			);
 			sourceTree = "<group>";
 		};
-		76CC7DB91CB41D07003398A8 /* Tests */ = {
+		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				768206971CBCEA94008B2B5A /* Tests.swift */,
-				7682069E1CBCEC82008B2B5A /* BucketSort.swift */,
-				768206961CBCEA94008B2B5A /* Info.plist */,
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				76E90BEA1CBFB317009E04FE /* Tests.swift */,
+				76E90BEC1CBFB322009E04FE /* BucketSort.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
 			name = Tests;
-			path = TestTests;
+			path = TestsTests;
 			sourceTree = "<group>";
 		};
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		76CC7DB51CB41D07003398A8 /* Tests */ = {
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 76CC7DC21CB41D07003398A8 /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
 			buildPhases = (
-				76CC7DB21CB41D07003398A8 /* Sources */,
-				76CC7DB31CB41D07003398A8 /* Frameworks */,
-				76CC7DB41CB41D07003398A8 /* Resources */,
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
 			);
 			buildRules = (
 			);
 			dependencies = (
 			);
 			name = Tests;
-			productName = TestTests;
-			productReference = 7682069D1CBCEC47008B2B5A /* Tests.temp_caseinsensitive_rename.xctest */;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
 
 /* Begin PBXProject section */
-		76CC7D9A1CB41D03003398A8 /* Project object */ = {
+		7B2BBC691C779D710067B71D /* Project object */ = {
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0730;
-				ORGANIZATIONNAME = "Barbara M. Rodeker";
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
-					76CC7DB51CB41D07003398A8 = {
-						CreatedOnToolsVersion = 7.3;
-						DevelopmentTeam = 6V43LV5QCY;
-						TestTargetID = 76CC7DA11CB41D03003398A8;
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
 					};
 				};
 			};
-			buildConfigurationList = 76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Tests" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -92,18 +99,18 @@
 				en,
 				Base,
 			);
-			mainGroup = 76CC7D991CB41D03003398A8;
-			productRefGroup = 76CC7D991CB41D03003398A8;
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				76CC7DB51CB41D07003398A8 /* Tests */,
+				7B2BBC7F1C779D720067B71D /* Tests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
-		76CC7DB41CB41D07003398A8 /* Resources */ = {
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -113,23 +120,22 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
-		76CC7DB21CB41D07003398A8 /* Sources */ = {
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				768206991CBCEA94008B2B5A /* Tests.swift in Sources */,
-				7682069F1CBCEC82008B2B5A /* BucketSort.swift in Sources */,
+				76E90BEB1CBFB317009E04FE /* Tests.swift in Sources */,
+				76E90BED1CBFB322009E04FE /* BucketSort.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
 /* End PBXSourcesBuildPhase section */
 
 /* Begin XCBuildConfiguration section */
-		76CC7DBD1CB41D07003398A8 /* Debug */ = {
+		7B2BBC871C779D720067B71D /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_ANALYZER_NONNULL = YES;
 				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
@@ -143,7 +149,7 @@
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				CODE_SIGN_IDENTITY = "-";
 				COPY_PHASE_STRIP = NO;
 				DEBUG_INFORMATION_FORMAT = dwarf;
 				ENABLE_STRICT_OBJC_MSGSEND = YES;
@@ -162,19 +168,18 @@
 				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
 				GCC_WARN_UNUSED_FUNCTION = YES;
 				GCC_WARN_UNUSED_VARIABLE = YES;
-				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = YES;
 				ONLY_ACTIVE_ARCH = YES;
-				SDKROOT = iphoneos;
+				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 			};
 			name = Debug;
 		};
-		76CC7DBE1CB41D07003398A8 /* Release */ = {
+		7B2BBC881C779D720067B71D /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ALWAYS_SEARCH_USER_PATHS = NO;
-				CLANG_ANALYZER_NONNULL = YES;
 				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
@@ -188,7 +193,7 @@
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
-				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				CODE_SIGN_IDENTITY = "-";
 				COPY_PHASE_STRIP = NO;
 				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
 				ENABLE_NS_ASSERTIONS = NO;
@@ -201,62 +206,59 @@
 				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
 				GCC_WARN_UNUSED_FUNCTION = YES;
 				GCC_WARN_UNUSED_VARIABLE = YES;
-				IPHONEOS_DEPLOYMENT_TARGET = 9.3;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
-				SDKROOT = iphoneos;
-				VALIDATE_PRODUCT = YES;
+				SDKROOT = macosx;
 			};
 			name = Release;
 		};
-		76CC7DC31CB41D07003398A8 /* Debug */ = {
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
-				BUNDLE_LOADER = "";
 				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
-				PRODUCT_NAME = Tests.temp_caseinsensitive_rename;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
 			};
 			name = Debug;
 		};
-		76CC7DC41CB41D07003398A8 /* Release */ = {
+		7B2BBC8E1C779D720067B71D /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
-				BUNDLE_LOADER = "";
 				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.algorithmsclub.Tests;
-				PRODUCT_NAME = Tests.temp_caseinsensitive_rename;
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Test.app/Test";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
 			};
 			name = Release;
 		};
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		76CC7D9D1CB41D03003398A8 /* Build configuration list for PBXProject "Tests" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
-				76CC7DBD1CB41D07003398A8 /* Debug */,
-				76CC7DBE1CB41D07003398A8 /* Release */,
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		76CC7DC21CB41D07003398A8 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
-				76CC7DC31CB41D07003398A8 /* Debug */,
-				76CC7DC41CB41D07003398A8 /* Release */,
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
-	rootObject = 76CC7D9A1CB41D03003398A8 /* Project object */;
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
 }
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 574e1d2ea..74dd9450b 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0720"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -16,8 +16,8 @@
             skipped = "NO">
             <BuildableReference
                BuildableIdentifier = "primary"
-               BlueprintIdentifier = "76CC7DB51CB41D07003398A8"
-               BuildableName = "Tests.temp_caseinsensitive_rename.xctest"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
                BlueprintName = "Tests"
                ReferencedContainer = "container:Tests.xcodeproj">
             </BuildableReference>

From 5873dd5a50fadf0e674143acb3d8bd0b5b8c4d66 Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Thu, 14 Apr 2016 14:11:45 +0200
Subject: [PATCH 0251/1679] Adding time performance & alternatives.

---
 Bucket Sort/README.markdown | 80 +++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index 5c785993e..576937359 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -12,6 +12,18 @@ A more complete definition could be
 >
 Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, and is a cousin of radix sort in the most to least significant digit flavour. Bucket sort is a generalization of pigeonhole sort. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity estimates involve the number of buckets. [1](https://en.wikipedia.org/wiki/Bucket_sort)
 
+## Performance
+
+Performance for execution time:  
+  
+| Case  | Performance |
+|:-------------: |:---------------:|
+| Worst       |  O(n^2) |
+| Best      | 	Omega(n + k)        |
+|  Average | 	Theta(n + k)       | 
+  
+Where **n** = #elements and **k** = #buckets  
+
 
 ## Pseudocode
 
@@ -117,5 +129,73 @@ The algorithm is designed to sort integers, so all the elements to be sorted sho
         func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
     }
 
+### Custom Sorter and Distributor
+
+The current implementation make use of the following implementations for *Sorter* and *Distributor*.  
+
+*Sorter*  
+
+    public struct InsertionSorter: Sorter {
+    
+        public init() {}
+    
+        public func sort<T:Sortable>(items: [T]) -> [T] {
+            var results = items
+            for i in 0 ..< results.count {
+                var j = i
+                while ( j > 0 && results[j-1] > results[j]) {
+                
+                    let auxiliar = results[j-1]
+                    results[j-1] = results[j]
+                    results[j] = auxiliar
+                
+                    j -= 1
+                }
+            }
+            return results
+        }
+    }
+
+*Distributor*  
+
+    /*
+    * An example of a simple distribution function that send every elements to
+    * the bucket representing the range in which it fits.An
+    *
+    * If the range of values to sort is 0..<49 i.e, there could be 5 buckets of capacity = 10
+    * So every element will be classified by the ranges:
+    *
+    * -  0 ..< 10
+    * - 10 ..< 20
+    * - 20 ..< 30
+    * - 30 ..< 40
+    * - 40 ..< 50
+    *
+    * By following the formula: element / capacity = #ofBucket
+    */
+    public struct RangeDistributor: Distributor {
+    
+         public init() {}
+    
+         public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
+         let value = element.toInt()
+         let bucketCapacity = buckets.first!.capacity
+        
+         let bucketIndex = value / bucketCapacity
+         buckets[bucketIndex].add(element)
+        }
+    }
+
+### Make your own version
+
+By reusing this code and implementing your own *Sorter* and *Distributor* you can experiment with different versions.
+
+## Other variations of Bucket Sort
+
+The following are some of the variation to the General Bucket Sort implemented here:
 
+- [Proxmap Sort](https://en.wikipedia.org/wiki/Bucket_sort#ProxmapSort)
+- [Histogram Sort](https://en.wikipedia.org/wiki/Bucket_sort#Histogram_sort)
+- [Postman Sort](https://en.wikipedia.org/wiki/Bucket_sort#Postman.27s_sort)
+- [Shuffle Sort](https://en.wikipedia.org/wiki/Bucket_sort#Shuffle_sort)
 

From 36962170d25c437f19c3b2070b705b2e32905097 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:20:06 -0400
Subject: [PATCH 0252/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 6e4542f6d..de11425d7 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1 +1,2 @@
-Radix Tree README
+# Radix Tree
+---

From e1ac122d9a90ba79dbf3bdf8ee3a0f58c72ce650 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:25:38 -0400
Subject: [PATCH 0253/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index de11425d7..99f4502b9 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,2 +1,3 @@
 # Radix Tree
 ---
+A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen (here)[https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg]

From 5fffd6913884e44f57cfd66d6d55085a34aa50fa Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:26:12 -0400
Subject: [PATCH 0254/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 99f4502b9..9ce08dff4 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,3 +1,3 @@
 # Radix Tree
 ---
-A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen (here)[https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg]
+A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen [here](https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg).

From adb8a6b4262a59ec76f0534d7974b298ca77ddbd Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:27:15 -0400
Subject: [PATCH 0255/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 9ce08dff4..a52c8f8ab 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,3 +1,3 @@
 # Radix Tree
----
+--
 A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen [here](https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg).

From 2b28ee4ba2cfaff1dc127eee6c969edb32ec0467 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:27:24 -0400
Subject: [PATCH 0256/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index a52c8f8ab..e3de0a161 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,3 +1,3 @@
 # Radix Tree
---
+-
 A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen [here](https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg).

From 180ce9e06161ddecc1dc5e860b67f2ada249b645 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:27:31 -0400
Subject: [PATCH 0257/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index e3de0a161..7f803e215 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,3 +1,3 @@
 # Radix Tree
--
+
 A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen [here](https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg).

From 831b27ad870da93d1789716701d5c5d7d64ede7e Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 10:31:34 -0400
Subject: [PATCH 0258/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 7f803e215..0d9a10125 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,3 +1,7 @@
 # Radix Tree
 
 A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen [here](https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg).
+
+## Operations
+
+Typical operations on a radix tree include lookup, insertion, deletion, find predecessor, find successor, and find all strings with common prefix. The running time of lookup, insertion, and deletion is O(k) where k is the length of the key. This is different from most trees because these operations usually run in O(logn) time where n is the number of nodes in the tree.

From 3b30576efb6e49be0ca9c90894387f7056a87fba Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:02:59 -0400
Subject: [PATCH 0259/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 0d9a10125..733f5ec0c 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -5,3 +5,7 @@ A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used
 ## Operations
 
 Typical operations on a radix tree include lookup, insertion, deletion, find predecessor, find successor, and find all strings with common prefix. The running time of lookup, insertion, and deletion is O(k) where k is the length of the key. This is different from most trees because these operations usually run in O(logn) time where n is the number of nodes in the tree.
+
+## See Also
+
+[Radix Tree - Wikipedia](https://en.wikipedia.org/wiki/Radix_tree)

From da404ce3e973d6a8e41e1ae9b40f1ee685a03b95 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:11:23 -0400
Subject: [PATCH 0260/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 733f5ec0c..1b41d1a93 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,6 +1,6 @@
 # Radix Tree
 
-A radix tree (or radix trie, compact prefix tree) is a space-optimized tree used for constructing associative arrays that are usually expressed as strings. Edges in radix trees store strings. If you started at the root of the tree and traversed down to any node that has no children, concatenating the edges in order of traversal would result in a stored word. An example can be seen [here](https://en.wikipedia.org/wiki/Radix_tree#/media/File:Patricia_trie.svg).
+A radix tree is a tree where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses and by traversing from the root to any leaf in the tree, (by concatenating all the labels of edges along the way) you can find any string. This is a radix tree:
 
 ## Operations
 

From 8a6f269288593b24d5e726e557c7f487595aeb3c Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:11:43 -0400
Subject: [PATCH 0261/1679] Create test.md

---
 Radix-Tree/Images/test.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Radix-Tree/Images/test.md

diff --git a/Radix-Tree/Images/test.md b/Radix-Tree/Images/test.md
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/Radix-Tree/Images/test.md
@@ -0,0 +1 @@
+

From 49543eac600925e4a1a34a0aeb11225d82d6d10b Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:12:38 -0400
Subject: [PATCH 0262/1679] Uploaded radixtree.png

---
 Radix-Tree/Images/radixtree.png | Bin 0 -> 24072 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Radix-Tree/Images/radixtree.png

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From e9f4bf40d83cff0302a5258343ca96232aaa0b4e Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:12:53 -0400
Subject: [PATCH 0263/1679] Delete test.md

---
 Radix-Tree/Images/test.md | 1 -
 1 file changed, 1 deletion(-)
 delete mode 100644 Radix-Tree/Images/test.md

diff --git a/Radix-Tree/Images/test.md b/Radix-Tree/Images/test.md
deleted file mode 100644
index 8b1378917..000000000
--- a/Radix-Tree/Images/test.md
+++ /dev/null
@@ -1 +0,0 @@
-

From be4e1a9180aa6c1a6be294249550a1b4589ea584 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:13:56 -0400
Subject: [PATCH 0264/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 1b41d1a93..db6dfe7b8 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,6 +1,7 @@
 # Radix Tree
 
 A radix tree is a tree where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses and by traversing from the root to any leaf in the tree, (by concatenating all the labels of edges along the way) you can find any string. This is a radix tree:
+![](/Images/radixtree.png)
 
 ## Operations
 

From 2e16592b4c3cf2f183bf293cad6fd4183e43aba4 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 14 Apr 2016 12:14:33 -0400
Subject: [PATCH 0265/1679] Update README.markdown

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index db6dfe7b8..eecbeb6f3 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -1,7 +1,7 @@
 # Radix Tree
 
 A radix tree is a tree where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses and by traversing from the root to any leaf in the tree, (by concatenating all the labels of edges along the way) you can find any string. This is a radix tree:
-![](/Images/radixtree.png)
+![](/Radix-Tree/Images/radixtree.png)
 
 ## Operations
 

From d74c1aa5f440424af52160d69d9744be42da15bb Mon Sep 17 00:00:00 2001
From: Luisa Herrmann <herrlui@gmail.com>
Date: Fri, 15 Apr 2016 16:49:25 +0200
Subject: [PATCH 0266/1679] Add minimum edit distance for strings

---
 .../MinimumEditDistance.swift                 | 27 +++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 Minimum Edit Distance/MinimumEditDistance.swift

diff --git a/Minimum Edit Distance/MinimumEditDistance.swift b/Minimum Edit Distance/MinimumEditDistance.swift
new file mode 100644
index 000000000..b03c76f8c
--- /dev/null
+++ b/Minimum Edit Distance/MinimumEditDistance.swift	
@@ -0,0 +1,27 @@
+extension String {
+    
+    public func minimumEditDistance(other: String) -> Int {
+        let m = self.characters.count
+        let n = other.characters.count
+        var matrix = [[Int]](count: m+1, repeatedValue: [Int](count: n+1, repeatedValue: 0))
+        
+        for index in 1...m {
+            matrix[index][0]=index
+        }
+        for index in 1...n {
+            matrix[0][index]=index
+        }
+        
+        for (i, selfChar) in self.characters.enumerate() {
+            for (j, otherChar) in other.characters.enumerate() {
+                if otherChar == selfChar {
+                    matrix[i+1][j+1] = matrix[i][j]
+                } else {
+                    matrix[i+1][j+1] = min(matrix[i][j]+1, matrix[i+1][j]+1, matrix[i][j+1]+1)
+                }
+                
+            }
+        }
+        return matrix[m][n]
+    }
+}

From f3da019e1f12018c5a0eeb3e36733601ab60ee3a Mon Sep 17 00:00:00 2001
From: Luisa Herrmann <herrlui@gmail.com>
Date: Sun, 17 Apr 2016 16:11:30 +0200
Subject: [PATCH 0267/1679] added README.markdown and some comments in the code

---
 .../MinimumEditDistance.swift                 |  7 ++
 Minimum Edit Distance/README.markdown         | 65 +++++++++++++++++++
 2 files changed, 72 insertions(+)
 create mode 100644 Minimum Edit Distance/README.markdown

diff --git a/Minimum Edit Distance/MinimumEditDistance.swift b/Minimum Edit Distance/MinimumEditDistance.swift
index b03c76f8c..8008e03ba 100644
--- a/Minimum Edit Distance/MinimumEditDistance.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.swift	
@@ -5,18 +5,25 @@ extension String {
         let n = other.characters.count
         var matrix = [[Int]](count: m+1, repeatedValue: [Int](count: n+1, repeatedValue: 0))
         
+        
+        // initialize matrix
         for index in 1...m {
+            // the distance of any first string to an empty second string
             matrix[index][0]=index
         }
         for index in 1...n {
+            // the distance of any second string to an empty first string
             matrix[0][index]=index
         }
         
+        // compute Levenshtein distance
         for (i, selfChar) in self.characters.enumerate() {
             for (j, otherChar) in other.characters.enumerate() {
                 if otherChar == selfChar {
+                    // substitution of equal symbols with cost 0
                     matrix[i+1][j+1] = matrix[i][j]
                 } else {
+                    // minimum of the cost of insertion, deletion, or substitution added to the already computed costs in the corresponding cells
                     matrix[i+1][j+1] = min(matrix[i][j]+1, matrix[i+1][j]+1, matrix[i][j+1]+1)
                 }
                 
diff --git a/Minimum Edit Distance/README.markdown b/Minimum Edit Distance/README.markdown
new file mode 100644
index 000000000..d72e0dbda
--- /dev/null
+++ b/Minimum Edit Distance/README.markdown	
@@ -0,0 +1,65 @@
+# Minimum Edit Distance
+
+The minimum edit distance is a possibility to measure the similarity of two strings *w* and *u* by counting costs of operations which are necessary to transform *w* into *u* (or vice versa).
+
+### Algorithm using Levenshtein distance
+
+A common distance measure is given by the *Levenshtein distance*, which allows the following three transformation operations:
+
+* **Inseration** (*ε→x*) of a single symbol *x* with **cost 1**,
+* **Deletion** (*x→ε*) of a single symbol *x* with **cost 1**, and
+* **Substitution** (*x→y*) of two single symbols *x, y* with **cost 1** if *x≠y* and with **cost 0** otherwise.
+
+When transforming a string by a sequence of operations, the costs of the single operations are added to obtain the (minimal) edit distance. For example, the string *Door* can be transformed by the operations *o→l*, *r→l*, *ε→s* to the string *Dolls*, which results in a minimum edit distance of 3.
+
+To avoid exponential time complexity, the minimum edit distance of two strings in the usual is computed using *dynamic programming*. For this in a matrix
+
+```swift
+var matrix = [[Int]](count: m+1, repeatedValue: [Int](count: n+1, repeatedValue: 0))
+```
+
+already computed minimal edit distances of prefixes of *w* and *u* (of length *m* and *n*, respectively) are used to fill the matrix. In a first step the matrix is initialized by filling the first row and the first column as follows:
+
+```swift
+// initialize matrix
+for index in 1...m {
+    // the distance of any prefix of the first string to an empty second string
+    matrix[index][0]=index
+}
+for index in 1...n {
+    // the distance of any prefix of the second string to an empty first string
+    matrix[0][index]=index
+}
+```
+Then in each cell the minimum of the cost of insertion, deletion, or substitution added to the already computed costs in the corresponding cells is chosen. In this way the matrix is filled iteratively:
+
+```swift
+// compute Levenshtein distance
+for (i, selfChar) in self.characters.enumerate() {
+    for (j, otherChar) in other.characters.enumerate() {
+        if otherChar == selfChar {
+            // substitution of equal symbols with cost 0
+            matrix[i+1][j+1] = matrix[i][j]
+        } else {
+            // minimum of the cost of insertion, deletion, or substitution added 
+            // to the already computed costs in the corresponing cells
+            matrix[i+1][j+1] = min(matrix[i][j]+1, matrix[i+1][j]+1, matrix[i][j+1]+1)
+        }
+                
+    }
+}
+```
+
+After applying this algorithm, the minimal edit distance can be read from the rightmost bottom cell and is returned.
+
+```swift
+return matrix[m][n]
+```
+
+This algorithm has a time complexity of Θ(*mn*).
+
+### Other distance measures
+
+**todo**
+
+*Written for Swift Algorithm Club by Luisa Herrmann*
\ No newline at end of file

From 11d7e8a46cbd3b9037593506ad7e55172eff7479 Mon Sep 17 00:00:00 2001
From: Steven Scally <scalls@rpi.edu>
Date: Thu, 21 Apr 2016 18:17:26 -0400
Subject: [PATCH 0268/1679] Testing two approaches to a RadixTree

---
 Radix-Tree/EdgeTree.swift  | 149 +++++++++++++++++++++++++++++++++++++
 Radix-Tree/RadixTree.swift | 123 ++++++++++++++++++++++++++++++
 2 files changed, 272 insertions(+)
 create mode 100644 Radix-Tree/EdgeTree.swift
 create mode 100644 Radix-Tree/RadixTree.swift

diff --git a/Radix-Tree/EdgeTree.swift b/Radix-Tree/EdgeTree.swift
new file mode 100644
index 000000000..06a8b0b7a
--- /dev/null
+++ b/Radix-Tree/EdgeTree.swift
@@ -0,0 +1,149 @@
+class Root {
+
+	var children: [Edge]
+
+	init() {
+		children = [Edge]()
+	}
+
+}
+
+class Edge: Root {
+
+	var parent: Edge?
+	var label: String
+
+	init(_ label: String) {
+		self.label = label
+		super.init()
+	}
+
+}
+
+class EdgeTree {
+
+	var root: Root
+
+	init() {
+		root = Root()
+	}
+
+	func insert(_ str: String) -> Bool {
+
+		//Account for a blank input
+		if str == "" {
+			return true
+		}
+
+		//Account for an empty tree
+		if root.children.count == 0 {
+			root.children.append( Edge(str) )
+			return true
+		}
+
+		var searchStr = str
+		var currEdge = root
+
+		while (true) {
+
+			var i = 0
+
+			for e in currEdge.children {
+
+				//Get the shared 
+				var shared = sharedPrefix(searchStr, e.label)
+				var index  = shared.startIndex
+
+				//The search string is equal to the shared string
+				//so the string already exists in the tree
+				if searchStr == shared {
+					return false
+				}
+
+				//The child's label is a prefix of the search string
+				else if e.label.hasPrefix(shared) {
+
+					for _ in 1...shared.characters.count {
+						index = index.successor()
+					}
+
+					//Substring the search string so that the prefix is removed
+					searchStr = searchStr.substringFromIndex(index)
+
+					//Set currNode to e
+					currEdge = e
+					break
+
+				}
+
+
+				//The child's label and the search string share a prefix
+				else if shared.characters.count > 0 {
+
+					//Cut the prefix off from both the search string and label
+					var labelIndex = e.label.characters.startIndex
+
+					for _ in 1...shared.characters.count {
+						index = index.successor()
+						labelIndex = labelIndex.successor()
+					}
+
+					searchStr = searchStr.substringFromIndex(index)
+					e.label = e.label.substringFromIndex(labelIndex)
+
+					//Create a new edge whose label is the shared string
+					//its parent is currEdge.parent and add a child with
+					//label = searchStr
+					//Also add it to the parent's children
+					let newEdge = Edge(shared)
+					newEdge.children.append( Edge(searchStr) )
+					newEdge.parent = e.parent
+					currEdge.children.append(newEdge)
+
+					//Remove this edge from the parent's child list
+					currEdge.children.remove(at: i)
+
+					//Set this edge's parent to the prefix node
+					e.parent = newEdge.parent
+					return true
+
+				}
+
+				//They don't share a prefix (go to next child)
+				i += 1
+
+			}
+
+			//No children share a prefix, so create a new child
+			currEdge.children.append( Edge(searchStr) )
+			return true
+		}
+	}
+}
+
+//Returns the prefix that is shared between the two input strings
+//i.e. sharedPrefix("court", "coral") -> "co"
+func sharedPrefix(_ str1: String, _ str2: String) -> String {
+
+	var temp = ""
+
+	var c1 = str1.characters.startIndex
+	var c2 = str2.characters.startIndex
+
+	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+
+		if str1[c1] == str2[c2] {
+			temp.append( str1[c1] )
+			c1 = c1.successor()
+			c2 = c2.successor()
+		}
+
+		else {
+			return temp
+		}
+
+	}
+
+	return temp
+
+}
\ No newline at end of file
diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
new file mode 100644
index 000000000..27dfbd8dc
--- /dev/null
+++ b/Radix-Tree/RadixTree.swift
@@ -0,0 +1,123 @@
+import Foundation
+
+
+public class RadixNode {
+	public var parent: RadixNode?
+	public var children = [(childNode: RadixNode, childEdgeLabel: String)]()
+
+	public init() {
+
+	}
+
+	public init(value: String) {
+		self.children.append((childNode: RadixNode(), childEdgeLabel: value))
+	}
+
+	public func addChild(_ node: RadixNode, _ label: String) {
+		children.append((node, label))
+		node.parent = self
+	}
+
+	public func getChildren() -> [(childNode: RadixNode, childEdgeLabel: String)] {
+		return children
+	}
+
+	public func getChildAt(i: Int) -> (RadixNode, String)? {
+		if i >= children.count {
+			return nil
+		}
+		return children[i]
+	}
+
+	public func getParent() -> RadixNode? {
+		return parent
+	}
+
+	public func isLeaf() -> Bool {
+		return children.count == 0
+	}
+}
+
+public class RadixTree {
+	public var root: RadixNode
+
+	//Construct an "empty" RadixTree with a single node
+	public init() {
+		root = RadixNode()
+	}
+
+	public init(value: String) {
+		self.root = RadixNode(value: value)
+	}
+
+	public func find(str: String, node: RadixNode?) -> Bool {
+		var currNode: RadixNode
+		var search = str
+		if (node == nil) {
+			currNode = self.root
+		}
+		else {
+			currNode = node!
+		}
+		if (str == "") {
+			return true
+		} 
+		else {
+			for n in 0...currNode.children.count-1 {
+				if (str.hasPrefix(currNode.children[n].childEdgeLabel)) {
+					let elementsFound = currNode.children[n].childEdgeLabel.characters.count
+					search = search.substringFromIndex(search.startIndex.advanced(by: elementsFound))
+					currNode = currNode.children[n].childNode
+					find(str: search, node: currNode)
+				}
+			}
+		}
+		return false
+	}
+
+	public func insert(str: String, node: RadixNode?) -> Bool {
+		var search = str
+		var currNode: RadixNode
+		if (node == nil) {
+			currNode = self.root
+		}
+		else {
+			currNode = node!
+		}
+		//Case 0: str == "" (it is already in the tree)
+		//			-> return false
+		if (str == "") {
+			return false
+		}
+		else {
+			for c in currNode.children {
+
+			//Temp is the string of the prefix that the label and the
+			//  search string have in common.
+			//let temp = currNode.children[c].childEdgeLabel.sharePrefix(str)
+
+			//Case 3: currNode has a child that shares some prefix with str
+			//			-> little bit more complicated
+			//if temp == 0 {
+
+				//Remove the shared characters from both the search string and
+				//  label
+				//currNode.children[c].childEdgeLabel.substringFromIndex(temp.count)
+				//str.substringFromIndex(temp.count)
+
+
+			//}
+			
+
+			//Case 1: currNode has no children that share a prefix with str
+			//			-> create a new child for currNode		
+
+
+			//Case 2: currNode has a child whose label is a prefix of str
+			//			-> recurse down
+
+			}
+		}
+		return false
+	}
+}
\ No newline at end of file

From 27d92a6848e7aa06daeea7d18e6ef488a8c0856e Mon Sep 17 00:00:00 2001
From: Keita Ito <keitaitok@gmail.com>
Date: Thu, 21 Apr 2016 17:59:29 -0700
Subject: [PATCH 0269/1679] Fix code snippet

---
 Graph/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index b76fae732..8e88f80eb 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -234,7 +234,7 @@ public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vert
   adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
 }
 
-public func weightFrom(sourceVertex: GraphVertex<T>, toDestinationVertex: GraphVertex<T>) -> Double? {
+public func weightFrom(sourceVertex: Vertex<T>, toDestinationVertex: Vertex<T>) -> Double? {
   return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
 }
 ```

From 6894b2e7a0d09f97dc3a6e2636e52a16ed58d15e Mon Sep 17 00:00:00 2001
From: Keita Ito <keitaitok@gmail.com>
Date: Thu, 21 Apr 2016 18:04:19 -0700
Subject: [PATCH 0270/1679] Fix typo

---
 Boyer-Moore/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index a8f2c9f7a..ad1d3bc73 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -143,7 +143,7 @@ See also: [a detailed analysis](http://www.inf.fh-flensburg.de/lang/algorithmen/
 
 A variation on the above algorithm is the [Boyer-Moore-Horspool algorithm](https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm).
 
-Like the regular Boyer-Moore algorithm, it uses the `skipTable` to skip ahead a number of characters. The difference is in how we check partial matches. In the above version, it a partial match is found but it's not a complete match, we skip ahead by just one character. In this revised version, we also use the skip table in that situation.
+Like the regular Boyer-Moore algorithm, it uses the `skipTable` to skip ahead a number of characters. The difference is in how we check partial matches. In the above version, if a partial match is found but it's not a complete match, we skip ahead by just one character. In this revised version, we also use the skip table in that situation.
 
 Here's an implementation of the Boyer-Moore-Horspool algorithm:
 

From d18b61132b81ac02ff23c39a2e11648b16a17dd5 Mon Sep 17 00:00:00 2001
From: Keita Ito <keitaitok@gmail.com>
Date: Thu, 21 Apr 2016 18:23:21 -0700
Subject: [PATCH 0271/1679] Fix code snippet by adding forced unwrapping

---
 Linked List/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 24360e2b5..e78735350 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -408,7 +408,7 @@ If you don't have a reference to the node, you can use `removeLast()` or `remove
   public func removeAtIndex(index: Int) -> T {
     let node = nodeAtIndex(index)
     assert(node != nil)
-    return removeNode(node)
+    return removeNode(node!)
   }
 ```
 

From 2eb7e9f144b0b099be48149da4524925453ee4e2 Mon Sep 17 00:00:00 2001
From: Jayson Tung <JFTung@users.noreply.github.com>
Date: Sat, 23 Apr 2016 15:27:13 -0400
Subject: [PATCH 0272/1679] Begin converting BinarySearchTree.swift to
 ThreadedBinaryTree.swift

---
 Threaded Binary Tree/ThreadedBinaryTree.swift | 380 ++++++++++++++++++
 1 file changed, 380 insertions(+)
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTree.swift

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
new file mode 100644
index 000000000..f83dd4592
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTree.swift	
@@ -0,0 +1,380 @@
+/*
+  A threaded binary tree based on this club's binary search tree implementation.
+
+  Each node stores a value and two children. The left child contains a smaller
+  value; the right a larger (or equal) value.
+  
+  Any nodes that lack either a left or right child instead keep track of their
+  in-order predecessor and/or successor.
+
+  This tree allows duplicate elements.
+
+  This tree does not automatically balance itself. To make sure it is balanced,
+  you should insert new values in randomized order, not in sorted order.
+*/
+public class ThreadedBinaryTree<T: Comparable> {
+  private(set) public var value: T
+  private(set) public var parent: ThreadedBinaryTree?
+  private(set) public var left: ThreadedBinaryTree?
+  private(set) public var right: ThreadedBinaryTree?
+
+  public init(value: T) {
+    self.value = value
+  }
+
+  public convenience init(array: [T]) {
+    precondition(array.count > 0)
+    self.init(value: array.first!)
+    for v in array.dropFirst() {
+      insert(v, parent: self)
+    }
+  }
+
+  public var isRoot: Bool {
+    return parent == nil
+  }
+
+  public var isLeaf: Bool {
+    return left == nil && right == nil
+  }
+
+  public var isLeftChild: Bool {
+    return parent?.left === self
+  }
+
+  public var isRightChild: Bool {
+    return parent?.right === self
+  }
+
+  public var hasLeftChild: Bool {
+    return left != nil
+  }
+
+  public var hasRightChild: Bool {
+    return right != nil
+  }
+
+  public var hasAnyChild: Bool {
+    return hasLeftChild || hasRightChild
+  }
+
+  public var hasBothChildren: Bool {
+    return hasLeftChild && hasRightChild
+  }
+
+  /* How many nodes are in this subtree. Performance: O(n). */
+  public var count: Int {
+    return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+  }
+}
+
+// MARK: - Adding items
+
+extension ThreadedBinaryTree {
+  /*
+    Inserts a new element into the tree. You should only insert elements
+    at the root, to make to sure this remains a valid binary tree!
+    Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func insert(value: T) {
+    insert(value, parent: self)
+  }
+  
+  private func insert(value: T, parent: ThreadedBinaryTree) {
+    if value < self.value {
+      if let left = left {
+        left.insert(value, parent: left)
+      } else {
+        left = ThreadedBinaryTree(value: value)
+        left?.parent = parent
+      }
+    } else {
+      if let right = right {
+        right.insert(value, parent: right)
+      } else {
+        right = ThreadedBinaryTree(value: value)
+        right?.parent = parent
+      }
+    }
+  }
+}
+
+// MARK: - Deleting items
+
+extension ThreadedBinaryTree {
+  /*
+    Deletes a node from the tree.
+
+    Returns the node that has replaced this removed one (or nil if this was a
+    leaf node). That is primarily useful for when you delete the root node, in
+    which case the tree gets a new root.
+
+    Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func remove() -> ThreadedBinaryTree? {
+    let replacement: ThreadedBinaryTree?
+
+    if let left = left {
+      if let right = right {
+        replacement = removeNodeWithTwoChildren(left, right)
+      } else {
+        // This node only has a left child. The left child replaces the node.
+        replacement = left
+      }
+    } else if let right = right {
+      // This node only has a right child. The right child replaces the node.
+      replacement = right
+    } else {
+      // This node has no children. We just disconnect it from its parent.
+      replacement = nil
+    }
+
+    reconnectParentToNode(replacement)
+
+    // The current node is no longer part of the tree, so clean it up.
+    parent = nil
+    left = nil
+    right = nil
+
+    return replacement
+  }
+
+  private func removeNodeWithTwoChildren(left: ThreadedBinaryTree, _ right: BinarySearchTree) -> BinarySearchTree {
+    // This node has two children. It must be replaced by the smallest
+    // child that is larger than this node's value, which is the leftmost
+    // descendent of the right child.
+    let successor = right.minimum()
+
+    // If this in-order successor has a right child of its own (it cannot
+    // have a left child by definition), then that must take its place.
+    successor.remove()
+
+    // Connect our left child with the new node.
+    successor.left = left
+    left.parent = successor
+
+    // Connect our right child with the new node. If the right child does
+    // not have any left children of its own, then the in-order successor
+    // *is* the right child.
+    if right !== successor {
+      successor.right = right
+      right.parent = successor
+    } else {
+      successor.right = nil
+    }
+
+    // And finally, connect the successor node to our parent.
+    return successor
+  }
+
+  private func reconnectParentToNode(node: ThreadedBinaryTree?) {
+    if let parent = parent {
+      if isLeftChild {
+        parent.left = node
+      } else {
+        parent.right = node
+      }
+    }
+    node?.parent = parent
+  }
+}
+
+// MARK: - Searching
+
+extension ThreadedBinaryTree {
+  /*
+    Finds the "highest" node with the specified value.
+    Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func search(value: T) -> ThreadedBinaryTree? {
+    var node: ThreadedBinaryTree? = self
+    while case let n? = node {
+      if value < n.value {
+        node = n.left
+      } else if value > n.value {
+        node = n.right
+      } else {
+        return node
+      }
+    }
+    return nil
+  }
+
+  /*
+  // Recursive version of search
+  public func search(value: T) -> ThreadedBinaryTree? {
+    if value < self.value {
+      return left?.search(value)
+    } else if value > self.value {
+      return right?.search(value)
+    } else {
+      return self  // found it!
+    }
+  }
+  */
+  
+  public func contains(value: T) -> Bool {
+    return search(value) != nil
+  }
+
+  /*
+    Returns the leftmost descendent. O(h) time.
+  */
+  public func minimum() -> ThreadedBinaryTree {
+    var node = self
+    while case let next? = node.left {
+      node = next
+    }
+    return node
+  }
+  
+  /*
+    Returns the rightmost descendent. O(h) time.
+  */
+  public func maximum() -> ThreadedBinaryTree {
+    var node = self
+    while case let next? = node.right {
+      node = next
+    }
+    return node
+  }
+  
+  /*
+    Calculates the depth of this node, i.e. the distance to the root.
+    Takes O(h) time.
+  */
+  public func depth() -> Int {
+    var node = self
+    var edges = 0
+    while case let parent? = node.parent {
+      node = parent
+      edges += 1
+    }
+    return edges
+  }
+  
+  /*
+    Calculates the height of this node, i.e. the distance to the lowest leaf.
+    Since this looks at all children of this node, performance is O(n).
+  */
+  public func height() -> Int {
+    if isLeaf {
+      return 0
+    } else {
+      return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+    }
+  }
+
+  /*
+    Finds the node whose value precedes our value in sorted order.
+  */
+  public func predecessor() -> ThreadedBinaryTree<T>? {
+    if let left = left {
+      return left.maximum()
+    } else {
+      var node = self
+      while case let parent? = node.parent {
+        if parent.value < value { return parent }
+        node = parent
+      }
+      return nil
+    }
+  }
+
+  /*
+    Finds the node whose value succeeds our value in sorted order.
+  */
+  public func successor() -> ThreadedBinaryTree<T>? {
+    if let right = right {
+      return right.minimum()
+    } else {
+      var node = self
+      while case let parent? = node.parent {
+        if parent.value > value { return parent }
+        node = parent
+      }
+      return nil
+    }
+  }
+}
+
+// MARK: - Traversal
+
+extension ThreadedBinaryTree {
+  public func traverseInOrder(@noescape process: T -> Void) {
+    left?.traverseInOrder(process)
+    process(value)
+    right?.traverseInOrder(process)
+  }
+  
+  public func traversePreOrder(@noescape process: T -> Void) {
+    process(value)
+    left?.traversePreOrder(process)
+    right?.traversePreOrder(process)
+  }
+  
+  public func traversePostOrder(@noescape process: T -> Void) {
+    left?.traversePostOrder(process)
+    right?.traversePostOrder(process)
+    process(value)
+  }
+
+  /*
+    Performs an in-order traversal and collects the results in an array.
+  */
+  public func map(@noescape formula: T -> T) -> [T] {
+    var a = [T]()
+    if let left = left { a += left.map(formula) }
+    a.append(formula(value))
+    if let right = right { a += right.map(formula) }
+    return a
+  }
+}
+
+/*
+  Is this binary tree a valid binary search tree?
+*/
+extension ThreadedBinaryTree {
+  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
+    if value < minValue || value > maxValue { return false }
+    let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+    let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+    return leftBST && rightBST
+  }
+}
+
+// MARK: - Debugging
+
+extension ThreadedBinaryTree: CustomStringConvertible {
+  public var description: String {
+    var s = ""
+    if let left = left {
+      s += "(\(left.description)) <- "
+    }
+    s += "\(value)"
+    if let right = right {
+      s += " -> (\(right.description))"
+    }
+    return s
+  }
+}
+
+extension ThreadedBinaryTree: CustomDebugStringConvertible {
+  public var debugDescription: String {
+    var s = "value: \(value)"
+    if let parent = parent {
+      s += ", parent: \(parent.value)"
+    }
+    if let left = left {
+      s += ", left = [" + left.debugDescription + "]"
+    }
+    if let right = right {
+      s += ", right = [" + right.debugDescription + "]"
+    }
+    return s
+  }
+
+  public func toArray() -> [T] {
+    return map { $0 }
+  }
+}

From 6065c25c9257c9c8aa9ec0cfa42429034791c70a Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 13:57:32 -0400
Subject: [PATCH 0273/1679] Removed Adjacency List directory and EdgeTree.swift
 class in Radix Tree directory

---
 Adjacency-List/README.markdown |   1 -
 "Adjacency\\ List"             |   1 -
 Radix-Tree/EdgeTree.swift      | 149 ---------------------------------
 3 files changed, 151 deletions(-)
 delete mode 100644 Adjacency-List/README.markdown
 delete mode 100644 "Adjacency\\ List"
 delete mode 100644 Radix-Tree/EdgeTree.swift

diff --git a/Adjacency-List/README.markdown b/Adjacency-List/README.markdown
deleted file mode 100644
index aebd1a631..000000000
--- a/Adjacency-List/README.markdown
+++ /dev/null
@@ -1 +0,0 @@
-Adjacency List README
diff --git "a/Adjacency\\ List" "b/Adjacency\\ List"
deleted file mode 100644
index 8b1378917..000000000
--- "a/Adjacency\\ List"	
+++ /dev/null
@@ -1 +0,0 @@
-
diff --git a/Radix-Tree/EdgeTree.swift b/Radix-Tree/EdgeTree.swift
deleted file mode 100644
index 06a8b0b7a..000000000
--- a/Radix-Tree/EdgeTree.swift
+++ /dev/null
@@ -1,149 +0,0 @@
-class Root {
-
-	var children: [Edge]
-
-	init() {
-		children = [Edge]()
-	}
-
-}
-
-class Edge: Root {
-
-	var parent: Edge?
-	var label: String
-
-	init(_ label: String) {
-		self.label = label
-		super.init()
-	}
-
-}
-
-class EdgeTree {
-
-	var root: Root
-
-	init() {
-		root = Root()
-	}
-
-	func insert(_ str: String) -> Bool {
-
-		//Account for a blank input
-		if str == "" {
-			return true
-		}
-
-		//Account for an empty tree
-		if root.children.count == 0 {
-			root.children.append( Edge(str) )
-			return true
-		}
-
-		var searchStr = str
-		var currEdge = root
-
-		while (true) {
-
-			var i = 0
-
-			for e in currEdge.children {
-
-				//Get the shared 
-				var shared = sharedPrefix(searchStr, e.label)
-				var index  = shared.startIndex
-
-				//The search string is equal to the shared string
-				//so the string already exists in the tree
-				if searchStr == shared {
-					return false
-				}
-
-				//The child's label is a prefix of the search string
-				else if e.label.hasPrefix(shared) {
-
-					for _ in 1...shared.characters.count {
-						index = index.successor()
-					}
-
-					//Substring the search string so that the prefix is removed
-					searchStr = searchStr.substringFromIndex(index)
-
-					//Set currNode to e
-					currEdge = e
-					break
-
-				}
-
-
-				//The child's label and the search string share a prefix
-				else if shared.characters.count > 0 {
-
-					//Cut the prefix off from both the search string and label
-					var labelIndex = e.label.characters.startIndex
-
-					for _ in 1...shared.characters.count {
-						index = index.successor()
-						labelIndex = labelIndex.successor()
-					}
-
-					searchStr = searchStr.substringFromIndex(index)
-					e.label = e.label.substringFromIndex(labelIndex)
-
-					//Create a new edge whose label is the shared string
-					//its parent is currEdge.parent and add a child with
-					//label = searchStr
-					//Also add it to the parent's children
-					let newEdge = Edge(shared)
-					newEdge.children.append( Edge(searchStr) )
-					newEdge.parent = e.parent
-					currEdge.children.append(newEdge)
-
-					//Remove this edge from the parent's child list
-					currEdge.children.remove(at: i)
-
-					//Set this edge's parent to the prefix node
-					e.parent = newEdge.parent
-					return true
-
-				}
-
-				//They don't share a prefix (go to next child)
-				i += 1
-
-			}
-
-			//No children share a prefix, so create a new child
-			currEdge.children.append( Edge(searchStr) )
-			return true
-		}
-	}
-}
-
-//Returns the prefix that is shared between the two input strings
-//i.e. sharedPrefix("court", "coral") -> "co"
-func sharedPrefix(_ str1: String, _ str2: String) -> String {
-
-	var temp = ""
-
-	var c1 = str1.characters.startIndex
-	var c2 = str2.characters.startIndex
-
-	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
-
-		if str1[c1] == str2[c2] {
-			temp.append( str1[c1] )
-			c1 = c1.successor()
-			c2 = c2.successor()
-		}
-
-		else {
-			return temp
-		}
-
-	}
-
-	return temp
-
-}
\ No newline at end of file

From 6d5d92a2c423aab6c11f8b0ca12bcf4326e9b155 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 13:58:52 -0400
Subject: [PATCH 0274/1679] Removed Adjacency List from README.markdown

---
 README.markdown | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 9a536bb63..2f883c287 100644
--- a/README.markdown
+++ b/README.markdown
@@ -174,7 +174,6 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
 - [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
 - All Paths
-- [Adjacency List](Adjacency-List/) :construction:
 
 ## Puzzles
 

From 32c558b8f4fb8bb964d1fcdf3aff40a045afb447 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 14:03:47 -0400
Subject: [PATCH 0275/1679] Added main.swift to the Radix-Tree directory and
 updated RadixTree.swift class

---
 Radix-Tree/main.swift | 63 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 Radix-Tree/main.swift

diff --git a/Radix-Tree/main.swift b/Radix-Tree/main.swift
new file mode 100644
index 000000000..cad669697
--- /dev/null
+++ b/Radix-Tree/main.swift
@@ -0,0 +1,63 @@
+var radix = RadixTree()
+var radix2 = RadixTree()
+var radixWiki = RadixTree()
+
+print("-------------------------------------------------")
+radix.printTree()
+print("--------------------------------------------------")
+radix.insert( "courting" )
+radix.printTree()
+print("-------------------------------------------------")
+radix.insert( "coral" )
+radix.printTree()
+print("--------------------------------------------------")
+radix.insert( "courted" )
+radix.printTree()
+print("---------------------------------------------------")
+print( radix.insert( "corals") )
+radix.printTree()
+
+print( radixWiki.insert("romanus") )
+print( radixWiki.insert("rubicundus") )
+print( radixWiki.insert("rubicon") )
+print( radixWiki.insert("romane") )
+print( radixWiki.insert("ruber") )
+print( radixWiki.insert("rubens") )
+print( radixWiki.insert("romulus") )
+radixWiki.insert("start")
+radixWiki.insert("shoot")
+radixWiki.insert("shit")
+radixWiki.insert("starch")
+radixWiki.insert("steven")
+
+radixWiki.insert("compute")
+radixWiki.insert("compatible")
+radixWiki.insert("construction")
+radixWiki.insert("coral")
+radixWiki.insert("crude")
+radixWiki.insert("chalk")
+radixWiki.insert("chime")
+radixWiki.insert("courting")
+radixWiki.insert("courted")
+
+print("PRINT TEST-------------------------------")
+radixWiki.printTree()
+
+// let h = radix.height()
+// let h2 = radix2.height()
+// let hwiki = radixWiki.height()
+// print("Height of tree: \(h)")
+// print("height of second tree: \(h2)")
+// print("Height of wikipedia tree: \(hwiki)")
+
+// print(radixWiki.root.level())
+// print(radixWiki.root.children[0].level())
+// print(radixWiki.root.children[0].children[0].level())
+// print(radixWiki.root.children[0].children[0].children[0].level())
+
+// print("\t\t\t\t\t\ttest")
+// print("PRINT TEST-------------------------------")
+// radixWiki.printTree()
+
+// print("PRINT TEST-------------------------------")
+// radix.printTree()
\ No newline at end of file

From cf7c08731baf2e7e8f7678a800427bb78cc84840 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 14:19:06 -0400
Subject: [PATCH 0276/1679] Updated RadixTree.swift and main.swift

---
 Radix-Tree/RadixTree.swift | 278 +++++++++++++++++++++++++------------
 Radix-Tree/main.swift      |  32 +++--
 2 files changed, 208 insertions(+), 102 deletions(-)

diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
index 27dfbd8dc..b58dee309 100644
--- a/Radix-Tree/RadixTree.swift
+++ b/Radix-Tree/RadixTree.swift
@@ -1,123 +1,227 @@
 import Foundation
 
+class Root {
 
-public class RadixNode {
-	public var parent: RadixNode?
-	public var children = [(childNode: RadixNode, childEdgeLabel: String)]()
+	var children: [Edge]
 
-	public init() {
-
-	}
-
-	public init(value: String) {
-		self.children.append((childNode: RadixNode(), childEdgeLabel: value))
-	}
-
-	public func addChild(_ node: RadixNode, _ label: String) {
-		children.append((node, label))
-		node.parent = self
-	}
-
-	public func getChildren() -> [(childNode: RadixNode, childEdgeLabel: String)] {
-		return children
+	init() {
+		children = [Edge]()
 	}
 
-	public func getChildAt(i: Int) -> (RadixNode, String)? {
-		if i >= children.count {
-			return nil
+	func height() -> Int {
+		if children.count == 0 {
+			return 1
+		}
+		else {
+			var max = 1
+			for c in children {
+				if c.height() > max {
+					max = c.height()
+				}
+			}
+			return 1 + max
 		}
-		return children[i]
 	}
 
-	public func getParent() -> RadixNode? {
-		return parent
+	func level() -> Int {
+		return 0
 	}
 
-	public func isLeaf() -> Bool {
-		return children.count == 0
+	func printRoot() {
+		//print("children: \(children.count)")
+		//print("split at: \(children.count/2-1)")
+		if (children.count > 1) {
+			for c in 0...children.count/2-1 {
+				children[c].printEdge()
+				print("|")
+			}
+		}
+		else if children.count > 0 {
+			children[0].printEdge()
+		}
+		print("ROOT")
+		//print("second half starts at: \(children.count/2)")
+		if children.count > 1 {
+			for c in children.count/2...children.count-1 {
+				children[c].printEdge()
+				print("|")
+			}
+		}
+		print()
 	}
 }
 
-public class RadixTree {
-	public var root: RadixNode
+class Edge: Root {
 
-	//Construct an "empty" RadixTree with a single node
-	public init() {
-		root = RadixNode()
-	}
+	var parent: Root?
+	var label: String
 
-	public init(value: String) {
-		self.root = RadixNode(value: value)
+	init(_ label: String) {	//Edge(label: "label")
+		self.label = label
+		super.init()
 	}
 
-	public func find(str: String, node: RadixNode?) -> Bool {
-		var currNode: RadixNode
-		var search = str
-		if (node == nil) {
-			currNode = self.root
+	override
+	func level() -> Int {
+		if parent != nil {
+			return 1 + parent!.level()
 		}
 		else {
-			currNode = node!
-		}
-		if (str == "") {
-			return true
-		} 
-		else {
-			for n in 0...currNode.children.count-1 {
-				if (str.hasPrefix(currNode.children[n].childEdgeLabel)) {
-					let elementsFound = currNode.children[n].childEdgeLabel.characters.count
-					search = search.substringFromIndex(search.startIndex.advanced(by: elementsFound))
-					currNode = currNode.children[n].childNode
-					find(str: search, node: currNode)
-				}
-			}
+			return 1
 		}
-		return false
 	}
 
-	public func insert(str: String, node: RadixNode?) -> Bool {
-		var search = str
-		var currNode: RadixNode
-		if (node == nil) {
-			currNode = self.root
+	func printEdge() {
+		if children.count > 1 {
+			for c in 0...children.count/2-1 {
+				children[c].printEdge()
+			}
 		}
-		else {
-			currNode = node!
+		else if children.count > 0 {
+			children[0].printEdge()
+		}
+		for x in 1...level() {
+			if x == level() {
+				print("|------>", terminator: "")
+			}
+			else if x == 1 {
+				print("|       ", terminator: "")
+			}
+			else if x == level()-1 {
+				print("|       ", terminator: "")
+			}
+			else {
+				print("|       ", terminator: "")
+			}
 		}
-		//Case 0: str == "" (it is already in the tree)
-		//			-> return false
-		if (str == "") {
-			return false
+		print(label)
+		if children.count == 0 {
+			for _ in 1...level() {
+				print("|       ", terminator: "")
+			}
+			print()
 		}
-		else {
-			for c in currNode.children {
-
-			//Temp is the string of the prefix that the label and the
-			//  search string have in common.
-			//let temp = currNode.children[c].childEdgeLabel.sharePrefix(str)
-
-			//Case 3: currNode has a child that shares some prefix with str
-			//			-> little bit more complicated
-			//if temp == 0 {
+		if children.count > 1 {
+			for c in children.count/2...children.count-1 {
+				children[c].printEdge()
+			}
+		}
+	}
+}
 
-				//Remove the shared characters from both the search string and
-				//  label
-				//currNode.children[c].childEdgeLabel.substringFromIndex(temp.count)
-				//str.substringFromIndex(temp.count)
+class RadixTree {
 
+	var root: Root
 
-			//}
-			
+	init() {
+		root = Root()
+	}
 
-			//Case 1: currNode has no children that share a prefix with str
-			//			-> create a new child for currNode		
+	func height() -> Int {
+		return root.height() - 1
+	}
 
+	func insert(_ str: String) -> Bool {
+		//Account for a blank input
+		if str == "" {
+			return true
+		}
+		//Account for an empty tree
+		if root.children.count == 0 {
+			root.children.append( Edge(str) )
+			return true
+		}
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			var i = 0
+			if currEdge.children.count == 0 {
+				let newEdge = Edge(searchStr)
+				currEdge.children.append(newEdge)
+				newEdge.parent = currEdge
+			}
+			for e in currEdge.children {
+				//Get the shared 
+				var shared = sharedPrefix(searchStr, e.label)
+				var index  = shared.startIndex
+				//The search string is equal to the shared string
+				//so the string already exists in the tree
+				if searchStr == shared {
+					return false
+				}
+				else if shared == e.label {
+					currEdge = e
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+				//The child's label and the search string share a prefix
+				else if shared.characters.count > 0 {
+					//Cut the prefix off from both the search string and label
+					var labelIndex = e.label.characters.startIndex
+					//Create index objects and move them to after the shared prefix
+					for _ in 1...shared.characters.count {
+						index = index.successor()
+						labelIndex = labelIndex.successor()
+					}
+					//Substring both the search string and the label from the shared prefix
+					searchStr = searchStr.substringFromIndex(index)
+					e.label = e.label.substringFromIndex(labelIndex)
+					//Create 2 new edges and update parent/children values
+					let newEdge = Edge(e.label)
+					e.label = shared
+					for ec in e.children {
+						newEdge.children.append(ec)
+					}
+					newEdge.parent = e
+					e.children.removeAll()
+					for nec in newEdge.children {
+						nec.parent = newEdge
+					}
+					e.children.append(newEdge)
+					let newEdge2 = Edge(searchStr)
+					newEdge2.parent = e
+					e.children.append(newEdge2)
+					return true
+				}
+				//They don't share a prefix (go to next child)
+				i += 1
+			}
+			if (!found) {
+				//No children share a prefix, so create a new child
+				let newEdge = Edge(searchStr)
+				currEdge.children.append(newEdge)
+				newEdge.parent = currEdge
+				return true
+			}
+		}
+	}
 
-			//Case 2: currNode has a child whose label is a prefix of str
-			//			-> recurse down
+	func printTree() {
+		root.printRoot()
+	}
+}
 
-			}
+//Returns the prefix that is shared between the two input strings
+//i.e. sharedPrefix("court", "coral") -> "co"
+func sharedPrefix(_ str1: String, _ str2: String) -> String {
+	var temp = ""
+	var c1 = str1.characters.startIndex
+	var c2 = str2.characters.startIndex
+	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+		if str1[c1] == str2[c2] {
+			temp.append( str1[c1] )
+			c1 = c1.successor()
+			c2 = c2.successor()
+		}
+		else {
+			return temp
 		}
-		return false
 	}
+	return temp
 }
\ No newline at end of file
diff --git a/Radix-Tree/main.swift b/Radix-Tree/main.swift
index cad669697..148766834 100644
--- a/Radix-Tree/main.swift
+++ b/Radix-Tree/main.swift
@@ -40,24 +40,26 @@ radixWiki.insert("chime")
 radixWiki.insert("courting")
 radixWiki.insert("courted")
 
+radixWiki.insert("rubicunduses")
+
 print("PRINT TEST-------------------------------")
 radixWiki.printTree()
 
-// let h = radix.height()
-// let h2 = radix2.height()
-// let hwiki = radixWiki.height()
-// print("Height of tree: \(h)")
-// print("height of second tree: \(h2)")
-// print("Height of wikipedia tree: \(hwiki)")
+let h = radix.height()
+let h2 = radix2.height()
+let hwiki = radixWiki.height()
+print("Height of tree: \(h)")
+print("height of second tree: \(h2)")
+print("Height of wikipedia tree: \(hwiki)")
 
-// print(radixWiki.root.level())
-// print(radixWiki.root.children[0].level())
-// print(radixWiki.root.children[0].children[0].level())
-// print(radixWiki.root.children[0].children[0].children[0].level())
+print(radixWiki.root.level())
+print(radixWiki.root.children[0].level())
+print(radixWiki.root.children[0].children[0].level())
+print(radixWiki.root.children[0].children[0].children[0].level())
 
-// print("\t\t\t\t\t\ttest")
-// print("PRINT TEST-------------------------------")
-// radixWiki.printTree()
+print("\t\t\t\t\t\ttest")
+print("PRINT TEST-------------------------------")
+radixWiki.printTree()
 
-// print("PRINT TEST-------------------------------")
-// radix.printTree()
\ No newline at end of file
+print("PRINT TEST-------------------------------")
+radix.printTree()
\ No newline at end of file

From 7b1a04510509eef72185d81a8f78d263b13a92b4 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 15:02:46 -0400
Subject: [PATCH 0277/1679] Added find() to RadixTree class

---
 Radix-Tree/RadixTree.swift | 62 ++++++++++++++++++++++++++++++++++++--
 Radix-Tree/main.swift      | 53 +++++++-------------------------
 2 files changed, 70 insertions(+), 45 deletions(-)

diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
index b58dee309..39448fa27 100644
--- a/Radix-Tree/RadixTree.swift
+++ b/Radix-Tree/RadixTree.swift
@@ -124,7 +124,7 @@ class RadixTree {
 	func insert(_ str: String) -> Bool {
 		//Account for a blank input
 		if str == "" {
-			return true
+			return false
 		}
 		//Account for an empty tree
 		if root.children.count == 0 {
@@ -135,7 +135,6 @@ class RadixTree {
 		var currEdge = root
 		while (true) {
 			var found = false
-			var i = 0
 			if currEdge.children.count == 0 {
 				let newEdge = Edge(searchStr)
 				currEdge.children.append(newEdge)
@@ -190,7 +189,6 @@ class RadixTree {
 					return true
 				}
 				//They don't share a prefix (go to next child)
-				i += 1
 			}
 			if (!found) {
 				//No children share a prefix, so create a new child
@@ -202,6 +200,64 @@ class RadixTree {
 		}
 	}
 
+	func find(_ str: String) -> Bool {
+		//A radix tree always contains the empty string
+		if str == "" {
+			return true
+		}
+		//If there are no children then the string cannot be in the tree
+		else if root.children.count == 0 {
+			return false
+		}
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			for c in currEdge.children {
+				//First check if the search string and the child's label are equal
+				//  if so the string is in the tree, return true
+				if searchStr == c.label {
+					return true
+				}
+				//If that is not true, find the shared string b/t the search string
+				//  and the label
+				var shared = sharedPrefix(searchStr, c.label)
+				//If the shared string is equal to the label, update the curent node
+				//  and run it back
+				if shared == c.label {
+					currEdge = c
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+				//If the shared string is empty, go to the next children
+				else if shared.characters.count == 0 {
+					continue
+				}
+				//If the search string and the child's label only share some characters,
+				//  the string is not in the tree, return false
+				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
+				  shared.characters.count < c.label.characters.count {
+				  	return false
+				}
+			}
+			if !found {
+				return false
+			}
+		}
+		//Start at the root
+			//If a child's label is a prefix of the search string
+			//  Cut the prefix off of the search string and 
+			//    start looking through that child's children
+			//If a child's label == searchStr, return true
+
+		//If none of the children's labels are a prefix of the search string
+	}
+
 	func printTree() {
 		root.printRoot()
 	}
diff --git a/Radix-Tree/main.swift b/Radix-Tree/main.swift
index 148766834..b53ffb9ec 100644
--- a/Radix-Tree/main.swift
+++ b/Radix-Tree/main.swift
@@ -1,29 +1,13 @@
 var radix = RadixTree()
-var radix2 = RadixTree()
 var radixWiki = RadixTree()
 
-print("-------------------------------------------------")
-radix.printTree()
-print("--------------------------------------------------")
-radix.insert( "courting" )
-radix.printTree()
-print("-------------------------------------------------")
-radix.insert( "coral" )
-radix.printTree()
-print("--------------------------------------------------")
-radix.insert( "courted" )
-radix.printTree()
-print("---------------------------------------------------")
-print( radix.insert( "corals") )
-radix.printTree()
-
-print( radixWiki.insert("romanus") )
-print( radixWiki.insert("rubicundus") )
-print( radixWiki.insert("rubicon") )
-print( radixWiki.insert("romane") )
-print( radixWiki.insert("ruber") )
-print( radixWiki.insert("rubens") )
-print( radixWiki.insert("romulus") )
+radixWiki.insert("romanus")
+radixWiki.insert("rubicundus")
+radixWiki.insert("rubicon")
+radixWiki.insert("romane")
+radixWiki.insert("ruber")
+radixWiki.insert("rubens")
+radixWiki.insert("romulus")
 radixWiki.insert("start")
 radixWiki.insert("shoot")
 radixWiki.insert("shit")
@@ -42,24 +26,9 @@ radixWiki.insert("courted")
 
 radixWiki.insert("rubicunduses")
 
-print("PRINT TEST-------------------------------")
-radixWiki.printTree()
-
-let h = radix.height()
-let h2 = radix2.height()
-let hwiki = radixWiki.height()
-print("Height of tree: \(h)")
-print("height of second tree: \(h2)")
-print("Height of wikipedia tree: \(hwiki)")
-
-print(radixWiki.root.level())
-print(radixWiki.root.children[0].level())
-print(radixWiki.root.children[0].children[0].level())
-print(radixWiki.root.children[0].children[0].children[0].level())
-
-print("\t\t\t\t\t\ttest")
-print("PRINT TEST-------------------------------")
 radixWiki.printTree()
 
-print("PRINT TEST-------------------------------")
-radix.printTree()
\ No newline at end of file
+print("FIND TESTS")
+print(radixWiki.find("courts"))
+print(radixWiki.find("rubicunduses"))
+print(radixWiki.find(""))
\ No newline at end of file

From 7386c4d80ec7597b28708fe4ac5ec44dbb5f2e36 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 15:21:34 -0400
Subject: [PATCH 0278/1679] Updated RadixTree's README.markdown

---
 Radix-Tree/README.markdown | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index eecbeb6f3..9c126760e 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -3,10 +3,22 @@
 A radix tree is a tree where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses and by traversing from the root to any leaf in the tree, (by concatenating all the labels of edges along the way) you can find any string. This is a radix tree:
 ![](/Radix-Tree/Images/radixtree.png)
 
+## Implemenation
+
+The RadixTree class itself has one member variable, root, of type Root. The Root is the top of every RadixTree. Every node that is added, removed, looked up, etc. is a child, a child of a child, etc. of that root. The rest of the tree is represented as an Edge, which inherits Root. The different between Edge and Root is that Edges have a label (of type String) and a parent (of type Root?) member variables. This approach is a little different from the conventional way of creating Tree data structures but is easier to wrap your head around (see the picture above).
+
 ## Operations
 
 Typical operations on a radix tree include lookup, insertion, deletion, find predecessor, find successor, and find all strings with common prefix. The running time of lookup, insertion, and deletion is O(k) where k is the length of the key. This is different from most trees because these operations usually run in O(logn) time where n is the number of nodes in the tree.
 
+### Find
+
+The find function returns true if the String you are searching for is in the tree and false if it is not. Every RadixTree contains at the very least one String ("") so find("") will always return true. A String is considered "in the tree" if the String you are searching for is a concatenation of Edge labels while traversing downwards or a prefix of that concatenation. For example, if you look at the example tree above, find("roma") will return true because it is a prefix of the traversal "r"->"om"->"an". On the other hand, find("romans") will return false.
+
+### Insert
+
+The insert function returns true if the String you are trying to insert was successfully inserted into the RadixTree and false if the String is already in the tree. Similarly to find(""), insert("") will always return false because an empty RadixTree contains "" by default.
+
 ## See Also
 
 [Radix Tree - Wikipedia](https://en.wikipedia.org/wiki/Radix_tree)

From f11d617fe9641f5bb425c0dd810621c22aa8d184 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 15:22:41 -0400
Subject: [PATCH 0279/1679] Updated RadixTree's README.markdown

---
 Radix-Tree/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 9c126760e..918c8324c 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -11,11 +11,11 @@ The RadixTree class itself has one member variable, root, of type Root. The Root
 
 Typical operations on a radix tree include lookup, insertion, deletion, find predecessor, find successor, and find all strings with common prefix. The running time of lookup, insertion, and deletion is O(k) where k is the length of the key. This is different from most trees because these operations usually run in O(logn) time where n is the number of nodes in the tree.
 
-### Find
+### Find(_ str: String) -> Bool
 
 The find function returns true if the String you are searching for is in the tree and false if it is not. Every RadixTree contains at the very least one String ("") so find("") will always return true. A String is considered "in the tree" if the String you are searching for is a concatenation of Edge labels while traversing downwards or a prefix of that concatenation. For example, if you look at the example tree above, find("roma") will return true because it is a prefix of the traversal "r"->"om"->"an". On the other hand, find("romans") will return false.
 
-### Insert
+### Insert(_ str: String) -> Bool
 
 The insert function returns true if the String you are trying to insert was successfully inserted into the RadixTree and false if the String is already in the tree. Similarly to find(""), insert("") will always return false because an empty RadixTree contains "" by default.
 

From c648c8fc4be6224b57a76715260d8dcf59c8aa3b Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 15:30:51 -0400
Subject: [PATCH 0280/1679] Added more to RadixTree's README

---
 Radix-Tree/README.markdown | 25 +++++++++++++++++++++++--
 1 file changed, 23 insertions(+), 2 deletions(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 918c8324c..129d0add4 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -11,14 +11,35 @@ The RadixTree class itself has one member variable, root, of type Root. The Root
 
 Typical operations on a radix tree include lookup, insertion, deletion, find predecessor, find successor, and find all strings with common prefix. The running time of lookup, insertion, and deletion is O(k) where k is the length of the key. This is different from most trees because these operations usually run in O(logn) time where n is the number of nodes in the tree.
 
-### Find(_ str: String) -> Bool
+### RadixTree.find(_ str: String) -> Bool
 
 The find function returns true if the String you are searching for is in the tree and false if it is not. Every RadixTree contains at the very least one String ("") so find("") will always return true. A String is considered "in the tree" if the String you are searching for is a concatenation of Edge labels while traversing downwards or a prefix of that concatenation. For example, if you look at the example tree above, find("roma") will return true because it is a prefix of the traversal "r"->"om"->"an". On the other hand, find("romans") will return false.
 
-### Insert(_ str: String) -> Bool
+### RadixTree.insert(_ str: String) -> Bool
 
 The insert function returns true if the String you are trying to insert was successfully inserted into the RadixTree and false if the String is already in the tree. Similarly to find(""), insert("") will always return false because an empty RadixTree contains "" by default.
 
+### RadixTree.remove(_ str: String) -> Bool
+
+THIS IS NOT IMPLEMENTED YET
+
+### Root.level() -> Int
+
+The level function returns how far down in the tree the Root or Edge in question is. A Root object will always return 0. A child of the Root will return 1, a child of a child of the root will return 2, etc.
+
+### RadixTree.height() -> Int
+
+The height function returns an Int equal to the highest level in the Tree. An empty tree will return 0.
+
+### RadixTree.printTree()
+
+The printTree function was used to visualize the tree itself. This function is a little buggy and not perfect yet but gets the job done thus far.
+
+### sharedPrefix(_ str1: String, _ str2: String) ->
+
+The sharedPrefix function is a non-member function in the RadixTree.swift file. It takes in two String objects and returns the shared prefix between them. For example,
+sharedPrefix("apples", "oranges") will return "" and sharedPrefix("court", "coral") will return "co". This function is used in the implementation of the find, insert, and remove functions.
+
 ## See Also
 
 [Radix Tree - Wikipedia](https://en.wikipedia.org/wiki/Radix_tree)

From a6d58ec2cdf4f11ffe7ac6260c4c26d25583e77c Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 15:31:34 -0400
Subject: [PATCH 0281/1679] Fixed typo in RadixTree's README

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index 129d0add4..ef405bcb0 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -35,7 +35,7 @@ The height function returns an Int equal to the highest level in the Tree. An em
 
 The printTree function was used to visualize the tree itself. This function is a little buggy and not perfect yet but gets the job done thus far.
 
-### sharedPrefix(_ str1: String, _ str2: String) ->
+### sharedPrefix(_ str1: String, _ str2: String) -> String
 
 The sharedPrefix function is a non-member function in the RadixTree.swift file. It takes in two String objects and returns the shared prefix between them. For example,
 sharedPrefix("apples", "oranges") will return "" and sharedPrefix("court", "coral") will return "co". This function is used in the implementation of the find, insert, and remove functions.

From 42e259f0a8cae284cda4826e3e0f7211ccdd696f Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Tue, 26 Apr 2016 17:21:39 -0400
Subject: [PATCH 0282/1679] Added remove() to the RadixTree class

---
 Radix-Tree/RadixTree.swift | 73 ++++++++++++++++++++++++++++++++++----
 Radix-Tree/main.swift      | 22 ++++++++++--
 2 files changed, 86 insertions(+), 9 deletions(-)

diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
index 39448fa27..994a38dbe 100644
--- a/Radix-Tree/RadixTree.swift
+++ b/Radix-Tree/RadixTree.swift
@@ -71,6 +71,18 @@ class Edge: Root {
 		}
 	}
 
+	func erase() {
+		print("Testing erase on: \(label)")
+		self.parent = nil
+		if children.count > 0 {
+			for _ in 0...children.count-1 {
+				children[0].erase()
+				children.remove(at: 0)
+			}
+		}
+		print("Removed: \(label)")
+	}
+
 	func printEdge() {
 		if children.count > 1 {
 			for c in 0...children.count/2-1 {
@@ -238,6 +250,10 @@ class RadixTree {
 				else if shared.characters.count == 0 {
 					continue
 				}
+				//If the shared string matches the search string, return true
+				else if shared == searchStr {
+					return true
+				}
 				//If the search string and the child's label only share some characters,
 				//  the string is not in the tree, return false
 				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
@@ -249,13 +265,58 @@ class RadixTree {
 				return false
 			}
 		}
-		//Start at the root
-			//If a child's label is a prefix of the search string
-			//  Cut the prefix off of the search string and 
-			//    start looking through that child's children
-			//If a child's label == searchStr, return true
+	}
 
-		//If none of the children's labels are a prefix of the search string
+	func remove(_ str: String) -> Bool {
+		print("Tryna remove: \(str)")
+		//You cannot remove the empty string from the tree
+		if str == "" {
+			return false
+		}
+		//If the tree is empty, you cannot remove anything
+		else if root.children.count == 0 {
+			return false
+		}
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			print("Search string: \(searchStr)")
+			//If currEdge has no children, then the searchStr is not in the tree
+			if currEdge.children.count == 0 {
+				return false
+			}
+			for c in 0...currEdge.children.count-1 {
+				//If the child's label matches the search string, remove that child
+				//  and everything below it in the tree
+				print("Looking at: \(currEdge.children[c].label)")
+				if currEdge.children[c].label == searchStr {
+					print("MATCH FOUND")
+					currEdge.children[c].erase()
+					print("ERASED WORKED")
+					currEdge.children.remove(at: c)
+					print("EDGE LABEL MATCH REMOVE")
+					return true
+				}
+				//Find the shared string
+				var shared = sharedPrefix(searchStr, currEdge.children[c].label)
+				//If the shared string is equal to the child's string, go down a level
+				if shared == currEdge.children[c].label {
+					currEdge = currEdge.children[c]
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+			}
+			//If there is no match, then the searchStr is not in the tree
+			if !found {
+				return false
+			}
+		}
 	}
 
 	func printTree() {
diff --git a/Radix-Tree/main.swift b/Radix-Tree/main.swift
index b53ffb9ec..6cffe1c20 100644
--- a/Radix-Tree/main.swift
+++ b/Radix-Tree/main.swift
@@ -29,6 +29,22 @@ radixWiki.insert("rubicunduses")
 radixWiki.printTree()
 
 print("FIND TESTS")
-print(radixWiki.find("courts"))
-print(radixWiki.find("rubicunduses"))
-print(radixWiki.find(""))
\ No newline at end of file
+print(radixWiki.find("courts")) // false
+print(radixWiki.find("r")) // true
+print(radixWiki.find("ro")) // true
+print(radixWiki.find("rom")) // true
+print(radixWiki.find("roma")) // true
+print(radixWiki.find("roman")) // true
+print(radixWiki.find("romane")) // true
+print(radixWiki.find("romans")) // false
+print(radixWiki.find("steve")) // true
+
+print("REMOVE TESTS")
+
+print(radixWiki.remove("c"))
+radixWiki.printTree()
+
+print(radixWiki.remove("rub"))
+radixWiki.printTree()
+
+print(radixWiki.remove("stevenson"))
\ No newline at end of file

From ad134fdbaf12919e8d349131ac422b29a9632a0e Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 10:44:22 -0400
Subject: [PATCH 0283/1679] Added debugged Insert and Find

---
 Trie/trie       | Bin 23362 -> 38270 bytes
 Trie/trie.swift |  58 +++++++++++++++++++++++++++++++++++++++++++-----
 2 files changed, 52 insertions(+), 6 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index 9459e471d729d947cf78e2e3b199647501c58738..327aac89484ab9a8360ca3e5e09e046d904d095d 100755
GIT binary patch
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 391300739..50a2b544a 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -1,12 +1,12 @@
 public class Node {
   var character: String?
   var parent: Node?
-  var children: [Node?]
+  var children: [String:Node]
   var isAWord: Bool
 
   init(c: String){
     self.character = c
-    self.children = []
+    self.children = [String:Node]()
     self.isAWord = false
     }
 
@@ -44,7 +44,7 @@ public class Node {
 }
 
 public class Trie {
-  var root: Node
+  var root = Node(c: "")
   var nodes: [Node]
 
   init() {
@@ -53,17 +53,63 @@ public class Trie {
     self.nodes.append(self.root)
   }
 
+  func find(key: String) -> (key: String, found: Bool) {
+    var currentNode = self.root
 
-  func insertWord(w: String) -> Void {
+    for c in key.characters {
+      if currentNode.children[String(c)] == nil {
+        return(key, false)
+      }
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    return(key, currentNode.isValidWord())
+  }
+
+  func insert(w: String) -> (word: String, inserted: Bool) {
+
+    var currentNode = self.root
+    var length = w.characters.count
+
+    for c in w.characters {
+      if currentNode.children[String(c)] != nil {
+        currentNode = currentNode.children[String(c)]!
+        length -= 1
+      }
+    }
+
+    if length == 0 {
+      if(currentNode.isValidWord()) {
+        return (w, false)
+      }
 
+      currentNode.isWord()
+      return (w, true)
+    }
+
+    let choppedWord = String(w.characters.suffix(length))
+
+    print(choppedWord)
+    for c in choppedWord.characters {
+      currentNode.children[String(c)] = Node(c: String(c))
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    currentNode.isWord()
+    return (w, true)
   }
 
 }
 
 print("tests")
 
-var x: Node = Node(c: "c")
+/*var x: Node = Node(c: "c")
 print(x.char())
 print(x.isValidWord())
 x.isWord()
-print(x.isValidWord())
+print(x.isValidWord())*/
+
+
+var T: Trie = Trie()
+print(T.insert("Hello"))
+print(T.find("Hello"))

From 05e402ae68971dce2297f6c77d601d49567c9441 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 11:09:48 -0400
Subject: [PATCH 0284/1679] got rid of debugging statements

---
 Trie/trie.swift | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/Trie/trie.swift b/Trie/trie.swift
index 50a2b544a..b8beb0293 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -46,6 +46,8 @@ public class Node {
 public class Trie {
   var root = Node(c: "")
   var nodes: [Node]
+  var wordList: [String]
+  var wordCount = 0
 
   init() {
     self.root = Node(c: "")
@@ -84,21 +86,29 @@ public class Trie {
       }
 
       currentNode.isWord()
+      wordList.append(w)
+      wordCount += 1
       return (w, true)
     }
 
     let choppedWord = String(w.characters.suffix(length))
 
-    print(choppedWord)
     for c in choppedWord.characters {
       currentNode.children[String(c)] = Node(c: String(c))
       currentNode = currentNode.children[String(c)]!
     }
 
     currentNode.isWord()
+    wordList.append(w)
+    wordCount += 1
     return (w, true)
   }
 
+  func remove(w: String) {
+
+
+  }
+
 }
 
 print("tests")

From 9dd86baa52481c578449c0b0774c8cc706fb8a4e Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 11:53:12 -0400
Subject: [PATCH 0285/1679] Added a few functions for usage, working on remove

---
 Trie/trie       | Bin 38270 -> 43930 bytes
 Trie/trie.swift |  30 +++++++++++++++++++++++++++++-
 2 files changed, 29 insertions(+), 1 deletion(-)

diff --git a/Trie/trie b/Trie/trie
index 327aac89484ab9a8360ca3e5e09e046d904d095d..c4dc38f8f44778777f5a4f81f5e8b56679323a28 100755
GIT binary patch
literal 43930
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zqh4{fA<$iqoitx45Ej#>*gCK(IZc4c4Ysy%XA~=iYBB2&MDfksDO=qgRq(Q>9shX6
tt*G(vYr7ihtzFIjaM;)BZ)(M0taL|wkwBX}62i;4u#e(#M`@Sj{{qgX79Rir

diff --git a/Trie/trie.swift b/Trie/trie.swift
index b8beb0293..4aa54d41f 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -53,6 +53,7 @@ public class Trie {
     self.root = Node(c: "")
     self.nodes = []
     self.nodes.append(self.root)
+    self.wordList = []
   }
 
   func find(key: String) -> (key: String, found: Bool) {
@@ -104,11 +105,38 @@ public class Trie {
     return (w, true)
   }
 
-  func remove(w: String) {
+  func remove(w: String) -> (word: String, removed: Bool){
+    var currentNode = self.root
+
+    for c in w.characters {
+      if(currentNode.children[String(c)]) == nil{
+        return (w, false)
+      }
+
+      currentNode = currentNode.children[String(c)]!
+
+    }
 
+    return (w, false)
 
+
+  }
+
+  func isEmpty() -> Bool {
+    return wordCount == 0
+  }
+
+  func count() -> Int {
+    return wordCount
+  }
+
+  func getWords() -> [String] {
+    return wordList
   }
 
+  func contains(w: String) -> Bool {
+    return find(w).found
+  }
 }
 
 print("tests")

From 2e12fbea4c2bc384a1689e3a6d6967615d6fe063 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 14:17:25 -0400
Subject: [PATCH 0286/1679] Tweaked somethings

---
 Trie/trie       | Bin 43930 -> 44196 bytes
 Trie/trie.swift |  12 ++++++++++++
 2 files changed, 12 insertions(+)

diff --git a/Trie/trie b/Trie/trie
index c4dc38f8f44778777f5a4f81f5e8b56679323a28..8160f90759b17a39108b47fd5e0fce35dd7a9ea0 100755
GIT binary patch
delta 6060
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 4aa54d41f..b3cc9c381 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -19,6 +19,9 @@ public class Node {
     self.character = c
   }
 
+  func isLeaf() -> Bool{
+    return self.children.count == 0
+  }
   //For Testing purposes
   func getParent() -> Node {
     return parent!
@@ -137,6 +140,15 @@ public class Trie {
   func contains(w: String) -> Bool {
     return find(w).found
   }
+
+  func isPrefix(w: String) -> Bool {
+    return true
+  }
+
+  func findPrefix(w: String) -> (key: String, found: Bool) {
+    return (w, true)
+  }
+
 }
 
 print("tests")

From b879d555f81c8f918926263be83dd2a737e6ce65 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Thu, 28 Apr 2016 14:49:31 -0400
Subject: [PATCH 0287/1679] Remove Fibonacci Heap

---
 Fibonacci Heap/README.markdown | 9 ---------
 README.markdown                | 2 +-
 2 files changed, 1 insertion(+), 10 deletions(-)
 delete mode 100644 Fibonacci Heap/README.markdown

diff --git a/Fibonacci Heap/README.markdown b/Fibonacci Heap/README.markdown
deleted file mode 100644
index c973701b2..000000000
--- a/Fibonacci Heap/README.markdown	
+++ /dev/null
@@ -1,9 +0,0 @@
-# Fibonacci Heap
-
-Under construction.
-
-## See also 
-
-[Fibonacci Heap on Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_heap).
-
-*Written for the Swift Algorithm Club by Jayson Tung*
diff --git a/README.markdown b/README.markdown
index fa6e263bc..a6b492154 100644
--- a/README.markdown
+++ b/README.markdown
@@ -149,7 +149,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
-- [Fibonacci Heap](Fibonacci\ Heap/) :construction:
+- Fibonacci Heap
 - [Trie](Trie/) :construction:
 - [B-Tree](B Tree/) :construction:
 

From 07f3856c0795d4369e7b15aa7dd2b6d59997712e Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 17:43:10 -0400
Subject: [PATCH 0288/1679] Bunch of stuff

---
 Trie/trie       | Bin 44196 -> 50574 bytes
 Trie/trie.swift | 154 +++++++++++++++++++++++++++++-------------------
 2 files changed, 94 insertions(+), 60 deletions(-)

diff --git a/Trie/trie b/Trie/trie
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index b3cc9c381..d0b156933 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -1,13 +1,15 @@
 public class Node {
-  var character: String?
-  var parent: Node?
-  var children: [String:Node]
-  var isAWord: Bool
+  private var character: String?
+  private var parent: Node?
+  private var children: [String:Node]
+  private var isAWord: Bool
 
-  init(c: String){
+
+  init(c: String?, p: Node?){
     self.character = c
     self.children = [String:Node]()
     self.isAWord = false
+    self.parent = p
     }
 
   //Easier getter function, probably will make it more swift like
@@ -15,7 +17,7 @@ public class Node {
     return self.character!
   }
 
-  func changeChar(c: String) -> Void {
+  func update(c: String?) -> Void {
     self.character = c
   }
 
@@ -27,6 +29,13 @@ public class Node {
     return parent!
   }
 
+  func setParent(node: Node) -> Void {
+    self.parent = node
+  }
+
+  func getChildAt(s: String) -> Node {
+    return self.children[s]!
+  }
   //Is this node marked as the end of a word?
   func isValidWord() -> Bool{
     return self.isAWord
@@ -44,18 +53,24 @@ public class Node {
   func isRoot() -> Bool {
     return self.character == ""
   }
+
+  func numChildren() -> Int {
+    return self.children.count
+  }
+
+  func getChildren() -> [String: Node] {
+    return self.children
+  }
+
 }
 
 public class Trie {
-  var root = Node(c: "")
-  var nodes: [Node]
-  var wordList: [String]
-  var wordCount = 0
+  private var root: Node
+  private var wordList: [String]
+  private var wordCount = 0
 
   init() {
-    self.root = Node(c: "")
-    self.nodes = []
-    self.nodes.append(self.root)
+    self.root = Node(c: "", p: nil)
     self.wordList = []
   }
 
@@ -72,33 +87,47 @@ public class Trie {
     return(key, currentNode.isValidWord())
   }
 
+  func isEmpty() -> Bool {
+    return wordCount == 0
+  }
+
+  func count() -> Int {
+    return wordCount
+  }
+
+  func getWords() -> [String] {
+    return wordList
+  }
+
+  func contains(w: String) -> Bool {
+    return find(w.lowercaseString).found
+  }
+
+  func isPrefix(w: String) -> Bool {
+    return true
+  }
+
   func insert(w: String) -> (word: String, inserted: Bool) {
 
+    let word = w.lowercaseString
     var currentNode = self.root
-    var length = w.characters.count
+    var length = word.characters.count
+
+    if self.contains(word) {
+      return (w, false)
+    }
 
-    for c in w.characters {
+    for c in word.characters {
       if currentNode.children[String(c)] != nil {
         currentNode = currentNode.children[String(c)]!
         length -= 1
       }
     }
 
-    if length == 0 {
-      if(currentNode.isValidWord()) {
-        return (w, false)
-      }
-
-      currentNode.isWord()
-      wordList.append(w)
-      wordCount += 1
-      return (w, true)
-    }
-
-    let choppedWord = String(w.characters.suffix(length))
+    let remainingChars = String(word.characters.suffix(length))
 
-    for c in choppedWord.characters {
-      currentNode.children[String(c)] = Node(c: String(c))
+    for c in remainingChars.characters {
+      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
       currentNode = currentNode.children[String(c)]!
     }
 
@@ -109,45 +138,40 @@ public class Trie {
   }
 
   func remove(w: String) -> (word: String, removed: Bool){
-    var currentNode = self.root
 
-    for c in w.characters {
-      if(currentNode.children[String(c)]) == nil{
-        return (w, false)
-      }
-
-      currentNode = currentNode.children[String(c)]!
+    let word = w.lowercaseString
+    var currentNode = self.root
 
+    if(!self.contains(w)) {
+      return (w, false)
     }
 
-    return (w, false)
-
-
-  }
-
-  func isEmpty() -> Bool {
-    return wordCount == 0
-  }
+    for c in word.characters {
+      if currentNode.children[String(c)] != nil {
+        currentNode = currentNode.children[String(c)]!
+      }
+    }
+    var x = currentNode.char()
+    while currentNode.getParent().numChildren() == 1 {
+      currentNode = currentNode.getParent()
+      currentNode.children[x] = nil
+      x = currentNode.char()
+    }
 
-  func count() -> Int {
-    return wordCount
-  }
+    wordCount -= 1
 
-  func getWords() -> [String] {
-    return wordList
-  }
+    var index = 0
+    for item in wordList{
+      if item == w {
+        wordList.removeAtIndex(index)
+      }
+      index += 1
+    }
 
-  func contains(w: String) -> Bool {
-    return find(w).found
+    return (w, true)
   }
 
-  func isPrefix(w: String) -> Bool {
-    return true
-  }
 
-  func findPrefix(w: String) -> (key: String, found: Bool) {
-    return (w, true)
-  }
 
 }
 
@@ -161,5 +185,15 @@ print(x.isValidWord())*/
 
 
 var T: Trie = Trie()
-print(T.insert("Hello"))
-print(T.find("Hello"))
+T.insert("Hello")
+T.insert("Hey")
+T.insert("YOLO")
+T.insert("Him")
+assert(T.count() == 4, "Count function failed")
+assert(T.contains("Hey") == true)
+assert(T.contains("Hello")==true)
+print("trying remove")
+T.remove("Him")
+assert(T.count() == 3)
+assert(T.contains("Him") == false, "Test failed")
+assert(T.wordList.count == 3)

From 3c985848500329311061a23df494c60e5baadf8c Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 17:44:31 -0400
Subject: [PATCH 0289/1679] Remove Counting Sort

---
 Counting-Sort/ReadMe.md | 7 -------
 1 file changed, 7 deletions(-)
 delete mode 100644 Counting-Sort/ReadMe.md

diff --git a/Counting-Sort/ReadMe.md b/Counting-Sort/ReadMe.md
deleted file mode 100644
index 30b7fbb98..000000000
--- a/Counting-Sort/ReadMe.md
+++ /dev/null
@@ -1,7 +0,0 @@
-# Counting Sort
-
-Under Construction.
-
-See also [Wikipedia](https://en.wikipedia.org/wiki/Counting_Sort).
-
-*Written for the Swift Algorithm Club by Christian Encarnacion*

From 1d87ed163902d5c0b553a212ac7cbd072a5712f8 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 17:48:36 -0400
Subject: [PATCH 0290/1679] Fixed Order of Deletion for Remove function in Trie
 class

---
 Trie/trie       | Bin 50574 -> 50582 bytes
 Trie/trie.swift |   3 ++-
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/Trie/trie b/Trie/trie
index a92296a75854658e2faea8776b4fa06b93878428..35d8d33f32d84a74c13e27100c3a12585bf2c19a 100755
GIT binary patch
delta 12659
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index d0b156933..bba82b357 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -29,7 +29,7 @@ public class Node {
     return parent!
   }
 
-  func setParent(node: Node) -> Void {
+  func setParent(node: Node?) -> Void {
     self.parent = node
   }
 
@@ -154,6 +154,7 @@ public class Trie {
     var x = currentNode.char()
     while currentNode.getParent().numChildren() == 1 {
       currentNode = currentNode.getParent()
+      currentNode.children[x]!.setParent(nil)
       currentNode.children[x] = nil
       x = currentNode.char()
     }

From f985b1bd2f2c5035e79420d4d392b4144f5c3b18 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 28 Apr 2016 17:55:20 -0400
Subject: [PATCH 0291/1679] Made some conditions more swift like

---
 Trie/trie       | Bin 50582 -> 50497 bytes
 Trie/trie.swift |  16 ++++++++--------
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index 35d8d33f32d84a74c13e27100c3a12585bf2c19a..9f97126c25ecb61209501230e7efeddd6f236300 100755
GIT binary patch
delta 16863
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lY+<qGnU4l}CzdVoUfNdw>^~fd|GNkgkCe1M{6d@i{{lw9xwQZQ

diff --git a/Trie/trie.swift b/Trie/trie.swift
index bba82b357..4a06a30ae 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -118,8 +118,8 @@ public class Trie {
     }
 
     for c in word.characters {
-      if currentNode.children[String(c)] != nil {
-        currentNode = currentNode.children[String(c)]!
+      if let child = currentNode.children[String(c)] {
+        currentNode = child
         length -= 1
       }
     }
@@ -147,16 +147,16 @@ public class Trie {
     }
 
     for c in word.characters {
-      if currentNode.children[String(c)] != nil {
-        currentNode = currentNode.children[String(c)]!
+      if let child = currentNode.children[String(c)] {
+        currentNode = child
       }
     }
-    var x = currentNode.char()
+    var character = currentNode.char()
     while currentNode.getParent().numChildren() == 1 {
       currentNode = currentNode.getParent()
-      currentNode.children[x]!.setParent(nil)
-      currentNode.children[x] = nil
-      x = currentNode.char()
+      currentNode.children[character]!.setParent(nil)
+      currentNode.children[character] = nil
+      character = currentNode.char()
     }
 
     wordCount -= 1

From 0c2f57d8f41f1e9400785a8584997d62a52463dd Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Fri, 29 Apr 2016 12:55:35 +0200
Subject: [PATCH 0292/1679] Update: example step by step and descr changes

---
 Bucket Sort/README.markdown | 68 ++++++++++++++++++++++++++++++++-----
 1 file changed, 60 insertions(+), 8 deletions(-)

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index 576937359..398f76e34 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -1,20 +1,16 @@
 # Bucket Sort
 
-## Definition
 [Bucket Sort or Bin Sort](https://en.wikipedia.org/wiki/Bucket_sort) is a distributed sorting algorithm, which sort elements from an array by performing these steps:  
 
-1) Distribute the elements into buckets or bin.  
+1) Distribute the elements into buckets or bins.  
 2) Sort each bucket individually.  
 3) Merge the buckets in order to produce a sort array as results.  
 
-A more complete definition could be
 
->
-Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, and is a cousin of radix sort in the most to least significant digit flavour. Bucket sort is a generalization of pigeonhole sort. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity estimates involve the number of buckets. [1](https://en.wikipedia.org/wiki/Bucket_sort)
+See the algorithm in action [here](https://www.cs.usfca.edu/~galles/visualization/BucketSort.html) and [here](http://www.algostructure.com/sorting/bucketsort.php).
 
-## Performance
 
-Performance for execution time:  
+The performance for execution time is:  
   
 | Case  | Performance |
 |:-------------: |:---------------:|
@@ -24,10 +20,13 @@ Performance for execution time:
   
 Where **n** = #elements and **k** = #buckets  
 
+On the **best case** the algorithm distributes the elements uniformily between buckets, a few elements are placed on each bucket and sorting the buckets is *O(1)*. Rearranging the elements is one more run through the initial list.  
+On the **worst case** the elements are sent all to the same bucket, making the process takes *O(n^2)*.  
+
 
 ## Pseudocode
 
-A [pseudocode](https://en.wikipedia.org/wiki/Bucket_sort#Pseudocode) of the algorithm is as follows:  
+A [pseudocode](https://en.wikipedia.org/wiki/Bucket_sort#Pseudocode) of the algorithm can be as follows:  
 
     function bucketSort(array, n) is
         buckets ← new array of n empty lists
@@ -48,6 +47,59 @@ A [pseudocode](https://en.wikipedia.org/wiki/Bucket_sort#Pseudocode) of the algo
 
 ![sorting each bucket and merge](https://upload.wikimedia.org/wikipedia/commons/3/39/Bucket_sort_2.png)
 
+##An example
+
+### Input  
+
+Suppose we have the following list of elements:  `[2, 56, 4, 77, 26, 98, 55]`.  
+And we define 10 buckets will be used. To determine the capacity of each bucket we need to know the `maximum element value`, in this case `98`.  
+
+So the buckets are:    
+* `bucket 1`: from 0 to 9
+* `bucket 2`: from 10 to 19
+* `bucket 3`: from 20 to 29
+*  and so on.
+
+### Distribution
+
+Now we need to choose a distribution function.  
+
+`bucketNumber = ( elementValue / totalNumberOfBuckets) + 1`  
+   
+Such that applying that function we distribute all the elements in the buckets.  
+In our example it is like following:  
+  
+1. Apply the distribution function to `2`. `bucketNumber = (2 / 10) + 1 = 1`
+2. Apply the distribution function to `56`. `bucketNumber = (56 / 10) + 1 = 6`
+3. Apply the distribution function to `4`. `bucketNumber = (4 / 10) + 1 = 1`
+4. Apply the distribution function to `77`. `bucketNumber = (77 / 10) + 1 = 8`
+5. Apply the distribution function to `26`. `bucketNumber = (26 / 10) + 1 = 3`
+6. Apply the distribution function to `98`. `bucketNumber = (98 / 10) + 1 = 10`
+7. Apply the distribution function to `55`. `bucketNumber = (55 / 10) + 1 = 6`
+
+Our buckets will be filled now:  
+
+**1**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[2, 4]`  
+**2**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[]`  
+**3**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[26]`  
+**4**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[]`  
+**5**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[]`  
+**6**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[55, 56]`  
+**7**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[]`  
+**8**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[77]`  
+**9**  <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[]`  
+**10** <img src="https://pixabay.com/static/uploads/photo/2014/03/24/17/21/pail-295491_960_720.png" width="40">: `[98]`  
+
+We can choose to insert the elements in every bucket in order, or sort every bucket after distributing all the elements.  
+
+### Put the elements back in the list 
+
+Finally we go through all the buckets and put the elements back in the list:  
+  
+  `[2,  4,  26,  55,  56,  77,  98]`  
+  
+
+
 ##Swift implementation
 
 ###Classes

From 3ead1ddc4923b8e7965690ccf4287a55275272c9 Mon Sep 17 00:00:00 2001
From: axptwig <raghua@rpi.edu>
Date: Fri, 29 Apr 2016 11:33:09 -0400
Subject: [PATCH 0293/1679] Update RBTree.swift

---
 Red Black Trees/RBTree.swift | 225 ++++++++++++++++++++++++-----------
 1 file changed, 153 insertions(+), 72 deletions(-)

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index 12f97b21f..33c165b4e 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -1,86 +1,167 @@
-public class RBTNode {
-    var color: Int?
-    var left: RBTNode?
-    var right: RBTNode?
-    var parent: RBTNode?
-    var data: Int
 
-    init(data: Int) {
-        self.data = data
-        self.left = nil
-        self.right = nil
-        self.parent = nil
-        self.color = nil
-    }
-
-    public var isLeaf: Bool {
-    return left == nil && right == nil
+public class  RBTNode{
+  private(set) public var color: Bool
+  private(set) public var left: RBTNode!
+  private(set) public var right: RBTNode!
+  private(set) public var parent: RBTNode!
+  private(set) public var data: Int
+  init(){
+    self.data = -1
+    self.color = true
+    self.left = nil
+    self.right = nil
+    self.parent = nil
   }
-
-  public var isLeftChild: Bool {
-    return parent?.left === self
-  }
-
-  public var isRightChild: Bool {
-    return parent?.right === self
-  }
-
-  public var hasLeftChild: Bool {
-    return left != nil
-  }
-
-  public var hasRightChild: Bool {
-    return right != nil
-  }
-
-  public var hasAnyChild: Bool {
-    return hasLeftChild || hasRightChild
-  }
-
-  public var hasBothChildren: Bool {
-    return hasLeftChild && hasRightChild
+  init(rootData: Int){
+    self.data = rootData
+    self.color = true
+    self.left = nil
+    self.right = nil
+    self.parent = nil
   }
 }
+public class RBTree {
 
-extension RBTNode {
-  public func insert(value: Int) {
-    insert(value, parent: self)
-  }
-  private func insert(value: Int, parent: RBTNode) {
-    if value < self.data {
-      if let left = left {
-        left.insert(value, parent: left)
-      } else {
-        left = RBTNode(data: value)
-        left?.parent = parent
+    private(set) public var root: RBTNode?
+    init(rootData: Int) {
+      root = RBTNode(rootData: rootData)
+    }
+    init(){
+      root = nil
+    }
+    public func depth()->Int{
+      let n = depth(root!)
+      return n
+    }
+    private func depth(rooty:RBTNode?)->Int{
+      if(rooty == nil){
+        return 0
       }
-    } else {
-      if let right = right {
-        right.insert(value, parent: right)
-      } else {
-        right = RBTNode(data: value)
-        right?.parent = parent
+      else{
+        return 1+(max(depth(root!.left),depth(root!.right)))
+      }
+    }
+
+    public func inOrder(){
+      inOrder(root)
+    }
+    private func inOrder(root: RBTNode?){
+      if(root == nil){
+        print("nil")
+        return
       }
+      inOrder(root!.left)
+      print("Data: \(root!.data) Color: \(root!.color)")
+      inOrder(root!.right)
     }
+
+    private func leftRotate(x: RBTNode) {
+        let newRoot = x.right
+        x.right = newRoot.left
+          if (newRoot.left !== nil) {
+            newRoot.left.parent = x
+          }
+          newRoot.parent = x.parent
+          if(x.parent === nil) {
+            root = newRoot
+          } else if (x === x.parent.left) {
+            x.parent.left = newRoot
+          } else {
+            x.parent.right = newRoot
+          }
+          newRoot.left = x
+          x.parent = newRoot
   }
+  private func rightRotate(x: RBTNode) {
+    let newRoot = x.left
+    x.left = newRoot.right 
+    if newRoot.right !== nil {
+      newRoot.right.parent = x
+    }
+    newRoot.parent = x.parent
+    if x.parent === nil {
+      root = newRoot
+    } else if x === x.parent.right {
+      x.parent.right = newRoot
+    } else {
+      x.parent.left = newRoot
+    }
+    newRoot.right = x
+    x.parent = newRoot
 }
-extension RBTNode{
-  public func inOrder(root: RBTNode?){
-    if(root == nil){
-      return
+
+
+    private func insertFixup(){}
+    public func insert(value: Int) {
+      insert(value, parent: root!)
+      //insertFixUp()
     }
-    inOrder(root!.left)
-    print(root!.data)
-    inOrder(root!.right)
-  }
+    private func insert(value: Int, parent: RBTNode) {
+        if value < parent.data {
+          if let left = parent.left {
+            insert(value, parent: left)
+          } else {
+            parent.left = RBTNode(rootData: value)
+            parent.left?.parent = parent
+          }
+        } else {
+          if let right = parent.right {
+            insert(value, parent: right)
+          } else {
+            parent.right = RBTNode(rootData: value)
+            parent.right?.parent = parent
+          }
+        }
+      }
+      public func find(data: Int)->RBTNode?{
+        return find(root!,data: data)
+      }
+      private func find(root: RBTNode, data: Int)->RBTNode?{
+          if data == root.data{
+            return root
+          }
+          if root.data != data && root.right == nil && root.left == nil {
+            return nil
+          }
+          else if data > root.data{
+            return find(root.right, data: data)
+          }
+          else if data < root.data{
+            return find(root.left, data: data)
+          }
+          else{
+            return nil
+          }
+      }
 }
 
-var me = RBTNode(data: 5)
-var me2 = RBTNode(data: 6)
+var tree = RBTree(rootData: 8)
+tree.insert(9)
+tree.insert(6)
+tree.insert(5)
+tree.insert(4)
+tree.insert(3)
+tree.inOrder()
+print("_________________________")
+let x = tree.root!
+print("root: \(tree.root!.data)")
+tree.rightRotate(x)
+print("root: \(tree.root!.data)")
+tree.inOrder()
+
+let t = tree.find(234)
+if t == nil{
+  print("ASDASD")
+}
+//how you access certain elements
+//let root = tree.root!.left!
+//if(root.parent === nil){
+//  print("niggs")
+//}
+//else{
+//  print(root.parent.data)
+//}
 
-me.insert(4)
-me.insert(3)
-me.insert(2)
-me.insert(1)
-me.insert(0)
-me.inOrder(me) //stupid way to call this
+//print(tree.root!.data)
+//print(tree.root!.right!.data)
+//print(tree.root!.left!.data)

From c59f47500f12138a8e688e9022407e7fed2f54bd Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Fri, 29 Apr 2016 12:05:38 -0400
Subject: [PATCH 0294/1679] Removed debug prints

---
 Radix-Tree/RadixTree.swift | 17 +++++------------
 Radix-Tree/main.swift      |  5 ++++-
 2 files changed, 9 insertions(+), 13 deletions(-)

diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
index 994a38dbe..89c3cb7ef 100644
--- a/Radix-Tree/RadixTree.swift
+++ b/Radix-Tree/RadixTree.swift
@@ -28,8 +28,6 @@ class Root {
 	}
 
 	func printRoot() {
-		//print("children: \(children.count)")
-		//print("split at: \(children.count/2-1)")
 		if (children.count > 1) {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
@@ -40,7 +38,6 @@ class Root {
 			children[0].printEdge()
 		}
 		print("ROOT")
-		//print("second half starts at: \(children.count/2)")
 		if children.count > 1 {
 			for c in children.count/2...children.count-1 {
 				children[c].printEdge()
@@ -72,7 +69,6 @@ class Edge: Root {
 	}
 
 	func erase() {
-		print("Testing erase on: \(label)")
 		self.parent = nil
 		if children.count > 0 {
 			for _ in 0...children.count-1 {
@@ -80,7 +76,6 @@ class Edge: Root {
 				children.remove(at: 0)
 			}
 		}
-		print("Removed: \(label)")
 	}
 
 	func printEdge() {
@@ -268,10 +263,13 @@ class RadixTree {
 	}
 
 	func remove(_ str: String) -> Bool {
-		print("Tryna remove: \(str)")
 		//You cannot remove the empty string from the tree
 		if str == "" {
-			return false
+			for c in root.children {
+				c.erase()
+				root.children.remove(at: 0)
+			}
+			return true
 		}
 		//If the tree is empty, you cannot remove anything
 		else if root.children.count == 0 {
@@ -281,7 +279,6 @@ class RadixTree {
 		var currEdge = root
 		while (true) {
 			var found = false
-			print("Search string: \(searchStr)")
 			//If currEdge has no children, then the searchStr is not in the tree
 			if currEdge.children.count == 0 {
 				return false
@@ -289,13 +286,9 @@ class RadixTree {
 			for c in 0...currEdge.children.count-1 {
 				//If the child's label matches the search string, remove that child
 				//  and everything below it in the tree
-				print("Looking at: \(currEdge.children[c].label)")
 				if currEdge.children[c].label == searchStr {
-					print("MATCH FOUND")
 					currEdge.children[c].erase()
-					print("ERASED WORKED")
 					currEdge.children.remove(at: c)
-					print("EDGE LABEL MATCH REMOVE")
 					return true
 				}
 				//Find the shared string
diff --git a/Radix-Tree/main.swift b/Radix-Tree/main.swift
index 6cffe1c20..ba1528046 100644
--- a/Radix-Tree/main.swift
+++ b/Radix-Tree/main.swift
@@ -47,4 +47,7 @@ radixWiki.printTree()
 print(radixWiki.remove("rub"))
 radixWiki.printTree()
 
-print(radixWiki.remove("stevenson"))
\ No newline at end of file
+print(radixWiki.remove("stevenson"))
+
+print(radixWiki.remove(""))
+radixWiki.printTree()
\ No newline at end of file

From 927cbf64ee2183982a6c7ad826f8c500eaed9e53 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Fri, 29 Apr 2016 12:09:24 -0400
Subject: [PATCH 0295/1679] Added documentation for RadixTree.remove()

---
 Radix-Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index ef405bcb0..e187c806b 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -21,7 +21,7 @@ The insert function returns true if the String you are trying to insert was succ
 
 ### RadixTree.remove(_ str: String) -> Bool
 
-THIS IS NOT IMPLEMENTED YET
+The remove function returns true if the String is removed and false if the String is not in the tree. When a string is removed, any other Strings that have a prefix of the removed String are removed as well. For example, remove("rom") will also remove "roman", "rome", and "romulus" if those Strings are in the tree as well. Calling remove("") will remove all Strings in the tree.
 
 ### Root.level() -> Int
 

From efe4d94c263fbc3f0d1295ab06cd783918f13101 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Fri, 29 Apr 2016 12:16:27 -0400
Subject: [PATCH 0296/1679] Added credit to wikipedia for the image

---
 Radix-Tree/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
index e187c806b..ce1dde6b7 100644
--- a/Radix-Tree/README.markdown
+++ b/Radix-Tree/README.markdown
@@ -2,6 +2,7 @@
 
 A radix tree is a tree where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses and by traversing from the root to any leaf in the tree, (by concatenating all the labels of edges along the way) you can find any string. This is a radix tree:
 ![](/Radix-Tree/Images/radixtree.png)
+(Image from en.wikipedia.org)
 
 ## Implemenation
 

From bcf9ade4ff49f467513cd67fdf08a218270fe454 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Fri, 29 Apr 2016 12:54:16 -0400
Subject: [PATCH 0297/1679] Added more inline comments

---
 Radix-Tree/RadixTree.swift | 69 +++++++++++++++++++++++++++-----------
 Radix-Tree/main.swift      |  2 ++
 2 files changed, 52 insertions(+), 19 deletions(-)

diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
index 89c3cb7ef..93ca95495 100644
--- a/Radix-Tree/RadixTree.swift
+++ b/Radix-Tree/RadixTree.swift
@@ -1,5 +1,6 @@
 import Foundation
 
+//The root is the top of the Radix Tree
 class Root {
 
 	var children: [Edge]
@@ -8,10 +9,14 @@ class Root {
 		children = [Edge]()
 	}
 
+	//The height functions returns the length (in number of edges) of the longest
+	//  traversal down the tree
 	func height() -> Int {
+		//Base case: no children: the tree has a height of 1
 		if children.count == 0 {
 			return 1
 		}
+		//Recursion: find the max height of a root's child and return 1 + that max
 		else {
 			var max = 1
 			for c in children {
@@ -23,11 +28,16 @@ class Root {
 		}
 	}
 
+	//The level function returns how far down in the tree a Root/Edge is
+	//A root's level is always 0
 	func level() -> Int {
 		return 0
 	}
 
+	//printRoot is a recursive function that prints the tree for debugging/
+	//  visualization purposes
 	func printRoot() {
+		//Print the first half of the children
 		if (children.count > 1) {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
@@ -37,7 +47,9 @@ class Root {
 		else if children.count > 0 {
 			children[0].printEdge()
 		}
+		//Then print the root
 		print("ROOT")
+		//Print the second half of the children
 		if children.count > 1 {
 			for c in children.count/2...children.count-1 {
 				children[c].printEdge()
@@ -48,6 +60,7 @@ class Root {
 	}
 }
 
+//Edges are what actually store the Strings in the tree
 class Edge: Root {
 
 	var parent: Root?
@@ -58,19 +71,25 @@ class Edge: Root {
 		super.init()
 	}
 
+	//The Edge class overrides root's level function
 	override
 	func level() -> Int {
+		//Recurse up the tree incrementing level by one until the root is reached
 		if parent != nil {
 			return 1 + parent!.level()
 		}
+		//If an edge has no parent, it's level is one
+		//  NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
 		else {
 			return 1
 		}
 	}
 
+	//Erase erases a specific edge (and all edges below it in the tree)
 	func erase() {
 		self.parent = nil
 		if children.count > 0 {
+			//For each child, erase it, then remove it from the children array
 			for _ in 0...children.count-1 {
 				children[0].erase()
 				children.remove(at: 0)
@@ -78,7 +97,10 @@ class Edge: Root {
 		}
 	}
 
+	//printEdge is used in printRoot to print the tree
+	//  It follows a similar structure to printRoot
 	func printEdge() {
+		//Print the first half of the edge's children
 		if children.count > 1 {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
@@ -87,21 +109,17 @@ class Edge: Root {
 		else if children.count > 0 {
 			children[0].printEdge()
 		}
+		//Tab over once up to the edge's level
 		for x in 1...level() {
 			if x == level() {
 				print("|------>", terminator: "")
 			}
-			else if x == 1 {
-				print("|       ", terminator: "")
-			}
-			else if x == level()-1 {
-				print("|       ", terminator: "")
-			}
 			else {
 				print("|       ", terminator: "")
 			}
 		}
 		print(label)
+		//Print the second half of the edge's children
 		if children.count == 0 {
 			for _ in 1...level() {
 				print("|       ", terminator: "")
@@ -124,38 +142,47 @@ class RadixTree {
 		root = Root()
 	}
 
+	//Returns the height of the tree by calling the root's height function
 	func height() -> Int {
 		return root.height() - 1
 	}
 
+	//Inserts a string into the tree
 	func insert(_ str: String) -> Bool {
 		//Account for a blank input
+		//  The empty string is already in the tree
 		if str == "" {
 			return false
 		}
-		//Account for an empty tree
-		if root.children.count == 0 {
-			root.children.append( Edge(str) )
-			return true
-		}
+		//searchStr is the parameter of the function
+		//  it will be substringed as the function traverses down the tree
 		var searchStr = str
+		//currEdge is the current Edge (or Root) in question
 		var currEdge = root
 		while (true) {
 			var found = false
+			//If the current Edge has no children then the remaining searchStr is
+			//  created as a child
 			if currEdge.children.count == 0 {
 				let newEdge = Edge(searchStr)
 				currEdge.children.append(newEdge)
 				newEdge.parent = currEdge
+				return true
 			}
+			//Loop through all of the children
 			for e in currEdge.children {
-				//Get the shared 
+				//Get the shared prefix betweeen the child in question and the
+				//  search string
 				var shared = sharedPrefix(searchStr, e.label)
 				var index  = shared.startIndex
-				//The search string is equal to the shared string
-				//so the string already exists in the tree
+				//If the search string is equal to the shared string,
+				//  the string already exists in the tree
 				if searchStr == shared {
 					return false
 				}
+				//If the child's label is equal to the shared string, you have to
+				//  traverse another level down the tree, so substring the search
+				//  string, break the loop, and run it back
 				else if shared == e.label {
 					currEdge = e
 					var tempIndex = searchStr.startIndex
@@ -166,16 +193,18 @@ class RadixTree {
 					found = true
 					break
 				}
-				//The child's label and the search string share a prefix
+				//If the child's label and the search string share a partial prefix,
+				//  then both the label and the search string need to be substringed
+				//  and a new branch needs to be created
 				else if shared.characters.count > 0 {
-					//Cut the prefix off from both the search string and label
 					var labelIndex = e.label.characters.startIndex
 					//Create index objects and move them to after the shared prefix
 					for _ in 1...shared.characters.count {
 						index = index.successor()
 						labelIndex = labelIndex.successor()
 					}
-					//Substring both the search string and the label from the shared prefix
+					//Substring both the search string and the label from the
+					//  shared prefix
 					searchStr = searchStr.substringFromIndex(index)
 					e.label = e.label.substringFromIndex(labelIndex)
 					//Create 2 new edges and update parent/children values
@@ -195,10 +224,10 @@ class RadixTree {
 					e.children.append(newEdge2)
 					return true
 				}
-				//They don't share a prefix (go to next child)
+				//If they don't share a prefix, go to next child
 			}
+			//If none of the children share a prefix, you have to create a new child
 			if (!found) {
-				//No children share a prefix, so create a new child
 				let newEdge = Edge(searchStr)
 				currEdge.children.append(newEdge)
 				newEdge.parent = currEdge
@@ -207,6 +236,7 @@ class RadixTree {
 		}
 	}
 
+	//Tells you if a string is in the tree
 	func find(_ str: String) -> Bool {
 		//A radix tree always contains the empty string
 		if str == "" {
@@ -216,6 +246,7 @@ class RadixTree {
 		else if root.children.count == 0 {
 			return false
 		}
+		//searchStr and currEdge have the same functionality as insert()
 		var searchStr = str
 		var currEdge = root
 		while (true) {
diff --git a/Radix-Tree/main.swift b/Radix-Tree/main.swift
index ba1528046..6495e5e1b 100644
--- a/Radix-Tree/main.swift
+++ b/Radix-Tree/main.swift
@@ -13,6 +13,8 @@ radixWiki.insert("shoot")
 radixWiki.insert("shit")
 radixWiki.insert("starch")
 radixWiki.insert("steven")
+radixWiki.insert("shart")
+radixWiki.insert("shard")
 
 radixWiki.insert("compute")
 radixWiki.insert("compatible")

From 2f209a30b81c657210b3d05090836678f014a837 Mon Sep 17 00:00:00 2001
From: scalls <scalls@rpi.edu>
Date: Fri, 29 Apr 2016 13:01:48 -0400
Subject: [PATCH 0298/1679] Added more inline comments

---
 Radix-Tree/RadixTree.swift | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
index 93ca95495..6f1f8fa57 100644
--- a/Radix-Tree/RadixTree.swift
+++ b/Radix-Tree/RadixTree.swift
@@ -251,6 +251,7 @@ class RadixTree {
 		var currEdge = root
 		while (true) {
 			var found = false
+			//Loop through currEdge's children
 			for c in currEdge.children {
 				//First check if the search string and the child's label are equal
 				//  if so the string is in the tree, return true
@@ -260,8 +261,8 @@ class RadixTree {
 				//If that is not true, find the shared string b/t the search string
 				//  and the label
 				var shared = sharedPrefix(searchStr, c.label)
-				//If the shared string is equal to the label, update the curent node
-				//  and run it back
+				//If the shared string is equal to the label, update the curent node,
+				//  break the loop, and run it back
 				if shared == c.label {
 					currEdge = c
 					var tempIndex = searchStr.startIndex
@@ -272,7 +273,7 @@ class RadixTree {
 					found = true
 					break
 				}
-				//If the shared string is empty, go to the next children
+				//If the shared string is empty, go to the next child
 				else if shared.characters.count == 0 {
 					continue
 				}
@@ -287,14 +288,16 @@ class RadixTree {
 				  	return false
 				}
 			}
+			//If nothing was found, return false
 			if !found {
 				return false
 			}
 		}
 	}
 
+	//Removes a string from the tree
 	func remove(_ str: String) -> Bool {
-		//You cannot remove the empty string from the tree
+		//Removing the empty string removes everything in the tree
 		if str == "" {
 			for c in root.children {
 				c.erase()
@@ -306,6 +309,7 @@ class RadixTree {
 		else if root.children.count == 0 {
 			return false
 		}
+		//searchStr and currEdge have the same functionality as in insert() and find()
 		var searchStr = str
 		var currEdge = root
 		while (true) {
@@ -314,6 +318,7 @@ class RadixTree {
 			if currEdge.children.count == 0 {
 				return false
 			}
+			//Loop through the children
 			for c in 0...currEdge.children.count-1 {
 				//If the child's label matches the search string, remove that child
 				//  and everything below it in the tree
@@ -343,6 +348,7 @@ class RadixTree {
 		}
 	}
 
+	//Prints the tree by calling the root's print function
 	func printTree() {
 		root.printRoot()
 	}

From 7fc446a8c1527b298c5e1f00bb5bec91b29454cb Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Fri, 29 Apr 2016 15:06:27 -0400
Subject: [PATCH 0299/1679] Implemented print Trie, but encountered insert bug

---
 Trie/trie       | Bin 50497 -> 55843 bytes
 Trie/trie.swift | 106 +++++++++++++++++++++++++++++++++++++++++++++---
 2 files changed, 101 insertions(+), 5 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index 9f97126c25ecb61209501230e7efeddd6f236300..352d06dbbdcbd17995b5c5478ae75c2b2d1272d1 100755
GIT binary patch
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 4a06a30ae..12800315b 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -62,6 +62,28 @@ public class Node {
     return self.children
   }
 
+  func printNode(var indent: String, leaf: Bool) -> Void {
+
+    print(indent, terminator: "")
+    if(leaf) {
+      print("\\-", terminator: "")
+      indent += " "
+    }
+    else {
+      print("|-", terminator: "")
+      indent += "| "
+    }
+
+    print(self.char())
+
+    var i = 0
+    for (_, node) in self.children {
+      node.printNode(indent, leaf: i == self.getChildren().count-1)
+      i+=1
+    }
+
+  }
+
 }
 
 public class Trie {
@@ -103,8 +125,26 @@ public class Trie {
     return find(w.lowercaseString).found
   }
 
-  func isPrefix(w: String) -> Bool {
-    return true
+  func isPrefix(w: String) -> (node: Node?, found: Bool) {
+    var currentNode = self.root
+
+    let word = w.lowercaseString
+    if !self.contains(w) {
+      return (nil,false)
+    }
+
+    for c in word.characters {
+      if let child = currentNode.children[String(c)] {
+        print("I make it here")
+        currentNode = child
+      }
+    }
+
+    if currentNode.getChildren().count > 0 {
+      return (currentNode, true)
+    }
+
+    return (nil, false)
   }
 
   func insert(w: String) -> (word: String, inserted: Bool) {
@@ -118,7 +158,9 @@ public class Trie {
     }
 
     for c in word.characters {
+      print(c)
       if let child = currentNode.children[String(c)] {
+        print(child.char())
         currentNode = child
         length -= 1
       }
@@ -172,7 +214,51 @@ public class Trie {
     return (w, true)
   }
 
+  private func getChildrenWithPrefix(node: Node, var word: String, var words: [String]) -> [String] {
+
+    if node.isLeaf() {
+      word += node.char()
 
+      words.append(word)
+
+    }
+
+    for (child, n) in node.getChildren() {
+      word += child
+      getChildrenWithPrefix(n, word: word, words: words)
+    }
+
+    return words
+  }
+
+  func findPrefix(p: String) -> [String] {
+    if self.isPrefix(p).found {
+      print("here")
+      return getChildrenWithPrefix(self.isPrefix(p).node!, word: "", words: [])
+    }
+
+    return []
+  }
+
+
+  private func removeAllHelper(node: Node, w: String) {
+
+    if(node.getChildren().count == 0) {
+
+    }
+
+
+
+  }
+
+
+  func removeAll(w: String) {
+
+  }
+
+  func printTrie() {
+    self.root.printNode("", leaf: true)
+  }
 
 }
 
@@ -186,15 +272,25 @@ print(x.isValidWord())*/
 
 
 var T: Trie = Trie()
-T.insert("Hello")
+/*T.insert("Hello")
 T.insert("Hey")
 T.insert("YOLO")
 T.insert("Him")
 assert(T.count() == 4, "Count function failed")
 assert(T.contains("Hey") == true)
-assert(T.contains("Hello")==true)
+assert(T.contains("Hello") == true)
 print("trying remove")
 T.remove("Him")
 assert(T.count() == 3)
 assert(T.contains("Him") == false, "Test failed")
-assert(T.wordList.count == 3)
+assert(T.wordList.count == 3)*/
+
+
+//T.insert("Hello")
+//T.insert("Hi")
+T.insert("Hey")
+//T.insert("Hallo")
+T.insert("Henry")
+T.printTrie()
+//assert(T.contains("He") == true)
+//print(T.findPrefix("H"))

From 16ee33f94944cc68b0b459fee9f0a2b165d79339 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Fri, 29 Apr 2016 16:30:55 -0400
Subject: [PATCH 0300/1679] Fixed a bug in the insert function

---
 Trie/trie       | Bin 55843 -> 55991 bytes
 Trie/trie.swift |  17 +++++++++--------
 2 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index 352d06dbbdcbd17995b5c5478ae75c2b2d1272d1..640d11ed4f90f1f725c18d7ff50bfca6d283926d 100755
GIT binary patch
delta 17037
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z_}(vkPX>6J5`20WS+5Vyl^l!ddn9Wq%3$KtVA<xQMD1=5XkVSra-^MY`j|)b^Q2Ff
zG2fb&%>kBK;=*BTRsj+%)oi{#P^_l?T9e;qlYU2;5p5(Z{BIAIy#8tD`-Ts@fB3?>
b!iH60br(<6bg|s|sL)Tx*M0r&2i^Y%q`|q7

diff --git a/Trie/trie.swift b/Trie/trie.swift
index 12800315b..0ea606908 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -157,17 +157,18 @@ public class Trie {
       return (w, false)
     }
 
-    for c in word.characters {
-      print(c)
-      if let child = currentNode.children[String(c)] {
-        print(child.char())
-        currentNode = child
-        length -= 1
-      }
+    var index = 0
+    var c = Array(word.characters)[index]
+
+    while let child = currentNode.children[String(c)] {
+      currentNode = child
+      length -= 1
+      index += 1
+      c = Array(word.characters)[index]
     }
 
     let remainingChars = String(word.characters.suffix(length))
-
+    print(remainingChars)
     for c in remainingChars.characters {
       currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
       currentNode = currentNode.children[String(c)]!

From bd7398bfed9491c075af79217adf799322cdfd95 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Fri, 29 Apr 2016 18:02:34 -0400
Subject: [PATCH 0301/1679] Fixed a bug where Remove was removing one node less
 than it should have.

---
 Trie/trie       | Bin 55991 -> 60243 bytes
 Trie/trie.swift |  37 ++++++++++++++++++++++++-------------
 2 files changed, 24 insertions(+), 13 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index 640d11ed4f90f1f725c18d7ff50bfca6d283926d..bb9ae602fe57355dc14252eafd3f27d85b53f7b5 100755
GIT binary patch
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 0ea606908..f4e9913d5 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -183,23 +183,29 @@ public class Trie {
   func remove(w: String) -> (word: String, removed: Bool){
 
     let word = w.lowercaseString
-    var currentNode = self.root
 
     if(!self.contains(w)) {
       return (w, false)
     }
+    var currentNode = self.root
 
     for c in word.characters {
-      if let child = currentNode.children[String(c)] {
-        currentNode = child
-      }
+      currentNode = currentNode.getChildAt(String(c))
     }
-    var character = currentNode.char()
-    while currentNode.getParent().numChildren() == 1 {
-      currentNode = currentNode.getParent()
-      currentNode.children[character]!.setParent(nil)
-      currentNode.children[character] = nil
-      character = currentNode.char()
+
+    if currentNode.numChildren() > 0 {
+      currentNode.isNotWord()
+    } else {
+      var character = currentNode.char()
+      while(currentNode.numChildren() < 1) {
+        currentNode = currentNode.getParent()
+        print(currentNode.char())
+        currentNode.children[character]!.setParent(nil)
+        currentNode.children[character]!.update(nil)
+        currentNode.children[character] = nil
+        character = currentNode.char()
+
+      }
     }
 
     wordCount -= 1
@@ -288,10 +294,15 @@ assert(T.wordList.count == 3)*/
 
 
 //T.insert("Hello")
-//T.insert("Hi")
+T.insert("Hi")
 T.insert("Hey")
 //T.insert("Hallo")
 T.insert("Henry")
 T.printTrie()
-//assert(T.contains("He") == true)
-//print(T.findPrefix("H"))
+assert(T.contains("Henry") == true)
+T.remove("Henry")
+assert(T.contains("Henry") == false)
+//assert(T.count() == 4)
+assert(T.isPrefix("Hen").found == false)
+T.printTrie()
+print(T.findPrefix("H"))

From 8fe2ec240dfc325f64ad8cb0b0561c4bcab47dda Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Fri, 29 Apr 2016 18:04:48 -0400
Subject: [PATCH 0302/1679] Removed some debugging print statements

---
 Trie/trie.swift | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Trie/trie.swift b/Trie/trie.swift
index f4e9913d5..6faf2e655 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -135,7 +135,6 @@ public class Trie {
 
     for c in word.characters {
       if let child = currentNode.children[String(c)] {
-        print("I make it here")
         currentNode = child
       }
     }
@@ -199,7 +198,6 @@ public class Trie {
       var character = currentNode.char()
       while(currentNode.numChildren() < 1) {
         currentNode = currentNode.getParent()
-        print(currentNode.char())
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
         currentNode.children[character] = nil

From aa32c46b5aa44f95f1e11b6c9556e71663180444 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Mon, 2 May 2016 11:47:08 -0400
Subject: [PATCH 0303/1679] Added a merge function, still debugging findPrefix

---
 Trie/trie       | Bin 60243 -> 61374 bytes
 Trie/trie.swift |  96 ++++++++++++++++++++++++++++++------------------
 2 files changed, 60 insertions(+), 36 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index bb9ae602fe57355dc14252eafd3f27d85b53f7b5..6df0edeec95fbb06b251185dd4af79c852fd0a9e 100755
GIT binary patch
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 6faf2e655..4169bd208 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -62,6 +62,7 @@ public class Node {
     return self.children
   }
 
+
   func printNode(var indent: String, leaf: Bool) -> Void {
 
     print(indent, terminator: "")
@@ -96,17 +97,36 @@ public class Trie {
     self.wordList = []
   }
 
-  func find(key: String) -> (key: String, found: Bool) {
+  init(wordList: Set<String>) {
+
+    self.root = Node(c: "", p: nil)
+    self.wordList = []
+
+    for word in wordList {
+      let op = self.insert(word)
+      if(op.inserted){
+        self.wordList.append(word)
+      }
+    }
+  }
+
+  func merge(other: Trie) -> Trie{
+    let newWorldList = Set(self.getWords() + other.getWords())
+
+    return Trie(wordList: newWorldList)
+  }
+
+  func find(key: String) -> (node: Node?, found: Bool) {
     var currentNode = self.root
 
     for c in key.characters {
       if currentNode.children[String(c)] == nil {
-        return(key, false)
+        return(nil, false)
       }
       currentNode = currentNode.children[String(c)]!
     }
 
-    return(key, currentNode.isValidWord())
+    return(currentNode, currentNode.isValidWord())
   }
 
   func isEmpty() -> Bool {
@@ -125,21 +145,20 @@ public class Trie {
     return find(w.lowercaseString).found
   }
 
-  func isPrefix(w: String) -> (node: Node?, found: Bool) {
-    var currentNode = self.root
+  func isPrefix(p: String) -> (node: Node?, found: Bool) {
+    let prefixP = p.lowercaseString
 
-    let word = w.lowercaseString
-    if !self.contains(w) {
-      return (nil,false)
-    }
+    var currentNode = self.root
 
-    for c in word.characters {
-      if let child = currentNode.children[String(c)] {
-        currentNode = child
+    for c in prefixP.characters {
+      if currentNode.children[String(c)] == nil{
+        return (nil, false)
       }
+
+      currentNode = currentNode.children[String(c)]!
     }
 
-    if currentNode.getChildren().count > 0 {
+    if currentNode.numChildren() > 0 {
       return (currentNode, true)
     }
 
@@ -167,7 +186,6 @@ public class Trie {
     }
 
     let remainingChars = String(word.characters.suffix(length))
-    print(remainingChars)
     for c in remainingChars.characters {
       currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
       currentNode = currentNode.children[String(c)]!
@@ -196,7 +214,7 @@ public class Trie {
       currentNode.isNotWord()
     } else {
       var character = currentNode.char()
-      while(currentNode.numChildren() < 1) {
+      while(currentNode.numChildren() == 0) {
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
@@ -221,25 +239,32 @@ public class Trie {
 
   private func getChildrenWithPrefix(node: Node, var word: String, var words: [String]) -> [String] {
 
-    if node.isLeaf() {
-      word += node.char()
+    print(word)
 
+    if node.isLeaf() && node.isValidWord() {
       words.append(word)
+      print(words)
 
-    }
+    } else {
 
-    for (child, n) in node.getChildren() {
-      word += child
-      getChildrenWithPrefix(n, word: word, words: words)
+      for (child, n) in node.getChildren(){
+        print(child)
+        word += child
+        getChildrenWithPrefix(n, word: word, words: words)
+      }
     }
 
     return words
   }
 
   func findPrefix(p: String) -> [String] {
+    print("Entered")
+
+
+    //var (node, pFound: Bool) = self.isPrefix(p)
     if self.isPrefix(p).found {
-      print("here")
-      return getChildrenWithPrefix(self.isPrefix(p).node!, word: "", words: [])
+      print("I found the prefix!")
+      return getChildrenWithPrefix(self.isPrefix(p).node!, word: p.lowercaseString, words: [])
     }
 
     return []
@@ -277,6 +302,16 @@ print(x.isValidWord())*/
 
 
 var T: Trie = Trie()
+T.insert("Hello")
+T.insert("Hi")
+T.insert("Hey")
+T.insert("Hallo")
+T.insert("Henry")
+var U: Trie = Trie(wordList: Set(["Hey", "HO", "hello", "yolo"]))
+var V: Trie = T.merge(U)
+T.printTrie()
+U.printTrie()
+V.printTrie()
 /*T.insert("Hello")
 T.insert("Hey")
 T.insert("YOLO")
@@ -290,17 +325,6 @@ assert(T.count() == 3)
 assert(T.contains("Him") == false, "Test failed")
 assert(T.wordList.count == 3)*/
 
-
-//T.insert("Hello")
-T.insert("Hi")
-T.insert("Hey")
-//T.insert("Hallo")
-T.insert("Henry")
-T.printTrie()
-assert(T.contains("Henry") == true)
-T.remove("Henry")
-assert(T.contains("Henry") == false)
-//assert(T.count() == 4)
-assert(T.isPrefix("Hen").found == false)
 T.printTrie()
-print(T.findPrefix("H"))
+print(T.find(""))
+//print(T.findPrefix("H"))

From 3a7f20d1f9dc0a8c208e9630740aca16cf0d77c0 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Mon, 2 May 2016 20:10:08 +0200
Subject: [PATCH 0304/1679] Small tweaks to the text

---
 Bucket Sort/BucketSort.swift |   2 +-
 Bucket Sort/README.markdown  | 252 ++++++++++++++++++-----------------
 README.markdown              |   2 +-
 3 files changed, 131 insertions(+), 125 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 0c75ce40a..c28eb0284 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -28,7 +28,7 @@ import Foundation
 
 
 /**
-    Perform buckets srot algorithm on the given input elements.
+    Performs bucket sort algorithm on the given input elements.
     [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
  
     - Parameter elements:     Array of Sortable elements
diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index 398f76e34..f6e318c1f 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -1,15 +1,13 @@
 # Bucket Sort
 
-[Bucket Sort or Bin Sort](https://en.wikipedia.org/wiki/Bucket_sort) is a distributed sorting algorithm, which sort elements from an array by performing these steps:  
+Bucket Sort, also known as Bin Sort, is a distributed sorting algorithm, which sort elements from an array by performing these steps:  
 
 1) Distribute the elements into buckets or bins.  
 2) Sort each bucket individually.  
-3) Merge the buckets in order to produce a sort array as results.  
-
+3) Merge the buckets in order to produce a sorted array as the result.
 
 See the algorithm in action [here](https://www.cs.usfca.edu/~galles/visualization/BucketSort.html) and [here](http://www.algostructure.com/sorting/bucketsort.php).
 
-
 The performance for execution time is:  
   
 | Case  | Performance |
@@ -18,11 +16,11 @@ The performance for execution time is:
 | Best      | 	Omega(n + k)        |
 |  Average | 	Theta(n + k)       | 
   
-Where **n** = #elements and **k** = #buckets  
+Where **n** = the number of elements and **k** is the number of buckets.
 
-On the **best case** the algorithm distributes the elements uniformily between buckets, a few elements are placed on each bucket and sorting the buckets is *O(1)*. Rearranging the elements is one more run through the initial list.  
-On the **worst case** the elements are sent all to the same bucket, making the process takes *O(n^2)*.  
+In the *best case*, the algorithm distributes the elements uniformily between buckets, a few elements are placed on each bucket and sorting the buckets is **O(1)**. Rearranging the elements is one more run through the initial list.  
 
+In the *worst case*, the elements are sent all to the same bucket, making the process take **O(n^2)**.
 
 ## Pseudocode
 
@@ -39,22 +37,22 @@ A [pseudocode](https://en.wikipedia.org/wiki/Bucket_sort#Pseudocode) of the algo
 
 ## Graphically explained
 
-###Distribute elements in buckets  
+1) Distribute elements in buckets:
 
 ![distribution step](https://upload.wikimedia.org/wikipedia/commons/6/61/Bucket_sort_1.png)
 
-###Sorting inside every bucket and merging  
+2) Sorting inside every bucket and merging:
 
 ![sorting each bucket and merge](https://upload.wikimedia.org/wikipedia/commons/3/39/Bucket_sort_2.png)
 
-##An example
+## An example
 
 ### Input  
 
-Suppose we have the following list of elements:  `[2, 56, 4, 77, 26, 98, 55]`.  
-And we define 10 buckets will be used. To determine the capacity of each bucket we need to know the `maximum element value`, in this case `98`.  
+Suppose we have the following list of elements: `[2, 56, 4, 77, 26, 98, 55]`. Let's use 10 buckets. To determine the capacity of each bucket we need to know the *maximum element value*, in this case `98`.  
 
 So the buckets are:    
+
 * `bucket 1`: from 0 to 9
 * `bucket 2`: from 10 to 19
 * `bucket 3`: from 20 to 29
@@ -64,10 +62,11 @@ So the buckets are:
 
 Now we need to choose a distribution function.  
 
-`bucketNumber = ( elementValue / totalNumberOfBuckets) + 1`  
+`bucketNumber = (elementValue / totalNumberOfBuckets) + 1`  
    
-Such that applying that function we distribute all the elements in the buckets.  
-In our example it is like following:  
+Such that by applying that function we distribute all the elements in the buckets.  
+
+In our example it is like the following:  
   
 1. Apply the distribution function to `2`. `bucketNumber = (2 / 10) + 1 = 1`
 2. Apply the distribution function to `56`. `bucketNumber = (56 / 10) + 1 = 6`
@@ -99,87 +98,95 @@ Finally we go through all the buckets and put the elements back in the list:
   `[2,  4,  26,  55,  56,  77,  98]`  
   
 
+## Swift implementation
 
-##Swift implementation
+Here is a diagram that shows the functions, data structures and protocols for our bucker sort implementation:
 
-###Classes
+![classes](Docs/BucketSort.png)
 
-![classes](https://github.com/barbaramartina/swift-algorithm-club/blob/BucketSort/Bucket%20Sort/Docs/BucketSort.png)
+#### Main function
 
-###Code
+`bucketSort()` is a generic function that can apply the algorithm to any element of type `T`, as long as `T` is `Sortable`.
 
-Bucket Sort implementation use the following functions, data structures and protocols:
+```swift
+public func bucketSort<T:Sortable>(elements: [T], 
+                                distributor: Distributor, 
+                                     sorter: Sorter, 
+                                    buckets: [Bucket<T>]) -> [T] {
+	precondition(allPositiveNumbers(elements))
+	precondition(enoughSpaceInBuckets(buckets, elements: elements))
 
-####Main function
+	var bucketsCopy = buckets
+	for elem in elements {
+		distributor.distribute(elem, buckets: &bucketsCopy)
+	}
 
-`bucketSort` is a generic function that can apply the algorithm to any element of type T, as long as T is Sortable.
+	var results = [T]()
 
-    public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
-        precondition(allPositiveNumbers(elements))
-        precondition(enoughSpaceInBuckets(buckets, elements: elements))
-    
-        var bucketsCopy = buckets
-        for elem in elements {
-            distributor.distribute(elem, buckets: &bucketsCopy)
-         }
-    
-        var results = [T]()
-    
-       for bucket in bucketsCopy {
-            results += bucket.sort(sorter)
-        }
-    
-        return results
-     }
+	for bucket in bucketsCopy {
+		results += bucket.sort(sorter)
+	}
 
+	return results
+}
+```
 
-####Bucket
+#### Bucket
 
-    public struct Bucket<T:Sortable> {
-        var elements: [T]
-        let capacity: Int
-    
-        public init(capacity: Int) {
-            self.capacity = capacity
-            elements = [T]()
-        }
-    
-        public mutating func add(item: T) {
-            if (elements.count < capacity) {
-                elements.append(item)
-            }
-         }
-    
-         public func sort(algorithm: Sorter) -> [T] {
-            return algorithm.sort(elements)
-         }
-    }
+```swift
+public struct Bucket<T:Sortable> {
+	var elements: [T]
+	let capacity: Int
 
-####Sortable
+	public init(capacity: Int) {
+		self.capacity = capacity
+		elements = [T]()
+	}
 
-    public protocol Sortable: IntConvertible, Comparable {
-    }
+	public mutating func add(item: T) {
+		if (elements.count < capacity) {
+			elements.append(item)
+		}
+	}
 
-####IntConvertible
+	public func sort(algorithm: Sorter) -> [T] {
+		return algorithm.sort(elements)
+	}
+}
+```
 
-The algorithm is designed to sort integers, so all the elements to be sorted should be mapped to an integer value.
+#### Sortable
+
+```swift
+public protocol Sortable: IntConvertible, Comparable {
+}
+```
 
-    public protocol IntConvertible {
-        func toInt() -> Int
-    }
+#### IntConvertible
+
+The algorithm is designed to sort integers, so all the elements to be sorted should be mapped to an integer value.
 
+```swift
+public protocol IntConvertible {
+	func toInt() -> Int
+}
+```
 
-####Sorter
+#### Sorter
 
-    public protocol Sorter {
-        func sort<T:Sortable>(items: [T]) -> [T]
-    }
+```swift
+public protocol Sorter {
+	func sort<T:Sortable>(items: [T]) -> [T]
+}
+```
 
-####Distributor
+#### Distributor
 
-    public protocol Distributor {
-        func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
-    }
+```swift
+public protocol Distributor {
+	func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
+}
+```
 
 ### Custom Sorter and Distributor
 
@@ -187,56 +194,54 @@ The current implementation make use of the following implementations for *Sorter
 
 *Sorter*  
 
-    public struct InsertionSorter: Sorter {
-    
-        public init() {}
-    
-        public func sort<T:Sortable>(items: [T]) -> [T] {
-            var results = items
-            for i in 0 ..< results.count {
-                var j = i
-                while ( j > 0 && results[j-1] > results[j]) {
-                
-                    let auxiliar = results[j-1]
-                    results[j-1] = results[j]
-                    results[j] = auxiliar
-                
-                    j -= 1
-                }
-            }
-            return results
-        }
-    }
+```swift
+public struct InsertionSorter: Sorter {
+	public func sort<T:Sortable>(items: [T]) -> [T] {
+		var results = items
+		for i in 0 ..< results.count {
+			var j = i
+			while ( j > 0 && results[j-1] > results[j]) {
+			
+				let auxiliar = results[j-1]
+				results[j-1] = results[j]
+				results[j] = auxiliar
+			
+				j -= 1
+			}
+		}
+		return results
+	}
+}
+```
 
 *Distributor*  
 
-    /*
-    * An example of a simple distribution function that send every elements to
-    * the bucket representing the range in which it fits.An
-    *
-    * If the range of values to sort is 0..<49 i.e, there could be 5 buckets of capacity = 10
-    * So every element will be classified by the ranges:
-    *
-    * -  0 ..< 10
-    * - 10 ..< 20
-    * - 20 ..< 30
-    * - 30 ..< 40
-    * - 40 ..< 50
-    *
-    * By following the formula: element / capacity = #ofBucket
-    */
-    public struct RangeDistributor: Distributor {
-    
-         public init() {}
-    
-         public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
-         let value = element.toInt()
-         let bucketCapacity = buckets.first!.capacity
-        
-         let bucketIndex = value / bucketCapacity
-         buckets[bucketIndex].add(element)
-        }
-    }
+```swift
+/*
+ * An example of a simple distribution function that send every elements to
+ * the bucket representing the range in which it fits.
+ *
+ * If the range of values to sort is 0..<49 i.e, there could be 5 buckets of capacity = 10
+ * So every element will be classified by the ranges:
+ *
+ * -  0 ..< 10
+ * - 10 ..< 20
+ * - 20 ..< 30
+ * - 30 ..< 40
+ * - 40 ..< 50
+ *
+ * By following the formula: element / capacity = #ofBucket
+ */
+public struct RangeDistributor: Distributor {
+	 public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
+	 let value = element.toInt()
+	 let bucketCapacity = buckets.first!.capacity
+	
+	 let bucketIndex = value / bucketCapacity
+	 buckets[bucketIndex].add(element)
+	}
+}
+```
 
 ### Make your own version
 
@@ -244,10 +249,11 @@ By reusing this code and implementing your own *Sorter* and *Distributor* you ca
 
 ## Other variations of Bucket Sort
 
-The following are some of the variation to the General Bucket Sort implemented here:
+The following are some of the variation to the general [Bucket Sort](https://en.wikipedia.org/wiki/Bucket_sort) implemented here:
 
 - [Proxmap Sort](https://en.wikipedia.org/wiki/Bucket_sort#ProxmapSort)
 - [Histogram Sort](https://en.wikipedia.org/wiki/Bucket_sort#Histogram_sort)
 - [Postman Sort](https://en.wikipedia.org/wiki/Bucket_sort#Postman.27s_sort)
 - [Shuffle Sort](https://en.wikipedia.org/wiki/Bucket_sort#Shuffle_sort)
 
+*Written for Swift Algorithm Club by Barbara Rodeker. Images from Wikipedia.*
diff --git a/README.markdown b/README.markdown
index abbc39cc5..bbc10fb8d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -72,7 +72,7 @@ Fast sorts:
 
 Special-purpose sorts:
 
-- Bucket Sort
+- [Bucket Sort](Bucket Sort/) :construction:
 - [Counting Sort](Counting Sort/)
 - Radix Sort
 - [Topological Sort](Topological Sort/)

From 6ec2d66c80eea2b583fc06e770b8f34a74c42308 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Mon, 2 May 2016 14:39:40 -0400
Subject: [PATCH 0305/1679] Finished Remove all, fixed a duplication error in
 constructor

---
 Trie/trie       | Bin 61374 -> 65115 bytes
 Trie/trie.swift |  49 +++++++++++++++++++++++-------------------------
 2 files changed, 23 insertions(+), 26 deletions(-)

diff --git a/Trie/trie b/Trie/trie
index 6df0edeec95fbb06b251185dd4af79c852fd0a9e..f4fc8cdf7379094f875f742142542a09096220b0 100755
GIT binary patch
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 4169bd208..e377bdbbf 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -104,16 +104,12 @@ public class Trie {
 
     for word in wordList {
       let op = self.insert(word)
-      if(op.inserted){
-        self.wordList.append(word)
-      }
     }
   }
 
   func merge(other: Trie) -> Trie{
-    let newWorldList = Set(self.getWords() + other.getWords())
-
-    return Trie(wordList: newWorldList)
+    let newWordList = Set(self.getWords() + other.getWords())
+    return Trie(wordList: newWordList)
   }
 
   func find(key: String) -> (node: Node?, found: Bool) {
@@ -198,7 +194,6 @@ public class Trie {
   }
 
   func remove(w: String) -> (word: String, removed: Bool){
-
     let word = w.lowercaseString
 
     if(!self.contains(w)) {
@@ -210,17 +205,23 @@ public class Trie {
       currentNode = currentNode.getChildAt(String(c))
     }
 
+    print("I make it here " + w)
     if currentNode.numChildren() > 0 {
+      //print("Hello?")
       currentNode.isNotWord()
     } else {
       var character = currentNode.char()
-      while(currentNode.numChildren() == 0) {
+      var i = 0
+      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
+        print("Do I die here?")
+        print(currentNode.getParent().char())
+        i+=1
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
         currentNode.children[character] = nil
         character = currentNode.char()
-
+        print(i)
       }
     }
 
@@ -267,25 +268,18 @@ public class Trie {
       return getChildrenWithPrefix(self.isPrefix(p).node!, word: p.lowercaseString, words: [])
     }
 
-    return []
+    return ["HE"]
   }
 
 
-  private func removeAllHelper(node: Node, w: String) {
-
-    if(node.getChildren().count == 0) {
-
+  func removeAll() -> Void {
+    for word in wordList {
+      self.remove(word)
     }
-
-
-
+    self.root.update(nil)
   }
 
 
-  func removeAll(w: String) {
-
-  }
-
   func printTrie() {
     self.root.printNode("", leaf: true)
   }
@@ -309,9 +303,12 @@ T.insert("Hallo")
 T.insert("Henry")
 var U: Trie = Trie(wordList: Set(["Hey", "HO", "hello", "yolo"]))
 var V: Trie = T.merge(U)
-T.printTrie()
-U.printTrie()
-V.printTrie()
+//T.printTrie()
+//U.printTrie()
+//V.printTrie()
+print(V.getWords())
+V.removeAll()
+//V.printTrie()
 /*T.insert("Hello")
 T.insert("Hey")
 T.insert("YOLO")
@@ -325,6 +322,6 @@ assert(T.count() == 3)
 assert(T.contains("Him") == false, "Test failed")
 assert(T.wordList.count == 3)*/
 
-T.printTrie()
-print(T.find(""))
+//T.printTrie()
+//print(T.find(""))
 //print(T.findPrefix("H"))

From 8d0a20cfb142dadc359086f7ea18094100cfa7be Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Mon, 2 May 2016 14:44:16 -0400
Subject: [PATCH 0306/1679] Got rid of unnecessary debugging print statements
 and variable declarations.

---
 Trie/trie.swift | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/Trie/trie.swift b/Trie/trie.swift
index e377bdbbf..4758e10fd 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -103,7 +103,7 @@ public class Trie {
     self.wordList = []
 
     for word in wordList {
-      let op = self.insert(word)
+      self.insert(word)
     }
   }
 
@@ -205,23 +205,17 @@ public class Trie {
       currentNode = currentNode.getChildAt(String(c))
     }
 
-    print("I make it here " + w)
     if currentNode.numChildren() > 0 {
-      //print("Hello?")
       currentNode.isNotWord()
     } else {
       var character = currentNode.char()
-      var i = 0
       while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
-        print("Do I die here?")
         print(currentNode.getParent().char())
-        i+=1
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
         currentNode.children[character] = nil
         character = currentNode.char()
-        print(i)
       }
     }
 

From 006e74db51e5618e90e81fe3d9a917a3be1f3fa7 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Mon, 2 May 2016 19:13:37 -0400
Subject: [PATCH 0307/1679] Add first draft of Threaded Binary Tree, with some
 images

---
 Threaded Binary Tree/Images/AddOne.png        | Bin 0 -> 15851 bytes
 Threaded Binary Tree/Images/AddTwo.png        | Bin 0 -> 17141 bytes
 Threaded Binary Tree/Images/Base.png          | Bin 0 -> 11907 bytes
 Threaded Binary Tree/Images/DelOne.png        | Bin 0 -> 17173 bytes
 Threaded Binary Tree/Images/DelThree.png      | Bin 0 -> 11596 bytes
 Threaded Binary Tree/Images/DelTwo.png        | Bin 0 -> 13594 bytes
 Threaded Binary Tree/Images/Full.png          | Bin 0 -> 12426 bytes
 Threaded Binary Tree/Images/Partial.png       | Bin 0 -> 11218 bytes
 Threaded Binary Tree/README.markdown          |  54 +-
 Threaded Binary Tree/ThreadedBinaryTree.swift | 171 +++++-
 .../ThreadedBinaryTreeBackup.swift            | 543 ++++++++++++++++++
 11 files changed, 738 insertions(+), 30 deletions(-)
 create mode 100644 Threaded Binary Tree/Images/AddOne.png
 create mode 100644 Threaded Binary Tree/Images/AddTwo.png
 create mode 100644 Threaded Binary Tree/Images/Base.png
 create mode 100644 Threaded Binary Tree/Images/DelOne.png
 create mode 100644 Threaded Binary Tree/Images/DelThree.png
 create mode 100644 Threaded Binary Tree/Images/DelTwo.png
 create mode 100644 Threaded Binary Tree/Images/Full.png
 create mode 100644 Threaded Binary Tree/Images/Partial.png
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTreeBackup.swift

diff --git a/Threaded Binary Tree/Images/AddOne.png b/Threaded Binary Tree/Images/AddOne.png
new file mode 100644
index 0000000000000000000000000000000000000000..12509733c9c6222e8442fe5306aa69bb5a78df21
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diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index d75809d7d..bc812ee6a 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -20,16 +20,18 @@ children last.
 
 In-order traversal of any binary tree generally goes as follows:
 
+```swift
+func traverse(n: Node?) {
+	if (n == nil) { return
+	} else {
+		traverse(n.left)
+		visit(n)
+		traverse(n.right)
+	}
+}
 ```
-traverse(n):
-	if (n == NULL) return
-	else:
-		traverse(n->left)
-		visit n
-		traverse(n->right)
-```
-Where `n` is a pointer to a node in the tree (or `NULL`), each node stores
-pointers to its children as `left` and `right`, and "visiting" a node can mean
+Where `n` is a a node in the tree (or `nil`), each node stores
+its children as `left` and `right`, and "visiting" a node can mean
 performing any desired action on it.  We would call this function by passing to
 it the root of the tree we wish to traverse.
 
@@ -48,9 +50,9 @@ A threaded binary tree fixes this problem.
 An in-order traversal of a tree yields a linear ordering of the nodes.  Thus
 each node has both a predecessor and a successor (except for the first and last
 nodes, which only have a successor or a predecessor respectively).  In a
-threaded binary tree, each left child pointer that would normally be `NULL`
+threaded binary tree, each left child pointer that would normally be `nil`
 instead points to the node's predecessor (if it exists), and each right child
-pointer that would normally be `NULL` instead points to the node's successor
+pointer that would normally be `nil` instead points to the node's successor
 (if it exists).  This is what separates threaded binary trees from standard
 binary trees.
 
@@ -80,31 +82,31 @@ threaded binary tree is much more efficient than the recursive algorithm
 outlined above.  We use these predecessor/successor attributes to great effect
 in this new algorithm (note that this is for a forward traversal):
 
-```
+```swift
 traverse(root):
-	if (root == NULL) return
+	if (root == nil) return
  
     // Find the leftmost Node
-    Node *n = root
-	while (n->left != NULL):
-		n = n->left
+    Node n = root
+	while (n.left != nil):
+		n = n.left
  
-    while (n != NULL):
+    while (n != nil):
 		visit n
 
         // If this Node is a thread Node, then go to its in-order successor
-        if (n->rightThread):
-            n = n->right
+        if (n.rightThread):
+            n = n.right
  
 		// Else go to the leftmost Node in its right subtree
         else:
-            n = n->right
-			while (n->left != NULL):
-				n = n->left
+            n = n.right
+			while (n.left != nil):
+				n = n.left
 ```
 Where:
-- `root` is a pointer to the root of the tree (or `NULL`).
-- Each node stores pointers to its children or predecessor/successor as `left`
+- `root` is the root of the tree (or `nil`).
+- Each node stores its children or predecessor/successor as `left`
   and `right`.
 - "Visiting" a node can mean performing any desired action on it.
 - The booleans `leftThread` and `rightThread` keep track of whether `left` and
@@ -113,8 +115,8 @@ Where:
 	- While `leftThread` is not used here, it would be used in a backwards
 	  traversal in a double threaded tree or a single threaded tree "pointing"
 	  the other direction.
-- The first node in the traversal has `leftThread = true` and `left = NULL`
-- The last node in the traversal has `rightThread = true` and `right = NULL`
+- The first node in the traversal has `leftThread = true` and `left = nil`
+- The last node in the traversal has `rightThread = true` and `right = nil`
 
 
 ## An example
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
index f83dd4592..10f955580 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.swift	
@@ -1,5 +1,6 @@
 /*
-  A threaded binary tree based on this club's binary search tree implementation.
+  A Threaded Binary Tree.
+  Based on this club's Binary Search Tree implementation.
 
   Each node stores a value and two children. The left child contains a smaller
   value; the right a larger (or equal) value.
@@ -18,6 +19,10 @@ public class ThreadedBinaryTree<T: Comparable> {
   private(set) public var left: ThreadedBinaryTree?
   private(set) public var right: ThreadedBinaryTree?
 
+  //threaded
+  private(set) public var leftThread: ThreadedBinaryTree?
+  private(set) public var rightThread: ThreadedBinaryTree?
+
   public init(value: T) {
     self.value = value
   }
@@ -87,6 +92,10 @@ extension ThreadedBinaryTree {
       } else {
         left = ThreadedBinaryTree(value: value)
         left?.parent = parent
+        //threaded
+        left?.leftThread = leftThread
+        left?.rightThread = parent
+        leftThread = nil
       }
     } else {
       if let right = right {
@@ -94,6 +103,10 @@ extension ThreadedBinaryTree {
       } else {
         right = ThreadedBinaryTree(value: value)
         right?.parent = parent
+        //threaded
+        right?.rightThread = rightThread
+        right?.leftThread = parent
+        rightThread = nil
       }
     }
   }
@@ -103,7 +116,7 @@ extension ThreadedBinaryTree {
 
 extension ThreadedBinaryTree {
   /*
-    Deletes a node from the tree.
+    Deletes the "highest" node with the specified value.
 
     Returns the node that has replaced this removed one (or nil if this was a
     leaf node). That is primarily useful for when you delete the root node, in
@@ -111,22 +124,45 @@ extension ThreadedBinaryTree {
 
     Performance: runs in O(h) time, where h is the height of the tree.
   */
+  //threaded
+  public func remove(value: T) -> ThreadedBinaryTree? {
+    return search(value)?.remove()
+  }
+
+  /*
+    Deletes "this" node from the tree.
+  */
   public func remove() -> ThreadedBinaryTree? {
     let replacement: ThreadedBinaryTree?
 
     if let left = left {
       if let right = right {
         replacement = removeNodeWithTwoChildren(left, right)
+        //threaded
+        replacement?.leftThread = leftThread
+        replacement?.rightThread = rightThread
+        left.maximum().rightThread = replacement
+        right.minimum().leftThread = replacement
       } else {
         // This node only has a left child. The left child replaces the node.
         replacement = left
+        //threaded
+        left.maximum().rightThread = rightThread
       }
     } else if let right = right {
       // This node only has a right child. The right child replaces the node.
       replacement = right
+      //threaded
+      right.minimum().leftThread = leftThread
     } else {
       // This node has no children. We just disconnect it from its parent.
       replacement = nil
+      //threaded
+      if isLeftChild {
+        parent?.leftThread = leftThread
+      } else {
+        parent?.rightThread = rightThread
+      }
     }
 
     reconnectParentToNode(replacement)
@@ -135,11 +171,14 @@ extension ThreadedBinaryTree {
     parent = nil
     left = nil
     right = nil
+    //threaded
+    leftThread = nil
+    rightThread = nil
 
     return replacement
   }
 
-  private func removeNodeWithTwoChildren(left: ThreadedBinaryTree, _ right: BinarySearchTree) -> BinarySearchTree {
+  private func removeNodeWithTwoChildren(left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
     // This node has two children. It must be replaced by the smallest
     // child that is larger than this node's value, which is the leftmost
     // descendent of the right child.
@@ -272,12 +311,16 @@ extension ThreadedBinaryTree {
     if let left = left {
       return left.maximum()
     } else {
+      /*
       var node = self
       while case let parent? = node.parent {
         if parent.value < value { return parent }
         node = parent
       }
       return nil
+      */
+      //threaded
+      return leftThread
     }
   }
 
@@ -288,12 +331,16 @@ extension ThreadedBinaryTree {
     if let right = right {
       return right.minimum()
     } else {
+      /*
       var node = self
       while case let parent? = node.parent {
         if parent.value > value { return parent }
         node = parent
       }
       return nil
+      */
+      //threaded
+      return rightThread
     }
   }
 }
@@ -302,9 +349,22 @@ extension ThreadedBinaryTree {
 
 extension ThreadedBinaryTree {
   public func traverseInOrder(@noescape process: T -> Void) {
+    /*
     left?.traverseInOrder(process)
     process(value)
     right?.traverseInOrder(process)
+    */
+    //threaded
+    var n: ThreadedBinaryTree
+    n = minimum()
+    while true {
+      process(n.value)
+      if let successor = n.successor() {
+        n = successor
+      } else {
+        break
+      }
+    }
   }
   
   public func traversePreOrder(@noescape process: T -> Void) {
@@ -332,7 +392,7 @@ extension ThreadedBinaryTree {
 }
 
 /*
-  Is this binary tree a valid binary search tree?
+  Is this threaded binary tree a valid binary search tree?
 */
 extension ThreadedBinaryTree {
   public func isBST(minValue minValue: T, maxValue: T) -> Bool {
@@ -343,6 +403,35 @@ extension ThreadedBinaryTree {
   }
 }
 
+/*
+  Is this binary tree properly threaded?
+  Either left or leftThread (but not both) must be nil (likewise for right).
+  The first and last nodes in the in-order traversal are exempt from this,
+  as the first has leftThread = nil, and the last has rightThread = nil.
+*/
+//threaded
+extension ThreadedBinaryTree {
+  public func isThreaded() -> Bool {
+    if self === minimum() {
+      if left != nil && leftThread != nil {
+        return false
+      }
+    } else if (left == nil && leftThread == nil) || (left != nil && leftThread != nil) {
+      return false
+    }
+    if self === maximum() {
+      if right != nil && rightThread != nil {
+        return false
+      }
+    } else if (right == nil && rightThread == nil) || (right != nil && rightThread != nil) {
+      return false
+    }
+    let leftThreaded = left?.isThreaded() ?? true
+    let rightThreaded = right?.isThreaded() ?? true
+    return leftThreaded && rightThreaded
+  }
+}
+
 // MARK: - Debugging
 
 extension ThreadedBinaryTree: CustomStringConvertible {
@@ -371,6 +460,13 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     if let right = right {
       s += ", right = [" + right.debugDescription + "]"
     }
+    //threaded
+    if let leftThread = leftThread {
+      s += ", leftThread: \(leftThread.value)"
+    }
+    if let rightThread = rightThread {
+      s += ", rightThread: \(rightThread.value)"
+    }
     return s
   }
 
@@ -378,3 +474,70 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     return map { $0 }
   }
 }
+
+/*
+  TESTS
+  I don't have an Apple computer, so I can't make a Playground or any of that
+  fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree class.
+  It follows the illustrations in the README.
+*/
+
+// Simple little debug function to make testing output pretty
+private func check(tree: ThreadedBinaryTree<Int>) {
+  print("Overview:")
+  print(tree)
+  print("Debug Info:")
+  print(tree.debugDescription)
+  print("In-Order Traversal:")
+  let myArray = tree.toArray()
+  for node in myArray {
+    print(node)
+  }
+  if tree.isThreaded() {
+    print("This threaded binary tree is VALID.")
+  } else {
+    print("This threaded binary tree is INVALID.")
+  }
+}
+  
+
+print("\nFull Balanced Binary Tree with 7 Nodes")
+let fullTree = ThreadedBinaryTree<Int>(value: 4)
+fullTree.insert(2)
+fullTree.insert(6)
+fullTree.insert(1)
+fullTree.insert(3)
+fullTree.insert(5)
+fullTree.insert(7)
+check(fullTree)
+
+
+print("\n\nUnbalanced Binary Tree with 5 Nodes")
+let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
+check(tree)
+
+print("\nInsert 10")
+tree.insert(10)
+check(tree)
+
+print("\nInsert 4")
+tree.insert(4)
+check(tree)
+
+print("\nRemove 13 (Not in the Tree)")
+tree.remove(13)
+check(tree)
+
+print("\nRemove 5")
+tree.remove(5)
+check(tree)
+
+print("\nRemove 7")
+tree.remove(7)
+check(tree)
+
+print("\nRemove 10")
+tree.remove(10)
+check(tree)
+
+print("\n\nDone with Tests!\n")
diff --git a/Threaded Binary Tree/ThreadedBinaryTreeBackup.swift b/Threaded Binary Tree/ThreadedBinaryTreeBackup.swift
new file mode 100644
index 000000000..10f955580
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTreeBackup.swift	
@@ -0,0 +1,543 @@
+/*
+  A Threaded Binary Tree.
+  Based on this club's Binary Search Tree implementation.
+
+  Each node stores a value and two children. The left child contains a smaller
+  value; the right a larger (or equal) value.
+  
+  Any nodes that lack either a left or right child instead keep track of their
+  in-order predecessor and/or successor.
+
+  This tree allows duplicate elements.
+
+  This tree does not automatically balance itself. To make sure it is balanced,
+  you should insert new values in randomized order, not in sorted order.
+*/
+public class ThreadedBinaryTree<T: Comparable> {
+  private(set) public var value: T
+  private(set) public var parent: ThreadedBinaryTree?
+  private(set) public var left: ThreadedBinaryTree?
+  private(set) public var right: ThreadedBinaryTree?
+
+  //threaded
+  private(set) public var leftThread: ThreadedBinaryTree?
+  private(set) public var rightThread: ThreadedBinaryTree?
+
+  public init(value: T) {
+    self.value = value
+  }
+
+  public convenience init(array: [T]) {
+    precondition(array.count > 0)
+    self.init(value: array.first!)
+    for v in array.dropFirst() {
+      insert(v, parent: self)
+    }
+  }
+
+  public var isRoot: Bool {
+    return parent == nil
+  }
+
+  public var isLeaf: Bool {
+    return left == nil && right == nil
+  }
+
+  public var isLeftChild: Bool {
+    return parent?.left === self
+  }
+
+  public var isRightChild: Bool {
+    return parent?.right === self
+  }
+
+  public var hasLeftChild: Bool {
+    return left != nil
+  }
+
+  public var hasRightChild: Bool {
+    return right != nil
+  }
+
+  public var hasAnyChild: Bool {
+    return hasLeftChild || hasRightChild
+  }
+
+  public var hasBothChildren: Bool {
+    return hasLeftChild && hasRightChild
+  }
+
+  /* How many nodes are in this subtree. Performance: O(n). */
+  public var count: Int {
+    return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+  }
+}
+
+// MARK: - Adding items
+
+extension ThreadedBinaryTree {
+  /*
+    Inserts a new element into the tree. You should only insert elements
+    at the root, to make to sure this remains a valid binary tree!
+    Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func insert(value: T) {
+    insert(value, parent: self)
+  }
+  
+  private func insert(value: T, parent: ThreadedBinaryTree) {
+    if value < self.value {
+      if let left = left {
+        left.insert(value, parent: left)
+      } else {
+        left = ThreadedBinaryTree(value: value)
+        left?.parent = parent
+        //threaded
+        left?.leftThread = leftThread
+        left?.rightThread = parent
+        leftThread = nil
+      }
+    } else {
+      if let right = right {
+        right.insert(value, parent: right)
+      } else {
+        right = ThreadedBinaryTree(value: value)
+        right?.parent = parent
+        //threaded
+        right?.rightThread = rightThread
+        right?.leftThread = parent
+        rightThread = nil
+      }
+    }
+  }
+}
+
+// MARK: - Deleting items
+
+extension ThreadedBinaryTree {
+  /*
+    Deletes the "highest" node with the specified value.
+
+    Returns the node that has replaced this removed one (or nil if this was a
+    leaf node). That is primarily useful for when you delete the root node, in
+    which case the tree gets a new root.
+
+    Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  //threaded
+  public func remove(value: T) -> ThreadedBinaryTree? {
+    return search(value)?.remove()
+  }
+
+  /*
+    Deletes "this" node from the tree.
+  */
+  public func remove() -> ThreadedBinaryTree? {
+    let replacement: ThreadedBinaryTree?
+
+    if let left = left {
+      if let right = right {
+        replacement = removeNodeWithTwoChildren(left, right)
+        //threaded
+        replacement?.leftThread = leftThread
+        replacement?.rightThread = rightThread
+        left.maximum().rightThread = replacement
+        right.minimum().leftThread = replacement
+      } else {
+        // This node only has a left child. The left child replaces the node.
+        replacement = left
+        //threaded
+        left.maximum().rightThread = rightThread
+      }
+    } else if let right = right {
+      // This node only has a right child. The right child replaces the node.
+      replacement = right
+      //threaded
+      right.minimum().leftThread = leftThread
+    } else {
+      // This node has no children. We just disconnect it from its parent.
+      replacement = nil
+      //threaded
+      if isLeftChild {
+        parent?.leftThread = leftThread
+      } else {
+        parent?.rightThread = rightThread
+      }
+    }
+
+    reconnectParentToNode(replacement)
+
+    // The current node is no longer part of the tree, so clean it up.
+    parent = nil
+    left = nil
+    right = nil
+    //threaded
+    leftThread = nil
+    rightThread = nil
+
+    return replacement
+  }
+
+  private func removeNodeWithTwoChildren(left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
+    // This node has two children. It must be replaced by the smallest
+    // child that is larger than this node's value, which is the leftmost
+    // descendent of the right child.
+    let successor = right.minimum()
+
+    // If this in-order successor has a right child of its own (it cannot
+    // have a left child by definition), then that must take its place.
+    successor.remove()
+
+    // Connect our left child with the new node.
+    successor.left = left
+    left.parent = successor
+
+    // Connect our right child with the new node. If the right child does
+    // not have any left children of its own, then the in-order successor
+    // *is* the right child.
+    if right !== successor {
+      successor.right = right
+      right.parent = successor
+    } else {
+      successor.right = nil
+    }
+
+    // And finally, connect the successor node to our parent.
+    return successor
+  }
+
+  private func reconnectParentToNode(node: ThreadedBinaryTree?) {
+    if let parent = parent {
+      if isLeftChild {
+        parent.left = node
+      } else {
+        parent.right = node
+      }
+    }
+    node?.parent = parent
+  }
+}
+
+// MARK: - Searching
+
+extension ThreadedBinaryTree {
+  /*
+    Finds the "highest" node with the specified value.
+    Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func search(value: T) -> ThreadedBinaryTree? {
+    var node: ThreadedBinaryTree? = self
+    while case let n? = node {
+      if value < n.value {
+        node = n.left
+      } else if value > n.value {
+        node = n.right
+      } else {
+        return node
+      }
+    }
+    return nil
+  }
+
+  /*
+  // Recursive version of search
+  public func search(value: T) -> ThreadedBinaryTree? {
+    if value < self.value {
+      return left?.search(value)
+    } else if value > self.value {
+      return right?.search(value)
+    } else {
+      return self  // found it!
+    }
+  }
+  */
+  
+  public func contains(value: T) -> Bool {
+    return search(value) != nil
+  }
+
+  /*
+    Returns the leftmost descendent. O(h) time.
+  */
+  public func minimum() -> ThreadedBinaryTree {
+    var node = self
+    while case let next? = node.left {
+      node = next
+    }
+    return node
+  }
+  
+  /*
+    Returns the rightmost descendent. O(h) time.
+  */
+  public func maximum() -> ThreadedBinaryTree {
+    var node = self
+    while case let next? = node.right {
+      node = next
+    }
+    return node
+  }
+  
+  /*
+    Calculates the depth of this node, i.e. the distance to the root.
+    Takes O(h) time.
+  */
+  public func depth() -> Int {
+    var node = self
+    var edges = 0
+    while case let parent? = node.parent {
+      node = parent
+      edges += 1
+    }
+    return edges
+  }
+  
+  /*
+    Calculates the height of this node, i.e. the distance to the lowest leaf.
+    Since this looks at all children of this node, performance is O(n).
+  */
+  public func height() -> Int {
+    if isLeaf {
+      return 0
+    } else {
+      return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+    }
+  }
+
+  /*
+    Finds the node whose value precedes our value in sorted order.
+  */
+  public func predecessor() -> ThreadedBinaryTree<T>? {
+    if let left = left {
+      return left.maximum()
+    } else {
+      /*
+      var node = self
+      while case let parent? = node.parent {
+        if parent.value < value { return parent }
+        node = parent
+      }
+      return nil
+      */
+      //threaded
+      return leftThread
+    }
+  }
+
+  /*
+    Finds the node whose value succeeds our value in sorted order.
+  */
+  public func successor() -> ThreadedBinaryTree<T>? {
+    if let right = right {
+      return right.minimum()
+    } else {
+      /*
+      var node = self
+      while case let parent? = node.parent {
+        if parent.value > value { return parent }
+        node = parent
+      }
+      return nil
+      */
+      //threaded
+      return rightThread
+    }
+  }
+}
+
+// MARK: - Traversal
+
+extension ThreadedBinaryTree {
+  public func traverseInOrder(@noescape process: T -> Void) {
+    /*
+    left?.traverseInOrder(process)
+    process(value)
+    right?.traverseInOrder(process)
+    */
+    //threaded
+    var n: ThreadedBinaryTree
+    n = minimum()
+    while true {
+      process(n.value)
+      if let successor = n.successor() {
+        n = successor
+      } else {
+        break
+      }
+    }
+  }
+  
+  public func traversePreOrder(@noescape process: T -> Void) {
+    process(value)
+    left?.traversePreOrder(process)
+    right?.traversePreOrder(process)
+  }
+  
+  public func traversePostOrder(@noescape process: T -> Void) {
+    left?.traversePostOrder(process)
+    right?.traversePostOrder(process)
+    process(value)
+  }
+
+  /*
+    Performs an in-order traversal and collects the results in an array.
+  */
+  public func map(@noescape formula: T -> T) -> [T] {
+    var a = [T]()
+    if let left = left { a += left.map(formula) }
+    a.append(formula(value))
+    if let right = right { a += right.map(formula) }
+    return a
+  }
+}
+
+/*
+  Is this threaded binary tree a valid binary search tree?
+*/
+extension ThreadedBinaryTree {
+  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
+    if value < minValue || value > maxValue { return false }
+    let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+    let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+    return leftBST && rightBST
+  }
+}
+
+/*
+  Is this binary tree properly threaded?
+  Either left or leftThread (but not both) must be nil (likewise for right).
+  The first and last nodes in the in-order traversal are exempt from this,
+  as the first has leftThread = nil, and the last has rightThread = nil.
+*/
+//threaded
+extension ThreadedBinaryTree {
+  public func isThreaded() -> Bool {
+    if self === minimum() {
+      if left != nil && leftThread != nil {
+        return false
+      }
+    } else if (left == nil && leftThread == nil) || (left != nil && leftThread != nil) {
+      return false
+    }
+    if self === maximum() {
+      if right != nil && rightThread != nil {
+        return false
+      }
+    } else if (right == nil && rightThread == nil) || (right != nil && rightThread != nil) {
+      return false
+    }
+    let leftThreaded = left?.isThreaded() ?? true
+    let rightThreaded = right?.isThreaded() ?? true
+    return leftThreaded && rightThreaded
+  }
+}
+
+// MARK: - Debugging
+
+extension ThreadedBinaryTree: CustomStringConvertible {
+  public var description: String {
+    var s = ""
+    if let left = left {
+      s += "(\(left.description)) <- "
+    }
+    s += "\(value)"
+    if let right = right {
+      s += " -> (\(right.description))"
+    }
+    return s
+  }
+}
+
+extension ThreadedBinaryTree: CustomDebugStringConvertible {
+  public var debugDescription: String {
+    var s = "value: \(value)"
+    if let parent = parent {
+      s += ", parent: \(parent.value)"
+    }
+    if let left = left {
+      s += ", left = [" + left.debugDescription + "]"
+    }
+    if let right = right {
+      s += ", right = [" + right.debugDescription + "]"
+    }
+    //threaded
+    if let leftThread = leftThread {
+      s += ", leftThread: \(leftThread.value)"
+    }
+    if let rightThread = rightThread {
+      s += ", rightThread: \(rightThread.value)"
+    }
+    return s
+  }
+
+  public func toArray() -> [T] {
+    return map { $0 }
+  }
+}
+
+/*
+  TESTS
+  I don't have an Apple computer, so I can't make a Playground or any of that
+  fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree class.
+  It follows the illustrations in the README.
+*/
+
+// Simple little debug function to make testing output pretty
+private func check(tree: ThreadedBinaryTree<Int>) {
+  print("Overview:")
+  print(tree)
+  print("Debug Info:")
+  print(tree.debugDescription)
+  print("In-Order Traversal:")
+  let myArray = tree.toArray()
+  for node in myArray {
+    print(node)
+  }
+  if tree.isThreaded() {
+    print("This threaded binary tree is VALID.")
+  } else {
+    print("This threaded binary tree is INVALID.")
+  }
+}
+  
+
+print("\nFull Balanced Binary Tree with 7 Nodes")
+let fullTree = ThreadedBinaryTree<Int>(value: 4)
+fullTree.insert(2)
+fullTree.insert(6)
+fullTree.insert(1)
+fullTree.insert(3)
+fullTree.insert(5)
+fullTree.insert(7)
+check(fullTree)
+
+
+print("\n\nUnbalanced Binary Tree with 5 Nodes")
+let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
+check(tree)
+
+print("\nInsert 10")
+tree.insert(10)
+check(tree)
+
+print("\nInsert 4")
+tree.insert(4)
+check(tree)
+
+print("\nRemove 13 (Not in the Tree)")
+tree.remove(13)
+check(tree)
+
+print("\nRemove 5")
+tree.remove(5)
+check(tree)
+
+print("\nRemove 7")
+tree.remove(7)
+check(tree)
+
+print("\nRemove 10")
+tree.remove(10)
+check(tree)
+
+print("\n\nDone with Tests!\n")

From ac9abb4ae8ed5589911630cd85d1f7588a7dd0d8 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Mon, 2 May 2016 20:55:09 -0400
Subject: [PATCH 0308/1679] Touch up ThreadedBinaryTree and begin testing

---
 Threaded Binary Tree/README.markdown          |  53 +++----
 Threaded Binary Tree/ThreadedBinaryTree.swift | 132 +++++++++---------
 2 files changed, 92 insertions(+), 93 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index bc812ee6a..d78030e4b 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -22,18 +22,18 @@ In-order traversal of any binary tree generally goes as follows:
 
 ```swift
 func traverse(n: Node?) {
-	if (n == nil) { return
-	} else {
-		traverse(n.left)
-		visit(n)
-		traverse(n.right)
-	}
+  if (n == nil) { return
+  } else {
+    traverse(n.left)
+    visit(n)
+    traverse(n.right)
+  }
 }
 ```
-Where `n` is a a node in the tree (or `nil`), each node stores
-its children as `left` and `right`, and "visiting" a node can mean
-performing any desired action on it.  We would call this function by passing to
-it the root of the tree we wish to traverse.
+Where `n` is a a node in the tree (or `nil`), each node stores its children as
+`left` and `right`, and "visiting" a node can mean performing any desired
+action on it.  We would call this function by passing to it the root of the
+tree we wish to traverse.
 
 While simple and understandable, this algorithm uses stack space proportional
 to the height of the tree due to its recursive nature.  If the tree has **n**
@@ -83,26 +83,19 @@ outlined above.  We use these predecessor/successor attributes to great effect
 in this new algorithm (note that this is for a forward traversal):
 
 ```swift
-traverse(root):
-	if (root == nil) return
- 
-    // Find the leftmost Node
-    Node n = root
-	while (n.left != nil):
-		n = n.left
- 
-    while (n != nil):
-		visit n
-
-        // If this Node is a thread Node, then go to its in-order successor
-        if (n.rightThread):
-            n = n.right
- 
-		// Else go to the leftmost Node in its right subtree
-        else:
-            n = n.right
-			while (n.left != nil):
-				n = n.left
+func traverse(root: Node) {
+  var n: ThreadedBinaryTree
+  // Start at the leftmost Node
+  n = root.minimum()
+  while true {
+    visit(n)
+    if let successor = n.successor() {
+      n = successor
+    } else {
+      break
+    }
+  }
+}
 ```
 Where:
 - `root` is the root of the tree (or `nil`).
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
index 10f955580..b1ae8d0bf 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.swift	
@@ -19,7 +19,7 @@ public class ThreadedBinaryTree<T: Comparable> {
   private(set) public var left: ThreadedBinaryTree?
   private(set) public var right: ThreadedBinaryTree?
 
-  //threaded
+  //THREADED
   private(set) public var leftThread: ThreadedBinaryTree?
   private(set) public var rightThread: ThreadedBinaryTree?
 
@@ -92,7 +92,7 @@ extension ThreadedBinaryTree {
       } else {
         left = ThreadedBinaryTree(value: value)
         left?.parent = parent
-        //threaded
+        //THREADED
         left?.leftThread = leftThread
         left?.rightThread = parent
         leftThread = nil
@@ -103,7 +103,7 @@ extension ThreadedBinaryTree {
       } else {
         right = ThreadedBinaryTree(value: value)
         right?.parent = parent
-        //threaded
+        //THREADED
         right?.rightThread = rightThread
         right?.leftThread = parent
         rightThread = nil
@@ -124,7 +124,7 @@ extension ThreadedBinaryTree {
 
     Performance: runs in O(h) time, where h is the height of the tree.
   */
-  //threaded
+  //THREADED
   public func remove(value: T) -> ThreadedBinaryTree? {
     return search(value)?.remove()
   }
@@ -138,7 +138,7 @@ extension ThreadedBinaryTree {
     if let left = left {
       if let right = right {
         replacement = removeNodeWithTwoChildren(left, right)
-        //threaded
+        //THREADED
         replacement?.leftThread = leftThread
         replacement?.rightThread = rightThread
         left.maximum().rightThread = replacement
@@ -146,18 +146,18 @@ extension ThreadedBinaryTree {
       } else {
         // This node only has a left child. The left child replaces the node.
         replacement = left
-        //threaded
+        //THREADED
         left.maximum().rightThread = rightThread
       }
     } else if let right = right {
       // This node only has a right child. The right child replaces the node.
       replacement = right
-      //threaded
+      //THREADED
       right.minimum().leftThread = leftThread
     } else {
       // This node has no children. We just disconnect it from its parent.
       replacement = nil
-      //threaded
+      //THREADED
       if isLeftChild {
         parent?.leftThread = leftThread
       } else {
@@ -171,7 +171,7 @@ extension ThreadedBinaryTree {
     parent = nil
     left = nil
     right = nil
-    //threaded
+    //THREADED
     leftThread = nil
     rightThread = nil
 
@@ -241,13 +241,14 @@ extension ThreadedBinaryTree {
 
   /*
   // Recursive version of search
+  // Educational but undesirable due to the overhead cost of recursion
   public func search(value: T) -> ThreadedBinaryTree? {
     if value < self.value {
       return left?.search(value)
     } else if value > self.value {
       return right?.search(value)
     } else {
-      return self  // found it!
+      return self
     }
   }
   */
@@ -311,15 +312,7 @@ extension ThreadedBinaryTree {
     if let left = left {
       return left.maximum()
     } else {
-      /*
-      var node = self
-      while case let parent? = node.parent {
-        if parent.value < value { return parent }
-        node = parent
-      }
-      return nil
-      */
-      //threaded
+      //THREADED
       return leftThread
     }
   }
@@ -331,15 +324,7 @@ extension ThreadedBinaryTree {
     if let right = right {
       return right.minimum()
     } else {
-      /*
-      var node = self
-      while case let parent? = node.parent {
-        if parent.value > value { return parent }
-        node = parent
-      }
-      return nil
-      */
-      //threaded
+      //THREADED
       return rightThread
     }
   }
@@ -348,17 +333,12 @@ extension ThreadedBinaryTree {
 // MARK: - Traversal
 
 extension ThreadedBinaryTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
-    /*
-    left?.traverseInOrder(process)
-    process(value)
-    right?.traverseInOrder(process)
-    */
-    //threaded
+  //THREADED
+  public func traverseInOrderForward(@noescape visit: T -> Void) {
     var n: ThreadedBinaryTree
     n = minimum()
     while true {
-      process(n.value)
+      visit(n.value)
       if let successor = n.successor() {
         n = successor
       } else {
@@ -366,17 +346,31 @@ extension ThreadedBinaryTree {
       }
     }
   }
+
+  //THREADED
+  public func traverseInOrderBackward(@noescape visit: T -> Void) {
+    var n: ThreadedBinaryTree
+    n = maximum()
+    while true {
+      visit(n.value)
+      if let predecessor = n.predecessor() {
+        n = predecessor
+      } else {
+        break
+      }
+    }
+  }
   
-  public func traversePreOrder(@noescape process: T -> Void) {
-    process(value)
-    left?.traversePreOrder(process)
-    right?.traversePreOrder(process)
+  public func traversePreOrder(@noescape visit: T -> Void) {
+    visit(value)
+    left?.traversePreOrder(visit)
+    right?.traversePreOrder(visit)
   }
   
-  public func traversePostOrder(@noescape process: T -> Void) {
-    left?.traversePostOrder(process)
-    right?.traversePostOrder(process)
-    process(value)
+  public func traversePostOrder(@noescape visit: T -> Void) {
+    left?.traversePostOrder(visit)
+    right?.traversePostOrder(visit)
+    visit(value)
   }
 
   /*
@@ -384,33 +378,41 @@ extension ThreadedBinaryTree {
   */
   public func map(@noescape formula: T -> T) -> [T] {
     var a = [T]()
-    if let left = left { a += left.map(formula) }
-    a.append(formula(value))
-    if let right = right { a += right.map(formula) }
+    //THREADED
+    var n: ThreadedBinaryTree
+    n = minimum()
+    while true {
+      a.append(formula(n.value))
+      if let successor = n.successor() {
+        n = successor
+      } else {
+        break
+      }
+    }
     return a
   }
 }
 
-/*
-  Is this threaded binary tree a valid binary search tree?
-*/
+// MARK: - Verification
+
 extension ThreadedBinaryTree {
+  /*
+    Is this threaded binary tree a valid binary search tree?
+  */
   public func isBST(minValue minValue: T, maxValue: T) -> Bool {
     if value < minValue || value > maxValue { return false }
     let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
     let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
     return leftBST && rightBST
   }
-}
 
-/*
-  Is this binary tree properly threaded?
-  Either left or leftThread (but not both) must be nil (likewise for right).
-  The first and last nodes in the in-order traversal are exempt from this,
-  as the first has leftThread = nil, and the last has rightThread = nil.
-*/
-//threaded
-extension ThreadedBinaryTree {
+  /*
+    Is this binary tree properly threaded?
+    Either left or leftThread (but not both) must be nil (likewise for right).
+    The first and last nodes in the in-order traversal are exempt from this,
+    as the first has leftThread = nil, and the last has rightThread = nil.
+  */
+  //THREADED
   public func isThreaded() -> Bool {
     if self === minimum() {
       if left != nil && leftThread != nil {
@@ -460,7 +462,7 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     if let right = right {
       s += ", right = [" + right.debugDescription + "]"
     }
-    //threaded
+    //THREADED
     if let leftThread = leftThread {
       s += ", leftThread: \(leftThread.value)"
     }
@@ -479,12 +481,12 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
   TESTS
   I don't have an Apple computer, so I can't make a Playground or any of that
   fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree class.
-  It follows the illustrations in the README.
+  It follows the examples in the README.
 */
 
 // Simple little debug function to make testing output pretty
 private func check(tree: ThreadedBinaryTree<Int>) {
-  print("Overview:")
+  print("\(tree.count) Total Nodes:");
   print(tree)
   print("Debug Info:")
   print(tree.debugDescription)
@@ -499,7 +501,11 @@ private func check(tree: ThreadedBinaryTree<Int>) {
     print("This threaded binary tree is INVALID.")
   }
 }
-  
+
+
+print("\nTree with Single Node")
+let emptyTree = ThreadedBinaryTree<Int>(value: 1)
+check(emptyTree)
 
 print("\nFull Balanced Binary Tree with 7 Nodes")
 let fullTree = ThreadedBinaryTree<Int>(value: 4)

From 0bf400802f7d5f824936529192254fee5c487439 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Mon, 2 May 2016 22:46:36 -0400
Subject: [PATCH 0309/1679] Add traversal details to Threaded README

---
 Threaded Binary Tree/README.markdown | 114 +++++++++++++++++++++------
 1 file changed, 88 insertions(+), 26 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index d78030e4b..ad8337f83 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -2,7 +2,7 @@
 
 A threaded binary tree is a special kind of [binary tree](../Binary Tree/) (a
 tree in which each node has at most two children) that maintains a few extra
-pointers to allow cheap and fast **in-order traversal** of the tree.
+variables to allow cheap and fast **in-order traversal** of the tree.
 
 If you don't know what a tree is or what it is for, then [read this
 first](../Tree/).
@@ -50,11 +50,10 @@ A threaded binary tree fixes this problem.
 An in-order traversal of a tree yields a linear ordering of the nodes.  Thus
 each node has both a predecessor and a successor (except for the first and last
 nodes, which only have a successor or a predecessor respectively).  In a
-threaded binary tree, each left child pointer that would normally be `nil`
-instead points to the node's predecessor (if it exists), and each right child
-pointer that would normally be `nil` instead points to the node's successor
-(if it exists).  This is what separates threaded binary trees from standard
-binary trees.
+threaded binary tree, each left child that would normally be `nil` instead
+stores the node's predecessor (if it exists), and each right child that would
+normally be `nil` instead stores the node's successor (if it exists).  This is
+what separates threaded binary trees from standard binary trees.
 
 There are two types of threaded binary trees:  single threaded and double
 threaded:
@@ -75,20 +74,70 @@ has a right child but no left child, it will track its predecessor in place of
 its left child.
 
 
+## Representation
+
+Before we go into detail about the methods that we can apply to threaded binary
+trees, it might be a good idea to explain how we will be representing the tree.
+The core of this data structure is the `ThreadedBinaryTree<T: Comparable>`
+class.  Each instance of this class represents a node with six member
+variables:  `value`, `parent`, `left`, `right`, `leftThread`, and
+`rightThread`.  Of all of these, only `value` is required.  The other five are
+Swift *optionals*.
+- `value: T` is the value of this node (e.g. 1, 2, A, B, etc.)
+- `parent: ThreadedBinaryTree?` is the parent of this node (if it exists)
+- `left: ThreadedBinaryTree?` is the left child of this node (if it exists)
+- `right: ThreadedBinaryTree?` is the right child of this node (if it exists)
+- `leftThread: ThreadedBinaryTree?` is the in-order predecessor of this node
+- `rightThread: ThreadedBinaryTree?` is the in-order successor of this node
+
+Now we are ready to go over some of the member functions in our
+`ThreadedBinaryTree` class.
+
+
 ## Traversal algorithm
 
+Let's start with the main reason we're using a threaded binary tree.  It is now
+very easy to find the in-order predecessor and the in-order successor of any
+node in the tree.  If the node has no left/right child, we can simply return
+the node's leftThread/rightThread.  Otherwise, it is trivial to move down the
+tree and find the correct node.
+
+```swift
+  func predecessor() -> ThreadedBinaryTree<T>? {
+    if let left = left {
+      return left.maximum()
+    } else {
+      return leftThread
+    }
+  }
+
+  func successor() -> ThreadedBinaryTree<T>? {
+    if let right = right {
+      return right.minimum()
+    } else {
+      return rightThread
+    }
+  }
+```
+> Note: `maximum()` and `minimum()` are methods of `ThreadedBinaryTree` which
+return the largest/smallest node in a given sub-tree.  See [the
+implementation](ThreadedBinaryTree.swift) for more detail.
+
+Because these are `ThreadedBinaryTree` methods, we can call
+`node.predecessor()` or `node.successor()` to obtain the predecessor or
+successor of any `node`, provided that `node` is a `ThreadedBinaryTree` object.
+
 Because predecessors and/or successors are tracked, an in-order traversal of a
 threaded binary tree is much more efficient than the recursive algorithm
 outlined above.  We use these predecessor/successor attributes to great effect
-in this new algorithm (note that this is for a forward traversal):
+in this new algorithm for both forward and backward traversals:
 
 ```swift
-func traverse(root: Node) {
+func traverseInOrderForward(visit: T -> Void) {
   var n: ThreadedBinaryTree
-  // Start at the leftmost Node
-  n = root.minimum()
+  n = minimum()
   while true {
-    visit(n)
+    visit(n.value)
     if let successor = n.successor() {
       n = successor
     } else {
@@ -96,23 +145,35 @@ func traverse(root: Node) {
     }
   }
 }
+
+func traverseInOrderBackward(visit: T -> Void) {
+  var n: ThreadedBinaryTree
+  n = maximum()
+  while true {
+    visit(n.value)
+    if let predecessor = n.predecessor() {
+      n = predecessor
+    } else {
+      break
+    }
+  }
+}
 ```
-Where:
-- `root` is the root of the tree (or `nil`).
-- Each node stores its children or predecessor/successor as `left`
-  and `right`.
-- "Visiting" a node can mean performing any desired action on it.
-- The booleans `leftThread` and `rightThread` keep track of whether `left` and
-  `right` point to a child or a predecessor/successor.
-	- They are `true` for predecessors/successors, and `false` for children.
-	- While `leftThread` is not used here, it would be used in a backwards
-	  traversal in a double threaded tree or a single threaded tree "pointing"
-	  the other direction.
-- The first node in the traversal has `leftThread = true` and `left = nil`
-- The last node in the traversal has `rightThread = true` and `right = nil`
+Again, this a method of `ThreadedBinaryTree`, so we'd call it like
+`node.traverseInorderForward(visitFunction)`.  Note that we are able to specify
+a function that executes on each node as they are visited.  This function can
+be anything you want, as long as it accepts `T` (the type of the values of the
+nodes of the tree) and has no return value.
+
 
+## Insertion and deletion
 
-## An example
+The quick in-order traversal that a threaded binary trees gives us comes at a
+small cost.  Inserting/deleting nodes becomes more complicated, as we have to
+continuously manage the `leftThread` and `rightThread` variables.  It is best
+to explain this with an example.  Please note that this requires knowledge of
+binary search trees, so make sure you have [read this first](../Binary Search
+Tree/).
 
 
 ### Still under construction.
@@ -121,4 +182,5 @@ Where:
 
 [Threaded Binary Tree on Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree).
 
-*Written for the Swift Algorithm Club by Jayson Tung*
+*Written for the Swift Algorithm Club by [Jayson
+Tung](https://github.com/JFTung)*

From 791456994bb225b1b83d5c3a14f3649e4cf5f4ec Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Mon, 2 May 2016 22:58:05 -0400
Subject: [PATCH 0310/1679] Fix README link and delete unnecessary backup

---
 Threaded Binary Tree/README.markdown          |  16 +-
 .../ThreadedBinaryTreeBackup.swift            | 543 ------------------
 2 files changed, 8 insertions(+), 551 deletions(-)
 delete mode 100644 Threaded Binary Tree/ThreadedBinaryTreeBackup.swift

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index ad8337f83..ba654ea07 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -4,8 +4,8 @@ A threaded binary tree is a special kind of [binary tree](../Binary Tree/) (a
 tree in which each node has at most two children) that maintains a few extra
 variables to allow cheap and fast **in-order traversal** of the tree.
 
-If you don't know what a tree is or what it is for, then [read this
-first](../Tree/).
+If you don't know what a tree is or what it is for, then
+[read this first](../Tree/).
 
 
 ## In-order traversal
@@ -120,8 +120,8 @@ tree and find the correct node.
   }
 ```
 > Note: `maximum()` and `minimum()` are methods of `ThreadedBinaryTree` which
-return the largest/smallest node in a given sub-tree.  See [the
-implementation](ThreadedBinaryTree.swift) for more detail.
+return the largest/smallest node in a given sub-tree.  See
+[the implementation](ThreadedBinaryTree.swift) for more detail.
 
 Because these are `ThreadedBinaryTree` methods, we can call
 `node.predecessor()` or `node.successor()` to obtain the predecessor or
@@ -172,8 +172,8 @@ The quick in-order traversal that a threaded binary trees gives us comes at a
 small cost.  Inserting/deleting nodes becomes more complicated, as we have to
 continuously manage the `leftThread` and `rightThread` variables.  It is best
 to explain this with an example.  Please note that this requires knowledge of
-binary search trees, so make sure you have [read this first](../Binary Search
-Tree/).
+binary search trees, so make sure you have
+[read this first](../Binary Search Tree/).
 
 
 ### Still under construction.
@@ -182,5 +182,5 @@ Tree/).
 
 [Threaded Binary Tree on Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree).
 
-*Written for the Swift Algorithm Club by [Jayson
-Tung](https://github.com/JFTung)*
+*Written for the Swift Algorithm Club by
+[Jayson Tung](https://github.com/JFTung)*
diff --git a/Threaded Binary Tree/ThreadedBinaryTreeBackup.swift b/Threaded Binary Tree/ThreadedBinaryTreeBackup.swift
deleted file mode 100644
index 10f955580..000000000
--- a/Threaded Binary Tree/ThreadedBinaryTreeBackup.swift	
+++ /dev/null
@@ -1,543 +0,0 @@
-/*
-  A Threaded Binary Tree.
-  Based on this club's Binary Search Tree implementation.
-
-  Each node stores a value and two children. The left child contains a smaller
-  value; the right a larger (or equal) value.
-  
-  Any nodes that lack either a left or right child instead keep track of their
-  in-order predecessor and/or successor.
-
-  This tree allows duplicate elements.
-
-  This tree does not automatically balance itself. To make sure it is balanced,
-  you should insert new values in randomized order, not in sorted order.
-*/
-public class ThreadedBinaryTree<T: Comparable> {
-  private(set) public var value: T
-  private(set) public var parent: ThreadedBinaryTree?
-  private(set) public var left: ThreadedBinaryTree?
-  private(set) public var right: ThreadedBinaryTree?
-
-  //threaded
-  private(set) public var leftThread: ThreadedBinaryTree?
-  private(set) public var rightThread: ThreadedBinaryTree?
-
-  public init(value: T) {
-    self.value = value
-  }
-
-  public convenience init(array: [T]) {
-    precondition(array.count > 0)
-    self.init(value: array.first!)
-    for v in array.dropFirst() {
-      insert(v, parent: self)
-    }
-  }
-
-  public var isRoot: Bool {
-    return parent == nil
-  }
-
-  public var isLeaf: Bool {
-    return left == nil && right == nil
-  }
-
-  public var isLeftChild: Bool {
-    return parent?.left === self
-  }
-
-  public var isRightChild: Bool {
-    return parent?.right === self
-  }
-
-  public var hasLeftChild: Bool {
-    return left != nil
-  }
-
-  public var hasRightChild: Bool {
-    return right != nil
-  }
-
-  public var hasAnyChild: Bool {
-    return hasLeftChild || hasRightChild
-  }
-
-  public var hasBothChildren: Bool {
-    return hasLeftChild && hasRightChild
-  }
-
-  /* How many nodes are in this subtree. Performance: O(n). */
-  public var count: Int {
-    return (left?.count ?? 0) + 1 + (right?.count ?? 0)
-  }
-}
-
-// MARK: - Adding items
-
-extension ThreadedBinaryTree {
-  /*
-    Inserts a new element into the tree. You should only insert elements
-    at the root, to make to sure this remains a valid binary tree!
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func insert(value: T) {
-    insert(value, parent: self)
-  }
-  
-  private func insert(value: T, parent: ThreadedBinaryTree) {
-    if value < self.value {
-      if let left = left {
-        left.insert(value, parent: left)
-      } else {
-        left = ThreadedBinaryTree(value: value)
-        left?.parent = parent
-        //threaded
-        left?.leftThread = leftThread
-        left?.rightThread = parent
-        leftThread = nil
-      }
-    } else {
-      if let right = right {
-        right.insert(value, parent: right)
-      } else {
-        right = ThreadedBinaryTree(value: value)
-        right?.parent = parent
-        //threaded
-        right?.rightThread = rightThread
-        right?.leftThread = parent
-        rightThread = nil
-      }
-    }
-  }
-}
-
-// MARK: - Deleting items
-
-extension ThreadedBinaryTree {
-  /*
-    Deletes the "highest" node with the specified value.
-
-    Returns the node that has replaced this removed one (or nil if this was a
-    leaf node). That is primarily useful for when you delete the root node, in
-    which case the tree gets a new root.
-
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  //threaded
-  public func remove(value: T) -> ThreadedBinaryTree? {
-    return search(value)?.remove()
-  }
-
-  /*
-    Deletes "this" node from the tree.
-  */
-  public func remove() -> ThreadedBinaryTree? {
-    let replacement: ThreadedBinaryTree?
-
-    if let left = left {
-      if let right = right {
-        replacement = removeNodeWithTwoChildren(left, right)
-        //threaded
-        replacement?.leftThread = leftThread
-        replacement?.rightThread = rightThread
-        left.maximum().rightThread = replacement
-        right.minimum().leftThread = replacement
-      } else {
-        // This node only has a left child. The left child replaces the node.
-        replacement = left
-        //threaded
-        left.maximum().rightThread = rightThread
-      }
-    } else if let right = right {
-      // This node only has a right child. The right child replaces the node.
-      replacement = right
-      //threaded
-      right.minimum().leftThread = leftThread
-    } else {
-      // This node has no children. We just disconnect it from its parent.
-      replacement = nil
-      //threaded
-      if isLeftChild {
-        parent?.leftThread = leftThread
-      } else {
-        parent?.rightThread = rightThread
-      }
-    }
-
-    reconnectParentToNode(replacement)
-
-    // The current node is no longer part of the tree, so clean it up.
-    parent = nil
-    left = nil
-    right = nil
-    //threaded
-    leftThread = nil
-    rightThread = nil
-
-    return replacement
-  }
-
-  private func removeNodeWithTwoChildren(left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
-    // This node has two children. It must be replaced by the smallest
-    // child that is larger than this node's value, which is the leftmost
-    // descendent of the right child.
-    let successor = right.minimum()
-
-    // If this in-order successor has a right child of its own (it cannot
-    // have a left child by definition), then that must take its place.
-    successor.remove()
-
-    // Connect our left child with the new node.
-    successor.left = left
-    left.parent = successor
-
-    // Connect our right child with the new node. If the right child does
-    // not have any left children of its own, then the in-order successor
-    // *is* the right child.
-    if right !== successor {
-      successor.right = right
-      right.parent = successor
-    } else {
-      successor.right = nil
-    }
-
-    // And finally, connect the successor node to our parent.
-    return successor
-  }
-
-  private func reconnectParentToNode(node: ThreadedBinaryTree?) {
-    if let parent = parent {
-      if isLeftChild {
-        parent.left = node
-      } else {
-        parent.right = node
-      }
-    }
-    node?.parent = parent
-  }
-}
-
-// MARK: - Searching
-
-extension ThreadedBinaryTree {
-  /*
-    Finds the "highest" node with the specified value.
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func search(value: T) -> ThreadedBinaryTree? {
-    var node: ThreadedBinaryTree? = self
-    while case let n? = node {
-      if value < n.value {
-        node = n.left
-      } else if value > n.value {
-        node = n.right
-      } else {
-        return node
-      }
-    }
-    return nil
-  }
-
-  /*
-  // Recursive version of search
-  public func search(value: T) -> ThreadedBinaryTree? {
-    if value < self.value {
-      return left?.search(value)
-    } else if value > self.value {
-      return right?.search(value)
-    } else {
-      return self  // found it!
-    }
-  }
-  */
-  
-  public func contains(value: T) -> Bool {
-    return search(value) != nil
-  }
-
-  /*
-    Returns the leftmost descendent. O(h) time.
-  */
-  public func minimum() -> ThreadedBinaryTree {
-    var node = self
-    while case let next? = node.left {
-      node = next
-    }
-    return node
-  }
-  
-  /*
-    Returns the rightmost descendent. O(h) time.
-  */
-  public func maximum() -> ThreadedBinaryTree {
-    var node = self
-    while case let next? = node.right {
-      node = next
-    }
-    return node
-  }
-  
-  /*
-    Calculates the depth of this node, i.e. the distance to the root.
-    Takes O(h) time.
-  */
-  public func depth() -> Int {
-    var node = self
-    var edges = 0
-    while case let parent? = node.parent {
-      node = parent
-      edges += 1
-    }
-    return edges
-  }
-  
-  /*
-    Calculates the height of this node, i.e. the distance to the lowest leaf.
-    Since this looks at all children of this node, performance is O(n).
-  */
-  public func height() -> Int {
-    if isLeaf {
-      return 0
-    } else {
-      return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
-    }
-  }
-
-  /*
-    Finds the node whose value precedes our value in sorted order.
-  */
-  public func predecessor() -> ThreadedBinaryTree<T>? {
-    if let left = left {
-      return left.maximum()
-    } else {
-      /*
-      var node = self
-      while case let parent? = node.parent {
-        if parent.value < value { return parent }
-        node = parent
-      }
-      return nil
-      */
-      //threaded
-      return leftThread
-    }
-  }
-
-  /*
-    Finds the node whose value succeeds our value in sorted order.
-  */
-  public func successor() -> ThreadedBinaryTree<T>? {
-    if let right = right {
-      return right.minimum()
-    } else {
-      /*
-      var node = self
-      while case let parent? = node.parent {
-        if parent.value > value { return parent }
-        node = parent
-      }
-      return nil
-      */
-      //threaded
-      return rightThread
-    }
-  }
-}
-
-// MARK: - Traversal
-
-extension ThreadedBinaryTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
-    /*
-    left?.traverseInOrder(process)
-    process(value)
-    right?.traverseInOrder(process)
-    */
-    //threaded
-    var n: ThreadedBinaryTree
-    n = minimum()
-    while true {
-      process(n.value)
-      if let successor = n.successor() {
-        n = successor
-      } else {
-        break
-      }
-    }
-  }
-  
-  public func traversePreOrder(@noescape process: T -> Void) {
-    process(value)
-    left?.traversePreOrder(process)
-    right?.traversePreOrder(process)
-  }
-  
-  public func traversePostOrder(@noescape process: T -> Void) {
-    left?.traversePostOrder(process)
-    right?.traversePostOrder(process)
-    process(value)
-  }
-
-  /*
-    Performs an in-order traversal and collects the results in an array.
-  */
-  public func map(@noescape formula: T -> T) -> [T] {
-    var a = [T]()
-    if let left = left { a += left.map(formula) }
-    a.append(formula(value))
-    if let right = right { a += right.map(formula) }
-    return a
-  }
-}
-
-/*
-  Is this threaded binary tree a valid binary search tree?
-*/
-extension ThreadedBinaryTree {
-  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
-    if value < minValue || value > maxValue { return false }
-    let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
-    let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
-    return leftBST && rightBST
-  }
-}
-
-/*
-  Is this binary tree properly threaded?
-  Either left or leftThread (but not both) must be nil (likewise for right).
-  The first and last nodes in the in-order traversal are exempt from this,
-  as the first has leftThread = nil, and the last has rightThread = nil.
-*/
-//threaded
-extension ThreadedBinaryTree {
-  public func isThreaded() -> Bool {
-    if self === minimum() {
-      if left != nil && leftThread != nil {
-        return false
-      }
-    } else if (left == nil && leftThread == nil) || (left != nil && leftThread != nil) {
-      return false
-    }
-    if self === maximum() {
-      if right != nil && rightThread != nil {
-        return false
-      }
-    } else if (right == nil && rightThread == nil) || (right != nil && rightThread != nil) {
-      return false
-    }
-    let leftThreaded = left?.isThreaded() ?? true
-    let rightThreaded = right?.isThreaded() ?? true
-    return leftThreaded && rightThreaded
-  }
-}
-
-// MARK: - Debugging
-
-extension ThreadedBinaryTree: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if let left = left {
-      s += "(\(left.description)) <- "
-    }
-    s += "\(value)"
-    if let right = right {
-      s += " -> (\(right.description))"
-    }
-    return s
-  }
-}
-
-extension ThreadedBinaryTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = "value: \(value)"
-    if let parent = parent {
-      s += ", parent: \(parent.value)"
-    }
-    if let left = left {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = right {
-      s += ", right = [" + right.debugDescription + "]"
-    }
-    //threaded
-    if let leftThread = leftThread {
-      s += ", leftThread: \(leftThread.value)"
-    }
-    if let rightThread = rightThread {
-      s += ", rightThread: \(rightThread.value)"
-    }
-    return s
-  }
-
-  public func toArray() -> [T] {
-    return map { $0 }
-  }
-}
-
-/*
-  TESTS
-  I don't have an Apple computer, so I can't make a Playground or any of that
-  fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree class.
-  It follows the illustrations in the README.
-*/
-
-// Simple little debug function to make testing output pretty
-private func check(tree: ThreadedBinaryTree<Int>) {
-  print("Overview:")
-  print(tree)
-  print("Debug Info:")
-  print(tree.debugDescription)
-  print("In-Order Traversal:")
-  let myArray = tree.toArray()
-  for node in myArray {
-    print(node)
-  }
-  if tree.isThreaded() {
-    print("This threaded binary tree is VALID.")
-  } else {
-    print("This threaded binary tree is INVALID.")
-  }
-}
-  
-
-print("\nFull Balanced Binary Tree with 7 Nodes")
-let fullTree = ThreadedBinaryTree<Int>(value: 4)
-fullTree.insert(2)
-fullTree.insert(6)
-fullTree.insert(1)
-fullTree.insert(3)
-fullTree.insert(5)
-fullTree.insert(7)
-check(fullTree)
-
-
-print("\n\nUnbalanced Binary Tree with 5 Nodes")
-let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
-check(tree)
-
-print("\nInsert 10")
-tree.insert(10)
-check(tree)
-
-print("\nInsert 4")
-tree.insert(4)
-check(tree)
-
-print("\nRemove 13 (Not in the Tree)")
-tree.remove(13)
-check(tree)
-
-print("\nRemove 5")
-tree.remove(5)
-check(tree)
-
-print("\nRemove 7")
-tree.remove(7)
-check(tree)
-
-print("\nRemove 10")
-tree.remove(10)
-check(tree)
-
-print("\n\nDone with Tests!\n")

From 75a94e38556a1de73cc3b4cf46c1d7115b365a97 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Tue, 3 May 2016 12:28:09 -0400
Subject: [PATCH 0311/1679] Finish threaded bin. tree images

---
 Threaded Binary Tree/Images/DelOne.png        | Bin 17173 -> 0 bytes
 Threaded Binary Tree/Images/DelThree.png      | Bin 11596 -> 0 bytes
 Threaded Binary Tree/Images/DelTwo.png        | Bin 13594 -> 0 bytes
 .../Images/{AddOne.png => Insert1.png}        | Bin
 .../Images/{AddTwo.png => Insert2.png}        | Bin
 Threaded Binary Tree/Images/Insert3.png       | Bin 0 -> 20386 bytes
 Threaded Binary Tree/Images/Remove1.png       | Bin 0 -> 17019 bytes
 Threaded Binary Tree/Images/Remove2.png       | Bin 0 -> 14090 bytes
 Threaded Binary Tree/Images/Remove3.png       | Bin 0 -> 12835 bytes
 Threaded Binary Tree/Images/Remove4.png       | Bin 0 -> 11934 bytes
 Threaded Binary Tree/README.markdown          |  53 ++++++++++++++++++
 Threaded Binary Tree/ThreadedBinaryTree.swift |  50 ++++++++++-------
 12 files changed, 84 insertions(+), 19 deletions(-)
 delete mode 100644 Threaded Binary Tree/Images/DelOne.png
 delete mode 100644 Threaded Binary Tree/Images/DelThree.png
 delete mode 100644 Threaded Binary Tree/Images/DelTwo.png
 rename Threaded Binary Tree/Images/{AddOne.png => Insert1.png} (100%)
 rename Threaded Binary Tree/Images/{AddTwo.png => Insert2.png} (100%)
 create mode 100644 Threaded Binary Tree/Images/Insert3.png
 create mode 100644 Threaded Binary Tree/Images/Remove1.png
 create mode 100644 Threaded Binary Tree/Images/Remove2.png
 create mode 100644 Threaded Binary Tree/Images/Remove3.png
 create mode 100644 Threaded Binary Tree/Images/Remove4.png

diff --git a/Threaded Binary Tree/Images/DelOne.png b/Threaded Binary Tree/Images/DelOne.png
deleted file mode 100644
index ded6abbe8cbad71af128c58c8e9eefd3189acece..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

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diff --git a/Threaded Binary Tree/Images/AddOne.png b/Threaded Binary Tree/Images/Insert1.png
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diff --git a/Threaded Binary Tree/Images/AddTwo.png b/Threaded Binary Tree/Images/Insert2.png
similarity index 100%
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HcmV?d00001

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index ba654ea07..91d7a9ecb 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -73,6 +73,26 @@ need to keep track of both.  For example, in a double threaded tree, if a node
 has a right child but no left child, it will track its predecessor in place of
 its left child.
 
+Here is a valid "full" threaded binary tree:
+
+![Full](/Images/Full.png)
+
+While the following threaded binary tree is not "full," it is still valid.  The
+structure of the tree does not matter as long as it follows the definition of a
+binary search tree:
+
+![Partial](/Images/Partial.png)
+
+The solid lines denote the links between parents and children, while the dotted
+lines denote the "threads."  The important thing to note here is how the
+children and thread edges interact with each other.  Every node besides the
+root has one entering edge (from its parent), and two leaving edges: one to the
+left and one to the right.  The left leaving edge goes to the node's left child
+if it exists, and to its in-order predecessor if it does not.  The right
+leaving edge goes to the node's right child if it exists, and to its in-order
+successor if it does not.  The exceptions are the left-most node and the
+right-most node, which do not have a predecessor or successor, respectively.
+
 
 ## Representation
 
@@ -175,6 +195,39 @@ to explain this with an example.  Please note that this requires knowledge of
 binary search trees, so make sure you have
 [read this first](../Binary Search Tree/).
 
+Base:
+
+![Base](/Images/Base.png)
+
+Insert1:
+
+![Insert1](/Images/Insert1.png)
+
+Insert2:
+
+![Insert2](/Images/Insert2.png)
+
+Insert3:
+
+![Insert3](/Images/Insert3.png)
+
+Remove1:
+
+![Remove1](/Images/Remove1.png)
+
+Remove2:
+
+![Remove2](/Images/Remove2.png)
+
+Remove3:
+
+![Remove3](/Images/Remove3.png)
+
+Remove4:
+
+![Remove4](/Images/Remove4.png)
+
+
 
 ### Still under construction.
 
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
index b1ae8d0bf..c4fd2f4de 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.swift	
@@ -485,20 +485,24 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
 */
 
 // Simple little debug function to make testing output pretty
-private func check(tree: ThreadedBinaryTree<Int>) {
-  print("\(tree.count) Total Nodes:");
-  print(tree)
-  print("Debug Info:")
-  print(tree.debugDescription)
-  print("In-Order Traversal:")
-  let myArray = tree.toArray()
-  for node in myArray {
-    print(node)
-  }
-  if tree.isThreaded() {
-    print("This threaded binary tree is VALID.")
+private func check(tree: ThreadedBinaryTree<Int>?) {
+  if let tree = tree {
+    print("\(tree.count) Total Nodes:");
+    print(tree)
+    print("Debug Info:")
+    print(tree.debugDescription)
+    print("In-Order Traversal:")
+    let myArray = tree.toArray()
+    for node in myArray {
+      print(node)
+    }
+    if tree.isThreaded() {
+      print("This threaded binary tree is VALID.")
+    } else {
+      print("This threaded binary tree is INVALID.")
+    }
   } else {
-    print("This threaded binary tree is INVALID.")
+    print("This tree is nil.")
   }
 }
 
@@ -530,20 +534,28 @@ print("\nInsert 4")
 tree.insert(4)
 check(tree)
 
-print("\nRemove 13 (Not in the Tree)")
-tree.remove(13)
+print("\nInsert 15")
+tree.insert(15)
 check(tree)
 
-print("\nRemove 5")
-tree.remove(5)
+print("\nRemove 13 (Not in the Tree)")
+tree.remove(13)
 check(tree)
 
 print("\nRemove 7")
 tree.remove(7)
 check(tree)
 
-print("\nRemove 10")
-tree.remove(10)
+print("\nRemove 5")
+tree.remove(5)
 check(tree)
 
+print("\nRemove 9 (root)")
+let newRoot = tree.remove(9)
+check(newRoot)
+
+print("\nRemove 12")
+newRoot?.remove(12)
+check(newRoot)
+
 print("\n\nDone with Tests!\n")

From 74f9ad5ff5bd8c177ecacde6b8101be8478ed7db Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Tue, 3 May 2016 12:33:14 -0400
Subject: [PATCH 0312/1679] Fix broken README links

---
 Threaded Binary Tree/README.markdown | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 91d7a9ecb..155404b66 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -75,13 +75,13 @@ its left child.
 
 Here is a valid "full" threaded binary tree:
 
-![Full](/Images/Full.png)
+![Full](Images/Full.png)
 
 While the following threaded binary tree is not "full," it is still valid.  The
 structure of the tree does not matter as long as it follows the definition of a
 binary search tree:
 
-![Partial](/Images/Partial.png)
+![Partial](Images/Partial.png)
 
 The solid lines denote the links between parents and children, while the dotted
 lines denote the "threads."  The important thing to note here is how the
@@ -197,35 +197,35 @@ binary search trees, so make sure you have
 
 Base:
 
-![Base](/Images/Base.png)
+![Base](Images/Base.png)
 
 Insert1:
 
-![Insert1](/Images/Insert1.png)
+![Insert1](Images/Insert1.png)
 
 Insert2:
 
-![Insert2](/Images/Insert2.png)
+![Insert2](Images/Insert2.png)
 
 Insert3:
 
-![Insert3](/Images/Insert3.png)
+![Insert3](Images/Insert3.png)
 
 Remove1:
 
-![Remove1](/Images/Remove1.png)
+![Remove1](Images/Remove1.png)
 
 Remove2:
 
-![Remove2](/Images/Remove2.png)
+![Remove2](Images/Remove2.png)
 
 Remove3:
 
-![Remove3](/Images/Remove3.png)
+![Remove3](Images/Remove3.png)
 
 Remove4:
 
-![Remove4](/Images/Remove4.png)
+![Remove4](Images/Remove4.png)
 
 
 

From ab7bafa62dec6878bdc23233f71acec7df29f966 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Tue, 3 May 2016 14:06:35 -0400
Subject: [PATCH 0313/1679] Scrapped current findPrefix() implementation

---
 Trie/trie       | Bin 65115 -> 60968 bytes
 Trie/trie.swift |  30 ------------------------------
 2 files changed, 30 deletions(-)

diff --git a/Trie/trie b/Trie/trie
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diff --git a/Trie/trie.swift b/Trie/trie.swift
index 4758e10fd..341f4c708 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -210,7 +210,6 @@ public class Trie {
     } else {
       var character = currentNode.char()
       while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
-        print(currentNode.getParent().char())
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
@@ -232,37 +231,8 @@ public class Trie {
     return (w, true)
   }
 
-  private func getChildrenWithPrefix(node: Node, var word: String, var words: [String]) -> [String] {
-
-    print(word)
-
-    if node.isLeaf() && node.isValidWord() {
-      words.append(word)
-      print(words)
-
-    } else {
-
-      for (child, n) in node.getChildren(){
-        print(child)
-        word += child
-        getChildrenWithPrefix(n, word: word, words: words)
-      }
-    }
-
-    return words
-  }
-
   func findPrefix(p: String) -> [String] {
-    print("Entered")
-
-
-    //var (node, pFound: Bool) = self.isPrefix(p)
-    if self.isPrefix(p).found {
-      print("I found the prefix!")
-      return getChildrenWithPrefix(self.isPrefix(p).node!, word: p.lowercaseString, words: [])
-    }
 
-    return ["HE"]
   }
 
 

From 461127f55a13eae90b68f602cab7f2cd0da2010e Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Tue, 3 May 2016 14:51:14 -0400
Subject: [PATCH 0314/1679] Revamped directory structure to allow for importing
 of modules from implemented data structures

---
 Trie/.build/debug/Trie                        | Bin 0 -> 95508 bytes
 Trie/.build/debug/Trie.a                      | Bin 0 -> 125236 bytes
 Trie/.build/debug/Trie.o/Trie/Queue.d         |   3 +
 Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps | 316 +++++++++++
 .../debug/Trie.o/Trie/Queue~partial.swiftdoc  | Bin 0 -> 540 bytes
 .../Trie.o/Trie/Queue~partial.swiftmodule     | Bin 0 -> 11788 bytes
 Trie/.build/debug/Trie.o/Trie/main.d          |   3 +
 Trie/.build/debug/Trie.o/Trie/main.swiftdeps  | 202 +++++++
 .../debug/Trie.o/Trie/main~partial.swiftdoc   | Bin 0 -> 540 bytes
 .../Trie.o/Trie/main~partial.swiftmodule      | Bin 0 -> 31660 bytes
 .../.build/debug/Trie.o/Trie/master.swiftdeps |   7 +
 .../debug/Trie.o/Trie/output-file-map.json    |  23 +
 Trie/.build/debug/Trie.o/Trie/trie.d          |   3 +
 Trie/.build/debug/Trie.o/Trie/trie.swiftdeps  | 504 +++++++++++++++++
 .../debug/Trie.o/Trie/trie~partial.swiftdoc   | Bin 0 -> 540 bytes
 .../Trie.o/Trie/trie~partial.swiftmodule      | Bin 0 -> 53928 bytes
 Trie/.build/debug/Trie.o/build.db             | Bin 0 -> 15360 bytes
 Trie/.build/debug/Trie.o/llbuild.yaml         |  29 +
 .../.build/debug/Trie.o/sources/Queue.swift.o | Bin 0 -> 23440 bytes
 Trie/.build/debug/Trie.o/sources/main.swift.o | Bin 0 -> 13864 bytes
 Trie/.build/debug/Trie.o/sources/trie.swift.o | Bin 0 -> 94800 bytes
 Trie/.build/debug/Trie.swiftdoc               | Bin 0 -> 540 bytes
 Trie/.build/debug/Trie.swiftmodule            | Bin 0 -> 20724 bytes
 .../build.db                                  | Bin 0 -> 7168 bytes
 .../llbuild.yaml                              |  29 +
 .../Queue.d                                   |   3 +
 .../Queue.swiftdeps                           | 316 +++++++++++
 .../master.swiftdeps                          |   6 +
 .../output-file-map.json                      |  17 +
 .../trie.d                                    |   3 +
 .../trie.swiftdeps                            | 513 ++++++++++++++++++
 Trie/Package.swift                            |   6 +
 Trie/Package.swift~                           |   5 +
 Trie/sources/Queue.swift                      |  47 ++
 Trie/sources/main.swift                       |  34 ++
 Trie/{ => sources}/trie.swift                 |  44 +-
 36 files changed, 2072 insertions(+), 41 deletions(-)
 create mode 100755 Trie/.build/debug/Trie
 create mode 100644 Trie/.build/debug/Trie.a
 create mode 100644 Trie/.build/debug/Trie.o/Trie/Queue.d
 create mode 100644 Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
 create mode 100644 Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc
 create mode 100644 Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule
 create mode 100644 Trie/.build/debug/Trie.o/Trie/main.d
 create mode 100644 Trie/.build/debug/Trie.o/Trie/main.swiftdeps
 create mode 100644 Trie/.build/debug/Trie.o/Trie/main~partial.swiftdoc
 create mode 100644 Trie/.build/debug/Trie.o/Trie/main~partial.swiftmodule
 create mode 100644 Trie/.build/debug/Trie.o/Trie/master.swiftdeps
 create mode 100644 Trie/.build/debug/Trie.o/Trie/output-file-map.json
 create mode 100644 Trie/.build/debug/Trie.o/Trie/trie.d
 create mode 100644 Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
 create mode 100644 Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc
 create mode 100644 Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule
 create mode 100644 Trie/.build/debug/Trie.o/build.db
 create mode 100644 Trie/.build/debug/Trie.o/llbuild.yaml
 create mode 100644 Trie/.build/debug/Trie.o/sources/Queue.swift.o
 create mode 100644 Trie/.build/debug/Trie.o/sources/main.swift.o
 create mode 100644 Trie/.build/debug/Trie.o/sources/trie.swift.o
 create mode 100644 Trie/.build/debug/Trie.swiftdoc
 create mode 100644 Trie/.build/debug/Trie.swiftmodule
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/build.db
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d
 create mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps
 create mode 100644 Trie/Package.swift
 create mode 100644 Trie/Package.swift~
 create mode 100644 Trie/sources/Queue.swift
 create mode 100644 Trie/sources/main.swift
 rename Trie/{ => sources}/trie.swift (85%)

diff --git a/Trie/.build/debug/Trie b/Trie/.build/debug/Trie
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diff --git a/Trie/.build/debug/Trie.o/Trie/Queue.d b/Trie/.build/debug/Trie.o/Trie/Queue.d
new file mode 100644
index 000000000..f39f80cfd
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/Queue.d
@@ -0,0 +1,3 @@
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+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps b/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
new file mode 100644
index 000000000..ccc0e26c1
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
@@ -0,0 +1,316 @@
+### Swift dependencies file v0 ###
+provides-top-level:
+- "Queue"
+provides-nominal:
+- "V4Trie5Queue"
+provides-member:
+- ["V4Trie5Queue", ""]
+depends-top-level:
+- "FloatLiteralType"
+- "IntegerLiteralType"
+- "Queue"
+- "Bool"
+- !private "-"
+- !private "/"
+- !private "=="
+- !private "<"
+- "Int"
+- !private ">"
+- !private "Double"
+- !private "&&"
+- !private "+="
+depends-member:
+- !private ["Ps16AbsoluteValuable", "init"]
+- ["Sa", "Generator"]
+- ["Sa", "Index"]
+- ["Sa", "SubSequence"]
+- ["Sa", "_Element"]
+- !private ["Sa", "append"]
+- !private ["Sa", "count"]
+- !private ["Sa", "deinit"]
+- ["Sa", "init"]
+- !private ["Sa", "removeFirst"]
+- !private ["Sa", "subscript"]
+- ["Ps23ArrayLiteralConvertible", "Generator"]
+- ["Ps23ArrayLiteralConvertible", "Index"]
+- ["Ps23ArrayLiteralConvertible", "SubSequence"]
+- ["Ps23ArrayLiteralConvertible", "_Element"]
+- !private ["Ps23ArrayLiteralConvertible", "append"]
+- !private ["Ps23ArrayLiteralConvertible", "count"]
+- ["Ps23ArrayLiteralConvertible", "init"]
+- !private ["Ps23ArrayLiteralConvertible", "removeFirst"]
+- !private ["Ps23ArrayLiteralConvertible", "subscript"]
+- ["Vs10ArraySlice", "Generator"]
+- ["Vs10ArraySlice", "Index"]
+- ["Ps22BidirectionalIndexType", "Distance"]
+- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
+- ["Ps21BitwiseOperationsType", "Distance"]
+- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
+- !private ["Sb", "_getBuiltinLogicValue"]
+- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
+- ["Ps11CVarArgType", "Distance"]
+- ["Ps11CVarArgType", "IntegerLiteralType"]
+- !private ["Ps11CVarArgType", "init"]
+- ["Ps14CollectionType", "Generator"]
+- ["Ps14CollectionType", "Index"]
+- ["Ps14CollectionType", "SubSequence"]
+- ["Ps14CollectionType", "_Element"]
+- !private ["Ps14CollectionType", "append"]
+- !private ["Ps14CollectionType", "count"]
+- ["Ps14CollectionType", "init"]
+- !private ["Ps14CollectionType", "removeFirst"]
+- !private ["Ps14CollectionType", "subscript"]
+- ["Ps10Comparable", "Distance"]
+- ["Ps10Comparable", "IntegerLiteralType"]
+- !private ["Ps10Comparable", "init"]
+- ["Ps28CustomDebugStringConvertible", "Generator"]
+- ["Ps28CustomDebugStringConvertible", "Index"]
+- ["Ps28CustomDebugStringConvertible", "Some"]
+- ["Ps28CustomDebugStringConvertible", "SubSequence"]
+- ["Ps28CustomDebugStringConvertible", "_Element"]
+- !private ["Ps28CustomDebugStringConvertible", "append"]
+- !private ["Ps28CustomDebugStringConvertible", "count"]
+- ["Ps28CustomDebugStringConvertible", "init"]
+- !private ["Ps28CustomDebugStringConvertible", "removeFirst"]
+- !private ["Ps28CustomDebugStringConvertible", "subscript"]
+- ["Ps23CustomStringConvertible", "Distance"]
+- ["Ps23CustomStringConvertible", "Generator"]
+- ["Ps23CustomStringConvertible", "Index"]
+- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
+- ["Ps23CustomStringConvertible", "SubSequence"]
+- ["Ps23CustomStringConvertible", "_Element"]
+- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps23CustomStringConvertible", "append"]
+- !private ["Ps23CustomStringConvertible", "count"]
+- ["Ps23CustomStringConvertible", "init"]
+- !private ["Ps23CustomStringConvertible", "removeFirst"]
+- !private ["Ps23CustomStringConvertible", "subscript"]
+- !private ["Sd", "init"]
+- ["Ps9Equatable", "Distance"]
+- ["Ps9Equatable", "IntegerLiteralType"]
+- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
+- !private ["Ps9Equatable", "init"]
+- !private ["Ps23FloatLiteralConvertible", "init"]
+- !private ["Ps17FloatingPointType", "init"]
+- ["Ps16ForwardIndexType", "Distance"]
+- ["Ps16ForwardIndexType", "IntegerLiteralType"]
+- ["Ps13GeneratorType", "Element"]
+- ["Ps8Hashable", "Distance"]
+- ["Ps8Hashable", "IntegerLiteralType"]
+- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
+- !private ["Ps8Hashable", "init"]
+- ["Ps9Indexable", "Generator"]
+- ["Ps9Indexable", "Index"]
+- ["Ps9Indexable", "SubSequence"]
+- ["Ps9Indexable", "_Element"]
+- !private ["Ps9Indexable", "append"]
+- !private ["Ps9Indexable", "count"]
+- ["Ps9Indexable", "init"]
+- !private ["Ps9Indexable", "removeFirst"]
+- !private ["Ps9Indexable", "subscript"]
+- ["Vs17IndexingGenerator", "Element"]
+- ["Si", "Distance"]
+- ["Si", "IntegerLiteralType"]
+- ["Ps21IntegerArithmeticType", "Distance"]
+- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps25IntegerLiteralConvertible", "Distance"]
+- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps25IntegerLiteralConvertible", "init"]
+- ["Ps11IntegerType", "Distance"]
+- ["Ps11IntegerType", "IntegerLiteralType"]
+- ["Ps14MirrorPathType", "Distance"]
+- ["Ps14MirrorPathType", "IntegerLiteralType"]
+- ["Ps21MutableCollectionType", "Generator"]
+- ["Ps21MutableCollectionType", "Index"]
+- ["Ps21MutableCollectionType", "SubSequence"]
+- ["Ps21MutableCollectionType", "_Element"]
+- !private ["Ps21MutableCollectionType", "append"]
+- !private ["Ps21MutableCollectionType", "count"]
+- ["Ps21MutableCollectionType", "init"]
+- !private ["Ps21MutableCollectionType", "removeFirst"]
+- !private ["Ps21MutableCollectionType", "subscript"]
+- ["Ps16MutableIndexable", "Generator"]
+- ["Ps16MutableIndexable", "Index"]
+- ["Ps16MutableIndexable", "SubSequence"]
+- ["Ps16MutableIndexable", "_Element"]
+- !private ["Ps16MutableIndexable", "append"]
+- !private ["Ps16MutableIndexable", "count"]
+- ["Ps16MutableIndexable", "init"]
+- !private ["Ps16MutableIndexable", "removeFirst"]
+- !private ["Ps16MutableIndexable", "subscript"]
+- ["Ps16MutableSliceable", "Generator"]
+- ["Ps16MutableSliceable", "Index"]
+- ["Ps16MutableSliceable", "SubSequence"]
+- ["Ps16MutableSliceable", "_Element"]
+- !private ["Ps16MutableSliceable", "append"]
+- !private ["Ps16MutableSliceable", "count"]
+- ["Ps16MutableSliceable", "init"]
+- !private ["Ps16MutableSliceable", "removeFirst"]
+- !private ["Ps16MutableSliceable", "subscript"]
+- ["Ps21NilLiteralConvertible", "Some"]
+- ["Sq", "Some"]
+- ["V4Trie5Queue", "Bool"]
+- !private ["V4Trie5Queue", "Double"]
+- ["V4Trie5Queue", "Int"]
+- ["V4Trie5Queue", "T"]
+- !private ["V4Trie5Queue", "array"]
+- ["V4Trie5Queue", "count"]
+- ["V4Trie5Queue", "dequeue"]
+- ["V4Trie5Queue", "enqueue"]
+- !private ["V4Trie5Queue", "head"]
+- ["V4Trie5Queue", "init"]
+- ["V4Trie5Queue", "isEmpty"]
+- ["V4Trie5Queue", "peek"]
+- ["Ps21RandomAccessIndexType", "Distance"]
+- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
+- ["Ps30RangeReplaceableCollectionType", "Generator"]
+- ["Ps30RangeReplaceableCollectionType", "Index"]
+- ["Ps30RangeReplaceableCollectionType", "SubSequence"]
+- ["Ps30RangeReplaceableCollectionType", "_Element"]
+- !private ["Ps30RangeReplaceableCollectionType", "append"]
+- !private ["Ps30RangeReplaceableCollectionType", "count"]
+- ["Ps30RangeReplaceableCollectionType", "init"]
+- !private ["Ps30RangeReplaceableCollectionType", "removeFirst"]
+- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
+- ["Ps12SequenceType", "Element"]
+- ["Ps12SequenceType", "Generator"]
+- ["Ps12SequenceType", "Index"]
+- ["Ps12SequenceType", "SubSequence"]
+- ["Ps12SequenceType", "_Element"]
+- !private ["Ps12SequenceType", "append"]
+- !private ["Ps12SequenceType", "count"]
+- ["Ps12SequenceType", "init"]
+- !private ["Ps12SequenceType", "removeFirst"]
+- !private ["Ps12SequenceType", "subscript"]
+- ["Ps17SignedIntegerType", "Distance"]
+- ["Ps17SignedIntegerType", "IntegerLiteralType"]
+- ["Ps16SignedNumberType", "Distance"]
+- ["Ps16SignedNumberType", "IntegerLiteralType"]
+- !private ["Ps16SignedNumberType", "init"]
+- !private ["Vs5Slice", "Generator"]
+- !private ["Vs5Slice", "Index"]
+- !private ["Vs5Slice", "SubSequence"]
+- !private ["Vs5Slice", "_Element"]
+- ["Ps10Strideable", "Distance"]
+- ["Ps10Strideable", "IntegerLiteralType"]
+- !private ["Ps10Strideable", "init"]
+- ["Ps10_ArrayType", "Generator"]
+- ["Ps10_ArrayType", "Index"]
+- ["Ps10_ArrayType", "SubSequence"]
+- ["Ps10_ArrayType", "_Element"]
+- !private ["Ps10_ArrayType", "append"]
+- !private ["Ps10_ArrayType", "count"]
+- ["Ps10_ArrayType", "init"]
+- !private ["Ps10_ArrayType", "removeFirst"]
+- !private ["Ps10_ArrayType", "subscript"]
+- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps31_BuiltinFloatLiteralConvertible", "init"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps33_BuiltinIntegerLiteralConvertible", "init"]
+- !private ["Ps19_CVarArgAlignedType", "init"]
+- !private ["Ps22_CVarArgPassedAsDouble", "init"]
+- ["Ps24_DestructorSafeContainer", "Generator"]
+- ["Ps24_DestructorSafeContainer", "Index"]
+- ["Ps24_DestructorSafeContainer", "SubSequence"]
+- ["Ps24_DestructorSafeContainer", "_Element"]
+- !private ["Ps24_DestructorSafeContainer", "append"]
+- !private ["Ps24_DestructorSafeContainer", "count"]
+- ["Ps24_DestructorSafeContainer", "init"]
+- !private ["Ps24_DestructorSafeContainer", "removeFirst"]
+- !private ["Ps24_DestructorSafeContainer", "subscript"]
+- ["Ps14_Incrementable", "Distance"]
+- ["Ps14_Incrementable", "IntegerLiteralType"]
+- ["Ps22_IntegerArithmeticType", "Distance"]
+- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps12_IntegerType", "Distance"]
+- ["Ps12_IntegerType", "IntegerLiteralType"]
+- ["Ps22_RandomAccessAmbiguity", "Distance"]
+- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Distance"]
+- ["Ps12_Reflectable", "Generator"]
+- ["Ps12_Reflectable", "Index"]
+- ["Ps12_Reflectable", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Some"]
+- ["Ps12_Reflectable", "SubSequence"]
+- ["Ps12_Reflectable", "_Element"]
+- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
+- !private ["Ps12_Reflectable", "append"]
+- !private ["Ps12_Reflectable", "count"]
+- ["Ps12_Reflectable", "init"]
+- !private ["Ps12_Reflectable", "removeFirst"]
+- !private ["Ps12_Reflectable", "subscript"]
+- ["Ps18_SignedIntegerType", "Distance"]
+- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
+depends-nominal:
+- !private "Ps16AbsoluteValuable"
+- "Sa"
+- "Ps23ArrayLiteralConvertible"
+- "Vs10ArraySlice"
+- "Ps22BidirectionalIndexType"
+- "Ps21BitwiseOperationsType"
+- !private "Sb"
+- !private "Ps25BooleanLiteralConvertible"
+- !private "Ps11BooleanType"
+- "Ps11CVarArgType"
+- "Ps14CollectionType"
+- "Ps10Comparable"
+- "Ps28CustomDebugStringConvertible"
+- "Ps23CustomStringConvertible"
+- !private "Sd"
+- "Ps9Equatable"
+- !private "Ps23FloatLiteralConvertible"
+- !private "Ps17FloatingPointType"
+- "Ps16ForwardIndexType"
+- "Ps13GeneratorType"
+- "Ps8Hashable"
+- "Ps9Indexable"
+- "Vs17IndexingGenerator"
+- "Si"
+- "Ps21IntegerArithmeticType"
+- "Ps25IntegerLiteralConvertible"
+- "Ps11IntegerType"
+- "Ps14MirrorPathType"
+- "Ps21MutableCollectionType"
+- "Ps16MutableIndexable"
+- "Ps16MutableSliceable"
+- "Ps21NilLiteralConvertible"
+- "Sq"
+- "V4Trie5Queue"
+- "Ps21RandomAccessIndexType"
+- "Ps30RangeReplaceableCollectionType"
+- "Ps12SequenceType"
+- "Ps17SignedIntegerType"
+- "Ps16SignedNumberType"
+- !private "Vs5Slice"
+- "Ps10Strideable"
+- "Ps10_ArrayType"
+- !private "Ps33_BuiltinBooleanLiteralConvertible"
+- !private "Ps31_BuiltinFloatLiteralConvertible"
+- "Ps33_BuiltinIntegerLiteralConvertible"
+- !private "Ps19_CVarArgAlignedType"
+- !private "Ps22_CVarArgPassedAsDouble"
+- "Ps24_DestructorSafeContainer"
+- "Ps14_Incrementable"
+- "Ps22_IntegerArithmeticType"
+- "Ps12_IntegerType"
+- "Ps22_RandomAccessAmbiguity"
+- "Ps12_Reflectable"
+- "Ps18_SignedIntegerType"
+depends-dynamic-lookup:
+depends-external:
+- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
+- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
+interface-hash: "b268b101cc2bc2706939fa25905dab4d"
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diff --git a/Trie/.build/debug/Trie.o/Trie/main.d b/Trie/.build/debug/Trie.o/Trie/main.d
new file mode 100644
index 000000000..73abc24e4
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/main.d
@@ -0,0 +1,3 @@
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/main.swiftdeps b/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
new file mode 100644
index 000000000..923f0f821
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
@@ -0,0 +1,202 @@
+### Swift dependencies file v0 ###
+provides-top-level:
+- "T"
+- "U"
+- "V"
+provides-nominal:
+provides-member:
+depends-top-level:
+- "StringLiteralType"
+- "Set"
+- "Array"
+- "print"
+- "Trie"
+- "V"
+- "T"
+- "U"
+depends-member:
+- ["Ps9AnyObject", "getWords"]
+- ["Ps9AnyObject", "init"]
+- ["Ps9AnyObject", "insert"]
+- ["Ps9AnyObject", "merge"]
+- ["Ps9AnyObject", "removeAll"]
+- ["Sa", "Element"]
+- ["Sa", "Generator"]
+- ["Sa", "Index"]
+- ["Sa", "_Element"]
+- ["Ps23ArrayLiteralConvertible", "Element"]
+- ["Ps23ArrayLiteralConvertible", "Generator"]
+- ["Ps23ArrayLiteralConvertible", "Index"]
+- ["Ps23ArrayLiteralConvertible", "_Element"]
+- ["Ps23ArrayLiteralConvertible", "init"]
+- ["Ps22BidirectionalIndexType", "Distance"]
+- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
+- ["Ps21BitwiseOperationsType", "Distance"]
+- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
+- ["Ps11CVarArgType", "Distance"]
+- ["Ps11CVarArgType", "IntegerLiteralType"]
+- ["Ps14CollectionType", "Element"]
+- ["Ps14CollectionType", "Generator"]
+- ["Ps14CollectionType", "Index"]
+- ["Ps14CollectionType", "_Element"]
+- ["Ps14CollectionType", "init"]
+- ["Ps10Comparable", "Distance"]
+- ["Ps10Comparable", "IntegerLiteralType"]
+- ["Ps28CustomDebugStringConvertible", "Element"]
+- ["Ps28CustomDebugStringConvertible", "Generator"]
+- ["Ps28CustomDebugStringConvertible", "Index"]
+- ["Ps28CustomDebugStringConvertible", "_Element"]
+- ["Ps28CustomDebugStringConvertible", "init"]
+- ["Ps23CustomStringConvertible", "Distance"]
+- ["Ps23CustomStringConvertible", "Element"]
+- ["Ps23CustomStringConvertible", "Generator"]
+- ["Ps23CustomStringConvertible", "Index"]
+- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
+- ["Ps23CustomStringConvertible", "_Element"]
+- ["Ps23CustomStringConvertible", "init"]
+- ["Ps9Equatable", "Distance"]
+- ["Ps9Equatable", "IntegerLiteralType"]
+- ["Ps9Equatable", "init"]
+- ["Ps16ForwardIndexType", "Distance"]
+- ["Ps16ForwardIndexType", "IntegerLiteralType"]
+- ["Ps13GeneratorType", "Element"]
+- ["Ps8Hashable", "Distance"]
+- ["Ps8Hashable", "IntegerLiteralType"]
+- ["Ps8Hashable", "init"]
+- ["Ps9Indexable", "Element"]
+- ["Ps9Indexable", "Generator"]
+- ["Ps9Indexable", "Index"]
+- ["Ps9Indexable", "_Element"]
+- ["Ps9Indexable", "init"]
+- ["Vs17IndexingGenerator", "Element"]
+- ["Si", "Distance"]
+- ["Si", "IntegerLiteralType"]
+- ["Si", "deinit"]
+- ["Ps21IntegerArithmeticType", "Distance"]
+- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps25IntegerLiteralConvertible", "Distance"]
+- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
+- ["Ps11IntegerType", "Distance"]
+- ["Ps11IntegerType", "IntegerLiteralType"]
+- ["Ps14MirrorPathType", "Distance"]
+- ["Ps14MirrorPathType", "IntegerLiteralType"]
+- ["Ps21MutableCollectionType", "Element"]
+- ["Ps21MutableCollectionType", "Generator"]
+- ["Ps21MutableCollectionType", "Index"]
+- ["Ps21MutableCollectionType", "_Element"]
+- ["Ps16MutableIndexable", "Element"]
+- ["Ps16MutableIndexable", "Generator"]
+- ["Ps16MutableIndexable", "Index"]
+- ["Ps16MutableIndexable", "_Element"]
+- ["Ps16MutableSliceable", "Element"]
+- ["Ps16MutableSliceable", "Generator"]
+- ["Ps16MutableSliceable", "Index"]
+- ["Ps16MutableSliceable", "_Element"]
+- ["Ps21RandomAccessIndexType", "Distance"]
+- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
+- ["Ps30RangeReplaceableCollectionType", "Element"]
+- ["Ps30RangeReplaceableCollectionType", "Generator"]
+- ["Ps30RangeReplaceableCollectionType", "Index"]
+- ["Ps30RangeReplaceableCollectionType", "_Element"]
+- ["Ps12SequenceType", "Element"]
+- ["Ps12SequenceType", "Generator"]
+- ["Ps12SequenceType", "Index"]
+- ["Ps12SequenceType", "_Element"]
+- ["Ps12SequenceType", "init"]
+- ["Vs3Set", "init"]
+- ["Ps17SignedIntegerType", "Distance"]
+- ["Ps17SignedIntegerType", "IntegerLiteralType"]
+- ["Ps16SignedNumberType", "Distance"]
+- ["Ps16SignedNumberType", "IntegerLiteralType"]
+- ["Ps10Strideable", "Distance"]
+- ["Ps10Strideable", "IntegerLiteralType"]
+- ["C4Trie4Trie", "getWords"]
+- ["C4Trie4Trie", "init"]
+- ["C4Trie4Trie", "insert"]
+- ["C4Trie4Trie", "merge"]
+- ["C4Trie4Trie", "removeAll"]
+- ["Ps10_ArrayType", "Element"]
+- ["Ps10_ArrayType", "Generator"]
+- ["Ps10_ArrayType", "Index"]
+- ["Ps10_ArrayType", "_Element"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
+- ["Ps24_DestructorSafeContainer", "Element"]
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diff --git a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
new file mode 100644
index 000000000..5539f705b
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
@@ -0,0 +1,7 @@
+version: "Swift version 2.2-dev (LLVM 3ebdbb2c7e, Clang f66c5bb67b, Swift 0ddf238ad7)"
+options: "1cfa30eacd63a1262ef0618da5cf7605"
+build_time: [515616404, 830067000]
+inputs:
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift": [515616359, 0]
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": [515616400, 0]
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": [512710161, 0]
diff --git a/Trie/.build/debug/Trie.o/Trie/output-file-map.json b/Trie/.build/debug/Trie.o/Trie/output-file-map.json
new file mode 100644
index 000000000..be714f4c6
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/output-file-map.json
@@ -0,0 +1,23 @@
+{
+  "": {
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/master.swiftdeps"
+  },
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift": {
+    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main.d",
+    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o",
+    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main~partial.swiftmodule",
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main.swiftdeps"
+  },
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": {
+    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie.d",
+    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o",
+    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule",
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps"
+  },
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": {
+    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue.d",
+    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o",
+    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule",
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps"
+  }
+}
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.d b/Trie/.build/debug/Trie.o/Trie/trie.d
new file mode 100644
index 000000000..98996f58e
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/trie.d
@@ -0,0 +1,3 @@
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
new file mode 100644
index 000000000..35e802978
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
@@ -0,0 +1,504 @@
+### Swift dependencies file v0 ###
+provides-top-level:
+- "Node"
+- "Trie"
+provides-nominal:
+- "C4Trie4Node"
+- "C4Trie4Trie"
+provides-member:
+- ["C4Trie4Node", ""]
+- ["C4Trie4Trie", ""]
+depends-top-level:
+- "Int"
+- !private "UnicodeScalarType"
+- !private "Array"
+- "Node"
+- "Void"
+- !private "=="
+- "IntegerLiteralType"
+- !private "+="
+- "Trie"
+- "FloatLiteralType"
+- "Set"
+- !private "BooleanLiteralType"
+- !private "-"
+- "Bool"
+- !private "print"
+- !private "-="
+- "String"
+- !private "&&"
+- !private "!"
+- !private "Queue"
+- !private "+"
+- !private "StringLiteralType"
+- !private ">"
+depends-member:
+- !private ["Vs12AnyGenerator", "Element"]
+- !private ["Ps9AnyObject", "Array"]
+- !private ["Ps9AnyObject", "Node"]
+- !private ["Ps9AnyObject", "Queue"]
+- !private ["Ps9AnyObject", "Set"]
+- !private ["Ps9AnyObject", "String"]
+- !private ["Ps9AnyObject", "Trie"]
+- !private ["Ps9AnyObject", "char"]
+- !private ["Ps9AnyObject", "character"]
+- !private ["Ps9AnyObject", "children"]
+- !private ["Ps9AnyObject", "contains"]
+- !private ["Ps9AnyObject", "find"]
+- !private ["Ps9AnyObject", "getChildAt"]
+- !private ["Ps9AnyObject", "getChildren"]
+- !private ["Ps9AnyObject", "getParent"]
+- !private ["Ps9AnyObject", "getWords"]
+- !private ["Ps9AnyObject", "init"]
+- !private ["Ps9AnyObject", "insert"]
+- !private ["Ps9AnyObject", "isAWord"]
+- !private ["Ps9AnyObject", "isNotWord"]
+- !private ["Ps9AnyObject", "isRoot"]
+- !private ["Ps9AnyObject", "isValidWord"]
+- !private ["Ps9AnyObject", "isWord"]
+- !private ["Ps9AnyObject", "numChildren"]
+- !private ["Ps9AnyObject", "parent"]
+- !private ["Ps9AnyObject", "print"]
+- !private ["Ps9AnyObject", "printNode"]
+- !private ["Ps9AnyObject", "remove"]
+- !private ["Ps9AnyObject", "root"]
+- !private ["Ps9AnyObject", "setParent"]
+- !private ["Ps9AnyObject", "update"]
+- !private ["Ps9AnyObject", "wordCount"]
+- !private ["Ps9AnyObject", "wordList"]
+- ["Ps9AnyObject", ""]
+- !private ["Vs11AnySequence", "Generator"]
+- !private ["Vs11AnySequence", "deinit"]
+- !private ["Sa", "Element"]
+- !private ["Sa", "Generator"]
+- !private ["Sa", "Index"]
+- !private ["Sa", "SubSequence"]
+- !private ["Sa", "_Element"]
+- !private ["Sa", "append"]
+- !private ["Sa", "deinit"]
+- !private ["Sa", "init"]
+- !private ["Sa", "removeAtIndex"]
+- !private ["Sa", "subscript"]
+- !private ["Ps23ArrayLiteralConvertible", "Element"]
+- !private ["Ps23ArrayLiteralConvertible", "Generator"]
+- !private ["Ps23ArrayLiteralConvertible", "Index"]
+- !private ["Ps23ArrayLiteralConvertible", "SubSequence"]
+- !private ["Ps23ArrayLiteralConvertible", "_Element"]
+- !private ["Ps23ArrayLiteralConvertible", "append"]
+- !private ["Ps23ArrayLiteralConvertible", "init"]
+- !private ["Ps23ArrayLiteralConvertible", "removeAtIndex"]
+- !private ["Ps23ArrayLiteralConvertible", "subscript"]
+- !private ["Vs10ArraySlice", "Generator"]
+- !private ["Vs10ArraySlice", "Index"]
+- !private ["Ps22BidirectionalIndexType", "Distance"]
+- !private ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
+- !private ["Ps21BitwiseOperationsType", "Distance"]
+- !private ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
+- !private ["Sb", "_getBuiltinLogicValue"]
+- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
+- !private ["Ps11CVarArgType", "Distance"]
+- !private ["Ps11CVarArgType", "IntegerLiteralType"]
+- !private ["VSS13CharacterView", "Generator"]
+- !private ["VSS13CharacterView", "Index"]
+- !private ["VSS13CharacterView", "SubSequence"]
+- !private ["VSS13CharacterView", "_Element"]
+- !private ["VSS13CharacterView", "count"]
+- !private ["VSS13CharacterView", "deinit"]
+- !private ["VSS13CharacterView", "suffix"]
+- !private ["Ps14CollectionType", "Element"]
+- !private ["Ps14CollectionType", "Generator"]
+- !private ["Ps14CollectionType", "Index"]
+- !private ["Ps14CollectionType", "SubSequence"]
+- !private ["Ps14CollectionType", "_Element"]
+- !private ["Ps14CollectionType", "append"]
+- !private ["Ps14CollectionType", "count"]
+- !private ["Ps14CollectionType", "init"]
+- !private ["Ps14CollectionType", "removeAtIndex"]
+- !private ["Ps14CollectionType", "subscript"]
+- !private ["Ps14CollectionType", "suffix"]
+- !private ["Ps10Comparable", "Distance"]
+- !private ["Ps10Comparable", "IntegerLiteralType"]
+- !private ["Ps10Comparable", "_DisabledRangeIndex"]
+- !private ["Ps10Comparable", "characters"]
+- !private ["Ps10Comparable", "init"]
+- !private ["Ps10Comparable", "lowercaseString"]
+- !private ["Ps28CustomDebugStringConvertible", "Element"]
+- !private ["Ps28CustomDebugStringConvertible", "Generator"]
+- !private ["Ps28CustomDebugStringConvertible", "Index"]
+- ["Ps28CustomDebugStringConvertible", "Some"]
+- !private ["Ps28CustomDebugStringConvertible", "SubSequence"]
+- !private ["Ps28CustomDebugStringConvertible", "_Element"]
+- !private ["Ps28CustomDebugStringConvertible", "append"]
+- !private ["Ps28CustomDebugStringConvertible", "characters"]
+- !private ["Ps28CustomDebugStringConvertible", "count"]
+- !private ["Ps28CustomDebugStringConvertible", "init"]
+- !private ["Ps28CustomDebugStringConvertible", "lowercaseString"]
+- !private ["Ps28CustomDebugStringConvertible", "removeAtIndex"]
+- !private ["Ps28CustomDebugStringConvertible", "subscript"]
+- !private ["Ps23CustomStringConvertible", "Distance"]
+- !private ["Ps23CustomStringConvertible", "Element"]
+- !private ["Ps23CustomStringConvertible", "Generator"]
+- !private ["Ps23CustomStringConvertible", "Index"]
+- !private ["Ps23CustomStringConvertible", "IntegerLiteralType"]
+- !private ["Ps23CustomStringConvertible", "SubSequence"]
+- !private ["Ps23CustomStringConvertible", "_Element"]
+- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps23CustomStringConvertible", "append"]
+- !private ["Ps23CustomStringConvertible", "count"]
+- !private ["Ps23CustomStringConvertible", "init"]
+- !private ["Ps23CustomStringConvertible", "removeAtIndex"]
+- !private ["Ps23CustomStringConvertible", "subscript"]
+- !private ["Vs10Dictionary", "Generator"]
+- !private ["Vs10Dictionary", "Index"]
+- !private ["Vs10Dictionary", "SubSequence"]
+- !private ["Vs10Dictionary", "_Element"]
+- !private ["Vs10Dictionary", "count"]
+- !private ["Vs10Dictionary", "deinit"]
+- !private ["Vs10Dictionary", "init"]
+- !private ["Vs10Dictionary", "subscript"]
+- !private ["Vs19DictionaryGenerator", "Element"]
+- !private ["Vs15DictionaryIndex", "Distance"]
+- !private ["Vs15DictionaryIndex", "_DisabledRangeIndex"]
+- !private ["Ps28DictionaryLiteralConvertible", "Generator"]
+- !private ["Ps28DictionaryLiteralConvertible", "Index"]
+- !private ["Ps28DictionaryLiteralConvertible", "SubSequence"]
+- !private ["Ps28DictionaryLiteralConvertible", "_Element"]
+- !private ["Ps28DictionaryLiteralConvertible", "count"]
+- !private ["Ps28DictionaryLiteralConvertible", "init"]
+- !private ["Ps28DictionaryLiteralConvertible", "subscript"]
+- !private ["Ps9Equatable", "Distance"]
+- !private ["Ps9Equatable", "Generator"]
+- !private ["Ps9Equatable", "IntegerLiteralType"]
+- !private ["Ps9Equatable", "_DisabledRangeIndex"]
+- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
+- !private ["Ps9Equatable", "characters"]
+- !private ["Ps9Equatable", "init"]
+- !private ["Ps9Equatable", "lowercaseString"]
+- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "characters"]
+- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "init"]
+- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
+- !private ["Ps16ForwardIndexType", "Distance"]
+- !private ["Ps16ForwardIndexType", "IntegerLiteralType"]
+- !private ["Ps16ForwardIndexType", "_DisabledRangeIndex"]
+- !private ["Ps13GeneratorType", "Element"]
+- !private ["Ps8Hashable", "Distance"]
+- !private ["Ps8Hashable", "Generator"]
+- !private ["Ps8Hashable", "IntegerLiteralType"]
+- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
+- !private ["Ps8Hashable", "characters"]
+- !private ["Ps8Hashable", "init"]
+- !private ["Ps8Hashable", "lowercaseString"]
+- !private ["VVSS13CharacterView5Index", "Distance"]
+- !private ["Ps9Indexable", "Element"]
+- !private ["Ps9Indexable", "Generator"]
+- !private ["Ps9Indexable", "Index"]
+- !private ["Ps9Indexable", "SubSequence"]
+- !private ["Ps9Indexable", "_Element"]
+- !private ["Ps9Indexable", "append"]
+- !private ["Ps9Indexable", "count"]
+- !private ["Ps9Indexable", "init"]
+- !private ["Ps9Indexable", "removeAtIndex"]
+- !private ["Ps9Indexable", "subscript"]
+- !private ["Ps9Indexable", "suffix"]
+- !private ["Vs17IndexingGenerator", "Element"]
+- !private ["Si", "Distance"]
+- !private ["Si", "IntegerLiteralType"]
+- !private ["Ps21IntegerArithmeticType", "Distance"]
+- !private ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
+- !private ["Ps25IntegerLiteralConvertible", "Distance"]
+- !private ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps11IntegerType", "Distance"]
+- !private ["Ps11IntegerType", "IntegerLiteralType"]
+- !private ["Ps14MirrorPathType", "Distance"]
+- !private ["Ps14MirrorPathType", "IntegerLiteralType"]
+- !private ["Ps14MirrorPathType", "characters"]
+- !private ["Ps14MirrorPathType", "init"]
+- !private ["Ps14MirrorPathType", "lowercaseString"]
+- !private ["Ps21MutableCollectionType", "Element"]
+- !private ["Ps21MutableCollectionType", "Generator"]
+- !private ["Ps21MutableCollectionType", "Index"]
+- !private ["Ps21MutableCollectionType", "SubSequence"]
+- !private ["Ps21MutableCollectionType", "_Element"]
+- !private ["Ps21MutableCollectionType", "append"]
+- !private ["Ps21MutableCollectionType", "init"]
+- !private ["Ps21MutableCollectionType", "removeAtIndex"]
+- !private ["Ps21MutableCollectionType", "subscript"]
+- !private ["Ps16MutableIndexable", "Element"]
+- !private ["Ps16MutableIndexable", "Generator"]
+- !private ["Ps16MutableIndexable", "Index"]
+- !private ["Ps16MutableIndexable", "SubSequence"]
+- !private ["Ps16MutableIndexable", "_Element"]
+- !private ["Ps16MutableIndexable", "append"]
+- !private ["Ps16MutableIndexable", "init"]
+- !private ["Ps16MutableIndexable", "removeAtIndex"]
+- !private ["Ps16MutableIndexable", "subscript"]
+- !private ["Ps16MutableSliceable", "Element"]
+- !private ["Ps16MutableSliceable", "Generator"]
+- !private ["Ps16MutableSliceable", "Index"]
+- !private ["Ps16MutableSliceable", "SubSequence"]
+- !private ["Ps16MutableSliceable", "_Element"]
+- !private ["Ps16MutableSliceable", "append"]
+- !private ["Ps16MutableSliceable", "init"]
+- !private ["Ps16MutableSliceable", "removeAtIndex"]
+- !private ["Ps16MutableSliceable", "subscript"]
+- ["Ps21NilLiteralConvertible", "Some"]
+- ["C4Trie4Node", "Bool"]
+- ["C4Trie4Node", "Int"]
+- ["C4Trie4Node", "Node"]
+- ["C4Trie4Node", "String"]
+- ["C4Trie4Node", "Void"]
+- ["C4Trie4Node", "char"]
+- !private ["C4Trie4Node", "character"]
+- !private ["C4Trie4Node", "children"]
+- ["C4Trie4Node", "deinit"]
+- ["C4Trie4Node", "getChildAt"]
+- ["C4Trie4Node", "getChildren"]
+- ["C4Trie4Node", "getParent"]
+- ["C4Trie4Node", "init"]
+- !private ["C4Trie4Node", "isAWord"]
+- ["C4Trie4Node", "isLeaf"]
+- ["C4Trie4Node", "isNotWord"]
+- ["C4Trie4Node", "isRoot"]
+- ["C4Trie4Node", "isValidWord"]
+- ["C4Trie4Node", "isWord"]
+- ["C4Trie4Node", "numChildren"]
+- !private ["C4Trie4Node", "parent"]
+- !private ["C4Trie4Node", "print"]
+- ["C4Trie4Node", "printNode"]
+- ["C4Trie4Node", "setParent"]
+- ["C4Trie4Node", "update"]
+- ["Sq", "Some"]
+- !private ["Sq", "deinit"]
+- !private ["Ps16OutputStreamType", "characters"]
+- !private ["Ps16OutputStreamType", "init"]
+- !private ["Ps16OutputStreamType", "lowercaseString"]
+- !private ["V4Trie5Queue", "init"]
+- !private ["Ps21RandomAccessIndexType", "Distance"]
+- !private ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
+- !private ["Ps30RangeReplaceableCollectionType", "Element"]
+- !private ["Ps30RangeReplaceableCollectionType", "Generator"]
+- !private ["Ps30RangeReplaceableCollectionType", "Index"]
+- !private ["Ps30RangeReplaceableCollectionType", "SubSequence"]
+- !private ["Ps30RangeReplaceableCollectionType", "_Element"]
+- !private ["Ps30RangeReplaceableCollectionType", "append"]
+- !private ["Ps30RangeReplaceableCollectionType", "count"]
+- !private ["Ps30RangeReplaceableCollectionType", "init"]
+- !private ["Ps30RangeReplaceableCollectionType", "removeAtIndex"]
+- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
+- !private ["Ps30RangeReplaceableCollectionType", "suffix"]
+- !private ["Ps12SequenceType", "Element"]
+- !private ["Ps12SequenceType", "Generator"]
+- !private ["Ps12SequenceType", "Index"]
+- !private ["Ps12SequenceType", "SubSequence"]
+- !private ["Ps12SequenceType", "_Element"]
+- !private ["Ps12SequenceType", "append"]
+- !private ["Ps12SequenceType", "count"]
+- !private ["Ps12SequenceType", "init"]
+- !private ["Ps12SequenceType", "removeAtIndex"]
+- !private ["Ps12SequenceType", "subscript"]
+- !private ["Ps12SequenceType", "suffix"]
+- !private ["Vs3Set", "Generator"]
+- !private ["Vs3Set", "init"]
+- !private ["Vs12SetGenerator", "Element"]
+- !private ["Ps17SignedIntegerType", "Distance"]
+- !private ["Ps17SignedIntegerType", "IntegerLiteralType"]
+- !private ["Ps16SignedNumberType", "Distance"]
+- !private ["Ps16SignedNumberType", "IntegerLiteralType"]
+- !private ["Vs5Slice", "Generator"]
+- !private ["Vs5Slice", "Index"]
+- !private ["Vs5Slice", "SubSequence"]
+- !private ["Vs5Slice", "_Element"]
+- !private ["Vs5Slice", "deinit"]
+- !private ["Ps10Streamable", "characters"]
+- !private ["Ps10Streamable", "init"]
+- !private ["Ps10Streamable", "lowercaseString"]
+- !private ["Ps10Strideable", "Distance"]
+- !private ["Ps10Strideable", "IntegerLiteralType"]
+- !private ["SS", "characters"]
+- !private ["SS", "init"]
+- !private ["SS", "lowercaseString"]
+- !private ["Ps30StringInterpolationConvertible", "characters"]
+- !private ["Ps30StringInterpolationConvertible", "init"]
+- !private ["Ps30StringInterpolationConvertible", "lowercaseString"]
+- !private ["Ps24StringLiteralConvertible", "characters"]
+- !private ["Ps24StringLiteralConvertible", "init"]
+- !private ["Ps24StringLiteralConvertible", "lowercaseString"]
+- !private ["C4Trie4Trie", "Array"]
+- ["C4Trie4Trie", "Bool"]
+- ["C4Trie4Trie", "Int"]
+- ["C4Trie4Trie", "Node"]
+- !private ["C4Trie4Trie", "Queue"]
+- ["C4Trie4Trie", "Set"]
+- ["C4Trie4Trie", "String"]
+- ["C4Trie4Trie", "Trie"]
+- ["C4Trie4Trie", "contains"]
+- ["C4Trie4Trie", "count"]
+- ["C4Trie4Trie", "deinit"]
+- ["C4Trie4Trie", "find"]
+- ["C4Trie4Trie", "findPrefix"]
+- ["C4Trie4Trie", "getWords"]
+- ["C4Trie4Trie", "init"]
+- ["C4Trie4Trie", "insert"]
+- ["C4Trie4Trie", "isEmpty"]
+- ["C4Trie4Trie", "isPrefix"]
+- ["C4Trie4Trie", "merge"]
+- ["C4Trie4Trie", "printTrie"]
+- ["C4Trie4Trie", "remove"]
+- ["C4Trie4Trie", "removeAll"]
+- !private ["C4Trie4Trie", "root"]
+- !private ["C4Trie4Trie", "wordCount"]
+- !private ["C4Trie4Trie", "wordList"]
+- !private ["Ps31UnicodeScalarLiteralConvertible", "characters"]
+- !private ["Ps31UnicodeScalarLiteralConvertible", "init"]
+- !private ["Ps31UnicodeScalarLiteralConvertible", "lowercaseString"]
+- !private ["Ps10_ArrayType", "Element"]
+- !private ["Ps10_ArrayType", "Generator"]
+- !private ["Ps10_ArrayType", "Index"]
+- !private ["Ps10_ArrayType", "SubSequence"]
+- !private ["Ps10_ArrayType", "_Element"]
+- !private ["Ps10_ArrayType", "append"]
+- !private ["Ps10_ArrayType", "init"]
+- !private ["Ps10_ArrayType", "removeAtIndex"]
+- !private ["Ps10_ArrayType", "subscript"]
+- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "characters"]
+- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "init"]
+- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
+- !private ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
+- !private ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps32_BuiltinStringLiteralConvertible", "characters"]
+- !private ["Ps32_BuiltinStringLiteralConvertible", "init"]
+- !private ["Ps32_BuiltinStringLiteralConvertible", "lowercaseString"]
+- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "characters"]
+- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "init"]
+- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "lowercaseString"]
+- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "characters"]
+- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "init"]
+- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "lowercaseString"]
+- !private ["Ps24_DestructorSafeContainer", "Element"]
+- !private ["Ps24_DestructorSafeContainer", "Generator"]
+- !private ["Ps24_DestructorSafeContainer", "Index"]
+- !private ["Ps24_DestructorSafeContainer", "SubSequence"]
+- !private ["Ps24_DestructorSafeContainer", "_Element"]
+- !private ["Ps24_DestructorSafeContainer", "append"]
+- !private ["Ps24_DestructorSafeContainer", "init"]
+- !private ["Ps24_DestructorSafeContainer", "removeAtIndex"]
+- !private ["Ps24_DestructorSafeContainer", "subscript"]
+- !private ["Ps14_Incrementable", "Distance"]
+- !private ["Ps14_Incrementable", "IntegerLiteralType"]
+- !private ["Ps14_Incrementable", "_DisabledRangeIndex"]
+- !private ["Ps22_IntegerArithmeticType", "Distance"]
+- !private ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
+- !private ["Ps12_IntegerType", "Distance"]
+- !private ["Ps12_IntegerType", "IntegerLiteralType"]
+- !private ["Vs26_OptionalNilComparisonType", "deinit"]
+- !private ["Ps22_RandomAccessAmbiguity", "Distance"]
+- !private ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
+- !private ["Ps12_Reflectable", "Distance"]
+- !private ["Ps12_Reflectable", "Element"]
+- !private ["Ps12_Reflectable", "Generator"]
+- !private ["Ps12_Reflectable", "Index"]
+- !private ["Ps12_Reflectable", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Some"]
+- !private ["Ps12_Reflectable", "SubSequence"]
+- !private ["Ps12_Reflectable", "_Element"]
+- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
+- !private ["Ps12_Reflectable", "append"]
+- !private ["Ps12_Reflectable", "characters"]
+- !private ["Ps12_Reflectable", "count"]
+- !private ["Ps12_Reflectable", "init"]
+- !private ["Ps12_Reflectable", "lowercaseString"]
+- !private ["Ps12_Reflectable", "removeAtIndex"]
+- !private ["Ps12_Reflectable", "subscript"]
+- !private ["Ps18_SignedIntegerType", "Distance"]
+- !private ["Ps18_SignedIntegerType", "IntegerLiteralType"]
+depends-nominal:
+- !private "Vs12AnyGenerator"
+- "Ps9AnyObject"
+- !private "Vs11AnySequence"
+- !private "Sa"
+- !private "Ps23ArrayLiteralConvertible"
+- !private "Vs10ArraySlice"
+- !private "Ps22BidirectionalIndexType"
+- !private "Ps21BitwiseOperationsType"
+- !private "Sb"
+- !private "Ps25BooleanLiteralConvertible"
+- !private "Ps11BooleanType"
+- !private "Ps11CVarArgType"
+- !private "VSS13CharacterView"
+- !private "Ps14CollectionType"
+- !private "Ps10Comparable"
+- "Ps28CustomDebugStringConvertible"
+- !private "Ps23CustomStringConvertible"
+- !private "Vs10Dictionary"
+- !private "Vs19DictionaryGenerator"
+- !private "Vs15DictionaryIndex"
+- !private "Ps28DictionaryLiteralConvertible"
+- !private "Ps9Equatable"
+- !private "Ps41ExtendedGraphemeClusterLiteralConvertible"
+- !private "Ps16ForwardIndexType"
+- !private "Ps13GeneratorType"
+- !private "Ps8Hashable"
+- !private "VVSS13CharacterView5Index"
+- !private "Ps9Indexable"
+- !private "Vs17IndexingGenerator"
+- !private "Si"
+- !private "Ps21IntegerArithmeticType"
+- !private "Ps25IntegerLiteralConvertible"
+- !private "Ps11IntegerType"
+- !private "Ps14MirrorPathType"
+- !private "Ps21MutableCollectionType"
+- !private "Ps16MutableIndexable"
+- !private "Ps16MutableSliceable"
+- "Ps21NilLiteralConvertible"
+- "C4Trie4Node"
+- "Sq"
+- !private "Ps16OutputStreamType"
+- !private "V4Trie5Queue"
+- !private "Ps21RandomAccessIndexType"
+- !private "Ps30RangeReplaceableCollectionType"
+- !private "Ps12SequenceType"
+- !private "Vs3Set"
+- !private "Vs12SetGenerator"
+- !private "Ps17SignedIntegerType"
+- !private "Ps16SignedNumberType"
+- !private "Vs5Slice"
+- !private "Ps10Streamable"
+- !private "Ps10Strideable"
+- !private "SS"
+- !private "Ps30StringInterpolationConvertible"
+- !private "Ps24StringLiteralConvertible"
+- "C4Trie4Trie"
+- !private "Ps31UnicodeScalarLiteralConvertible"
+- !private "Ps10_ArrayType"
+- !private "Ps33_BuiltinBooleanLiteralConvertible"
+- !private "Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible"
+- !private "Ps33_BuiltinIntegerLiteralConvertible"
+- !private "Ps32_BuiltinStringLiteralConvertible"
+- !private "Ps37_BuiltinUTF16StringLiteralConvertible"
+- !private "Ps39_BuiltinUnicodeScalarLiteralConvertible"
+- !private "Ps24_DestructorSafeContainer"
+- !private "Ps14_Incrementable"
+- !private "Ps22_IntegerArithmeticType"
+- !private "Ps12_IntegerType"
+- !private "Vs26_OptionalNilComparisonType"
+- !private "Ps22_RandomAccessAmbiguity"
+- "Ps12_Reflectable"
+- !private "Ps18_SignedIntegerType"
+depends-dynamic-lookup:
+depends-external:
+- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
+- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
+interface-hash: "fd9fdb3a4bd3dfc789eaf1430eb72c67"
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diff --git a/Trie/.build/debug/Trie.o/llbuild.yaml b/Trie/.build/debug/Trie.o/llbuild.yaml
new file mode 100644
index 000000000..8607eca74
--- /dev/null
+++ b/Trie/.build/debug/Trie.o/llbuild.yaml
@@ -0,0 +1,29 @@
+client:
+  name: swift-build
+
+tools: {}
+
+targets:
+  "": [<Trie>]
+  Trie: [<Trie>]
+
+commands:
+  <Trie-swiftc>:
+    tool: swift-compiler
+    executable: "/home/christian/swiftv2/usr/bin/swiftc"
+    inputs: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
+    outputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
+    module-name: "Trie"
+    module-output-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule"
+    is-library: false
+    sources: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
+    objects: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
+    import-paths: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug"]
+    temps-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie"
+    other-args: ["-j8","-Onone","-g","-I","/usr/local/include"]
+  <Trie>:
+    tool: shell
+    inputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
+    outputs: ["<Trie>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie"]
+    args: ["/home/christian/swiftv2/usr/bin/swiftc","-o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o","-g","-L/usr/local/lib"]
+    description: "Linking Executable:  .build/debug/Trie"
diff --git a/Trie/.build/debug/Trie.o/sources/Queue.swift.o b/Trie/.build/debug/Trie.o/sources/Queue.swift.o
new file mode 100644
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diff --git a/Trie/.build/debug/Trie.o/sources/trie.swift.o b/Trie/.build/debug/Trie.o/sources/trie.swift.o
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diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/build.db b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/build.db
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diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml
new file mode 100644
index 000000000..5e1bc6390
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml
@@ -0,0 +1,29 @@
+client:
+  name: swift-build
+
+tools: {}
+
+targets:
+  "": [<package_name_here_and_keep_quote_marks>]
+  package_name_here_and_keep_quote_marks: [<package_name_here_and_keep_quote_marks>]
+
+commands:
+  <package_name_here_and_keep_quote_marks-swiftc>:
+    tool: swift-compiler
+    executable: "/home/christian/swiftv2/usr/bin/swiftc"
+    inputs: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
+    outputs: ["<package_name_here_and_keep_quote_marks-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.swiftmodule","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o"]
+    module-name: "package_name_here_and_keep_quote_marks"
+    module-output-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.swiftmodule"
+    is-library: true
+    sources: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
+    objects: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o"]
+    import-paths: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug"]
+    temps-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks"
+    other-args: ["-j8","-Onone","-g","-enable-testing","-I","/usr/local/include"]
+  <package_name_here_and_keep_quote_marks>:
+    tool: shell
+    inputs: ["<package_name_here_and_keep_quote_marks-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o"]
+    outputs: ["<package_name_here_and_keep_quote_marks>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.a"]
+    args: ["/bin/sh","-c","rm -f '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.a'; ar cr '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.a' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o'"]
+    description: "Linking Library:  .build/debug/package_name_here_and_keep_quote_marks.a"
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d
new file mode 100644
index 000000000..2b2aa612f
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d
@@ -0,0 +1,3 @@
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps
new file mode 100644
index 000000000..eaa595090
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps
@@ -0,0 +1,316 @@
+### Swift dependencies file v0 ###
+provides-top-level:
+- "Queue"
+provides-nominal:
+- "V38package_name_here_and_keep_quote_marks5Queue"
+provides-member:
+- ["V38package_name_here_and_keep_quote_marks5Queue", ""]
+depends-top-level:
+- "Queue"
+- !private "/"
+- !private "&&"
+- !private "Double"
+- !private "-"
+- "Bool"
+- "FloatLiteralType"
+- "IntegerLiteralType"
+- !private ">"
+- !private "=="
+- "Int"
+- !private "<"
+- !private "+="
+depends-member:
+- !private ["Ps16AbsoluteValuable", "init"]
+- ["Sa", "Generator"]
+- ["Sa", "Index"]
+- ["Sa", "SubSequence"]
+- ["Sa", "_Element"]
+- !private ["Sa", "append"]
+- !private ["Sa", "count"]
+- !private ["Sa", "deinit"]
+- ["Sa", "init"]
+- !private ["Sa", "removeFirst"]
+- !private ["Sa", "subscript"]
+- ["Ps23ArrayLiteralConvertible", "Generator"]
+- ["Ps23ArrayLiteralConvertible", "Index"]
+- ["Ps23ArrayLiteralConvertible", "SubSequence"]
+- ["Ps23ArrayLiteralConvertible", "_Element"]
+- !private ["Ps23ArrayLiteralConvertible", "append"]
+- !private ["Ps23ArrayLiteralConvertible", "count"]
+- ["Ps23ArrayLiteralConvertible", "init"]
+- !private ["Ps23ArrayLiteralConvertible", "removeFirst"]
+- !private ["Ps23ArrayLiteralConvertible", "subscript"]
+- ["Vs10ArraySlice", "Generator"]
+- ["Vs10ArraySlice", "Index"]
+- ["Ps22BidirectionalIndexType", "Distance"]
+- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
+- ["Ps21BitwiseOperationsType", "Distance"]
+- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
+- !private ["Sb", "_getBuiltinLogicValue"]
+- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
+- ["Ps11CVarArgType", "Distance"]
+- ["Ps11CVarArgType", "IntegerLiteralType"]
+- !private ["Ps11CVarArgType", "init"]
+- ["Ps14CollectionType", "Generator"]
+- ["Ps14CollectionType", "Index"]
+- ["Ps14CollectionType", "SubSequence"]
+- ["Ps14CollectionType", "_Element"]
+- !private ["Ps14CollectionType", "append"]
+- !private ["Ps14CollectionType", "count"]
+- ["Ps14CollectionType", "init"]
+- !private ["Ps14CollectionType", "removeFirst"]
+- !private ["Ps14CollectionType", "subscript"]
+- ["Ps10Comparable", "Distance"]
+- ["Ps10Comparable", "IntegerLiteralType"]
+- !private ["Ps10Comparable", "init"]
+- ["Ps28CustomDebugStringConvertible", "Generator"]
+- ["Ps28CustomDebugStringConvertible", "Index"]
+- ["Ps28CustomDebugStringConvertible", "Some"]
+- ["Ps28CustomDebugStringConvertible", "SubSequence"]
+- ["Ps28CustomDebugStringConvertible", "_Element"]
+- !private ["Ps28CustomDebugStringConvertible", "append"]
+- !private ["Ps28CustomDebugStringConvertible", "count"]
+- ["Ps28CustomDebugStringConvertible", "init"]
+- !private ["Ps28CustomDebugStringConvertible", "removeFirst"]
+- !private ["Ps28CustomDebugStringConvertible", "subscript"]
+- ["Ps23CustomStringConvertible", "Distance"]
+- ["Ps23CustomStringConvertible", "Generator"]
+- ["Ps23CustomStringConvertible", "Index"]
+- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
+- ["Ps23CustomStringConvertible", "SubSequence"]
+- ["Ps23CustomStringConvertible", "_Element"]
+- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps23CustomStringConvertible", "append"]
+- !private ["Ps23CustomStringConvertible", "count"]
+- ["Ps23CustomStringConvertible", "init"]
+- !private ["Ps23CustomStringConvertible", "removeFirst"]
+- !private ["Ps23CustomStringConvertible", "subscript"]
+- !private ["Sd", "init"]
+- ["Ps9Equatable", "Distance"]
+- ["Ps9Equatable", "IntegerLiteralType"]
+- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
+- !private ["Ps9Equatable", "init"]
+- !private ["Ps23FloatLiteralConvertible", "init"]
+- !private ["Ps17FloatingPointType", "init"]
+- ["Ps16ForwardIndexType", "Distance"]
+- ["Ps16ForwardIndexType", "IntegerLiteralType"]
+- ["Ps13GeneratorType", "Element"]
+- ["Ps8Hashable", "Distance"]
+- ["Ps8Hashable", "IntegerLiteralType"]
+- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
+- !private ["Ps8Hashable", "init"]
+- ["Ps9Indexable", "Generator"]
+- ["Ps9Indexable", "Index"]
+- ["Ps9Indexable", "SubSequence"]
+- ["Ps9Indexable", "_Element"]
+- !private ["Ps9Indexable", "append"]
+- !private ["Ps9Indexable", "count"]
+- ["Ps9Indexable", "init"]
+- !private ["Ps9Indexable", "removeFirst"]
+- !private ["Ps9Indexable", "subscript"]
+- ["Vs17IndexingGenerator", "Element"]
+- ["Si", "Distance"]
+- ["Si", "IntegerLiteralType"]
+- ["Ps21IntegerArithmeticType", "Distance"]
+- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps25IntegerLiteralConvertible", "Distance"]
+- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps25IntegerLiteralConvertible", "init"]
+- ["Ps11IntegerType", "Distance"]
+- ["Ps11IntegerType", "IntegerLiteralType"]
+- ["Ps14MirrorPathType", "Distance"]
+- ["Ps14MirrorPathType", "IntegerLiteralType"]
+- ["Ps21MutableCollectionType", "Generator"]
+- ["Ps21MutableCollectionType", "Index"]
+- ["Ps21MutableCollectionType", "SubSequence"]
+- ["Ps21MutableCollectionType", "_Element"]
+- !private ["Ps21MutableCollectionType", "append"]
+- !private ["Ps21MutableCollectionType", "count"]
+- ["Ps21MutableCollectionType", "init"]
+- !private ["Ps21MutableCollectionType", "removeFirst"]
+- !private ["Ps21MutableCollectionType", "subscript"]
+- ["Ps16MutableIndexable", "Generator"]
+- ["Ps16MutableIndexable", "Index"]
+- ["Ps16MutableIndexable", "SubSequence"]
+- ["Ps16MutableIndexable", "_Element"]
+- !private ["Ps16MutableIndexable", "append"]
+- !private ["Ps16MutableIndexable", "count"]
+- ["Ps16MutableIndexable", "init"]
+- !private ["Ps16MutableIndexable", "removeFirst"]
+- !private ["Ps16MutableIndexable", "subscript"]
+- ["Ps16MutableSliceable", "Generator"]
+- ["Ps16MutableSliceable", "Index"]
+- ["Ps16MutableSliceable", "SubSequence"]
+- ["Ps16MutableSliceable", "_Element"]
+- !private ["Ps16MutableSliceable", "append"]
+- !private ["Ps16MutableSliceable", "count"]
+- ["Ps16MutableSliceable", "init"]
+- !private ["Ps16MutableSliceable", "removeFirst"]
+- !private ["Ps16MutableSliceable", "subscript"]
+- ["Ps21NilLiteralConvertible", "Some"]
+- ["Sq", "Some"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "Bool"]
+- !private ["V38package_name_here_and_keep_quote_marks5Queue", "Double"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "Int"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "T"]
+- !private ["V38package_name_here_and_keep_quote_marks5Queue", "array"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "count"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "dequeue"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "enqueue"]
+- !private ["V38package_name_here_and_keep_quote_marks5Queue", "head"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "init"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "isEmpty"]
+- ["V38package_name_here_and_keep_quote_marks5Queue", "peek"]
+- ["Ps21RandomAccessIndexType", "Distance"]
+- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
+- ["Ps30RangeReplaceableCollectionType", "Generator"]
+- ["Ps30RangeReplaceableCollectionType", "Index"]
+- ["Ps30RangeReplaceableCollectionType", "SubSequence"]
+- ["Ps30RangeReplaceableCollectionType", "_Element"]
+- !private ["Ps30RangeReplaceableCollectionType", "append"]
+- !private ["Ps30RangeReplaceableCollectionType", "count"]
+- ["Ps30RangeReplaceableCollectionType", "init"]
+- !private ["Ps30RangeReplaceableCollectionType", "removeFirst"]
+- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
+- ["Ps12SequenceType", "Element"]
+- ["Ps12SequenceType", "Generator"]
+- ["Ps12SequenceType", "Index"]
+- ["Ps12SequenceType", "SubSequence"]
+- ["Ps12SequenceType", "_Element"]
+- !private ["Ps12SequenceType", "append"]
+- !private ["Ps12SequenceType", "count"]
+- ["Ps12SequenceType", "init"]
+- !private ["Ps12SequenceType", "removeFirst"]
+- !private ["Ps12SequenceType", "subscript"]
+- ["Ps17SignedIntegerType", "Distance"]
+- ["Ps17SignedIntegerType", "IntegerLiteralType"]
+- ["Ps16SignedNumberType", "Distance"]
+- ["Ps16SignedNumberType", "IntegerLiteralType"]
+- !private ["Ps16SignedNumberType", "init"]
+- !private ["Vs5Slice", "Generator"]
+- !private ["Vs5Slice", "Index"]
+- !private ["Vs5Slice", "SubSequence"]
+- !private ["Vs5Slice", "_Element"]
+- ["Ps10Strideable", "Distance"]
+- ["Ps10Strideable", "IntegerLiteralType"]
+- !private ["Ps10Strideable", "init"]
+- ["Ps10_ArrayType", "Generator"]
+- ["Ps10_ArrayType", "Index"]
+- ["Ps10_ArrayType", "SubSequence"]
+- ["Ps10_ArrayType", "_Element"]
+- !private ["Ps10_ArrayType", "append"]
+- !private ["Ps10_ArrayType", "count"]
+- ["Ps10_ArrayType", "init"]
+- !private ["Ps10_ArrayType", "removeFirst"]
+- !private ["Ps10_ArrayType", "subscript"]
+- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps31_BuiltinFloatLiteralConvertible", "init"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps33_BuiltinIntegerLiteralConvertible", "init"]
+- !private ["Ps19_CVarArgAlignedType", "init"]
+- !private ["Ps22_CVarArgPassedAsDouble", "init"]
+- ["Ps24_DestructorSafeContainer", "Generator"]
+- ["Ps24_DestructorSafeContainer", "Index"]
+- ["Ps24_DestructorSafeContainer", "SubSequence"]
+- ["Ps24_DestructorSafeContainer", "_Element"]
+- !private ["Ps24_DestructorSafeContainer", "append"]
+- !private ["Ps24_DestructorSafeContainer", "count"]
+- ["Ps24_DestructorSafeContainer", "init"]
+- !private ["Ps24_DestructorSafeContainer", "removeFirst"]
+- !private ["Ps24_DestructorSafeContainer", "subscript"]
+- ["Ps14_Incrementable", "Distance"]
+- ["Ps14_Incrementable", "IntegerLiteralType"]
+- ["Ps22_IntegerArithmeticType", "Distance"]
+- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps12_IntegerType", "Distance"]
+- ["Ps12_IntegerType", "IntegerLiteralType"]
+- ["Ps22_RandomAccessAmbiguity", "Distance"]
+- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Distance"]
+- ["Ps12_Reflectable", "Generator"]
+- ["Ps12_Reflectable", "Index"]
+- ["Ps12_Reflectable", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Some"]
+- ["Ps12_Reflectable", "SubSequence"]
+- ["Ps12_Reflectable", "_Element"]
+- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
+- !private ["Ps12_Reflectable", "append"]
+- !private ["Ps12_Reflectable", "count"]
+- ["Ps12_Reflectable", "init"]
+- !private ["Ps12_Reflectable", "removeFirst"]
+- !private ["Ps12_Reflectable", "subscript"]
+- ["Ps18_SignedIntegerType", "Distance"]
+- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
+depends-nominal:
+- !private "Ps16AbsoluteValuable"
+- "Sa"
+- "Ps23ArrayLiteralConvertible"
+- "Vs10ArraySlice"
+- "Ps22BidirectionalIndexType"
+- "Ps21BitwiseOperationsType"
+- !private "Sb"
+- !private "Ps25BooleanLiteralConvertible"
+- !private "Ps11BooleanType"
+- "Ps11CVarArgType"
+- "Ps14CollectionType"
+- "Ps10Comparable"
+- "Ps28CustomDebugStringConvertible"
+- "Ps23CustomStringConvertible"
+- !private "Sd"
+- "Ps9Equatable"
+- !private "Ps23FloatLiteralConvertible"
+- !private "Ps17FloatingPointType"
+- "Ps16ForwardIndexType"
+- "Ps13GeneratorType"
+- "Ps8Hashable"
+- "Ps9Indexable"
+- "Vs17IndexingGenerator"
+- "Si"
+- "Ps21IntegerArithmeticType"
+- "Ps25IntegerLiteralConvertible"
+- "Ps11IntegerType"
+- "Ps14MirrorPathType"
+- "Ps21MutableCollectionType"
+- "Ps16MutableIndexable"
+- "Ps16MutableSliceable"
+- "Ps21NilLiteralConvertible"
+- "Sq"
+- "V38package_name_here_and_keep_quote_marks5Queue"
+- "Ps21RandomAccessIndexType"
+- "Ps30RangeReplaceableCollectionType"
+- "Ps12SequenceType"
+- "Ps17SignedIntegerType"
+- "Ps16SignedNumberType"
+- !private "Vs5Slice"
+- "Ps10Strideable"
+- "Ps10_ArrayType"
+- !private "Ps33_BuiltinBooleanLiteralConvertible"
+- !private "Ps31_BuiltinFloatLiteralConvertible"
+- "Ps33_BuiltinIntegerLiteralConvertible"
+- !private "Ps19_CVarArgAlignedType"
+- !private "Ps22_CVarArgPassedAsDouble"
+- "Ps24_DestructorSafeContainer"
+- "Ps14_Incrementable"
+- "Ps22_IntegerArithmeticType"
+- "Ps12_IntegerType"
+- "Ps22_RandomAccessAmbiguity"
+- "Ps12_Reflectable"
+- "Ps18_SignedIntegerType"
+depends-dynamic-lookup:
+depends-external:
+- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
+- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
+interface-hash: "b268b101cc2bc2706939fa25905dab4d"
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps
new file mode 100644
index 000000000..d0814f65b
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps
@@ -0,0 +1,6 @@
+version: "Swift version 2.2-dev (LLVM 3ebdbb2c7e, Clang f66c5bb67b, Swift 0ddf238ad7)"
+options: "4b4cb3e8efe303c8a39bf9409934d3d3"
+build_time: [515615518, 682291000]
+inputs:
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": !dirty [515615193, 0]
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": !dirty [512710161, 0]
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json
new file mode 100644
index 000000000..5b65a86c0
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json
@@ -0,0 +1,17 @@
+{
+  "": {
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps"
+  },
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": {
+    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d",
+    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o",
+    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie~partial.swiftmodule",
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps"
+  },
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": {
+    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d",
+    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o",
+    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue~partial.swiftmodule",
+    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps"
+  }
+}
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d
new file mode 100644
index 000000000..eefb6fd8d
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d
@@ -0,0 +1,3 @@
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps
new file mode 100644
index 000000000..39eba9f00
--- /dev/null
+++ b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps
@@ -0,0 +1,513 @@
+### Swift dependencies file v0 ###
+provides-top-level:
+- "Node"
+- "Trie"
+- "T"
+- "U"
+- "V"
+provides-nominal:
+- "C38package_name_here_and_keep_quote_marks4Node"
+- "C38package_name_here_and_keep_quote_marks4Trie"
+provides-member:
+- ["C38package_name_here_and_keep_quote_marks4Node", ""]
+- ["C38package_name_here_and_keep_quote_marks4Trie", ""]
+depends-top-level:
+- "Trie"
+- "print"
+- "Bool"
+- !private "-="
+- "StringLiteralType"
+- !private ">"
+- !private "&&"
+- !private "Queue"
+- "U"
+- "Int"
+- "V"
+- !private "BooleanLiteralType"
+- "Node"
+- "FloatLiteralType"
+- "Set"
+- "Array"
+- !private "+"
+- !private "-"
+- !private "UnicodeScalarType"
+- "IntegerLiteralType"
+- !private "=="
+- "Void"
+- !private "+="
+- "T"
+- !private "!"
+- "String"
+depends-member:
+- !private ["Vs12AnyGenerator", "Element"]
+- !private ["Ps9AnyObject", "Array"]
+- !private ["Ps9AnyObject", "Node"]
+- !private ["Ps9AnyObject", "Queue"]
+- !private ["Ps9AnyObject", "Set"]
+- !private ["Ps9AnyObject", "String"]
+- !private ["Ps9AnyObject", "Trie"]
+- !private ["Ps9AnyObject", "char"]
+- !private ["Ps9AnyObject", "character"]
+- !private ["Ps9AnyObject", "children"]
+- !private ["Ps9AnyObject", "contains"]
+- !private ["Ps9AnyObject", "find"]
+- !private ["Ps9AnyObject", "getChildAt"]
+- !private ["Ps9AnyObject", "getChildren"]
+- !private ["Ps9AnyObject", "getParent"]
+- ["Ps9AnyObject", "getWords"]
+- ["Ps9AnyObject", "init"]
+- ["Ps9AnyObject", "insert"]
+- !private ["Ps9AnyObject", "isAWord"]
+- !private ["Ps9AnyObject", "isNotWord"]
+- !private ["Ps9AnyObject", "isRoot"]
+- !private ["Ps9AnyObject", "isValidWord"]
+- !private ["Ps9AnyObject", "isWord"]
+- ["Ps9AnyObject", "merge"]
+- !private ["Ps9AnyObject", "numChildren"]
+- !private ["Ps9AnyObject", "parent"]
+- !private ["Ps9AnyObject", "print"]
+- !private ["Ps9AnyObject", "printNode"]
+- !private ["Ps9AnyObject", "remove"]
+- ["Ps9AnyObject", "removeAll"]
+- !private ["Ps9AnyObject", "root"]
+- !private ["Ps9AnyObject", "setParent"]
+- !private ["Ps9AnyObject", "update"]
+- !private ["Ps9AnyObject", "wordCount"]
+- !private ["Ps9AnyObject", "wordList"]
+- ["Ps9AnyObject", ""]
+- !private ["Vs11AnySequence", "Generator"]
+- !private ["Vs11AnySequence", "deinit"]
+- ["Sa", "Element"]
+- ["Sa", "Generator"]
+- ["Sa", "Index"]
+- !private ["Sa", "SubSequence"]
+- ["Sa", "_Element"]
+- !private ["Sa", "append"]
+- !private ["Sa", "deinit"]
+- !private ["Sa", "init"]
+- !private ["Sa", "removeAtIndex"]
+- !private ["Sa", "subscript"]
+- ["Ps23ArrayLiteralConvertible", "Element"]
+- ["Ps23ArrayLiteralConvertible", "Generator"]
+- ["Ps23ArrayLiteralConvertible", "Index"]
+- !private ["Ps23ArrayLiteralConvertible", "SubSequence"]
+- ["Ps23ArrayLiteralConvertible", "_Element"]
+- !private ["Ps23ArrayLiteralConvertible", "append"]
+- ["Ps23ArrayLiteralConvertible", "init"]
+- !private ["Ps23ArrayLiteralConvertible", "removeAtIndex"]
+- !private ["Ps23ArrayLiteralConvertible", "subscript"]
+- !private ["Vs10ArraySlice", "Generator"]
+- !private ["Vs10ArraySlice", "Index"]
+- ["Ps22BidirectionalIndexType", "Distance"]
+- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
+- ["Ps21BitwiseOperationsType", "Distance"]
+- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
+- !private ["Sb", "_getBuiltinLogicValue"]
+- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
+- ["Ps11CVarArgType", "Distance"]
+- ["Ps11CVarArgType", "IntegerLiteralType"]
+- !private ["VSS13CharacterView", "Generator"]
+- !private ["VSS13CharacterView", "Index"]
+- !private ["VSS13CharacterView", "SubSequence"]
+- !private ["VSS13CharacterView", "_Element"]
+- !private ["VSS13CharacterView", "count"]
+- !private ["VSS13CharacterView", "deinit"]
+- !private ["VSS13CharacterView", "suffix"]
+- ["Ps14CollectionType", "Element"]
+- ["Ps14CollectionType", "Generator"]
+- ["Ps14CollectionType", "Index"]
+- !private ["Ps14CollectionType", "SubSequence"]
+- ["Ps14CollectionType", "_Element"]
+- !private ["Ps14CollectionType", "append"]
+- !private ["Ps14CollectionType", "count"]
+- ["Ps14CollectionType", "init"]
+- !private ["Ps14CollectionType", "removeAtIndex"]
+- !private ["Ps14CollectionType", "subscript"]
+- !private ["Ps14CollectionType", "suffix"]
+- ["Ps10Comparable", "Distance"]
+- ["Ps10Comparable", "IntegerLiteralType"]
+- !private ["Ps10Comparable", "_DisabledRangeIndex"]
+- !private ["Ps10Comparable", "characters"]
+- !private ["Ps10Comparable", "init"]
+- !private ["Ps10Comparable", "lowercaseString"]
+- ["Ps28CustomDebugStringConvertible", "Element"]
+- ["Ps28CustomDebugStringConvertible", "Generator"]
+- ["Ps28CustomDebugStringConvertible", "Index"]
+- ["Ps28CustomDebugStringConvertible", "Some"]
+- !private ["Ps28CustomDebugStringConvertible", "SubSequence"]
+- ["Ps28CustomDebugStringConvertible", "_Element"]
+- !private ["Ps28CustomDebugStringConvertible", "append"]
+- !private ["Ps28CustomDebugStringConvertible", "characters"]
+- !private ["Ps28CustomDebugStringConvertible", "count"]
+- ["Ps28CustomDebugStringConvertible", "init"]
+- !private ["Ps28CustomDebugStringConvertible", "lowercaseString"]
+- !private ["Ps28CustomDebugStringConvertible", "removeAtIndex"]
+- !private ["Ps28CustomDebugStringConvertible", "subscript"]
+- ["Ps23CustomStringConvertible", "Distance"]
+- ["Ps23CustomStringConvertible", "Element"]
+- ["Ps23CustomStringConvertible", "Generator"]
+- ["Ps23CustomStringConvertible", "Index"]
+- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
+- !private ["Ps23CustomStringConvertible", "SubSequence"]
+- ["Ps23CustomStringConvertible", "_Element"]
+- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps23CustomStringConvertible", "append"]
+- !private ["Ps23CustomStringConvertible", "count"]
+- ["Ps23CustomStringConvertible", "init"]
+- !private ["Ps23CustomStringConvertible", "removeAtIndex"]
+- !private ["Ps23CustomStringConvertible", "subscript"]
+- !private ["Vs10Dictionary", "Generator"]
+- !private ["Vs10Dictionary", "Index"]
+- !private ["Vs10Dictionary", "SubSequence"]
+- !private ["Vs10Dictionary", "_Element"]
+- !private ["Vs10Dictionary", "count"]
+- !private ["Vs10Dictionary", "deinit"]
+- !private ["Vs10Dictionary", "init"]
+- !private ["Vs10Dictionary", "subscript"]
+- !private ["Vs19DictionaryGenerator", "Element"]
+- !private ["Vs15DictionaryIndex", "Distance"]
+- !private ["Vs15DictionaryIndex", "_DisabledRangeIndex"]
+- !private ["Ps28DictionaryLiteralConvertible", "Generator"]
+- !private ["Ps28DictionaryLiteralConvertible", "Index"]
+- !private ["Ps28DictionaryLiteralConvertible", "SubSequence"]
+- !private ["Ps28DictionaryLiteralConvertible", "_Element"]
+- !private ["Ps28DictionaryLiteralConvertible", "count"]
+- !private ["Ps28DictionaryLiteralConvertible", "init"]
+- !private ["Ps28DictionaryLiteralConvertible", "subscript"]
+- ["Ps9Equatable", "Distance"]
+- !private ["Ps9Equatable", "Generator"]
+- ["Ps9Equatable", "IntegerLiteralType"]
+- !private ["Ps9Equatable", "_DisabledRangeIndex"]
+- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
+- !private ["Ps9Equatable", "characters"]
+- ["Ps9Equatable", "init"]
+- !private ["Ps9Equatable", "lowercaseString"]
+- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "characters"]
+- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "init"]
+- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
+- ["Ps16ForwardIndexType", "Distance"]
+- ["Ps16ForwardIndexType", "IntegerLiteralType"]
+- !private ["Ps16ForwardIndexType", "_DisabledRangeIndex"]
+- ["Ps13GeneratorType", "Element"]
+- ["Ps8Hashable", "Distance"]
+- !private ["Ps8Hashable", "Generator"]
+- ["Ps8Hashable", "IntegerLiteralType"]
+- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
+- !private ["Ps8Hashable", "characters"]
+- ["Ps8Hashable", "init"]
+- !private ["Ps8Hashable", "lowercaseString"]
+- !private ["VVSS13CharacterView5Index", "Distance"]
+- ["Ps9Indexable", "Element"]
+- ["Ps9Indexable", "Generator"]
+- ["Ps9Indexable", "Index"]
+- !private ["Ps9Indexable", "SubSequence"]
+- ["Ps9Indexable", "_Element"]
+- !private ["Ps9Indexable", "append"]
+- !private ["Ps9Indexable", "count"]
+- ["Ps9Indexable", "init"]
+- !private ["Ps9Indexable", "removeAtIndex"]
+- !private ["Ps9Indexable", "subscript"]
+- !private ["Ps9Indexable", "suffix"]
+- ["Vs17IndexingGenerator", "Element"]
+- ["Si", "Distance"]
+- ["Si", "IntegerLiteralType"]
+- ["Si", "deinit"]
+- ["Ps21IntegerArithmeticType", "Distance"]
+- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps25IntegerLiteralConvertible", "Distance"]
+- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
+- ["Ps11IntegerType", "Distance"]
+- ["Ps11IntegerType", "IntegerLiteralType"]
+- ["Ps14MirrorPathType", "Distance"]
+- ["Ps14MirrorPathType", "IntegerLiteralType"]
+- !private ["Ps14MirrorPathType", "characters"]
+- !private ["Ps14MirrorPathType", "init"]
+- !private ["Ps14MirrorPathType", "lowercaseString"]
+- ["Ps21MutableCollectionType", "Element"]
+- ["Ps21MutableCollectionType", "Generator"]
+- ["Ps21MutableCollectionType", "Index"]
+- !private ["Ps21MutableCollectionType", "SubSequence"]
+- ["Ps21MutableCollectionType", "_Element"]
+- !private ["Ps21MutableCollectionType", "append"]
+- !private ["Ps21MutableCollectionType", "init"]
+- !private ["Ps21MutableCollectionType", "removeAtIndex"]
+- !private ["Ps21MutableCollectionType", "subscript"]
+- ["Ps16MutableIndexable", "Element"]
+- ["Ps16MutableIndexable", "Generator"]
+- ["Ps16MutableIndexable", "Index"]
+- !private ["Ps16MutableIndexable", "SubSequence"]
+- ["Ps16MutableIndexable", "_Element"]
+- !private ["Ps16MutableIndexable", "append"]
+- !private ["Ps16MutableIndexable", "init"]
+- !private ["Ps16MutableIndexable", "removeAtIndex"]
+- !private ["Ps16MutableIndexable", "subscript"]
+- ["Ps16MutableSliceable", "Element"]
+- ["Ps16MutableSliceable", "Generator"]
+- ["Ps16MutableSliceable", "Index"]
+- !private ["Ps16MutableSliceable", "SubSequence"]
+- ["Ps16MutableSliceable", "_Element"]
+- !private ["Ps16MutableSliceable", "append"]
+- !private ["Ps16MutableSliceable", "init"]
+- !private ["Ps16MutableSliceable", "removeAtIndex"]
+- !private ["Ps16MutableSliceable", "subscript"]
+- ["Ps21NilLiteralConvertible", "Some"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "Bool"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "Int"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "Node"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "String"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "Void"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "char"]
+- !private ["C38package_name_here_and_keep_quote_marks4Node", "character"]
+- !private ["C38package_name_here_and_keep_quote_marks4Node", "children"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "deinit"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "getChildAt"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "getChildren"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "getParent"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "init"]
+- !private ["C38package_name_here_and_keep_quote_marks4Node", "isAWord"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "isLeaf"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "isNotWord"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "isRoot"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "isValidWord"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "isWord"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "numChildren"]
+- !private ["C38package_name_here_and_keep_quote_marks4Node", "parent"]
+- !private ["C38package_name_here_and_keep_quote_marks4Node", "print"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "printNode"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "setParent"]
+- ["C38package_name_here_and_keep_quote_marks4Node", "update"]
+- ["Sq", "Some"]
+- !private ["Sq", "deinit"]
+- !private ["Ps16OutputStreamType", "characters"]
+- !private ["Ps16OutputStreamType", "init"]
+- !private ["Ps16OutputStreamType", "lowercaseString"]
+- !private ["V38package_name_here_and_keep_quote_marks5Queue", "init"]
+- ["Ps21RandomAccessIndexType", "Distance"]
+- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
+- ["Ps30RangeReplaceableCollectionType", "Element"]
+- ["Ps30RangeReplaceableCollectionType", "Generator"]
+- ["Ps30RangeReplaceableCollectionType", "Index"]
+- !private ["Ps30RangeReplaceableCollectionType", "SubSequence"]
+- ["Ps30RangeReplaceableCollectionType", "_Element"]
+- !private ["Ps30RangeReplaceableCollectionType", "append"]
+- !private ["Ps30RangeReplaceableCollectionType", "count"]
+- !private ["Ps30RangeReplaceableCollectionType", "init"]
+- !private ["Ps30RangeReplaceableCollectionType", "removeAtIndex"]
+- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
+- !private ["Ps30RangeReplaceableCollectionType", "suffix"]
+- ["Ps12SequenceType", "Element"]
+- ["Ps12SequenceType", "Generator"]
+- ["Ps12SequenceType", "Index"]
+- !private ["Ps12SequenceType", "SubSequence"]
+- ["Ps12SequenceType", "_Element"]
+- !private ["Ps12SequenceType", "append"]
+- !private ["Ps12SequenceType", "count"]
+- ["Ps12SequenceType", "init"]
+- !private ["Ps12SequenceType", "removeAtIndex"]
+- !private ["Ps12SequenceType", "subscript"]
+- !private ["Ps12SequenceType", "suffix"]
+- !private ["Vs3Set", "Generator"]
+- ["Vs3Set", "init"]
+- !private ["Vs12SetGenerator", "Element"]
+- ["Ps17SignedIntegerType", "Distance"]
+- ["Ps17SignedIntegerType", "IntegerLiteralType"]
+- ["Ps16SignedNumberType", "Distance"]
+- ["Ps16SignedNumberType", "IntegerLiteralType"]
+- !private ["Vs5Slice", "Generator"]
+- !private ["Vs5Slice", "Index"]
+- !private ["Vs5Slice", "SubSequence"]
+- !private ["Vs5Slice", "_Element"]
+- !private ["Vs5Slice", "deinit"]
+- !private ["Ps10Streamable", "characters"]
+- !private ["Ps10Streamable", "init"]
+- !private ["Ps10Streamable", "lowercaseString"]
+- ["Ps10Strideable", "Distance"]
+- ["Ps10Strideable", "IntegerLiteralType"]
+- !private ["SS", "characters"]
+- !private ["SS", "init"]
+- !private ["SS", "lowercaseString"]
+- !private ["Ps30StringInterpolationConvertible", "characters"]
+- !private ["Ps30StringInterpolationConvertible", "init"]
+- !private ["Ps30StringInterpolationConvertible", "lowercaseString"]
+- !private ["Ps24StringLiteralConvertible", "characters"]
+- !private ["Ps24StringLiteralConvertible", "init"]
+- !private ["Ps24StringLiteralConvertible", "lowercaseString"]
+- !private ["C38package_name_here_and_keep_quote_marks4Trie", "Array"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "Bool"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "Int"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "Node"]
+- !private ["C38package_name_here_and_keep_quote_marks4Trie", "Queue"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "Set"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "String"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "Trie"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "contains"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "count"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "deinit"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "find"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "findPrefix"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "getWords"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "init"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "insert"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "isEmpty"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "isPrefix"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "merge"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "printTrie"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "remove"]
+- ["C38package_name_here_and_keep_quote_marks4Trie", "removeAll"]
+- !private ["C38package_name_here_and_keep_quote_marks4Trie", "root"]
+- !private ["C38package_name_here_and_keep_quote_marks4Trie", "wordCount"]
+- !private ["C38package_name_here_and_keep_quote_marks4Trie", "wordList"]
+- !private ["Ps31UnicodeScalarLiteralConvertible", "characters"]
+- !private ["Ps31UnicodeScalarLiteralConvertible", "init"]
+- !private ["Ps31UnicodeScalarLiteralConvertible", "lowercaseString"]
+- ["Ps10_ArrayType", "Element"]
+- ["Ps10_ArrayType", "Generator"]
+- ["Ps10_ArrayType", "Index"]
+- !private ["Ps10_ArrayType", "SubSequence"]
+- ["Ps10_ArrayType", "_Element"]
+- !private ["Ps10_ArrayType", "append"]
+- !private ["Ps10_ArrayType", "init"]
+- !private ["Ps10_ArrayType", "removeAtIndex"]
+- !private ["Ps10_ArrayType", "subscript"]
+- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
+- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "characters"]
+- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "init"]
+- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
+- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
+- !private ["Ps32_BuiltinStringLiteralConvertible", "characters"]
+- !private ["Ps32_BuiltinStringLiteralConvertible", "init"]
+- !private ["Ps32_BuiltinStringLiteralConvertible", "lowercaseString"]
+- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "characters"]
+- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "init"]
+- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "lowercaseString"]
+- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "characters"]
+- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "init"]
+- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "lowercaseString"]
+- ["Ps24_DestructorSafeContainer", "Element"]
+- ["Ps24_DestructorSafeContainer", "Generator"]
+- ["Ps24_DestructorSafeContainer", "Index"]
+- !private ["Ps24_DestructorSafeContainer", "SubSequence"]
+- ["Ps24_DestructorSafeContainer", "_Element"]
+- !private ["Ps24_DestructorSafeContainer", "append"]
+- !private ["Ps24_DestructorSafeContainer", "init"]
+- !private ["Ps24_DestructorSafeContainer", "removeAtIndex"]
+- !private ["Ps24_DestructorSafeContainer", "subscript"]
+- ["Ps14_Incrementable", "Distance"]
+- ["Ps14_Incrementable", "IntegerLiteralType"]
+- !private ["Ps14_Incrementable", "_DisabledRangeIndex"]
+- ["Ps22_IntegerArithmeticType", "Distance"]
+- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
+- ["Ps12_IntegerType", "Distance"]
+- ["Ps12_IntegerType", "IntegerLiteralType"]
+- !private ["Vs26_OptionalNilComparisonType", "deinit"]
+- ["Ps22_RandomAccessAmbiguity", "Distance"]
+- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Distance"]
+- ["Ps12_Reflectable", "Element"]
+- ["Ps12_Reflectable", "Generator"]
+- ["Ps12_Reflectable", "Index"]
+- ["Ps12_Reflectable", "IntegerLiteralType"]
+- ["Ps12_Reflectable", "Some"]
+- !private ["Ps12_Reflectable", "SubSequence"]
+- ["Ps12_Reflectable", "_Element"]
+- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
+- !private ["Ps12_Reflectable", "append"]
+- !private ["Ps12_Reflectable", "characters"]
+- !private ["Ps12_Reflectable", "count"]
+- ["Ps12_Reflectable", "init"]
+- !private ["Ps12_Reflectable", "lowercaseString"]
+- !private ["Ps12_Reflectable", "removeAtIndex"]
+- !private ["Ps12_Reflectable", "subscript"]
+- ["Ps18_SignedIntegerType", "Distance"]
+- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
+depends-nominal:
+- !private "Vs12AnyGenerator"
+- "Ps9AnyObject"
+- !private "Vs11AnySequence"
+- "Sa"
+- "Ps23ArrayLiteralConvertible"
+- !private "Vs10ArraySlice"
+- "Ps22BidirectionalIndexType"
+- "Ps21BitwiseOperationsType"
+- !private "Sb"
+- !private "Ps25BooleanLiteralConvertible"
+- !private "Ps11BooleanType"
+- "Ps11CVarArgType"
+- !private "VSS13CharacterView"
+- "Ps14CollectionType"
+- "Ps10Comparable"
+- "Ps28CustomDebugStringConvertible"
+- "Ps23CustomStringConvertible"
+- !private "Vs10Dictionary"
+- !private "Vs19DictionaryGenerator"
+- !private "Vs15DictionaryIndex"
+- !private "Ps28DictionaryLiteralConvertible"
+- "Ps9Equatable"
+- !private "Ps41ExtendedGraphemeClusterLiteralConvertible"
+- "Ps16ForwardIndexType"
+- "Ps13GeneratorType"
+- "Ps8Hashable"
+- !private "VVSS13CharacterView5Index"
+- "Ps9Indexable"
+- "Vs17IndexingGenerator"
+- "Si"
+- "Ps21IntegerArithmeticType"
+- "Ps25IntegerLiteralConvertible"
+- "Ps11IntegerType"
+- "Ps14MirrorPathType"
+- "Ps21MutableCollectionType"
+- "Ps16MutableIndexable"
+- "Ps16MutableSliceable"
+- "Ps21NilLiteralConvertible"
+- "C38package_name_here_and_keep_quote_marks4Node"
+- "Sq"
+- !private "Ps16OutputStreamType"
+- !private "V38package_name_here_and_keep_quote_marks5Queue"
+- "Ps21RandomAccessIndexType"
+- "Ps30RangeReplaceableCollectionType"
+- "Ps12SequenceType"
+- "Vs3Set"
+- !private "Vs12SetGenerator"
+- "Ps17SignedIntegerType"
+- "Ps16SignedNumberType"
+- !private "Vs5Slice"
+- !private "Ps10Streamable"
+- "Ps10Strideable"
+- !private "SS"
+- !private "Ps30StringInterpolationConvertible"
+- !private "Ps24StringLiteralConvertible"
+- "C38package_name_here_and_keep_quote_marks4Trie"
+- !private "Ps31UnicodeScalarLiteralConvertible"
+- "Ps10_ArrayType"
+- !private "Ps33_BuiltinBooleanLiteralConvertible"
+- !private "Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible"
+- "Ps33_BuiltinIntegerLiteralConvertible"
+- !private "Ps32_BuiltinStringLiteralConvertible"
+- !private "Ps37_BuiltinUTF16StringLiteralConvertible"
+- !private "Ps39_BuiltinUnicodeScalarLiteralConvertible"
+- "Ps24_DestructorSafeContainer"
+- "Ps14_Incrementable"
+- "Ps22_IntegerArithmeticType"
+- "Ps12_IntegerType"
+- !private "Vs26_OptionalNilComparisonType"
+- "Ps22_RandomAccessAmbiguity"
+- "Ps12_Reflectable"
+- "Ps18_SignedIntegerType"
+depends-dynamic-lookup:
+depends-external:
+- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
+- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
+- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
+interface-hash: "f003b1876d32aa37e370054fb3e811bb"
diff --git a/Trie/Package.swift b/Trie/Package.swift
new file mode 100644
index 000000000..fc323a1ec
--- /dev/null
+++ b/Trie/Package.swift
@@ -0,0 +1,6 @@
+import PackageDescription
+
+let package = Package(
+    name: "Trie",
+    targets: []
+)
diff --git a/Trie/Package.swift~ b/Trie/Package.swift~
new file mode 100644
index 000000000..c9e5942b1
--- /dev/null
+++ b/Trie/Package.swift~
@@ -0,0 +1,5 @@
+import PackageDescription
+
+let package = Package(
+    name: "package_name_here_and_keep_quote_marks"
+)
diff --git a/Trie/sources/Queue.swift b/Trie/sources/Queue.swift
new file mode 100644
index 000000000..efc573442
--- /dev/null
+++ b/Trie/sources/Queue.swift
@@ -0,0 +1,47 @@
+/*
+  First-in first-out queue (FIFO)
+
+  New elements are added to the end of the queue. Dequeuing pulls elements from
+  the front of the queue.
+
+  Enqueuing and dequeuing are O(1) operations.
+*/
+public struct Queue<T> {
+  private var array = [T?]()
+  private var head = 0
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
+
+    let percentage = Double(head)/Double(array.count)
+    if array.count > 50 && percentage > 0.25 {
+      array.removeFirst(head)
+      head = 0
+    }
+    
+    return element
+  }
+  
+  public func peek() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
+  }
+}
diff --git a/Trie/sources/main.swift b/Trie/sources/main.swift
new file mode 100644
index 000000000..e88bbc713
--- /dev/null
+++ b/Trie/sources/main.swift
@@ -0,0 +1,34 @@
+
+print("tests")
+
+
+var T: Trie = Trie()
+T.insert("Hello")
+T.insert("Hi")
+T.insert("Hey")
+T.insert("Hallo")
+T.insert("Henry")
+var U: Trie = Trie(wordList: Set(["Hey", "HO", "hello", "yolo"]))
+var V: Trie = T.merge(U)
+//T.printTrie()
+//U.printTrie()
+//V.printTrie()
+print(V.getWords())
+V.removeAll()
+//V.printTrie()
+/*T.insert("Hello")
+T.insert("Hey")
+T.insert("YOLO")
+T.insert("Him")
+assert(T.count() == 4, "Count function failed")
+assert(T.contains("Hey") == true)
+assert(T.contains("Hello") == true)
+print("trying remove")
+T.remove("Him")
+assert(T.count() == 3)
+assert(T.contains("Him") == false, "Test failed")
+assert(T.wordList.count == 3)*/
+
+//T.printTrie()
+//print(T.find(""))
+//print(T.findPrefix("H"))
diff --git a/Trie/trie.swift b/Trie/sources/trie.swift
similarity index 85%
rename from Trie/trie.swift
rename to Trie/sources/trie.swift
index 341f4c708..bf1b44156 100644
--- a/Trie/trie.swift
+++ b/Trie/sources/trie.swift
@@ -233,10 +233,12 @@ public class Trie {
 
   func findPrefix(p: String) -> [String] {
 
+    var q: Queue = Queue<String>()
+    return []
   }
 
 
-  func removeAll() -> Void {
+  func removeAll()  {
     for word in wordList {
       self.remove(word)
     }
@@ -249,43 +251,3 @@ public class Trie {
   }
 
 }
-
-print("tests")
-
-/*var x: Node = Node(c: "c")
-print(x.char())
-print(x.isValidWord())
-x.isWord()
-print(x.isValidWord())*/
-
-
-var T: Trie = Trie()
-T.insert("Hello")
-T.insert("Hi")
-T.insert("Hey")
-T.insert("Hallo")
-T.insert("Henry")
-var U: Trie = Trie(wordList: Set(["Hey", "HO", "hello", "yolo"]))
-var V: Trie = T.merge(U)
-//T.printTrie()
-//U.printTrie()
-//V.printTrie()
-print(V.getWords())
-V.removeAll()
-//V.printTrie()
-/*T.insert("Hello")
-T.insert("Hey")
-T.insert("YOLO")
-T.insert("Him")
-assert(T.count() == 4, "Count function failed")
-assert(T.contains("Hey") == true)
-assert(T.contains("Hello") == true)
-print("trying remove")
-T.remove("Him")
-assert(T.count() == 3)
-assert(T.contains("Him") == false, "Test failed")
-assert(T.wordList.count == 3)*/
-
-//T.printTrie()
-//print(T.find(""))
-//print(T.findPrefix("H"))

From 3d0bb6de0aa0bf87b933680407881d511cc9cbea Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Tue, 3 May 2016 16:12:48 -0400
Subject: [PATCH 0315/1679] Finally got findPrefix() workinggit add .git add .!

---
 Trie/.build/debug/Trie                        | Bin 95508 -> 103286 bytes
 Trie/.build/debug/Trie.o/Trie/main.swiftdeps  |  15 +++--
 .../.build/debug/Trie.o/Trie/master.swiftdeps |   6 +-
 Trie/.build/debug/Trie.o/Trie/trie.swiftdeps  |  62 +++++++++++++-----
 .../Trie.o/Trie/trie~partial.swiftmodule      | Bin 53928 -> 66240 bytes
 Trie/.build/debug/Trie.o/build.db             | Bin 15360 -> 15360 bytes
 Trie/.build/debug/Trie.o/sources/main.swift.o | Bin 13864 -> 14800 bytes
 Trie/.build/debug/Trie.o/sources/trie.swift.o | Bin 94800 -> 107904 bytes
 Trie/.build/debug/Trie.swiftmodule            | Bin 20724 -> 21236 bytes
 Trie/sources/main.swift                       |   3 +-
 Trie/sources/trie.swift                       |  38 ++++++++++-
 11 files changed, 94 insertions(+), 30 deletions(-)

diff --git a/Trie/.build/debug/Trie b/Trie/.build/debug/Trie
index 3635f7c44a43c8b6f0aeab91e0d200109e211888..188a7c4d0c444c157c71e7da34a6ba76d6069ca5 100755
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diff --git a/Trie/.build/debug/Trie.o/Trie/main.swiftdeps b/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
index 923f0f821..d126051a2 100644
--- a/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
+++ b/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
@@ -6,15 +6,17 @@ provides-top-level:
 provides-nominal:
 provides-member:
 depends-top-level:
-- "StringLiteralType"
-- "Set"
-- "Array"
-- "print"
 - "Trie"
+- "U"
+- "Array"
 - "V"
+- "print"
+- "StringLiteralType"
 - "T"
-- "U"
+- "Set"
+- "UnicodeScalarType"
 depends-member:
+- ["Ps9AnyObject", "findPrefix"]
 - ["Ps9AnyObject", "getWords"]
 - ["Ps9AnyObject", "init"]
 - ["Ps9AnyObject", "insert"]
@@ -110,6 +112,7 @@ depends-member:
 - ["Ps16SignedNumberType", "IntegerLiteralType"]
 - ["Ps10Strideable", "Distance"]
 - ["Ps10Strideable", "IntegerLiteralType"]
+- ["C4Trie4Trie", "findPrefix"]
 - ["C4Trie4Trie", "getWords"]
 - ["C4Trie4Trie", "init"]
 - ["C4Trie4Trie", "insert"]
@@ -199,4 +202,4 @@ depends-external:
 - "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
 - "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
 - "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "80fed5d587327a0a97180685d884fa09"
+interface-hash: "57319b836b718d38040ac7809f4446f7"
diff --git a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
index 5539f705b..3f65c9e2b 100644
--- a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
+++ b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
@@ -1,7 +1,7 @@
 version: "Swift version 2.2-dev (LLVM 3ebdbb2c7e, Clang f66c5bb67b, Swift 0ddf238ad7)"
 options: "1cfa30eacd63a1262ef0618da5cf7605"
-build_time: [515616404, 830067000]
+build_time: [515621198, 271577000]
 inputs:
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift": [515616359, 0]
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": [515616400, 0]
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift": [515620938, 0]
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": [515621195, 0]
   "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": [512710161, 0]
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
index 35e802978..6f65d2492 100644
--- a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
+++ b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
@@ -9,29 +9,30 @@ provides-member:
 - ["C4Trie4Node", ""]
 - ["C4Trie4Trie", ""]
 depends-top-level:
-- "Int"
+- !private "StringLiteralType"
 - !private "UnicodeScalarType"
-- !private "Array"
-- "Node"
-- "Void"
-- !private "=="
-- "IntegerLiteralType"
-- !private "+="
-- "Trie"
-- "FloatLiteralType"
-- "Set"
-- !private "BooleanLiteralType"
+- !private "&&"
 - !private "-"
+- "String"
+- !private "BooleanLiteralType"
 - "Bool"
-- !private "print"
 - !private "-="
-- "String"
-- !private "&&"
+- "Trie"
+- "FloatLiteralType"
+- "Int"
+- !private "+"
+- "IntegerLiteralType"
 - !private "!"
+- !private "+="
+- !private "print"
+- !private "!=="
+- "Set"
+- "Node"
+- "Void"
+- !private "=="
 - !private "Queue"
-- !private "+"
-- !private "StringLiteralType"
 - !private ">"
+- !private "Array"
 depends-member:
 - !private ["Vs12AnyGenerator", "Element"]
 - !private ["Ps9AnyObject", "Array"]
@@ -53,6 +54,7 @@ depends-member:
 - !private ["Ps9AnyObject", "insert"]
 - !private ["Ps9AnyObject", "isAWord"]
 - !private ["Ps9AnyObject", "isNotWord"]
+- !private ["Ps9AnyObject", "isPrefix"]
 - !private ["Ps9AnyObject", "isRoot"]
 - !private ["Ps9AnyObject", "isValidWord"]
 - !private ["Ps9AnyObject", "isWord"]
@@ -64,6 +66,7 @@ depends-member:
 - !private ["Ps9AnyObject", "root"]
 - !private ["Ps9AnyObject", "setParent"]
 - !private ["Ps9AnyObject", "update"]
+- !private ["Ps9AnyObject", "visited"]
 - !private ["Ps9AnyObject", "wordCount"]
 - !private ["Ps9AnyObject", "wordList"]
 - ["Ps9AnyObject", ""]
@@ -92,6 +95,7 @@ depends-member:
 - !private ["Vs10ArraySlice", "Index"]
 - !private ["Ps22BidirectionalIndexType", "Distance"]
 - !private ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
+- !private ["Ps22BidirectionalIndexType", "_DisabledRangeIndex"]
 - !private ["Ps21BitwiseOperationsType", "Distance"]
 - !private ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
 - !private ["Sb", "_getBuiltinLogicValue"]
@@ -105,6 +109,7 @@ depends-member:
 - !private ["VSS13CharacterView", "_Element"]
 - !private ["VSS13CharacterView", "count"]
 - !private ["VSS13CharacterView", "deinit"]
+- !private ["VSS13CharacterView", "reverse"]
 - !private ["VSS13CharacterView", "suffix"]
 - !private ["Ps14CollectionType", "Element"]
 - !private ["Ps14CollectionType", "Generator"]
@@ -115,6 +120,7 @@ depends-member:
 - !private ["Ps14CollectionType", "count"]
 - !private ["Ps14CollectionType", "init"]
 - !private ["Ps14CollectionType", "removeAtIndex"]
+- !private ["Ps14CollectionType", "reverse"]
 - !private ["Ps14CollectionType", "subscript"]
 - !private ["Ps14CollectionType", "suffix"]
 - !private ["Ps10Comparable", "Distance"]
@@ -190,6 +196,8 @@ depends-member:
 - !private ["Ps8Hashable", "init"]
 - !private ["Ps8Hashable", "lowercaseString"]
 - !private ["VVSS13CharacterView5Index", "Distance"]
+- !private ["VVSS13CharacterView5Index", "_DisabledRangeIndex"]
+- !private ["VVSS13CharacterView5Index", "deinit"]
 - !private ["Ps9Indexable", "Element"]
 - !private ["Ps9Indexable", "Generator"]
 - !private ["Ps9Indexable", "Index"]
@@ -199,6 +207,7 @@ depends-member:
 - !private ["Ps9Indexable", "count"]
 - !private ["Ps9Indexable", "init"]
 - !private ["Ps9Indexable", "removeAtIndex"]
+- !private ["Ps9Indexable", "reverse"]
 - !private ["Ps9Indexable", "subscript"]
 - !private ["Ps9Indexable", "suffix"]
 - !private ["Vs17IndexingGenerator", "Element"]
@@ -268,11 +277,14 @@ depends-member:
 - ["C4Trie4Node", "printNode"]
 - ["C4Trie4Node", "setParent"]
 - ["C4Trie4Node", "update"]
+- !private ["C4Trie4Node", "visited"]
 - ["Sq", "Some"]
 - !private ["Sq", "deinit"]
 - !private ["Ps16OutputStreamType", "characters"]
 - !private ["Ps16OutputStreamType", "init"]
 - !private ["Ps16OutputStreamType", "lowercaseString"]
+- !private ["V4Trie5Queue", "dequeue"]
+- !private ["V4Trie5Queue", "enqueue"]
 - !private ["V4Trie5Queue", "init"]
 - !private ["Ps21RandomAccessIndexType", "Distance"]
 - !private ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
@@ -285,8 +297,15 @@ depends-member:
 - !private ["Ps30RangeReplaceableCollectionType", "count"]
 - !private ["Ps30RangeReplaceableCollectionType", "init"]
 - !private ["Ps30RangeReplaceableCollectionType", "removeAtIndex"]
+- !private ["Ps30RangeReplaceableCollectionType", "reverse"]
 - !private ["Ps30RangeReplaceableCollectionType", "subscript"]
 - !private ["Ps30RangeReplaceableCollectionType", "suffix"]
+- !private ["Vs17ReverseCollection", "Generator"]
+- !private ["Vs17ReverseCollection", "Index"]
+- !private ["Vs17ReverseCollection", "_Element"]
+- !private ["Vs17ReverseCollection", "deinit"]
+- !private ["Vs12ReverseIndex", "Distance"]
+- !private ["Ps16ReverseIndexType", "Distance"]
 - !private ["Ps12SequenceType", "Element"]
 - !private ["Ps12SequenceType", "Generator"]
 - !private ["Ps12SequenceType", "Index"]
@@ -296,6 +315,7 @@ depends-member:
 - !private ["Ps12SequenceType", "count"]
 - !private ["Ps12SequenceType", "init"]
 - !private ["Ps12SequenceType", "removeAtIndex"]
+- !private ["Ps12SequenceType", "reverse"]
 - !private ["Ps12SequenceType", "subscript"]
 - !private ["Ps12SequenceType", "suffix"]
 - !private ["Vs3Set", "Generator"]
@@ -402,6 +422,7 @@ depends-member:
 - !private ["Ps12_Reflectable", "IntegerLiteralType"]
 - ["Ps12_Reflectable", "Some"]
 - !private ["Ps12_Reflectable", "SubSequence"]
+- !private ["Ps12_Reflectable", "_DisabledRangeIndex"]
 - !private ["Ps12_Reflectable", "_Element"]
 - !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
 - !private ["Ps12_Reflectable", "append"]
@@ -411,6 +432,9 @@ depends-member:
 - !private ["Ps12_Reflectable", "lowercaseString"]
 - !private ["Ps12_Reflectable", "removeAtIndex"]
 - !private ["Ps12_Reflectable", "subscript"]
+- !private ["Ps22_ReverseCollectionType", "Generator"]
+- !private ["Ps22_ReverseCollectionType", "Index"]
+- !private ["Ps22_ReverseCollectionType", "_Element"]
 - !private ["Ps18_SignedIntegerType", "Distance"]
 - !private ["Ps18_SignedIntegerType", "IntegerLiteralType"]
 depends-nominal:
@@ -458,6 +482,9 @@ depends-nominal:
 - !private "V4Trie5Queue"
 - !private "Ps21RandomAccessIndexType"
 - !private "Ps30RangeReplaceableCollectionType"
+- !private "Vs17ReverseCollection"
+- !private "Vs12ReverseIndex"
+- !private "Ps16ReverseIndexType"
 - !private "Ps12SequenceType"
 - !private "Vs3Set"
 - !private "Vs12SetGenerator"
@@ -485,6 +512,7 @@ depends-nominal:
 - !private "Vs26_OptionalNilComparisonType"
 - !private "Ps22_RandomAccessAmbiguity"
 - "Ps12_Reflectable"
+- !private "Ps22_ReverseCollectionType"
 - !private "Ps18_SignedIntegerType"
 depends-dynamic-lookup:
 depends-external:
@@ -501,4 +529,4 @@ depends-external:
 - "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
 - "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
 - "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "fd9fdb3a4bd3dfc789eaf1430eb72c67"
+interface-hash: "eefc37d55a335afd501967035d9090a5"
diff --git a/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule b/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule
index adcffc2d393f212f2788c24b04011d6603038431..f9e33b421a684ed26ac2066848785167312f0845 100644
GIT binary patch
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index 0028fe224f5e646cb2855a04c20247cf4e075b37..1b9a387ff0a346fbfbed4bd7a4a3a64c8bb116ee 100644
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diff --git a/Trie/.build/debug/Trie.o/sources/main.swift.o b/Trie/.build/debug/Trie.o/sources/main.swift.o
index c44e7e0254fa8c98846d9e01de765def37b2da8c..625ca7c5217d193b2ef840d5fe9a49e9ed441651 100644
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diff --git a/Trie/.build/debug/Trie.o/sources/trie.swift.o b/Trie/.build/debug/Trie.o/sources/trie.swift.o
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diff --git a/Trie/.build/debug/Trie.swiftmodule b/Trie/.build/debug/Trie.swiftmodule
index 9c1463f850e9a3df6dac26495e6a4be9822ca2dd..e387c6b3e3b7fafc2d6e5435918866b17cfd6302 100644
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diff --git a/Trie/sources/main.swift b/Trie/sources/main.swift
index e88bbc713..8f95afdf7 100644
--- a/Trie/sources/main.swift
+++ b/Trie/sources/main.swift
@@ -8,6 +8,7 @@ T.insert("Hi")
 T.insert("Hey")
 T.insert("Hallo")
 T.insert("Henry")
+T.insert("YELLO")
 var U: Trie = Trie(wordList: Set(["Hey", "HO", "hello", "yolo"]))
 var V: Trie = T.merge(U)
 //T.printTrie()
@@ -31,4 +32,4 @@ assert(T.wordList.count == 3)*/
 
 //T.printTrie()
 //print(T.find(""))
-//print(T.findPrefix("H"))
+print(T.findPrefix("H"))
diff --git a/Trie/sources/trie.swift b/Trie/sources/trie.swift
index bf1b44156..9088d2b70 100644
--- a/Trie/sources/trie.swift
+++ b/Trie/sources/trie.swift
@@ -3,13 +3,14 @@ public class Node {
   private var parent: Node?
   private var children: [String:Node]
   private var isAWord: Bool
-
+  private var visited: Bool  //only for findPrefix
 
   init(c: String?, p: Node?){
     self.character = c
     self.children = [String:Node]()
     self.isAWord = false
     self.parent = p
+    self.visited = false
     }
 
   //Easier getter function, probably will make it more swift like
@@ -233,8 +234,39 @@ public class Trie {
 
   func findPrefix(p: String) -> [String] {
 
-    var q: Queue = Queue<String>()
-    return []
+    if !self.isPrefix(p).found {
+      return []
+    }
+
+    var q: Queue = Queue<Node>()
+    var n: Node = self.isPrefix(p).node!
+
+    var wordsWithPrefix: [String] = []
+    var word = p
+    var tmp = ""
+    q.enqueue(n)
+
+    while let current = q.dequeue() {
+      for (char, child) in current.getChildren() {
+        if(!child.visited) {
+          q.enqueue(child)
+          child.visited = true
+          if(child.isValidWord()) {
+            var currentNode = child
+            while currentNode !== n {
+              tmp += currentNode.char()
+              currentNode = currentNode.getParent()
+            }
+            tmp = String(tmp.characters.reverse())
+            wordsWithPrefix.append(word + tmp)
+          }
+        }
+        tmp = ""
+      }
+    }
+
+
+    return wordsWithPrefix
   }
 
 

From 002c70b07ec33e17128277be09b7a20481adfc4e Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Tue, 3 May 2016 16:18:03 -0400
Subject: [PATCH 0316/1679] Fixed commit message....

---
 Trie/sources/trie.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Trie/sources/trie.swift b/Trie/sources/trie.swift
index 9088d2b70..092b497dc 100644
--- a/Trie/sources/trie.swift
+++ b/Trie/sources/trie.swift
@@ -259,9 +259,9 @@ public class Trie {
             }
             tmp = String(tmp.characters.reverse())
             wordsWithPrefix.append(word + tmp)
+            tmp = ""
           }
         }
-        tmp = ""
       }
     }
 

From 6f886298c9fd1cab41776684a8e477d0d72d2d46 Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Tue, 3 May 2016 17:23:49 -0400
Subject: [PATCH 0317/1679] fixed insertion and rotations

---
 Red Black Trees/RBTree.swift  | 145 +++++++++++++++++++++++++----
 Red Black Trees/RBTree.swift~ | 167 ++++++++++++++++++++++++++++++++++
 2 files changed, 294 insertions(+), 18 deletions(-)
 create mode 100644 Red Black Trees/RBTree.swift~

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index 33c165b4e..cd43b8255 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -1,4 +1,3 @@
-
 public class  RBTNode{
   private(set) public var color: Bool
   private(set) public var left: RBTNode!
@@ -14,17 +13,37 @@ public class  RBTNode{
   }
   init(rootData: Int){
     self.data = rootData
-    self.color = true
+    self.color = true //0is black 1 is red
     self.left = nil
     self.right = nil
     self.parent = nil
   }
+  public func grandparent()->RBTNode?{
+    if(self.parent === nil || self.parent.parent === nil){
+      return nil
+    }
+    else{
+      return self.parent.parent
+    }
+  }
+  public func sibling()->RBTNode?{
+      if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
+        return nil
+      }
+      if(self === self.parent!.left!){
+        return self.parent!.right!
+      }
+      else{
+        return self.parent!.left!
+      }
+  }
 }
 public class RBTree {
 
     private(set) public var root: RBTNode?
     init(rootData: Int) {
       root = RBTNode(rootData: rootData)
+      root!.color = false
     }
     init(){
       root = nil
@@ -47,7 +66,6 @@ public class RBTree {
     }
     private func inOrder(root: RBTNode?){
       if(root == nil){
-        print("nil")
         return
       }
       inOrder(root!.left)
@@ -74,7 +92,7 @@ public class RBTree {
   }
   private func rightRotate(x: RBTNode) {
     let newRoot = x.left
-    x.left = newRoot.right 
+    x.left = newRoot.right
     if newRoot.right !== nil {
       newRoot.right.parent = x
     }
@@ -90,14 +108,94 @@ public class RBTree {
     x.parent = newRoot
 }
 
+public func insertFixup(value: Int){
+  let inserted = find(value)
+
+  if(inserted == nil){
+    print("INSERTEDNILLLLLLLL")
+  }
+  print("inserted: ")
+  print(inserted!.data)
+  insertCase1(inserted)
+}
+public func insertCase1(inserted: RBTNode?){
+  let myroot = self.root!
+  if myroot === inserted!{
+    self.root!.color = false
+    print("ITS THE ROOT")
+    print("insert case 1: The root was nil and we inserted a black node at root")
+  }
+  insertCase2(inserted!)
+}
+public func insertCase2(inserted: RBTNode?){
+  if inserted!.parent!.color == false{
+      print("Insert case 2: parent is black so nothing to change")
+      return
+  }
+  insertCase3(inserted!)
+}
+public func insertCase3(inserted: RBTNode?){
+  if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
+    print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
+    inserted!.parent!.color = false
+    inserted!.parent!.sibling()!.color = false
+    let g = inserted!.grandparent
+    g()!.color = true
+    if(g()!.parent == nil){
+      g()!.color = false
+    }
+  }
+  insertCase4(inserted)
+}
+//THIS ONE MAY BE BROKEN!?!?!?!?
+public func insertCase4(var inserted: RBTNode?){
+  if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
+    print("case 4")
+    rightRotate(inserted!.parent)
+    inserted! = inserted!.left
+  }
+  else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
+     print("case 4")
+    leftRotate(inserted!.parent)
+    inserted! = inserted!.right
+  }
+  insertCase5(inserted)
+}
+public func insertCase5(inserted: RBTNode?){
+  if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
+      if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
+        print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
+        inserted!.parent.color = false
+        inserted!.grandparent()?.color = true
+        if(inserted! === inserted!.parent!.left){
+          print("its on the left")
+          rightRotate(inserted!.grandparent()!)
+        }
+      }
+      else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
+        print("insert case 5: RIGHT RIGHT")
+        inserted!.parent.color = false
+        inserted!.grandparent()?.color = true
+
+          print("Its on the right")
+          leftRotate(inserted!.grandparent()!)
+
+      }
+  }
+
+  print("weve reached the end boys")
+}
 
-    private func insertFixup(){}
     public func insert(value: Int) {
       insert(value, parent: root!)
-      //insertFixUp()
+      insertFixup(value)
     }
     private func insert(value: Int, parent: RBTNode) {
-        if value < parent.data {
+        if self.root == nil{
+          self.root = RBTNode(rootData: value)
+          return
+        }
+        else if value < parent.data {
           if let left = parent.left {
             insert(value, parent: left)
           } else {
@@ -116,6 +214,7 @@ public class RBTree {
       public func find(data: Int)->RBTNode?{
         return find(root!,data: data)
       }
+
       private func find(root: RBTNode, data: Int)->RBTNode?{
           if data == root.data{
             return root
@@ -140,19 +239,28 @@ tree.insert(9)
 tree.insert(6)
 tree.insert(5)
 tree.insert(4)
-tree.insert(3)
-tree.inOrder()
-print("_________________________")
-let x = tree.root!
-print("root: \(tree.root!.data)")
-tree.rightRotate(x)
-print("root: \(tree.root!.data)")
+tree.insert(40)
+tree.insert(400)
+tree.insert(430)
+
 tree.inOrder()
 
-let t = tree.find(234)
-if t == nil{
-  print("ASDASD")
-}
+//print("_________________________")
+//let x = tree.root!
+//print("sibling: \(tree.root!.left!.sibling()!.data)")
+//print("root: \(tree.root!.data)")
+//tree.rightRotate(x)
+//print("root: \(tree.root!.data)")
+//tree.inOrder()
+
+//let l = tree.root!.left!
+//let r = tree.root!.right!
+//print(l.data)
+//print(r.data)
+//if tree.root!.parent == nil{
+//  print("ASDASD")
+//}
+
 //how you access certain elements
 //let root = tree.root!.left!
 //if(root.parent === nil){
@@ -165,3 +273,4 @@ if t == nil{
 //print(tree.root!.data)
 //print(tree.root!.right!.data)
 //print(tree.root!.left!.data)
+
diff --git a/Red Black Trees/RBTree.swift~ b/Red Black Trees/RBTree.swift~
new file mode 100644
index 000000000..33c165b4e
--- /dev/null
+++ b/Red Black Trees/RBTree.swift~	
@@ -0,0 +1,167 @@
+
+public class  RBTNode{
+  private(set) public var color: Bool
+  private(set) public var left: RBTNode!
+  private(set) public var right: RBTNode!
+  private(set) public var parent: RBTNode!
+  private(set) public var data: Int
+  init(){
+    self.data = -1
+    self.color = true
+    self.left = nil
+    self.right = nil
+    self.parent = nil
+  }
+  init(rootData: Int){
+    self.data = rootData
+    self.color = true
+    self.left = nil
+    self.right = nil
+    self.parent = nil
+  }
+}
+public class RBTree {
+
+    private(set) public var root: RBTNode?
+    init(rootData: Int) {
+      root = RBTNode(rootData: rootData)
+    }
+    init(){
+      root = nil
+    }
+    public func depth()->Int{
+      let n = depth(root!)
+      return n
+    }
+    private func depth(rooty:RBTNode?)->Int{
+      if(rooty == nil){
+        return 0
+      }
+      else{
+        return 1+(max(depth(root!.left),depth(root!.right)))
+      }
+    }
+
+    public func inOrder(){
+      inOrder(root)
+    }
+    private func inOrder(root: RBTNode?){
+      if(root == nil){
+        print("nil")
+        return
+      }
+      inOrder(root!.left)
+      print("Data: \(root!.data) Color: \(root!.color)")
+      inOrder(root!.right)
+    }
+
+    private func leftRotate(x: RBTNode) {
+        let newRoot = x.right
+        x.right = newRoot.left
+          if (newRoot.left !== nil) {
+            newRoot.left.parent = x
+          }
+          newRoot.parent = x.parent
+          if(x.parent === nil) {
+            root = newRoot
+          } else if (x === x.parent.left) {
+            x.parent.left = newRoot
+          } else {
+            x.parent.right = newRoot
+          }
+          newRoot.left = x
+          x.parent = newRoot
+  }
+  private func rightRotate(x: RBTNode) {
+    let newRoot = x.left
+    x.left = newRoot.right 
+    if newRoot.right !== nil {
+      newRoot.right.parent = x
+    }
+    newRoot.parent = x.parent
+    if x.parent === nil {
+      root = newRoot
+    } else if x === x.parent.right {
+      x.parent.right = newRoot
+    } else {
+      x.parent.left = newRoot
+    }
+    newRoot.right = x
+    x.parent = newRoot
+}
+
+
+    private func insertFixup(){}
+    public func insert(value: Int) {
+      insert(value, parent: root!)
+      //insertFixUp()
+    }
+    private func insert(value: Int, parent: RBTNode) {
+        if value < parent.data {
+          if let left = parent.left {
+            insert(value, parent: left)
+          } else {
+            parent.left = RBTNode(rootData: value)
+            parent.left?.parent = parent
+          }
+        } else {
+          if let right = parent.right {
+            insert(value, parent: right)
+          } else {
+            parent.right = RBTNode(rootData: value)
+            parent.right?.parent = parent
+          }
+        }
+      }
+      public func find(data: Int)->RBTNode?{
+        return find(root!,data: data)
+      }
+      private func find(root: RBTNode, data: Int)->RBTNode?{
+          if data == root.data{
+            return root
+          }
+          if root.data != data && root.right == nil && root.left == nil {
+            return nil
+          }
+          else if data > root.data{
+            return find(root.right, data: data)
+          }
+          else if data < root.data{
+            return find(root.left, data: data)
+          }
+          else{
+            return nil
+          }
+      }
+}
+
+var tree = RBTree(rootData: 8)
+tree.insert(9)
+tree.insert(6)
+tree.insert(5)
+tree.insert(4)
+tree.insert(3)
+tree.inOrder()
+print("_________________________")
+let x = tree.root!
+print("root: \(tree.root!.data)")
+tree.rightRotate(x)
+print("root: \(tree.root!.data)")
+tree.inOrder()
+
+let t = tree.find(234)
+if t == nil{
+  print("ASDASD")
+}
+//how you access certain elements
+//let root = tree.root!.left!
+//if(root.parent === nil){
+//  print("niggs")
+//}
+//else{
+//  print(root.parent.data)
+//}
+
+//print(tree.root!.data)
+//print(tree.root!.right!.data)
+//print(tree.root!.left!.data)

From c6d34032b824957aa410f2279e25132afc396f7b Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Tue, 3 May 2016 17:36:10 -0400
Subject: [PATCH 0318/1679] Finalize ThreadedBinaryTree implementation

---
 Threaded Binary Tree/README.markdown          |  52 ++++++-
 Threaded Binary Tree/ThreadedBinaryTree.swift | 136 +++---------------
 .../ThreadedBinaryTreeTests.swift             |  89 ++++++++++++
 3 files changed, 151 insertions(+), 126 deletions(-)
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTreeTests.swift

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 155404b66..1b35f39e2 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -185,25 +185,56 @@ a function that executes on each node as they are visited.  This function can
 be anything you want, as long as it accepts `T` (the type of the values of the
 nodes of the tree) and has no return value.
 
+Let's walk through a forward traversal of a tree by hand to get a better idea
+of how a computer would do it.  For example, take this simple threaded tree:
+
+![Base](Images/Base.png)
+
+We start at the root of the tree, **9**.  Note that we don't `visit(9)` yet.
+From there we want to go to the `minimum()` node in the tree, which is **2** in
+this case.  We then `visit(2)` and see that it has a `rightThread`, and thus
+we immediately know what its `successor()` is.  We follow the thread to **5**,
+which does not have any leaving threads.  Therefore, after we `visit(5)`, we go
+to the `minimum()` node in its `right` subtree, which is **7**.  We then
+`visit(7)` and see that it has a `rightThread`, which we follow to get back to
+**9**.  *Now* we `visit(9)`, and after noticing that it has no `rightThread`,
+we go to the `minimum()` node in its `right` subtree, which is **12**.  This
+node has a `rightThread` that leads to `nil`, which signals that we have
+completed the traversal!  We visited the nodes in order **2, 5, 7, 9, 12**,
+which intuitively makes sense, as that is their natural increasing order.
+
+A backward traversal would be very similar, but you would replace `right`,
+`rightThread`, `minimum()`, and `successor()` with `left`, `leftThread`,
+`maximum()`, and `predecessor()`.
+
+
 
 ## Insertion and deletion
 
 The quick in-order traversal that a threaded binary trees gives us comes at a
 small cost.  Inserting/deleting nodes becomes more complicated, as we have to
-continuously manage the `leftThread` and `rightThread` variables.  It is best
-to explain this with an example.  Please note that this requires knowledge of
-binary search trees, so make sure you have
+continuously manage the `leftThread` and `rightThread` variables.  Rather than
+walking through some boring code, it is best to explain this with an example
+(although you can read through [the implementation](ThreadedBinaryTree.swift)
+if you want to know the finer details).  Please note that this requires
+knowledge of binary search trees, so make sure you have 
 [read this first](../Binary Search Tree/).
 
-Base:
+> Note: we do allow duplicate nodes in this implementation of a threaded binary
+> tree.  We break ties by defaulting insertion to the right.
+
+Let's start with the same tree that we used for the above traversal example:
 
 ![Base](Images/Base.png)
 
-Insert1:
+Suppose we `insert(10)` into this tree.  The resulting graph would look like
+this, with the changes highlighted in red:
 
 ![Insert1](Images/Insert1.png)
 
-Insert2:
+If you've done your homework and are familiar with binary search trees, the
+placement of the node should not surprise you.  What's new is how we maintain
+the threads between nodes.
 
 ![Insert2](Images/Insert2.png)
 
@@ -228,8 +259,15 @@ Remove4:
 ![Remove4](Images/Remove4.png)
 
 
+## Miscellaneous methods
+
+There are many other smaller operations that a threaded binary tree can do,
+such as `searching()` for a node in the tree, finding the `depth()` or
+`height()` of a node, etc.  You can check
+[the implementation](ThreadedBinaryTree.swift) for the full technical details.
+Many of these methods are inherent to binary search trees as well, so you can
+find [further documentation here](../Binary Search Tree/).
 
-### Still under construction.
 
 ## See also 
 
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
index c4fd2f4de..a046d4378 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.swift	
@@ -8,7 +8,7 @@
   Any nodes that lack either a left or right child instead keep track of their
   in-order predecessor and/or successor.
 
-  This tree allows duplicate elements.
+  This tree allows duplicate elements (we break ties by defaulting right).
 
   This tree does not automatically balance itself. To make sure it is balanced,
   you should insert new values in randomized order, not in sorted order.
@@ -18,8 +18,6 @@ public class ThreadedBinaryTree<T: Comparable> {
   private(set) public var parent: ThreadedBinaryTree?
   private(set) public var left: ThreadedBinaryTree?
   private(set) public var right: ThreadedBinaryTree?
-
-  //THREADED
   private(set) public var leftThread: ThreadedBinaryTree?
   private(set) public var rightThread: ThreadedBinaryTree?
 
@@ -92,9 +90,8 @@ extension ThreadedBinaryTree {
       } else {
         left = ThreadedBinaryTree(value: value)
         left?.parent = parent
-        //THREADED
-        left?.leftThread = leftThread
         left?.rightThread = parent
+        left?.leftThread = leftThread
         leftThread = nil
       }
     } else {
@@ -103,9 +100,8 @@ extension ThreadedBinaryTree {
       } else {
         right = ThreadedBinaryTree(value: value)
         right?.parent = parent
-        //THREADED
-        right?.rightThread = rightThread
         right?.leftThread = parent
+        right?.rightThread = rightThread
         rightThread = nil
       }
     }
@@ -124,7 +120,6 @@ extension ThreadedBinaryTree {
 
     Performance: runs in O(h) time, where h is the height of the tree.
   */
-  //THREADED
   public func remove(value: T) -> ThreadedBinaryTree? {
     return search(value)?.remove()
   }
@@ -138,7 +133,6 @@ extension ThreadedBinaryTree {
     if let left = left {
       if let right = right {
         replacement = removeNodeWithTwoChildren(left, right)
-        //THREADED
         replacement?.leftThread = leftThread
         replacement?.rightThread = rightThread
         left.maximum().rightThread = replacement
@@ -146,18 +140,15 @@ extension ThreadedBinaryTree {
       } else {
         // This node only has a left child. The left child replaces the node.
         replacement = left
-        //THREADED
         left.maximum().rightThread = rightThread
       }
     } else if let right = right {
       // This node only has a right child. The right child replaces the node.
       replacement = right
-      //THREADED
       right.minimum().leftThread = leftThread
     } else {
       // This node has no children. We just disconnect it from its parent.
       replacement = nil
-      //THREADED
       if isLeftChild {
         parent?.leftThread = leftThread
       } else {
@@ -171,7 +162,6 @@ extension ThreadedBinaryTree {
     parent = nil
     left = nil
     right = nil
-    //THREADED
     leftThread = nil
     rightThread = nil
 
@@ -312,7 +302,6 @@ extension ThreadedBinaryTree {
     if let left = left {
       return left.maximum()
     } else {
-      //THREADED
       return leftThread
     }
   }
@@ -324,7 +313,6 @@ extension ThreadedBinaryTree {
     if let right = right {
       return right.minimum()
     } else {
-      //THREADED
       return rightThread
     }
   }
@@ -333,7 +321,6 @@ extension ThreadedBinaryTree {
 // MARK: - Traversal
 
 extension ThreadedBinaryTree {
-  //THREADED
   public func traverseInOrderForward(@noescape visit: T -> Void) {
     var n: ThreadedBinaryTree
     n = minimum()
@@ -347,7 +334,6 @@ extension ThreadedBinaryTree {
     }
   }
 
-  //THREADED
   public func traverseInOrderBackward(@noescape visit: T -> Void) {
     var n: ThreadedBinaryTree
     n = maximum()
@@ -378,7 +364,6 @@ extension ThreadedBinaryTree {
   */
   public func map(@noescape formula: T -> T) -> [T] {
     var a = [T]()
-    //THREADED
     var n: ThreadedBinaryTree
     n = minimum()
     while true {
@@ -412,20 +397,17 @@ extension ThreadedBinaryTree {
     The first and last nodes in the in-order traversal are exempt from this,
     as the first has leftThread = nil, and the last has rightThread = nil.
   */
-  //THREADED
   public func isThreaded() -> Bool {
-    if self === minimum() {
-      if left != nil && leftThread != nil {
-        return false
-      }
-    } else if (left == nil && leftThread == nil) || (left != nil && leftThread != nil) {
+    if left == nil && leftThread == nil {
+      if self !== minimum() { return false }
+    }
+    if left != nil && leftThread != nil {
       return false
     }
-    if self === maximum() {
-      if right != nil && rightThread != nil {
-        return false
-      }
-    } else if (right == nil && rightThread == nil) || (right != nil && rightThread != nil) {
+    if right == nil && rightThread == nil {
+      if self !== maximum() { return false }
+    }
+    if right != nil && rightThread != nil {
       return false
     }
     let leftThreaded = left?.isThreaded() ?? true
@@ -456,19 +438,18 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     if let parent = parent {
       s += ", parent: \(parent.value)"
     }
-    if let left = left {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = right {
-      s += ", right = [" + right.debugDescription + "]"
-    }
-    //THREADED
     if let leftThread = leftThread {
       s += ", leftThread: \(leftThread.value)"
     }
     if let rightThread = rightThread {
       s += ", rightThread: \(rightThread.value)"
     }
+    if let left = left {
+      s += ", left = [" + left.debugDescription + "]"
+    }
+    if let right = right {
+      s += ", right = [" + right.debugDescription + "]"
+    }
     return s
   }
 
@@ -476,86 +457,3 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     return map { $0 }
   }
 }
-
-/*
-  TESTS
-  I don't have an Apple computer, so I can't make a Playground or any of that
-  fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree class.
-  It follows the examples in the README.
-*/
-
-// Simple little debug function to make testing output pretty
-private func check(tree: ThreadedBinaryTree<Int>?) {
-  if let tree = tree {
-    print("\(tree.count) Total Nodes:");
-    print(tree)
-    print("Debug Info:")
-    print(tree.debugDescription)
-    print("In-Order Traversal:")
-    let myArray = tree.toArray()
-    for node in myArray {
-      print(node)
-    }
-    if tree.isThreaded() {
-      print("This threaded binary tree is VALID.")
-    } else {
-      print("This threaded binary tree is INVALID.")
-    }
-  } else {
-    print("This tree is nil.")
-  }
-}
-
-
-print("\nTree with Single Node")
-let emptyTree = ThreadedBinaryTree<Int>(value: 1)
-check(emptyTree)
-
-print("\nFull Balanced Binary Tree with 7 Nodes")
-let fullTree = ThreadedBinaryTree<Int>(value: 4)
-fullTree.insert(2)
-fullTree.insert(6)
-fullTree.insert(1)
-fullTree.insert(3)
-fullTree.insert(5)
-fullTree.insert(7)
-check(fullTree)
-
-
-print("\n\nUnbalanced Binary Tree with 5 Nodes")
-let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
-check(tree)
-
-print("\nInsert 10")
-tree.insert(10)
-check(tree)
-
-print("\nInsert 4")
-tree.insert(4)
-check(tree)
-
-print("\nInsert 15")
-tree.insert(15)
-check(tree)
-
-print("\nRemove 13 (Not in the Tree)")
-tree.remove(13)
-check(tree)
-
-print("\nRemove 7")
-tree.remove(7)
-check(tree)
-
-print("\nRemove 5")
-tree.remove(5)
-check(tree)
-
-print("\nRemove 9 (root)")
-let newRoot = tree.remove(9)
-check(newRoot)
-
-print("\nRemove 12")
-newRoot?.remove(12)
-check(newRoot)
-
-print("\n\nDone with Tests!\n")
diff --git a/Threaded Binary Tree/ThreadedBinaryTreeTests.swift b/Threaded Binary Tree/ThreadedBinaryTreeTests.swift
new file mode 100644
index 000000000..550df424d
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTreeTests.swift	
@@ -0,0 +1,89 @@
+/*
+  TESTS
+  I don't have access to an Apple computer, so I can't make a Playground or any
+  of that fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree
+  class.  It follows the examples in the README.
+*/
+
+// Simple little debug function to make testing output pretty
+func check(tree: ThreadedBinaryTree<Int>?) {
+  if let tree = tree {
+    print("\(tree.count) Total Nodes:");
+    print(tree)
+    print("Debug Info:")
+    print(tree.debugDescription)
+    print("In-Order Traversal:")
+    let myArray = tree.toArray()
+    for node in myArray {
+      print(node)
+    }
+    if tree.isBST(minValue: Int.min, maxValue: Int.max) {
+      print("This is a VALID binary search tree.")
+    } else {
+      print("This is an INVALID binary search tree.")
+    }
+    if tree.isThreaded() {
+      print("This is a VALID threaded binary tree.")
+    } else {
+      print("This is an INVALID threaded binary tree.")
+    }
+  } else {
+    print("This tree is nil.")
+  }
+}
+
+
+print("\nTree with Single Node")
+let emptyTree = ThreadedBinaryTree<Int>(value: 1)
+check(emptyTree)
+
+
+print("\nFull Balanced Binary Tree with 7 Nodes")
+let fullTree = ThreadedBinaryTree<Int>(value: 4)
+fullTree.insert(2)
+fullTree.insert(1)
+fullTree.insert(6)
+fullTree.insert(5)
+fullTree.insert(3)
+fullTree.insert(7)
+check(fullTree)
+
+
+print("\n\nBase Binary Tree with 5 Nodes")
+let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
+check(tree)
+
+print("\nInsert 10")
+tree.insert(10)
+check(tree)
+
+print("\nInsert 4")
+tree.insert(4)
+check(tree)
+
+print("\nInsert 15")
+tree.insert(15)
+check(tree)
+
+print("\nRemove 13 (Not in the Tree)")
+tree.remove(13)
+check(tree)
+
+print("\nRemove 7")
+tree.remove(7)
+check(tree)
+
+print("\nRemove 5")
+tree.remove(5)
+check(tree)
+
+print("\nRemove 9 (root)")
+let newRoot = tree.remove(9)
+check(newRoot)
+
+print("\nRemove 12")
+newRoot?.remove(12)
+check(newRoot)
+
+
+print("\n\nDone with Tests!\n")

From ba9b1bb2fa6e49f9eb9f733cf5312508bf99d517 Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Tue, 3 May 2016 20:01:16 -0400
Subject: [PATCH 0319/1679] added delete helpers

---
 Red Black Trees/RBTree.swift  |  63 ++++++++++++---
 Red Black Trees/RBTree.swift~ | 145 +++++++++++++++++++++++++++++-----
 2 files changed, 181 insertions(+), 27 deletions(-)

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index cd43b8255..69d49b230 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -37,6 +37,37 @@ public class  RBTNode{
         return self.parent!.left!
       }
   }
+  public func replaceNode(n1: RBTNode, n2: RBTNode){
+    var temp = n1.data
+    var temp_color = n1.color
+    n1.data = n2.data
+    n1.color = n2.color
+    n2.data = temp
+    n2.color = temp_color
+  }
+  public func minimum(var node: RBTNode)->RBTNode {
+    while node.left !== nil{
+      node = node.left
+    }
+    return node
+  }
+  public func successorOfNode(var node: RBTNode) -> RBTNode? {
+    if node.right !== nil {
+      return minimum(node.right)
+    }
+    var successor = node.parent
+    while successor !== nil && node === successor.right {
+      node = successor
+      successor = successor.parent
+    }
+    return successor
+  }
+  public func maximum(var rootNode: RBTNode) -> RBTNode{
+    while rootNode.right !== nil {
+      rootNode = rootNode.right
+    }
+    return rootNode
+  }
 }
 public class RBTree {
 
@@ -118,7 +149,7 @@ public func insertFixup(value: Int){
   print(inserted!.data)
   insertCase1(inserted)
 }
-public func insertCase1(inserted: RBTNode?){
+private func insertCase1(inserted: RBTNode?){
   let myroot = self.root!
   if myroot === inserted!{
     self.root!.color = false
@@ -127,14 +158,14 @@ public func insertCase1(inserted: RBTNode?){
   }
   insertCase2(inserted!)
 }
-public func insertCase2(inserted: RBTNode?){
+private func insertCase2(inserted: RBTNode?){
   if inserted!.parent!.color == false{
       print("Insert case 2: parent is black so nothing to change")
       return
   }
   insertCase3(inserted!)
 }
-public func insertCase3(inserted: RBTNode?){
+private func insertCase3(inserted: RBTNode?){
   if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
     print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
     inserted!.parent!.color = false
@@ -148,7 +179,7 @@ public func insertCase3(inserted: RBTNode?){
   insertCase4(inserted)
 }
 //THIS ONE MAY BE BROKEN!?!?!?!?
-public func insertCase4(var inserted: RBTNode?){
+private func insertCase4(var inserted: RBTNode?){
   if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
     print("case 4")
     rightRotate(inserted!.parent)
@@ -161,7 +192,7 @@ public func insertCase4(var inserted: RBTNode?){
   }
   insertCase5(inserted)
 }
-public func insertCase5(inserted: RBTNode?){
+private func insertCase5(inserted: RBTNode?){
   if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
       if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
         print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
@@ -179,10 +210,8 @@ public func insertCase5(inserted: RBTNode?){
 
           print("Its on the right")
           leftRotate(inserted!.grandparent()!)
-
       }
   }
-
   print("weve reached the end boys")
 }
 
@@ -232,6 +261,17 @@ public func insertCase5(inserted: RBTNode?){
             return nil
           }
       }
+
+      //DELETION HELPER FUNCTIONS
+      public func remove(value: Int){
+          let toRemove = find(value)
+          if(toRemove == nil){
+            return
+          }
+      }
+
+
+
 }
 
 var tree = RBTree(rootData: 8)
@@ -242,7 +282,12 @@ tree.insert(4)
 tree.insert(40)
 tree.insert(400)
 tree.insert(430)
-
+var t = tree.root!
+var min = t.minimum(t)
+print("MIN: \(min.data)")
+var x = tree.root!.left
+tree.inOrder()
+t.replaceNode(t,n2:x)
 tree.inOrder()
 
 //print("_________________________")
@@ -264,7 +309,7 @@ tree.inOrder()
 //how you access certain elements
 //let root = tree.root!.left!
 //if(root.parent === nil){
-//  print("niggs")
+//  print("nil")
 //}
 //else{
 //  print(root.parent.data)
diff --git a/Red Black Trees/RBTree.swift~ b/Red Black Trees/RBTree.swift~
index 33c165b4e..cd43b8255 100644
--- a/Red Black Trees/RBTree.swift~	
+++ b/Red Black Trees/RBTree.swift~	
@@ -1,4 +1,3 @@
-
 public class  RBTNode{
   private(set) public var color: Bool
   private(set) public var left: RBTNode!
@@ -14,17 +13,37 @@ public class  RBTNode{
   }
   init(rootData: Int){
     self.data = rootData
-    self.color = true
+    self.color = true //0is black 1 is red
     self.left = nil
     self.right = nil
     self.parent = nil
   }
+  public func grandparent()->RBTNode?{
+    if(self.parent === nil || self.parent.parent === nil){
+      return nil
+    }
+    else{
+      return self.parent.parent
+    }
+  }
+  public func sibling()->RBTNode?{
+      if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
+        return nil
+      }
+      if(self === self.parent!.left!){
+        return self.parent!.right!
+      }
+      else{
+        return self.parent!.left!
+      }
+  }
 }
 public class RBTree {
 
     private(set) public var root: RBTNode?
     init(rootData: Int) {
       root = RBTNode(rootData: rootData)
+      root!.color = false
     }
     init(){
       root = nil
@@ -47,7 +66,6 @@ public class RBTree {
     }
     private func inOrder(root: RBTNode?){
       if(root == nil){
-        print("nil")
         return
       }
       inOrder(root!.left)
@@ -74,7 +92,7 @@ public class RBTree {
   }
   private func rightRotate(x: RBTNode) {
     let newRoot = x.left
-    x.left = newRoot.right 
+    x.left = newRoot.right
     if newRoot.right !== nil {
       newRoot.right.parent = x
     }
@@ -90,14 +108,94 @@ public class RBTree {
     x.parent = newRoot
 }
 
+public func insertFixup(value: Int){
+  let inserted = find(value)
+
+  if(inserted == nil){
+    print("INSERTEDNILLLLLLLL")
+  }
+  print("inserted: ")
+  print(inserted!.data)
+  insertCase1(inserted)
+}
+public func insertCase1(inserted: RBTNode?){
+  let myroot = self.root!
+  if myroot === inserted!{
+    self.root!.color = false
+    print("ITS THE ROOT")
+    print("insert case 1: The root was nil and we inserted a black node at root")
+  }
+  insertCase2(inserted!)
+}
+public func insertCase2(inserted: RBTNode?){
+  if inserted!.parent!.color == false{
+      print("Insert case 2: parent is black so nothing to change")
+      return
+  }
+  insertCase3(inserted!)
+}
+public func insertCase3(inserted: RBTNode?){
+  if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
+    print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
+    inserted!.parent!.color = false
+    inserted!.parent!.sibling()!.color = false
+    let g = inserted!.grandparent
+    g()!.color = true
+    if(g()!.parent == nil){
+      g()!.color = false
+    }
+  }
+  insertCase4(inserted)
+}
+//THIS ONE MAY BE BROKEN!?!?!?!?
+public func insertCase4(var inserted: RBTNode?){
+  if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
+    print("case 4")
+    rightRotate(inserted!.parent)
+    inserted! = inserted!.left
+  }
+  else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
+     print("case 4")
+    leftRotate(inserted!.parent)
+    inserted! = inserted!.right
+  }
+  insertCase5(inserted)
+}
+public func insertCase5(inserted: RBTNode?){
+  if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
+      if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
+        print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
+        inserted!.parent.color = false
+        inserted!.grandparent()?.color = true
+        if(inserted! === inserted!.parent!.left){
+          print("its on the left")
+          rightRotate(inserted!.grandparent()!)
+        }
+      }
+      else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
+        print("insert case 5: RIGHT RIGHT")
+        inserted!.parent.color = false
+        inserted!.grandparent()?.color = true
+
+          print("Its on the right")
+          leftRotate(inserted!.grandparent()!)
+
+      }
+  }
+
+  print("weve reached the end boys")
+}
 
-    private func insertFixup(){}
     public func insert(value: Int) {
       insert(value, parent: root!)
-      //insertFixUp()
+      insertFixup(value)
     }
     private func insert(value: Int, parent: RBTNode) {
-        if value < parent.data {
+        if self.root == nil{
+          self.root = RBTNode(rootData: value)
+          return
+        }
+        else if value < parent.data {
           if let left = parent.left {
             insert(value, parent: left)
           } else {
@@ -116,6 +214,7 @@ public class RBTree {
       public func find(data: Int)->RBTNode?{
         return find(root!,data: data)
       }
+
       private func find(root: RBTNode, data: Int)->RBTNode?{
           if data == root.data{
             return root
@@ -140,19 +239,28 @@ tree.insert(9)
 tree.insert(6)
 tree.insert(5)
 tree.insert(4)
-tree.insert(3)
-tree.inOrder()
-print("_________________________")
-let x = tree.root!
-print("root: \(tree.root!.data)")
-tree.rightRotate(x)
-print("root: \(tree.root!.data)")
+tree.insert(40)
+tree.insert(400)
+tree.insert(430)
+
 tree.inOrder()
 
-let t = tree.find(234)
-if t == nil{
-  print("ASDASD")
-}
+//print("_________________________")
+//let x = tree.root!
+//print("sibling: \(tree.root!.left!.sibling()!.data)")
+//print("root: \(tree.root!.data)")
+//tree.rightRotate(x)
+//print("root: \(tree.root!.data)")
+//tree.inOrder()
+
+//let l = tree.root!.left!
+//let r = tree.root!.right!
+//print(l.data)
+//print(r.data)
+//if tree.root!.parent == nil{
+//  print("ASDASD")
+//}
+
 //how you access certain elements
 //let root = tree.root!.left!
 //if(root.parent === nil){
@@ -165,3 +273,4 @@ if t == nil{
 //print(tree.root!.data)
 //print(tree.root!.right!.data)
 //print(tree.root!.left!.data)
+

From df9e4f6887fe0933ca589b8d832b10482c038a5e Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Tue, 3 May 2016 20:07:12 -0400
Subject: [PATCH 0320/1679] added predecessor

---
 Red Black Trees/RBTree.swift  | 13 +++++-
 Red Black Trees/RBTree.swift~ | 74 ++++++++++++++++++++++++++++++-----
 2 files changed, 77 insertions(+), 10 deletions(-)

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index 69d49b230..4cb0c2fcb 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -51,7 +51,7 @@ public class  RBTNode{
     }
     return node
   }
-  public func successorOfNode(var node: RBTNode) -> RBTNode? {
+  public func successor(var node: RBTNode) -> RBTNode? {
     if node.right !== nil {
       return minimum(node.right)
     }
@@ -62,6 +62,17 @@ public class  RBTNode{
     }
     return successor
   }
+  public func predecessor(var node: RBTNode) -> RBTNode{
+    if node.left !== nil {
+      return minimum(node.left)
+    }
+    var successor = node.parent
+    while successor !== nil && node === successor.left {
+      node = successor
+      successor = successor.parent
+    }
+    return successor
+  }
   public func maximum(var rootNode: RBTNode) -> RBTNode{
     while rootNode.right !== nil {
       rootNode = rootNode.right
diff --git a/Red Black Trees/RBTree.swift~ b/Red Black Trees/RBTree.swift~
index cd43b8255..4cb0c2fcb 100644
--- a/Red Black Trees/RBTree.swift~	
+++ b/Red Black Trees/RBTree.swift~	
@@ -37,6 +37,48 @@ public class  RBTNode{
         return self.parent!.left!
       }
   }
+  public func replaceNode(n1: RBTNode, n2: RBTNode){
+    var temp = n1.data
+    var temp_color = n1.color
+    n1.data = n2.data
+    n1.color = n2.color
+    n2.data = temp
+    n2.color = temp_color
+  }
+  public func minimum(var node: RBTNode)->RBTNode {
+    while node.left !== nil{
+      node = node.left
+    }
+    return node
+  }
+  public func successor(var node: RBTNode) -> RBTNode? {
+    if node.right !== nil {
+      return minimum(node.right)
+    }
+    var successor = node.parent
+    while successor !== nil && node === successor.right {
+      node = successor
+      successor = successor.parent
+    }
+    return successor
+  }
+  public func predecessor(var node: RBTNode) -> RBTNode{
+    if node.left !== nil {
+      return minimum(node.left)
+    }
+    var successor = node.parent
+    while successor !== nil && node === successor.left {
+      node = successor
+      successor = successor.parent
+    }
+    return successor
+  }
+  public func maximum(var rootNode: RBTNode) -> RBTNode{
+    while rootNode.right !== nil {
+      rootNode = rootNode.right
+    }
+    return rootNode
+  }
 }
 public class RBTree {
 
@@ -118,7 +160,7 @@ public func insertFixup(value: Int){
   print(inserted!.data)
   insertCase1(inserted)
 }
-public func insertCase1(inserted: RBTNode?){
+private func insertCase1(inserted: RBTNode?){
   let myroot = self.root!
   if myroot === inserted!{
     self.root!.color = false
@@ -127,14 +169,14 @@ public func insertCase1(inserted: RBTNode?){
   }
   insertCase2(inserted!)
 }
-public func insertCase2(inserted: RBTNode?){
+private func insertCase2(inserted: RBTNode?){
   if inserted!.parent!.color == false{
       print("Insert case 2: parent is black so nothing to change")
       return
   }
   insertCase3(inserted!)
 }
-public func insertCase3(inserted: RBTNode?){
+private func insertCase3(inserted: RBTNode?){
   if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
     print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
     inserted!.parent!.color = false
@@ -148,7 +190,7 @@ public func insertCase3(inserted: RBTNode?){
   insertCase4(inserted)
 }
 //THIS ONE MAY BE BROKEN!?!?!?!?
-public func insertCase4(var inserted: RBTNode?){
+private func insertCase4(var inserted: RBTNode?){
   if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
     print("case 4")
     rightRotate(inserted!.parent)
@@ -161,7 +203,7 @@ public func insertCase4(var inserted: RBTNode?){
   }
   insertCase5(inserted)
 }
-public func insertCase5(inserted: RBTNode?){
+private func insertCase5(inserted: RBTNode?){
   if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
       if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
         print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
@@ -179,10 +221,8 @@ public func insertCase5(inserted: RBTNode?){
 
           print("Its on the right")
           leftRotate(inserted!.grandparent()!)
-
       }
   }
-
   print("weve reached the end boys")
 }
 
@@ -232,6 +272,17 @@ public func insertCase5(inserted: RBTNode?){
             return nil
           }
       }
+
+      //DELETION HELPER FUNCTIONS
+      public func remove(value: Int){
+          let toRemove = find(value)
+          if(toRemove == nil){
+            return
+          }
+      }
+
+
+
 }
 
 var tree = RBTree(rootData: 8)
@@ -242,7 +293,12 @@ tree.insert(4)
 tree.insert(40)
 tree.insert(400)
 tree.insert(430)
-
+var t = tree.root!
+var min = t.minimum(t)
+print("MIN: \(min.data)")
+var x = tree.root!.left
+tree.inOrder()
+t.replaceNode(t,n2:x)
 tree.inOrder()
 
 //print("_________________________")
@@ -264,7 +320,7 @@ tree.inOrder()
 //how you access certain elements
 //let root = tree.root!.left!
 //if(root.parent === nil){
-//  print("niggs")
+//  print("nil")
 //}
 //else{
 //  print(root.parent.data)

From 8fdc1aff72210bc093c6e80b01af10e53df412cc Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Tue, 3 May 2016 22:36:59 -0400
Subject: [PATCH 0321/1679] Complete rough draft of Thread. Bin. Tree README

---
 Threaded Binary Tree/README.markdown | 116 ++++++++++++++++++++++-----
 1 file changed, 95 insertions(+), 21 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 1b35f39e2..e3a27eb4b 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -2,7 +2,10 @@
 
 A threaded binary tree is a special kind of [binary tree](../Binary Tree/) (a
 tree in which each node has at most two children) that maintains a few extra
-variables to allow cheap and fast **in-order traversal** of the tree.
+variables to allow cheap and fast **in-order traversal** of the tree.  We will
+explore the general structure of threaded binary trees, as well as
+[the Swift implementation](ThreadedBinaryTree.swift) of a fully functioning
+threaded binary tree.
 
 If you don't know what a tree is or what it is for, then
 [read this first](../Tree/).
@@ -11,14 +14,15 @@ If you don't know what a tree is or what it is for, then
 ## In-order traversal
 
 The main motivation behind using a threaded binary tree over a simpler and
-smaller standard binary tree is to increase the speed of **in-order traversal**
+smaller standard binary tree is to increase the speed of in-order traversal
 of the tree.  An in-order traversal of a binary tree visits the nodes in the
 order in which they are stored, which matches the underlying ordering of a
 [binary search tree](../Binary Search Tree/).  The idea is to visit all the
 left children of a node first, then visit the node itself, and visit the left
 children last.
 
-In-order traversal of any binary tree generally goes as follows:
+In-order traversal of any binary tree generally goes as follows (using Swift
+syntax):
 
 ```swift
 func traverse(n: Node?) {
@@ -48,15 +52,15 @@ A threaded binary tree fixes this problem.
 ## Predecessors and successors
 
 An in-order traversal of a tree yields a linear ordering of the nodes.  Thus
-each node has both a predecessor and a successor (except for the first and last
-nodes, which only have a successor or a predecessor respectively).  In a
-threaded binary tree, each left child that would normally be `nil` instead
+each node has both a **predecessor** and a **successor** (except for the first
+and last nodes, which only have a successor or a predecessor respectively).  In
+a threaded binary tree, each left child that would normally be `nil` instead
 stores the node's predecessor (if it exists), and each right child that would
 normally be `nil` instead stores the node's successor (if it exists).  This is
 what separates threaded binary trees from standard binary trees.
 
-There are two types of threaded binary trees:  single threaded and double
-threaded:
+There are two types of threaded binary trees:  **single threaded** and **double
+threaded**:
 - A single threaded tree keeps track of **either** the in-order predecessor
   **or** successor (left **or** right).
 - A double threaded tree keeps track of **both** the in-order predecessor
@@ -110,7 +114,8 @@ Swift *optionals*.
 - `leftThread: ThreadedBinaryTree?` is the in-order predecessor of this node
 - `rightThread: ThreadedBinaryTree?` is the in-order successor of this node
 
-Now we are ready to go over some of the member functions in our
+As we are storing both `leftThread` and `rightThread`, this is a double
+threaded tree. Now we are ready to go over some of the member functions in our
 `ThreadedBinaryTree` class.
 
 
@@ -118,9 +123,9 @@ Now we are ready to go over some of the member functions in our
 
 Let's start with the main reason we're using a threaded binary tree.  It is now
 very easy to find the in-order predecessor and the in-order successor of any
-node in the tree.  If the node has no left/right child, we can simply return
-the node's leftThread/rightThread.  Otherwise, it is trivial to move down the
-tree and find the correct node.
+node in the tree.  If the node has no `left`/`right` child, we can simply
+return the node's `leftThread`/`rightThread`.  Otherwise, it is trivial to move
+down the tree and find the correct node.
 
 ```swift
   func predecessor() -> ThreadedBinaryTree<T>? {
@@ -227,37 +232,104 @@ Let's start with the same tree that we used for the above traversal example:
 
 ![Base](Images/Base.png)
 
-Suppose we `insert(10)` into this tree.  The resulting graph would look like
+Suppose we insert **10** into this tree.  The resulting graph would look like
 this, with the changes highlighted in red:
 
 ![Insert1](Images/Insert1.png)
 
 If you've done your homework and are familiar with binary search trees, the
-placement of the node should not surprise you.  What's new is how we maintain
-the threads between nodes.
+placement of this node should not surprise you.  What's new is how we maintain
+the threads between nodes.  So we know that we want to insert **10** as
+**12**'s `left` child.  The first thing we do is set **12**'s `left` child to
+**10**, and set **10**'s `parent` to **12**.  Because **10** is being inserted
+on the `left`, and **10** has no children of its own, we can safely set
+**10**'s `rightThread` to its `parent` **12**.  What about **10**'s
+`leftThread`?  Because we know that **10** < **12**, and **10** is the only
+`left` child of **12**, we can safely set **10**'s `leftThread` to **12**'s
+(now outdated) `leftThread`.  Finally we set **12**'s `leftThread = nil`, as it
+now has a `left` child.
+
+Let's now insert another node, **4**, into the tree:
 
 ![Insert2](Images/Insert2.png)
 
-Insert3:
+While we are inserting **4** as a `right` child, it follows the exact same
+process as above, but mirrored (swap `left` and `right`).  For the sake of
+completeness, we'll insert one final node, **15**:
 
 ![Insert3](Images/Insert3.png)
 
-Remove1:
+Now that we have a fairly crowded tree, let's try removing some nodes.
+Compared to insertion, deletion is a little more complicated.  Let's start with
+something simple, like removing **7**, which has no children:
 
 ![Remove1](Images/Remove1.png)
 
-Remove2:
+Before we can just throw **7** away, we have to perform some clean-up.  In this
+case, because **7** is a `right` child and has no children itself, we can
+simply set the `rightThread` of **7**'s `parent`(**5**) to **7**'s (now
+outdated) `rightThread`.  Then we can just set **7**'s `parent`, `left`,
+`right`, `leftThread`, and `rightThread` to `nil`, effectively removing it from
+the tree.
+
+Let's try something a little harder.  Say we remove **5** from the tree:
 
 ![Remove2](Images/Remove2.png)
 
-Remove3:
+This is a little trickier, as **5** has some children that we have to deal
+with.  The core idea is to replace **5** with its first child, **2**.  To
+accomplish this, we of course set **2**'s `parent` to **9** and set **9**'s
+`left` child to **2**.  Note that **4**'s `rightThread` used to be **5**, but
+we are removing **5**, so it needs to change.  It is now important to
+understand two important properties of threaded binary trees:
+
+1. For the rightmost node **m** in the `left` subtree of any node **n**,
+**m**'s `rightThread` is **n**.
+2. For the leftmost node **m** in the `right` subtree of any node **n**,
+**m**'s `leftThread` is **n**.
+
+Note how this property held true before the removal of **5**, as **4** was the
+rightmost node in **5**'s `left` subtree.  In order to maintain this property,
+we must set **4**'s `rightThread` to **9**, as **4** is now the rightmost node
+in **9**'s `left` subtree.  To completely remove **5**, all we now have to do
+is set **5**'s `parent`, `left`, `right`, `leftThread`, and `rightThread` to
+`nil`.
+
+How about we do something crazy?  What would happen if we tried to remove
+**9**, the root node?  This is the resulting tree:
 
 ![Remove3](Images/Remove3.png)
 
-Remove4:
+Whenever we want to remove a node that has two children, we take a slightly
+different approach than the above examples.  The basic idea is to replace the
+node that we want to remove with the leftmost node in its `right`  subtree,
+which we call the replacement node.
+
+> Note: we could also replace the node with the rightmost node in its `left`
+> subtree.  Choosing left or right is mostly an arbitrary decision.
+
+Once we find the replacement node, **10** in this case, we remove it from the
+tree using the algorithms outlined above.  This ensures that the edges in the
+`right` subtree remain correct.  From there it is easy to replace **9** with
+**10**, as we just have to update the edges leaving **10**.  Now all we have to
+do is fiddle with the threads in order to maintain the two properties outlined
+above.  In this case, **12**'s `leftThread` is now **10**. Node **9** is no
+longer needed, so we can finish teh removal process by setting all of its
+variables to `nil`.
+
+In order to illustrate how to remove a node that has only a `right` child,
+we'll remove one final node, **12** from the tree:
 
 ![Remove4](Images/Remove4.png)
 
+The process to remove **12** is identical to the process we used to remove
+**5**, but mirrored.  **5** had a `left` child, while **12** has a `right`
+child, but the core algorithm is the same.
+
+That is a quick overview of how insertion and deletion work in threaded binary
+trees.  More detail can of course be found in
+[the implementation](ThreadedBinaryTree.swift).
+
 
 ## Miscellaneous methods
 
@@ -271,7 +343,9 @@ find [further documentation here](../Binary Search Tree/).
 
 ## See also 
 
-[Threaded Binary Tree on Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree).
+[Threaded Binary Tree on Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree)
 
 *Written for the Swift Algorithm Club by
 [Jayson Tung](https://github.com/JFTung)*
+
+*Images made using www.draw.io*

From 6ab41aad8ac66675af43e7690854371624355597 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Tue, 3 May 2016 22:55:08 -0400
Subject: [PATCH 0322/1679] Finished Radix Sort Implementation

---
 Radix-Sort/radixSort       | Bin 0 -> 20310 bytes
 Radix-Sort/radixSort.swift |  42 +++++++++++++++++++++++++++++++++++++
 2 files changed, 42 insertions(+)
 create mode 100755 Radix-Sort/radixSort
 create mode 100644 Radix-Sort/radixSort.swift

diff --git a/Radix-Sort/radixSort b/Radix-Sort/radixSort
new file mode 100755
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QqHj!kR$tua|5y(DADjR>DF6Tf

literal 0
HcmV?d00001

diff --git a/Radix-Sort/radixSort.swift b/Radix-Sort/radixSort.swift
new file mode 100644
index 000000000..47bdb0fd1
--- /dev/null
+++ b/Radix-Sort/radixSort.swift
@@ -0,0 +1,42 @@
+func radixSort(inout arr: [Int] ) {
+
+  let radix = 10
+  var done = false
+  var index: Int
+  var digit = 1
+
+  while !done {
+    done = true
+
+    var buckets: [[Int]] = []
+
+    for _ in 1...radix {
+      buckets.append([])
+    }
+
+
+    for number in arr  {
+      index = number / digit
+      buckets[index % radix].append(number)
+      if done && index > 0 {
+        done = false
+      }
+    }
+
+    var i = 0
+
+    for j in 0..<radix {
+      let bucket = buckets[j]
+      for number in bucket {
+        arr[i] = number
+        i += 1
+      }
+    }
+
+    digit *= radix
+  }
+}
+
+var a: [Int] = [0, 69, 28, 14, 32, 1, 1, 1111, 1111111, 55, 123, 236626456256, 9393, 23, 66]
+radixSort(&a)
+print(a)

From ab3f24a9df3198e334be6256a129fe000ebbb376 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Tue, 3 May 2016 23:28:23 -0400
Subject: [PATCH 0323/1679] Finalize Threaded Binary Tree README

---
 Threaded Binary Tree/README.markdown | 44 +++++++++++++++-------------
 1 file changed, 23 insertions(+), 21 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index e3a27eb4b..048a1f23d 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -14,14 +14,15 @@ If you don't know what a tree is or what it is for, then
 ## In-order traversal
 
 The main motivation behind using a threaded binary tree over a simpler and
-smaller standard binary tree is to increase the speed of in-order traversal
+smaller standard binary tree is to increase the speed of an in-order traversal
 of the tree.  An in-order traversal of a binary tree visits the nodes in the
 order in which they are stored, which matches the underlying ordering of a
-[binary search tree](../Binary Search Tree/).  The idea is to visit all the
-left children of a node first, then visit the node itself, and visit the left
+[binary search tree](../Binary Search Tree/).  Thus threaded binary trees are
+almost always binary search trees too.  The idea is to visit all the left
+children of a node first, then visit the node itself, and visit the left
 children last.
 
-In-order traversal of any binary tree generally goes as follows (using Swift
+An in-order traversal of any binary tree generally goes as follows (using Swift
 syntax):
 
 ```swift
@@ -68,8 +69,8 @@ threaded**:
 
 Using a single or double threaded tree depends on what we want to accomplish.
 If we only need to traverse the tree in one direction (either forward or
-backward), use a single threaded tree.  If we want to traverse in both
-directions, use a double threaded tree.
+backward), then we use a single threaded tree.  If we want to traverse in both
+directions, then we use a double threaded tree.
 
 It is important to note that each node stores either its predecessor or its
 left child, and either its successor or its right child.  The nodes do not
@@ -77,7 +78,7 @@ need to keep track of both.  For example, in a double threaded tree, if a node
 has a right child but no left child, it will track its predecessor in place of
 its left child.
 
-Here is a valid "full" threaded binary tree:
+Here is an example valid "full" threaded binary tree:
 
 ![Full](Images/Full.png)
 
@@ -106,11 +107,11 @@ The core of this data structure is the `ThreadedBinaryTree<T: Comparable>`
 class.  Each instance of this class represents a node with six member
 variables:  `value`, `parent`, `left`, `right`, `leftThread`, and
 `rightThread`.  Of all of these, only `value` is required.  The other five are
-Swift *optionals*.
+Swift *optionals* (they may be `nil`).
 - `value: T` is the value of this node (e.g. 1, 2, A, B, etc.)
-- `parent: ThreadedBinaryTree?` is the parent of this node (if it exists)
-- `left: ThreadedBinaryTree?` is the left child of this node (if it exists)
-- `right: ThreadedBinaryTree?` is the right child of this node (if it exists)
+- `parent: ThreadedBinaryTree?` is the parent of this node
+- `left: ThreadedBinaryTree?` is the left child of this node
+- `right: ThreadedBinaryTree?` is the right child of this node
 - `leftThread: ThreadedBinaryTree?` is the in-order predecessor of this node
 - `rightThread: ThreadedBinaryTree?` is the in-order successor of this node
 
@@ -213,7 +214,6 @@ A backward traversal would be very similar, but you would replace `right`,
 `maximum()`, and `predecessor()`.
 
 
-
 ## Insertion and deletion
 
 The quick in-order traversal that a threaded binary trees gives us comes at a
@@ -288,12 +288,12 @@ understand two important properties of threaded binary trees:
 2. For the leftmost node **m** in the `right` subtree of any node **n**,
 **m**'s `leftThread` is **n**.
 
-Note how this property held true before the removal of **5**, as **4** was the
-rightmost node in **5**'s `left` subtree.  In order to maintain this property,
-we must set **4**'s `rightThread` to **9**, as **4** is now the rightmost node
-in **9**'s `left` subtree.  To completely remove **5**, all we now have to do
-is set **5**'s `parent`, `left`, `right`, `leftThread`, and `rightThread` to
-`nil`.
+Note how these properties held true before the removal of **5**, as **4** was
+the rightmost node in **5**'s `left` subtree.  In order to maintain this
+property, we must set **4**'s `rightThread` to **9**, as **4** is now the
+rightmost node in **9**'s `left` subtree.  To completely remove **5**, all we
+now have to do is set **5**'s `parent`, `left`, `right`, `leftThread`, and
+`rightThread` to `nil`.
 
 How about we do something crazy?  What would happen if we tried to remove
 **9**, the root node?  This is the resulting tree:
@@ -314,7 +314,7 @@ tree using the algorithms outlined above.  This ensures that the edges in the
 **10**, as we just have to update the edges leaving **10**.  Now all we have to
 do is fiddle with the threads in order to maintain the two properties outlined
 above.  In this case, **12**'s `leftThread` is now **10**. Node **9** is no
-longer needed, so we can finish teh removal process by setting all of its
+longer needed, so we can finish the removal process by setting all of its
 variables to `nil`.
 
 In order to illustrate how to remove a node that has only a `right` child,
@@ -326,8 +326,10 @@ The process to remove **12** is identical to the process we used to remove
 **5**, but mirrored.  **5** had a `left` child, while **12** has a `right`
 child, but the core algorithm is the same.
 
-That is a quick overview of how insertion and deletion work in threaded binary
-trees.  More detail can of course be found in
+And that's it!  This was just a quick overview of how insertion and deletion
+work in threaded binary trees, but if you understood these examples, you should
+be able to insert or remove any node from any tree you want.  More detail can
+of course be found in
 [the implementation](ThreadedBinaryTree.swift).
 
 

From d13f9d078d9dec034d7b9f5abfbb426078cacfab Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Wed, 4 May 2016 16:39:36 -0400
Subject: [PATCH 0324/1679] Fix various typos in Threaded README

---
 Threaded Binary Tree/README.markdown | 39 ++++++++++++++--------------
 1 file changed, 19 insertions(+), 20 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 048a1f23d..0c533ad63 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -17,10 +17,10 @@ The main motivation behind using a threaded binary tree over a simpler and
 smaller standard binary tree is to increase the speed of an in-order traversal
 of the tree.  An in-order traversal of a binary tree visits the nodes in the
 order in which they are stored, which matches the underlying ordering of a
-[binary search tree](../Binary Search Tree/).  Thus threaded binary trees are
-almost always binary search trees too.  The idea is to visit all the left
-children of a node first, then visit the node itself, and visit the left
-children last.
+[binary search tree](../Binary Search Tree/).  This means most threaded binary
+trees are also binary search trees.  The idea is to visit all the left children
+of a node first, then visit the node itself, and then visit the right children
+last.
 
 An in-order traversal of any binary tree generally goes as follows (using Swift
 syntax):
@@ -89,25 +89,24 @@ binary search tree:
 ![Partial](Images/Partial.png)
 
 The solid lines denote the links between parents and children, while the dotted
-lines denote the "threads."  The important thing to note here is how the
-children and thread edges interact with each other.  Every node besides the
-root has one entering edge (from its parent), and two leaving edges: one to the
-left and one to the right.  The left leaving edge goes to the node's left child
-if it exists, and to its in-order predecessor if it does not.  The right
-leaving edge goes to the node's right child if it exists, and to its in-order
-successor if it does not.  The exceptions are the left-most node and the
-right-most node, which do not have a predecessor or successor, respectively.
+lines denote the "threads."  It is important to note how the children and
+thread edges interact with each other.  Every node besides the root has one
+entering edge (from its parent), and two leaving edges: one to the left and one
+to the right.  The left leaving edge goes to the node's left child if it
+exists, and to its in-order predecessor if it does not.  The right leaving edge
+goes to the node's right child if it exists, and to its in-order successor if
+it does not.  The exceptions are the left-most node and the right-most node,
+which do not have a predecessor or successor, respectively.
 
 
 ## Representation
 
-Before we go into detail about the methods that we can apply to threaded binary
-trees, it might be a good idea to explain how we will be representing the tree.
-The core of this data structure is the `ThreadedBinaryTree<T: Comparable>`
-class.  Each instance of this class represents a node with six member
-variables:  `value`, `parent`, `left`, `right`, `leftThread`, and
-`rightThread`.  Of all of these, only `value` is required.  The other five are
-Swift *optionals* (they may be `nil`).
+Before we go into detail about the methods of a threaded binary tree, we should
+first explain how the tree itself is represented.  The core of this data
+structure is the `ThreadedBinaryTree<T: Comparable>` class.  Each instance of
+this class represents a node with six member variables:  `value`, `parent`,
+`left`, `right`, `leftThread`, and `rightThread`.  Of all of these, only
+`value` is required.  The other five are Swift *optionals* (they may be `nil`).
 - `value: T` is the value of this node (e.g. 1, 2, A, B, etc.)
 - `parent: ThreadedBinaryTree?` is the parent of this node
 - `left: ThreadedBinaryTree?` is the left child of this node
@@ -185,7 +184,7 @@ func traverseInOrderBackward(visit: T -> Void) {
   }
 }
 ```
-Again, this a method of `ThreadedBinaryTree`, so we'd call it like
+Again, this a method of `ThreadedBinaryTree`, so we'd call it via
 `node.traverseInorderForward(visitFunction)`.  Note that we are able to specify
 a function that executes on each node as they are visited.  This function can
 be anything you want, as long as it accepts `T` (the type of the values of the

From 6644f8b4011617af2ec0188275f038634e4d68e3 Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Wed, 4 May 2016 17:05:00 -0400
Subject: [PATCH 0325/1679] added delete

---
 Red Black Trees/RBTree.swift | 228 ++++++++++++++++++++++++++---------
 1 file changed, 170 insertions(+), 58 deletions(-)

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index 4cb0c2fcb..dab7e1fd8 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -13,11 +13,14 @@ public class  RBTNode{
   }
   init(rootData: Int){
     self.data = rootData
-    self.color = true //0is black 1 is red
+    self.color = true //0 is black 1 is red
     self.left = nil
     self.right = nil
     self.parent = nil
   }
+  deinit{
+    print("Node: \(self.data) is bein deinitialized")
+  }
   public func grandparent()->RBTNode?{
     if(self.parent === nil || self.parent.parent === nil){
       return nil
@@ -37,48 +40,9 @@ public class  RBTNode{
         return self.parent!.left!
       }
   }
-  public func replaceNode(n1: RBTNode, n2: RBTNode){
-    var temp = n1.data
-    var temp_color = n1.color
-    n1.data = n2.data
-    n1.color = n2.color
-    n2.data = temp
-    n2.color = temp_color
-  }
-  public func minimum(var node: RBTNode)->RBTNode {
-    while node.left !== nil{
-      node = node.left
-    }
-    return node
-  }
-  public func successor(var node: RBTNode) -> RBTNode? {
-    if node.right !== nil {
-      return minimum(node.right)
-    }
-    var successor = node.parent
-    while successor !== nil && node === successor.right {
-      node = successor
-      successor = successor.parent
-    }
-    return successor
-  }
-  public func predecessor(var node: RBTNode) -> RBTNode{
-    if node.left !== nil {
-      return minimum(node.left)
-    }
-    var successor = node.parent
-    while successor !== nil && node === successor.left {
-      node = successor
-      successor = successor.parent
-    }
-    return successor
-  }
-  public func maximum(var rootNode: RBTNode) -> RBTNode{
-    while rootNode.right !== nil {
-      rootNode = rootNode.right
-    }
-    return rootNode
-  }
+
+
+
 }
 public class RBTree {
 
@@ -189,16 +153,16 @@ private func insertCase3(inserted: RBTNode?){
   }
   insertCase4(inserted)
 }
-//THIS ONE MAY BE BROKEN!?!?!?!?
+
 private func insertCase4(var inserted: RBTNode?){
   if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
     print("case 4")
-    rightRotate(inserted!.parent)
+    leftRotate(inserted!.parent)
     inserted! = inserted!.left
   }
   else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
      print("case 4")
-    leftRotate(inserted!.parent)
+    rightRotate(inserted!.parent)
     inserted! = inserted!.right
   }
   insertCase5(inserted)
@@ -280,26 +244,174 @@ private func insertCase5(inserted: RBTNode?){
             return
           }
       }
+      public func replaceNode(n1: RBTNode, n2: RBTNode){
+        var temp = n1.data
+        var temp_color = n1.color
+        n1.data = n2.data
+        n1.color = n2.color
+        n2.data = temp
+        n2.color = temp_color
+      }
+      public func minimum(var node: RBTNode)->RBTNode {
+        while node.left !== nil{
+          node = node.left
+        }
+        return node
+      }
+      public func successor(var node: RBTNode) -> RBTNode? {
+        if node.right !== nil {
+          return minimum(node.right)
+        }
+        var successor = node.parent
+        while successor !== nil && node === successor.right {
+          node = successor
+          successor = successor.parent
+        }
+        return successor
+      }
+      public func predecessor(var node: RBTNode) -> RBTNode{
+        if node.left !== nil {
+          return minimum(node.left)
+        }
+        var successor = node.parent
+        while successor !== nil && node === successor.left {
+          node = successor
+          successor = successor.parent
+        }
+        return successor
+      }
+      public func maximum(var rootNode: RBTNode) -> RBTNode{
+        while rootNode.right !== nil {
+          rootNode = rootNode.right
+        }
+        return rootNode
+      }
+  private func deletionFixup(x: RBTNode) {}
+
+  public func delete(x: Int){
+    let toDel = find(x)
+    deleteNode(toDel!)
+  }
+  private func deleteNode(var toDel: RBTNode?){
+    print("DELETE CASE 0")
+    if(toDel!.left == nil && toDel!.right == nil && toDel!.color == true){
+      print("IM IN HERE")
+      //DEINIT NOT BEING CALLED AGAIN?
+      toDel = nil
+      return
+    }
+    if(toDel!.left !== nil && toDel!.right !== nil){
+      var pred = maximum(toDel!.left!)
+      toDel!.data = pred.data
+      toDel! = pred
+    }
+    var child: RBTNode? = nil
 
+    if(toDel!.right === nil){
+      child = toDel!.left
+    }
+    else{
+       child = toDel!.right
+    }
+
+    if(toDel!.color == false){
+      toDel!.color = child!.color
+      deleteCase1(toDel!)
+    }
 
+    if(child !== nil){
+      replaceNode(toDel!, n2: child!)
 
+      if(toDel!.parent === nil && child !== nil){
+        child!.color = false
+      }
+    }
+    print("This statement isnt actually deleting the object??? V")
+    toDel = nil
+  }
+  private func deleteCase1(var toDel: RBTNode?){
+      print("DELETE CASE 1")
+      if(toDel?.parent === nil){
+        return
+      }
+      else{
+        deleteCase2(toDel)
+      }
+  }
+  private func deleteCase2(var toDel: RBTNode?){
+    print("DELETE CASE 2")
+    var sibling = toDel!.sibling()
+    if(sibling?.color == true){
+       toDel!.parent.color = true;
+       sibling?.color = false
+       if(toDel! === toDel!.parent.left){
+         leftRotate(toDel!.parent)
+       }
+       else{
+         rightRotate(toDel!.parent)
+       }
+       deleteCase3(toDel!)
+    }
+  }
+  private func deleteCase3(var toDel: RBTNode?){
+    print("DELETE CASE 3")
+    if(toDel!.parent?.color == false && toDel!.sibling()?.color == false && toDel!.sibling()?.left!.color == false && toDel!.sibling()?.right!.color == false){
+        toDel!.sibling()?.color = true
+        toDel!.parent?.color = false
+    }
+    else{
+      deleteCase4(toDel)
+    }
+  }
+  private func deleteCase4(var toDel: RBTNode?){
+    print("DELETE CASE 4")
+    if(toDel!.parent?.color == true && toDel!.sibling()?.color == false && toDel!.sibling()?.left!.color == false && toDel!.sibling()?.right!.color == false){
+        toDel!.sibling()?.color = true
+        toDel!.parent.color = false
+    }
+    else{
+      deleteCase5(toDel)
+    }
+  }
+  private func deleteCase5(var toDel:RBTNode?){
+    print("DELETE CASE 5")
+    if(toDel! === toDel!.parent?.left && toDel!.sibling()?.color == false && toDel!.sibling()?.left.color == true && toDel!.sibling()?.right.color == false){
+      toDel!.sibling()?.color = true
+      toDel!.sibling()?.left?.color = false
+      rightRotate(toDel!.sibling()!)
+    }
+    else if(toDel! === toDel!.parent?.right && toDel!.sibling()?.color == false && toDel!.sibling()?.left.color == false && toDel!.sibling()?.right.color == true){
+      toDel!.sibling()?.color = true
+      toDel!.sibling()?.right?.color = false
+      leftRotate(toDel!.sibling()!)
+    }
+  }
+  private func deleteCase6(var toDel: RBTNode?){
+    print("DELETE CASE 6")
+    let color = toDel!.sibling()?.color
+    toDel!.parent?.color = color!
+    toDel!.parent?.color = false
+    if(toDel! === toDel!.parent.left){
+        toDel!.sibling()?.right?.color = false
+        leftRotate(toDel!.parent!)
+    }
+    else{
+      toDel!.sibling()?.left?.color = false
+      rightRotate(toDel!.parent!)
+    }
+  }
 }
 
+
+
 var tree = RBTree(rootData: 8)
-tree.insert(9)
+
 tree.insert(6)
-tree.insert(5)
-tree.insert(4)
-tree.insert(40)
-tree.insert(400)
-tree.insert(430)
-var t = tree.root!
-var min = t.minimum(t)
-print("MIN: \(min.data)")
-var x = tree.root!.left
-tree.inOrder()
-t.replaceNode(t,n2:x)
+tree.delete(6)
 tree.inOrder()
+print("_______")
+
+
 
 //print("_________________________")
 //let x = tree.root!

From ead1fc37b587c7b2021750c6fcc4bf1e8e55b8fa Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Wed, 4 May 2016 20:36:43 -0400
Subject: [PATCH 0326/1679] Update ReadMe.md

---
 Radix-Sort/ReadMe.md | 26 +++++++++++++++++++++++++-
 1 file changed, 25 insertions(+), 1 deletion(-)

diff --git a/Radix-Sort/ReadMe.md b/Radix-Sort/ReadMe.md
index 27dcf6eb3..5bdb931ca 100644
--- a/Radix-Sort/ReadMe.md
+++ b/Radix-Sort/ReadMe.md
@@ -1,6 +1,30 @@
 # Radix Sort
 
-Under Construction.
+Radix sort is a sorting algorithm that takes as input an array of integers and uses a sorting subroutine( that is often another efficient sorting algorith) to sort the integers by their radix, or rather their digit.  Counting Sort, and Bucket Sort are often times used as the subroutine for Radix Sort.
+
+##Example
+
+* Input Array: [170, 45, 75, 90, 802, 24, 2, 66]
+* Output Array (Sorted):  [2, 24, 45, 66, 75, 90, 170, 802]
+
+###Step 1:
+The first step in this algorithm is to define the digit or rather the "base" or radix that we will use to sort.
+For this example we will let radix = 10, since the integers we are working with in the example are of base 10.
+
+###Step 2:
+The next step is to simply iterate n times (where n is the number of digits in the largest integer in the input array), and upon each iteration perform a sorting subroutine on the current digit in question.
+
+###Algorithm in Action
+
+Let's take a look at our example input array.
+
+The largest integer in our array is 802, and it has three digits (ones, tens, hundreds).  So our algorithm will iterate three times whilst performing some sorting algorithm on the digits of each integer.
+
+* Iteration 1:  170, 90, 802, 2, 24, 45, 75, 66
+* Iteration 2:  802, 2, 24, 45, 66, 170, 75, 90
+* Iteration 3:  2, 24, 45, 66, 75, 90, 170, 802
+
+
 
 See also [Wikipedia](https://en.wikipedia.org/wiki/Radix_Sort).
 

From 1a07781dfe4a40fa0523202fd5dac0171ac81e48 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 11:00:15 -0400
Subject: [PATCH 0327/1679] Provided a temporary fix for insert function,
 finished radix sort readme, commented Trie and Node classes.

---
 Radix-Sort/radixSort.swift                    |  29 +--
 Trie/.build/debug/Trie.a                      | Bin 125236 -> 139282 bytes
 Trie/.build/debug/Trie.o/Trie/Queue.d         |   6 +-
 Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps |  16 +-
 .../Trie.o/Trie/Queue~partial.swiftmodule     | Bin 11788 -> 11608 bytes
 .../.build/debug/Trie.o/Trie/master.swiftdeps |   7 +-
 .../debug/Trie.o/Trie/output-file-map.json    |   6 -
 Trie/.build/debug/Trie.o/Trie/trie.d          |   6 +-
 Trie/.build/debug/Trie.o/Trie/trie.swiftdeps  |  34 ++--
 .../Trie.o/Trie/trie~partial.swiftmodule      | Bin 66240 -> 66060 bytes
 Trie/.build/debug/Trie.o/build.db             | Bin 15360 -> 15360 bytes
 Trie/.build/debug/Trie.o/llbuild.yaml         |  20 +-
 .../.build/debug/Trie.o/sources/Queue.swift.o | Bin 23440 -> 23408 bytes
 Trie/.build/debug/Trie.o/sources/trie.swift.o | Bin 107904 -> 107872 bytes
 Trie/.build/debug/Trie.swiftmodule            | Bin 21236 -> 20828 bytes
 Trie/sources/main.swift                       |  35 ----
 Trie/sources/trie.swift                       | 190 +++++++++++++++++-
 Trie/tests/LinuxMain.swift                    |   8 +
 Trie/tests/Trie/TrieTest.swift                |  26 +++
 19 files changed, 276 insertions(+), 107 deletions(-)
 delete mode 100644 Trie/sources/main.swift
 create mode 100644 Trie/tests/LinuxMain.swift
 create mode 100644 Trie/tests/Trie/TrieTest.swift

diff --git a/Radix-Sort/radixSort.swift b/Radix-Sort/radixSort.swift
index 47bdb0fd1..64166e88a 100644
--- a/Radix-Sort/radixSort.swift
+++ b/Radix-Sort/radixSort.swift
@@ -1,14 +1,23 @@
+/*
+
+  Sorting Algorithm that sorts an input array of integers digit by digit.
+
+*/
+
+
 func radixSort(inout arr: [Int] ) {
 
-  let radix = 10
+
+  let radix = 10  //Here we define our radix to be 10
   var done = false
   var index: Int
-  var digit = 1
+  var digit = 1  //Which digit are we on?
+
 
-  while !done {
-    done = true
+  while !done {  //While our  sorting is not completed
+    done = true  //Assume it is done for now
 
-    var buckets: [[Int]] = []
+    var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
 
     for _ in 1...radix {
       buckets.append([])
@@ -16,9 +25,9 @@ func radixSort(inout arr: [Int] ) {
 
 
     for number in arr  {
-      index = number / digit
+      index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
-      if done && index > 0 {
+      if done && index > 0 {  //If we arent done, continue to finish, otherwise we are done
         done = false
       }
     }
@@ -33,10 +42,6 @@ func radixSort(inout arr: [Int] ) {
       }
     }
 
-    digit *= radix
+    digit *= radix  //Move to the next digit
   }
 }
-
-var a: [Int] = [0, 69, 28, 14, 32, 1, 1, 1111, 1111111, 55, 123, 236626456256, 9393, 23, 66]
-radixSort(&a)
-print(a)
diff --git a/Trie/.build/debug/Trie.a b/Trie/.build/debug/Trie.a
index 6683c390836e5dea9352d1ab823aa4057f36435f..8a6855460ced86d852718c4d574c11b94b8e9168 100644
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diff --git a/Trie/.build/debug/Trie.o/Trie/Queue.d b/Trie/.build/debug/Trie.o/Trie/Queue.d
index f39f80cfd..bc5d30531 100644
--- a/Trie/.build/debug/Trie.o/Trie/Queue.d
+++ b/Trie/.build/debug/Trie.o/Trie/Queue.d
@@ -1,3 +1,3 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps b/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
index ccc0e26c1..6151adec1 100644
--- a/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
+++ b/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
@@ -6,19 +6,19 @@ provides-nominal:
 provides-member:
 - ["V4Trie5Queue", ""]
 depends-top-level:
-- "FloatLiteralType"
-- "IntegerLiteralType"
 - "Queue"
+- !private "Double"
+- !private "&&"
+- "Int"
 - "Bool"
+- "IntegerLiteralType"
+- !private "<"
 - !private "-"
-- !private "/"
 - !private "=="
-- !private "<"
-- "Int"
-- !private ">"
-- !private "Double"
-- !private "&&"
 - !private "+="
+- !private ">"
+- !private "/"
+- "FloatLiteralType"
 depends-member:
 - !private ["Ps16AbsoluteValuable", "init"]
 - ["Sa", "Generator"]
diff --git a/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule b/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule
index 267c48a56b4a095c3a6463ff17bcb74be262f696..1594ec4d238b3a285e3e18a9dbfd52390d125f0e 100644
GIT binary patch
delta 404
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delta 584
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diff --git a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
index 3f65c9e2b..e309a3241 100644
--- a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
+++ b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
@@ -1,7 +1,6 @@
 version: "Swift version 2.2-dev (LLVM 3ebdbb2c7e, Clang f66c5bb67b, Swift 0ddf238ad7)"
-options: "1cfa30eacd63a1262ef0618da5cf7605"
-build_time: [515621198, 271577000]
+options: "b9e1edeb018f28952094455e51afbd70"
+build_time: [515622447, 803412000]
 inputs:
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift": [515620938, 0]
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": [515621195, 0]
+  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": [515621876, 0]
   "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": [512710161, 0]
diff --git a/Trie/.build/debug/Trie.o/Trie/output-file-map.json b/Trie/.build/debug/Trie.o/Trie/output-file-map.json
index be714f4c6..6583c1858 100644
--- a/Trie/.build/debug/Trie.o/Trie/output-file-map.json
+++ b/Trie/.build/debug/Trie.o/Trie/output-file-map.json
@@ -2,12 +2,6 @@
   "": {
     "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/master.swiftdeps"
   },
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift": {
-    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main.d",
-    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o",
-    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main~partial.swiftmodule",
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main.swiftdeps"
-  },
   "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": {
     "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie.d",
     "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o",
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.d b/Trie/.build/debug/Trie.o/Trie/trie.d
index 98996f58e..6afbabc4c 100644
--- a/Trie/.build/debug/Trie.o/Trie/trie.d
+++ b/Trie/.build/debug/Trie.o/Trie/trie.d
@@ -1,3 +1,3 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
+/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
index 6f65d2492..c56a23f66 100644
--- a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
+++ b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
@@ -9,30 +9,30 @@ provides-member:
 - ["C4Trie4Node", ""]
 - ["C4Trie4Trie", ""]
 depends-top-level:
-- !private "StringLiteralType"
-- !private "UnicodeScalarType"
-- !private "&&"
+- "FloatLiteralType"
 - !private "-"
-- "String"
-- !private "BooleanLiteralType"
-- "Bool"
-- !private "-="
+- !private "&&"
 - "Trie"
-- "FloatLiteralType"
-- "Int"
-- !private "+"
-- "IntegerLiteralType"
-- !private "!"
-- !private "+="
+- !private "BooleanLiteralType"
+- !private "UnicodeScalarType"
+- "Node"
 - !private "print"
-- !private "!=="
 - "Set"
-- "Node"
-- "Void"
 - !private "=="
+- !private "Array"
+- !private "+="
+- "IntegerLiteralType"
+- !private "!"
+- !private "StringLiteralType"
+- "Int"
 - !private "Queue"
+- "Void"
 - !private ">"
-- !private "Array"
+- !private "!=="
+- !private "-="
+- "Bool"
+- !private "+"
+- "String"
 depends-member:
 - !private ["Vs12AnyGenerator", "Element"]
 - !private ["Ps9AnyObject", "Array"]
diff --git a/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule b/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule
index f9e33b421a684ed26ac2066848785167312f0845..e7406d6766930d93bf2df20bf71744e783feb822 100644
GIT binary patch
delta 2355
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diff --git a/Trie/.build/debug/Trie.o/build.db b/Trie/.build/debug/Trie.o/build.db
index 1b9a387ff0a346fbfbed4bd7a4a3a64c8bb116ee..2b1683e2e9ba3866b1bce6151f2ed62617ddbcac 100644
GIT binary patch
delta 1323
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delta 1285
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diff --git a/Trie/.build/debug/Trie.o/llbuild.yaml b/Trie/.build/debug/Trie.o/llbuild.yaml
index 8607eca74..7f699a487 100644
--- a/Trie/.build/debug/Trie.o/llbuild.yaml
+++ b/Trie/.build/debug/Trie.o/llbuild.yaml
@@ -11,19 +11,19 @@ commands:
   <Trie-swiftc>:
     tool: swift-compiler
     executable: "/home/christian/swiftv2/usr/bin/swiftc"
-    inputs: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
-    outputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
+    inputs: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
+    outputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
     module-name: "Trie"
     module-output-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule"
-    is-library: false
-    sources: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
-    objects: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
+    is-library: true
+    sources: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
+    objects: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
     import-paths: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug"]
     temps-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie"
-    other-args: ["-j8","-Onone","-g","-I","/usr/local/include"]
+    other-args: ["-j8","-Onone","-g","-enable-testing","-I","/usr/local/include"]
   <Trie>:
     tool: shell
-    inputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
-    outputs: ["<Trie>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie"]
-    args: ["/home/christian/swiftv2/usr/bin/swiftc","-o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o","-g","-L/usr/local/lib"]
-    description: "Linking Executable:  .build/debug/Trie"
+    inputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
+    outputs: ["<Trie>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.a"]
+    args: ["/bin/sh","-c","rm -f '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.a'; ar cr '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.a' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o'"]
+    description: "Linking Library:  .build/debug/Trie.a"
diff --git a/Trie/.build/debug/Trie.o/sources/Queue.swift.o b/Trie/.build/debug/Trie.o/sources/Queue.swift.o
index efac8c7a3782cff0aaa917c7375533ce4bf89c97..068c988f70a207bd47b06b045f22a76272695d32 100644
GIT binary patch
delta 1714
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delta 1703
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diff --git a/Trie/.build/debug/Trie.o/sources/trie.swift.o b/Trie/.build/debug/Trie.o/sources/trie.swift.o
index fc047f2cdfbf51fcca8f6f7dcddd0d202f73415f..35fa7256f2ff05ec4eaf4d7cc3f3e31fe2ff4dbb 100644
GIT binary patch
delta 6367
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diff --git a/Trie/.build/debug/Trie.swiftmodule b/Trie/.build/debug/Trie.swiftmodule
index e387c6b3e3b7fafc2d6e5435918866b17cfd6302..078d7a6e1f4157ce427046619f65d62ae669b16e 100644
GIT binary patch
delta 7588
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diff --git a/Trie/sources/main.swift b/Trie/sources/main.swift
deleted file mode 100644
index 8f95afdf7..000000000
--- a/Trie/sources/main.swift
+++ /dev/null
@@ -1,35 +0,0 @@
-
-print("tests")
-
-
-var T: Trie = Trie()
-T.insert("Hello")
-T.insert("Hi")
-T.insert("Hey")
-T.insert("Hallo")
-T.insert("Henry")
-T.insert("YELLO")
-var U: Trie = Trie(wordList: Set(["Hey", "HO", "hello", "yolo"]))
-var V: Trie = T.merge(U)
-//T.printTrie()
-//U.printTrie()
-//V.printTrie()
-print(V.getWords())
-V.removeAll()
-//V.printTrie()
-/*T.insert("Hello")
-T.insert("Hey")
-T.insert("YOLO")
-T.insert("Him")
-assert(T.count() == 4, "Count function failed")
-assert(T.contains("Hey") == true)
-assert(T.contains("Hello") == true)
-print("trying remove")
-T.remove("Him")
-assert(T.count() == 3)
-assert(T.contains("Him") == false, "Test failed")
-assert(T.wordList.count == 3)*/
-
-//T.printTrie()
-//print(T.find(""))
-print(T.findPrefix("H"))
diff --git a/Trie/sources/trie.swift b/Trie/sources/trie.swift
index 092b497dc..b3a8fb4f5 100644
--- a/Trie/sources/trie.swift
+++ b/Trie/sources/trie.swift
@@ -1,3 +1,16 @@
+/*
+  A Trie (Pre-fix Tree)
+
+  Some of the functionality of the trie makes use of the Queue implementation for this project.
+
+
+  Every node in the Trie stores a bit of information pertainining to what it references:
+    -Character (letter of an inserted word)
+    -Parent  (Letter that comes before the current letter in some word)
+    -Children (Words that have more letters than available in the prefix)
+    -isAWord (Does the current letter mark the end of a known inserted word?)
+    -visited (Mainly for the findPrefix() function)
+*/
 public class Node {
   private var character: String?
   private var parent: Node?
@@ -13,58 +26,135 @@ public class Node {
     self.visited = false
     }
 
-  //Easier getter function, probably will make it more swift like
+  /*
+    Function Name:  char()
+    Input:  N/A
+    Output:  String
+    Functionality: Returns the associated value of the node
+  */
   func char() -> String {
     return self.character!
   }
 
-  func update(c: String?) -> Void {
+  /*
+    Function Name:  update
+    Input: String
+    Output: N/A
+    Functionality: Updates the associated value of the node
+  */
+  func update(c: String?) {
     self.character = c
   }
 
+  /*
+    Function Name:  isLeaf
+    Input:  N/A
+    Output:  Bool
+    Functionality: Returns true if the node is a leaf node, false otherwise
+  */
   func isLeaf() -> Bool{
     return self.children.count == 0
   }
-  //For Testing purposes
+
+  /*
+    Function Name:  getParent
+    Input:  N/A
+    Output:  Node
+    Functionality: Returns the parent node of the current node
+  */
   func getParent() -> Node {
     return parent!
   }
 
-  func setParent(node: Node?) -> Void {
+  /*
+    Function Name:  setParent
+    Input:  Node
+    Output:  N/A
+    Functionality: Changes the parent of the current node to the passed node
+  */
+
+  func setParent(node: Node?) {
     self.parent = node
   }
 
+  /*
+    Function Name:  getChildAt
+    Input:  String
+    Output:  Node
+    Functionality:  returns the child node that holds the specific passed letter
+  */
   func getChildAt(s: String) -> Node {
     return self.children[s]!
   }
-  //Is this node marked as the end of a word?
+
+  /*
+    Function Name:  isValidWord
+    Input:  N/A
+    Output:  Bool
+    Functionality: Returns whether or not the current node marks the end of a valid word
+  */
   func isValidWord() -> Bool{
     return self.isAWord
   }
 
-  //Setters
-  func isWord() -> Void {
+  /*
+    Function Name:  isWord
+    Input:  N/A
+    Output:  N/A
+    Functionality:  the current node is indeed a word
+  */
+  func isWord() {
     self.isAWord = true
   }
 
-  func isNotWord() -> Void {
+  /*
+    Function Name: isNotWord
+    Input:  N/A
+    Output:  N/A
+    Functionality:  marks the current node as not a word
+  */
+  func isNotWord() {
     self.isAWord = false
   }
 
+  /*
+    Function Name:  isRoot
+    Input: N/A
+    Output: Bool
+    Functionality:  Returns whether or not the current node is the root of the trie
+  */
   func isRoot() -> Bool {
     return self.character == ""
   }
 
+  /*
+    Function Name:  numChildren
+    Input:  N/A
+    Output:  Int
+    Functionality:  Returns the number of immediate letters that follow the current node
+  */
   func numChildren() -> Int {
     return self.children.count
   }
 
+  /*
+    Function Name:  getChildren
+    Input:  N/A
+    Output:  [String: Node]
+    Functionality:  Returns the letters that immediately follow the current node's value for possible word segments that follow
+  */
   func getChildren() -> [String: Node] {
     return self.children
   }
 
 
-  func printNode(var indent: String, leaf: Bool) -> Void {
+  /*
+    Function Name:  printNode
+    Input:  String, Bool
+    Output:  N/A
+    Functionality:  prints to the console a string representation of the current node in the trie
+  */
+  func printNode(var indent: String, leaf: Bool) {
 
     print(indent, terminator: "")
     if(leaf) {
@@ -88,6 +178,13 @@ public class Node {
 
 }
 
+
+/*
+  The Trie class has the following attributes:
+    -root (the root of the trie)
+    -wordList (the words that currently exist in the trie)
+    -wordCount (the number of words in the trie)
+*/
 public class Trie {
   private var root: Node
   private var wordList: [String]
@@ -108,11 +205,23 @@ public class Trie {
     }
   }
 
+  /*
+    Function Name: merge
+    Input:  Trie
+    Output:  Trie
+    Functionality:  Merges two tries into one and returns the merged trie
+  */
   func merge(other: Trie) -> Trie{
     let newWordList = Set(self.getWords() + other.getWords())
     return Trie(wordList: newWordList)
   }
 
+  /*
+    Function Name:  find
+    Input:  String
+    Output:  (Node?, Bool)
+    Functionality:  Looks for a specific key and returns a tuple that has a reference to the node(if found) and true/false depending on if it was found
+  */
   func find(key: String) -> (node: Node?, found: Bool) {
     var currentNode = self.root
 
@@ -126,22 +235,52 @@ public class Trie {
     return(currentNode, currentNode.isValidWord())
   }
 
+  /*
+    Function Name: isEmpty
+    Input:  N/A
+    Output:  Bool
+    Functionality:  returns true if the trie is empty, false otherwise
+  */
   func isEmpty() -> Bool {
     return wordCount == 0
   }
 
+  /*
+    Function Name:  count
+    Input:  N/A
+    Output:  Int
+    Functionality:  returns the number of words in the trie
+  */
   func count() -> Int {
     return wordCount
   }
 
+  /*
+    Function Name:  getWords
+    Input:  N/A
+    Output:  [String]
+    Functionality:  returns the list of words that exist in the trie
+  */
   func getWords() -> [String] {
     return wordList
   }
 
+  /*
+    Function Name:  contains
+    Input:  String
+    Output:  Bool
+    Functionality:  returns true if the tries has the word passed, false otherwise
+  */
   func contains(w: String) -> Bool {
     return find(w.lowercaseString).found
   }
 
+  /*
+    Function Name:  isPrefix
+    Input:  String
+    Output: (Node?, Bool)
+    Functionality:  returns a tuple containing a reference to the final node in the prefix (if it exists) and true/false depending on whether or not the prefix exists in the trie
+  */
   func isPrefix(p: String) -> (node: Node?, found: Bool) {
     let prefixP = p.lowercaseString
 
@@ -162,8 +301,15 @@ public class Trie {
     return (nil, false)
   }
 
+  /*
+    Function Name:  insert
+    Input:  String
+    Output:  (String, Bool)
+    Functionality:  Inserts a word int othe trie.  Returns a tuple containing the word attempted to be added, and true/false depending on whether or not the insertion was successful
+  */
   func insert(w: String) -> (word: String, inserted: Bool) {
 
+    print(w)
     let word = w.lowercaseString
     var currentNode = self.root
     var length = word.characters.count
@@ -182,6 +328,7 @@ public class Trie {
       c = Array(word.characters)[index]
     }
 
+    print(length)
     let remainingChars = String(word.characters.suffix(length))
     for c in remainingChars.characters {
       currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
@@ -194,6 +341,12 @@ public class Trie {
     return (w, true)
   }
 
+  /*
+    Function Name:  remove
+    Input:  String
+    Output:  (String, Bool)
+    Functionality:  Removes the specified key from the trie if it exists, returns tuple containing the word attempted to be removed and true/false if the removal was succesful
+  */
   func remove(w: String) -> (word: String, removed: Bool){
     let word = w.lowercaseString
 
@@ -211,6 +364,7 @@ public class Trie {
     } else {
       var character = currentNode.char()
       while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
+        print("I make it here")
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
@@ -232,6 +386,12 @@ public class Trie {
     return (w, true)
   }
 
+  /*
+    Function Name: findPrefix
+    Input:  String
+    Output:  [String]
+    Functionality:  returns a list containing all words in the trie that have the specified prefix
+  */
   func findPrefix(p: String) -> [String] {
 
     if !self.isPrefix(p).found {
@@ -270,6 +430,12 @@ public class Trie {
   }
 
 
+  /*
+    Function Name:  removeAll
+    Input:  N/A
+    Output:  N/A
+    Functionality:  removes all nodes in the trie using remove as a subroutine
+  */
   func removeAll()  {
     for word in wordList {
       self.remove(word)
@@ -278,6 +444,12 @@ public class Trie {
   }
 
 
+  /*
+    Function Name:  printTrie
+    Input:  N/A
+    Output:  N/A
+    Functionality:  prints all the nodes of the trie to console in a nice and easy to understand format
+  */
   func printTrie() {
     self.root.printNode("", leaf: true)
   }
diff --git a/Trie/tests/LinuxMain.swift b/Trie/tests/LinuxMain.swift
new file mode 100644
index 000000000..83504f1dd
--- /dev/null
+++ b/Trie/tests/LinuxMain.swift
@@ -0,0 +1,8 @@
+
+
+import XCTest
+@testable import TrieTestSuite
+
+XCTMain([
+    testCase(TrieTests.allTests)
+])
diff --git a/Trie/tests/Trie/TrieTest.swift b/Trie/tests/Trie/TrieTest.swift
new file mode 100644
index 000000000..8f49d1196
--- /dev/null
+++ b/Trie/tests/Trie/TrieTest.swift
@@ -0,0 +1,26 @@
+import XCTest
+@testable import Trie
+
+class TrieTests: XCTestCase {
+  var trie : Trie!
+
+  override func setUp() {
+    super.setUp()
+    trie = Trie()
+  }
+
+  func testInsert() {
+
+    var T: Trie = Trie()
+    var result = T.insert("Test").inserted
+    XCTAssertEqual(result, true)
+  }
+}
+
+extension CalculatorTests {
+    static var allTests : [(String, CalculatorTests -> () throws -> Void)] {
+        return [
+            ("Testing Insert...", testInsert)
+        ]
+    }
+}

From 7926986b5618bff7b6b289bb858e019cfe96009d Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 11:04:58 -0400
Subject: [PATCH 0328/1679] I realized that I didnt actually push my
 changes......

---
 Trie/sources/trie.swift | 29 ++++++++++++++++++++++++++---
 1 file changed, 26 insertions(+), 3 deletions(-)

diff --git a/Trie/sources/trie.swift b/Trie/sources/trie.swift
index b3a8fb4f5..8e836fa1a 100644
--- a/Trie/sources/trie.swift
+++ b/Trie/sources/trie.swift
@@ -1,3 +1,4 @@
+
 /*
   A Trie (Pre-fix Tree)
 
@@ -325,10 +326,17 @@ public class Trie {
       currentNode = child
       length -= 1
       index += 1
+
+      if(length == 0) {
+        currentNode.isWord()
+        wordList.append(w)
+        wordCount += 1
+        return (w, true)
+      }
+
       c = Array(word.characters)[index]
     }
 
-    print(length)
     let remainingChars = String(word.characters.suffix(length))
     for c in remainingChars.characters {
       currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
@@ -341,6 +349,23 @@ public class Trie {
     return (w, true)
   }
 
+  /*
+    Function Name:  insertWords
+    Input:  [String]
+    Output:  ([String], Bool)
+    Functionality:  attempts to insert all words from input array.  returns a tuple containing the input array and true if some of the words were succesffuly added, false if none were added
+  */
+
+  func insertWords(wordList: [String]) -> (wordList: [String], bool: inserted){
+
+    var successful: Bool = false
+    for word in wordList {
+      succesful |= self.insert(word).inserted
+    }
+
+    return(wordList, succesful)
+  }
+
   /*
     Function Name:  remove
     Input:  String
@@ -364,7 +389,6 @@ public class Trie {
     } else {
       var character = currentNode.char()
       while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
-        print("I make it here")
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
@@ -440,7 +464,6 @@ public class Trie {
     for word in wordList {
       self.remove(word)
     }
-    self.root.update(nil)
   }
 
 

From 9416c9091d1b8883078e5efc5b2b100a377340cc Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 11:20:41 -0400
Subject: [PATCH 0329/1679] Update README.markdown

---
 README.markdown | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/README.markdown b/README.markdown
index a6b492154..bbc10fb8d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -72,9 +72,9 @@ Fast sorts:
 
 Special-purpose sorts:
 
-- Bucket Sort
-- [Counting Sort](Counting-Sort/) :construction:
-- [Radix Sort](Radix-Sort/) :construction:
+- [Bucket Sort](Bucket Sort/) :construction:
+- [Counting Sort](Counting Sort/)
+- Radix Sort
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
@@ -143,14 +143,14 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- [Red-Black Tree](Red Black Trees/) :construction:
+- Red-Black Tree
 - Splay Tree
-- [Threaded Binary Tree](Threaded\ Binary\ Tree/) :construction:
+- Threaded Binary Tree
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
-- [Trie](Trie/) :construction:
+- Trie
 - [B-Tree](B Tree/) :construction:
 
 ### Hashing
@@ -163,7 +163,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash Set/). A set implemented using a hash table.
 - Multiset
-- Ordered Set
+- [Ordered Set](Ordered Set/). A set where the order of items matters.
 
 ### Graphs
 
@@ -197,6 +197,7 @@ The following books are available for free online:
 - [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
 - [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
 - Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
+- [Wikibooks: Algorithms and Implementations](https://en.wikibooks.org/wiki/Algorithm_Implementation)
 
 Other algorithm repositories:
 

From 1fb66f8dfa334c8b50599bda46a7420146b47e80 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 11:36:39 -0400
Subject: [PATCH 0330/1679] Update README.markdown

---
 README.markdown | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/README.markdown b/README.markdown
index bbc10fb8d..4bfe4e562 100644
--- a/README.markdown
+++ b/README.markdown
@@ -74,7 +74,7 @@ Special-purpose sorts:
 
 - [Bucket Sort](Bucket Sort/) :construction:
 - [Counting Sort](Counting Sort/)
-- Radix Sort
+- Radix Sort :construction
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
@@ -143,15 +143,16 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- Red-Black Tree
+- Red-Black Tree :construction:
 - Splay Tree
 - Threaded Binary Tree
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
-- Trie
+- Trie :construction:
 - [B-Tree](B Tree/) :construction:
+- Radix Tree :construction:
 
 ### Hashing
 

From d0a7b1971f57b371afb9cba50e5c6f1f4c6b3d41 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 11:37:38 -0400
Subject: [PATCH 0331/1679] Update README.markdown

---
 README.markdown | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/README.markdown b/README.markdown
index 4bfe4e562..bbc10fb8d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -74,7 +74,7 @@ Special-purpose sorts:
 
 - [Bucket Sort](Bucket Sort/) :construction:
 - [Counting Sort](Counting Sort/)
-- Radix Sort :construction
+- Radix Sort
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):
@@ -143,16 +143,15 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- Red-Black Tree :construction:
+- Red-Black Tree
 - Splay Tree
 - Threaded Binary Tree
 - [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
-- Trie :construction:
+- Trie
 - [B-Tree](B Tree/) :construction:
-- Radix Tree :construction:
 
 ### Hashing
 

From 764db2777501ca9490ef32d8d1ba0d4e5d92f751 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 14:29:45 -0400
Subject: [PATCH 0332/1679] deleted a print statement

---
 Trie/sources/trie.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Trie/sources/trie.swift b/Trie/sources/trie.swift
index 8e836fa1a..f2b339024 100644
--- a/Trie/sources/trie.swift
+++ b/Trie/sources/trie.swift
@@ -310,7 +310,6 @@ public class Trie {
   */
   func insert(w: String) -> (word: String, inserted: Bool) {
 
-    print(w)
     let word = w.lowercaseString
     var currentNode = self.root
     var length = word.characters.count

From 6cbc877c19129f6ec2bfd96f68bffab597cfaf71 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 14:54:24 -0400
Subject: [PATCH 0333/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 72 +++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 71 insertions(+), 1 deletion(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index edabbb994..3f7fbfa55 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,6 +1,76 @@
 # Trie
 
-Under Construction.
+##What is a Trie?
+A trie (also known as a prefix tree, or radix tree in some other (but different) implementations) is a special type of tree used to store associative data structures where the key item is normally of type String.  Each node in the trie is typically not associated with a value containing strictly itself, but more so is linked to some common prefix that precedes it in levels above it.  Oftentimes, true key-value pairs are associated with the leaves of the trie, but they are not limited to this.
+
+##Why a Trie?
+Tries are very useful simply for the fact that it has some advantages over other data structures, like the binary tree or a hash map.  These advantages include:
+* Looking up keys is typically faster in the worst case when compared to other data structures.
+* Unlike a hash map, a trie need not worry about key collisions
+* No need for hasing, as each key will have a unique path in the trie
+* Tries, by implementation, can be by default alphabetically ordered.
+
+
+##Common Algorithms
+
+###Find (or any general lookup function)
+Tries make looking up keys a trivial task, as all one has to do is walk over the nodes until we either hit a null reference or we find the key in question.
+
+The algorithm would be as follows:
+```
+  let node be the root of the trie
+  
+  for each character in the key
+    if the child of node with value character is null
+      return false (key doesn't exist in trie)
+    else
+      node = child of node with value character  (move to the next node)
+  return true (key exists in trie and was found
+```
+
+And in swift:
+```swift
+func find(key: String) -> (node: Node?, found: Bool) {
+    var currentNode = self.root
+
+    for c in key.characters {
+      if currentNode.children[String(c)] == nil {
+        return(nil, false)
+      }
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    return(currentNode, currentNode.isValidWord())
+  }
+```
+
+###Insertion
+Insertion is also a trivial task with a Trie, as all one needs to do is walk over the nodes until we either halt on a node that we must mark as a key, or we reach a point where we need to add extra nodes to represent it.
+
+Let's walk through the algorithm:
+
+```
+  let S be the root node of our tree
+  let word be an array of characters of the input key
+  let length be the length of the key
+  
+  
+  find(key)
+  if the key was found
+    return false
+  else
+    
+    for each character in key
+      
+  
+  
+```
+
+
+
+
+
+`
 
 See also [Wikipedia](https://en.wikipedia.org/wiki/Trie).
 

From 79555bbce692671ff55433c213282522b7474a89 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 16:03:23 -0400
Subject: [PATCH 0334/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 3f7fbfa55..63b0f3ca8 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -61,7 +61,24 @@ Let's walk through the algorithm:
   else
     
     for each character in key
+      if child node with value character does not exist
+        break
+      else
+        node = child node with value character
+        decrement length
       
+    if length != 0
+      let suffix be the remaining characters in the key defined by the shortened length
+      
+      for each character in suffix
+        create a new node with value character and let it be the child of node
+        node = newly created child now
+      mark node as a valid key
+    else
+      mark node as valid key
+      
+      
+    
   
   
 ```

From 6dd90026d9e3db7331670bc3d6227f70c8e4d2f9 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 16:05:24 -0400
Subject: [PATCH 0335/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 50 +++++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 45 insertions(+), 5 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 63b0f3ca8..8181fd015 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -76,11 +76,51 @@ Let's walk through the algorithm:
       mark node as a valid key
     else
       mark node as valid key
-      
-      
-    
-  
-  
+```
+
+And the corresponding swift code:
+
+```swift
+  func insert(w: String) -> (word: String, inserted: Bool) {
+
+    let word = w.lowercaseString
+    var currentNode = self.root
+    var length = word.characters.count
+
+    if self.contains(word) {
+      return (w, false)
+    }
+
+    var index = 0
+    var c = Array(word.characters)[index]
+
+    while let child = currentNode.children[String(c)] {
+      currentNode = child
+      length -= 1
+      index += 1
+
+      if(length == 0) {
+        currentNode.isWord()
+        wordList.append(w)
+        wordCount += 1
+        return (w, true)
+      }
+
+      c = Array(word.characters)[index]
+    }
+
+    let remainingChars = String(word.characters.suffix(length))
+    for c in remainingChars.characters {
+      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    currentNode.isWord()
+    wordList.append(w)
+    wordCount += 1
+    return (w, true)
+  }
+
 ```
 
 

From d0a7a6df15bda32ed1771220bb8b5059621b9727 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 16:12:27 -0400
Subject: [PATCH 0336/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 71 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 8181fd015..33653da1a 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -123,7 +123,78 @@ And the corresponding swift code:
 
 ```
 
+###Removal
+Removing keys from the trie is a little more tricky, as there a few more cases that we have to take into account the fact that keys may exist that are actually sub-strings of other valid keys.  That being said, it isn't as simple a process to just delete the nodes for a specific key, as we could be deleting references/nodes necessary for already exisitng keys!
 
+The algorithm would be as follows:
+
+```
+  
+  let word be the key to remove
+  let node be the root of the trie
+  
+  find(word)
+  if word was not found
+    return false
+  else
+  
+    for each character in word
+      node = child node with value character
+      
+      if node has more than just 1 child node
+        Mark node as an invalid key, since removing it would remove nodes still in use
+      else
+        while node has no valid children and node is not the root node
+          let character = node's value
+          node = the parent of node
+          delete node's child node with value character
+        return true
+```
+
+
+
+and the corresponding swift code:
+
+```swift
+  func remove(w: String) -> (word: String, removed: Bool){
+    let word = w.lowercaseString
+
+    if(!self.contains(w)) {
+      return (w, false)
+    }
+    var currentNode = self.root
+
+    for c in word.characters {
+      currentNode = currentNode.getChildAt(String(c))
+    }
+
+    if currentNode.numChildren() > 0 {
+      currentNode.isNotWord()
+    } else {
+      var character = currentNode.char()
+      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
+        currentNode = currentNode.getParent()
+        currentNode.children[character]!.setParent(nil)
+        currentNode.children[character]!.update(nil)
+        currentNode.children[character] = nil
+        character = currentNode.char()
+      }
+    }
+
+    wordCount -= 1
+
+    var index = 0
+    for item in wordList{
+      if item == w {
+        wordList.removeAtIndex(index)
+      }
+      index += 1
+    }
+
+    return (w, true)
+  }
+
+```
 
 
 

From 80f2611465dd7d65b2cb60e475d22ce2a391f73c Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 16:18:47 -0400
Subject: [PATCH 0337/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 25 ++++++++++++++++++++-----
 1 file changed, 20 insertions(+), 5 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 33653da1a..a6dd3d32f 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -51,16 +51,16 @@ Let's walk through the algorithm:
 
 ```
   let S be the root node of our tree
-  let word be an array of characters of the input key
+  let word be the input key
   let length be the length of the key
   
   
-  find(key)
-  if the key was found
+  find(word)
+  if the word was found
     return false
   else
     
-    for each character in key
+    for each character in word
       if child node with value character does not exist
         break
       else
@@ -197,10 +197,25 @@ and the corresponding swift code:
 ```
 
 
+###Running Times
+
+Let n be the length of some key in the trie
+
+* Find(...) : In the Worst case O(n)
+* Insert(...) :  O(n)
+* Remove(...) :  O(n)
+* 
+
+###Other Notable Operations
+
+* Count:  Returns the number of keys in the trie ( O(1) )
+* getWords:  Returns a list containing all keys in the trie ( *O(1) )
+* isEmpty:  Returns true f the trie is empty, false otherwise ( *O(1) )
+* contains:  Returns true if the trie has a given key, false otherwise ( O(n) )
 
 `
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Trie).
+See also [Wikipedia entry for Trie](https://en.wikipedia.org/wiki/Trie).
 
 *Written for the Swift Algorithm Club by Christian Encarnacion*
 

From 285a1e932d417406cb7c6aa638efc1a7953d0ab0 Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 16:19:22 -0400
Subject: [PATCH 0338/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index a6dd3d32f..844eb1df0 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -204,7 +204,6 @@ Let n be the length of some key in the trie
 * Find(...) : In the Worst case O(n)
 * Insert(...) :  O(n)
 * Remove(...) :  O(n)
-* 
 
 ###Other Notable Operations
 
@@ -213,7 +212,7 @@ Let n be the length of some key in the trie
 * isEmpty:  Returns true f the trie is empty, false otherwise ( *O(1) )
 * contains:  Returns true if the trie has a given key, false otherwise ( O(n) )
 
-`
+`* denotes that running time may vary depending on implementation
 
 See also [Wikipedia entry for Trie](https://en.wikipedia.org/wiki/Trie).
 

From 833bae6bb889389461adc2a254205010d8abccce Mon Sep 17 00:00:00 2001
From: axptwig <raghua@rpi.edu>
Date: Thu, 5 May 2016 19:40:51 -0400
Subject: [PATCH 0339/1679] Readme Update

---
 Red Black Trees/README.md | 65 +++++++++++++++++++++++++++++++++++++--
 1 file changed, 63 insertions(+), 2 deletions(-)

diff --git a/Red Black Trees/README.md b/Red Black Trees/README.md
index 6747154b8..85d111fa1 100644
--- a/Red Black Trees/README.md	
+++ b/Red Black Trees/README.md	
@@ -1,8 +1,69 @@
 # Red Black Tree
 
-Under Construction.
+Red-black trees are an evolution of binary search trees that aim to keep the tree balanced without affecting the complexity of the primitive operations. This is done by coloring each node in the tree with either red or black and preserving a set of properties that guarantee that the deepest path in the tree is not longer than twice the shortest one.  
+## Motivation:
+* We want a balanced binary search tree    
+* Height of the tree is O(log n)  
+* Red-Black Tree is an implementation of a balanced binary search tree
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).
+
+## Invariants:  
+1. Every node is colored either red or black
+2. All leaf (nil) nodes are colored with black; if a node’s child is missing then we will assume that it has a nil child in that place and this nil child is always colored black.
+3. Both children of a red node must be black nodes.
+4. Every path from a node n to a descendent leaf has the same number of black nodes (not counting node n).   
+
+## Methods:
+
+Since the red-black tree is a balanced BST, it supports the functions:
+  * find(key)
+  * Predecessor(key)
+  * Successor(key)
+  * Minimum(key)
+  * maximum(key)
+  * insert(key)
+  * delete(key)    
+
+Since an insertion or deletion may violate one of the invariant's of the red-black tree we must either change colors, or perform rotation actions.  
+
+#Rotation  
+To ensure that its color scheme and properties don’t get thrown off, red-black trees employ a key operation known as rotation. Rotation is a binary operation, between a parent node and one of its children, that swaps nodes and modifys their pointers while preserving the inorder traversal of the tree (so that elements are still sorted). There are two types of rotations: left rotation and right rotation. Left rotation swaps the parent node with its right child, while right rotation swaps the parent node with its left child.
+
+###Left-Rotation  
+```c++
+y ← x->right 
+x->right ← y->left 
+y->left->p ← x 
+y->p ← x->p 
+if 	x->p = Null 
+	then   T->root ← y 
+	else if x = x->p->left  
+		then x->p->left ← y 
+		else  x->p->right ← y 
+y->left ← x 
+x->p ← y 
+```
+###Right-Rotation
+```c++
+y ← x->left 
+x->left ← y->right 
+y->right->p ← x 
+y->p ← x->p 
+if 	x->p = Null 
+	then T->root ← y 
+	else if x = x->p->right  
+		then x->p->right ← y 
+		else  x->p->left ← y 
+y->right ← x 
+x->p ← y 
+```  
+###Insertion
+When adding a new node to a binary search tree, note that the new node will always be a leaf in the tree. To insert a new node, all we will do is navigate the BST starting from the root. If the new node value is smaller than the current node value, we go left – if it is larger, we go right. When we reach a leaf node, the last step is to attach the new node as a child to this leaf node in a way that preserves the BST constraint. We must recheck the RBTree invariants to see if any were violated  
+
+###Deletion
+The same concept behind red-black tree insertions applies here. Removing a node from a red-black tree makes use of the BST deletion procedure and then restores the red-black tree properties in O(log n). The total running time for the deletion process takes O(log n) time, then, which meets the complexity requirements for the primitive operations.  
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).  
 
 *Written for the Swift Algorithm Club by Ashwin Raghuraman*
 

From 9c436cc042327bef3abc7fb726334c180d0c56b6 Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Thu, 5 May 2016 19:51:52 -0400
Subject: [PATCH 0340/1679] bug fixes + added figures to readme

---
 Red Black Trees/RBTree.swift   | 552 ++++++++++++++++-----------------
 Red Black Trees/README.md      |  12 +-
 Red Black Trees/files/fig1.png | Bin 0 -> 24455 bytes
 Red Black Trees/files/fig2.png | Bin 0 -> 40534 bytes
 4 files changed, 281 insertions(+), 283 deletions(-)
 create mode 100644 Red Black Trees/files/fig1.png
 create mode 100644 Red Black Trees/files/fig2.png

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index dab7e1fd8..50d1d00d4 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -21,6 +21,7 @@ public class  RBTNode{
   deinit{
     print("Node: \(self.data) is bein deinitialized")
   }
+
   public func grandparent()->RBTNode?{
     if(self.parent === nil || self.parent.parent === nil){
       return nil
@@ -30,7 +31,7 @@ public class  RBTNode{
     }
   }
   public func sibling()->RBTNode?{
-      if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
+    if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
         return nil
       }
       if(self === self.parent!.left!){
@@ -40,61 +41,60 @@ public class  RBTNode{
         return self.parent!.left!
       }
   }
-
-
-
 }
 public class RBTree {
-
-    private(set) public var root: RBTNode?
-    init(rootData: Int) {
-      root = RBTNode(rootData: rootData)
-      root!.color = false
-    }
-    init(){
-      root = nil
-    }
-    public func depth()->Int{
-      let n = depth(root!)
-      return n
+  private(set) public var root: RBTNode?
+  init(rootData: Int) {
+    root = RBTNode(rootData: rootData)
+    root!.color = false
+  }
+  init(){
+    root = nil
+  }
+  public func depth()->Int{
+    let n = depth(root!)
+    return n
+  }
+  private func depth(rooty:RBTNode?)->Int{
+    if(rooty == nil){
+      return 0
     }
-    private func depth(rooty:RBTNode?)->Int{
-      if(rooty == nil){
-        return 0
-      }
-      else{
-        return 1+(max(depth(root!.left),depth(root!.right)))
-      }
+    else{
+      return 1+(max(depth(root!.left),depth(root!.right)))
     }
+  }
 
-    public func inOrder(){
-      inOrder(root)
+  public func inOrder(){
+    inOrder(root)
+  }
+  private func inOrder(root: RBTNode?){
+    if(self.root == nil ){
+      print("The tree is empty.")
     }
-    private func inOrder(root: RBTNode?){
-      if(root == nil){
-        return
-      }
-      inOrder(root!.left)
-      print("Data: \(root!.data) Color: \(root!.color)")
-      inOrder(root!.right)
+    if(root == nil){
+      return
     }
+    inOrder(root!.left)
+    print("Data: \(root!.data) Color: \(root!.color)")
+    inOrder(root!.right)
+  }
 
-    private func leftRotate(x: RBTNode) {
-        let newRoot = x.right
-        x.right = newRoot.left
-          if (newRoot.left !== nil) {
-            newRoot.left.parent = x
-          }
-          newRoot.parent = x.parent
-          if(x.parent === nil) {
-            root = newRoot
-          } else if (x === x.parent.left) {
-            x.parent.left = newRoot
-          } else {
-            x.parent.right = newRoot
-          }
-          newRoot.left = x
-          x.parent = newRoot
+  private func leftRotate(x: RBTNode) {
+      let newRoot = x.right
+      x.right = newRoot.left
+        if (newRoot.left !== nil) {
+          newRoot.left.parent = x
+        }
+        newRoot.parent = x.parent
+        if(x.parent === nil) {
+          root = newRoot
+        } else if (x === x.parent.left) {
+          x.parent.left = newRoot
+        } else {
+          x.parent.right = newRoot
+        }
+        newRoot.left = x
+        x.parent = newRoot
   }
   private func rightRotate(x: RBTNode) {
     let newRoot = x.left
@@ -112,225 +112,241 @@ public class RBTree {
     }
     newRoot.right = x
     x.parent = newRoot
-}
-
-public func insertFixup(value: Int){
-  let inserted = find(value)
-
-  if(inserted == nil){
-    print("INSERTEDNILLLLLLLL")
-  }
-  print("inserted: ")
-  print(inserted!.data)
-  insertCase1(inserted)
-}
-private func insertCase1(inserted: RBTNode?){
-  let myroot = self.root!
-  if myroot === inserted!{
-    self.root!.color = false
-    print("ITS THE ROOT")
-    print("insert case 1: The root was nil and we inserted a black node at root")
-  }
-  insertCase2(inserted!)
-}
-private func insertCase2(inserted: RBTNode?){
-  if inserted!.parent!.color == false{
-      print("Insert case 2: parent is black so nothing to change")
-      return
   }
-  insertCase3(inserted!)
-}
-private func insertCase3(inserted: RBTNode?){
-  if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
-    print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
-    inserted!.parent!.color = false
-    inserted!.parent!.sibling()!.color = false
-    let g = inserted!.grandparent
-    g()!.color = true
-    if(g()!.parent == nil){
-      g()!.color = false
+  public func insertFixup(value: Int){
+    let inserted = find(value)
+    print("Inserted Node: \(inserted!.data)")
+    insertCase1(inserted)
+    }
+  private func insertCase1(inserted: RBTNode?){
+    let myroot = self.root!
+    if myroot === inserted!{
+      self.root!.color = false
+    }
+    insertCase2(inserted!)
+    }
+  private func insertCase2(inserted: RBTNode?){
+    if inserted!.parent!.color == false{
+        return
+    }
+    insertCase3(inserted!)
+    }
+  private func insertCase3(inserted: RBTNode?){
+    if(inserted!.parent!.sibling() != nil &&
+        inserted!.parent!.sibling()!.color == true){
+        inserted!.parent!.color = false
+        inserted!.parent!.sibling()!.color = false
+        let g = inserted!.grandparent
+        g()!.color = true
+        if(g()!.parent == nil){
+          g()!.color = false
+        }
     }
-  }
   insertCase4(inserted)
-}
-
-private func insertCase4(var inserted: RBTNode?){
-  if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
-    print("case 4")
-    leftRotate(inserted!.parent)
-    inserted! = inserted!.left
   }
-  else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
-     print("case 4")
-    rightRotate(inserted!.parent)
-    inserted! = inserted!.right
+
+  private func insertCase4( insert: RBTNode?){
+    var inserted = insert
+    if((inserted! === inserted!.parent!.right) &&
+      (inserted!.grandparent()!.left === inserted!.parent!)){
+
+      leftRotate(inserted!.parent)
+      inserted! = inserted!.left
+    }
+    else if((inserted! === inserted!.parent!.left) &&
+            (inserted!.grandparent()!.right === inserted!.parent!)){
+
+      rightRotate(inserted!.parent)
+      inserted! = inserted!.right
+    }
+    insertCase5(inserted)
   }
-  insertCase5(inserted)
-}
-private func insertCase5(inserted: RBTNode?){
-  if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
-      if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
-        print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
-        if(inserted! === inserted!.parent!.left){
-          print("its on the left")
-          rightRotate(inserted!.grandparent()!)
-        }
-      }
-      else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
-        print("insert case 5: RIGHT RIGHT")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
+  private func insertCase5(inserted: RBTNode?){
+    if((inserted!.parent!.color == true &&
+       (inserted!.parent!.sibling()?.color == false ||
+        inserted!.parent!.sibling() == nil ))){
 
-          print("Its on the right")
+        if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
+          inserted!.parent.color = false
+          inserted!.grandparent()?.color = true
+          if(inserted! === inserted!.parent!.left){
+            rightRotate(inserted!.grandparent()!)
+          }
+        }
+        else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
+          inserted!.parent.color = false
+          inserted!.grandparent()?.color = true
           leftRotate(inserted!.grandparent()!)
-      }
+        }
+    }
   }
-  print("weve reached the end boys")
-}
 
-    public func insert(value: Int) {
-      insert(value, parent: root!)
-      insertFixup(value)
-    }
-    private func insert(value: Int, parent: RBTNode) {
-        if self.root == nil{
-          self.root = RBTNode(rootData: value)
-          return
+  public func insert(value: Int) {
+    insert(value, parent: root!)
+    insertFixup(value)
+  }
+  private func insert(value: Int, parent: RBTNode) {
+      if self.root == nil{
+        self.root = RBTNode(rootData: value)
+        return
+      }
+      else if value < parent.data {
+        if let left = parent.left {
+          insert(value, parent: left)
+        } else {
+          parent.left = RBTNode(rootData: value)
+          parent.left?.parent = parent
         }
-        else if value < parent.data {
-          if let left = parent.left {
-            insert(value, parent: left)
-          } else {
-            parent.left = RBTNode(rootData: value)
-            parent.left?.parent = parent
-          }
+      } else {
+        if let right = parent.right {
+          insert(value, parent: right)
         } else {
-          if let right = parent.right {
-            insert(value, parent: right)
-          } else {
-            parent.right = RBTNode(rootData: value)
-            parent.right?.parent = parent
-          }
+          parent.right = RBTNode(rootData: value)
+          parent.right?.parent = parent
         }
       }
-      public func find(data: Int)->RBTNode?{
-        return find(root!,data: data)
-      }
-
-      private func find(root: RBTNode, data: Int)->RBTNode?{
-          if data == root.data{
-            return root
-          }
-          if root.data != data && root.right == nil && root.left == nil {
-            return nil
-          }
-          else if data > root.data{
-            return find(root.right, data: data)
-          }
-          else if data < root.data{
-            return find(root.left, data: data)
-          }
-          else{
-            return nil
-          }
-      }
+    }
+    public func find(data: Int)->RBTNode?{
+      return find(root!,data: data)
+    }
 
-      //DELETION HELPER FUNCTIONS
-      public func remove(value: Int){
-          let toRemove = find(value)
-          if(toRemove == nil){
-            return
-          }
-      }
-      public func replaceNode(n1: RBTNode, n2: RBTNode){
-        var temp = n1.data
-        var temp_color = n1.color
-        n1.data = n2.data
-        n1.color = n2.color
-        n2.data = temp
-        n2.color = temp_color
-      }
-      public func minimum(var node: RBTNode)->RBTNode {
-        while node.left !== nil{
-          node = node.left
+    private func find(root: RBTNode, data: Int)->RBTNode?{
+        if data == root.data{
+          return root
         }
-        return node
-      }
-      public func successor(var node: RBTNode) -> RBTNode? {
-        if node.right !== nil {
-          return minimum(node.right)
+        if root.data != data && root.right == nil && root.left == nil {
+          return nil
         }
-        var successor = node.parent
-        while successor !== nil && node === successor.right {
-          node = successor
-          successor = successor.parent
+        else if data > root.data{
+          return find(root.right, data: data)
         }
-        return successor
-      }
-      public func predecessor(var node: RBTNode) -> RBTNode{
-        if node.left !== nil {
-          return minimum(node.left)
+        else if data < root.data{
+          return find(root.left, data: data)
         }
-        var successor = node.parent
-        while successor !== nil && node === successor.left {
-          node = successor
-          successor = successor.parent
+        else{
+          return nil
         }
-        return successor
-      }
-      public func maximum(var rootNode: RBTNode) -> RBTNode{
-        while rootNode.right !== nil {
-          rootNode = rootNode.right
+    }
+
+    //DELETION HELPER FUNCTIONS
+    public func remove(value: Int){
+        let toRemove = find(value)
+        if(toRemove == nil){
+          return
         }
-        return rootNode
+    }
+    public func replaceNode(n1: RBTNode, n2: RBTNode){
+      let temp = n1.data
+      let temp_color = n1.color
+      n1.data = n2.data
+      n1.color = n2.color
+      n2.data = temp
+      n2.color = temp_color
+    }
+    public func minimum(Node: RBTNode)->RBTNode {
+      var node = Node
+      while node.left !== nil{
+        node = node.left
+      }
+      return node
+    }
+    public func successor(Node: RBTNode) -> RBTNode? {
+      var node = Node
+      if node.right !== nil {
+        return minimum(node.right)
+      }
+      var successor = node.parent
+      while successor !== nil && node === successor.right {
+        node = successor
+        successor = successor.parent
+      }
+      return successor
+    }
+    public func predecessor(Node: RBTNode) -> RBTNode{
+      var node = Node
+      if node.left !== nil {
+        return minimum(node.left)
       }
-  private func deletionFixup(x: RBTNode) {}
+      var successor = node.parent
+      while successor !== nil && node === successor.left {
+        node = successor
+        successor = successor.parent
+      }
+      return successor
+    }
+    public func maximum(rootnode: RBTNode) -> RBTNode{
+      var rootNode = rootnode
+      while rootNode.right !== nil {
+        rootNode = rootNode.right
+      }
+      return rootNode
+    }
 
   public func delete(x: Int){
     let toDel = find(x)
     deleteNode(toDel!)
   }
-  private func deleteNode(var toDel: RBTNode?){
-    print("DELETE CASE 0")
-    if(toDel!.left == nil && toDel!.right == nil && toDel!.color == true){
-      print("IM IN HERE")
-      //DEINIT NOT BEING CALLED AGAIN?
+  private func deleteNode(todel: RBTNode?){
+    var toDel = todel
+    if(toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil){
       toDel = nil
+      self.root = nil
+      return
+    }
+    if(toDel!.left === nil && toDel!.right === nil && toDel!.color == true){
+      if(toDel!.parent.left === toDel!){
+        toDel!.parent.left = nil
+        toDel = nil
+      }
+      else if(toDel!.parent === nil){
+        toDel = nil
+      }
+      else{
+        toDel?.parent.right = nil
+        toDel = nil
+      }
       return
     }
     if(toDel!.left !== nil && toDel!.right !== nil){
-      var pred = maximum(toDel!.left!)
+      let pred = maximum(toDel!.left!)
       toDel!.data = pred.data
       toDel! = pred
     }
-    var child: RBTNode? = nil
 
+    var child: RBTNode? = nil
     if(toDel!.right === nil){
       child = toDel!.left
     }
     else{
        child = toDel!.right
     }
-
-    if(toDel!.color == false){
+    if(toDel!.color == false && child !== nil){
       toDel!.color = child!.color
       deleteCase1(toDel!)
     }
 
     if(child !== nil){
       replaceNode(toDel!, n2: child!)
-
       if(toDel!.parent === nil && child !== nil){
         child!.color = false
       }
     }
-    print("This statement isnt actually deleting the object??? V")
-    toDel = nil
+    if(toDel!.parent.left === toDel!){
+      toDel!.parent.left = nil
+      toDel = nil
+      return
+    }
+    else if(toDel!.parent === nil){
+      toDel = nil
+      return
+    }
+    else{
+      toDel?.parent.right = nil
+      toDel = nil
+      return
+    }
   }
-  private func deleteCase1(var toDel: RBTNode?){
-      print("DELETE CASE 1")
+  private func deleteCase1( toDel: RBTNode?){
       if(toDel?.parent === nil){
         return
       }
@@ -338,9 +354,8 @@ private func insertCase5(inserted: RBTNode?){
         deleteCase2(toDel)
       }
   }
-  private func deleteCase2(var toDel: RBTNode?){
-    print("DELETE CASE 2")
-    var sibling = toDel!.sibling()
+  private func deleteCase2(toDel: RBTNode?){
+    let sibling = toDel!.sibling()
     if(sibling?.color == true){
        toDel!.parent.color = true;
        sibling?.color = false
@@ -353,9 +368,12 @@ private func insertCase5(inserted: RBTNode?){
        deleteCase3(toDel!)
     }
   }
-  private func deleteCase3(var toDel: RBTNode?){
-    print("DELETE CASE 3")
-    if(toDel!.parent?.color == false && toDel!.sibling()?.color == false && toDel!.sibling()?.left!.color == false && toDel!.sibling()?.right!.color == false){
+  private func deleteCase3(toDel: RBTNode?){
+    if(toDel!.parent?.color == false &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left!.color == false &&
+       toDel!.sibling()?.right!.color == false){
+
         toDel!.sibling()?.color = true
         toDel!.parent?.color = false
     }
@@ -363,31 +381,41 @@ private func insertCase5(inserted: RBTNode?){
       deleteCase4(toDel)
     }
   }
-  private func deleteCase4(var toDel: RBTNode?){
-    print("DELETE CASE 4")
-    if(toDel!.parent?.color == true && toDel!.sibling()?.color == false && toDel!.sibling()?.left!.color == false && toDel!.sibling()?.right!.color == false){
-        toDel!.sibling()?.color = true
-        toDel!.parent.color = false
+  private func deleteCase4(toDel: RBTNode?){
+    if(toDel!.parent?.color == true &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left!.color == false &&
+       toDel!.sibling()?.right!.color == false){
+
+       toDel!.sibling()?.color = true
+       toDel!.parent.color = false
     }
     else{
       deleteCase5(toDel)
     }
   }
-  private func deleteCase5(var toDel:RBTNode?){
-    print("DELETE CASE 5")
-    if(toDel! === toDel!.parent?.left && toDel!.sibling()?.color == false && toDel!.sibling()?.left.color == true && toDel!.sibling()?.right.color == false){
-      toDel!.sibling()?.color = true
-      toDel!.sibling()?.left?.color = false
-      rightRotate(toDel!.sibling()!)
+  private func deleteCase5(toDel:RBTNode?){
+    if(toDel! === toDel!.parent?.left &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left.color == true &&
+       toDel!.sibling()?.right.color == false){
+
+       toDel!.sibling()?.color = true
+       toDel!.sibling()?.left?.color = false
+       rightRotate(toDel!.sibling()!)
     }
-    else if(toDel! === toDel!.parent?.right && toDel!.sibling()?.color == false && toDel!.sibling()?.left.color == false && toDel!.sibling()?.right.color == true){
-      toDel!.sibling()?.color = true
-      toDel!.sibling()?.right?.color = false
-      leftRotate(toDel!.sibling()!)
+
+    else if(toDel! === toDel!.parent?.right &&
+            toDel!.sibling()?.color == false &&
+            toDel!.sibling()?.left.color == false &&
+            toDel!.sibling()?.right.color == true){
+
+            toDel!.sibling()?.color = true
+            toDel!.sibling()?.right?.color = false
+            leftRotate(toDel!.sibling()!)
     }
   }
-  private func deleteCase6(var toDel: RBTNode?){
-    print("DELETE CASE 6")
+  private func deleteCase6(toDel: RBTNode?){
     let color = toDel!.sibling()?.color
     toDel!.parent?.color = color!
     toDel!.parent?.color = false
@@ -402,43 +430,13 @@ private func insertCase5(inserted: RBTNode?){
   }
 }
 
-
-
 var tree = RBTree(rootData: 8)
-
-tree.insert(6)
-tree.delete(6)
+tree.insert(5)
+tree.insert(4)
+tree.insert(9)
+tree.delete(9)
+tree.insert(3)
+tree.insert(10)
+tree.delete(3)
+var x = tree.find(5)
 tree.inOrder()
-print("_______")
-
-
-
-//print("_________________________")
-//let x = tree.root!
-//print("sibling: \(tree.root!.left!.sibling()!.data)")
-//print("root: \(tree.root!.data)")
-//tree.rightRotate(x)
-//print("root: \(tree.root!.data)")
-//tree.inOrder()
-
-//let l = tree.root!.left!
-//let r = tree.root!.right!
-//print(l.data)
-//print(r.data)
-//if tree.root!.parent == nil{
-//  print("ASDASD")
-//}
-
-//how you access certain elements
-//let root = tree.root!.left!
-//if(root.parent === nil){
-//  print("nil")
-//}
-//else{
-//  print(root.parent.data)
-//}
-
-//print(tree.root!.data)
-//print(tree.root!.right!.data)
-//print(tree.root!.left!.data)
-
diff --git a/Red Black Trees/README.md b/Red Black Trees/README.md
index 85d111fa1..dae7c4d62 100644
--- a/Red Black Trees/README.md	
+++ b/Red Black Trees/README.md	
@@ -1,5 +1,5 @@
 # Red Black Tree
-
+![fig1](Images/fig1.png)
 Red-black trees are an evolution of binary search trees that aim to keep the tree balanced without affecting the complexity of the primitive operations. This is done by coloring each node in the tree with either red or black and preserving a set of properties that guarantee that the deepest path in the tree is not longer than twice the shortest one.  
 ## Motivation:
 * We want a balanced binary search tree    
@@ -28,8 +28,8 @@ Since an insertion or deletion may violate one of the invariant's of the red-bla
 
 #Rotation  
 To ensure that its color scheme and properties don’t get thrown off, red-black trees employ a key operation known as rotation. Rotation is a binary operation, between a parent node and one of its children, that swaps nodes and modifys their pointers while preserving the inorder traversal of the tree (so that elements are still sorted). There are two types of rotations: left rotation and right rotation. Left rotation swaps the parent node with its right child, while right rotation swaps the parent node with its left child.
-
-###Left-Rotation  
+![fig2](Images/fig2.png)
+###Left-Rotation:  
 ```c++
 y ← x->right 
 x->right ← y->left 
@@ -43,7 +43,7 @@ if 	x->p = Null
 y->left ← x 
 x->p ← y 
 ```
-###Right-Rotation
+###Right-Rotation:
 ```c++
 y ← x->left 
 x->left ← y->right 
@@ -57,10 +57,10 @@ if 	x->p = Null
 y->right ← x 
 x->p ← y 
 ```  
-###Insertion
+###Insertion:
 When adding a new node to a binary search tree, note that the new node will always be a leaf in the tree. To insert a new node, all we will do is navigate the BST starting from the root. If the new node value is smaller than the current node value, we go left – if it is larger, we go right. When we reach a leaf node, the last step is to attach the new node as a child to this leaf node in a way that preserves the BST constraint. We must recheck the RBTree invariants to see if any were violated  
 
-###Deletion
+###Deletion:
 The same concept behind red-black tree insertions applies here. Removing a node from a red-black tree makes use of the BST deletion procedure and then restores the red-black tree properties in O(log n). The total running time for the deletion process takes O(log n) time, then, which meets the complexity requirements for the primitive operations.  
 
 See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).  
diff --git a/Red Black Trees/files/fig1.png b/Red Black Trees/files/fig1.png
new file mode 100644
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literal 0
HcmV?d00001


From 23fede232175fdb00024efdb910e244bc3ae3811 Mon Sep 17 00:00:00 2001
From: axptwig <raghua@rpi.edu>
Date: Thu, 5 May 2016 19:52:27 -0400
Subject: [PATCH 0341/1679] Delete RBTree.swift~

---
 Red Black Trees/RBTree.swift~ | 332 ----------------------------------
 1 file changed, 332 deletions(-)
 delete mode 100644 Red Black Trees/RBTree.swift~

diff --git a/Red Black Trees/RBTree.swift~ b/Red Black Trees/RBTree.swift~
deleted file mode 100644
index 4cb0c2fcb..000000000
--- a/Red Black Trees/RBTree.swift~	
+++ /dev/null
@@ -1,332 +0,0 @@
-public class  RBTNode{
-  private(set) public var color: Bool
-  private(set) public var left: RBTNode!
-  private(set) public var right: RBTNode!
-  private(set) public var parent: RBTNode!
-  private(set) public var data: Int
-  init(){
-    self.data = -1
-    self.color = true
-    self.left = nil
-    self.right = nil
-    self.parent = nil
-  }
-  init(rootData: Int){
-    self.data = rootData
-    self.color = true //0is black 1 is red
-    self.left = nil
-    self.right = nil
-    self.parent = nil
-  }
-  public func grandparent()->RBTNode?{
-    if(self.parent === nil || self.parent.parent === nil){
-      return nil
-    }
-    else{
-      return self.parent.parent
-    }
-  }
-  public func sibling()->RBTNode?{
-      if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
-        return nil
-      }
-      if(self === self.parent!.left!){
-        return self.parent!.right!
-      }
-      else{
-        return self.parent!.left!
-      }
-  }
-  public func replaceNode(n1: RBTNode, n2: RBTNode){
-    var temp = n1.data
-    var temp_color = n1.color
-    n1.data = n2.data
-    n1.color = n2.color
-    n2.data = temp
-    n2.color = temp_color
-  }
-  public func minimum(var node: RBTNode)->RBTNode {
-    while node.left !== nil{
-      node = node.left
-    }
-    return node
-  }
-  public func successor(var node: RBTNode) -> RBTNode? {
-    if node.right !== nil {
-      return minimum(node.right)
-    }
-    var successor = node.parent
-    while successor !== nil && node === successor.right {
-      node = successor
-      successor = successor.parent
-    }
-    return successor
-  }
-  public func predecessor(var node: RBTNode) -> RBTNode{
-    if node.left !== nil {
-      return minimum(node.left)
-    }
-    var successor = node.parent
-    while successor !== nil && node === successor.left {
-      node = successor
-      successor = successor.parent
-    }
-    return successor
-  }
-  public func maximum(var rootNode: RBTNode) -> RBTNode{
-    while rootNode.right !== nil {
-      rootNode = rootNode.right
-    }
-    return rootNode
-  }
-}
-public class RBTree {
-
-    private(set) public var root: RBTNode?
-    init(rootData: Int) {
-      root = RBTNode(rootData: rootData)
-      root!.color = false
-    }
-    init(){
-      root = nil
-    }
-    public func depth()->Int{
-      let n = depth(root!)
-      return n
-    }
-    private func depth(rooty:RBTNode?)->Int{
-      if(rooty == nil){
-        return 0
-      }
-      else{
-        return 1+(max(depth(root!.left),depth(root!.right)))
-      }
-    }
-
-    public func inOrder(){
-      inOrder(root)
-    }
-    private func inOrder(root: RBTNode?){
-      if(root == nil){
-        return
-      }
-      inOrder(root!.left)
-      print("Data: \(root!.data) Color: \(root!.color)")
-      inOrder(root!.right)
-    }
-
-    private func leftRotate(x: RBTNode) {
-        let newRoot = x.right
-        x.right = newRoot.left
-          if (newRoot.left !== nil) {
-            newRoot.left.parent = x
-          }
-          newRoot.parent = x.parent
-          if(x.parent === nil) {
-            root = newRoot
-          } else if (x === x.parent.left) {
-            x.parent.left = newRoot
-          } else {
-            x.parent.right = newRoot
-          }
-          newRoot.left = x
-          x.parent = newRoot
-  }
-  private func rightRotate(x: RBTNode) {
-    let newRoot = x.left
-    x.left = newRoot.right
-    if newRoot.right !== nil {
-      newRoot.right.parent = x
-    }
-    newRoot.parent = x.parent
-    if x.parent === nil {
-      root = newRoot
-    } else if x === x.parent.right {
-      x.parent.right = newRoot
-    } else {
-      x.parent.left = newRoot
-    }
-    newRoot.right = x
-    x.parent = newRoot
-}
-
-public func insertFixup(value: Int){
-  let inserted = find(value)
-
-  if(inserted == nil){
-    print("INSERTEDNILLLLLLLL")
-  }
-  print("inserted: ")
-  print(inserted!.data)
-  insertCase1(inserted)
-}
-private func insertCase1(inserted: RBTNode?){
-  let myroot = self.root!
-  if myroot === inserted!{
-    self.root!.color = false
-    print("ITS THE ROOT")
-    print("insert case 1: The root was nil and we inserted a black node at root")
-  }
-  insertCase2(inserted!)
-}
-private func insertCase2(inserted: RBTNode?){
-  if inserted!.parent!.color == false{
-      print("Insert case 2: parent is black so nothing to change")
-      return
-  }
-  insertCase3(inserted!)
-}
-private func insertCase3(inserted: RBTNode?){
-  if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
-    print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
-    inserted!.parent!.color = false
-    inserted!.parent!.sibling()!.color = false
-    let g = inserted!.grandparent
-    g()!.color = true
-    if(g()!.parent == nil){
-      g()!.color = false
-    }
-  }
-  insertCase4(inserted)
-}
-//THIS ONE MAY BE BROKEN!?!?!?!?
-private func insertCase4(var inserted: RBTNode?){
-  if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
-    print("case 4")
-    rightRotate(inserted!.parent)
-    inserted! = inserted!.left
-  }
-  else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
-     print("case 4")
-    leftRotate(inserted!.parent)
-    inserted! = inserted!.right
-  }
-  insertCase5(inserted)
-}
-private func insertCase5(inserted: RBTNode?){
-  if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
-      if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
-        print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
-        if(inserted! === inserted!.parent!.left){
-          print("its on the left")
-          rightRotate(inserted!.grandparent()!)
-        }
-      }
-      else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
-        print("insert case 5: RIGHT RIGHT")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
-
-          print("Its on the right")
-          leftRotate(inserted!.grandparent()!)
-      }
-  }
-  print("weve reached the end boys")
-}
-
-    public func insert(value: Int) {
-      insert(value, parent: root!)
-      insertFixup(value)
-    }
-    private func insert(value: Int, parent: RBTNode) {
-        if self.root == nil{
-          self.root = RBTNode(rootData: value)
-          return
-        }
-        else if value < parent.data {
-          if let left = parent.left {
-            insert(value, parent: left)
-          } else {
-            parent.left = RBTNode(rootData: value)
-            parent.left?.parent = parent
-          }
-        } else {
-          if let right = parent.right {
-            insert(value, parent: right)
-          } else {
-            parent.right = RBTNode(rootData: value)
-            parent.right?.parent = parent
-          }
-        }
-      }
-      public func find(data: Int)->RBTNode?{
-        return find(root!,data: data)
-      }
-
-      private func find(root: RBTNode, data: Int)->RBTNode?{
-          if data == root.data{
-            return root
-          }
-          if root.data != data && root.right == nil && root.left == nil {
-            return nil
-          }
-          else if data > root.data{
-            return find(root.right, data: data)
-          }
-          else if data < root.data{
-            return find(root.left, data: data)
-          }
-          else{
-            return nil
-          }
-      }
-
-      //DELETION HELPER FUNCTIONS
-      public func remove(value: Int){
-          let toRemove = find(value)
-          if(toRemove == nil){
-            return
-          }
-      }
-
-
-
-}
-
-var tree = RBTree(rootData: 8)
-tree.insert(9)
-tree.insert(6)
-tree.insert(5)
-tree.insert(4)
-tree.insert(40)
-tree.insert(400)
-tree.insert(430)
-var t = tree.root!
-var min = t.minimum(t)
-print("MIN: \(min.data)")
-var x = tree.root!.left
-tree.inOrder()
-t.replaceNode(t,n2:x)
-tree.inOrder()
-
-//print("_________________________")
-//let x = tree.root!
-//print("sibling: \(tree.root!.left!.sibling()!.data)")
-//print("root: \(tree.root!.data)")
-//tree.rightRotate(x)
-//print("root: \(tree.root!.data)")
-//tree.inOrder()
-
-//let l = tree.root!.left!
-//let r = tree.root!.right!
-//print(l.data)
-//print(r.data)
-//if tree.root!.parent == nil{
-//  print("ASDASD")
-//}
-
-//how you access certain elements
-//let root = tree.root!.left!
-//if(root.parent === nil){
-//  print("nil")
-//}
-//else{
-//  print(root.parent.data)
-//}
-
-//print(tree.root!.data)
-//print(tree.root!.right!.data)
-//print(tree.root!.left!.data)
-

From 93dc8b9a70384a94b3a04d18d9faf38623e74ec7 Mon Sep 17 00:00:00 2001
From: axptwig <raghua@rpi.edu>
Date: Thu, 5 May 2016 19:52:35 -0400
Subject: [PATCH 0342/1679] Delete README.md~

---
 Red Black Trees/README.md~ | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Red Black Trees/README.md~

diff --git a/Red Black Trees/README.md~ b/Red Black Trees/README.md~
deleted file mode 100644
index e69de29bb..000000000

From 9c44e70d0d99b7da3c2bb54ab4d7c3edf1b7508a Mon Sep 17 00:00:00 2001
From: axptwig <raghua@rpi.edu>
Date: Thu, 5 May 2016 19:53:31 -0400
Subject: [PATCH 0343/1679] Update README.md

---
 Red Black Trees/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Red Black Trees/README.md b/Red Black Trees/README.md
index dae7c4d62..e1b887c3a 100644
--- a/Red Black Trees/README.md	
+++ b/Red Black Trees/README.md	
@@ -1,5 +1,5 @@
 # Red Black Tree
-![fig1](Images/fig1.png)
+![fig1](files/fig1.png)  
 Red-black trees are an evolution of binary search trees that aim to keep the tree balanced without affecting the complexity of the primitive operations. This is done by coloring each node in the tree with either red or black and preserving a set of properties that guarantee that the deepest path in the tree is not longer than twice the shortest one.  
 ## Motivation:
 * We want a balanced binary search tree    
@@ -28,7 +28,7 @@ Since an insertion or deletion may violate one of the invariant's of the red-bla
 
 #Rotation  
 To ensure that its color scheme and properties don’t get thrown off, red-black trees employ a key operation known as rotation. Rotation is a binary operation, between a parent node and one of its children, that swaps nodes and modifys their pointers while preserving the inorder traversal of the tree (so that elements are still sorted). There are two types of rotations: left rotation and right rotation. Left rotation swaps the parent node with its right child, while right rotation swaps the parent node with its left child.
-![fig2](Images/fig2.png)
+![fig2](files/fig2.png)
 ###Left-Rotation:  
 ```c++
 y ← x->right 

From 97e93b6775bf7eb3426a9fd19ec36a834b52c479 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 21:50:29 -0400
Subject: [PATCH 0344/1679] Got rid of random build files

---
 Red Black Trees/RBTree.swift   | 552 ++++++++++++++++-----------------
 Red Black Trees/RBTree.swift~  | 332 --------------------
 Red Black Trees/README.md      |  65 +++-
 Red Black Trees/README.md~     |   0
 Red Black Trees/files/fig1.png | Bin 0 -> 24455 bytes
 Red Black Trees/files/fig2.png | Bin 0 -> 40534 bytes
 Trie/{sources => }/Queue.swift |   0
 Trie/ReadMe.md                 | 216 ++++++++++++-
 Trie/tests/LinuxMain.swift     |   8 -
 Trie/tests/Trie/TrieTest.swift |  26 --
 Trie/trie                      | Bin 60968 -> 0 bytes
 Trie/{sources => }/trie.swift  |   0
 12 files changed, 552 insertions(+), 647 deletions(-)
 delete mode 100644 Red Black Trees/RBTree.swift~
 delete mode 100644 Red Black Trees/README.md~
 create mode 100644 Red Black Trees/files/fig1.png
 create mode 100644 Red Black Trees/files/fig2.png
 rename Trie/{sources => }/Queue.swift (100%)
 delete mode 100644 Trie/tests/LinuxMain.swift
 delete mode 100644 Trie/tests/Trie/TrieTest.swift
 delete mode 100755 Trie/trie
 rename Trie/{sources => }/trie.swift (100%)

diff --git a/Red Black Trees/RBTree.swift b/Red Black Trees/RBTree.swift
index dab7e1fd8..50d1d00d4 100644
--- a/Red Black Trees/RBTree.swift	
+++ b/Red Black Trees/RBTree.swift	
@@ -21,6 +21,7 @@ public class  RBTNode{
   deinit{
     print("Node: \(self.data) is bein deinitialized")
   }
+
   public func grandparent()->RBTNode?{
     if(self.parent === nil || self.parent.parent === nil){
       return nil
@@ -30,7 +31,7 @@ public class  RBTNode{
     }
   }
   public func sibling()->RBTNode?{
-      if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
+    if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
         return nil
       }
       if(self === self.parent!.left!){
@@ -40,61 +41,60 @@ public class  RBTNode{
         return self.parent!.left!
       }
   }
-
-
-
 }
 public class RBTree {
-
-    private(set) public var root: RBTNode?
-    init(rootData: Int) {
-      root = RBTNode(rootData: rootData)
-      root!.color = false
-    }
-    init(){
-      root = nil
-    }
-    public func depth()->Int{
-      let n = depth(root!)
-      return n
+  private(set) public var root: RBTNode?
+  init(rootData: Int) {
+    root = RBTNode(rootData: rootData)
+    root!.color = false
+  }
+  init(){
+    root = nil
+  }
+  public func depth()->Int{
+    let n = depth(root!)
+    return n
+  }
+  private func depth(rooty:RBTNode?)->Int{
+    if(rooty == nil){
+      return 0
     }
-    private func depth(rooty:RBTNode?)->Int{
-      if(rooty == nil){
-        return 0
-      }
-      else{
-        return 1+(max(depth(root!.left),depth(root!.right)))
-      }
+    else{
+      return 1+(max(depth(root!.left),depth(root!.right)))
     }
+  }
 
-    public func inOrder(){
-      inOrder(root)
+  public func inOrder(){
+    inOrder(root)
+  }
+  private func inOrder(root: RBTNode?){
+    if(self.root == nil ){
+      print("The tree is empty.")
     }
-    private func inOrder(root: RBTNode?){
-      if(root == nil){
-        return
-      }
-      inOrder(root!.left)
-      print("Data: \(root!.data) Color: \(root!.color)")
-      inOrder(root!.right)
+    if(root == nil){
+      return
     }
+    inOrder(root!.left)
+    print("Data: \(root!.data) Color: \(root!.color)")
+    inOrder(root!.right)
+  }
 
-    private func leftRotate(x: RBTNode) {
-        let newRoot = x.right
-        x.right = newRoot.left
-          if (newRoot.left !== nil) {
-            newRoot.left.parent = x
-          }
-          newRoot.parent = x.parent
-          if(x.parent === nil) {
-            root = newRoot
-          } else if (x === x.parent.left) {
-            x.parent.left = newRoot
-          } else {
-            x.parent.right = newRoot
-          }
-          newRoot.left = x
-          x.parent = newRoot
+  private func leftRotate(x: RBTNode) {
+      let newRoot = x.right
+      x.right = newRoot.left
+        if (newRoot.left !== nil) {
+          newRoot.left.parent = x
+        }
+        newRoot.parent = x.parent
+        if(x.parent === nil) {
+          root = newRoot
+        } else if (x === x.parent.left) {
+          x.parent.left = newRoot
+        } else {
+          x.parent.right = newRoot
+        }
+        newRoot.left = x
+        x.parent = newRoot
   }
   private func rightRotate(x: RBTNode) {
     let newRoot = x.left
@@ -112,225 +112,241 @@ public class RBTree {
     }
     newRoot.right = x
     x.parent = newRoot
-}
-
-public func insertFixup(value: Int){
-  let inserted = find(value)
-
-  if(inserted == nil){
-    print("INSERTEDNILLLLLLLL")
-  }
-  print("inserted: ")
-  print(inserted!.data)
-  insertCase1(inserted)
-}
-private func insertCase1(inserted: RBTNode?){
-  let myroot = self.root!
-  if myroot === inserted!{
-    self.root!.color = false
-    print("ITS THE ROOT")
-    print("insert case 1: The root was nil and we inserted a black node at root")
-  }
-  insertCase2(inserted!)
-}
-private func insertCase2(inserted: RBTNode?){
-  if inserted!.parent!.color == false{
-      print("Insert case 2: parent is black so nothing to change")
-      return
   }
-  insertCase3(inserted!)
-}
-private func insertCase3(inserted: RBTNode?){
-  if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
-    print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
-    inserted!.parent!.color = false
-    inserted!.parent!.sibling()!.color = false
-    let g = inserted!.grandparent
-    g()!.color = true
-    if(g()!.parent == nil){
-      g()!.color = false
+  public func insertFixup(value: Int){
+    let inserted = find(value)
+    print("Inserted Node: \(inserted!.data)")
+    insertCase1(inserted)
+    }
+  private func insertCase1(inserted: RBTNode?){
+    let myroot = self.root!
+    if myroot === inserted!{
+      self.root!.color = false
+    }
+    insertCase2(inserted!)
+    }
+  private func insertCase2(inserted: RBTNode?){
+    if inserted!.parent!.color == false{
+        return
+    }
+    insertCase3(inserted!)
+    }
+  private func insertCase3(inserted: RBTNode?){
+    if(inserted!.parent!.sibling() != nil &&
+        inserted!.parent!.sibling()!.color == true){
+        inserted!.parent!.color = false
+        inserted!.parent!.sibling()!.color = false
+        let g = inserted!.grandparent
+        g()!.color = true
+        if(g()!.parent == nil){
+          g()!.color = false
+        }
     }
-  }
   insertCase4(inserted)
-}
-
-private func insertCase4(var inserted: RBTNode?){
-  if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
-    print("case 4")
-    leftRotate(inserted!.parent)
-    inserted! = inserted!.left
   }
-  else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
-     print("case 4")
-    rightRotate(inserted!.parent)
-    inserted! = inserted!.right
+
+  private func insertCase4( insert: RBTNode?){
+    var inserted = insert
+    if((inserted! === inserted!.parent!.right) &&
+      (inserted!.grandparent()!.left === inserted!.parent!)){
+
+      leftRotate(inserted!.parent)
+      inserted! = inserted!.left
+    }
+    else if((inserted! === inserted!.parent!.left) &&
+            (inserted!.grandparent()!.right === inserted!.parent!)){
+
+      rightRotate(inserted!.parent)
+      inserted! = inserted!.right
+    }
+    insertCase5(inserted)
   }
-  insertCase5(inserted)
-}
-private func insertCase5(inserted: RBTNode?){
-  if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
-      if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
-        print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
-        if(inserted! === inserted!.parent!.left){
-          print("its on the left")
-          rightRotate(inserted!.grandparent()!)
-        }
-      }
-      else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
-        print("insert case 5: RIGHT RIGHT")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
+  private func insertCase5(inserted: RBTNode?){
+    if((inserted!.parent!.color == true &&
+       (inserted!.parent!.sibling()?.color == false ||
+        inserted!.parent!.sibling() == nil ))){
 
-          print("Its on the right")
+        if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
+          inserted!.parent.color = false
+          inserted!.grandparent()?.color = true
+          if(inserted! === inserted!.parent!.left){
+            rightRotate(inserted!.grandparent()!)
+          }
+        }
+        else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
+          inserted!.parent.color = false
+          inserted!.grandparent()?.color = true
           leftRotate(inserted!.grandparent()!)
-      }
+        }
+    }
   }
-  print("weve reached the end boys")
-}
 
-    public func insert(value: Int) {
-      insert(value, parent: root!)
-      insertFixup(value)
-    }
-    private func insert(value: Int, parent: RBTNode) {
-        if self.root == nil{
-          self.root = RBTNode(rootData: value)
-          return
+  public func insert(value: Int) {
+    insert(value, parent: root!)
+    insertFixup(value)
+  }
+  private func insert(value: Int, parent: RBTNode) {
+      if self.root == nil{
+        self.root = RBTNode(rootData: value)
+        return
+      }
+      else if value < parent.data {
+        if let left = parent.left {
+          insert(value, parent: left)
+        } else {
+          parent.left = RBTNode(rootData: value)
+          parent.left?.parent = parent
         }
-        else if value < parent.data {
-          if let left = parent.left {
-            insert(value, parent: left)
-          } else {
-            parent.left = RBTNode(rootData: value)
-            parent.left?.parent = parent
-          }
+      } else {
+        if let right = parent.right {
+          insert(value, parent: right)
         } else {
-          if let right = parent.right {
-            insert(value, parent: right)
-          } else {
-            parent.right = RBTNode(rootData: value)
-            parent.right?.parent = parent
-          }
+          parent.right = RBTNode(rootData: value)
+          parent.right?.parent = parent
         }
       }
-      public func find(data: Int)->RBTNode?{
-        return find(root!,data: data)
-      }
-
-      private func find(root: RBTNode, data: Int)->RBTNode?{
-          if data == root.data{
-            return root
-          }
-          if root.data != data && root.right == nil && root.left == nil {
-            return nil
-          }
-          else if data > root.data{
-            return find(root.right, data: data)
-          }
-          else if data < root.data{
-            return find(root.left, data: data)
-          }
-          else{
-            return nil
-          }
-      }
+    }
+    public func find(data: Int)->RBTNode?{
+      return find(root!,data: data)
+    }
 
-      //DELETION HELPER FUNCTIONS
-      public func remove(value: Int){
-          let toRemove = find(value)
-          if(toRemove == nil){
-            return
-          }
-      }
-      public func replaceNode(n1: RBTNode, n2: RBTNode){
-        var temp = n1.data
-        var temp_color = n1.color
-        n1.data = n2.data
-        n1.color = n2.color
-        n2.data = temp
-        n2.color = temp_color
-      }
-      public func minimum(var node: RBTNode)->RBTNode {
-        while node.left !== nil{
-          node = node.left
+    private func find(root: RBTNode, data: Int)->RBTNode?{
+        if data == root.data{
+          return root
         }
-        return node
-      }
-      public func successor(var node: RBTNode) -> RBTNode? {
-        if node.right !== nil {
-          return minimum(node.right)
+        if root.data != data && root.right == nil && root.left == nil {
+          return nil
         }
-        var successor = node.parent
-        while successor !== nil && node === successor.right {
-          node = successor
-          successor = successor.parent
+        else if data > root.data{
+          return find(root.right, data: data)
         }
-        return successor
-      }
-      public func predecessor(var node: RBTNode) -> RBTNode{
-        if node.left !== nil {
-          return minimum(node.left)
+        else if data < root.data{
+          return find(root.left, data: data)
         }
-        var successor = node.parent
-        while successor !== nil && node === successor.left {
-          node = successor
-          successor = successor.parent
+        else{
+          return nil
         }
-        return successor
-      }
-      public func maximum(var rootNode: RBTNode) -> RBTNode{
-        while rootNode.right !== nil {
-          rootNode = rootNode.right
+    }
+
+    //DELETION HELPER FUNCTIONS
+    public func remove(value: Int){
+        let toRemove = find(value)
+        if(toRemove == nil){
+          return
         }
-        return rootNode
+    }
+    public func replaceNode(n1: RBTNode, n2: RBTNode){
+      let temp = n1.data
+      let temp_color = n1.color
+      n1.data = n2.data
+      n1.color = n2.color
+      n2.data = temp
+      n2.color = temp_color
+    }
+    public func minimum(Node: RBTNode)->RBTNode {
+      var node = Node
+      while node.left !== nil{
+        node = node.left
+      }
+      return node
+    }
+    public func successor(Node: RBTNode) -> RBTNode? {
+      var node = Node
+      if node.right !== nil {
+        return minimum(node.right)
+      }
+      var successor = node.parent
+      while successor !== nil && node === successor.right {
+        node = successor
+        successor = successor.parent
+      }
+      return successor
+    }
+    public func predecessor(Node: RBTNode) -> RBTNode{
+      var node = Node
+      if node.left !== nil {
+        return minimum(node.left)
       }
-  private func deletionFixup(x: RBTNode) {}
+      var successor = node.parent
+      while successor !== nil && node === successor.left {
+        node = successor
+        successor = successor.parent
+      }
+      return successor
+    }
+    public func maximum(rootnode: RBTNode) -> RBTNode{
+      var rootNode = rootnode
+      while rootNode.right !== nil {
+        rootNode = rootNode.right
+      }
+      return rootNode
+    }
 
   public func delete(x: Int){
     let toDel = find(x)
     deleteNode(toDel!)
   }
-  private func deleteNode(var toDel: RBTNode?){
-    print("DELETE CASE 0")
-    if(toDel!.left == nil && toDel!.right == nil && toDel!.color == true){
-      print("IM IN HERE")
-      //DEINIT NOT BEING CALLED AGAIN?
+  private func deleteNode(todel: RBTNode?){
+    var toDel = todel
+    if(toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil){
       toDel = nil
+      self.root = nil
+      return
+    }
+    if(toDel!.left === nil && toDel!.right === nil && toDel!.color == true){
+      if(toDel!.parent.left === toDel!){
+        toDel!.parent.left = nil
+        toDel = nil
+      }
+      else if(toDel!.parent === nil){
+        toDel = nil
+      }
+      else{
+        toDel?.parent.right = nil
+        toDel = nil
+      }
       return
     }
     if(toDel!.left !== nil && toDel!.right !== nil){
-      var pred = maximum(toDel!.left!)
+      let pred = maximum(toDel!.left!)
       toDel!.data = pred.data
       toDel! = pred
     }
-    var child: RBTNode? = nil
 
+    var child: RBTNode? = nil
     if(toDel!.right === nil){
       child = toDel!.left
     }
     else{
        child = toDel!.right
     }
-
-    if(toDel!.color == false){
+    if(toDel!.color == false && child !== nil){
       toDel!.color = child!.color
       deleteCase1(toDel!)
     }
 
     if(child !== nil){
       replaceNode(toDel!, n2: child!)
-
       if(toDel!.parent === nil && child !== nil){
         child!.color = false
       }
     }
-    print("This statement isnt actually deleting the object??? V")
-    toDel = nil
+    if(toDel!.parent.left === toDel!){
+      toDel!.parent.left = nil
+      toDel = nil
+      return
+    }
+    else if(toDel!.parent === nil){
+      toDel = nil
+      return
+    }
+    else{
+      toDel?.parent.right = nil
+      toDel = nil
+      return
+    }
   }
-  private func deleteCase1(var toDel: RBTNode?){
-      print("DELETE CASE 1")
+  private func deleteCase1( toDel: RBTNode?){
       if(toDel?.parent === nil){
         return
       }
@@ -338,9 +354,8 @@ private func insertCase5(inserted: RBTNode?){
         deleteCase2(toDel)
       }
   }
-  private func deleteCase2(var toDel: RBTNode?){
-    print("DELETE CASE 2")
-    var sibling = toDel!.sibling()
+  private func deleteCase2(toDel: RBTNode?){
+    let sibling = toDel!.sibling()
     if(sibling?.color == true){
        toDel!.parent.color = true;
        sibling?.color = false
@@ -353,9 +368,12 @@ private func insertCase5(inserted: RBTNode?){
        deleteCase3(toDel!)
     }
   }
-  private func deleteCase3(var toDel: RBTNode?){
-    print("DELETE CASE 3")
-    if(toDel!.parent?.color == false && toDel!.sibling()?.color == false && toDel!.sibling()?.left!.color == false && toDel!.sibling()?.right!.color == false){
+  private func deleteCase3(toDel: RBTNode?){
+    if(toDel!.parent?.color == false &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left!.color == false &&
+       toDel!.sibling()?.right!.color == false){
+
         toDel!.sibling()?.color = true
         toDel!.parent?.color = false
     }
@@ -363,31 +381,41 @@ private func insertCase5(inserted: RBTNode?){
       deleteCase4(toDel)
     }
   }
-  private func deleteCase4(var toDel: RBTNode?){
-    print("DELETE CASE 4")
-    if(toDel!.parent?.color == true && toDel!.sibling()?.color == false && toDel!.sibling()?.left!.color == false && toDel!.sibling()?.right!.color == false){
-        toDel!.sibling()?.color = true
-        toDel!.parent.color = false
+  private func deleteCase4(toDel: RBTNode?){
+    if(toDel!.parent?.color == true &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left!.color == false &&
+       toDel!.sibling()?.right!.color == false){
+
+       toDel!.sibling()?.color = true
+       toDel!.parent.color = false
     }
     else{
       deleteCase5(toDel)
     }
   }
-  private func deleteCase5(var toDel:RBTNode?){
-    print("DELETE CASE 5")
-    if(toDel! === toDel!.parent?.left && toDel!.sibling()?.color == false && toDel!.sibling()?.left.color == true && toDel!.sibling()?.right.color == false){
-      toDel!.sibling()?.color = true
-      toDel!.sibling()?.left?.color = false
-      rightRotate(toDel!.sibling()!)
+  private func deleteCase5(toDel:RBTNode?){
+    if(toDel! === toDel!.parent?.left &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left.color == true &&
+       toDel!.sibling()?.right.color == false){
+
+       toDel!.sibling()?.color = true
+       toDel!.sibling()?.left?.color = false
+       rightRotate(toDel!.sibling()!)
     }
-    else if(toDel! === toDel!.parent?.right && toDel!.sibling()?.color == false && toDel!.sibling()?.left.color == false && toDel!.sibling()?.right.color == true){
-      toDel!.sibling()?.color = true
-      toDel!.sibling()?.right?.color = false
-      leftRotate(toDel!.sibling()!)
+
+    else if(toDel! === toDel!.parent?.right &&
+            toDel!.sibling()?.color == false &&
+            toDel!.sibling()?.left.color == false &&
+            toDel!.sibling()?.right.color == true){
+
+            toDel!.sibling()?.color = true
+            toDel!.sibling()?.right?.color = false
+            leftRotate(toDel!.sibling()!)
     }
   }
-  private func deleteCase6(var toDel: RBTNode?){
-    print("DELETE CASE 6")
+  private func deleteCase6(toDel: RBTNode?){
     let color = toDel!.sibling()?.color
     toDel!.parent?.color = color!
     toDel!.parent?.color = false
@@ -402,43 +430,13 @@ private func insertCase5(inserted: RBTNode?){
   }
 }
 
-
-
 var tree = RBTree(rootData: 8)
-
-tree.insert(6)
-tree.delete(6)
+tree.insert(5)
+tree.insert(4)
+tree.insert(9)
+tree.delete(9)
+tree.insert(3)
+tree.insert(10)
+tree.delete(3)
+var x = tree.find(5)
 tree.inOrder()
-print("_______")
-
-
-
-//print("_________________________")
-//let x = tree.root!
-//print("sibling: \(tree.root!.left!.sibling()!.data)")
-//print("root: \(tree.root!.data)")
-//tree.rightRotate(x)
-//print("root: \(tree.root!.data)")
-//tree.inOrder()
-
-//let l = tree.root!.left!
-//let r = tree.root!.right!
-//print(l.data)
-//print(r.data)
-//if tree.root!.parent == nil{
-//  print("ASDASD")
-//}
-
-//how you access certain elements
-//let root = tree.root!.left!
-//if(root.parent === nil){
-//  print("nil")
-//}
-//else{
-//  print(root.parent.data)
-//}
-
-//print(tree.root!.data)
-//print(tree.root!.right!.data)
-//print(tree.root!.left!.data)
-
diff --git a/Red Black Trees/RBTree.swift~ b/Red Black Trees/RBTree.swift~
deleted file mode 100644
index 4cb0c2fcb..000000000
--- a/Red Black Trees/RBTree.swift~	
+++ /dev/null
@@ -1,332 +0,0 @@
-public class  RBTNode{
-  private(set) public var color: Bool
-  private(set) public var left: RBTNode!
-  private(set) public var right: RBTNode!
-  private(set) public var parent: RBTNode!
-  private(set) public var data: Int
-  init(){
-    self.data = -1
-    self.color = true
-    self.left = nil
-    self.right = nil
-    self.parent = nil
-  }
-  init(rootData: Int){
-    self.data = rootData
-    self.color = true //0is black 1 is red
-    self.left = nil
-    self.right = nil
-    self.parent = nil
-  }
-  public func grandparent()->RBTNode?{
-    if(self.parent === nil || self.parent.parent === nil){
-      return nil
-    }
-    else{
-      return self.parent.parent
-    }
-  }
-  public func sibling()->RBTNode?{
-      if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
-        return nil
-      }
-      if(self === self.parent!.left!){
-        return self.parent!.right!
-      }
-      else{
-        return self.parent!.left!
-      }
-  }
-  public func replaceNode(n1: RBTNode, n2: RBTNode){
-    var temp = n1.data
-    var temp_color = n1.color
-    n1.data = n2.data
-    n1.color = n2.color
-    n2.data = temp
-    n2.color = temp_color
-  }
-  public func minimum(var node: RBTNode)->RBTNode {
-    while node.left !== nil{
-      node = node.left
-    }
-    return node
-  }
-  public func successor(var node: RBTNode) -> RBTNode? {
-    if node.right !== nil {
-      return minimum(node.right)
-    }
-    var successor = node.parent
-    while successor !== nil && node === successor.right {
-      node = successor
-      successor = successor.parent
-    }
-    return successor
-  }
-  public func predecessor(var node: RBTNode) -> RBTNode{
-    if node.left !== nil {
-      return minimum(node.left)
-    }
-    var successor = node.parent
-    while successor !== nil && node === successor.left {
-      node = successor
-      successor = successor.parent
-    }
-    return successor
-  }
-  public func maximum(var rootNode: RBTNode) -> RBTNode{
-    while rootNode.right !== nil {
-      rootNode = rootNode.right
-    }
-    return rootNode
-  }
-}
-public class RBTree {
-
-    private(set) public var root: RBTNode?
-    init(rootData: Int) {
-      root = RBTNode(rootData: rootData)
-      root!.color = false
-    }
-    init(){
-      root = nil
-    }
-    public func depth()->Int{
-      let n = depth(root!)
-      return n
-    }
-    private func depth(rooty:RBTNode?)->Int{
-      if(rooty == nil){
-        return 0
-      }
-      else{
-        return 1+(max(depth(root!.left),depth(root!.right)))
-      }
-    }
-
-    public func inOrder(){
-      inOrder(root)
-    }
-    private func inOrder(root: RBTNode?){
-      if(root == nil){
-        return
-      }
-      inOrder(root!.left)
-      print("Data: \(root!.data) Color: \(root!.color)")
-      inOrder(root!.right)
-    }
-
-    private func leftRotate(x: RBTNode) {
-        let newRoot = x.right
-        x.right = newRoot.left
-          if (newRoot.left !== nil) {
-            newRoot.left.parent = x
-          }
-          newRoot.parent = x.parent
-          if(x.parent === nil) {
-            root = newRoot
-          } else if (x === x.parent.left) {
-            x.parent.left = newRoot
-          } else {
-            x.parent.right = newRoot
-          }
-          newRoot.left = x
-          x.parent = newRoot
-  }
-  private func rightRotate(x: RBTNode) {
-    let newRoot = x.left
-    x.left = newRoot.right
-    if newRoot.right !== nil {
-      newRoot.right.parent = x
-    }
-    newRoot.parent = x.parent
-    if x.parent === nil {
-      root = newRoot
-    } else if x === x.parent.right {
-      x.parent.right = newRoot
-    } else {
-      x.parent.left = newRoot
-    }
-    newRoot.right = x
-    x.parent = newRoot
-}
-
-public func insertFixup(value: Int){
-  let inserted = find(value)
-
-  if(inserted == nil){
-    print("INSERTEDNILLLLLLLL")
-  }
-  print("inserted: ")
-  print(inserted!.data)
-  insertCase1(inserted)
-}
-private func insertCase1(inserted: RBTNode?){
-  let myroot = self.root!
-  if myroot === inserted!{
-    self.root!.color = false
-    print("ITS THE ROOT")
-    print("insert case 1: The root was nil and we inserted a black node at root")
-  }
-  insertCase2(inserted!)
-}
-private func insertCase2(inserted: RBTNode?){
-  if inserted!.parent!.color == false{
-      print("Insert case 2: parent is black so nothing to change")
-      return
-  }
-  insertCase3(inserted!)
-}
-private func insertCase3(inserted: RBTNode?){
-  if(inserted!.parent!.sibling() != nil && inserted!.parent!.sibling()!.color == true){
-    print("insert case3: If both the parent P and the uncle U are red, then both of them can be repainted black and the grandparent G ")
-    inserted!.parent!.color = false
-    inserted!.parent!.sibling()!.color = false
-    let g = inserted!.grandparent
-    g()!.color = true
-    if(g()!.parent == nil){
-      g()!.color = false
-    }
-  }
-  insertCase4(inserted)
-}
-//THIS ONE MAY BE BROKEN!?!?!?!?
-private func insertCase4(var inserted: RBTNode?){
-  if((inserted! === inserted!.parent!.right) && (inserted!.grandparent()!.left === inserted!.parent!)){
-    print("case 4")
-    rightRotate(inserted!.parent)
-    inserted! = inserted!.left
-  }
-  else if((inserted! === inserted!.parent!.left) && (inserted!.grandparent()!.right === inserted!.parent!)){
-     print("case 4")
-    leftRotate(inserted!.parent)
-    inserted! = inserted!.right
-  }
-  insertCase5(inserted)
-}
-private func insertCase5(inserted: RBTNode?){
-  if((inserted!.parent!.color == true && (inserted!.parent!.sibling()?.color == false || inserted!.parent!.sibling() == nil ))){
-      if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
-        print("insert case 5: The parent P is red but the uncle U is black/nil, the current node N is the left child of P, and P is the left child of its parent G")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
-        if(inserted! === inserted!.parent!.left){
-          print("its on the left")
-          rightRotate(inserted!.grandparent()!)
-        }
-      }
-      else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
-        print("insert case 5: RIGHT RIGHT")
-        inserted!.parent.color = false
-        inserted!.grandparent()?.color = true
-
-          print("Its on the right")
-          leftRotate(inserted!.grandparent()!)
-      }
-  }
-  print("weve reached the end boys")
-}
-
-    public func insert(value: Int) {
-      insert(value, parent: root!)
-      insertFixup(value)
-    }
-    private func insert(value: Int, parent: RBTNode) {
-        if self.root == nil{
-          self.root = RBTNode(rootData: value)
-          return
-        }
-        else if value < parent.data {
-          if let left = parent.left {
-            insert(value, parent: left)
-          } else {
-            parent.left = RBTNode(rootData: value)
-            parent.left?.parent = parent
-          }
-        } else {
-          if let right = parent.right {
-            insert(value, parent: right)
-          } else {
-            parent.right = RBTNode(rootData: value)
-            parent.right?.parent = parent
-          }
-        }
-      }
-      public func find(data: Int)->RBTNode?{
-        return find(root!,data: data)
-      }
-
-      private func find(root: RBTNode, data: Int)->RBTNode?{
-          if data == root.data{
-            return root
-          }
-          if root.data != data && root.right == nil && root.left == nil {
-            return nil
-          }
-          else if data > root.data{
-            return find(root.right, data: data)
-          }
-          else if data < root.data{
-            return find(root.left, data: data)
-          }
-          else{
-            return nil
-          }
-      }
-
-      //DELETION HELPER FUNCTIONS
-      public func remove(value: Int){
-          let toRemove = find(value)
-          if(toRemove == nil){
-            return
-          }
-      }
-
-
-
-}
-
-var tree = RBTree(rootData: 8)
-tree.insert(9)
-tree.insert(6)
-tree.insert(5)
-tree.insert(4)
-tree.insert(40)
-tree.insert(400)
-tree.insert(430)
-var t = tree.root!
-var min = t.minimum(t)
-print("MIN: \(min.data)")
-var x = tree.root!.left
-tree.inOrder()
-t.replaceNode(t,n2:x)
-tree.inOrder()
-
-//print("_________________________")
-//let x = tree.root!
-//print("sibling: \(tree.root!.left!.sibling()!.data)")
-//print("root: \(tree.root!.data)")
-//tree.rightRotate(x)
-//print("root: \(tree.root!.data)")
-//tree.inOrder()
-
-//let l = tree.root!.left!
-//let r = tree.root!.right!
-//print(l.data)
-//print(r.data)
-//if tree.root!.parent == nil{
-//  print("ASDASD")
-//}
-
-//how you access certain elements
-//let root = tree.root!.left!
-//if(root.parent === nil){
-//  print("nil")
-//}
-//else{
-//  print(root.parent.data)
-//}
-
-//print(tree.root!.data)
-//print(tree.root!.right!.data)
-//print(tree.root!.left!.data)
-
diff --git a/Red Black Trees/README.md b/Red Black Trees/README.md
index 6747154b8..e1b887c3a 100644
--- a/Red Black Trees/README.md	
+++ b/Red Black Trees/README.md	
@@ -1,8 +1,69 @@
 # Red Black Tree
+![fig1](files/fig1.png)  
+Red-black trees are an evolution of binary search trees that aim to keep the tree balanced without affecting the complexity of the primitive operations. This is done by coloring each node in the tree with either red or black and preserving a set of properties that guarantee that the deepest path in the tree is not longer than twice the shortest one.  
+## Motivation:
+* We want a balanced binary search tree    
+* Height of the tree is O(log n)  
+* Red-Black Tree is an implementation of a balanced binary search tree
 
-Under Construction.
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).
+## Invariants:  
+1. Every node is colored either red or black
+2. All leaf (nil) nodes are colored with black; if a node’s child is missing then we will assume that it has a nil child in that place and this nil child is always colored black.
+3. Both children of a red node must be black nodes.
+4. Every path from a node n to a descendent leaf has the same number of black nodes (not counting node n).   
+
+## Methods:
+
+Since the red-black tree is a balanced BST, it supports the functions:
+  * find(key)
+  * Predecessor(key)
+  * Successor(key)
+  * Minimum(key)
+  * maximum(key)
+  * insert(key)
+  * delete(key)    
+
+Since an insertion or deletion may violate one of the invariant's of the red-black tree we must either change colors, or perform rotation actions.  
+
+#Rotation  
+To ensure that its color scheme and properties don’t get thrown off, red-black trees employ a key operation known as rotation. Rotation is a binary operation, between a parent node and one of its children, that swaps nodes and modifys their pointers while preserving the inorder traversal of the tree (so that elements are still sorted). There are two types of rotations: left rotation and right rotation. Left rotation swaps the parent node with its right child, while right rotation swaps the parent node with its left child.
+![fig2](files/fig2.png)
+###Left-Rotation:  
+```c++
+y ← x->right 
+x->right ← y->left 
+y->left->p ← x 
+y->p ← x->p 
+if 	x->p = Null 
+	then   T->root ← y 
+	else if x = x->p->left  
+		then x->p->left ← y 
+		else  x->p->right ← y 
+y->left ← x 
+x->p ← y 
+```
+###Right-Rotation:
+```c++
+y ← x->left 
+x->left ← y->right 
+y->right->p ← x 
+y->p ← x->p 
+if 	x->p = Null 
+	then T->root ← y 
+	else if x = x->p->right  
+		then x->p->right ← y 
+		else  x->p->left ← y 
+y->right ← x 
+x->p ← y 
+```  
+###Insertion:
+When adding a new node to a binary search tree, note that the new node will always be a leaf in the tree. To insert a new node, all we will do is navigate the BST starting from the root. If the new node value is smaller than the current node value, we go left – if it is larger, we go right. When we reach a leaf node, the last step is to attach the new node as a child to this leaf node in a way that preserves the BST constraint. We must recheck the RBTree invariants to see if any were violated  
+
+###Deletion:
+The same concept behind red-black tree insertions applies here. Removing a node from a red-black tree makes use of the BST deletion procedure and then restores the red-black tree properties in O(log n). The total running time for the deletion process takes O(log n) time, then, which meets the complexity requirements for the primitive operations.  
+
+See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).  
 
 *Written for the Swift Algorithm Club by Ashwin Raghuraman*
 
diff --git a/Red Black Trees/README.md~ b/Red Black Trees/README.md~
deleted file mode 100644
index e69de29bb..000000000
diff --git a/Red Black Trees/files/fig1.png b/Red Black Trees/files/fig1.png
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index 0000000000000000000000000000000000000000..7a91eb6932feddfc00890e16aeec6e1a079a75b9
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diff --git a/Trie/sources/Queue.swift b/Trie/Queue.swift
similarity index 100%
rename from Trie/sources/Queue.swift
rename to Trie/Queue.swift
diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index edabbb994..844eb1df0 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,8 +1,220 @@
 # Trie
 
-Under Construction.
+##What is a Trie?
+A trie (also known as a prefix tree, or radix tree in some other (but different) implementations) is a special type of tree used to store associative data structures where the key item is normally of type String.  Each node in the trie is typically not associated with a value containing strictly itself, but more so is linked to some common prefix that precedes it in levels above it.  Oftentimes, true key-value pairs are associated with the leaves of the trie, but they are not limited to this.
 
-See also [Wikipedia](https://en.wikipedia.org/wiki/Trie).
+##Why a Trie?
+Tries are very useful simply for the fact that it has some advantages over other data structures, like the binary tree or a hash map.  These advantages include:
+* Looking up keys is typically faster in the worst case when compared to other data structures.
+* Unlike a hash map, a trie need not worry about key collisions
+* No need for hasing, as each key will have a unique path in the trie
+* Tries, by implementation, can be by default alphabetically ordered.
+
+
+##Common Algorithms
+
+###Find (or any general lookup function)
+Tries make looking up keys a trivial task, as all one has to do is walk over the nodes until we either hit a null reference or we find the key in question.
+
+The algorithm would be as follows:
+```
+  let node be the root of the trie
+  
+  for each character in the key
+    if the child of node with value character is null
+      return false (key doesn't exist in trie)
+    else
+      node = child of node with value character  (move to the next node)
+  return true (key exists in trie and was found
+```
+
+And in swift:
+```swift
+func find(key: String) -> (node: Node?, found: Bool) {
+    var currentNode = self.root
+
+    for c in key.characters {
+      if currentNode.children[String(c)] == nil {
+        return(nil, false)
+      }
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    return(currentNode, currentNode.isValidWord())
+  }
+```
+
+###Insertion
+Insertion is also a trivial task with a Trie, as all one needs to do is walk over the nodes until we either halt on a node that we must mark as a key, or we reach a point where we need to add extra nodes to represent it.
+
+Let's walk through the algorithm:
+
+```
+  let S be the root node of our tree
+  let word be the input key
+  let length be the length of the key
+  
+  
+  find(word)
+  if the word was found
+    return false
+  else
+    
+    for each character in word
+      if child node with value character does not exist
+        break
+      else
+        node = child node with value character
+        decrement length
+      
+    if length != 0
+      let suffix be the remaining characters in the key defined by the shortened length
+      
+      for each character in suffix
+        create a new node with value character and let it be the child of node
+        node = newly created child now
+      mark node as a valid key
+    else
+      mark node as valid key
+```
+
+And the corresponding swift code:
+
+```swift
+  func insert(w: String) -> (word: String, inserted: Bool) {
+
+    let word = w.lowercaseString
+    var currentNode = self.root
+    var length = word.characters.count
+
+    if self.contains(word) {
+      return (w, false)
+    }
+
+    var index = 0
+    var c = Array(word.characters)[index]
+
+    while let child = currentNode.children[String(c)] {
+      currentNode = child
+      length -= 1
+      index += 1
+
+      if(length == 0) {
+        currentNode.isWord()
+        wordList.append(w)
+        wordCount += 1
+        return (w, true)
+      }
+
+      c = Array(word.characters)[index]
+    }
+
+    let remainingChars = String(word.characters.suffix(length))
+    for c in remainingChars.characters {
+      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    currentNode.isWord()
+    wordList.append(w)
+    wordCount += 1
+    return (w, true)
+  }
+
+```
+
+###Removal
+Removing keys from the trie is a little more tricky, as there a few more cases that we have to take into account the fact that keys may exist that are actually sub-strings of other valid keys.  That being said, it isn't as simple a process to just delete the nodes for a specific key, as we could be deleting references/nodes necessary for already exisitng keys!
+
+The algorithm would be as follows:
+
+```
+  
+  let word be the key to remove
+  let node be the root of the trie
+  
+  find(word)
+  if word was not found
+    return false
+  else
+  
+    for each character in word
+      node = child node with value character
+      
+      if node has more than just 1 child node
+        Mark node as an invalid key, since removing it would remove nodes still in use
+      else
+        while node has no valid children and node is not the root node
+          let character = node's value
+          node = the parent of node
+          delete node's child node with value character
+        return true
+```
+
+
+
+and the corresponding swift code:
+
+```swift
+  func remove(w: String) -> (word: String, removed: Bool){
+    let word = w.lowercaseString
+
+    if(!self.contains(w)) {
+      return (w, false)
+    }
+    var currentNode = self.root
+
+    for c in word.characters {
+      currentNode = currentNode.getChildAt(String(c))
+    }
+
+    if currentNode.numChildren() > 0 {
+      currentNode.isNotWord()
+    } else {
+      var character = currentNode.char()
+      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
+        currentNode = currentNode.getParent()
+        currentNode.children[character]!.setParent(nil)
+        currentNode.children[character]!.update(nil)
+        currentNode.children[character] = nil
+        character = currentNode.char()
+      }
+    }
+
+    wordCount -= 1
+
+    var index = 0
+    for item in wordList{
+      if item == w {
+        wordList.removeAtIndex(index)
+      }
+      index += 1
+    }
+
+    return (w, true)
+  }
+
+```
+
+
+###Running Times
+
+Let n be the length of some key in the trie
+
+* Find(...) : In the Worst case O(n)
+* Insert(...) :  O(n)
+* Remove(...) :  O(n)
+
+###Other Notable Operations
+
+* Count:  Returns the number of keys in the trie ( O(1) )
+* getWords:  Returns a list containing all keys in the trie ( *O(1) )
+* isEmpty:  Returns true f the trie is empty, false otherwise ( *O(1) )
+* contains:  Returns true if the trie has a given key, false otherwise ( O(n) )
+
+`* denotes that running time may vary depending on implementation
+
+See also [Wikipedia entry for Trie](https://en.wikipedia.org/wiki/Trie).
 
 *Written for the Swift Algorithm Club by Christian Encarnacion*
 
diff --git a/Trie/tests/LinuxMain.swift b/Trie/tests/LinuxMain.swift
deleted file mode 100644
index 83504f1dd..000000000
--- a/Trie/tests/LinuxMain.swift
+++ /dev/null
@@ -1,8 +0,0 @@
-
-
-import XCTest
-@testable import TrieTestSuite
-
-XCTMain([
-    testCase(TrieTests.allTests)
-])
diff --git a/Trie/tests/Trie/TrieTest.swift b/Trie/tests/Trie/TrieTest.swift
deleted file mode 100644
index 8f49d1196..000000000
--- a/Trie/tests/Trie/TrieTest.swift
+++ /dev/null
@@ -1,26 +0,0 @@
-import XCTest
-@testable import Trie
-
-class TrieTests: XCTestCase {
-  var trie : Trie!
-
-  override func setUp() {
-    super.setUp()
-    trie = Trie()
-  }
-
-  func testInsert() {
-
-    var T: Trie = Trie()
-    var result = T.insert("Test").inserted
-    XCTAssertEqual(result, true)
-  }
-}
-
-extension CalculatorTests {
-    static var allTests : [(String, CalculatorTests -> () throws -> Void)] {
-        return [
-            ("Testing Insert...", testInsert)
-        ]
-    }
-}
diff --git a/Trie/trie b/Trie/trie
deleted file mode 100755
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diff --git a/Trie/sources/trie.swift b/Trie/trie.swift
similarity index 100%
rename from Trie/sources/trie.swift
rename to Trie/trie.swift

From d1874e83857c8503ac8f9bb17104ddf272e6c12c Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 21:56:02 -0400
Subject: [PATCH 0345/1679] Merged Queue with Trie

---
 Trie/Package.swift |   6 -
 Trie/Queue.swift   |  47 -----
 Trie/trie.swift    |  41 ++++
 Trie/trie.swift~   | 479 +++++++++++++++++++++++++++++++++++++++++++++
 4 files changed, 520 insertions(+), 53 deletions(-)
 delete mode 100644 Trie/Package.swift
 delete mode 100644 Trie/Queue.swift
 create mode 100644 Trie/trie.swift~

diff --git a/Trie/Package.swift b/Trie/Package.swift
deleted file mode 100644
index fc323a1ec..000000000
--- a/Trie/Package.swift
+++ /dev/null
@@ -1,6 +0,0 @@
-import PackageDescription
-
-let package = Package(
-    name: "Trie",
-    targets: []
-)
diff --git a/Trie/Queue.swift b/Trie/Queue.swift
deleted file mode 100644
index efc573442..000000000
--- a/Trie/Queue.swift
+++ /dev/null
@@ -1,47 +0,0 @@
-/*
-  First-in first-out queue (FIFO)
-
-  New elements are added to the end of the queue. Dequeuing pulls elements from
-  the front of the queue.
-
-  Enqueuing and dequeuing are O(1) operations.
-*/
-public struct Queue<T> {
-  private var array = [T?]()
-  private var head = 0
-  
-  public var isEmpty: Bool {
-    return count == 0
-  }
-
-  public var count: Int {
-    return array.count - head
-  }
-  
-  public mutating func enqueue(element: T) {
-    array.append(element)
-  }
-  
-  public mutating func dequeue() -> T? {
-    guard head < array.count, let element = array[head] else { return nil }
-
-    array[head] = nil
-    head += 1
-
-    let percentage = Double(head)/Double(array.count)
-    if array.count > 50 && percentage > 0.25 {
-      array.removeFirst(head)
-      head = 0
-    }
-    
-    return element
-  }
-  
-  public func peek() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array[head]
-    }
-  }
-}
diff --git a/Trie/trie.swift b/Trie/trie.swift
index f2b339024..352ca26cc 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -1,4 +1,45 @@
+/*
+  Queue implementation (taken from repository, needed for findPrefix())
+*/
+public struct Queue<T> {
+  private var array = [T?]()
+  private var head = 0
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+
+    array[head] = nil
+    head += 1
 
+    let percentage = Double(head)/Double(array.count)
+    if array.count > 50 && percentage > 0.25 {
+      array.removeFirst(head)
+      head = 0
+    }
+    
+    return element
+  }
+  
+  public func peek() -> T? {
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
+  }
+}
 /*
   A Trie (Pre-fix Tree)
 
diff --git a/Trie/trie.swift~ b/Trie/trie.swift~
new file mode 100644
index 000000000..f2b339024
--- /dev/null
+++ b/Trie/trie.swift~
@@ -0,0 +1,479 @@
+
+/*
+  A Trie (Pre-fix Tree)
+
+  Some of the functionality of the trie makes use of the Queue implementation for this project.
+
+
+  Every node in the Trie stores a bit of information pertainining to what it references:
+    -Character (letter of an inserted word)
+    -Parent  (Letter that comes before the current letter in some word)
+    -Children (Words that have more letters than available in the prefix)
+    -isAWord (Does the current letter mark the end of a known inserted word?)
+    -visited (Mainly for the findPrefix() function)
+*/
+public class Node {
+  private var character: String?
+  private var parent: Node?
+  private var children: [String:Node]
+  private var isAWord: Bool
+  private var visited: Bool  //only for findPrefix
+
+  init(c: String?, p: Node?){
+    self.character = c
+    self.children = [String:Node]()
+    self.isAWord = false
+    self.parent = p
+    self.visited = false
+    }
+
+  /*
+    Function Name:  char()
+    Input:  N/A
+    Output:  String
+    Functionality: Returns the associated value of the node
+  */
+  func char() -> String {
+    return self.character!
+  }
+
+  /*
+    Function Name:  update
+    Input: String
+    Output: N/A
+    Functionality: Updates the associated value of the node
+  */
+  func update(c: String?) {
+    self.character = c
+  }
+
+  /*
+    Function Name:  isLeaf
+    Input:  N/A
+    Output:  Bool
+    Functionality: Returns true if the node is a leaf node, false otherwise
+  */
+  func isLeaf() -> Bool{
+    return self.children.count == 0
+  }
+
+  /*
+    Function Name:  getParent
+    Input:  N/A
+    Output:  Node
+    Functionality: Returns the parent node of the current node
+  */
+  func getParent() -> Node {
+    return parent!
+  }
+
+  /*
+    Function Name:  setParent
+    Input:  Node
+    Output:  N/A
+    Functionality: Changes the parent of the current node to the passed node
+  */
+
+  func setParent(node: Node?) {
+    self.parent = node
+  }
+
+  /*
+    Function Name:  getChildAt
+    Input:  String
+    Output:  Node
+    Functionality:  returns the child node that holds the specific passed letter
+  */
+  func getChildAt(s: String) -> Node {
+    return self.children[s]!
+  }
+
+  /*
+    Function Name:  isValidWord
+    Input:  N/A
+    Output:  Bool
+    Functionality: Returns whether or not the current node marks the end of a valid word
+  */
+  func isValidWord() -> Bool{
+    return self.isAWord
+  }
+
+  /*
+    Function Name:  isWord
+    Input:  N/A
+    Output:  N/A
+    Functionality:  the current node is indeed a word
+  */
+  func isWord() {
+    self.isAWord = true
+  }
+
+  /*
+    Function Name: isNotWord
+    Input:  N/A
+    Output:  N/A
+    Functionality:  marks the current node as not a word
+  */
+  func isNotWord() {
+    self.isAWord = false
+  }
+
+  /*
+    Function Name:  isRoot
+    Input: N/A
+    Output: Bool
+    Functionality:  Returns whether or not the current node is the root of the trie
+  */
+  func isRoot() -> Bool {
+    return self.character == ""
+  }
+
+  /*
+    Function Name:  numChildren
+    Input:  N/A
+    Output:  Int
+    Functionality:  Returns the number of immediate letters that follow the current node
+  */
+  func numChildren() -> Int {
+    return self.children.count
+  }
+
+  /*
+    Function Name:  getChildren
+    Input:  N/A
+    Output:  [String: Node]
+    Functionality:  Returns the letters that immediately follow the current node's value for possible word segments that follow
+  */
+  func getChildren() -> [String: Node] {
+    return self.children
+  }
+
+
+  /*
+    Function Name:  printNode
+    Input:  String, Bool
+    Output:  N/A
+    Functionality:  prints to the console a string representation of the current node in the trie
+  */
+  func printNode(var indent: String, leaf: Bool) {
+
+    print(indent, terminator: "")
+    if(leaf) {
+      print("\\-", terminator: "")
+      indent += " "
+    }
+    else {
+      print("|-", terminator: "")
+      indent += "| "
+    }
+
+    print(self.char())
+
+    var i = 0
+    for (_, node) in self.children {
+      node.printNode(indent, leaf: i == self.getChildren().count-1)
+      i+=1
+    }
+
+  }
+
+}
+
+
+/*
+  The Trie class has the following attributes:
+    -root (the root of the trie)
+    -wordList (the words that currently exist in the trie)
+    -wordCount (the number of words in the trie)
+*/
+public class Trie {
+  private var root: Node
+  private var wordList: [String]
+  private var wordCount = 0
+
+  init() {
+    self.root = Node(c: "", p: nil)
+    self.wordList = []
+  }
+
+  init(wordList: Set<String>) {
+
+    self.root = Node(c: "", p: nil)
+    self.wordList = []
+
+    for word in wordList {
+      self.insert(word)
+    }
+  }
+
+  /*
+    Function Name: merge
+    Input:  Trie
+    Output:  Trie
+    Functionality:  Merges two tries into one and returns the merged trie
+  */
+  func merge(other: Trie) -> Trie{
+    let newWordList = Set(self.getWords() + other.getWords())
+    return Trie(wordList: newWordList)
+  }
+
+  /*
+    Function Name:  find
+    Input:  String
+    Output:  (Node?, Bool)
+    Functionality:  Looks for a specific key and returns a tuple that has a reference to the node(if found) and true/false depending on if it was found
+  */
+  func find(key: String) -> (node: Node?, found: Bool) {
+    var currentNode = self.root
+
+    for c in key.characters {
+      if currentNode.children[String(c)] == nil {
+        return(nil, false)
+      }
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    return(currentNode, currentNode.isValidWord())
+  }
+
+  /*
+    Function Name: isEmpty
+    Input:  N/A
+    Output:  Bool
+    Functionality:  returns true if the trie is empty, false otherwise
+  */
+  func isEmpty() -> Bool {
+    return wordCount == 0
+  }
+
+  /*
+    Function Name:  count
+    Input:  N/A
+    Output:  Int
+    Functionality:  returns the number of words in the trie
+  */
+  func count() -> Int {
+    return wordCount
+  }
+
+  /*
+    Function Name:  getWords
+    Input:  N/A
+    Output:  [String]
+    Functionality:  returns the list of words that exist in the trie
+  */
+  func getWords() -> [String] {
+    return wordList
+  }
+
+  /*
+    Function Name:  contains
+    Input:  String
+    Output:  Bool
+    Functionality:  returns true if the tries has the word passed, false otherwise
+  */
+  func contains(w: String) -> Bool {
+    return find(w.lowercaseString).found
+  }
+
+  /*
+    Function Name:  isPrefix
+    Input:  String
+    Output: (Node?, Bool)
+    Functionality:  returns a tuple containing a reference to the final node in the prefix (if it exists) and true/false depending on whether or not the prefix exists in the trie
+  */
+  func isPrefix(p: String) -> (node: Node?, found: Bool) {
+    let prefixP = p.lowercaseString
+
+    var currentNode = self.root
+
+    for c in prefixP.characters {
+      if currentNode.children[String(c)] == nil{
+        return (nil, false)
+      }
+
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    if currentNode.numChildren() > 0 {
+      return (currentNode, true)
+    }
+
+    return (nil, false)
+  }
+
+  /*
+    Function Name:  insert
+    Input:  String
+    Output:  (String, Bool)
+    Functionality:  Inserts a word int othe trie.  Returns a tuple containing the word attempted to be added, and true/false depending on whether or not the insertion was successful
+  */
+  func insert(w: String) -> (word: String, inserted: Bool) {
+
+    let word = w.lowercaseString
+    var currentNode = self.root
+    var length = word.characters.count
+
+    if self.contains(word) {
+      return (w, false)
+    }
+
+    var index = 0
+    var c = Array(word.characters)[index]
+
+    while let child = currentNode.children[String(c)] {
+      currentNode = child
+      length -= 1
+      index += 1
+
+      if(length == 0) {
+        currentNode.isWord()
+        wordList.append(w)
+        wordCount += 1
+        return (w, true)
+      }
+
+      c = Array(word.characters)[index]
+    }
+
+    let remainingChars = String(word.characters.suffix(length))
+    for c in remainingChars.characters {
+      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
+      currentNode = currentNode.children[String(c)]!
+    }
+
+    currentNode.isWord()
+    wordList.append(w)
+    wordCount += 1
+    return (w, true)
+  }
+
+  /*
+    Function Name:  insertWords
+    Input:  [String]
+    Output:  ([String], Bool)
+    Functionality:  attempts to insert all words from input array.  returns a tuple containing the input array and true if some of the words were succesffuly added, false if none were added
+  */
+
+  func insertWords(wordList: [String]) -> (wordList: [String], bool: inserted){
+
+    var successful: Bool = false
+    for word in wordList {
+      succesful |= self.insert(word).inserted
+    }
+
+    return(wordList, succesful)
+  }
+
+  /*
+    Function Name:  remove
+    Input:  String
+    Output:  (String, Bool)
+    Functionality:  Removes the specified key from the trie if it exists, returns tuple containing the word attempted to be removed and true/false if the removal was succesful
+  */
+  func remove(w: String) -> (word: String, removed: Bool){
+    let word = w.lowercaseString
+
+    if(!self.contains(w)) {
+      return (w, false)
+    }
+    var currentNode = self.root
+
+    for c in word.characters {
+      currentNode = currentNode.getChildAt(String(c))
+    }
+
+    if currentNode.numChildren() > 0 {
+      currentNode.isNotWord()
+    } else {
+      var character = currentNode.char()
+      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
+        currentNode = currentNode.getParent()
+        currentNode.children[character]!.setParent(nil)
+        currentNode.children[character]!.update(nil)
+        currentNode.children[character] = nil
+        character = currentNode.char()
+      }
+    }
+
+    wordCount -= 1
+
+    var index = 0
+    for item in wordList{
+      if item == w {
+        wordList.removeAtIndex(index)
+      }
+      index += 1
+    }
+
+    return (w, true)
+  }
+
+  /*
+    Function Name: findPrefix
+    Input:  String
+    Output:  [String]
+    Functionality:  returns a list containing all words in the trie that have the specified prefix
+  */
+  func findPrefix(p: String) -> [String] {
+
+    if !self.isPrefix(p).found {
+      return []
+    }
+
+    var q: Queue = Queue<Node>()
+    var n: Node = self.isPrefix(p).node!
+
+    var wordsWithPrefix: [String] = []
+    var word = p
+    var tmp = ""
+    q.enqueue(n)
+
+    while let current = q.dequeue() {
+      for (char, child) in current.getChildren() {
+        if(!child.visited) {
+          q.enqueue(child)
+          child.visited = true
+          if(child.isValidWord()) {
+            var currentNode = child
+            while currentNode !== n {
+              tmp += currentNode.char()
+              currentNode = currentNode.getParent()
+            }
+            tmp = String(tmp.characters.reverse())
+            wordsWithPrefix.append(word + tmp)
+            tmp = ""
+          }
+        }
+      }
+    }
+
+
+    return wordsWithPrefix
+  }
+
+
+  /*
+    Function Name:  removeAll
+    Input:  N/A
+    Output:  N/A
+    Functionality:  removes all nodes in the trie using remove as a subroutine
+  */
+  func removeAll()  {
+    for word in wordList {
+      self.remove(word)
+    }
+  }
+
+
+  /*
+    Function Name:  printTrie
+    Input:  N/A
+    Output:  N/A
+    Functionality:  prints all the nodes of the trie to console in a nice and easy to understand format
+  */
+  func printTrie() {
+    self.root.printNode("", leaf: true)
+  }
+
+}

From d6b64083de1e334a5dc5d2a4ab667329c8cdfc43 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 21:57:56 -0400
Subject: [PATCH 0346/1679] Got rid of build files

---
 Trie/.build/debug/Trie                        | Bin 103286 -> 0 bytes
 Trie/.build/debug/Trie.a                      | Bin 139282 -> 0 bytes
 Trie/.build/debug/Trie.o/Trie/Queue.d         |   3 -
 Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps | 316 -----------
 .../debug/Trie.o/Trie/Queue~partial.swiftdoc  | Bin 540 -> 0 bytes
 .../Trie.o/Trie/Queue~partial.swiftmodule     | Bin 11608 -> 0 bytes
 Trie/.build/debug/Trie.o/Trie/main.d          |   3 -
 Trie/.build/debug/Trie.o/Trie/main.swiftdeps  | 205 -------
 .../debug/Trie.o/Trie/main~partial.swiftdoc   | Bin 540 -> 0 bytes
 .../Trie.o/Trie/main~partial.swiftmodule      | Bin 31660 -> 0 bytes
 .../.build/debug/Trie.o/Trie/master.swiftdeps |   6 -
 .../debug/Trie.o/Trie/output-file-map.json    |  17 -
 Trie/.build/debug/Trie.o/Trie/trie.d          |   3 -
 Trie/.build/debug/Trie.o/Trie/trie.swiftdeps  | 532 ------------------
 .../debug/Trie.o/Trie/trie~partial.swiftdoc   | Bin 540 -> 0 bytes
 .../Trie.o/Trie/trie~partial.swiftmodule      | Bin 66060 -> 0 bytes
 Trie/.build/debug/Trie.o/build.db             | Bin 15360 -> 0 bytes
 Trie/.build/debug/Trie.o/llbuild.yaml         |  29 -
 .../.build/debug/Trie.o/sources/Queue.swift.o | Bin 23408 -> 0 bytes
 Trie/.build/debug/Trie.o/sources/main.swift.o | Bin 14800 -> 0 bytes
 Trie/.build/debug/Trie.o/sources/trie.swift.o | Bin 107872 -> 0 bytes
 Trie/.build/debug/Trie.swiftdoc               | Bin 540 -> 0 bytes
 Trie/.build/debug/Trie.swiftmodule            | Bin 20828 -> 0 bytes
 .../build.db                                  | Bin 7168 -> 0 bytes
 .../llbuild.yaml                              |  29 -
 .../Queue.d                                   |   3 -
 .../Queue.swiftdeps                           | 316 -----------
 .../master.swiftdeps                          |   6 -
 .../output-file-map.json                      |  17 -
 .../trie.d                                    |   3 -
 .../trie.swiftdeps                            | 513 -----------------
 Trie/Package.swift~                           |   5 -
 Trie/trie.swift~                              | 479 ----------------
 33 files changed, 2485 deletions(-)
 delete mode 100755 Trie/.build/debug/Trie
 delete mode 100644 Trie/.build/debug/Trie.a
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/Queue.d
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/main.d
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/main.swiftdeps
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/main~partial.swiftdoc
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/main~partial.swiftmodule
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/master.swiftdeps
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/output-file-map.json
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/trie.d
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc
 delete mode 100644 Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule
 delete mode 100644 Trie/.build/debug/Trie.o/build.db
 delete mode 100644 Trie/.build/debug/Trie.o/llbuild.yaml
 delete mode 100644 Trie/.build/debug/Trie.o/sources/Queue.swift.o
 delete mode 100644 Trie/.build/debug/Trie.o/sources/main.swift.o
 delete mode 100644 Trie/.build/debug/Trie.o/sources/trie.swift.o
 delete mode 100644 Trie/.build/debug/Trie.swiftdoc
 delete mode 100644 Trie/.build/debug/Trie.swiftmodule
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/build.db
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d
 delete mode 100644 Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps
 delete mode 100644 Trie/Package.swift~
 delete mode 100644 Trie/trie.swift~

diff --git a/Trie/.build/debug/Trie b/Trie/.build/debug/Trie
deleted file mode 100755
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diff --git a/Trie/.build/debug/Trie.o/Trie/Queue.d b/Trie/.build/debug/Trie.o/Trie/Queue.d
deleted file mode 100644
index bc5d30531..000000000
--- a/Trie/.build/debug/Trie.o/Trie/Queue.d
+++ /dev/null
@@ -1,3 +0,0 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps b/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
deleted file mode 100644
index 6151adec1..000000000
--- a/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps
+++ /dev/null
@@ -1,316 +0,0 @@
-### Swift dependencies file v0 ###
-provides-top-level:
-- "Queue"
-provides-nominal:
-- "V4Trie5Queue"
-provides-member:
-- ["V4Trie5Queue", ""]
-depends-top-level:
-- "Queue"
-- !private "Double"
-- !private "&&"
-- "Int"
-- "Bool"
-- "IntegerLiteralType"
-- !private "<"
-- !private "-"
-- !private "=="
-- !private "+="
-- !private ">"
-- !private "/"
-- "FloatLiteralType"
-depends-member:
-- !private ["Ps16AbsoluteValuable", "init"]
-- ["Sa", "Generator"]
-- ["Sa", "Index"]
-- ["Sa", "SubSequence"]
-- ["Sa", "_Element"]
-- !private ["Sa", "append"]
-- !private ["Sa", "count"]
-- !private ["Sa", "deinit"]
-- ["Sa", "init"]
-- !private ["Sa", "removeFirst"]
-- !private ["Sa", "subscript"]
-- ["Ps23ArrayLiteralConvertible", "Generator"]
-- ["Ps23ArrayLiteralConvertible", "Index"]
-- ["Ps23ArrayLiteralConvertible", "SubSequence"]
-- ["Ps23ArrayLiteralConvertible", "_Element"]
-- !private ["Ps23ArrayLiteralConvertible", "append"]
-- !private ["Ps23ArrayLiteralConvertible", "count"]
-- ["Ps23ArrayLiteralConvertible", "init"]
-- !private ["Ps23ArrayLiteralConvertible", "removeFirst"]
-- !private ["Ps23ArrayLiteralConvertible", "subscript"]
-- ["Vs10ArraySlice", "Generator"]
-- ["Vs10ArraySlice", "Index"]
-- ["Ps22BidirectionalIndexType", "Distance"]
-- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
-- ["Ps21BitwiseOperationsType", "Distance"]
-- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
-- !private ["Sb", "_getBuiltinLogicValue"]
-- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
-- ["Ps11CVarArgType", "Distance"]
-- ["Ps11CVarArgType", "IntegerLiteralType"]
-- !private ["Ps11CVarArgType", "init"]
-- ["Ps14CollectionType", "Generator"]
-- ["Ps14CollectionType", "Index"]
-- ["Ps14CollectionType", "SubSequence"]
-- ["Ps14CollectionType", "_Element"]
-- !private ["Ps14CollectionType", "append"]
-- !private ["Ps14CollectionType", "count"]
-- ["Ps14CollectionType", "init"]
-- !private ["Ps14CollectionType", "removeFirst"]
-- !private ["Ps14CollectionType", "subscript"]
-- ["Ps10Comparable", "Distance"]
-- ["Ps10Comparable", "IntegerLiteralType"]
-- !private ["Ps10Comparable", "init"]
-- ["Ps28CustomDebugStringConvertible", "Generator"]
-- ["Ps28CustomDebugStringConvertible", "Index"]
-- ["Ps28CustomDebugStringConvertible", "Some"]
-- ["Ps28CustomDebugStringConvertible", "SubSequence"]
-- ["Ps28CustomDebugStringConvertible", "_Element"]
-- !private ["Ps28CustomDebugStringConvertible", "append"]
-- !private ["Ps28CustomDebugStringConvertible", "count"]
-- ["Ps28CustomDebugStringConvertible", "init"]
-- !private ["Ps28CustomDebugStringConvertible", "removeFirst"]
-- !private ["Ps28CustomDebugStringConvertible", "subscript"]
-- ["Ps23CustomStringConvertible", "Distance"]
-- ["Ps23CustomStringConvertible", "Generator"]
-- ["Ps23CustomStringConvertible", "Index"]
-- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
-- ["Ps23CustomStringConvertible", "SubSequence"]
-- ["Ps23CustomStringConvertible", "_Element"]
-- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps23CustomStringConvertible", "append"]
-- !private ["Ps23CustomStringConvertible", "count"]
-- ["Ps23CustomStringConvertible", "init"]
-- !private ["Ps23CustomStringConvertible", "removeFirst"]
-- !private ["Ps23CustomStringConvertible", "subscript"]
-- !private ["Sd", "init"]
-- ["Ps9Equatable", "Distance"]
-- ["Ps9Equatable", "IntegerLiteralType"]
-- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
-- !private ["Ps9Equatable", "init"]
-- !private ["Ps23FloatLiteralConvertible", "init"]
-- !private ["Ps17FloatingPointType", "init"]
-- ["Ps16ForwardIndexType", "Distance"]
-- ["Ps16ForwardIndexType", "IntegerLiteralType"]
-- ["Ps13GeneratorType", "Element"]
-- ["Ps8Hashable", "Distance"]
-- ["Ps8Hashable", "IntegerLiteralType"]
-- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
-- !private ["Ps8Hashable", "init"]
-- ["Ps9Indexable", "Generator"]
-- ["Ps9Indexable", "Index"]
-- ["Ps9Indexable", "SubSequence"]
-- ["Ps9Indexable", "_Element"]
-- !private ["Ps9Indexable", "append"]
-- !private ["Ps9Indexable", "count"]
-- ["Ps9Indexable", "init"]
-- !private ["Ps9Indexable", "removeFirst"]
-- !private ["Ps9Indexable", "subscript"]
-- ["Vs17IndexingGenerator", "Element"]
-- ["Si", "Distance"]
-- ["Si", "IntegerLiteralType"]
-- ["Ps21IntegerArithmeticType", "Distance"]
-- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps25IntegerLiteralConvertible", "Distance"]
-- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps25IntegerLiteralConvertible", "init"]
-- ["Ps11IntegerType", "Distance"]
-- ["Ps11IntegerType", "IntegerLiteralType"]
-- ["Ps14MirrorPathType", "Distance"]
-- ["Ps14MirrorPathType", "IntegerLiteralType"]
-- ["Ps21MutableCollectionType", "Generator"]
-- ["Ps21MutableCollectionType", "Index"]
-- ["Ps21MutableCollectionType", "SubSequence"]
-- ["Ps21MutableCollectionType", "_Element"]
-- !private ["Ps21MutableCollectionType", "append"]
-- !private ["Ps21MutableCollectionType", "count"]
-- ["Ps21MutableCollectionType", "init"]
-- !private ["Ps21MutableCollectionType", "removeFirst"]
-- !private ["Ps21MutableCollectionType", "subscript"]
-- ["Ps16MutableIndexable", "Generator"]
-- ["Ps16MutableIndexable", "Index"]
-- ["Ps16MutableIndexable", "SubSequence"]
-- ["Ps16MutableIndexable", "_Element"]
-- !private ["Ps16MutableIndexable", "append"]
-- !private ["Ps16MutableIndexable", "count"]
-- ["Ps16MutableIndexable", "init"]
-- !private ["Ps16MutableIndexable", "removeFirst"]
-- !private ["Ps16MutableIndexable", "subscript"]
-- ["Ps16MutableSliceable", "Generator"]
-- ["Ps16MutableSliceable", "Index"]
-- ["Ps16MutableSliceable", "SubSequence"]
-- ["Ps16MutableSliceable", "_Element"]
-- !private ["Ps16MutableSliceable", "append"]
-- !private ["Ps16MutableSliceable", "count"]
-- ["Ps16MutableSliceable", "init"]
-- !private ["Ps16MutableSliceable", "removeFirst"]
-- !private ["Ps16MutableSliceable", "subscript"]
-- ["Ps21NilLiteralConvertible", "Some"]
-- ["Sq", "Some"]
-- ["V4Trie5Queue", "Bool"]
-- !private ["V4Trie5Queue", "Double"]
-- ["V4Trie5Queue", "Int"]
-- ["V4Trie5Queue", "T"]
-- !private ["V4Trie5Queue", "array"]
-- ["V4Trie5Queue", "count"]
-- ["V4Trie5Queue", "dequeue"]
-- ["V4Trie5Queue", "enqueue"]
-- !private ["V4Trie5Queue", "head"]
-- ["V4Trie5Queue", "init"]
-- ["V4Trie5Queue", "isEmpty"]
-- ["V4Trie5Queue", "peek"]
-- ["Ps21RandomAccessIndexType", "Distance"]
-- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
-- ["Ps30RangeReplaceableCollectionType", "Generator"]
-- ["Ps30RangeReplaceableCollectionType", "Index"]
-- ["Ps30RangeReplaceableCollectionType", "SubSequence"]
-- ["Ps30RangeReplaceableCollectionType", "_Element"]
-- !private ["Ps30RangeReplaceableCollectionType", "append"]
-- !private ["Ps30RangeReplaceableCollectionType", "count"]
-- ["Ps30RangeReplaceableCollectionType", "init"]
-- !private ["Ps30RangeReplaceableCollectionType", "removeFirst"]
-- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
-- ["Ps12SequenceType", "Element"]
-- ["Ps12SequenceType", "Generator"]
-- ["Ps12SequenceType", "Index"]
-- ["Ps12SequenceType", "SubSequence"]
-- ["Ps12SequenceType", "_Element"]
-- !private ["Ps12SequenceType", "append"]
-- !private ["Ps12SequenceType", "count"]
-- ["Ps12SequenceType", "init"]
-- !private ["Ps12SequenceType", "removeFirst"]
-- !private ["Ps12SequenceType", "subscript"]
-- ["Ps17SignedIntegerType", "Distance"]
-- ["Ps17SignedIntegerType", "IntegerLiteralType"]
-- ["Ps16SignedNumberType", "Distance"]
-- ["Ps16SignedNumberType", "IntegerLiteralType"]
-- !private ["Ps16SignedNumberType", "init"]
-- !private ["Vs5Slice", "Generator"]
-- !private ["Vs5Slice", "Index"]
-- !private ["Vs5Slice", "SubSequence"]
-- !private ["Vs5Slice", "_Element"]
-- ["Ps10Strideable", "Distance"]
-- ["Ps10Strideable", "IntegerLiteralType"]
-- !private ["Ps10Strideable", "init"]
-- ["Ps10_ArrayType", "Generator"]
-- ["Ps10_ArrayType", "Index"]
-- ["Ps10_ArrayType", "SubSequence"]
-- ["Ps10_ArrayType", "_Element"]
-- !private ["Ps10_ArrayType", "append"]
-- !private ["Ps10_ArrayType", "count"]
-- ["Ps10_ArrayType", "init"]
-- !private ["Ps10_ArrayType", "removeFirst"]
-- !private ["Ps10_ArrayType", "subscript"]
-- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps31_BuiltinFloatLiteralConvertible", "init"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps33_BuiltinIntegerLiteralConvertible", "init"]
-- !private ["Ps19_CVarArgAlignedType", "init"]
-- !private ["Ps22_CVarArgPassedAsDouble", "init"]
-- ["Ps24_DestructorSafeContainer", "Generator"]
-- ["Ps24_DestructorSafeContainer", "Index"]
-- ["Ps24_DestructorSafeContainer", "SubSequence"]
-- ["Ps24_DestructorSafeContainer", "_Element"]
-- !private ["Ps24_DestructorSafeContainer", "append"]
-- !private ["Ps24_DestructorSafeContainer", "count"]
-- ["Ps24_DestructorSafeContainer", "init"]
-- !private ["Ps24_DestructorSafeContainer", "removeFirst"]
-- !private ["Ps24_DestructorSafeContainer", "subscript"]
-- ["Ps14_Incrementable", "Distance"]
-- ["Ps14_Incrementable", "IntegerLiteralType"]
-- ["Ps22_IntegerArithmeticType", "Distance"]
-- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps12_IntegerType", "Distance"]
-- ["Ps12_IntegerType", "IntegerLiteralType"]
-- ["Ps22_RandomAccessAmbiguity", "Distance"]
-- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Distance"]
-- ["Ps12_Reflectable", "Generator"]
-- ["Ps12_Reflectable", "Index"]
-- ["Ps12_Reflectable", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Some"]
-- ["Ps12_Reflectable", "SubSequence"]
-- ["Ps12_Reflectable", "_Element"]
-- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
-- !private ["Ps12_Reflectable", "append"]
-- !private ["Ps12_Reflectable", "count"]
-- ["Ps12_Reflectable", "init"]
-- !private ["Ps12_Reflectable", "removeFirst"]
-- !private ["Ps12_Reflectable", "subscript"]
-- ["Ps18_SignedIntegerType", "Distance"]
-- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
-depends-nominal:
-- !private "Ps16AbsoluteValuable"
-- "Sa"
-- "Ps23ArrayLiteralConvertible"
-- "Vs10ArraySlice"
-- "Ps22BidirectionalIndexType"
-- "Ps21BitwiseOperationsType"
-- !private "Sb"
-- !private "Ps25BooleanLiteralConvertible"
-- !private "Ps11BooleanType"
-- "Ps11CVarArgType"
-- "Ps14CollectionType"
-- "Ps10Comparable"
-- "Ps28CustomDebugStringConvertible"
-- "Ps23CustomStringConvertible"
-- !private "Sd"
-- "Ps9Equatable"
-- !private "Ps23FloatLiteralConvertible"
-- !private "Ps17FloatingPointType"
-- "Ps16ForwardIndexType"
-- "Ps13GeneratorType"
-- "Ps8Hashable"
-- "Ps9Indexable"
-- "Vs17IndexingGenerator"
-- "Si"
-- "Ps21IntegerArithmeticType"
-- "Ps25IntegerLiteralConvertible"
-- "Ps11IntegerType"
-- "Ps14MirrorPathType"
-- "Ps21MutableCollectionType"
-- "Ps16MutableIndexable"
-- "Ps16MutableSliceable"
-- "Ps21NilLiteralConvertible"
-- "Sq"
-- "V4Trie5Queue"
-- "Ps21RandomAccessIndexType"
-- "Ps30RangeReplaceableCollectionType"
-- "Ps12SequenceType"
-- "Ps17SignedIntegerType"
-- "Ps16SignedNumberType"
-- !private "Vs5Slice"
-- "Ps10Strideable"
-- "Ps10_ArrayType"
-- !private "Ps33_BuiltinBooleanLiteralConvertible"
-- !private "Ps31_BuiltinFloatLiteralConvertible"
-- "Ps33_BuiltinIntegerLiteralConvertible"
-- !private "Ps19_CVarArgAlignedType"
-- !private "Ps22_CVarArgPassedAsDouble"
-- "Ps24_DestructorSafeContainer"
-- "Ps14_Incrementable"
-- "Ps22_IntegerArithmeticType"
-- "Ps12_IntegerType"
-- "Ps22_RandomAccessAmbiguity"
-- "Ps12_Reflectable"
-- "Ps18_SignedIntegerType"
-depends-dynamic-lookup:
-depends-external:
-- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
-- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "b268b101cc2bc2706939fa25905dab4d"
diff --git a/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc b/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftdoc
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diff --git a/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule b/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule
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diff --git a/Trie/.build/debug/Trie.o/Trie/main.d b/Trie/.build/debug/Trie.o/Trie/main.d
deleted file mode 100644
index 73abc24e4..000000000
--- a/Trie/.build/debug/Trie.o/Trie/main.d
+++ /dev/null
@@ -1,3 +0,0 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/main.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/main~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/main.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/main.swiftdeps b/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
deleted file mode 100644
index d126051a2..000000000
--- a/Trie/.build/debug/Trie.o/Trie/main.swiftdeps
+++ /dev/null
@@ -1,205 +0,0 @@
-### Swift dependencies file v0 ###
-provides-top-level:
-- "T"
-- "U"
-- "V"
-provides-nominal:
-provides-member:
-depends-top-level:
-- "Trie"
-- "U"
-- "Array"
-- "V"
-- "print"
-- "StringLiteralType"
-- "T"
-- "Set"
-- "UnicodeScalarType"
-depends-member:
-- ["Ps9AnyObject", "findPrefix"]
-- ["Ps9AnyObject", "getWords"]
-- ["Ps9AnyObject", "init"]
-- ["Ps9AnyObject", "insert"]
-- ["Ps9AnyObject", "merge"]
-- ["Ps9AnyObject", "removeAll"]
-- ["Sa", "Element"]
-- ["Sa", "Generator"]
-- ["Sa", "Index"]
-- ["Sa", "_Element"]
-- ["Ps23ArrayLiteralConvertible", "Element"]
-- ["Ps23ArrayLiteralConvertible", "Generator"]
-- ["Ps23ArrayLiteralConvertible", "Index"]
-- ["Ps23ArrayLiteralConvertible", "_Element"]
-- ["Ps23ArrayLiteralConvertible", "init"]
-- ["Ps22BidirectionalIndexType", "Distance"]
-- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
-- ["Ps21BitwiseOperationsType", "Distance"]
-- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
-- ["Ps11CVarArgType", "Distance"]
-- ["Ps11CVarArgType", "IntegerLiteralType"]
-- ["Ps14CollectionType", "Element"]
-- ["Ps14CollectionType", "Generator"]
-- ["Ps14CollectionType", "Index"]
-- ["Ps14CollectionType", "_Element"]
-- ["Ps14CollectionType", "init"]
-- ["Ps10Comparable", "Distance"]
-- ["Ps10Comparable", "IntegerLiteralType"]
-- ["Ps28CustomDebugStringConvertible", "Element"]
-- ["Ps28CustomDebugStringConvertible", "Generator"]
-- ["Ps28CustomDebugStringConvertible", "Index"]
-- ["Ps28CustomDebugStringConvertible", "_Element"]
-- ["Ps28CustomDebugStringConvertible", "init"]
-- ["Ps23CustomStringConvertible", "Distance"]
-- ["Ps23CustomStringConvertible", "Element"]
-- ["Ps23CustomStringConvertible", "Generator"]
-- ["Ps23CustomStringConvertible", "Index"]
-- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
-- ["Ps23CustomStringConvertible", "_Element"]
-- ["Ps23CustomStringConvertible", "init"]
-- ["Ps9Equatable", "Distance"]
-- ["Ps9Equatable", "IntegerLiteralType"]
-- ["Ps9Equatable", "init"]
-- ["Ps16ForwardIndexType", "Distance"]
-- ["Ps16ForwardIndexType", "IntegerLiteralType"]
-- ["Ps13GeneratorType", "Element"]
-- ["Ps8Hashable", "Distance"]
-- ["Ps8Hashable", "IntegerLiteralType"]
-- ["Ps8Hashable", "init"]
-- ["Ps9Indexable", "Element"]
-- ["Ps9Indexable", "Generator"]
-- ["Ps9Indexable", "Index"]
-- ["Ps9Indexable", "_Element"]
-- ["Ps9Indexable", "init"]
-- ["Vs17IndexingGenerator", "Element"]
-- ["Si", "Distance"]
-- ["Si", "IntegerLiteralType"]
-- ["Si", "deinit"]
-- ["Ps21IntegerArithmeticType", "Distance"]
-- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps25IntegerLiteralConvertible", "Distance"]
-- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
-- ["Ps11IntegerType", "Distance"]
-- ["Ps11IntegerType", "IntegerLiteralType"]
-- ["Ps14MirrorPathType", "Distance"]
-- ["Ps14MirrorPathType", "IntegerLiteralType"]
-- ["Ps21MutableCollectionType", "Element"]
-- ["Ps21MutableCollectionType", "Generator"]
-- ["Ps21MutableCollectionType", "Index"]
-- ["Ps21MutableCollectionType", "_Element"]
-- ["Ps16MutableIndexable", "Element"]
-- ["Ps16MutableIndexable", "Generator"]
-- ["Ps16MutableIndexable", "Index"]
-- ["Ps16MutableIndexable", "_Element"]
-- ["Ps16MutableSliceable", "Element"]
-- ["Ps16MutableSliceable", "Generator"]
-- ["Ps16MutableSliceable", "Index"]
-- ["Ps16MutableSliceable", "_Element"]
-- ["Ps21RandomAccessIndexType", "Distance"]
-- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
-- ["Ps30RangeReplaceableCollectionType", "Element"]
-- ["Ps30RangeReplaceableCollectionType", "Generator"]
-- ["Ps30RangeReplaceableCollectionType", "Index"]
-- ["Ps30RangeReplaceableCollectionType", "_Element"]
-- ["Ps12SequenceType", "Element"]
-- ["Ps12SequenceType", "Generator"]
-- ["Ps12SequenceType", "Index"]
-- ["Ps12SequenceType", "_Element"]
-- ["Ps12SequenceType", "init"]
-- ["Vs3Set", "init"]
-- ["Ps17SignedIntegerType", "Distance"]
-- ["Ps17SignedIntegerType", "IntegerLiteralType"]
-- ["Ps16SignedNumberType", "Distance"]
-- ["Ps16SignedNumberType", "IntegerLiteralType"]
-- ["Ps10Strideable", "Distance"]
-- ["Ps10Strideable", "IntegerLiteralType"]
-- ["C4Trie4Trie", "findPrefix"]
-- ["C4Trie4Trie", "getWords"]
-- ["C4Trie4Trie", "init"]
-- ["C4Trie4Trie", "insert"]
-- ["C4Trie4Trie", "merge"]
-- ["C4Trie4Trie", "removeAll"]
-- ["Ps10_ArrayType", "Element"]
-- ["Ps10_ArrayType", "Generator"]
-- ["Ps10_ArrayType", "Index"]
-- ["Ps10_ArrayType", "_Element"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
-- ["Ps24_DestructorSafeContainer", "Element"]
-- ["Ps24_DestructorSafeContainer", "Generator"]
-- ["Ps24_DestructorSafeContainer", "Index"]
-- ["Ps24_DestructorSafeContainer", "_Element"]
-- ["Ps14_Incrementable", "Distance"]
-- ["Ps14_Incrementable", "IntegerLiteralType"]
-- ["Ps22_IntegerArithmeticType", "Distance"]
-- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps12_IntegerType", "Distance"]
-- ["Ps12_IntegerType", "IntegerLiteralType"]
-- ["Ps22_RandomAccessAmbiguity", "Distance"]
-- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Distance"]
-- ["Ps12_Reflectable", "Element"]
-- ["Ps12_Reflectable", "Generator"]
-- ["Ps12_Reflectable", "Index"]
-- ["Ps12_Reflectable", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "_Element"]
-- ["Ps12_Reflectable", "init"]
-- ["Ps18_SignedIntegerType", "Distance"]
-- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
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-- "Sa"
-- "Ps23ArrayLiteralConvertible"
-- "Ps22BidirectionalIndexType"
-- "Ps21BitwiseOperationsType"
-- "Ps11CVarArgType"
-- "Ps14CollectionType"
-- "Ps10Comparable"
-- "Ps28CustomDebugStringConvertible"
-- "Ps23CustomStringConvertible"
-- "Ps9Equatable"
-- "Ps16ForwardIndexType"
-- "Ps13GeneratorType"
-- "Ps8Hashable"
-- "Ps9Indexable"
-- "Vs17IndexingGenerator"
-- "Si"
-- "Ps21IntegerArithmeticType"
-- "Ps25IntegerLiteralConvertible"
-- "Ps11IntegerType"
-- "Ps14MirrorPathType"
-- "Ps21MutableCollectionType"
-- "Ps16MutableIndexable"
-- "Ps16MutableSliceable"
-- "Ps21RandomAccessIndexType"
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-- "Ps12SequenceType"
-- "Vs3Set"
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-- "C4Trie4Trie"
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-- "Ps24_DestructorSafeContainer"
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-- "Ps12_IntegerType"
-- "Ps22_RandomAccessAmbiguity"
-- "Ps12_Reflectable"
-- "Ps18_SignedIntegerType"
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-- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
-- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "57319b836b718d38040ac7809f4446f7"
diff --git a/Trie/.build/debug/Trie.o/Trie/main~partial.swiftdoc b/Trie/.build/debug/Trie.o/Trie/main~partial.swiftdoc
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diff --git a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps b/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
deleted file mode 100644
index e309a3241..000000000
--- a/Trie/.build/debug/Trie.o/Trie/master.swiftdeps
+++ /dev/null
@@ -1,6 +0,0 @@
-version: "Swift version 2.2-dev (LLVM 3ebdbb2c7e, Clang f66c5bb67b, Swift 0ddf238ad7)"
-options: "b9e1edeb018f28952094455e51afbd70"
-build_time: [515622447, 803412000]
-inputs:
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": [515621876, 0]
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": [512710161, 0]
diff --git a/Trie/.build/debug/Trie.o/Trie/output-file-map.json b/Trie/.build/debug/Trie.o/Trie/output-file-map.json
deleted file mode 100644
index 6583c1858..000000000
--- a/Trie/.build/debug/Trie.o/Trie/output-file-map.json
+++ /dev/null
@@ -1,17 +0,0 @@
-{
-  "": {
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/master.swiftdeps"
-  },
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": {
-    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie.d",
-    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o",
-    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule",
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps"
-  },
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": {
-    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue.d",
-    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o",
-    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue~partial.swiftmodule",
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/Queue.swiftdeps"
-  }
-}
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.d b/Trie/.build/debug/Trie.o/Trie/trie.d
deleted file mode 100644
index 6afbabc4c..000000000
--- a/Trie/.build/debug/Trie.o/Trie/trie.d
+++ /dev/null
@@ -1,3 +0,0 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps b/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
deleted file mode 100644
index c56a23f66..000000000
--- a/Trie/.build/debug/Trie.o/Trie/trie.swiftdeps
+++ /dev/null
@@ -1,532 +0,0 @@
-### Swift dependencies file v0 ###
-provides-top-level:
-- "Node"
-- "Trie"
-provides-nominal:
-- "C4Trie4Node"
-- "C4Trie4Trie"
-provides-member:
-- ["C4Trie4Node", ""]
-- ["C4Trie4Trie", ""]
-depends-top-level:
-- "FloatLiteralType"
-- !private "-"
-- !private "&&"
-- "Trie"
-- !private "BooleanLiteralType"
-- !private "UnicodeScalarType"
-- "Node"
-- !private "print"
-- "Set"
-- !private "=="
-- !private "Array"
-- !private "+="
-- "IntegerLiteralType"
-- !private "!"
-- !private "StringLiteralType"
-- "Int"
-- !private "Queue"
-- "Void"
-- !private ">"
-- !private "!=="
-- !private "-="
-- "Bool"
-- !private "+"
-- "String"
-depends-member:
-- !private ["Vs12AnyGenerator", "Element"]
-- !private ["Ps9AnyObject", "Array"]
-- !private ["Ps9AnyObject", "Node"]
-- !private ["Ps9AnyObject", "Queue"]
-- !private ["Ps9AnyObject", "Set"]
-- !private ["Ps9AnyObject", "String"]
-- !private ["Ps9AnyObject", "Trie"]
-- !private ["Ps9AnyObject", "char"]
-- !private ["Ps9AnyObject", "character"]
-- !private ["Ps9AnyObject", "children"]
-- !private ["Ps9AnyObject", "contains"]
-- !private ["Ps9AnyObject", "find"]
-- !private ["Ps9AnyObject", "getChildAt"]
-- !private ["Ps9AnyObject", "getChildren"]
-- !private ["Ps9AnyObject", "getParent"]
-- !private ["Ps9AnyObject", "getWords"]
-- !private ["Ps9AnyObject", "init"]
-- !private ["Ps9AnyObject", "insert"]
-- !private ["Ps9AnyObject", "isAWord"]
-- !private ["Ps9AnyObject", "isNotWord"]
-- !private ["Ps9AnyObject", "isPrefix"]
-- !private ["Ps9AnyObject", "isRoot"]
-- !private ["Ps9AnyObject", "isValidWord"]
-- !private ["Ps9AnyObject", "isWord"]
-- !private ["Ps9AnyObject", "numChildren"]
-- !private ["Ps9AnyObject", "parent"]
-- !private ["Ps9AnyObject", "print"]
-- !private ["Ps9AnyObject", "printNode"]
-- !private ["Ps9AnyObject", "remove"]
-- !private ["Ps9AnyObject", "root"]
-- !private ["Ps9AnyObject", "setParent"]
-- !private ["Ps9AnyObject", "update"]
-- !private ["Ps9AnyObject", "visited"]
-- !private ["Ps9AnyObject", "wordCount"]
-- !private ["Ps9AnyObject", "wordList"]
-- ["Ps9AnyObject", ""]
-- !private ["Vs11AnySequence", "Generator"]
-- !private ["Vs11AnySequence", "deinit"]
-- !private ["Sa", "Element"]
-- !private ["Sa", "Generator"]
-- !private ["Sa", "Index"]
-- !private ["Sa", "SubSequence"]
-- !private ["Sa", "_Element"]
-- !private ["Sa", "append"]
-- !private ["Sa", "deinit"]
-- !private ["Sa", "init"]
-- !private ["Sa", "removeAtIndex"]
-- !private ["Sa", "subscript"]
-- !private ["Ps23ArrayLiteralConvertible", "Element"]
-- !private ["Ps23ArrayLiteralConvertible", "Generator"]
-- !private ["Ps23ArrayLiteralConvertible", "Index"]
-- !private ["Ps23ArrayLiteralConvertible", "SubSequence"]
-- !private ["Ps23ArrayLiteralConvertible", "_Element"]
-- !private ["Ps23ArrayLiteralConvertible", "append"]
-- !private ["Ps23ArrayLiteralConvertible", "init"]
-- !private ["Ps23ArrayLiteralConvertible", "removeAtIndex"]
-- !private ["Ps23ArrayLiteralConvertible", "subscript"]
-- !private ["Vs10ArraySlice", "Generator"]
-- !private ["Vs10ArraySlice", "Index"]
-- !private ["Ps22BidirectionalIndexType", "Distance"]
-- !private ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
-- !private ["Ps22BidirectionalIndexType", "_DisabledRangeIndex"]
-- !private ["Ps21BitwiseOperationsType", "Distance"]
-- !private ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
-- !private ["Sb", "_getBuiltinLogicValue"]
-- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
-- !private ["Ps11CVarArgType", "Distance"]
-- !private ["Ps11CVarArgType", "IntegerLiteralType"]
-- !private ["VSS13CharacterView", "Generator"]
-- !private ["VSS13CharacterView", "Index"]
-- !private ["VSS13CharacterView", "SubSequence"]
-- !private ["VSS13CharacterView", "_Element"]
-- !private ["VSS13CharacterView", "count"]
-- !private ["VSS13CharacterView", "deinit"]
-- !private ["VSS13CharacterView", "reverse"]
-- !private ["VSS13CharacterView", "suffix"]
-- !private ["Ps14CollectionType", "Element"]
-- !private ["Ps14CollectionType", "Generator"]
-- !private ["Ps14CollectionType", "Index"]
-- !private ["Ps14CollectionType", "SubSequence"]
-- !private ["Ps14CollectionType", "_Element"]
-- !private ["Ps14CollectionType", "append"]
-- !private ["Ps14CollectionType", "count"]
-- !private ["Ps14CollectionType", "init"]
-- !private ["Ps14CollectionType", "removeAtIndex"]
-- !private ["Ps14CollectionType", "reverse"]
-- !private ["Ps14CollectionType", "subscript"]
-- !private ["Ps14CollectionType", "suffix"]
-- !private ["Ps10Comparable", "Distance"]
-- !private ["Ps10Comparable", "IntegerLiteralType"]
-- !private ["Ps10Comparable", "_DisabledRangeIndex"]
-- !private ["Ps10Comparable", "characters"]
-- !private ["Ps10Comparable", "init"]
-- !private ["Ps10Comparable", "lowercaseString"]
-- !private ["Ps28CustomDebugStringConvertible", "Element"]
-- !private ["Ps28CustomDebugStringConvertible", "Generator"]
-- !private ["Ps28CustomDebugStringConvertible", "Index"]
-- ["Ps28CustomDebugStringConvertible", "Some"]
-- !private ["Ps28CustomDebugStringConvertible", "SubSequence"]
-- !private ["Ps28CustomDebugStringConvertible", "_Element"]
-- !private ["Ps28CustomDebugStringConvertible", "append"]
-- !private ["Ps28CustomDebugStringConvertible", "characters"]
-- !private ["Ps28CustomDebugStringConvertible", "count"]
-- !private ["Ps28CustomDebugStringConvertible", "init"]
-- !private ["Ps28CustomDebugStringConvertible", "lowercaseString"]
-- !private ["Ps28CustomDebugStringConvertible", "removeAtIndex"]
-- !private ["Ps28CustomDebugStringConvertible", "subscript"]
-- !private ["Ps23CustomStringConvertible", "Distance"]
-- !private ["Ps23CustomStringConvertible", "Element"]
-- !private ["Ps23CustomStringConvertible", "Generator"]
-- !private ["Ps23CustomStringConvertible", "Index"]
-- !private ["Ps23CustomStringConvertible", "IntegerLiteralType"]
-- !private ["Ps23CustomStringConvertible", "SubSequence"]
-- !private ["Ps23CustomStringConvertible", "_Element"]
-- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps23CustomStringConvertible", "append"]
-- !private ["Ps23CustomStringConvertible", "count"]
-- !private ["Ps23CustomStringConvertible", "init"]
-- !private ["Ps23CustomStringConvertible", "removeAtIndex"]
-- !private ["Ps23CustomStringConvertible", "subscript"]
-- !private ["Vs10Dictionary", "Generator"]
-- !private ["Vs10Dictionary", "Index"]
-- !private ["Vs10Dictionary", "SubSequence"]
-- !private ["Vs10Dictionary", "_Element"]
-- !private ["Vs10Dictionary", "count"]
-- !private ["Vs10Dictionary", "deinit"]
-- !private ["Vs10Dictionary", "init"]
-- !private ["Vs10Dictionary", "subscript"]
-- !private ["Vs19DictionaryGenerator", "Element"]
-- !private ["Vs15DictionaryIndex", "Distance"]
-- !private ["Vs15DictionaryIndex", "_DisabledRangeIndex"]
-- !private ["Ps28DictionaryLiteralConvertible", "Generator"]
-- !private ["Ps28DictionaryLiteralConvertible", "Index"]
-- !private ["Ps28DictionaryLiteralConvertible", "SubSequence"]
-- !private ["Ps28DictionaryLiteralConvertible", "_Element"]
-- !private ["Ps28DictionaryLiteralConvertible", "count"]
-- !private ["Ps28DictionaryLiteralConvertible", "init"]
-- !private ["Ps28DictionaryLiteralConvertible", "subscript"]
-- !private ["Ps9Equatable", "Distance"]
-- !private ["Ps9Equatable", "Generator"]
-- !private ["Ps9Equatable", "IntegerLiteralType"]
-- !private ["Ps9Equatable", "_DisabledRangeIndex"]
-- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
-- !private ["Ps9Equatable", "characters"]
-- !private ["Ps9Equatable", "init"]
-- !private ["Ps9Equatable", "lowercaseString"]
-- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "characters"]
-- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "init"]
-- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
-- !private ["Ps16ForwardIndexType", "Distance"]
-- !private ["Ps16ForwardIndexType", "IntegerLiteralType"]
-- !private ["Ps16ForwardIndexType", "_DisabledRangeIndex"]
-- !private ["Ps13GeneratorType", "Element"]
-- !private ["Ps8Hashable", "Distance"]
-- !private ["Ps8Hashable", "Generator"]
-- !private ["Ps8Hashable", "IntegerLiteralType"]
-- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
-- !private ["Ps8Hashable", "characters"]
-- !private ["Ps8Hashable", "init"]
-- !private ["Ps8Hashable", "lowercaseString"]
-- !private ["VVSS13CharacterView5Index", "Distance"]
-- !private ["VVSS13CharacterView5Index", "_DisabledRangeIndex"]
-- !private ["VVSS13CharacterView5Index", "deinit"]
-- !private ["Ps9Indexable", "Element"]
-- !private ["Ps9Indexable", "Generator"]
-- !private ["Ps9Indexable", "Index"]
-- !private ["Ps9Indexable", "SubSequence"]
-- !private ["Ps9Indexable", "_Element"]
-- !private ["Ps9Indexable", "append"]
-- !private ["Ps9Indexable", "count"]
-- !private ["Ps9Indexable", "init"]
-- !private ["Ps9Indexable", "removeAtIndex"]
-- !private ["Ps9Indexable", "reverse"]
-- !private ["Ps9Indexable", "subscript"]
-- !private ["Ps9Indexable", "suffix"]
-- !private ["Vs17IndexingGenerator", "Element"]
-- !private ["Si", "Distance"]
-- !private ["Si", "IntegerLiteralType"]
-- !private ["Ps21IntegerArithmeticType", "Distance"]
-- !private ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
-- !private ["Ps25IntegerLiteralConvertible", "Distance"]
-- !private ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps11IntegerType", "Distance"]
-- !private ["Ps11IntegerType", "IntegerLiteralType"]
-- !private ["Ps14MirrorPathType", "Distance"]
-- !private ["Ps14MirrorPathType", "IntegerLiteralType"]
-- !private ["Ps14MirrorPathType", "characters"]
-- !private ["Ps14MirrorPathType", "init"]
-- !private ["Ps14MirrorPathType", "lowercaseString"]
-- !private ["Ps21MutableCollectionType", "Element"]
-- !private ["Ps21MutableCollectionType", "Generator"]
-- !private ["Ps21MutableCollectionType", "Index"]
-- !private ["Ps21MutableCollectionType", "SubSequence"]
-- !private ["Ps21MutableCollectionType", "_Element"]
-- !private ["Ps21MutableCollectionType", "append"]
-- !private ["Ps21MutableCollectionType", "init"]
-- !private ["Ps21MutableCollectionType", "removeAtIndex"]
-- !private ["Ps21MutableCollectionType", "subscript"]
-- !private ["Ps16MutableIndexable", "Element"]
-- !private ["Ps16MutableIndexable", "Generator"]
-- !private ["Ps16MutableIndexable", "Index"]
-- !private ["Ps16MutableIndexable", "SubSequence"]
-- !private ["Ps16MutableIndexable", "_Element"]
-- !private ["Ps16MutableIndexable", "append"]
-- !private ["Ps16MutableIndexable", "init"]
-- !private ["Ps16MutableIndexable", "removeAtIndex"]
-- !private ["Ps16MutableIndexable", "subscript"]
-- !private ["Ps16MutableSliceable", "Element"]
-- !private ["Ps16MutableSliceable", "Generator"]
-- !private ["Ps16MutableSliceable", "Index"]
-- !private ["Ps16MutableSliceable", "SubSequence"]
-- !private ["Ps16MutableSliceable", "_Element"]
-- !private ["Ps16MutableSliceable", "append"]
-- !private ["Ps16MutableSliceable", "init"]
-- !private ["Ps16MutableSliceable", "removeAtIndex"]
-- !private ["Ps16MutableSliceable", "subscript"]
-- ["Ps21NilLiteralConvertible", "Some"]
-- ["C4Trie4Node", "Bool"]
-- ["C4Trie4Node", "Int"]
-- ["C4Trie4Node", "Node"]
-- ["C4Trie4Node", "String"]
-- ["C4Trie4Node", "Void"]
-- ["C4Trie4Node", "char"]
-- !private ["C4Trie4Node", "character"]
-- !private ["C4Trie4Node", "children"]
-- ["C4Trie4Node", "deinit"]
-- ["C4Trie4Node", "getChildAt"]
-- ["C4Trie4Node", "getChildren"]
-- ["C4Trie4Node", "getParent"]
-- ["C4Trie4Node", "init"]
-- !private ["C4Trie4Node", "isAWord"]
-- ["C4Trie4Node", "isLeaf"]
-- ["C4Trie4Node", "isNotWord"]
-- ["C4Trie4Node", "isRoot"]
-- ["C4Trie4Node", "isValidWord"]
-- ["C4Trie4Node", "isWord"]
-- ["C4Trie4Node", "numChildren"]
-- !private ["C4Trie4Node", "parent"]
-- !private ["C4Trie4Node", "print"]
-- ["C4Trie4Node", "printNode"]
-- ["C4Trie4Node", "setParent"]
-- ["C4Trie4Node", "update"]
-- !private ["C4Trie4Node", "visited"]
-- ["Sq", "Some"]
-- !private ["Sq", "deinit"]
-- !private ["Ps16OutputStreamType", "characters"]
-- !private ["Ps16OutputStreamType", "init"]
-- !private ["Ps16OutputStreamType", "lowercaseString"]
-- !private ["V4Trie5Queue", "dequeue"]
-- !private ["V4Trie5Queue", "enqueue"]
-- !private ["V4Trie5Queue", "init"]
-- !private ["Ps21RandomAccessIndexType", "Distance"]
-- !private ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
-- !private ["Ps30RangeReplaceableCollectionType", "Element"]
-- !private ["Ps30RangeReplaceableCollectionType", "Generator"]
-- !private ["Ps30RangeReplaceableCollectionType", "Index"]
-- !private ["Ps30RangeReplaceableCollectionType", "SubSequence"]
-- !private ["Ps30RangeReplaceableCollectionType", "_Element"]
-- !private ["Ps30RangeReplaceableCollectionType", "append"]
-- !private ["Ps30RangeReplaceableCollectionType", "count"]
-- !private ["Ps30RangeReplaceableCollectionType", "init"]
-- !private ["Ps30RangeReplaceableCollectionType", "removeAtIndex"]
-- !private ["Ps30RangeReplaceableCollectionType", "reverse"]
-- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
-- !private ["Ps30RangeReplaceableCollectionType", "suffix"]
-- !private ["Vs17ReverseCollection", "Generator"]
-- !private ["Vs17ReverseCollection", "Index"]
-- !private ["Vs17ReverseCollection", "_Element"]
-- !private ["Vs17ReverseCollection", "deinit"]
-- !private ["Vs12ReverseIndex", "Distance"]
-- !private ["Ps16ReverseIndexType", "Distance"]
-- !private ["Ps12SequenceType", "Element"]
-- !private ["Ps12SequenceType", "Generator"]
-- !private ["Ps12SequenceType", "Index"]
-- !private ["Ps12SequenceType", "SubSequence"]
-- !private ["Ps12SequenceType", "_Element"]
-- !private ["Ps12SequenceType", "append"]
-- !private ["Ps12SequenceType", "count"]
-- !private ["Ps12SequenceType", "init"]
-- !private ["Ps12SequenceType", "removeAtIndex"]
-- !private ["Ps12SequenceType", "reverse"]
-- !private ["Ps12SequenceType", "subscript"]
-- !private ["Ps12SequenceType", "suffix"]
-- !private ["Vs3Set", "Generator"]
-- !private ["Vs3Set", "init"]
-- !private ["Vs12SetGenerator", "Element"]
-- !private ["Ps17SignedIntegerType", "Distance"]
-- !private ["Ps17SignedIntegerType", "IntegerLiteralType"]
-- !private ["Ps16SignedNumberType", "Distance"]
-- !private ["Ps16SignedNumberType", "IntegerLiteralType"]
-- !private ["Vs5Slice", "Generator"]
-- !private ["Vs5Slice", "Index"]
-- !private ["Vs5Slice", "SubSequence"]
-- !private ["Vs5Slice", "_Element"]
-- !private ["Vs5Slice", "deinit"]
-- !private ["Ps10Streamable", "characters"]
-- !private ["Ps10Streamable", "init"]
-- !private ["Ps10Streamable", "lowercaseString"]
-- !private ["Ps10Strideable", "Distance"]
-- !private ["Ps10Strideable", "IntegerLiteralType"]
-- !private ["SS", "characters"]
-- !private ["SS", "init"]
-- !private ["SS", "lowercaseString"]
-- !private ["Ps30StringInterpolationConvertible", "characters"]
-- !private ["Ps30StringInterpolationConvertible", "init"]
-- !private ["Ps30StringInterpolationConvertible", "lowercaseString"]
-- !private ["Ps24StringLiteralConvertible", "characters"]
-- !private ["Ps24StringLiteralConvertible", "init"]
-- !private ["Ps24StringLiteralConvertible", "lowercaseString"]
-- !private ["C4Trie4Trie", "Array"]
-- ["C4Trie4Trie", "Bool"]
-- ["C4Trie4Trie", "Int"]
-- ["C4Trie4Trie", "Node"]
-- !private ["C4Trie4Trie", "Queue"]
-- ["C4Trie4Trie", "Set"]
-- ["C4Trie4Trie", "String"]
-- ["C4Trie4Trie", "Trie"]
-- ["C4Trie4Trie", "contains"]
-- ["C4Trie4Trie", "count"]
-- ["C4Trie4Trie", "deinit"]
-- ["C4Trie4Trie", "find"]
-- ["C4Trie4Trie", "findPrefix"]
-- ["C4Trie4Trie", "getWords"]
-- ["C4Trie4Trie", "init"]
-- ["C4Trie4Trie", "insert"]
-- ["C4Trie4Trie", "isEmpty"]
-- ["C4Trie4Trie", "isPrefix"]
-- ["C4Trie4Trie", "merge"]
-- ["C4Trie4Trie", "printTrie"]
-- ["C4Trie4Trie", "remove"]
-- ["C4Trie4Trie", "removeAll"]
-- !private ["C4Trie4Trie", "root"]
-- !private ["C4Trie4Trie", "wordCount"]
-- !private ["C4Trie4Trie", "wordList"]
-- !private ["Ps31UnicodeScalarLiteralConvertible", "characters"]
-- !private ["Ps31UnicodeScalarLiteralConvertible", "init"]
-- !private ["Ps31UnicodeScalarLiteralConvertible", "lowercaseString"]
-- !private ["Ps10_ArrayType", "Element"]
-- !private ["Ps10_ArrayType", "Generator"]
-- !private ["Ps10_ArrayType", "Index"]
-- !private ["Ps10_ArrayType", "SubSequence"]
-- !private ["Ps10_ArrayType", "_Element"]
-- !private ["Ps10_ArrayType", "append"]
-- !private ["Ps10_ArrayType", "init"]
-- !private ["Ps10_ArrayType", "removeAtIndex"]
-- !private ["Ps10_ArrayType", "subscript"]
-- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "characters"]
-- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "init"]
-- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
-- !private ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
-- !private ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps32_BuiltinStringLiteralConvertible", "characters"]
-- !private ["Ps32_BuiltinStringLiteralConvertible", "init"]
-- !private ["Ps32_BuiltinStringLiteralConvertible", "lowercaseString"]
-- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "characters"]
-- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "init"]
-- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "lowercaseString"]
-- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "characters"]
-- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "init"]
-- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "lowercaseString"]
-- !private ["Ps24_DestructorSafeContainer", "Element"]
-- !private ["Ps24_DestructorSafeContainer", "Generator"]
-- !private ["Ps24_DestructorSafeContainer", "Index"]
-- !private ["Ps24_DestructorSafeContainer", "SubSequence"]
-- !private ["Ps24_DestructorSafeContainer", "_Element"]
-- !private ["Ps24_DestructorSafeContainer", "append"]
-- !private ["Ps24_DestructorSafeContainer", "init"]
-- !private ["Ps24_DestructorSafeContainer", "removeAtIndex"]
-- !private ["Ps24_DestructorSafeContainer", "subscript"]
-- !private ["Ps14_Incrementable", "Distance"]
-- !private ["Ps14_Incrementable", "IntegerLiteralType"]
-- !private ["Ps14_Incrementable", "_DisabledRangeIndex"]
-- !private ["Ps22_IntegerArithmeticType", "Distance"]
-- !private ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
-- !private ["Ps12_IntegerType", "Distance"]
-- !private ["Ps12_IntegerType", "IntegerLiteralType"]
-- !private ["Vs26_OptionalNilComparisonType", "deinit"]
-- !private ["Ps22_RandomAccessAmbiguity", "Distance"]
-- !private ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
-- !private ["Ps12_Reflectable", "Distance"]
-- !private ["Ps12_Reflectable", "Element"]
-- !private ["Ps12_Reflectable", "Generator"]
-- !private ["Ps12_Reflectable", "Index"]
-- !private ["Ps12_Reflectable", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Some"]
-- !private ["Ps12_Reflectable", "SubSequence"]
-- !private ["Ps12_Reflectable", "_DisabledRangeIndex"]
-- !private ["Ps12_Reflectable", "_Element"]
-- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
-- !private ["Ps12_Reflectable", "append"]
-- !private ["Ps12_Reflectable", "characters"]
-- !private ["Ps12_Reflectable", "count"]
-- !private ["Ps12_Reflectable", "init"]
-- !private ["Ps12_Reflectable", "lowercaseString"]
-- !private ["Ps12_Reflectable", "removeAtIndex"]
-- !private ["Ps12_Reflectable", "subscript"]
-- !private ["Ps22_ReverseCollectionType", "Generator"]
-- !private ["Ps22_ReverseCollectionType", "Index"]
-- !private ["Ps22_ReverseCollectionType", "_Element"]
-- !private ["Ps18_SignedIntegerType", "Distance"]
-- !private ["Ps18_SignedIntegerType", "IntegerLiteralType"]
-depends-nominal:
-- !private "Vs12AnyGenerator"
-- "Ps9AnyObject"
-- !private "Vs11AnySequence"
-- !private "Sa"
-- !private "Ps23ArrayLiteralConvertible"
-- !private "Vs10ArraySlice"
-- !private "Ps22BidirectionalIndexType"
-- !private "Ps21BitwiseOperationsType"
-- !private "Sb"
-- !private "Ps25BooleanLiteralConvertible"
-- !private "Ps11BooleanType"
-- !private "Ps11CVarArgType"
-- !private "VSS13CharacterView"
-- !private "Ps14CollectionType"
-- !private "Ps10Comparable"
-- "Ps28CustomDebugStringConvertible"
-- !private "Ps23CustomStringConvertible"
-- !private "Vs10Dictionary"
-- !private "Vs19DictionaryGenerator"
-- !private "Vs15DictionaryIndex"
-- !private "Ps28DictionaryLiteralConvertible"
-- !private "Ps9Equatable"
-- !private "Ps41ExtendedGraphemeClusterLiteralConvertible"
-- !private "Ps16ForwardIndexType"
-- !private "Ps13GeneratorType"
-- !private "Ps8Hashable"
-- !private "VVSS13CharacterView5Index"
-- !private "Ps9Indexable"
-- !private "Vs17IndexingGenerator"
-- !private "Si"
-- !private "Ps21IntegerArithmeticType"
-- !private "Ps25IntegerLiteralConvertible"
-- !private "Ps11IntegerType"
-- !private "Ps14MirrorPathType"
-- !private "Ps21MutableCollectionType"
-- !private "Ps16MutableIndexable"
-- !private "Ps16MutableSliceable"
-- "Ps21NilLiteralConvertible"
-- "C4Trie4Node"
-- "Sq"
-- !private "Ps16OutputStreamType"
-- !private "V4Trie5Queue"
-- !private "Ps21RandomAccessIndexType"
-- !private "Ps30RangeReplaceableCollectionType"
-- !private "Vs17ReverseCollection"
-- !private "Vs12ReverseIndex"
-- !private "Ps16ReverseIndexType"
-- !private "Ps12SequenceType"
-- !private "Vs3Set"
-- !private "Vs12SetGenerator"
-- !private "Ps17SignedIntegerType"
-- !private "Ps16SignedNumberType"
-- !private "Vs5Slice"
-- !private "Ps10Streamable"
-- !private "Ps10Strideable"
-- !private "SS"
-- !private "Ps30StringInterpolationConvertible"
-- !private "Ps24StringLiteralConvertible"
-- "C4Trie4Trie"
-- !private "Ps31UnicodeScalarLiteralConvertible"
-- !private "Ps10_ArrayType"
-- !private "Ps33_BuiltinBooleanLiteralConvertible"
-- !private "Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible"
-- !private "Ps33_BuiltinIntegerLiteralConvertible"
-- !private "Ps32_BuiltinStringLiteralConvertible"
-- !private "Ps37_BuiltinUTF16StringLiteralConvertible"
-- !private "Ps39_BuiltinUnicodeScalarLiteralConvertible"
-- !private "Ps24_DestructorSafeContainer"
-- !private "Ps14_Incrementable"
-- !private "Ps22_IntegerArithmeticType"
-- !private "Ps12_IntegerType"
-- !private "Vs26_OptionalNilComparisonType"
-- !private "Ps22_RandomAccessAmbiguity"
-- "Ps12_Reflectable"
-- !private "Ps22_ReverseCollectionType"
-- !private "Ps18_SignedIntegerType"
-depends-dynamic-lookup:
-depends-external:
-- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
-- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "eefc37d55a335afd501967035d9090a5"
diff --git a/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc b/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftdoc
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GIT binary patch
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diff --git a/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule b/Trie/.build/debug/Trie.o/Trie/trie~partial.swiftmodule
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diff --git a/Trie/.build/debug/Trie.o/llbuild.yaml b/Trie/.build/debug/Trie.o/llbuild.yaml
deleted file mode 100644
index 7f699a487..000000000
--- a/Trie/.build/debug/Trie.o/llbuild.yaml
+++ /dev/null
@@ -1,29 +0,0 @@
-client:
-  name: swift-build
-
-tools: {}
-
-targets:
-  "": [<Trie>]
-  Trie: [<Trie>]
-
-commands:
-  <Trie-swiftc>:
-    tool: swift-compiler
-    executable: "/home/christian/swiftv2/usr/bin/swiftc"
-    inputs: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
-    outputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
-    module-name: "Trie"
-    module-output-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.swiftmodule"
-    is-library: true
-    sources: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
-    objects: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
-    import-paths: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug"]
-    temps-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/Trie"
-    other-args: ["-j8","-Onone","-g","-enable-testing","-I","/usr/local/include"]
-  <Trie>:
-    tool: shell
-    inputs: ["<Trie-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o"]
-    outputs: ["<Trie>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.a"]
-    args: ["/bin/sh","-c","rm -f '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.a'; ar cr '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.a' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/trie.swift.o' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/Trie.o/sources/Queue.swift.o'"]
-    description: "Linking Library:  .build/debug/Trie.a"
diff --git a/Trie/.build/debug/Trie.o/sources/Queue.swift.o b/Trie/.build/debug/Trie.o/sources/Queue.swift.o
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diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/build.db b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/build.db
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index 1c00411e4402e025363b0e2c481337daff6a3f53..0000000000000000000000000000000000000000
GIT binary patch
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diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml
deleted file mode 100644
index 5e1bc6390..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/llbuild.yaml
+++ /dev/null
@@ -1,29 +0,0 @@
-client:
-  name: swift-build
-
-tools: {}
-
-targets:
-  "": [<package_name_here_and_keep_quote_marks>]
-  package_name_here_and_keep_quote_marks: [<package_name_here_and_keep_quote_marks>]
-
-commands:
-  <package_name_here_and_keep_quote_marks-swiftc>:
-    tool: swift-compiler
-    executable: "/home/christian/swiftv2/usr/bin/swiftc"
-    inputs: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
-    outputs: ["<package_name_here_and_keep_quote_marks-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.swiftmodule","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o"]
-    module-name: "package_name_here_and_keep_quote_marks"
-    module-output-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.swiftmodule"
-    is-library: true
-    sources: ["/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift","/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift"]
-    objects: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o"]
-    import-paths: ["/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug"]
-    temps-path: "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks"
-    other-args: ["-j8","-Onone","-g","-enable-testing","-I","/usr/local/include"]
-  <package_name_here_and_keep_quote_marks>:
-    tool: shell
-    inputs: ["<package_name_here_and_keep_quote_marks-swiftc>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o"]
-    outputs: ["<package_name_here_and_keep_quote_marks>","/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.a"]
-    args: ["/bin/sh","-c","rm -f '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.a'; ar cr '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.a' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o' '/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o'"]
-    description: "Linking Library:  .build/debug/package_name_here_and_keep_quote_marks.a"
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d
deleted file mode 100644
index 2b2aa612f..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d
+++ /dev/null
@@ -1,3 +0,0 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps
deleted file mode 100644
index eaa595090..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps
+++ /dev/null
@@ -1,316 +0,0 @@
-### Swift dependencies file v0 ###
-provides-top-level:
-- "Queue"
-provides-nominal:
-- "V38package_name_here_and_keep_quote_marks5Queue"
-provides-member:
-- ["V38package_name_here_and_keep_quote_marks5Queue", ""]
-depends-top-level:
-- "Queue"
-- !private "/"
-- !private "&&"
-- !private "Double"
-- !private "-"
-- "Bool"
-- "FloatLiteralType"
-- "IntegerLiteralType"
-- !private ">"
-- !private "=="
-- "Int"
-- !private "<"
-- !private "+="
-depends-member:
-- !private ["Ps16AbsoluteValuable", "init"]
-- ["Sa", "Generator"]
-- ["Sa", "Index"]
-- ["Sa", "SubSequence"]
-- ["Sa", "_Element"]
-- !private ["Sa", "append"]
-- !private ["Sa", "count"]
-- !private ["Sa", "deinit"]
-- ["Sa", "init"]
-- !private ["Sa", "removeFirst"]
-- !private ["Sa", "subscript"]
-- ["Ps23ArrayLiteralConvertible", "Generator"]
-- ["Ps23ArrayLiteralConvertible", "Index"]
-- ["Ps23ArrayLiteralConvertible", "SubSequence"]
-- ["Ps23ArrayLiteralConvertible", "_Element"]
-- !private ["Ps23ArrayLiteralConvertible", "append"]
-- !private ["Ps23ArrayLiteralConvertible", "count"]
-- ["Ps23ArrayLiteralConvertible", "init"]
-- !private ["Ps23ArrayLiteralConvertible", "removeFirst"]
-- !private ["Ps23ArrayLiteralConvertible", "subscript"]
-- ["Vs10ArraySlice", "Generator"]
-- ["Vs10ArraySlice", "Index"]
-- ["Ps22BidirectionalIndexType", "Distance"]
-- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
-- ["Ps21BitwiseOperationsType", "Distance"]
-- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
-- !private ["Sb", "_getBuiltinLogicValue"]
-- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
-- ["Ps11CVarArgType", "Distance"]
-- ["Ps11CVarArgType", "IntegerLiteralType"]
-- !private ["Ps11CVarArgType", "init"]
-- ["Ps14CollectionType", "Generator"]
-- ["Ps14CollectionType", "Index"]
-- ["Ps14CollectionType", "SubSequence"]
-- ["Ps14CollectionType", "_Element"]
-- !private ["Ps14CollectionType", "append"]
-- !private ["Ps14CollectionType", "count"]
-- ["Ps14CollectionType", "init"]
-- !private ["Ps14CollectionType", "removeFirst"]
-- !private ["Ps14CollectionType", "subscript"]
-- ["Ps10Comparable", "Distance"]
-- ["Ps10Comparable", "IntegerLiteralType"]
-- !private ["Ps10Comparable", "init"]
-- ["Ps28CustomDebugStringConvertible", "Generator"]
-- ["Ps28CustomDebugStringConvertible", "Index"]
-- ["Ps28CustomDebugStringConvertible", "Some"]
-- ["Ps28CustomDebugStringConvertible", "SubSequence"]
-- ["Ps28CustomDebugStringConvertible", "_Element"]
-- !private ["Ps28CustomDebugStringConvertible", "append"]
-- !private ["Ps28CustomDebugStringConvertible", "count"]
-- ["Ps28CustomDebugStringConvertible", "init"]
-- !private ["Ps28CustomDebugStringConvertible", "removeFirst"]
-- !private ["Ps28CustomDebugStringConvertible", "subscript"]
-- ["Ps23CustomStringConvertible", "Distance"]
-- ["Ps23CustomStringConvertible", "Generator"]
-- ["Ps23CustomStringConvertible", "Index"]
-- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
-- ["Ps23CustomStringConvertible", "SubSequence"]
-- ["Ps23CustomStringConvertible", "_Element"]
-- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps23CustomStringConvertible", "append"]
-- !private ["Ps23CustomStringConvertible", "count"]
-- ["Ps23CustomStringConvertible", "init"]
-- !private ["Ps23CustomStringConvertible", "removeFirst"]
-- !private ["Ps23CustomStringConvertible", "subscript"]
-- !private ["Sd", "init"]
-- ["Ps9Equatable", "Distance"]
-- ["Ps9Equatable", "IntegerLiteralType"]
-- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
-- !private ["Ps9Equatable", "init"]
-- !private ["Ps23FloatLiteralConvertible", "init"]
-- !private ["Ps17FloatingPointType", "init"]
-- ["Ps16ForwardIndexType", "Distance"]
-- ["Ps16ForwardIndexType", "IntegerLiteralType"]
-- ["Ps13GeneratorType", "Element"]
-- ["Ps8Hashable", "Distance"]
-- ["Ps8Hashable", "IntegerLiteralType"]
-- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
-- !private ["Ps8Hashable", "init"]
-- ["Ps9Indexable", "Generator"]
-- ["Ps9Indexable", "Index"]
-- ["Ps9Indexable", "SubSequence"]
-- ["Ps9Indexable", "_Element"]
-- !private ["Ps9Indexable", "append"]
-- !private ["Ps9Indexable", "count"]
-- ["Ps9Indexable", "init"]
-- !private ["Ps9Indexable", "removeFirst"]
-- !private ["Ps9Indexable", "subscript"]
-- ["Vs17IndexingGenerator", "Element"]
-- ["Si", "Distance"]
-- ["Si", "IntegerLiteralType"]
-- ["Ps21IntegerArithmeticType", "Distance"]
-- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps25IntegerLiteralConvertible", "Distance"]
-- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps25IntegerLiteralConvertible", "init"]
-- ["Ps11IntegerType", "Distance"]
-- ["Ps11IntegerType", "IntegerLiteralType"]
-- ["Ps14MirrorPathType", "Distance"]
-- ["Ps14MirrorPathType", "IntegerLiteralType"]
-- ["Ps21MutableCollectionType", "Generator"]
-- ["Ps21MutableCollectionType", "Index"]
-- ["Ps21MutableCollectionType", "SubSequence"]
-- ["Ps21MutableCollectionType", "_Element"]
-- !private ["Ps21MutableCollectionType", "append"]
-- !private ["Ps21MutableCollectionType", "count"]
-- ["Ps21MutableCollectionType", "init"]
-- !private ["Ps21MutableCollectionType", "removeFirst"]
-- !private ["Ps21MutableCollectionType", "subscript"]
-- ["Ps16MutableIndexable", "Generator"]
-- ["Ps16MutableIndexable", "Index"]
-- ["Ps16MutableIndexable", "SubSequence"]
-- ["Ps16MutableIndexable", "_Element"]
-- !private ["Ps16MutableIndexable", "append"]
-- !private ["Ps16MutableIndexable", "count"]
-- ["Ps16MutableIndexable", "init"]
-- !private ["Ps16MutableIndexable", "removeFirst"]
-- !private ["Ps16MutableIndexable", "subscript"]
-- ["Ps16MutableSliceable", "Generator"]
-- ["Ps16MutableSliceable", "Index"]
-- ["Ps16MutableSliceable", "SubSequence"]
-- ["Ps16MutableSliceable", "_Element"]
-- !private ["Ps16MutableSliceable", "append"]
-- !private ["Ps16MutableSliceable", "count"]
-- ["Ps16MutableSliceable", "init"]
-- !private ["Ps16MutableSliceable", "removeFirst"]
-- !private ["Ps16MutableSliceable", "subscript"]
-- ["Ps21NilLiteralConvertible", "Some"]
-- ["Sq", "Some"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "Bool"]
-- !private ["V38package_name_here_and_keep_quote_marks5Queue", "Double"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "Int"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "T"]
-- !private ["V38package_name_here_and_keep_quote_marks5Queue", "array"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "count"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "dequeue"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "enqueue"]
-- !private ["V38package_name_here_and_keep_quote_marks5Queue", "head"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "init"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "isEmpty"]
-- ["V38package_name_here_and_keep_quote_marks5Queue", "peek"]
-- ["Ps21RandomAccessIndexType", "Distance"]
-- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
-- ["Ps30RangeReplaceableCollectionType", "Generator"]
-- ["Ps30RangeReplaceableCollectionType", "Index"]
-- ["Ps30RangeReplaceableCollectionType", "SubSequence"]
-- ["Ps30RangeReplaceableCollectionType", "_Element"]
-- !private ["Ps30RangeReplaceableCollectionType", "append"]
-- !private ["Ps30RangeReplaceableCollectionType", "count"]
-- ["Ps30RangeReplaceableCollectionType", "init"]
-- !private ["Ps30RangeReplaceableCollectionType", "removeFirst"]
-- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
-- ["Ps12SequenceType", "Element"]
-- ["Ps12SequenceType", "Generator"]
-- ["Ps12SequenceType", "Index"]
-- ["Ps12SequenceType", "SubSequence"]
-- ["Ps12SequenceType", "_Element"]
-- !private ["Ps12SequenceType", "append"]
-- !private ["Ps12SequenceType", "count"]
-- ["Ps12SequenceType", "init"]
-- !private ["Ps12SequenceType", "removeFirst"]
-- !private ["Ps12SequenceType", "subscript"]
-- ["Ps17SignedIntegerType", "Distance"]
-- ["Ps17SignedIntegerType", "IntegerLiteralType"]
-- ["Ps16SignedNumberType", "Distance"]
-- ["Ps16SignedNumberType", "IntegerLiteralType"]
-- !private ["Ps16SignedNumberType", "init"]
-- !private ["Vs5Slice", "Generator"]
-- !private ["Vs5Slice", "Index"]
-- !private ["Vs5Slice", "SubSequence"]
-- !private ["Vs5Slice", "_Element"]
-- ["Ps10Strideable", "Distance"]
-- ["Ps10Strideable", "IntegerLiteralType"]
-- !private ["Ps10Strideable", "init"]
-- ["Ps10_ArrayType", "Generator"]
-- ["Ps10_ArrayType", "Index"]
-- ["Ps10_ArrayType", "SubSequence"]
-- ["Ps10_ArrayType", "_Element"]
-- !private ["Ps10_ArrayType", "append"]
-- !private ["Ps10_ArrayType", "count"]
-- ["Ps10_ArrayType", "init"]
-- !private ["Ps10_ArrayType", "removeFirst"]
-- !private ["Ps10_ArrayType", "subscript"]
-- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps31_BuiltinFloatLiteralConvertible", "init"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps33_BuiltinIntegerLiteralConvertible", "init"]
-- !private ["Ps19_CVarArgAlignedType", "init"]
-- !private ["Ps22_CVarArgPassedAsDouble", "init"]
-- ["Ps24_DestructorSafeContainer", "Generator"]
-- ["Ps24_DestructorSafeContainer", "Index"]
-- ["Ps24_DestructorSafeContainer", "SubSequence"]
-- ["Ps24_DestructorSafeContainer", "_Element"]
-- !private ["Ps24_DestructorSafeContainer", "append"]
-- !private ["Ps24_DestructorSafeContainer", "count"]
-- ["Ps24_DestructorSafeContainer", "init"]
-- !private ["Ps24_DestructorSafeContainer", "removeFirst"]
-- !private ["Ps24_DestructorSafeContainer", "subscript"]
-- ["Ps14_Incrementable", "Distance"]
-- ["Ps14_Incrementable", "IntegerLiteralType"]
-- ["Ps22_IntegerArithmeticType", "Distance"]
-- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps12_IntegerType", "Distance"]
-- ["Ps12_IntegerType", "IntegerLiteralType"]
-- ["Ps22_RandomAccessAmbiguity", "Distance"]
-- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Distance"]
-- ["Ps12_Reflectable", "Generator"]
-- ["Ps12_Reflectable", "Index"]
-- ["Ps12_Reflectable", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Some"]
-- ["Ps12_Reflectable", "SubSequence"]
-- ["Ps12_Reflectable", "_Element"]
-- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
-- !private ["Ps12_Reflectable", "append"]
-- !private ["Ps12_Reflectable", "count"]
-- ["Ps12_Reflectable", "init"]
-- !private ["Ps12_Reflectable", "removeFirst"]
-- !private ["Ps12_Reflectable", "subscript"]
-- ["Ps18_SignedIntegerType", "Distance"]
-- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
-depends-nominal:
-- !private "Ps16AbsoluteValuable"
-- "Sa"
-- "Ps23ArrayLiteralConvertible"
-- "Vs10ArraySlice"
-- "Ps22BidirectionalIndexType"
-- "Ps21BitwiseOperationsType"
-- !private "Sb"
-- !private "Ps25BooleanLiteralConvertible"
-- !private "Ps11BooleanType"
-- "Ps11CVarArgType"
-- "Ps14CollectionType"
-- "Ps10Comparable"
-- "Ps28CustomDebugStringConvertible"
-- "Ps23CustomStringConvertible"
-- !private "Sd"
-- "Ps9Equatable"
-- !private "Ps23FloatLiteralConvertible"
-- !private "Ps17FloatingPointType"
-- "Ps16ForwardIndexType"
-- "Ps13GeneratorType"
-- "Ps8Hashable"
-- "Ps9Indexable"
-- "Vs17IndexingGenerator"
-- "Si"
-- "Ps21IntegerArithmeticType"
-- "Ps25IntegerLiteralConvertible"
-- "Ps11IntegerType"
-- "Ps14MirrorPathType"
-- "Ps21MutableCollectionType"
-- "Ps16MutableIndexable"
-- "Ps16MutableSliceable"
-- "Ps21NilLiteralConvertible"
-- "Sq"
-- "V38package_name_here_and_keep_quote_marks5Queue"
-- "Ps21RandomAccessIndexType"
-- "Ps30RangeReplaceableCollectionType"
-- "Ps12SequenceType"
-- "Ps17SignedIntegerType"
-- "Ps16SignedNumberType"
-- !private "Vs5Slice"
-- "Ps10Strideable"
-- "Ps10_ArrayType"
-- !private "Ps33_BuiltinBooleanLiteralConvertible"
-- !private "Ps31_BuiltinFloatLiteralConvertible"
-- "Ps33_BuiltinIntegerLiteralConvertible"
-- !private "Ps19_CVarArgAlignedType"
-- !private "Ps22_CVarArgPassedAsDouble"
-- "Ps24_DestructorSafeContainer"
-- "Ps14_Incrementable"
-- "Ps22_IntegerArithmeticType"
-- "Ps12_IntegerType"
-- "Ps22_RandomAccessAmbiguity"
-- "Ps12_Reflectable"
-- "Ps18_SignedIntegerType"
-depends-dynamic-lookup:
-depends-external:
-- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
-- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "b268b101cc2bc2706939fa25905dab4d"
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps
deleted file mode 100644
index d0814f65b..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps
+++ /dev/null
@@ -1,6 +0,0 @@
-version: "Swift version 2.2-dev (LLVM 3ebdbb2c7e, Clang f66c5bb67b, Swift 0ddf238ad7)"
-options: "4b4cb3e8efe303c8a39bf9409934d3d3"
-build_time: [515615518, 682291000]
-inputs:
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": !dirty [515615193, 0]
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": !dirty [512710161, 0]
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json
deleted file mode 100644
index 5b65a86c0..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/output-file-map.json
+++ /dev/null
@@ -1,17 +0,0 @@
-{
-  "": {
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/master.swiftdeps"
-  },
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift": {
-    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d",
-    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o",
-    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie~partial.swiftmodule",
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps"
-  },
-  "/home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift": {
-    "dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.d",
-    "object": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/Queue.swift.o",
-    "swiftmodule": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue~partial.swiftmodule",
-    "swift-dependencies": "/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/Queue.swiftdeps"
-  }
-}
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d
deleted file mode 100644
index eefb6fd8d..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.d
+++ /dev/null
@@ -1,3 +0,0 @@
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/sources/trie.swift.o : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie~partial.swiftmodule : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
-/home/christian/Desktop/swift-algorithm-club/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie~partial.swiftdoc : /home/christian/Desktop/swift-algorithm-club/Trie/sources/trie.swift /home/christian/Desktop/swift-algorithm-club/Trie/sources/Queue.swift /home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule /home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h /home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h /home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h /home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h /home/christian/swiftv2/usr/lib/swift/shims/RefCount.h /home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h /home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h /home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h /home/christian/swiftv2/usr/lib/swift/shims/module.map
diff --git a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps b/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps
deleted file mode 100644
index 39eba9f00..000000000
--- a/Trie/.build/debug/package_name_here_and_keep_quote_marks.o/package_name_here_and_keep_quote_marks/trie.swiftdeps
+++ /dev/null
@@ -1,513 +0,0 @@
-### Swift dependencies file v0 ###
-provides-top-level:
-- "Node"
-- "Trie"
-- "T"
-- "U"
-- "V"
-provides-nominal:
-- "C38package_name_here_and_keep_quote_marks4Node"
-- "C38package_name_here_and_keep_quote_marks4Trie"
-provides-member:
-- ["C38package_name_here_and_keep_quote_marks4Node", ""]
-- ["C38package_name_here_and_keep_quote_marks4Trie", ""]
-depends-top-level:
-- "Trie"
-- "print"
-- "Bool"
-- !private "-="
-- "StringLiteralType"
-- !private ">"
-- !private "&&"
-- !private "Queue"
-- "U"
-- "Int"
-- "V"
-- !private "BooleanLiteralType"
-- "Node"
-- "FloatLiteralType"
-- "Set"
-- "Array"
-- !private "+"
-- !private "-"
-- !private "UnicodeScalarType"
-- "IntegerLiteralType"
-- !private "=="
-- "Void"
-- !private "+="
-- "T"
-- !private "!"
-- "String"
-depends-member:
-- !private ["Vs12AnyGenerator", "Element"]
-- !private ["Ps9AnyObject", "Array"]
-- !private ["Ps9AnyObject", "Node"]
-- !private ["Ps9AnyObject", "Queue"]
-- !private ["Ps9AnyObject", "Set"]
-- !private ["Ps9AnyObject", "String"]
-- !private ["Ps9AnyObject", "Trie"]
-- !private ["Ps9AnyObject", "char"]
-- !private ["Ps9AnyObject", "character"]
-- !private ["Ps9AnyObject", "children"]
-- !private ["Ps9AnyObject", "contains"]
-- !private ["Ps9AnyObject", "find"]
-- !private ["Ps9AnyObject", "getChildAt"]
-- !private ["Ps9AnyObject", "getChildren"]
-- !private ["Ps9AnyObject", "getParent"]
-- ["Ps9AnyObject", "getWords"]
-- ["Ps9AnyObject", "init"]
-- ["Ps9AnyObject", "insert"]
-- !private ["Ps9AnyObject", "isAWord"]
-- !private ["Ps9AnyObject", "isNotWord"]
-- !private ["Ps9AnyObject", "isRoot"]
-- !private ["Ps9AnyObject", "isValidWord"]
-- !private ["Ps9AnyObject", "isWord"]
-- ["Ps9AnyObject", "merge"]
-- !private ["Ps9AnyObject", "numChildren"]
-- !private ["Ps9AnyObject", "parent"]
-- !private ["Ps9AnyObject", "print"]
-- !private ["Ps9AnyObject", "printNode"]
-- !private ["Ps9AnyObject", "remove"]
-- ["Ps9AnyObject", "removeAll"]
-- !private ["Ps9AnyObject", "root"]
-- !private ["Ps9AnyObject", "setParent"]
-- !private ["Ps9AnyObject", "update"]
-- !private ["Ps9AnyObject", "wordCount"]
-- !private ["Ps9AnyObject", "wordList"]
-- ["Ps9AnyObject", ""]
-- !private ["Vs11AnySequence", "Generator"]
-- !private ["Vs11AnySequence", "deinit"]
-- ["Sa", "Element"]
-- ["Sa", "Generator"]
-- ["Sa", "Index"]
-- !private ["Sa", "SubSequence"]
-- ["Sa", "_Element"]
-- !private ["Sa", "append"]
-- !private ["Sa", "deinit"]
-- !private ["Sa", "init"]
-- !private ["Sa", "removeAtIndex"]
-- !private ["Sa", "subscript"]
-- ["Ps23ArrayLiteralConvertible", "Element"]
-- ["Ps23ArrayLiteralConvertible", "Generator"]
-- ["Ps23ArrayLiteralConvertible", "Index"]
-- !private ["Ps23ArrayLiteralConvertible", "SubSequence"]
-- ["Ps23ArrayLiteralConvertible", "_Element"]
-- !private ["Ps23ArrayLiteralConvertible", "append"]
-- ["Ps23ArrayLiteralConvertible", "init"]
-- !private ["Ps23ArrayLiteralConvertible", "removeAtIndex"]
-- !private ["Ps23ArrayLiteralConvertible", "subscript"]
-- !private ["Vs10ArraySlice", "Generator"]
-- !private ["Vs10ArraySlice", "Index"]
-- ["Ps22BidirectionalIndexType", "Distance"]
-- ["Ps22BidirectionalIndexType", "IntegerLiteralType"]
-- ["Ps21BitwiseOperationsType", "Distance"]
-- ["Ps21BitwiseOperationsType", "IntegerLiteralType"]
-- !private ["Sb", "_getBuiltinLogicValue"]
-- !private ["Ps25BooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps11BooleanType", "_getBuiltinLogicValue"]
-- ["Ps11CVarArgType", "Distance"]
-- ["Ps11CVarArgType", "IntegerLiteralType"]
-- !private ["VSS13CharacterView", "Generator"]
-- !private ["VSS13CharacterView", "Index"]
-- !private ["VSS13CharacterView", "SubSequence"]
-- !private ["VSS13CharacterView", "_Element"]
-- !private ["VSS13CharacterView", "count"]
-- !private ["VSS13CharacterView", "deinit"]
-- !private ["VSS13CharacterView", "suffix"]
-- ["Ps14CollectionType", "Element"]
-- ["Ps14CollectionType", "Generator"]
-- ["Ps14CollectionType", "Index"]
-- !private ["Ps14CollectionType", "SubSequence"]
-- ["Ps14CollectionType", "_Element"]
-- !private ["Ps14CollectionType", "append"]
-- !private ["Ps14CollectionType", "count"]
-- ["Ps14CollectionType", "init"]
-- !private ["Ps14CollectionType", "removeAtIndex"]
-- !private ["Ps14CollectionType", "subscript"]
-- !private ["Ps14CollectionType", "suffix"]
-- ["Ps10Comparable", "Distance"]
-- ["Ps10Comparable", "IntegerLiteralType"]
-- !private ["Ps10Comparable", "_DisabledRangeIndex"]
-- !private ["Ps10Comparable", "characters"]
-- !private ["Ps10Comparable", "init"]
-- !private ["Ps10Comparable", "lowercaseString"]
-- ["Ps28CustomDebugStringConvertible", "Element"]
-- ["Ps28CustomDebugStringConvertible", "Generator"]
-- ["Ps28CustomDebugStringConvertible", "Index"]
-- ["Ps28CustomDebugStringConvertible", "Some"]
-- !private ["Ps28CustomDebugStringConvertible", "SubSequence"]
-- ["Ps28CustomDebugStringConvertible", "_Element"]
-- !private ["Ps28CustomDebugStringConvertible", "append"]
-- !private ["Ps28CustomDebugStringConvertible", "characters"]
-- !private ["Ps28CustomDebugStringConvertible", "count"]
-- ["Ps28CustomDebugStringConvertible", "init"]
-- !private ["Ps28CustomDebugStringConvertible", "lowercaseString"]
-- !private ["Ps28CustomDebugStringConvertible", "removeAtIndex"]
-- !private ["Ps28CustomDebugStringConvertible", "subscript"]
-- ["Ps23CustomStringConvertible", "Distance"]
-- ["Ps23CustomStringConvertible", "Element"]
-- ["Ps23CustomStringConvertible", "Generator"]
-- ["Ps23CustomStringConvertible", "Index"]
-- ["Ps23CustomStringConvertible", "IntegerLiteralType"]
-- !private ["Ps23CustomStringConvertible", "SubSequence"]
-- ["Ps23CustomStringConvertible", "_Element"]
-- !private ["Ps23CustomStringConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps23CustomStringConvertible", "append"]
-- !private ["Ps23CustomStringConvertible", "count"]
-- ["Ps23CustomStringConvertible", "init"]
-- !private ["Ps23CustomStringConvertible", "removeAtIndex"]
-- !private ["Ps23CustomStringConvertible", "subscript"]
-- !private ["Vs10Dictionary", "Generator"]
-- !private ["Vs10Dictionary", "Index"]
-- !private ["Vs10Dictionary", "SubSequence"]
-- !private ["Vs10Dictionary", "_Element"]
-- !private ["Vs10Dictionary", "count"]
-- !private ["Vs10Dictionary", "deinit"]
-- !private ["Vs10Dictionary", "init"]
-- !private ["Vs10Dictionary", "subscript"]
-- !private ["Vs19DictionaryGenerator", "Element"]
-- !private ["Vs15DictionaryIndex", "Distance"]
-- !private ["Vs15DictionaryIndex", "_DisabledRangeIndex"]
-- !private ["Ps28DictionaryLiteralConvertible", "Generator"]
-- !private ["Ps28DictionaryLiteralConvertible", "Index"]
-- !private ["Ps28DictionaryLiteralConvertible", "SubSequence"]
-- !private ["Ps28DictionaryLiteralConvertible", "_Element"]
-- !private ["Ps28DictionaryLiteralConvertible", "count"]
-- !private ["Ps28DictionaryLiteralConvertible", "init"]
-- !private ["Ps28DictionaryLiteralConvertible", "subscript"]
-- ["Ps9Equatable", "Distance"]
-- !private ["Ps9Equatable", "Generator"]
-- ["Ps9Equatable", "IntegerLiteralType"]
-- !private ["Ps9Equatable", "_DisabledRangeIndex"]
-- !private ["Ps9Equatable", "_getBuiltinLogicValue"]
-- !private ["Ps9Equatable", "characters"]
-- ["Ps9Equatable", "init"]
-- !private ["Ps9Equatable", "lowercaseString"]
-- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "characters"]
-- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "init"]
-- !private ["Ps41ExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
-- ["Ps16ForwardIndexType", "Distance"]
-- ["Ps16ForwardIndexType", "IntegerLiteralType"]
-- !private ["Ps16ForwardIndexType", "_DisabledRangeIndex"]
-- ["Ps13GeneratorType", "Element"]
-- ["Ps8Hashable", "Distance"]
-- !private ["Ps8Hashable", "Generator"]
-- ["Ps8Hashable", "IntegerLiteralType"]
-- !private ["Ps8Hashable", "_getBuiltinLogicValue"]
-- !private ["Ps8Hashable", "characters"]
-- ["Ps8Hashable", "init"]
-- !private ["Ps8Hashable", "lowercaseString"]
-- !private ["VVSS13CharacterView5Index", "Distance"]
-- ["Ps9Indexable", "Element"]
-- ["Ps9Indexable", "Generator"]
-- ["Ps9Indexable", "Index"]
-- !private ["Ps9Indexable", "SubSequence"]
-- ["Ps9Indexable", "_Element"]
-- !private ["Ps9Indexable", "append"]
-- !private ["Ps9Indexable", "count"]
-- ["Ps9Indexable", "init"]
-- !private ["Ps9Indexable", "removeAtIndex"]
-- !private ["Ps9Indexable", "subscript"]
-- !private ["Ps9Indexable", "suffix"]
-- ["Vs17IndexingGenerator", "Element"]
-- ["Si", "Distance"]
-- ["Si", "IntegerLiteralType"]
-- ["Si", "deinit"]
-- ["Ps21IntegerArithmeticType", "Distance"]
-- ["Ps21IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps25IntegerLiteralConvertible", "Distance"]
-- ["Ps25IntegerLiteralConvertible", "IntegerLiteralType"]
-- ["Ps11IntegerType", "Distance"]
-- ["Ps11IntegerType", "IntegerLiteralType"]
-- ["Ps14MirrorPathType", "Distance"]
-- ["Ps14MirrorPathType", "IntegerLiteralType"]
-- !private ["Ps14MirrorPathType", "characters"]
-- !private ["Ps14MirrorPathType", "init"]
-- !private ["Ps14MirrorPathType", "lowercaseString"]
-- ["Ps21MutableCollectionType", "Element"]
-- ["Ps21MutableCollectionType", "Generator"]
-- ["Ps21MutableCollectionType", "Index"]
-- !private ["Ps21MutableCollectionType", "SubSequence"]
-- ["Ps21MutableCollectionType", "_Element"]
-- !private ["Ps21MutableCollectionType", "append"]
-- !private ["Ps21MutableCollectionType", "init"]
-- !private ["Ps21MutableCollectionType", "removeAtIndex"]
-- !private ["Ps21MutableCollectionType", "subscript"]
-- ["Ps16MutableIndexable", "Element"]
-- ["Ps16MutableIndexable", "Generator"]
-- ["Ps16MutableIndexable", "Index"]
-- !private ["Ps16MutableIndexable", "SubSequence"]
-- ["Ps16MutableIndexable", "_Element"]
-- !private ["Ps16MutableIndexable", "append"]
-- !private ["Ps16MutableIndexable", "init"]
-- !private ["Ps16MutableIndexable", "removeAtIndex"]
-- !private ["Ps16MutableIndexable", "subscript"]
-- ["Ps16MutableSliceable", "Element"]
-- ["Ps16MutableSliceable", "Generator"]
-- ["Ps16MutableSliceable", "Index"]
-- !private ["Ps16MutableSliceable", "SubSequence"]
-- ["Ps16MutableSliceable", "_Element"]
-- !private ["Ps16MutableSliceable", "append"]
-- !private ["Ps16MutableSliceable", "init"]
-- !private ["Ps16MutableSliceable", "removeAtIndex"]
-- !private ["Ps16MutableSliceable", "subscript"]
-- ["Ps21NilLiteralConvertible", "Some"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "Bool"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "Int"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "Node"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "String"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "Void"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "char"]
-- !private ["C38package_name_here_and_keep_quote_marks4Node", "character"]
-- !private ["C38package_name_here_and_keep_quote_marks4Node", "children"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "deinit"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "getChildAt"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "getChildren"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "getParent"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "init"]
-- !private ["C38package_name_here_and_keep_quote_marks4Node", "isAWord"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "isLeaf"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "isNotWord"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "isRoot"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "isValidWord"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "isWord"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "numChildren"]
-- !private ["C38package_name_here_and_keep_quote_marks4Node", "parent"]
-- !private ["C38package_name_here_and_keep_quote_marks4Node", "print"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "printNode"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "setParent"]
-- ["C38package_name_here_and_keep_quote_marks4Node", "update"]
-- ["Sq", "Some"]
-- !private ["Sq", "deinit"]
-- !private ["Ps16OutputStreamType", "characters"]
-- !private ["Ps16OutputStreamType", "init"]
-- !private ["Ps16OutputStreamType", "lowercaseString"]
-- !private ["V38package_name_here_and_keep_quote_marks5Queue", "init"]
-- ["Ps21RandomAccessIndexType", "Distance"]
-- ["Ps21RandomAccessIndexType", "IntegerLiteralType"]
-- ["Ps30RangeReplaceableCollectionType", "Element"]
-- ["Ps30RangeReplaceableCollectionType", "Generator"]
-- ["Ps30RangeReplaceableCollectionType", "Index"]
-- !private ["Ps30RangeReplaceableCollectionType", "SubSequence"]
-- ["Ps30RangeReplaceableCollectionType", "_Element"]
-- !private ["Ps30RangeReplaceableCollectionType", "append"]
-- !private ["Ps30RangeReplaceableCollectionType", "count"]
-- !private ["Ps30RangeReplaceableCollectionType", "init"]
-- !private ["Ps30RangeReplaceableCollectionType", "removeAtIndex"]
-- !private ["Ps30RangeReplaceableCollectionType", "subscript"]
-- !private ["Ps30RangeReplaceableCollectionType", "suffix"]
-- ["Ps12SequenceType", "Element"]
-- ["Ps12SequenceType", "Generator"]
-- ["Ps12SequenceType", "Index"]
-- !private ["Ps12SequenceType", "SubSequence"]
-- ["Ps12SequenceType", "_Element"]
-- !private ["Ps12SequenceType", "append"]
-- !private ["Ps12SequenceType", "count"]
-- ["Ps12SequenceType", "init"]
-- !private ["Ps12SequenceType", "removeAtIndex"]
-- !private ["Ps12SequenceType", "subscript"]
-- !private ["Ps12SequenceType", "suffix"]
-- !private ["Vs3Set", "Generator"]
-- ["Vs3Set", "init"]
-- !private ["Vs12SetGenerator", "Element"]
-- ["Ps17SignedIntegerType", "Distance"]
-- ["Ps17SignedIntegerType", "IntegerLiteralType"]
-- ["Ps16SignedNumberType", "Distance"]
-- ["Ps16SignedNumberType", "IntegerLiteralType"]
-- !private ["Vs5Slice", "Generator"]
-- !private ["Vs5Slice", "Index"]
-- !private ["Vs5Slice", "SubSequence"]
-- !private ["Vs5Slice", "_Element"]
-- !private ["Vs5Slice", "deinit"]
-- !private ["Ps10Streamable", "characters"]
-- !private ["Ps10Streamable", "init"]
-- !private ["Ps10Streamable", "lowercaseString"]
-- ["Ps10Strideable", "Distance"]
-- ["Ps10Strideable", "IntegerLiteralType"]
-- !private ["SS", "characters"]
-- !private ["SS", "init"]
-- !private ["SS", "lowercaseString"]
-- !private ["Ps30StringInterpolationConvertible", "characters"]
-- !private ["Ps30StringInterpolationConvertible", "init"]
-- !private ["Ps30StringInterpolationConvertible", "lowercaseString"]
-- !private ["Ps24StringLiteralConvertible", "characters"]
-- !private ["Ps24StringLiteralConvertible", "init"]
-- !private ["Ps24StringLiteralConvertible", "lowercaseString"]
-- !private ["C38package_name_here_and_keep_quote_marks4Trie", "Array"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "Bool"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "Int"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "Node"]
-- !private ["C38package_name_here_and_keep_quote_marks4Trie", "Queue"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "Set"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "String"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "Trie"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "contains"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "count"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "deinit"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "find"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "findPrefix"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "getWords"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "init"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "insert"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "isEmpty"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "isPrefix"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "merge"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "printTrie"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "remove"]
-- ["C38package_name_here_and_keep_quote_marks4Trie", "removeAll"]
-- !private ["C38package_name_here_and_keep_quote_marks4Trie", "root"]
-- !private ["C38package_name_here_and_keep_quote_marks4Trie", "wordCount"]
-- !private ["C38package_name_here_and_keep_quote_marks4Trie", "wordList"]
-- !private ["Ps31UnicodeScalarLiteralConvertible", "characters"]
-- !private ["Ps31UnicodeScalarLiteralConvertible", "init"]
-- !private ["Ps31UnicodeScalarLiteralConvertible", "lowercaseString"]
-- ["Ps10_ArrayType", "Element"]
-- ["Ps10_ArrayType", "Generator"]
-- ["Ps10_ArrayType", "Index"]
-- !private ["Ps10_ArrayType", "SubSequence"]
-- ["Ps10_ArrayType", "_Element"]
-- !private ["Ps10_ArrayType", "append"]
-- !private ["Ps10_ArrayType", "init"]
-- !private ["Ps10_ArrayType", "removeAtIndex"]
-- !private ["Ps10_ArrayType", "subscript"]
-- !private ["Ps33_BuiltinBooleanLiteralConvertible", "_getBuiltinLogicValue"]
-- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "characters"]
-- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "init"]
-- !private ["Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible", "lowercaseString"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "Distance"]
-- ["Ps33_BuiltinIntegerLiteralConvertible", "IntegerLiteralType"]
-- !private ["Ps32_BuiltinStringLiteralConvertible", "characters"]
-- !private ["Ps32_BuiltinStringLiteralConvertible", "init"]
-- !private ["Ps32_BuiltinStringLiteralConvertible", "lowercaseString"]
-- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "characters"]
-- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "init"]
-- !private ["Ps37_BuiltinUTF16StringLiteralConvertible", "lowercaseString"]
-- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "characters"]
-- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "init"]
-- !private ["Ps39_BuiltinUnicodeScalarLiteralConvertible", "lowercaseString"]
-- ["Ps24_DestructorSafeContainer", "Element"]
-- ["Ps24_DestructorSafeContainer", "Generator"]
-- ["Ps24_DestructorSafeContainer", "Index"]
-- !private ["Ps24_DestructorSafeContainer", "SubSequence"]
-- ["Ps24_DestructorSafeContainer", "_Element"]
-- !private ["Ps24_DestructorSafeContainer", "append"]
-- !private ["Ps24_DestructorSafeContainer", "init"]
-- !private ["Ps24_DestructorSafeContainer", "removeAtIndex"]
-- !private ["Ps24_DestructorSafeContainer", "subscript"]
-- ["Ps14_Incrementable", "Distance"]
-- ["Ps14_Incrementable", "IntegerLiteralType"]
-- !private ["Ps14_Incrementable", "_DisabledRangeIndex"]
-- ["Ps22_IntegerArithmeticType", "Distance"]
-- ["Ps22_IntegerArithmeticType", "IntegerLiteralType"]
-- ["Ps12_IntegerType", "Distance"]
-- ["Ps12_IntegerType", "IntegerLiteralType"]
-- !private ["Vs26_OptionalNilComparisonType", "deinit"]
-- ["Ps22_RandomAccessAmbiguity", "Distance"]
-- ["Ps22_RandomAccessAmbiguity", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Distance"]
-- ["Ps12_Reflectable", "Element"]
-- ["Ps12_Reflectable", "Generator"]
-- ["Ps12_Reflectable", "Index"]
-- ["Ps12_Reflectable", "IntegerLiteralType"]
-- ["Ps12_Reflectable", "Some"]
-- !private ["Ps12_Reflectable", "SubSequence"]
-- ["Ps12_Reflectable", "_Element"]
-- !private ["Ps12_Reflectable", "_getBuiltinLogicValue"]
-- !private ["Ps12_Reflectable", "append"]
-- !private ["Ps12_Reflectable", "characters"]
-- !private ["Ps12_Reflectable", "count"]
-- ["Ps12_Reflectable", "init"]
-- !private ["Ps12_Reflectable", "lowercaseString"]
-- !private ["Ps12_Reflectable", "removeAtIndex"]
-- !private ["Ps12_Reflectable", "subscript"]
-- ["Ps18_SignedIntegerType", "Distance"]
-- ["Ps18_SignedIntegerType", "IntegerLiteralType"]
-depends-nominal:
-- !private "Vs12AnyGenerator"
-- "Ps9AnyObject"
-- !private "Vs11AnySequence"
-- "Sa"
-- "Ps23ArrayLiteralConvertible"
-- !private "Vs10ArraySlice"
-- "Ps22BidirectionalIndexType"
-- "Ps21BitwiseOperationsType"
-- !private "Sb"
-- !private "Ps25BooleanLiteralConvertible"
-- !private "Ps11BooleanType"
-- "Ps11CVarArgType"
-- !private "VSS13CharacterView"
-- "Ps14CollectionType"
-- "Ps10Comparable"
-- "Ps28CustomDebugStringConvertible"
-- "Ps23CustomStringConvertible"
-- !private "Vs10Dictionary"
-- !private "Vs19DictionaryGenerator"
-- !private "Vs15DictionaryIndex"
-- !private "Ps28DictionaryLiteralConvertible"
-- "Ps9Equatable"
-- !private "Ps41ExtendedGraphemeClusterLiteralConvertible"
-- "Ps16ForwardIndexType"
-- "Ps13GeneratorType"
-- "Ps8Hashable"
-- !private "VVSS13CharacterView5Index"
-- "Ps9Indexable"
-- "Vs17IndexingGenerator"
-- "Si"
-- "Ps21IntegerArithmeticType"
-- "Ps25IntegerLiteralConvertible"
-- "Ps11IntegerType"
-- "Ps14MirrorPathType"
-- "Ps21MutableCollectionType"
-- "Ps16MutableIndexable"
-- "Ps16MutableSliceable"
-- "Ps21NilLiteralConvertible"
-- "C38package_name_here_and_keep_quote_marks4Node"
-- "Sq"
-- !private "Ps16OutputStreamType"
-- !private "V38package_name_here_and_keep_quote_marks5Queue"
-- "Ps21RandomAccessIndexType"
-- "Ps30RangeReplaceableCollectionType"
-- "Ps12SequenceType"
-- "Vs3Set"
-- !private "Vs12SetGenerator"
-- "Ps17SignedIntegerType"
-- "Ps16SignedNumberType"
-- !private "Vs5Slice"
-- !private "Ps10Streamable"
-- "Ps10Strideable"
-- !private "SS"
-- !private "Ps30StringInterpolationConvertible"
-- !private "Ps24StringLiteralConvertible"
-- "C38package_name_here_and_keep_quote_marks4Trie"
-- !private "Ps31UnicodeScalarLiteralConvertible"
-- "Ps10_ArrayType"
-- !private "Ps33_BuiltinBooleanLiteralConvertible"
-- !private "Ps49_BuiltinExtendedGraphemeClusterLiteralConvertible"
-- "Ps33_BuiltinIntegerLiteralConvertible"
-- !private "Ps32_BuiltinStringLiteralConvertible"
-- !private "Ps37_BuiltinUTF16StringLiteralConvertible"
-- !private "Ps39_BuiltinUnicodeScalarLiteralConvertible"
-- "Ps24_DestructorSafeContainer"
-- "Ps14_Incrementable"
-- "Ps22_IntegerArithmeticType"
-- "Ps12_IntegerType"
-- !private "Vs26_OptionalNilComparisonType"
-- "Ps22_RandomAccessAmbiguity"
-- "Ps12_Reflectable"
-- "Ps18_SignedIntegerType"
-depends-dynamic-lookup:
-depends-external:
-- "/home/christian/swiftv2/usr/lib/swift/linux/x86_64/Swift.swiftmodule"
-- "/home/christian/swiftv2/usr/lib/swift/shims/UnicodeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStdint.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/SwiftStddef.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/LibcShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeStubs.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RuntimeShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/RefCount.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/HeapObject.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/GlobalObjects.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/FoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/CoreFoundationShims.h"
-- "/home/christian/swiftv2/usr/lib/swift/shims/module.map"
-interface-hash: "f003b1876d32aa37e370054fb3e811bb"
diff --git a/Trie/Package.swift~ b/Trie/Package.swift~
deleted file mode 100644
index c9e5942b1..000000000
--- a/Trie/Package.swift~
+++ /dev/null
@@ -1,5 +0,0 @@
-import PackageDescription
-
-let package = Package(
-    name: "package_name_here_and_keep_quote_marks"
-)
diff --git a/Trie/trie.swift~ b/Trie/trie.swift~
deleted file mode 100644
index f2b339024..000000000
--- a/Trie/trie.swift~
+++ /dev/null
@@ -1,479 +0,0 @@
-
-/*
-  A Trie (Pre-fix Tree)
-
-  Some of the functionality of the trie makes use of the Queue implementation for this project.
-
-
-  Every node in the Trie stores a bit of information pertainining to what it references:
-    -Character (letter of an inserted word)
-    -Parent  (Letter that comes before the current letter in some word)
-    -Children (Words that have more letters than available in the prefix)
-    -isAWord (Does the current letter mark the end of a known inserted word?)
-    -visited (Mainly for the findPrefix() function)
-*/
-public class Node {
-  private var character: String?
-  private var parent: Node?
-  private var children: [String:Node]
-  private var isAWord: Bool
-  private var visited: Bool  //only for findPrefix
-
-  init(c: String?, p: Node?){
-    self.character = c
-    self.children = [String:Node]()
-    self.isAWord = false
-    self.parent = p
-    self.visited = false
-    }
-
-  /*
-    Function Name:  char()
-    Input:  N/A
-    Output:  String
-    Functionality: Returns the associated value of the node
-  */
-  func char() -> String {
-    return self.character!
-  }
-
-  /*
-    Function Name:  update
-    Input: String
-    Output: N/A
-    Functionality: Updates the associated value of the node
-  */
-  func update(c: String?) {
-    self.character = c
-  }
-
-  /*
-    Function Name:  isLeaf
-    Input:  N/A
-    Output:  Bool
-    Functionality: Returns true if the node is a leaf node, false otherwise
-  */
-  func isLeaf() -> Bool{
-    return self.children.count == 0
-  }
-
-  /*
-    Function Name:  getParent
-    Input:  N/A
-    Output:  Node
-    Functionality: Returns the parent node of the current node
-  */
-  func getParent() -> Node {
-    return parent!
-  }
-
-  /*
-    Function Name:  setParent
-    Input:  Node
-    Output:  N/A
-    Functionality: Changes the parent of the current node to the passed node
-  */
-
-  func setParent(node: Node?) {
-    self.parent = node
-  }
-
-  /*
-    Function Name:  getChildAt
-    Input:  String
-    Output:  Node
-    Functionality:  returns the child node that holds the specific passed letter
-  */
-  func getChildAt(s: String) -> Node {
-    return self.children[s]!
-  }
-
-  /*
-    Function Name:  isValidWord
-    Input:  N/A
-    Output:  Bool
-    Functionality: Returns whether or not the current node marks the end of a valid word
-  */
-  func isValidWord() -> Bool{
-    return self.isAWord
-  }
-
-  /*
-    Function Name:  isWord
-    Input:  N/A
-    Output:  N/A
-    Functionality:  the current node is indeed a word
-  */
-  func isWord() {
-    self.isAWord = true
-  }
-
-  /*
-    Function Name: isNotWord
-    Input:  N/A
-    Output:  N/A
-    Functionality:  marks the current node as not a word
-  */
-  func isNotWord() {
-    self.isAWord = false
-  }
-
-  /*
-    Function Name:  isRoot
-    Input: N/A
-    Output: Bool
-    Functionality:  Returns whether or not the current node is the root of the trie
-  */
-  func isRoot() -> Bool {
-    return self.character == ""
-  }
-
-  /*
-    Function Name:  numChildren
-    Input:  N/A
-    Output:  Int
-    Functionality:  Returns the number of immediate letters that follow the current node
-  */
-  func numChildren() -> Int {
-    return self.children.count
-  }
-
-  /*
-    Function Name:  getChildren
-    Input:  N/A
-    Output:  [String: Node]
-    Functionality:  Returns the letters that immediately follow the current node's value for possible word segments that follow
-  */
-  func getChildren() -> [String: Node] {
-    return self.children
-  }
-
-
-  /*
-    Function Name:  printNode
-    Input:  String, Bool
-    Output:  N/A
-    Functionality:  prints to the console a string representation of the current node in the trie
-  */
-  func printNode(var indent: String, leaf: Bool) {
-
-    print(indent, terminator: "")
-    if(leaf) {
-      print("\\-", terminator: "")
-      indent += " "
-    }
-    else {
-      print("|-", terminator: "")
-      indent += "| "
-    }
-
-    print(self.char())
-
-    var i = 0
-    for (_, node) in self.children {
-      node.printNode(indent, leaf: i == self.getChildren().count-1)
-      i+=1
-    }
-
-  }
-
-}
-
-
-/*
-  The Trie class has the following attributes:
-    -root (the root of the trie)
-    -wordList (the words that currently exist in the trie)
-    -wordCount (the number of words in the trie)
-*/
-public class Trie {
-  private var root: Node
-  private var wordList: [String]
-  private var wordCount = 0
-
-  init() {
-    self.root = Node(c: "", p: nil)
-    self.wordList = []
-  }
-
-  init(wordList: Set<String>) {
-
-    self.root = Node(c: "", p: nil)
-    self.wordList = []
-
-    for word in wordList {
-      self.insert(word)
-    }
-  }
-
-  /*
-    Function Name: merge
-    Input:  Trie
-    Output:  Trie
-    Functionality:  Merges two tries into one and returns the merged trie
-  */
-  func merge(other: Trie) -> Trie{
-    let newWordList = Set(self.getWords() + other.getWords())
-    return Trie(wordList: newWordList)
-  }
-
-  /*
-    Function Name:  find
-    Input:  String
-    Output:  (Node?, Bool)
-    Functionality:  Looks for a specific key and returns a tuple that has a reference to the node(if found) and true/false depending on if it was found
-  */
-  func find(key: String) -> (node: Node?, found: Bool) {
-    var currentNode = self.root
-
-    for c in key.characters {
-      if currentNode.children[String(c)] == nil {
-        return(nil, false)
-      }
-      currentNode = currentNode.children[String(c)]!
-    }
-
-    return(currentNode, currentNode.isValidWord())
-  }
-
-  /*
-    Function Name: isEmpty
-    Input:  N/A
-    Output:  Bool
-    Functionality:  returns true if the trie is empty, false otherwise
-  */
-  func isEmpty() -> Bool {
-    return wordCount == 0
-  }
-
-  /*
-    Function Name:  count
-    Input:  N/A
-    Output:  Int
-    Functionality:  returns the number of words in the trie
-  */
-  func count() -> Int {
-    return wordCount
-  }
-
-  /*
-    Function Name:  getWords
-    Input:  N/A
-    Output:  [String]
-    Functionality:  returns the list of words that exist in the trie
-  */
-  func getWords() -> [String] {
-    return wordList
-  }
-
-  /*
-    Function Name:  contains
-    Input:  String
-    Output:  Bool
-    Functionality:  returns true if the tries has the word passed, false otherwise
-  */
-  func contains(w: String) -> Bool {
-    return find(w.lowercaseString).found
-  }
-
-  /*
-    Function Name:  isPrefix
-    Input:  String
-    Output: (Node?, Bool)
-    Functionality:  returns a tuple containing a reference to the final node in the prefix (if it exists) and true/false depending on whether or not the prefix exists in the trie
-  */
-  func isPrefix(p: String) -> (node: Node?, found: Bool) {
-    let prefixP = p.lowercaseString
-
-    var currentNode = self.root
-
-    for c in prefixP.characters {
-      if currentNode.children[String(c)] == nil{
-        return (nil, false)
-      }
-
-      currentNode = currentNode.children[String(c)]!
-    }
-
-    if currentNode.numChildren() > 0 {
-      return (currentNode, true)
-    }
-
-    return (nil, false)
-  }
-
-  /*
-    Function Name:  insert
-    Input:  String
-    Output:  (String, Bool)
-    Functionality:  Inserts a word int othe trie.  Returns a tuple containing the word attempted to be added, and true/false depending on whether or not the insertion was successful
-  */
-  func insert(w: String) -> (word: String, inserted: Bool) {
-
-    let word = w.lowercaseString
-    var currentNode = self.root
-    var length = word.characters.count
-
-    if self.contains(word) {
-      return (w, false)
-    }
-
-    var index = 0
-    var c = Array(word.characters)[index]
-
-    while let child = currentNode.children[String(c)] {
-      currentNode = child
-      length -= 1
-      index += 1
-
-      if(length == 0) {
-        currentNode.isWord()
-        wordList.append(w)
-        wordCount += 1
-        return (w, true)
-      }
-
-      c = Array(word.characters)[index]
-    }
-
-    let remainingChars = String(word.characters.suffix(length))
-    for c in remainingChars.characters {
-      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
-      currentNode = currentNode.children[String(c)]!
-    }
-
-    currentNode.isWord()
-    wordList.append(w)
-    wordCount += 1
-    return (w, true)
-  }
-
-  /*
-    Function Name:  insertWords
-    Input:  [String]
-    Output:  ([String], Bool)
-    Functionality:  attempts to insert all words from input array.  returns a tuple containing the input array and true if some of the words were succesffuly added, false if none were added
-  */
-
-  func insertWords(wordList: [String]) -> (wordList: [String], bool: inserted){
-
-    var successful: Bool = false
-    for word in wordList {
-      succesful |= self.insert(word).inserted
-    }
-
-    return(wordList, succesful)
-  }
-
-  /*
-    Function Name:  remove
-    Input:  String
-    Output:  (String, Bool)
-    Functionality:  Removes the specified key from the trie if it exists, returns tuple containing the word attempted to be removed and true/false if the removal was succesful
-  */
-  func remove(w: String) -> (word: String, removed: Bool){
-    let word = w.lowercaseString
-
-    if(!self.contains(w)) {
-      return (w, false)
-    }
-    var currentNode = self.root
-
-    for c in word.characters {
-      currentNode = currentNode.getChildAt(String(c))
-    }
-
-    if currentNode.numChildren() > 0 {
-      currentNode.isNotWord()
-    } else {
-      var character = currentNode.char()
-      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
-        currentNode = currentNode.getParent()
-        currentNode.children[character]!.setParent(nil)
-        currentNode.children[character]!.update(nil)
-        currentNode.children[character] = nil
-        character = currentNode.char()
-      }
-    }
-
-    wordCount -= 1
-
-    var index = 0
-    for item in wordList{
-      if item == w {
-        wordList.removeAtIndex(index)
-      }
-      index += 1
-    }
-
-    return (w, true)
-  }
-
-  /*
-    Function Name: findPrefix
-    Input:  String
-    Output:  [String]
-    Functionality:  returns a list containing all words in the trie that have the specified prefix
-  */
-  func findPrefix(p: String) -> [String] {
-
-    if !self.isPrefix(p).found {
-      return []
-    }
-
-    var q: Queue = Queue<Node>()
-    var n: Node = self.isPrefix(p).node!
-
-    var wordsWithPrefix: [String] = []
-    var word = p
-    var tmp = ""
-    q.enqueue(n)
-
-    while let current = q.dequeue() {
-      for (char, child) in current.getChildren() {
-        if(!child.visited) {
-          q.enqueue(child)
-          child.visited = true
-          if(child.isValidWord()) {
-            var currentNode = child
-            while currentNode !== n {
-              tmp += currentNode.char()
-              currentNode = currentNode.getParent()
-            }
-            tmp = String(tmp.characters.reverse())
-            wordsWithPrefix.append(word + tmp)
-            tmp = ""
-          }
-        }
-      }
-    }
-
-
-    return wordsWithPrefix
-  }
-
-
-  /*
-    Function Name:  removeAll
-    Input:  N/A
-    Output:  N/A
-    Functionality:  removes all nodes in the trie using remove as a subroutine
-  */
-  func removeAll()  {
-    for word in wordList {
-      self.remove(word)
-    }
-  }
-
-
-  /*
-    Function Name:  printTrie
-    Input:  N/A
-    Output:  N/A
-    Functionality:  prints all the nodes of the trie to console in a nice and easy to understand format
-  */
-  func printTrie() {
-    self.root.printNode("", leaf: true)
-  }
-
-}

From d5648e1ceceee4caeee56750da670f5162a9278c Mon Sep 17 00:00:00 2001
From: Christian Encarnacion <encarc@rpi.edu>
Date: Thu, 5 May 2016 21:59:06 -0400
Subject: [PATCH 0347/1679] Update trie.swift

---
 Trie/trie.swift | 8 --------
 1 file changed, 8 deletions(-)

diff --git a/Trie/trie.swift b/Trie/trie.swift
index 352ca26cc..b62d3f598 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -31,14 +31,6 @@ public struct Queue<T> {
     
     return element
   }
-  
-  public func peek() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array[head]
-    }
-  }
 }
 /*
   A Trie (Pre-fix Tree)

From 1649935a6d946c8ff5781cb5730c31acec50a0c6 Mon Sep 17 00:00:00 2001
From: Jayson Tung <jaysontung@gmail.com>
Date: Thu, 5 May 2016 22:05:41 -0400
Subject: [PATCH 0348/1679] Remove unnecessary files

---
 .Rhistory            |   0
 README.markdown      |   1 -
 README.markdown~     | 212 -------------------------------------------
 Radix-Sort/radixSort | Bin 20310 -> 0 bytes
 4 files changed, 213 deletions(-)
 delete mode 100644 .Rhistory
 delete mode 100644 README.markdown~
 delete mode 100755 Radix-Sort/radixSort

diff --git a/.Rhistory b/.Rhistory
deleted file mode 100644
index e69de29bb..000000000
diff --git a/README.markdown b/README.markdown
index 480d8f26a..bbc10fb8d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -210,4 +210,3 @@ Other algorithm repositories:
 All content is licensed under the terms of the MIT open source license.
 
 [![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)
-
diff --git a/README.markdown~ b/README.markdown~
deleted file mode 100644
index bbc10fb8d..000000000
--- a/README.markdown~
+++ /dev/null
@@ -1,212 +0,0 @@
-# Welcome to the Swift Algorithm Club!
-
-Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.
-
-If you're a computer science student who needs to learn this stuff for exams -- or if you're a self-taught programmer who wants to brush up on the theory behind your craft -- you've come to the right place!
-
-The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
-
-All code is compatible with **Xcode 7.3** and **Swift 2.2**. We'll keep this updated with the latest version of Swift.
-
-This is a work in progress. More algorithms will be added soon. :-) 
-
-:heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
-
-## Important links
-
-[What are algorithms and data structures?](What are Algorithms.markdown) Pancakes!
-
-[Why learn algorithms?](Why Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
-
-[Big-O notation](Big-O Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
-
-[Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
-
-[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
-
-## Where to start?
-
-If you're new to algorithms and data structures, here are a few good ones to start out with:
-
-- [Stack](Stack/)
-- [Queue](Queue/)
-- [Insertion Sort](Insertion Sort/)
-- [Binary Search](Binary Search/) and [Binary Search Tree](Binary Search Tree/)
-- [Merge Sort](Merge Sort/)
-- [Boyer-Moore string search](Boyer-Moore/)
-
-## The algorithms
-
-### Searching
-
-- [Linear Search](Linear Search/). Find an element in an array.
-- [Binary Search](Binary Search/). Quickly find elements in a sorted array.
-- [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
-- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
-- [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
-- [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
-- [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
-
-### String Search
-
-- [Brute-Force String Search](Brute-Force String Search/). A naive method.
-- [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
-- Rabin-Karp
-- [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
-
-### Sorting
-
-It's fun to see how sorting algorithms work, but in practice you'll almost never have to provide your own sorting routines. Swift's own `sort()` is more than up to the job. But if you're curious, read on...
-
-Basic sorts:
-
-- [Insertion Sort](Insertion Sort/)
-- [Selection Sort](Selection Sort/)
-- [Shell Sort](Shell Sort/)
-
-Fast sorts:
-
-- [Quicksort](Quicksort/)
-- [Merge Sort](Merge Sort/)
-- [Heap Sort](Heap Sort/)
-
-Special-purpose sorts:
-
-- [Bucket Sort](Bucket Sort/) :construction:
-- [Counting Sort](Counting Sort/)
-- Radix Sort
-- [Topological Sort](Topological Sort/)
-
-Bad sorting algorithms (don't use these!):
-
-- [Bubble Sort](Bubble Sort/)
-
-### Compression
-
-- [Run-Length Encoding (RLE)](Run-Length Encoding/). Store repeated values as a single byte and a count.
-- [Huffman Coding](Huffman Coding/). Store more common elements using a smaller number of bits.
-
-### Miscellaneous
-
-- [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
-
-### Mathematics
-
-- [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
-- [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
-- [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
-- Statistics
-
-### Machine learning
-
-- [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
-- k-Nearest Neighbors
-- Linear Regression
-- Logistic Regression
-- Neural Networks
-- PageRank
-
-## Data structures
-
-The choice of data structure for a particular task depends on a few things.
-
-First, there is the shape of your data and the kinds of operations that you'll need to perform on it. If you want to look up objects by a key you need some kind of dictionary; if your data is hierarchical in nature you want a tree structure of some sort; if your data is sequential you want a stack or queue.
-
-Second, it matters what particular operations you'll be performing most, as certain data structures are optimized for certain actions. For example, if you often need to find the most important object in a collection, then a heap or priority queue is more optimal than a plain array.
-
-Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types is sufficient, but sometimes you may want something more fancy...
-
-### Variations on arrays
-
-- [Array2D](Array2D/). A two-dimensional array with fixed dimensions. Useful for board games.
-- [Bit Set](Bit Set/). A fixed-size sequence of *n* bits.
-- [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
-- [Ordered Array](Ordered Array/). An array that is always sorted.
-
-### Queues
-
-- [Stack](Stack/). Last-in, first-out!
-- [Queue](Queue/). First-in, first-out!
-- [Deque](Deque/). A double-ended queue.
-- [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
-- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements. :construction:
-- [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
-
-### Lists
-
-- [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
-- Skip List
-
-### Trees
-
-- [Tree](Tree/). A general-purpose tree structure.
-- [Binary Tree](Binary Tree/). A tree where each node has at most two children.
-- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
-- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
-- Red-Black Tree
-- Splay Tree
-- Threaded Binary Tree
-- [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
-- kd-Tree
-- [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
-- Fibonacci Heap
-- Trie
-- [B-Tree](B Tree/) :construction:
-
-### Hashing
-
-- [Hash Table](Hash Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
-- Hash Functions
-
-### Sets
-
-- [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
-- [Hash Set](Hash Set/). A set implemented using a hash table.
-- Multiset
-- [Ordered Set](Ordered Set/). A set where the order of items matters.
-
-### Graphs
-
-- [Graph](Graph/)
-- [Breadth-First Search (BFS)](Breadth-First Search/)
-- [Depth-First Search (DFS)](Depth-First Search/)
-- [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
-- [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
-- All Paths
-
-## Puzzles
-
-A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see [here](http://elementsofprogramminginterviews.com/) and [here](http://www.crackingthecodinginterview.com).
-
-- [Two-Sum Problem](Two-Sum Problem/)
-- [Fizz Buzz](Fizz Buzz/)
-- [Monty Hall Problem](Monty Hall Problem/)
-
-## Learn more!
-
-For more information, check out these great books:
-
-- [Introduction to Algorithms](https://mitpress.mit.edu/books/introduction-algorithms) by Cormen, Leiserson, Rivest, Stein
-- [The Algorithm Design Manual](http://www.algorist.com) by Skiena
-- [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
-- [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
-
-The following books are available for free online:
-
-- [Algorithms](http://www.beust.com/algorithms.pdf) by Dasgupta, Papadimitriou, Vazirani
-- [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
-- [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
-- Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
-- [Wikibooks: Algorithms and Implementations](https://en.wikibooks.org/wiki/Algorithm_Implementation)
-
-Other algorithm repositories:
-
-- [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
-- [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
-- [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
-
-## License
-
-All content is licensed under the terms of the MIT open source license.
-
-[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)
diff --git a/Radix-Sort/radixSort b/Radix-Sort/radixSort
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From a125a854f5832136f561e7bddf09b31f5e4d3ce3 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 22:12:31 -0400
Subject: [PATCH 0349/1679] Got rid of binary

---
 Radix-Sort/radixSort | Bin 20310 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100755 Radix-Sort/radixSort

diff --git a/Radix-Sort/radixSort b/Radix-Sort/radixSort
deleted file mode 100755
index 6ebfbe215703f5c207e9c454062125f9e1fc466d..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

literal 20310
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From ea555cc06ca40fd8052664dcfc1a2cb2e8a7e9d9 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Thu, 5 May 2016 22:39:05 -0400
Subject: [PATCH 0350/1679] Fixed a logic bug

---
 Trie/trie.swift | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Trie/trie.swift b/Trie/trie.swift
index b62d3f598..f50363749 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -4,7 +4,7 @@
 public struct Queue<T> {
   private var array = [T?]()
   private var head = 0
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
@@ -12,11 +12,11 @@ public struct Queue<T> {
   public var count: Int {
     return array.count - head
   }
-  
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
-  
+
   public mutating func dequeue() -> T? {
     guard head < array.count, let element = array[head] else { return nil }
 
@@ -28,7 +28,7 @@ public struct Queue<T> {
       array.removeFirst(head)
       head = 0
     }
-    
+
     return element
   }
 }
@@ -388,11 +388,11 @@ public class Trie {
     Functionality:  attempts to insert all words from input array.  returns a tuple containing the input array and true if some of the words were succesffuly added, false if none were added
   */
 
-  func insertWords(wordList: [String]) -> (wordList: [String], bool: inserted){
+  func insertWords(wordList: [String]) -> (wordList: [String], inserted: Bool){
 
-    var successful: Bool = false
+    var succesful: Bool = false
     for word in wordList {
-      succesful |= self.insert(word).inserted
+      succesful = self.insert(word).inserted || succesful
     }
 
     return(wordList, succesful)

From fc76bafd2452eabb6f8462eb966c6016be1125fd Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Fri, 6 May 2016 11:03:05 +0200
Subject: [PATCH 0351/1679] Cleanup of text and code

We're not using Swift 3 yet. ;-)
---
 README.markdown                               |   2 +-
 .../Images/radixtree.png                      | Bin
 Radix Tree/README.markdown                    |  72 ++++
 .../RadixTree.playground/Contents.swift       |   6 +-
 .../Sources/RadixTree.swift                   | 385 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 Radix Tree/RadixTree.swift                    | 385 ++++++++++++++++++
 Radix-Tree/README.markdown                    |  46 ---
 Radix-Tree/RadixTree.swift                    | 374 -----------------
 9 files changed, 850 insertions(+), 424 deletions(-)
 rename {Radix-Tree => Radix Tree}/Images/radixtree.png (100%)
 create mode 100644 Radix Tree/README.markdown
 rename Radix-Tree/main.swift => Radix Tree/RadixTree.playground/Contents.swift (94%)
 create mode 100644 Radix Tree/RadixTree.playground/Sources/RadixTree.swift
 create mode 100644 Radix Tree/RadixTree.playground/contents.xcplayground
 create mode 100644 Radix Tree/RadixTree.swift
 delete mode 100644 Radix-Tree/README.markdown
 delete mode 100644 Radix-Tree/RadixTree.swift

diff --git a/README.markdown b/README.markdown
index 3c441f428..51aa0a60a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -152,7 +152,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - Fibonacci Heap
 - Trie
 - [B-Tree](B Tree/) :construction:
-- [Radix Tree](Radix-Tree/) :construction:
+- [Radix Tree](Radix Tree/) :construction:
 
 ### Hashing
 
diff --git a/Radix-Tree/Images/radixtree.png b/Radix Tree/Images/radixtree.png
similarity index 100%
rename from Radix-Tree/Images/radixtree.png
rename to Radix Tree/Images/radixtree.png
diff --git a/Radix Tree/README.markdown b/Radix Tree/README.markdown
new file mode 100644
index 000000000..3fb1ab986
--- /dev/null
+++ b/Radix Tree/README.markdown	
@@ -0,0 +1,72 @@
+# Radix Tree
+
+A radix tree is a [tree](../Tree/) where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses. By traversing from the root to any leaf in the tree, concatenating all the labels of edges along the way, you can find any string.
+
+This is an example of a radix tree (image from wikipedia.org):
+
+![](Images/radixtree.png)
+
+## Implemenation
+
+The radix tree is represented by a `RadixTree` object. This class has one member variable, `root`, of type `Root`. The `Root` is the object at the top of every `RadixTree`. 
+
+Every other node is of type `Edge` and is a child (or child of a child, etc.) of the root. 
+
+The difference between `Edge` and `Root` is that edges have a label (of type `String`) and a reference to a parent node. 
+
+This approach is a little different from the conventional way of creating tree data structures but is easier to wrap your head around (see the picture above).
+
+## Operations
+
+Typical operations on a radix tree are:
+
+- lookup
+- insertion
+- deletion
+- find predecessor
+- find successor
+- find all strings with common prefix
+
+The running time of lookup, insertion, and deletion is **O(k)** where **k** is the length of the key. This is different from most trees because these operations usually run in **O(log n)** time where **n** is the number of nodes in the tree.
+
+### Lookup
+
+The `find()` function returns true if the string you are searching for is in the tree and false if it is not. 
+
+Every `RadixTree` contains at the very least the empty string `""` so `find("")` will always return true. 
+
+A string is considered "in the tree" if the text you are searching for is a concatenation of `Edge` labels while traversing downwards, or a prefix of that concatenation.
+
+For example, if you look at the example tree above, `find("roma")` will return true because it is a prefix of the traversal `"r" -> "om" -> "an"`. 
+
+On the other hand, `find("romans")` will return false.
+
+### Insertion
+
+The `insert()` function lets you add new strings to the radix tree.
+
+This function returns true if the string you are trying to insert was successfully inserted into the `RadixTree` and false if the string is already in the tree.
+
+### Deletion
+
+The `remove()` removes a string from the tree. When a string is removed, any other strings that have a prefix of the removed string are removed as well. 
+
+For example, `remove("rom")` will also remove `"roman"`, `"rome"`, and `"romulus"` if those strings are in the tree as well. Calling `remove("")` will remove all strings in the tree.
+
+### printTree()
+
+You can use the `printTree()` function to visualize the tree. This function is a little buggy and not perfect yet but gets the job done thus far.
+
+### Helper functions
+
+The `sharedPrefix()` function is a non-member function in the **RadixTree.swift** file. It takes in two `String` objects and returns the shared prefix between them. 
+
+For example, `sharedPrefix("apples", "oranges")` will return `""`, and `sharedPrefix("court", "coral")` will return `"co"`. 
+
+This function is used in the implementation of the `find()`, `insert()`, and `remove()` functions.
+
+## See also
+
+[Radix Tree - Wikipedia](https://en.wikipedia.org/wiki/Radix_tree)
+
+*Written for Swift Algorithm Club by Steven Scally*
diff --git a/Radix-Tree/main.swift b/Radix Tree/RadixTree.playground/Contents.swift
similarity index 94%
rename from Radix-Tree/main.swift
rename to Radix Tree/RadixTree.playground/Contents.swift
index 6495e5e1b..e161e48a2 100644
--- a/Radix-Tree/main.swift
+++ b/Radix Tree/RadixTree.playground/Contents.swift	
@@ -30,7 +30,7 @@ radixWiki.insert("rubicunduses")
 
 radixWiki.printTree()
 
-print("FIND TESTS")
+print("\n\nFIND TESTS")
 print(radixWiki.find("courts")) // false
 print(radixWiki.find("r")) // true
 print(radixWiki.find("ro")) // true
@@ -41,7 +41,7 @@ print(radixWiki.find("romane")) // true
 print(radixWiki.find("romans")) // false
 print(radixWiki.find("steve")) // true
 
-print("REMOVE TESTS")
+print("\n\nREMOVE TESTS")
 
 print(radixWiki.remove("c"))
 radixWiki.printTree()
@@ -52,4 +52,4 @@ radixWiki.printTree()
 print(radixWiki.remove("stevenson"))
 
 print(radixWiki.remove(""))
-radixWiki.printTree()
\ No newline at end of file
+radixWiki.printTree()
diff --git a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift
new file mode 100644
index 000000000..8b11e2508
--- /dev/null
+++ b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
@@ -0,0 +1,385 @@
+import Foundation
+
+// The root is the top of the Radix Tree
+public class Root {
+	var children: [Edge]
+
+	public init() {
+		children = [Edge]()
+	}
+
+	// Returns the length (in number of edges) of the longest traversal down the tree.
+	public func height() -> Int {
+		// Base case: no children: the tree has a height of 1
+		if children.count == 0 {
+			return 1
+		}
+		// Recursion: find the max height of a root's child and return 1 + that max
+		else {
+			var max = 1
+			for c in children {
+				if c.height() > max {
+					max = c.height()
+				}
+			}
+			return 1 + max
+		}
+	}
+
+	// Returns how far down in the tree a Root/Edge is.
+	// A root's level is always 0.
+	public func level() -> Int {
+		return 0
+	}
+
+	// Prints the tree for debugging/visualization purposes.
+	public func printRoot() {
+		// Print the first half of the children
+		if (children.count > 1) {
+			for c in 0...children.count/2-1 {
+				children[c].printEdge()
+				print("|")
+			}
+		}
+		else if children.count > 0 {
+			children[0].printEdge()
+		}
+		// Then print the root
+		print("ROOT")
+		// Print the second half of the children
+		if children.count > 1 {
+			for c in children.count/2...children.count-1 {
+				children[c].printEdge()
+				print("|")
+			}
+		}
+		print()
+	}
+}
+
+// Edges are what actually store the Strings in the tree
+public class Edge: Root {
+	var parent: Root?
+	var label: String
+
+	public init(_ label: String) {
+		self.label = label
+		super.init()
+	}
+
+	public override func level() -> Int {
+		// Recurse up the tree incrementing level by one until the root is reached
+		if parent != nil {
+			return 1 + parent!.level()
+		}
+		// If an edge has no parent, it's level is one
+		// NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
+		else {
+			return 1
+		}
+	}
+
+	// Erases a specific edge (and all edges below it in the tree).
+	public func erase() {
+		self.parent = nil
+		if children.count > 0 {
+			// For each child, erase it, then remove it from the children array.
+			for _ in 0...children.count-1 {
+				children[0].erase()
+				children.removeAtIndex(0)
+			}
+		}
+	}
+
+	// Prints the tree for debugging/visualization purposes.
+	public func printEdge() {
+		// Print the first half of the edge's children
+		if children.count > 1 {
+			for c in 0...children.count/2-1 {
+				children[c].printEdge()
+			}
+		}
+		else if children.count > 0 {
+			children[0].printEdge()
+		}
+		// Tab over once up to the edge's level
+		for x in 1...level() {
+			if x == level() {
+				print("|------>", terminator: "")
+			}
+			else {
+				print("|       ", terminator: "")
+			}
+		}
+		print(label)
+		// Print the second half of the edge's children
+		if children.count == 0 {
+			for _ in 1...level() {
+				print("|       ", terminator: "")
+			}
+			print()
+		}
+		if children.count > 1 {
+			for c in children.count/2...children.count-1 {
+				children[c].printEdge()
+			}
+		}
+	}
+}
+
+public class RadixTree {
+	var root: Root
+
+	public init() {
+		root = Root()
+	}
+
+	// Returns the height of the tree by calling the root's height function.
+	public func height() -> Int {
+		return root.height() - 1
+	}
+
+	// Inserts a string into the tree.
+	public func insert(str: String) -> Bool {
+		//Account for a blank input. The empty string is already in the tree.
+		if str == "" {
+			return false
+		}
+
+		// searchStr is the parameter of the function
+		// it will be substringed as the function traverses down the tree
+		var searchStr = str
+
+		// currEdge is the current Edge (or Root) in question
+		var currEdge = root
+
+		while (true) {
+			var found = false
+
+			// If the current Edge has no children then the remaining searchStr is
+			// created as a child
+			if currEdge.children.count == 0 {
+				let newEdge = Edge(searchStr)
+				currEdge.children.append(newEdge)
+				newEdge.parent = currEdge
+				return true
+			}
+
+			// Loop through all of the children
+			for e in currEdge.children {
+				// Get the shared prefix between the child in question and the
+				// search string
+				let shared = sharedPrefix(searchStr, e.label)
+				var index  = shared.startIndex
+
+				// If the search string is equal to the shared string,
+				// the string already exists in the tree
+				if searchStr == shared {
+					return false
+				}
+
+				// If the child's label is equal to the shared string, you have to
+				// traverse another level down the tree, so substring the search
+				// string, break the loop, and run it back
+				else if shared == e.label {
+					currEdge = e
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+
+				// If the child's label and the search string share a partial prefix,
+				// then both the label and the search string need to be substringed
+				// and a new branch needs to be created
+				else if shared.characters.count > 0 {
+					var labelIndex = e.label.characters.startIndex
+
+					// Create index objects and move them to after the shared prefix
+					for _ in 1...shared.characters.count {
+						index = index.successor()
+						labelIndex = labelIndex.successor()
+					}
+
+					// Substring both the search string and the label from the shared prefix
+					searchStr = searchStr.substringFromIndex(index)
+					e.label = e.label.substringFromIndex(labelIndex)
+
+					// Create 2 new edges and update parent/children values
+					let newEdge = Edge(e.label)
+					e.label = shared
+					for ec in e.children {
+						newEdge.children.append(ec)
+					}
+					newEdge.parent = e
+					e.children.removeAll()
+					for nec in newEdge.children {
+						nec.parent = newEdge
+					}
+					e.children.append(newEdge)
+					let newEdge2 = Edge(searchStr)
+					newEdge2.parent = e
+					e.children.append(newEdge2)
+					return true
+				}
+				// If they don't share a prefix, go to next child
+			}
+
+			// If none of the children share a prefix, you have to create a new child
+			if !found {
+				let newEdge = Edge(searchStr)
+				currEdge.children.append(newEdge)
+				newEdge.parent = currEdge
+				return true
+			}
+		}
+	}
+
+	// Tells you if a string is in the tree
+	public func find(str: String) -> Bool {
+		// A radix tree always contains the empty string
+		if str == "" {
+			return true
+		}
+		// If there are no children then the string cannot be in the tree
+		else if root.children.count == 0 {
+			return false
+		}
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			// Loop through currEdge's children
+			for c in currEdge.children {
+				// First check if the search string and the child's label are equal
+				// if so the string is in the tree, return true
+				if searchStr == c.label {
+					return true
+				}
+
+				// If that is not true, find the shared string b/t the search string
+				// and the label
+				let shared = sharedPrefix(searchStr, c.label)
+
+				// If the shared string is equal to the label, update the curent node,
+				// break the loop, and run it back
+				if shared == c.label {
+					currEdge = c
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+
+				// If the shared string is empty, go to the next child
+				else if shared.characters.count == 0 {
+					continue
+				}
+
+				// If the shared string matches the search string, return true
+				else if shared == searchStr {
+					return true
+				}
+
+				// If the search string and the child's label only share some characters,
+				// the string is not in the tree, return false
+				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
+				  shared.characters.count < c.label.characters.count {
+				  	return false
+				}
+			}
+
+			// If nothing was found, return false
+			if !found {
+				return false
+			}
+		}
+	}
+
+	// Removes a string from the tree
+	public func remove(str: String) -> Bool {
+		// Removing the empty string removes everything in the tree
+		if str == "" {
+			for c in root.children {
+				c.erase()
+				root.children.removeAtIndex(0)
+			}
+			return true
+		}
+		// If the tree is empty, you cannot remove anything
+		else if root.children.count == 0 {
+			return false
+		}
+
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			// If currEdge has no children, then the searchStr is not in the tree
+			if currEdge.children.count == 0 {
+				return false
+			}
+
+			// Loop through the children
+			for c in 0...currEdge.children.count-1 {
+				// If the child's label matches the search string, remove that child
+				// and everything below it in the tree
+				if currEdge.children[c].label == searchStr {
+					currEdge.children[c].erase()
+					currEdge.children.removeAtIndex(c)
+					return true
+				}
+
+				// Find the shared string
+				let shared = sharedPrefix(searchStr, currEdge.children[c].label)
+
+				// If the shared string is equal to the child's string, go down a level
+				if shared == currEdge.children[c].label {
+					currEdge = currEdge.children[c]
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+			}
+
+			// If there is no match, then the searchStr is not in the tree
+			if !found {
+				return false
+			}
+		}
+	}
+
+	// Prints the tree by calling the root's print function
+	public func printTree() {
+		root.printRoot()
+	}
+}
+
+// Returns the prefix that is shared between the two input strings
+// i.e. sharedPrefix("court", "coral") -> "co"
+public func sharedPrefix(str1: String, _ str2: String) -> String {
+	var temp = ""
+	var c1 = str1.characters.startIndex
+	var c2 = str2.characters.startIndex
+	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+		if str1[c1] == str2[c2] {
+			temp.append( str1[c1] )
+			c1 = c1.successor()
+			c2 = c2.successor()
+		}
+		else {
+			return temp
+		}
+	}
+	return temp
+}
diff --git a/Radix Tree/RadixTree.playground/contents.xcplayground b/Radix Tree/RadixTree.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Radix Tree/RadixTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Radix Tree/RadixTree.swift b/Radix Tree/RadixTree.swift
new file mode 100644
index 000000000..8b11e2508
--- /dev/null
+++ b/Radix Tree/RadixTree.swift	
@@ -0,0 +1,385 @@
+import Foundation
+
+// The root is the top of the Radix Tree
+public class Root {
+	var children: [Edge]
+
+	public init() {
+		children = [Edge]()
+	}
+
+	// Returns the length (in number of edges) of the longest traversal down the tree.
+	public func height() -> Int {
+		// Base case: no children: the tree has a height of 1
+		if children.count == 0 {
+			return 1
+		}
+		// Recursion: find the max height of a root's child and return 1 + that max
+		else {
+			var max = 1
+			for c in children {
+				if c.height() > max {
+					max = c.height()
+				}
+			}
+			return 1 + max
+		}
+	}
+
+	// Returns how far down in the tree a Root/Edge is.
+	// A root's level is always 0.
+	public func level() -> Int {
+		return 0
+	}
+
+	// Prints the tree for debugging/visualization purposes.
+	public func printRoot() {
+		// Print the first half of the children
+		if (children.count > 1) {
+			for c in 0...children.count/2-1 {
+				children[c].printEdge()
+				print("|")
+			}
+		}
+		else if children.count > 0 {
+			children[0].printEdge()
+		}
+		// Then print the root
+		print("ROOT")
+		// Print the second half of the children
+		if children.count > 1 {
+			for c in children.count/2...children.count-1 {
+				children[c].printEdge()
+				print("|")
+			}
+		}
+		print()
+	}
+}
+
+// Edges are what actually store the Strings in the tree
+public class Edge: Root {
+	var parent: Root?
+	var label: String
+
+	public init(_ label: String) {
+		self.label = label
+		super.init()
+	}
+
+	public override func level() -> Int {
+		// Recurse up the tree incrementing level by one until the root is reached
+		if parent != nil {
+			return 1 + parent!.level()
+		}
+		// If an edge has no parent, it's level is one
+		// NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
+		else {
+			return 1
+		}
+	}
+
+	// Erases a specific edge (and all edges below it in the tree).
+	public func erase() {
+		self.parent = nil
+		if children.count > 0 {
+			// For each child, erase it, then remove it from the children array.
+			for _ in 0...children.count-1 {
+				children[0].erase()
+				children.removeAtIndex(0)
+			}
+		}
+	}
+
+	// Prints the tree for debugging/visualization purposes.
+	public func printEdge() {
+		// Print the first half of the edge's children
+		if children.count > 1 {
+			for c in 0...children.count/2-1 {
+				children[c].printEdge()
+			}
+		}
+		else if children.count > 0 {
+			children[0].printEdge()
+		}
+		// Tab over once up to the edge's level
+		for x in 1...level() {
+			if x == level() {
+				print("|------>", terminator: "")
+			}
+			else {
+				print("|       ", terminator: "")
+			}
+		}
+		print(label)
+		// Print the second half of the edge's children
+		if children.count == 0 {
+			for _ in 1...level() {
+				print("|       ", terminator: "")
+			}
+			print()
+		}
+		if children.count > 1 {
+			for c in children.count/2...children.count-1 {
+				children[c].printEdge()
+			}
+		}
+	}
+}
+
+public class RadixTree {
+	var root: Root
+
+	public init() {
+		root = Root()
+	}
+
+	// Returns the height of the tree by calling the root's height function.
+	public func height() -> Int {
+		return root.height() - 1
+	}
+
+	// Inserts a string into the tree.
+	public func insert(str: String) -> Bool {
+		//Account for a blank input. The empty string is already in the tree.
+		if str == "" {
+			return false
+		}
+
+		// searchStr is the parameter of the function
+		// it will be substringed as the function traverses down the tree
+		var searchStr = str
+
+		// currEdge is the current Edge (or Root) in question
+		var currEdge = root
+
+		while (true) {
+			var found = false
+
+			// If the current Edge has no children then the remaining searchStr is
+			// created as a child
+			if currEdge.children.count == 0 {
+				let newEdge = Edge(searchStr)
+				currEdge.children.append(newEdge)
+				newEdge.parent = currEdge
+				return true
+			}
+
+			// Loop through all of the children
+			for e in currEdge.children {
+				// Get the shared prefix between the child in question and the
+				// search string
+				let shared = sharedPrefix(searchStr, e.label)
+				var index  = shared.startIndex
+
+				// If the search string is equal to the shared string,
+				// the string already exists in the tree
+				if searchStr == shared {
+					return false
+				}
+
+				// If the child's label is equal to the shared string, you have to
+				// traverse another level down the tree, so substring the search
+				// string, break the loop, and run it back
+				else if shared == e.label {
+					currEdge = e
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+
+				// If the child's label and the search string share a partial prefix,
+				// then both the label and the search string need to be substringed
+				// and a new branch needs to be created
+				else if shared.characters.count > 0 {
+					var labelIndex = e.label.characters.startIndex
+
+					// Create index objects and move them to after the shared prefix
+					for _ in 1...shared.characters.count {
+						index = index.successor()
+						labelIndex = labelIndex.successor()
+					}
+
+					// Substring both the search string and the label from the shared prefix
+					searchStr = searchStr.substringFromIndex(index)
+					e.label = e.label.substringFromIndex(labelIndex)
+
+					// Create 2 new edges and update parent/children values
+					let newEdge = Edge(e.label)
+					e.label = shared
+					for ec in e.children {
+						newEdge.children.append(ec)
+					}
+					newEdge.parent = e
+					e.children.removeAll()
+					for nec in newEdge.children {
+						nec.parent = newEdge
+					}
+					e.children.append(newEdge)
+					let newEdge2 = Edge(searchStr)
+					newEdge2.parent = e
+					e.children.append(newEdge2)
+					return true
+				}
+				// If they don't share a prefix, go to next child
+			}
+
+			// If none of the children share a prefix, you have to create a new child
+			if !found {
+				let newEdge = Edge(searchStr)
+				currEdge.children.append(newEdge)
+				newEdge.parent = currEdge
+				return true
+			}
+		}
+	}
+
+	// Tells you if a string is in the tree
+	public func find(str: String) -> Bool {
+		// A radix tree always contains the empty string
+		if str == "" {
+			return true
+		}
+		// If there are no children then the string cannot be in the tree
+		else if root.children.count == 0 {
+			return false
+		}
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			// Loop through currEdge's children
+			for c in currEdge.children {
+				// First check if the search string and the child's label are equal
+				// if so the string is in the tree, return true
+				if searchStr == c.label {
+					return true
+				}
+
+				// If that is not true, find the shared string b/t the search string
+				// and the label
+				let shared = sharedPrefix(searchStr, c.label)
+
+				// If the shared string is equal to the label, update the curent node,
+				// break the loop, and run it back
+				if shared == c.label {
+					currEdge = c
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+
+				// If the shared string is empty, go to the next child
+				else if shared.characters.count == 0 {
+					continue
+				}
+
+				// If the shared string matches the search string, return true
+				else if shared == searchStr {
+					return true
+				}
+
+				// If the search string and the child's label only share some characters,
+				// the string is not in the tree, return false
+				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
+				  shared.characters.count < c.label.characters.count {
+				  	return false
+				}
+			}
+
+			// If nothing was found, return false
+			if !found {
+				return false
+			}
+		}
+	}
+
+	// Removes a string from the tree
+	public func remove(str: String) -> Bool {
+		// Removing the empty string removes everything in the tree
+		if str == "" {
+			for c in root.children {
+				c.erase()
+				root.children.removeAtIndex(0)
+			}
+			return true
+		}
+		// If the tree is empty, you cannot remove anything
+		else if root.children.count == 0 {
+			return false
+		}
+
+		var searchStr = str
+		var currEdge = root
+		while (true) {
+			var found = false
+			// If currEdge has no children, then the searchStr is not in the tree
+			if currEdge.children.count == 0 {
+				return false
+			}
+
+			// Loop through the children
+			for c in 0...currEdge.children.count-1 {
+				// If the child's label matches the search string, remove that child
+				// and everything below it in the tree
+				if currEdge.children[c].label == searchStr {
+					currEdge.children[c].erase()
+					currEdge.children.removeAtIndex(c)
+					return true
+				}
+
+				// Find the shared string
+				let shared = sharedPrefix(searchStr, currEdge.children[c].label)
+
+				// If the shared string is equal to the child's string, go down a level
+				if shared == currEdge.children[c].label {
+					currEdge = currEdge.children[c]
+					var tempIndex = searchStr.startIndex
+					for _ in 1...shared.characters.count {
+						tempIndex = tempIndex.successor()
+					}
+					searchStr = searchStr.substringFromIndex(tempIndex)
+					found = true
+					break
+				}
+			}
+
+			// If there is no match, then the searchStr is not in the tree
+			if !found {
+				return false
+			}
+		}
+	}
+
+	// Prints the tree by calling the root's print function
+	public func printTree() {
+		root.printRoot()
+	}
+}
+
+// Returns the prefix that is shared between the two input strings
+// i.e. sharedPrefix("court", "coral") -> "co"
+public func sharedPrefix(str1: String, _ str2: String) -> String {
+	var temp = ""
+	var c1 = str1.characters.startIndex
+	var c2 = str2.characters.startIndex
+	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+		if str1[c1] == str2[c2] {
+			temp.append( str1[c1] )
+			c1 = c1.successor()
+			c2 = c2.successor()
+		}
+		else {
+			return temp
+		}
+	}
+	return temp
+}
diff --git a/Radix-Tree/README.markdown b/Radix-Tree/README.markdown
deleted file mode 100644
index ce1dde6b7..000000000
--- a/Radix-Tree/README.markdown
+++ /dev/null
@@ -1,46 +0,0 @@
-# Radix Tree
-
-A radix tree is a tree where a node can have any number of children. Each edge leading from a node to a child has a label (usually a string). A radix tree is often used to store strings or IP addresses and by traversing from the root to any leaf in the tree, (by concatenating all the labels of edges along the way) you can find any string. This is a radix tree:
-![](/Radix-Tree/Images/radixtree.png)
-(Image from en.wikipedia.org)
-
-## Implemenation
-
-The RadixTree class itself has one member variable, root, of type Root. The Root is the top of every RadixTree. Every node that is added, removed, looked up, etc. is a child, a child of a child, etc. of that root. The rest of the tree is represented as an Edge, which inherits Root. The different between Edge and Root is that Edges have a label (of type String) and a parent (of type Root?) member variables. This approach is a little different from the conventional way of creating Tree data structures but is easier to wrap your head around (see the picture above).
-
-## Operations
-
-Typical operations on a radix tree include lookup, insertion, deletion, find predecessor, find successor, and find all strings with common prefix. The running time of lookup, insertion, and deletion is O(k) where k is the length of the key. This is different from most trees because these operations usually run in O(logn) time where n is the number of nodes in the tree.
-
-### RadixTree.find(_ str: String) -> Bool
-
-The find function returns true if the String you are searching for is in the tree and false if it is not. Every RadixTree contains at the very least one String ("") so find("") will always return true. A String is considered "in the tree" if the String you are searching for is a concatenation of Edge labels while traversing downwards or a prefix of that concatenation. For example, if you look at the example tree above, find("roma") will return true because it is a prefix of the traversal "r"->"om"->"an". On the other hand, find("romans") will return false.
-
-### RadixTree.insert(_ str: String) -> Bool
-
-The insert function returns true if the String you are trying to insert was successfully inserted into the RadixTree and false if the String is already in the tree. Similarly to find(""), insert("") will always return false because an empty RadixTree contains "" by default.
-
-### RadixTree.remove(_ str: String) -> Bool
-
-The remove function returns true if the String is removed and false if the String is not in the tree. When a string is removed, any other Strings that have a prefix of the removed String are removed as well. For example, remove("rom") will also remove "roman", "rome", and "romulus" if those Strings are in the tree as well. Calling remove("") will remove all Strings in the tree.
-
-### Root.level() -> Int
-
-The level function returns how far down in the tree the Root or Edge in question is. A Root object will always return 0. A child of the Root will return 1, a child of a child of the root will return 2, etc.
-
-### RadixTree.height() -> Int
-
-The height function returns an Int equal to the highest level in the Tree. An empty tree will return 0.
-
-### RadixTree.printTree()
-
-The printTree function was used to visualize the tree itself. This function is a little buggy and not perfect yet but gets the job done thus far.
-
-### sharedPrefix(_ str1: String, _ str2: String) -> String
-
-The sharedPrefix function is a non-member function in the RadixTree.swift file. It takes in two String objects and returns the shared prefix between them. For example,
-sharedPrefix("apples", "oranges") will return "" and sharedPrefix("court", "coral") will return "co". This function is used in the implementation of the find, insert, and remove functions.
-
-## See Also
-
-[Radix Tree - Wikipedia](https://en.wikipedia.org/wiki/Radix_tree)
diff --git a/Radix-Tree/RadixTree.swift b/Radix-Tree/RadixTree.swift
deleted file mode 100644
index 6f1f8fa57..000000000
--- a/Radix-Tree/RadixTree.swift
+++ /dev/null
@@ -1,374 +0,0 @@
-import Foundation
-
-//The root is the top of the Radix Tree
-class Root {
-
-	var children: [Edge]
-
-	init() {
-		children = [Edge]()
-	}
-
-	//The height functions returns the length (in number of edges) of the longest
-	//  traversal down the tree
-	func height() -> Int {
-		//Base case: no children: the tree has a height of 1
-		if children.count == 0 {
-			return 1
-		}
-		//Recursion: find the max height of a root's child and return 1 + that max
-		else {
-			var max = 1
-			for c in children {
-				if c.height() > max {
-					max = c.height()
-				}
-			}
-			return 1 + max
-		}
-	}
-
-	//The level function returns how far down in the tree a Root/Edge is
-	//A root's level is always 0
-	func level() -> Int {
-		return 0
-	}
-
-	//printRoot is a recursive function that prints the tree for debugging/
-	//  visualization purposes
-	func printRoot() {
-		//Print the first half of the children
-		if (children.count > 1) {
-			for c in 0...children.count/2-1 {
-				children[c].printEdge()
-				print("|")
-			}
-		}
-		else if children.count > 0 {
-			children[0].printEdge()
-		}
-		//Then print the root
-		print("ROOT")
-		//Print the second half of the children
-		if children.count > 1 {
-			for c in children.count/2...children.count-1 {
-				children[c].printEdge()
-				print("|")
-			}
-		}
-		print()
-	}
-}
-
-//Edges are what actually store the Strings in the tree
-class Edge: Root {
-
-	var parent: Root?
-	var label: String
-
-	init(_ label: String) {	//Edge(label: "label")
-		self.label = label
-		super.init()
-	}
-
-	//The Edge class overrides root's level function
-	override
-	func level() -> Int {
-		//Recurse up the tree incrementing level by one until the root is reached
-		if parent != nil {
-			return 1 + parent!.level()
-		}
-		//If an edge has no parent, it's level is one
-		//  NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
-		else {
-			return 1
-		}
-	}
-
-	//Erase erases a specific edge (and all edges below it in the tree)
-	func erase() {
-		self.parent = nil
-		if children.count > 0 {
-			//For each child, erase it, then remove it from the children array
-			for _ in 0...children.count-1 {
-				children[0].erase()
-				children.remove(at: 0)
-			}
-		}
-	}
-
-	//printEdge is used in printRoot to print the tree
-	//  It follows a similar structure to printRoot
-	func printEdge() {
-		//Print the first half of the edge's children
-		if children.count > 1 {
-			for c in 0...children.count/2-1 {
-				children[c].printEdge()
-			}
-		}
-		else if children.count > 0 {
-			children[0].printEdge()
-		}
-		//Tab over once up to the edge's level
-		for x in 1...level() {
-			if x == level() {
-				print("|------>", terminator: "")
-			}
-			else {
-				print("|       ", terminator: "")
-			}
-		}
-		print(label)
-		//Print the second half of the edge's children
-		if children.count == 0 {
-			for _ in 1...level() {
-				print("|       ", terminator: "")
-			}
-			print()
-		}
-		if children.count > 1 {
-			for c in children.count/2...children.count-1 {
-				children[c].printEdge()
-			}
-		}
-	}
-}
-
-class RadixTree {
-
-	var root: Root
-
-	init() {
-		root = Root()
-	}
-
-	//Returns the height of the tree by calling the root's height function
-	func height() -> Int {
-		return root.height() - 1
-	}
-
-	//Inserts a string into the tree
-	func insert(_ str: String) -> Bool {
-		//Account for a blank input
-		//  The empty string is already in the tree
-		if str == "" {
-			return false
-		}
-		//searchStr is the parameter of the function
-		//  it will be substringed as the function traverses down the tree
-		var searchStr = str
-		//currEdge is the current Edge (or Root) in question
-		var currEdge = root
-		while (true) {
-			var found = false
-			//If the current Edge has no children then the remaining searchStr is
-			//  created as a child
-			if currEdge.children.count == 0 {
-				let newEdge = Edge(searchStr)
-				currEdge.children.append(newEdge)
-				newEdge.parent = currEdge
-				return true
-			}
-			//Loop through all of the children
-			for e in currEdge.children {
-				//Get the shared prefix betweeen the child in question and the
-				//  search string
-				var shared = sharedPrefix(searchStr, e.label)
-				var index  = shared.startIndex
-				//If the search string is equal to the shared string,
-				//  the string already exists in the tree
-				if searchStr == shared {
-					return false
-				}
-				//If the child's label is equal to the shared string, you have to
-				//  traverse another level down the tree, so substring the search
-				//  string, break the loop, and run it back
-				else if shared == e.label {
-					currEdge = e
-					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
-					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
-					found = true
-					break
-				}
-				//If the child's label and the search string share a partial prefix,
-				//  then both the label and the search string need to be substringed
-				//  and a new branch needs to be created
-				else if shared.characters.count > 0 {
-					var labelIndex = e.label.characters.startIndex
-					//Create index objects and move them to after the shared prefix
-					for _ in 1...shared.characters.count {
-						index = index.successor()
-						labelIndex = labelIndex.successor()
-					}
-					//Substring both the search string and the label from the
-					//  shared prefix
-					searchStr = searchStr.substringFromIndex(index)
-					e.label = e.label.substringFromIndex(labelIndex)
-					//Create 2 new edges and update parent/children values
-					let newEdge = Edge(e.label)
-					e.label = shared
-					for ec in e.children {
-						newEdge.children.append(ec)
-					}
-					newEdge.parent = e
-					e.children.removeAll()
-					for nec in newEdge.children {
-						nec.parent = newEdge
-					}
-					e.children.append(newEdge)
-					let newEdge2 = Edge(searchStr)
-					newEdge2.parent = e
-					e.children.append(newEdge2)
-					return true
-				}
-				//If they don't share a prefix, go to next child
-			}
-			//If none of the children share a prefix, you have to create a new child
-			if (!found) {
-				let newEdge = Edge(searchStr)
-				currEdge.children.append(newEdge)
-				newEdge.parent = currEdge
-				return true
-			}
-		}
-	}
-
-	//Tells you if a string is in the tree
-	func find(_ str: String) -> Bool {
-		//A radix tree always contains the empty string
-		if str == "" {
-			return true
-		}
-		//If there are no children then the string cannot be in the tree
-		else if root.children.count == 0 {
-			return false
-		}
-		//searchStr and currEdge have the same functionality as insert()
-		var searchStr = str
-		var currEdge = root
-		while (true) {
-			var found = false
-			//Loop through currEdge's children
-			for c in currEdge.children {
-				//First check if the search string and the child's label are equal
-				//  if so the string is in the tree, return true
-				if searchStr == c.label {
-					return true
-				}
-				//If that is not true, find the shared string b/t the search string
-				//  and the label
-				var shared = sharedPrefix(searchStr, c.label)
-				//If the shared string is equal to the label, update the curent node,
-				//  break the loop, and run it back
-				if shared == c.label {
-					currEdge = c
-					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
-					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
-					found = true
-					break
-				}
-				//If the shared string is empty, go to the next child
-				else if shared.characters.count == 0 {
-					continue
-				}
-				//If the shared string matches the search string, return true
-				else if shared == searchStr {
-					return true
-				}
-				//If the search string and the child's label only share some characters,
-				//  the string is not in the tree, return false
-				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-				  shared.characters.count < c.label.characters.count {
-				  	return false
-				}
-			}
-			//If nothing was found, return false
-			if !found {
-				return false
-			}
-		}
-	}
-
-	//Removes a string from the tree
-	func remove(_ str: String) -> Bool {
-		//Removing the empty string removes everything in the tree
-		if str == "" {
-			for c in root.children {
-				c.erase()
-				root.children.remove(at: 0)
-			}
-			return true
-		}
-		//If the tree is empty, you cannot remove anything
-		else if root.children.count == 0 {
-			return false
-		}
-		//searchStr and currEdge have the same functionality as in insert() and find()
-		var searchStr = str
-		var currEdge = root
-		while (true) {
-			var found = false
-			//If currEdge has no children, then the searchStr is not in the tree
-			if currEdge.children.count == 0 {
-				return false
-			}
-			//Loop through the children
-			for c in 0...currEdge.children.count-1 {
-				//If the child's label matches the search string, remove that child
-				//  and everything below it in the tree
-				if currEdge.children[c].label == searchStr {
-					currEdge.children[c].erase()
-					currEdge.children.remove(at: c)
-					return true
-				}
-				//Find the shared string
-				var shared = sharedPrefix(searchStr, currEdge.children[c].label)
-				//If the shared string is equal to the child's string, go down a level
-				if shared == currEdge.children[c].label {
-					currEdge = currEdge.children[c]
-					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
-					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
-					found = true
-					break
-				}
-			}
-			//If there is no match, then the searchStr is not in the tree
-			if !found {
-				return false
-			}
-		}
-	}
-
-	//Prints the tree by calling the root's print function
-	func printTree() {
-		root.printRoot()
-	}
-}
-
-//Returns the prefix that is shared between the two input strings
-//i.e. sharedPrefix("court", "coral") -> "co"
-func sharedPrefix(_ str1: String, _ str2: String) -> String {
-	var temp = ""
-	var c1 = str1.characters.startIndex
-	var c2 = str2.characters.startIndex
-	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
-		if str1[c1] == str2[c2] {
-			temp.append( str1[c1] )
-			c1 = c1.successor()
-			c2 = c2.successor()
-		}
-		else {
-			return temp
-		}
-	}
-	return temp
-}
\ No newline at end of file

From 6f9ef9bbc986aa31b6676fdc5285452085d54f8b Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Fri, 6 May 2016 08:35:18 -0400
Subject: [PATCH 0352/1679] Radix-Sort -> Radix Sort, Got rid of unnecessary
 ()'s in Trie

---
 {Radix-Sort => Radix Sort}/ReadMe.md       |  0
 {Radix-Sort => Radix Sort}/radixSort.swift |  0
 Trie/trie.swift                            | 10 +++++-----
 3 files changed, 5 insertions(+), 5 deletions(-)
 rename {Radix-Sort => Radix Sort}/ReadMe.md (100%)
 rename {Radix-Sort => Radix Sort}/radixSort.swift (100%)

diff --git a/Radix-Sort/ReadMe.md b/Radix Sort/ReadMe.md
similarity index 100%
rename from Radix-Sort/ReadMe.md
rename to Radix Sort/ReadMe.md
diff --git a/Radix-Sort/radixSort.swift b/Radix Sort/radixSort.swift
similarity index 100%
rename from Radix-Sort/radixSort.swift
rename to Radix Sort/radixSort.swift
diff --git a/Trie/trie.swift b/Trie/trie.swift
index f50363749..839c4350b 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -191,7 +191,7 @@ public class Node {
   func printNode(var indent: String, leaf: Bool) {
 
     print(indent, terminator: "")
-    if(leaf) {
+    if leaf {
       print("\\-", terminator: "")
       indent += " "
     }
@@ -359,7 +359,7 @@ public class Trie {
       length -= 1
       index += 1
 
-      if(length == 0) {
+      if length == 0 {
         currentNode.isWord()
         wordList.append(w)
         wordCount += 1
@@ -407,7 +407,7 @@ public class Trie {
   func remove(w: String) -> (word: String, removed: Bool){
     let word = w.lowercaseString
 
-    if(!self.contains(w)) {
+    if !self.contains(w) {
       return (w, false)
     }
     var currentNode = self.root
@@ -464,10 +464,10 @@ public class Trie {
 
     while let current = q.dequeue() {
       for (char, child) in current.getChildren() {
-        if(!child.visited) {
+        if !child.visited {
           q.enqueue(child)
           child.visited = true
-          if(child.isValidWord()) {
+          if child.isValidWord() {
             var currentNode = child
             while currentNode !== n {
               tmp += currentNode.char()

From 9857cb7073b2e970cbb4dca8ab3cab52435e3eb9 Mon Sep 17 00:00:00 2001
From: Thukor <encarc@rpi.edu>
Date: Fri, 6 May 2016 09:45:42 -0400
Subject: [PATCH 0353/1679] Renamed Red Black Trees -> Red-Black Tree

---
 {Red Black Trees => Red-Black Tree}/RBTree.swift   |   0
 {Red Black Trees => Red-Black Tree}/README.md      |   0
 {Red Black Trees => Red-Black Tree}/files/fig1.png | Bin
 {Red Black Trees => Red-Black Tree}/files/fig2.png | Bin
 4 files changed, 0 insertions(+), 0 deletions(-)
 rename {Red Black Trees => Red-Black Tree}/RBTree.swift (100%)
 rename {Red Black Trees => Red-Black Tree}/README.md (100%)
 rename {Red Black Trees => Red-Black Tree}/files/fig1.png (100%)
 rename {Red Black Trees => Red-Black Tree}/files/fig2.png (100%)

diff --git a/Red Black Trees/RBTree.swift b/Red-Black Tree/RBTree.swift
similarity index 100%
rename from Red Black Trees/RBTree.swift
rename to Red-Black Tree/RBTree.swift
diff --git a/Red Black Trees/README.md b/Red-Black Tree/README.md
similarity index 100%
rename from Red Black Trees/README.md
rename to Red-Black Tree/README.md
diff --git a/Red Black Trees/files/fig1.png b/Red-Black Tree/files/fig1.png
similarity index 100%
rename from Red Black Trees/files/fig1.png
rename to Red-Black Tree/files/fig1.png
diff --git a/Red Black Trees/files/fig2.png b/Red-Black Tree/files/fig2.png
similarity index 100%
rename from Red Black Trees/files/fig2.png
rename to Red-Black Tree/files/fig2.png

From 3aa88de547fad9b7f8ab2dbbd968c1f456f1a88f Mon Sep 17 00:00:00 2001
From: Ashwin <raghua@rpi.edu>
Date: Fri, 6 May 2016 16:54:41 +0000
Subject: [PATCH 0354/1679] inline comments

---
 Red-Black Tree/RBTree.swift  |  48 +++-
 Red-Black Tree/RBTree.swift~ | 477 +++++++++++++++++++++++++++++++++++
 2 files changed, 519 insertions(+), 6 deletions(-)
 create mode 100644 Red-Black Tree/RBTree.swift~

diff --git a/Red-Black Tree/RBTree.swift b/Red-Black Tree/RBTree.swift
index 50d1d00d4..8b2653297 100644
--- a/Red-Black Tree/RBTree.swift	
+++ b/Red-Black Tree/RBTree.swift	
@@ -55,6 +55,7 @@ public class RBTree {
     let n = depth(root!)
     return n
   }
+  //return the max depth of the tree
   private func depth(rooty:RBTNode?)->Int{
     if(rooty == nil){
       return 0
@@ -67,6 +68,7 @@ public class RBTree {
   public func inOrder(){
     inOrder(root)
   }
+  //Prints the in order traversal of the current tree
   private func inOrder(root: RBTNode?){
     if(self.root == nil ){
       print("The tree is empty.")
@@ -78,7 +80,14 @@ public class RBTree {
     print("Data: \(root!.data) Color: \(root!.color)")
     inOrder(root!.right)
   }
-
+   /*
+   Basic Algorithm:
+     Let Q be P's right child.
+     Set P's right child to be Q's left child.
+     [Set Q's left-child's parent to P]
+     Set Q's left child to be P.
+     [Set P's parent to Q]
+  */
   private func leftRotate(x: RBTNode) {
       let newRoot = x.right
       x.right = newRoot.left
@@ -96,6 +105,14 @@ public class RBTree {
         newRoot.left = x
         x.parent = newRoot
   }
+  /*
+   Basic Algorithm:
+     Let P be Q's left child.
+     Set Q's left child to be P's right child.
+     [Set P's right-child's parent to Q]
+     Set P's right child to be Q.
+     [Set Q's parent to P]
+  */
   private func rightRotate(x: RBTNode) {
     let newRoot = x.left
     x.left = newRoot.right
@@ -118,6 +135,7 @@ public class RBTree {
     print("Inserted Node: \(inserted!.data)")
     insertCase1(inserted)
     }
+  //Case where root is the only node
   private func insertCase1(inserted: RBTNode?){
     let myroot = self.root!
     if myroot === inserted!{
@@ -125,12 +143,14 @@ public class RBTree {
     }
     insertCase2(inserted!)
     }
+  //Case for inserting a node as a child of a black node
   private func insertCase2(inserted: RBTNode?){
     if inserted!.parent!.color == false{
         return
     }
     insertCase3(inserted!)
     }
+  //Insert case for if the parent is black and parent's siblng is black
   private func insertCase3(inserted: RBTNode?){
     if(inserted!.parent!.sibling() != nil &&
         inserted!.parent!.sibling()!.color == true){
@@ -144,7 +164,7 @@ public class RBTree {
     }
   insertCase4(inserted)
   }
-
+  //Insert case for Node N is left of parent and parent is right of grandparent
   private func insertCase4( insert: RBTNode?){
     var inserted = insert
     if((inserted! === inserted!.parent!.right) &&
@@ -161,6 +181,7 @@ public class RBTree {
     }
     insertCase5(inserted)
   }
+  //Insert case for Node n where parent is red and parent's sibling is black
   private func insertCase5(inserted: RBTNode?){
     if((inserted!.parent!.color == true &&
        (inserted!.parent!.sibling()?.color == false ||
@@ -185,6 +206,7 @@ public class RBTree {
     insert(value, parent: root!)
     insertFixup(value)
   }
+  //Basic BST insert implementation
   private func insert(value: Int, parent: RBTNode) {
       if self.root == nil{
         self.root = RBTNode(rootData: value)
@@ -209,7 +231,7 @@ public class RBTree {
     public func find(data: Int)->RBTNode?{
       return find(root!,data: data)
     }
-
+    //Returns the reference to the RBTNode whos data was requested
     private func find(root: RBTNode, data: Int)->RBTNode?{
         if data == root.data{
           return root
@@ -235,6 +257,7 @@ public class RBTree {
           return
         }
     }
+    //Transplant the positions of two nodes in the RBTree
     public func replaceNode(n1: RBTNode, n2: RBTNode){
       let temp = n1.data
       let temp_color = n1.color
@@ -243,6 +266,7 @@ public class RBTree {
       n2.data = temp
       n2.color = temp_color
     }
+    //returns the node with the minimum value in the subtree
     public func minimum(Node: RBTNode)->RBTNode {
       var node = Node
       while node.left !== nil{
@@ -250,6 +274,7 @@ public class RBTree {
       }
       return node
     }
+    //Returns the next largest node in the tree
     public func successor(Node: RBTNode) -> RBTNode? {
       var node = Node
       if node.right !== nil {
@@ -262,6 +287,7 @@ public class RBTree {
       }
       return successor
     }
+    //Returns the next smallest node in the tree
     public func predecessor(Node: RBTNode) -> RBTNode{
       var node = Node
       if node.left !== nil {
@@ -274,6 +300,7 @@ public class RBTree {
       }
       return successor
     }
+    //Returns the node with the largest value in the subtree
     public func maximum(rootnode: RBTNode) -> RBTNode{
       var rootNode = rootnode
       while rootNode.right !== nil {
@@ -281,18 +308,21 @@ public class RBTree {
       }
       return rootNode
     }
-
+  //call to remove a node from the tree
   public func delete(x: Int){
     let toDel = find(x)
     deleteNode(toDel!)
   }
+  //Function call for removing a node
   private func deleteNode(todel: RBTNode?){
     var toDel = todel
+    //case for if todel is the only node in the tree
     if(toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil){
       toDel = nil
       self.root = nil
       return
     }
+    //case for if toDell is a red node w/ no children
     if(toDel!.left === nil && toDel!.right === nil && toDel!.color == true){
       if(toDel!.parent.left === toDel!){
         toDel!.parent.left = nil
@@ -307,12 +337,13 @@ public class RBTree {
       }
       return
     }
+    //case for toDel having two children
     if(toDel!.left !== nil && toDel!.right !== nil){
       let pred = maximum(toDel!.left!)
       toDel!.data = pred.data
       toDel! = pred
     }
-
+    //case for toDel having one child
     var child: RBTNode? = nil
     if(toDel!.right === nil){
       child = toDel!.left
@@ -346,6 +377,7 @@ public class RBTree {
       return
     }
   }
+  //delete case for if parent is nil after deletion
   private func deleteCase1( toDel: RBTNode?){
       if(toDel?.parent === nil){
         return
@@ -354,6 +386,7 @@ public class RBTree {
         deleteCase2(toDel)
       }
   }
+  //case to fix tree after deletion and sibling is red
   private func deleteCase2(toDel: RBTNode?){
     let sibling = toDel!.sibling()
     if(sibling?.color == true){
@@ -368,6 +401,7 @@ public class RBTree {
        deleteCase3(toDel!)
     }
   }
+  //delete case for fixing tree when parnet is black and sibling is black and sibling.children are also black
   private func deleteCase3(toDel: RBTNode?){
     if(toDel!.parent?.color == false &&
        toDel!.sibling()?.color == false &&
@@ -394,6 +428,7 @@ public class RBTree {
       deleteCase5(toDel)
     }
   }
+  //delete case for fixing tree if toDel is a left child and sibling(n) is black and children of sibling(n) are black and white respectibely
   private func deleteCase5(toDel:RBTNode?){
     if(toDel! === toDel!.parent?.left &&
        toDel!.sibling()?.color == false &&
@@ -404,7 +439,7 @@ public class RBTree {
        toDel!.sibling()?.left?.color = false
        rightRotate(toDel!.sibling()!)
     }
-
+    //opposite case
     else if(toDel! === toDel!.parent?.right &&
             toDel!.sibling()?.color == false &&
             toDel!.sibling()?.left.color == false &&
@@ -415,6 +450,7 @@ public class RBTree {
             leftRotate(toDel!.sibling()!)
     }
   }
+  //final rotations to be done after deleting a black node from the tree
   private func deleteCase6(toDel: RBTNode?){
     let color = toDel!.sibling()?.color
     toDel!.parent?.color = color!
diff --git a/Red-Black Tree/RBTree.swift~ b/Red-Black Tree/RBTree.swift~
new file mode 100644
index 000000000..46abc897b
--- /dev/null
+++ b/Red-Black Tree/RBTree.swift~	
@@ -0,0 +1,477 @@
+public class  RBTNode{
+  private(set) public var color: Bool
+  private(set) public var left: RBTNode!
+  private(set) public var right: RBTNode!
+  private(set) public var parent: RBTNode!
+  private(set) public var data: Int
+  init(){
+    self.data = -1
+    self.color = true
+    self.left = nil
+    self.right = nil
+    self.parent = nil
+  }
+  init(rootData: Int){
+    self.data = rootData
+    self.color = true //0 is black 1 is red
+    self.left = nil
+    self.right = nil
+    self.parent = nil
+  }
+  deinit{
+    print("Node: \(self.data) is bein deinitialized")
+  }
+
+  public func grandparent()->RBTNode?{
+    if(self.parent === nil || self.parent.parent === nil){
+      return nil
+    }
+    else{
+      return self.parent.parent
+    }
+  }
+  public func sibling()->RBTNode?{
+    if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
+        return nil
+      }
+      if(self === self.parent!.left!){
+        return self.parent!.right!
+      }
+      else{
+        return self.parent!.left!
+      }
+  }
+}
+public class RBTree {
+  private(set) public var root: RBTNode?
+  init(rootData: Int) {
+    root = RBTNode(rootData: rootData)
+    root!.color = false
+  }
+  init(){
+    root = nil
+  }
+  public func depth()->Int{
+    let n = depth(root!)
+    return n
+  }
+  //return the max depth of the tree
+  private func depth(rooty:RBTNode?)->Int{
+    if(rooty == nil){
+      return 0
+    }
+    else{
+      return 1+(max(depth(root!.left),depth(root!.right)))
+    }
+  }
+
+  public func inOrder(){
+    inOrder(root)
+  }
+  //Prints the in order traversal of the current tree
+  private func inOrder(root: RBTNode?){
+    if(self.root == nil ){
+      print("The tree is empty.")
+    }
+    if(root == nil){
+      return
+    }
+    inOrder(root!.left)
+    print("Data: \(root!.data) Color: \(root!.color)")
+    inOrder(root!.right)
+  }
+   /*
+   Basic Algorithm:
+     Let Q be P's right child.
+     Set P's right child to be Q's left child.
+     [Set Q's left-child's parent to P]
+     Set Q's left child to be P.
+     [Set P's parent to Q]
+  */
+  private func leftRotate(x: RBTNode) {
+      let newRoot = x.right
+      x.right = newRoot.left
+        if (newRoot.left !== nil) {
+          newRoot.left.parent = x
+        }
+        newRoot.parent = x.parent
+        if(x.parent === nil) {
+          root = newRoot
+        } else if (x === x.parent.left) {
+          x.parent.left = newRoot
+        } else {
+          x.parent.right = newRoot
+        }
+        newRoot.left = x
+        x.parent = newRoot
+  }
+  /*
+   Basic Algorithm:
+     Let P be Q's left child.
+     Set Q's left child to be P's right child.
+     [Set P's right-child's parent to Q]
+     Set P's right child to be Q.
+     [Set Q's parent to P]
+  */
+  private func rightRotate(x: RBTNode) {
+    let newRoot = x.left
+    x.left = newRoot.right
+    if newRoot.right !== nil {
+      newRoot.right.parent = x
+    }
+    newRoot.parent = x.parent
+    if x.parent === nil {
+      root = newRoot
+    } else if x === x.parent.right {
+      x.parent.right = newRoot
+    } else {
+      x.parent.left = newRoot
+    }
+    newRoot.right = x
+    x.parent = newRoot
+  }
+  public func insertFixup(value: Int){
+    let inserted = find(value)
+    print("Inserted Node: \(inserted!.data)")
+    insertCase1(inserted)
+    }
+  //Case where root is the only node
+  private func insertCase1(inserted: RBTNode?){
+    let myroot = self.root!
+    if myroot === inserted!{
+      self.root!.color = false
+    }
+    insertCase2(inserted!)
+    }
+  //Case for inserting a node as a child of a black node
+  private func insertCase2(inserted: RBTNode?){
+    if inserted!.parent!.color == false{
+        return
+    }
+    insertCase3(inserted!)
+    }
+  //Insert case for if the parent is black and parent's siblng is black
+  private func insertCase3(inserted: RBTNode?){
+    if(inserted!.parent!.sibling() != nil &&
+        inserted!.parent!.sibling()!.color == true){
+        inserted!.parent!.color = false
+        inserted!.parent!.sibling()!.color = false
+        let g = inserted!.grandparent
+        g()!.color = true
+        if(g()!.parent == nil){
+          g()!.color = false
+        }
+    }
+  insertCase4(inserted)
+  }
+  //Insert case for Node N is left of parent and parent is right of grandparent
+  private func insertCase4( insert: RBTNode?){
+    var inserted = insert
+    if((inserted! === inserted!.parent!.right) &&
+      (inserted!.grandparent()!.left === inserted!.parent!)){
+
+      leftRotate(inserted!.parent)
+      inserted! = inserted!.left
+    }
+    else if((inserted! === inserted!.parent!.left) &&
+            (inserted!.grandparent()!.right === inserted!.parent!)){
+
+      rightRotate(inserted!.parent)
+      inserted! = inserted!.right
+    }
+    insertCase5(inserted)
+  }
+  //Insert case for Node n where parent is red and parent's sibling is black
+  private func insertCase5(inserted: RBTNode?){
+    if((inserted!.parent!.color == true &&
+       (inserted!.parent!.sibling()?.color == false ||
+        inserted!.parent!.sibling() == nil ))){
+
+        if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
+          inserted!.parent.color = false
+          inserted!.grandparent()?.color = true
+          if(inserted! === inserted!.parent!.left){
+            rightRotate(inserted!.grandparent()!)
+          }
+        }
+        else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
+          inserted!.parent.color = false
+          inserted!.grandparent()?.color = true
+          leftRotate(inserted!.grandparent()!)
+        }
+    }
+  }
+
+  public func insert(value: Int) {
+    insert(value, parent: root!)
+    insertFixup(value)
+  }
+  //Basic BST insert implementation
+  private func insert(value: Int, parent: RBTNode) {
+      if self.root == nil{
+        self.root = RBTNode(rootData: value)
+        return
+      }
+      else if value < parent.data {
+        if let left = parent.left {
+          insert(value, parent: left)
+        } else {
+          parent.left = RBTNode(rootData: value)
+          parent.left?.parent = parent
+        }
+      } else {
+        if let right = parent.right {
+          insert(value, parent: right)
+        } else {
+          parent.right = RBTNode(rootData: value)
+          parent.right?.parent = parent
+        }
+      }
+    }
+    public func find(data: Int)->RBTNode?{
+      return find(root!,data: data)
+    }
+    //Returns the reference to the RBTNode whos data was requested
+    private func find(root: RBTNode, data: Int)->RBTNode?{
+        if data == root.data{
+          return root
+        }
+        if root.data != data && root.right == nil && root.left == nil {
+          return nil
+        }
+        else if data > root.data{
+          return find(root.right, data: data)
+        }
+        else if data < root.data{
+          return find(root.left, data: data)
+        }
+        else{
+          return nil
+        }
+    }
+
+    //DELETION HELPER FUNCTIONS
+    public func remove(value: Int){
+        let toRemove = find(value)
+        if(toRemove == nil){
+          return
+        }
+    }
+    //Transplant the positions of two nodes in the RBTree
+    public func replaceNode(n1: RBTNode, n2: RBTNode){
+      let temp = n1.data
+      let temp_color = n1.color
+      n1.data = n2.data
+      n1.color = n2.color
+      n2.data = temp
+      n2.color = temp_color
+    }
+    //returns the node with the minimum value in the subtree
+    public func minimum(Node: RBTNode)->RBTNode {
+      var node = Node
+      while node.left !== nil{
+        node = node.left
+      }
+      return node
+    }
+    //Returns the next largest node in the tree
+    public func successor(Node: RBTNode) -> RBTNode? {
+      var node = Node
+      if node.right !== nil {
+        return minimum(node.right)
+      }
+      var successor = node.parent
+      while successor !== nil && node === successor.right {
+        node = successor
+        successor = successor.parent
+      }
+      return successor
+    }
+    //Returns the next smallest node in the tree
+    public func predecessor(Node: RBTNode) -> RBTNode{
+      var node = Node
+      if node.left !== nil {
+        return minimum(node.left)
+      }
+      var successor = node.parent
+      while successor !== nil && node === successor.left {
+        node = successor
+        successor = successor.parent
+      }
+      return successor
+    }
+    //Returns the node with the largest value in the subtree
+    public func maximum(rootnode: RBTNode) -> RBTNode{
+      var rootNode = rootnode
+      while rootNode.right !== nil {
+        rootNode = rootNode.right
+      }
+      return rootNode
+    }
+  //call to remove a node from the tree
+  public func delete(x: Int){
+    let toDel = find(x)
+    deleteNode(toDel!)
+  }
+  //Function call for removing a node
+  private func deleteNode(todel: RBTNode?){
+    var toDel = todel
+    //case for if todel is the only node in the tree
+    if(toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil){
+      toDel = nil
+      self.root = nil
+      return
+    }
+    //case for if toDell is a red node w/ no children
+    if(toDel!.left === nil && toDel!.right === nil && toDel!.color == true){
+      if(toDel!.parent.left === toDel!){
+        toDel!.parent.left = nil
+        toDel = nil
+      }
+      else if(toDel!.parent === nil){
+        toDel = nil
+      }
+      else{
+        toDel?.parent.right = nil
+        toDel = nil
+      }
+      return
+    }
+    //case for toDel having two children
+    if(toDel!.left !== nil && toDel!.right !== nil){
+      let pred = maximum(toDel!.left!)
+      toDel!.data = pred.data
+      toDel! = pred
+    }
+    //case for toDel having one child
+    var child: RBTNode? = nil
+    if(toDel!.right === nil){
+      child = toDel!.left
+    }
+    else{
+       child = toDel!.right
+    }
+    if(toDel!.color == false && child !== nil){
+      toDel!.color = child!.color
+      deleteCase1(toDel!)
+    }
+
+    if(child !== nil){
+      replaceNode(toDel!, n2: child!)
+      if(toDel!.parent === nil && child !== nil){
+        child!.color = false
+      }
+    }
+    if(toDel!.parent.left === toDel!){
+      toDel!.parent.left = nil
+      toDel = nil
+      return
+    }
+    else if(toDel!.parent === nil){
+      toDel = nil
+      return
+    }
+    else{
+      toDel?.parent.right = nil
+      toDel = nil
+      return
+    }
+  }
+  //delete case for if parent is nil after deletion
+  private func deleteCase1( toDel: RBTNode?){
+      if(toDel?.parent === nil){
+        return
+      }
+      else{
+        deleteCase2(toDel)
+      }
+  }
+  //case to fix tree after deletion and sibling is red
+  private func deleteCase2(toDel: RBTNode?){
+    let sibling = toDel!.sibling()
+    if(sibling?.color == true){
+       toDel!.parent.color = true;
+       sibling?.color = false
+       if(toDel! === toDel!.parent.left){
+         leftRotate(toDel!.parent)
+       }
+       else{
+         rightRotate(toDel!.parent)
+       }
+       deleteCase3(toDel!)
+    }
+  }
+  //delete case for fixing tree when parnet is black and sibling is black and sibling.children are also black
+  private func deleteCase3(toDel: RBTNode?){
+    if(toDel!.parent?.color == false &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left!.color == false &&
+       toDel!.sibling()?.right!.color == false){
+
+        toDel!.sibling()?.color = true
+        toDel!.parent?.color = false
+    }
+    else{
+      deleteCase4(toDel)
+    }
+  }
+  private func deleteCase4(toDel: RBTNode?){
+    if(toDel!.parent?.color == true &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left!.color == false &&
+       toDel!.sibling()?.right!.color == false){
+
+       toDel!.sibling()?.color = true
+       toDel!.parent.color = false
+    }
+    else{
+      deleteCase5(toDel)
+    }
+  }
+  //delete case for fixing tree if toDel is a left child and sibling(n) is black and children of sibling(n) are black and white respectibely
+  private func deleteCase5(toDel:RBTNode?){
+    if(toDel! === toDel!.parent?.left &&
+       toDel!.sibling()?.color == false &&
+       toDel!.sibling()?.left.color == true &&
+       toDel!.sibling()?.right.color == false){
+
+       toDel!.sibling()?.color = true
+       toDel!.sibling()?.left?.color = false
+       rightRotate(toDel!.sibling()!)
+    }
+    //opposite case
+    else if(toDel! === toDel!.parent?.right &&
+            toDel!.sibling()?.color == false &&
+            toDel!.sibling()?.left.color == false &&
+            toDel!.sibling()?.right.color == true){
+
+            toDel!.sibling()?.color = true
+            toDel!.sibling()?.right?.color = false
+            leftRotate(toDel!.sibling()!)
+    }
+  }
+  private func deleteCase6(toDel: RBTNode?){
+    let color = toDel!.sibling()?.color
+    toDel!.parent?.color = color!
+    toDel!.parent?.color = false
+    if(toDel! === toDel!.parent.left){
+        toDel!.sibling()?.right?.color = false
+        leftRotate(toDel!.parent!)
+    }
+    else{
+      toDel!.sibling()?.left?.color = false
+      rightRotate(toDel!.parent!)
+    }
+  }
+}
+
+var tree = RBTree(rootData: 8)
+tree.insert(5)
+tree.insert(4)
+tree.insert(9)
+tree.delete(9)
+tree.insert(3)
+tree.insert(10)
+tree.delete(3)
+var x = tree.find(5)
+tree.inOrder()

From 610b532b8720f2a04efd02831205057be4b26765 Mon Sep 17 00:00:00 2001
From: axptwig <raghua@rpi.edu>
Date: Fri, 6 May 2016 16:55:36 +0000
Subject: [PATCH 0355/1679] Delete RBTree.swift~

removed temp
---
 Red-Black Tree/RBTree.swift~ | 477 -----------------------------------
 1 file changed, 477 deletions(-)
 delete mode 100644 Red-Black Tree/RBTree.swift~

diff --git a/Red-Black Tree/RBTree.swift~ b/Red-Black Tree/RBTree.swift~
deleted file mode 100644
index 46abc897b..000000000
--- a/Red-Black Tree/RBTree.swift~	
+++ /dev/null
@@ -1,477 +0,0 @@
-public class  RBTNode{
-  private(set) public var color: Bool
-  private(set) public var left: RBTNode!
-  private(set) public var right: RBTNode!
-  private(set) public var parent: RBTNode!
-  private(set) public var data: Int
-  init(){
-    self.data = -1
-    self.color = true
-    self.left = nil
-    self.right = nil
-    self.parent = nil
-  }
-  init(rootData: Int){
-    self.data = rootData
-    self.color = true //0 is black 1 is red
-    self.left = nil
-    self.right = nil
-    self.parent = nil
-  }
-  deinit{
-    print("Node: \(self.data) is bein deinitialized")
-  }
-
-  public func grandparent()->RBTNode?{
-    if(self.parent === nil || self.parent.parent === nil){
-      return nil
-    }
-    else{
-      return self.parent.parent
-    }
-  }
-  public func sibling()->RBTNode?{
-    if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
-        return nil
-      }
-      if(self === self.parent!.left!){
-        return self.parent!.right!
-      }
-      else{
-        return self.parent!.left!
-      }
-  }
-}
-public class RBTree {
-  private(set) public var root: RBTNode?
-  init(rootData: Int) {
-    root = RBTNode(rootData: rootData)
-    root!.color = false
-  }
-  init(){
-    root = nil
-  }
-  public func depth()->Int{
-    let n = depth(root!)
-    return n
-  }
-  //return the max depth of the tree
-  private func depth(rooty:RBTNode?)->Int{
-    if(rooty == nil){
-      return 0
-    }
-    else{
-      return 1+(max(depth(root!.left),depth(root!.right)))
-    }
-  }
-
-  public func inOrder(){
-    inOrder(root)
-  }
-  //Prints the in order traversal of the current tree
-  private func inOrder(root: RBTNode?){
-    if(self.root == nil ){
-      print("The tree is empty.")
-    }
-    if(root == nil){
-      return
-    }
-    inOrder(root!.left)
-    print("Data: \(root!.data) Color: \(root!.color)")
-    inOrder(root!.right)
-  }
-   /*
-   Basic Algorithm:
-     Let Q be P's right child.
-     Set P's right child to be Q's left child.
-     [Set Q's left-child's parent to P]
-     Set Q's left child to be P.
-     [Set P's parent to Q]
-  */
-  private func leftRotate(x: RBTNode) {
-      let newRoot = x.right
-      x.right = newRoot.left
-        if (newRoot.left !== nil) {
-          newRoot.left.parent = x
-        }
-        newRoot.parent = x.parent
-        if(x.parent === nil) {
-          root = newRoot
-        } else if (x === x.parent.left) {
-          x.parent.left = newRoot
-        } else {
-          x.parent.right = newRoot
-        }
-        newRoot.left = x
-        x.parent = newRoot
-  }
-  /*
-   Basic Algorithm:
-     Let P be Q's left child.
-     Set Q's left child to be P's right child.
-     [Set P's right-child's parent to Q]
-     Set P's right child to be Q.
-     [Set Q's parent to P]
-  */
-  private func rightRotate(x: RBTNode) {
-    let newRoot = x.left
-    x.left = newRoot.right
-    if newRoot.right !== nil {
-      newRoot.right.parent = x
-    }
-    newRoot.parent = x.parent
-    if x.parent === nil {
-      root = newRoot
-    } else if x === x.parent.right {
-      x.parent.right = newRoot
-    } else {
-      x.parent.left = newRoot
-    }
-    newRoot.right = x
-    x.parent = newRoot
-  }
-  public func insertFixup(value: Int){
-    let inserted = find(value)
-    print("Inserted Node: \(inserted!.data)")
-    insertCase1(inserted)
-    }
-  //Case where root is the only node
-  private func insertCase1(inserted: RBTNode?){
-    let myroot = self.root!
-    if myroot === inserted!{
-      self.root!.color = false
-    }
-    insertCase2(inserted!)
-    }
-  //Case for inserting a node as a child of a black node
-  private func insertCase2(inserted: RBTNode?){
-    if inserted!.parent!.color == false{
-        return
-    }
-    insertCase3(inserted!)
-    }
-  //Insert case for if the parent is black and parent's siblng is black
-  private func insertCase3(inserted: RBTNode?){
-    if(inserted!.parent!.sibling() != nil &&
-        inserted!.parent!.sibling()!.color == true){
-        inserted!.parent!.color = false
-        inserted!.parent!.sibling()!.color = false
-        let g = inserted!.grandparent
-        g()!.color = true
-        if(g()!.parent == nil){
-          g()!.color = false
-        }
-    }
-  insertCase4(inserted)
-  }
-  //Insert case for Node N is left of parent and parent is right of grandparent
-  private func insertCase4( insert: RBTNode?){
-    var inserted = insert
-    if((inserted! === inserted!.parent!.right) &&
-      (inserted!.grandparent()!.left === inserted!.parent!)){
-
-      leftRotate(inserted!.parent)
-      inserted! = inserted!.left
-    }
-    else if((inserted! === inserted!.parent!.left) &&
-            (inserted!.grandparent()!.right === inserted!.parent!)){
-
-      rightRotate(inserted!.parent)
-      inserted! = inserted!.right
-    }
-    insertCase5(inserted)
-  }
-  //Insert case for Node n where parent is red and parent's sibling is black
-  private func insertCase5(inserted: RBTNode?){
-    if((inserted!.parent!.color == true &&
-       (inserted!.parent!.sibling()?.color == false ||
-        inserted!.parent!.sibling() == nil ))){
-
-        if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
-          inserted!.parent.color = false
-          inserted!.grandparent()?.color = true
-          if(inserted! === inserted!.parent!.left){
-            rightRotate(inserted!.grandparent()!)
-          }
-        }
-        else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
-          inserted!.parent.color = false
-          inserted!.grandparent()?.color = true
-          leftRotate(inserted!.grandparent()!)
-        }
-    }
-  }
-
-  public func insert(value: Int) {
-    insert(value, parent: root!)
-    insertFixup(value)
-  }
-  //Basic BST insert implementation
-  private func insert(value: Int, parent: RBTNode) {
-      if self.root == nil{
-        self.root = RBTNode(rootData: value)
-        return
-      }
-      else if value < parent.data {
-        if let left = parent.left {
-          insert(value, parent: left)
-        } else {
-          parent.left = RBTNode(rootData: value)
-          parent.left?.parent = parent
-        }
-      } else {
-        if let right = parent.right {
-          insert(value, parent: right)
-        } else {
-          parent.right = RBTNode(rootData: value)
-          parent.right?.parent = parent
-        }
-      }
-    }
-    public func find(data: Int)->RBTNode?{
-      return find(root!,data: data)
-    }
-    //Returns the reference to the RBTNode whos data was requested
-    private func find(root: RBTNode, data: Int)->RBTNode?{
-        if data == root.data{
-          return root
-        }
-        if root.data != data && root.right == nil && root.left == nil {
-          return nil
-        }
-        else if data > root.data{
-          return find(root.right, data: data)
-        }
-        else if data < root.data{
-          return find(root.left, data: data)
-        }
-        else{
-          return nil
-        }
-    }
-
-    //DELETION HELPER FUNCTIONS
-    public func remove(value: Int){
-        let toRemove = find(value)
-        if(toRemove == nil){
-          return
-        }
-    }
-    //Transplant the positions of two nodes in the RBTree
-    public func replaceNode(n1: RBTNode, n2: RBTNode){
-      let temp = n1.data
-      let temp_color = n1.color
-      n1.data = n2.data
-      n1.color = n2.color
-      n2.data = temp
-      n2.color = temp_color
-    }
-    //returns the node with the minimum value in the subtree
-    public func minimum(Node: RBTNode)->RBTNode {
-      var node = Node
-      while node.left !== nil{
-        node = node.left
-      }
-      return node
-    }
-    //Returns the next largest node in the tree
-    public func successor(Node: RBTNode) -> RBTNode? {
-      var node = Node
-      if node.right !== nil {
-        return minimum(node.right)
-      }
-      var successor = node.parent
-      while successor !== nil && node === successor.right {
-        node = successor
-        successor = successor.parent
-      }
-      return successor
-    }
-    //Returns the next smallest node in the tree
-    public func predecessor(Node: RBTNode) -> RBTNode{
-      var node = Node
-      if node.left !== nil {
-        return minimum(node.left)
-      }
-      var successor = node.parent
-      while successor !== nil && node === successor.left {
-        node = successor
-        successor = successor.parent
-      }
-      return successor
-    }
-    //Returns the node with the largest value in the subtree
-    public func maximum(rootnode: RBTNode) -> RBTNode{
-      var rootNode = rootnode
-      while rootNode.right !== nil {
-        rootNode = rootNode.right
-      }
-      return rootNode
-    }
-  //call to remove a node from the tree
-  public func delete(x: Int){
-    let toDel = find(x)
-    deleteNode(toDel!)
-  }
-  //Function call for removing a node
-  private func deleteNode(todel: RBTNode?){
-    var toDel = todel
-    //case for if todel is the only node in the tree
-    if(toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil){
-      toDel = nil
-      self.root = nil
-      return
-    }
-    //case for if toDell is a red node w/ no children
-    if(toDel!.left === nil && toDel!.right === nil && toDel!.color == true){
-      if(toDel!.parent.left === toDel!){
-        toDel!.parent.left = nil
-        toDel = nil
-      }
-      else if(toDel!.parent === nil){
-        toDel = nil
-      }
-      else{
-        toDel?.parent.right = nil
-        toDel = nil
-      }
-      return
-    }
-    //case for toDel having two children
-    if(toDel!.left !== nil && toDel!.right !== nil){
-      let pred = maximum(toDel!.left!)
-      toDel!.data = pred.data
-      toDel! = pred
-    }
-    //case for toDel having one child
-    var child: RBTNode? = nil
-    if(toDel!.right === nil){
-      child = toDel!.left
-    }
-    else{
-       child = toDel!.right
-    }
-    if(toDel!.color == false && child !== nil){
-      toDel!.color = child!.color
-      deleteCase1(toDel!)
-    }
-
-    if(child !== nil){
-      replaceNode(toDel!, n2: child!)
-      if(toDel!.parent === nil && child !== nil){
-        child!.color = false
-      }
-    }
-    if(toDel!.parent.left === toDel!){
-      toDel!.parent.left = nil
-      toDel = nil
-      return
-    }
-    else if(toDel!.parent === nil){
-      toDel = nil
-      return
-    }
-    else{
-      toDel?.parent.right = nil
-      toDel = nil
-      return
-    }
-  }
-  //delete case for if parent is nil after deletion
-  private func deleteCase1( toDel: RBTNode?){
-      if(toDel?.parent === nil){
-        return
-      }
-      else{
-        deleteCase2(toDel)
-      }
-  }
-  //case to fix tree after deletion and sibling is red
-  private func deleteCase2(toDel: RBTNode?){
-    let sibling = toDel!.sibling()
-    if(sibling?.color == true){
-       toDel!.parent.color = true;
-       sibling?.color = false
-       if(toDel! === toDel!.parent.left){
-         leftRotate(toDel!.parent)
-       }
-       else{
-         rightRotate(toDel!.parent)
-       }
-       deleteCase3(toDel!)
-    }
-  }
-  //delete case for fixing tree when parnet is black and sibling is black and sibling.children are also black
-  private func deleteCase3(toDel: RBTNode?){
-    if(toDel!.parent?.color == false &&
-       toDel!.sibling()?.color == false &&
-       toDel!.sibling()?.left!.color == false &&
-       toDel!.sibling()?.right!.color == false){
-
-        toDel!.sibling()?.color = true
-        toDel!.parent?.color = false
-    }
-    else{
-      deleteCase4(toDel)
-    }
-  }
-  private func deleteCase4(toDel: RBTNode?){
-    if(toDel!.parent?.color == true &&
-       toDel!.sibling()?.color == false &&
-       toDel!.sibling()?.left!.color == false &&
-       toDel!.sibling()?.right!.color == false){
-
-       toDel!.sibling()?.color = true
-       toDel!.parent.color = false
-    }
-    else{
-      deleteCase5(toDel)
-    }
-  }
-  //delete case for fixing tree if toDel is a left child and sibling(n) is black and children of sibling(n) are black and white respectibely
-  private func deleteCase5(toDel:RBTNode?){
-    if(toDel! === toDel!.parent?.left &&
-       toDel!.sibling()?.color == false &&
-       toDel!.sibling()?.left.color == true &&
-       toDel!.sibling()?.right.color == false){
-
-       toDel!.sibling()?.color = true
-       toDel!.sibling()?.left?.color = false
-       rightRotate(toDel!.sibling()!)
-    }
-    //opposite case
-    else if(toDel! === toDel!.parent?.right &&
-            toDel!.sibling()?.color == false &&
-            toDel!.sibling()?.left.color == false &&
-            toDel!.sibling()?.right.color == true){
-
-            toDel!.sibling()?.color = true
-            toDel!.sibling()?.right?.color = false
-            leftRotate(toDel!.sibling()!)
-    }
-  }
-  private func deleteCase6(toDel: RBTNode?){
-    let color = toDel!.sibling()?.color
-    toDel!.parent?.color = color!
-    toDel!.parent?.color = false
-    if(toDel! === toDel!.parent.left){
-        toDel!.sibling()?.right?.color = false
-        leftRotate(toDel!.parent!)
-    }
-    else{
-      toDel!.sibling()?.left?.color = false
-      rightRotate(toDel!.parent!)
-    }
-  }
-}
-
-var tree = RBTree(rootData: 8)
-tree.insert(5)
-tree.insert(4)
-tree.insert(9)
-tree.delete(9)
-tree.insert(3)
-tree.insert(10)
-tree.delete(3)
-var x = tree.find(5)
-tree.inOrder()

From a62271d5c68fd4b3b6bae11764e653b4c2fa4553 Mon Sep 17 00:00:00 2001
From: Andrew McKnight <amcknight2718@gmail.com>
Date: Thu, 5 May 2016 20:37:44 -0400
Subject: [PATCH 0356/1679] Implement Floyd-Warshall algorith for All-Pairs
 Shortest Paths

- implement as one of a possible family of algorithms to compute APSP; towards
that end, some protocols are defined for a general APSP algorithm and its
result structure

Changes to Graph data structure:
- track vertex objects in an array as they are created for random access later
- make Vertex.index public for use by external algorithms
- conform to CustomStringConvertible class for printing descriptions
---
 .travis.yml                                   |   5 +-
 .../APSP/APSP.playground/Contents.swift       |  29 ++
 .../APSP.playground/contents.xcplayground     |   4 +
 .../APSP/APSP.playground/timeline.xctimeline  |  16 +
 .../APSP/APSP.xcodeproj/project.pbxproj       | 423 ++++++++++++++++++
 .../xcshareddata/xcschemes/APSP.xcscheme      |  91 ++++
 .../xcshareddata/xcschemes/APSPTests.xcscheme |  56 +++
 All-Pairs Shortest Paths/APSP/APSP/APSP.h     |  19 +
 All-Pairs Shortest Paths/APSP/APSP/APSP.swift |  33 ++
 .../APSP/APSP/FloydWarshall.swift             | 200 +++++++++
 .../APSP/APSP/Helpers.swift                   |  60 +++
 All-Pairs Shortest Paths/APSP/APSP/Info.plist |  28 ++
 .../APSP/APSPTests/APSPTests.swift            | 119 +++++
 .../APSP/APSPTests/Info.plist                 |  24 +
 All-Pairs Shortest Paths/README.md            |  76 ++++
 All-Pairs Shortest Paths/img/d0.png           | Bin 0 -> 26452 bytes
 All-Pairs Shortest Paths/img/d1.png           | Bin 0 -> 25961 bytes
 All-Pairs Shortest Paths/img/d2.png           | Bin 0 -> 25837 bytes
 All-Pairs Shortest Paths/img/d3.png           | Bin 0 -> 25924 bytes
 .../img/example_graph.png                     | Bin 0 -> 10320 bytes
 .../img/original_adjacency_matrix.png         | Bin 0 -> 23853 bytes
 All-Pairs Shortest Paths/img/pi0.png          | Bin 0 -> 10557 bytes
 All-Pairs Shortest Paths/img/pi1.png          | Bin 0 -> 10564 bytes
 All-Pairs Shortest Paths/img/pi2.png          | Bin 0 -> 10799 bytes
 All-Pairs Shortest Paths/img/pi3.png          | Bin 0 -> 10831 bytes
 .../img/weight_comparison_formula.png         | Bin 0 -> 28752 bytes
 Graph/AdjacencyMatrix.swift                   |  38 +-
 .../timeline.xctimeline                       |   5 +
 README.markdown                               |   2 +-
 29 files changed, 1222 insertions(+), 6 deletions(-)
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP/APSP.h
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP/APSP.swift
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP/Helpers.swift
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP/Info.plist
 create mode 100644 All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
 create mode 100644 All-Pairs Shortest Paths/APSP/APSPTests/Info.plist
 create mode 100644 All-Pairs Shortest Paths/README.md
 create mode 100644 All-Pairs Shortest Paths/img/d0.png
 create mode 100644 All-Pairs Shortest Paths/img/d1.png
 create mode 100644 All-Pairs Shortest Paths/img/d2.png
 create mode 100644 All-Pairs Shortest Paths/img/d3.png
 create mode 100644 All-Pairs Shortest Paths/img/example_graph.png
 create mode 100644 All-Pairs Shortest Paths/img/original_adjacency_matrix.png
 create mode 100644 All-Pairs Shortest Paths/img/pi0.png
 create mode 100644 All-Pairs Shortest Paths/img/pi1.png
 create mode 100644 All-Pairs Shortest Paths/img/pi2.png
 create mode 100644 All-Pairs Shortest Paths/img/pi3.png
 create mode 100644 All-Pairs Shortest Paths/img/weight_comparison_formula.png

diff --git a/.travis.yml b/.travis.yml
index a980968be..294f4e158 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 language: objective-c
-osx_image: xcode7.2
+osx_image: xcode7.3
 
 script:
 
@@ -23,4 +23,5 @@ script:
 - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
\ No newline at end of file
+- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
\ No newline at end of file
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
new file mode 100644
index 000000000..e14966113
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
@@ -0,0 +1,29 @@
+//: Playground - noun: a place where people can play
+
+import APSP
+
+var graph = Graph<String>()
+
+let v1 = graph.createVertex("Montreal")
+let v2 = graph.createVertex("New York")
+let v3 = graph.createVertex("Boston")
+let v4 = graph.createVertex("Portland")
+let v5 = graph.createVertex("Portsmouth")
+
+graph.connect(v1, to: v2, withWeight: 3)
+graph.connect(v1, to: v5, withWeight: -4)
+graph.connect(v1, to: v3, withWeight: 8)
+
+graph.connect(v2, to: v4, withWeight: 1)
+graph.connect(v2, to: v5, withWeight: 7)
+
+graph.connect(v3, to: v2, withWeight: 4)
+
+graph.connect(v4, to: v1, withWeight: 2)
+graph.connect(v4, to: v3, withWeight: -5)
+
+graph.connect(v5, to: v4, withWeight: 6)
+
+let result = FloydWarshall<String>.apply(graph)
+
+let path = result.path(fromVertex: v1, toVertex: v4, inGraph: graph)
\ No newline at end of file
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground b/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline
new file mode 100644
index 000000000..522661fa7
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=790&amp;EndingColumnNumber=44&amp;EndingLineNumber=28&amp;StartingColumnNumber=3&amp;StartingLineNumber=27&amp;Timestamp=484286078.350375"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=4&amp;CharacterRangeLoc=727&amp;EndingColumnNumber=9&amp;EndingLineNumber=28&amp;StartingColumnNumber=5&amp;StartingLineNumber=28&amp;Timestamp=484286078.357412"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..7df369cd7
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -0,0 +1,423 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		493D8DE31CDD2A1C0089795A /* APSPTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DE21CDD2A1C0089795A /* APSPTests.swift */; };
+		493D8DF41CDD5B960089795A /* APSP.h in Headers */ = {isa = PBXBuildFile; fileRef = 493D8DF31CDD5B960089795A /* APSP.h */; settings = {ATTRIBUTES = (Public, ); }; };
+		493D8DF91CDD5B9B0089795A /* FloydWarshall.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DD81CDC38C60089795A /* FloydWarshall.swift */; };
+		493D8DFA1CDD5B9E0089795A /* Helpers.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DDA1CDD29C80089795A /* Helpers.swift */; };
+		493D8DFB1CDD5BDE0089795A /* AdjacencyMatrix.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DB91CDC34D00089795A /* AdjacencyMatrix.swift */; };
+		49BFA27A1CDD93F400522D66 /* APSP.swift in Sources */ = {isa = PBXBuildFile; fileRef = 49BFA2791CDD93F400522D66 /* APSP.swift */; };
+		49BFA2801CDE742900522D66 /* APSP.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = 493D8DF11CDD5B960089795A /* APSP.framework */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
+		49BFA27E1CDE742700522D66 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 493D8D7E1CDC2DAE0089795A /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = 493D8DF01CDD5B960089795A;
+			remoteInfo = APSP;
+		};
+/* End PBXContainerItemProxy section */
+
+/* Begin PBXFileReference section */
+		493D8DB91CDC34D00089795A /* AdjacencyMatrix.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AdjacencyMatrix.swift; sourceTree = "<group>"; };
+		493D8DD81CDC38C60089795A /* FloydWarshall.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = FloydWarshall.swift; sourceTree = "<group>"; };
+		493D8DDA1CDD29C80089795A /* Helpers.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Helpers.swift; sourceTree = "<group>"; };
+		493D8DE01CDD2A1C0089795A /* APSPTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = APSPTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		493D8DE21CDD2A1C0089795A /* APSPTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = APSPTests.swift; sourceTree = "<group>"; };
+		493D8DE41CDD2A1C0089795A /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		493D8DF11CDD5B960089795A /* APSP.framework */ = {isa = PBXFileReference; explicitFileType = wrapper.framework; includeInIndex = 0; path = APSP.framework; sourceTree = BUILT_PRODUCTS_DIR; };
+		493D8DF31CDD5B960089795A /* APSP.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = APSP.h; sourceTree = "<group>"; };
+		493D8DF51CDD5B960089795A /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		49BFA2791CDD93F400522D66 /* APSP.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = APSP.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
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+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				49BFA2801CDE742900522D66 /* APSP.framework in Frameworks */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		493D8DED1CDD5B960089795A /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
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+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		493D8D7D1CDC2DAE0089795A = {
+			isa = PBXGroup;
+			children = (
+				493D8DB71CDC34D00089795A /* Graph */,
+				493D8D881CDC2DAE0089795A /* APSP */,
+				493D8DE11CDD2A1C0089795A /* APSPTests */,
+				493D8D871CDC2DAE0089795A /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		493D8D871CDC2DAE0089795A /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				493D8DE01CDD2A1C0089795A /* APSPTests.xctest */,
+				493D8DF11CDD5B960089795A /* APSP.framework */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		493D8D881CDC2DAE0089795A /* APSP */ = {
+			isa = PBXGroup;
+			children = (
+				493D8DF31CDD5B960089795A /* APSP.h */,
+				49BFA2791CDD93F400522D66 /* APSP.swift */,
+				493D8DD81CDC38C60089795A /* FloydWarshall.swift */,
+				493D8DDA1CDD29C80089795A /* Helpers.swift */,
+				493D8DF51CDD5B960089795A /* Info.plist */,
+			);
+			path = APSP;
+			sourceTree = "<group>";
+		};
+		493D8DB71CDC34D00089795A /* Graph */ = {
+			isa = PBXGroup;
+			children = (
+				493D8DB91CDC34D00089795A /* AdjacencyMatrix.swift */,
+			);
+			name = Graph;
+			path = ../../Graph;
+			sourceTree = "<group>";
+		};
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+			isa = PBXGroup;
+			children = (
+				493D8DE21CDD2A1C0089795A /* APSPTests.swift */,
+				493D8DE41CDD2A1C0089795A /* Info.plist */,
+			);
+			path = APSPTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXHeadersBuildPhase section */
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+			buildActionMask = 2147483647;
+			files = (
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+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXHeadersBuildPhase section */
+
+/* Begin PBXNativeTarget section */
+		493D8DDF1CDD2A1C0089795A /* APSPTests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 493D8DE51CDD2A1C0089795A /* Build configuration list for PBXNativeTarget "APSPTests" */;
+			buildPhases = (
+				493D8DDC1CDD2A1C0089795A /* Sources */,
+				493D8DDD1CDD2A1C0089795A /* Frameworks */,
+				493D8DDE1CDD2A1C0089795A /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				49BFA27F1CDE742700522D66 /* PBXTargetDependency */,
+			);
+			name = APSPTests;
+			productName = APSPTests;
+			productReference = 493D8DE01CDD2A1C0089795A /* APSPTests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+		493D8DF01CDD5B960089795A /* APSP */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 493D8DF61CDD5B960089795A /* Build configuration list for PBXNativeTarget "APSP" */;
+			buildPhases = (
+				493D8DEC1CDD5B960089795A /* Sources */,
+				493D8DED1CDD5B960089795A /* Frameworks */,
+				493D8DEE1CDD5B960089795A /* Headers */,
+				493D8DEF1CDD5B960089795A /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = APSP;
+			productName = APSP;
+			productReference = 493D8DF11CDD5B960089795A /* APSP.framework */;
+			productType = "com.apple.product-type.framework";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		493D8D7E1CDC2DAE0089795A /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0730;
+				LastUpgradeCheck = 0730;
+				ORGANIZATIONNAME = "Andrew McKnight";
+				TargetAttributes = {
+					493D8DDF1CDD2A1C0089795A = {
+						CreatedOnToolsVersion = 7.3;
+					};
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+					};
+				};
+			};
+			buildConfigurationList = 493D8D811CDC2DAE0089795A /* Build configuration list for PBXProject "APSP" */;
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+				en,
+			);
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+			projectRoot = "";
+			targets = (
+				493D8DDF1CDD2A1C0089795A /* APSPTests */,
+				493D8DF01CDD5B960089795A /* APSP */,
+			);
+		};
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+			);
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+			files = (
+			);
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+			buildActionMask = 2147483647;
+			files = (
+				493D8DE31CDD2A1C0089795A /* APSPTests.swift in Sources */,
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+			);
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+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin PBXTargetDependency section */
+		49BFA27F1CDE742700522D66 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			target = 493D8DF01CDD5B960089795A /* APSP */;
+			targetProxy = 49BFA27E1CDE742700522D66 /* PBXContainerItemProxy */;
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+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
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+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
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+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
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+				SDKROOT = macosx;
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+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = APSPTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSPTests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		493D8DE71CDD2A1C0089795A /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = APSPTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSPTests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+		493D8DF71CDD5B960089795A /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				CURRENT_PROJECT_VERSION = 1;
+				DEFINES_MODULE = YES;
+				DYLIB_COMPATIBILITY_VERSION = 1;
+				DYLIB_CURRENT_VERSION = 1;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				FRAMEWORK_VERSION = A;
+				INFOPLIST_FILE = APSP/Info.plist;
+				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSP;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SKIP_INSTALL = YES;
+				VERSIONING_SYSTEM = "apple-generic";
+				VERSION_INFO_PREFIX = "";
+			};
+			name = Debug;
+		};
+		493D8DF81CDD5B960089795A /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				CURRENT_PROJECT_VERSION = 1;
+				DEFINES_MODULE = YES;
+				DYLIB_COMPATIBILITY_VERSION = 1;
+				DYLIB_CURRENT_VERSION = 1;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				FRAMEWORK_VERSION = A;
+				INFOPLIST_FILE = APSP/Info.plist;
+				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSP;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SKIP_INSTALL = YES;
+				VERSIONING_SYSTEM = "apple-generic";
+				VERSION_INFO_PREFIX = "";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		493D8D811CDC2DAE0089795A /* Build configuration list for PBXProject "APSP" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				493D8D8B1CDC2DAE0089795A /* Debug */,
+				493D8D8C1CDC2DAE0089795A /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		493D8DE51CDD2A1C0089795A /* Build configuration list for PBXNativeTarget "APSPTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				493D8DE61CDD2A1C0089795A /* Debug */,
+				493D8DE71CDD2A1C0089795A /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		493D8DF61CDD5B960089795A /* Build configuration list for PBXNativeTarget "APSP" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				493D8DF71CDD5B960089795A /* Debug */,
+				493D8DF81CDD5B960089795A /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 493D8D7E1CDC2DAE0089795A /* Project object */;
+}
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme
new file mode 100644
index 000000000..475997aa9
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
@@ -0,0 +1,91 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "493D8DF01CDD5B960089795A"
+               BuildableName = "APSP.framework"
+               BlueprintName = "APSP"
+               ReferencedContainer = "container:APSP.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "493D8DF01CDD5B960089795A"
+            BuildableName = "APSP.framework"
+            BlueprintName = "APSP"
+            ReferencedContainer = "container:APSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "493D8DF01CDD5B960089795A"
+            BuildableName = "APSP.framework"
+            BlueprintName = "APSP"
+            ReferencedContainer = "container:APSP.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "493D8DF01CDD5B960089795A"
+            BuildableName = "APSP.framework"
+            BlueprintName = "APSP"
+            ReferencedContainer = "container:APSP.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme
new file mode 100644
index 000000000..867745024
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "493D8DDF1CDD2A1C0089795A"
+               BuildableName = "APSPTests.xctest"
+               BlueprintName = "APSPTests"
+               ReferencedContainer = "container:APSP.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/All-Pairs Shortest Paths/APSP/APSP/APSP.h b/All-Pairs Shortest Paths/APSP/APSP/APSP.h
new file mode 100644
index 000000000..59613bceb
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP/APSP.h	
@@ -0,0 +1,19 @@
+//
+//  APSP.h
+//  APSP
+//
+//  Created by Andrew McKnight on 5/6/16.
+//  Copyright © 2016 Andrew McKnight. All rights reserved.
+//
+
+#import <Cocoa/Cocoa.h>
+
+//! Project version number for APSP.
+FOUNDATION_EXPORT double APSPVersionNumber;
+
+//! Project version string for APSP.
+FOUNDATION_EXPORT const unsigned char APSPVersionString[];
+
+// In this header, you should import all the public headers of your framework using statements like #import <APSP/PublicHeader.h>
+
+
diff --git a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift
new file mode 100644
index 000000000..22ad4a958
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
@@ -0,0 +1,33 @@
+//
+//  Base.swift
+//  APSP
+//
+//  Created by Andrew McKnight on 5/6/16.
+//  Copyright © 2016 Andrew McKnight. All rights reserved.
+//
+
+import Foundation
+
+/**
+ APSPAlgorithm is a protocol for encapsulating an All-Pairs Shortest Paths algorithm. It provides a single function `apply` that accepts a `Graph` and returns an object conforming to `APSPResult`.
+ */
+protocol APSPAlgorithm {
+
+  associatedtype Q
+  associatedtype P: APSPResult
+
+  static func apply(graph: Graph<Q>) -> P
+
+}
+
+/**
+ APSPResult is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the APSP solution according to the algorithm used.
+ */
+protocol APSPResult {
+
+  associatedtype T
+
+  func distance(fromVertex from: Vertex<T>, toVertex to: Vertex<T>) -> Double?
+  func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: Graph<T>) -> [T]?
+
+}
diff --git a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
new file mode 100644
index 000000000..976d3138c
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
@@ -0,0 +1,200 @@
+//
+//  FloydWarshall.swift
+//  APSP
+//
+//  Created by Andrew McKnight on 5/5/16.
+//  Copyright © 2016 Andrew McKnight. All rights reserved.
+//
+
+import Foundation
+
+private typealias Distances = [[Double]]
+private typealias Predecessors = [[Int?]]
+private typealias StepResult = (distances: Distances, predecessors: Predecessors)
+
+/**
+ Encapsulation of the Floyd-Warshall All-Pairs Shortest Paths algorithm, conforming to the APSPAlgorithm protocol.
+
+ - note: In all complexity bounds, `V` is the number of vertices in the graph, and `E` is the number of edges.
+ */
+public struct FloydWarshall<T>: APSPAlgorithm {
+
+  typealias Q = T
+  typealias P = FloydWarshallResult<T>
+
+  /**
+   Floyd-Warshall algorithm for computing all-pairs shortest paths in a weighted directed graph.
+
+   - precondition: `graph` must have no negative weight cycles
+   - complexity: `Θ(V^3)` time, `Θ(V^2)` space
+   - returns a `FloydWarshallResult` struct which can be queried for shortest paths and their total weights
+   */
+  public static func apply<T>(graph: Graph<T>) -> FloydWarshallResult<T> {
+
+    var previousDistance = constructInitialDistanceMatrix(graph)
+    var previousPredecessor = constructInitialPredecessorMatrix(previousDistance)
+    for intermediateIdx in 0 ..< graph.vertices.count {
+      let nextResult = nextStep(intermediateIdx, previousDistances: previousDistance, previousPredecessors: previousPredecessor, graph: graph)
+      previousDistance = nextResult.distances
+      previousPredecessor = nextResult.predecessors
+
+//      // uncomment to see each new weight matrix
+//      print("  D(\(k)):\n")
+//      printMatrix(nextResult.distances)
+//
+//      // uncomment to see each new predecessor matrix
+//      print("  ∏(\(k)):\n")
+//      printIntMatrix(nextResult.predecessors)
+    }
+    return FloydWarshallResult<T>(weights: previousDistance, predecessors: previousPredecessor)
+
+  }
+
+  /**
+   For each iteration of `intermediateIdx`, perform the comparison for the dynamic algorith, checking for each pair of start/end vertices, whether a path taken through another vertex produces a shorter path.
+
+   - complexity: `Θ(V^2)` time/space
+   - returns: a tuple containing the next distance matrix with weights of currently known shortest paths and the corresponding predecessor matrix
+   */
+  static private func nextStep<T>(intermediateIdx: Int, previousDistances: Distances, previousPredecessors: Predecessors, graph: Graph<T>) -> StepResult {
+
+    let vertexCount = graph.adjacencyMatrix.count
+    var nextDistances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
+    var nextPredecessors = Array(count: vertexCount, repeatedValue: Array<Int?>(count: vertexCount, repeatedValue: nil))
+
+    for fromIdx in 0 ..< vertexCount {
+      for toIndex in 0 ..< vertexCount {
+//        printMatrix(previousDistances, i: fromIdx, j: toIdx, k: intermediateIdx) // uncomment to see each comparison being made
+        let originalPathWeight = previousDistances[fromIdx][toIndex]
+        let newPathWeightBefore = previousDistances[fromIdx][intermediateIdx]
+        let newPathWeightAfter = previousDistances[intermediateIdx][toIndex]
+
+        let minimum = min(originalPathWeight, newPathWeightBefore + newPathWeightAfter)
+        nextDistances[fromIdx][toIndex] = minimum
+
+        var predecessor: Int?
+        if originalPathWeight <= newPathWeightBefore + newPathWeightAfter {
+          predecessor = previousPredecessors[fromIdx][toIndex]
+        } else {
+          predecessor = previousPredecessors[intermediateIdx][toIndex]
+        }
+        nextPredecessors[fromIdx][toIndex] = predecessor
+      }
+    }
+    return (nextDistances, nextPredecessors)
+
+  }
+
+  /** 
+   We need to convert the value system in Graph's adjacency matrix to the one we need to perform the algorithm. We need the actual weight between two vertices, or infinity if no edge exists, represented by nil in Graph.adjacencyMatrix. Also set the weight to 0 on the diagonal.
+   
+   - complexity: `Θ(V^2)` time/space
+   - returns: weighted adjacency matrix in form ready for processing with Floyd-Warshall
+   */
+  static private func constructInitialDistanceMatrix<T>(graph: Graph<T>) -> Distances {
+
+    let vertexCount = graph.adjacencyMatrix.count
+    var distances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
+
+    for fromIdx in 0 ..< vertexCount {
+      for toIdx in 0 ..< vertexCount {
+        if fromIdx == toIdx {
+          distances[fromIdx][toIdx] = 0.0
+        } else if let w = graph.adjacencyMatrix[fromIdx][toIdx] {
+          distances[fromIdx][toIdx] = w
+        }
+      }
+    }
+
+    return distances
+
+  }
+
+  /**
+   Make the initial predecessor index matrix. Initially each value is equal to it's row index, it's "from" index when querying into it.
+   
+   - complexity: `Θ(V^2)` time/space
+  */
+  static private func constructInitialPredecessorMatrix(distances: Distances) -> Predecessors {
+
+    let vertexCount = distances.count
+    var predecessors = Array(count: vertexCount, repeatedValue: Array<Int?>(count: vertexCount, repeatedValue: nil))
+
+    for fromIdx in 0 ..< vertexCount {
+      for toIdx in 0 ..< vertexCount {
+        if fromIdx != toIdx && distances[fromIdx][toIdx] < Double.infinity {
+          predecessors[fromIdx][toIdx] = fromIdx
+        }
+      }
+    }
+
+    return predecessors
+
+  }
+
+}
+
+/**
+ FloydWarshallResult encapsulates the result of the computation, namely the minimized distance adjacency matrix, and the matrix of predecessor indices.
+ 
+ It conforms to the APSPResult procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
+ */
+public struct FloydWarshallResult<T>: APSPResult {
+
+  private var weights: Distances
+  private var predecessors: Predecessors
+
+  /**
+   - returns: the total weight of the path from a starting vertex to a destination. This value is the minimal connected weight between the two vertices.
+   - complexity: `Θ(1)` time/space
+   */
+  public func distance(fromVertex from: Vertex<T>, toVertex to: Vertex<T>) -> Double? {
+
+    return weights[from.index][to.index]
+
+  }
+
+  /**
+   - returns: the reconstructed path from a starting vertex to a destination, as an array containing the data property of each vertex
+   - complexity: `Θ(V)` time, `Θ(V^2)` space
+   */
+  public func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: Graph<T>) -> [T]? {
+
+    if let path = recursePathFrom(predecessors, fromVertex: from, toVertex: to, path: [ to ], inGraph: graph) {
+      let pathValues = path.map() { vertex in
+        vertex.data
+      }
+      return pathValues
+    }
+    return nil
+
+  }
+
+  /**
+   The recursive component to rebuilding the shortest path between two vertices using the predecessor graph.
+
+   - returns: the list of predecessors discovered so far
+   */
+  private func recursePathFrom(predecessors: [[Int?]], fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>], inGraph graph: Graph<T>) -> [Vertex<T>]? {
+
+    if from.index == to.index {
+      return [ from, to ]
+    }
+
+    if let predecessor = predecessors[from.index][to.index] {
+      let predecessorVertex = graph.vertices[predecessor]
+      if predecessor == from.index {
+        let newPath = [ from, to ]
+        return newPath
+      } else {
+        let buildPath = recursePathFrom(predecessors, fromVertex: from, toVertex: predecessorVertex, path: path, inGraph: graph)
+        let newPath = buildPath! + [ to ]
+        return newPath
+      }
+    }
+
+    return nil
+    
+  }
+
+}
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift
new file mode 100644
index 000000000..c6f22e879
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
@@ -0,0 +1,60 @@
+//
+//  Helpers.swift
+//  APSP
+//
+//  Created by Andrew McKnight on 5/6/16.
+//  Copyright © 2016 Andrew McKnight. All rights reserved.
+//
+
+import Foundation
+
+/**
+ Print a matrix, optionally specifying only the cells to display with the triplet (i, j, k) -> matrix[i][j], matrix[i][k], matrix[k][j]
+ */
+func printMatrix(matrix: [[Double]], i: Int = -1, j: Int = -1, k: Int = -1) {
+
+  if i >= 0 {
+    print("  k: \(k); i: \(i); j: \(j)\n")
+  }
+
+  var grid = [String]()
+
+  let n = matrix.count
+  for x in 0..<n {
+    var row = ""
+    for y in 0..<n {
+      if i < 0 || ( x == i && y == j ) || ( x == i && y == k ) || ( x == k && y == j ) {
+        let value = NSString(format: "%.1f", matrix[x][y])
+        row += "\(matrix[x][y] >= 0 ? " " : "")\(value) "
+      } else {
+        row += "  .  "
+      }
+    }
+    grid.append(row)
+  }
+  print((grid as NSArray).componentsJoinedByString("\n"))
+  print(" =======================")
+
+}
+
+func printIntMatrix(matrix: [[Int?]]) {
+
+  var grid = [String]()
+
+  let n = matrix.count
+  for x in 0..<n {
+    var row = ""
+    for y in 0..<n {
+      if let value = matrix[x][y] {
+        let valueString = NSString(format: "%i", value)
+        row += "\(matrix[x][y] >= 0 ? " " : "")\(valueString) "
+      } else {
+        row += "  ø  "
+      }
+    }
+    grid.append(row)
+  }
+  print((grid as NSArray).componentsJoinedByString("\n"))
+  print(" =======================")
+
+}
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Info.plist b/All-Pairs Shortest Paths/APSP/APSP/Info.plist
new file mode 100644
index 000000000..9bf850304
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP/Info.plist	
@@ -0,0 +1,28 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>FMWK</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>$(CURRENT_PROJECT_VERSION)</string>
+	<key>NSHumanReadableCopyright</key>
+	<string>Copyright © 2016 Andrew McKnight. All rights reserved.</string>
+	<key>NSPrincipalClass</key>
+	<string></string>
+</dict>
+</plist>
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
new file mode 100644
index 000000000..47b71b3ea
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -0,0 +1,119 @@
+//
+//  APSPTests.swift
+//  APSPTests
+//
+//  Created by Andrew McKnight on 5/6/16.
+//  Copyright © 2016 Andrew McKnight. All rights reserved.
+//
+
+import APSP
+import XCTest
+
+struct TestCase<T> {
+
+  var from: Vertex<T>
+  var to: Vertex<T>
+  var expectedPath: [T]
+  var expectedDistance: Double
+
+}
+
+class APSPTests: XCTestCase {
+
+  func testExampleFromBook() {
+
+    var graph = Graph<String>()
+    let v1 = graph.createVertex("Montreal")
+    let v2 = graph.createVertex("New York")
+    let v3 = graph.createVertex("Boston")
+    let v4 = graph.createVertex("Portland")
+    let v5 = graph.createVertex("Portsmouth")
+
+    graph.connect(v1, to: v2, withWeight: 3)
+    graph.connect(v1, to: v5, withWeight: -4)
+    graph.connect(v1, to: v3, withWeight: 8)
+
+    graph.connect(v2, to: v4, withWeight: 1)
+    graph.connect(v2, to: v5, withWeight: 7)
+
+    graph.connect(v3, to: v2, withWeight: 4)
+
+    graph.connect(v4, to: v1, withWeight: 2)
+    graph.connect(v4, to: v3, withWeight: -5)
+
+    graph.connect(v5, to: v4, withWeight: 6)
+
+    let result = FloydWarshall<String>.apply(graph)
+
+    let cases = [
+      TestCase<String>(from: v1, to: v4, expectedPath: ["Montreal", "Portsmouth", "Portland"], expectedDistance: 2),
+      TestCase<String>(from: v1, to: v5, expectedPath: ["Montreal", "Portsmouth"], expectedDistance: -4),
+      TestCase<String>(from: v2, to: v1, expectedPath: ["New York", "Portland", "Montreal"], expectedDistance: 3),
+      TestCase<String>(from: v2, to: v3, expectedPath: ["New York", "Portland", "Boston"], expectedDistance: -4),
+      TestCase<String>(from: v2, to: v4, expectedPath: ["New York", "Portland"], expectedDistance: 1),
+      TestCase<String>(from: v2, to: v5, expectedPath: ["New York", "Portland", "Montreal", "Portsmouth"], expectedDistance: -1),
+      TestCase<String>(from: v3, to: v1, expectedPath: ["Boston", "New York", "Portland", "Montreal"], expectedDistance: 7),
+      TestCase<String>(from: v3, to: v2, expectedPath: ["Boston", "New York"], expectedDistance: 4),
+      TestCase<String>(from: v3, to: v4, expectedPath: ["Boston", "New York", "Portland"], expectedDistance: 5),
+      TestCase<String>(from: v3, to: v5, expectedPath: ["Boston", "New York", "Portland", "Montreal", "Portsmouth"], expectedDistance: 3),
+      TestCase<String>(from: v4, to: v1, expectedPath: ["Portland", "Montreal"], expectedDistance: 2),
+      TestCase<String>(from: v4, to: v2, expectedPath: ["Portland", "Boston", "New York"], expectedDistance: -1),
+      TestCase<String>(from: v4, to: v3, expectedPath: ["Portland", "Boston"], expectedDistance: -5),
+      TestCase<String>(from: v4, to: v5, expectedPath: ["Portland", "Montreal", "Portsmouth"], expectedDistance: -2),
+      TestCase<String>(from: v5, to: v1, expectedPath: ["Portsmouth", "Portland", "Montreal"], expectedDistance: 8),
+      TestCase<String>(from: v5, to: v2, expectedPath: ["Portsmouth", "Portland", "Boston", "New York"], expectedDistance: 5),
+      TestCase<String>(from: v5, to: v3, expectedPath: ["Portsmouth", "Portland", "Boston"], expectedDistance: 1),
+      TestCase<String>(from: v5, to: v4, expectedPath: ["Portsmouth", "Portland"], expectedDistance: 6),
+      ]
+
+    for testCase: TestCase<String> in cases {
+      if let computedPath = result.path(fromVertex: testCase.from, toVertex: testCase.to, inGraph: graph),
+              computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
+        XCTAssert(computedDistance == testCase.expectedDistance, "expected distance \(testCase.expectedDistance) but got \(computedDistance)")
+        XCTAssert(computedPath == testCase.expectedPath, "expected path \(testCase.expectedPath) but got \(computedPath)")
+      }
+    }
+
+  }
+
+  func testExampleFromReadme() {
+
+    var graph = Graph<Int>()
+    let v1 = graph.createVertex(1)
+    let v2 = graph.createVertex(2)
+    let v3 = graph.createVertex(3)
+    let v4 = graph.createVertex(4)
+
+    graph.connect(v1, to: v2, withWeight: 4)
+    graph.connect(v1, to: v3, withWeight: 1)
+    graph.connect(v1, to: v4, withWeight: 3)
+
+    graph.connect(v2, to: v3, withWeight: 8)
+    graph.connect(v2, to: v4, withWeight: -2)
+
+    graph.connect(v3, to: v4, withWeight: -5)
+
+    let result = FloydWarshall<Int>.apply(graph)
+
+    let cases = [
+      TestCase<Int>(from: v1, to: v2, expectedPath: [1, 2], expectedDistance: 4),
+      TestCase<Int>(from: v1, to: v3, expectedPath: [1, 3], expectedDistance: 1),
+      TestCase<Int>(from: v1, to: v4, expectedPath: [1, 3, 4], expectedDistance: -4),
+
+      TestCase<Int>(from: v2, to: v3, expectedPath: [2, 3], expectedDistance: 8),
+      TestCase<Int>(from: v2, to: v4, expectedPath: [2, 4], expectedDistance: -2),
+
+      TestCase<Int>(from: v3, to: v4, expectedPath: [3, 4], expectedDistance: -5),
+    ]
+
+    for testCase: TestCase<Int> in cases {
+      if let computedPath = result.path(fromVertex: testCase.from, toVertex: testCase.to, inGraph: graph),
+        computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
+        XCTAssert(computedDistance == testCase.expectedDistance, "expected distance \(testCase.expectedDistance) but got \(computedDistance)")
+        XCTAssert(computedPath == testCase.expectedPath, "expected path \(testCase.expectedPath) but got \(computedPath)")
+      }
+    }
+
+  }
+
+}
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/Info.plist b/All-Pairs Shortest Paths/APSP/APSPTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/All-Pairs Shortest Paths/README.md b/All-Pairs Shortest Paths/README.md
new file mode 100644
index 000000000..8a75c8b73
--- /dev/null
+++ b/All-Pairs Shortest Paths/README.md	
@@ -0,0 +1,76 @@
+# All-Pairs Shortest Paths
+
+The All-Pairs shortest path problem simultaneously computes the shortest path from each node in the graph to each other node, provded a path exists for each pair. In the naive approach, we could simply compute a single-source shortest path from each node to each other node. The number of shortest paths computed is then bound by `O(V^2)`, where `V` is the number of vertices in the graph. Because SSSP is also bounded by `O(V^2)`, the total running time for the naive approach would be `O(V^4)`.
+
+However, by applying a dynamic approach on the adjacency matrix of the graph, a running time of `Θ(V^3)` is achievable, using the `Floyd-Warshall` algorithm. Floyd-Warshall iterates through an adjacency matrix, and for each pair of start(`i`) and end(`j`) vertices it considers if the current distance between them is greater than a path taken through another vertex(`k`) in the graph (if paths `i` ~> `k` and `k` ~> `j` exist). It moves through an adjacency matrix for every vertex `k` applying its comparison for each pair (`i`, `j`), so for each `k` a new adjacency matrix `D(k)` is derived, where each value `d(k)[i][j]` is defined as:
+
+<img src="img/weight_comparison_formula.png" width="400px" />
+
+where `w[i][j]` is the weight of the edge connecting vertex `i` to vertex `j` in the graph's original adjacency matrix. 
+
+When the algorithm memoizes each refined adjacency and predecessor matrix, its space complexity is `Θ(V^3)`, which can be optimised to `Θ(V^2)` by only memoizing the latest refinements. Reconstructing paths is a recursive procedure which requires `Θ(V)` time and `Θ(V^2)` space.
+
+# Example
+
+For the following weighted directed graph
+
+<img src="img/example_graph.png" width="200px" />
+
+the adjacency matrix representation `w` is
+
+<img src="img/original_adjacency_matrix.png" width="200px" />
+
+### Calculating shortest paths' weights
+
+At the beginning of the algorithm, `D(0)` is the same as `w`, with the following exceptions to accomodate the comparison function:
+
+1. vertices with no path connecting them have the `ø` replaced with `∞` 
+2. the diagonal has all `0`s
+
+Here are all the adjacency matrices derived when perform Floyd-Warshall on the above graph:
+
+<img src="img/d0.png" width="200px" />
+<img src="img/d1.png" width="200px" />
+
+<img src="img/d2.png" width="200px" />
+<img src="img/d3.png" width="200px" />
+
+with the last being the result, which tells for each pair of starting and ending vertices, the total weight of the shortest path connecting them. During the step where `k = 2`, the comparison that winds up changing the top right value from `2` to `-4` goes like this:
+
+	k = 2, i = 0, j = 3
+	d(k-1)[i][j] => d(1)[0][3] = 2
+	d(k-1)[i][k] => d(1)[0][2] = 1
+	d(k-1)[j][k] => d(1)[2][3] = -5
+
+therefore `min(2, 2 + -5) => min(2, -4)` produces a new weight of `-4` for the element at `d(2)[0][3]`, meaning that the shortest known path 1 ~> 4 before this step was from 1 -> 2 -> 4 with a total weight of -2, and afterwards we discovered a shorter path from 1 -> 3 -> 4 with a total weight of -4.
+
+### Reconstructing shortest paths
+
+This algorithm finds only the lengths of the shortest paths between all pairs of nodes; a separate bookkeeping structure must be maintained to track predecessors' indices and reconstruct the shortest paths afterwards. The predecessor matrices at each step for the above graph follow:
+
+<img src="img/pi0.png" width="200px" />
+<img src="img/pi1.png" width="200px" />
+
+<img src="img/pi2.png" width="200px" />
+<img src="img/pi3.png" width="200px" />
+
+# Project Structure
+
+The provided xcworkspace allows working in the playground, which imports the APSP framework target from the xcodeproj. Build the framework target and rerun the playground to get started. There is also a test target in the xcodeproj. 
+
+In the framework:
+
+- protocols for All-Pairs Shortest Paths algorithms and results structures
+- an implementation of the Floyd-Warshall algorithm
+
+# TODO
+
+- Implement naive `Θ(V^4)` method for comparison
+- Implement Johnson's algorithm for sparse graphs
+- Implement other cool optimized versions
+
+# References
+
+Chapter 25 of Introduction to Algorithms, Third Edition by Cormen, Leiserson, Rivest and Stein [https://mitpress.mit.edu/books/introduction-algorithms](https://mitpress.mit.edu/books/introduction-algorithms)
+
+*Written for Swift Algorithm Club by [Andrew McKnight](https://github.com/armcknight)*
\ No newline at end of file
diff --git a/All-Pairs Shortest Paths/img/d0.png b/All-Pairs Shortest Paths/img/d0.png
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diff --git a/All-Pairs Shortest Paths/img/d2.png b/All-Pairs Shortest Paths/img/d2.png
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diff --git a/All-Pairs Shortest Paths/img/example_graph.png b/All-Pairs Shortest Paths/img/example_graph.png
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z;_nr>%!G*&>@f`Fl1y$5{YW4u0}hpfFrEeYOxjQ6TmQ^>qc#4X|5%jJEI`L4&|#+k
zQdPhP$vL1VJVfy)R;hyq0@o)QVI!OjNB!k0)<3<Ktb*dr<^?WGqW@~ILY=??<Xk=X
z{Xbf!$=k3(-a?}!it@+zo0CgeawVBQ;j?FPxuDLneT5hQOBM3}dzubr-@XtL|6caf
zj49&F?<lfi?rgp@&jSw~s&t}2^WXo=2m*^D1N1DHQmOV|Zl5+Pa2!O)n<*~!wCwVF
zfTWBzY1MXIy4tyrk5??NM;-YC;3fJ;S{=!O$7ha|w*Py46*vwraRhKpdD4&qc1cY$
zYdx>Eb$$>NTv&ch`yVp&0cA$#(<)LacIe1IISIgdxXF^GDfcJNQkjtM7m31y3RkV=
zr-XmpNhDZV2HB0NiV4X6@^67U&u4&hKBW~)@~_|p2b0$y7r(Fe?+m?kf&aD?KwHmP
zfyF5j{{Xm1z^_x1;a8zRd(rZ8<vA^Vhd1p$;;=NAJNds40K#YqYIXQ#-u%;?hKe%#
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tLN1W6H&VX=`}P0n`u{eXPI`jB>V8*Vvx*5ZcLn$;Kh=0rreG2B{{R={3vmDd

literal 0
HcmV?d00001

diff --git a/Graph/AdjacencyMatrix.swift b/Graph/AdjacencyMatrix.swift
index 85a16d94f..d1d35ac02 100644
--- a/Graph/AdjacencyMatrix.swift
+++ b/Graph/AdjacencyMatrix.swift
@@ -1,12 +1,19 @@
+import Foundation
+
 public struct Vertex<T> {
   public var data: T
-  private let index: Int
+  public let index: Int
 }
 
+
+
 public struct Graph<T> {
   // If adjacencyMatrix[i][j] is not nil, then there is an edge from
   // vertex i to vertex j.
-  private var adjacencyMatrix: [[Double?]] = []
+  var adjacencyMatrix: [[Double?]] = []
+  var vertices: [Vertex<T>] = []
+
+  public init() {}
   
   // Adds a new vertex to the matrix.
   // Performance: possibly O(n^2) because of the resizing of the matrix.
@@ -22,9 +29,34 @@ public struct Graph<T> {
     let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
     adjacencyMatrix.append(newRow)
 
+    vertices.append(vertex)
     return vertex
   }
-  
+}
+
+extension Graph: CustomStringConvertible {
+  public var description: String {
+    get {
+      var grid = [String]()
+      let n = self.adjacencyMatrix.count
+      for i in 0..<n {
+        var row = ""
+        for j in 0..<n {
+          if let value = self.adjacencyMatrix[i][j] {
+            let number = NSString(format: "%.1f", value)
+            row += "\(value >= 0 ? " " : "")\(number) "
+          } else {
+            row += "  ø  "
+          }
+        }
+        grid.append(row)
+      }
+      return (grid as NSArray).componentsJoinedByString("\n")
+    }
+  }
+}
+
+extension Graph {
   // Creates a directed edge source -----> dest.
   public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
     adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline
index bf468afec..60cd19e82 100644
--- a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline	
+++ b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline	
@@ -2,5 +2,10 @@
 <Timeline
    version = "3.0">
    <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=28&amp;CharacterRangeLoc=3390&amp;EndingColumnNumber=29&amp;EndingLineNumber=97&amp;StartingColumnNumber=1&amp;StartingLineNumber=97&amp;Timestamp=484381589.889495"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
    </TimelineItems>
 </Timeline>
diff --git a/README.markdown b/README.markdown
index bbc10fb8d..4f2001ce6 100644
--- a/README.markdown
+++ b/README.markdown
@@ -172,7 +172,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Depth-First Search (DFS)](Depth-First Search/)
 - [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
 - [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
-- All Paths
+- [All-Pairs Shortest Paths](All-Pairs Shortest Paths/)
 
 ## Puzzles
 

From fc64b1e04002078c8fb85b7e750368811e690029 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Sun, 8 May 2016 19:04:48 +0200
Subject: [PATCH 0357/1679] Rename README.md to .markdown

---
 All-Pairs Shortest Paths/{README.md => README.markdown} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename All-Pairs Shortest Paths/{README.md => README.markdown} (100%)

diff --git a/All-Pairs Shortest Paths/README.md b/All-Pairs Shortest Paths/README.markdown
similarity index 100%
rename from All-Pairs Shortest Paths/README.md
rename to All-Pairs Shortest Paths/README.markdown

From c41a631cfdfe7394ecff9c8903ecb1cd0a95217b Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Mon, 9 May 2016 09:11:50 +0200
Subject: [PATCH 0358/1679] No longer gitignore xcworkspace

---
 .gitignore                                                 | 1 -
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../project.xcworkspace/contents.xcworkspacedata           | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 79 files changed, 546 insertions(+), 1 deletion(-)
 create mode 100644 AVL Tree/AVLTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 AVL Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Array2D/Array2D.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Array2D/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Binary Tree/BinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bit Set/BitSet.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bloom Filter/BloomFilter.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Brute-Force String Search/BruteForceStringSearch.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bucket Sort/BucketSort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Combinatorics/Combinatorics.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Count Occurrences/CountOccurrences.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Counting Sort/CountingSort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Deque/Deque.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 GCD/GCD.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Graph/Graph.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Hash Set/HashSet.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Hash Table/HashTable.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Huffman Coding/Huffman.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Insertion Sort/InsertionSort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 K-Means/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Kth Largest Element/kthLargest.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Linear Search/LinearSearch.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Linked List/LinkedList.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Longest Common Subsequence/LongestCommonSubsequence.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Longest Common Subsequence/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Merge Sort/MergeSort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Monty Hall Problem/MontyHall.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Ordered Array/OrderedArray.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Queue/Queue.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Quicksort/Quicksort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Radix Tree/RadixTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Ring Buffer/RingBuffer.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Run-Length Encoding/RLE.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Segment Tree/SegmentTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Select Minimum Maximum/SelectMinimumMaximum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Select Minimum Maximum/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Selection Sampling/SelectionSampling.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Selection Sort/SelectionSort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Selection Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Shell Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Shortest Path (Unweighted)/ShortestPath.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Shuffle/Shuffle.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Shunting Yard/ShuntingYard.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Stack/Stack.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Topological Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Topological Sort/Topological Sort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Tree/Tree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Union-Find/UnionFind.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/.gitignore b/.gitignore
index 189605960..c2f483cba 100644
--- a/.gitignore
+++ b/.gitignore
@@ -8,7 +8,6 @@ DerivedData/
 *.perspectivev3
 *.xccheckout
 *.moved-aside
-*.xcworkspace
 *.xcuserstate
 
 xcuserdata
diff --git a/AVL Tree/AVLTree.playground/playground.xcworkspace/contents.xcworkspacedata b/AVL Tree/AVLTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/AVL Tree/AVLTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/AVL Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/AVL Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/AVL Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Array2D/Array2D.playground/playground.xcworkspace/contents.xcworkspacedata b/Array2D/Array2D.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Array2D/Array2D.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Array2D/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Array2D/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Array2D/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Binary Tree/BinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Binary Tree/BinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Binary Tree/BinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bit Set/BitSet.playground/playground.xcworkspace/contents.xcworkspacedata b/Bit Set/BitSet.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bit Set/BitSet.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bloom Filter/BloomFilter.playground/playground.xcworkspace/contents.xcworkspacedata b/Bloom Filter/BloomFilter.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bloom Filter/BloomFilter.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata b/Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Brute-Force String Search/BruteForceStringSearch.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bucket Sort/BucketSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Bucket Sort/BucketSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Combinatorics/Combinatorics.playground/playground.xcworkspace/contents.xcworkspacedata b/Combinatorics/Combinatorics.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Combinatorics/Combinatorics.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Count Occurrences/CountOccurrences.playground/playground.xcworkspace/contents.xcworkspacedata b/Count Occurrences/CountOccurrences.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Count Occurrences/CountOccurrences.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Counting Sort/CountingSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Counting Sort/CountingSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Counting Sort/CountingSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Depth-First Search/DepthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Depth-First Search/DepthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Depth-First Search/DepthFirstSearch.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Deque/Deque.playground/playground.xcworkspace/contents.xcworkspacedata b/Deque/Deque.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Deque/Deque.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/GCD/GCD.playground/playground.xcworkspace/contents.xcworkspacedata b/GCD/GCD.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/GCD/GCD.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Graph/Graph.playground/playground.xcworkspace/contents.xcworkspacedata b/Graph/Graph.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Graph/Graph.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Hash Set/HashSet.playground/playground.xcworkspace/contents.xcworkspacedata b/Hash Set/HashSet.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Hash Set/HashSet.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Hash Table/HashTable.playground/playground.xcworkspace/contents.xcworkspacedata b/Hash Table/HashTable.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Hash Table/HashTable.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Huffman Coding/Huffman.playground/playground.xcworkspace/contents.xcworkspacedata b/Huffman Coding/Huffman.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Huffman Coding/Huffman.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Insertion Sort/InsertionSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Insertion Sort/InsertionSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Insertion Sort/InsertionSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Kth Largest Element/kthLargest.playground/playground.xcworkspace/contents.xcworkspacedata b/Kth Largest Element/kthLargest.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Kth Largest Element/kthLargest.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Linear Search/LinearSearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Linear Search/LinearSearch.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Linear Search/LinearSearch.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Linked List/LinkedList.playground/playground.xcworkspace/contents.xcworkspacedata b/Linked List/LinkedList.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Linked List/LinkedList.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/playground.xcworkspace/contents.xcworkspacedata b/Longest Common Subsequence/LongestCommonSubsequence.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Merge Sort/MergeSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Merge Sort/MergeSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Merge Sort/MergeSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Monty Hall Problem/MontyHall.playground/playground.xcworkspace/contents.xcworkspacedata b/Monty Hall Problem/MontyHall.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Monty Hall Problem/MontyHall.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Ordered Array/OrderedArray.playground/playground.xcworkspace/contents.xcworkspacedata b/Ordered Array/OrderedArray.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Ordered Array/OrderedArray.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata b/Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Queue/Queue.playground/playground.xcworkspace/contents.xcworkspacedata b/Queue/Queue.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Queue/Queue.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Queue/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Quicksort/Quicksort.playground/playground.xcworkspace/contents.xcworkspacedata b/Quicksort/Quicksort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Quicksort/Quicksort.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Radix Tree/RadixTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Radix Tree/RadixTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Radix Tree/RadixTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Ring Buffer/RingBuffer.playground/playground.xcworkspace/contents.xcworkspacedata b/Ring Buffer/RingBuffer.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Ring Buffer/RingBuffer.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Run-Length Encoding/RLE.playground/playground.xcworkspace/contents.xcworkspacedata b/Run-Length Encoding/RLE.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Run-Length Encoding/RLE.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Segment Tree/SegmentTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Segment Tree/SegmentTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Segment Tree/SegmentTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/playground.xcworkspace/contents.xcworkspacedata b/Select Minimum Maximum/SelectMinimumMaximum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Select Minimum Maximum/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Select Minimum Maximum/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Select Minimum Maximum/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Selection Sampling/SelectionSampling.playground/playground.xcworkspace/contents.xcworkspacedata b/Selection Sampling/SelectionSampling.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Selection Sampling/SelectionSampling.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Selection Sort/SelectionSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Selection Sort/SelectionSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Selection Sort/SelectionSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Selection Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Selection Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Selection Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Shell Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Shell Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Shell Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/playground.xcworkspace/contents.xcworkspacedata b/Shortest Path (Unweighted)/ShortestPath.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Shuffle/Shuffle.playground/playground.xcworkspace/contents.xcworkspacedata b/Shuffle/Shuffle.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Shuffle/Shuffle.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/contents.xcworkspacedata b/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Stack/Stack.playground/playground.xcworkspace/contents.xcworkspacedata b/Stack/Stack.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Stack/Stack.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Topological Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Topological Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Topological Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Topological Sort/Topological Sort.playground/playground.xcworkspace/contents.xcworkspacedata b/Topological Sort/Topological Sort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Topological Sort/Topological Sort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Tree/Tree.playground/playground.xcworkspace/contents.xcworkspacedata b/Tree/Tree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Tree/Tree.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata b/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata b/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Union-Find/UnionFind.playground/playground.xcworkspace/contents.xcworkspacedata b/Union-Find/UnionFind.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Union-Find/UnionFind.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 4ab746d22aef252ba3b966c28c41b2dd774580a0 Mon Sep 17 00:00:00 2001
From: Andrew McKnight <amcknight2718@gmail.com>
Date: Mon, 9 May 2016 08:36:25 -0400
Subject: [PATCH 0359/1679] add xcworkspace

---
 .../playground.xcworkspace/contents.xcworkspacedata    |  7 +++++++
 .../xcshareddata/WorkspaceSettings.xcsettings          |  8 ++++++++
 .../APSP/APSP.xcworkspace/contents.xcworkspacedata     | 10 ++++++++++
 .../xcshareddata/WorkspaceSettings.xcsettings          |  8 ++++++++
 4 files changed, 33 insertions(+)
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcworkspace/contents.xcworkspacedata
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/playground.xcworkspace/contents.xcworkspacedata b/All-Pairs Shortest Paths/APSP/APSP.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/contents.xcworkspacedata b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..615e34ecd
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,10 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "group:APSP.playground">
+   </FileRef>
+   <FileRef
+      location = "container:APSP.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>

From 47249d08f7b99d1672096ef7c9c2a3ea894a4d90 Mon Sep 17 00:00:00 2001
From: Kevin Connor <kevin@striiv.com>
Date: Thu, 12 May 2016 12:30:21 -0700
Subject: [PATCH 0360/1679] fix broken link

---
 Shortest Path (Unweighted)/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Shortest Path (Unweighted)/README.markdown b/Shortest Path (Unweighted)/README.markdown
index 64ae52a80..0107964ae 100644
--- a/Shortest Path (Unweighted)/README.markdown	
+++ b/Shortest Path (Unweighted)/README.markdown	
@@ -97,6 +97,6 @@ This will output:
 	Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
 	Node(label: g, distance: 2), Node(label: h, distance: 3)
 
-> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum Spanning Tree/) on how you can convert the graph into a tree by removing edges.
+> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum Spanning Tree (Unweighted)/) on how you can convert the graph into a tree by removing edges.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*

From b41213f8a9ec0f130d9121c50a7f1d608efb26e2 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 14 May 2016 17:36:49 +1200
Subject: [PATCH 0361/1679] Updating build status badge to point to
 RayWenderlich repository

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index e3d9fd9cf..1c7ca4300 100644
--- a/README.markdown
+++ b/README.markdown
@@ -210,4 +210,4 @@ Other algorithm repositories:
 
 All content is licensed under the terms of the MIT open source license.
 
-[![Build Status](https://travis-ci.org/hollance/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/hollance/swift-algorithm-club)
+[![Build Status](https://travis-ci.org/raywenderlich/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/raywenderlich/swift-algorithm-club)

From 4c7920d581cd9e4aa7388f3710ee72d36aaea364 Mon Sep 17 00:00:00 2001
From: Vinay Jain <vinay.jn7@gmail.com>
Date: Tue, 17 May 2016 18:51:16 +0530
Subject: [PATCH 0362/1679] Replaced Array2D with Swift inbuilt 2D array

---
 Combinatorics/Combinatorics.swift | 31 ++++++++++++++++---------------
 1 file changed, 16 insertions(+), 15 deletions(-)

diff --git a/Combinatorics/Combinatorics.swift b/Combinatorics/Combinatorics.swift
index eb67fb53f..de82618c3 100644
--- a/Combinatorics/Combinatorics.swift
+++ b/Combinatorics/Combinatorics.swift
@@ -100,21 +100,22 @@ func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
   the calculation of much larger numbers, at the cost of temporary storage
   space for the cached values.
 */
+
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array2D(columns: n + 1, rows: n + 1, initialValue: 0)
-  
-  for i in 0...n {
-    bc[i, 0] = 1
-    bc[i, i] = 1
-  }
-  
-  if n > 0 {
-    for i in 1...n {
-      for j in 1..<i {
-        bc[i, j] = bc[i - 1, j - 1] + bc[i - 1, j]
-      }
+    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+    
+    for i in 0...n {
+        bc[i][0] = 1
+        bc[i][i] = 1
     }
-  }
-  
-  return bc[n, k]
+    
+    if n > 0 {
+        for i in 1...n {
+            for j in 1..<i {
+                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+            }
+        }
+    }
+    
+    return bc[n][k]
 }

From 002f9c652bbfbce0df366c769d61fb2258a82250 Mon Sep 17 00:00:00 2001
From: Vinay Jain <vinay.jn7@gmail.com>
Date: Tue, 17 May 2016 18:52:58 +0530
Subject: [PATCH 0363/1679] Updated ReadMe

Replaced Array2D with Swift inbuilt 2D array
---
 Combinatorics/README.markdown | 32 ++++++++++++++++----------------
 1 file changed, 16 insertions(+), 16 deletions(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 6e16e93c3..45e48693d 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -366,26 +366,26 @@ The following code calculates Pascal's triangle in order to find the `C(n, k)` y
 
 ```swift
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array2D(columns: n + 1, rows: n + 1, initialValue: 0)
-
-  for i in 0...n {
-    bc[i, 0] = 1
-    bc[i, i] = 1
-  }
-
-  if n > 0 {
-    for i in 1...n {
-      for j in 1..<i {
-        bc[i, j] = bc[i - 1, j - 1] + bc[i - 1, j]
-      }
+    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+    
+    for i in 0...n {
+        bc[i][0] = 1
+        bc[i][i] = 1
     }
-  }
-
-  return bc[n, k]
+    
+    if n > 0 {
+        for i in 1...n {
+            for j in 1..<i {
+                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+            }
+        }
+    }
+    
+    return bc[n][k]
 }
 ```
 
-This uses [Array2D](../Array2D/) as helper code because Swift doesn't have a built-in two-dimensional array. The algorithm itself is quite simple: the first loop fills in the 1s at the outer edges of the triangle. The other loops calculate each number in the triangle by adding up the two numbers from the previous row.
+The algorithm itself is quite simple: the first loop fills in the 1s at the outer edges of the triangle. The other loops calculate each number in the triangle by adding up the two numbers from the previous row.
 
 Now you can calculate `C(66, 33)` without any problems:
 

From 2d3238cda763a7319ed37af3c6c5e76973c8c33c Mon Sep 17 00:00:00 2001
From: Vinay Jain <vinay.jn7@gmail.com>
Date: Fri, 20 May 2016 16:07:35 +0530
Subject: [PATCH 0364/1679] Changed Array2d to Swift standard 2d array in
 playground

---
 .../Combinatorics.playground/Contents.swift   | 205 +++++++++---------
 1 file changed, 103 insertions(+), 102 deletions(-)

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 2cafaa0c1..1ac77a5c4 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -2,13 +2,13 @@
 
 /* Calculates n! */
 func factorial(n: Int) -> Int {
-  var n = n
-  var result = 1
-  while n > 1 {
-    result *= n
-    n -= 1
-  }
-  return result
+    var n = n
+    var result = 1
+    while n > 1 {
+        result *= n
+        n -= 1
+    }
+    return result
 }
 
 factorial(5)
@@ -17,17 +17,17 @@ factorial(20)
 
 
 /*
-  Calculates P(n, k), the number of permutations of n distinct symbols
-  in groups of size k.
-*/
+ Calculates P(n, k), the number of permutations of n distinct symbols
+ in groups of size k.
+ */
 func permutations(n: Int, _ k: Int) -> Int {
-  var n = n
-  var answer = n
-  for _ in 1..<k {
-    n -= 1
-    answer *= n
-  }
-  return answer
+    var n = n
+    var answer = n
+    for _ in 1..<k {
+        n -= 1
+        answer *= n
+    }
+    return answer
 }
 
 permutations(5, 3)
@@ -37,22 +37,22 @@ permutations(9, 4)
 
 
 /*
-  Prints out all the permutations of the given array.
-  Original algorithm by Niklaus Wirth.
-  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
-*/
+ Prints out all the permutations of the given array.
+ Original algorithm by Niklaus Wirth.
+ See also Dr.Dobb's Magazine June 1993, Algorithm Alley
+ */
 func permuteWirth<T>(a: [T], _ n: Int) {
-  if n == 0 {
-    print(a)   // display the current permutation
-  } else {
-    var a = a
-    permuteWirth(a, n - 1)
-    for i in 0..<n {
-      swap(&a[i], &a[n])
-      permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
+    if n == 0 {
+        print(a)   // display the current permutation
+    } else {
+        var a = a
+        permuteWirth(a, n - 1)
+        for i in 0..<n {
+            swap(&a[i], &a[n])
+            permuteWirth(a, n - 1)
+            swap(&a[i], &a[n])
+        }
     }
-  }
 }
 
 let letters = ["a", "b", "c", "d", "e"]
@@ -66,30 +66,30 @@ permuteWirth(xyz, 2)
 
 
 /*
-  Prints out all the permutations of an n-element collection.
-
-  The initial array must be initialized with all zeros. The algorithm
-  uses 0 as a flag that indicates more work to be done on each level
-  of the recursion.
-
-  Original algorithm by Robert Sedgewick.
-  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
-*/
+ Prints out all the permutations of an n-element collection.
+ 
+ The initial array must be initialized with all zeros. The algorithm
+ uses 0 as a flag that indicates more work to be done on each level
+ of the recursion.
+ 
+ Original algorithm by Robert Sedgewick.
+ See also Dr.Dobb's Magazine June 1993, Algorithm Alley
+ */
 func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
-  var a = a
-  pos += 1
-  a[n] = pos
-  if pos == a.count - 1 {
-    print(a)              // display the current permutation
-  } else {
-    for i in 0..<a.count {
-      if a[i] == 0 {
-        permuteSedgewick(a, i, &pos)
-      }
+    var a = a
+    pos += 1
+    a[n] = pos
+    if pos == a.count - 1 {
+        print(a)              // display the current permutation
+    } else {
+        for i in 0..<a.count {
+            if a[i] == 0 {
+                permuteSedgewick(a, i, &pos)
+            }
+        }
     }
-  }
-  pos -= 1
-  a[n] = 0
+    pos -= 1
+    a[n] = 0
 }
 
 print("\nSedgewick permutations:")
@@ -100,11 +100,11 @@ permuteSedgewick(numbers, 0, &pos)
 
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. how many different selections
-  of size k out of a total number of distinct elements (n) you can make.
-*/
+ Calculates C(n, k), or "n-choose-k", i.e. how many different selections
+ of size k out of a total number of distinct elements (n) you can make.
+ */
 func combinations(n: Int, _ k: Int) -> Int {
-  return permutations(n, k) / factorial(k)
+    return permutations(n, k) / factorial(k)
 }
 
 combinations(3, 2)
@@ -112,23 +112,23 @@ combinations(28, 5)
 
 print("\nCombinations:")
 for i in 1...20 {
-  print("\(20)-choose-\(i) = \(combinations(20, i))")
+    print("\(20)-choose-\(i) = \(combinations(20, i))")
 }
 
 
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-  k things out of n possibilities.
-*/
+ Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+ k things out of n possibilities.
+ */
 func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
-  var result = 1
+    var result = 1
     
-  for i in 0..<k {
-    result *= (n - i)
-    result /= (i + 1)
-  }
-  return result
+    for i in 0..<k {
+        result *= (n - i)
+        result /= (i + 1)
+    }
+    return result
 }
 
 quickBinomialCoefficient(8, 2)
@@ -138,47 +138,48 @@ quickBinomialCoefficient(30, 15)
 
 /* Supporting code because Swift doesn't have a built-in 2D array. */
 struct Array2D<T> {
-  let columns: Int
-  let rows: Int
-  private var array: [T]
-  
-  init(columns: Int, rows: Int, initialValue: T) {
-    self.columns = columns
-    self.rows = rows
-    array = .init(count: rows*columns, repeatedValue: initialValue)
-  }
-  
-  subscript(column: Int, row: Int) -> T {
-    get { return array[row*columns + column] }
-    set { array[row*columns + column] = newValue }
-  }
+    let columns: Int
+    let rows: Int
+    private var array: [T]
+    
+    init(columns: Int, rows: Int, initialValue: T) {
+        self.columns = columns
+        self.rows = rows
+        array = .init(count: rows*columns, repeatedValue: initialValue)
+    }
+    
+    subscript(column: Int, row: Int) -> T {
+        get { return array[row*columns + column] }
+        set { array[row*columns + column] = newValue }
+    }
 }
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-  k things out of n possibilities.
+ Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+ k things out of n possibilities.
+ 
+ Thanks to the dynamic programming, this algorithm from Skiena allows for
+ the calculation of much larger numbers, at the cost of temporary storage
+ space for the cached values.
+ */
 
-  Thanks to the dynamic programming, this algorithm from Skiena allows for
-  the calculation of much larger numbers, at the cost of temporary storage
-  space for the cached values.
-*/
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array2D(columns: n + 1, rows: n + 1, initialValue: 0)
-  
-  for i in 0...n {
-    bc[i, 0] = 1
-    bc[i, i] = 1
-  }
-  
-  if n > 0 {
-    for i in 1...n {
-      for j in 1..<i {
-        bc[i, j] = bc[i - 1, j - 1] + bc[i - 1, j]
-      }
+    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+    
+    for i in 0...n {
+        bc[i][0] = 1
+        bc[i][i] = 1
     }
-  }
-  
-  return bc[n, k]
+    
+    if n > 0 {
+        for i in 1...n {
+            for j in 1..<i {
+                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+            }
+        }
+    }
+    
+    return bc[n][k]
 }
 
 binomialCoefficient(30, 15)

From 0a7781df36b78d734d5545457dbee6c9fb3015e6 Mon Sep 17 00:00:00 2001
From: Marcio Klepacz <marcioklepacz@gmail.com>
Date: Wed, 25 May 2016 11:48:11 +0200
Subject: [PATCH 0365/1679] Adds AlgorithmVisualizer to README

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index e3d9fd9cf..ab309f724 100644
--- a/README.markdown
+++ b/README.markdown
@@ -205,6 +205,7 @@ Other algorithm repositories:
 - [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
 - [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
 - [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
+- [AlgorithmVisualizer](http://jasonpark.me/AlgorithmVisualizer/). Visualize algorithms on your browser.
 
 ## License
 

From 5234381da1e6a85f1b405a458880dca47f5c910a Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 25 May 2016 23:29:50 +1200
Subject: [PATCH 0366/1679] Removing B-Tree as it has no content and has not
 been updated in 3 months.

---
 B Tree/README.markdown | 8 --------
 README.markdown        | 2 +-
 2 files changed, 1 insertion(+), 9 deletions(-)
 delete mode 100644 B Tree/README.markdown

diff --git a/B Tree/README.markdown b/B Tree/README.markdown
deleted file mode 100644
index a96d59be2..000000000
--- a/B Tree/README.markdown	
+++ /dev/null
@@ -1,8 +0,0 @@
-# B Tree
-
-Under Construction.
-
-See also [Wikipedia](https://en.wikipedia.org/wiki/B-tree).
-
-*Written by Jeroen Houtzager*
-
diff --git a/README.markdown b/README.markdown
index 1c7ca4300..65c3b2b0d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -151,7 +151,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - Trie
-- [B-Tree](B Tree/) :construction:
+- B-Tree
 - [Radix Tree](Radix Tree/) :construction:
 
 ### Hashing

From 636fee82741d6f1bae1f28177d0008ee34afd44f Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 26 May 2016 22:56:15 +1200
Subject: [PATCH 0367/1679] Bounded Priority Queue - adding updated
 implementation from Matthijs + updating readme

---
 .../Contents.swift                            | 104 ++++++++++
 .../Sources/BoundedPriorityQueue.swift        | 137 ++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../BoundedPriorityQueue.swift                | 145 ++++++++-----
 Bounded Priority Queue/README.markdown        | 143 ++++++++-----
 .../Tests/BoundedPriorityQueueTests.swift     | 196 +++++++++---------
 7 files changed, 528 insertions(+), 208 deletions(-)
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
new file mode 100644
index 000000000..b4977d6ce
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -0,0 +1,104 @@
+struct Message: Comparable, CustomStringConvertible {
+  let name: String
+  let priority: Int
+  
+  var description: String {
+    return "\(name):\(priority)"
+  }
+}
+
+func ==(m1: Message, m2: Message) -> Bool {
+  return m1.priority == m2.priority
+}
+
+func <(m1: Message, m2: Message) -> Bool {
+  return m1.priority < m2.priority
+}
+
+
+
+let queue = BoundedPriorityQueue<Message>(maxElements: 5)
+queue.count
+
+queue.enqueue(Message(name: "hello", priority: 100))
+queue.count
+queue.peek()
+print(queue)
+
+queue.enqueue(Message(name: "there", priority: 99))
+queue.count
+queue.peek()
+print(queue)
+
+queue.enqueue(Message(name: "world", priority: 150))
+queue.count
+queue.peek()
+print(queue)
+
+queue.enqueue(Message(name: "swift", priority: 110))
+queue.count
+queue.peek()
+print(queue)
+
+queue.enqueue(Message(name: "is", priority: 30))
+queue.count
+queue.peek()
+print(queue)
+
+// At this point, the queue is:
+// <world:150, swift:110, hello:100, there:99, is:30, >
+
+
+
+// Try to insert an item with a really low priority. This should not get added.
+queue.enqueue(Message(name: "very", priority: -1))
+queue.count    // 5
+queue.peek()
+print(queue)   // still same as before
+
+// Try to insert an item with medium priority. This gets added and the lowest
+// priority item is removed.
+queue.enqueue(Message(name: "cool", priority: 120))
+queue.count
+queue.peek()
+print(queue)
+
+// Try to insert an item with very high priority. This gets added and the 
+// lowest priority item is removed.
+queue.enqueue(Message(name: "!!!", priority: 500))
+queue.count
+queue.peek()
+print(queue)
+
+
+
+// Test dequeuing
+queue.dequeue()
+queue.count
+queue.peek()
+print(queue)
+
+queue.dequeue()
+queue.count
+queue.peek()
+print(queue)
+
+queue.dequeue()
+queue.count
+queue.peek()
+print(queue)
+
+queue.dequeue()
+queue.count
+queue.peek()
+print(queue)
+
+queue.dequeue()
+queue.count
+queue.peek()
+print(queue)
+
+queue.dequeue()
+queue.count
+queue.peek()
+print(queue)
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift
new file mode 100644
index 000000000..99f00d70c
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
@@ -0,0 +1,137 @@
+public class LinkedListNode<T: Comparable> {
+  var value: T
+  var next: LinkedListNode?
+  var previous: LinkedListNode?
+  
+  public init(value: T) {
+    self.value = value
+  }
+}
+
+public class BoundedPriorityQueue<T: Comparable> {
+  private typealias Node = LinkedListNode<T>
+
+  private(set) public var count = 0
+  private var head: Node?
+  private var tail: Node?
+  private var maxElements: Int
+
+  public init(maxElements: Int) {
+    self.maxElements = maxElements
+  }
+
+  public var isEmpty: Bool {
+    return count == 0
+  }
+
+  public func peek() -> T? {
+    return head?.value
+  }
+
+  public func enqueue(value: T) {
+    if let node = insert(value, after: findInsertionPoint(value)) {
+      // If the newly inserted node is the last one in the list, then update
+      // the tail pointer.
+      if node.next == nil {
+        tail = node
+      }
+
+      // If the queue is full, then remove an element from the back.
+      count += 1
+      if count > maxElements {
+        removeLeastImportantElement()
+      }
+    }
+  }
+
+  private func insert(value: T, after: Node?) -> Node? {
+    if let previous = after {
+
+      // If the queue is full and we have to insert at the end of the list,
+      // then there's no reason to insert the new value.
+      if count == maxElements && previous.next == nil {
+        print("Queue is full and priority of new object is too small")
+        return nil
+      }
+
+      // Put the new node in between previous and previous.next (if exists).
+      let node = Node(value: value)
+      node.next = previous.next
+      previous.next?.previous = node
+      previous.next = node
+      node.previous = previous
+      return node
+    
+    } else if let first = head {
+      // Have to insert at the head, so shift the existing head up once place.
+      head = Node(value: value)
+      head!.next = first
+      first.previous = head
+      return head
+
+    } else {
+      // This is the very first item in the queue.
+      head = Node(value: value)
+      return head
+    }
+  }
+
+  /* Find the node after which to insert the new value. If this returns nil,
+     the new value should be inserted at the head of the list. */
+  private func findInsertionPoint(value: T) -> Node? {
+    var node = head
+    var prev: Node? = nil
+    
+    while let current = node where value < current.value {
+      prev = node
+      node = current.next
+    }
+    return prev
+  }
+
+  private func removeLeastImportantElement() {
+    if let last = tail {
+      tail = last.previous
+      tail?.next = nil
+      count -= 1
+    }
+
+    // Note: Instead of using a tail pointer, we could just scan from the new
+    // node until the end. Then nodes also don't need a previous pointer. But
+    // this is much slower on large lists.
+  }
+
+  public func dequeue() -> T? {
+    if let first = head {
+      count -= 1
+      if count == 0 {
+        head = nil
+        tail = nil
+      } else {
+        head = first.next
+        head!.previous = nil
+      }
+      return first.value
+    } else {
+      return nil
+    }
+  }
+}
+
+extension LinkedListNode: CustomStringConvertible {
+  public var description: String {
+    return "\(value)"
+  }
+}
+
+extension BoundedPriorityQueue: CustomStringConvertible {
+  public var description: String {
+    var s = "<"
+    var node = head
+    while let current = node {
+      s += "\(current), "
+      node = current.next
+    }
+    return s + ">"
+  }
+}
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground b/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/contents.xcworkspacedata b/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.swift
index abee9e526..fbd8d5450 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.swift	
@@ -1,18 +1,10 @@
-//
-//  BoundedPriorityQueue.swift
-//
-//  Created by John Gill on 2/28/16.
-//
-
 public class LinkedListNode<T: Comparable> {
   var value: T
   var next: LinkedListNode?
   var previous: LinkedListNode?
-  
+
   public init(value: T) {
     self.value = value
-    self.next = nil
-    self.previous = nil
   }
 }
 
@@ -21,6 +13,7 @@ public class BoundedPriorityQueue<T: Comparable> {
 
   private(set) public var count = 0
   private var head: Node?
+  private var tail: Node?
   private var maxElements: Int
 
   public init(maxElements: Int) {
@@ -36,63 +29,109 @@ public class BoundedPriorityQueue<T: Comparable> {
   }
 
   public func enqueue(value: T) {
-    let newNode = Node(value: value)
+    if let node = insert(value, after: findInsertionPoint(value)) {
+      // If the newly inserted node is the last one in the list, then update
+      // the tail pointer.
+      if node.next == nil {
+        tail = node
+      }
 
-    if head == nil  {
-      head = newNode
-      count = 1
-      return
+      // If the queue is full, then remove an element from the back.
+      count += 1
+      if count > maxElements {
+        removeLeastImportantElement()
+      }
     }
+  }
 
-    var node = head
-    if count == maxElements && newNode.value > node!.value {
-      return
-    }
-    
-    while (node!.next != nil) && (newNode.value < node!.value) {
-      node = node!.next
-    }
-    
-    if newNode.value < node!.value {
-      newNode.next = node!.next
-      newNode.previous = node
-      
-      if newNode.next != nil {     /* TAIL */
-        newNode.next!.previous = newNode
+  private func insert(value: T, after: Node?) -> Node? {
+    if let previous = after {
+
+      // If the queue is full and we have to insert at the end of the list,
+      // then there's no reason to insert the new value.
+      if count == maxElements && previous.next == nil {
+        print("Queue is full and priority of new object is too small")
+        return nil
       }
-      node!.next = newNode
+
+      // Put the new node in between previous and previous.next (if exists).
+      let node = Node(value: value)
+      node.next = previous.next
+      previous.next?.previous = node
+      previous.next = node
+      node.previous = previous
+      return node
+
+    } else if let first = head {
+      // Have to insert at the head, so shift the existing head up once place.
+      head = Node(value: value)
+      head!.next = first
+      first.previous = head
+      return head
+
     } else {
-      newNode.previous = node!.previous
-      newNode.next = node
-      if node!.previous == nil {   /* HEAD */
-        head = newNode
-      } else {
-        node!.previous!.next = newNode
-      }
-      node!.previous = newNode
+      // This is the very first item in the queue.
+      head = Node(value: value)
+      return head
     }
+  }
+
+  /* Find the node after which to insert the new value. If this returns nil,
+   the new value should be inserted at the head of the list. */
+  private func findInsertionPoint(value: T) -> Node? {
+    var node = head
+    var prev: Node? = nil
 
-    if count == maxElements {
-      dequeue()
+    while let current = node where value < current.value {
+      prev = node
+      node = current.next
     }
-    count += 1
+    return prev
   }
-  
-  public func dequeue() -> T? {
-    if count == 0 {
-      return nil
+
+  private func removeLeastImportantElement() {
+    if let last = tail {
+      tail = last.previous
+      tail?.next = nil
+      count -= 1
     }
 
-    let retVal = head!.value
-    
-    if count == 1 {
-      head = nil
+    // Note: Instead of using a tail pointer, we could just scan from the new
+    // node until the end. Then nodes also don't need a previous pointer. But
+    // this is much slower on large lists.
+  }
+
+  public func dequeue() -> T? {
+    if let first = head {
+      count -= 1
+      if count == 0 {
+        head = nil
+        tail = nil
+      } else {
+        head = first.next
+        head!.previous = nil
+      }
+      return first.value
     } else {
-      head = head!.next
-      head!.previous = nil
+      return nil
     }
+  }
+}
+
+extension LinkedListNode: CustomStringConvertible {
+  public var description: String {
+    return "\(value)"
+  }
+}
 
-    count -= 1
-    return retVal
+extension BoundedPriorityQueue: CustomStringConvertible {
+  public var description: String {
+    var s = "<"
+    var node = head
+    while let current = node {
+      s += "\(current), "
+      node = current.next
+    }
+    return s + ">"
   }
 }
diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
index b62d87678..8d6ea1804 100644
--- a/Bounded Priority Queue/README.markdown	
+++ b/Bounded Priority Queue/README.markdown	
@@ -7,22 +7,22 @@ A bounded priority queue is similar to a regular [priority queue](../Priority Qu
 Suppose we have a bounded-priority-queue with maximum size 5 that has the following values and priorities:
 
 ```
-Value:    [ A,   B,    C,    D,   E   ]
-Priority: [ 0.1, 0.25, 1.33, 3.2, 4.6 ]
+Value:    [ A,   B,   C,    D,    E   ]
+Priority: [ 4.6, 3.2, 1.33, 0.25, 0.1 ]
 ```
 
-Here, we consider the object with the lowest priority value to be the most important (so this is a *min-priority* queue). The larger the priority value, the less we care about the object. So `A` is more important than `B`, `B` is more important than `C`, and so on.
+Here, we consider the object with the highest priority value to be the most important (so this is a *max-priority* queue). The larger the priority value, the more we care about the object. So `A` is more important than `B`, `B` is more important than `C`, and so on.
 
 Now we want to insert the element `F` with priority `0.4` into this bounded priority queue. Because the queue has maximum size 5, this will insert the element `F` but then evict the lowest-priority element (`E`), yielding the updated queue:
 
 ```
-Value:    [ A,   B,    F,   C,    D   ]
-Priority: [ 0.1, 0.25, 0.4, 1.33, 3.2 ]
+Value:    [ A,   B,   C,    F,   D    ]
+Priority: [ 4.6, 3.2, 1.33, 0.4, 0.25 ]
 ```
 
-`F` is inserted between `B` and `C` because of its priority value. It's less important than `B` but more important than `C`.
+`F` is inserted between `C` and `D` because of its priority value. It's less important than `C` but more important than `D`.
 
-Suppose that we wish to insert the element `G` with priority 4.0 into this BPQ. Because `G`'s priority value is greater than the maximum-priority element in the queue, upon inserting `G` it will immediately be evicted. In other words, inserting an element into a BPQ with priority greater than the maximum-priority element of the BPQ has no effect.
+Suppose that we wish to insert the element `G` with priority 0.1 into this BPQ. Because `G`'s priority value is less than the minimum-priority element in the queue, upon inserting `G` it will immediately be evicted. In other words, inserting an element into a BPQ with priority less than the minimum-priority element of the BPQ has no effect.
 
 ## Implementation
 
@@ -36,69 +36,100 @@ public class BoundedPriorityQueue<T: Comparable> {
 
   private(set) public var count = 0
   private var head: Node?
+  private var tail: Node?
   private var maxElements: Int
 
   public init(maxElements: Int) {
     self.maxElements = maxElements
   }
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
 
   public func peek() -> T? {
     return head?.value
-  } 
+  }
 ```
 
 The `BoundedPriorityQueue` class contains a doubly linked list of `LinkedListNode` objects. Nothing special here yet. The fun stuff happens in the `enqueue()` method:
 
 ```swift
-  public func enqueue(value: T) {
-    let newNode = Node(value: value)
-
-    if head == nil  {
-      head = newNode
-      count = 1
-      return
+public func enqueue(value: T) {
+  if let node = insert(value, after: findInsertionPoint(value)) {
+    // If the newly inserted node is the last one in the list, then update
+    // the tail pointer.
+    if node.next == nil {
+      tail = node
     }
 
-    var node = head
-    if count == maxElements && newNode.value > node!.value {
-      return
-    }
-    
-    while (node!.next != nil) && (newNode.value < node!.value) {
-      node = node!.next
-    }
-    
-    if newNode.value < node!.value {
-      newNode.next = node!.next
-      newNode.previous = node
-      
-      if newNode.next != nil {     /* TAIL */
-        newNode.next!.previous = newNode
-      }
-      node!.next = newNode
-    } else {
-      newNode.previous = node!.previous
-      newNode.next = node
-      if node!.previous == nil {   /* HEAD */
-        head = newNode
-      } else {
-        node!.previous!.next = newNode
-      }
-      node!.previous = newNode
+    // If the queue is full, then remove an element from the back.
+    count += 1
+    if count > maxElements {
+      removeLeastImportantElement()
     }
+  }
+}
+
+private func insert(value: T, after: Node?) -> Node? {
+  if let previous = after {
 
-    if count == maxElements {
-      dequeue()
+    // If the queue is full and we have to insert at the end of the list,
+    // then there's no reason to insert the new value.
+    if count == maxElements && previous.next == nil {
+      print("Queue is full and priority of new object is too small")
+      return nil
     }
-    count += 1
+
+    // Put the new node in between previous and previous.next (if exists).
+    let node = Node(value: value)
+    node.next = previous.next
+    previous.next?.previous = node
+    previous.next = node
+    node.previous = previous
+    return node
+
+  } else if let first = head {
+    // Have to insert at the head, so shift the existing head up once place.
+    head = Node(value: value)
+    head!.next = first
+    first.previous = head
+    return head
+
+  } else {
+    // This is the very first item in the queue.
+    head = Node(value: value)
+    return head
   }
+}
+
+/* Find the node after which to insert the new value. If this returns nil,
+   the new value should be inserted at the head of the list. */
+private func findInsertionPoint(value: T) -> Node? {
+  var node = head
+  var prev: Node? = nil
+
+  while let current = node where value < current.value {
+    prev = node
+    node = current.next
+  }
+  return prev
+}
+
+private func removeLeastImportantElement() {
+  if let last = tail {
+    tail = last.previous
+    tail?.next = nil
+    count -= 1
+  }
+
+  // Note: Instead of using a tail pointer, we could just scan from the new
+  // node until the end. Then nodes also don't need a previous pointer. But
+  // this is much slower on large lists.
+}
 ```
 
-We first check if the queue already has the maximum number of elements. If so, and the new priority value is greater than the `head` element's priority value, then there is no room for this new element and we return without inserting it.
+We first check if the queue already has the maximum number of elements. If so, and the new priority value is less than the `tail` element's priority value, then there is no room for this new element and we return without inserting it.
 
 If the new value is acceptable, then we search through the list to find the proper insertion location and update the `next` and `previous` pointers.
 
@@ -107,23 +138,21 @@ Lastly, if the queue has now reached the maximum number of elements, then we `de
 By keeping the most important element at the front of the list, it makes dequeueing very easy:
 
 ```swift
-  public func dequeue() -> T? {
+public func dequeue() -> T? {
+  if let first = head {
+    count -= 1
     if count == 0 {
-      return nil
-    }
-
-    let retVal = head!.value
-    
-    if count == 1 {
       head = nil
+      tail = nil
     } else {
-      head = head!.next
+      head = first.next
       head!.previous = nil
     }
-
-    count -= 1
-    return retVal
+    return first.value
+  } else {
+    return nil
   }
+}
 ```
 
 This simply removes the `head` element from the list and returns it.
diff --git a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift
index 772999e84..c6ab5d554 100644
--- a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
+++ b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
@@ -8,114 +8,114 @@ import Foundation
 import XCTest
 
 private struct Message: Comparable {
-    let name: String
-    let priority: Int
+  let name: String
+  let priority: Int
 }
 
 private func ==(m1: Message, m2: Message) -> Bool {
-    return m1.priority == m2.priority
+  return m1.priority == m2.priority
 }
 
 private func <(m1: Message, m2: Message) -> Bool {
-    return m1.priority < m2.priority
+  return m1.priority < m2.priority
 }
 
 private func >(m1: Message, m2: Message) -> Bool {
-    return m1.priority > m2.priority
+  return m1.priority > m2.priority
 }
 
 class BoundedPriorityQueueTest: XCTestCase {
-    func testEmpty() {
-        let queue = BoundedPriorityQueue<Message>(maxElements: 5)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.dequeue())
-    }
-
-    func testOneElement() {
-        let queue = BoundedPriorityQueue<Message>(maxElements: 5)
-
-        queue.enqueue(Message(name: "hello", priority: 100))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-
-        let result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 100)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-    }
-
-    func testMaxElements() {
-        let queue = BoundedPriorityQueue<Message>(maxElements: 5)
-        XCTAssertTrue(queue.isEmpty)
-
-        queue.enqueue(Message(name: "john", priority: 100))
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()?.priority, 100)
-
-        queue.enqueue(Message(name: "james", priority: 200))
-        XCTAssertEqual(queue.count, 2)
-        XCTAssertEqual(queue.peek()?.priority, 200)
-
-        queue.enqueue(Message(name: "mark", priority: 300))
-        XCTAssertEqual(queue.count, 3)
-        XCTAssertEqual(queue.peek()?.priority, 300)
-
-        queue.enqueue(Message(name: "ken", priority: 400))
-        XCTAssertEqual(queue.count, 4)
-        XCTAssertEqual(queue.peek()?.priority, 400)
-
-        queue.enqueue(Message(name: "thomas", priority: 500))
-        XCTAssertEqual(queue.count, 5)
-        XCTAssertEqual(queue.peek()?.priority, 500)
-
-        queue.enqueue(Message(name: "melanie", priority: 550))
-        XCTAssertEqual(queue.count, 5)
-        XCTAssertEqual(queue.peek()?.priority, 500)
-
-        queue.enqueue(Message(name: "lily", priority: 450))
-        XCTAssertEqual(queue.count, 5)
-        XCTAssertEqual(queue.peek()?.priority, 450)
-
-        queue.enqueue(Message(name: "fred", priority: 350))
-        XCTAssertEqual(queue.count, 5)
-        XCTAssertEqual(queue.peek()?.priority, 400)
-
-        queue.enqueue(Message(name: "rachel", priority: 50))
-        XCTAssertEqual(queue.count, 5)
-        XCTAssertEqual(queue.peek()?.priority, 350)
-
-        var result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 350)
-        XCTAssertEqual(queue.count, 4)
-
-        result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 300)
-        XCTAssertEqual(queue.count, 3)
-
-        result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 200)
-        XCTAssertEqual(queue.count, 2)
-
-        queue.enqueue(Message(name: "ryan", priority: 150))
-        XCTAssertEqual(queue.count, 3)
-        XCTAssertEqual(queue.peek()?.priority, 150)
-
-        result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 150)
-        XCTAssertEqual(queue.count, 2)
-
-        result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 100)
-        XCTAssertEqual(queue.count, 1)
-
-        result = queue.dequeue()
-        XCTAssertEqual(result!.priority, 50)
-        XCTAssertEqual(queue.count, 0)
-
-        result = queue.dequeue()
-        XCTAssertNil(result)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertTrue(queue.isEmpty)
-    }
+  func testEmpty() {
+    let queue = BoundedPriorityQueue<Message>(maxElements: 5)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.dequeue())
+  }
+
+  func testOneElement() {
+    let queue = BoundedPriorityQueue<Message>(maxElements: 5)
+
+    queue.enqueue(Message(name: "hello", priority: 100))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+
+    let result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 100)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+  }
+
+  func testMaxElements() {
+    let queue = BoundedPriorityQueue<Message>(maxElements: 5)
+    XCTAssertTrue(queue.isEmpty)
+
+    queue.enqueue(Message(name: "john", priority: 100))
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()?.priority, 100)
+
+    queue.enqueue(Message(name: "james", priority: 200))
+    XCTAssertEqual(queue.count, 2)
+    XCTAssertEqual(queue.peek()?.priority, 200)
+
+    queue.enqueue(Message(name: "mark", priority: 300))
+    XCTAssertEqual(queue.count, 3)
+    XCTAssertEqual(queue.peek()?.priority, 300)
+
+    queue.enqueue(Message(name: "ken", priority: 400))
+    XCTAssertEqual(queue.count, 4)
+    XCTAssertEqual(queue.peek()?.priority, 400)
+
+    queue.enqueue(Message(name: "thomas", priority: 500))
+    XCTAssertEqual(queue.count, 5)
+    XCTAssertEqual(queue.peek()?.priority, 500)
+
+    queue.enqueue(Message(name: "melanie", priority: 550))
+    XCTAssertEqual(queue.count, 5)
+    XCTAssertEqual(queue.peek()?.priority, 550)
+
+    queue.enqueue(Message(name: "lily", priority: 450))
+    XCTAssertEqual(queue.count, 5)
+    XCTAssertEqual(queue.peek()?.priority, 550)
+
+    queue.enqueue(Message(name: "fred", priority: 350))
+    XCTAssertEqual(queue.count, 5)
+    XCTAssertEqual(queue.peek()?.priority, 550)
+
+    queue.enqueue(Message(name: "rachel", priority: 50))
+    XCTAssertEqual(queue.count, 5)
+    XCTAssertEqual(queue.peek()?.priority, 550)
+
+    var result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 550)
+    XCTAssertEqual(queue.count, 4)
+
+    result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 500)
+    XCTAssertEqual(queue.count, 3)
+
+    result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 450)
+    XCTAssertEqual(queue.count, 2)
+
+    queue.enqueue(Message(name: "ryan", priority: 150))
+    XCTAssertEqual(queue.count, 3)
+    XCTAssertEqual(queue.peek()?.priority, 400)
+
+    result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 400)
+    XCTAssertEqual(queue.count, 2)
+
+    result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 350)
+    XCTAssertEqual(queue.count, 1)
+
+    result = queue.dequeue()
+    XCTAssertEqual(result!.priority, 150)
+    XCTAssertEqual(queue.count, 0)
+
+    result = queue.dequeue()
+    XCTAssertNil(result)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertTrue(queue.isEmpty)
+  }
 }

From d629c7e6d7fc63cd0b95b64f84aba216d4c41f71 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 1 Jun 2016 21:20:33 +1200
Subject: [PATCH 0368/1679] Indentation changes for combinatorics

---
 .../Combinatorics.playground/Contents.swift   | 156 +++++++++---------
 Combinatorics/Combinatorics.swift             |  86 +++++-----
 Combinatorics/README.markdown                 |  30 ++--
 3 files changed, 136 insertions(+), 136 deletions(-)

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 1ac77a5c4..6dde6a9e0 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -2,13 +2,13 @@
 
 /* Calculates n! */
 func factorial(n: Int) -> Int {
-    var n = n
-    var result = 1
-    while n > 1 {
-        result *= n
-        n -= 1
-    }
-    return result
+  var n = n
+  var result = 1
+  while n > 1 {
+    result *= n
+    n -= 1
+  }
+  return result
 }
 
 factorial(5)
@@ -21,13 +21,13 @@ factorial(20)
  in groups of size k.
  */
 func permutations(n: Int, _ k: Int) -> Int {
-    var n = n
-    var answer = n
-    for _ in 1..<k {
-        n -= 1
-        answer *= n
-    }
-    return answer
+  var n = n
+  var answer = n
+  for _ in 1..<k {
+    n -= 1
+    answer *= n
+  }
+  return answer
 }
 
 permutations(5, 3)
@@ -42,17 +42,17 @@ permutations(9, 4)
  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
  */
 func permuteWirth<T>(a: [T], _ n: Int) {
-    if n == 0 {
-        print(a)   // display the current permutation
-    } else {
-        var a = a
-        permuteWirth(a, n - 1)
-        for i in 0..<n {
-            swap(&a[i], &a[n])
-            permuteWirth(a, n - 1)
-            swap(&a[i], &a[n])
-        }
+  if n == 0 {
+    print(a)   // display the current permutation
+  } else {
+    var a = a
+    permuteWirth(a, n - 1)
+    for i in 0..<n {
+      swap(&a[i], &a[n])
+      permuteWirth(a, n - 1)
+      swap(&a[i], &a[n])
     }
+  }
 }
 
 let letters = ["a", "b", "c", "d", "e"]
@@ -67,29 +67,29 @@ permuteWirth(xyz, 2)
 
 /*
  Prints out all the permutations of an n-element collection.
- 
+
  The initial array must be initialized with all zeros. The algorithm
  uses 0 as a flag that indicates more work to be done on each level
  of the recursion.
- 
+
  Original algorithm by Robert Sedgewick.
  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
  */
 func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
-    var a = a
-    pos += 1
-    a[n] = pos
-    if pos == a.count - 1 {
-        print(a)              // display the current permutation
-    } else {
-        for i in 0..<a.count {
-            if a[i] == 0 {
-                permuteSedgewick(a, i, &pos)
-            }
-        }
+  var a = a
+  pos += 1
+  a[n] = pos
+  if pos == a.count - 1 {
+    print(a)              // display the current permutation
+  } else {
+    for i in 0..<a.count {
+      if a[i] == 0 {
+        permuteSedgewick(a, i, &pos)
+      }
     }
-    pos -= 1
-    a[n] = 0
+  }
+  pos -= 1
+  a[n] = 0
 }
 
 print("\nSedgewick permutations:")
@@ -104,7 +104,7 @@ permuteSedgewick(numbers, 0, &pos)
  of size k out of a total number of distinct elements (n) you can make.
  */
 func combinations(n: Int, _ k: Int) -> Int {
-    return permutations(n, k) / factorial(k)
+  return permutations(n, k) / factorial(k)
 }
 
 combinations(3, 2)
@@ -112,7 +112,7 @@ combinations(28, 5)
 
 print("\nCombinations:")
 for i in 1...20 {
-    print("\(20)-choose-\(i) = \(combinations(20, i))")
+  print("\(20)-choose-\(i) = \(combinations(20, i))")
 }
 
 
@@ -122,13 +122,13 @@ for i in 1...20 {
  k things out of n possibilities.
  */
 func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
-    var result = 1
-    
-    for i in 0..<k {
-        result *= (n - i)
-        result /= (i + 1)
-    }
-    return result
+  var result = 1
+
+  for i in 0..<k {
+    result *= (n - i)
+    result /= (i + 1)
+  }
+  return result
 }
 
 quickBinomialCoefficient(8, 2)
@@ -138,48 +138,48 @@ quickBinomialCoefficient(30, 15)
 
 /* Supporting code because Swift doesn't have a built-in 2D array. */
 struct Array2D<T> {
-    let columns: Int
-    let rows: Int
-    private var array: [T]
-    
-    init(columns: Int, rows: Int, initialValue: T) {
-        self.columns = columns
-        self.rows = rows
-        array = .init(count: rows*columns, repeatedValue: initialValue)
-    }
-    
-    subscript(column: Int, row: Int) -> T {
-        get { return array[row*columns + column] }
-        set { array[row*columns + column] = newValue }
-    }
+  let columns: Int
+  let rows: Int
+  private var array: [T]
+
+  init(columns: Int, rows: Int, initialValue: T) {
+    self.columns = columns
+    self.rows = rows
+    array = .init(count: rows*columns, repeatedValue: initialValue)
+  }
+
+  subscript(column: Int, row: Int) -> T {
+    get { return array[row*columns + column] }
+    set { array[row*columns + column] = newValue }
+  }
 }
 
 /*
  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
  k things out of n possibilities.
- 
+
  Thanks to the dynamic programming, this algorithm from Skiena allows for
  the calculation of much larger numbers, at the cost of temporary storage
  space for the cached values.
  */
 
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
-    
-    for i in 0...n {
-        bc[i][0] = 1
-        bc[i][i] = 1
-    }
-    
-    if n > 0 {
-        for i in 1...n {
-            for j in 1..<i {
-                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
-            }
-        }
+  var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+
+  for i in 0...n {
+    bc[i][0] = 1
+    bc[i][i] = 1
+  }
+
+  if n > 0 {
+    for i in 1...n {
+      for j in 1..<i {
+        bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+      }
     }
-    
-    return bc[n][k]
+  }
+
+  return bc[n][k]
 }
 
 binomialCoefficient(30, 15)
diff --git a/Combinatorics/Combinatorics.swift b/Combinatorics/Combinatorics.swift
index de82618c3..04ef98765 100644
--- a/Combinatorics/Combinatorics.swift
+++ b/Combinatorics/Combinatorics.swift
@@ -10,9 +10,9 @@ func factorial(n: Int) -> Int {
 }
 
 /*
-  Calculates P(n, k), the number of permutations of n distinct symbols
-  in groups of size k.
-*/
+ Calculates P(n, k), the number of permutations of n distinct symbols
+ in groups of size k.
+ */
 func permutations(n: Int, _ k: Int) -> Int {
   var n = n
   var answer = n
@@ -24,10 +24,10 @@ func permutations(n: Int, _ k: Int) -> Int {
 }
 
 /*
-  Prints out all the permutations of the given array.
-  Original algorithm by Niklaus Wirth.
-  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
-*/
+ Prints out all the permutations of the given array.
+ Original algorithm by Niklaus Wirth.
+ See also Dr.Dobb's Magazine June 1993, Algorithm Alley
+ */
 func permuteWirth<T>(a: [T], _ n: Int) {
   if n == 0 {
     print(a)   // display the current permutation
@@ -43,15 +43,15 @@ func permuteWirth<T>(a: [T], _ n: Int) {
 }
 
 /*
-  Prints out all the permutations of an n-element collection.
+ Prints out all the permutations of an n-element collection.
 
-  The initial array must be initialized with all zeros. The algorithm
-  uses 0 as a flag that indicates more work to be done on each level
-  of the recursion.
+ The initial array must be initialized with all zeros. The algorithm
+ uses 0 as a flag that indicates more work to be done on each level
+ of the recursion.
 
-  Original algorithm by Robert Sedgewick.
-  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
-*/
+ Original algorithm by Robert Sedgewick.
+ See also Dr.Dobb's Magazine June 1993, Algorithm Alley
+ */
 func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
   var a = a
   pos += 1
@@ -70,21 +70,21 @@ func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
 }
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. how many different selections
-  of size k out of a total number of distinct elements (n) you can make.
-  Doesn't work very well for large numbers.
-*/
+ Calculates C(n, k), or "n-choose-k", i.e. how many different selections
+ of size k out of a total number of distinct elements (n) you can make.
+ Doesn't work very well for large numbers.
+ */
 func combinations(n: Int, _ k: Int) -> Int {
   return permutations(n, k) / factorial(k)
 }
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-  k things out of n possibilities.
-*/
+ Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+ k things out of n possibilities.
+ */
 func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
   var result = 1
-    
+
   for i in 0..<k {
     result *= (n - i)
     result /= (i + 1)
@@ -93,29 +93,29 @@ func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
 }
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-  k things out of n possibilities.
+ Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+ k things out of n possibilities.
 
-  Thanks to the dynamic programming, this algorithm from Skiena allows for
-  the calculation of much larger numbers, at the cost of temporary storage
-  space for the cached values.
-*/
+ Thanks to the dynamic programming, this algorithm from Skiena allows for
+ the calculation of much larger numbers, at the cost of temporary storage
+ space for the cached values.
+ */
 
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
-    
-    for i in 0...n {
-        bc[i][0] = 1
-        bc[i][i] = 1
-    }
-    
-    if n > 0 {
-        for i in 1...n {
-            for j in 1..<i {
-                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
-            }
-        }
+  var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+
+  for i in 0...n {
+    bc[i][0] = 1
+    bc[i][i] = 1
+  }
+
+  if n > 0 {
+    for i in 1...n {
+      for j in 1..<i {
+        bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+      }
     }
-    
-    return bc[n][k]
+  }
+
+  return bc[n][k]
 }
diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 45e48693d..81a56261e 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -366,22 +366,22 @@ The following code calculates Pascal's triangle in order to find the `C(n, k)` y
 
 ```swift
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
-    
-    for i in 0...n {
-        bc[i][0] = 1
-        bc[i][i] = 1
-    }
-    
-    if n > 0 {
-        for i in 1...n {
-            for j in 1..<i {
-                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
-            }
-        }
+  var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+
+  for i in 0...n {
+    bc[i][0] = 1
+    bc[i][i] = 1
+  }
+
+  if n > 0 {
+    for i in 1...n {
+      for j in 1..<i {
+        bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+      }
     }
-    
-    return bc[n][k]
+  }
+
+  return bc[n][k]
 }
 ```
 

From 74ec882450a3fa8a09f576aa6b10c5bc6734328e Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 2 Jun 2016 00:40:47 +1200
Subject: [PATCH 0369/1679] Minor typo

---
 How to Contribute.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 385d712e0..1862eda0a 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -28,7 +28,7 @@ Just so you know, I will probably edit your text and code for grammar etc, just
 
 For the unit tests:
 
-- Add the unit test project to `.travis.yml` so they it be run on [Travis-CI](https://travis-ci.org/hollance/swift-algorithm-club). Add a line to `.travis.yml` like this:
+- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/hollance/swift-algorithm-club). Add a line to `.travis.yml` like this:
 
 ```
 - xcodebuild test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests

From 4a8ae7c7e2e912c9588690ed3bcc181a7fa4178f Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 2 Jun 2016 00:46:45 +1200
Subject: [PATCH 0370/1679] Updated links to point to new repository

---
 How to Contribute.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 1862eda0a..1e2f61b41 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -28,7 +28,7 @@ Just so you know, I will probably edit your text and code for grammar etc, just
 
 For the unit tests:
 
-- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/hollance/swift-algorithm-club). Add a line to `.travis.yml` like this:
+- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/raywenderlich/swift-algorithm-club). Add a line to `.travis.yml` like this:
 
 ```
 - xcodebuild test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
@@ -43,4 +43,4 @@ For the unit tests:
 
 ## Want to chat?
 
-This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/hollance/swift-algorithm-club/issues) and we'll talk!
+This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!

From 88f89491299675410f73b7014ddc9f2f9dd6a2d4 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 4 Jun 2016 19:18:52 +1200
Subject: [PATCH 0371/1679] Adding logo

---
 Images/SwiftAlgorithm-1024-transp.png | Bin 0 -> 46580 bytes
 README.markdown                       |   2 ++
 2 files changed, 2 insertions(+)
 create mode 100644 Images/SwiftAlgorithm-1024-transp.png

diff --git a/Images/SwiftAlgorithm-1024-transp.png b/Images/SwiftAlgorithm-1024-transp.png
new file mode 100644
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diff --git a/README.markdown b/README.markdown
index 41cb93a36..b6a37da08 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,3 +1,5 @@
+![Swift Algorithm Club](https://raw.githubusercontent.com/chris-pilcher/swift-algorithm-club/logo/Images/SwiftAlgorithm-1024-transp.png)
+
 # Welcome to the Swift Algorithm Club!
 
 Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.

From c0257e4c1deed5f4e6c8edbf98babb284683b3d1 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 4 Jun 2016 19:21:46 +1200
Subject: [PATCH 0372/1679] Image size change

---
 Images/SwiftAlgorithm-1024-transp.png | Bin 46580 -> 0 bytes
 Images/SwiftAlgorithm-410-transp.png  | Bin 0 -> 36570 bytes
 README.markdown                       |   2 +-
 3 files changed, 1 insertion(+), 1 deletion(-)
 delete mode 100644 Images/SwiftAlgorithm-1024-transp.png
 create mode 100644 Images/SwiftAlgorithm-410-transp.png

diff --git a/Images/SwiftAlgorithm-1024-transp.png b/Images/SwiftAlgorithm-1024-transp.png
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diff --git a/README.markdown b/README.markdown
index b6a37da08..2e6bbb94c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,4 +1,4 @@
-![Swift Algorithm Club](https://raw.githubusercontent.com/chris-pilcher/swift-algorithm-club/logo/Images/SwiftAlgorithm-1024-transp.png)
+![Swift Algorithm Club](https://raw.githubusercontent.com/chris-pilcher/swift-algorithm-club/logo/Images/SwiftAlgorithm-410-transp.png)
 
 # Welcome to the Swift Algorithm Club!
 

From c81cd526c30e67bdd6c724cd82af40b9fb0b555b Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 4 Jun 2016 19:24:05 +1200
Subject: [PATCH 0373/1679] Pointing logo to raywenderlich repository

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 2e6bbb94c..4d88ebdb0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,4 +1,4 @@
-![Swift Algorithm Club](https://raw.githubusercontent.com/chris-pilcher/swift-algorithm-club/logo/Images/SwiftAlgorithm-410-transp.png)
+![Swift Algorithm Club](https://raw.githubusercontent.com/raywenderlich/swift-algorithm-club/logo/Images/SwiftAlgorithm-410-transp.png)
 
 # Welcome to the Swift Algorithm Club!
 

From 4329e3b8ab9d1b3a3a3c8ee9b52ac3006b1884c2 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 4 Jun 2016 19:29:09 +1200
Subject: [PATCH 0374/1679] Relative logo image

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 4d88ebdb0..d13775410 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,4 +1,4 @@
-![Swift Algorithm Club](https://raw.githubusercontent.com/raywenderlich/swift-algorithm-club/logo/Images/SwiftAlgorithm-410-transp.png)
+![Swift Algorithm Club](/Images/SwiftAlgorithm-410-transp.png)
 
 # Welcome to the Swift Algorithm Club!
 

From ed59ea4cac70d6c65cb4e6b225cde01b355ef51c Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 22:11:28 +1200
Subject: [PATCH 0375/1679] Moved under construction pages to a different area

---
 How to Contribute.markdown  |  2 +-
 README.markdown             |  6 ++----
 Under Construction.markdown | 19 +++++++++++++++++++
 3 files changed, 22 insertions(+), 5 deletions(-)
 create mode 100644 Under Construction.markdown

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 1e2f61b41..dc1562327 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -6,7 +6,7 @@ Want to help out with the Swift Algorithm Club? Great!
 
 Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
 
-Things marked with :construction: need work.
+Algorithms in the [Under construction](Under Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
 
 New algorithms and data structures are always welcome (even if they aren't on the list).
 
diff --git a/README.markdown b/README.markdown
index d13775410..355e0c940 100644
--- a/README.markdown
+++ b/README.markdown
@@ -26,6 +26,8 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 [How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
 
+[Under construction](Under Construction.markdown). Algorithms that are under construction. 
+
 ## Where to start?
 
 If you're new to algorithms and data structures, here are a few good ones to start out with:
@@ -74,7 +76,6 @@ Fast sorts:
 
 Special-purpose sorts:
 
-- [Bucket Sort](Bucket Sort/) :construction:
 - [Counting Sort](Counting Sort/)
 - Radix Sort
 - [Topological Sort](Topological Sort/)
@@ -131,7 +132,6 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Queue](Queue/). First-in, first-out!
 - [Deque](Deque/). A double-ended queue.
 - [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
-- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements. :construction:
 - [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
 
 ### Lists
@@ -144,7 +144,6 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Tree](Tree/). A general-purpose tree structure.
 - [Binary Tree](Binary Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
-- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations. :construction:
 - Red-Black Tree
 - Splay Tree
 - Threaded Binary Tree
@@ -154,7 +153,6 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - Fibonacci Heap
 - Trie
 - B-Tree
-- [Radix Tree](Radix Tree/) :construction:
 
 ### Hashing
 
diff --git a/Under Construction.markdown b/Under Construction.markdown
new file mode 100644
index 000000000..b7cf7a696
--- /dev/null
+++ b/Under Construction.markdown	
@@ -0,0 +1,19 @@
+# Under Construction :construction:
+
+Here you'll find algorithms that are under construction. 
+
+**Suggestions and feedback are welcome!**
+
+Special-purpose sorts:
+
+- [Bucket Sort](Bucket Sort/)
+
+### Queues
+
+- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements.
+
+### Trees
+
+- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
+- [Radix Tree](Radix Tree/)
+

From 19edb529452884b9a7e55d0d078ac995f84dcf09 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 22:13:13 +1200
Subject: [PATCH 0376/1679] Under construction title

---
 Under Construction.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index b7cf7a696..e5b942950 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -1,10 +1,10 @@
 # Under Construction :construction:
 
-Here you'll find algorithms that are under construction. 
+Here you'll find algorithms that are currently under construction. 
 
 **Suggestions and feedback are welcome!**
 
-Special-purpose sorts:
+### Special-purpose sorts:
 
 - [Bucket Sort](Bucket Sort/)
 

From d0ebabdabc8d51932de73458a4247baeb19c96ba Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 22:13:51 +1200
Subject: [PATCH 0377/1679] Under construction formatting change

---
 Under Construction.markdown | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index e5b942950..0589c5491 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -1,8 +1,6 @@
 # Under Construction :construction:
 
-Here you'll find algorithms that are currently under construction. 
-
-**Suggestions and feedback are welcome!**
+Here you'll find algorithms that are currently under construction. Suggestions and feedback are welcome!
 
 ### Special-purpose sorts:
 

From cafb8e1813219ed67ff09986dbeac37a36a80360 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 22:14:31 +1200
Subject: [PATCH 0378/1679] Under construction page

---
 Under Construction.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index 0589c5491..f6d2852ea 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -1,6 +1,6 @@
 # Under Construction :construction:
 
-Here you'll find algorithms that are currently under construction. Suggestions and feedback are welcome!
+Here you'll find algorithms that are currently under construction. Suggestions and feedback is welcome!
 
 ### Special-purpose sorts:
 

From 475d23cedaee132d536c342045e764e4b3d5ceec Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 22:40:20 +1200
Subject: [PATCH 0379/1679] Update Under Construction.markdown

Added minimum edit distance link
---
 Under Construction.markdown | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index f6d2852ea..63e696f75 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -15,3 +15,6 @@ Here you'll find algorithms that are currently under construction. Suggestions a
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
 - [Radix Tree](Radix Tree/)
 
+### Miscellaneous
+
+- [Minimum Edit Distance](Minimum Edit Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.

From c6e6de525fa971e9864aba9eb444308712682037 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 23:04:55 +1200
Subject: [PATCH 0380/1679] Update Under Construction.markdown

Added link for ternary search tree.
---
 Under Construction.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index 63e696f75..83d48716b 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -13,6 +13,7 @@ Here you'll find algorithms that are currently under construction. Suggestions a
 ### Trees
 
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
+- [Ternary Search Tree](Ternary Search Tree/)
 - [Radix Tree](Radix Tree/)
 
 ### Miscellaneous

From af47d57057bde6f5850383a9a3ac3ab01e20c6ef Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 5 Jun 2016 23:54:59 +1200
Subject: [PATCH 0381/1679] Update Under Construction.markdown

Added link to Treap
---
 Under Construction.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index 83d48716b..f0befb3d9 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -19,3 +19,4 @@ Here you'll find algorithms that are currently under construction. Suggestions a
 ### Miscellaneous
 
 - [Minimum Edit Distance](Minimum Edit Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
+- [Treap](Treap/)

From 495303b9c02749766c6536ca54e7429ff1fc5171 Mon Sep 17 00:00:00 2001
From: Andrew McKnight <amcknight2718@gmail.com>
Date: Mon, 30 May 2016 13:22:42 -0400
Subject: [PATCH 0382/1679] refactor Graph implementation

- define an abstract class called AbstractGraph, with two concrete implementations: AdjacencyListGraph and AdjacencyMatrixGraph
- improve some method naming, especially those dealing with creating (un)directed edges
- make a framework target, and add xcodeproj and playground to a workspace to import the framework module so we don't need to duplicate the implementation in the playground
- update README to reflect the new implementations/concepts

consequently, the APSP implementation is updated to use the refactored Graph implementation, plus:
- improvements to doc comments
- remove redundant parameter in FloydWarshallResult.recursePathFrom
- changed the test case ported from the book to reflect the exact names of the graph vertices
---
 .../APSP/APSP.playground/Contents.swift       |  23 +-
 .../APSP/APSP.playground/timeline.xctimeline  |   4 +-
 .../APSP/APSP.xcodeproj/project.pbxproj       |  86 +++-
 All-Pairs Shortest Paths/APSP/APSP/APSP.h     |   1 -
 All-Pairs Shortest Paths/APSP/APSP/APSP.swift |  18 +-
 .../APSP/APSP/FloydWarshall.swift             |  58 +--
 .../APSP/APSP/Helpers.swift                   |   1 -
 All-Pairs Shortest Paths/APSP/APSP/Info.plist |   2 -
 .../APSP/APSPTests/APSPTests.swift            |  91 ++--
 Graph/AdjacencyList.swift                     |  39 --
 Graph/AdjacencyMatrix.swift                   |  75 ----
 Graph/Graph.playground/Contents.swift         |  45 ++
 .../Contents.swift                            |  87 ----
 .../timeline.xctimeline                       |   6 -
 .../Contents.swift                            |  99 ----
 .../timeline.xctimeline                       |  11 -
 Graph/Graph.playground/contents.xcplayground  |   7 +-
 Graph/Graph.xcodeproj/project.pbxproj         | 421 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   4 +
 .../xcshareddata/xcschemes/Graph.xcscheme     |  80 ++++
 .../xcschemes/GraphTests.xcscheme             |  56 +++
 .../contents.xcworkspacedata                  |  10 +
 .../xcshareddata/WorkspaceSettings.xcsettings |   8 +
 Graph/Graph/AdjacencyListGraph.swift          | 134 ++++++
 Graph/Graph/AdjacencyMatrixGraph.swift        | 107 +++++
 Graph/Graph/Edge.swift                        |  60 +++
 Graph/Graph/Graph.h                           |  18 +
 Graph/Graph/Graph.swift                       |  59 +++
 Graph/Graph/Info.plist                        |  26 ++
 Graph/Graph/Vertex.swift                      |  47 ++
 Graph/GraphTests/GraphTests.swift             |  57 +++
 Graph/GraphTests/Info.plist                   |  24 +
 Graph/README.markdown                         | 206 +++++----
 33 files changed, 1434 insertions(+), 536 deletions(-)
 delete mode 100644 Graph/AdjacencyList.swift
 delete mode 100644 Graph/AdjacencyMatrix.swift
 create mode 100644 Graph/Graph.playground/Contents.swift
 delete mode 100644 Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
 delete mode 100644 Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/timeline.xctimeline
 delete mode 100644 Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
 delete mode 100644 Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Graph/Graph.xcodeproj/project.pbxproj
 create mode 100644 Graph/Graph.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
 create mode 100644 Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
 create mode 100644 Graph/Graph.xcworkspace/contents.xcworkspacedata
 create mode 100644 Graph/Graph.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
 create mode 100644 Graph/Graph/AdjacencyListGraph.swift
 create mode 100644 Graph/Graph/AdjacencyMatrixGraph.swift
 create mode 100644 Graph/Graph/Edge.swift
 create mode 100644 Graph/Graph/Graph.h
 create mode 100644 Graph/Graph/Graph.swift
 create mode 100644 Graph/Graph/Info.plist
 create mode 100644 Graph/Graph/Vertex.swift
 create mode 100644 Graph/GraphTests/GraphTests.swift
 create mode 100644 Graph/GraphTests/Info.plist

diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
index e14966113..24c27cac8 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
@@ -1,8 +1,9 @@
 //: Playground - noun: a place where people can play
 
+import Graph
 import APSP
 
-var graph = Graph<String>()
+var graph = AdjacencyListGraph<String>()
 
 let v1 = graph.createVertex("Montreal")
 let v2 = graph.createVertex("New York")
@@ -10,20 +11,20 @@ let v3 = graph.createVertex("Boston")
 let v4 = graph.createVertex("Portland")
 let v5 = graph.createVertex("Portsmouth")
 
-graph.connect(v1, to: v2, withWeight: 3)
-graph.connect(v1, to: v5, withWeight: -4)
-graph.connect(v1, to: v3, withWeight: 8)
+graph.addDirectedEdge(v1, to: v2, withWeight: 3)
+graph.addDirectedEdge(v1, to: v5, withWeight: -4)
+graph.addDirectedEdge(v1, to: v3, withWeight: 8)
 
-graph.connect(v2, to: v4, withWeight: 1)
-graph.connect(v2, to: v5, withWeight: 7)
+graph.addDirectedEdge(v2, to: v4, withWeight: 1)
+graph.addDirectedEdge(v2, to: v5, withWeight: 7)
 
-graph.connect(v3, to: v2, withWeight: 4)
+graph.addDirectedEdge(v3, to: v2, withWeight: 4)
 
-graph.connect(v4, to: v1, withWeight: 2)
-graph.connect(v4, to: v3, withWeight: -5)
+graph.addDirectedEdge(v4, to: v1, withWeight: 2)
+graph.addDirectedEdge(v4, to: v3, withWeight: -5)
 
-graph.connect(v5, to: v4, withWeight: 6)
+graph.addDirectedEdge(v5, to: v4, withWeight: 6)
 
 let result = FloydWarshall<String>.apply(graph)
 
-let path = result.path(fromVertex: v1, toVertex: v4, inGraph: graph)
\ No newline at end of file
+let path = result.path(fromVertex: v1, toVertex: v4, inGraph: graph)
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline
index 522661fa7..2c73a4e3e 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=790&amp;EndingColumnNumber=44&amp;EndingLineNumber=28&amp;StartingColumnNumber=3&amp;StartingLineNumber=27&amp;Timestamp=484286078.350375"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=888&amp;EndingColumnNumber=44&amp;EndingLineNumber=29&amp;StartingColumnNumber=3&amp;StartingLineNumber=28&amp;Timestamp=486844329.035763"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=4&amp;CharacterRangeLoc=727&amp;EndingColumnNumber=9&amp;EndingLineNumber=28&amp;StartingColumnNumber=5&amp;StartingLineNumber=28&amp;Timestamp=484286078.357412"
+         documentLocation = "#CharacterRangeLen=4&amp;CharacterRangeLoc=825&amp;EndingColumnNumber=9&amp;EndingLineNumber=29&amp;StartingColumnNumber=5&amp;StartingLineNumber=29&amp;Timestamp=486844329.036018"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index 7df369cd7..e7e95bbb7 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -7,16 +7,37 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
+		491AA3821CE8C5F700A2E2C5 /* Graph.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = 491AA37F1CE8C5C900A2E2C5 /* Graph.framework */; };
 		493D8DE31CDD2A1C0089795A /* APSPTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DE21CDD2A1C0089795A /* APSPTests.swift */; };
 		493D8DF41CDD5B960089795A /* APSP.h in Headers */ = {isa = PBXBuildFile; fileRef = 493D8DF31CDD5B960089795A /* APSP.h */; settings = {ATTRIBUTES = (Public, ); }; };
 		493D8DF91CDD5B9B0089795A /* FloydWarshall.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DD81CDC38C60089795A /* FloydWarshall.swift */; };
 		493D8DFA1CDD5B9E0089795A /* Helpers.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DDA1CDD29C80089795A /* Helpers.swift */; };
-		493D8DFB1CDD5BDE0089795A /* AdjacencyMatrix.swift in Sources */ = {isa = PBXBuildFile; fileRef = 493D8DB91CDC34D00089795A /* AdjacencyMatrix.swift */; };
 		49BFA27A1CDD93F400522D66 /* APSP.swift in Sources */ = {isa = PBXBuildFile; fileRef = 49BFA2791CDD93F400522D66 /* APSP.swift */; };
 		49BFA2801CDE742900522D66 /* APSP.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = 493D8DF11CDD5B960089795A /* APSP.framework */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
+		491AA37E1CE8C5C900A2E2C5 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 491AA3791CE8C5C900A2E2C5 /* Graph.xcodeproj */;
+			proxyType = 2;
+			remoteGlobalIDString = 49BFA2FD1CDF886B00522D66;
+			remoteInfo = Graph;
+		};
+		491AA3801CE8C5C900A2E2C5 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 491AA3791CE8C5C900A2E2C5 /* Graph.xcodeproj */;
+			proxyType = 2;
+			remoteGlobalIDString = 49BFA3071CDF886B00522D66;
+			remoteInfo = GraphTests;
+		};
+		491AA3831CE8C5F900A2E2C5 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 491AA3791CE8C5C900A2E2C5 /* Graph.xcodeproj */;
+			proxyType = 1;
+			remoteGlobalIDString = 49BFA2FC1CDF886B00522D66;
+			remoteInfo = Graph;
+		};
 		49BFA27E1CDE742700522D66 /* PBXContainerItemProxy */ = {
 			isa = PBXContainerItemProxy;
 			containerPortal = 493D8D7E1CDC2DAE0089795A /* Project object */;
@@ -27,7 +48,7 @@
 /* End PBXContainerItemProxy section */
 
 /* Begin PBXFileReference section */
-		493D8DB91CDC34D00089795A /* AdjacencyMatrix.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AdjacencyMatrix.swift; sourceTree = "<group>"; };
+		491AA3791CE8C5C900A2E2C5 /* Graph.xcodeproj */ = {isa = PBXFileReference; lastKnownFileType = "wrapper.pb-project"; name = Graph.xcodeproj; path = ../../Graph/Graph.xcodeproj; sourceTree = "<group>"; };
 		493D8DD81CDC38C60089795A /* FloydWarshall.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = FloydWarshall.swift; sourceTree = "<group>"; };
 		493D8DDA1CDD29C80089795A /* Helpers.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Helpers.swift; sourceTree = "<group>"; };
 		493D8DE01CDD2A1C0089795A /* APSPTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = APSPTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
@@ -52,16 +73,26 @@
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				491AA3821CE8C5F700A2E2C5 /* Graph.framework in Frameworks */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
+		491AA37A1CE8C5C900A2E2C5 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				491AA37F1CE8C5C900A2E2C5 /* Graph.framework */,
+				491AA3811CE8C5C900A2E2C5 /* GraphTests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
 		493D8D7D1CDC2DAE0089795A = {
 			isa = PBXGroup;
 			children = (
-				493D8DB71CDC34D00089795A /* Graph */,
+				491AA3791CE8C5C900A2E2C5 /* Graph.xcodeproj */,
 				493D8D881CDC2DAE0089795A /* APSP */,
 				493D8DE11CDD2A1C0089795A /* APSPTests */,
 				493D8D871CDC2DAE0089795A /* Products */,
@@ -89,15 +120,6 @@
 			path = APSP;
 			sourceTree = "<group>";
 		};
-		493D8DB71CDC34D00089795A /* Graph */ = {
-			isa = PBXGroup;
-			children = (
-				493D8DB91CDC34D00089795A /* AdjacencyMatrix.swift */,
-			);
-			name = Graph;
-			path = ../../Graph;
-			sourceTree = "<group>";
-		};
 		493D8DE11CDD2A1C0089795A /* APSPTests */ = {
 			isa = PBXGroup;
 			children = (
@@ -151,6 +173,7 @@
 			buildRules = (
 			);
 			dependencies = (
+				491AA3841CE8C5F900A2E2C5 /* PBXTargetDependency */,
 			);
 			name = APSP;
 			productName = APSP;
@@ -165,7 +188,7 @@
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
 				LastUpgradeCheck = 0730;
-				ORGANIZATIONNAME = "Andrew McKnight";
+				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					493D8DDF1CDD2A1C0089795A = {
 						CreatedOnToolsVersion = 7.3;
@@ -185,6 +208,12 @@
 			mainGroup = 493D8D7D1CDC2DAE0089795A;
 			productRefGroup = 493D8D871CDC2DAE0089795A /* Products */;
 			projectDirPath = "";
+			projectReferences = (
+				{
+					ProductGroup = 491AA37A1CE8C5C900A2E2C5 /* Products */;
+					ProjectRef = 491AA3791CE8C5C900A2E2C5 /* Graph.xcodeproj */;
+				},
+			);
 			projectRoot = "";
 			targets = (
 				493D8DDF1CDD2A1C0089795A /* APSPTests */,
@@ -193,6 +222,23 @@
 		};
 /* End PBXProject section */
 
+/* Begin PBXReferenceProxy section */
+		491AA37F1CE8C5C900A2E2C5 /* Graph.framework */ = {
+			isa = PBXReferenceProxy;
+			fileType = wrapper.framework;
+			path = Graph.framework;
+			remoteRef = 491AA37E1CE8C5C900A2E2C5 /* PBXContainerItemProxy */;
+			sourceTree = BUILT_PRODUCTS_DIR;
+		};
+		491AA3811CE8C5C900A2E2C5 /* GraphTests.xctest */ = {
+			isa = PBXReferenceProxy;
+			fileType = wrapper.cfbundle;
+			path = GraphTests.xctest;
+			remoteRef = 491AA3801CE8C5C900A2E2C5 /* PBXContainerItemProxy */;
+			sourceTree = BUILT_PRODUCTS_DIR;
+		};
+/* End PBXReferenceProxy section */
+
 /* Begin PBXResourcesBuildPhase section */
 		493D8DDE1CDD2A1C0089795A /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
@@ -226,13 +272,17 @@
 				49BFA27A1CDD93F400522D66 /* APSP.swift in Sources */,
 				493D8DF91CDD5B9B0089795A /* FloydWarshall.swift in Sources */,
 				493D8DFA1CDD5B9E0089795A /* Helpers.swift in Sources */,
-				493D8DFB1CDD5BDE0089795A /* AdjacencyMatrix.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
 /* End PBXSourcesBuildPhase section */
 
 /* Begin PBXTargetDependency section */
+		491AA3841CE8C5F900A2E2C5 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			name = Graph;
+			targetProxy = 491AA3831CE8C5F900A2E2C5 /* PBXContainerItemProxy */;
+		};
 		49BFA27F1CDE742700522D66 /* PBXTargetDependency */ = {
 			isa = PBXTargetDependency;
 			target = 493D8DF01CDD5B960089795A /* APSP */;
@@ -329,7 +379,7 @@
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = APSPTests/Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSPTests;
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 			};
 			name = Debug;
@@ -340,7 +390,7 @@
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = APSPTests/Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSPTests;
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 			};
 			name = Release;
@@ -358,7 +408,7 @@
 				INFOPLIST_FILE = APSP/Info.plist;
 				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSP;
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				VERSIONING_SYSTEM = "apple-generic";
@@ -379,7 +429,7 @@
 				INFOPLIST_FILE = APSP/Info.plist;
 				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.armcknight.APSP;
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				VERSIONING_SYSTEM = "apple-generic";
diff --git a/All-Pairs Shortest Paths/APSP/APSP/APSP.h b/All-Pairs Shortest Paths/APSP/APSP/APSP.h
index 59613bceb..6936d5a21 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/APSP.h	
+++ b/All-Pairs Shortest Paths/APSP/APSP/APSP.h	
@@ -3,7 +3,6 @@
 //  APSP
 //
 //  Created by Andrew McKnight on 5/6/16.
-//  Copyright © 2016 Andrew McKnight. All rights reserved.
 //
 
 #import <Cocoa/Cocoa.h>
diff --git a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift
index 22ad4a958..bb773306e 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
@@ -3,31 +3,31 @@
 //  APSP
 //
 //  Created by Andrew McKnight on 5/6/16.
-//  Copyright © 2016 Andrew McKnight. All rights reserved.
 //
 
 import Foundation
+import Graph
 
 /**
- APSPAlgorithm is a protocol for encapsulating an All-Pairs Shortest Paths algorithm. It provides a single function `apply` that accepts a `Graph` and returns an object conforming to `APSPResult`.
+ `APSPAlgorithm` is a protocol for encapsulating an All-Pairs Shortest Paths algorithm. It provides a single function `apply` that accepts a subclass of `AbstractGraph` and returns an object conforming to `APSPResult`.
  */
-protocol APSPAlgorithm {
+public protocol APSPAlgorithm {
 
-  associatedtype Q
+  associatedtype Q: Hashable
   associatedtype P: APSPResult
 
-  static func apply(graph: Graph<Q>) -> P
+  static func apply(graph: AbstractGraph<Q>) -> P
 
 }
 
 /**
- APSPResult is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the APSP solution according to the algorithm used.
+ `APSPResult` is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the APSP solution according to the algorithm used.
  */
-protocol APSPResult {
+public protocol APSPResult {
 
-  associatedtype T
+  associatedtype T: Hashable
 
   func distance(fromVertex from: Vertex<T>, toVertex to: Vertex<T>) -> Double?
-  func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: Graph<T>) -> [T]?
+  func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]?
 
 }
diff --git a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
index 976d3138c..a655e215f 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
@@ -3,24 +3,24 @@
 //  APSP
 //
 //  Created by Andrew McKnight on 5/5/16.
-//  Copyright © 2016 Andrew McKnight. All rights reserved.
 //
 
 import Foundation
+import Graph
 
 private typealias Distances = [[Double]]
 private typealias Predecessors = [[Int?]]
 private typealias StepResult = (distances: Distances, predecessors: Predecessors)
 
 /**
- Encapsulation of the Floyd-Warshall All-Pairs Shortest Paths algorithm, conforming to the APSPAlgorithm protocol.
+ Encapsulation of the Floyd-Warshall All-Pairs Shortest Paths algorithm, conforming to the `APSPAlgorithm` protocol.
 
  - note: In all complexity bounds, `V` is the number of vertices in the graph, and `E` is the number of edges.
  */
-public struct FloydWarshall<T>: APSPAlgorithm {
+public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
 
-  typealias Q = T
-  typealias P = FloydWarshallResult<T>
+  public typealias Q = T
+  public typealias P = FloydWarshallResult<T>
 
   /**
    Floyd-Warshall algorithm for computing all-pairs shortest paths in a weighted directed graph.
@@ -29,7 +29,7 @@ public struct FloydWarshall<T>: APSPAlgorithm {
    - complexity: `Θ(V^3)` time, `Θ(V^2)` space
    - returns a `FloydWarshallResult` struct which can be queried for shortest paths and their total weights
    */
-  public static func apply<T>(graph: Graph<T>) -> FloydWarshallResult<T> {
+  public static func apply<T>(graph: AbstractGraph<T>) -> FloydWarshallResult<T> {
 
     var previousDistance = constructInitialDistanceMatrix(graph)
     var previousPredecessor = constructInitialPredecessorMatrix(previousDistance)
@@ -56,9 +56,9 @@ public struct FloydWarshall<T>: APSPAlgorithm {
    - complexity: `Θ(V^2)` time/space
    - returns: a tuple containing the next distance matrix with weights of currently known shortest paths and the corresponding predecessor matrix
    */
-  static private func nextStep<T>(intermediateIdx: Int, previousDistances: Distances, previousPredecessors: Predecessors, graph: Graph<T>) -> StepResult {
+  static private func nextStep<T>(intermediateIdx: Int, previousDistances: Distances, previousPredecessors: Predecessors, graph: AbstractGraph<T>) -> StepResult {
 
-    let vertexCount = graph.adjacencyMatrix.count
+    let vertexCount = graph.vertices.count
     var nextDistances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
     var nextPredecessors = Array(count: vertexCount, repeatedValue: Array<Int?>(count: vertexCount, repeatedValue: nil))
 
@@ -86,22 +86,26 @@ public struct FloydWarshall<T>: APSPAlgorithm {
   }
 
   /** 
-   We need to convert the value system in Graph's adjacency matrix to the one we need to perform the algorithm. We need the actual weight between two vertices, or infinity if no edge exists, represented by nil in Graph.adjacencyMatrix. Also set the weight to 0 on the diagonal.
+   We need to map the graph's weight domain onto the one required by the algorithm: the graph stores either a weight as a `Double` or `nil` if no edge exists between two vertices, but the algorithm needs a lack of an edge represented as ∞ for the `min` comparison to work correctly.
    
    - complexity: `Θ(V^2)` time/space
    - returns: weighted adjacency matrix in form ready for processing with Floyd-Warshall
    */
-  static private func constructInitialDistanceMatrix<T>(graph: Graph<T>) -> Distances {
+  static private func constructInitialDistanceMatrix<T>(graph: AbstractGraph<T>) -> Distances {
 
-    let vertexCount = graph.adjacencyMatrix.count
+    let vertices = graph.vertices
+
+    let vertexCount = graph.vertices.count
     var distances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
 
-    for fromIdx in 0 ..< vertexCount {
-      for toIdx in 0 ..< vertexCount {
-        if fromIdx == toIdx {
-          distances[fromIdx][toIdx] = 0.0
-        } else if let w = graph.adjacencyMatrix[fromIdx][toIdx] {
-          distances[fromIdx][toIdx] = w
+    for row in vertices {
+      for col in vertices {
+        let rowIdx = row.index
+        let colIdx = col.index
+        if rowIdx == colIdx {
+          distances[rowIdx][colIdx] = 0.0
+        } else if let w = graph.weightFrom(row, to: col) {
+          distances[rowIdx][colIdx] = w
         }
       }
     }
@@ -135,17 +139,17 @@ public struct FloydWarshall<T>: APSPAlgorithm {
 }
 
 /**
- FloydWarshallResult encapsulates the result of the computation, namely the minimized distance adjacency matrix, and the matrix of predecessor indices.
+ `FloydWarshallResult` encapsulates the result of the computation, namely the minimized distance adjacency matrix, and the matrix of predecessor indices.
  
- It conforms to the APSPResult procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
+ It conforms to the `APSPResult` procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
  */
-public struct FloydWarshallResult<T>: APSPResult {
+public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
 
   private var weights: Distances
   private var predecessors: Predecessors
 
   /**
-   - returns: the total weight of the path from a starting vertex to a destination. This value is the minimal connected weight between the two vertices.
+   - returns: the total weight of the path from a starting vertex to a destination. This value is the minimal connected weight between the two vertices, or `nil` if no path exists
    - complexity: `Θ(1)` time/space
    */
   public func distance(fromVertex from: Vertex<T>, toVertex to: Vertex<T>) -> Double? {
@@ -155,12 +159,12 @@ public struct FloydWarshallResult<T>: APSPResult {
   }
 
   /**
-   - returns: the reconstructed path from a starting vertex to a destination, as an array containing the data property of each vertex
+   - returns: the reconstructed path from a starting vertex to a destination, as an array containing the data property of each vertex, or `nil` if no path exists
    - complexity: `Θ(V)` time, `Θ(V^2)` space
    */
-  public func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: Graph<T>) -> [T]? {
+  public func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
 
-    if let path = recursePathFrom(predecessors, fromVertex: from, toVertex: to, path: [ to ], inGraph: graph) {
+    if let path = recursePathFrom(fromVertex: from, toVertex: to, path: [ to ], inGraph: graph) {
       let pathValues = path.map() { vertex in
         vertex.data
       }
@@ -171,11 +175,11 @@ public struct FloydWarshallResult<T>: APSPResult {
   }
 
   /**
-   The recursive component to rebuilding the shortest path between two vertices using the predecessor graph.
+   The recursive component to rebuilding the shortest path between two vertices using the predecessor matrix.
 
    - returns: the list of predecessors discovered so far
    */
-  private func recursePathFrom(predecessors: [[Int?]], fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>], inGraph graph: Graph<T>) -> [Vertex<T>]? {
+  private func recursePathFrom(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>], inGraph graph: AbstractGraph<T>) -> [Vertex<T>]? {
 
     if from.index == to.index {
       return [ from, to ]
@@ -187,7 +191,7 @@ public struct FloydWarshallResult<T>: APSPResult {
         let newPath = [ from, to ]
         return newPath
       } else {
-        let buildPath = recursePathFrom(predecessors, fromVertex: from, toVertex: predecessorVertex, path: path, inGraph: graph)
+        let buildPath = recursePathFrom(fromVertex: from, toVertex: predecessorVertex, path: path, inGraph: graph)
         let newPath = buildPath! + [ to ]
         return newPath
       }
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift
index c6f22e879..644454491 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
@@ -3,7 +3,6 @@
 //  APSP
 //
 //  Created by Andrew McKnight on 5/6/16.
-//  Copyright © 2016 Andrew McKnight. All rights reserved.
 //
 
 import Foundation
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Info.plist b/All-Pairs Shortest Paths/APSP/APSP/Info.plist
index 9bf850304..d3de8eefb 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/Info.plist	
+++ b/All-Pairs Shortest Paths/APSP/APSP/Info.plist	
@@ -20,8 +20,6 @@
 	<string>????</string>
 	<key>CFBundleVersion</key>
 	<string>$(CURRENT_PROJECT_VERSION)</string>
-	<key>NSHumanReadableCopyright</key>
-	<string>Copyright © 2016 Andrew McKnight. All rights reserved.</string>
 	<key>NSPrincipalClass</key>
 	<string></string>
 </dict>
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
index 47b71b3ea..52e87758c 100644
--- a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -3,13 +3,13 @@
 //  APSPTests
 //
 //  Created by Andrew McKnight on 5/6/16.
-//  Copyright © 2016 Andrew McKnight. All rights reserved.
 //
 
 import APSP
+import Graph
 import XCTest
 
-struct TestCase<T> {
+struct TestCase<T where T: Hashable> {
 
   var from: Vertex<T>
   var to: Vertex<T>
@@ -20,53 +20,56 @@ struct TestCase<T> {
 
 class APSPTests: XCTestCase {
 
+  /**
+   See Figure 25.1 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 690
+   */
   func testExampleFromBook() {
 
-    var graph = Graph<String>()
-    let v1 = graph.createVertex("Montreal")
-    let v2 = graph.createVertex("New York")
-    let v3 = graph.createVertex("Boston")
-    let v4 = graph.createVertex("Portland")
-    let v5 = graph.createVertex("Portsmouth")
+    let graph = AdjacencyMatrixGraph<Int>()
+    let v1 = graph.createVertex(1)
+    let v2 = graph.createVertex(2)
+    let v3 = graph.createVertex(3)
+    let v4 = graph.createVertex(4)
+    let v5 = graph.createVertex(5)
 
-    graph.connect(v1, to: v2, withWeight: 3)
-    graph.connect(v1, to: v5, withWeight: -4)
-    graph.connect(v1, to: v3, withWeight: 8)
+    graph.addDirectedEdge(v1, to: v2, withWeight: 3)
+    graph.addDirectedEdge(v1, to: v5, withWeight: -4)
+    graph.addDirectedEdge(v1, to: v3, withWeight: 8)
 
-    graph.connect(v2, to: v4, withWeight: 1)
-    graph.connect(v2, to: v5, withWeight: 7)
+    graph.addDirectedEdge(v2, to: v4, withWeight: 1)
+    graph.addDirectedEdge(v2, to: v5, withWeight: 7)
 
-    graph.connect(v3, to: v2, withWeight: 4)
+    graph.addDirectedEdge(v3, to: v2, withWeight: 4)
 
-    graph.connect(v4, to: v1, withWeight: 2)
-    graph.connect(v4, to: v3, withWeight: -5)
+    graph.addDirectedEdge(v4, to: v1, withWeight: 2)
+    graph.addDirectedEdge(v4, to: v3, withWeight: -5)
 
-    graph.connect(v5, to: v4, withWeight: 6)
+    graph.addDirectedEdge(v5, to: v4, withWeight: 6)
 
-    let result = FloydWarshall<String>.apply(graph)
+    let result = FloydWarshall<Int>.apply(graph)
 
     let cases = [
-      TestCase<String>(from: v1, to: v4, expectedPath: ["Montreal", "Portsmouth", "Portland"], expectedDistance: 2),
-      TestCase<String>(from: v1, to: v5, expectedPath: ["Montreal", "Portsmouth"], expectedDistance: -4),
-      TestCase<String>(from: v2, to: v1, expectedPath: ["New York", "Portland", "Montreal"], expectedDistance: 3),
-      TestCase<String>(from: v2, to: v3, expectedPath: ["New York", "Portland", "Boston"], expectedDistance: -4),
-      TestCase<String>(from: v2, to: v4, expectedPath: ["New York", "Portland"], expectedDistance: 1),
-      TestCase<String>(from: v2, to: v5, expectedPath: ["New York", "Portland", "Montreal", "Portsmouth"], expectedDistance: -1),
-      TestCase<String>(from: v3, to: v1, expectedPath: ["Boston", "New York", "Portland", "Montreal"], expectedDistance: 7),
-      TestCase<String>(from: v3, to: v2, expectedPath: ["Boston", "New York"], expectedDistance: 4),
-      TestCase<String>(from: v3, to: v4, expectedPath: ["Boston", "New York", "Portland"], expectedDistance: 5),
-      TestCase<String>(from: v3, to: v5, expectedPath: ["Boston", "New York", "Portland", "Montreal", "Portsmouth"], expectedDistance: 3),
-      TestCase<String>(from: v4, to: v1, expectedPath: ["Portland", "Montreal"], expectedDistance: 2),
-      TestCase<String>(from: v4, to: v2, expectedPath: ["Portland", "Boston", "New York"], expectedDistance: -1),
-      TestCase<String>(from: v4, to: v3, expectedPath: ["Portland", "Boston"], expectedDistance: -5),
-      TestCase<String>(from: v4, to: v5, expectedPath: ["Portland", "Montreal", "Portsmouth"], expectedDistance: -2),
-      TestCase<String>(from: v5, to: v1, expectedPath: ["Portsmouth", "Portland", "Montreal"], expectedDistance: 8),
-      TestCase<String>(from: v5, to: v2, expectedPath: ["Portsmouth", "Portland", "Boston", "New York"], expectedDistance: 5),
-      TestCase<String>(from: v5, to: v3, expectedPath: ["Portsmouth", "Portland", "Boston"], expectedDistance: 1),
-      TestCase<String>(from: v5, to: v4, expectedPath: ["Portsmouth", "Portland"], expectedDistance: 6),
+      TestCase<Int>(from: v1, to: v4, expectedPath: [1, 5, 4], expectedDistance: 2),
+      TestCase<Int>(from: v1, to: v5, expectedPath: [1, 5], expectedDistance: -4),
+      TestCase<Int>(from: v2, to: v1, expectedPath: [2, 4, 1], expectedDistance: 3),
+      TestCase<Int>(from: v2, to: v3, expectedPath: [2, 4, 3], expectedDistance: -4),
+      TestCase<Int>(from: v2, to: v4, expectedPath: [2, 4], expectedDistance: 1),
+      TestCase<Int>(from: v2, to: v5, expectedPath: [2, 4, 1, 5], expectedDistance: -1),
+      TestCase<Int>(from: v3, to: v1, expectedPath: [3, 2, 4, 1], expectedDistance: 7),
+      TestCase<Int>(from: v3, to: v2, expectedPath: [3, 2], expectedDistance: 4),
+      TestCase<Int>(from: v3, to: v4, expectedPath: [3, 2, 4], expectedDistance: 5),
+      TestCase<Int>(from: v3, to: v5, expectedPath: [3, 2, 4, 1, 5], expectedDistance: 3),
+      TestCase<Int>(from: v4, to: v1, expectedPath: [4, 1], expectedDistance: 2),
+      TestCase<Int>(from: v4, to: v2, expectedPath: [4, 3, 2], expectedDistance: -1),
+      TestCase<Int>(from: v4, to: v3, expectedPath: [4, 3], expectedDistance: -5),
+      TestCase<Int>(from: v4, to: v5, expectedPath: [4, 1, 5], expectedDistance: -2),
+      TestCase<Int>(from: v5, to: v1, expectedPath: [5, 4, 1], expectedDistance: 8),
+      TestCase<Int>(from: v5, to: v2, expectedPath: [5, 4, 3, 2], expectedDistance: 5),
+      TestCase<Int>(from: v5, to: v3, expectedPath: [5, 4, 3], expectedDistance: 1),
+      TestCase<Int>(from: v5, to: v4, expectedPath: [5, 4], expectedDistance: 6),
       ]
 
-    for testCase: TestCase<String> in cases {
+    for testCase: TestCase<Int> in cases {
       if let computedPath = result.path(fromVertex: testCase.from, toVertex: testCase.to, inGraph: graph),
               computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
         XCTAssert(computedDistance == testCase.expectedDistance, "expected distance \(testCase.expectedDistance) but got \(computedDistance)")
@@ -78,20 +81,20 @@ class APSPTests: XCTestCase {
 
   func testExampleFromReadme() {
 
-    var graph = Graph<Int>()
+    let graph = AdjacencyMatrixGraph<Int>()
     let v1 = graph.createVertex(1)
     let v2 = graph.createVertex(2)
     let v3 = graph.createVertex(3)
     let v4 = graph.createVertex(4)
 
-    graph.connect(v1, to: v2, withWeight: 4)
-    graph.connect(v1, to: v3, withWeight: 1)
-    graph.connect(v1, to: v4, withWeight: 3)
+    graph.addDirectedEdge(v1, to: v2, withWeight: 4)
+    graph.addDirectedEdge(v1, to: v3, withWeight: 1)
+    graph.addDirectedEdge(v1, to: v4, withWeight: 3)
 
-    graph.connect(v2, to: v3, withWeight: 8)
-    graph.connect(v2, to: v4, withWeight: -2)
+    graph.addDirectedEdge(v2, to: v3, withWeight: 8)
+    graph.addDirectedEdge(v2, to: v4, withWeight: -2)
 
-    graph.connect(v3, to: v4, withWeight: -5)
+    graph.addDirectedEdge(v3, to: v4, withWeight: -5)
 
     let result = FloydWarshall<Int>.apply(graph)
 
diff --git a/Graph/AdjacencyList.swift b/Graph/AdjacencyList.swift
deleted file mode 100644
index 3a8bc3006..000000000
--- a/Graph/AdjacencyList.swift
+++ /dev/null
@@ -1,39 +0,0 @@
-private var uniqueIDCounter = 0
-
-public struct Edge<T> {
-  public let from: Vertex<T>
-  public let to: Vertex<T>
-  public let weight: Double
-}
-
-public struct Vertex<T> {
-  public var data: T
-  public let uniqueID: Int
-  
-  private(set) public var edges: [Edge<T>] = []   // the adjacency list
-  
-  public init(data: T) {
-    self.data = data
-    uniqueID = uniqueIDCounter
-    uniqueIDCounter += 1
-  }
-
-  // Creates the directed edge: self -----> dest
-  public mutating func connectTo(destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
-    edges.append(Edge(from: self, to: destinationVertex, weight: weight))
-  }
-  
-  // Creates an undirected edge by making two directed edges: self ----> other, and other ----> self
-  public mutating func connectBetween(inout otherVertex: Vertex<T>, withWeight weight: Double = 0) {
-    connectTo(otherVertex, withWeight: weight)
-    otherVertex.connectTo(self, withWeight: weight)
-  }
-  
-  // Does this vertex have an edge -----> otherVertex?
-  public func edgeTo(otherVertex: Vertex<T>) -> Edge<T>? {
-    for e in edges where e.to.uniqueID == otherVertex.uniqueID {
-      return e
-    }
-    return nil
-  }
-}
diff --git a/Graph/AdjacencyMatrix.swift b/Graph/AdjacencyMatrix.swift
deleted file mode 100644
index d1d35ac02..000000000
--- a/Graph/AdjacencyMatrix.swift
+++ /dev/null
@@ -1,75 +0,0 @@
-import Foundation
-
-public struct Vertex<T> {
-  public var data: T
-  public let index: Int
-}
-
-
-
-public struct Graph<T> {
-  // If adjacencyMatrix[i][j] is not nil, then there is an edge from
-  // vertex i to vertex j.
-  var adjacencyMatrix: [[Double?]] = []
-  var vertices: [Vertex<T>] = []
-
-  public init() {}
-  
-  // Adds a new vertex to the matrix.
-  // Performance: possibly O(n^2) because of the resizing of the matrix.
-  public mutating func createVertex(data: T) -> Vertex<T> {
-    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
-    
-    // Expand each existing row to the right one column.
-    for i in 0..<adjacencyMatrix.count {
-      adjacencyMatrix[i].append(nil)
-    }
-    
-    // Add one new row at the bottom.
-    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
-    adjacencyMatrix.append(newRow)
-
-    vertices.append(vertex)
-    return vertex
-  }
-}
-
-extension Graph: CustomStringConvertible {
-  public var description: String {
-    get {
-      var grid = [String]()
-      let n = self.adjacencyMatrix.count
-      for i in 0..<n {
-        var row = ""
-        for j in 0..<n {
-          if let value = self.adjacencyMatrix[i][j] {
-            let number = NSString(format: "%.1f", value)
-            row += "\(value >= 0 ? " " : "")\(number) "
-          } else {
-            row += "  ø  "
-          }
-        }
-        grid.append(row)
-      }
-      return (grid as NSArray).componentsJoinedByString("\n")
-    }
-  }
-}
-
-extension Graph {
-  // Creates a directed edge source -----> dest.
-  public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
-  }
-  
-  // Creates an undirected edge by making 2 directed edges:
-  // some ----> other, and other ----> some.
-  public mutating func connect(someVertex: Vertex<T>, symmetricallyWithVertex withVertex: Vertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[someVertex.index][withVertex.index] = weight
-    adjacencyMatrix[withVertex.index][someVertex.index] = weight
-  }
-
-  public func weightFrom(sourceVertex: Vertex<T>, toDestinationVertex: Vertex<T>) -> Double? {
-    return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
-  }
-}
diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
new file mode 100644
index 000000000..4e6d98a11
--- /dev/null
+++ b/Graph/Graph.playground/Contents.swift
@@ -0,0 +1,45 @@
+import Graph
+
+// Create the vertices
+var adjacencyMatrixGraph = AdjacencyMatrixGraph<Int>()
+var adjacencyListGraph = AdjacencyListGraph<Int>()
+
+for graph in [ adjacencyMatrixGraph, adjacencyListGraph ] {
+
+  let v1 = graph.createVertex(1)
+  let v2 = graph.createVertex(2)
+  let v3 = graph.createVertex(3)
+  let v4 = graph.createVertex(4)
+  let v5 = graph.createVertex(5)
+
+  // Set up a cycle like so:
+  //               v5
+  //                ^
+  //                | (3.2)
+  //                |
+  // v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
+  // ^                                            |
+  // |                                            V
+  // ---------<-----------<---------(2.8)----<----|
+
+  graph.addDirectedEdge(v1, to: v2, withWeight: 1.0)
+  graph.addDirectedEdge(v2, to: v3, withWeight: 1.0)
+  graph.addDirectedEdge(v3, to: v4, withWeight: 4.5)
+  graph.addDirectedEdge(v4, to: v1, withWeight: 2.8)
+  graph.addDirectedEdge(v2, to: v5, withWeight: 3.2)
+
+  // Returns the weight of the edge from v1 to v2 (1.0)
+  graph.weightFrom(v1, to: v2)
+
+  // Returns the weight of the edge from v1 to v3 (nil, since there is not an edge)
+  graph.weightFrom(v1, to: v3)
+
+  // Returns the weight of the edge from v3 to v4 (4.5)
+  graph.weightFrom(v3, to: v4)
+
+  // Returns the weight of the edge from v4 to v1 (2.8)
+  graph.weightFrom(v4, to: v1)
+
+  print(graph)
+  print() // separate by a newline
+}
diff --git a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift
deleted file mode 100644
index f3c89b112..000000000
--- a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/Contents.swift	
+++ /dev/null
@@ -1,87 +0,0 @@
-//: # Graph using an adjacency list
-//:
-//: In an adjacency list implementation of a graph, each vertex stores an
-//: array of edges, indicating to which other vertices it has an edge.
-//: (Note the directionality: we only record "to" edges, not "from" edges.)
-
-private var uniqueIDCounter = 0
-
-public struct Edge<T> {
-  public let from: Vertex<T>
-  public let to: Vertex<T>
-  public let weight: Double
-}
-
-public struct Vertex<T> {
-  public var data: T
-  public let uniqueID: Int
-  
-  private(set) public var edges: [Edge<T>] = []   // the adjacency list
-  
-  public init(data: T) {
-    self.data = data
-    uniqueID = uniqueIDCounter
-    uniqueIDCounter += 1
-  }
-
-  // Creates the directed edge: self -----> dest
-  public mutating func connectTo(destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
-    edges.append(Edge(from: self, to: destinationVertex, weight: weight))
-  }
-  
-  // Creates an undirected edge by making two directed edges: self ----> other, and other ----> self
-  public mutating func connectBetween(inout otherVertex: Vertex<T>, withWeight weight: Double = 0) {
-    connectTo(otherVertex, withWeight: weight)
-    otherVertex.connectTo(self, withWeight: weight)
-  }
-  
-  // Does this vertex have an edge -----> otherVertex?
-  public func edgeTo(otherVertex: Vertex<T>) -> Edge<T>? {
-    for e in edges where e.to.uniqueID == otherVertex.uniqueID {
-      return e
-    }
-    return nil
-  }
-}
-
-
-
-//: ### Demo
-
-// Create the vertices
-var v1 = Vertex(data: 1)
-var v2 = Vertex(data: 2)
-var v3 = Vertex(data: 3)
-var v4 = Vertex(data: 4)
-var v5 = Vertex(data: 5)
-
-// Set up a cycle like so:
-//               v5
-//                ^
-//                | (3.2)
-//                |
-// v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
-// ^                                            |
-// |                                            V
-// ---------<-----------<---------(2.8)----<----|
-
-v1.connectTo(v2, withWeight: 1.0)
-v2.connectTo(v3, withWeight: 1.0)
-v3.connectTo(v4, withWeight: 4.5)
-v4.connectTo(v1, withWeight: 2.8)
-v2.connectTo(v5, withWeight: 3.2)
-
-
-// Returns the weight of the edge from v1 to v2 (1.0)
-v1.edgeTo(v2)?.weight
-
-// Returns the weight of the edge from v1 to v3 (nil, since there is not an edge)
-v1.edgeTo(v3)?.weight
-
-// Returns the weight of the edge from v3 to v4 (4.5)
-v3.edgeTo(v4)?.weight
-
-// Returns the weight of the edge from v4 to v1 (2.8)
-v4.edgeTo(v1)?.weight
-
-//: [Next: Adjacency Matrix](@next)
diff --git a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/timeline.xctimeline b/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Graph/Graph.playground/Pages/Adjacency List.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift
deleted file mode 100644
index 8d9fb5080..000000000
--- a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/Contents.swift	
+++ /dev/null
@@ -1,99 +0,0 @@
-//: [Previous: Adjacency List](@previous)
-
-//: # Graph using an adjacency matrix
-//:
-//: In an adjacency matrix implementation, each vertex is given an index 
-//: from `0..<V`, where `V` is the total number of vertices. The matrix is 
-//: a 2D array, with each entry indicating if the corresponding two vertices
-//: are connected, and the weight of that edge.
-//:
-//: For example, if `matrix[3][5] = 4.6`, then vertex #3 is connected to
-//: vertex #5, with a weight of 4.6. Note that vertex #5 is not necessarily
-//: connected back to vertex #3 (that would be recorded in `matrix[5][3]`).
-
-public struct Vertex<T> {
-  public var data: T
-  private let index: Int
-}
-
-public struct Graph<T> {
-  // If adjacencyMatrix[i][j] is not nil, then there is an edge from
-  // vertex i to vertex j.
-  private var adjacencyMatrix: [[Double?]] = []
-  
-  // Adds a new vertex to the matrix.
-  // Performance: possibly O(n^2) because of the resizing of the matrix.
-  public mutating func createVertex(data: T) -> Vertex<T> {
-    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
-    
-    // Expand each existing row to the right one column.
-    for i in 0..<adjacencyMatrix.count {
-      adjacencyMatrix[i].append(nil)
-    }
-    
-    // Add one new row at the bottom.
-    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
-    adjacencyMatrix.append(newRow)
-
-    return vertex
-  }
-  
-  // Creates a directed edge source -----> dest.
-  public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
-  }
-  
-  // Creates an undirected edge by making 2 directed edges:
-  // some ----> other, and other ----> some.
-  public mutating func connect(someVertex: Vertex<T>, symmetricallyWithVertex withVertex: Vertex<T>, withWeight weight: Double = 0) {
-    adjacencyMatrix[someVertex.index][withVertex.index] = weight
-    adjacencyMatrix[withVertex.index][someVertex.index] = weight
-  }
-
-  public func weightFrom(sourceVertex: Vertex<T>, toDestinationVertex: Vertex<T>) -> Double? {
-    return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
-  }
-}
-
-
-
-//: ### Demo
-
-// Create the vertices
-var graph = Graph<Int>()
-let v1 = graph.createVertex(1)
-let v2 = graph.createVertex(2)
-let v3 = graph.createVertex(3)
-let v4 = graph.createVertex(4)
-let v5 = graph.createVertex(5)
-
-// Set up a cycle like so:
-//               v5
-//                ^
-//                | (3.2)
-//                |
-// v1 ---(1)---> v2 ---(1)---> v3 ---(4.5)---> v4
-// ^                                            |
-// |                                            V
-// ---------<-----------<---------(2.8)----<----|
-
-graph.connect(v1, to: v2, withWeight: 1.0)
-graph.connect(v2, to: v3, withWeight: 1.0)
-graph.connect(v3, to: v4, withWeight: 4.5)
-graph.connect(v4, to: v1, withWeight: 2.8)
-graph.connect(v2, to: v5, withWeight: 3.2)
-
-// Returns the weight of the edge from v1 to v2 (1.0)
-graph.weightFrom(v1, toDestinationVertex: v2)
-
-// Returns the weight of the edge from v1 to v3 (nil, since there is not an edge)
-graph.weightFrom(v1, toDestinationVertex: v3)
-
-// Returns the weight of the edge from v3 to v4 (4.5)
-graph.weightFrom(v3, toDestinationVertex: v4)
-
-// Returns the weight of the edge from v4 to v1 (2.8)
-graph.weightFrom(v4, toDestinationVertex: v1)
-
-print(graph.adjacencyMatrix)
-
diff --git a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline b/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index 60cd19e82..000000000
--- a/Graph/Graph.playground/Pages/Adjacency Matrix.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,11 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-      <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=28&amp;CharacterRangeLoc=3390&amp;EndingColumnNumber=29&amp;EndingLineNumber=97&amp;StartingColumnNumber=1&amp;StartingLineNumber=97&amp;Timestamp=484381589.889495"
-         selectedRepresentationIndex = "0"
-         shouldTrackSuperviewWidth = "NO">
-      </LoggerValueHistoryTimelineItem>
-   </TimelineItems>
-</Timeline>
diff --git a/Graph/Graph.playground/contents.xcplayground b/Graph/Graph.playground/contents.xcplayground
index 32b5a98b9..50ce46d0b 100644
--- a/Graph/Graph.playground/contents.xcplayground
+++ b/Graph/Graph.playground/contents.xcplayground
@@ -1,7 +1,2 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='6.0' target-platform='ios' display-mode='rendered'>
-    <pages>
-        <page name='Adjacency List'/>
-        <page name='Adjacency Matrix'/>
-    </pages>
-</playground>
\ No newline at end of file
+<playground version='6.0' target-platform='osx' display-mode='rendered'/>
\ No newline at end of file
diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..0157eb377
--- /dev/null
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -0,0 +1,421 @@
+// !$*UTF8*$!
+{
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+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				CURRENT_PROJECT_VERSION = 1;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				VERSIONING_SYSTEM = "apple-generic";
+				VERSION_INFO_PREFIX = "";
+			};
+			name = Release;
+		};
+		49BFA3121CDF886B00522D66 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				DEFINES_MODULE = YES;
+				DYLIB_COMPATIBILITY_VERSION = 1;
+				DYLIB_CURRENT_VERSION = 1;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				FRAMEWORK_VERSION = A;
+				INFOPLIST_FILE = Graph/Info.plist;
+				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.Graph";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SKIP_INSTALL = YES;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		49BFA3131CDF886B00522D66 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				DEFINES_MODULE = YES;
+				DYLIB_COMPATIBILITY_VERSION = 1;
+				DYLIB_CURRENT_VERSION = 1;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				FRAMEWORK_VERSION = A;
+				INFOPLIST_FILE = Graph/Info.plist;
+				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.Graph";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SKIP_INSTALL = YES;
+			};
+			name = Release;
+		};
+		49BFA3151CDF886B00522D66 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = GraphTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.GraphTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Debug;
+		};
+		49BFA3161CDF886B00522D66 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = GraphTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.GraphTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		49BFA2F71CDF886B00522D66 /* Build configuration list for PBXProject "Graph" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				49BFA30F1CDF886B00522D66 /* Debug */,
+				49BFA3101CDF886B00522D66 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		49BFA3111CDF886B00522D66 /* Build configuration list for PBXNativeTarget "Graph" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				49BFA3121CDF886B00522D66 /* Debug */,
+				49BFA3131CDF886B00522D66 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		49BFA3141CDF886B00522D66 /* Build configuration list for PBXNativeTarget "GraphTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				49BFA3151CDF886B00522D66 /* Debug */,
+				49BFA3161CDF886B00522D66 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 49BFA2F41CDF886B00522D66 /* Project object */;
+}
diff --git a/Graph/Graph.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Graph/Graph.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..94b2795e2
--- /dev/null
+++ b/Graph/Graph.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+</Workspace>
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
new file mode 100644
index 000000000..a8ce1124d
--- /dev/null
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -0,0 +1,80 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA2FC1CDF886B00522D66"
+               BuildableName = "Graph.framework"
+               BlueprintName = "Graph"
+               ReferencedContainer = "container:Graph.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA2FC1CDF886B00522D66"
+            BuildableName = "Graph.framework"
+            BlueprintName = "Graph"
+            ReferencedContainer = "container:Graph.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA2FC1CDF886B00522D66"
+            BuildableName = "Graph.framework"
+            BlueprintName = "Graph"
+            ReferencedContainer = "container:Graph.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
new file mode 100644
index 000000000..8eb3c9fdf
--- /dev/null
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA3061CDF886B00522D66"
+               BuildableName = "GraphTests.xctest"
+               BlueprintName = "GraphTests"
+               ReferencedContainer = "container:Graph.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Graph/Graph.xcworkspace/contents.xcworkspacedata b/Graph/Graph.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..eea257206
--- /dev/null
+++ b/Graph/Graph.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,10 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "group:Graph.playground">
+   </FileRef>
+   <FileRef
+      location = "group:Graph.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Graph/Graph.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Graph/Graph.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Graph/Graph.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>
diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
new file mode 100644
index 000000000..fddd04033
--- /dev/null
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -0,0 +1,134 @@
+//
+//  AdjacencyListGraph.swift
+//  Graph
+//
+//  Created by Andrew McKnight on 5/13/16.
+//
+
+import Foundation
+
+private class EdgeList<T where T: Equatable, T: Hashable> {
+
+  var vertex: Vertex<T>
+  var edges: [Edge<T>]? = nil
+
+  init(vertex: Vertex<T>) {
+    self.vertex = vertex
+  }
+
+  func addEdge(edge: Edge<T>) {
+    edges?.append(edge)
+  }
+
+}
+
+public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGraph<T> {
+
+  private var adjacencyList: [EdgeList<T>] = []
+
+  public override init() {
+    super.init()
+  }
+
+  public override init(fromGraph graph: AbstractGraph<T>) {
+    super.init(fromGraph: graph)
+  }
+
+  public override var vertices: [Vertex<T>] {
+    get {
+      var vertices = [Vertex<T>]()
+      for edgeList in adjacencyList {
+        vertices.append(edgeList.vertex)
+      }
+      return vertices
+    }
+  }
+
+  public override var edges: [Edge<T>] {
+    get {
+      var allEdges = Set<Edge<T>>()
+      for edgeList in adjacencyList {
+        guard let edges = edgeList.edges else {
+          continue
+        }
+
+        for edge in edges {
+          allEdges.insert(edge)
+        }
+      }
+      return Array(allEdges)
+    }
+  }
+
+  public override func createVertex(data: T) -> Vertex<T> {
+    // check if the vertex already exists
+    let matchingVertices = vertices.filter() { vertex in
+      return vertex.data == data
+    }
+
+    if matchingVertices.count > 0 {
+      return matchingVertices.last!
+    }
+
+    // if the vertex doesn't exist, create a new one
+    let vertex = Vertex(data: data, index: adjacencyList.count)
+    adjacencyList.append(EdgeList(vertex: vertex))
+    return vertex
+  }
+
+  public override func addDirectedEdge(from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
+    // works
+    let edge = Edge(from: from, to: to, weight: weight)
+    let edgeList = adjacencyList[from.index]
+    if edgeList.edges?.count > 0 {
+      edgeList.addEdge(edge)
+    } else {
+      edgeList.edges = [edge]
+    }
+  }
+
+  public override func addUndirectedEdge(vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
+    addDirectedEdge(vertices.0, to: vertices.1, withWeight: weight)
+    addDirectedEdge(vertices.1, to: vertices.0, withWeight: weight)
+  }
+
+
+  public override func weightFrom(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
+    guard let edges = adjacencyList[sourceVertex.index].edges else {
+      return nil
+    }
+
+    for edge: Edge<T> in edges {
+      if edge.to == destinationVertex {
+        return edge.weight
+      }
+    }
+
+    return nil
+  }
+
+  public override var description: String {
+    get {
+      var rows = [String]()
+      for edgeList in adjacencyList {
+
+        guard let edges = edgeList.edges else {
+          continue
+        }
+
+        var row = [String]()
+        for edge in edges {
+          var value = "\(edge.to.data)"
+          if edge.weight != nil {
+            value = "(\(value): \(edge.weight!))"
+          }
+          row.append(value)
+        }
+
+        rows.append("\(edgeList.vertex.data) -> [\(row.joinWithSeparator(", "))]")
+      }
+
+      return rows.joinWithSeparator("\n")
+    }
+  }
+}
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
new file mode 100644
index 000000000..b2047797f
--- /dev/null
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -0,0 +1,107 @@
+//
+//  AdjacencyMatrixGraph.swift
+//  Graph
+//
+//  Created by Andrew McKnight on 5/13/16.
+//
+
+import Foundation
+
+public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGraph<T> {
+
+  // If adjacencyMatrix[i][j] is not nil, then there is an edge from
+  // vertex i to vertex j.
+  private var adjacencyMatrix: [[Double?]] = []
+  private var _vertices: [Vertex<T>] = []
+
+  public override init() {
+    super.init()
+  }
+
+  public override init(fromGraph graph: AbstractGraph<T>) {
+    super.init(fromGraph: graph)
+  }
+
+  public override var vertices: [Vertex<T>] {
+    get {
+      return _vertices
+    }
+  }
+
+  public override var edges: [Edge<T>] {
+    get {
+      var edges = [Edge<T>]()
+      for row in 0 ..< adjacencyMatrix.count {
+        for column in 0 ..< adjacencyMatrix.count {
+          if let weight = adjacencyMatrix[row][column] {
+            edges.append(Edge(from: vertices[row], to: vertices[column], weight: weight))
+          }
+        }
+      }
+      return edges
+    }
+  }
+
+  // Adds a new vertex to the matrix.
+  // Performance: possibly O(n^2) because of the resizing of the matrix.
+  public override func createVertex(data: T) -> Vertex<T> {
+    // check if the vertex already exists
+    let matchingVertices = vertices.filter() { vertex in
+      return vertex.data == data
+    }
+
+    if matchingVertices.count > 0 {
+      return matchingVertices.last!
+    }
+
+    // if the vertex doesn't exist, create a new one
+    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
+
+    // Expand each existing row to the right one column.
+    for i in 0 ..< adjacencyMatrix.count {
+      adjacencyMatrix[i].append(nil)
+    }
+
+    // Add one new row at the bottom.
+    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+    adjacencyMatrix.append(newRow)
+
+    _vertices.append(vertex)
+
+    return vertex
+  }
+
+  public override func addDirectedEdge(from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
+    adjacencyMatrix[from.index][to.index] = weight
+  }
+
+  public override func addUndirectedEdge(vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
+    addDirectedEdge(vertices.0, to: vertices.1, withWeight: weight)
+    addDirectedEdge(vertices.1, to: vertices.0, withWeight: weight)
+  }
+
+  public override func weightFrom(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
+    return adjacencyMatrix[sourceVertex.index][destinationVertex.index]
+  }
+
+  public override var description: String {
+    get {
+      var grid = [String]()
+      let n = self.adjacencyMatrix.count
+      for i in 0..<n {
+        var row = ""
+        for j in 0..<n {
+          if let value = self.adjacencyMatrix[i][j] {
+            let number = NSString(format: "%.1f", value)
+            row += "\(value >= 0 ? " " : "")\(number) "
+          } else {
+            row += "  ø  "
+          }
+        }
+        grid.append(row)
+      }
+      return (grid as NSArray).componentsJoinedByString("\n")
+    }
+  }
+
+}
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
new file mode 100644
index 000000000..5ce865af6
--- /dev/null
+++ b/Graph/Graph/Edge.swift
@@ -0,0 +1,60 @@
+//
+//  Edge.swift
+//  Graph
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import Foundation
+
+public struct Edge<T where T: Equatable, T: Hashable>: Equatable {
+  
+  public let from: Vertex<T>
+  public let to: Vertex<T>
+
+  public let weight: Double?
+
+}
+
+extension Edge: CustomStringConvertible {
+
+  public var description: String {
+    get {
+      guard let unwrappedWeight = weight else {
+        return "\(from.description) -> \(to.description)"
+      }
+      return "\(from.description) -(\(unwrappedWeight))-> \(to.description)"
+    }
+  }
+
+}
+
+extension Edge: Hashable {
+
+  public var hashValue: Int {
+    get {
+      var string = "\(from.description)\(to.description)"
+      if weight != nil {
+        string.appendContentsOf("\(weight!)")
+      }
+      return string.hashValue
+    }
+  }
+
+}
+
+public func ==<T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
+  guard lhs.from == rhs.from else {
+    return false
+  }
+
+  guard lhs.to == rhs.to else {
+    return false
+  }
+
+  guard lhs.weight == rhs.weight else {
+    return false
+  }
+
+  return true
+}
diff --git a/Graph/Graph/Graph.h b/Graph/Graph/Graph.h
new file mode 100644
index 000000000..085103b23
--- /dev/null
+++ b/Graph/Graph/Graph.h
@@ -0,0 +1,18 @@
+//
+//  Graph.h
+//  Graph
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+#import <Cocoa/Cocoa.h>
+
+//! Project version number for Graph.
+FOUNDATION_EXPORT double GraphVersionNumber;
+
+//! Project version string for Graph.
+FOUNDATION_EXPORT const unsigned char GraphVersionString[];
+
+// In this header, you should import all the public headers of your framework using statements like #import <Graph/PublicHeader.h>
+
+
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
new file mode 100644
index 000000000..4e27e989e
--- /dev/null
+++ b/Graph/Graph/Graph.swift
@@ -0,0 +1,59 @@
+//
+//  Graph.swift
+//  Graph
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import Foundation
+
+public class AbstractGraph<T where T: Equatable, T: Hashable>: CustomStringConvertible {
+
+  public init() {}
+
+  public init(fromGraph graph: AbstractGraph<T>) {
+    for edge in graph.edges {
+      let from = createVertex(edge.from.data)
+      let to = createVertex(edge.to.data)
+
+      addDirectedEdge(from, to: to, withWeight: edge.weight)
+    }
+  }
+
+  public var description: String {
+    get {
+      fatalError("abstract property accessed")
+    }
+  }
+
+  public var vertices: [Vertex<T>] {
+    get {
+      fatalError("abstract property accessed")
+    }
+  }
+
+  public var edges: [Edge<T>] {
+    get {
+      fatalError("abstract property accessed")
+    }
+  }
+
+  // Adds a new vertex to the matrix.
+  // Performance: possibly O(n^2) because of the resizing of the matrix.
+  public func createVertex(data: T) -> Vertex<T> {
+    fatalError("abstract function called")
+  }
+
+  public func addDirectedEdge(from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
+    fatalError("abstract function called")
+  }
+
+  public func addUndirectedEdge(vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
+    fatalError("abstract function called")
+  }
+
+  public func weightFrom(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
+    fatalError("abstract function called")
+  }
+
+}
diff --git a/Graph/Graph/Info.plist b/Graph/Graph/Info.plist
new file mode 100644
index 000000000..d3de8eefb
--- /dev/null
+++ b/Graph/Graph/Info.plist
@@ -0,0 +1,26 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>FMWK</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>$(CURRENT_PROJECT_VERSION)</string>
+	<key>NSPrincipalClass</key>
+	<string></string>
+</dict>
+</plist>
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
new file mode 100644
index 000000000..1223eb116
--- /dev/null
+++ b/Graph/Graph/Vertex.swift
@@ -0,0 +1,47 @@
+//
+//  Vertex.swift
+//  Graph
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import Foundation
+
+public struct Vertex<T where T: Equatable, T: Hashable>: Equatable {
+
+  public var data: T
+  public let index: Int
+
+}
+
+extension Vertex: CustomStringConvertible {
+
+  public var description: String {
+    get {
+      return "\(index): \(data)"
+    }
+  }
+
+}
+
+extension Vertex: Hashable {
+
+  public var hashValue: Int {
+    get {
+      return "\(data)\(index)".hashValue
+    }
+  }
+
+}
+
+public func ==<T: Equatable>(lhs: Vertex<T>, rhs: Vertex<T>) -> Bool {
+  guard lhs.index == rhs.index else {
+    return false
+  }
+
+  guard lhs.data == rhs.data else {
+    return false
+  }
+
+  return true
+}
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
new file mode 100644
index 000000000..e6360754e
--- /dev/null
+++ b/Graph/GraphTests/GraphTests.swift
@@ -0,0 +1,57 @@
+//
+//  GraphTests.swift
+//  GraphTests
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import XCTest
+@testable import Graph
+
+class GraphTests: XCTestCase {
+    
+  func testAdjacencyMatrixGraphDescription() {
+
+    let graph = AdjacencyMatrixGraph<String>()
+
+    let a = graph.createVertex("a")
+    let b = graph.createVertex("b")
+    let c = graph.createVertex("c")
+
+    graph.addDirectedEdge(a, to: b, withWeight: 1.0)
+    graph.addDirectedEdge(b, to: c, withWeight: 2.0)
+
+    let expectedValue = "  ø   1.0   ø  \n  ø    ø   2.0 \n  ø    ø    ø  "
+    XCTAssertEqual(graph.description, expectedValue)
+  }
+
+  func testAdjacencyListGraphDescription() {
+
+    let graph = AdjacencyListGraph<String>()
+
+    let a = graph.createVertex("a")
+    let b = graph.createVertex("b")
+    let c = graph.createVertex("c")
+
+    graph.addDirectedEdge(a, to: b, withWeight: 1.0)
+    graph.addDirectedEdge(b, to: c, withWeight: 2.0)
+    graph.addDirectedEdge(a, to: c, withWeight: -5.5)
+
+    let expectedValue = "a -> [(b: 1.0), (c: -5.5)]\nb -> [(c: 2.0)]"
+    XCTAssertEqual(graph.description, expectedValue)
+  }
+
+  func testAddingPreexistingVertex() {
+    let adjacencyList = AdjacencyListGraph<String>()
+    let adjacencyMatrix = AdjacencyMatrixGraph<String>()
+
+    for graph in [adjacencyList, adjacencyMatrix] {
+      let a = graph.createVertex("a")
+      let b = graph.createVertex("a")
+
+      XCTAssertEqual(a, b, "Should have returned the same vertex when creating a new one with identical data")
+      XCTAssertEqual(graph.vertices.count, 1, "Graph should only contain one vertex after trying to create two vertices with identical data")
+    }
+  }
+    
+}
diff --git a/Graph/GraphTests/Info.plist b/Graph/GraphTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Graph/GraphTests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Graph/README.markdown b/Graph/README.markdown
index 8e88f80eb..349add81a 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -80,12 +80,14 @@ There are two main strategies: adjacency list and adjacency matrix.
 
 ![Adjacency list](Images/AdjacencyList.png)
 
-The adjacency list describes outgoing edges. A has an edge to B but B does not have an edge back to A, so A does not appear in B's adjacency list.
+The adjacency list describes outgoing edges. A has an edge to B but B does not have an edge back to A, so A does not appear in B's adjacency list. Finding an edge or weight between two vertices can be expensive because there is no random access to edges–you must traverse the adjacency lists until it is found.
 
 **Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for vertex A, column for vertex B would have value 5.6:
 
 ![Adjacency matrix](Images/AdjacencyMatrix.png)
 
+Adding another vertex to the graph is expensive, because a new matrix structure must be created with enough space to hold the new row/column, and the existing structure must be copied into the new one.
+
 So which one should you use? Most of the time, the adjacency list is the right approach. What follows is a more detailed comparison between the two.
 
 Let *V* be the number of vertices in the graph, and *E* the number of edges.  Then we have:
@@ -103,159 +105,167 @@ In the case of a *sparse* graph, where each vertex is connected to only a handfu
 
 We'll show you sample implementations of both adjacency list and adjacency matrix.
 
-## The code: adjacency list
+## The code: edges and vertices
 
 The adjacency list for each vertex consists of `Edge` objects:
 
 ```swift
-public struct Edge<T> {
+public struct Edge<T where T: Equatable, T: Hashable>: Equatable {
+  
   public let from: Vertex<T>
   public let to: Vertex<T>
-  public let weight: Double
+
+  public let weight: Double?
 }
 ```
 
-This struct describes the "from" and "to" vertices and a weight value. Note that an `Edge` object is always directed, a one-way connection (shown as arrows in the illustrations above). If you want the connection to go both ways, you also need to add an `Edge` object to the adjacency list of the destination vertex.
+This struct describes the "from" and "to" vertices and a weight value. Note that an `Edge` object is always directed, a one-way connection (shown as arrows in the illustrations above). If you want an undirected connection, you also need to add an `Edge` object in the opposite direction. Each `Edge` optionally stores a weight, so they can be used to describe both weighted and unweighted graphs.
 
 The `Vertex` looks like this:
 
 ```swift
-private var uniqueIDCounter = 0
+public struct Vertex<T where T: Equatable, T: Hashable>: Equatable {
 
-public struct Vertex<T> {
   public var data: T
-  public let uniqueID: Int
-  
-  private(set) public var edges: [Edge<T>] = []
-  
-  public init(data: T) {
-    self.data = data
-    uniqueID = uniqueIDCounter
-    uniqueIDCounter += 1
-  }
+  public let index: Int
+
+}
 ```
 
-It stores arbitrary data with a generic type `T`. The vertex also has a unique identifier, which we use to compare equality later. The `edges` array is the adjacency list.
+It stores arbitrary data with a generic type `T`, which is `Hashable` to enforce uniqueness, and also `Equatable`. Vertices themselves are also `Equatable`.
+
+## The code: graphs
+
+> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
+
+Here's an example of a very simple graph:
+
+![Demo](Images/Demo1.png)
+
+We can represent it as an adjacency matrix or adjacency list. The classes implementing those concept both inherit a common API from `AbstractGraph`, so they can be created in an identical fashion, with different optimized data structures behind the scenes.
 
-To connect two vertices using a directed edge:
+Let's create some directed, weighted graphs, using each representation, to store the example:
 
 ```swift
-  public mutating func connectTo(destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
-    edges.append(Edge(from: self, to: destinationVertex, weight: weight))
-  }
+var adjacencyMatrixGraph = AdjacencyMatrixGraph<Int>()
+var adjacencyListGraph = AdjacencyListGraph<Int>()
+
+for graph in [ adjacencyMatrixGraph, adjacencyListGraph ] {
+
+  let v1 = graph.createVertex(1)
+  let v2 = graph.createVertex(2)
+  let v3 = graph.createVertex(3)
+  let v4 = graph.createVertex(4)
+  let v5 = graph.createVertex(5)
+
+  graph.addDirectedEdge(v1, to: v2, withWeight: 1.0)
+  graph.addDirectedEdge(v2, to: v3, withWeight: 1.0)
+  graph.addDirectedEdge(v3, to: v4, withWeight: 4.5)
+  graph.addDirectedEdge(v4, to: v1, withWeight: 2.8)
+  graph.addDirectedEdge(v2, to: v5, withWeight: 3.2)
+}
+
 ```
 
-As mentioned, to create an undirected edge you need to make two directed edges:
+As mentioned earlier, to create an undirected edge you need to make two directed edges. If we wanted undirected graphs, we'd call this method instead, which takes care of that work for us:
 
+```swift
+  graph.addUndirectedEdge(v1, to: v2, withWeight: 1.0)
+  graph.addUndirectedEdge(v2, to: v3, withWeight: 1.0)
+  graph.addUndirectedEdge(v3, to: v4, withWeight: 4.5)
+  graph.addUndirectedEdge(v4, to: v1, withWeight: 2.8)
+  graph.addUndirectedEdge(v2, to: v5, withWeight: 3.2)
 ```
-  public mutating func connectBetween(inout otherVertex: Vertex<T>, withWeight weight: Double = 0) {
-    connectTo(otherVertex, withWeight: weight)
-    otherVertex.connectTo(self, withWeight: weight)
-  }
-```
 
-There is also a method for checking adjacency, i.e. to determine if there is an edge between two vertices:
+We could provide `nil` as the values for the `withWeight` parameter in either case to make unweighted graphs.
+
+## The code: adjacency list
+
+To maintain the adjacency list, there is a class that maps a list of edges to a vertex. The graph simply maintains an array of such objects and modifies them as necessary.
 
 ```swift
-  public func edgeTo(otherVertex: Vertex<T>) -> Edge<T>? {
-    for e in edges where e.to.uniqueID == otherVertex.uniqueID {
-      return e
-    }
-    return nil
+private class EdgeList<T where T: Equatable, T: Hashable> {
+
+  var vertex: Vertex<T>
+  var edges: [Edge<T>]? = nil
+
+  init(vertex: Vertex<T>) {
+    self.vertex = vertex
   }
-```
 
-Here's an example of a very simple graph:
+  func addEdge(edge: Edge<T>) {
+    edges?.append(edge)
+  }
 
-![Demo](Images/Demo1.png)
+}
+``` 
 
-This is how you'd create it using `Vertex` objects:
+They are implemented as a class as opposed to structs so we can modify them by reference, in place, like when adding an edge to a new vertex, where the source vertex already has an edge list:
 
 ```swift
-var v1 = Vertex(data: 1)
-var v2 = Vertex(data: 2)
-var v3 = Vertex(data: 3)
-var v4 = Vertex(data: 4)
-var v5 = Vertex(data: 5)
-
-v1.connectTo(v2, withWeight: 1.0)
-v2.connectTo(v3, withWeight: 1.0)
-v3.connectTo(v4, withWeight: 4.5)
-v4.connectTo(v1, withWeight: 2.8)
-v2.connectTo(v5, withWeight: 3.2)
-```
+  public override func createVertex(data: T) -> Vertex<T> {
+    // check if the vertex already exists
+    let matchingVertices = vertices.filter() { vertex in
+      return vertex.data == data
+    }
 
-> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
+    if matchingVertices.count > 0 {
+      return matchingVertices.last!
+    }
 
-## The code: adjacency matrix
+    // if the vertex doesn't exist, create a new one
+    let vertex = Vertex(data: data, index: adjacencyList.count)
+    adjacencyList.append(EdgeList(vertex: vertex))
+    return vertex
+  }
+```
 
-We'll keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight.
+The adjacency list for the example looks like this: 
 
-```swift
-public struct Graph<T> {
-  private var adjacencyMatrix: [[Double?]] = []
-}
+```
+v1 -> [(v2: 1.0)]
+v2 -> [(v3: 1.0), (v5: 3.2)]
+v3 -> [(v4: 4.5)]
+v4 -> [(v1: 2.8)]
 ```
 
-If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
+where the general form `a -> [(b: w), ...]` means an edge exists from `a` to `b` with weight `w` (with possibly more edges connecting `a` to other vertices as well).
 
-To index into the matrix using vertices, we give each `Vertex` a unique integer index:
+## The code: adjacency matrix
 
-```swift
-public struct Vertex<T> {
-  public var data: T
-  private let index: Int
-}
-```
+We'll keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight. If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
 
-To create a new vertex, the graph must resize the matrix:
+To index into the matrix using vertices, we use the `index` property in `Vertex`, which is assigned when creating the vertex through the graph object. When creating a new vertex, the graph must resize the matrix:
 
 ```swift
-  public mutating func createVertex(data: T) -> Vertex<T> {
+  public override func createVertex(data: T) -> Vertex<T> {
+    // check if the vertex already exists
+    let matchingVertices = vertices.filter() { vertex in
+      return vertex.data == data
+    }
+
+    if matchingVertices.count > 0 {
+      return matchingVertices.last!
+    }
+
+    // if the vertex doesn't exist, create a new one
     let vertex = Vertex(data: data, index: adjacencyMatrix.count)
-    
+
     // Expand each existing row to the right one column.
-    for i in 0..<adjacencyMatrix.count {
+    for i in 0 ..< adjacencyMatrix.count {
       adjacencyMatrix[i].append(nil)
     }
-    
+
     // Add one new row at the bottom.
     let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
     adjacencyMatrix.append(newRow)
 
+    _vertices.append(vertex)
+
     return vertex
   }
 ```
 
-Once we have the matrix properly configured, adding edges and querying for edges are simple indexing operations into the matrix:
-
-```swift
-public mutating func connect(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>, withWeight weight: Double = 0) {
-  adjacencyMatrix[sourceVertex.index][destinationVertex.index] = weight
-}
-
-public func weightFrom(sourceVertex: Vertex<T>, toDestinationVertex: Vertex<T>) -> Double? {
-  return adjacencyMatrix[sourceVertex.index][toDestinationVertex.index]
-}
-```
-
-You use these objects as follows:
-
-```swift
-var graph = Graph<Int>()
-let v1 = graph.createVertex(1)
-let v2 = graph.createVertex(2)
-let v3 = graph.createVertex(3)
-let v4 = graph.createVertex(4)
-let v5 = graph.createVertex(5)
-
-graph.connect(v1, to: v2, withWeight: 1.0)
-graph.connect(v2, to: v3, withWeight: 1.0)
-graph.connect(v3, to: v4, withWeight: 4.5)
-graph.connect(v4, to: v1, withWeight: 2.8)
-graph.connect(v2, to: v5, withWeight: 3.2)
-```
-
 Then the adjacency matrix looks like this:
 
 	[[nil, 1.0, nil, nil, nil]    v1

From dd3ba8df3f9a24d521192af18a61a07d39134451 Mon Sep 17 00:00:00 2001
From: Andrew McKnight <amcknight2718@gmail.com>
Date: Mon, 30 May 2016 13:24:00 -0400
Subject: [PATCH 0383/1679] add project for SSSP with Bellman-Ford
 implementation

---
 .travis.yml                                   |   9 +-
 .../SSSP.playground/Contents.swift            |  28 ++
 .../SSSP.playground/contents.xcplayground     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../SSSP.xcodeproj/project.pbxproj            | 472 ++++++++++++++++++
 .../xcshareddata/xcschemes/SSSP.xcscheme      |  99 ++++
 .../xcshareddata/xcschemes/SSSPTests.xcscheme |  56 +++
 .../SSSP.xcworkspace/contents.xcworkspacedata |  10 +
 .../xcshareddata/WorkspaceSettings.xcsettings |   8 +
 .../SSSP/BellmanFord.swift                    | 136 +++++
 .../SSSP/Info.plist                           |  26 +
 .../SSSP/SSSP.h                               |  18 +
 .../SSSP/SSSP.swift                           |  32 ++
 .../SSSPTests/Info.plist                      |  24 +
 .../SSSPTests/SSSPTests.swift                 | 134 +++++
 15 files changed, 1059 insertions(+), 4 deletions(-)
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.playground/contents.xcplayground
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/contents.xcworkspacedata
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP/Info.plist
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP/SSSP.h
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSPTests/Info.plist
 create mode 100644 Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift

diff --git a/.travis.yml b/.travis.yml
index 294f4e158..b0210d197 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -3,17 +3,20 @@ osx_image: xcode7.3
 
 script:
 
+- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
@@ -21,7 +24,5 @@ script:
 - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
\ No newline at end of file
+- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
+- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
\ No newline at end of file
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift
new file mode 100644
index 000000000..ece36a663
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
@@ -0,0 +1,28 @@
+import Graph
+import SSSP
+
+let graph = AdjacencyMatrixGraph<String>()
+let s = graph.createVertex("s")
+let t = graph.createVertex("t")
+let x = graph.createVertex("x")
+let y = graph.createVertex("y")
+let z = graph.createVertex("z")
+
+graph.addDirectedEdge(s, to: t, withWeight: 6)
+graph.addDirectedEdge(s, to: y, withWeight: 7)
+
+graph.addDirectedEdge(t, to: x, withWeight: 5)
+graph.addDirectedEdge(t, to: y, withWeight: 8)
+graph.addDirectedEdge(t, to: z, withWeight: -4)
+
+graph.addDirectedEdge(x, to: t, withWeight: -2)
+
+graph.addDirectedEdge(y, to: x, withWeight: -3)
+graph.addDirectedEdge(y, to: z, withWeight: 9)
+
+graph.addDirectedEdge(z, to: s, withWeight: 2)
+graph.addDirectedEdge(z, to: x, withWeight: 7)
+
+let result = BellmanFord<String>.apply(graph, source: s)!
+
+let path = result.path(z, inGraph: graph)
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.playground/contents.xcplayground b/Single-Source Shortest Paths (Weighted)/SSSP.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.playground/playground.xcworkspace/contents.xcworkspacedata b/Single-Source Shortest Paths (Weighted)/SSSP.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..55893acfd
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
@@ -0,0 +1,472 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		49763FF21CF08FC500202EA9 /* Graph.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = 49763FEF1CF08FB100202EA9 /* Graph.framework */; };
+		49BFA2971CDF86E100522D66 /* SSSP.h in Headers */ = {isa = PBXBuildFile; fileRef = 49BFA2961CDF86E100522D66 /* SSSP.h */; settings = {ATTRIBUTES = (Public, ); }; };
+		49BFA29E1CDF86E100522D66 /* SSSP.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = 49BFA2931CDF86E100522D66 /* SSSP.framework */; };
+		49BFA2A31CDF86E100522D66 /* SSSPTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 49BFA2A21CDF86E100522D66 /* SSSPTests.swift */; };
+		49BFA2AE1CDF86FD00522D66 /* SSSP.swift in Sources */ = {isa = PBXBuildFile; fileRef = 49BFA2AD1CDF86FD00522D66 /* SSSP.swift */; };
+		49BFA2B01CDF870600522D66 /* BellmanFord.swift in Sources */ = {isa = PBXBuildFile; fileRef = 49BFA2AF1CDF870600522D66 /* BellmanFord.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
+		49763FEE1CF08FB100202EA9 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 49763FE91CF08FB100202EA9 /* Graph.xcodeproj */;
+			proxyType = 2;
+			remoteGlobalIDString = 49BFA2FD1CDF886B00522D66;
+			remoteInfo = Graph;
+		};
+		49763FF01CF08FB100202EA9 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 49763FE91CF08FB100202EA9 /* Graph.xcodeproj */;
+			proxyType = 2;
+			remoteGlobalIDString = 49BFA3071CDF886B00522D66;
+			remoteInfo = GraphTests;
+		};
+		49763FF31CF08FC900202EA9 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 49763FE91CF08FB100202EA9 /* Graph.xcodeproj */;
+			proxyType = 1;
+			remoteGlobalIDString = 49BFA2FC1CDF886B00522D66;
+			remoteInfo = Graph;
+		};
+		49BFA29F1CDF86E100522D66 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 49BFA28A1CDF86E100522D66 /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = 49BFA2921CDF86E100522D66;
+			remoteInfo = SSSP;
+		};
+/* End PBXContainerItemProxy section */
+
+/* Begin PBXFileReference section */
+		49763FE91CF08FB100202EA9 /* Graph.xcodeproj */ = {isa = PBXFileReference; lastKnownFileType = "wrapper.pb-project"; name = Graph.xcodeproj; path = ../Graph/Graph.xcodeproj; sourceTree = "<group>"; };
+		49BFA2931CDF86E100522D66 /* SSSP.framework */ = {isa = PBXFileReference; explicitFileType = wrapper.framework; includeInIndex = 0; path = SSSP.framework; sourceTree = BUILT_PRODUCTS_DIR; };
+		49BFA2961CDF86E100522D66 /* SSSP.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = SSSP.h; sourceTree = "<group>"; };
+		49BFA2981CDF86E100522D66 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		49BFA29D1CDF86E100522D66 /* SSSPTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = SSSPTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		49BFA2A21CDF86E100522D66 /* SSSPTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = SSSPTests.swift; sourceTree = "<group>"; };
+		49BFA2A41CDF86E100522D66 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		49BFA2AD1CDF86FD00522D66 /* SSSP.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = SSSP.swift; sourceTree = "<group>"; };
+		49BFA2AF1CDF870600522D66 /* BellmanFord.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BellmanFord.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		49BFA28F1CDF86E100522D66 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				49763FF21CF08FC500202EA9 /* Graph.framework in Frameworks */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		49BFA29A1CDF86E100522D66 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				49BFA29E1CDF86E100522D66 /* SSSP.framework in Frameworks */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		49763FEA1CF08FB100202EA9 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				49763FEF1CF08FB100202EA9 /* Graph.framework */,
+				49763FF11CF08FB100202EA9 /* GraphTests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		49BFA2891CDF86E100522D66 = {
+			isa = PBXGroup;
+			children = (
+				49763FE91CF08FB100202EA9 /* Graph.xcodeproj */,
+				49BFA2951CDF86E100522D66 /* SSSP */,
+				49BFA2A11CDF86E100522D66 /* SSSPTests */,
+				49BFA2941CDF86E100522D66 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		49BFA2941CDF86E100522D66 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				49BFA2931CDF86E100522D66 /* SSSP.framework */,
+				49BFA29D1CDF86E100522D66 /* SSSPTests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		49BFA2951CDF86E100522D66 /* SSSP */ = {
+			isa = PBXGroup;
+			children = (
+				49BFA2961CDF86E100522D66 /* SSSP.h */,
+				49BFA2AD1CDF86FD00522D66 /* SSSP.swift */,
+				49BFA2AF1CDF870600522D66 /* BellmanFord.swift */,
+				49BFA2981CDF86E100522D66 /* Info.plist */,
+			);
+			path = SSSP;
+			sourceTree = "<group>";
+		};
+		49BFA2A11CDF86E100522D66 /* SSSPTests */ = {
+			isa = PBXGroup;
+			children = (
+				49BFA2A21CDF86E100522D66 /* SSSPTests.swift */,
+				49BFA2A41CDF86E100522D66 /* Info.plist */,
+			);
+			path = SSSPTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXHeadersBuildPhase section */
+		49BFA2901CDF86E100522D66 /* Headers */ = {
+			isa = PBXHeadersBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				49BFA2971CDF86E100522D66 /* SSSP.h in Headers */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXHeadersBuildPhase section */
+
+/* Begin PBXNativeTarget section */
+		49BFA2921CDF86E100522D66 /* SSSP */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 49BFA2A71CDF86E100522D66 /* Build configuration list for PBXNativeTarget "SSSP" */;
+			buildPhases = (
+				49BFA28E1CDF86E100522D66 /* Sources */,
+				49BFA28F1CDF86E100522D66 /* Frameworks */,
+				49BFA2901CDF86E100522D66 /* Headers */,
+				49BFA2911CDF86E100522D66 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				49763FF41CF08FC900202EA9 /* PBXTargetDependency */,
+			);
+			name = SSSP;
+			productName = SSSP;
+			productReference = 49BFA2931CDF86E100522D66 /* SSSP.framework */;
+			productType = "com.apple.product-type.framework";
+		};
+		49BFA29C1CDF86E100522D66 /* SSSPTests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 49BFA2AA1CDF86E100522D66 /* Build configuration list for PBXNativeTarget "SSSPTests" */;
+			buildPhases = (
+				49BFA2991CDF86E100522D66 /* Sources */,
+				49BFA29A1CDF86E100522D66 /* Frameworks */,
+				49BFA29B1CDF86E100522D66 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				49BFA2A01CDF86E100522D66 /* PBXTargetDependency */,
+			);
+			name = SSSPTests;
+			productName = SSSPTests;
+			productReference = 49BFA29D1CDF86E100522D66 /* SSSPTests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		49BFA28A1CDF86E100522D66 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0730;
+				LastUpgradeCheck = 0730;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					49BFA2921CDF86E100522D66 = {
+						CreatedOnToolsVersion = 7.3;
+					};
+					49BFA29C1CDF86E100522D66 = {
+						CreatedOnToolsVersion = 7.3;
+					};
+				};
+			};
+			buildConfigurationList = 49BFA28D1CDF86E100522D66 /* Build configuration list for PBXProject "SSSP" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
+			mainGroup = 49BFA2891CDF86E100522D66;
+			productRefGroup = 49BFA2941CDF86E100522D66 /* Products */;
+			projectDirPath = "";
+			projectReferences = (
+				{
+					ProductGroup = 49763FEA1CF08FB100202EA9 /* Products */;
+					ProjectRef = 49763FE91CF08FB100202EA9 /* Graph.xcodeproj */;
+				},
+			);
+			projectRoot = "";
+			targets = (
+				49BFA2921CDF86E100522D66 /* SSSP */,
+				49BFA29C1CDF86E100522D66 /* SSSPTests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXReferenceProxy section */
+		49763FEF1CF08FB100202EA9 /* Graph.framework */ = {
+			isa = PBXReferenceProxy;
+			fileType = wrapper.framework;
+			path = Graph.framework;
+			remoteRef = 49763FEE1CF08FB100202EA9 /* PBXContainerItemProxy */;
+			sourceTree = BUILT_PRODUCTS_DIR;
+		};
+		49763FF11CF08FB100202EA9 /* GraphTests.xctest */ = {
+			isa = PBXReferenceProxy;
+			fileType = wrapper.cfbundle;
+			path = GraphTests.xctest;
+			remoteRef = 49763FF01CF08FB100202EA9 /* PBXContainerItemProxy */;
+			sourceTree = BUILT_PRODUCTS_DIR;
+		};
+/* End PBXReferenceProxy section */
+
+/* Begin PBXResourcesBuildPhase section */
+		49BFA2911CDF86E100522D66 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		49BFA29B1CDF86E100522D66 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		49BFA28E1CDF86E100522D66 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				49BFA2B01CDF870600522D66 /* BellmanFord.swift in Sources */,
+				49BFA2AE1CDF86FD00522D66 /* SSSP.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+		49BFA2991CDF86E100522D66 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				49BFA2A31CDF86E100522D66 /* SSSPTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin PBXTargetDependency section */
+		49763FF41CF08FC900202EA9 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			name = Graph;
+			targetProxy = 49763FF31CF08FC900202EA9 /* PBXContainerItemProxy */;
+		};
+		49BFA2A01CDF86E100522D66 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			target = 49BFA2921CDF86E100522D66 /* SSSP */;
+			targetProxy = 49BFA29F1CDF86E100522D66 /* PBXContainerItemProxy */;
+		};
+/* End PBXTargetDependency section */
+
+/* Begin XCBuildConfiguration section */
+		49BFA2A51CDF86E100522D66 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
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+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				CURRENT_PROJECT_VERSION = 1;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				VERSIONING_SYSTEM = "apple-generic";
+				VERSION_INFO_PREFIX = "";
+			};
+			name = Debug;
+		};
+		49BFA2A61CDF86E100522D66 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				CURRENT_PROJECT_VERSION = 1;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
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+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				VERSIONING_SYSTEM = "apple-generic";
+				VERSION_INFO_PREFIX = "";
+			};
+			name = Release;
+		};
+		49BFA2A81CDF86E100522D66 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				DEFINES_MODULE = YES;
+				DYLIB_COMPATIBILITY_VERSION = 1;
+				DYLIB_CURRENT_VERSION = 1;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				FRAMEWORK_VERSION = A;
+				INFOPLIST_FILE = SSSP/Info.plist;
+				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSP";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SKIP_INSTALL = YES;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		49BFA2A91CDF86E100522D66 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				DEFINES_MODULE = YES;
+				DYLIB_COMPATIBILITY_VERSION = 1;
+				DYLIB_CURRENT_VERSION = 1;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				FRAMEWORK_VERSION = A;
+				INFOPLIST_FILE = SSSP/Info.plist;
+				INSTALL_PATH = "$(LOCAL_LIBRARY_DIR)/Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSP";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SKIP_INSTALL = YES;
+			};
+			name = Release;
+		};
+		49BFA2AB1CDF86E100522D66 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = SSSPTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
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+				PRODUCT_NAME = "$(TARGET_NAME)";
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+		};
+		49BFA2AC1CDF86E100522D66 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = SSSPTests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		49BFA28D1CDF86E100522D66 /* Build configuration list for PBXProject "SSSP" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				49BFA2A51CDF86E100522D66 /* Debug */,
+				49BFA2A61CDF86E100522D66 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		49BFA2A71CDF86E100522D66 /* Build configuration list for PBXNativeTarget "SSSP" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				49BFA2A81CDF86E100522D66 /* Debug */,
+				49BFA2A91CDF86E100522D66 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		49BFA2AA1CDF86E100522D66 /* Build configuration list for PBXNativeTarget "SSSPTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				49BFA2AB1CDF86E100522D66 /* Debug */,
+				49BFA2AC1CDF86E100522D66 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 49BFA28A1CDF86E100522D66 /* Project object */;
+}
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme
new file mode 100644
index 000000000..9d28c18c4
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme	
@@ -0,0 +1,99 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA2921CDF86E100522D66"
+               BuildableName = "SSSP.framework"
+               BlueprintName = "SSSP"
+               ReferencedContainer = "container:SSSP.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA29C1CDF86E100522D66"
+               BuildableName = "SSSPTests.xctest"
+               BlueprintName = "SSSPTests"
+               ReferencedContainer = "container:SSSP.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA2921CDF86E100522D66"
+            BuildableName = "SSSP.framework"
+            BlueprintName = "SSSP"
+            ReferencedContainer = "container:SSSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA2921CDF86E100522D66"
+            BuildableName = "SSSP.framework"
+            BlueprintName = "SSSP"
+            ReferencedContainer = "container:SSSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA2921CDF86E100522D66"
+            BuildableName = "SSSP.framework"
+            BlueprintName = "SSSP"
+            ReferencedContainer = "container:SSSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme
new file mode 100644
index 000000000..38b6c1697
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA29C1CDF86E100522D66"
+               BuildableName = "SSSPTests.xctest"
+               BlueprintName = "SSSPTests"
+               ReferencedContainer = "container:SSSP.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/contents.xcworkspacedata b/Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..77aa9c473
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,10 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "group:SSSP.playground">
+   </FileRef>
+   <FileRef
+      location = "group:SSSP.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift
new file mode 100644
index 000000000..4c58e4d90
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
@@ -0,0 +1,136 @@
+//
+//  BellmanFord.swift
+//  SSSP
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import Foundation
+import Graph
+
+public struct BellmanFord<T where T: Hashable> {
+  public typealias Q = T
+}
+
+/**
+ Encapsulation of the Bellman-Ford Single-Source Shortest Paths algorithm, which operates on a general directed graph that may contain negative edge weights.
+ 
+ - note: In all complexity bounds, `V` is the number of vertices in the graph, and `E` is the number of edges.
+ */
+extension BellmanFord: SSSPAlgorithm {
+
+  /**
+   Compute the shortest path from `source` to each other vertex in `graph`, if such paths exist. Also report negative weight cycles reachable from `source`, which are cycles whose sum of edge weights is negative.
+
+   - precondition: `graph` must have no negative weight cycles
+   - complexity: `O(VE)` time, `Θ(V)` space
+   - returns a `BellmanFordResult` struct which can be queried for shortest paths and their total weights, or `nil` if a negative weight cycle exists
+ */
+  public static func apply(graph: AbstractGraph<T>, source: Vertex<Q>) -> BellmanFordResult<T>? {
+    let vertices = graph.vertices
+    let edges = graph.edges
+
+    var predecessors = Array<Int?>(count: vertices.count, repeatedValue: nil)
+    var weights = Array(count: vertices.count, repeatedValue: Double.infinity)
+    predecessors[source.index] = source.index
+    weights[source.index] = 0
+
+    for _ in 0 ..< vertices.count - 1 {
+      var weightsUpdated = false
+      edges.forEach() { edge in
+        let weight = edge.weight!
+        let relaxedDistance = weights[edge.from.index] + weight
+        let nextVertexIdx = edge.to.index
+        if relaxedDistance < weights[nextVertexIdx] {
+          predecessors[nextVertexIdx] = edge.from.index
+          weights[nextVertexIdx] = relaxedDistance
+          weightsUpdated = true
+        }
+      }
+      if !weightsUpdated {
+        break
+      }
+    }
+
+    // check for negative weight cycles reachable from the source vertex
+    // TODO: modify to incorporate solution to 24.1-4, pg 654, to set the weight of a path containing a negative weight cycle to -∞, instead of returning nil for the entire result
+    for edge in edges {
+      if weights[edge.to.index] > weights[edge.from.index] + edge.weight! {
+        return nil
+      }
+    }
+
+    return BellmanFordResult(predecessors: predecessors, weights: weights)
+  }
+
+}
+
+/**
+ `BellmanFordResult` encapsulates the result of the computation, namely the minimized distances, and the predecessor indices.
+
+ It conforms to the `SSSPResult` procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
+ */
+public struct BellmanFordResult<T where T: Hashable> {
+
+  private var predecessors: [Int?]
+  private var weights: [Double]
+
+}
+
+extension BellmanFordResult: SSSPResult {
+
+  /**
+   - returns: the total weight of the path from the source vertex to a destination. This value is the minimal connected weight between the two vertices, or `nil` if no path exists
+   - complexity: `Θ(1)` time/space
+   */
+  public func distance(to: Vertex<T>) -> Double? {
+    let distance = weights[to.index]
+
+    guard distance != Double.infinity else {
+      return nil
+    }
+
+    return distance
+  }
+
+  /**
+   - returns: the reconstructed path from the source vertex to a destination, as an array containing the data property of each vertex, or `nil` if no path exists
+   - complexity: `Θ(V)` time, `Θ(V^2)` space
+   */
+  public func path(to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
+    guard weights[to.index] != Double.infinity else {
+      return nil
+    }
+
+    guard let path = recursePath(to, inGraph: graph, path: [to]) else {
+      return nil
+    }
+    
+    return path.map() { vertex in
+      return vertex.data
+    }
+  }
+
+  /**
+   The recursive component to rebuilding the shortest path between two vertices using predecessors.
+
+   - returns: the list of predecessors discovered so far, or `nil` if the next vertex has no predecessor 
+   */
+  private func recursePath(to: Vertex<T>, inGraph graph: AbstractGraph<T>, path: [Vertex<T>]) -> [Vertex<T>]? {
+    guard let predecessorIdx = predecessors[to.index] else {
+      return nil
+    }
+
+    let predecessor = graph.vertices[predecessorIdx]
+    if predecessor.index == to.index {
+      return [ to ]
+    }
+
+    guard let buildPath = recursePath(predecessor, inGraph: graph, path: path) else {
+      return nil
+    }
+
+    return buildPath + [ to ]
+  }
+
+}
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/Info.plist b/Single-Source Shortest Paths (Weighted)/SSSP/Info.plist
new file mode 100644
index 000000000..d3de8eefb
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/Info.plist	
@@ -0,0 +1,26 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>FMWK</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>$(CURRENT_PROJECT_VERSION)</string>
+	<key>NSPrincipalClass</key>
+	<string></string>
+</dict>
+</plist>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.h b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.h
new file mode 100644
index 000000000..46cc4de16
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.h	
@@ -0,0 +1,18 @@
+//
+//  SSSP.h
+//  SSSP
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+#import <Cocoa/Cocoa.h>
+
+//! Project version number for SSSP.
+FOUNDATION_EXPORT double SSSPVersionNumber;
+
+//! Project version string for SSSP.
+FOUNDATION_EXPORT const unsigned char SSSPVersionString[];
+
+// In this header, you should import all the public headers of your framework using statements like #import <SSSP/PublicHeader.h>
+
+
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift
new file mode 100644
index 000000000..3d50731ca
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift	
@@ -0,0 +1,32 @@
+//
+//  SSSP.swift
+//  SSSP
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import Foundation
+import Graph
+
+/**
+ `SSSPAlgorithm` is a protocol for encapsulating a Single-Source Shortest Path algorithm. It provides a single function `apply` that accepts a subclass of `AbstractGraph` and returns an object conforming to `SSSPResult`.
+ */
+protocol SSSPAlgorithm {
+
+  associatedtype Q: Equatable, Hashable
+  associatedtype P: SSSPResult
+
+  static func apply(graph: AbstractGraph<Q>, source: Vertex<Q>) -> P?
+
+}
+
+/**
+ `SSSPResult` is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the SSSP solution according to the algorithm used.
+ */
+protocol SSSPResult {
+
+  associatedtype T: Equatable, Hashable
+
+  func distance(to: Vertex<T>) -> Double?
+  func path(to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]?
+}
diff --git a/Single-Source Shortest Paths (Weighted)/SSSPTests/Info.plist b/Single-Source Shortest Paths (Weighted)/SSSPTests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSPTests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift
new file mode 100644
index 000000000..1bb862b74
--- /dev/null
+++ b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
@@ -0,0 +1,134 @@
+//
+//  SSSPTests.swift
+//  SSSPTests
+//
+//  Created by Andrew McKnight on 5/8/16.
+//
+
+import Graph
+import XCTest
+@testable import SSSP
+
+class SSSPTests: XCTestCase {
+
+  /**
+   See Figure 24.4 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 652
+   */
+  func testExampleFromBook() {
+    let graph = AdjacencyMatrixGraph<String>()
+    let s = graph.createVertex("s")
+    let t = graph.createVertex("t")
+    let x = graph.createVertex("x")
+    let y = graph.createVertex("y")
+    let z = graph.createVertex("z")
+
+    graph.addDirectedEdge(s, to: t, withWeight: 6)
+    graph.addDirectedEdge(s, to: y, withWeight: 7)
+
+    graph.addDirectedEdge(t, to: x, withWeight: 5)
+    graph.addDirectedEdge(t, to: y, withWeight: 8)
+    graph.addDirectedEdge(t, to: z, withWeight: -4)
+
+    graph.addDirectedEdge(x, to: t, withWeight: -2)
+
+    graph.addDirectedEdge(y, to: x, withWeight: -3)
+    graph.addDirectedEdge(y, to: z, withWeight: 9)
+
+    graph.addDirectedEdge(z, to: s, withWeight: 2)
+    graph.addDirectedEdge(z, to: x, withWeight: 7)
+
+    let result = BellmanFord<String>.apply(graph, source: s)!
+
+    let expectedPath = ["s", "y", "x", "t", "z"]
+    let computedPath = result.path(z, inGraph: graph)!
+    XCTAssertEqual(expectedPath, computedPath, "expected path of \(expectedPath) but got \(computedPath)")
+
+    let expectedWeight = -2.0
+    let computedWeight = result.distance(z)
+    XCTAssertEqual(expectedWeight, computedWeight, "expected weight of \(expectedWeight) but got \(computedWeight)")
+  }
+
+  func testSimpleExample() {
+    let graph = AdjacencyMatrixGraph<String>()
+    let a = graph.createVertex("a")
+    let b = graph.createVertex("b")
+    let c = graph.createVertex("c")
+    let d = graph.createVertex("d")
+    let e = graph.createVertex("e")
+
+    graph.addDirectedEdge(a, to: b, withWeight: 4)
+    graph.addDirectedEdge(a, to: c, withWeight: 5)
+    graph.addDirectedEdge(a, to: d, withWeight: 8)
+
+    graph.addDirectedEdge(b, to: c, withWeight: -2)
+
+    graph.addDirectedEdge(c, to: e, withWeight: 4)
+
+    graph.addDirectedEdge(d, to: e, withWeight: 2)
+
+    graph.addDirectedEdge(e, to: d, withWeight: 1)
+
+    let result = BellmanFord<String>.apply(graph, source: a)!
+
+    let expectedPath = ["a", "b", "c", "e", "d"]
+    let computedPath = result.path(d, inGraph: graph)!
+    XCTAssertEqual(expectedPath, computedPath, "expected path of \(expectedPath) but got \(computedPath)")
+
+    let expectedWeight = 7.0
+    let computedWeight = result.distance(d)
+    XCTAssertEqual(expectedWeight, computedWeight, "expected weight of \(expectedWeight) but got \(computedWeight)")
+  }
+
+  /**
+   Construct a nearly bipartite graph, except one vertex only has out-edges. Then no path should exist from the source to that vertex.
+   */
+  func testGraphWithUnreachableVertex() {
+    let graph = AdjacencyMatrixGraph<String>()
+    let a = graph.createVertex("a")
+    let b = graph.createVertex("b")
+    let s = graph.createVertex("s")
+    let t = graph.createVertex("t")
+
+    graph.addDirectedEdge(a, to: s, withWeight: 9)
+    graph.addDirectedEdge(a, to: t, withWeight: 2)
+
+    graph.addDirectedEdge(b, to: a, withWeight: 1)
+    graph.addDirectedEdge(b, to: s, withWeight: 2)
+    graph.addDirectedEdge(b, to: t, withWeight: 3)
+
+    graph.addDirectedEdge(s, to: a, withWeight: 4)
+    graph.addDirectedEdge(s, to: t, withWeight: 1)
+
+    graph.addDirectedEdge(t, to: a, withWeight: 7)
+    graph.addDirectedEdge(t, to: s, withWeight: 5)
+
+    let result = BellmanFord<String>.apply(graph, source: a)!
+
+    XCTAssertNil(result.path(b, inGraph: graph), "a path should not be defined from a ~> b")
+    XCTAssertNil(result.distance(b), "a path should not be defined from a ~> b")
+    XCTAssertNotNil(result.path(s, inGraph: graph), "a path should be defined from a ~> s")
+    XCTAssertNotNil(result.distance(s), "a path should be defined from a ~> s")
+    XCTAssertNotNil(result.path(t, inGraph: graph), "a path should be defined from a ~> t")
+    XCTAssertNotNil(result.distance(t), "a path should be defined from a ~> t")
+  }
+
+  func testNegativeWeightCycle() {
+    let graph = AdjacencyMatrixGraph<String>()
+    let a = graph.createVertex("a")
+    let b = graph.createVertex("b")
+    let s = graph.createVertex("s")
+    let t = graph.createVertex("t")
+
+    graph.addDirectedEdge(a, to: t, withWeight: 2)
+
+    graph.addDirectedEdge(b, to: t, withWeight: 5)
+
+    graph.addDirectedEdge(s, to: a, withWeight: 4)
+    graph.addDirectedEdge(s, to: b, withWeight: 4)
+
+    graph.addDirectedEdge(t, to: s, withWeight: -15)
+
+    XCTAssertNil(BellmanFord<String>.apply(graph, source: s), "negative weight cycle not reported")
+  }
+
+}

From 6c5ed4bcd2b297f60d41be666b563bfa18b3c76e Mon Sep 17 00:00:00 2001
From: Andrew McKnight <amcknight2718@gmail.com>
Date: Wed, 1 Jun 2016 23:28:53 -0400
Subject: [PATCH 0384/1679] add and update readmes for SSSP

---
 README.markdown                               |   1 +
 .../README.markdown                           | 125 ++++++++++++++++++
 .../img/example_graph.png                     | Bin 0 -> 61490 bytes
 .../img/negative_cycle_example.png            | Bin 0 -> 40648 bytes
 4 files changed, 126 insertions(+)
 create mode 100644 Single-Source Shortest Paths (Weighted)/README.markdown
 create mode 100644 Single-Source Shortest Paths (Weighted)/img/example_graph.png
 create mode 100644 Single-Source Shortest Paths (Weighted)/img/negative_cycle_example.png

diff --git a/README.markdown b/README.markdown
index e3d9fd9cf..b433608eb 100644
--- a/README.markdown
+++ b/README.markdown
@@ -172,6 +172,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Breadth-First Search (BFS)](Breadth-First Search/)
 - [Depth-First Search (DFS)](Depth-First Search/)
 - [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
+- [Single-Source Shortest Paths](Single-Source Shortest Paths (Weighted)/)
 - [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
 - [All-Pairs Shortest Paths](All-Pairs Shortest Paths/)
 
diff --git a/Single-Source Shortest Paths (Weighted)/README.markdown b/Single-Source Shortest Paths (Weighted)/README.markdown
new file mode 100644
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+++ b/Single-Source Shortest Paths (Weighted)/README.markdown	
@@ -0,0 +1,125 @@
+# Single-Source Shortest Paths
+
+The Single-Source shortest path problem finds the shortest paths from a given source vertex to all other vertices in a directed weighted graph. Many variations exist on the problem, specifying whether or not edges may have negative values, whether cycles exist, or whether a path between a specific pair of vertices.
+
+## Bellman-Ford
+
+The Bellman-Ford shortest paths algorithm finds the shortest paths to all vertices from a given source vertex `s` in a directed graph that may contain negative edge weights. It iterates over all edges for each other vertex in the graph, applying a relaxation to the current state of known shortest path weights. The intuition here is that a path will not contain more vertices than are present in the graph, so performing a pass over all edges `|V|-1` number of times is sufficient to compare all possible paths. 
+
+At each step, a value is stored for each vertex `v`, which is the weight of the current known shortest path `s`~>`v`. This value remains 0 for the source vertex itself, and all others are initially `∞`. Then, they are "relaxed" by applying the following test to each edge `e = (u, v)` (where `u` is a source vertex and `v` is a destination vertex for the directed edge):
+
+	if weights[v] > weights[u] + e.weight {
+		weights[v] = weights[u] + e.weight
+	}
+
+Bellman-Ford in essence only computes the lengths of the shortest paths, but can optionally maintain a structure that memoizes the predecessor of each vertex on its shortest path from the source vertex.  Then the paths themselves can be reconstructed by recursing through this structure from a destination vertex to the source vertex. This is maintained by simply adding the statement
+
+	predecessors[v] = u
+	
+inside of the `if` statement's body above.
+
+### Example
+
+For the following weighted directed graph:
+
+<img src="img/example_graph.png" width="200px" />
+
+let's compute the shortest paths from vertex `s`. First, we prepare our `weights` and `predecessors` structures thusly:
+
+| weights | predecessors |
+| ------------- |:-------------:|
+| `weights[s] = 0` | `predecessors[s] = 1` |
+| `weights[t] = ∞` | `predecessors[t] = ø` |
+| `weights[x] = ∞` | `predecessors[x] = ø` |
+| `weights[y] = ∞` | `predecessors[y] = ø` |
+| `weights[z] = ∞` | `predecessors[z] = ø` |
+
+Here are their states after each relaxation iteration (each iteration is a pass over all edges, and there are 4 iterations total for this graph):
+
+###### Iteration 1:
+
+| weights | predecessors |
+| ------------- |:-------------:|
+| `weights[s] = 0` | `predecessors[s] = s` |
+| `weights[t] = 6` | `predecessors[t] = s` |
+| `weights[x] = 4` | `predecessors[x] = y` |
+| `weights[y] = 7` | `predecessors[y] = s` |
+| `weights[z] = 2` | `predecessors[z] = t` |
+
+###### Iteration 2:
+
+| weights | predecessors |
+| ------------- |:-------------:|
+| `weights[s] = 0` | `predecessors[s] = s` |
+| `weights[t] = 2` | `predecessors[t] = x` |
+| `weights[x] = 4` | `predecessors[x] = y` |
+| `weights[y] = 7` | `predecessors[y] = s` |
+| `weights[z] = 2` | `predecessors[z] = t` |
+
+###### Iteration 3:
+
+| weights | predecessors |
+| ------------- |:-------------:|
+| `weights[s] = 0` | `predecessors[s] = s` |
+| `weights[t] = 2` | `predecessors[t] = x` |
+| `weights[x] = 4` | `predecessors[x] = y` |
+| `weights[y] = 7` | `predecessors[y] = s` |
+| `weights[z] = -2` | `predecessors[z] = t` |
+
+###### Iteration 4:
+
+| weights | predecessors |
+| ------------- |:-------------:|
+| `weights[s] = 0` | `predecessors[s] = s` |
+| `weights[t] = 2` | `predecessors[t] = x` |
+| `weights[x] = 4` | `predecessors[x] = y` |
+| `weights[y] = 7` | `predecessors[y] = s` |
+| `weights[z] = -2` | `predecessors[z] = t` |
+
+#### Negative weight cycles
+
+An additional useful property of the solution structure is that it can answer whether or not a negative weight cycle exists in the graph and is reachable from the source vertex. A negative weight cycle is a cycle whose sum of edge weights is negative. This means that shortest paths are not well defined in the graph from the specified source, because you can decrease the weight of a path by reentering the cycle, pushing the path's weight towards `-∞`. After fully relaxing the paths, simply running a check over each edge `e = (u, v)` to see if the weight of the shortest path to `v` is greater than the path to `u`, plus the edge weight itself, signals that the edge has a negative weight and would decrease the shortest path's weight further. Since we know we've already performed the relaxations enough times according to the intuition stated above, we can safely assume this further decrease of weight will continue infinitely.
+
+##### Example
+
+For this example, we try to compute the shortest paths from `a`:
+
+<img src="img/negative_cycle_example.png" width="200px" />
+
+The cycle `a`->`t`->`s`->`a` has a total edge weight of -9, therefore shortest paths for `a`~>`t` and `a`~>`s` are not well-defined. `a`~>`b` is also not well-defined because `b`->`t`->`s` is also a negative weight cycle.
+
+This is confirmed after running the relaxation loop, and checking all the edges as mentioned above. For this graph, we would have after relaxation:
+
+| weights |
+| ------------- |
+| `weights[a] = -5` |
+| `weights[b] = -5` |
+| `weights[s] = -18` |
+| `weights[t] = -3` |
+
+One of the edge checks we would perform afterwards would be the following:
+
+	e = (s, a)
+	e.weight = 4
+	weight[a] > weight[s] + e.weight => -5 > -18 + 4 => -5 > -14 => true
+	
+Because this check is true, we know the graph has a negative weight cycle reachable from `a`.
+
+#### Complexity
+
+The relaxation step requires constant time (`O(1)`) as it simply performs comparisons. That step is performed once per edge (`Θ(|E|)`), and the edges are iterated over `|V|-1` times. This would mean a total complexity of `Θ(|V||E|)`, but there is an optimization we can make: if the outer loop executes and no changes are made to the recorded weights, we can safely terminate the relaxation phase, which means it may execute in `O(|V|)` steps instead of `Θ(|V|)` steps (that is, the best case for any size graph is actually a constant number of iterations; the worst case is still iterating `|V|-1` times).
+
+The check for negative weight cycles at the end is `O(|E|)` if we return once we find a hit. To find all negative weight cycles reachable from the source vertex, we'd have to iterate `Θ(|E|)` times (we currently do not attempt to report the cycles, we simply return a `nil` result if such a cycle is present).
+
+The total running time of Bellman-Ford is therefore `O(|V||E|)`.
+
+## TODO
+
+- Dijkstra's algorithm for computing SSSP on a directed non-negative weighted graph
+
+# References
+
+- Chapter 24 of Introduction to Algorithms, Third Edition by Cormen, Leiserson, Rivest and Stein [https://mitpress.mit.edu/books/introduction-algorithms](https://mitpress.mit.edu/books/introduction-algorithms)
+- Wikipedia: [Bellman–Ford algorithm](https://en.wikipedia.org/wiki/Bellman–Ford_algorithm)
+
+*Written for Swift Algorithm Club by [Andrew McKnight](https://github.com/armcknight)*
\ No newline at end of file
diff --git a/Single-Source Shortest Paths (Weighted)/img/example_graph.png b/Single-Source Shortest Paths (Weighted)/img/example_graph.png
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diff --git a/Single-Source Shortest Paths (Weighted)/img/negative_cycle_example.png b/Single-Source Shortest Paths (Weighted)/img/negative_cycle_example.png
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zsib*$N0L!tu1X(8q70rA;PA!;85{<&59g(zref2g(I9;^zT4QtBpc!S+om&@bl^|R
ce*gOhzqMNmM@BT$j|covDmoAAkTwzj5AKVE7ytkO

literal 0
HcmV?d00001


From 57b3c68766574bb3faea6c11357a19784bc2e7d3 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 7 Jun 2016 10:44:19 -0400
Subject: [PATCH 0385/1679] Giving credit to Matthijs, Chris, Kelvin, and
 contributors :]

---
 README.markdown | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/README.markdown b/README.markdown
index 10919f827..d36aec465 100644
--- a/README.markdown
+++ b/README.markdown
@@ -208,6 +208,14 @@ Other algorithm repositories:
 - [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
 - [AlgorithmVisualizer](http://jasonpark.me/AlgorithmVisualizer/). Visualize algorithms on your browser.
 
+## Credits
+
+The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
+
+It is now maintained by [Chris Pilcher](https://github.com/chris-pilcher) and [Kelvin Lau](https://github.com/kelvinlauKL).
+
+The Swift Algorithm Club is a a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How to Contribute.markdown)? :]
+
 ## License
 
 All content is licensed under the terms of the MIT open source license.

From df44023c572558f57a9905e7bc4355d4cf35757e Mon Sep 17 00:00:00 2001
From: schlagelk <kenny.schlagel+github@gmail.com>
Date: Tue, 7 Jun 2016 10:20:12 -0600
Subject: [PATCH 0386/1679] use swift guard statement consistently

---
 Quicksort/Quicksort.playground/Contents.swift | 24 +++++++++----------
 .../Quicksort.playground/timeline.xctimeline  |  6 -----
 Quicksort/Quicksort.swift                     | 17 +++++++------
 Quicksort/README.markdown                     | 17 +++++++------
 4 files changed, 27 insertions(+), 37 deletions(-)
 delete mode 100644 Quicksort/Quicksort.playground/timeline.xctimeline

diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 2d9ef3590..b88bafc12 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -6,20 +6,18 @@ import Foundation
 // *** Simple but inefficient version of quicksort ***
 
 func quicksort<T: Comparable>(a: [T]) -> [T] {
-  if a.count <= 1 {
-    return a
-  } else {
-    let pivot = a[a.count/2]
-    let less = a.filter { $0 < pivot }
-    let equal = a.filter { $0 == pivot }
-    let greater = a.filter { $0 > pivot }
-    
-    // Uncomment this following line to see in detail what the 
-    // pivot is in each step and how the subarrays are partitioned.
-    //print(pivot, less, equal, greater)
+  guard a.count > 1 else { return a }
+  
+  let pivot = a[a.count/2]
+  let less = a.filter { $0 < pivot }
+  let equal = a.filter { $0 == pivot }
+  let greater = a.filter { $0 > pivot }
+  
+  // Uncomment this following line to see in detail what the
+  // pivot is in each step and how the subarrays are partitioned.
+  //print(pivot, less, equal, greater)  return quicksort(less) + equal + quicksort(greater)
     
-    return quicksort(less) + equal + quicksort(greater)
-  }
+  return quicksort(less) + equal + quicksort(greater)
 }
 
 let list1 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
diff --git a/Quicksort/Quicksort.playground/timeline.xctimeline b/Quicksort/Quicksort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Quicksort/Quicksort.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Quicksort/Quicksort.swift b/Quicksort/Quicksort.swift
index 1d3b0602d..68c54ac5c 100644
--- a/Quicksort/Quicksort.swift
+++ b/Quicksort/Quicksort.swift
@@ -4,15 +4,14 @@ import Foundation
   Easy to understand but not very efficient.
 */
 func quicksort<T: Comparable>(a: [T]) -> [T] {
-  if a.count <= 1 {
-    return a
-  } else {
-    let pivot = a[a.count/2]
-    let less = a.filter { $0 < pivot }
-    let equal = a.filter { $0 == pivot }
-    let greater = a.filter { $0 > pivot }
-    return quicksort(less) + equal + quicksort(greater)
-  }
+  guard a.count > 1 else { return a }
+  
+  let pivot = a[a.count/2]
+  let less = a.filter { $0 < pivot }
+  let equal = a.filter { $0 == pivot }
+  let greater = a.filter { $0 > pivot }
+  
+  return quicksort(less) + equal + quicksort(greater)
 }
 
 // MARK: - Lomuto
diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index b8a908985..936f9f44c 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -8,15 +8,14 @@ Here's an implementation in Swift that should be easy to understand:
 
 ```swift
 func quicksort<T: Comparable>(a: [T]) -> [T] {
-  if a.count <= 1 {
-    return a
-  } else {
-    let pivot = a[a.count/2]
-    let less = a.filter { $0 < pivot }
-    let equal = a.filter { $0 == pivot }
-    let greater = a.filter { $0 > pivot }
-    return quicksort(less) + equal + quicksort(greater)
-  }
+  guard a.count > 1 else { return a }
+
+  let pivot = a[a.count/2]
+  let less = a.filter { $0 < pivot }
+  let equal = a.filter { $0 == pivot }
+  let greater = a.filter { $0 > pivot }
+  
+  return quicksort(less) + equal + quicksort(greater)
 }
 ```
 

From feeccfbd6eac6b97d3072734464f6bf695e581d0 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 8 Jun 2016 21:40:37 +1200
Subject: [PATCH 0387/1679] Update Under Construction.markdown

Added links to algorithms submitted in PR #102
---
 Under Construction.markdown | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index f0befb3d9..95ead4218 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -2,6 +2,11 @@
 
 Here you'll find algorithms that are currently under construction. Suggestions and feedback is welcome!
 
+### Sorting
+
+Special-purpose sorts:
+ - [Radix Sort](Radix Sort/)
+
 ### Special-purpose sorts:
 
 - [Bucket Sort](Bucket Sort/)
@@ -13,7 +18,10 @@ Here you'll find algorithms that are currently under construction. Suggestions a
 ### Trees
 
 - [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
+- [Red-Black Tree](Red-Black Tree/)
+- [Threaded Binary Tree](Threaded Binary Tree/)
 - [Ternary Search Tree](Ternary Search Tree/)
+- [Trie](Trie/)
 - [Radix Tree](Radix Tree/)
 
 ### Miscellaneous

From 2d4d59f24116e9647d81735562ef1380a009ae87 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 8 Jun 2016 21:51:41 +1200
Subject: [PATCH 0388/1679] Configure Travis CI to run SwiftLint

---
 .travis.yml          |  6 ++++++
 install_swiftlint.sh | 23 +++++++++++++++++++++++
 2 files changed, 29 insertions(+)
 create mode 100644 install_swiftlint.sh

diff --git a/.travis.yml b/.travis.yml
index b0210d197..e4c746b5e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,8 +1,14 @@
 language: objective-c
 osx_image: xcode7.3
 
+install:
+
+- ./install_swiftlint.sh
+
 script:
 
+- swiftlint
+
 - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
diff --git a/install_swiftlint.sh b/install_swiftlint.sh
new file mode 100644
index 000000000..b33d83de2
--- /dev/null
+++ b/install_swiftlint.sh
@@ -0,0 +1,23 @@
+#!/bin/bash
+
+# Installs the SwiftLint package.
+# Tries to get the precompiled .pkg file from Github, but if that
+# fails just recompiles from source.
+
+set -e
+
+SWIFTLINT_PKG_PATH="/tmp/SwiftLint.pkg"
+SWIFTLINT_PKG_URL="https://github.com/realm/SwiftLint/releases/download/0.10.0/SwiftLint.pkg"
+
+wget --output-document=$SWIFTLINT_PKG_PATH $SWIFTLINT_PKG_URL
+
+if [ -f $SWIFTLINT_PKG_PATH ]; then
+  echo "SwiftLint package exists! Installing it..."
+  sudo installer -pkg $SWIFTLINT_PKG_PATH -target /
+else
+  echo "SwiftLint package doesn't exist. Compiling from source..." &&
+  git clone https://github.com/realm/SwiftLint.git /tmp/SwiftLint &&
+  cd /tmp/SwiftLint &&
+  git submodule update --init --recursive &&
+  sudo make install
+fi

From 3df07d44b07d13e316d239ae921f0b3e9d59d606 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 8 Jun 2016 22:01:55 +1200
Subject: [PATCH 0389/1679] CHMOD install_swiftlint.sh

---
 install_swiftlint.sh | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 mode change 100644 => 100755 install_swiftlint.sh

diff --git a/install_swiftlint.sh b/install_swiftlint.sh
old mode 100644
new mode 100755

From e164943c9cabb53e6e34a21bf64f2bae4aec3da3 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 8 Jun 2016 23:53:04 +1200
Subject: [PATCH 0390/1679] Added basic SwiftLint config file. Fixing all
 linting errors.

---
 .swiftlint.yml                                |  25 ++
 AVL Tree/AVLTree.playground/Contents.swift    |   2 +-
 AVL Tree/Tests/AVLTreeTests.swift             |  40 ++-
 AVL Tree/Tests/TreeNodeTests.swift            |  46 ++--
 All-Pairs Shortest Paths/APSP/APSP/APSP.swift |   7 +-
 .../APSP/APSP/FloydWarshall.swift             |  41 +--
 Array2D/Array2D.playground/Contents.swift     |  17 +-
 .../Array2D.playground/timeline.xctimeline    |   6 -
 Array2D/Tests/Array2DTests.swift              |  40 +--
 .../Contents.swift                            |   2 +-
 .../Sources/BinarySearchTree.swift            |  14 +-
 .../Solution 1/BinarySearchTree.swift         |  14 +-
 .../Tests/BinarySearchTreeTests.swift         |   4 +-
 .../Sources/BinarySearchTree.swift            |  18 +-
 .../Solution 2/BinarySearchTree.swift         |  18 +-
 .../BinaryTree.playground/Contents.swift      |   8 +-
 .../BinaryTree.playground/timeline.xctimeline |   6 -
 Binary Tree/BinaryTree.swift                  |   6 +-
 Bit Set/BitSet.playground/Contents.swift      |   6 +-
 .../BitSet.playground/Sources/BitSet.swift    |  12 +-
 Bit Set/BitSet.swift                          |  12 +-
 .../BloomFilter.playground/Contents.swift     |  20 +-
 Bloom Filter/BloomFilter.swift                |  20 +-
 Bloom Filter/Tests/BloomFilterTests.swift     |  46 ++--
 .../Contents.swift                            |   8 +-
 .../Sources/BoundedPriorityQueue.swift        |   6 +-
 .../Tests/BoundedPriorityQueueTests.swift     |   6 +-
 .../BoyerMoore.playground/Contents.swift      |   8 +-
 Boyer-Moore/BoyerMoore.swift                  |  18 +-
 .../Sources/Edge.swift                        |   4 +-
 .../Sources/Graph.swift                       |   8 +-
 .../Sources/Node.swift                        |   6 +-
 Breadth-First Search/BreadthFirstSearch.swift |   2 +-
 Breadth-First Search/Tests/Graph.swift        |  20 +-
 .../BucketSort.playground/Contents.swift      |   5 +-
 .../Sources/BucketSort.swift                  |  40 +--
 Bucket Sort/BucketSort.swift                  |  54 ++--
 Bucket Sort/Tests/Tests.swift                 |  44 +--
 .../Combinatorics.playground/Contents.swift   |   1 -
 .../Contents.swift                            |   4 +-
 .../CountingSort.playground/Contents.swift    |   4 +-
 Counting Sort/CountingSort.swift              |   4 +-
 Counting Sort/Tests/CountingSortTest.swift    |   4 +-
 .../Sources/Edge.swift                        |   4 +-
 .../Sources/Graph.swift                       |   8 +-
 .../Sources/Node.swift                        |   6 +-
 Depth-First Search/Tests/Graph.swift          |  20 +-
 Deque/Deque-Optimized.swift                   |  16 +-
 Deque/Deque-Simple.swift                      |   2 +-
 Deque/Deque.playground/Contents.swift         |  16 +-
 GCD/GCD.playground/Contents.swift             |   2 +-
 Graph/Graph/Edge.swift                        |   4 +-
 Graph/GraphTests/GraphTests.swift             |   4 +-
 Hash Set/HashSet.playground/Contents.swift    |  12 +-
 Hash Set/HashSet.swift                        |  12 +-
 .../HashTable.playground/Contents.swift       |  18 +-
 Hash Table/HashTable.swift                    |  28 +-
 Heap/Heap.swift                               |  26 +-
 Heap/Tests/HeapTests.swift                    |   4 +-
 .../Huffman.playground/Contents.swift         |   8 +-
 .../Huffman.playground/Sources/Heap.swift     |  26 +-
 .../Huffman.playground/Sources/Huffman.swift  |  44 +--
 .../Sources/NSData+Bits.swift                 |   6 +-
 .../Sources/PriorityQueue.swift               |   2 +-
 Huffman Coding/Huffman.swift                  |  44 +--
 Huffman Coding/NSData+Bits.swift              |   6 +-
 K-Means/KMeans.swift                          |  30 +--
 K-Means/Tests/KMeansTests.swift               |  24 +-
 K-Means/Tests/Vector.swift                    |  18 +-
 .../kthLargest.playground/Contents.swift      |   4 +-
 Kth Largest Element/kthLargest.swift          |   8 +-
 .../LinkedList.playground/Contents.swift      |  30 +--
 Linked List/LinkedList.swift                  |  46 ++--
 .../Contents.swift                            |  12 +-
 .../LongestCommonSubsequence.swift            |  12 +-
 .../Tests/LongestCommonSubsequenceTests.swift |   8 +-
 .../MergeSort.playground/Contents.swift       |  10 +-
 Merge Sort/MergeSort.swift                    |  16 +-
 .../MinimumEditDistance.swift                 |  10 +-
 .../Sources/Edge.swift                        |   4 +-
 .../Sources/Graph.swift                       |   8 +-
 .../Sources/Node.swift                        |   6 +-
 .../Tests/Graph.swift                         |  20 +-
 .../OrderedArray.playground/Contents.swift    |  13 +-
 Ordered Array/OrderedArray.swift              |  16 +-
 .../Sources/OrderedSet.swift                  |  10 +-
 .../Sources/Player.swift                      |   6 +-
 Ordered Set/OrderedSet.swift                  |  10 +-
 Priority Queue/PriorityQueue.swift            |   2 +-
 Queue/Queue-Optimized.swift                   |  10 +-
 Queue/Queue.playground/Contents.swift         |   2 +-
 Quicksort/Quicksort.playground/Contents.swift |  20 +-
 Quicksort/Quicksort.swift                     |   8 +-
 Quicksort/Tests/QuicksortTests.swift          |   4 +-
 Radix Sort/radixSort.swift                    |   2 +-
 .../Sources/RadixTree.swift                   |  20 +-
 Radix Tree/RadixTree.swift                    |  20 +-
 Red-Black Tree/RBTree.swift                   | 251 ++++++++----------
 .../RingBuffer.playground/Contents.swift      |   8 +-
 Ring Buffer/RingBuffer.swift                  |  16 +-
 .../RLE.playground/Contents.swift             |  10 +-
 Run-Length Encoding/RLE.swift                 |  10 +-
 Run-Length Encoding/Tests/RLETests.swift      |   8 +-
 .../SegmentTree.playground/Contents.swift     |  15 +-
 Segment Tree/SegmentTree.swift                |  14 +-
 Select Minimum Maximum/Maximum.swift          |   2 +-
 .../Contents.swift                            |   3 +-
 .../Tests/MaximumTests.swift                  |   2 +-
 Select Minimum Maximum/Tests/TestHelper.swift |   2 +-
 .../Contents.swift                            |   6 +-
 Selection Sampling/SelectionSampling.swift    |   8 +-
 Selection Sort/SelectionSort.swift            |   4 +-
 Shell Sort/shellsort.swift                    |   2 +-
 .../Sources/Edge.swift                        |   4 +-
 .../Sources/Graph.swift                       |   8 +-
 .../Sources/Node.swift                        |   6 +-
 Shortest Path (Unweighted)/Tests/Graph.swift  |  20 +-
 .../Tests/ShortestPathTests.swift             |   2 +-
 .../ShuntingYard.playground/Contents.swift    |  69 +++--
 .../Sources/Stack.swift                       |  14 +-
 .../timeline.xctimeline                       |   6 -
 Shunting Yard/ShuntingYard.swift              |  50 ++--
 .../SSSP/BellmanFord.swift                    |  32 ++-
 .../SSSP/SSSP.swift                           |   8 +-
 Stack/Stack.playground/Contents.swift         |  14 +-
 .../TST.playground/Contents.swift             |  13 +-
 .../TST.playground/Sources/TSTNode.swift      |  16 +-
 .../Sources/TernarySearchTree.swift           |  52 ++--
 .../contents.xcworkspacedata                  |   7 +
 .../TST.playground/timeline.xctimeline        |   6 -
 Ternary Search Tree/TSTNode.swift             |  24 +-
 Ternary Search Tree/TernarySearchTree.swift   |  62 ++---
 Threaded Binary Tree/ThreadedBinaryTree.swift |  16 +-
 .../ThreadedBinaryTreeTests.swift             |   2 +-
 Topological Sort/Graph.swift                  |  14 +-
 .../Tests/TopologicalSortTests.swift          |   8 +-
 .../Sources/Graph.swift                       |  16 +-
 .../Sources/TopologicalSort1.swift            |  12 +-
 .../Sources/TopologicalSort3.swift            |   2 +-
 Topological Sort/TopologicalSort1.swift       |  14 +-
 Topological Sort/TopologicalSort3.swift       |   2 +-
 Treap/Treap.swift                             |  52 ++--
 .../contents.xcworkspacedata                  |   7 +
 Treap/Treap/Treap/AppDelegate.swift           |   1 -
 Treap/Treap/TreapTests/TreapTests.swift       |  13 +-
 Treap/TreapMergeSplit.swift                   |  53 ++--
 Tree/Tree.playground/Contents.swift           |   4 +-
 Tree/Tree.swift                               |   4 +-
 Trie/trie.swift                               |  43 +--
 .../Solution 1/2Sum.playground/Contents.swift |   2 +-
 Two-Sum Problem/Solution 1/2Sum.swift         |   4 +-
 .../Solution 2/2Sum.playground/Contents.swift |   2 +-
 .../UnionFind.playground/Contents.swift       |  14 +-
 Union-Find/UnionFind.swift                    |  10 +-
 154 files changed, 1240 insertions(+), 1232 deletions(-)
 create mode 100644 .swiftlint.yml
 delete mode 100644 Array2D/Array2D.playground/timeline.xctimeline
 delete mode 100644 Binary Tree/BinaryTree.playground/timeline.xctimeline
 delete mode 100644 Shunting Yard/ShuntingYard.playground/timeline.xctimeline
 create mode 100644 Ternary Search Tree/TST.playground/playground.xcworkspace/contents.xcworkspacedata
 delete mode 100644 Ternary Search Tree/TST.playground/timeline.xctimeline
 create mode 100644 Treap/Treap/Treap.xcodeproj/project.xcworkspace/contents.xcworkspacedata

diff --git a/.swiftlint.yml b/.swiftlint.yml
new file mode 100644
index 000000000..1434bf637
--- /dev/null
+++ b/.swiftlint.yml
@@ -0,0 +1,25 @@
+cyclomatic_complexity: 12
+file_length: 550
+function_body_length: 80
+function_parameter_count: 8
+line_length: 150
+type_body_length: 300
+variable_name:
+  min_length:
+    error: 1
+    warning: 1
+  excluded:
+    - N
+
+disabled_rules:
+  - valid_docs
+
+custom_rules:
+  smiley_face:
+    name: "Smiley Face"
+    regex: "(\:\))"
+    match_kinds: 
+      - comment
+      - string
+    message: "A closing parenthesis smiley :) creates a half-hearted smile, and thus is not preferred. Use :]"
+    severity: warning
diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 4b4e1f3e2..2b8ee8b59 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -24,4 +24,4 @@ tree.delete(5)
 tree.delete(2)
 tree.delete(1)
 tree.delete(4)
-tree.delete(3)
\ No newline at end of file
+tree.delete(3)
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 51e1211c3..065367bb6 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -9,15 +9,15 @@
 import XCTest
 
 class AVLTreeTests: XCTestCase {
-  
-  var tree : AVLTree<Int, String>?
+
+  var tree: AVLTree<Int, String>?
 
   override func setUp() {
     super.setUp()
-    
+
     tree = AVLTree()
   }
-  
+
   override func tearDown() {
     // Put teardown code here. This method is called after the invocation of each test method in the class.
     super.tearDown()
@@ -60,8 +60,8 @@ class AVLTreeTests: XCTestCase {
   }
 
   func testEmptyInitialization() {
-    let tree = AVLTree<Int,String>()
-    
+    let tree = AVLTree<Int, String>()
+
     XCTAssertEqual(tree.size, 0)
     XCTAssertNil(tree.root)
   }
@@ -71,45 +71,45 @@ class AVLTreeTests: XCTestCase {
       self.tree?.insert(5, "E")
     }
   }
-  
+
   func testMultipleInsertionsPerformance() {
     self.measureBlock {
       self.tree?.autopopulateWithNodes(50)
     }
   }
-  
+
   func testSearchExistentOnSmallTreePerformance() {
     self.measureBlock {
       self.tree?.search(2)
     }
   }
-  
+
   func testSearchExistentElementOnLargeTreePerformance() {
     self.measureBlock {
       self.tree?.autopopulateWithNodes(500)
       self.tree?.search(400)
     }
   }
-  
+
   func testMinimumOnPopulatedTree() {
     self.tree?.autopopulateWithNodes(500)
     let min = self.tree?.root?.minimum()
     XCTAssertNotNil(min, "Minimum function not working")
   }
-  
+
   func testMinimumOnSingleTreeNode() {
     let treeNode = TreeNode(key: 1, payload: "A")
     let min = treeNode.minimum()
-    
+
     XCTAssertNotNil(min, "Minimum on single node should be returned")
-    XCTAssertEqual(min?.payload,treeNode.payload)
+    XCTAssertEqual(min?.payload, treeNode.payload)
   }
-  
+
   func testDeleteExistentKey() {
     self.tree?.delete(1)
     XCTAssertNil(self.tree?.search(1), "Key should not exist anymore")
   }
-  
+
   func testDeleteNotExistentKey() {
     self.tree?.delete(1056)
     XCTAssertNil(self.tree?.search(1056), "Key should not exist")
@@ -122,7 +122,7 @@ class AVLTreeTests: XCTestCase {
       XCTAssertEqual(tree.size, i + 1, "Insert didn't update size correctly!")
     }
   }
-  
+
   func testDelete() {
     let permutations = [
       [5, 1, 4, 2, 3],
@@ -130,7 +130,7 @@ class AVLTreeTests: XCTestCase {
       [4, 5, 3, 2, 1],
       [3, 2, 5, 4, 1],
     ]
-    
+
     for p in permutations {
       let tree = AVLTree<Int, String>()
 
@@ -151,8 +151,8 @@ class AVLTreeTests: XCTestCase {
 }
 
 extension AVLTree where Key : SignedIntegerType {
-  func autopopulateWithNodes(count : Int) {
-    var k : Key = 1
+  func autopopulateWithNodes(count: Int) {
+    var k: Key = 1
     for _ in 0...count {
       self.insert(k)
       k = k + 1
@@ -185,5 +185,3 @@ extension AVLTree where Key : SignedIntegerType {
     }
   }
 }
-
-
diff --git a/AVL Tree/Tests/TreeNodeTests.swift b/AVL Tree/Tests/TreeNodeTests.swift
index c15721655..88b314e41 100644
--- a/AVL Tree/Tests/TreeNodeTests.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -9,50 +9,50 @@
 import XCTest
 
 class TreeNodeTests: XCTestCase {
-    
-    var root : TreeNode<String,String>?
-    var left : TreeNode<String,String>?
-    var right : TreeNode<String,String>?
-    
+
+    var root: TreeNode<String, String>?
+    var left: TreeNode<String, String>?
+    var right: TreeNode<String, String>?
+
     override func setUp() {
         super.setUp()
 
-        left = TreeNode<String,String>(key: "Name", payload: "Left")
-        right = TreeNode<String,String>(key: "Name", payload: "Right")
-        root = TreeNode<String,String>(key: "Name", payload: "Root", leftChild: left, rightChild: right, parent: nil, height: 0)
+        left = TreeNode<String, String>(key: "Name", payload: "Left")
+        right = TreeNode<String, String>(key: "Name", payload: "Right")
+        root = TreeNode<String, String>(key: "Name", payload: "Root", leftChild: left, rightChild: right, parent: nil, height: 0)
     }
-    
+
     override func tearDown() {
         // Put teardown code here. This method is called after the invocation of each test method in the class.
         super.tearDown()
     }
-    
-    
+
+
     func testSingleNodeCreationNOPayload() {
-        let treeNode = TreeNode<String,String>(key: "Building")
+        let treeNode = TreeNode<String, String>(key: "Building")
         XCTAssertNil(treeNode.payload, "Payload for this case should be nil")
     }
-    
+
     func testSingleNodeCreationWithPayload() {
         XCTAssertNotNil(self.root!, "Payload for this case should not be nil")
     }
-    
+
     func testIsRoot() {
         XCTAssertTrue(self.root!.isRoot)
     }
-    
+
     func testNotIsLeaf() {
         XCTAssertFalse(self.root!.isLeaf, "root node is not leaf")
     }
-    
+
     func testNotIsLeftChild() {
         XCTAssertFalse(self.root!.isLeftChild, "root node is not left child")
     }
-    
+
     func testNotIsRightChild() {
         XCTAssertFalse(self.root!.isRightChild, "root node is not right child")
     }
-    
+
     func testIsLeftChild() {
         XCTAssertTrue(self.left!.isLeftChild)
     }
@@ -64,21 +64,21 @@ class TreeNodeTests: XCTestCase {
     func isLeaf() {
         XCTAssertTrue(self.left!.isLeaf)
     }
-    
+
     func testHasAnyChild() {
         XCTAssertTrue(self.root!.hasAnyChild)
     }
-    
+
     func testNotHasAnyChild() {
         XCTAssertFalse(self.left!.hasAnyChild)
     }
-    
+
     func testHasBothChildren() {
         XCTAssertTrue(self.root!.hasBothChildren)
     }
-    
+
     func testNotHasBothChildren() {
         XCTAssertFalse(self.left!.hasBothChildren)
     }
-    
+
 }
diff --git a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift
index bb773306e..453f738b7 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
@@ -9,7 +9,9 @@ import Foundation
 import Graph
 
 /**
- `APSPAlgorithm` is a protocol for encapsulating an All-Pairs Shortest Paths algorithm. It provides a single function `apply` that accepts a subclass of `AbstractGraph` and returns an object conforming to `APSPResult`.
+ `APSPAlgorithm` is a protocol for encapsulating an All-Pairs Shortest Paths algorithm.
+ It provides a single function `apply` that accepts a subclass of `AbstractGraph` and
+ returns an object conforming to `APSPResult`.
  */
 public protocol APSPAlgorithm {
 
@@ -21,7 +23,8 @@ public protocol APSPAlgorithm {
 }
 
 /**
- `APSPResult` is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the APSP solution according to the algorithm used.
+ `APSPResult` is a protocol defining functions `distance` and `path`, allowing for opaque
+ queries into the actual data structures that represent the APSP solution according to the algorithm used.
  */
 public protocol APSPResult {
 
diff --git a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
index a655e215f..806c8677c 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
@@ -51,12 +51,16 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
   }
 
   /**
-   For each iteration of `intermediateIdx`, perform the comparison for the dynamic algorith, checking for each pair of start/end vertices, whether a path taken through another vertex produces a shorter path.
+   For each iteration of `intermediateIdx`, perform the comparison for the dynamic algorith,
+   checking for each pair of start/end vertices, whether a path taken through another vertex
+   produces a shorter path.
 
    - complexity: `Θ(V^2)` time/space
-   - returns: a tuple containing the next distance matrix with weights of currently known shortest paths and the corresponding predecessor matrix
+   - returns: a tuple containing the next distance matrix with weights of currently known
+   shortest paths and the corresponding predecessor matrix
    */
-  static private func nextStep<T>(intermediateIdx: Int, previousDistances: Distances, previousPredecessors: Predecessors, graph: AbstractGraph<T>) -> StepResult {
+  static private func nextStep<T>(intermediateIdx: Int, previousDistances: Distances,
+                               previousPredecessors: Predecessors, graph: AbstractGraph<T>) -> StepResult {
 
     let vertexCount = graph.vertices.count
     var nextDistances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
@@ -85,9 +89,11 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
 
   }
 
-  /** 
-   We need to map the graph's weight domain onto the one required by the algorithm: the graph stores either a weight as a `Double` or `nil` if no edge exists between two vertices, but the algorithm needs a lack of an edge represented as ∞ for the `min` comparison to work correctly.
-   
+  /**
+   We need to map the graph's weight domain onto the one required by the algorithm: the graph
+   stores either a weight as a `Double` or `nil` if no edge exists between two vertices, but
+   the algorithm needs a lack of an edge represented as ∞ for the `min` comparison to work correctly.
+
    - complexity: `Θ(V^2)` time/space
    - returns: weighted adjacency matrix in form ready for processing with Floyd-Warshall
    */
@@ -116,7 +122,7 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
 
   /**
    Make the initial predecessor index matrix. Initially each value is equal to it's row index, it's "from" index when querying into it.
-   
+
    - complexity: `Θ(V^2)` time/space
   */
   static private func constructInitialPredecessorMatrix(distances: Distances) -> Predecessors {
@@ -139,9 +145,11 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
 }
 
 /**
- `FloydWarshallResult` encapsulates the result of the computation, namely the minimized distance adjacency matrix, and the matrix of predecessor indices.
- 
- It conforms to the `APSPResult` procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
+ `FloydWarshallResult` encapsulates the result of the computation, namely the
+ minimized distance adjacency matrix, and the matrix of predecessor indices.
+
+ It conforms to the `APSPResult` procotol which provides methods to retrieve
+ distances and paths between given pairs of start and end nodes.
  */
 public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
 
@@ -149,7 +157,8 @@ public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
   private var predecessors: Predecessors
 
   /**
-   - returns: the total weight of the path from a starting vertex to a destination. This value is the minimal connected weight between the two vertices, or `nil` if no path exists
+   - returns: the total weight of the path from a starting vertex to a destination.
+   This value is the minimal connected weight between the two vertices, or `nil` if no path exists
    - complexity: `Θ(1)` time/space
    */
   public func distance(fromVertex from: Vertex<T>, toVertex to: Vertex<T>) -> Double? {
@@ -159,7 +168,8 @@ public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
   }
 
   /**
-   - returns: the reconstructed path from a starting vertex to a destination, as an array containing the data property of each vertex, or `nil` if no path exists
+   - returns: the reconstructed path from a starting vertex to a destination,
+   as an array containing the data property of each vertex, or `nil` if no path exists
    - complexity: `Θ(V)` time, `Θ(V^2)` space
    */
   public func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
@@ -175,11 +185,13 @@ public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
   }
 
   /**
-   The recursive component to rebuilding the shortest path between two vertices using the predecessor matrix.
+   The recursive component to rebuilding the shortest path between
+   two vertices using the predecessor matrix.
 
    - returns: the list of predecessors discovered so far
    */
-  private func recursePathFrom(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>], inGraph graph: AbstractGraph<T>) -> [Vertex<T>]? {
+  private func recursePathFrom(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>],
+                                          inGraph graph: AbstractGraph<T>) -> [Vertex<T>]? {
 
     if from.index == to.index {
       return [ from, to ]
@@ -198,7 +210,6 @@ public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
     }
 
     return nil
-    
   }
 
 }
diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index f73ba8b13..0bcb7b5b9 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -7,14 +7,14 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   private var array: [T]
-  
+
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(count: rows*columns, repeatedValue: initialValue)
   }
-  
-  public subscript(column: Int, row: Int)  -> T {
+
+  public subscript(column: Int, row: Int) -> T {
     get {
       return array[row*columns + column]
     }
@@ -51,14 +51,13 @@ print(matrix.array)
 
 // print out the 2D array with a reference around the grid
 for i in 0..<matrix.rows {
-  print("[", terminator: "");
+  print("[", terminator: "")
   for j in 0..<matrix.columns {
-    if (j == matrix.columns - 1) {
-      print("\(matrix[j, i])", terminator: "");
+    if j == matrix.columns - 1 {
+      print("\(matrix[j, i])", terminator: "")
     } else {
-      print("\(matrix[j, i]) ", terminator: "");
+      print("\(matrix[j, i]) ", terminator: "")
     }
   }
-  print("]");
+  print("]")
 }
-
diff --git a/Array2D/Array2D.playground/timeline.xctimeline b/Array2D/Array2D.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Array2D/Array2D.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Array2D/Tests/Array2DTests.swift b/Array2D/Tests/Array2DTests.swift
index 3383b5eb3..f4019a03a 100644
--- a/Array2D/Tests/Array2DTests.swift
+++ b/Array2D/Tests/Array2DTests.swift
@@ -9,65 +9,65 @@
 import XCTest
 
 class Array2DTest: XCTestCase {
-  
+
   override func setUp() {
     super.setUp()
   }
-  
+
   override func tearDown() {
     super.tearDown()
   }
-  
+
   func testIntegerArrayWithPositiveRowsAndColumns() {
     let array = Array2D<Int>(columns: 3, rows: 2, initialValue: 0)
-    
+
     XCTAssertEqual(array.columns, 3, "Column count setup failed")
     XCTAssertEqual(array.rows, 2, "Rows count setup failed")
-    XCTAssertEqual(array[2,1], 0, "Integer array: Initialization value is wrong")
+    XCTAssertEqual(array[2, 1], 0, "Integer array: Initialization value is wrong")
   }
-  
+
   func testStringArrayWithPositiveRowsAndColumns() {
     let array = Array2D<String>(columns: 3, rows: 2, initialValue: "empty")
-    
+
     XCTAssertEqual(array.columns, 3, "Column count setup failed")
     XCTAssertEqual(array.rows, 2, "Rows count setup failed")
-    XCTAssertEqual(array[2,1], "empty", "String array: Initialization value is wrong")
+    XCTAssertEqual(array[2, 1], "empty", "String array: Initialization value is wrong")
   }
-  
+
   func testCustomClassArrayWithPositiveRowsAndColumns() {
     let array = Array2D<TestElement>(columns: 3, rows: 2, initialValue: TestElement(identifier: "pepe"))
-    
+
     XCTAssertEqual(array.columns, 3, "Column count setup failed")
     XCTAssertEqual(array.rows, 2, "Rows count setup failed")
-    XCTAssertEqual(array[2,1], TestElement(identifier: "pepe"), "Custom Class array: Initialization value is wrong")
+    XCTAssertEqual(array[2, 1], TestElement(identifier: "pepe"), "Custom Class array: Initialization value is wrong")
   }
-  
+
   func testPerformanceOnSmallArray() {
     self.measureBlock {
       self.printArrayWith(columns: 2, rows: 2, inititalValue: 1)
     }
   }
-  
+
   //    func testPerformanceOnLargeArray() {
   //        self.measureBlock {
   //            self.printArrayWith(columns: 2000, rows: 2000, inititalValue: 1)
   //        }
   //    }
-  
-  private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int){
+
+  private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int) {
     let array = Array2D(columns: columns, rows: rows, initialValue: 4)
     for r in 0..<array.rows {
       for c in 0..<array.columns {
-        print("Array in [\(r), \(c)] value is: \(array[c,r])")
+        print("Array in [\(r), \(c)] value is: \(array[c, r])")
       }
     }
   }
-  
+
 }
 
-class TestElement : Equatable {
-  let identifier : String
-  
+class TestElement: Equatable {
+  let identifier: String
+
   init(identifier: String) {
     self.identifier = identifier
   }
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 1b9b070a1..4c2a6c358 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -49,7 +49,7 @@ if let node9 = tree.search(9) {
 }
 
 if let node1 = tree.search(1) {
-  // This makes it an invalid binary search tree because 100 is greater 
+  // This makes it an invalid binary search tree because 100 is greater
   // than the root, 7, and so must be in the right branch not in the left.
   tree.isBST(minValue: Int.min, maxValue: Int.max)  // true
   node1.insert(100)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 55683b639..a58ac075a 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -76,7 +76,7 @@ extension BinarySearchTree {
   public func insert(value: T) {
     insert(value, parent: self)
   }
-  
+
   private func insert(value: T, parent: BinarySearchTree) {
     if value < self.value {
       if let left = left {
@@ -209,7 +209,7 @@ extension BinarySearchTree {
     }
   }
   */
-  
+
   public func contains(value: T) -> Bool {
     return search(value) != nil
   }
@@ -224,7 +224,7 @@ extension BinarySearchTree {
     }
     return node
   }
-  
+
   /*
     Returns the rightmost descendent. O(h) time.
   */
@@ -235,7 +235,7 @@ extension BinarySearchTree {
     }
     return node
   }
-  
+
   /*
     Calculates the depth of this node, i.e. the distance to the root.
     Takes O(h) time.
@@ -249,7 +249,7 @@ extension BinarySearchTree {
     }
     return edges
   }
-  
+
   /*
     Calculates the height of this node, i.e. the distance to the lowest leaf.
     Since this looks at all children of this node, performance is O(n).
@@ -303,13 +303,13 @@ extension BinarySearchTree {
     process(value)
     right?.traverseInOrder(process)
   }
-  
+
   public func traversePreOrder(@noescape process: T -> Void) {
     process(value)
     left?.traversePreOrder(process)
     right?.traversePreOrder(process)
   }
-  
+
   public func traversePostOrder(@noescape process: T -> Void) {
     left?.traversePostOrder(process)
     right?.traversePostOrder(process)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.swift
index 55683b639..a58ac075a 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.swift	
@@ -76,7 +76,7 @@ extension BinarySearchTree {
   public func insert(value: T) {
     insert(value, parent: self)
   }
-  
+
   private func insert(value: T, parent: BinarySearchTree) {
     if value < self.value {
       if let left = left {
@@ -209,7 +209,7 @@ extension BinarySearchTree {
     }
   }
   */
-  
+
   public func contains(value: T) -> Bool {
     return search(value) != nil
   }
@@ -224,7 +224,7 @@ extension BinarySearchTree {
     }
     return node
   }
-  
+
   /*
     Returns the rightmost descendent. O(h) time.
   */
@@ -235,7 +235,7 @@ extension BinarySearchTree {
     }
     return node
   }
-  
+
   /*
     Calculates the depth of this node, i.e. the distance to the root.
     Takes O(h) time.
@@ -249,7 +249,7 @@ extension BinarySearchTree {
     }
     return edges
   }
-  
+
   /*
     Calculates the height of this node, i.e. the distance to the lowest leaf.
     Since this looks at all children of this node, performance is O(n).
@@ -303,13 +303,13 @@ extension BinarySearchTree {
     process(value)
     right?.traverseInOrder(process)
   }
-  
+
   public func traversePreOrder(@noescape process: T -> Void) {
     process(value)
     left?.traversePreOrder(process)
     right?.traversePreOrder(process)
   }
-  
+
   public func traversePostOrder(@noescape process: T -> Void) {
     left?.traversePostOrder(process)
     right?.traversePostOrder(process)
diff --git a/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift
index 46fdd7c8a..7c7fd069b 100755
--- a/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
+++ b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
@@ -302,9 +302,9 @@ class BinarySearchTreeTest: XCTestCase {
 
   func testRemoveRoot() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4, 9, 20, 11, 15, 13])
-    
+
     let node9 = tree.search(9)!
-    
+
     let newRoot = tree.remove()
     XCTAssertTrue(newRoot === node9)
     XCTAssertEqual(newRoot!.value, 9)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index d370eb691..ce2868bbf 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -7,7 +7,7 @@ public enum BinarySearchTree<T: Comparable> {
   case Empty
   case Leaf(T)
   indirect case Node(BinarySearchTree, T, BinarySearchTree)
-  
+
   /* How many nodes are in this subtree. Performance: O(n). */
   public var count: Int {
     switch self {
@@ -16,7 +16,7 @@ public enum BinarySearchTree<T: Comparable> {
     case let .Node(left, _, right): return left.count + 1 + right.count
     }
   }
-  
+
   /* Distance of this node to its lowest leaf. Performance: O(n). */
   public var height: Int {
     switch self {
@@ -25,7 +25,7 @@ public enum BinarySearchTree<T: Comparable> {
     case let .Node(left, _, right): return 1 + max(left.height, right.height)
     }
   }
-  
+
   /*
     Inserts a new element into the tree.
     Performance: runs in O(h) time, where h is the height of the tree.
@@ -34,14 +34,14 @@ public enum BinarySearchTree<T: Comparable> {
     switch self {
     case .Empty:
       return .Leaf(newValue)
-      
+
     case .Leaf(let value):
       if newValue < value {
         return .Node(.Leaf(newValue), value, .Empty)
       } else {
         return .Node(.Empty, value, .Leaf(newValue))
       }
-      
+
     case .Node(let left, let value, let right):
       if newValue < value {
         return .Node(left.insert(newValue), value, right)
@@ -50,7 +50,7 @@ public enum BinarySearchTree<T: Comparable> {
       }
     }
   }
-  
+
   /*
     Finds the "highest" node with the specified value.
     Performance: runs in O(h) time, where h is the height of the tree.
@@ -71,11 +71,11 @@ public enum BinarySearchTree<T: Comparable> {
       }
     }
   }
-  
+
   public func contains(x: T) -> Bool {
     return search(x) != nil
   }
-  
+
   /*
     Returns the leftmost descendent. O(h) time.
   */
@@ -91,7 +91,7 @@ public enum BinarySearchTree<T: Comparable> {
     }
     return prev
   }
-  
+
   /*
     Returns the rightmost descendent. O(h) time.
   */
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.swift
index d370eb691..ce2868bbf 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.swift	
@@ -7,7 +7,7 @@ public enum BinarySearchTree<T: Comparable> {
   case Empty
   case Leaf(T)
   indirect case Node(BinarySearchTree, T, BinarySearchTree)
-  
+
   /* How many nodes are in this subtree. Performance: O(n). */
   public var count: Int {
     switch self {
@@ -16,7 +16,7 @@ public enum BinarySearchTree<T: Comparable> {
     case let .Node(left, _, right): return left.count + 1 + right.count
     }
   }
-  
+
   /* Distance of this node to its lowest leaf. Performance: O(n). */
   public var height: Int {
     switch self {
@@ -25,7 +25,7 @@ public enum BinarySearchTree<T: Comparable> {
     case let .Node(left, _, right): return 1 + max(left.height, right.height)
     }
   }
-  
+
   /*
     Inserts a new element into the tree.
     Performance: runs in O(h) time, where h is the height of the tree.
@@ -34,14 +34,14 @@ public enum BinarySearchTree<T: Comparable> {
     switch self {
     case .Empty:
       return .Leaf(newValue)
-      
+
     case .Leaf(let value):
       if newValue < value {
         return .Node(.Leaf(newValue), value, .Empty)
       } else {
         return .Node(.Empty, value, .Leaf(newValue))
       }
-      
+
     case .Node(let left, let value, let right):
       if newValue < value {
         return .Node(left.insert(newValue), value, right)
@@ -50,7 +50,7 @@ public enum BinarySearchTree<T: Comparable> {
       }
     }
   }
-  
+
   /*
     Finds the "highest" node with the specified value.
     Performance: runs in O(h) time, where h is the height of the tree.
@@ -71,11 +71,11 @@ public enum BinarySearchTree<T: Comparable> {
       }
     }
   }
-  
+
   public func contains(x: T) -> Bool {
     return search(x) != nil
   }
-  
+
   /*
     Returns the leftmost descendent. O(h) time.
   */
@@ -91,7 +91,7 @@ public enum BinarySearchTree<T: Comparable> {
     }
     return prev
   }
-  
+
   /*
     Returns the rightmost descendent. O(h) time.
   */
diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index 5470f9741..b953b6a71 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -36,8 +36,8 @@ let node3 = BinaryTree.Node(.Empty, "3", .Empty)
 let nodeB = BinaryTree.Node(.Empty, "b", .Empty)
 
 // intermediate nodes on the left
-let Aminus10 = BinaryTree.Node(nodeA, "-", node10)
-let timesLeft = BinaryTree.Node(node5, "*", Aminus10)
+let aMinus10 = BinaryTree.Node(nodeA, "-", node10)
+let timesLeft = BinaryTree.Node(node5, "*", aMinus10)
 
 // intermediate nodes on the right
 let minus4 = BinaryTree.Node(.Empty, "-", node4)
@@ -60,7 +60,7 @@ extension BinaryTree {
       right.traverseInOrder(process)
     }
   }
-  
+
   public func traversePreOrder(@noescape process: T -> Void) {
     if case let .Node(left, value, right) = self {
       process(value)
@@ -68,7 +68,7 @@ extension BinaryTree {
       right.traversePreOrder(process)
     }
   }
-  
+
   public func traversePostOrder(@noescape process: T -> Void) {
     if case let .Node(left, value, right) = self {
       left.traversePostOrder(process)
diff --git a/Binary Tree/BinaryTree.playground/timeline.xctimeline b/Binary Tree/BinaryTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Tree/BinaryTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index edcb3b461..0c55af20e 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -6,7 +6,7 @@
 public indirect enum BinaryTree<T> {
   case Node(BinaryTree<T>, T, BinaryTree<T>)
   case Empty
-  
+
   public var count: Int {
     switch self {
     case let .Node(left, _, right):
@@ -36,7 +36,7 @@ extension BinaryTree {
       right.traverseInOrder(process)
     }
   }
-  
+
   public func traversePreOrder(@noescape process: T -> Void) {
     if case let .Node(left, value, right) = self {
       process(value)
@@ -44,7 +44,7 @@ extension BinaryTree {
       right.traversePreOrder(process)
     }
   }
-  
+
   public func traversePostOrder(@noescape process: T -> Void) {
     if case let .Node(left, value, right) = self {
       left.traversePostOrder(process)
diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 3cb56ccbb..77d371420 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -4,8 +4,8 @@
 var bits = BitSet(size: 140)
 
 // Initially, it looks like all zeros:
-// 0000000000000000000000000000000000000000000000000000000000000000 
-// 0000000000000000000000000000000000000000000000000000000000000000 
+// 0000000000000000000000000000000000000000000000000000000000000000
+// 0000000000000000000000000000000000000000000000000000000000000000
 // 0000000000000000000000000000000000000000000000000000000000000000
 print(bits)
 
@@ -63,7 +63,7 @@ c.cardinality  // 4
 print("")
 print(~a)  // 0111000000000000000000000000000000000000000000000000000000000000
 print(~b)  // 1101110000000000000000000000000000000000000000000000000000000000
-print(~c)  // 0101110000000000000000000000000000000000000000000000000000000000 
+print(~c)  // 0101110000000000000000000000000000000000000000000000000000000000
 
 (~a).cardinality  // 3
 (~b).cardinality  // 5
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index e54bf9cc8..46f51dbba 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -112,7 +112,7 @@ public struct BitSet {
       while x != 0 {
         let y = x & ~(x - 1)  // find lowest 1-bit
         x = x ^ y             // and erase it
-        ++count
+        count += 1
       }
     }
     return count
@@ -148,7 +148,7 @@ public struct BitSet {
 extension BitSet: Equatable {
 }
 
-public func ==(lhs: BitSet, rhs: BitSet) -> Bool {
+public func == (lhs: BitSet, rhs: BitSet) -> Bool {
   return lhs.words == rhs.words
 }
 
@@ -184,7 +184,7 @@ private func copyLargest(lhs: BitSet, _ rhs: BitSet) -> BitSet {
   That will strip off the higher bits from the larger BitSet when doing &.
 */
 
-public func &(lhs: BitSet, rhs: BitSet) -> BitSet {
+public func & (lhs: BitSet, rhs: BitSet) -> BitSet {
   let m = max(lhs.size, rhs.size)
   var out = BitSet(size: m)
   let n = min(lhs.words.count, rhs.words.count)
@@ -194,7 +194,7 @@ public func &(lhs: BitSet, rhs: BitSet) -> BitSet {
   return out
 }
 
-public func |(lhs: BitSet, rhs: BitSet) -> BitSet {
+public func | (lhs: BitSet, rhs: BitSet) -> BitSet {
   var out = copyLargest(lhs, rhs)
   let n = min(lhs.words.count, rhs.words.count)
   for i in 0..<n {
@@ -203,7 +203,7 @@ public func |(lhs: BitSet, rhs: BitSet) -> BitSet {
   return out
 }
 
-public func ^(lhs: BitSet, rhs: BitSet) -> BitSet {
+public func ^ (lhs: BitSet, rhs: BitSet) -> BitSet {
   var out = copyLargest(lhs, rhs)
   let n = min(lhs.words.count, rhs.words.count)
   for i in 0..<n {
@@ -212,7 +212,7 @@ public func ^(lhs: BitSet, rhs: BitSet) -> BitSet {
   return out
 }
 
-prefix public func ~(rhs: BitSet) -> BitSet {
+prefix public func ~ (rhs: BitSet) -> BitSet {
   var out = BitSet(size: rhs.size)
   for i in 0..<rhs.words.count {
     out.words[i] = ~rhs.words[i]
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index e54bf9cc8..46f51dbba 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -112,7 +112,7 @@ public struct BitSet {
       while x != 0 {
         let y = x & ~(x - 1)  // find lowest 1-bit
         x = x ^ y             // and erase it
-        ++count
+        count += 1
       }
     }
     return count
@@ -148,7 +148,7 @@ public struct BitSet {
 extension BitSet: Equatable {
 }
 
-public func ==(lhs: BitSet, rhs: BitSet) -> Bool {
+public func == (lhs: BitSet, rhs: BitSet) -> Bool {
   return lhs.words == rhs.words
 }
 
@@ -184,7 +184,7 @@ private func copyLargest(lhs: BitSet, _ rhs: BitSet) -> BitSet {
   That will strip off the higher bits from the larger BitSet when doing &.
 */
 
-public func &(lhs: BitSet, rhs: BitSet) -> BitSet {
+public func & (lhs: BitSet, rhs: BitSet) -> BitSet {
   let m = max(lhs.size, rhs.size)
   var out = BitSet(size: m)
   let n = min(lhs.words.count, rhs.words.count)
@@ -194,7 +194,7 @@ public func &(lhs: BitSet, rhs: BitSet) -> BitSet {
   return out
 }
 
-public func |(lhs: BitSet, rhs: BitSet) -> BitSet {
+public func | (lhs: BitSet, rhs: BitSet) -> BitSet {
   var out = copyLargest(lhs, rhs)
   let n = min(lhs.words.count, rhs.words.count)
   for i in 0..<n {
@@ -203,7 +203,7 @@ public func |(lhs: BitSet, rhs: BitSet) -> BitSet {
   return out
 }
 
-public func ^(lhs: BitSet, rhs: BitSet) -> BitSet {
+public func ^ (lhs: BitSet, rhs: BitSet) -> BitSet {
   var out = copyLargest(lhs, rhs)
   let n = min(lhs.words.count, rhs.words.count)
   for i in 0..<n {
@@ -212,7 +212,7 @@ public func ^(lhs: BitSet, rhs: BitSet) -> BitSet {
   return out
 }
 
-prefix public func ~(rhs: BitSet) -> BitSet {
+prefix public func ~ (rhs: BitSet) -> BitSet {
   var out = BitSet(size: rhs.size)
   for i in 0..<rhs.words.count {
     out.words[i] = ~rhs.words[i]
diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 0727ea439..ce59eecaa 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -3,44 +3,44 @@
 public class BloomFilter<T> {
   private var array: [Bool]
   private var hashFunctions: [T -> Int]
-  
+
   public init(size: Int = 1024, hashFunctions: [T -> Int]) {
     self.array = .init(count: size, repeatedValue: false)
     self.hashFunctions = hashFunctions
   }
-  
+
   private func computeHashes(value: T) -> [Int] {
     return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
   }
-  
+
   public func insert(element: T) {
     for hashValue in computeHashes(element) {
       array[hashValue] = true
     }
   }
-  
+
   public func insert(values: [T]) {
     for value in values {
       insert(value)
     }
   }
-  
+
   public func query(value: T) -> Bool {
     let hashValues = computeHashes(value)
-    
+
     // Map hashes to indices in the Bloom Filter
     let results = hashValues.map() { hashValue in array[hashValue] }
-    
+
     // All values must be 'true' for the query to return true
-    
+
     // This does NOT imply that the value is in the Bloom filter,
     // only that it may be. If the query returns false, however,
     // you can be certain that the value was not added.
-    
+
     let exists = results.reduce(true, combine: { $0 && $1 })
     return exists
   }
-  
+
   public func isEmpty() -> Bool {
     // As soon as the reduction hits a 'true' value, the && condition will fail.
     return array.reduce(true) { prev, next in prev && !next }
diff --git a/Bloom Filter/BloomFilter.swift b/Bloom Filter/BloomFilter.swift
index 83787ee7b..97a982f48 100644
--- a/Bloom Filter/BloomFilter.swift	
+++ b/Bloom Filter/BloomFilter.swift	
@@ -1,44 +1,44 @@
 public class BloomFilter<T> {
   private var array: [Bool]
   private var hashFunctions: [T -> Int]
-  
+
   public init(size: Int = 1024, hashFunctions: [T -> Int]) {
     self.array = .init(count: size, repeatedValue: false)
     self.hashFunctions = hashFunctions
   }
-  
+
   private func computeHashes(value: T) -> [Int] {
     return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
   }
-  
+
   public func insert(element: T) {
     for hashValue in computeHashes(element) {
       array[hashValue] = true
     }
   }
-  
+
   public func insert(values: [T]) {
     for value in values {
       insert(value)
     }
   }
-  
+
   public func query(value: T) -> Bool {
     let hashValues = computeHashes(value)
-    
+
     // Map hashes to indices in the Bloom Filter
     let results = hashValues.map() { hashValue in array[hashValue] }
-    
+
     // All values must be 'true' for the query to return true
-    
+
     // This does NOT imply that the value is in the Bloom filter,
     // only that it may be. If the query returns false, however,
     // you can be certain that the value was not added.
-    
+
     let exists = results.reduce(true, combine: { $0 && $1 })
     return exists
   }
-  
+
   public func isEmpty() -> Bool {
     // As soon as the reduction hits a 'true' value, the && condition will fail.
     return array.reduce(true) { prev, next in prev && !next }
diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 1248e0150..ffac8192d 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -5,72 +5,72 @@ import XCTest
 
 func djb2(x: String) -> Int {
     var hash = 5381
-    
+
     for char in x.characters {
         hash = ((hash << 5) &+ hash) &+ char.hashValue
     }
-    
+
     return Int(hash)
 }
 
 func sdbm(x: String) -> Int {
     var hash = 0
-    
+
     for char in x.characters {
-        hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash;
+        hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
     }
-    
+
     return Int(hash)
 }
 
 
 class BloomFilterTests: XCTestCase {
-    
+
     func testSingleHashFunction() {
         let bloom = BloomFilter<String>(hashFunctions: [djb2])
-        
+
         bloom.insert("Hello world!")
-        
+
         let result_good = bloom.query("Hello world!")
         let result_bad = bloom.query("Hello world")
-        
+
         XCTAssertTrue(result_good)
         XCTAssertFalse(result_bad)
     }
-    
+
     func testEmptyFilter() {
         let bloom = BloomFilter<String>(hashFunctions: [djb2])
-        
+
         let empty = bloom.isEmpty()
-        
+
         XCTAssertTrue(empty)
     }
-    
+
     func testMultipleHashFunctions() {
         let bloom = BloomFilter<String>(hashFunctions: [djb2, sdbm])
-        
+
         bloom.insert("Hello world!")
-        
+
         let result_good = bloom.query("Hello world!")
         let result_bad = bloom.query("Hello world")
-        
+
         XCTAssertTrue(result_good)
         XCTAssertFalse(result_bad)
     }
-    
+
     func testFalsePositive() {
         let bloom = BloomFilter<String>(size: 5, hashFunctions: [djb2, sdbm])
-        
+
         bloom.insert(["hello", "elloh", "llohe", "lohel", "ohell"])
-        
+
         print("Inserted")
-        
+
         let query = bloom.query("This wasn't inserted!")
-        
+
         // This is true even though we did not insert the value in the Bloom filter;
-        // the Bloom filter is capable of producing false positives but NOT 
+        // the Bloom filter is capable of producing false positives but NOT
         // false negatives.
-        
+
         XCTAssertTrue(query)
     }
 }
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index b4977d6ce..1bc678ccc 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -1,17 +1,17 @@
 struct Message: Comparable, CustomStringConvertible {
   let name: String
   let priority: Int
-  
+
   var description: String {
     return "\(name):\(priority)"
   }
 }
 
-func ==(m1: Message, m2: Message) -> Bool {
+func == (m1: Message, m2: Message) -> Bool {
   return m1.priority == m2.priority
 }
 
-func <(m1: Message, m2: Message) -> Bool {
+func < (m1: Message, m2: Message) -> Bool {
   return m1.priority < m2.priority
 }
 
@@ -63,7 +63,7 @@ queue.count
 queue.peek()
 print(queue)
 
-// Try to insert an item with very high priority. This gets added and the 
+// Try to insert an item with very high priority. This gets added and the
 // lowest priority item is removed.
 queue.enqueue(Message(name: "!!!", priority: 500))
 queue.count
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift
index 99f00d70c..58dc5034e 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
@@ -2,7 +2,7 @@ public class LinkedListNode<T: Comparable> {
   var value: T
   var next: LinkedListNode?
   var previous: LinkedListNode?
-  
+
   public init(value: T) {
     self.value = value
   }
@@ -61,7 +61,7 @@ public class BoundedPriorityQueue<T: Comparable> {
       previous.next = node
       node.previous = previous
       return node
-    
+
     } else if let first = head {
       // Have to insert at the head, so shift the existing head up once place.
       head = Node(value: value)
@@ -81,7 +81,7 @@ public class BoundedPriorityQueue<T: Comparable> {
   private func findInsertionPoint(value: T) -> Node? {
     var node = head
     var prev: Node? = nil
-    
+
     while let current = node where value < current.value {
       prev = node
       node = current.next
diff --git a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift
index c6ab5d554..b248c17ad 100644
--- a/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
+++ b/Bounded Priority Queue/Tests/BoundedPriorityQueueTests.swift	
@@ -12,15 +12,15 @@ private struct Message: Comparable {
   let priority: Int
 }
 
-private func ==(m1: Message, m2: Message) -> Bool {
+private func == (m1: Message, m2: Message) -> Bool {
   return m1.priority == m2.priority
 }
 
-private func <(m1: Message, m2: Message) -> Bool {
+private func < (m1: Message, m2: Message) -> Bool {
   return m1.priority < m2.priority
 }
 
-private func >(m1: Message, m2: Message) -> Bool {
+private func > (m1: Message, m2: Message) -> Bool {
   return m1.priority > m2.priority
 }
 
diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 926a76f93..433935133 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -5,16 +5,16 @@ extension String {
     let patternLength = pattern.characters.count
     assert(patternLength > 0)
     assert(patternLength <= self.characters.count)
-    
+
     var skipTable = [Character: Int]()
     for (i, c) in pattern.characters.enumerate() {
       skipTable[c] = patternLength - i - 1
     }
-    
+
     let p = pattern.endIndex.predecessor()
     let lastChar = pattern[p]
     var i = self.startIndex.advancedBy(patternLength - 1)
-    
+
     func backwards() -> String.Index? {
       var q = p
       var j = i
@@ -25,7 +25,7 @@ extension String {
       }
       return j
     }
-    
+
     while i < self.endIndex {
       let c = self[i]
       if c == lastChar {
diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore/BoyerMoore.swift
index 50aa88048..12a1d86c1 100644
--- a/Boyer-Moore/BoyerMoore.swift
+++ b/Boyer-Moore/BoyerMoore.swift
@@ -12,24 +12,24 @@ extension String {
     let patternLength = pattern.characters.count
     assert(patternLength > 0)
     assert(patternLength <= self.characters.count)
-    
+
     // Make the skip table. This table determines how far we skip ahead
     // when a character from the pattern is found.
     var skipTable = [Character: Int]()
     for (i, c) in pattern.characters.enumerate() {
       skipTable[c] = patternLength - i - 1
     }
-    
+
     // This points at the last character in the pattern.
     let p = pattern.endIndex.predecessor()
     let lastChar = pattern[p]
-    
+
     // The pattern is scanned right-to-left, so skip ahead in the string by
     // the length of the pattern. (Minus 1 because startIndex already points
     // at the first character in the source string.)
     var i = self.startIndex.advancedBy(patternLength - 1)
-    
-    // This is a helper function that steps backwards through both strings 
+
+    // This is a helper function that steps backwards through both strings
     // until we find a character that doesn’t match, or until we’ve reached
     // the beginning of the pattern.
     func backwards() -> String.Index? {
@@ -42,17 +42,17 @@ extension String {
       }
       return j
     }
-    
+
     // The main loop. Keep going until the end of the string is reached.
     while i < self.endIndex {
       let c = self[i]
-      
+
       // Does the current character match the last character from the pattern?
       if c == lastChar {
-        
+
         // There is a possible match. Do a brute-force search backwards.
         if let k = backwards() { return k }
-        
+
         // If no match, we can only safely skip one character ahead.
         i = i.successor()
       } else {
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift
index 3937a2cc7..9a58a1f96 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
@@ -1,4 +1,4 @@
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -6,6 +6,6 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
index e89d4ac97..8cfb2a09c 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -1,4 +1,4 @@
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -21,14 +21,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -50,6 +50,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift
index 9d8435ffa..37a3b3fdf 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
@@ -1,4 +1,4 @@
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
 
   public private(set) var label: String
@@ -23,10 +23,10 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Breadth-First Search/BreadthFirstSearch.swift b/Breadth-First Search/BreadthFirstSearch.swift
index 296bf42ed..aa396ac7b 100644
--- a/Breadth-First Search/BreadthFirstSearch.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.swift	
@@ -4,7 +4,7 @@ func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
 
   var nodesExplored = [source.label]
   source.visited = true
-  
+
   while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
diff --git a/Breadth-First Search/Tests/Graph.swift b/Breadth-First Search/Tests/Graph.swift
index 6f69ee800..ed71cab7c 100644
--- a/Breadth-First Search/Tests/Graph.swift	
+++ b/Breadth-First Search/Tests/Graph.swift	
@@ -1,6 +1,6 @@
 // MARK: - Edge
 
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -8,15 +8,15 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
 
 // MARK: - Node
 
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-  
+
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
@@ -39,17 +39,17 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
 
 // MARK: - Graph
 
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -72,14 +72,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -101,6 +101,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Bucket Sort/BucketSort.playground/Contents.swift b/Bucket Sort/BucketSort.playground/Contents.swift
index 32cd6ed29..f7383746c 100644
--- a/Bucket Sort/BucketSort.playground/Contents.swift	
+++ b/Bucket Sort/BucketSort.playground/Contents.swift	
@@ -37,10 +37,9 @@ extension Int: IntConvertible, Sortable {
 // MARK: Playing code
 //////////////////////////////////////
 
-let input = [1,2,4,6,10]
-let buckets = [Bucket<Int>(capacity: 15),Bucket<Int>(capacity: 15),Bucket<Int>(capacity: 15)]
+let input = [1, 2, 4, 6, 10]
+let buckets = [Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15)]
 
 let sortedElements = bucketSort(input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
 
 print(sortedElements)
-
diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index 8dfa80cd4..c93b96cb2 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -27,18 +27,18 @@ import Foundation
 //////////////////////////////////////
 
 
-public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
   var bucketsCopy = buckets
   for elem in elements {
     distributor.distribute(elem, buckets: &bucketsCopy)
   }
-  
+
   var results = [T]()
-  
+
   for bucket in buckets {
     results += bucket.sort(sorter)
   }
-  
+
   return results
 }
 
@@ -48,7 +48,7 @@ public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorte
 
 
 public protocol Distributor {
-  func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
+  func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
 }
 
 /*
@@ -67,13 +67,13 @@ public protocol Distributor {
  * By following the formula: element / capacity = #ofBucket
  */
 public struct RangeDistributor: Distributor {
-  
+
   public init() {}
-  
-  public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
+
+  public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
     let value = element.toInt()
     let bucketCapacity = buckets.first!.capacity
-    
+
     let bucketIndex = value / bucketCapacity
     buckets[bucketIndex].add(element)
   }
@@ -95,23 +95,23 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-  func sort<T:Sortable>(items: [T]) -> [T]
+  func sort<T: Sortable>(items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
-  
+
   public init() {}
-  
-  public func sort<T:Sortable>(items: [T]) -> [T] {
+
+  public func sort<T: Sortable>(items: [T]) -> [T] {
     var results = items
     for i in 0 ..< results.count {
       var j = i
-      while ( j > 0 && results[j-i] > results[j]) {
-        
+      while j > 0 && results[j-i] > results[j] {
+
         let auxiliar = results[i]
         results[i] = results[j]
         results[j] = auxiliar
-        
+
         j -= 1
       }
     }
@@ -126,18 +126,18 @@ public struct InsertionSorter: Sorter {
 public struct Bucket<T:Sortable> {
   var elements: [T]
   let capacity: Int
-  
+
   public init(capacity: Int) {
     self.capacity = capacity
     elements = [T]()
   }
-  
+
   public mutating func add(item: T) {
-    if (elements.count < capacity) {
+    if elements.count < capacity {
       elements.append(item)
     }
   }
-  
+
   public func sort(algorithm: Sorter) -> [T] {
     return algorithm.sort(elements)
   }
diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index c28eb0284..8363fd867 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -30,41 +30,41 @@ import Foundation
 /**
     Performs bucket sort algorithm on the given input elements.
     [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
- 
+
     - Parameter elements:     Array of Sortable elements
     - Parameter distributor:  Performs the distribution of each element of a bucket
     - Parameter sorter:       Performs the sorting inside each bucket, after all the elements are distributed
     - Parameter buckets:      An array of buckets
- 
+
     - Returns: A new array with sorted elements
  */
 
-public func bucketSort<T:Sortable>(elements: [T], distributor: Distributor,sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
     precondition(allPositiveNumbers(elements))
     precondition(enoughSpaceInBuckets(buckets, elements: elements))
-    
+
     var bucketsCopy = buckets
     for elem in elements {
         distributor.distribute(elem, buckets: &bucketsCopy)
     }
-    
+
     var results = [T]()
-    
+
     for bucket in bucketsCopy {
         results += bucket.sort(sorter)
     }
-    
+
     return results
 }
 
-private func allPositiveNumbers<T:Sortable>(array: [T]) -> Bool {
-    return array.filter{ $0.toInt() >= 0 }.count > 0
+private func allPositiveNumbers<T: Sortable>(array: [T]) -> Bool {
+    return array.filter { $0.toInt() >= 0 }.count > 0
 }
 
-private func enoughSpaceInBuckets<T:Sortable>(buckets: [Bucket<T>], elements: [T]) -> Bool {
+private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [T]) -> Bool {
     let maximumValue = elements.maxElement()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
- 
+
     return totalCapacity >= maximumValue
 }
 
@@ -74,7 +74,7 @@ private func enoughSpaceInBuckets<T:Sortable>(buckets: [Bucket<T>], elements: [T
 
 
 public protocol Distributor {
-    func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>])
+    func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
 }
 
 /*
@@ -93,13 +93,13 @@ public protocol Distributor {
  * By following the formula: element / capacity = #ofBucket
  */
 public struct RangeDistributor: Distributor {
-    
+
     public init() {}
-    
-    public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
+
+    public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
         let value = element.toInt()
         let bucketCapacity = buckets.first!.capacity
-        
+
         let bucketIndex = value / bucketCapacity
         buckets[bucketIndex].add(element)
     }
@@ -121,23 +121,23 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-    func sort<T:Sortable>(items: [T]) -> [T]
+    func sort<T: Sortable>(items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
-    
+
     public init() {}
-    
-    public func sort<T:Sortable>(items: [T]) -> [T] {
+
+    public func sort<T: Sortable>(items: [T]) -> [T] {
         var results = items
         for i in 0 ..< results.count {
             var j = i
-            while ( j > 0 && results[j-1] > results[j]) {
-                
+            while j > 0 && results[j-1] > results[j] {
+
                 let auxiliar = results[j-1]
                 results[j-1] = results[j]
                 results[j] = auxiliar
-                
+
                 j -= 1
             }
         }
@@ -152,18 +152,18 @@ public struct InsertionSorter: Sorter {
 public struct Bucket<T:Sortable> {
     var elements: [T]
     let capacity: Int
-    
+
     public init(capacity: Int) {
         self.capacity = capacity
         elements = [T]()
     }
-    
+
     public mutating func add(item: T) {
-        if (elements.count < capacity) {
+        if elements.count < capacity {
             elements.append(item)
         }
     }
-    
+
     public func sort(algorithm: Sorter) -> [T] {
         return algorithm.sort(elements)
     }
diff --git a/Bucket Sort/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
index f3b897b2b..22ac751de 100644
--- a/Bucket Sort/Tests/Tests.swift	
+++ b/Bucket Sort/Tests/Tests.swift	
@@ -9,79 +9,79 @@
 import XCTest
 
 class TestTests: XCTestCase {
-    
+
     var smallArray: [Int]?
 
     let total = 400
     let maximum = 1000
     var largeArray: [Int]?
-    
+
     var sparsedArray: [Int]?
-    
+
     override func setUp() {
         super.setUp()
-        
-        smallArray = [8,3,33,0,12,8,2,18]
-        
+
+        smallArray = [8, 3, 33, 0, 12, 8, 2, 18]
+
         largeArray = [Int]()
         for _ in 0..<total {
             largeArray!.append( random() % maximum )
         }
-        
+
         sparsedArray = [Int]()
-        sparsedArray = [10,400,1500,500]
+        sparsedArray = [10, 400, 1500, 500]
     }
-    
+
     override func tearDown() {
         // Put teardown code here. This method is called after the invocation of each test method in the class.
         super.tearDown()
     }
-    
+
     func testSmallArray() {
-        
+
         let results = performBucketSort(smallArray!, totalBuckets: 3)
         XCTAssert(isSorted(results))
     }
 
     func testBigArray() {
-        
+
         let results = performBucketSort(largeArray!, totalBuckets: 8)
         XCTAssert(isSorted(results))
     }
-    
+
     func testSparsedArray() {
-        
+
         let results = performBucketSort(sparsedArray!, totalBuckets: 3)
         XCTAssert(isSorted(results))
     }
-    
+
     // MARK: Private functions
-    
+
     private func performBucketSort(elements: [Int], totalBuckets: Int) -> [Int] {
 
         let value = (elements.maxElement()?.toInt())! + 1
         let capacityRequired = Int( ceil( Double(value) / Double(totalBuckets) ) )
-        
+
         var buckets = [Bucket<Int>]()
         for _ in 0..<totalBuckets {
             buckets.append(Bucket<Int>(capacity: capacityRequired))
         }
-        
+
         let results = bucketSort(smallArray!, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
         return results
     }
-    
+
     func isSorted(array: [Int]) -> Bool {
-        
+
         var index = 0
         var sorted = true
         while index < (array.count - 1) && sorted {
-            if (array[index] > array[index+1]) {
+            if array[index] > array[index+1] {
                 sorted = false
             }
             index += 1
         }
-        
+
         return sorted
     }
 }
diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 6dde6a9e0..5cb91967e 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -184,4 +184,3 @@ func binomialCoefficient(n: Int, _ k: Int) -> Int {
 
 binomialCoefficient(30, 15)
 binomialCoefficient(66, 33)
-
diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index 3a7ea9713..b90ba12ce 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -14,7 +14,7 @@ func countOccurrencesOfKey(key: Int, inArray a: [Int]) -> Int {
     }
     return low
   }
-  
+
   func rightBoundary() -> Int {
     var low = 0
     var high = a.count
@@ -28,7 +28,7 @@ func countOccurrencesOfKey(key: Int, inArray a: [Int]) -> Int {
     }
     return low
   }
-  
+
   return rightBoundary() - leftBoundary()
 }
 
diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 13249aea8..67d416f2f 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -8,11 +8,11 @@ func countingSort(array: [Int]) throws -> [Int] {
   guard array.count > 0 else {
     throw CountingSortError.ArrayEmpty
   }
-  
+
   // Step 1
   // Create an array to store the count of each element
   let maxElement = array.maxElement() ?? 0
-  
+
   var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
   for element in array {
     countArray[element] += 1
diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index 156782fef..ec8c5adcb 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -14,11 +14,11 @@ func countingSort(array: [Int]) throws -> [Int] {
   guard array.count > 0 else {
     throw CountingSortError.ArrayEmpty
   }
-  
+
   // Step 1
   // Create an array to store the count of each element
   let maxElement = array.maxElement() ?? 0
-  
+
   var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
   for element in array {
     countArray[element] += 1
diff --git a/Counting Sort/Tests/CountingSortTest.swift b/Counting Sort/Tests/CountingSortTest.swift
index fba639ba4..d8d73fc76 100644
--- a/Counting Sort/Tests/CountingSortTest.swift	
+++ b/Counting Sort/Tests/CountingSortTest.swift	
@@ -9,11 +9,11 @@
 import XCTest
 
 class CountingSort: XCTestCase {
-    
+
   func testCountingSort() {
     let sequence = [10, 8, 1, 2, 5, 8]
     let sortedSequence = [1, 2, 5, 8, 8, 10]
-    
+
     do {
       let afterCountingSort = try countingSort(sequence)
       XCTAssertEqual(afterCountingSort, sortedSequence)
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift
index 3937a2cc7..9a58a1f96 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
@@ -1,4 +1,4 @@
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -6,6 +6,6 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index e89d4ac97..8cfb2a09c 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -1,4 +1,4 @@
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -21,14 +21,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -50,6 +50,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift
index 9d8435ffa..37a3b3fdf 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
@@ -1,4 +1,4 @@
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
 
   public private(set) var label: String
@@ -23,10 +23,10 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Depth-First Search/Tests/Graph.swift b/Depth-First Search/Tests/Graph.swift
index 6f69ee800..ed71cab7c 100644
--- a/Depth-First Search/Tests/Graph.swift	
+++ b/Depth-First Search/Tests/Graph.swift	
@@ -1,6 +1,6 @@
 // MARK: - Edge
 
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -8,15 +8,15 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
 
 // MARK: - Node
 
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-  
+
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
@@ -39,17 +39,17 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
 
 // MARK: - Graph
 
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -72,14 +72,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -101,6 +101,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index 3b0d724dd..ea68059c0 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -7,25 +7,25 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
-  
+
   public init(capacity: Int = 10) {
     self.capacity = max(capacity, 1)
     array = .init(count: capacity, repeatedValue: nil)
     head = capacity
   }
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
-  
+
   public var count: Int {
     return array.count - head
   }
-  
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
-  
+
   public mutating func enqueueFront(element: T) {
     if head == 0 {
       capacity *= 2
@@ -52,7 +52,7 @@ public struct Deque<T> {
     }
     return element
   }
-  
+
   public mutating func dequeueBack() -> T? {
     if isEmpty {
       return nil
@@ -60,7 +60,7 @@ public struct Deque<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peekFront() -> T? {
     if isEmpty {
       return nil
@@ -68,7 +68,7 @@ public struct Deque<T> {
       return array[head]
     }
   }
-  
+
   public func peekBack() -> T? {
     if isEmpty {
       return nil
diff --git a/Deque/Deque-Simple.swift b/Deque/Deque-Simple.swift
index c1b2489a7..0ccba0caa 100644
--- a/Deque/Deque-Simple.swift
+++ b/Deque/Deque-Simple.swift
@@ -2,7 +2,7 @@
   Deque (pronounced "deck"), a double-ended queue
 
   This particular implementation is simple but not very efficient. Several
-  operations are O(n). A more efficient implementation would use a doubly 
+  operations are O(n). A more efficient implementation would use a doubly
   linked list or a circular buffer.
 */
 public struct Deque<T> {
diff --git a/Deque/Deque.playground/Contents.swift b/Deque/Deque.playground/Contents.swift
index e3cedd706..15bf1ee07 100644
--- a/Deque/Deque.playground/Contents.swift
+++ b/Deque/Deque.playground/Contents.swift
@@ -2,23 +2,23 @@
 
 public struct Deque<T> {
   private var array = [T]()
-  
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
-  
+
   public mutating func enqueueFront(element: T) {
     array.insert(element, atIndex: 0)
   }
-  
+
   public mutating func dequeue() -> T? {
     if isEmpty {
       return nil
@@ -26,7 +26,7 @@ public struct Deque<T> {
       return array.removeFirst()
     }
   }
-  
+
   public mutating func dequeueBack() -> T? {
     if isEmpty {
       return nil
@@ -34,11 +34,11 @@ public struct Deque<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peekFront() -> T? {
     return array.first
   }
-  
+
   public func peekBack() -> T? {
     return array.last
   }
diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 387d5de94..dedf6e293 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -16,7 +16,7 @@ func gcd(m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
   var r = min(m, n)
-  
+
   while r != 0 {
     a = b
     b = r
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 5ce865af6..a867e164a 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 public struct Edge<T where T: Equatable, T: Hashable>: Equatable {
-  
+
   public let from: Vertex<T>
   public let to: Vertex<T>
 
@@ -43,7 +43,7 @@ extension Edge: Hashable {
 
 }
 
-public func ==<T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
+public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
   guard lhs.from == rhs.from else {
     return false
   }
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index e6360754e..0a2c8042f 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -9,7 +9,7 @@ import XCTest
 @testable import Graph
 
 class GraphTests: XCTestCase {
-    
+
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()
@@ -53,5 +53,5 @@ class GraphTests: XCTestCase {
       XCTAssertEqual(graph.vertices.count, 1, "Graph should only contain one vertex after trying to create two vertices with identical data")
     }
   }
-    
+
 }
diff --git a/Hash Set/HashSet.playground/Contents.swift b/Hash Set/HashSet.playground/Contents.swift
index d49864fa3..636d4d925 100644
--- a/Hash Set/HashSet.playground/Contents.swift	
+++ b/Hash Set/HashSet.playground/Contents.swift	
@@ -2,27 +2,27 @@
 
 public struct HashSet<T: Hashable> {
   private var dictionary = Dictionary<T, Bool>()
-  
+
   public mutating func insert(element: T) {
     dictionary[element] = true
   }
-  
+
   public mutating func remove(element: T) {
     dictionary[element] = nil
   }
-  
+
   public func contains(element: T) -> Bool {
     return dictionary[element] != nil
   }
-  
+
   public func allElements() -> [T] {
     return Array(dictionary.keys)
   }
-  
+
   public var count: Int {
     return dictionary.count
   }
-  
+
   public var isEmpty: Bool {
     return dictionary.isEmpty
   }
diff --git a/Hash Set/HashSet.swift b/Hash Set/HashSet.swift
index 57f8f2219..303353574 100644
--- a/Hash Set/HashSet.swift	
+++ b/Hash Set/HashSet.swift	
@@ -1,26 +1,26 @@
 public struct HashSet<T: Hashable> {
   private var dictionary = Dictionary<T, Bool>()
-  
+
   public mutating func insert(element: T) {
     dictionary[element] = true
   }
-  
+
   public mutating func remove(element: T) {
     dictionary[element] = nil
   }
-  
+
   public func contains(element: T) -> Bool {
     return dictionary[element] != nil
   }
-  
+
   public func allElements() -> [T] {
     return Array(dictionary.keys)
   }
-  
+
   public var count: Int {
     return dictionary.count
   }
-  
+
   public var isEmpty: Bool {
     return dictionary.isEmpty
   }
diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index d5788176a..cda0919de 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -3,19 +3,19 @@
 public struct HashTable<Key: Hashable, Value> {
   private typealias Element = (key: Key, value: Value)
   private typealias Bucket = [Element]
-  
+
   private var buckets: [Bucket]
   private(set) var count = 0
-  
+
   public init(capacity: Int) {
     assert(capacity > 0)
     buckets = .init(count: capacity, repeatedValue: [])
   }
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
-  
+
   private func indexForKey(key: Key) -> Int {
     return abs(key.hashValue) % buckets.count
   }
@@ -34,7 +34,7 @@ extension HashTable {
       }
     }
   }
-  
+
   public func valueForKey(key: Key) -> Value? {
     let index = indexForKey(key)
 
@@ -48,7 +48,7 @@ extension HashTable {
 
   public mutating func updateValue(value: Value, forKey key: Key) -> Value? {
     let index = indexForKey(key)
-    
+
     // Do we already have this key in the bucket?
     for (i, element) in buckets[index].enumerate() {
       if element.key == key {
@@ -57,13 +57,13 @@ extension HashTable {
         return oldValue
       }
     }
-    
+
     // This key isn't in the bucket yet; add it to the chain.
     buckets[index].append((key: key, value: value))
     count += 1
     return nil
   }
-  
+
   public mutating func removeValueForKey(key: Key) -> Value? {
     let index = indexForKey(key)
 
@@ -77,7 +77,7 @@ extension HashTable {
     }
     return nil  // key not in hash table
   }
-  
+
   public mutating func removeAll() {
     buckets = .init(count: buckets.count, repeatedValue: [])
     count = 0
diff --git a/Hash Table/HashTable.swift b/Hash Table/HashTable.swift
index da9ca9064..46c73e284 100644
--- a/Hash Table/HashTable.swift	
+++ b/Hash Table/HashTable.swift	
@@ -14,7 +14,7 @@
   own bucket. In practice that is hard to achieve.
 
   When there is more than one hash value that maps to the same bucket index
-  -- a "collision" -- they are chained together, using an array. (Note that 
+  -- a "collision" -- they are chained together, using an array. (Note that
   more clever ways exist for dealing with the chaining issue.)
 
   While there are free buckets, inserting/retrieving/removing are O(1).
@@ -33,19 +33,19 @@
 public struct HashTable<Key: Hashable, Value> {
   private typealias Element = (key: Key, value: Value)
   private typealias Bucket = [Element]
-  
+
   private var buckets: [Bucket]
   private(set) var count = 0
-  
+
   public init(capacity: Int) {
     assert(capacity > 0)
     buckets = .init(count: capacity, repeatedValue: [])
   }
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
-  
+
   private func indexForKey(key: Key) -> Int {
     return abs(key.hashValue) % buckets.count
   }
@@ -66,10 +66,10 @@ extension HashTable {
       }
     }
   }
-  
+
   public func valueForKey(key: Key) -> Value? {
     let index = indexForKey(key)
-    
+
     for element in buckets[index] {
       if element.key == key {
         return element.value
@@ -77,10 +77,10 @@ extension HashTable {
     }
     return nil  // key not in hash table
   }
-  
+
   public mutating func updateValue(value: Value, forKey key: Key) -> Value? {
     let index = indexForKey(key)
-    
+
     // Do we already have this key in the bucket?
     for (i, element) in buckets[index].enumerate() {
       if element.key == key {
@@ -89,16 +89,16 @@ extension HashTable {
         return oldValue
       }
     }
-    
+
     // This key isn't in the bucket yet; add it to the chain.
     buckets[index].append((key: key, value: value))
     count += 1
     return nil
   }
-  
+
   public mutating func removeValueForKey(key: Key) -> Value? {
     let index = indexForKey(key)
-    
+
     // Find the element in the bucket's chain and remove it.
     for (i, element) in buckets[index].enumerate() {
       if element.key == key {
@@ -109,7 +109,7 @@ extension HashTable {
     }
     return nil  // key not in hash table
   }
-  
+
   public mutating func removeAll() {
     buckets = .init(count: buckets.count, repeatedValue: [])
     count = 0
@@ -128,7 +128,7 @@ extension HashTable {
     }
     return a
   }
-  
+
   public var values: [Value] {
     var a = [Value]()
     for bucket in buckets {
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 3293f75bb..64bd90cd8 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -6,10 +6,10 @@
 public struct Heap<T> {
   /** The array that stores the heap's nodes. */
   var elements = [T]()
-  
+
   /** Determines whether this is a max-heap (>) or min-heap (<). */
   private var isOrderedBefore: (T, T) -> Bool
- 
+
   /**
    * Creates an empty heap.
    * The sort function determines whether this is a min-heap or max-heap.
@@ -38,7 +38,7 @@ public struct Heap<T> {
     }
   }
   */
-  
+
   /**
    * Converts an array to a max-heap or min-heap in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
@@ -53,11 +53,11 @@ public struct Heap<T> {
   public var isEmpty: Bool {
     return elements.isEmpty
   }
-  
+
   public var count: Int {
     return elements.count
   }
-  
+
   /**
    * Returns the index of the parent of the element at index i.
    * The element at index 0 is the root of the tree and has no parent.
@@ -83,7 +83,7 @@ public struct Heap<T> {
   @inline(__always) func indexOfRightChild(i: Int) -> Int {
     return 2*i + 2
   }
-  
+
   /**
    * Returns the maximum value in the heap (for a max-heap) or the minimum
    * value (for a min-heap).
@@ -100,13 +100,13 @@ public struct Heap<T> {
     elements.append(value)
     shiftUp(index: elements.count - 1)
   }
-  
-  public mutating func insert<S : SequenceType where S.Generator.Element == T>(sequence: S) {
+
+  public mutating func insert<S: SequenceType where S.Generator.Element == T>(sequence: S) {
     for value in sequence {
       insert(value)
     }
   }
-  
+
   /**
    * Allows you to change an element. In a max-heap, the new element should be
    * larger than the old one; in a min-heap it should be smaller.
@@ -135,7 +135,7 @@ public struct Heap<T> {
       return value
     }
   }
-  
+
   /**
    * Removes an arbitrary node from the heap. Performance: O(log n). You need
    * to know the node's index, which may actually take O(n) steps to find.
@@ -149,9 +149,9 @@ public struct Heap<T> {
     }
     return elements.removeLast()
   }
-  
+
   /**
-   * Takes a child node and looks at its parents; if a parent is not larger 
+   * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
   mutating func shiftUp(index index: Int) {
@@ -167,7 +167,7 @@ public struct Heap<T> {
 
     elements[childIndex] = child
   }
-  
+
   mutating func shiftDown() {
     shiftDown(index: 0, heapSize: elements.count)
   }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index b038687ad..ec17560a5 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -6,7 +6,7 @@
 import XCTest
 
 class HeapTests: XCTestCase {
-  
+
   private func verifyMaxHeap(h: Heap<Int>) -> Bool {
     for i in 0..<h.count {
       let left = h.indexOfLeftChild(i)
@@ -62,7 +62,7 @@ class HeapTests: XCTestCase {
     heap.remove()
     XCTAssertTrue(heap.isEmpty)
   }
-  
+
   func testCount() {
     var heap = Heap<Int>(sort: >)
     XCTAssertEqual(0, heap.count)
diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index 99170fa91..b67f93a6a 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -5,18 +5,18 @@ import Foundation
 let s1 = "so much words wow many compression"
 if let originalData = s1.dataUsingEncoding(NSUTF8StringEncoding) {
   print(originalData.length)
-  
+
   let huffman1 = Huffman()
   let compressedData = huffman1.compressData(originalData)
   print(compressedData.length)
-  
+
   let frequencyTable = huffman1.frequencyTable()
   //print(frequencyTable)
-  
+
   let huffman2 = Huffman()
   let decompressedData = huffman2.decompressData(compressedData, frequencyTable: frequencyTable)
   print(decompressedData.length)
-  
+
   let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
   print(s2)
   assert(s1 == s2)
diff --git a/Huffman Coding/Huffman.playground/Sources/Heap.swift b/Huffman Coding/Huffman.playground/Sources/Heap.swift
index 3293f75bb..64bd90cd8 100644
--- a/Huffman Coding/Huffman.playground/Sources/Heap.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/Heap.swift	
@@ -6,10 +6,10 @@
 public struct Heap<T> {
   /** The array that stores the heap's nodes. */
   var elements = [T]()
-  
+
   /** Determines whether this is a max-heap (>) or min-heap (<). */
   private var isOrderedBefore: (T, T) -> Bool
- 
+
   /**
    * Creates an empty heap.
    * The sort function determines whether this is a min-heap or max-heap.
@@ -38,7 +38,7 @@ public struct Heap<T> {
     }
   }
   */
-  
+
   /**
    * Converts an array to a max-heap or min-heap in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
@@ -53,11 +53,11 @@ public struct Heap<T> {
   public var isEmpty: Bool {
     return elements.isEmpty
   }
-  
+
   public var count: Int {
     return elements.count
   }
-  
+
   /**
    * Returns the index of the parent of the element at index i.
    * The element at index 0 is the root of the tree and has no parent.
@@ -83,7 +83,7 @@ public struct Heap<T> {
   @inline(__always) func indexOfRightChild(i: Int) -> Int {
     return 2*i + 2
   }
-  
+
   /**
    * Returns the maximum value in the heap (for a max-heap) or the minimum
    * value (for a min-heap).
@@ -100,13 +100,13 @@ public struct Heap<T> {
     elements.append(value)
     shiftUp(index: elements.count - 1)
   }
-  
-  public mutating func insert<S : SequenceType where S.Generator.Element == T>(sequence: S) {
+
+  public mutating func insert<S: SequenceType where S.Generator.Element == T>(sequence: S) {
     for value in sequence {
       insert(value)
     }
   }
-  
+
   /**
    * Allows you to change an element. In a max-heap, the new element should be
    * larger than the old one; in a min-heap it should be smaller.
@@ -135,7 +135,7 @@ public struct Heap<T> {
       return value
     }
   }
-  
+
   /**
    * Removes an arbitrary node from the heap. Performance: O(log n). You need
    * to know the node's index, which may actually take O(n) steps to find.
@@ -149,9 +149,9 @@ public struct Heap<T> {
     }
     return elements.removeLast()
   }
-  
+
   /**
-   * Takes a child node and looks at its parents; if a parent is not larger 
+   * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
   mutating func shiftUp(index index: Int) {
@@ -167,7 +167,7 @@ public struct Heap<T> {
 
     elements[childIndex] = child
   }
-  
+
   mutating func shiftDown() {
     shiftDown(index: 0, heapSize: elements.count)
   }
diff --git a/Huffman Coding/Huffman.playground/Sources/Huffman.swift b/Huffman Coding/Huffman.playground/Sources/Huffman.swift
index 0b6da03af..d50b90d82 100644
--- a/Huffman Coding/Huffman.playground/Sources/Huffman.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/Huffman.swift	
@@ -1,19 +1,19 @@
 import Foundation
 
 /*
-  Basic implementation of Huffman encoding. It encodes bytes that occur often 
+  Basic implementation of Huffman encoding. It encodes bytes that occur often
   with a smaller number of bits than bytes that occur less frequently.
 
-  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 
-  1991 and October 1992. 
+  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February
+  1991 and October 1992.
 
   Note: This code is not optimized for speed but explanation.
 */
 public class Huffman {
-  /* Tree nodes don't use pointers to refer to each other, but simple integer 
+  /* Tree nodes don't use pointers to refer to each other, but simple integer
      indices. That allows us to use structs for the nodes. */
   typealias NodeIndex = Int
-  
+
   /* A node in the compression tree. Leaf nodes represent the actual bytes that
      are present in the input data. The count of an intermediary node is the sum
      of the counts of all nodes below it. The root node's count is the number of
@@ -25,29 +25,29 @@ public class Huffman {
     var left: NodeIndex = -1
     var right: NodeIndex = -1
   }
-  
-  /* The tree structure. The first 256 entries are for the leaf nodes (not all 
-     of those may be used, depending on the input). We add additional nodes as 
+
+  /* The tree structure. The first 256 entries are for the leaf nodes (not all
+     of those may be used, depending on the input). We add additional nodes as
      we build the tree. */
   var tree = [Node](count: 256, repeatedValue: Node())
 
   /* This is the last node we add to the tree. */
   var root: NodeIndex = -1
 
-  /* The frequency table describes how often a byte occurs in the input data. 
+  /* The frequency table describes how often a byte occurs in the input data.
      You need it to decompress the Huffman-encoded data. The frequency table
      should be serialized along with the compressed data. */
   public struct Freq {
     var byte: UInt8 = 0
     var count = 0
   }
-  
+
   public init() { }
 }
 
 extension Huffman {
-  /* To compress a block of data, first we need to count how often each byte 
-     occurs. These counts are stored in the first 256 nodes in the tree, i.e. 
+  /* To compress a block of data, first we need to count how often each byte
+     occurs. These counts are stored in the first 256 nodes in the tree, i.e.
      the leaf nodes. The frequency table used by decompression is derived from
      this. */
   private func countByteFrequency(data: NSData) {
@@ -59,7 +59,7 @@ extension Huffman {
       ptr = ptr.successor()
     }
   }
-  
+
   /* Takes a frequency table and rebuilds the tree. This is the first step of
      decompression. */
   private func restoreTree(frequencyTable: [Freq]) {
@@ -70,9 +70,9 @@ extension Huffman {
     }
     buildTree()
   }
-  
-  /* Returns the frequency table. This is the first 256 nodes from the tree but 
-     only those that are actually used, without the parent/left/right pointers. 
+
+  /* Returns the frequency table. This is the first 256 nodes from the tree but
+     only those that are actually used, without the parent/left/right pointers.
      You would serialize this along with the compressed file. */
   public func frequencyTable() -> [Freq] {
     var a = [Freq]()
@@ -109,7 +109,7 @@ extension Huffman {
       // Link the two nodes into their new parent node.
       tree[node1.index].parent = parentNode.index
       tree[node2.index].parent = parentNode.index
-      
+
       // Put the intermediate node back into the queue.
       queue.enqueue(parentNode)
     }
@@ -125,7 +125,7 @@ extension Huffman {
   public func compressData(data: NSData) -> NSData {
     countByteFrequency(data)
     buildTree()
-    
+
     let writer = BitWriter()
     var ptr = UnsafePointer<UInt8>(data.bytes)
     for _ in 0..<data.length {
@@ -137,8 +137,8 @@ extension Huffman {
     writer.flush()
     return writer.data
   }
-  
-  /* Recursively walks the tree from a leaf node up to the root, and then back 
+
+  /* Recursively walks the tree from a leaf node up to the root, and then back
      again. If a child is the right node, we emit a 0 bit; if it's the left node,
      we emit a 1 bit. */
   private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
@@ -172,8 +172,8 @@ extension Huffman {
     }
     return outData
   }
-  
-  /* Walks the tree from the root down to the leaf node. At every node, read the 
+
+  /* Walks the tree from the root down to the leaf node. At every node, read the
      next bit and use that to determine whether to step to the left or right.
      When we get to the leaf node, we simply return its index, which is equal to
      the original byte value. */
diff --git a/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift b/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift
index beb669dd1..0aa821f72 100644
--- a/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift	
@@ -5,7 +5,7 @@ public class BitWriter {
   public var data = NSMutableData()
   var outByte: UInt8 = 0
   var outCount = 0
-  
+
   public func writeBit(bit: Bool) {
     if outCount == 8 {
       data.appendBytes(&outByte, length: 1)
@@ -31,11 +31,11 @@ public class BitReader {
   var ptr: UnsafePointer<UInt8>
   var inByte: UInt8 = 0
   var inCount = 8
-  
+
   public init(data: NSData) {
     ptr = UnsafePointer<UInt8>(data.bytes)
   }
-  
+
   public func readBit() -> Bool {
     if inCount == 8 {
       inByte = ptr.memory    // load the next byte
diff --git a/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift b/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift
index 7a7cee34b..757a6c539 100644
--- a/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift	
@@ -3,7 +3,7 @@
   the queue.
 
   The heap is a natural data structure for a priority queue, so this object
-  simply wraps the Heap struct. 
+  simply wraps the Heap struct.
 
   All operations are O(lg n).
 
diff --git a/Huffman Coding/Huffman.swift b/Huffman Coding/Huffman.swift
index 0b6da03af..d50b90d82 100644
--- a/Huffman Coding/Huffman.swift	
+++ b/Huffman Coding/Huffman.swift	
@@ -1,19 +1,19 @@
 import Foundation
 
 /*
-  Basic implementation of Huffman encoding. It encodes bytes that occur often 
+  Basic implementation of Huffman encoding. It encodes bytes that occur often
   with a smaller number of bits than bytes that occur less frequently.
 
-  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February 
-  1991 and October 1992. 
+  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February
+  1991 and October 1992.
 
   Note: This code is not optimized for speed but explanation.
 */
 public class Huffman {
-  /* Tree nodes don't use pointers to refer to each other, but simple integer 
+  /* Tree nodes don't use pointers to refer to each other, but simple integer
      indices. That allows us to use structs for the nodes. */
   typealias NodeIndex = Int
-  
+
   /* A node in the compression tree. Leaf nodes represent the actual bytes that
      are present in the input data. The count of an intermediary node is the sum
      of the counts of all nodes below it. The root node's count is the number of
@@ -25,29 +25,29 @@ public class Huffman {
     var left: NodeIndex = -1
     var right: NodeIndex = -1
   }
-  
-  /* The tree structure. The first 256 entries are for the leaf nodes (not all 
-     of those may be used, depending on the input). We add additional nodes as 
+
+  /* The tree structure. The first 256 entries are for the leaf nodes (not all
+     of those may be used, depending on the input). We add additional nodes as
      we build the tree. */
   var tree = [Node](count: 256, repeatedValue: Node())
 
   /* This is the last node we add to the tree. */
   var root: NodeIndex = -1
 
-  /* The frequency table describes how often a byte occurs in the input data. 
+  /* The frequency table describes how often a byte occurs in the input data.
      You need it to decompress the Huffman-encoded data. The frequency table
      should be serialized along with the compressed data. */
   public struct Freq {
     var byte: UInt8 = 0
     var count = 0
   }
-  
+
   public init() { }
 }
 
 extension Huffman {
-  /* To compress a block of data, first we need to count how often each byte 
-     occurs. These counts are stored in the first 256 nodes in the tree, i.e. 
+  /* To compress a block of data, first we need to count how often each byte
+     occurs. These counts are stored in the first 256 nodes in the tree, i.e.
      the leaf nodes. The frequency table used by decompression is derived from
      this. */
   private func countByteFrequency(data: NSData) {
@@ -59,7 +59,7 @@ extension Huffman {
       ptr = ptr.successor()
     }
   }
-  
+
   /* Takes a frequency table and rebuilds the tree. This is the first step of
      decompression. */
   private func restoreTree(frequencyTable: [Freq]) {
@@ -70,9 +70,9 @@ extension Huffman {
     }
     buildTree()
   }
-  
-  /* Returns the frequency table. This is the first 256 nodes from the tree but 
-     only those that are actually used, without the parent/left/right pointers. 
+
+  /* Returns the frequency table. This is the first 256 nodes from the tree but
+     only those that are actually used, without the parent/left/right pointers.
      You would serialize this along with the compressed file. */
   public func frequencyTable() -> [Freq] {
     var a = [Freq]()
@@ -109,7 +109,7 @@ extension Huffman {
       // Link the two nodes into their new parent node.
       tree[node1.index].parent = parentNode.index
       tree[node2.index].parent = parentNode.index
-      
+
       // Put the intermediate node back into the queue.
       queue.enqueue(parentNode)
     }
@@ -125,7 +125,7 @@ extension Huffman {
   public func compressData(data: NSData) -> NSData {
     countByteFrequency(data)
     buildTree()
-    
+
     let writer = BitWriter()
     var ptr = UnsafePointer<UInt8>(data.bytes)
     for _ in 0..<data.length {
@@ -137,8 +137,8 @@ extension Huffman {
     writer.flush()
     return writer.data
   }
-  
-  /* Recursively walks the tree from a leaf node up to the root, and then back 
+
+  /* Recursively walks the tree from a leaf node up to the root, and then back
      again. If a child is the right node, we emit a 0 bit; if it's the left node,
      we emit a 1 bit. */
   private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
@@ -172,8 +172,8 @@ extension Huffman {
     }
     return outData
   }
-  
-  /* Walks the tree from the root down to the leaf node. At every node, read the 
+
+  /* Walks the tree from the root down to the leaf node. At every node, read the
      next bit and use that to determine whether to step to the left or right.
      When we get to the leaf node, we simply return its index, which is equal to
      the original byte value. */
diff --git a/Huffman Coding/NSData+Bits.swift b/Huffman Coding/NSData+Bits.swift
index beb669dd1..0aa821f72 100644
--- a/Huffman Coding/NSData+Bits.swift	
+++ b/Huffman Coding/NSData+Bits.swift	
@@ -5,7 +5,7 @@ public class BitWriter {
   public var data = NSMutableData()
   var outByte: UInt8 = 0
   var outCount = 0
-  
+
   public func writeBit(bit: Bool) {
     if outCount == 8 {
       data.appendBytes(&outByte, length: 1)
@@ -31,11 +31,11 @@ public class BitReader {
   var ptr: UnsafePointer<UInt8>
   var inByte: UInt8 = 0
   var inCount = 8
-  
+
   public init(data: NSData) {
     ptr = UnsafePointer<UInt8>(data.bytes)
   }
-  
+
   public func readBit() -> Bool {
     if inCount == 8 {
       inByte = ptr.memory    // load the next byte
diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 743cdc824..972fd7230 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -4,17 +4,17 @@ class KMeans<Label: Hashable> {
   let numCenters: Int
   let labels: [Label]
   private(set) var centroids = [Vector]()
-  
+
   init(labels: [Label]) {
     assert(labels.count > 1, "Exception: KMeans with less than 2 centers.")
     self.labels = labels
     self.numCenters = labels.count
   }
-  
+
   private func indexOfNearestCenter(x: Vector, centers: [Vector]) -> Int {
     var nearestDist = DBL_MAX
     var minIndex = 0
-    
+
     for (idx, center) in centers.enumerate() {
       let dist = x.distanceTo(center)
       if dist < nearestDist {
@@ -24,18 +24,18 @@ class KMeans<Label: Hashable> {
     }
     return minIndex
   }
-  
+
   func trainCenters(points: [Vector], convergeDistance: Double) {
     let zeroVector = Vector([Double](count: points[0].length, repeatedValue: 0))
-    
+
     // Randomly take k objects from the input data to make the initial centroids.
     var centers = reservoirSample(points, k: numCenters)
-    
+
     var centerMoveDist = 0.0
     repeat {
       // This array keeps track of which data points belong to which centroids.
       var classification: [[Vector]] = .init(count: numCenters, repeatedValue: [])
-      
+
       // For each data point, find the centroid that it is closest to.
       for p in points {
         let classIndex = indexOfNearestCenter(p, centers: centers)
@@ -47,30 +47,30 @@ class KMeans<Label: Hashable> {
       let newCenters = classification.map { assignedPoints in
         assignedPoints.reduce(zeroVector, combine: +) / Double(assignedPoints.count)
       }
-      
+
       // Find out how far each centroid moved since the last iteration. If it's
       // only a small distance, then we're done.
       centerMoveDist = 0.0
       for idx in 0..<numCenters {
         centerMoveDist += centers[idx].distanceTo(newCenters[idx])
       }
-      
+
       centers = newCenters
     } while centerMoveDist > convergeDistance
-    
+
     centroids = centers
   }
-  
+
   func fit(point: Vector) -> Label {
     assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
-    
+
     let centroidIndex = indexOfNearestCenter(point, centers: centroids)
     return labels[centroidIndex]
   }
-  
+
   func fit(points: [Vector]) -> [Label] {
     assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
-    
+
     return points.map(fit)
   }
 }
@@ -78,7 +78,7 @@ class KMeans<Label: Hashable> {
 // Pick k random elements from samples
 func reservoirSample<T>(samples: [T], k: Int) -> [T] {
   var result = [T]()
-  
+
   // Fill the result array with first k elements
   for i in 0..<k {
     result.append(samples[i])
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index 7a6803f63..179f9d418 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -21,27 +21,27 @@ class KMeansTests: XCTestCase {
     }
     return points
   }
-  
+
   func testSmall_2D() {
     let points = genPoints(10, numDimensions: 2)
-    
+
     print("\nCenters")
     let kmm = KMeans<Character>(labels: ["A", "B", "C"])
     kmm.trainCenters(points, convergeDistance: 0.01)
-    
+
     for (label, centroid) in zip(kmm.labels, kmm.centroids) {
       print("\(label): \(centroid)")
     }
-    
+
     print("\nClassifications")
     for (label, point) in zip(kmm.fit(points), points) {
       print("\(label): \(point)")
     }
   }
-  
+
   func testSmall_10D() {
     let points = genPoints(10, numDimensions: 10)
-    
+
     print("\nCenters")
     let kmm = KMeans<Int>(labels: [1, 2, 3])
     kmm.trainCenters(points, convergeDistance: 0.01)
@@ -49,23 +49,23 @@ class KMeansTests: XCTestCase {
       print(c)
     }
   }
-  
+
   func testLarge_2D() {
     let points = genPoints(10000, numDimensions: 2)
-    
+
     print("\nCenters")
-    let kmm = KMeans<Character>(labels: ["A","B","C","D","E"])
+    let kmm = KMeans<Character>(labels: ["A", "B", "C", "D", "E"])
     kmm.trainCenters(points, convergeDistance: 0.01)
     for c in kmm.centroids {
       print(c)
     }
   }
-  
+
   func testLarge_10D() {
     let points = genPoints(10000, numDimensions: 10)
-    
+
     print("\nCenters")
-    let kmm = KMeans<Int>(labels: [1,2,3,4,5])
+    let kmm = KMeans<Int>(labels: [1, 2, 3, 4, 5])
     kmm.trainCenters(points, convergeDistance: 0.01)
     for c in kmm.centroids {
       print(c)
diff --git a/K-Means/Tests/Vector.swift b/K-Means/Tests/Vector.swift
index 659bd914f..10baf9338 100644
--- a/K-Means/Tests/Vector.swift
+++ b/K-Means/Tests/Vector.swift
@@ -8,11 +8,11 @@ struct Vector: CustomStringConvertible, Equatable {
     self.data = data
     self.length = data.count
   }
-  
+
   var description: String {
     return "Vector (\(data)"
   }
-  
+
   func distanceTo(other: Vector) -> Double {
     var result = 0.0
     for idx in 0..<length {
@@ -22,7 +22,7 @@ struct Vector: CustomStringConvertible, Equatable {
   }
 }
 
-func ==(left: Vector, right: Vector) -> Bool {
+func == (left: Vector, right: Vector) -> Bool {
   for idx in 0..<left.length {
     if left.data[idx] != right.data[idx] {
       return false
@@ -31,7 +31,7 @@ func ==(left: Vector, right: Vector) -> Bool {
   return true
 }
 
-func +(left: Vector, right: Vector) -> Vector {
+func + (left: Vector, right: Vector) -> Vector {
   var results = [Double]()
   for idx in 0..<left.length {
     results.append(left.data[idx] + right.data[idx])
@@ -39,11 +39,11 @@ func +(left: Vector, right: Vector) -> Vector {
   return Vector(results)
 }
 
-func +=(inout left: Vector, right: Vector) {
+func += (inout left: Vector, right: Vector) {
   left = left + right
 }
 
-func -(left: Vector, right: Vector) -> Vector {
+func - (left: Vector, right: Vector) -> Vector {
   var results = [Double]()
   for idx in 0..<left.length {
     results.append(left.data[idx] - right.data[idx])
@@ -51,11 +51,11 @@ func -(left: Vector, right: Vector) -> Vector {
   return Vector(results)
 }
 
-func -=(inout left: Vector, right: Vector) {
+func -= (inout left: Vector, right: Vector) {
   left = left - right
 }
 
-func /(left:Vector, right: Double) -> Vector  {
+func / (left: Vector, right: Double) -> Vector {
   var results = [Double](count: left.length, repeatedValue: 0)
   for (idx, value) in left.data.enumerate() {
     results[idx] = value / right
@@ -63,6 +63,6 @@ func /(left:Vector, right: Double) -> Vector  {
   return Vector(results)
 }
 
-func /=(inout left: Vector, right: Double) {
+func /= (inout left: Vector, right: Double) {
   left = left / right
 }
diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 7f97bb271..628892d9c 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -45,7 +45,7 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
 
 public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
   var a = array
-  
+
   func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
     swap(&a, pivotIndex, high)
@@ -79,7 +79,7 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
       return a[low]
     }
   }
-  
+
   precondition(a.count > 0)
   return randomizedSelect(&a, 0, a.count - 1, k)
 }
diff --git a/Kth Largest Element/kthLargest.swift b/Kth Largest Element/kthLargest.swift
index 5bf781932..1f90b096f 100644
--- a/Kth Largest Element/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.swift	
@@ -48,13 +48,13 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
 */
 public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
   var a = array
-  
+
   func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
     swap(&a, pivotIndex, high)
     return a[high]
   }
-  
+
   func randomizedPartition<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> Int {
     let pivot = randomPivot(&a, low, high)
     var i = low
@@ -67,7 +67,7 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
     swap(&a, i, high)
     return i
   }
-  
+
   func randomizedSelect<T: Comparable>(inout a: [T], _ low: Int, _ high: Int, _ k: Int) -> T {
     if low < high {
       let p = randomizedPartition(&a, low, high)
@@ -82,7 +82,7 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
       return a[low]
     }
   }
-  
+
   precondition(a.count > 0)
   return randomizedSelect(&a, 0, a.count - 1, k)
 }
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index c09bed736..cc7ed3d59 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -14,15 +14,15 @@ public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
   private var head: Node?
-  
+
   public var isEmpty: Bool {
     return head == nil
   }
-  
+
   public var first: Node? {
     return head
   }
-  
+
   public var last: Node? {
     if var node = head {
       while case let next? = node.next {
@@ -33,7 +33,7 @@ public class LinkedList<T> {
       return nil
     }
   }
-  
+
   public var count: Int {
     if var node = head {
       var c = 1
@@ -46,7 +46,7 @@ public class LinkedList<T> {
       return 0
     }
   }
-  
+
   public func nodeAtIndex(index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -59,7 +59,7 @@ public class LinkedList<T> {
     }
     return nil
   }
-  
+
   public subscript(index: Int) -> T {
     let node = nodeAtIndex(index)
     assert(node != nil)
@@ -75,10 +75,10 @@ public class LinkedList<T> {
       head = newNode
     }
   }
-  
+
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-    
+
     var i = index
     var next = head
     var prev: Node?
@@ -92,10 +92,10 @@ public class LinkedList<T> {
 
     return (prev, next)
   }
-  
+
   public func insert(value: T, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index)
-    
+
     let newNode = Node(value: value)
     newNode.previous = prev
     newNode.next = next
@@ -106,7 +106,7 @@ public class LinkedList<T> {
       head = newNode
     }
   }
-  
+
   public func removeAll() {
     head = nil
   }
@@ -114,24 +114,24 @@ public class LinkedList<T> {
   public func removeNode(node: Node) -> T {
     let prev = node.previous
     let next = node.next
-    
+
     if let prev = prev {
       prev.next = next
     } else {
       head = next
     }
     next?.previous = prev
-    
+
     node.previous = nil
     node.next = nil
     return node.value
   }
-  
+
   public func removeLast() -> T {
     assert(!isEmpty)
     return removeNode(last!)
   }
-  
+
   public func removeAtIndex(index: Int) -> T {
     let node = nodeAtIndex(index)
     assert(node != nil)
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 8d2c27d7e..ef95a0b58 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -7,7 +7,7 @@ public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
   weak var previous: LinkedListNode?
-  
+
   public init(value: T) {
     self.value = value
   }
@@ -15,17 +15,17 @@ public class LinkedListNode<T> {
 
 public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
-  
+
   private var head: Node?
-  
+
   public var isEmpty: Bool {
     return head == nil
   }
-  
+
   public var first: Node? {
     return head
   }
-  
+
   public var last: Node? {
     if var node = head {
       while case let next? = node.next {
@@ -36,7 +36,7 @@ public class LinkedList<T> {
       return nil
     }
   }
-  
+
   public var count: Int {
     if var node = head {
       var c = 1
@@ -49,7 +49,7 @@ public class LinkedList<T> {
       return 0
     }
   }
-  
+
   public func nodeAtIndex(index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -62,13 +62,13 @@ public class LinkedList<T> {
     }
     return nil
   }
-  
+
   public subscript(index: Int) -> T {
     let node = nodeAtIndex(index)
     assert(node != nil)
     return node!.value
   }
-  
+
   public func append(value: T) {
     let newNode = Node(value: value)
     if let lastNode = last {
@@ -78,63 +78,63 @@ public class LinkedList<T> {
       head = newNode
     }
   }
-  
+
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-    
+
     var i = index
     var next = head
     var prev: Node?
-    
+
     while next != nil && i > 0 {
       i -= 1
       prev = next
       next = next!.next
     }
     assert(i == 0)  // if > 0, then specified index was too large
-    
+
     return (prev, next)
   }
-  
+
   public func insert(value: T, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index)
-    
+
     let newNode = Node(value: value)
     newNode.previous = prev
     newNode.next = next
     prev?.next = newNode
     next?.previous = newNode
-    
+
     if prev == nil {
       head = newNode
     }
   }
-  
+
   public func removeAll() {
     head = nil
   }
-  
+
   public func removeNode(node: Node) -> T {
     let prev = node.previous
     let next = node.next
-    
+
     if let prev = prev {
       prev.next = next
     } else {
       head = next
     }
     next?.previous = prev
-    
+
     node.previous = nil
     node.next = nil
     return node.value
   }
-  
+
   public func removeLast() -> T {
     assert(!isEmpty)
     return removeNode(last!)
   }
-  
+
   public func removeAtIndex(index: Int) -> T {
     let node = nodeAtIndex(index)
     assert(node != nil)
@@ -176,7 +176,7 @@ extension LinkedList {
     }
     return result
   }
-  
+
   public func filter(predicate: T -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index 0fa00d48b..bb6fa7c2a 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,9 +1,9 @@
 extension String {
   public func longestCommonSubsequence(other: String) -> String {
-    
+
     func lcsLength(other: String) -> [[Int]] {
       var matrix = [[Int]](count: self.characters.count+1, repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
-      
+
       for (i, selfChar) in self.characters.enumerate() {
         for (j, otherChar) in other.characters.enumerate() {
           if otherChar == selfChar {
@@ -15,14 +15,14 @@ extension String {
       }
       return matrix
     }
-    
+
     func backtrack(matrix: [[Int]]) -> String {
       var i = self.characters.count
       var j = other.characters.count
       var charInSequence = self.endIndex
-      
+
       var lcs = String()
-      
+
       while i >= 1 && j >= 1 {
         if matrix[i][j] == matrix[i][j - 1] {
           j -= 1
@@ -38,7 +38,7 @@ extension String {
       }
       return String(lcs.characters.reverse())
     }
-    
+
     return backtrack(lcsLength(other))
   }
 }
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.swift b/Longest Common Subsequence/LongestCommonSubsequence.swift
index d9dda1364..23d191102 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.swift	
@@ -1,6 +1,6 @@
 extension String {
   public func longestCommonSubsequence(other: String) -> String {
-    
+
     // Computes the length of the lcs using dynamic programming.
     // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] is the length
     // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
@@ -31,12 +31,12 @@ extension String {
     func backtrack(matrix: [[Int]]) -> String {
       var i = self.characters.count
       var j = other.characters.count
-      
+
       // charInSequence is in sync with i so we can get self[i]
       var charInSequence = self.endIndex
-      
+
       var lcs = String()
-      
+
       while i >= 1 && j >= 1 {
         // Indicates propagation without change: no new char was added to lcs.
         if matrix[i][j] == matrix[i][j - 1] {
@@ -57,12 +57,12 @@ extension String {
           lcs.append(self[charInSequence])
         }
       }
-      
+
       // Due to backtrack, chars were added in reverse order: reverse it back.
       // Append and reverse is faster than inserting at index 0.
       return String(lcs.characters.reverse())
     }
-    
+
     // Combine dynamic programming approach with backtrack to find the lcs.
     return backtrack(lcsLength(other))
   }
diff --git a/Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift b/Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift
index db388a65f..2498b6dd7 100644
--- a/Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift	
+++ b/Longest Common Subsequence/Tests/LongestCommonSubsequenceTests.swift	
@@ -2,26 +2,26 @@ import Foundation
 import XCTest
 
 class LongestCommonSubsequenceTests: XCTestCase {
-    
+
     func testLCSwithSelfIsSelf() {
         let a = "ABCDE"
 
         XCTAssertEqual(a, a.longestCommonSubsequence(a))
     }
-    
+
     func testLCSWithEmptyStringIsEmptyString() {
         let a = "ABCDE"
 
         XCTAssertEqual("", a.longestCommonSubsequence(""))
     }
-    
+
     func testLCSIsEmptyWhenNoCharMatches() {
         let a = "ABCDE"
         let b = "WXYZ"
 
         XCTAssertEqual("", a.longestCommonSubsequence(b))
     }
-    
+
     func testLCSIsNotCommutative() {
         let a = "ABCDEF"
         let b = "XAWDMVBEKD"
diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index 27e52ab09..a71a90136 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -52,20 +52,20 @@ func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   let n = a.count
   var z = [a, a]   // the two working arrays
   var d = 0        // z[d] is used for reading, z[1 - d] for writing
-  
+
   var width = 1
   while width < n {
-  
+
     var i = 0
     while i < n {
 
       var j = i
       var l = i
       var r = i + width
-      
+
       let lmax = min(l + width, n)
       let rmax = min(r + width, n)
-      
+
       while l < lmax && r < rmax {
         if isOrderedBefore(z[d][l], z[d][r]) {
           z[1 - d][j] = z[d][l]
@@ -89,7 +89,7 @@ func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
       i += width*2
     }
-    
+
     width *= 2   // in each step, the subarray to merge becomes larger
     d = 1 - d    // swap active array
   }
diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index 35bf7b5f8..968484dd1 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -1,6 +1,6 @@
 //
 //  Mergesort.swift
-//  
+//
 //
 //  Created by Kelvin Lau on 2016-02-03.
 //
@@ -63,20 +63,20 @@ func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   let n = a.count
   var z = [a, a]   // the two working arrays
   var d = 0        // z[d] is used for reading, z[1 - d] for writing
-  
+
   var width = 1
   while width < n {
-    
+
     var i = 0
     while i < n {
-      
+
       var j = i
       var l = i
       var r = i + width
-      
+
       let lmax = min(l + width, n)
       let rmax = min(r + width, n)
-      
+
       while l < lmax && r < rmax {
         if isOrderedBefore(z[d][l], z[d][r]) {
           z[1 - d][j] = z[d][l]
@@ -97,10 +97,10 @@ func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
         j += 1
         r += 1
       }
-      
+
       i += width*2
     }
-    
+
     width *= 2   // in each step, the subarray to merge becomes larger
     d = 1 - d    // swap active array
   }
diff --git a/Minimum Edit Distance/MinimumEditDistance.swift b/Minimum Edit Distance/MinimumEditDistance.swift
index 8008e03ba..a128b2dab 100644
--- a/Minimum Edit Distance/MinimumEditDistance.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.swift	
@@ -1,11 +1,11 @@
 extension String {
-    
+
     public func minimumEditDistance(other: String) -> Int {
         let m = self.characters.count
         let n = other.characters.count
         var matrix = [[Int]](count: m+1, repeatedValue: [Int](count: n+1, repeatedValue: 0))
-        
-        
+
+
         // initialize matrix
         for index in 1...m {
             // the distance of any first string to an empty second string
@@ -15,7 +15,7 @@ extension String {
             // the distance of any second string to an empty first string
             matrix[0][index]=index
         }
-        
+
         // compute Levenshtein distance
         for (i, selfChar) in self.characters.enumerate() {
             for (j, otherChar) in other.characters.enumerate() {
@@ -26,7 +26,7 @@ extension String {
                     // minimum of the cost of insertion, deletion, or substitution added to the already computed costs in the corresponding cells
                     matrix[i+1][j+1] = min(matrix[i][j]+1, matrix[i+1][j]+1, matrix[i][j+1]+1)
                 }
-                
+
             }
         }
         return matrix[m][n]
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Edge.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Edge.swift
index 3937a2cc7..9a58a1f96 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Edge.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Edge.swift	
@@ -1,4 +1,4 @@
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -6,6 +6,6 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift
index e89d4ac97..8cfb2a09c 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -1,4 +1,4 @@
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -21,14 +21,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -50,6 +50,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift
index 9d8435ffa..37a3b3fdf 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift	
@@ -1,4 +1,4 @@
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
 
   public private(set) var label: String
@@ -23,10 +23,10 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift
index 6f69ee800..ed71cab7c 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift	
@@ -1,6 +1,6 @@
 // MARK: - Edge
 
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -8,15 +8,15 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
 
 // MARK: - Node
 
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-  
+
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
@@ -39,17 +39,17 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
 
 // MARK: - Graph
 
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -72,14 +72,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -101,6 +101,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index b83e9c62a..aae146ca2 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -2,7 +2,7 @@
 
 public struct OrderedArray<T: Comparable> {
   private var array = [T]()
-  
+
   public init(array: [T]) {
     self.array = array.sort()
   }
@@ -10,23 +10,23 @@ public struct OrderedArray<T: Comparable> {
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public subscript(index: Int) -> T {
     return array[index]
   }
-  
+
   public mutating func removeAtIndex(index: Int) -> T {
     return array.removeAtIndex(index)
   }
-  
+
   public mutating func removeAll() {
     array.removeAll()
   }
-  
+
   public mutating func insert(newElement: T) -> Int {
     let i = findInsertionPoint(newElement)
     array.insert(newElement, atIndex: i)
@@ -79,4 +79,3 @@ a              // [-1, 1, 3, 4, 5, 7, 9]
 a.insert(-2)   // inserted at index 0
 a.insert(10)   // inserted at index 8
 a              // [-2, -1, 1, 3, 4, 5, 7, 9, 10]
-
diff --git a/Ordered Array/OrderedArray.swift b/Ordered Array/OrderedArray.swift
index e6e1ca79f..f92311445 100644
--- a/Ordered Array/OrderedArray.swift	
+++ b/Ordered Array/OrderedArray.swift	
@@ -4,37 +4,37 @@
 */
 public struct OrderedArray<T: Comparable> {
   private var array = [T]()
-  
+
   public init(array: [T]) {
     self.array = array.sort()
   }
-  
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public subscript(index: Int) -> T {
     return array[index]
   }
-  
+
   public mutating func removeAtIndex(index: Int) -> T {
     return array.removeAtIndex(index)
   }
-  
+
   public mutating func removeAll() {
     array.removeAll()
   }
-  
+
   public mutating func insert(newElement: T) -> Int {
     let i = findInsertionPoint(newElement)
     array.insert(newElement, atIndex: i)
     return i
   }
-  
+
   private func findInsertionPoint(newElement: T) -> Int {
     var range = 0..<array.count
     while range.startIndex < range.endIndex {
diff --git a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
index 5f5a73fa2..a8b3b0966 100644
--- a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
@@ -1,4 +1,4 @@
-/* 
+/*
   An Ordered Set is a collection where all items in the set follow an ordering,
   usually ordered from 'least' to 'most'. The way you value and compare items
   can be user-defined.
@@ -14,7 +14,7 @@ public struct OrderedSet<T: Comparable> {
   }
 
   // Inserts an item. Performance: O(n)
-  public mutating func insert(item: T){
+  public mutating func insert(item: T) {
     if exists(item) {
       return  // don't add an item if it already exists
     }
@@ -60,7 +60,7 @@ public struct OrderedSet<T: Comparable> {
       } else {
         // When we get here, we've landed on an item whose value is equal to the
         // value of the item we're looking for, but the items themselves are not
-        // equal. We need to check the items with the same value to the right 
+        // equal. We need to check the items with the same value to the right
         // and to the left in order to find an exact match.
 
         // Check to the right.
@@ -86,7 +86,7 @@ public struct OrderedSet<T: Comparable> {
     return nil
   }
 
-  // Returns the item at the given index. 
+  // Returns the item at the given index.
   // Assertion fails if the index is out of the range of [0, count).
   public subscript(index: Int) -> T {
     assert(index >= 0 && index < count)
@@ -103,7 +103,7 @@ public struct OrderedSet<T: Comparable> {
     return count == 0 ? nil : internalSet[0]
   }
 
-  // Returns the k-th largest element in the set, if k is in the range 
+  // Returns the k-th largest element in the set, if k is in the range
   // [1, count]. Returns nil otherwise.
   public func kLargest(k: Int) -> T? {
     return k > count || k <= 0 ? nil : internalSet[count - k]
diff --git a/Ordered Set/OrderedSet.playground/Sources/Player.swift b/Ordered Set/OrderedSet.playground/Sources/Player.swift
index 7b8175107..9357744db 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Player.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/Player.swift	
@@ -15,14 +15,14 @@ public struct Player: Comparable {
   }
 }
 
-// Player x is equal to Player y if and only if both players have the 
+// Player x is equal to Player y if and only if both players have the
 // same name and number of points.
-public func ==(x: Player, y: Player) -> Bool {
+public func == (x: Player, y: Player) -> Bool {
   return x.name == y.name && x.points == y.points
 }
 
 // Player x is less than Player y if x has less points than y.
-public func <(x: Player, y: Player) -> Bool {
+public func < (x: Player, y: Player) -> Bool {
   return x.points < y.points
 }
 
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index 5f5a73fa2..a8b3b0966 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -1,4 +1,4 @@
-/* 
+/*
   An Ordered Set is a collection where all items in the set follow an ordering,
   usually ordered from 'least' to 'most'. The way you value and compare items
   can be user-defined.
@@ -14,7 +14,7 @@ public struct OrderedSet<T: Comparable> {
   }
 
   // Inserts an item. Performance: O(n)
-  public mutating func insert(item: T){
+  public mutating func insert(item: T) {
     if exists(item) {
       return  // don't add an item if it already exists
     }
@@ -60,7 +60,7 @@ public struct OrderedSet<T: Comparable> {
       } else {
         // When we get here, we've landed on an item whose value is equal to the
         // value of the item we're looking for, but the items themselves are not
-        // equal. We need to check the items with the same value to the right 
+        // equal. We need to check the items with the same value to the right
         // and to the left in order to find an exact match.
 
         // Check to the right.
@@ -86,7 +86,7 @@ public struct OrderedSet<T: Comparable> {
     return nil
   }
 
-  // Returns the item at the given index. 
+  // Returns the item at the given index.
   // Assertion fails if the index is out of the range of [0, count).
   public subscript(index: Int) -> T {
     assert(index >= 0 && index < count)
@@ -103,7 +103,7 @@ public struct OrderedSet<T: Comparable> {
     return count == 0 ? nil : internalSet[0]
   }
 
-  // Returns the k-th largest element in the set, if k is in the range 
+  // Returns the k-th largest element in the set, if k is in the range
   // [1, count]. Returns nil otherwise.
   public func kLargest(k: Int) -> T? {
     return k > count || k <= 0 ? nil : internalSet[count - k]
diff --git a/Priority Queue/PriorityQueue.swift b/Priority Queue/PriorityQueue.swift
index 7a7cee34b..757a6c539 100644
--- a/Priority Queue/PriorityQueue.swift	
+++ b/Priority Queue/PriorityQueue.swift	
@@ -3,7 +3,7 @@
   the queue.
 
   The heap is a natural data structure for a priority queue, so this object
-  simply wraps the Heap struct. 
+  simply wraps the Heap struct.
 
   All operations are O(lg n).
 
diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index efc573442..5a9d04394 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -9,7 +9,7 @@
 public struct Queue<T> {
   private var array = [T?]()
   private var head = 0
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
@@ -17,11 +17,11 @@ public struct Queue<T> {
   public var count: Int {
     return array.count - head
   }
-  
+
   public mutating func enqueue(element: T) {
     array.append(element)
   }
-  
+
   public mutating func dequeue() -> T? {
     guard head < array.count, let element = array[head] else { return nil }
 
@@ -33,10 +33,10 @@ public struct Queue<T> {
       array.removeFirst(head)
       head = 0
     }
-    
+
     return element
   }
-  
+
   public func peek() -> T? {
     if isEmpty {
       return nil
diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index da556d156..0c48afd5b 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -1,7 +1,7 @@
 /*
   Queue
 
-  A queue is a list where you can only insert new items at the back and 
+  A queue is a list where you can only insert new items at the back and
   remove items from the front. This ensures that the first item you enqueue
   is also the first item you dequeue. First come, first serve!
 
diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index b88bafc12..0894ae61b 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -7,16 +7,16 @@ import Foundation
 
 func quicksort<T: Comparable>(a: [T]) -> [T] {
   guard a.count > 1 else { return a }
-  
+
   let pivot = a[a.count/2]
   let less = a.filter { $0 < pivot }
   let equal = a.filter { $0 == pivot }
   let greater = a.filter { $0 > pivot }
-  
+
   // Uncomment this following line to see in detail what the
   // pivot is in each step and how the subarrays are partitioned.
   //print(pivot, less, equal, greater)  return quicksort(less) + equal + quicksort(greater)
-    
+
   return quicksort(less) + equal + quicksort(greater)
 }
 
@@ -36,7 +36,7 @@ quicksort(list1)
 */
 func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
   let pivot = a[high]
-  
+
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
@@ -44,7 +44,7 @@ func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
       i += 1
     }
   }
-  
+
   (a[i], a[high]) = (a[high], a[i])
   return i
 }
@@ -79,11 +79,11 @@ func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
   let pivot = a[low]
   var i = low - 1
   var j = high + 1
-  
+
   while true {
     repeat { j -= 1 } while a[j] > pivot
     repeat { i += 1 } while a[i] < pivot
-    
+
     if i < j {
       swap(&a[i], &a[j])
     } else {
@@ -120,7 +120,7 @@ func quicksortRandom<T: Comparable>(inout a: [T], low: Int, high: Int) {
   if low < high {
     let pivotIndex = random(min: low, max: high)
     (a[pivotIndex], a[high]) = (a[high], a[pivotIndex])
-    
+
     let p = partitionLomuto(&a, low: low, high: high)
     quicksortRandom(&a, low: low, high: p - 1)
     quicksortRandom(&a, low: p + 1, high: high)
@@ -151,11 +151,11 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
 */
 func partitionDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
   let pivot = a[pivotIndex]
-  
+
   var smaller = low
   var equal = low
   var larger = high
-  
+
   while equal <= larger {
     if a[equal] < pivot {
       swap(&a, smaller, equal)
diff --git a/Quicksort/Quicksort.swift b/Quicksort/Quicksort.swift
index 68c54ac5c..6448dd815 100644
--- a/Quicksort/Quicksort.swift
+++ b/Quicksort/Quicksort.swift
@@ -5,12 +5,12 @@ import Foundation
 */
 func quicksort<T: Comparable>(a: [T]) -> [T] {
   guard a.count > 1 else { return a }
-  
+
   let pivot = a[a.count/2]
   let less = a.filter { $0 < pivot }
   let equal = a.filter { $0 == pivot }
   let greater = a.filter { $0 > pivot }
-  
+
   return quicksort(less) + equal + quicksort(greater)
 }
 
@@ -45,7 +45,7 @@ func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
       i += 1
     }
   }
-  
+
   // Swap the pivot element with the first element that is greater than
   // the pivot. Now the pivot sits between the <= and > regions and the
   // array is properly partitioned.
@@ -88,7 +88,7 @@ func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
   while true {
     repeat { j -= 1 } while a[j] > pivot
     repeat { i += 1 } while a[i] < pivot
-    
+
     if i < j {
       swap(&a[i], &a[j])
     } else {
diff --git a/Quicksort/Tests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
index ef95f1095..00135b31f 100644
--- a/Quicksort/Tests/QuicksortTests.swift
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -4,9 +4,9 @@ class QuicksortTests: XCTestCase {
   func testQuicksort() {
     checkSortAlgorithm(quicksort)
   }
-  
+
   private typealias QuicksortFunction = (inout [Int], low: Int, high: Int) -> Void
-  
+
   private func checkQuicksort(function: QuicksortFunction) {
     checkSortAlgorithm { (a: [Int]) -> [Int] in
       var b = a
diff --git a/Radix Sort/radixSort.swift b/Radix Sort/radixSort.swift
index 64166e88a..31a783db7 100644
--- a/Radix Sort/radixSort.swift	
+++ b/Radix Sort/radixSort.swift	
@@ -24,7 +24,7 @@ func radixSort(inout arr: [Int] ) {
     }
 
 
-    for number in arr  {
+    for number in arr {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
       if done && index > 0 {  //If we arent done, continue to finish, otherwise we are done
diff --git a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift
index 8b11e2508..3cba5254a 100644
--- a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
+++ b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
@@ -35,13 +35,12 @@ public class Root {
 	// Prints the tree for debugging/visualization purposes.
 	public func printRoot() {
 		// Print the first half of the children
-		if (children.count > 1) {
+		if children.count > 1 {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
 				print("|")
 			}
-		}
-		else if children.count > 0 {
+		} else if children.count > 0 {
 			children[0].printEdge()
 		}
 		// Then print the root
@@ -98,16 +97,14 @@ public class Edge: Root {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
 			}
-		}
-		else if children.count > 0 {
+		} else if children.count > 0 {
 			children[0].printEdge()
 		}
 		// Tab over once up to the edge's level
 		for x in 1...level() {
 			if x == level() {
 				print("|------>", terminator: "")
-			}
-			else {
+			} else {
 				print("|       ", terminator: "")
 			}
 		}
@@ -153,7 +150,7 @@ public class RadixTree {
 		// currEdge is the current Edge (or Root) in question
 		var currEdge = root
 
-		while (true) {
+		while true {
 			var found = false
 
 			// If the current Edge has no children then the remaining searchStr is
@@ -250,7 +247,7 @@ public class RadixTree {
 		}
 		var searchStr = str
 		var currEdge = root
-		while (true) {
+		while true {
 			var found = false
 			// Loop through currEdge's children
 			for c in currEdge.children {
@@ -319,7 +316,7 @@ public class RadixTree {
 
 		var searchStr = str
 		var currEdge = root
-		while (true) {
+		while true {
 			var found = false
 			// If currEdge has no children, then the searchStr is not in the tree
 			if currEdge.children.count == 0 {
@@ -376,8 +373,7 @@ public func sharedPrefix(str1: String, _ str2: String) -> String {
 			temp.append( str1[c1] )
 			c1 = c1.successor()
 			c2 = c2.successor()
-		}
-		else {
+		} else {
 			return temp
 		}
 	}
diff --git a/Radix Tree/RadixTree.swift b/Radix Tree/RadixTree.swift
index 8b11e2508..3cba5254a 100644
--- a/Radix Tree/RadixTree.swift	
+++ b/Radix Tree/RadixTree.swift	
@@ -35,13 +35,12 @@ public class Root {
 	// Prints the tree for debugging/visualization purposes.
 	public func printRoot() {
 		// Print the first half of the children
-		if (children.count > 1) {
+		if children.count > 1 {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
 				print("|")
 			}
-		}
-		else if children.count > 0 {
+		} else if children.count > 0 {
 			children[0].printEdge()
 		}
 		// Then print the root
@@ -98,16 +97,14 @@ public class Edge: Root {
 			for c in 0...children.count/2-1 {
 				children[c].printEdge()
 			}
-		}
-		else if children.count > 0 {
+		} else if children.count > 0 {
 			children[0].printEdge()
 		}
 		// Tab over once up to the edge's level
 		for x in 1...level() {
 			if x == level() {
 				print("|------>", terminator: "")
-			}
-			else {
+			} else {
 				print("|       ", terminator: "")
 			}
 		}
@@ -153,7 +150,7 @@ public class RadixTree {
 		// currEdge is the current Edge (or Root) in question
 		var currEdge = root
 
-		while (true) {
+		while true {
 			var found = false
 
 			// If the current Edge has no children then the remaining searchStr is
@@ -250,7 +247,7 @@ public class RadixTree {
 		}
 		var searchStr = str
 		var currEdge = root
-		while (true) {
+		while true {
 			var found = false
 			// Loop through currEdge's children
 			for c in currEdge.children {
@@ -319,7 +316,7 @@ public class RadixTree {
 
 		var searchStr = str
 		var currEdge = root
-		while (true) {
+		while true {
 			var found = false
 			// If currEdge has no children, then the searchStr is not in the tree
 			if currEdge.children.count == 0 {
@@ -376,8 +373,7 @@ public func sharedPrefix(str1: String, _ str2: String) -> String {
 			temp.append( str1[c1] )
 			c1 = c1.successor()
 			c2 = c2.successor()
-		}
-		else {
+		} else {
 			return temp
 		}
 	}
diff --git a/Red-Black Tree/RBTree.swift b/Red-Black Tree/RBTree.swift
index 8b2653297..fe7f34a72 100644
--- a/Red-Black Tree/RBTree.swift	
+++ b/Red-Black Tree/RBTree.swift	
@@ -1,43 +1,41 @@
-public class  RBTNode{
+public class  RBTNode {
   private(set) public var color: Bool
   private(set) public var left: RBTNode!
   private(set) public var right: RBTNode!
   private(set) public var parent: RBTNode!
   private(set) public var data: Int
-  init(){
+  init() {
     self.data = -1
     self.color = true
     self.left = nil
     self.right = nil
     self.parent = nil
   }
-  init(rootData: Int){
+  init(rootData: Int) {
     self.data = rootData
     self.color = true //0 is black 1 is red
     self.left = nil
     self.right = nil
     self.parent = nil
   }
-  deinit{
+  deinit {
     print("Node: \(self.data) is bein deinitialized")
   }
 
-  public func grandparent()->RBTNode?{
-    if(self.parent === nil || self.parent.parent === nil){
+  public func grandparent() -> RBTNode? {
+    if self.parent === nil || self.parent.parent === nil {
       return nil
-    }
-    else{
+    } else {
       return self.parent.parent
     }
   }
-  public func sibling()->RBTNode?{
-    if(self.parent === nil || self.parent.right === nil || self.parent.left === nil){
+  public func sibling() -> RBTNode? {
+    if self.parent === nil || self.parent.right === nil || self.parent.left === nil {
         return nil
       }
-      if(self === self.parent!.left!){
+      if self === self.parent!.left! {
         return self.parent!.right!
-      }
-      else{
+      } else {
         return self.parent!.left!
       }
   }
@@ -48,32 +46,31 @@ public class RBTree {
     root = RBTNode(rootData: rootData)
     root!.color = false
   }
-  init(){
+  init() {
     root = nil
   }
-  public func depth()->Int{
+  public func depth() -> Int {
     let n = depth(root!)
     return n
   }
   //return the max depth of the tree
-  private func depth(rooty:RBTNode?)->Int{
-    if(rooty == nil){
+  private func depth(rooty: RBTNode?) -> Int {
+    if rooty == nil {
       return 0
-    }
-    else{
-      return 1+(max(depth(root!.left),depth(root!.right)))
+    } else {
+      return 1+(max(depth(root!.left), depth(root!.right)))
     }
   }
 
-  public func inOrder(){
+  public func inOrder() {
     inOrder(root)
   }
   //Prints the in order traversal of the current tree
-  private func inOrder(root: RBTNode?){
-    if(self.root == nil ){
+  private func inOrder(root: RBTNode?) {
+    if self.root == nil {
       print("The tree is empty.")
     }
-    if(root == nil){
+    if root == nil {
       return
     }
     inOrder(root!.left)
@@ -91,13 +88,13 @@ public class RBTree {
   private func leftRotate(x: RBTNode) {
       let newRoot = x.right
       x.right = newRoot.left
-        if (newRoot.left !== nil) {
+        if newRoot.left !== nil {
           newRoot.left.parent = x
         }
         newRoot.parent = x.parent
-        if(x.parent === nil) {
+        if x.parent === nil {
           root = newRoot
-        } else if (x === x.parent.left) {
+        } else if x === x.parent.left {
           x.parent.left = newRoot
         } else {
           x.parent.right = newRoot
@@ -130,51 +127,50 @@ public class RBTree {
     newRoot.right = x
     x.parent = newRoot
   }
-  public func insertFixup(value: Int){
+  public func insertFixup(value: Int) {
     let inserted = find(value)
     print("Inserted Node: \(inserted!.data)")
     insertCase1(inserted)
     }
   //Case where root is the only node
-  private func insertCase1(inserted: RBTNode?){
+  private func insertCase1(inserted: RBTNode?) {
     let myroot = self.root!
-    if myroot === inserted!{
+    if myroot === inserted! {
       self.root!.color = false
     }
     insertCase2(inserted!)
     }
   //Case for inserting a node as a child of a black node
-  private func insertCase2(inserted: RBTNode?){
-    if inserted!.parent!.color == false{
+  private func insertCase2(inserted: RBTNode?) {
+    if inserted!.parent!.color == false {
         return
     }
     insertCase3(inserted!)
     }
   //Insert case for if the parent is black and parent's siblng is black
-  private func insertCase3(inserted: RBTNode?){
-    if(inserted!.parent!.sibling() != nil &&
-        inserted!.parent!.sibling()!.color == true){
+  private func insertCase3(inserted: RBTNode?) {
+    if inserted!.parent!.sibling() != nil &&
+        inserted!.parent!.sibling()!.color == true {
         inserted!.parent!.color = false
         inserted!.parent!.sibling()!.color = false
         let g = inserted!.grandparent
         g()!.color = true
-        if(g()!.parent == nil){
+        if g()!.parent == nil {
           g()!.color = false
         }
     }
   insertCase4(inserted)
   }
   //Insert case for Node N is left of parent and parent is right of grandparent
-  private func insertCase4( insert: RBTNode?){
+  private func insertCase4( insert: RBTNode?) {
     var inserted = insert
-    if((inserted! === inserted!.parent!.right) &&
-      (inserted!.grandparent()!.left === inserted!.parent!)){
+    if (inserted! === inserted!.parent!.right) &&
+      (inserted!.grandparent()!.left === inserted!.parent!) {
 
       leftRotate(inserted!.parent)
       inserted! = inserted!.left
-    }
-    else if((inserted! === inserted!.parent!.left) &&
-            (inserted!.grandparent()!.right === inserted!.parent!)){
+    } else if (inserted! === inserted!.parent!.left) &&
+            (inserted!.grandparent()!.right === inserted!.parent!) {
 
       rightRotate(inserted!.parent)
       inserted! = inserted!.right
@@ -182,19 +178,18 @@ public class RBTree {
     insertCase5(inserted)
   }
   //Insert case for Node n where parent is red and parent's sibling is black
-  private func insertCase5(inserted: RBTNode?){
-    if((inserted!.parent!.color == true &&
+  private func insertCase5(inserted: RBTNode?) {
+    if inserted!.parent!.color == true &&
        (inserted!.parent!.sibling()?.color == false ||
-        inserted!.parent!.sibling() == nil ))){
+        inserted!.parent!.sibling() == nil) {
 
-        if(inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent!){
+        if inserted! === inserted!.parent!.left && inserted!.grandparent()!.left === inserted!.parent! {
           inserted!.parent.color = false
           inserted!.grandparent()?.color = true
-          if(inserted! === inserted!.parent!.left){
+          if inserted! === inserted!.parent!.left {
             rightRotate(inserted!.grandparent()!)
           }
-        }
-        else if(inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent!){
+        } else if inserted! === inserted!.parent!.right && inserted!.grandparent()!.right === inserted!.parent! {
           inserted!.parent.color = false
           inserted!.grandparent()?.color = true
           leftRotate(inserted!.grandparent()!)
@@ -208,11 +203,10 @@ public class RBTree {
   }
   //Basic BST insert implementation
   private func insert(value: Int, parent: RBTNode) {
-      if self.root == nil{
+      if self.root == nil {
         self.root = RBTNode(rootData: value)
         return
-      }
-      else if value < parent.data {
+      } else if value < parent.data {
         if let left = parent.left {
           insert(value, parent: left)
         } else {
@@ -228,37 +222,34 @@ public class RBTree {
         }
       }
     }
-    public func find(data: Int)->RBTNode?{
-      return find(root!,data: data)
+    public func find(data: Int) -> RBTNode? {
+      return find(root!, data: data)
     }
     //Returns the reference to the RBTNode whos data was requested
-    private func find(root: RBTNode, data: Int)->RBTNode?{
-        if data == root.data{
+    private func find(root: RBTNode, data: Int) -> RBTNode? {
+        if data == root.data {
           return root
         }
         if root.data != data && root.right == nil && root.left == nil {
           return nil
-        }
-        else if data > root.data{
+        } else if data > root.data {
           return find(root.right, data: data)
-        }
-        else if data < root.data{
+        } else if data < root.data {
           return find(root.left, data: data)
-        }
-        else{
+        } else {
           return nil
         }
     }
 
     //DELETION HELPER FUNCTIONS
-    public func remove(value: Int){
+    public func remove(value: Int) {
         let toRemove = find(value)
-        if(toRemove == nil){
+        if toRemove == nil {
           return
         }
     }
     //Transplant the positions of two nodes in the RBTree
-    public func replaceNode(n1: RBTNode, n2: RBTNode){
+    public func replaceNode(n1: RBTNode, n2: RBTNode) {
       let temp = n1.data
       let temp_color = n1.color
       n1.data = n2.data
@@ -267,41 +258,41 @@ public class RBTree {
       n2.color = temp_color
     }
     //returns the node with the minimum value in the subtree
-    public func minimum(Node: RBTNode)->RBTNode {
-      var node = Node
-      while node.left !== nil{
-        node = node.left
+    public func minimum(node: RBTNode) -> RBTNode {
+      var minimumNode = node
+      while minimumNode.left !== nil {
+        minimumNode = minimumNode.left
       }
-      return node
+      return minimumNode
     }
     //Returns the next largest node in the tree
-    public func successor(Node: RBTNode) -> RBTNode? {
-      var node = Node
-      if node.right !== nil {
-        return minimum(node.right)
+    public func successor(node: RBTNode) -> RBTNode? {
+      var nextLargestNode = node
+      if nextLargestNode.right !== nil {
+        return minimum(nextLargestNode.right)
       }
-      var successor = node.parent
-      while successor !== nil && node === successor.right {
-        node = successor
+      var successor = nextLargestNode.parent
+      while successor !== nil && nextLargestNode === successor.right {
+        nextLargestNode = successor
         successor = successor.parent
       }
       return successor
     }
     //Returns the next smallest node in the tree
-    public func predecessor(Node: RBTNode) -> RBTNode{
-      var node = Node
-      if node.left !== nil {
-        return minimum(node.left)
+    public func predecessor(node: RBTNode) -> RBTNode {
+      var nextSmallestNode = node
+      if nextSmallestNode.left !== nil {
+        return minimum(nextSmallestNode.left)
       }
-      var successor = node.parent
-      while successor !== nil && node === successor.left {
-        node = successor
+      var successor = nextSmallestNode.parent
+      while successor !== nil && nextSmallestNode === successor.left {
+        nextSmallestNode = successor
         successor = successor.parent
       }
       return successor
     }
     //Returns the node with the largest value in the subtree
-    public func maximum(rootnode: RBTNode) -> RBTNode{
+    public func maximum(rootnode: RBTNode) -> RBTNode {
       var rootNode = rootnode
       while rootNode.right !== nil {
         rootNode = rootNode.right
@@ -309,141 +300,132 @@ public class RBTree {
       return rootNode
     }
   //call to remove a node from the tree
-  public func delete(x: Int){
+  public func delete(x: Int) {
     let toDel = find(x)
     deleteNode(toDel!)
   }
   //Function call for removing a node
-  private func deleteNode(todel: RBTNode?){
+  private func deleteNode(todel: RBTNode?) {
     var toDel = todel
     //case for if todel is the only node in the tree
-    if(toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil){
+    if toDel!.left === nil && toDel!.right === nil && toDel!.parent === nil {
       toDel = nil
       self.root = nil
       return
     }
     //case for if toDell is a red node w/ no children
-    if(toDel!.left === nil && toDel!.right === nil && toDel!.color == true){
-      if(toDel!.parent.left === toDel!){
+    if toDel!.left === nil && toDel!.right === nil && toDel!.color == true {
+      if toDel!.parent.left === toDel! {
         toDel!.parent.left = nil
         toDel = nil
-      }
-      else if(toDel!.parent === nil){
+      } else if toDel!.parent === nil {
         toDel = nil
-      }
-      else{
+      } else {
         toDel?.parent.right = nil
         toDel = nil
       }
       return
     }
     //case for toDel having two children
-    if(toDel!.left !== nil && toDel!.right !== nil){
+    if toDel!.left !== nil && toDel!.right !== nil {
       let pred = maximum(toDel!.left!)
       toDel!.data = pred.data
       toDel! = pred
     }
     //case for toDel having one child
     var child: RBTNode? = nil
-    if(toDel!.right === nil){
+    if toDel!.right === nil {
       child = toDel!.left
-    }
-    else{
+    } else {
        child = toDel!.right
     }
-    if(toDel!.color == false && child !== nil){
+    if toDel!.color == false && child !== nil {
       toDel!.color = child!.color
       deleteCase1(toDel!)
     }
 
-    if(child !== nil){
+    if child !== nil {
       replaceNode(toDel!, n2: child!)
-      if(toDel!.parent === nil && child !== nil){
+      if toDel!.parent === nil && child !== nil {
         child!.color = false
       }
     }
-    if(toDel!.parent.left === toDel!){
+    if toDel!.parent.left === toDel! {
       toDel!.parent.left = nil
       toDel = nil
       return
-    }
-    else if(toDel!.parent === nil){
+    } else if toDel!.parent === nil {
       toDel = nil
       return
-    }
-    else{
+    } else {
       toDel?.parent.right = nil
       toDel = nil
       return
     }
   }
   //delete case for if parent is nil after deletion
-  private func deleteCase1( toDel: RBTNode?){
-      if(toDel?.parent === nil){
+  private func deleteCase1( toDel: RBTNode?) {
+      if toDel?.parent === nil {
         return
-      }
-      else{
+      } else {
         deleteCase2(toDel)
       }
   }
   //case to fix tree after deletion and sibling is red
-  private func deleteCase2(toDel: RBTNode?){
+  private func deleteCase2(toDel: RBTNode?) {
     let sibling = toDel!.sibling()
-    if(sibling?.color == true){
-       toDel!.parent.color = true;
+    if sibling?.color == true {
+       toDel!.parent.color = true
        sibling?.color = false
-       if(toDel! === toDel!.parent.left){
+       if toDel! === toDel!.parent.left {
          leftRotate(toDel!.parent)
-       }
-       else{
+       } else {
          rightRotate(toDel!.parent)
        }
        deleteCase3(toDel!)
     }
   }
   //delete case for fixing tree when parnet is black and sibling is black and sibling.children are also black
-  private func deleteCase3(toDel: RBTNode?){
-    if(toDel!.parent?.color == false &&
+  private func deleteCase3(toDel: RBTNode?) {
+    if toDel!.parent?.color == false &&
        toDel!.sibling()?.color == false &&
        toDel!.sibling()?.left!.color == false &&
-       toDel!.sibling()?.right!.color == false){
+       toDel!.sibling()?.right!.color == false {
 
         toDel!.sibling()?.color = true
         toDel!.parent?.color = false
-    }
-    else{
+    } else {
       deleteCase4(toDel)
     }
   }
-  private func deleteCase4(toDel: RBTNode?){
-    if(toDel!.parent?.color == true &&
+  private func deleteCase4(toDel: RBTNode?) {
+    if toDel!.parent?.color == true &&
        toDel!.sibling()?.color == false &&
        toDel!.sibling()?.left!.color == false &&
-       toDel!.sibling()?.right!.color == false){
+       toDel!.sibling()?.right!.color == false {
 
        toDel!.sibling()?.color = true
        toDel!.parent.color = false
-    }
-    else{
+    } else {
       deleteCase5(toDel)
     }
   }
   //delete case for fixing tree if toDel is a left child and sibling(n) is black and children of sibling(n) are black and white respectibely
-  private func deleteCase5(toDel:RBTNode?){
-    if(toDel! === toDel!.parent?.left &&
+  private func deleteCase5(toDel: RBTNode?) {
+    if toDel! === toDel!.parent?.left &&
        toDel!.sibling()?.color == false &&
        toDel!.sibling()?.left.color == true &&
-       toDel!.sibling()?.right.color == false){
+       toDel!.sibling()?.right.color == false {
 
        toDel!.sibling()?.color = true
        toDel!.sibling()?.left?.color = false
        rightRotate(toDel!.sibling()!)
     }
     //opposite case
-    else if(toDel! === toDel!.parent?.right &&
+    else if toDel! === toDel!.parent?.right &&
             toDel!.sibling()?.color == false &&
             toDel!.sibling()?.left.color == false &&
-            toDel!.sibling()?.right.color == true){
+            toDel!.sibling()?.right.color == true {
 
             toDel!.sibling()?.color = true
             toDel!.sibling()?.right?.color = false
@@ -451,15 +433,14 @@ public class RBTree {
     }
   }
   //final rotations to be done after deleting a black node from the tree
-  private func deleteCase6(toDel: RBTNode?){
+  private func deleteCase6(toDel: RBTNode?) {
     let color = toDel!.sibling()?.color
     toDel!.parent?.color = color!
     toDel!.parent?.color = false
-    if(toDel! === toDel!.parent.left){
+    if toDel! === toDel!.parent.left {
         toDel!.sibling()?.right?.color = false
         leftRotate(toDel!.parent!)
-    }
-    else{
+    } else {
       toDel!.sibling()?.left?.color = false
       rightRotate(toDel!.parent!)
     }
diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index 5e6c4d6eb..a7522c366 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -4,11 +4,11 @@ public struct RingBuffer<T> {
   private var array: [T?]
   private var readIndex = 0
   private var writeIndex = 0
-  
+
   public init(count: Int) {
     array = [T?](count: count, repeatedValue: nil)
   }
-  
+
   public mutating func write(element: T) -> Bool {
     if !isFull {
       array[writeIndex % array.count] = element
@@ -18,7 +18,7 @@ public struct RingBuffer<T> {
       return false
     }
   }
-  
+
   public mutating func read() -> T? {
     if !isEmpty {
       let element = array[readIndex % array.count]
@@ -32,7 +32,7 @@ public struct RingBuffer<T> {
   private var availableSpaceForReading: Int {
     return writeIndex - readIndex
   }
-  
+
   public var isEmpty: Bool {
     return availableSpaceForReading == 0
   }
diff --git a/Ring Buffer/RingBuffer.swift b/Ring Buffer/RingBuffer.swift
index 3176ab1fc..7e845aa74 100644
--- a/Ring Buffer/RingBuffer.swift	
+++ b/Ring Buffer/RingBuffer.swift	
@@ -14,11 +14,11 @@ public struct RingBuffer<T> {
   private var array: [T?]
   private var readIndex = 0
   private var writeIndex = 0
-  
+
   public init(count: Int) {
     array = [T?](count: count, repeatedValue: nil)
   }
-  
+
   /* Returns false if out of space. */
   public mutating func write(element: T) -> Bool {
     if !isFull {
@@ -29,7 +29,7 @@ public struct RingBuffer<T> {
       return false
     }
   }
-  
+
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
     if !isEmpty {
@@ -40,20 +40,20 @@ public struct RingBuffer<T> {
       return nil
     }
   }
-  
+
   private var availableSpaceForReading: Int {
     return writeIndex - readIndex
   }
-  
+
   public var isEmpty: Bool {
     return availableSpaceForReading == 0
   }
-  
+
   private var availableSpaceForWriting: Int {
     return array.count - availableSpaceForReading
   }
-  
+
   public var isFull: Bool {
     return availableSpaceForWriting == 0
   }
-}
\ No newline at end of file
+}
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index b79cdf9e6..41dcae3b1 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -11,12 +11,12 @@ extension NSData {
     if length > 0 {
       var ptr = UnsafePointer<UInt8>(bytes)
       let end = ptr + length
-      
+
       while ptr < end {
         var count = 0
         var byte = ptr.memory
         var next = byte
-        
+
         // Is the next byte the same? Keep reading until we find a different
         // value, or we reach the end of the data, or the run is 64 bytes.
         while next == byte && ptr < end && count < 64 {
@@ -36,7 +36,7 @@ extension NSData {
     }
     return data
   }
-  
+
   /*
     Converts a run-length encoded NSData back to the original.
   */
@@ -47,11 +47,11 @@ extension NSData {
       let end = ptr + length
 
       while ptr < end {
-        // Read the next byte. This is either a single value less than 192, 
+        // Read the next byte. This is either a single value less than 192,
         // or the start of a byte run.
         var byte = ptr.memory
         ptr = ptr.advancedBy(1)
-        
+
         if byte < 192 {                       // single value
           data.appendBytes(&byte, length: 1)
 
diff --git a/Run-Length Encoding/RLE.swift b/Run-Length Encoding/RLE.swift
index f26299cf1..b62c59c63 100644
--- a/Run-Length Encoding/RLE.swift	
+++ b/Run-Length Encoding/RLE.swift	
@@ -9,12 +9,12 @@ extension NSData {
     if length > 0 {
       var ptr = UnsafePointer<UInt8>(bytes)
       let end = ptr + length
-      
+
       while ptr < end {
         var count = 0
         var byte = ptr.memory
         var next = byte
-        
+
         // Is the next byte the same? Keep reading until we find a different
         // value, or we reach the end of the data, or the run is 64 bytes.
         while next == byte && ptr < end && count < 64 {
@@ -34,7 +34,7 @@ extension NSData {
     }
     return data
   }
-  
+
   /*
     Converts a run-length encoded NSData back to the original.
   */
@@ -45,11 +45,11 @@ extension NSData {
       let end = ptr + length
 
       while ptr < end {
-        // Read the next byte. This is either a single value less than 192, 
+        // Read the next byte. This is either a single value less than 192,
         // or the start of a byte run.
         var byte = ptr.memory
         ptr = ptr.advancedBy(1)
-        
+
         if byte < 192 {                       // single value
           data.appendBytes(&byte, length: 1)
 
diff --git a/Run-Length Encoding/Tests/RLETests.swift b/Run-Length Encoding/Tests/RLETests.swift
index a55f74fdc..f4b2f8d7d 100644
--- a/Run-Length Encoding/Tests/RLETests.swift	
+++ b/Run-Length Encoding/Tests/RLETests.swift	
@@ -36,17 +36,17 @@ class RLETests: XCTestCase {
     let bytes: [UInt8] = []
     encodeAndDecode(bytes)
   }
-  
+
   func testOneByteWithLowValue() {
     let bytes: [UInt8] = [ 0x80 ]
     encodeAndDecode(bytes)
   }
-  
+
   func testOneByteWithHighValue() {
     let bytes: [UInt8] = [ 0xD0 ]
     encodeAndDecode(bytes)
   }
-  
+
   func testSimpleCases() {
     let bytes: [UInt8] = [
       0x00,
@@ -96,7 +96,7 @@ class RLETests: XCTestCase {
     bufferWithSpans(66)
     bufferWithSpans(80)
   }
-  
+
   func testRandomBytes() {
     for _ in 0..<10 {
       let length = 1 + Int(arc4random_uniform(2048))
diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index e74591e56..14b7f57cf 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -1,14 +1,14 @@
 //: Playground - noun: a place where people can play
 
 public class SegmentTree<T> {
-  
+
   private var value: T
   private var function: (T, T) -> T
   private var leftBound: Int
   private var rightBound: Int
   private var leftChild: SegmentTree<T>?
   private var rightChild: SegmentTree<T>?
-  
+
   public init(array: [T], leftBound: Int, rightBound: Int, function: (T, T) -> T) {
     self.leftBound = leftBound
     self.rightBound = rightBound
@@ -23,19 +23,19 @@ public class SegmentTree<T> {
       value = function(leftChild!.value, rightChild!.value)
     }
   }
-  
+
   public convenience init(array: [T], function: (T, T) -> T) {
     self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
   }
-  
+
   public func queryWithLeftBound(leftBound: Int, rightBound: Int) -> T {
     if self.leftBound == leftBound && self.rightBound == rightBound {
       return self.value
     }
-    
+
     guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-    
+
     if leftChild.rightBound < leftBound {
       return rightChild.queryWithLeftBound(leftBound, rightBound: rightBound)
     } else if rightChild.leftBound > rightBound {
@@ -83,7 +83,7 @@ func gcd(m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
   var r = min(m, n)
-  
+
   while r != 0 {
     a = b
     b = r
@@ -137,4 +137,3 @@ stringSegmentTree.replaceItemAtIndex(4, withItem: " swift")
 stringSegmentTree.replaceItemAtIndex(5, withItem: "!")
 
 print(stringSegmentTree.queryWithLeftBound(0, rightBound: 5))
-
diff --git a/Segment Tree/SegmentTree.swift b/Segment Tree/SegmentTree.swift
index e616255ec..608d5151a 100644
--- a/Segment Tree/SegmentTree.swift	
+++ b/Segment Tree/SegmentTree.swift	
@@ -1,6 +1,6 @@
 /*
   Segment tree
-  
+
   Performance:
     building the tree is O(n)
     query is O(log n)
@@ -8,14 +8,14 @@
 */
 
 public class SegmentTree<T> {
-  
+
   private var value: T
   private var function: (T, T) -> T
   private var leftBound: Int
   private var rightBound: Int
   private var leftChild: SegmentTree<T>?
   private var rightChild: SegmentTree<T>?
-  
+
   public init(array: [T], leftBound: Int, rightBound: Int, function: (T, T) -> T) {
     self.leftBound = leftBound
     self.rightBound = rightBound
@@ -30,19 +30,19 @@ public class SegmentTree<T> {
       value = function(leftChild!.value, rightChild!.value)
     }
   }
-  
+
   public convenience init(array: [T], function: (T, T) -> T) {
     self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
   }
-  
+
   public func queryWithLeftBound(leftBound: Int, rightBound: Int) -> T {
     if self.leftBound == leftBound && self.rightBound == rightBound {
       return self.value
     }
-    
+
     guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-    
+
     if leftChild.rightBound < leftBound {
       return rightChild.queryWithLeftBound(leftBound, rightBound: rightBound)
     } else if rightChild.leftBound > rightBound {
diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index eb0204b0e..8c78ba478 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -6,7 +6,7 @@ func maximum<T: Comparable>(var array: [T]) -> T? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var maximum = array.removeFirst()
   for element in array {
     maximum = element > maximum ? element : maximum
diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index 450b6624e..ef92ac1e6 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -25,8 +25,7 @@ func maximum<T: Comparable>(var array: [T]) -> T? {
 }
 
 // Compare in pairs to find minimum and maximum
-func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)?
-{
+func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)? {
   guard !array.isEmpty else {
     return nil
   }
diff --git a/Select Minimum Maximum/Tests/MaximumTests.swift b/Select Minimum Maximum/Tests/MaximumTests.swift
index 38bcf483b..cd63ac0a3 100644
--- a/Select Minimum Maximum/Tests/MaximumTests.swift	
+++ b/Select Minimum Maximum/Tests/MaximumTests.swift	
@@ -30,7 +30,7 @@ class MaximumTests: XCTestCase {
     let array = [ 9, 8, 6, 4, 3 ]
 
     let result = maximum(array)
-    
+
     XCTAssertEqual(result, 9)
   }
 
diff --git a/Select Minimum Maximum/Tests/TestHelper.swift b/Select Minimum Maximum/Tests/TestHelper.swift
index 7afe751d0..cd782d305 100644
--- a/Select Minimum Maximum/Tests/TestHelper.swift	
+++ b/Select Minimum Maximum/Tests/TestHelper.swift	
@@ -1,5 +1,5 @@
 import Foundation
 
 func createRandomList(numberOfElements: Int) -> [UInt32] {
-  return (1...numberOfElements).map{_ in arc4random()}
+  return (1...numberOfElements).map {_ in arc4random()}
 }
diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index 4afbe4f03..f6032137b 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -25,13 +25,13 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var examined = 0
   var selected = 0
   var b = [T]()
-  
+
   while selected < requested {
     examined += 1
-    
+
     // Calculate random variable 0.0 <= r < 1.0 (exclusive!).
     let r = Double(arc4random()) / 0x100000000
-    
+
     let leftToExamine = a.count - examined + 1
     let leftToAdd = requested - selected
 
diff --git a/Selection Sampling/SelectionSampling.swift b/Selection Sampling/SelectionSampling.swift
index d562481c6..1e6257908 100644
--- a/Selection Sampling/SelectionSampling.swift	
+++ b/Selection Sampling/SelectionSampling.swift	
@@ -30,7 +30,7 @@ func reservoirSample<T>(from a: [T], count k: Int) -> [T] {
   precondition(a.count >= k)
 
   var result = [T]()
-  
+
   // Fill the result array with first k elements.
   for i in 0..<k {
     result.append(a[i])
@@ -59,13 +59,13 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var examined = 0
   var selected = 0
   var b = [T]()
-  
+
   while selected < requested {
     examined += 1
-    
+
     // Calculate random variable 0.0 <= r < 1.0 (exclusive!).
     let r = Double(arc4random()) / 0x100000000
-    
+
     let leftToExamine = a.count - examined + 1
     let leftToAdd = requested - selected
 
diff --git a/Selection Sort/SelectionSort.swift b/Selection Sort/SelectionSort.swift
index 4c50688e5..9d7b45ad8 100644
--- a/Selection Sort/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.swift	
@@ -3,7 +3,7 @@ func selectionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
   var a = array
   for x in 0 ..< a.count - 1 {
-    
+
     // Find the lowest value in the rest of the array.
     var lowest = x
     for y in x + 1 ..< a.count {
@@ -11,7 +11,7 @@ func selectionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
         lowest = y
       }
     }
-    
+
     // Swap the lowest value with the current array index.
     if x != lowest {
       swap(&a[x], &a[lowest])
diff --git a/Shell Sort/shellsort.swift b/Shell Sort/shellsort.swift
index 5b2c73763..489a92ebc 100644
--- a/Shell Sort/shellsort.swift	
+++ b/Shell Sort/shellsort.swift	
@@ -21,7 +21,7 @@
 // SOFTWARE.
 
 public func insertionSort(inout list: [Int], start: Int, gap: Int) {
-  for i in (start + gap).stride(to: list.count, by: gap){
+  for i in (start + gap).stride(to: list.count, by: gap) {
     let currentValue = list[i]
     var pos = i
     while pos >= gap && list[pos - gap] > currentValue {
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Edge.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Edge.swift
index 3937a2cc7..9a58a1f96 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Edge.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Edge.swift	
@@ -1,4 +1,4 @@
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -6,6 +6,6 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift
index e89d4ac97..8cfb2a09c 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift	
@@ -1,4 +1,4 @@
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -21,14 +21,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -50,6 +50,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift
index 9d8435ffa..37a3b3fdf 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift	
@@ -1,4 +1,4 @@
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
 
   public private(set) var label: String
@@ -23,10 +23,10 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index 6f69ee800..ed71cab7c 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -1,6 +1,6 @@
 // MARK: - Edge
 
-public class Edge : Equatable {
+public class Edge: Equatable {
   public var neighbor: Node
 
   public init(neighbor: Node) {
@@ -8,15 +8,15 @@ public class Edge : Equatable {
   }
 }
 
-public func ==(lhs: Edge, rhs: Edge) -> Bool {
+public func == (lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
 
 // MARK: - Node
 
-public class Node : CustomStringConvertible, Equatable {
+public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-  
+
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
@@ -39,17 +39,17 @@ public class Node : CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
+    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
   }
 }
 
-public func ==(lhs: Node, rhs: Node) -> Bool {
+public func == (lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
 
 // MARK: - Graph
 
-public class Graph : CustomStringConvertible, Equatable {
+public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
 
   public init() {
@@ -72,14 +72,14 @@ public class Graph : CustomStringConvertible, Equatable {
 
     for node in nodes {
       if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
+        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
       }
     }
     return description
   }
 
   public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter{ $0.label == label }.first!
+    return nodes.filter { $0.label == label }.first!
   }
 
   public func duplicate() -> Graph {
@@ -101,6 +101,6 @@ public class Graph : CustomStringConvertible, Equatable {
   }
 }
 
-public func ==(lhs: Graph, rhs: Graph) -> Bool {
+public func == (lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift
index 17c9264a1..003f3cf20 100644
--- a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
+++ b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
@@ -86,4 +86,4 @@ class ShortestPathTests: XCTestCase {
     XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeH.label).distance, 1)
     XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeI.label).distance, 2)
   }
-}
\ No newline at end of file
+}
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index 52b952d1f..04fed7739 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -12,7 +12,7 @@ public enum OperatorType: CustomStringConvertible {
   case Multiply
   case Percent
   case Exponent
-  
+
   public var description: String {
     switch self {
       case Add:
@@ -36,7 +36,7 @@ public enum TokenType: CustomStringConvertible {
   case CloseBracket
   case Operator(OperatorToken)
   case Operand(Double)
-  
+
   public var description: String {
     switch self {
       case OpenBracket:
@@ -53,11 +53,11 @@ public enum TokenType: CustomStringConvertible {
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-  
+
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-  
+
   var precedence: Int {
     switch operatorType {
       case .Add, .Subtract:
@@ -68,44 +68,44 @@ public struct OperatorToken: CustomStringConvertible {
         return 10
     }
   }
-  
+
   var associativity: OperatorAssociativity {
     switch operatorType {
       case .Add, .Subtract, .Divide, .Multiply, .Percent:
-        return .LeftAssociative;
+        return .LeftAssociative
       case .Exponent:
         return .RightAssociative
     }
   }
-  
+
   public var description: String {
     return operatorType.description
   }
 }
 
-func <=(left: OperatorToken, right: OperatorToken) -> Bool {
+func <= (left: OperatorToken, right: OperatorToken) -> Bool {
   return left.precedence <= right.precedence
 }
 
-func <(left: OperatorToken, right: OperatorToken) -> Bool {
+func < (left: OperatorToken, right: OperatorToken) -> Bool {
   return left.precedence < right.precedence
 }
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-  
+
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-  
+
   init(operand: Double) {
     tokenType = .Operand(operand)
   }
-  
+
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-  
+
   var isOpenBracket: Bool {
     switch tokenType {
       case .OpenBracket:
@@ -114,7 +114,7 @@ public struct Token: CustomStringConvertible {
         return false
     }
   }
-  
+
   var isOperator: Bool {
     switch tokenType {
       case .Operator(_):
@@ -123,7 +123,7 @@ public struct Token: CustomStringConvertible {
         return false
     }
   }
-  
+
   var operatorToken: OperatorToken? {
     switch tokenType {
       case .Operator(let operatorToken):
@@ -132,7 +132,7 @@ public struct Token: CustomStringConvertible {
         return nil
     }
   }
-  
+
   public var description: String {
     return tokenType.description
   }
@@ -140,27 +140,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-  
+
   public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-  
+
   public func addOperand(operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-  
+
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .OpenBracket))
     return self
   }
-  
+
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .CloseBracket))
     return self
   }
-  
+
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -172,7 +172,7 @@ public func reversePolishNotation(expression: [Token]) -> String {
 
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-  
+
   for token in expression {
     switch token.tokenType {
       case .Operand(_):
@@ -191,7 +191,7 @@ public func reversePolishNotation(expression: [Token]) -> String {
           if !tempToken.isOperator {
             break
           }
-          
+
           if let tempOperatorToken = tempToken.operatorToken {
             if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
                 || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
@@ -204,19 +204,34 @@ public func reversePolishNotation(expression: [Token]) -> String {
         tokenStack.push(token)
     }
   }
-  
+
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-  
+
   return reversePolishNotation.map({token in token.description}).joinWithSeparator(" ")
 }
 
 
 // Simple demo
 
-let expr = InfixExpressionBuilder().addOperand(3).addOperator(.Add).addOperand(4).addOperator(.Multiply).addOperand(2).addOperator(.Divide).addOpenBracket().addOperand(1).addOperator(.Subtract).addOperand(5).addCloseBracket().addOperator(.Exponent).addOperand(2).addOperator(.Exponent).addOperand(3).build()
+let expr = InfixExpressionBuilder()
+  .addOperand(3)
+  .addOperator(.Add)
+  .addOperand(4)
+  .addOperator(.Multiply)
+  .addOperand(2)
+  .addOperator(.Divide)
+  .addOpenBracket()
+  .addOperand(1)
+  .addOperator(.Subtract)
+  .addOperand(5)
+  .addCloseBracket()
+  .addOperator(.Exponent)
+  .addOperand(2)
+  .addOperator(.Exponent)
+  .addOperand(3)
+  .build()
 
 print(expr.description)
 print(reversePolishNotation(expr))
-
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index 93feb2ca1..0df342af5 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -2,23 +2,23 @@ import Foundation
 
 public struct Stack<T> {
     private var array = [T]()
-    
+
     public init() {
         array = []
     }
-    
+
     public var isEmpty: Bool {
         return array.isEmpty
     }
-    
+
     public var count: Int {
         return array.count
     }
-    
+
     public mutating func push(element: T) {
         array.append(element)
     }
-    
+
     public mutating func pop() -> T? {
         if isEmpty {
             return nil
@@ -26,7 +26,7 @@ public struct Stack<T> {
             return array.removeLast()
         }
     }
-    
+
     public func peek() -> T? {
         return array.last
     }
@@ -40,4 +40,4 @@ extension Stack: SequenceType {
             return curr.pop()
         }
     }
-}
\ No newline at end of file
+}
diff --git a/Shunting Yard/ShuntingYard.playground/timeline.xctimeline b/Shunting Yard/ShuntingYard.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Shunting Yard/ShuntingYard.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Shunting Yard/ShuntingYard.swift b/Shunting Yard/ShuntingYard.swift
index 1da67990d..5159c9172 100644
--- a/Shunting Yard/ShuntingYard.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -18,7 +18,7 @@ public enum OperatorType: CustomStringConvertible {
   case Multiply
   case Percent
   case Exponent
-  
+
   public var description: String {
     switch self {
       case Add:
@@ -42,7 +42,7 @@ public enum TokenType: CustomStringConvertible {
   case CloseBracket
   case Operator(OperatorToken)
   case Operand(Double)
-  
+
   public var description: String {
     switch self {
       case OpenBracket:
@@ -59,11 +59,11 @@ public enum TokenType: CustomStringConvertible {
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-  
+
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-  
+
   var precedence: Int {
     switch operatorType {
       case .Add, .Subtract:
@@ -74,44 +74,44 @@ public struct OperatorToken: CustomStringConvertible {
         return 10
     }
   }
-  
+
   var associativity: OperatorAssociativity {
     switch operatorType {
       case .Add, .Subtract, .Divide, .Multiply, .Percent:
-        return .LeftAssociative;
+        return .LeftAssociative
       case .Exponent:
         return .RightAssociative
     }
   }
-  
+
   public var description: String {
     return operatorType.description
   }
 }
 
-func <=(left: OperatorToken, right: OperatorToken) -> Bool {
+func <= (left: OperatorToken, right: OperatorToken) -> Bool {
   return left.precedence <= right.precedence
 }
 
-func <(left: OperatorToken, right: OperatorToken) -> Bool {
+func < (left: OperatorToken, right: OperatorToken) -> Bool {
   return left.precedence < right.precedence
 }
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-  
+
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-  
+
   init(operand: Double) {
     tokenType = .Operand(operand)
   }
-  
+
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-  
+
   var isOpenBracket: Bool {
     switch tokenType {
       case .OpenBracket:
@@ -120,7 +120,7 @@ public struct Token: CustomStringConvertible {
         return false
     }
   }
-  
+
   var isOperator: Bool {
     switch tokenType {
       case .Operator(_):
@@ -129,7 +129,7 @@ public struct Token: CustomStringConvertible {
         return false
     }
   }
-  
+
   var operatorToken: OperatorToken? {
     switch tokenType {
       case .Operator(let operatorToken):
@@ -138,7 +138,7 @@ public struct Token: CustomStringConvertible {
         return nil
     }
   }
-  
+
   public var description: String {
     return tokenType.description
   }
@@ -146,27 +146,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-  
+
   public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-  
+
   public func addOperand(operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-  
+
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .OpenBracket))
     return self
   }
-  
+
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .CloseBracket))
     return self
   }
-  
+
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -178,7 +178,7 @@ public func reversePolishNotation(expression: [Token]) -> String {
 
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-  
+
   for token in expression {
     switch token.tokenType {
       case .Operand(_):
@@ -197,7 +197,7 @@ public func reversePolishNotation(expression: [Token]) -> String {
           if !tempToken.isOperator {
             break
           }
-          
+
           if let tempOperatorToken = tempToken.operatorToken {
             if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
                 || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
@@ -210,10 +210,10 @@ public func reversePolishNotation(expression: [Token]) -> String {
         tokenStack.push(token)
     }
   }
-  
+
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-  
+
   return reversePolishNotation.map({token in token.description}).joinWithSeparator(" ")
 }
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift
index 4c58e4d90..e2114c963 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
@@ -13,18 +13,22 @@ public struct BellmanFord<T where T: Hashable> {
 }
 
 /**
- Encapsulation of the Bellman-Ford Single-Source Shortest Paths algorithm, which operates on a general directed graph that may contain negative edge weights.
- 
+ Encapsulation of the Bellman-Ford Single-Source Shortest Paths algorithm,
+ which operates on a general directed graph that may contain negative edge weights.
+
  - note: In all complexity bounds, `V` is the number of vertices in the graph, and `E` is the number of edges.
  */
 extension BellmanFord: SSSPAlgorithm {
 
   /**
-   Compute the shortest path from `source` to each other vertex in `graph`, if such paths exist. Also report negative weight cycles reachable from `source`, which are cycles whose sum of edge weights is negative.
+   Compute the shortest path from `source` to each other vertex in `graph`,
+   if such paths exist. Also report negative weight cycles reachable from `source`,
+   which are cycles whose sum of edge weights is negative.
 
    - precondition: `graph` must have no negative weight cycles
    - complexity: `O(VE)` time, `Θ(V)` space
-   - returns a `BellmanFordResult` struct which can be queried for shortest paths and their total weights, or `nil` if a negative weight cycle exists
+   - returns a `BellmanFordResult` struct which can be queried for
+   shortest paths and their total weights, or `nil` if a negative weight cycle exists
  */
   public static func apply(graph: AbstractGraph<T>, source: Vertex<Q>) -> BellmanFordResult<T>? {
     let vertices = graph.vertices
@@ -53,7 +57,9 @@ extension BellmanFord: SSSPAlgorithm {
     }
 
     // check for negative weight cycles reachable from the source vertex
-    // TODO: modify to incorporate solution to 24.1-4, pg 654, to set the weight of a path containing a negative weight cycle to -∞, instead of returning nil for the entire result
+    // TO DO: modify to incorporate solution to 24.1-4, pg 654, to set the
+    //       weight of a path containing a negative weight cycle to -∞,
+    //       instead of returning nil for the entire result
     for edge in edges {
       if weights[edge.to.index] > weights[edge.from.index] + edge.weight! {
         return nil
@@ -66,9 +72,11 @@ extension BellmanFord: SSSPAlgorithm {
 }
 
 /**
- `BellmanFordResult` encapsulates the result of the computation, namely the minimized distances, and the predecessor indices.
+ `BellmanFordResult` encapsulates the result of the computation,
+ namely the minimized distances, and the predecessor indices.
 
- It conforms to the `SSSPResult` procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
+ It conforms to the `SSSPResult` procotol which provides methods to
+ retrieve distances and paths between given pairs of start and end nodes.
  */
 public struct BellmanFordResult<T where T: Hashable> {
 
@@ -80,7 +88,8 @@ public struct BellmanFordResult<T where T: Hashable> {
 extension BellmanFordResult: SSSPResult {
 
   /**
-   - returns: the total weight of the path from the source vertex to a destination. This value is the minimal connected weight between the two vertices, or `nil` if no path exists
+   - returns: the total weight of the path from the source vertex to a destination.
+   This value is the minimal connected weight between the two vertices, or `nil` if no path exists
    - complexity: `Θ(1)` time/space
    */
   public func distance(to: Vertex<T>) -> Double? {
@@ -94,7 +103,8 @@ extension BellmanFordResult: SSSPResult {
   }
 
   /**
-   - returns: the reconstructed path from the source vertex to a destination, as an array containing the data property of each vertex, or `nil` if no path exists
+   - returns: the reconstructed path from the source vertex to a destination,
+   as an array containing the data property of each vertex, or `nil` if no path exists
    - complexity: `Θ(V)` time, `Θ(V^2)` space
    */
   public func path(to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
@@ -105,7 +115,7 @@ extension BellmanFordResult: SSSPResult {
     guard let path = recursePath(to, inGraph: graph, path: [to]) else {
       return nil
     }
-    
+
     return path.map() { vertex in
       return vertex.data
     }
@@ -114,7 +124,7 @@ extension BellmanFordResult: SSSPResult {
   /**
    The recursive component to rebuilding the shortest path between two vertices using predecessors.
 
-   - returns: the list of predecessors discovered so far, or `nil` if the next vertex has no predecessor 
+   - returns: the list of predecessors discovered so far, or `nil` if the next vertex has no predecessor
    */
   private func recursePath(to: Vertex<T>, inGraph graph: AbstractGraph<T>, path: [Vertex<T>]) -> [Vertex<T>]? {
     guard let predecessorIdx = predecessors[to.index] else {
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift
index 3d50731ca..8e3afc40a 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift	
@@ -9,7 +9,9 @@ import Foundation
 import Graph
 
 /**
- `SSSPAlgorithm` is a protocol for encapsulating a Single-Source Shortest Path algorithm. It provides a single function `apply` that accepts a subclass of `AbstractGraph` and returns an object conforming to `SSSPResult`.
+ `SSSPAlgorithm` is a protocol for encapsulating a Single-Source Shortest Path algorithm.
+ It provides a single function `apply` that accepts a subclass of `AbstractGraph` and returns
+ an object conforming to `SSSPResult`.
  */
 protocol SSSPAlgorithm {
 
@@ -21,7 +23,9 @@ protocol SSSPAlgorithm {
 }
 
 /**
- `SSSPResult` is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the SSSP solution according to the algorithm used.
+ `SSSPResult` is a protocol defining functions `distance` and `path`, allowing
+ for opaque queries into the actual data structures that represent the SSSP
+ solution according to the algorithm used.
  */
 protocol SSSPResult {
 
diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 51567669c..242dbf518 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,11 +1,11 @@
 /*
   Stack
 
-  A stack is like an array but with limited functionality. You can only push 
+  A stack is like an array but with limited functionality. You can only push
   to add a new element to the top of the stack, pop to remove the element from
   the top, and peek at the top element without popping it off.
 
-  A stack gives you a LIFO or last-in first-out order. The element you pushed 
+  A stack gives you a LIFO or last-in first-out order. The element you pushed
   last is the first one to come off with the next pop.
 
   Push and pop are O(1) operations.
@@ -13,19 +13,19 @@
 
 public struct Stack<T> {
   private var array = [T]()
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public mutating func push(element: T) {
     array.append(element)
   }
-  
+
   public mutating func pop() -> T? {
     if isEmpty {
       return nil
@@ -33,7 +33,7 @@ public struct Stack<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peek() -> T? {
     return array.last
   }
diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index cc2225057..6b1fe3eaa 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -11,24 +11,24 @@ let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ01234567
 func randomAlphaNumericString(length: Int) -> String {
     let allowedCharsCount = UInt32(allowedChars.characters.count)
     var randomString = ""
-    
+
     for _ in (0..<length) {
         let randomNum = Int(arc4random_uniform(allowedCharsCount))
         let newCharacter = allowedChars[allowedChars.startIndex.advancedBy(randomNum)]
         randomString += String(newCharacter)
     }
-    
+
     return randomString
 }
 
-var testStrings: [(key:String, data:String)] = []
+var testStrings: [(key: String, data: String)] = []
 let testCount = 30
 for _ in (1...testCount) {
     let randomLength = Int(arc4random_uniform(10))
     let key = randomAlphaNumericString(randomLength)
     let data = randomAlphaNumericString(randomLength)
 //    print("Key: \(key) Data: \(data)")
-    
+
     if key != "" && data != "" {
         testStrings.append((key, data))
         treeOfStrings.insert(data, withKey: key)
@@ -37,7 +37,7 @@ for _ in (1...testCount) {
 
 for aTest in testStrings {
     let data = treeOfStrings.find(aTest.key)
-    
+
     if data == nil {
         print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
     }
@@ -52,7 +52,7 @@ for _ in (1...testCount) {
     let randomNum = Int(arc4random_uniform(UInt32.max))
     let randomLength = Int(arc4random_uniform(10))
     let key = randomAlphaNumericString(randomLength)
-    
+
     if key != "" {
         testNums.append((key, randomNum))
         treeOfInts.insert(randomNum, withKey: key)
@@ -68,4 +68,3 @@ for aTest in testNums {
         print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
     }
 }
-
diff --git a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift
index b6030400f..efdfd4299 100644
--- a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
@@ -1,6 +1,6 @@
 //
 //  TSTNode.swift
-//  
+//
 //
 //  Created by Siddharth Atre on 3/15/16.
 //
@@ -13,21 +13,21 @@ class TSTNode<Element> {
     var key: Character
     var data: Element?
     var hasData: Bool
-    
+
     //Children
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
-    
-    
+
+
     init(key: Character, data: Element?) {
         self.key = key
         self.data = data
         self.hasData = (data != nil)
     }
-    
-    init(key:Character) {
+
+    init(key: Character) {
         self.key = key
         self.data = nil
         self.hasData = false
     }
-    
-}
\ No newline at end of file
+
+}
diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index 1bbc1c390..43c4453e3 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -1,6 +1,6 @@
 //
 //  TernarySearchTree.swift
-//  
+//
 //
 //  Created by Siddharth Atre on 3/15/16.
 //
@@ -10,44 +10,44 @@ import Foundation
 
 
 public class TernarySearchTree<Element> {
-    
+
     var root: TSTNode<Element>?
-    
+
     public init() {}
-    
+
     //MARK: - Insertion
-    
-    public func insert(data:Element, withKey key: String) -> Bool{
+
+    public func insert(data: Element, withKey key: String) -> Bool {
         return insertNode(&root, withData: data, andKey: key, atIndex: 0)
-        
+
     }
-    
+
     private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
-        
+
         //sanity check.
-        if(key.characters.count == 0) {
+        if key.characters.count == 0 {
             return false
         }
-        
+
         //create a new node if necessary.
-        if(aNode == nil) {
+        if aNode == nil {
             let index = key.startIndex.advancedBy(charIndex)
             aNode = TSTNode<Element>(key: key[index])
         }
-        
+
         //if current char is less than the current node's char, go left
         let index = key.startIndex.advancedBy(charIndex)
-        if(key[index] < aNode!.key) {
+        if key[index] < aNode!.key {
             return insertNode(&aNode!.left, withData: data, andKey: key, atIndex: charIndex)
         }
             //if it's greater, go right.
-        else if(key[index] > aNode!.key) {
+        else if key[index] > aNode!.key {
             return insertNode(&aNode!.right, withData: data, andKey: key, atIndex: charIndex)
         }
             //current char is equal to the current nodes, go middle
         else {
             //continue down the middle.
-            if(charIndex + 1 < key.characters.count) {
+            if charIndex + 1 < key.characters.count {
                 return insertNode(&aNode!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
             }
                 //otherwise, all done.
@@ -58,23 +58,23 @@ public class TernarySearchTree<Element> {
             }
         }
     }
-    
-    
+
+
     //MARK: - Finding
-    
-    
-    public func find(key:String) -> Element? {
+
+
+    public func find(key: String) -> Element? {
         return findNode(root, withKey: key, atIndex: 0)
     }
-    
-    
+
+
     private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
-        
+
         //Given key does not exist in tree.
         if aNode == nil {
             return nil
         }
-        
+
         let index = key.startIndex.advancedBy(charIndex)
         //go left
         if key[index] < aNode!.key {
@@ -93,4 +93,4 @@ public class TernarySearchTree<Element> {
             }
         }
     }
-}
\ No newline at end of file
+}
diff --git a/Ternary Search Tree/TST.playground/playground.xcworkspace/contents.xcworkspacedata b/Ternary Search Tree/TST.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Ternary Search Tree/TST.playground/timeline.xctimeline b/Ternary Search Tree/TST.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ternary Search Tree/TST.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Ternary Search Tree/TSTNode.swift b/Ternary Search Tree/TSTNode.swift
index 95376591f..16f1ba2cf 100644
--- a/Ternary Search Tree/TSTNode.swift	
+++ b/Ternary Search Tree/TSTNode.swift	
@@ -1,6 +1,6 @@
 //
 //  TSTNode.swift
-//  
+//
 //
 //  Created by Siddharth Atre on 3/15/16.
 //
@@ -9,27 +9,27 @@
 import Foundation
 
 /**
- This class represents a node in the Ternary Search Tree. 
- A node has two main data members, the key and the data. 
+ This class represents a node in the Ternary Search Tree.
+ A node has two main data members, the key and the data.
  All nodes in a TST must have keys, but only some will have data.
  This can be seen in the way the data variable is of Optional type.
 */
 class TSTNode<Element> {
     //Member properties of a particular node.
-    
+
     /// The key that identifies this node.
     var key: Character
     /// The data stored in this node. May be `nil`
     var data: Element?
     /// Boolean flag to depict whether this node holds data or not.
     var hasData: Bool
-    
+
     /// The children of this node
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
-    
+
     /**
      Initializer for key and/or data
-     
+
      - parameter key:  The key to set for this node.
      - parameter data: The optional data to set in this node.
      */
@@ -38,16 +38,16 @@ class TSTNode<Element> {
         self.data = data
         self.hasData = (data != nil)
     }
-    
+
     /**
      Make a node that only has a key
-    
+
      - parameter key: The key to ascribe to this node.
      */
-    init(key:Character) {
+    init(key: Character) {
         self.key = key
         self.data = nil
         self.hasData = false
     }
-    
-}
\ No newline at end of file
+
+}
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 5187e1e78..2f143bead 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -1,6 +1,6 @@
 //
 //  TernarySearchTree.swift
-//  
+//
 //
 //  Created by Siddharth Atre on 3/15/16.
 //
@@ -14,65 +14,65 @@ Data structure uses key-value mappings. Keys are strings used to map to any data
 See README for more information.
 */
 public class TernarySearchTree<Element> {
-    
+
     /// A reference to the root node of this TST
     var root: TSTNode<Element>?
-    
+
     /**
      Standard initializer
      */
     public init() {}
-    
+
     //MARK: - Insertion
-    
+
     /**
     Public insertion method.
-    
+
     - parameter data: The value to store in this TST.
     - parameter key:  The key to associate with this value.
-    
+
     - returns: Value indicating insertion success/failure.
     */
-    public func insert(data:Element, withKey key: String) -> Bool{
+    public func insert(data: Element, withKey key: String) -> Bool {
         return insertNode(&root, withData: data, andKey: key, atIndex: 0)
     }
-    
+
     /**
      Helper method for insertion that does the actual legwork. Insertion is performed recursively.
-     
+
      - parameter aNode:     The current node to insert below.
      - parameter data:      The data being inserted.
      - parameter key:       The key being used to find an insertion location for the given data
      - parameter charIndex: The index of the character in the key string to use to for the next node.
-     
+
      - returns: Value indicating insertion success/failure.
      */
     private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
-        
+
         //sanity check.
-        if(key.characters.count == 0) {
+        if key.characters.count == 0 {
             return false
         }
-        
+
         //create a new node if necessary.
-        if(aNode == nil) {
+        if aNode == nil {
             let index = key.startIndex.advancedBy(charIndex)
             aNode = TSTNode<Element>(key: key[index])
         }
-        
+
         //if current char is less than the current node's char, go left
         let index = key.startIndex.advancedBy(charIndex)
-        if(key[index] < aNode!.key) {
+        if key[index] < aNode!.key {
             return insertNode(&aNode!.left, withData: data, andKey: key, atIndex: charIndex)
         }
             //if it's greater, go right.
-        else if(key[index] > aNode!.key) {
+        else if key[index] > aNode!.key {
             return insertNode(&aNode!.right, withData: data, andKey: key, atIndex: charIndex)
         }
             //current char is equal to the current nodes, go middle
         else {
             //continue down the middle.
-            if(charIndex + 1 < key.characters.count) {
+            if charIndex + 1 < key.characters.count {
                 return insertNode(&aNode!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
             }
                 //otherwise, all done.
@@ -83,37 +83,37 @@ public class TernarySearchTree<Element> {
             }
         }
     }
-    
-    
+
+
     //MARK: - Finding
-    
+
     /**
     Public find method.
-    
+
     - parameter key: Search for an object associated with this key.
-    
+
     - returns: The element, if found. Otherwise, nil.
     */
-    public func find(key:String) -> Element? {
+    public func find(key: String) -> Element? {
         return findNode(root, withKey: key, atIndex: 0)
     }
-    
+
     /**
      Helper method that performs actual legwork of find operation. Implemented recursively.
-    
+
      - parameter aNode:     The current node being evaluated.
      - parameter key:       The key being used for the search.
      - parameter charIndex: The index of the current char in the search key
-     
+
      - returns: The element, if found. Nil otherwise.
      */
     private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
-        
+
         //Given key does not exist in tree.
         if aNode == nil {
             return nil
         }
-        
+
         let index = key.startIndex.advancedBy(charIndex)
         //go left
         if key[index] < aNode!.key {
@@ -132,4 +132,4 @@ public class TernarySearchTree<Element> {
             }
         }
     }
-}
\ No newline at end of file
+}
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
index a046d4378..98a23d013 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.swift	
@@ -4,7 +4,7 @@
 
   Each node stores a value and two children. The left child contains a smaller
   value; the right a larger (or equal) value.
-  
+
   Any nodes that lack either a left or right child instead keep track of their
   in-order predecessor and/or successor.
 
@@ -82,7 +82,7 @@ extension ThreadedBinaryTree {
   public func insert(value: T) {
     insert(value, parent: self)
   }
-  
+
   private func insert(value: T, parent: ThreadedBinaryTree) {
     if value < self.value {
       if let left = left {
@@ -242,7 +242,7 @@ extension ThreadedBinaryTree {
     }
   }
   */
-  
+
   public func contains(value: T) -> Bool {
     return search(value) != nil
   }
@@ -257,7 +257,7 @@ extension ThreadedBinaryTree {
     }
     return node
   }
-  
+
   /*
     Returns the rightmost descendent. O(h) time.
   */
@@ -268,7 +268,7 @@ extension ThreadedBinaryTree {
     }
     return node
   }
-  
+
   /*
     Calculates the depth of this node, i.e. the distance to the root.
     Takes O(h) time.
@@ -282,7 +282,7 @@ extension ThreadedBinaryTree {
     }
     return edges
   }
-  
+
   /*
     Calculates the height of this node, i.e. the distance to the lowest leaf.
     Since this looks at all children of this node, performance is O(n).
@@ -346,13 +346,13 @@ extension ThreadedBinaryTree {
       }
     }
   }
-  
+
   public func traversePreOrder(@noescape visit: T -> Void) {
     visit(value)
     left?.traversePreOrder(visit)
     right?.traversePreOrder(visit)
   }
-  
+
   public func traversePostOrder(@noescape visit: T -> Void) {
     left?.traversePostOrder(visit)
     right?.traversePostOrder(visit)
diff --git a/Threaded Binary Tree/ThreadedBinaryTreeTests.swift b/Threaded Binary Tree/ThreadedBinaryTreeTests.swift
index 550df424d..514c0db63 100644
--- a/Threaded Binary Tree/ThreadedBinaryTreeTests.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTreeTests.swift	
@@ -8,7 +8,7 @@
 // Simple little debug function to make testing output pretty
 func check(tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {
-    print("\(tree.count) Total Nodes:");
+    print("\(tree.count) Total Nodes:")
     print(tree)
     print("Debug Info:")
     print(tree.debugDescription)
diff --git a/Topological Sort/Graph.swift b/Topological Sort/Graph.swift
index 5db37ad45..173676537 100644
--- a/Topological Sort/Graph.swift	
+++ b/Topological Sort/Graph.swift	
@@ -1,26 +1,26 @@
 public class Graph: CustomStringConvertible {
   public typealias Node = String
-  
+
   private(set) public var adjacencyLists: [Node : [Node]]
 
   public init() {
     adjacencyLists = [Node : [Node]]()
   }
-  
+
   public func addNode(value: Node) -> Node {
     adjacencyLists[value] = []
     return value
   }
-  
+
   public func addEdge(fromNode from: Node, toNode to: Node) -> Bool {
     adjacencyLists[from]?.append(to)
     return adjacencyLists[from] != nil ? true : false
   }
-  
+
   public var description: String {
     return adjacencyLists.description
   }
-  
+
   public func adjacencyList(forNode node: Node) -> [Node]? {
     for (key, adjacencyList) in adjacencyLists {
       if key == node {
@@ -36,11 +36,11 @@ extension Graph {
 
   func calculateInDegreeOfNodes() -> [Node : InDegree] {
     var inDegrees = [Node : InDegree]()
-    
+
     for (node, _) in adjacencyLists {
       inDegrees[node] = 0
     }
-    
+
     for (_, adjacencyList) in adjacencyLists {
       for nodeInList in adjacencyList {
         inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
diff --git a/Topological Sort/Tests/TopologicalSortTests.swift b/Topological Sort/Tests/TopologicalSortTests.swift
index 441422703..5acdcf2ae 100644
--- a/Topological Sort/Tests/TopologicalSortTests.swift	
+++ b/Topological Sort/Tests/TopologicalSortTests.swift	
@@ -17,7 +17,7 @@ extension Graph {
 }
 
 class TopologicalSort: XCTestCase {
-  
+
   // The topological sort is valid if a node does not have any of its
   // predecessors in its adjacency list.
   func checkIsValidTopologicalSort(graph: Graph, _ a: [Graph.Node]) {
@@ -29,10 +29,10 @@ class TopologicalSort: XCTestCase {
       }
     }
   }
-  
+
   func testTopologicalSort() {
     let graph = Graph()
-    
+
     let node5 = graph.addNode("5")
     let node7 = graph.addNode("7")
     let node3 = graph.addNode("3")
@@ -41,7 +41,7 @@ class TopologicalSort: XCTestCase {
     let node2 = graph.addNode("2")
     let node9 = graph.addNode("9")
     let node10 = graph.addNode("10")
-    
+
     graph.addEdge(fromNode: node5, toNode: node11)
     graph.addEdge(fromNode: node7, toNode: node11)
     graph.addEdge(fromNode: node7, toNode: node8)
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index 7fbadb6ce..173676537 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -1,26 +1,26 @@
 public class Graph: CustomStringConvertible {
   public typealias Node = String
-  
+
   private(set) public var adjacencyLists: [Node : [Node]]
-  
+
   public init() {
     adjacencyLists = [Node : [Node]]()
   }
-  
+
   public func addNode(value: Node) -> Node {
     adjacencyLists[value] = []
     return value
   }
-  
+
   public func addEdge(fromNode from: Node, toNode to: Node) -> Bool {
     adjacencyLists[from]?.append(to)
     return adjacencyLists[from] != nil ? true : false
   }
-  
+
   public var description: String {
     return adjacencyLists.description
   }
-  
+
   public func adjacencyList(forNode node: Node) -> [Node]? {
     for (key, adjacencyList) in adjacencyLists {
       if key == node {
@@ -36,11 +36,11 @@ extension Graph {
 
   func calculateInDegreeOfNodes() -> [Node : InDegree] {
     var inDegrees = [Node : InDegree]()
-    
+
     for (node, _) in adjacencyLists {
       inDegrees[node] = 0
     }
-    
+
     for (_, adjacencyList) in adjacencyLists {
       for nodeInList in adjacencyList {
         inDegrees[nodeInList] = (inDegrees[nodeInList] ?? 0) + 1
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index a7be2803c..7f1aca5e7 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -1,7 +1,7 @@
 extension Graph {
   private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
     var result = [Node]()
-    
+
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
         if let seen = visited[nodeInAdjacencyList] where !seen {
@@ -9,30 +9,30 @@ extension Graph {
         }
       }
     }
-    
+
     visited[source] = true
     return [source] + result
   }
 
   /* Topological sort using depth-first search. */
   public func topologicalSort() -> [Node] {
-    
+
     let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
     }).map({ node, indegree in
       return node
     })
-    
+
     var visited = [Node : Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
     }
-    
+
     var result = [Node]()
     for startNode in startNodes {
       result = depthFirstSearch(startNode, visited: &visited) + result
     }
-    
+
     return result
   }
 }
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift
index 24a6189fa..cdc479b41 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift	
@@ -6,7 +6,7 @@
 extension Graph {
   public func topologicalSortAlternative() -> [Node] {
     var stack = [Node]()
-    
+
     var visited = [Node: Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index e134bf9ce..7f1aca5e7 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -1,7 +1,7 @@
 extension Graph {
   private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
     var result = [Node]()
-    
+
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
         if let seen = visited[nodeInAdjacencyList] where !seen {
@@ -9,30 +9,30 @@ extension Graph {
         }
       }
     }
-    
+
     visited[source] = true
     return [source] + result
   }
-  
+
   /* Topological sort using depth-first search. */
   public func topologicalSort() -> [Node] {
-    
+
     let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
     }).map({ node, indegree in
       return node
     })
-    
+
     var visited = [Node : Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
     }
-    
+
     var result = [Node]()
     for startNode in startNodes {
       result = depthFirstSearch(startNode, visited: &visited) + result
     }
-    
+
     return result
   }
 }
diff --git a/Topological Sort/TopologicalSort3.swift b/Topological Sort/TopologicalSort3.swift
index 24a6189fa..cdc479b41 100644
--- a/Topological Sort/TopologicalSort3.swift	
+++ b/Topological Sort/TopologicalSort3.swift	
@@ -6,7 +6,7 @@
 extension Graph {
   public func topologicalSortAlternative() -> [Node] {
     var stack = [Node]()
-    
+
     var visited = [Node: Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 5413a17c2..e1d1d4892 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -46,7 +46,7 @@ public indirect enum Treap<Key: Comparable, Element> {
             return nil
         }
     }
-    
+
     public func contains(key: Key) -> Bool {
         switch self {
         case .Empty:
@@ -61,7 +61,7 @@ public indirect enum Treap<Key: Comparable, Element> {
             return false
         }
     }
-    
+
     public var depth: Int {
         get {
             switch self {
@@ -76,43 +76,39 @@ public indirect enum Treap<Key: Comparable, Element> {
                 let rightDepth = right.depth
                 return 1 + max(leftDepth, rightDepth)
             }
-            
+
         }
     }
-    
+
     public var count: Int {
         get {
             return Treap.countHelper(self)
         }
     }
-    
-    private static func countHelper(treap: Treap<Key, Element>) -> Int
-    {
-        if case let .Node(_, _, _, left, right) = treap
-        {
+
+    private static func countHelper(treap: Treap<Key, Element>) -> Int {
+        if case let .Node(_, _, _, left, right) = treap {
             return countHelper(left) + 1 + countHelper(right)
         }
-        
+
         return 0
     }
 }
 
 internal func leftRotate<Key: Comparable, Element>(tree: Treap<Key, Element>) -> Treap<Key, Element> {
     if case let .Node(key, val, p, .Node(leftKey, leftVal, leftP, leftLeft, leftRight), right) = tree {
-        return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: Treap.Node(key: key, val: val, p: p, left: leftRight, right: right))
-    }
-    else
-    {
+        return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft,
+                     right: Treap.Node(key: key, val: val, p: p, left: leftRight, right: right))
+    } else {
         return .Empty
     }
 }
 
 internal func rightRotate<Key: Comparable, Element>(tree: Treap<Key, Element>) -> Treap<Key, Element> {
     if case let .Node(key, val, p, left, .Node(rightKey, rightVal, rightP, rightLeft, rightRight)) = tree {
-        return .Node(key: rightKey, val: rightVal, p: rightP, left: Treap.Node(key: key, val: val, p: p, left: left, right: rightLeft), right: rightRight)
-    }
-    else
-    {
+        return .Node(key: rightKey, val: rightVal, p: rightP,
+                     left: Treap.Node(key: key, val: val, p: p, left: left, right: rightLeft), right: rightRight)
+    } else {
         return .Empty
     }
 }
@@ -129,10 +125,11 @@ public extension Treap {
         default: // should never happen
             return .Empty
         }
-        
+
     }
-    
-    private func insertAndBalance(nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap, _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
+
+    private func insertAndBalance(nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap,
+                                  _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
         let newChild: Treap<Key, Element>
         let newNode: Treap<Key, Element>
         let rotate: (Treap) -> Treap
@@ -140,27 +137,24 @@ public extension Treap {
             newChild = left.set(key, val: val, p: p)
             newNode = .Node(key: nodeKey, val: nodeVal, p: nodeP, left: newChild, right: right)
             rotate = leftRotate
-        }
-        else if key > nodeKey {
+        } else if key > nodeKey {
             newChild = right.set(key, val: val, p: p)
             newNode = .Node(key: nodeKey, val: nodeVal, p: nodeP, left: left, right: newChild)
             rotate = rightRotate
-        }
-        else {
+        } else {
             // It should be impossible to reach here
             newChild = .Empty
             newNode = .Empty
             return newNode
         }
-        
+
         if case let .Node(_, _, newChildP, _, _) = newChild where newChildP < nodeP {
             return rotate(newNode)
-        }
-        else {
+        } else {
             return newNode
         }
     }
-    
+
     internal func delete(key: Key) throws -> Treap {
         switch self {
         case .Empty:
diff --git a/Treap/Treap/Treap.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Treap/Treap/Treap.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Treap/Treap/Treap.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Treap/Treap/Treap/AppDelegate.swift b/Treap/Treap/Treap/AppDelegate.swift
index 1813d840b..a6a68a40c 100644
--- a/Treap/Treap/Treap/AppDelegate.swift
+++ b/Treap/Treap/Treap/AppDelegate.swift
@@ -41,4 +41,3 @@ class AppDelegate: NSObject, NSApplicationDelegate {
 
 
 }
-
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index 496e2f940..5f43a376f 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -22,21 +22,23 @@ LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.*/
 
+// swiftlint:disable force_try
+
 import XCTest
 @testable import Treap
 
 class TreapTests: XCTestCase {
-    
+
     override func setUp() {
         super.setUp()
         // Put setup code here. This method is called before the invocation of each test method in the class.
     }
-    
+
     override func tearDown() {
         // Put teardown code here. This method is called after the invocation of each test method in the class.
         super.tearDown()
     }
-    
+
     func testSanity() {
         var treap = Treap<Int, String>.Empty
         treap = treap.set(5, val: "a").set(7, val: "b")
@@ -62,12 +64,11 @@ class TreapTests: XCTestCase {
 
     func testFairlyBalancedCollection() {
         var treap = Treap<Int, Int?>()
-        for i in 0..<1000
-        {
+        for i in 0..<1000 {
             treap[i] = Optional<Int>.None
         }
         let depth = treap.depth
         XCTAssert(depth > 0 && depth < 30)
     }
-    
+
 }
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index 51929893b..277cb40b7 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -24,39 +24,32 @@ THE SOFTWARE.*/
 
 import Foundation
 public extension Treap {
-    internal func split(key: Key) -> (left: Treap, right: Treap)
-    {
+    internal func split(key: Key) -> (left: Treap, right: Treap) {
         var current = self
         let val: Element
-        if let newVal = self.get(key)
-        {
+        if let newVal = self.get(key) {
+          // swiftlint:disable force_try
             current = try! current.delete(key)
+          // swiftlint:enable force_try
             val = newVal
-        }
-        else if case let .Node(_, newVal, _, _, _) = self
-        {
+        } else if case let .Node(_, newVal, _, _, _) = self {
             val = newVal
-        }
-        else
-        {
+        } else {
             fatalError("No values in treap")
         }
-        
+
         switch self {
         case .Node:
-            if case let .Node(_, _, _, left, right) = current.set(key, val: val, p: -1)
-            {
+            if case let .Node(_, _, _, left, right) = current.set(key, val: val, p: -1) {
                 return (left: left, right: right)
-            }
-            else
-            {
+            } else {
                 return (left: .Empty, right: .Empty)
             }
         default:
             return (left: .Empty, right: .Empty)
         }
     }
-    
+
     internal var leastKey: Key? {
         switch self {
         case .Empty:
@@ -67,7 +60,7 @@ public extension Treap {
             return left.leastKey
         }
     }
-    
+
     internal var mostKey: Key? {
         switch self {
         case .Empty:
@@ -86,13 +79,11 @@ internal func merge<Key: Comparable, Element>(left: Treap<Key, Element>, right:
         return right
     case (_, .Empty):
         return left
-        
+
     case let (.Node(leftKey, leftVal, leftP, leftLeft, leftRight), .Node(rightKey, rightVal, rightP, rightLeft, rightRight)):
         if leftP < rightP {
             return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: merge(leftRight, right: right))
-        }
-        else
-        {
+        } else {
             return .Node(key: rightKey, val: rightVal, p: rightP, left: merge(rightLeft, right: left), right: rightRight)
         }
     default:
@@ -101,29 +92,25 @@ internal func merge<Key: Comparable, Element>(left: Treap<Key, Element>, right:
     return .Empty
 }
 
-extension Treap: CustomStringConvertible
-{
+extension Treap: CustomStringConvertible {
     public var description: String {
         get {
             return Treap.descHelper(self, indent: 0)
         }
     }
-    
-    private static func descHelper(treap: Treap<Key, Element>, indent: Int) -> String
-    {
+
+    private static func descHelper(treap: Treap<Key, Element>, indent: Int) -> String {
         if case let .Node(key, value, priority, left, right) = treap {
             var result = ""
             let tabs = String(count: indent, repeatedValue: Character("\t"))
-            
+
             result += descHelper(left, indent: indent + 1)
             result += "\n" + tabs + "\(key), \(value), \(priority)\n"
             result += descHelper(right, indent: indent + 1)
-            
+
             return result
-        }
-        else
-        {
+        } else {
             return ""
         }
     }
-}
\ No newline at end of file
+}
diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 966870bdf..c8ee8fe71 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -2,14 +2,14 @@
 
 public class TreeNode<T> {
   public var value: T
-  
+
   public var parent: TreeNode?
   public var children = [TreeNode<T>]()
 
   public init(value: T) {
     self.value = value
   }
-  
+
   public func addChild(node: TreeNode<T>) {
     children.append(node)
     node.parent = self
diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index 5c027141c..89f1a39da 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -1,13 +1,13 @@
 public class TreeNode<T> {
   public var value: T
-  
+
   public var parent: TreeNode?
   public var children = [TreeNode<T>]()
 
   public init(value: T) {
     self.value = value
   }
-  
+
   public func addChild(node: TreeNode<T>) {
     children.append(node)
     node.parent = self
diff --git a/Trie/trie.swift b/Trie/trie.swift
index 839c4350b..9ebfba8bc 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -52,7 +52,7 @@ public class Node {
   private var isAWord: Bool
   private var visited: Bool  //only for findPrefix
 
-  init(c: String?, p: Node?){
+  init(c: String?, p: Node?) {
     self.character = c
     self.children = [String:Node]()
     self.isAWord = false
@@ -86,7 +86,7 @@ public class Node {
     Output:  Bool
     Functionality: Returns true if the node is a leaf node, false otherwise
   */
-  func isLeaf() -> Bool{
+  func isLeaf() -> Bool {
     return self.children.count == 0
   }
 
@@ -127,7 +127,7 @@ public class Node {
     Output:  Bool
     Functionality: Returns whether or not the current node marks the end of a valid word
   */
-  func isValidWord() -> Bool{
+  func isValidWord() -> Bool {
     return self.isAWord
   }
 
@@ -194,8 +194,7 @@ public class Node {
     if leaf {
       print("\\-", terminator: "")
       indent += " "
-    }
-    else {
+    } else {
       print("|-", terminator: "")
       indent += "| "
     }
@@ -245,7 +244,7 @@ public class Trie {
     Output:  Trie
     Functionality:  Merges two tries into one and returns the merged trie
   */
-  func merge(other: Trie) -> Trie{
+  func merge(other: Trie) -> Trie {
     let newWordList = Set(self.getWords() + other.getWords())
     return Trie(wordList: newWordList)
   }
@@ -254,7 +253,9 @@ public class Trie {
     Function Name:  find
     Input:  String
     Output:  (Node?, Bool)
-    Functionality:  Looks for a specific key and returns a tuple that has a reference to the node(if found) and true/false depending on if it was found
+    Functionality:  Looks for a specific key and returns a tuple that
+                    has a reference to the node(if found) and true/false
+                    depending on if it was found
   */
   func find(key: String) -> (node: Node?, found: Bool) {
     var currentNode = self.root
@@ -313,7 +314,9 @@ public class Trie {
     Function Name:  isPrefix
     Input:  String
     Output: (Node?, Bool)
-    Functionality:  returns a tuple containing a reference to the final node in the prefix (if it exists) and true/false depending on whether or not the prefix exists in the trie
+    Functionality:  returns a tuple containing a reference to the final
+                    node in the prefix (if it exists) and true/false
+                    depending on whether or not the prefix exists in the trie
   */
   func isPrefix(p: String) -> (node: Node?, found: Bool) {
     let prefixP = p.lowercaseString
@@ -321,7 +324,7 @@ public class Trie {
     var currentNode = self.root
 
     for c in prefixP.characters {
-      if currentNode.children[String(c)] == nil{
+      if currentNode.children[String(c)] == nil {
         return (nil, false)
       }
 
@@ -339,7 +342,9 @@ public class Trie {
     Function Name:  insert
     Input:  String
     Output:  (String, Bool)
-    Functionality:  Inserts a word int othe trie.  Returns a tuple containing the word attempted to be added, and true/false depending on whether or not the insertion was successful
+    Functionality:  Inserts a word int othe trie.  Returns a tuple containing
+                    the word attempted to be added, and true/false depending on
+                    whether or not the insertion was successful
   */
   func insert(w: String) -> (word: String, inserted: Bool) {
 
@@ -385,10 +390,12 @@ public class Trie {
     Function Name:  insertWords
     Input:  [String]
     Output:  ([String], Bool)
-    Functionality:  attempts to insert all words from input array.  returns a tuple containing the input array and true if some of the words were succesffuly added, false if none were added
+    Functionality:  attempts to insert all words from input array.  returns a tuple
+                    containing the input array and true if some of the words were
+                    succesffuly added, false if none were added
   */
 
-  func insertWords(wordList: [String]) -> (wordList: [String], inserted: Bool){
+  func insertWords(wordList: [String]) -> (wordList: [String], inserted: Bool) {
 
     var succesful: Bool = false
     for word in wordList {
@@ -402,9 +409,11 @@ public class Trie {
     Function Name:  remove
     Input:  String
     Output:  (String, Bool)
-    Functionality:  Removes the specified key from the trie if it exists, returns tuple containing the word attempted to be removed and true/false if the removal was succesful
+    Functionality:  Removes the specified key from the trie if it exists, returns
+                    tuple containing the word attempted to be removed and true/false
+                    if the removal was succesful
   */
-  func remove(w: String) -> (word: String, removed: Bool){
+  func remove(w: String) -> (word: String, removed: Bool) {
     let word = w.lowercaseString
 
     if !self.contains(w) {
@@ -420,7 +429,7 @@ public class Trie {
       currentNode.isNotWord()
     } else {
       var character = currentNode.char()
-      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
+      while currentNode.numChildren() == 0 && !currentNode.isRoot() {
         currentNode = currentNode.getParent()
         currentNode.children[character]!.setParent(nil)
         currentNode.children[character]!.update(nil)
@@ -432,7 +441,7 @@ public class Trie {
     wordCount -= 1
 
     var index = 0
-    for item in wordList{
+    for item in wordList {
       if item == w {
         wordList.removeAtIndex(index)
       }
@@ -492,7 +501,7 @@ public class Trie {
     Output:  N/A
     Functionality:  removes all nodes in the trie using remove as a subroutine
   */
-  func removeAll()  {
+  func removeAll() {
     for word in wordList {
       self.remove(word)
     }
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 5fee2deb4..11c95b96c 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -2,7 +2,7 @@
 
 func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
-  
+
   for i in 0 ..< a.count {
     if let newK = map[a[i]] {
       return (newK, i)
diff --git a/Two-Sum Problem/Solution 1/2Sum.swift b/Two-Sum Problem/Solution 1/2Sum.swift
index 0f438c11d..b3ef54790 100644
--- a/Two-Sum Problem/Solution 1/2Sum.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.swift	
@@ -4,12 +4,12 @@
 
   Uses a dictionary to store differences between the target and each element.
   If any value in the dictionary equals an element in the array, they sum to k.
-  
+
   This is an O(n) solution.
 */
 func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
-  
+
   for i in 0 ..< a.count {
     if let newK = map[a[i]] {
       return (newK, i)
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index 07883e251..1d6b0a9c8 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -3,7 +3,7 @@
 func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
   var j = a.count - 1
-  
+
   while i < j {
     let sum = a[i] + a[j]
     if sum == k {
diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index dd57514cd..5747b15b5 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -4,13 +4,13 @@ public struct UnionFind<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public mutating func addSetWith(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(index: Int) -> Int {
     if parent[index] == index {
       return index
@@ -19,7 +19,7 @@ public struct UnionFind<T: Hashable> {
       return parent[index]
     }
   }
-  
+
   public mutating func setOf(element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -27,7 +27,7 @@ public struct UnionFind<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -41,7 +41,7 @@ public struct UnionFind<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
       return firstSet == secondSet
@@ -114,7 +114,3 @@ print(dsuForStrings.inSameSet("border", and: "best"))
 
 print(dsuForStrings.inSameSet("amazing", and: "boy"))
 print(dsuForStrings.inSameSet("all", and: "border"))
-
-
-
-
diff --git a/Union-Find/UnionFind.swift b/Union-Find/UnionFind.swift
index f1500e6c9..4323b80d4 100644
--- a/Union-Find/UnionFind.swift
+++ b/Union-Find/UnionFind.swift
@@ -11,13 +11,13 @@ public struct UnionFind<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public mutating func addSetWith(element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(index: Int) -> Int {
     if parent[index] == index {
       return index
@@ -26,7 +26,7 @@ public struct UnionFind<T: Hashable> {
       return parent[index]
     }
   }
-  
+
   public mutating func setOf(element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -34,7 +34,7 @@ public struct UnionFind<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -56,4 +56,4 @@ public struct UnionFind<T: Hashable> {
       return false
     }
   }
-}
\ No newline at end of file
+}

From 6a8a677e5a943423f4fc60a1d6bd67ee8f25a652 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 9 Jun 2016 00:03:57 +1200
Subject: [PATCH 0391/1679] Added instructions for running SwiftLint to the
 "How to Contribute" page

---
 How to Contribute.markdown | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index dc1562327..94e69ae68 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -23,6 +23,15 @@ To keep this a high quality repo, please follow this process when submitting you
 3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
 4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. If you wrote it, you deserve the credit and fame.
 5. Add a playground and/or unit tests.
+6. Run [SwiftLint](https://github.com/realm/SwiftLint)  
+  - [Install](https://github.com/realm/SwiftLint#installation)
+  - Open terminal and run the `swiftlint` command:
+
+```
+cd path/to/swift-algorithm-club
+swiftlint
+```
+
 
 Just so you know, I will probably edit your text and code for grammar etc, just to ensure a certain level of polish.
 

From e90de2840daf9b77f71550dc11a0b600dd8a3756 Mon Sep 17 00:00:00 2001
From: Kevin Randrup <kevinrandrup@gmail.com>
Date: Wed, 8 Jun 2016 22:22:48 -0400
Subject: [PATCH 0392/1679] Added swift-algorithm-cllub.workspace so all
 projects can be viewed together.

Using a workspace brings all of the projects together in a single window with all of the code highlighting, search and documentation features that Xcode brings. I found it extremely useful when viewing/comparing multiple projects.
---
 .../contents.xcworkspacedata                  | 2103 +++++++++++++++++
 1 file changed, 2103 insertions(+)
 create mode 100644 swift-algorithm-club.xcworkspace/contents.xcworkspacedata

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..1ec94e727
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,2103 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "group:README.markdown">
+   </FileRef>
+   <FileRef
+      location = "group:LICENSE.txt">
+   </FileRef>
+   <FileRef
+      location = "group:Algorithm Design.markdown">
+   </FileRef>
+   <FileRef
+      location = "group:Big-O Notation.markdown">
+   </FileRef>
+   <FileRef
+      location = "group:How to Contribute.markdown">
+   </FileRef>
+   <FileRef
+      location = "group:Under Construction.markdown">
+   </FileRef>
+   <FileRef
+      location = "group:What are Algorithms.markdown">
+   </FileRef>
+   <FileRef
+      location = "group:Why Algorithms.markdown">
+   </FileRef>
+   <Group
+      location = "group:All-Pairs Shortest Paths"
+      name = "All-Pairs Shortest Paths">
+      <Group
+         location = "group:APSP"
+         name = "APSP">
+         <Group
+            location = "group:APSP"
+            name = "APSP">
+            <FileRef
+               location = "group:APSP.h">
+            </FileRef>
+            <FileRef
+               location = "group:APSP.swift">
+            </FileRef>
+            <FileRef
+               location = "group:FloydWarshall.swift">
+            </FileRef>
+            <FileRef
+               location = "group:Helpers.swift">
+            </FileRef>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:APSP.playground">
+         </FileRef>
+         <FileRef
+            location = "group:APSP.xcodeproj">
+         </FileRef>
+         <FileRef
+            location = "group:APSP.xcworkspace">
+         </FileRef>
+         <Group
+            location = "group:APSPTests"
+            name = "APSPTests">
+            <FileRef
+               location = "group:APSPTests.swift">
+            </FileRef>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+         </Group>
+      </Group>
+      <Group
+         location = "group:img"
+         name = "img">
+         <FileRef
+            location = "group:d0.png">
+         </FileRef>
+         <FileRef
+            location = "group:d1.png">
+         </FileRef>
+         <FileRef
+            location = "group:d2.png">
+         </FileRef>
+         <FileRef
+            location = "group:d3.png">
+         </FileRef>
+         <FileRef
+            location = "group:example_graph.png">
+         </FileRef>
+         <FileRef
+            location = "group:original_adjacency_matrix.png">
+         </FileRef>
+         <FileRef
+            location = "group:pi0.png">
+         </FileRef>
+         <FileRef
+            location = "group:pi1.png">
+         </FileRef>
+         <FileRef
+            location = "group:pi2.png">
+         </FileRef>
+         <FileRef
+            location = "group:pi3.png">
+         </FileRef>
+         <FileRef
+            location = "group:weight_comparison_formula.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Array2D"
+      name = "Array2D">
+      <FileRef
+         location = "group:Array2D.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Array2D.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Array2DTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
+   <Group
+      location = "group:AVL Tree"
+      name = "AVL Tree">
+      <FileRef
+         location = "group:AVLTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:AVLTree.swift">
+      </FileRef>
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:Balanced.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Balanced.png">
+         </FileRef>
+         <FileRef
+            location = "group:BalanceNotOK.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:BalanceNotOK.png">
+         </FileRef>
+         <FileRef
+            location = "group:BalanceOK.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:BalanceOK.png">
+         </FileRef>
+         <FileRef
+            location = "group:Height.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Height.png">
+         </FileRef>
+         <FileRef
+            location = "group:Unbalanced.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Unbalanced.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:AVLTreeTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+         <FileRef
+            location = "group:TreeNodeTests.swift">
+         </FileRef>
+      </Group>
+   </Group>
+   <Group
+      location = "group:Binary Search"
+      name = "Binary Search">
+      <FileRef
+         location = "group:BinarySearch.playground">
+      </FileRef>
+      <FileRef
+         location = "group:BinarySearch.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:BinarySearchTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
+   <Group
+      location = "group:Binary Search Tree"
+      name = "Binary Search Tree">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:DeleteLeaf.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:DeleteLeaf.png">
+         </FileRef>
+         <FileRef
+            location = "group:DeleteOneChild.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:DeleteOneChild.png">
+         </FileRef>
+         <FileRef
+            location = "group:DeleteTwoChildren.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:DeleteTwoChildren.png">
+         </FileRef>
+         <FileRef
+            location = "group:MinimumMaximum.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:MinimumMaximum.png">
+         </FileRef>
+         <FileRef
+            location = "group:Searching.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Searching.png">
+         </FileRef>
+         <FileRef
+            location = "group:Traversing.graffle">
+         </FileRef>
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+               name = "Assets.xcassets">
+               <Group
+                  location = "group:AppIcon.appiconset"
+                  name = "AppIcon.appiconset">
+                  <FileRef
+                     location = "group:Contents.json">
+                  </FileRef>
+               </Group>
+            </Group>
+            <Group
+               location = "group:Base.lproj"
+               name = "Base.lproj">
+               <FileRef
+                  location = "group:MainMenu.xib">
+               </FileRef>
+            </Group>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Treap.xcodeproj">
+         </FileRef>
+         <Group
+            location = "group:TreapTests"
+            name = "TreapTests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:TreapTests.swift">
+            </FileRef>
+         </Group>
+      </Group>
+      <FileRef
+         location = "group:Treap.swift">
+      </FileRef>
+      <FileRef
+         location = "group:TreapCollectionType.swift">
+      </FileRef>
+      <FileRef
+         location = "group:TreapMergeSplit.swift">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Tree"
+      name = "Tree">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:Cycles.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Cycles.png">
+         </FileRef>
+         <FileRef
+            location = "group:Example.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Example.png">
+         </FileRef>
+         <FileRef
+            location = "group:ParentChildren.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:ParentChildren.png">
+         </FileRef>
+         <FileRef
+            location = "group:Tree.graffle">
+         </FileRef>
+         <FileRef
+            location = "group:Tree.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:Tree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Tree.swift">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Trie"
+      name = "Trie">
+      <FileRef
+         location = "group:ReadMe.md">
+      </FileRef>
+      <FileRef
+         location = "group:trie.swift">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Two-Sum Problem"
+      name = "Two-Sum Problem">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Solution 1"
+         name = "Solution 1">
+         <FileRef
+            location = "group:2Sum.playground">
+         </FileRef>
+         <FileRef
+            location = "group:2Sum.swift">
+         </FileRef>
+      </Group>
+      <Group
+         location = "group:Solution 2"
+         name = "Solution 2">
+         <FileRef
+            location = "group:2Sum.playground">
+         </FileRef>
+         <FileRef
+            location = "group:2Sum.swift">
+         </FileRef>
+      </Group>
+   </Group>
+   <Group
+      location = "group:Union-Find"
+      name = "Union-Find">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:AfterFind.png">
+         </FileRef>
+         <FileRef
+            location = "group:AfterUnion.png">
+         </FileRef>
+         <FileRef
+            location = "group:BeforeFind.png">
+         </FileRef>
+         <FileRef
+            location = "group:BeforeUnion.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:UnionFind.playground">
+      </FileRef>
+      <FileRef
+         location = "group:UnionFind.swift">
+      </FileRef>
+   </Group>
+</Workspace>

From 38d225247a7f7396ee30dbd08955db0cb8d14f59 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 10 Jun 2016 13:40:39 +1200
Subject: [PATCH 0393/1679] Fix for #141

---
 Fizz Buzz/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Fizz Buzz/README.markdown b/Fizz Buzz/README.markdown
index 0ce1e2c42..e4cf485ff 100644
--- a/Fizz Buzz/README.markdown	
+++ b/Fizz Buzz/README.markdown	
@@ -18,7 +18,7 @@ The modulus operator returns the remainder after an integer division. Here is an
 
 | Division      | Division Result            | Modulus         | Modulus Result  |
 | ------------- | -------------------------- | --------------- | ---------------:|
-| 1 / 3       | 0 with a remainder of 3  | 1 % 3         | 3             |
+| 1 / 3       | 0 with a remainder of 3  | 1 % 3         | 1             |
 | 5 / 3       | 1 with a remainder of 2  | 5 % 3         | 2             |
 | 16 / 3      | 5 with a remainder of 1  | 16 % 3        | 1             |
 

From 8596b64870c95cd4b902c46155a2b8a096c7adef Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 20:08:14 +1200
Subject: [PATCH 0394/1679] Changing from xcodebuild to xctool

---
 .travis.yml                | 46 +++++++++++++++++++-------------------
 How to Contribute.markdown |  2 +-
 2 files changed, 24 insertions(+), 24 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index b0210d197..685ad9235 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -3,26 +3,26 @@ osx_image: xcode7.3
 
 script:
 
-- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
\ No newline at end of file
+- xctool test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
+- xctool test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
+- xctool test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index dc1562327..9aa0b07ca 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -31,7 +31,7 @@ For the unit tests:
 - Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/raywenderlich/swift-algorithm-club). Add a line to `.travis.yml` like this:
 
 ```
-- xcodebuild test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
 ```
 
 - Configure the Test project's scheme to run on Travis-CI:

From fa813a787ee5fa5b4f21c8c0c3acf805f01aeffa Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 21:06:08 +1200
Subject: [PATCH 0395/1679] Configure tests projects for running for xctool

---
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/APSPTests.xcscheme | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 15 ++++++--
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/SSSPTests.xcscheme | 34 +++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 34 +++++++++++++++++++
 23 files changed, 760 insertions(+), 3 deletions(-)

diff --git a/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme
index 867745024..cd141a407 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "493D8DDF1CDD2A1C0089795A"
+               BuildableName = "APSPTests.xctest"
+               BlueprintName = "APSPTests"
+               ReferencedContainer = "container:APSP.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "493D8DDF1CDD2A1C0089795A"
+            BuildableName = "APSPTests.xctest"
+            BlueprintName = "APSPTests"
+            ReferencedContainer = "container:APSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "493D8DDF1CDD2A1C0089795A"
+            BuildableName = "APSPTests.xctest"
+            BlueprintName = "APSPTests"
+            ReferencedContainer = "container:APSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 81f549cef..a563876e7 100644
--- a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "B80894DF1C852D100018730E"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "B80894DF1C852D100018730E"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "B80894DF1C852D100018730E"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 19caeb2ad..3d7f342b3 100644
--- a/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -9,9 +9,9 @@
          <BuildActionEntry
             buildForTesting = "YES"
             buildForRunning = "YES"
-            buildForProfiling = "YES"
-            buildForArchiving = "YES"
-            buildForAnalyzing = "YES">
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "4716C7A61C93750500F6C1C0"
@@ -39,6 +39,15 @@
             </BuildableReference>
          </TestableReference>
       </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "4716C7A61C93750500F6C1C0"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </TestAction>
diff --git a/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Shell Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme
index 38b6c1697..6efceaf20 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA29C1CDF86E100522D66"
+               BuildableName = "SSSPTests.xctest"
+               BlueprintName = "SSSPTests"
+               ReferencedContainer = "container:SSSP.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA29C1CDF86E100522D66"
+            BuildableName = "SSSPTests.xctest"
+            BlueprintName = "SSSPTests"
+            ReferencedContainer = "container:SSSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA29C1CDF86E100522D66"
+            BuildableName = "SSSPTests.xctest"
+            BlueprintName = "SSSPTests"
+            ReferencedContainer = "container:SSSP.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">

From d8cf0504a9581e292ae9f48f6f51f7750e4ae5d0 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 21:21:12 +1200
Subject: [PATCH 0396/1679] Added test projects that were missing from
 .travis.yml

---
 .travis.yml                                   |   8 ++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  34 ++++++
 .../xcschemes/GraphTests.xcscheme             |  34 ++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  34 ++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  34 ++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  34 ++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  90 ++++++++++++++++
 .../xcshareddata/xcschemes/Treap.xcscheme     | 101 ++++++++++++++++++
 8 files changed, 369 insertions(+)
 create mode 100644 Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme

diff --git a/.travis.yml b/.travis.yml
index 685ad9235..94fdde89e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,14 +9,19 @@ script:
 - xctool test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Depth-First Search/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests
 - xctool test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
@@ -24,5 +29,8 @@ script:
 - xctool test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xctool test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
diff --git a/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index 8eb3c9fdf..b5a957429 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "49BFA3061CDF886B00522D66"
+               BuildableName = "GraphTests.xctest"
+               BlueprintName = "GraphTests"
+               ReferencedContainer = "container:Graph.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA3061CDF886B00522D66"
+            BuildableName = "GraphTests.xctest"
+            BlueprintName = "GraphTests"
+            ReferencedContainer = "container:Graph.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "49BFA3061CDF886B00522D66"
+            BuildableName = "GraphTests.xctest"
+            BlueprintName = "GraphTests"
+            ReferencedContainer = "container:Graph.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 74dd9450b..8ef8d8581 100644
--- a/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -5,6 +5,22 @@
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
@@ -36,6 +52,15 @@
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -45,6 +70,15 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..3eb165e19
--- /dev/null
+++ b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
+               BuildableName = "TreapTests.xctest"
+               BlueprintName = "TreapTests"
+               ReferencedContainer = "container:Treap.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
+               BuildableName = "TreapTests.xctest"
+               BlueprintName = "TreapTests"
+               ReferencedContainer = "container:Treap.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
+            BuildableName = "TreapTests.xctest"
+            BlueprintName = "TreapTests"
+            ReferencedContainer = "container:Treap.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
+            BuildableName = "TreapTests.xctest"
+            BlueprintName = "TreapTests"
+            ReferencedContainer = "container:Treap.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme
new file mode 100644
index 000000000..566c370e1
--- /dev/null
+++ b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme
@@ -0,0 +1,101 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
+               BuildableName = "Treap.app"
+               BlueprintName = "Treap"
+               ReferencedContainer = "container:Treap.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
+               BuildableName = "TreapTests.xctest"
+               BlueprintName = "TreapTests"
+               ReferencedContainer = "container:Treap.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
+            BuildableName = "Treap.app"
+            BlueprintName = "Treap"
+            ReferencedContainer = "container:Treap.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
+            BuildableName = "Treap.app"
+            BlueprintName = "Treap"
+            ReferencedContainer = "container:Treap.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
+            BuildableName = "Treap.app"
+            BlueprintName = "Treap"
+            ReferencedContainer = "container:Treap.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 298ba4f7179e63da39c5b3bfef43d6bce8a415a3 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 21:23:09 +1200
Subject: [PATCH 0397/1679] Removing super user permission requirement to speed
 up build

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 94fdde89e..d56dd3cc4 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,6 @@
 language: objective-c
 osx_image: xcode7.3
+sudo: false
 
 script:
 

From d4f5614deed539afd342180068400eb1c07c244a Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 21:47:28 +1200
Subject: [PATCH 0398/1679] Removed treap tests as project is a cocoa
 application and causes Travis CI to terminate.

---
 .travis.yml | 1 -
 1 file changed, 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index d56dd3cc4..b14f5d490 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -34,4 +34,3 @@ script:
 - xctool test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xctool test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests

From fe59cad3ed62e4f386114df984feeb0279c465da Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 22:04:09 +1200
Subject: [PATCH 0399/1679] Missing escape character for Depth-First search

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index b14f5d490..0b14e9a40 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -14,7 +14,7 @@ script:
 - xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Depth-First Search/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests
 - xctool test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 3d0655003c8cd97dd3eb1d6b284d6c848f685451 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 22:22:19 +1200
Subject: [PATCH 0400/1679] Making Depth-First search test scheme "shared" so
 that it will run on Travis

---
 .../xcshareddata/xcschemes/Tests.xcscheme     | 99 +++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..e5bd10d97
--- /dev/null
+++ b/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,99 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From e38391108d765dde7be00cff881b1ce5fa50923f Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 22:41:49 +1200
Subject: [PATCH 0401/1679] Turning off auto create schemes for depth first
 search

---
 .../xcshareddata/WorkspaceSettings.xcsettings             | 8 ++++++++
 1 file changed, 8 insertions(+)
 create mode 100644 Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>

From 7839c760fdd77ac964a94c1617c06c0c36a0f34a Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 11 Jun 2016 23:00:35 +1200
Subject: [PATCH 0402/1679] Turning off auto create schemes for bounded
 priority queue

---
 .../xcshareddata/WorkspaceSettings.xcsettings |  8 ++
 .../xcshareddata/xcschemes/Tests.xcscheme     | 90 +++++++++++++++++++
 2 files changed, 98 insertions(+)
 create mode 100644 Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
 create mode 100644 Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..0416248f1
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "B80004B21C83E342001FE2D7"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "B80004B21C83E342001FE2D7"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "B80004B21C83E342001FE2D7"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "B80004B21C83E342001FE2D7"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 9f62cf3d424ba1cf041bd089dfa9f91c4ddae426 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sun, 12 Jun 2016 15:09:59 +1200
Subject: [PATCH 0403/1679] Fix for #144 stack pop function is unnecessarily
 complex

---
 Stack/README.markdown                      | 6 +-----
 Stack/Stack.playground/Contents.swift      | 6 +-----
 Stack/Stack.playground/timeline.xctimeline | 6 ------
 Stack/Stack.swift                          | 8 ++------
 4 files changed, 4 insertions(+), 22 deletions(-)
 delete mode 100644 Stack/Stack.playground/timeline.xctimeline

diff --git a/Stack/README.markdown b/Stack/README.markdown
index 6e832b69b..17770643b 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -57,11 +57,7 @@ public struct Stack<T> {
   }
 
   public mutating func pop() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array.removeLast()
-    }
+    return array.popLast()
   }
 
   public func peek() -> T? {
diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 51567669c..96e86e18a 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -27,11 +27,7 @@ public struct Stack<T> {
   }
   
   public mutating func pop() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array.removeLast()
-    }
+    return array.popLast()
   }
   
   public func peek() -> T? {
diff --git a/Stack/Stack.playground/timeline.xctimeline b/Stack/Stack.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Stack/Stack.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 96c1ff284..454b66fa0 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -19,11 +19,7 @@ public struct Stack<T> {
   }
 
   public mutating func pop() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array.removeLast()
-    }
+    return array.popLast()
   }
 
   public func peek() -> T? {
@@ -34,7 +30,7 @@ public struct Stack<T> {
 extension Stack: SequenceType {
     public func generate() -> AnyGenerator<T> {
         var curr = self
-        return anyGenerator {
+        return AnyGenerator {
             _ -> T? in
             return curr.pop()
         }

From 07de50d9f9ed1fa5d6e0f17b6125e9e5bc748df8 Mon Sep 17 00:00:00 2001
From: "Michael C. Rael" <michael.c.rael@gmail.com>
Date: Sun, 12 Jun 2016 09:52:39 -0600
Subject: [PATCH 0404/1679] Added Greedy Set Cover algorithm (unweighted) as
 extension to Set.

---
 SetCover.swift                                | 33 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  7 ++++
 2 files changed, 40 insertions(+)
 create mode 100644 SetCover.swift

diff --git a/SetCover.swift b/SetCover.swift
new file mode 100644
index 000000000..3a61140a8
--- /dev/null
+++ b/SetCover.swift
@@ -0,0 +1,33 @@
+extension Set {
+    func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
+        var result: [Set<Element>]? = [Set<Element>]()
+        var remainingSet = self
+        
+        func largestIntersectingSet() -> Set<Element>? {
+            var largestIntersectionLength = 0
+            var largestSet: Set<Element>?
+            
+            for set in array {
+                let intersectionLength = remainingSet.intersect(set).count
+                if intersectionLength > largestIntersectionLength {
+                    largestIntersectionLength = intersectionLength
+                    largestSet = set
+                }
+            }
+            
+            return largestSet
+        }
+        
+        while remainingSet.count != 0 {
+            guard let largestSet = largestIntersectingSet() else { break }
+            result!.append(largestSet)
+            remainingSet = remainingSet.subtract(largestSet)
+        }
+        
+        if remainingSet.count != 0 || self.count == 0 {
+            result = nil
+        }
+        
+        return result
+    }
+}
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 1ec94e727..1fdf194f5 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1628,6 +1628,13 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "container:"
+      name = "Set Cover (Unweighted)">
+      <FileRef
+         location = "group:SetCover.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Shell Sort"
       name = "Shell Sort">

From 9c0c08382dfd5da8cbe7f4a7abdb6a04db415fb6 Mon Sep 17 00:00:00 2001
From: "Michael C. Rael" <michael.c.rael@gmail.com>
Date: Sun, 12 Jun 2016 10:08:12 -0600
Subject: [PATCH 0405/1679] Added playground, separating algorthm source from
 playground source.

---
 SetCover.playground/Contents.swift            | 31 +++++++++++++
 .../Sources/RandomArrayOfSets.swift           | 43 +++++++++++++++++++
 SetCover.playground/Sources/SetCover.swift    | 33 ++++++++++++++
 SetCover.playground/contents.xcplayground     |  4 ++
 .../contents.xcworkspacedata                  |  3 ++
 5 files changed, 114 insertions(+)
 create mode 100644 SetCover.playground/Contents.swift
 create mode 100644 SetCover.playground/Sources/RandomArrayOfSets.swift
 create mode 100644 SetCover.playground/Sources/SetCover.swift
 create mode 100644 SetCover.playground/contents.xcplayground

diff --git a/SetCover.playground/Contents.swift b/SetCover.playground/Contents.swift
new file mode 100644
index 000000000..3822f16e3
--- /dev/null
+++ b/SetCover.playground/Contents.swift
@@ -0,0 +1,31 @@
+let universe1 = Set(1...7)
+let array1 = randomArrayOfSets(covering: universe1)
+let cover1 = universe1.cover(from: array1)
+
+let universe2 = Set(1...10)
+let array2: Array<Set<Int>> = [[1,2,3,4,5,6,7], [8,9]]
+let cover2 = universe2.cover(from: array2)
+
+let universe3 = Set(["tall", "heavy"])
+let array3: Array<Set<String>> = [["tall", "light"], ["short", "heavy"], ["tall", "heavy", "young"]]
+let cover3 = universe3.cover(from: array3)
+
+let universe4 = Set(["tall", "heavy", "green"])
+let cover4 = universe4.cover(from: array3)
+
+let universe5: Set<Int> = [16, 32, 64]
+let array5: Array<Set<Int>> = [[16,17,18], [16,32,128], [1,2,3], [32,64,128]]
+let cover5 = universe5.cover(from: array5)
+
+let universe6: Set<Int> = [24, 89, 132, 90, 22]
+let array6 = randomArrayOfSets(covering: universe6)
+let cover6 = universe6.cover(from: array6)
+
+let universe7: Set<String> = ["fast", "cheap", "good"]
+let array7 = randomArrayOfSets(covering: universe7, minArraySizeFactor: 20.0, maxSetSizeFactor: 0.7)
+let cover7 = universe7.cover(from: array7)
+
+let emptySet = Set<Int>()
+let coverTest1 = emptySet.cover(from: array1)
+let coverTest2 = universe1.cover(from: Array<Set<Int>>())
+let coverTest3 = emptySet.cover(from: Array<Set<Int>>())
\ No newline at end of file
diff --git a/SetCover.playground/Sources/RandomArrayOfSets.swift b/SetCover.playground/Sources/RandomArrayOfSets.swift
new file mode 100644
index 000000000..301fbf5f2
--- /dev/null
+++ b/SetCover.playground/Sources/RandomArrayOfSets.swift
@@ -0,0 +1,43 @@
+import Foundation
+
+public func randomArrayOfSets<T>(covering universe: Set<T>,
+                       minArraySizeFactor: Double = 0.8,
+                       maxSetSizeFactor: Double = 0.6) -> Array<Set<T>> {
+    var result = [Set<T>]()
+    var ongoingUnion = Set<T>()
+    
+    let minArraySize = Int(Double(universe.count) * minArraySizeFactor)
+    var maxSetSize = Int(Double(universe.count) * maxSetSizeFactor)
+    if maxSetSize > universe.count {
+        maxSetSize = universe.count
+    }
+    
+    while true {
+        var generatedSet = Set<T>()
+        let targetSetSize = Int(arc4random_uniform(UInt32(maxSetSize)) + 1)
+        
+        while true {
+            let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
+            for (setIndex, value) in universe.enumerate() {
+                if setIndex == randomUniverseIndex {
+                    generatedSet.insert(value)
+                    break
+                }
+            }
+            
+            if generatedSet.count == targetSetSize {
+                result.append(generatedSet)
+                ongoingUnion = ongoingUnion.union(generatedSet)
+                break
+            }
+        }
+        
+        if result.count >= minArraySize {
+            if ongoingUnion == universe {
+                break
+            }
+        }
+    }
+    
+    return result
+}
\ No newline at end of file
diff --git a/SetCover.playground/Sources/SetCover.swift b/SetCover.playground/Sources/SetCover.swift
new file mode 100644
index 000000000..7f4cec314
--- /dev/null
+++ b/SetCover.playground/Sources/SetCover.swift
@@ -0,0 +1,33 @@
+public extension Set {
+    func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
+        var result: [Set<Element>]? = [Set<Element>]()
+        var remainingSet = self
+        
+        func largestIntersectingSet() -> Set<Element>? {
+            var largestIntersectionLength = 0
+            var largestSet: Set<Element>?
+            
+            for set in array {
+                let intersectionLength = remainingSet.intersect(set).count
+                if intersectionLength > largestIntersectionLength {
+                    largestIntersectionLength = intersectionLength
+                    largestSet = set
+                }
+            }
+            
+            return largestSet
+        }
+        
+        while remainingSet.count != 0 {
+            guard let largestSet = largestIntersectingSet() else { break }
+            result!.append(largestSet)
+            remainingSet = remainingSet.subtract(largestSet)
+        }
+        
+        if remainingSet.count != 0 || self.count == 0 {
+            result = nil
+        }
+        
+        return result
+    }
+}
\ No newline at end of file
diff --git a/SetCover.playground/contents.xcplayground b/SetCover.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/SetCover.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 1fdf194f5..e1f4380e7 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1634,6 +1634,9 @@
       <FileRef
          location = "group:SetCover.swift">
       </FileRef>
+      <FileRef
+         location = "group:SetCover.playground">
+      </FileRef>
    </Group>
    <Group
       location = "group:Shell Sort"

From 0139874c00ec5f90a386e76834392f540bde0d75 Mon Sep 17 00:00:00 2001
From: "Michael C. Rael" <michael.c.rael@gmail.com>
Date: Sun, 12 Jun 2016 10:21:44 -0600
Subject: [PATCH 0406/1679] Added directory for all files.

---
 Set Cover (Unweighted)/README.markdown        |  0
 .../SetCover.playground}/Contents.swift       |  0
 .../Sources/RandomArrayOfSets.swift           | 43 +++++++++++++++++++
 .../Sources/SetCover.swift                    | 33 ++++++++++++++
 .../contents.xcplayground                     |  0
 Set Cover (Unweighted)/SetCover.swift         | 33 ++++++++++++++
 .../Sources/RandomArrayOfSets.swift           | 43 -------------------
 SetCover.playground/Sources/SetCover.swift    | 33 --------------
 SetCover.swift                                | 33 --------------
 .../contents.xcworkspacedata                  |  7 ++-
 10 files changed, 114 insertions(+), 111 deletions(-)
 create mode 100644 Set Cover (Unweighted)/README.markdown
 rename {SetCover.playground => Set Cover (Unweighted)/SetCover.playground}/Contents.swift (100%)
 create mode 100644 Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift
 create mode 100644 Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift
 rename {SetCover.playground => Set Cover (Unweighted)/SetCover.playground}/contents.xcplayground (100%)
 create mode 100644 Set Cover (Unweighted)/SetCover.swift
 delete mode 100644 SetCover.playground/Sources/RandomArrayOfSets.swift
 delete mode 100644 SetCover.playground/Sources/SetCover.swift
 delete mode 100644 SetCover.swift

diff --git a/Set Cover (Unweighted)/README.markdown b/Set Cover (Unweighted)/README.markdown
new file mode 100644
index 000000000..e69de29bb
diff --git a/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
similarity index 100%
rename from SetCover.playground/Contents.swift
rename to Set Cover (Unweighted)/SetCover.playground/Contents.swift
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift
new file mode 100644
index 000000000..64253014b
--- /dev/null
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
@@ -0,0 +1,43 @@
+import Foundation
+
+public func randomArrayOfSets<T>(covering universe: Set<T>,
+                              minArraySizeFactor: Double = 0.8,
+                              maxSetSizeFactor: Double = 0.6) -> Array<Set<T>> {
+  var result = [Set<T>]()
+  var ongoingUnion = Set<T>()
+  
+  let minArraySize = Int(Double(universe.count) * minArraySizeFactor)
+  var maxSetSize = Int(Double(universe.count) * maxSetSizeFactor)
+  if maxSetSize > universe.count {
+    maxSetSize = universe.count
+  }
+  
+  while true {
+    var generatedSet = Set<T>()
+    let targetSetSize = Int(arc4random_uniform(UInt32(maxSetSize)) + 1)
+    
+    while true {
+      let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
+      for (setIndex, value) in universe.enumerate() {
+        if setIndex == randomUniverseIndex {
+          generatedSet.insert(value)
+          break
+        }
+      }
+      
+      if generatedSet.count == targetSetSize {
+        result.append(generatedSet)
+        ongoingUnion = ongoingUnion.union(generatedSet)
+        break
+      }
+    }
+    
+    if result.count >= minArraySize {
+      if ongoingUnion == universe {
+        break
+      }
+    }
+  }
+  
+  return result
+}
\ No newline at end of file
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift
new file mode 100644
index 000000000..8e608cb52
--- /dev/null
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
@@ -0,0 +1,33 @@
+public extension Set {
+  func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
+    var result: [Set<Element>]? = [Set<Element>]()
+    var remainingSet = self
+    
+    func largestIntersectingSet() -> Set<Element>? {
+      var largestIntersectionLength = 0
+      var largestSet: Set<Element>?
+      
+      for set in array {
+        let intersectionLength = remainingSet.intersect(set).count
+        if intersectionLength > largestIntersectionLength {
+          largestIntersectionLength = intersectionLength
+          largestSet = set
+        }
+      }
+      
+      return largestSet
+    }
+    
+    while remainingSet.count != 0 {
+      guard let largestSet = largestIntersectingSet() else { break }
+      result!.append(largestSet)
+      remainingSet = remainingSet.subtract(largestSet)
+    }
+    
+    if remainingSet.count != 0 || self.count == 0 {
+      result = nil
+    }
+    
+    return result
+  }
+}
\ No newline at end of file
diff --git a/SetCover.playground/contents.xcplayground b/Set Cover (Unweighted)/SetCover.playground/contents.xcplayground
similarity index 100%
rename from SetCover.playground/contents.xcplayground
rename to Set Cover (Unweighted)/SetCover.playground/contents.xcplayground
diff --git a/Set Cover (Unweighted)/SetCover.swift b/Set Cover (Unweighted)/SetCover.swift
new file mode 100644
index 000000000..58ffade9d
--- /dev/null
+++ b/Set Cover (Unweighted)/SetCover.swift	
@@ -0,0 +1,33 @@
+extension Set {
+  func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
+    var result: [Set<Element>]? = [Set<Element>]()
+    var remainingSet = self
+    
+    func largestIntersectingSet() -> Set<Element>? {
+      var largestIntersectionLength = 0
+      var largestSet: Set<Element>?
+      
+      for set in array {
+        let intersectionLength = remainingSet.intersect(set).count
+        if intersectionLength > largestIntersectionLength {
+          largestIntersectionLength = intersectionLength
+          largestSet = set
+        }
+      }
+      
+      return largestSet
+    }
+    
+    while remainingSet.count != 0 {
+      guard let largestSet = largestIntersectingSet() else { break }
+      result!.append(largestSet)
+      remainingSet = remainingSet.subtract(largestSet)
+    }
+    
+    if remainingSet.count != 0 || self.count == 0 {
+      result = nil
+    }
+    
+    return result
+  }
+}
\ No newline at end of file
diff --git a/SetCover.playground/Sources/RandomArrayOfSets.swift b/SetCover.playground/Sources/RandomArrayOfSets.swift
deleted file mode 100644
index 301fbf5f2..000000000
--- a/SetCover.playground/Sources/RandomArrayOfSets.swift
+++ /dev/null
@@ -1,43 +0,0 @@
-import Foundation
-
-public func randomArrayOfSets<T>(covering universe: Set<T>,
-                       minArraySizeFactor: Double = 0.8,
-                       maxSetSizeFactor: Double = 0.6) -> Array<Set<T>> {
-    var result = [Set<T>]()
-    var ongoingUnion = Set<T>()
-    
-    let minArraySize = Int(Double(universe.count) * minArraySizeFactor)
-    var maxSetSize = Int(Double(universe.count) * maxSetSizeFactor)
-    if maxSetSize > universe.count {
-        maxSetSize = universe.count
-    }
-    
-    while true {
-        var generatedSet = Set<T>()
-        let targetSetSize = Int(arc4random_uniform(UInt32(maxSetSize)) + 1)
-        
-        while true {
-            let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
-            for (setIndex, value) in universe.enumerate() {
-                if setIndex == randomUniverseIndex {
-                    generatedSet.insert(value)
-                    break
-                }
-            }
-            
-            if generatedSet.count == targetSetSize {
-                result.append(generatedSet)
-                ongoingUnion = ongoingUnion.union(generatedSet)
-                break
-            }
-        }
-        
-        if result.count >= minArraySize {
-            if ongoingUnion == universe {
-                break
-            }
-        }
-    }
-    
-    return result
-}
\ No newline at end of file
diff --git a/SetCover.playground/Sources/SetCover.swift b/SetCover.playground/Sources/SetCover.swift
deleted file mode 100644
index 7f4cec314..000000000
--- a/SetCover.playground/Sources/SetCover.swift
+++ /dev/null
@@ -1,33 +0,0 @@
-public extension Set {
-    func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
-        var result: [Set<Element>]? = [Set<Element>]()
-        var remainingSet = self
-        
-        func largestIntersectingSet() -> Set<Element>? {
-            var largestIntersectionLength = 0
-            var largestSet: Set<Element>?
-            
-            for set in array {
-                let intersectionLength = remainingSet.intersect(set).count
-                if intersectionLength > largestIntersectionLength {
-                    largestIntersectionLength = intersectionLength
-                    largestSet = set
-                }
-            }
-            
-            return largestSet
-        }
-        
-        while remainingSet.count != 0 {
-            guard let largestSet = largestIntersectingSet() else { break }
-            result!.append(largestSet)
-            remainingSet = remainingSet.subtract(largestSet)
-        }
-        
-        if remainingSet.count != 0 || self.count == 0 {
-            result = nil
-        }
-        
-        return result
-    }
-}
\ No newline at end of file
diff --git a/SetCover.swift b/SetCover.swift
deleted file mode 100644
index 3a61140a8..000000000
--- a/SetCover.swift
+++ /dev/null
@@ -1,33 +0,0 @@
-extension Set {
-    func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
-        var result: [Set<Element>]? = [Set<Element>]()
-        var remainingSet = self
-        
-        func largestIntersectingSet() -> Set<Element>? {
-            var largestIntersectionLength = 0
-            var largestSet: Set<Element>?
-            
-            for set in array {
-                let intersectionLength = remainingSet.intersect(set).count
-                if intersectionLength > largestIntersectionLength {
-                    largestIntersectionLength = intersectionLength
-                    largestSet = set
-                }
-            }
-            
-            return largestSet
-        }
-        
-        while remainingSet.count != 0 {
-            guard let largestSet = largestIntersectingSet() else { break }
-            result!.append(largestSet)
-            remainingSet = remainingSet.subtract(largestSet)
-        }
-        
-        if remainingSet.count != 0 || self.count == 0 {
-            result = nil
-        }
-        
-        return result
-    }
-}
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index e1f4380e7..4e0f19dc2 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1632,10 +1632,13 @@
       location = "container:"
       name = "Set Cover (Unweighted)">
       <FileRef
-         location = "group:SetCover.swift">
+         location = "group:Set Cover (Unweighted)/README.markdown">
       </FileRef>
       <FileRef
-         location = "group:SetCover.playground">
+         location = "group:Set Cover (Unweighted)/SetCover.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Set Cover (Unweighted)/SetCover.swift">
       </FileRef>
    </Group>
    <Group

From e963e97214cd436909b5d498f1fb217ad98ccc20 Mon Sep 17 00:00:00 2001
From: "Michael C. Rael" <michael.c.rael@gmail.com>
Date: Sun, 12 Jun 2016 10:36:12 -0600
Subject: [PATCH 0407/1679] Started work on the README file.

---
 Set Cover (Unweighted)/README.markdown | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/Set Cover (Unweighted)/README.markdown b/Set Cover (Unweighted)/README.markdown
index e69de29bb..68538cc60 100644
--- a/Set Cover (Unweighted)/README.markdown	
+++ b/Set Cover (Unweighted)/README.markdown	
@@ -0,0 +1,13 @@
+# Set Cover (Unweighted)
+
+A cover 
+
+If you have a set (also called the universe in the mathematical descriptions of the problem)
+
+## The algorithm
+
+## See also
+
+[Set cover problem on Wikipedia](https://en.wikipedia.org/wiki/Set_cover_problem)
+
+*Written for Swift Algorithm Club by [Michael C. Rael](https://github.com/mrael2)*
\ No newline at end of file

From a573bb240c2d5e8acf90faf599c59f8def6d7461 Mon Sep 17 00:00:00 2001
From: "Michael C. Rael" <michael.c.rael@gmail.com>
Date: Sun, 12 Jun 2016 11:34:31 -0600
Subject: [PATCH 0408/1679] Work in progress on README.

---
 Set Cover (Unweighted)/README.markdown | 18 ++++++++++++++++--
 1 file changed, 16 insertions(+), 2 deletions(-)

diff --git a/Set Cover (Unweighted)/README.markdown b/Set Cover (Unweighted)/README.markdown
index 68538cc60..48b5f3bfa 100644
--- a/Set Cover (Unweighted)/README.markdown	
+++ b/Set Cover (Unweighted)/README.markdown	
@@ -1,11 +1,25 @@
 # Set Cover (Unweighted)
 
-A cover 
+If you have a group of sets, this algorithm finds a subset of those sets within that group whose union will cover an initial set that you're trying to match. The initial set is also known as the universe.
 
-If you have a set (also called the universe in the mathematical descriptions of the problem)
+For example, suppose you have a universe of `{1, 5, 7}` and you want to find the sets which cover the universe within the following group of sets:
+
+> {8, 4, 2}
+> {3, 1}
+> {7, 6, 5, 4}
+> {2}
+> {1, 2, 3}
+
+You can see that the sets `{3, 1} {7, 6, 5, 4}` when unioned together will cover the universe of `{1, 5, 7}`. Yes, there may be additional elements in the sets returned by the algorithm, but every element in the universe is represented.
+
+If there is no cover within the group of sets, the function returns nil. For example, if your universe is `{7, 9}`, there is no combination of sets within the grouping above that will yield a cover.
 
 ## The algorithm
 
+The Greedy Set Cover algorithm (unweighted) is provided here. It's known as greedy because it uses the largest intersecting set from the group of sets first before examining other sets in the group.
+
+The function (named `cover`) is provided as an extension of the Swift type `Set`. The function takes a single parameter, which is an array of sets. This array represents the group, and the set itself represents the universe.
+
 ## See also
 
 [Set cover problem on Wikipedia](https://en.wikipedia.org/wiki/Set_cover_problem)

From 0ecf394d200cd6866d8443b72d5fd16430506f1a Mon Sep 17 00:00:00 2001
From: Michal Dabrowski <michal.dabrowski@daftcode.pl>
Date: Tue, 14 Jun 2016 20:45:43 +0200
Subject: [PATCH 0409/1679] Added, tested and implemented edges from vertex
 function in graph

---
 Graph/Graph/AdjacencyListGraph.swift   |   8 +-
 Graph/Graph/AdjacencyMatrixGraph.swift |  15 +++-
 Graph/Graph/Graph.swift                |   7 +-
 Graph/GraphTests/GraphTests.swift      | 103 ++++++++++++++++++++++++-
 4 files changed, 126 insertions(+), 7 deletions(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index fddd04033..562a48514 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -26,11 +26,11 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
 
   private var adjacencyList: [EdgeList<T>] = []
 
-  public override init() {
+  public required init() {
     super.init()
   }
 
-  public override init(fromGraph graph: AbstractGraph<T>) {
+  public required init(fromGraph graph: AbstractGraph<T>) {
     super.init(fromGraph: graph)
   }
 
@@ -107,6 +107,10 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
     return nil
   }
 
+  public override func edgesFrom(sourceVertex: Vertex<T>) -> [Edge<T>] {
+    return adjacencyList[sourceVertex.index].edges ?? []
+  }
+
   public override var description: String {
     get {
       var rows = [String]()
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index b2047797f..6b19bcfcc 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -14,11 +14,11 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
   private var adjacencyMatrix: [[Double?]] = []
   private var _vertices: [Vertex<T>] = []
 
-  public override init() {
+  public required init() {
     super.init()
   }
 
-  public override init(fromGraph graph: AbstractGraph<T>) {
+  public required init(fromGraph graph: AbstractGraph<T>) {
     super.init(fromGraph: graph)
   }
 
@@ -84,6 +84,17 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
     return adjacencyMatrix[sourceVertex.index][destinationVertex.index]
   }
 
+  public override func edgesFrom(sourceVertex: Vertex<T>) -> [Edge<T>] {
+    var outEdges = [Edge<T>]()
+    let fromIndex = sourceVertex.index
+    for column in 0..<adjacencyMatrix.count {
+      if let weight = adjacencyMatrix[fromIndex][column] {
+        outEdges.append(Edge(from: sourceVertex, to: vertices[column], weight: weight))
+      }
+    }
+    return outEdges
+  }
+
   public override var description: String {
     get {
       var grid = [String]()
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
index 4e27e989e..75b4bddec 100644
--- a/Graph/Graph/Graph.swift
+++ b/Graph/Graph/Graph.swift
@@ -9,9 +9,9 @@ import Foundation
 
 public class AbstractGraph<T where T: Equatable, T: Hashable>: CustomStringConvertible {
 
-  public init() {}
+  public required init() {}
 
-  public init(fromGraph graph: AbstractGraph<T>) {
+  public required init(fromGraph graph: AbstractGraph<T>) {
     for edge in graph.edges {
       let from = createVertex(edge.from.data)
       let to = createVertex(edge.to.data)
@@ -56,4 +56,7 @@ public class AbstractGraph<T where T: Equatable, T: Hashable>: CustomStringConve
     fatalError("abstract function called")
   }
 
+  public func edgesFrom(sourceVertex: Vertex<T>) -> [Edge<T>] {
+    fatalError("abstract function called")
+  }
 }
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index e6360754e..3b9c4645c 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -53,5 +53,106 @@ class GraphTests: XCTestCase {
       XCTAssertEqual(graph.vertices.count, 1, "Graph should only contain one vertex after trying to create two vertices with identical data")
     }
   }
-    
+
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(graphType: AbstractGraph<Int>.Type) {
+    let graph = graphType.init()
+
+    let a = graph.createVertex(1)
+    let b = graph.createVertex(2)
+
+    graph.addDirectedEdge(a, to: b, withWeight: 1.0)
+
+    let edgesFromA = graph.edgesFrom(a)
+    let edgesFromB = graph.edgesFrom(b)
+
+    XCTAssertEqual(edgesFromA.count, 1)
+    XCTAssertEqual(edgesFromB.count, 0)
+
+    XCTAssertEqual(edgesFromA.first?.to, b)
+  }
+
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(graphType: AbstractGraph<Int>.Type) {
+    let graph = graphType.init()
+
+    let a = graph.createVertex(1)
+    let b = graph.createVertex(2)
+
+    graph.addUndirectedEdge((a, b), withWeight: 1.0)
+
+    let edgesFromA = graph.edgesFrom(a)
+    let edgesFromB = graph.edgesFrom(b)
+
+    XCTAssertEqual(edgesFromA.count, 1)
+    XCTAssertEqual(edgesFromB.count, 1)
+
+    XCTAssertEqual(edgesFromA.first?.to, b)
+    XCTAssertEqual(edgesFromB.first?.to, a)
+  }
+
+  func testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(graphType: AbstractGraph<Int>.Type) {
+    let graph = graphType.init()
+
+    let a = graph.createVertex(1)
+    let b = graph.createVertex(2)
+
+    XCTAssertEqual(graph.edgesFrom(a).count, 0)
+    XCTAssertEqual(graph.edgesFrom(b).count, 0)
+  }
+
+  func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(graphType: AbstractGraph<Int>.Type) {
+    let graph = graphType.init()
+    let verticesCount = 100
+    var vertices: [Vertex<Int>] = []
+
+    for i in 0..<verticesCount {
+      vertices.append(graph.createVertex(i))
+    }
+
+    for i in 0..<verticesCount {
+      for j in i+1..<verticesCount {
+        graph.addDirectedEdge(vertices[i], to: vertices[j], withWeight: 1)
+      }
+    }
+
+    for i in 0..<verticesCount {
+      let outEdges = graph.edgesFrom(vertices[i])
+      let toVertices = outEdges.map {return $0.to}
+      XCTAssertEqual(outEdges.count, verticesCount - i - 1)
+      for j in i+1..<verticesCount {
+        XCTAssertTrue(toVertices.contains(vertices[j]))
+      }
+    }
+  }
+
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedMatrixGraph() {
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(AdjacencyMatrixGraph<Int>)
+  }
+
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedMatrixGraph() {
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(AdjacencyMatrixGraph<Int>)
+  }
+
+  func testEdgesFromReturnsNoInNoEdgeMatrixGraph() {
+    testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(AdjacencyMatrixGraph<Int>)
+  }
+
+  func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedMatrixGraph() {
+    testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(AdjacencyMatrixGraph<Int>)
+  }
+
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedListGraph() {
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(AdjacencyListGraph<Int>)
+  }
+
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedListGraph() {
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(AdjacencyListGraph<Int>)
+  }
+
+  func testEdgesFromReturnsNoInNoEdgeListGraph() {
+    testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(AdjacencyListGraph<Int>)
+  }
+
+  func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedListGraph() {
+    testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(AdjacencyListGraph<Int>)
+  }
 }

From 5005c28b606b61fc26d73f03f350cd3c97e56b2f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Viktor?= <aqviktor@gmail.com>
Date: Fri, 17 Jun 2016 10:39:54 +0200
Subject: [PATCH 0410/1679] Added B-Tree

---
 BTree/BTree.playground/Contents.swift         |  10 +
 BTree/BTree.playground/Sources/BTree.swift    | 473 ++++++++++++++++++
 BTree/BTree.playground/contents.xcplayground  |   4 +
 .../contents.xcworkspacedata                  |   7 +
 BTree/BTree.swift                             | 473 ++++++++++++++++++
 BTree/Images/BTree20.png                      | Bin 0 -> 16592 bytes
 BTree/Images/InsertionSplit.png               | Bin 0 -> 17998 bytes
 BTree/Images/MergingNodes.png                 | Bin 0 -> 8359 bytes
 BTree/Images/MovingKey.png                    | Bin 0 -> 12354 bytes
 BTree/Images/Node.png                         | Bin 0 -> 6255 bytes
 BTree/README.md                               | 172 +++++++
 BTree/Tests/Tests.xcodeproj/project.pbxproj   | 268 ++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     | 100 ++++
 BTree/Tests/Tests/BTreeNodeTests.swift        |  54 ++
 BTree/Tests/Tests/BTreeTests.swift            | 257 ++++++++++
 BTree/Tests/Tests/Info.plist                  |  24 +
 17 files changed, 1849 insertions(+)
 create mode 100644 BTree/BTree.playground/Contents.swift
 create mode 100644 BTree/BTree.playground/Sources/BTree.swift
 create mode 100644 BTree/BTree.playground/contents.xcplayground
 create mode 100644 BTree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 BTree/BTree.swift
 create mode 100644 BTree/Images/BTree20.png
 create mode 100644 BTree/Images/InsertionSplit.png
 create mode 100644 BTree/Images/MergingNodes.png
 create mode 100644 BTree/Images/MovingKey.png
 create mode 100644 BTree/Images/Node.png
 create mode 100644 BTree/README.md
 create mode 100644 BTree/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 BTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 BTree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 BTree/Tests/Tests/BTreeNodeTests.swift
 create mode 100644 BTree/Tests/Tests/BTreeTests.swift
 create mode 100644 BTree/Tests/Tests/Info.plist

diff --git a/BTree/BTree.playground/Contents.swift b/BTree/BTree.playground/Contents.swift
new file mode 100644
index 000000000..7d2973f77
--- /dev/null
+++ b/BTree/BTree.playground/Contents.swift
@@ -0,0 +1,10 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+let bTree = BTree<Int, Int>(order: 1)!
+
+bTree.insertValue(1, forKey: 1)
+bTree.insertValue(2, forKey: 2)
+bTree.insertValue(3, forKey: 3)
+bTree.insertValue(4, forKey: 4)
diff --git a/BTree/BTree.playground/Sources/BTree.swift b/BTree/BTree.playground/Sources/BTree.swift
new file mode 100644
index 000000000..16c4eabe4
--- /dev/null
+++ b/BTree/BTree.playground/Sources/BTree.swift
@@ -0,0 +1,473 @@
+// The MIT License (MIT)
+
+// Copyright (c) 2016 Viktor Szilárd Simkó (aqviktor[at]gmail.com)
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+/*
+ B-Tree
+	
+ A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
+ */
+
+// MARK: - BTreeNode class
+
+class BTreeNode<Key: Comparable, Value> {
+  unowned var ownerTree: BTree<Key, Value>
+  
+  private var keys = [Key]()
+  var values = [Value]()
+  var children: [BTreeNode]?
+  
+  var isLeaf: Bool {
+    return children == nil
+  }
+  
+  var numberOfKeys: Int {
+    return keys.count
+  }
+  
+  init(ownerTree: BTree<Key, Value>) {
+    self.ownerTree = ownerTree
+  }
+  
+  convenience init(ownerTree: BTree<Key, Value>, keys: [Key],
+                   values: [Value], children: [BTreeNode]? = nil) {
+    self.init(ownerTree: ownerTree)
+    self.keys += keys
+    self.values += values
+    self.children = children
+  }
+}
+
+// MARK: BTreeNode extesnion: Searching
+
+extension BTreeNode {
+ func valueForKey(key: Key) -> Value? {
+    var index = keys.startIndex
+    
+    while index.successor() < keys.endIndex && keys[index] < key {
+      index = index.successor()
+    }
+    
+    if key == keys[index] {
+      return values[index]
+    } else if key < keys[index] {
+      return children?[index].valueForKey(key)
+    } else {
+      return children?[index.successor()].valueForKey(key)
+    }
+  }
+}
+
+// MARK: BTreeNode extension: Travelsals
+
+extension BTreeNode {
+  func traverseKeysInOrder(@noescape process: Key -> Void) {
+    for i in 0..<numberOfKeys {
+      children?[i].traverseKeysInOrder(process)
+      process(keys[i])
+    }
+    
+    children?.last?.traverseKeysInOrder(process)
+  }
+}
+
+// MARK: BTreeNode extension: Insertion
+
+extension BTreeNode {
+  func insertValue(value: Value, forKey key: Key) {
+    var index = keys.startIndex
+    
+    while index < keys.endIndex && keys[index] < key {
+      index = index.successor()
+    }
+    
+    if index < keys.endIndex && keys[index] == key {
+      values[index] = value
+      return
+    }
+    
+    if isLeaf {
+      keys.insert(key, atIndex: index)
+      values.insert(value, atIndex: index)
+      ownerTree.numberOfKeys += 1
+    } else {
+      children![index].insertValue(value, forKey: key)
+      if children![index].numberOfKeys > ownerTree.order * 2 {
+        splitChild(children![index], atIndex: index)
+      }
+    }
+  }
+  
+  private func splitChild(child: BTreeNode, atIndex index: Int) {
+    let middleIndex = child.numberOfKeys / 2
+    keys.insert(child.keys[middleIndex], atIndex: index)
+    values.insert(child.values[middleIndex], atIndex: index)
+    child.keys.removeAtIndex(middleIndex)
+    child.values.removeAtIndex(middleIndex)
+    
+    let rightSibling = BTreeNode(
+      ownerTree: ownerTree,
+      keys: Array(child.keys[middleIndex..<child.keys.endIndex]),
+      values: Array(child.values[middleIndex..<child.values.endIndex])
+    )
+    child.keys.removeRange(middleIndex..<child.keys.endIndex)
+    child.values.removeRange(middleIndex..<child.values.endIndex)
+    
+    children!.insert(rightSibling, atIndex: index.successor())
+    
+    if child.children != nil {
+      rightSibling.children = Array(
+        child.children![middleIndex.successor()..<child.children!.endIndex]
+      )
+      child.children!.removeRange(middleIndex.successor()..<child.children!.endIndex)
+    }
+  }
+}
+
+// MARK: BTreeNode extension: Removal
+
+private enum BTreeNodePosition {
+  case Left
+  case Right
+}
+
+extension BTreeNode {
+  private var inorderPredecessor: BTreeNode {
+    if isLeaf {
+      return self
+    } else {
+      return children!.last!.inorderPredecessor
+    }
+  }
+  
+  func removeKey(key: Key) {
+    var index = keys.startIndex
+    
+    while index.successor() < keys.endIndex && keys[index] < key {
+      index = index.successor()
+    }
+    
+    if keys[index] == key {
+      if isLeaf {
+        keys.removeAtIndex(index)
+        values.removeAtIndex(index)
+        ownerTree.numberOfKeys -= 1
+      } else {
+        let predecessor = children![index].inorderPredecessor
+        keys[index] = predecessor.keys.last!
+        values[index] = predecessor.values.last!
+        children![index].removeKey(keys[index])
+        if children![index].numberOfKeys < ownerTree.order {
+          fixChildWithLessNodesThanOrder(children![index], atIndex: index)
+        }
+      }
+    } else if key < keys[index] {
+      // We should go to left child...
+      
+      if let leftChild = children?[index] {
+        leftChild.removeKey(key)
+        if leftChild.numberOfKeys < ownerTree.order {
+          fixChildWithLessNodesThanOrder(leftChild, atIndex: index)
+        }
+      } else {
+        print("The key:\(key) is not in the tree.")
+      }
+    } else {
+      // We should go to right child...
+      
+      if let rightChild = children?[index.successor()] {
+        rightChild.removeKey(key)
+        if rightChild.numberOfKeys < ownerTree.order {
+          fixChildWithLessNodesThanOrder(rightChild, atIndex: index.successor())
+        }
+      } else {
+        print("The key:\(key) is not in the tree")
+      }
+    }
+  }
+  
+  private func fixChildWithLessNodesThanOrder(child: BTreeNode, atIndex index: Int) {
+    
+    if index.predecessor() >= 0 &&
+       children![index.predecessor()].numberOfKeys > ownerTree.order {
+      
+      moveKeyAtIndex(index.predecessor(), toNode: child,
+                     fromNode: children![index.predecessor()], atPosition: .Left)
+      
+    } else if index.successor() < children!.count &&
+              children![index.successor()].numberOfKeys > ownerTree.order {
+      
+      moveKeyAtIndex(index, toNode: child,
+                     fromNode: children![index.successor()], atPosition: .Right)
+      
+    } else if index.predecessor() >= 0 {
+      mergeChild(child, withIndex: index, toNodeAtPosition: .Left)
+    } else {
+      mergeChild(child, withIndex: index, toNodeAtPosition: .Right)
+    }
+  }
+  
+  private func moveKeyAtIndex(keyIndex: Int, toNode targetNode: BTreeNode,
+                             fromNode: BTreeNode, atPosition position: BTreeNodePosition) {
+    switch position {
+    case .Left:
+      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.startIndex)
+      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.startIndex)
+      keys[keyIndex] = fromNode.keys.last!
+      values[keyIndex] = fromNode.values.last!
+      fromNode.keys.removeLast()
+      fromNode.values.removeLast()
+      if !targetNode.isLeaf {
+        targetNode.children!.insert(fromNode.children!.last!,
+                                    atIndex: targetNode.children!.startIndex)
+        fromNode.children!.removeLast()
+      }
+      
+    case .Right:
+      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.endIndex)
+      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.endIndex)
+      keys[keyIndex] = fromNode.keys.first!
+      values[keyIndex] = fromNode.values.first!
+      fromNode.keys.removeFirst()
+      fromNode.values.removeFirst()
+      if !targetNode.isLeaf {
+        targetNode.children!.insert(fromNode.children!.first!,
+                                    atIndex: targetNode.children!.endIndex)
+        fromNode.children!.removeFirst()
+      }
+    }
+  }
+  
+  private func mergeChild(child: BTreeNode, withIndex index: Int, toNodeAtPosition position: BTreeNodePosition) {
+    switch position {
+    case .Left:
+      // We can merge to the left sibling
+      
+      children![index.predecessor()].keys = children![index.predecessor()].keys +
+        [keys[index.predecessor()]] + child.keys
+      
+      children![index.predecessor()].values = children![index.predecessor()].values +
+        [values[index.predecessor()]] + child.values
+      
+      keys.removeAtIndex(index.predecessor())
+      values.removeAtIndex(index.predecessor())
+      
+      if !child.isLeaf {
+        children![index.predecessor()].children =
+          children![index.predecessor()].children! + child.children!
+      }
+      
+    case .Right:
+      // We should merge to the right sibling
+      
+      children![index.successor()].keys = child.keys + [keys[index]] +
+        children![index.successor()].keys
+      
+      children![index.successor()].values = child.values + [values[index]] +
+        children![index.successor()].values
+      
+      keys.removeAtIndex(index)
+      values.removeAtIndex(index)
+      
+      if !child.isLeaf {
+        children![index.successor()].children =
+          child.children! + children![index.successor()].children!
+      }
+    }
+    children!.removeAtIndex(index)
+  }
+}
+
+// MARK: BTreeNode extension: Conversion
+
+extension BTreeNode {
+  func inorderArrayFromKeys() -> [Key] {
+    var array = [Key] ()
+    
+    for i in 0..<numberOfKeys {
+      if let returnedArray = children?[i].inorderArrayFromKeys() {
+        array += returnedArray
+      }
+      array += [keys[i]]
+    }
+    
+    if let returnedArray = children?.last?.inorderArrayFromKeys() {
+      array += returnedArray
+    }
+    
+    return array
+  }
+}
+
+// MARK: BTreeNode extension: Description
+
+extension BTreeNode: CustomStringConvertible {
+  var description: String {
+    var str = "\(keys)"
+    
+    if !isLeaf {
+      for child in children! {
+        str += child.description
+      }
+    }
+    
+    return str
+  }
+}
+
+// MARK: - BTree class
+
+public class BTree<Key: Comparable, Value> {
+  
+  /**
+   The order of the B-Tree
+   
+   The number of keys in every node should be in the [order, 2*order] range,
+   except the root node which is allowed to contain less keys than the value of order.
+   */
+  public let order: Int
+  
+  /// The root node of the tree
+  var rootNode: BTreeNode<Key, Value>!
+  
+  private(set) public var numberOfKeys = 0
+  
+  /**
+   Designated initializer for the tree
+   
+   - parameters:
+   - order: The order of the tree.
+   */
+  public init?(order: Int) {
+    guard order > 0 else {
+      print("Order has to be greater than 0.")
+      return nil
+    }
+    self.order = order
+    rootNode = BTreeNode<Key, Value>(ownerTree: self)
+  }
+}
+
+// MARK: BTree extension: Travelsals
+
+extension BTree {
+  public func traverseKeysInOrder(@noescape process: Key -> Void) {
+    rootNode.traverseKeysInOrder(process)
+  }
+}
+
+// MARK: BTree extension: Subscript
+
+extension BTree {
+  public subscript (key: Key) -> Value? {
+    return valueForKey(key)
+  }
+}
+
+// MARK: BTree extension: Value for Key
+
+extension BTree {
+  public func valueForKey(key: Key) -> Value? {
+    guard rootNode.numberOfKeys > 0 else {
+      return nil
+    }
+    
+    return rootNode.valueForKey(key)
+  }
+}
+
+// MARK: BTree extension: Insertion
+
+extension BTree {
+  public func insertValue(value: Value, forKey key: Key) {
+    rootNode.insertValue(value, forKey: key)
+    
+    if rootNode.numberOfKeys > order * 2 {
+      splitRoot()
+    }
+  }
+  
+  private func splitRoot() {
+    let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
+    
+    let newRoot = BTreeNode<Key, Value>(
+      ownerTree: self,
+      keys: [rootNode.keys[middleIndexOfOldRoot]],
+      values: [rootNode.values[middleIndexOfOldRoot]],
+      children: [rootNode]
+    )
+    rootNode.keys.removeAtIndex(middleIndexOfOldRoot)
+    rootNode.values.removeAtIndex(middleIndexOfOldRoot)
+    
+    let newRightChild = BTreeNode<Key, Value>(
+      ownerTree: self,
+      keys: Array(rootNode.keys[middleIndexOfOldRoot..<rootNode.keys.endIndex]),
+      values: Array(rootNode.values[middleIndexOfOldRoot..<rootNode.values.endIndex])
+    )
+    rootNode.keys.removeRange(middleIndexOfOldRoot..<rootNode.keys.endIndex)
+    rootNode.values.removeRange(middleIndexOfOldRoot..<rootNode.values.endIndex)
+    
+    if rootNode.children != nil {
+      newRightChild.children = Array(
+        rootNode.children![middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex]
+      )
+      rootNode.children!.removeRange(
+        middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex
+      )
+    }
+    
+    newRoot.children!.append(newRightChild)
+    rootNode = newRoot
+  }
+}
+
+// MARK: BTree extension: Removal
+
+extension BTree {
+  public func removeKey(key: Key) {
+    guard rootNode.numberOfKeys > 0 else {
+      return
+    }
+    
+    rootNode.removeKey(key)
+    
+    if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
+      rootNode = rootNode.children!.first!
+    }
+  }
+}
+
+// MARK: BTree extension: Conversion
+
+extension BTree {
+  public func inorderArrayFromKeys() -> [Key] {
+    return rootNode.inorderArrayFromKeys()
+  }
+}
+
+// MARK: BTree extension: Decription
+
+extension BTree: CustomStringConvertible {
+  // Returns a String containing the preorder representation of the nodes
+  public var description: String {
+    return rootNode.description
+  }
+}
diff --git a/BTree/BTree.playground/contents.xcplayground b/BTree/BTree.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/BTree/BTree.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/BTree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata b/BTree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/BTree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/BTree/BTree.swift b/BTree/BTree.swift
new file mode 100644
index 000000000..16c4eabe4
--- /dev/null
+++ b/BTree/BTree.swift
@@ -0,0 +1,473 @@
+// The MIT License (MIT)
+
+// Copyright (c) 2016 Viktor Szilárd Simkó (aqviktor[at]gmail.com)
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+/*
+ B-Tree
+	
+ A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
+ */
+
+// MARK: - BTreeNode class
+
+class BTreeNode<Key: Comparable, Value> {
+  unowned var ownerTree: BTree<Key, Value>
+  
+  private var keys = [Key]()
+  var values = [Value]()
+  var children: [BTreeNode]?
+  
+  var isLeaf: Bool {
+    return children == nil
+  }
+  
+  var numberOfKeys: Int {
+    return keys.count
+  }
+  
+  init(ownerTree: BTree<Key, Value>) {
+    self.ownerTree = ownerTree
+  }
+  
+  convenience init(ownerTree: BTree<Key, Value>, keys: [Key],
+                   values: [Value], children: [BTreeNode]? = nil) {
+    self.init(ownerTree: ownerTree)
+    self.keys += keys
+    self.values += values
+    self.children = children
+  }
+}
+
+// MARK: BTreeNode extesnion: Searching
+
+extension BTreeNode {
+ func valueForKey(key: Key) -> Value? {
+    var index = keys.startIndex
+    
+    while index.successor() < keys.endIndex && keys[index] < key {
+      index = index.successor()
+    }
+    
+    if key == keys[index] {
+      return values[index]
+    } else if key < keys[index] {
+      return children?[index].valueForKey(key)
+    } else {
+      return children?[index.successor()].valueForKey(key)
+    }
+  }
+}
+
+// MARK: BTreeNode extension: Travelsals
+
+extension BTreeNode {
+  func traverseKeysInOrder(@noescape process: Key -> Void) {
+    for i in 0..<numberOfKeys {
+      children?[i].traverseKeysInOrder(process)
+      process(keys[i])
+    }
+    
+    children?.last?.traverseKeysInOrder(process)
+  }
+}
+
+// MARK: BTreeNode extension: Insertion
+
+extension BTreeNode {
+  func insertValue(value: Value, forKey key: Key) {
+    var index = keys.startIndex
+    
+    while index < keys.endIndex && keys[index] < key {
+      index = index.successor()
+    }
+    
+    if index < keys.endIndex && keys[index] == key {
+      values[index] = value
+      return
+    }
+    
+    if isLeaf {
+      keys.insert(key, atIndex: index)
+      values.insert(value, atIndex: index)
+      ownerTree.numberOfKeys += 1
+    } else {
+      children![index].insertValue(value, forKey: key)
+      if children![index].numberOfKeys > ownerTree.order * 2 {
+        splitChild(children![index], atIndex: index)
+      }
+    }
+  }
+  
+  private func splitChild(child: BTreeNode, atIndex index: Int) {
+    let middleIndex = child.numberOfKeys / 2
+    keys.insert(child.keys[middleIndex], atIndex: index)
+    values.insert(child.values[middleIndex], atIndex: index)
+    child.keys.removeAtIndex(middleIndex)
+    child.values.removeAtIndex(middleIndex)
+    
+    let rightSibling = BTreeNode(
+      ownerTree: ownerTree,
+      keys: Array(child.keys[middleIndex..<child.keys.endIndex]),
+      values: Array(child.values[middleIndex..<child.values.endIndex])
+    )
+    child.keys.removeRange(middleIndex..<child.keys.endIndex)
+    child.values.removeRange(middleIndex..<child.values.endIndex)
+    
+    children!.insert(rightSibling, atIndex: index.successor())
+    
+    if child.children != nil {
+      rightSibling.children = Array(
+        child.children![middleIndex.successor()..<child.children!.endIndex]
+      )
+      child.children!.removeRange(middleIndex.successor()..<child.children!.endIndex)
+    }
+  }
+}
+
+// MARK: BTreeNode extension: Removal
+
+private enum BTreeNodePosition {
+  case Left
+  case Right
+}
+
+extension BTreeNode {
+  private var inorderPredecessor: BTreeNode {
+    if isLeaf {
+      return self
+    } else {
+      return children!.last!.inorderPredecessor
+    }
+  }
+  
+  func removeKey(key: Key) {
+    var index = keys.startIndex
+    
+    while index.successor() < keys.endIndex && keys[index] < key {
+      index = index.successor()
+    }
+    
+    if keys[index] == key {
+      if isLeaf {
+        keys.removeAtIndex(index)
+        values.removeAtIndex(index)
+        ownerTree.numberOfKeys -= 1
+      } else {
+        let predecessor = children![index].inorderPredecessor
+        keys[index] = predecessor.keys.last!
+        values[index] = predecessor.values.last!
+        children![index].removeKey(keys[index])
+        if children![index].numberOfKeys < ownerTree.order {
+          fixChildWithLessNodesThanOrder(children![index], atIndex: index)
+        }
+      }
+    } else if key < keys[index] {
+      // We should go to left child...
+      
+      if let leftChild = children?[index] {
+        leftChild.removeKey(key)
+        if leftChild.numberOfKeys < ownerTree.order {
+          fixChildWithLessNodesThanOrder(leftChild, atIndex: index)
+        }
+      } else {
+        print("The key:\(key) is not in the tree.")
+      }
+    } else {
+      // We should go to right child...
+      
+      if let rightChild = children?[index.successor()] {
+        rightChild.removeKey(key)
+        if rightChild.numberOfKeys < ownerTree.order {
+          fixChildWithLessNodesThanOrder(rightChild, atIndex: index.successor())
+        }
+      } else {
+        print("The key:\(key) is not in the tree")
+      }
+    }
+  }
+  
+  private func fixChildWithLessNodesThanOrder(child: BTreeNode, atIndex index: Int) {
+    
+    if index.predecessor() >= 0 &&
+       children![index.predecessor()].numberOfKeys > ownerTree.order {
+      
+      moveKeyAtIndex(index.predecessor(), toNode: child,
+                     fromNode: children![index.predecessor()], atPosition: .Left)
+      
+    } else if index.successor() < children!.count &&
+              children![index.successor()].numberOfKeys > ownerTree.order {
+      
+      moveKeyAtIndex(index, toNode: child,
+                     fromNode: children![index.successor()], atPosition: .Right)
+      
+    } else if index.predecessor() >= 0 {
+      mergeChild(child, withIndex: index, toNodeAtPosition: .Left)
+    } else {
+      mergeChild(child, withIndex: index, toNodeAtPosition: .Right)
+    }
+  }
+  
+  private func moveKeyAtIndex(keyIndex: Int, toNode targetNode: BTreeNode,
+                             fromNode: BTreeNode, atPosition position: BTreeNodePosition) {
+    switch position {
+    case .Left:
+      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.startIndex)
+      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.startIndex)
+      keys[keyIndex] = fromNode.keys.last!
+      values[keyIndex] = fromNode.values.last!
+      fromNode.keys.removeLast()
+      fromNode.values.removeLast()
+      if !targetNode.isLeaf {
+        targetNode.children!.insert(fromNode.children!.last!,
+                                    atIndex: targetNode.children!.startIndex)
+        fromNode.children!.removeLast()
+      }
+      
+    case .Right:
+      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.endIndex)
+      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.endIndex)
+      keys[keyIndex] = fromNode.keys.first!
+      values[keyIndex] = fromNode.values.first!
+      fromNode.keys.removeFirst()
+      fromNode.values.removeFirst()
+      if !targetNode.isLeaf {
+        targetNode.children!.insert(fromNode.children!.first!,
+                                    atIndex: targetNode.children!.endIndex)
+        fromNode.children!.removeFirst()
+      }
+    }
+  }
+  
+  private func mergeChild(child: BTreeNode, withIndex index: Int, toNodeAtPosition position: BTreeNodePosition) {
+    switch position {
+    case .Left:
+      // We can merge to the left sibling
+      
+      children![index.predecessor()].keys = children![index.predecessor()].keys +
+        [keys[index.predecessor()]] + child.keys
+      
+      children![index.predecessor()].values = children![index.predecessor()].values +
+        [values[index.predecessor()]] + child.values
+      
+      keys.removeAtIndex(index.predecessor())
+      values.removeAtIndex(index.predecessor())
+      
+      if !child.isLeaf {
+        children![index.predecessor()].children =
+          children![index.predecessor()].children! + child.children!
+      }
+      
+    case .Right:
+      // We should merge to the right sibling
+      
+      children![index.successor()].keys = child.keys + [keys[index]] +
+        children![index.successor()].keys
+      
+      children![index.successor()].values = child.values + [values[index]] +
+        children![index.successor()].values
+      
+      keys.removeAtIndex(index)
+      values.removeAtIndex(index)
+      
+      if !child.isLeaf {
+        children![index.successor()].children =
+          child.children! + children![index.successor()].children!
+      }
+    }
+    children!.removeAtIndex(index)
+  }
+}
+
+// MARK: BTreeNode extension: Conversion
+
+extension BTreeNode {
+  func inorderArrayFromKeys() -> [Key] {
+    var array = [Key] ()
+    
+    for i in 0..<numberOfKeys {
+      if let returnedArray = children?[i].inorderArrayFromKeys() {
+        array += returnedArray
+      }
+      array += [keys[i]]
+    }
+    
+    if let returnedArray = children?.last?.inorderArrayFromKeys() {
+      array += returnedArray
+    }
+    
+    return array
+  }
+}
+
+// MARK: BTreeNode extension: Description
+
+extension BTreeNode: CustomStringConvertible {
+  var description: String {
+    var str = "\(keys)"
+    
+    if !isLeaf {
+      for child in children! {
+        str += child.description
+      }
+    }
+    
+    return str
+  }
+}
+
+// MARK: - BTree class
+
+public class BTree<Key: Comparable, Value> {
+  
+  /**
+   The order of the B-Tree
+   
+   The number of keys in every node should be in the [order, 2*order] range,
+   except the root node which is allowed to contain less keys than the value of order.
+   */
+  public let order: Int
+  
+  /// The root node of the tree
+  var rootNode: BTreeNode<Key, Value>!
+  
+  private(set) public var numberOfKeys = 0
+  
+  /**
+   Designated initializer for the tree
+   
+   - parameters:
+   - order: The order of the tree.
+   */
+  public init?(order: Int) {
+    guard order > 0 else {
+      print("Order has to be greater than 0.")
+      return nil
+    }
+    self.order = order
+    rootNode = BTreeNode<Key, Value>(ownerTree: self)
+  }
+}
+
+// MARK: BTree extension: Travelsals
+
+extension BTree {
+  public func traverseKeysInOrder(@noescape process: Key -> Void) {
+    rootNode.traverseKeysInOrder(process)
+  }
+}
+
+// MARK: BTree extension: Subscript
+
+extension BTree {
+  public subscript (key: Key) -> Value? {
+    return valueForKey(key)
+  }
+}
+
+// MARK: BTree extension: Value for Key
+
+extension BTree {
+  public func valueForKey(key: Key) -> Value? {
+    guard rootNode.numberOfKeys > 0 else {
+      return nil
+    }
+    
+    return rootNode.valueForKey(key)
+  }
+}
+
+// MARK: BTree extension: Insertion
+
+extension BTree {
+  public func insertValue(value: Value, forKey key: Key) {
+    rootNode.insertValue(value, forKey: key)
+    
+    if rootNode.numberOfKeys > order * 2 {
+      splitRoot()
+    }
+  }
+  
+  private func splitRoot() {
+    let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
+    
+    let newRoot = BTreeNode<Key, Value>(
+      ownerTree: self,
+      keys: [rootNode.keys[middleIndexOfOldRoot]],
+      values: [rootNode.values[middleIndexOfOldRoot]],
+      children: [rootNode]
+    )
+    rootNode.keys.removeAtIndex(middleIndexOfOldRoot)
+    rootNode.values.removeAtIndex(middleIndexOfOldRoot)
+    
+    let newRightChild = BTreeNode<Key, Value>(
+      ownerTree: self,
+      keys: Array(rootNode.keys[middleIndexOfOldRoot..<rootNode.keys.endIndex]),
+      values: Array(rootNode.values[middleIndexOfOldRoot..<rootNode.values.endIndex])
+    )
+    rootNode.keys.removeRange(middleIndexOfOldRoot..<rootNode.keys.endIndex)
+    rootNode.values.removeRange(middleIndexOfOldRoot..<rootNode.values.endIndex)
+    
+    if rootNode.children != nil {
+      newRightChild.children = Array(
+        rootNode.children![middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex]
+      )
+      rootNode.children!.removeRange(
+        middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex
+      )
+    }
+    
+    newRoot.children!.append(newRightChild)
+    rootNode = newRoot
+  }
+}
+
+// MARK: BTree extension: Removal
+
+extension BTree {
+  public func removeKey(key: Key) {
+    guard rootNode.numberOfKeys > 0 else {
+      return
+    }
+    
+    rootNode.removeKey(key)
+    
+    if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
+      rootNode = rootNode.children!.first!
+    }
+  }
+}
+
+// MARK: BTree extension: Conversion
+
+extension BTree {
+  public func inorderArrayFromKeys() -> [Key] {
+    return rootNode.inorderArrayFromKeys()
+  }
+}
+
+// MARK: BTree extension: Decription
+
+extension BTree: CustomStringConvertible {
+  // Returns a String containing the preorder representation of the nodes
+  public var description: String {
+    return rootNode.description
+  }
+}
diff --git a/BTree/Images/BTree20.png b/BTree/Images/BTree20.png
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diff --git a/BTree/README.md b/BTree/README.md
new file mode 100644
index 000000000..0a25c44c3
--- /dev/null
+++ b/BTree/README.md
@@ -0,0 +1,172 @@
+# B-Tree
+
+A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
+
+### Properties
+
+A B-Tree of order *n* satisfies the following properties:
+ - Every node has at most *2n* keys.
+ - Every node (except root) has at least *n* keys.
+ - Eyery non-leaf node with *k* keys has *k+1* children.
+ - The keys in all nodes are sorted in increasing order. 
+ - The subtree between two keys *k* and *l* of a non-leaf node contains all the keys between *k* and *l*.
+ - All leaves appear at the same level.
+
+A second order B-Tree with keys from 1 to 20 looks like this:
+
+![A B-Tree with 20 keys.](Images/BTree20.png)
+
+### The representation of a B-Tree node in code
+
+```swift
+class BTreeNode<Key: Comparable, Value> {
+  unowned var ownerTree: BTree<Key, Value>
+  
+  private var keys = [Key]()
+  var children: [BTreeNode]?
+  
+  ...
+}
+```
+
+The main parts of a node are two arrays:
+ - An array containing the keys
+ - An array containing the children
+
+![Node.](Images/Node.png)
+
+Nodes also have a reference to the tree they belong to.  
+This is necessary because nodes have to know the order of the tree.
+
+*Note: The array containing the children is an Optional, because leaf nodes don't have children.*
+
+## Searching
+
+1. Searching for a key `k` begins at the root node.
+2. We perform a linear search on the keys of the node, until we find a key `l` that is not less than `k`,  
+   or reach the end of the array.
+3. If `k == l` then we have found the key.
+4. If `k < l`: 
+    - If the node we are on is not a leaf, then we go to the left child of `l`, and perform the steps 3.-5. again.
+    - If we are on a leaf, then `k` is not in the tree.
+5. If we have reached the end of the array:
+    - If we are on a non-leaf node, then we go to the last child of the node, and perform the steps 3.-5. again.
+    - If we are on a leaf, then `k` is not in the tree.
+
+### The code
+
+`valueForKey(_:)` method searches for the given key and if it's in the tree,  
+it returns the value associated with it, else it returns `nil`.
+
+## Insertion
+
+Keys can only be inserted to leaf nodes.
+
+1. Perform a search for the key `k` we want to insert.
+2. If we haven't found it and we are on a leaf node, we can insert it.
+ - If after the search the key `l` which we are standing on is greater than `k`:  
+   We insert `k` to the position before `l`.
+ - Else:  
+   We insert `k` to the position after `l`.
+
+After insertion we should check if the number of keys in the node is in the correct range.  
+If there are more keys in the node than `order*2`, we need to split the node.
+
+####Splitting a node
+
+1. Move up the middle key of the node we want to split, to its parent (if it has one).  
+2. If it hasn't got a parent(it is the root), then create a new root and insert to it.  
+   Also add the old root as the left child of the new root.
+3. Split the node into two by moving the keys (and children, if it's a non-leaf) that were after the middle key
+   to a new node.  
+4. Add the new node as a right child for the key that we have moved up.  
+
+After splitting a node it is possible that the parent node will also contain too many keys, so we need to split it also.  
+In the worst case the splitting goes up to the root (in this case the height of the tree increases).
+
+An insertion to a first order tree looks like this:
+
+![Splitting](Images/InsertionSplit.png)
+
+### The code
+
+The method `insertValue(_:forKey:)` does the insertion.
+After it has inserted a key, as the recursion goes up every node checks the number of keys in its child.  
+if a node has too many keys, its parent calls the `splitChild(_:atIndex:)` method on it.
+
+The root node is checked by the tree itself.  
+If the root has too many nodes after the insertion the tree calls the `splitRoot()` method.
+
+## Removal
+
+Keys can only be removed from leaf nodes.
+
+1. Perform a search for the key `k` we want to remove.
+2. If we have found it:
+   - If we are on a leaf node:  
+     We can remove the key.
+   - Else:  
+     We overwrite `k` with its inorder predecessor `p`, then we remove `p` from the leaf node.
+
+After a key have been removed from a node we should check that the node has enough keys.
+If a node has fewer keys than the order of the tree, then we should move a key to it,  
+or merge it with one of its siblings.
+
+####Moving a key to the child
+
+If the problematic node has a nearest sibling that has more keys than the order of the tree,  
+we should perform this operation on the tree, else we should merge the node with one of its siblings.
+
+Let's say the child we want to fix `c1` is at index `i` in its parent node's children array.
+
+If the child `c2` at index `i-1` has more keys than the order of the tree:  
+
+1. We move the key at index `i-1` from the parent node to the child `c1`'s keys array at index `0`.
+2. We move the last key from `c2` to the parent's keys array at index `i-1`.
+3. (If `c1` is non-leaf) We move the last children from `c1` to `c2`'s children array at index 0.
+
+Else:  
+
+1. We move the key at index `i` from the parent node to the end of child `c1`'s keys array.
+2. We move the first key from `c2` to the parent's keys array at index `i`.
+3. (If `c1` isn't a leaf) We move the first children from `c2` to the end of `c1`'s children array. 
+
+![Moving Key](Images/MovingKey.png)
+
+####Merging two nodes
+
+Let's say we want to merge the child `c1` at index `i` in its parent's children array.
+
+If `c1` has a left sibling `c2`:
+
+1. We move the key from the parent at index `i-1` to the end of `c2`'s keys array.
+2. We move the keys and the children(if it's a non-leaf) from `c1` to the end of `c2`'s keys and children array.
+3. We remove the children at index `i` from the parent node.
+
+Else if `c1` only has a right sibling `c2`:
+
+1. We move the key from the parent at index `i` to the beginning of `c2`'s keys array.
+2. We move the keys and the children(if it's a non-leaf) from `c1` to the beginning of `c2`'s keys and children array.
+3. We remove the children at index `i` from the parent node.
+
+After merging it is possible that now the parent node contains too few keys,  
+so in the worst case merging also can go up to the root, in which case the height of the tree decreases.
+
+![Merging Nodes](Images/MergingNodes.png)
+
+### The code
+
+- `removeKey(_:)` method removes the given key from the tree. After a key has been deleted,  
+  every node checks the number of keys in its child. If a child has less nodes than the order of the tree,
+  it calls the `fixChildWithLessNodesThanOrder(_:atIndex:)` method.  
+
+- `fixChildWithLessNodesThanOrder(_:atIndex:)` method decides which way to fix the child (by moving a key to it,
+  or by merging it), then calls `moveKeyAtIndex(keyIndex:toNode:fromNode:atPosition:)` or 
+  `mergeChild(_:withIndex:toNodeAtPosition:)` method according to its choice.
+
+## See also
+
+[Wikipedia](https://en.wikipedia.org/wiki/B-tree)  
+[GeeksforGeeks](http://www.geeksforgeeks.org/b-tree-set-1-introduction-2/)
+
+*Written for Swift Algorithm Club by Viktor Szilárd Simkó*
diff --git a/BTree/Tests/Tests.xcodeproj/project.pbxproj b/BTree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..0780f04c8
--- /dev/null
+++ b/BTree/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,268 @@
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diff --git a/BTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/BTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/BTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/BTree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/BTree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..d9200547d
--- /dev/null
+++ b/BTree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,100 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0730"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "C66702771D0EEE25008CD769"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "C66702771D0EEE25008CD769"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "C66702771D0EEE25008CD769"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "C66702771D0EEE25008CD769"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
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+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "C66702771D0EEE25008CD769"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
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+</Scheme>
diff --git a/BTree/Tests/Tests/BTreeNodeTests.swift b/BTree/Tests/Tests/BTreeNodeTests.swift
new file mode 100644
index 000000000..07457d937
--- /dev/null
+++ b/BTree/Tests/Tests/BTreeNodeTests.swift
@@ -0,0 +1,54 @@
+//
+//  BTreeNodeTests.swift
+//  BTree
+//
+//  Created by Viktor Szilárd Simkó on 13/06/16.
+//  Copyright © 2016 Viktor Szilárd Simkó. All rights reserved.
+//
+
+import XCTest
+
+class BTreeNodeTests: XCTestCase {
+  
+  let ownerTree = BTree<Int, Int>(order: 2)!
+  var root: BTreeNode<Int, Int>!
+  var leftChild: BTreeNode<Int, Int>!
+  var rightChild: BTreeNode<Int, Int>!
+  
+  override func setUp() {
+    super.setUp()
+    
+    root = BTreeNode(ownerTree: ownerTree)
+    leftChild = BTreeNode(ownerTree: ownerTree)
+    rightChild = BTreeNode(ownerTree: ownerTree)
+    
+    root.insertValue(1, forKey: 1)
+    root.children = [leftChild, rightChild]
+  }
+  
+  func testIsLeafRoot() {
+    XCTAssertFalse(root.isLeaf)
+  }
+  
+  func testIsLeafLeaf() {
+    XCTAssertTrue(leftChild.isLeaf)
+    XCTAssertTrue(rightChild.isLeaf)
+  }
+  
+  func testOwner() {
+    XCTAssert(root.ownerTree === ownerTree)
+    XCTAssert(leftChild.ownerTree === ownerTree)
+    XCTAssert(rightChild.ownerTree === ownerTree)
+  }
+  
+  func testNumberOfKeys() {
+    XCTAssertEqual(root.numberOfKeys, 1)
+    XCTAssertEqual(leftChild.numberOfKeys, 0)
+    XCTAssertEqual(rightChild.numberOfKeys, 0)
+  }
+  
+  func testChildren() {
+    XCTAssertEqual(root.children!.count, 2)
+  }
+}
+
diff --git a/BTree/Tests/Tests/BTreeTests.swift b/BTree/Tests/Tests/BTreeTests.swift
new file mode 100644
index 000000000..77337c5e4
--- /dev/null
+++ b/BTree/Tests/Tests/BTreeTests.swift
@@ -0,0 +1,257 @@
+//
+//  BTreeTests.swift
+//  BTreeTests
+//
+//  Created by Viktor Szilárd Simkó on 09/06/16.
+//  Copyright © 2016 Viktor Szilárd Simkó. All rights reserved.
+//
+
+import XCTest
+
+class BTreeTests: XCTestCase {
+  var bTree: BTree<Int, Int>!
+  
+  override func setUp() {
+    super.setUp()
+    bTree = BTree<Int, Int>(order: 3)!
+  }
+  
+  // MARK: - Tests on empty tree
+  
+  func testOrder() {
+    XCTAssertEqual(bTree.order, 3)
+  }
+  
+  func testRootNode() {
+    XCTAssertNotNil(bTree.rootNode)
+  }
+  
+  func testNumberOfNodesOnEmptyTree() {
+    XCTAssertEqual(bTree.numberOfKeys, 0)
+  }
+  
+  func testInorderTraversalOfEmptyTree() {
+    bTree.traverseKeysInOrder { i in
+      XCTFail("Inorder travelsal fail.")
+    }
+  }
+  
+  func testSubscriptOnEmptyTree() {
+    XCTAssertEqual(bTree[1], nil)
+  }
+  
+  func testSearchEmptyTree() {
+    XCTAssertEqual(bTree.valueForKey(1), nil)
+  }
+  
+  func testInsertToEmptyTree() {
+    bTree.insertValue(1, forKey: 1)
+    
+    XCTAssertEqual(bTree[1]!, 1)
+  }
+  
+  func testRemoveFromEmptyTree() {
+    bTree.removeKey(1)
+    XCTAssertEqual(bTree.description, "[]")
+  }
+  
+  func testInorderArrayFromEmptyTree() {
+    XCTAssertEqual(bTree.inorderArrayFromKeys(), [Int]())
+  }
+  
+  func testDescriptionOfEmptyTree() {
+    XCTAssertEqual(bTree.description, "[]")
+  }
+  
+  // MARK: - Travelsal
+  
+  func testInorderTravelsal() {
+    for i in 1...20 {
+      bTree.insertValue(i, forKey: i)
+    }
+    
+    var j = 1
+    
+    bTree.traverseKeysInOrder { i in
+      XCTAssertEqual(i, j)
+      j += 1
+    }
+  }
+  
+  // MARK: - Searching
+  
+  func testSearchForMaximum() {
+    for i in 1...20 {
+      bTree.insertValue(i, forKey: i)
+    }
+    
+    XCTAssertEqual(bTree.valueForKey(20)!, 20)
+  }
+  
+  func testSearchForMinimum() {
+    for i in 1...20 {
+      bTree.insertValue(i, forKey: i)
+    }
+    
+    XCTAssertEqual(bTree.valueForKey(1)!, 1)
+  }
+  
+  // MARK: - Insertion
+  
+  func testInsertion() {
+    bTree.insertKeysUpTo(20)
+    
+    XCTAssertEqual(bTree.numberOfKeys, 20)
+    
+    for i in 1...20 {
+      XCTAssertNotNil(bTree[i])
+    }
+    
+    do {
+      try bTree.checkBalanced()
+    } catch {
+      XCTFail("BTree is not balanced")
+    }
+    
+    XCTAssertEqual(bTree.description,
+                   "[4, 8, 12, 16][1, 2, 3][5, 6, 7][9, 10, 11][13, 14, 15][17, 18, 19, 20]")
+  }
+  
+  // MARK: - Removal
+  
+  func testRemoveMaximum() {
+    for i in 1...20 {
+      bTree.insertValue(i, forKey: i)
+    }
+    
+    bTree.removeKey(20)
+    
+    XCTAssertNil(bTree[20])
+    
+    do {
+      try bTree.checkBalanced()
+    } catch {
+      XCTFail("BTree is not balanced")
+    }
+  }
+  
+  func testRemoveMinimum() {
+    bTree.insertKeysUpTo(20)
+    
+    bTree.removeKey(1)
+    
+    XCTAssertNil(bTree[1])
+    
+    do {
+      try bTree.checkBalanced()
+    } catch {
+      XCTFail("BTree is not balanced")
+    }
+  }
+  
+  func testRemoveSome() {
+    bTree.insertKeysUpTo(20)
+    
+    bTree.removeKey(6)
+    bTree.removeKey(9)
+    
+    XCTAssertNil(bTree[6])
+    XCTAssertNil(bTree[9])
+    
+    do {
+      try bTree.checkBalanced()
+    } catch {
+      XCTFail("BTree is not balanced")
+    }
+    
+    XCTAssertEqual(bTree.description,
+                   "[7, 12, 16][1, 2, 3, 4, 5][8, 10, 11][13, 14, 15][17, 18, 19, 20]")
+  }
+  
+  func testRemoveSomeFrom2ndOrder() {
+    bTree = BTree<Int, Int>(order: 2)!
+    bTree.insertKeysUpTo(20)
+    
+    bTree.removeKey(6)
+    bTree.removeKey(9)
+    
+    XCTAssertNil(bTree[6])
+    XCTAssertNil(bTree[9])
+    
+    do {
+      try bTree.checkBalanced()
+    } catch {
+      XCTFail("BTree is not balanced")
+    }
+    
+    XCTAssertEqual(bTree.description,
+                   "[12][4, 8][1, 2, 3][5, 7][10, 11][15, 18][13, 14][16, 17][19, 20]")
+  }
+  
+  func testRemoveAll() {
+    bTree.insertKeysUpTo(20)
+    
+    XCTAssertEqual(bTree.numberOfKeys, 20)
+    
+    for i in (1...20).reverse() {
+      bTree.removeKey(i)
+    }
+    
+    do {
+      try bTree.checkBalanced()
+    } catch {
+      XCTFail("BTree is not balanced")
+    }
+    
+    XCTAssertEqual(bTree.numberOfKeys, 0)
+  }
+  
+  // MARK: - InorderArray
+  
+	func testInorderArray() {
+    bTree.insertKeysUpTo(20)
+		
+		let returnedArray = bTree.inorderArrayFromKeys()
+		let targetArray = Array<Int>(1...20)
+		
+		XCTAssertEqual(returnedArray, targetArray)
+	}
+}
+
+enum BTreeError: ErrorType {
+  case TooManyNodes
+  case TooFewNodes
+}
+
+extension BTreeNode {
+  func checkBalanced(isRoot root: Bool) throws {
+    if numberOfKeys > ownerTree.order * 2 {
+      throw BTreeError.TooManyNodes
+    } else if !root && numberOfKeys < ownerTree.order {
+      throw BTreeError.TooFewNodes
+    }
+    
+    if !isLeaf {
+      for child in children! {
+        try child.checkBalanced(isRoot: false)
+      }
+    }
+  }
+}
+
+extension BTree where Key: SignedIntegerType, Value: SignedIntegerType {
+  func insertKeysUpTo(to: Int) {
+    var k: Key = 1
+    var v: Value = 1
+    
+    for _ in 1...to {
+      insertValue(v, forKey: k)
+      k = k + 1
+      v = v + 1
+    }
+  }
+  
+  func checkBalanced() throws {
+    try rootNode.checkBalanced(isRoot: true)
+  }
+}
diff --git a/BTree/Tests/Tests/Info.plist b/BTree/Tests/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/BTree/Tests/Tests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>

From 01248c5725728cfe8f56b06c7f44a55353c7d469 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Viktor?= <aqviktor@gmail.com>
Date: Fri, 17 Jun 2016 10:50:17 +0200
Subject: [PATCH 0411/1679] cleaned up tests

---
 BTree/Tests/Tests/BTreeTests.swift | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/BTree/Tests/Tests/BTreeTests.swift b/BTree/Tests/Tests/BTreeTests.swift
index 77337c5e4..947781478 100644
--- a/BTree/Tests/Tests/BTreeTests.swift
+++ b/BTree/Tests/Tests/BTreeTests.swift
@@ -112,9 +112,6 @@ class BTreeTests: XCTestCase {
     } catch {
       XCTFail("BTree is not balanced")
     }
-    
-    XCTAssertEqual(bTree.description,
-                   "[4, 8, 12, 16][1, 2, 3][5, 6, 7][9, 10, 11][13, 14, 15][17, 18, 19, 20]")
   }
   
   // MARK: - Removal
@@ -163,9 +160,6 @@ class BTreeTests: XCTestCase {
     } catch {
       XCTFail("BTree is not balanced")
     }
-    
-    XCTAssertEqual(bTree.description,
-                   "[7, 12, 16][1, 2, 3, 4, 5][8, 10, 11][13, 14, 15][17, 18, 19, 20]")
   }
   
   func testRemoveSomeFrom2ndOrder() {
@@ -183,9 +177,6 @@ class BTreeTests: XCTestCase {
     } catch {
       XCTFail("BTree is not balanced")
     }
-    
-    XCTAssertEqual(bTree.description,
-                   "[12][4, 8][1, 2, 3][5, 7][10, 11][15, 18][13, 14][16, 17][19, 20]")
   }
   
   func testRemoveAll() {

From c40de6e3685f70244b265dedb3a54a8f6384cdd4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Viktor?= <aqviktor@gmail.com>
Date: Fri, 17 Jun 2016 10:56:05 +0200
Subject: [PATCH 0412/1679] added test in .travis.yml

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 0b14e9a40..a7861ed76 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -13,6 +13,7 @@ script:
 - xctool test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./BTree\ BTree/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests

From 25e470ca002e3b7e104eb646a92843e9226980d4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Viktor?= <aqviktor@gmail.com>
Date: Fri, 17 Jun 2016 11:08:41 +0200
Subject: [PATCH 0413/1679] renamed folder

---
 .travis.yml                                         |   2 +-
 {BTree => B-Tree}/BTree.playground/Contents.swift   |   0
 .../BTree.playground/Sources/BTree.swift            |   0
 .../BTree.playground/contents.xcplayground          |   0
 .../playground.xcworkspace/contents.xcworkspacedata |   0
 {BTree => B-Tree}/BTree.swift                       |   0
 {BTree => B-Tree}/Images/BTree20.png                | Bin
 {BTree => B-Tree}/Images/InsertionSplit.png         | Bin
 {BTree => B-Tree}/Images/MergingNodes.png           | Bin
 {BTree => B-Tree}/Images/MovingKey.png              | Bin
 {BTree => B-Tree}/Images/Node.png                   | Bin
 {BTree => B-Tree}/README.md                         |   0
 .../Tests/Tests.xcodeproj/project.pbxproj           |   0
 .../project.xcworkspace/contents.xcworkspacedata    |   0
 .../xcshareddata/xcschemes/Tests.xcscheme           |   0
 {BTree => B-Tree}/Tests/Tests/BTreeNodeTests.swift  |   0
 {BTree => B-Tree}/Tests/Tests/BTreeTests.swift      |   0
 {BTree => B-Tree}/Tests/Tests/Info.plist            |   0
 18 files changed, 1 insertion(+), 1 deletion(-)
 rename {BTree => B-Tree}/BTree.playground/Contents.swift (100%)
 rename {BTree => B-Tree}/BTree.playground/Sources/BTree.swift (100%)
 rename {BTree => B-Tree}/BTree.playground/contents.xcplayground (100%)
 rename {BTree => B-Tree}/BTree.playground/playground.xcworkspace/contents.xcworkspacedata (100%)
 rename {BTree => B-Tree}/BTree.swift (100%)
 rename {BTree => B-Tree}/Images/BTree20.png (100%)
 rename {BTree => B-Tree}/Images/InsertionSplit.png (100%)
 rename {BTree => B-Tree}/Images/MergingNodes.png (100%)
 rename {BTree => B-Tree}/Images/MovingKey.png (100%)
 rename {BTree => B-Tree}/Images/Node.png (100%)
 rename {BTree => B-Tree}/README.md (100%)
 rename {BTree => B-Tree}/Tests/Tests.xcodeproj/project.pbxproj (100%)
 rename {BTree => B-Tree}/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata (100%)
 rename {BTree => B-Tree}/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme (100%)
 rename {BTree => B-Tree}/Tests/Tests/BTreeNodeTests.swift (100%)
 rename {BTree => B-Tree}/Tests/Tests/BTreeTests.swift (100%)
 rename {BTree => B-Tree}/Tests/Tests/Info.plist (100%)

diff --git a/.travis.yml b/.travis.yml
index a7861ed76..019948716 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -13,7 +13,7 @@ script:
 - xctool test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./BTree\ BTree/Tests/Tests.xcodeproj -scheme Tests
+- xctool test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests
diff --git a/BTree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
similarity index 100%
rename from BTree/BTree.playground/Contents.swift
rename to B-Tree/BTree.playground/Contents.swift
diff --git a/BTree/BTree.playground/Sources/BTree.swift b/B-Tree/BTree.playground/Sources/BTree.swift
similarity index 100%
rename from BTree/BTree.playground/Sources/BTree.swift
rename to B-Tree/BTree.playground/Sources/BTree.swift
diff --git a/BTree/BTree.playground/contents.xcplayground b/B-Tree/BTree.playground/contents.xcplayground
similarity index 100%
rename from BTree/BTree.playground/contents.xcplayground
rename to B-Tree/BTree.playground/contents.xcplayground
diff --git a/BTree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata b/B-Tree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from BTree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata
rename to B-Tree/BTree.playground/playground.xcworkspace/contents.xcworkspacedata
diff --git a/BTree/BTree.swift b/B-Tree/BTree.swift
similarity index 100%
rename from BTree/BTree.swift
rename to B-Tree/BTree.swift
diff --git a/BTree/Images/BTree20.png b/B-Tree/Images/BTree20.png
similarity index 100%
rename from BTree/Images/BTree20.png
rename to B-Tree/Images/BTree20.png
diff --git a/BTree/Images/InsertionSplit.png b/B-Tree/Images/InsertionSplit.png
similarity index 100%
rename from BTree/Images/InsertionSplit.png
rename to B-Tree/Images/InsertionSplit.png
diff --git a/BTree/Images/MergingNodes.png b/B-Tree/Images/MergingNodes.png
similarity index 100%
rename from BTree/Images/MergingNodes.png
rename to B-Tree/Images/MergingNodes.png
diff --git a/BTree/Images/MovingKey.png b/B-Tree/Images/MovingKey.png
similarity index 100%
rename from BTree/Images/MovingKey.png
rename to B-Tree/Images/MovingKey.png
diff --git a/BTree/Images/Node.png b/B-Tree/Images/Node.png
similarity index 100%
rename from BTree/Images/Node.png
rename to B-Tree/Images/Node.png
diff --git a/BTree/README.md b/B-Tree/README.md
similarity index 100%
rename from BTree/README.md
rename to B-Tree/README.md
diff --git a/BTree/Tests/Tests.xcodeproj/project.pbxproj b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
similarity index 100%
rename from BTree/Tests/Tests.xcodeproj/project.pbxproj
rename to B-Tree/Tests/Tests.xcodeproj/project.pbxproj
diff --git a/BTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from BTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/BTree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 100%
rename from BTree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
diff --git a/BTree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
similarity index 100%
rename from BTree/Tests/Tests/BTreeNodeTests.swift
rename to B-Tree/Tests/Tests/BTreeNodeTests.swift
diff --git a/BTree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
similarity index 100%
rename from BTree/Tests/Tests/BTreeTests.swift
rename to B-Tree/Tests/Tests/BTreeTests.swift
diff --git a/BTree/Tests/Tests/Info.plist b/B-Tree/Tests/Tests/Info.plist
similarity index 100%
rename from BTree/Tests/Tests/Info.plist
rename to B-Tree/Tests/Tests/Info.plist

From 7dd0cb5cca1baa5115b5e111454d279cef42ad03 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Viktor?= <aqviktor@gmail.com>
Date: Fri, 17 Jun 2016 13:59:36 +0200
Subject: [PATCH 0414/1679] Added playground contents.

---
 B-Tree/BTree.playground/Contents.swift | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index 7d2973f77..186718bbd 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -8,3 +8,19 @@ bTree.insertValue(1, forKey: 1)
 bTree.insertValue(2, forKey: 2)
 bTree.insertValue(3, forKey: 3)
 bTree.insertValue(4, forKey: 4)
+
+bTree.valueForKey(3)
+bTree[3]
+
+bTree.removeKey(2)
+
+bTree.traverseKeysInOrder {
+  key in
+  print(key)
+}
+
+bTree.numberOfKeys
+
+bTree.order
+
+bTree.inorderArrayFromKeys()
\ No newline at end of file

From 396924baef1ec0bfad18d7105ec86419676f6d0c Mon Sep 17 00:00:00 2001
From: "Michael C. Rael" <michael.c.rael@gmail.com>
Date: Sat, 18 Jun 2016 09:38:31 -0600
Subject: [PATCH 0415/1679] Completed documentation. Also changed external
 parameter name in cover from 'from' to 'within'.

---
 Set Cover (Unweighted)/README.markdown        | 12 ++++++++---
 .../SetCover.playground/Contents.swift        | 20 +++++++++----------
 .../Sources/SetCover.swift                    |  2 +-
 Set Cover (Unweighted)/SetCover.swift         |  2 +-
 4 files changed, 21 insertions(+), 15 deletions(-)

diff --git a/Set Cover (Unweighted)/README.markdown b/Set Cover (Unweighted)/README.markdown
index 48b5f3bfa..fde032438 100644
--- a/Set Cover (Unweighted)/README.markdown	
+++ b/Set Cover (Unweighted)/README.markdown	
@@ -10,16 +10,22 @@ For example, suppose you have a universe of `{1, 5, 7}` and you want to find the
 > {2}
 > {1, 2, 3}
 
-You can see that the sets `{3, 1} {7, 6, 5, 4}` when unioned together will cover the universe of `{1, 5, 7}`. Yes, there may be additional elements in the sets returned by the algorithm, but every element in the universe is represented.
+You can see that the sets `{3, 1} {7, 6, 5, 4}` when unioned together will cover the universe of `{1, 5, 7}`. Yes, there may be additional elements in the sets returned by the algorithm, but every element in the universe is represented in the cover itself.
 
-If there is no cover within the group of sets, the function returns nil. For example, if your universe is `{7, 9}`, there is no combination of sets within the grouping above that will yield a cover.
+There may be cases where no cover exists. For example, if your universe is `{7, 9}`, there is no combination of sets within the group above that will yield a cover.
 
 ## The algorithm
 
-The Greedy Set Cover algorithm (unweighted) is provided here. It's known as greedy because it uses the largest intersecting set from the group of sets first before examining other sets in the group.
+The Greedy Set Cover algorithm (unweighted) is provided here. It's known as greedy because it uses the largest intersecting set from the group of sets first before examining other sets in the group. This is part of the reason why the cover may have additional elements which are not part of the universe.
 
 The function (named `cover`) is provided as an extension of the Swift type `Set`. The function takes a single parameter, which is an array of sets. This array represents the group, and the set itself represents the universe.
 
+One of the first things done in `cover` is to make a copy of the universe in `remainingSet`. Then, the algorithm enters a `while` loop in which a call to `largestIntersectingSet` is made. The value returned from `largestIntersectingSet` is the set which has the most elements in common with the remaining universe identified by `remainingSet`. If all sets have nothing in common, `largestIntersectingSet` returns `nil`.
+
+If the result from `largestIntersectingSet` is not nil, that result is subtracted from `remainingSet` (reducing its size), and the loop continues until `remainingSet` has zero length (meaning a cover has been found) or until `largestIntersectingSet` returns `nil`.
+
+If there is no cover within the group of sets, `cover` returns `nil`.
+
 ## See also
 
 [Set cover problem on Wikipedia](https://en.wikipedia.org/wiki/Set_cover_problem)
diff --git a/Set Cover (Unweighted)/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
index 3822f16e3..6fac33e6d 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
@@ -1,31 +1,31 @@
 let universe1 = Set(1...7)
 let array1 = randomArrayOfSets(covering: universe1)
-let cover1 = universe1.cover(from: array1)
+let cover1 = universe1.cover(within: array1)
 
 let universe2 = Set(1...10)
 let array2: Array<Set<Int>> = [[1,2,3,4,5,6,7], [8,9]]
-let cover2 = universe2.cover(from: array2)
+let cover2 = universe2.cover(within: array2)
 
 let universe3 = Set(["tall", "heavy"])
 let array3: Array<Set<String>> = [["tall", "light"], ["short", "heavy"], ["tall", "heavy", "young"]]
-let cover3 = universe3.cover(from: array3)
+let cover3 = universe3.cover(within: array3)
 
 let universe4 = Set(["tall", "heavy", "green"])
-let cover4 = universe4.cover(from: array3)
+let cover4 = universe4.cover(within: array3)
 
 let universe5: Set<Int> = [16, 32, 64]
 let array5: Array<Set<Int>> = [[16,17,18], [16,32,128], [1,2,3], [32,64,128]]
-let cover5 = universe5.cover(from: array5)
+let cover5 = universe5.cover(within: array5)
 
 let universe6: Set<Int> = [24, 89, 132, 90, 22]
 let array6 = randomArrayOfSets(covering: universe6)
-let cover6 = universe6.cover(from: array6)
+let cover6 = universe6.cover(within: array6)
 
 let universe7: Set<String> = ["fast", "cheap", "good"]
 let array7 = randomArrayOfSets(covering: universe7, minArraySizeFactor: 20.0, maxSetSizeFactor: 0.7)
-let cover7 = universe7.cover(from: array7)
+let cover7 = universe7.cover(within: array7)
 
 let emptySet = Set<Int>()
-let coverTest1 = emptySet.cover(from: array1)
-let coverTest2 = universe1.cover(from: Array<Set<Int>>())
-let coverTest3 = emptySet.cover(from: Array<Set<Int>>())
\ No newline at end of file
+let coverTest1 = emptySet.cover(within: array1)
+let coverTest2 = universe1.cover(within: Array<Set<Int>>())
+let coverTest3 = emptySet.cover(within: Array<Set<Int>>())
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift
index 8e608cb52..c739a595a 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
@@ -1,5 +1,5 @@
 public extension Set {
-  func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
+  func cover(within array: Array<Set<Element>>) -> Array<Set<Element>>? {
     var result: [Set<Element>]? = [Set<Element>]()
     var remainingSet = self
     
diff --git a/Set Cover (Unweighted)/SetCover.swift b/Set Cover (Unweighted)/SetCover.swift
index 58ffade9d..587da4d9d 100644
--- a/Set Cover (Unweighted)/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.swift	
@@ -1,5 +1,5 @@
 extension Set {
-  func cover(from array: Array<Set<Element>>) -> Array<Set<Element>>? {
+  func cover(within array: Array<Set<Element>>) -> Array<Set<Element>>? {
     var result: [Set<Element>]? = [Set<Element>]()
     var remainingSet = self
     

From f81304b29683e25e6b8947c5f96ab124ff1bbf97 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 26 Jun 2016 17:15:23 -0700
Subject: [PATCH 0416/1679] Fixed some typos

---
 B-Tree/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/B-Tree/README.md b/B-Tree/README.md
index 0a25c44c3..28b617ca1 100644
--- a/B-Tree/README.md
+++ b/B-Tree/README.md
@@ -7,7 +7,7 @@ A B-Tree is a self-balancing search tree, in which nodes can have more than two
 A B-Tree of order *n* satisfies the following properties:
  - Every node has at most *2n* keys.
  - Every node (except root) has at least *n* keys.
- - Eyery non-leaf node with *k* keys has *k+1* children.
+ - Every non-leaf node with *k* keys has *k+1* children.
  - The keys in all nodes are sorted in increasing order. 
  - The subtree between two keys *k* and *l* of a non-leaf node contains all the keys between *k* and *l*.
  - All leaves appear at the same level.
@@ -47,10 +47,10 @@ This is necessary because nodes have to know the order of the tree.
    or reach the end of the array.
 3. If `k == l` then we have found the key.
 4. If `k < l`: 
-    - If the node we are on is not a leaf, then we go to the left child of `l`, and perform the steps 3.-5. again.
+    - If the node we are on is not a leaf, then we go to the left child of `l`, and perform the steps 3 - 5 again.
     - If we are on a leaf, then `k` is not in the tree.
 5. If we have reached the end of the array:
-    - If we are on a non-leaf node, then we go to the last child of the node, and perform the steps 3.-5. again.
+    - If we are on a non-leaf node, then we go to the last child of the node, and perform the steps 3 - 5 again.
     - If we are on a leaf, then `k` is not in the tree.
 
 ### The code

From d680e0648f07e5ddf8912d5fa2bc845ba25ec18e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Viktor?= <aqviktor@gmail.com>
Date: Mon, 27 Jun 2016 09:35:56 +0200
Subject: [PATCH 0417/1679] Fixed link to B-Tree in README.md

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index d36aec465..c125742fc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -152,7 +152,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - Trie
-- B-Tree
+- [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
 
 ### Hashing
 

From 1da67165b48b33ff421fd8dfd2ac9883e5bdb83e Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 27 Jun 2016 21:17:12 -0700
Subject: [PATCH 0418/1679] Altered the tree diagram so that one of the leafs
 is actually labeled as a leaf rather than a node

---
 Tree/Images/Tree.png | Bin 19207 -> 21989 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/Tree/Images/Tree.png b/Tree/Images/Tree.png
index 751dac2e33741afc1489102e8dcd1642f018360b..59ef800cbac28467b3ebcd9d5e51e0b2eec4f09f 100644
GIT binary patch
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znm}sc3kT;8Tp2hIede*Q^Au+94&m~{+6gY>T}Rxma_Vvc?86H}(G!&>Y^PxReR4An
z$kD=<kbJ4xb708DlW_mU$DvI`^1vu!8Y=7}Q*j47v|Z5{tO-zjV{dFMY^C!HDiI9~
z%d>#$1*)6l9OM)BSV=43^977|#dU>nl2ncUE<Z^!myd<r*kqqk&$%}x6apkOVNNs2
z5nzr6xwsud&uIHML!5NjZ@sGD10)+<H*WkJ_^;$;z?lIc(XUl(<jIAcHB4Fo;AP6F
z_x5(+>Rmwm0y6>jw>+4@abG(TD?J(8yX}7U6}7(63xVYn|EAa$n-4(EB2j0+_Iv`o
z{=X+{&*S7zY=P;ODi9p40tC~f7NH~v|IDG^9|Ged&>d>D=m*yoJ`NhC{a)`<h<Ev#
zYKZMK>~GgB?9Mt5cl1Djp_)4g{rV`a8T^vTY|!UwU{A?)KEwdARck7T@3<~XO7m^T
zxgDWJMEeX+`W>BrD~mk?eV$w=^z+}g>TI_JSPIN^1@@OSupggTu<o1<Id1&7ZhgRx
z2~(|rU3|yTVez<rI^w^1g#qgrkD;94KU<eG*4CwBL}B=M*#oMHvmoN$e+3{vB1}_z
y1ds3(D7GeNS_~uBn8{8XdGP;x86WH%*DvOWTZTse4e;Ys5Orl8r5XjBJO39VcFscp


From 1cfb7de3ff686532b816469f9251272b7c7fec15 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 28 Jun 2016 16:09:53 +0200
Subject: [PATCH 0419/1679] Removing swiftlint warnings from Set Cover
 (Unweighted)

---
 .../SetCover.playground/Contents.swift             |  4 ++--
 .../Sources/RandomArrayOfSets.swift                | 14 +++++++-------
 .../SetCover.playground/Sources/SetCover.swift     | 14 +++++++-------
 Set Cover (Unweighted)/SetCover.swift              | 14 +++++++-------
 4 files changed, 23 insertions(+), 23 deletions(-)

diff --git a/Set Cover (Unweighted)/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
index 6fac33e6d..dcf998a66 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
@@ -3,7 +3,7 @@ let array1 = randomArrayOfSets(covering: universe1)
 let cover1 = universe1.cover(within: array1)
 
 let universe2 = Set(1...10)
-let array2: Array<Set<Int>> = [[1,2,3,4,5,6,7], [8,9]]
+let array2: Array<Set<Int>> = [[1, 2, 3, 4, 5, 6, 7], [8, 9]]
 let cover2 = universe2.cover(within: array2)
 
 let universe3 = Set(["tall", "heavy"])
@@ -14,7 +14,7 @@ let universe4 = Set(["tall", "heavy", "green"])
 let cover4 = universe4.cover(within: array3)
 
 let universe5: Set<Int> = [16, 32, 64]
-let array5: Array<Set<Int>> = [[16,17,18], [16,32,128], [1,2,3], [32,64,128]]
+let array5: Array<Set<Int>> = [[16, 17, 18], [16, 32, 128], [1, 2, 3], [32, 64, 128]]
 let cover5 = universe5.cover(within: array5)
 
 let universe6: Set<Int> = [24, 89, 132, 90, 22]
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift
index 64253014b..b64d8d70e 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
@@ -5,17 +5,17 @@ public func randomArrayOfSets<T>(covering universe: Set<T>,
                               maxSetSizeFactor: Double = 0.6) -> Array<Set<T>> {
   var result = [Set<T>]()
   var ongoingUnion = Set<T>()
-  
+
   let minArraySize = Int(Double(universe.count) * minArraySizeFactor)
   var maxSetSize = Int(Double(universe.count) * maxSetSizeFactor)
   if maxSetSize > universe.count {
     maxSetSize = universe.count
   }
-  
+
   while true {
     var generatedSet = Set<T>()
     let targetSetSize = Int(arc4random_uniform(UInt32(maxSetSize)) + 1)
-    
+
     while true {
       let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
       for (setIndex, value) in universe.enumerate() {
@@ -24,20 +24,20 @@ public func randomArrayOfSets<T>(covering universe: Set<T>,
           break
         }
       }
-      
+
       if generatedSet.count == targetSetSize {
         result.append(generatedSet)
         ongoingUnion = ongoingUnion.union(generatedSet)
         break
       }
     }
-    
+
     if result.count >= minArraySize {
       if ongoingUnion == universe {
         break
       }
     }
   }
-  
+
   return result
-}
\ No newline at end of file
+}
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift
index c739a595a..0e93caf0b 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
@@ -2,11 +2,11 @@ public extension Set {
   func cover(within array: Array<Set<Element>>) -> Array<Set<Element>>? {
     var result: [Set<Element>]? = [Set<Element>]()
     var remainingSet = self
-    
+
     func largestIntersectingSet() -> Set<Element>? {
       var largestIntersectionLength = 0
       var largestSet: Set<Element>?
-      
+
       for set in array {
         let intersectionLength = remainingSet.intersect(set).count
         if intersectionLength > largestIntersectionLength {
@@ -14,20 +14,20 @@ public extension Set {
           largestSet = set
         }
       }
-      
+
       return largestSet
     }
-    
+
     while remainingSet.count != 0 {
       guard let largestSet = largestIntersectingSet() else { break }
       result!.append(largestSet)
       remainingSet = remainingSet.subtract(largestSet)
     }
-    
+
     if remainingSet.count != 0 || self.count == 0 {
       result = nil
     }
-    
+
     return result
   }
-}
\ No newline at end of file
+}
diff --git a/Set Cover (Unweighted)/SetCover.swift b/Set Cover (Unweighted)/SetCover.swift
index 587da4d9d..86be6729b 100644
--- a/Set Cover (Unweighted)/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.swift	
@@ -2,11 +2,11 @@ extension Set {
   func cover(within array: Array<Set<Element>>) -> Array<Set<Element>>? {
     var result: [Set<Element>]? = [Set<Element>]()
     var remainingSet = self
-    
+
     func largestIntersectingSet() -> Set<Element>? {
       var largestIntersectionLength = 0
       var largestSet: Set<Element>?
-      
+
       for set in array {
         let intersectionLength = remainingSet.intersect(set).count
         if intersectionLength > largestIntersectionLength {
@@ -14,20 +14,20 @@ extension Set {
           largestSet = set
         }
       }
-      
+
       return largestSet
     }
-    
+
     while remainingSet.count != 0 {
       guard let largestSet = largestIntersectingSet() else { break }
       result!.append(largestSet)
       remainingSet = remainingSet.subtract(largestSet)
     }
-    
+
     if remainingSet.count != 0 || self.count == 0 {
       result = nil
     }
-    
+
     return result
   }
-}
\ No newline at end of file
+}

From 31935d9ac62b7ad4d3a8464d855211cf29ece79e Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 28 Jun 2016 17:07:39 +0200
Subject: [PATCH 0420/1679] Set cover (unweighted) - replacing count = 0
 conditions with isEmpty

---
 .../SetCover.playground/Sources/SetCover.swift             | 4 ++--
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 Set Cover (Unweighted)/SetCover.swift                      | 4 ++--
 3 files changed, 11 insertions(+), 4 deletions(-)
 create mode 100644 Set Cover (Unweighted)/SetCover.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift
index 0e93caf0b..8d40e1fda 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
@@ -18,13 +18,13 @@ public extension Set {
       return largestSet
     }
 
-    while remainingSet.count != 0 {
+    while !remainingSet.isEmpty {
       guard let largestSet = largestIntersectingSet() else { break }
       result!.append(largestSet)
       remainingSet = remainingSet.subtract(largestSet)
     }
 
-    if remainingSet.count != 0 || self.count == 0 {
+    if !remainingSet.isEmpty || isEmpty {
       result = nil
     }
 
diff --git a/Set Cover (Unweighted)/SetCover.playground/playground.xcworkspace/contents.xcworkspacedata b/Set Cover (Unweighted)/SetCover.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Set Cover (Unweighted)/SetCover.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Set Cover (Unweighted)/SetCover.swift b/Set Cover (Unweighted)/SetCover.swift
index 86be6729b..d67dfbfa9 100644
--- a/Set Cover (Unweighted)/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.swift	
@@ -18,13 +18,13 @@ extension Set {
       return largestSet
     }
 
-    while remainingSet.count != 0 {
+    while !remainingSet.isEmpty {
       guard let largestSet = largestIntersectingSet() else { break }
       result!.append(largestSet)
       remainingSet = remainingSet.subtract(largestSet)
     }
 
-    if remainingSet.count != 0 || self.count == 0 {
+    if !remainingSet.isEmpty || isEmpty {
       result = nil
     }
 

From dfec36d031bfaa1e861da559498a4ebd6b367364 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 28 Jun 2016 17:09:33 +0200
Subject: [PATCH 0421/1679] Set cover (unweighted) - adding link on under
 construction page

---
 Under Construction.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index 95ead4218..555d778e6 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -28,3 +28,4 @@ Special-purpose sorts:
 
 - [Minimum Edit Distance](Minimum Edit Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
 - [Treap](Treap/)
+- [Set Cover (Unweighted)][Set Cover (Unweighted)/]

From 824d06c19cddd5855e36e7ee3239ddd5c09d93b6 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 28 Jun 2016 17:10:50 +0200
Subject: [PATCH 0422/1679] Set cover (unweighted) - adding link on under
 construction page

---
 Under Construction.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Under Construction.markdown b/Under Construction.markdown
index 555d778e6..0c59d90c1 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -28,4 +28,4 @@ Special-purpose sorts:
 
 - [Minimum Edit Distance](Minimum Edit Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
 - [Treap](Treap/)
-- [Set Cover (Unweighted)][Set Cover (Unweighted)/]
+- [Set Cover (Unweighted)](Set Cover (Unweighted)/)

From 912c21d455aa7cda0579d9ffc68bdb211b5cfdee Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 30 Jun 2016 10:50:21 -0700
Subject: [PATCH 0423/1679] Fixed a typo in the main readme markdown file

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index c125742fc..b1947a6c8 100644
--- a/README.markdown
+++ b/README.markdown
@@ -214,7 +214,7 @@ The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://
 
 It is now maintained by [Chris Pilcher](https://github.com/chris-pilcher) and [Kelvin Lau](https://github.com/kelvinlauKL).
 
-The Swift Algorithm Club is a a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How to Contribute.markdown)? :]
+The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How to Contribute.markdown)? :]
 
 ## License
 

From c77a74803bc87a59cfac94f9bda8a5291b68ba68 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andre=CC=81s=20Pesate?= <andres.pesate@mobgen.com>
Date: Fri, 1 Jul 2016 15:30:58 +0200
Subject: [PATCH 0424/1679] Added preconditions to subscript to avoid unwanted
 changes or crashes.

---
 Array2D/Array2D.swift | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Array2D/Array2D.swift b/Array2D/Array2D.swift
index ca84275f3..6177974d7 100644
--- a/Array2D/Array2D.swift
+++ b/Array2D/Array2D.swift
@@ -19,6 +19,9 @@ public struct Array2D<T> {
       return array[row*columns + column]
     }
     set {
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+        
       array[row*columns + column] = newValue
     }
   }

From 358ea45332f92c6d2a29d64c7c786a0acf1784da Mon Sep 17 00:00:00 2001
From: Stephen Rutstein <Stephen.Rutstein@target.com>
Date: Wed, 13 Jul 2016 23:20:12 -0500
Subject: [PATCH 0425/1679] Palindromes swift file, playground, and README file
 added

---
 .../Palindromes.playground/Contents.swift     | 36 +++++++++++
 .../contents.xcplayground                     |  4 ++
 Palindromes/Palindromes.swift                 | 21 ++++++
 Palindromes/README.markdown                   | 64 +++++++++++++++++++
 4 files changed, 125 insertions(+)
 create mode 100644 Palindromes/Palindromes.playground/Contents.swift
 create mode 100644 Palindromes/Palindromes.playground/contents.xcplayground
 create mode 100644 Palindromes/Palindromes.swift
 create mode 100644 Palindromes/README.markdown

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
new file mode 100644
index 000000000..c89231d09
--- /dev/null
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -0,0 +1,36 @@
+import Cocoa
+
+public func palindromeCheck (text: String?) -> Bool {
+  if let text = text {
+    let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
+    let length: Int = mutableText.characters.count
+    
+    if length < 1 {
+      return false
+    }
+    
+    if length == 1 {
+      return true
+    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.endIndex.predecessor()] {
+      let range = Range<String.Index>(mutableText.startIndex.successor()..<mutableText.endIndex.predecessor())
+      return palindromeCheck(mutableText.substringWithRange(range))
+    }
+  }
+  
+  return false
+}
+
+// Test to check that non-palindromes are handled correctly:
+palindromeCheck("owls")
+
+// Test to check that palindromes are accurately found (regardless of case and whitespace:
+palindromeCheck("lol")
+palindromeCheck("race car")
+palindromeCheck("Race fast Safe car")
+
+// Test to check that palindromes are found regardless of case:
+palindromeCheck("HelloLLEH")
+
+// Test that nil and empty Strings return false:
+palindromeCheck("")
+palindromeCheck(nil)
diff --git a/Palindromes/Palindromes.playground/contents.xcplayground b/Palindromes/Palindromes.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Palindromes/Palindromes.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
new file mode 100644
index 000000000..96269fe23
--- /dev/null
+++ b/Palindromes/Palindromes.swift
@@ -0,0 +1,21 @@
+import Cocoa
+
+public func palindromeCheck (text: String?) -> Bool {
+  if let text = text {
+    let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
+    let length: Int = mutableText.characters.count
+    
+    if length < 1 {
+      return false
+    }
+    
+    if length == 1 {
+      return true
+    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.endIndex.predecessor()] {
+      let range = Range<String.Index>(mutableText.startIndex.successor()..<mutableText.endIndex.predecessor())
+      return palindromeCheck(mutableText.substringWithRange(range))
+    }
+  }
+  
+  return false
+}
diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
new file mode 100644
index 000000000..d27605ed4
--- /dev/null
+++ b/Palindromes/README.markdown
@@ -0,0 +1,64 @@
+# Palindromes
+
+A palindrome is a word or phrase that is spelled the exact same when read forwards or backwards. 
+For this example puzzle, palindromes will not take case into account, meaning that uppercase and
+lowercase text will be treated the same. In addition, spaces will not be considered, allowing 
+for multi-word phrases to constitute palindromes too. 
+
+Algorithms that check for palindromes are a common programming interview question. 
+
+## Example 
+
+The word "radar" is spelled the exact same both forwards and backwards, and as a result is a palindrome. 
+The phrase "race car" is another common palindrome that is spelled the same forwards and backwards. 
+
+## Algorithm 
+
+To check for palindromes, the first and last characters of a String must be compared for equality. 
+When the first and last characters are the same, they are removed from the String, resulting in a 
+substring starting with the second character and ending at the second to last character. 
+
+In this implementation of a palindrome checker, recursion is used to check each substring of the 
+original String. 
+
+## The code 
+
+Here is a recursive implementation of this in Swift: 
+
+``swift
+func palindromeCheck (text: String?) -> Bool {
+  if let text = text {
+    let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
+    let length: Int = mutableText.characters.count
+    
+    if length < 1 {
+      return false
+    }
+
+    if length == 1 {
+      return true
+    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.endIndex.predecessor()] {
+      let range = Range<String.Index>(mutableText.startIndex.successor()..<mutableText.endIndex.predecessor())
+      return palindromeCheck(mutableText.substringWithRange(range))
+    }
+  }
+
+  return false
+}
+``
+
+
+This code can be tested in a playground using the following: 
+
+``swift
+palindromeCheck("Race car")
+``
+
+Since the phrase "Race car" is a palindrome, this will return true. 
+
+## Additional Resources
+
+[Palindrome Wikipedia](https://en.wikipedia.org/wiki/Palindrome)
+
+
+*Written by [Stephen Rutstein](https://github.com/srutstein21)*

From b5e983d72abb5a976d09a318f562ff816333b7da Mon Sep 17 00:00:00 2001
From: srutstein21 <srutstein@wisc.edu>
Date: Wed, 13 Jul 2016 23:24:07 -0500
Subject: [PATCH 0426/1679] Updated README

---
 Palindromes/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index d27605ed4..a595408ca 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -25,7 +25,7 @@ original String.
 
 Here is a recursive implementation of this in Swift: 
 
-``swift
+```swift
 func palindromeCheck (text: String?) -> Bool {
   if let text = text {
     let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
@@ -45,7 +45,7 @@ func palindromeCheck (text: String?) -> Bool {
 
   return false
 }
-``
+```
 
 
 This code can be tested in a playground using the following: 

From 58c0128fb7d1235ae39ad23782db76543fe65fe8 Mon Sep 17 00:00:00 2001
From: srutstein21 <srutstein@wisc.edu>
Date: Wed, 13 Jul 2016 23:25:13 -0500
Subject: [PATCH 0427/1679] Updating markdown format for README

---
 Palindromes/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index a595408ca..a0696ff93 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -50,9 +50,9 @@ func palindromeCheck (text: String?) -> Bool {
 
 This code can be tested in a playground using the following: 
 
-``swift
+```swift
 palindromeCheck("Race car")
-``
+```
 
 Since the phrase "Race car" is a palindrome, this will return true. 
 

From d67c81f1f82bec733a60e8819539c7b4781b32e2 Mon Sep 17 00:00:00 2001
From: lionel0806 <lixiansir@gmail.com>
Date: Thu, 14 Jul 2016 23:27:11 +0800
Subject: [PATCH 0428/1679] Processing index out of bounds

---
 Heap/Heap.swift            |  4 ++++
 Heap/Tests/HeapTests.swift | 11 +++++++++++
 2 files changed, 15 insertions(+)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 64bd90cd8..bf7031abe 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -112,6 +112,8 @@ public struct Heap<T> {
    * larger than the old one; in a min-heap it should be smaller.
    */
   public mutating func replace(index i: Int, value: T) {
+    guard i < elements.count else { return }
+    
     assert(isOrderedBefore(value, elements[i]))
     elements[i] = value
     shiftUp(index: i)
@@ -141,6 +143,8 @@ public struct Heap<T> {
    * to know the node's index, which may actually take O(n) steps to find.
    */
   public mutating func removeAtIndex(i: Int) -> T? {
+    guard i < elements.count else { return nil }
+    
     let size = elements.count - 1
     if i != size {
       swap(&elements[i], &elements[size])
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index ec17560a5..6178a8094 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -196,6 +196,12 @@ class HeapTests: XCTestCase {
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
 
+    //test index out of bounds
+    let v = h.removeAtIndex(10)
+    XCTAssertEqual(v, nil)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    
     let v1 = h.removeAtIndex(5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
@@ -308,5 +314,10 @@ class HeapTests: XCTestCase {
     h.replace(index: 5, value: 13)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+    
+    //test index out of bounds
+    h.replace(index: 20, value: 2)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
   }
 }

From 5524ef40ca461c445e40952011560fee391f414f Mon Sep 17 00:00:00 2001
From: Lukas Schramm <schramm98@icloud.com>
Date: Sat, 16 Jul 2016 17:41:37 +0200
Subject: [PATCH 0429/1679] Added SlowSort

---
 Slow Sort/README.markdown                     | 50 +++++++++++++++++++
 Slow Sort/SlowSort.swift                      | 28 +++++++++++
 .../contents.xcworkspacedata                  |  7 +++
 3 files changed, 85 insertions(+)
 create mode 100644 Slow Sort/README.markdown
 create mode 100644 Slow Sort/SlowSort.swift

diff --git a/Slow Sort/README.markdown b/Slow Sort/README.markdown
new file mode 100644
index 000000000..f8cc743cc
--- /dev/null
+++ b/Slow Sort/README.markdown	
@@ -0,0 +1,50 @@
+# Slow Sort
+
+Goal: Sort an array of numbers from low to high (or high to low).
+
+You are given an array of numbers and need to put them in the right order. The insertion sort algorithm works as follows:
+
+We can decompose the problem of sorting n numbers in ascending order into
+
+1. find the maximum of the numbers
+ 1. find the maximum of the first n/2 elements
+ 2. find the maximum of the remaining n/2 elements
+ 3. find the largest of those two maxima
+2. sorting the remaining ones
+
+## The code
+
+Here is an implementation of slow sort in Swift:
+
+```swift
+public func slowsort(_ i: Int, _ j: Int) {
+    if i>=j {
+        return
+    }
+    let m = (i+j)/2
+    slowsort(i,m)
+    slowsort(m+1,j)
+    if numberList[j] < numberList[m] {
+        let temp = numberList[j]
+        numberList[j] = numberList[m]
+        numberList[m] = temp
+    }
+    slowsort(i,j-1)
+}
+```
+
+## Performance
+
+| Case  | Performance |
+|:-------------: |:---------------:|
+| Worst       |  slow |
+| Best      | 	O(n^(log(n)/(2+e))))        |
+|  Average | 	O(n^(log(n)/2))       | 
+
+## See also
+
+[Slow Sort explanation in the Internet](http://c2.com/cgi/wiki?SlowSort)
+
+*Written for Swift Algorithm Club by Lukas Schramm*
+
+(used the Insertion Sort Readme as template)
\ No newline at end of file
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
new file mode 100644
index 000000000..c21a77fd8
--- /dev/null
+++ b/Slow Sort/SlowSort.swift	
@@ -0,0 +1,28 @@
+//
+//  SlowSort.swift
+//  
+//
+//  Created by Pope Lukas Schramm (Dabendorf Orthodox Religion) on 16-07-16.
+//
+//
+
+var numberList = [1,12,9,17,13,12]
+
+public func slowsort(_ i: Int, _ j: Int) {
+    if i>=j {
+        return
+    }
+    let m = (i+j)/2
+    slowsort(i,m)
+    slowsort(m+1,j)
+    if numberList[j] < numberList[m] {
+        let temp = numberList[j]
+        numberList[j] = numberList[m]
+        numberList[m] = temp
+    }
+    slowsort(i,j-1)
+}
+
+
+slowsort(0,numberList.count-1)
+print(numberList)
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4e0f19dc2..3feeaa5c2 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1019,6 +1019,13 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "container:"
+      name = "Slow Sort">
+      <FileRef
+         location = "group:Slow Sort/SlowSort.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Huffman Coding"
       name = "Huffman Coding">

From 185e7caab77acdb6ae830f17ed1ab9ce6774d78b Mon Sep 17 00:00:00 2001
From: Stephen Rutstein <Stephen.Rutstein@target.com>
Date: Sun, 17 Jul 2016 00:59:48 -0500
Subject: [PATCH 0430/1679] Added files for Comb Sort

---
 Comb Sort/Comb Sort.playground/Contents.swift | 50 ++++++++++++
 .../contents.xcplayground                     |  4 +
 .../contents.xcworkspacedata                  |  7 ++
 Comb Sort/Comb Sort.swift                     | 36 +++++++++
 Comb Sort/README.markdown                     | 78 +++++++++++++++++++
 5 files changed, 175 insertions(+)
 create mode 100644 Comb Sort/Comb Sort.playground/Contents.swift
 create mode 100644 Comb Sort/Comb Sort.playground/contents.xcplayground
 create mode 100644 Comb Sort/Comb Sort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Comb Sort/Comb Sort.swift
 create mode 100644 Comb Sort/README.markdown

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
new file mode 100644
index 000000000..3bc03546a
--- /dev/null
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -0,0 +1,50 @@
+// Comb Sort Function
+// Created by Stephen Rutstein
+// 7-16-2016
+
+import Cocoa
+
+func combSort (input: [Int]) -> [Int] {
+    var copy: [Int] = input
+    var gap = copy.count
+    let shrink = 1.3
+    
+    while gap > 1 {
+        gap = (Int)(Double(gap) / shrink)
+        if gap < 1 {
+            gap = 1
+        }
+        
+        var index = 0
+        while !(index + gap >= copy.count) {
+            if copy[index] > copy[index + gap] {
+                swap(&copy[index], &copy[index + gap])
+            }
+            index += 1
+        }
+    }
+    return copy
+}
+
+// A function to swap two integer values
+// Used for swapping within the array of values.
+func swap (inout a: Int, inout b: Int) {
+    let temp = a
+    a = b
+    b = temp
+}
+
+// Test Comb Sort with small array of ten values
+let array: [Int] = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
+combSort(array)
+
+// Test Comb Sort with large array of 1000 random values
+var bigArray = [Int](count: 1000, repeatedValue: 0)
+var i = 0
+while i < 1000 {
+    bigArray[i] = Int(arc4random_uniform(1000) + 1)
+    i += 1
+}
+combSort(bigArray)
+
+
diff --git a/Comb Sort/Comb Sort.playground/contents.xcplayground b/Comb Sort/Comb Sort.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Comb Sort/Comb Sort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Comb Sort/Comb Sort.playground/playground.xcworkspace/contents.xcworkspacedata b/Comb Sort/Comb Sort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Comb Sort/Comb Sort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Comb Sort/Comb Sort.swift b/Comb Sort/Comb Sort.swift
new file mode 100644
index 000000000..7abba8c7f
--- /dev/null
+++ b/Comb Sort/Comb Sort.swift	
@@ -0,0 +1,36 @@
+//  Comb Sort.swift
+//  Comb Sort
+//
+//  Created by Stephen.Rutstein on 7/16/16.
+//  Copyright © 2016 Stephen.Rutstein. All rights reserved.
+//
+
+import Foundation
+
+func combSort (input: [Int]) -> [Int] {
+    var copy: [Int] = input
+    var gap = copy.count
+    let shrink = 1.3
+    
+    while gap > 1 {
+        gap = (Int)(Double(gap) / shrink)
+        if gap < 1 {
+            gap = 1
+        }
+        
+        var index = 0
+        while !(index + gap >= copy.count) {
+            if copy[index] > copy[index + gap] {
+                swap(&copy[index], &copy[index + gap])
+            }
+            index += 1
+        }
+    }
+    return copy
+}
+
+func swap (inout a: Int, inout b: Int) {
+    let temp = a
+    a = b
+    b = temp
+}
diff --git a/Comb Sort/README.markdown b/Comb Sort/README.markdown
new file mode 100644
index 000000000..fedbc5705
--- /dev/null
+++ b/Comb Sort/README.markdown	
@@ -0,0 +1,78 @@
+# Comb Sort
+
+A common issue for Bubble Sort is when small values are located near the end of an array. 
+This problem severely slows down Bubble Sort, as it must move the small value -- or _turtle_ -- 
+through nearly the entire array. Bubble Sort works by checking the current index of an array 
+against the next index, and when those two values are unsorted, they are swapped into place. 
+As a result, the values bubble into their rightful place within the array. 
+
+Comb Sort improves upon Bubble Sort by dealing with these turtles near the end of the array. 
+The value of the current index of the array is compared against one a set distance away. This 
+removes a worst-case scenario of Bubble Sort, and greatly improves on the time complexity of Bubble Sort. 
+
+## Example 
+
+A step-by-step example of how Comb Sort works, and differs from Bubble Sort, can be seen [here](http://www.exforsys.com/tutorials/c-algorithms/comb-sort.html). 
+
+Here is a visual to see Comb Sort in effect: 
+![](https://upload.wikimedia.org/wikipedia/commons/4/46/Comb_sort_demo.gif)
+
+## Algorithm 
+
+Similar to Bubble Sort, two values within an array are compared. When the lower index value 
+is larger than the higher index value, and thus out of place within the array, they are 
+swapped. Unlike Bubble Sort, the value being compared against is a set distance away. This 
+value -- the _gap_ -- is slowly decreased through iterations. 
+
+## The Code 
+
+Here is a Swift implementation of Comb Sort: 
+
+```swift
+func combSort (input: [Int]) -> [Int] {
+    var copy: [Int] = input
+    var gap = copy.count
+    let shrink = 1.3
+
+    while gap > 1 {
+        gap = (Int)(Double(gap) / shrink)
+        if gap < 1 {
+            gap = 1
+        }
+    
+        var index = 0
+        while !(index + gap >= copy.count) {
+            if copy[index] > copy[index + gap] {
+                swap(&copy[index], &copy[index + gap])
+            }
+            index += 1
+        }
+    }
+    return copy
+}
+```
+
+This code can be tested in a playground by calling this method with a paramaterized array to sort: 
+
+```swift
+combSort(example_array_of_values)
+```
+
+This will sort the values of the array into ascending order -- increasing in value.  
+
+## Performance
+
+Comb Sort was created to improve upon the worst case time complexity of Bubble Sort. With Comb 
+Sort, the worst case scenario for performance is exponential -- O(n^2). At best though, Comb Sort 
+performs at O(n logn) time complexity. This creates a drastic improvement over Bubble Sort's performance. 
+
+Similar to Bubble Sort, the space complexity for Comb Sort is constant -- O(1). 
+This is extremely space efficient as it sorts the array in place. 
+
+
+## Additional Resources
+
+[Comb Sort Wikipedia](https://en.wikipedia.org/wiki/Comb_sort)
+
+
+*Written for the _Swift Algorithm Club_ by [Stephen Rutstein](https://github.com/srutstein21)*

From 0951ea332ec1ec7b8e700321d1558fd1ea4b35bc Mon Sep 17 00:00:00 2001
From: Stephen Rutstein <Stephen.Rutstein@target.com>
Date: Sun, 17 Jul 2016 01:03:35 -0500
Subject: [PATCH 0431/1679] Quick change to the read me file to fix spacing

---
 Comb Sort/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Comb Sort/README.markdown b/Comb Sort/README.markdown
index fedbc5705..d30d429b3 100644
--- a/Comb Sort/README.markdown	
+++ b/Comb Sort/README.markdown	
@@ -15,6 +15,7 @@ removes a worst-case scenario of Bubble Sort, and greatly improves on the time c
 A step-by-step example of how Comb Sort works, and differs from Bubble Sort, can be seen [here](http://www.exforsys.com/tutorials/c-algorithms/comb-sort.html). 
 
 Here is a visual to see Comb Sort in effect: 
+
 ![](https://upload.wikimedia.org/wikipedia/commons/4/46/Comb_sort_demo.gif)
 
 ## Algorithm 

From ab2d1a2c7c4017c0c3a37011abe82883ba9a565f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 17 Jul 2016 08:49:31 -0700
Subject: [PATCH 0432/1679] Tweaks to palindrome article. Linked up Palindrome
 alg on front page

---
 Palindromes/Palindromes.playground/Contents.swift          | 4 ++--
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 Palindromes/Palindromes.swift                              | 4 ++--
 Palindromes/README.markdown                                | 4 ++--
 README.markdown                                            | 1 +
 5 files changed, 14 insertions(+), 6 deletions(-)
 create mode 100644 Palindromes/Palindromes.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index c89231d09..b548182af 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -2,10 +2,10 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
+    let mutableText = text.stringByTrimmingCharactersInSet(.whitespaceCharacterSet()).lowercaseString
     let length: Int = mutableText.characters.count
     
-    if length < 1 {
+    guard length >= 1 else {
       return false
     }
     
diff --git a/Palindromes/Palindromes.playground/playground.xcworkspace/contents.xcworkspacedata b/Palindromes/Palindromes.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Palindromes/Palindromes.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 96269fe23..61e7740ab 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -2,10 +2,10 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
+    let mutableText = text.stringByTrimmingCharactersInSet(.whitespaceCharacterSet()).lowercaseString
     let length: Int = mutableText.characters.count
     
-    if length < 1 {
+    guard length >= 1 else {
       return false
     }
     
diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index a0696ff93..3df775e31 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -28,10 +28,10 @@ Here is a recursive implementation of this in Swift:
 ```swift
 func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet()).lowercaseString
+    let mutableText = text.stringByTrimmingCharactersInSet(.whitespaceCharacterSet()).lowercaseString
     let length: Int = mutableText.characters.count
     
-    if length < 1 {
+    guard length >= 1 {
       return false
     }
 
diff --git a/README.markdown b/README.markdown
index b1947a6c8..3d011a178 100644
--- a/README.markdown
+++ b/README.markdown
@@ -183,6 +183,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Two-Sum Problem](Two-Sum Problem/)
 - [Fizz Buzz](Fizz Buzz/)
 - [Monty Hall Problem](Monty Hall Problem/)
+- [Finding Palindromes](Palindromes/)
 
 ## Learn more!
 

From 790533767da1213c2886ae3f7790b950b14b702d Mon Sep 17 00:00:00 2001
From: jamesharrop <James@Jamess-MBP.lan>
Date: Sun, 17 Jul 2016 21:15:17 +0100
Subject: [PATCH 0433/1679] First draft of Linear Regression

First draft
---
 .../Contents.swift                            | 23 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++++
 .../contents.xcworkspacedata                  |  7 ++++++
 Linear Regression/README.markdown             | 19 +++++++++++++++
 4 files changed, 53 insertions(+)
 create mode 100644 Linear Regression/LinearRegression.playground/Contents.swift
 create mode 100644 Linear Regression/LinearRegression.playground/contents.xcplayground
 create mode 100644 Linear Regression/LinearRegression.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Linear Regression/README.markdown

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
new file mode 100644
index 000000000..2b111ce68
--- /dev/null
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -0,0 +1,23 @@
+// Linear Regression
+
+import Foundation
+
+let carAge: [Double] = [10, 8, 3, 3, 2, 1]
+let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
+var intercept = 10000.0
+var slope = -1000.0
+let alpha = 0.0001
+let numberOfCarAdvertsWeSaw = carPrice.count
+
+func h(carAge: Double) -> Double {
+    return intercept + slope * carAge
+}
+
+for n in 1...10000 {
+    for i in 1...numberOfCarAdvertsWeSaw {
+        intercept += alpha * (carPrice[i-1] - h(carAge[i-1])) * 1
+        slope += alpha * (carPrice[i-1] - h(carAge[i-1])) * carAge[i-1]
+    }
+}
+
+print("A car age 4 years is predicted to be worth £\(Int(h(4)))")
diff --git a/Linear Regression/LinearRegression.playground/contents.xcplayground b/Linear Regression/LinearRegression.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Linear Regression/LinearRegression.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Linear Regression/LinearRegression.playground/playground.xcworkspace/contents.xcworkspacedata b/Linear Regression/LinearRegression.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Linear Regression/LinearRegression.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
new file mode 100644
index 000000000..1aa03fbe8
--- /dev/null
+++ b/Linear Regression/README.markdown	
@@ -0,0 +1,19 @@
+# Linear Regression
+## First draft version of this document
+
+Linear regression is a technique for creating a model of the relationship between two (or more) variable quantities.
+
+For example, let's say we are planning to sell a car. We are not sure how much money to ask for. So we look at recent advertisments for the asking prices of other cars. There are a lot of variables we could look at - for example: make, model, engine size. To simplify our task, we collect data on just the age of the car and the price:
+
+Age (in years)| Price (in £)
+--------------|-------------
+10 | 500
+8 | 400
+3 | 7,000
+3 | 8,500
+2 | 11,000
+1 | 10,500
+
+Our car is 4 years old. How can we set a price for our car based on the data in this table?
+
+*Written for Swift Algorithm Club by James Harrop*
\ No newline at end of file

From 9f96077964cbf5d300888034ccf89bfe3ce44612 Mon Sep 17 00:00:00 2001
From: John Pham <hprobotic@gmail.com>
Date: Mon, 18 Jul 2016 16:23:19 +0700
Subject: [PATCH 0434/1679] Remove comma at end of array

---
 Merge Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 023e18b32..a24c71f2f 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -19,7 +19,7 @@ Assume you're given an array of *n* numbers and you need to put them in the righ
 
 Let's say the numbers to sort are `[2, 1, 5, 4, 9]`. This is your unsorted pile. The goal is to keep splitting the pile until you can't split anymore. 
 
-First, split the array into two halves: `[2, 1,]` and `[5, 4, 9]`. Can you keep splitting them? Yes you can!
+First, split the array into two halves: `[2, 1]` and `[5, 4, 9]`. Can you keep splitting them? Yes you can!
 
 Focus on the left pile. `[2, 1]` will split into `[2]` and `[1]`. Can you keep splitting them? No. Time to check the other pile.
 

From 236c4e4b632f45e0d487eae168291ca836ed570f Mon Sep 17 00:00:00 2001
From: jamesharrop <James@Jamess-MBP.lan>
Date: Fri, 22 Jul 2016 22:03:23 +0100
Subject: [PATCH 0435/1679] Playground and readme file completed

---
 Linear Regression/Images/graph1.png           | Bin 0 -> 22918 bytes
 Linear Regression/Images/graph2.png           | Bin 0 -> 43570 bytes
 Linear Regression/Images/graph3.png           | Bin 0 -> 31467 bytes
 .../Contents.swift                            |  47 ++++--
 Linear Regression/README.markdown             | 149 +++++++++++++++++-
 5 files changed, 185 insertions(+), 11 deletions(-)
 create mode 100644 Linear Regression/Images/graph1.png
 create mode 100644 Linear Regression/Images/graph2.png
 create mode 100644 Linear Regression/Images/graph3.png

diff --git a/Linear Regression/Images/graph1.png b/Linear Regression/Images/graph1.png
new file mode 100644
index 0000000000000000000000000000000000000000..bffe838ef01e2d68a8b00963276fa0dc141e40ea
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diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 2b111ce68..07ebe6a5d 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -4,20 +4,47 @@ import Foundation
 
 let carAge: [Double] = [10, 8, 3, 3, 2, 1]
 let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
-var intercept = 10000.0
-var slope = -1000.0
-let alpha = 0.0001
-let numberOfCarAdvertsWeSaw = carPrice.count
+var intercept = 0.0
+var slope = 0.0
 
-func h(carAge: Double) -> Double {
+func predictedCarPrice(carAge: Double) -> Double {
     return intercept + slope * carAge
 }
 
-for n in 1...10000 {
-    for i in 1...numberOfCarAdvertsWeSaw {
-        intercept += alpha * (carPrice[i-1] - h(carAge[i-1])) * 1
-        slope += alpha * (carPrice[i-1] - h(carAge[i-1])) * carAge[i-1]
+// An iterative approach
+
+let numberOfCarAdvertsWeSaw = carPrice.count - 1
+let numberOfIterations = 100
+let alpha = 0.0001
+
+for n in 1...numberOfIterations {
+    for i in 0...numberOfCarAdvertsWeSaw {
+        let difference = carPrice[i] - predictedCarPrice(carAge[i])
+        intercept += alpha * difference
+        slope += alpha * difference * carAge[i]
     }
 }
 
-print("A car age 4 years is predicted to be worth £\(Int(h(4)))")
+print("A car age of 4 years is predicted to be worth £\(Int(predictedCarPrice(4)))")
+
+// A closed form solution
+
+func average(input: [Double]) -> Double {
+    return input.reduce(0, combine: +) / Double(input.count)
+}
+
+func multiply(input1: [Double], _ input2: [Double]) -> [Double] {
+    return input1.enumerate().map({ (index, element) in return element*input2[index] })
+}
+
+func linearRegression(xVariable: [Double], _ yVariable: [Double]) -> (Double -> Double) {
+    let sum1 = average(multiply(xVariable, yVariable)) - average(xVariable) * average(yVariable)
+    let sum2 = average(multiply(xVariable, xVariable)) - pow(average(xVariable), 2)
+    let slope = sum1 / sum2
+    let intercept = average(yVariable) - slope * average(xVariable)
+    return { intercept + slope * $0 }
+}
+
+let result = linearRegression(carAge, carPrice)(4)
+
+print("A car of age 4 years is predicted to be worth £\(Int(result))")
diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 1aa03fbe8..e78514df5 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -1,5 +1,4 @@
 # Linear Regression
-## First draft version of this document
 
 Linear regression is a technique for creating a model of the relationship between two (or more) variable quantities.
 
@@ -16,4 +15,152 @@ Age (in years)| Price (in £)
 
 Our car is 4 years old. How can we set a price for our car based on the data in this table?
 
+Let's start by looking at the data plotted out:
+
+![graph1](Images/graph1.png)
+
+We could imagine a straight line drawn through the points on this graph. It's not (in this case) going to go exactly through every point, but we could place the line so that it goes as close to all the points as possible.
+
+To say this in another way, we want to make the distance from the line to each point as small as possible. This is most often done by minimising the square of the distance from the line to each point.
+
+We can describe the straight line in terms of two variables:
+
+1. The point at which it crosses the y-axis i.e. the predicted price of a brand new car. This is the *intercept*.
+2. The *slope* of the line - i.e. for every year of age, how much does the price change.
+
+This is the equation for our line:
+
+$$
+carPrice = slope \times carAge + intercept 
+$$
+
+How can we find the best values for the intercept and the slope? Let's look at two different ways to do this.
+
+## An iterative approach
+One approach is to start with some arbitrary values for the intercept and the slope. We work out what small changes we make to these values to move our line closer to the data points. Then we repeat this multiple times. Eventually our line will approach the optimum position.
+
+First let's set up our data structures. We will use two Swift arrays for the car age and the car price:
+
+```swift
+let carAge: [Double] = [10, 8, 3, 3, 2, 1]
+let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
+```
+
+This is how we can represent our straight line:
+
+```swift
+var intercept = 0.0
+var slope = 0.0
+func predictedCarPrice(carAge: Double) -> Double {
+    return intercept + slope * carAge
+}
+```
+Now for the code which will perform the iterations:
+
+```swift
+let numberOfCarAdvertsWeSaw = carPrice.count - 1
+let iterations = 2000
+let alpha = 0.0001
+
+for n in 1...iterations {
+    for i in 0...numberOfCarAdvertsWeSaw {
+        let difference = carPrice[i] - predictedCarPrice(carAge[i])
+        intercept += alpha * difference
+        slope += alpha * difference * carAge[i]
+    }
+}
+```
+
+```alpha``` is a factor that determines how much closer we move to the correct solution with each iteration. If this factor is too large then our program will not converge on the correct solution.
+
+The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
+
+We want to minimse the square of the distance between the line and the points. Let's define a function J which represents this distance - for simplicity we consider only one point here:
+
+$$
+J \propto ((slope.carAge+intercept) - carPrice))^2
+$$
+
+In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope:
+
+$$
+\frac{\partial J}{\partial (slope)} \propto (slope.carAge+intercept) - carPrice).carAge
+$$
+
+And similarly for the intercept:
+
+$$
+\frac{\partial J}{\partial (intercept)} \propto
+(slope.carAge+intercept) - carPrice)
+$$
+
+We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
+
+Looking at the code, it intuitively makes sense - the larger the difference between the current predicted car Price and the actual car price, and the larger the value of ```alpha```, the greater the adjustments to the intercept and the slope.
+
+It can take a lot of iterations to approach the ideal values. Let's look at how the intercept and slope change as we increase the number of iterations:
+
+Iterations | Intercept | Slope | Predicted value of a 4 year old car
+:---------:|:---------:|:-----:|:------------------------:
+0 | 0 | 0 | 0
+2000 | 4112 | -113 | 3659 
+6000 | 8564 | -764 | 5507 
+10000 | 10517 | -1049 | 6318 
+14000 | 11374 | -1175 | 6673 
+18000 | 11750 | -1230 | 6829 
+
+Here is the same data shown as a graph. Each of the blue lines on the graph represents a row in the table above.
+
+![graph2](Images/graph2.png)
+
+After 18,000 iterations it looks as if the line is getting closer to what we would expect (just by looking) to be the correct line of best fit. Also, each additional 2,000 iterations has less and less effect on the final result - the values of the intercept and the slope are converging on the correct values.
+
+##A closed form solution
+
+There is another way we can calculate the line of best fit, without having to do multiple iterations. We can solve the equations describing the least squares minimisation and just work out the intercept and slope directly. 
+
+First we need some helper functions. This one calculates the average (the mean) of an array of Doubles:
+
+```swift
+func average(input: [Double]) -> Double {
+    return input.reduce(0, combine: +) / Double(input.count)
+}
+```
+We are using the ```reduce``` Swift function to sum up all the elements of the array, and then divide that by the number of elements. This gives us the mean value.
+
+We also need to be able to multiply each element in an array by the corresponding element in another array, to create a new array. Here is a function which will do this:
+
+```swift
+func multiply(input1: [Double], _ input2: [Double]) -> [Double] {
+    return input1.enumerate().map({ (index, element) in return element*input2[index] })
+}
+```
+
+We are using the ```map``` function to multiply each element.
+
+Finally, the function which fits the line to the data:
+
+```swift
+func linearRegression(xVariable: [Double], _ yVariable: [Double]) -> (Double -> Double) {
+    let sum1 = average(multiply(xVariable, yVariable)) - average(xVariable) * average(yVariable)
+    let sum2 = average(multiply(xVariable, xVariable)) - pow(average(xVariable), 2)
+    let slope = sum1 / sum2
+    let intercept = average(yVariable) - slope * average(xVariable)
+    return { intercept + slope * $0 }
+}
+```
+This function takes as arguments two arrays of Doubles, and returns a function which is the line of best fit. The formulas to calculate the slope and the intercept can be derived from our definition of the function J. Let's see how the output from this line fits our data:
+
+![graph3](Images/graph3.png)
+
+Using this line, we would predict a price for our 4 year old car of £6952.
+
+
+##Summary
+We've seen two different ways to implement a simple linear regression in Swift. An obvious question is: why bother with the iterative approach at all? 
+
+Well, the line we've found doesn't fit the data perfectly. For one thing, the graph includes some negative values at high car ages! Possibly we would have to pay someone to tow away a very old car... but really these negative values just show that we have not modelled the real life situation very accurately. The relationship between the car age and the car price is not linear but instead is some other function. We also know that a car's price is not just related to its age but also other factors such as the make, model and engine size of the car. We would need to use additional variables to describe these other factors. 
+
+It turns out that in some of these more complicated models, the iterative approach is the only viable or efficient approach. This can also occur when the arrays of data are very large and may be sparsely populated with data values.
+
 *Written for Swift Algorithm Club by James Harrop*
\ No newline at end of file

From 0abfd03de68af02f62d1b41298e364d634362e15 Mon Sep 17 00:00:00 2001
From: jamesharrop <James@Jamess-MBP.lan>
Date: Fri, 22 Jul 2016 22:11:22 +0100
Subject: [PATCH 0436/1679] Removed LaTex equations

---
 Linear Regression/README.markdown | 26 ++++----------------------
 1 file changed, 4 insertions(+), 22 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index e78514df5..3fc16ff31 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -30,9 +30,8 @@ We can describe the straight line in terms of two variables:
 
 This is the equation for our line:
 
-$$
-carPrice = slope \times carAge + intercept 
-$$
+carPrice = slope * carAge + intercept 
+
 
 How can we find the best values for the intercept and the slope? Let's look at two different ways to do this.
 
@@ -75,26 +74,9 @@ for n in 1...iterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimse the square of the distance between the line and the points. Let's define a function J which represents this distance - for simplicity we consider only one point here:
-
-$$
-J \propto ((slope.carAge+intercept) - carPrice))^2
-$$
-
-In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope:
-
-$$
-\frac{\partial J}{\partial (slope)} \propto (slope.carAge+intercept) - carPrice).carAge
-$$
-
-And similarly for the intercept:
-
-$$
-\frac{\partial J}{\partial (intercept)} \propto
-(slope.carAge+intercept) - carPrice)
-$$
+We want to minimse the square of the distance between the line and the points. We define a function J which represents this distance - for simplicity we consider only one point here. This function J is proprotional to  ((slope.carAge+intercept) - carPrice))^2
 
-We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
+In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 
 Looking at the code, it intuitively makes sense - the larger the difference between the current predicted car Price and the actual car price, and the larger the value of ```alpha```, the greater the adjustments to the intercept and the slope.
 

From a9aa744dd0a389bb6f2efa8b9c9e9a65ace0a8d9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 28 Jul 2016 07:03:07 -0700
Subject: [PATCH 0437/1679] Indexed the Linear Regression article in the main
 read.me file. Also made a code style change.

---
 Linear Regression/LinearRegression.playground/Contents.swift | 4 ++--
 README.markdown                                              | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 07ebe6a5d..585471487 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -13,12 +13,12 @@ func predictedCarPrice(carAge: Double) -> Double {
 
 // An iterative approach
 
-let numberOfCarAdvertsWeSaw = carPrice.count - 1
+let numberOfCarAdvertsWeSaw = carPrice.count
 let numberOfIterations = 100
 let alpha = 0.0001
 
 for n in 1...numberOfIterations {
-    for i in 0...numberOfCarAdvertsWeSaw {
+    for i in 0..<numberOfCarAdvertsWeSaw {
         let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference
         slope += alpha * difference * carAge[i]
diff --git a/README.markdown b/README.markdown
index 3d011a178..35dad0aff 100644
--- a/README.markdown
+++ b/README.markdown
@@ -104,7 +104,7 @@ Bad sorting algorithms (don't use these!):
 
 - [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
-- Linear Regression
+- [Linear Regression](Linear Regression/)
 - Logistic Regression
 - Neural Networks
 - PageRank

From 797fd0a029266aef1e42e8bb11f45faa21a232db Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 28 Jul 2016 07:03:49 -0700
Subject: [PATCH 0438/1679] Minor code style change in read.me file of Linear
 Regression

---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 3fc16ff31..c04e3b3dc 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -57,12 +57,12 @@ func predictedCarPrice(carAge: Double) -> Double {
 Now for the code which will perform the iterations:
 
 ```swift
-let numberOfCarAdvertsWeSaw = carPrice.count - 1
+let numberOfCarAdvertsWeSaw = carPrice.count
 let iterations = 2000
 let alpha = 0.0001
 
 for n in 1...iterations {
-    for i in 0...numberOfCarAdvertsWeSaw {
+    for i in 0..<numberOfCarAdvertsWeSaw {
         let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference
         slope += alpha * difference * carAge[i]

From a80282ccd475892bd63116ca32ed235ce2264924 Mon Sep 17 00:00:00 2001
From: Nagasawa Hiroki <civokjots10.pico@gmail.com>
Date: Sun, 31 Jul 2016 09:56:27 +0900
Subject: [PATCH 0439/1679] Add public access in Tree

---
 Tree/Tree.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index 89f1a39da..39d1f3df5 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -25,7 +25,7 @@ extension TreeNode: CustomStringConvertible {
 }
 
 extension TreeNode where T: Equatable {
-  func search(value: T) -> TreeNode? {
+  public func search(value: T) -> TreeNode? {
     if value == self.value {
       return self
     }

From c95bec277b89eda7992abfe4716281d3bf136301 Mon Sep 17 00:00:00 2001
From: Tim Camber <tim@camber.us>
Date: Mon, 1 Aug 2016 12:59:24 -0400
Subject: [PATCH 0440/1679] Adds Knuth-Morris-Pratt to Substring Searches

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 35dad0aff..418cb1fa8 100644
--- a/README.markdown
+++ b/README.markdown
@@ -55,6 +55,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 
 - [Brute-Force String Search](Brute-Force String Search/). A naive method.
 - [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
+- Knuth-Morris-Pratt
 - Rabin-Karp
 - [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
 

From 9c5aad72a5bf760088377ce0dc4ee0113337de9d Mon Sep 17 00:00:00 2001
From: Ian Alexander Rahman <ianrahman@users.noreply.github.com>
Date: Mon, 1 Aug 2016 22:02:35 -0400
Subject: [PATCH 0441/1679] Minor grammatical fixes

---
 K-Means/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/K-Means/README.markdown b/K-Means/README.markdown
index bebcf225b..774cc18d2 100644
--- a/K-Means/README.markdown
+++ b/K-Means/README.markdown
@@ -45,11 +45,11 @@ The selection of initial centroids was fortuitous! We found the lower left clust
 
 #### Bad clustering
 
-The next two examples highlight the unpredictability of k-Means and how it not always finds the best clustering.
+The next two examples highlight the unpredictability of k-Means and how it does not always find the best clustering.
 
 ![Bad Clustering 1](Images/k_means_bad1.png)
 
-As you can see in this one, the initial centroids were all a little too close to one another, and the blue one didn't quite get to a good place. By adjusting the convergence distance we should be able to get it better.
+As you can see in this example, the initial centroids were all a little too close to one another, and the blue one didn't quite get to a good place. By adjusting the convergence distance we should be able to improve the fit of our centroids to the data.
 
 ![Bad Clustering 1](Images/k_means_bad2.png)
 

From 4d56039855507bdbe090f8ecb1b7dc52b9ab6329 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 3 Aug 2016 22:41:05 -0700
Subject: [PATCH 0442/1679] Minor styling fixes to comb sort

---
 Comb Sort/Comb Sort.playground/Contents.swift | 48 ++++++++-----------
 1 file changed, 20 insertions(+), 28 deletions(-)

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index 3bc03546a..2d6155b50 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -5,45 +5,37 @@
 import Cocoa
 
 func combSort (input: [Int]) -> [Int] {
-    var copy: [Int] = input
-    var gap = copy.count
-    let shrink = 1.3
-    
-    while gap > 1 {
-        gap = (Int)(Double(gap) / shrink)
-        if gap < 1 {
-            gap = 1
-        }
-        
-        var index = 0
-        while !(index + gap >= copy.count) {
-            if copy[index] > copy[index + gap] {
-                swap(&copy[index], &copy[index + gap])
-            }
-            index += 1
-        }
+  var copy = input
+  var gap = copy.count
+  let shrink = 1.3
+
+  while gap > 1 {
+    gap = Int(Double(gap) / shrink)
+    if gap < 1 {
+      gap = 1
     }
-    return copy
-}
 
-// A function to swap two integer values
-// Used for swapping within the array of values.
-func swap (inout a: Int, inout b: Int) {
-    let temp = a
-    a = b
-    b = temp
+    var index = 0
+    while index + gap < copy.count {
+      if copy[index] > copy[index + gap] {
+        swap(&copy[index], &copy[index + gap])
+      }
+      index += 1
+    }
+  }
+  return copy
 }
 
 // Test Comb Sort with small array of ten values
-let array: [Int] = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
+let array = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
 combSort(array)
 
 // Test Comb Sort with large array of 1000 random values
 var bigArray = [Int](count: 1000, repeatedValue: 0)
 var i = 0
 while i < 1000 {
-    bigArray[i] = Int(arc4random_uniform(1000) + 1)
-    i += 1
+  bigArray[i] = Int(arc4random_uniform(1000) + 1)
+  i += 1
 }
 combSort(bigArray)
 

From 5046c1f6fd1496528ac7a072100aa625a31be03c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 3 Aug 2016 22:43:42 -0700
Subject: [PATCH 0443/1679] Added Comb Sort to main readme file

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 35dad0aff..233bd94f3 100644
--- a/README.markdown
+++ b/README.markdown
@@ -92,6 +92,7 @@ Bad sorting algorithms (don't use these!):
 ### Miscellaneous
 
 - [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
+- [Comb Sort](Comb Sort/). An improve upon the Bubble Sort algorithm.
 
 ### Mathematics
 

From bbee485a20d3f8ce77243d110506abce87fd0042 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Wed, 17 Aug 2016 19:36:23 +0200
Subject: [PATCH 0444/1679] Create README.md

---
 Skip-List/README.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Skip-List/README.md

diff --git a/Skip-List/README.md b/Skip-List/README.md
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/Skip-List/README.md
@@ -0,0 +1 @@
+

From 559c0b1c7039a87c769c10545f5731fad0da39e0 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 18 Aug 2016 22:43:03 +1200
Subject: [PATCH 0445/1679] Xcode auto migration to Swift 3

---
 AVL Tree/AVLTree.swift                        | 62 +++++++++----------
 AVL Tree/Tests/AVLTreeTests.swift             | 24 +++----
 .../Tests/Tests.xcodeproj/project.pbxproj     |  3 +
 3 files changed, 46 insertions(+), 43 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 580a51e8e..427d3da11 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -20,16 +20,16 @@
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.
 
-public class TreeNode<Key: Comparable, Payload> {
+open class TreeNode<Key: Comparable, Payload> {
   public typealias Node = TreeNode<Key, Payload>
 
-  public var payload: Payload?
+  open var payload: Payload?
 
-  private var key: Key
+  fileprivate var key: Key
   internal var leftChild: Node?
   internal var rightChild: Node?
-  private var height: Int
-  weak private var parent: Node?
+  fileprivate var height: Int
+  weak fileprivate var parent: Node?
 
   public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
     self.key = key
@@ -51,46 +51,46 @@ public class TreeNode<Key: Comparable, Payload> {
     self.init(key: key, payload: nil)
   }
 
-  public var isRoot: Bool {
+  open var isRoot: Bool {
     return parent == nil
   }
 
-  public var isLeaf: Bool {
+  open var isLeaf: Bool {
     return rightChild == nil && leftChild == nil
   }
 
-  public var isLeftChild: Bool {
+  open var isLeftChild: Bool {
     return parent?.leftChild === self
   }
 
-  public var isRightChild: Bool {
+  open var isRightChild: Bool {
     return parent?.rightChild === self
   }
 
-  public var hasLeftChild: Bool {
+  open var hasLeftChild: Bool {
     return leftChild != nil
   }
 
-  public var hasRightChild: Bool {
+  open var hasRightChild: Bool {
     return rightChild != nil
   }
 
-  public var hasAnyChild: Bool {
+  open var hasAnyChild: Bool {
     return leftChild != nil || rightChild != nil
   }
 
-  public var hasBothChildren: Bool {
+  open var hasBothChildren: Bool {
     return leftChild != nil && rightChild != nil
   }
 }
 
 // MARK: - The AVL tree
 
-public class AVLTree<Key: Comparable, Payload> {
+open class AVLTree<Key: Comparable, Payload> {
   public typealias Node = TreeNode<Key, Payload>
 
-  private(set) public var root: Node?
-  private(set) public var size = 0
+  fileprivate(set) open var root: Node?
+  fileprivate(set) open var size = 0
 
   public init() { }
 }
@@ -119,7 +119,7 @@ extension AVLTree {
     set { insert(key, newValue) }
   }
 
-  public func search(input: Key) -> Payload? {
+  public func search(_ input: Key) -> Payload? {
     if let result = search(input, root) {
       return result.payload
     } else {
@@ -127,7 +127,7 @@ extension AVLTree {
     }
   }
 
-  private func search(key: Key, _ node: Node?) -> Node? {
+  fileprivate func search(_ key: Key, _ node: Node?) -> Node? {
     if let node = node {
       if key == node.key {
         return node
@@ -144,7 +144,7 @@ extension AVLTree {
 // MARK: - Inserting new items
 
 extension AVLTree {
-  public func insert(key: Key, _ payload: Payload? = nil) {
+  public func insert(_ key: Key, _ payload: Payload? = nil) {
     if let root = root {
       insert(key, payload, root)
     } else {
@@ -153,7 +153,7 @@ extension AVLTree {
     size += 1
   }
 
-  private func insert(input: Key, _ payload: Payload?, _ node: Node) {
+  fileprivate func insert(_ input: Key, _ payload: Payload?, _ node: Node) {
     if input < node.key {
       if let child = node.leftChild {
         insert(input, payload, child)
@@ -177,7 +177,7 @@ extension AVLTree {
 // MARK: - Balancing tree
 
 extension AVLTree {
-  private func updateHeightUpwards(node: Node?) {
+  fileprivate func updateHeightUpwards(_ node: Node?) {
     if let node = node {
       let lHeight = node.leftChild?.height ?? 0
       let rHeight = node.rightChild?.height ?? 0
@@ -186,13 +186,13 @@ extension AVLTree {
     }
   }
 
-  private func lrDifference(node: Node?) -> Int {
+  fileprivate func lrDifference(_ node: Node?) -> Int {
     let lHeight = node?.leftChild?.height ?? 0
     let rHeight = node?.rightChild?.height ?? 0
     return lHeight - rHeight
   }
 
-  private func balance(node: Node?) {
+  fileprivate func balance(_ node: Node?) {
     guard let node = node else {
       return
     }
@@ -200,8 +200,8 @@ extension AVLTree {
     updateHeightUpwards(node.leftChild)
     updateHeightUpwards(node.rightChild)
 
-    var nodes = [Node?](count: 3, repeatedValue: nil)
-    var subtrees = [Node?](count: 4, repeatedValue: nil)
+    var nodes = [Node?](repeating: nil, count: 3)
+    var subtrees = [Node?](repeating: nil, count: 4)
     let nodeParent = node.parent
 
     let lrFactor = lrDifference(node)
@@ -295,7 +295,7 @@ extension AVLTree {
 // MARK: - Displaying tree
 
 extension AVLTree {
-  private func display(node: Node?, level: Int) {
+  fileprivate func display(_ node: Node?, level: Int) {
     if let node = node {
       display(node.rightChild, level: level + 1)
       print("")
@@ -310,7 +310,7 @@ extension AVLTree {
     }
   }
 
-  public func display(node: Node) {
+  public func display(_ node: Node) {
     display(node, level: 0)
     print("")
   }
@@ -319,7 +319,7 @@ extension AVLTree {
 // MARK: - Delete node
 
 extension AVLTree {
-  public func delete(key: Key) {
+  public func delete(_ key: Key) {
     if size == 1 {
       root = nil
       size -= 1
@@ -329,7 +329,7 @@ extension AVLTree {
     }
   }
 
-  private func delete(node: Node) {
+  fileprivate func delete(_ node: Node) {
     if node.isLeaf {
       // Just remove and balance up
       if let parent = node.parent {
@@ -351,11 +351,11 @@ extension AVLTree {
       }
     } else {
       // Handle stem cases
-      if let replacement = node.leftChild?.maximum() where replacement !== node {
+      if let replacement = node.leftChild?.maximum() , replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(replacement)
-      } else if let replacement = node.rightChild?.minimum() where replacement !== node {
+      } else if let replacement = node.rightChild?.minimum() , replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(replacement)
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 065367bb6..637f499e9 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -67,25 +67,25 @@ class AVLTreeTests: XCTestCase {
   }
 
   func testSingleInsertionPerformance() {
-    self.measureBlock {
+    self.measure {
       self.tree?.insert(5, "E")
     }
   }
 
   func testMultipleInsertionsPerformance() {
-    self.measureBlock {
+    self.measure {
       self.tree?.autopopulateWithNodes(50)
     }
   }
 
   func testSearchExistentOnSmallTreePerformance() {
-    self.measureBlock {
+    self.measure {
       self.tree?.search(2)
     }
   }
 
   func testSearchExistentElementOnLargeTreePerformance() {
-    self.measureBlock {
+    self.measure {
       self.tree?.autopopulateWithNodes(500)
       self.tree?.search(400)
     }
@@ -150,8 +150,8 @@ class AVLTreeTests: XCTestCase {
   }
 }
 
-extension AVLTree where Key : SignedIntegerType {
-  func autopopulateWithNodes(count: Int) {
+extension AVLTree where Key : SignedInteger {
+  func autopopulateWithNodes(_ count: Int) {
     var k: Key = 1
     for _ in 0...count {
       self.insert(k)
@@ -160,12 +160,12 @@ extension AVLTree where Key : SignedIntegerType {
   }
 }
 
-enum AVLTreeError: ErrorType {
-  case NotBalanced
+enum AVLTreeError: Error {
+  case notBalanced
 }
 
-extension AVLTree where Key : SignedIntegerType {
-  func height(node: Node?) -> Int {
+extension AVLTree where Key : SignedInteger {
+  func height(_ node: Node?) -> Int {
     if let node = node {
       let lHeight = height(node.leftChild)
       let rHeight = height(node.rightChild)
@@ -175,10 +175,10 @@ extension AVLTree where Key : SignedIntegerType {
     return 0
   }
 
-  func inOrderCheckBalanced(node: Node?) throws {
+  func inOrderCheckBalanced(_ node: Node?) throws {
     if let node = node {
       guard abs(height(node.leftChild) - height(node.rightChild)) <= 1 else {
-        throw AVLTreeError.NotBalanced
+        throw AVLTreeError.notBalanced
       }
       try inOrderCheckBalanced(node.leftChild)
       try inOrderCheckBalanced(node.rightChild)
diff --git a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj
index dfaf44e8d..079f0010b 100644
--- a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -91,6 +91,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -224,6 +225,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +237,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 4683bb9bf30ce68aa005111dfd3fd7b852a9091b Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 18 Aug 2016 22:49:37 +1200
Subject: [PATCH 0446/1679] Updating project to recommended settings

---
 AVL Tree/Tests/Tests.xcodeproj/project.pbxproj             | 7 ++++++-
 .../Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme  | 2 +-
 2 files changed, 7 insertions(+), 2 deletions(-)

diff --git a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj
index 079f0010b..64c244747 100644
--- a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,7 +86,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -150,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -194,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -214,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
diff --git a/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/AVL Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From cfb23c46449ff643235fa2cd337bb6514406e41a Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 18 Aug 2016 23:44:10 +1200
Subject: [PATCH 0447/1679] Removing "open" access level that was automatically
 included in auto migration to swift 3. Removing underscore labels.

---
 AVL Tree/AVLTree.swift            | 102 +++++++++++++++---------------
 AVL Tree/Tests/AVLTreeTests.swift |  34 +++++-----
 2 files changed, 68 insertions(+), 68 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 427d3da11..b4b97f0d6 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -20,10 +20,10 @@
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.
 
-open class TreeNode<Key: Comparable, Payload> {
+public class TreeNode<Key: Comparable, Payload> {
   public typealias Node = TreeNode<Key, Payload>
 
-  open var payload: Payload?
+  var payload: Payload?
 
   fileprivate var key: Key
   internal var leftChild: Node?
@@ -51,35 +51,35 @@ open class TreeNode<Key: Comparable, Payload> {
     self.init(key: key, payload: nil)
   }
 
-  open var isRoot: Bool {
+  var isRoot: Bool {
     return parent == nil
   }
 
-  open var isLeaf: Bool {
+  var isLeaf: Bool {
     return rightChild == nil && leftChild == nil
   }
 
-  open var isLeftChild: Bool {
+  var isLeftChild: Bool {
     return parent?.leftChild === self
   }
 
-  open var isRightChild: Bool {
+  var isRightChild: Bool {
     return parent?.rightChild === self
   }
 
-  open var hasLeftChild: Bool {
+  var hasLeftChild: Bool {
     return leftChild != nil
   }
 
-  open var hasRightChild: Bool {
+  var hasRightChild: Bool {
     return rightChild != nil
   }
 
-  open var hasAnyChild: Bool {
+  var hasAnyChild: Bool {
     return leftChild != nil || rightChild != nil
   }
 
-  open var hasBothChildren: Bool {
+  var hasBothChildren: Bool {
     return leftChild != nil && rightChild != nil
   }
 }
@@ -89,8 +89,8 @@ open class TreeNode<Key: Comparable, Payload> {
 open class AVLTree<Key: Comparable, Payload> {
   public typealias Node = TreeNode<Key, Payload>
 
-  fileprivate(set) open var root: Node?
-  fileprivate(set) open var size = 0
+  fileprivate(set) var root: Node?
+  fileprivate(set) var size = 0
 
   public init() { }
 }
@@ -115,26 +115,26 @@ extension TreeNode {
 
 extension AVLTree {
   subscript(key: Key) -> Payload? {
-    get { return search(key) }
-    set { insert(key, newValue) }
+    get { return search(input: key) }
+    set { insert(key: key, payload: newValue) }
   }
 
-  public func search(_ input: Key) -> Payload? {
-    if let result = search(input, root) {
+  public func search(input: Key) -> Payload? {
+    if let result = search(key: input, node: root) {
       return result.payload
     } else {
       return nil
     }
   }
 
-  fileprivate func search(_ key: Key, _ node: Node?) -> Node? {
+  fileprivate func search(key: Key, node: Node?) -> Node? {
     if let node = node {
       if key == node.key {
         return node
       } else if key < node.key {
-        return search(key, node.leftChild)
+        return search(key: key, node: node.leftChild)
       } else {
-        return search(key, node.rightChild)
+        return search(key: key, node: node.rightChild)
       }
     }
     return nil
@@ -144,31 +144,31 @@ extension AVLTree {
 // MARK: - Inserting new items
 
 extension AVLTree {
-  public func insert(_ key: Key, _ payload: Payload? = nil) {
+  public func insert(key: Key, payload: Payload? = nil) {
     if let root = root {
-      insert(key, payload, root)
+      insert(input: key, payload: payload, node: root)
     } else {
       root = Node(key: key, payload: payload)
     }
     size += 1
   }
 
-  fileprivate func insert(_ input: Key, _ payload: Payload?, _ node: Node) {
+  private func insert(input: Key, payload: Payload?, node: Node) {
     if input < node.key {
       if let child = node.leftChild {
-        insert(input, payload, child)
+        insert(input: input, payload: payload, node: child)
       } else {
         let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.leftChild = child
-        balance(child)
+        balance(node: child)
       }
     } else {
       if let child = node.rightChild {
-        insert(input, payload, child)
+        insert(input: input, payload: payload, node: child)
       } else {
         let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.rightChild = child
-        balance(child)
+        balance(node: child)
       }
     }
   }
@@ -177,37 +177,37 @@ extension AVLTree {
 // MARK: - Balancing tree
 
 extension AVLTree {
-  fileprivate func updateHeightUpwards(_ node: Node?) {
+  fileprivate func updateHeightUpwards(node: Node?) {
     if let node = node {
       let lHeight = node.leftChild?.height ?? 0
       let rHeight = node.rightChild?.height ?? 0
       node.height = max(lHeight, rHeight) + 1
-      updateHeightUpwards(node.parent)
+      updateHeightUpwards(node: node.parent)
     }
   }
 
-  fileprivate func lrDifference(_ node: Node?) -> Int {
+  fileprivate func lrDifference(node: Node?) -> Int {
     let lHeight = node?.leftChild?.height ?? 0
     let rHeight = node?.rightChild?.height ?? 0
     return lHeight - rHeight
   }
 
-  fileprivate func balance(_ node: Node?) {
+  fileprivate func balance(node: Node?) {
     guard let node = node else {
       return
     }
 
-    updateHeightUpwards(node.leftChild)
-    updateHeightUpwards(node.rightChild)
+    updateHeightUpwards(node: node.leftChild)
+    updateHeightUpwards(node: node.rightChild)
 
     var nodes = [Node?](repeating: nil, count: 3)
     var subtrees = [Node?](repeating: nil, count: 4)
     let nodeParent = node.parent
 
-    let lrFactor = lrDifference(node)
+    let lrFactor = lrDifference(node: node)
     if lrFactor > 1 {
       // left-left or left-right
-      if lrDifference(node.leftChild) > 0 {
+      if lrDifference(node: node.leftChild) > 0 {
         // left-left
         nodes[0] = node
         nodes[2] = node.leftChild
@@ -230,7 +230,7 @@ extension AVLTree {
       }
     } else if lrFactor < -1 {
       // right-left or right-right
-      if lrDifference(node.rightChild) < 0 {
+      if lrDifference(node: node.rightChild) < 0 {
         // right-right
         nodes[1] = node
         nodes[2] = node.rightChild
@@ -253,7 +253,7 @@ extension AVLTree {
       }
     } else {
       // Don't need to balance 'node', go for parent
-      balance(node.parent)
+      balance(node: node.parent)
       return
     }
 
@@ -285,19 +285,19 @@ extension AVLTree {
     nodes[0]?.rightChild = subtrees[3]
     subtrees[3]?.parent = nodes[0]
 
-    updateHeightUpwards(nodes[1])    // Update height from left
-    updateHeightUpwards(nodes[0])    // Update height from right
+    updateHeightUpwards(node: nodes[1])    // Update height from left
+    updateHeightUpwards(node: nodes[0])    // Update height from right
 
-    balance(nodes[2]?.parent)
+    balance(node: nodes[2]?.parent)
   }
 }
 
 // MARK: - Displaying tree
 
 extension AVLTree {
-  fileprivate func display(_ node: Node?, level: Int) {
+  fileprivate func display(node: Node?, level: Int) {
     if let node = node {
-      display(node.rightChild, level: level + 1)
+      display(node: node.rightChild, level: level + 1)
       print("")
       if node.isRoot {
         print("Root -> ", terminator: "")
@@ -306,12 +306,12 @@ extension AVLTree {
         print("        ", terminator:  "")
       }
       print("(\(node.key):\(node.height))", terminator: "")
-      display(node.leftChild, level: level + 1)
+      display(node: node.leftChild, level: level + 1)
     }
   }
 
-  public func display(_ node: Node) {
-    display(node, level: 0)
+  public func display(node: Node) {
+    display(node: node, level: 0)
     print("")
   }
 }
@@ -319,17 +319,17 @@ extension AVLTree {
 // MARK: - Delete node
 
 extension AVLTree {
-  public func delete(_ key: Key) {
+  public func delete(key: Key) {
     if size == 1 {
       root = nil
       size -= 1
-    } else if let node = search(key, root) {
-      delete(node)
+    } else if let node = search(key: key, node: root) {
+      delete(node: node)
       size -= 1
     }
   }
 
-  fileprivate func delete(_ node: Node) {
+  private func delete(node: Node) {
     if node.isLeaf {
       // Just remove and balance up
       if let parent = node.parent {
@@ -344,7 +344,7 @@ extension AVLTree {
           parent.rightChild = nil
         }
 
-        balance(parent)
+        balance(node: parent)
       } else {
         // at root
         root = nil
@@ -354,11 +354,11 @@ extension AVLTree {
       if let replacement = node.leftChild?.maximum() , replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
-        delete(replacement)
+        delete(node: replacement)
       } else if let replacement = node.rightChild?.minimum() , replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
-        delete(replacement)
+        delete(node: replacement)
       }
     }
   }
diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 637f499e9..51607d7c3 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -37,7 +37,7 @@ class AVLTreeTests: XCTestCase {
     self.tree?.autopopulateWithNodes(5)
 
     for i in 6...10 {
-      self.tree?.insert(i)
+      self.tree?.insert(key: i)
       do {
         try self.tree?.inOrderCheckBalanced(self.tree?.root)
       } catch _ {
@@ -50,7 +50,7 @@ class AVLTreeTests: XCTestCase {
     self.tree?.autopopulateWithNodes(5)
 
     for i in 1...6 {
-      self.tree?.delete(i)
+      self.tree?.delete(key: i)
       do {
         try self.tree?.inOrderCheckBalanced(self.tree?.root)
       } catch _ {
@@ -68,7 +68,7 @@ class AVLTreeTests: XCTestCase {
 
   func testSingleInsertionPerformance() {
     self.measure {
-      self.tree?.insert(5, "E")
+      self.tree?.insert(key: 5, payload: "E")
     }
   }
 
@@ -80,14 +80,14 @@ class AVLTreeTests: XCTestCase {
 
   func testSearchExistentOnSmallTreePerformance() {
     self.measure {
-      self.tree?.search(2)
+      self.tree?.search(input: 2)
     }
   }
 
   func testSearchExistentElementOnLargeTreePerformance() {
     self.measure {
       self.tree?.autopopulateWithNodes(500)
-      self.tree?.search(400)
+      self.tree?.search(input: 400)
     }
   }
 
@@ -106,19 +106,19 @@ class AVLTreeTests: XCTestCase {
   }
 
   func testDeleteExistentKey() {
-    self.tree?.delete(1)
-    XCTAssertNil(self.tree?.search(1), "Key should not exist anymore")
+    self.tree?.delete(key: 1)
+    XCTAssertNil(self.tree?.search(input: 1), "Key should not exist anymore")
   }
 
   func testDeleteNotExistentKey() {
-    self.tree?.delete(1056)
-    XCTAssertNil(self.tree?.search(1056), "Key should not exist")
+    self.tree?.delete(key: 1056)
+    XCTAssertNil(self.tree?.search(input: 1056), "Key should not exist")
   }
 
   func testInsertSize() {
     let tree = AVLTree<Int, String>()
     for i in 0...5 {
-      tree.insert(i, "")
+      tree.insert(key: i, payload: "")
       XCTAssertEqual(tree.size, i + 1, "Insert didn't update size correctly!")
     }
   }
@@ -134,15 +134,15 @@ class AVLTreeTests: XCTestCase {
     for p in permutations {
       let tree = AVLTree<Int, String>()
 
-      tree.insert(1, "five")
-      tree.insert(2, "four")
-      tree.insert(3, "three")
-      tree.insert(4, "two")
-      tree.insert(5, "one")
+      tree.insert(key: 1, payload: "five")
+      tree.insert(key: 2, payload: "four")
+      tree.insert(key: 3, payload: "three")
+      tree.insert(key: 4, payload: "two")
+      tree.insert(key: 5, payload: "one")
 
       var count = tree.size
       for i in p {
-        tree.delete(i)
+        tree.delete(key: i)
         count -= 1
         XCTAssertEqual(tree.size, count, "Delete didn't update size correctly!")
       }
@@ -154,7 +154,7 @@ extension AVLTree where Key : SignedInteger {
   func autopopulateWithNodes(_ count: Int) {
     var k: Key = 1
     for _ in 0...count {
-      self.insert(k)
+      self.insert(key: k)
       k = k + 1
     }
   }

From b094e0fde016e4cb19693a5eb3c67745c6bd9b02 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 18 Aug 2016 23:45:28 +1200
Subject: [PATCH 0448/1679] Updating travis build to Xcode 8. Commenting out
 projects that have not yet been migrated.

---
 .travis.yml | 64 ++++++++++++++++++++++++++---------------------------
 1 file changed, 32 insertions(+), 32 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 7f13f64eb..b01dfd26a 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 language: objective-c
-osx_image: xcode7.3
+osx_image: xcode8
 sudo: false
 
 install:
@@ -8,34 +8,34 @@ install:
 
 script:
 
-- xctool test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-- xctool test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests
-- xctool test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-- xctool test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
-- xctool test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
+# - xctool test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+ - xctool test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests
+# - xctool test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
+# - xctool test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+# - xctool test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 8df51248547fe53cf199bc6ad7cea39d8e85d8d4 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Thu, 18 Aug 2016 23:51:01 +1200
Subject: [PATCH 0449/1679] Removing "expression not used" warnings in test

---
 AVL Tree/Tests/AVLTreeTests.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 51607d7c3..7765c6d29 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -80,14 +80,14 @@ class AVLTreeTests: XCTestCase {
 
   func testSearchExistentOnSmallTreePerformance() {
     self.measure {
-      self.tree?.search(input: 2)
+      print(self.tree?.search(input: 2))
     }
   }
 
   func testSearchExistentElementOnLargeTreePerformance() {
     self.measure {
       self.tree?.autopopulateWithNodes(500)
-      self.tree?.search(input: 400)
+      print(self.tree?.search(input: 400))
     }
   }
 

From f0ad3f504b4bcf7bff71dd58ac37916990e59fc5 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 19 Aug 2016 00:05:37 +1200
Subject: [PATCH 0450/1679] Disabling swift lint until all projects can be
 built in Xcode 8

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index b01dfd26a..0cb6dc728 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,7 +4,7 @@ sudo: false
 
 install:
 
-- ./install_swiftlint.sh
+# - ./install_swiftlint.sh
 
 script:
 

From 9537cf8722778a7ecdaa0b3bf5bc9109e12da4c2 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 19 Aug 2016 00:09:55 +1200
Subject: [PATCH 0451/1679] Trying to resolve build error "*** Terminating app
 due to uncaught exception 'NSInternalInconsistencyException', reason: 'Got
 error while trying to deserialize event 'User defaults from command line:':
 The data is not in the correct format.'"

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 0cb6dc728..b8199a4a3 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,6 +1,6 @@
 language: objective-c
 osx_image: xcode8
-sudo: false
+# sudo: false
 
 install:
 

From 2813695209a888e6f01364d79d9c3cc2a60f3fad Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 19 Aug 2016 00:14:20 +1200
Subject: [PATCH 0452/1679] Changing to xcodebuild as xctool fails to run
 tests. Terminating app due to uncaught exception
 'NSInternalInconsistencyException', reason: 'Got error while trying to
 deserialize event 'User defaults from command line:': The data is not in the
 correct format.'

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index b8199a4a3..228faab79 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -10,7 +10,7 @@ script:
 
 # - xctool test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
 # - xctool test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
- - xctool test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 # - xctool test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xctool test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 # - xctool test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests

From 0267f61a4abd42606c7d5be4c7c5cec189944ad7 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 19 Aug 2016 00:20:27 +1200
Subject: [PATCH 0453/1679] Changing xctool to xcodebuild for all tests

---
 .travis.yml | 60 ++++++++++++++++++++++++++---------------------------
 1 file changed, 30 insertions(+), 30 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 228faab79..970f85aa8 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -8,34 +8,34 @@ install:
 
 script:
 
-# - xctool test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-# - xctool test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
+# - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Graph/Graph.xcodeproj -scheme GraphTests
-# - xctool test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-# - xctool test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
-# - xctool test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
+# - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
+# - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From c104087a821fef3b2058095ea70490a152d7fc80 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 19 Aug 2016 00:35:32 +1200
Subject: [PATCH 0454/1679] Updating playground

---
 AVL Tree/AVLTree.playground/Contents.swift    |  22 ++--
 .../AVLTree.playground/Sources/AVLTree.swift  | 108 +++++++++---------
 .../AVLTree.playground/timeline.xctimeline    |   6 -
 3 files changed, 65 insertions(+), 71 deletions(-)
 delete mode 100644 AVL Tree/AVLTree.playground/timeline.xctimeline

diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 2b8ee8b59..409dfdc49 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -2,26 +2,26 @@
 
 let tree = AVLTree<Int, String>()
 
-tree.insert(5, "five")
+tree.insert(key: 5, payload: "five")
 print(tree)
 
-tree.insert(4, "four")
+tree.insert(key: 4, payload: "four")
 print(tree)
 
-tree.insert(3, "three")
+tree.insert(key: 3, payload: "three")
 print(tree)
 
-tree.insert(2, "two")
+tree.insert(key: 2, payload: "two")
 print(tree)
 
-tree.insert(1, "one")
+tree.insert(key: 1, payload: "one")
 print(tree)
 print(tree.debugDescription)
 
-let node = tree.search(2)   // "two"
+let node = tree.search(input: 2)   // "two"
 
-tree.delete(5)
-tree.delete(2)
-tree.delete(1)
-tree.delete(4)
-tree.delete(3)
+tree.delete(key: 5)
+tree.delete(key: 2)
+tree.delete(key: 1)
+tree.delete(key: 4)
+tree.delete(key: 3)
diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index 580a51e8e..b4b97f0d6 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -23,13 +23,13 @@
 public class TreeNode<Key: Comparable, Payload> {
   public typealias Node = TreeNode<Key, Payload>
 
-  public var payload: Payload?
+  var payload: Payload?
 
-  private var key: Key
+  fileprivate var key: Key
   internal var leftChild: Node?
   internal var rightChild: Node?
-  private var height: Int
-  weak private var parent: Node?
+  fileprivate var height: Int
+  weak fileprivate var parent: Node?
 
   public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
     self.key = key
@@ -51,46 +51,46 @@ public class TreeNode<Key: Comparable, Payload> {
     self.init(key: key, payload: nil)
   }
 
-  public var isRoot: Bool {
+  var isRoot: Bool {
     return parent == nil
   }
 
-  public var isLeaf: Bool {
+  var isLeaf: Bool {
     return rightChild == nil && leftChild == nil
   }
 
-  public var isLeftChild: Bool {
+  var isLeftChild: Bool {
     return parent?.leftChild === self
   }
 
-  public var isRightChild: Bool {
+  var isRightChild: Bool {
     return parent?.rightChild === self
   }
 
-  public var hasLeftChild: Bool {
+  var hasLeftChild: Bool {
     return leftChild != nil
   }
 
-  public var hasRightChild: Bool {
+  var hasRightChild: Bool {
     return rightChild != nil
   }
 
-  public var hasAnyChild: Bool {
+  var hasAnyChild: Bool {
     return leftChild != nil || rightChild != nil
   }
 
-  public var hasBothChildren: Bool {
+  var hasBothChildren: Bool {
     return leftChild != nil && rightChild != nil
   }
 }
 
 // MARK: - The AVL tree
 
-public class AVLTree<Key: Comparable, Payload> {
+open class AVLTree<Key: Comparable, Payload> {
   public typealias Node = TreeNode<Key, Payload>
 
-  private(set) public var root: Node?
-  private(set) public var size = 0
+  fileprivate(set) var root: Node?
+  fileprivate(set) var size = 0
 
   public init() { }
 }
@@ -115,26 +115,26 @@ extension TreeNode {
 
 extension AVLTree {
   subscript(key: Key) -> Payload? {
-    get { return search(key) }
-    set { insert(key, newValue) }
+    get { return search(input: key) }
+    set { insert(key: key, payload: newValue) }
   }
 
   public func search(input: Key) -> Payload? {
-    if let result = search(input, root) {
+    if let result = search(key: input, node: root) {
       return result.payload
     } else {
       return nil
     }
   }
 
-  private func search(key: Key, _ node: Node?) -> Node? {
+  fileprivate func search(key: Key, node: Node?) -> Node? {
     if let node = node {
       if key == node.key {
         return node
       } else if key < node.key {
-        return search(key, node.leftChild)
+        return search(key: key, node: node.leftChild)
       } else {
-        return search(key, node.rightChild)
+        return search(key: key, node: node.rightChild)
       }
     }
     return nil
@@ -144,31 +144,31 @@ extension AVLTree {
 // MARK: - Inserting new items
 
 extension AVLTree {
-  public func insert(key: Key, _ payload: Payload? = nil) {
+  public func insert(key: Key, payload: Payload? = nil) {
     if let root = root {
-      insert(key, payload, root)
+      insert(input: key, payload: payload, node: root)
     } else {
       root = Node(key: key, payload: payload)
     }
     size += 1
   }
 
-  private func insert(input: Key, _ payload: Payload?, _ node: Node) {
+  private func insert(input: Key, payload: Payload?, node: Node) {
     if input < node.key {
       if let child = node.leftChild {
-        insert(input, payload, child)
+        insert(input: input, payload: payload, node: child)
       } else {
         let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.leftChild = child
-        balance(child)
+        balance(node: child)
       }
     } else {
       if let child = node.rightChild {
-        insert(input, payload, child)
+        insert(input: input, payload: payload, node: child)
       } else {
         let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
         node.rightChild = child
-        balance(child)
+        balance(node: child)
       }
     }
   }
@@ -177,37 +177,37 @@ extension AVLTree {
 // MARK: - Balancing tree
 
 extension AVLTree {
-  private func updateHeightUpwards(node: Node?) {
+  fileprivate func updateHeightUpwards(node: Node?) {
     if let node = node {
       let lHeight = node.leftChild?.height ?? 0
       let rHeight = node.rightChild?.height ?? 0
       node.height = max(lHeight, rHeight) + 1
-      updateHeightUpwards(node.parent)
+      updateHeightUpwards(node: node.parent)
     }
   }
 
-  private func lrDifference(node: Node?) -> Int {
+  fileprivate func lrDifference(node: Node?) -> Int {
     let lHeight = node?.leftChild?.height ?? 0
     let rHeight = node?.rightChild?.height ?? 0
     return lHeight - rHeight
   }
 
-  private func balance(node: Node?) {
+  fileprivate func balance(node: Node?) {
     guard let node = node else {
       return
     }
 
-    updateHeightUpwards(node.leftChild)
-    updateHeightUpwards(node.rightChild)
+    updateHeightUpwards(node: node.leftChild)
+    updateHeightUpwards(node: node.rightChild)
 
-    var nodes = [Node?](count: 3, repeatedValue: nil)
-    var subtrees = [Node?](count: 4, repeatedValue: nil)
+    var nodes = [Node?](repeating: nil, count: 3)
+    var subtrees = [Node?](repeating: nil, count: 4)
     let nodeParent = node.parent
 
-    let lrFactor = lrDifference(node)
+    let lrFactor = lrDifference(node: node)
     if lrFactor > 1 {
       // left-left or left-right
-      if lrDifference(node.leftChild) > 0 {
+      if lrDifference(node: node.leftChild) > 0 {
         // left-left
         nodes[0] = node
         nodes[2] = node.leftChild
@@ -230,7 +230,7 @@ extension AVLTree {
       }
     } else if lrFactor < -1 {
       // right-left or right-right
-      if lrDifference(node.rightChild) < 0 {
+      if lrDifference(node: node.rightChild) < 0 {
         // right-right
         nodes[1] = node
         nodes[2] = node.rightChild
@@ -253,7 +253,7 @@ extension AVLTree {
       }
     } else {
       // Don't need to balance 'node', go for parent
-      balance(node.parent)
+      balance(node: node.parent)
       return
     }
 
@@ -285,19 +285,19 @@ extension AVLTree {
     nodes[0]?.rightChild = subtrees[3]
     subtrees[3]?.parent = nodes[0]
 
-    updateHeightUpwards(nodes[1])    // Update height from left
-    updateHeightUpwards(nodes[0])    // Update height from right
+    updateHeightUpwards(node: nodes[1])    // Update height from left
+    updateHeightUpwards(node: nodes[0])    // Update height from right
 
-    balance(nodes[2]?.parent)
+    balance(node: nodes[2]?.parent)
   }
 }
 
 // MARK: - Displaying tree
 
 extension AVLTree {
-  private func display(node: Node?, level: Int) {
+  fileprivate func display(node: Node?, level: Int) {
     if let node = node {
-      display(node.rightChild, level: level + 1)
+      display(node: node.rightChild, level: level + 1)
       print("")
       if node.isRoot {
         print("Root -> ", terminator: "")
@@ -306,12 +306,12 @@ extension AVLTree {
         print("        ", terminator:  "")
       }
       print("(\(node.key):\(node.height))", terminator: "")
-      display(node.leftChild, level: level + 1)
+      display(node: node.leftChild, level: level + 1)
     }
   }
 
   public func display(node: Node) {
-    display(node, level: 0)
+    display(node: node, level: 0)
     print("")
   }
 }
@@ -323,8 +323,8 @@ extension AVLTree {
     if size == 1 {
       root = nil
       size -= 1
-    } else if let node = search(key, root) {
-      delete(node)
+    } else if let node = search(key: key, node: root) {
+      delete(node: node)
       size -= 1
     }
   }
@@ -344,21 +344,21 @@ extension AVLTree {
           parent.rightChild = nil
         }
 
-        balance(parent)
+        balance(node: parent)
       } else {
         // at root
         root = nil
       }
     } else {
       // Handle stem cases
-      if let replacement = node.leftChild?.maximum() where replacement !== node {
+      if let replacement = node.leftChild?.maximum() , replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
-        delete(replacement)
-      } else if let replacement = node.rightChild?.minimum() where replacement !== node {
+        delete(node: replacement)
+      } else if let replacement = node.rightChild?.minimum() , replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
-        delete(replacement)
+        delete(node: replacement)
       }
     }
   }
diff --git a/AVL Tree/AVLTree.playground/timeline.xctimeline b/AVL Tree/AVLTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/AVL Tree/AVLTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From cd9c8246e7c14c89503b642ee25ab12888a30f63 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Fri, 19 Aug 2016 00:45:38 +1200
Subject: [PATCH 0455/1679] Updating readme. Removing mentions of methods that
 are not contained in the AVLTree.swift file.

---
 AVL Tree/README.markdown | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 744d9a272..159f9e1dc 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -56,11 +56,7 @@ Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary searc
 
 > **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary Search Tree/). It will make the rest of the AVL tree easier to understand.
 
-The interesting bits are in the following methods:
-
-- `updateBalance()`. Called after inserting a new node. This may cause the node's parent to be rebalanced.
-- `rebalance()`. Figures out how to rotate the nodes to restore the balance.
-- `rotateRight()` and `rotateLeft()` perform the actual rotations.
+The interesting bits are in the `balance()` method which is called after inserting or deleting a node. 
 
 ## See also
 

From aec3405f297ae40832057b8b29486ca54e012c17 Mon Sep 17 00:00:00 2001
From: lenli <leonard.li@gmail.com>
Date: Fri, 19 Aug 2016 18:00:48 -0400
Subject: [PATCH 0456/1679] Upgrade binary search code and test to Swift 3.0

---
 .../BinarySearch.playground/Contents.swift    |  59 ++------
 .../Sources/BinarySearch.swift                |  52 +++++++
 Binary Search/BinarySearch.swift              |  64 ++++++---
 Binary Search/README.markdown                 | 131 +++++++++---------
 .../project.pbxproj                           |  30 ++--
 .../contents.xcworkspacedata                  |   0
 .../xcshareddata/xcschemes/Tests.xcscheme     |  26 ++--
 7 files changed, 207 insertions(+), 155 deletions(-)
 create mode 100644 Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
 rename Binary Search/Tests/{Tests.xcodeproj => BinarySearchTests.xcodeproj}/project.pbxproj (89%)
 rename Binary Search/Tests/{Tests.xcodeproj => BinarySearchTests.xcodeproj}/project.xcworkspace/contents.xcworkspacedata (100%)
 rename Binary Search/Tests/{Tests.xcodeproj => BinarySearchTests.xcodeproj}/xcshareddata/xcschemes/Tests.xcscheme (77%)

diff --git a/Binary Search/BinarySearch.playground/Contents.swift b/Binary Search/BinarySearch.playground/Contents.swift
index fdfd37d8f..cccf9f8ac 100644
--- a/Binary Search/BinarySearch.playground/Contents.swift	
+++ b/Binary Search/BinarySearch.playground/Contents.swift	
@@ -4,53 +4,16 @@
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
 // Binary search requires that the array is sorted from low to high
-let sorted = numbers.sort()
+let sorted = numbers.sorted()
 
-/*
-  The recursive version of binary search.
-*/
-func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> Int? {
-  if range.startIndex >= range.endIndex {
-    return nil
-  } else {
-    let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-    if a[midIndex] > key {
-      return binarySearch(a, key: key, range: range.startIndex ..< midIndex)
-    } else if a[midIndex] < key {
-      return binarySearch(a, key: key, range: midIndex + 1 ..< range.endIndex)
-    } else {
-      return midIndex
-    }
-  }
-}
+// Using recursive solution
+binarySearch(a: sorted, key: 2, range: 0 ..< sorted.count)   // gives 0
+binarySearch(a: sorted, key: 67, range: 0 ..< sorted.count)  // gives 18
+binarySearch(a: sorted, key: 43, range: 0 ..< sorted.count)  // gives 13
+binarySearch(a: sorted, key: 42, range: 0 ..< sorted.count)  // nil
 
-binarySearch(sorted, key: 2, range: 0 ..< sorted.count)   // gives 0
-binarySearch(sorted, key: 67, range: 0 ..< sorted.count)  // gives 18
-binarySearch(sorted, key: 43, range: 0 ..< sorted.count)  // gives 13
-binarySearch(sorted, key: 42, range: 0 ..< sorted.count)  // nil
-
-/*
-  The iterative version of binary search.
-
-  Notice how similar these functions are. The difference is that this one
-  uses a while loop, while the other calls itself recursively.
-*/
-func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
-  var range = 0..<a.count
-  while range.startIndex < range.endIndex {
-    let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-    if a[midIndex] == key {
-      return midIndex
-    } else if a[midIndex] < key {
-      range.startIndex = midIndex + 1
-    } else {
-      range.endIndex = midIndex
-    }
-  }
-  return nil
-}
-
-binarySearch(sorted, key: 2)   // gives 0
-binarySearch(sorted, key: 67)  // gives 18
-binarySearch(sorted, key: 43)  // gives 13
-binarySearch(sorted, key: 42)  // nil
+// Using iterative solution
+binarySearch(a: sorted, key: 2)   // gives 0
+binarySearch(a: sorted, key: 67)  // gives 18
+binarySearch(a: sorted, key: 43)  // gives 13
+binarySearch(a: sorted, key: 42)  // nil
diff --git a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift b/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
new file mode 100644
index 000000000..a7a24bd3a
--- /dev/null
+++ b/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift	
@@ -0,0 +1,52 @@
+/**
+ Binary Search
+ 
+ Recursively splits the array in half until the value is found.
+ 
+ If there is more than one occurrence of the search key in the array, then
+ there is no guarantee which one it finds.
+ 
+ Note: The array must be sorted!
+ **/
+
+import Foundation
+
+// The recursive version of binary search.
+
+public func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> Int? {
+    if range.lowerBound >= range.upperBound {
+        return nil
+    } else {
+        let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
+        if a[midIndex] > key {
+            return binarySearch(a: a, key: key, range: range.lowerBound ..< midIndex)
+        } else if a[midIndex] < key {
+            return binarySearch(a: a, key: key, range: midIndex + 1 ..< range.upperBound)
+        } else {
+            return midIndex
+        }
+    }
+}
+
+/**
+ The iterative version of binary search.
+ 
+ Notice how similar these functions are. The difference is that this one
+ uses a while loop, while the other calls itself recursively.
+ **/
+
+public func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
+    var lowerBound = 0
+    var upperBound = a.count
+    while lowerBound < upperBound {
+        let midIndex = lowerBound + (upperBound - lowerBound) / 2
+        if a[midIndex] == key {
+            return midIndex
+        } else if a[midIndex] < key {
+            lowerBound = midIndex + 1
+        } else {
+            upperBound = midIndex
+        }
+    }
+    return nil
+}
diff --git a/Binary Search/BinarySearch.swift b/Binary Search/BinarySearch.swift
index 5bcdf4152..d6623e355 100644
--- a/Binary Search/BinarySearch.swift	
+++ b/Binary Search/BinarySearch.swift	
@@ -1,24 +1,52 @@
-/*
-  Binary Search
+/**
+ Binary Search
+ 
+ Recursively splits the array in half until the value is found.
+ 
+ If there is more than one occurrence of the search key in the array, then
+ there is no guarantee which one it finds.
+ 
+ Note: The array must be sorted!
+ **/
 
-  Recursively splits the array in half until the value is found.
+import Foundation
 
-  If there is more than one occurrence of the search key in the array, then
-  there is no guarantee which one it finds.
+// The recursive version of binary search.
 
-  Note: The array must be sorted!
-*/
-func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
-  var range = 0..<a.count
-  while range.startIndex < range.endIndex {
-    let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-    if a[midIndex] == key {
-      return midIndex
-    } else if a[midIndex] < key {
-      range.startIndex = midIndex + 1
+public func binarySearch<T: Comparable>(_ a: [T], key: T, range: Range<Int>) -> Int? {
+    if range.lowerBound >= range.upperBound {
+        return nil
     } else {
-      range.endIndex = midIndex
+        let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
+        if a[midIndex] > key {
+            return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
+        } else if a[midIndex] < key {
+            return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
+        } else {
+            return midIndex
+        }
     }
-  }
-  return nil
+}
+
+/**
+ The iterative version of binary search.
+ 
+ Notice how similar these functions are. The difference is that this one
+ uses a while loop, while the other calls itself recursively.
+ **/
+
+public func binarySearch<T: Comparable>(_ a: [T], key: T) -> Int? {
+    var lowerBound = 0
+    var upperBound = a.count
+    while lowerBound < upperBound {
+        let midIndex = lowerBound + (upperBound - lowerBound) / 2
+        if a[midIndex] == key {
+            return midIndex
+        } else if a[midIndex] < key {
+            lowerBound = midIndex + 1
+        } else {
+            upperBound = midIndex
+        }
+    }
+    return nil
 }
diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 8c5d8f0f1..6fb6e9985 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -16,12 +16,12 @@ The built-in `indexOf()` function performs a [linear search](../Linear Search/).
 
 ```swift
 func linearSearch<T: Equatable>(a: [T], _ key: T) -> Int? {
-  for i in 0 ..< a.count {
-    if a[i] == key {
-      return i
-    }
-  }
-  return nil
+for i in 0 ..< a.count {
+if a[i] == key {
+return i
+}
+}
+return nil
 }
 ```
 
@@ -58,27 +58,27 @@ Here is a recursive implementation of binary search in Swift:
 
 ```swift
 func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> Int? {
-  if range.startIndex >= range.endIndex {
-    // If we get here, then the search key is not present in the array.
-    return nil
-
-  } else {
-    // Calculate where to split the array.
-    let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-    
-    // Is the search key in the left half?
-    if a[midIndex] > key {
-      return binarySearch(a, key: key, range: range.startIndex ..< midIndex)
-      
-    // Is the search key in the right half?
-    } else if a[midIndex] < key {
-      return binarySearch(a, key: key, range: midIndex + 1 ..< range.endIndex)
-      
-    // If we get here, then we've found the search key!
-    } else {
-      return midIndex
-    }
-  }
+if range.lowerBound >= range.upperBound {
+// If we get here, then the search key is not present in the array.
+return nil
+
+} else {
+// Calculate where to split the array.
+let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
+
+// Is the search key in the left half?
+if a[midIndex] > key {
+return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
+
+// Is the search key in the right half?
+} else if a[midIndex] < key {
+return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
+
+// If we get here, then we've found the search key!
+} else {
+return midIndex
+}
+}
 }
 ```
 
@@ -94,7 +94,7 @@ Note that the `numbers` array is sorted. The binary search algorithm does not wo
 
 I said that binary search works by splitting the array in half, but we don't actually create two new arrays. Instead, we keep track of these splits using a Swift `Range` object. Initially, this range covers the entire array, `0 ..< numbers.count`.  As we split the array, the range becomes smaller and smaller.
 
-> **Note:** One thing to be aware of is that `range.endIndex` always points one beyond the last element. In the example, the range is `0..<19` because there are 19 numbers in the array, and so `range.startIndex = 0` and `range.endIndex = 19`. But in our array the last element is at index 18, not 19, since we start counting from 0. Just keep this in mind when working with ranges: the `endIndex` is always one more than the index of the last element.
+> **Note:** One thing to be aware of is that `range.upperBound` always points one beyond the last element. In the example, the range is `0..<19` because there are 19 numbers in the array, and so `range.lowerBound = 0` and `range.upperBound = 19`. But in our array the last element is at index 18, not 19, since we start counting from 0. Just keep this in mind when working with ranges: the `upperBound` is always one more than the index of the last element.
 
 ## Stepping through the example
 
@@ -102,76 +102,76 @@ It might be useful to look at how the algorithm works in detail.
 
 The array from the above example consists of 19 numbers and looks like this when sorted:
 
-	[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
 
 We're trying to determine if the number `43` is in this array.
 
 To split the array in half, we need to know the index of the object in the middle. That's determined by this line:
 
 ```swift
-    let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
+let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
 ```
 
-Initially, the range has `startIndex = 0` and `endIndex = 19`. Filling in these values, we find that `midIndex` is `0 + (19 - 0)/2 = 19/2 = 9`. It's actually `9.5` but because we're using integers, the answer is rounded down.
+Initially, the range has `lowerBound = 0` and `upperBound = 19`. Filling in these values, we find that `midIndex` is `0 + (19 - 0)/2 = 19/2 = 9`. It's actually `9.5` but because we're using integers, the answer is rounded down.
 
 In the next figure, the `*` shows the middle item. As you can see, the number of items on each side is the same, so we're split right down the middle.
 
-	[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
-                                      *
+[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+*
 
 Now binary search will determine which half to use. The relevant section from the code is:
 
 ```swift
-    if a[midIndex] > key {
-      // use left half
-    } else if a[midIndex] < key {
-      // use right half
-    } else {
-      return midIndex
-    }
+if a[midIndex] > key {
+// use left half
+} else if a[midIndex] < key {
+// use right half
+} else {
+return midIndex
+}
 ```
 
 In this case, `a[midIndex] = 29`. That's less than the search key, so we can safely conclude that the search key will never be in the left half of the array. After all, the left half only contains numbers smaller than `29`. Hence, the search key must be in the right half somewhere (or not in the array at all).
 
-Now we can simply repeat the binary search, but on the array interval from `midIndex + 1` to `range.endIndex`:
+Now we can simply repeat the binary search, but on the array interval from `midIndex + 1` to `range.upperBound`:
 
-	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
 
 Since we no longer need to concern ourselves with the left half of the array, I've marked that with `x`'s. From now on we'll only look at the right half, which starts at array index 10.
 
 We calculate the index of the new middle element: `midIndex = 10 + (19 - 10)/2 = 14`, and split the array down the middle again.
 
-	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
-	                                                 *
+[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+*
 
 As you can see, `a[14]` is indeed the middle element of the array's right half.
 
 Is the search key greater or smaller than `a[14]`? It's smaller because `43 < 47`. This time we're taking the left half and ignore the larger numbers on the right:
 
-	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
+[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
 
 The new `midIndex` is here:
 
-	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
-	                                     *
+[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
+*
 
 The search key is greater than `37`, so continue with the right side:
 
-	[ x, x, x, x, x, x, x, x, x, x | x, x | 41, 43 | x, x, x, x, x ]
-	                                        *
+[ x, x, x, x, x, x, x, x, x, x | x, x | 41, 43 | x, x, x, x, x ]
+*
 
 Again, the search key is greater, so split once more and take the right side:
 
-	[ x, x, x, x, x, x, x, x, x, x | x, x | x | 43 | x, x, x, x, x ]
-	                                            *
+[ x, x, x, x, x, x, x, x, x, x | x, x | x | 43 | x, x, x, x, x ]
+*
 
 And now we're done. The search key equals the array element we're looking at, so we've finally found what we were searching for: number `43` is at array index `13`. w00t!
 
 It may have seemed like a lot of work, but in reality it only took four steps to find the search key in the array, which sounds about right because `log_2(19) = 4.23`. With a linear search, it would have taken 14 steps.
 
-What would happen if we were to search for `42` instead of `43`? In that case, we can't split up the array any further. The `range.endIndex` becomes smaller than `range.startIndex`. That tells the algorithm the search key is not in the array and it returns `nil`.
+What would happen if we were to search for `42` instead of `43`? In that case, we can't split up the array any further. The `range.upperBound` becomes smaller than `range.lowerBound`. That tells the algorithm the search key is not in the array and it returns `nil`.
 
-> **Note:** Many implementations of binary search calculate `midIndex = (startIndex + endIndex) / 2`. This contains a subtle bug that only appears with very large arrays, because `startIndex + endIndex` may overflow the maximum number an integer can hold. This situation is unlikely to happen on a 64-bit CPU, but it definitely can on 32-bit machines.
+> **Note:** Many implementations of binary search calculate `midIndex = (lowerBound + upperBound) / 2`. This contains a subtle bug that only appears with very large arrays, because `lowerBound + upperBound` may overflow the maximum number an integer can hold. This situation is unlikely to happen on a 64-bit CPU, but it definitely can on 32-bit machines.
 
 ## Iterative vs recursive
 
@@ -181,18 +181,19 @@ Here is an iterative implementation of binary search in Swift:
 
 ```swift
 func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
-  var range = 0..<a.count
-  while range.startIndex < range.endIndex {
-    let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-    if a[midIndex] == key {
-      return midIndex
-    } else if a[midIndex] < key {
-      range.startIndex = midIndex + 1
-    } else {
-      range.endIndex = midIndex
-    }
-  }
-  return nil
+var lowerBound = 0
+var upperBound = a.count
+while lowerBound < upperBound {
+let midIndex = lowerBound + (upperBound - lowerBound) / 2
+if a[midIndex] == key {
+return midIndex
+} else if a[midIndex] < key {
+lowerBound = midIndex + 1
+} else {
+upperBound = midIndex
+}
+}
+return nil
 }
 ```
 
diff --git a/Binary Search/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search/Tests/BinarySearchTests.xcodeproj/project.pbxproj
similarity index 89%
rename from Binary Search/Tests/Tests.xcodeproj/project.pbxproj
rename to Binary Search/Tests/BinarySearchTests.xcodeproj/project.pbxproj
index 9ed1ab1a8..2db8ac5b6 100644
--- a/Binary Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search/Tests/BinarySearchTests.xcodeproj/project.pbxproj	
@@ -12,7 +12,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC801C779D720067B71D /* BinarySearchTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = BinarySearchTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BinarySearchTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BinarySearchTests.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3CF1C77A263003CECC7 /* BinarySearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearch.swift; path = ../BinarySearch.swift; sourceTree = SOURCE_ROOT; };
@@ -40,7 +40,7 @@
 		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC801C779D720067B71D /* Tests.xctest */,
+				7B2BBC801C779D720067B71D /* BinarySearchTests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -59,9 +59,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* Tests */ = {
+		7B2BBC7F1C779D720067B71D /* BinarySearchTests */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "BinarySearchTests" */;
 			buildPhases = (
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
@@ -71,9 +71,9 @@
 			);
 			dependencies = (
 			);
-			name = Tests;
+			name = BinarySearchTests;
 			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productReference = 7B2BBC801C779D720067B71D /* BinarySearchTests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -83,15 +83,16 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
-			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "BinarySearchTests" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -104,7 +105,7 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				7B2BBC7F1C779D720067B71D /* Tests */,
+				7B2BBC7F1C779D720067B71D /* BinarySearchTests */,
 			);
 		};
 /* End PBXProject section */
@@ -145,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -189,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -220,6 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,13 +238,14 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "BinarySearchTests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC871C779D720067B71D /* Debug */,
@@ -246,7 +254,7 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "BinarySearchTests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC8D1C779D720067B71D /* Debug */,
diff --git a/Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Binary Search/Tests/BinarySearchTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Binary Search/Tests/BinarySearchTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search/Tests/BinarySearchTests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 77%
rename from Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Binary Search/Tests/BinarySearchTests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..d6cd9152b 100644
--- a/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search/Tests/BinarySearchTests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -15,9 +15,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
+               BuildableName = "BinarySearchTests.xctest"
+               BlueprintName = "BinarySearchTests"
+               ReferencedContainer = "container:BinarySearchTests.xcodeproj">
             </BuildableReference>
          </BuildActionEntry>
       </BuildActionEntries>
@@ -33,9 +33,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
+               BuildableName = "BinarySearchTests.xctest"
+               BlueprintName = "BinarySearchTests"
+               ReferencedContainer = "container:BinarySearchTests.xcodeproj">
             </BuildableReference>
          </TestableReference>
       </Testables>
@@ -56,9 +56,9 @@
          <BuildableReference
             BuildableIdentifier = "primary"
             BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "Tests.xctest"
-            BlueprintName = "Tests"
-            ReferencedContainer = "container:Tests.xcodeproj">
+            BuildableName = "BinarySearchTests.xctest"
+            BlueprintName = "BinarySearchTests"
+            ReferencedContainer = "container:BinarySearchTests.xcodeproj">
          </BuildableReference>
       </MacroExpansion>
       <AdditionalOptions>
@@ -74,9 +74,9 @@
          <BuildableReference
             BuildableIdentifier = "primary"
             BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "Tests.xctest"
-            BlueprintName = "Tests"
-            ReferencedContainer = "container:Tests.xcodeproj">
+            BuildableName = "BinarySearchTests.xctest"
+            BlueprintName = "BinarySearchTests"
+            ReferencedContainer = "container:BinarySearchTests.xcodeproj">
          </BuildableReference>
       </MacroExpansion>
    </ProfileAction>

From fba86e174042e95692f8e8b3a6e989bdba5b4141 Mon Sep 17 00:00:00 2001
From: lenli <leonard.li@gmail.com>
Date: Fri, 19 Aug 2016 18:14:22 -0400
Subject: [PATCH 0457/1679] Fix code indentation on Binary Search readme

---
 Binary Search/README.markdown | 86 +++++++++++++++++------------------
 1 file changed, 43 insertions(+), 43 deletions(-)

diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 6fb6e9985..0faa46128 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -16,12 +16,12 @@ The built-in `indexOf()` function performs a [linear search](../Linear Search/).
 
 ```swift
 func linearSearch<T: Equatable>(a: [T], _ key: T) -> Int? {
-for i in 0 ..< a.count {
-if a[i] == key {
-return i
-}
-}
-return nil
+    for i in 0 ..< a.count {
+        if a[i] == key {
+            return i
+        }
+    }
+    return nil
 }
 ```
 
@@ -58,27 +58,27 @@ Here is a recursive implementation of binary search in Swift:
 
 ```swift
 func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> Int? {
-if range.lowerBound >= range.upperBound {
-// If we get here, then the search key is not present in the array.
-return nil
-
-} else {
-// Calculate where to split the array.
-let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
-
-// Is the search key in the left half?
-if a[midIndex] > key {
-return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
-
-// Is the search key in the right half?
-} else if a[midIndex] < key {
-return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
-
-// If we get here, then we've found the search key!
-} else {
-return midIndex
-}
-}
+    if range.lowerBound >= range.upperBound {
+        // If we get here, then the search key is not present in the array.
+        return nil
+
+    } else {
+        // Calculate where to split the array.
+        let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
+
+        // Is the search key in the left half?
+        if a[midIndex] > key {
+            return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
+
+        // Is the search key in the right half?
+        } else if a[midIndex] < key {
+            return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
+
+        // If we get here, then we've found the search key!
+        } else {
+            return midIndex
+        }
+    }
 }
 ```
 
@@ -123,11 +123,11 @@ Now binary search will determine which half to use. The relevant section from th
 
 ```swift
 if a[midIndex] > key {
-// use left half
+    // use left half
 } else if a[midIndex] < key {
-// use right half
+    // use right half
 } else {
-return midIndex
+    return midIndex
 }
 ```
 
@@ -181,19 +181,19 @@ Here is an iterative implementation of binary search in Swift:
 
 ```swift
 func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
-var lowerBound = 0
-var upperBound = a.count
-while lowerBound < upperBound {
-let midIndex = lowerBound + (upperBound - lowerBound) / 2
-if a[midIndex] == key {
-return midIndex
-} else if a[midIndex] < key {
-lowerBound = midIndex + 1
-} else {
-upperBound = midIndex
-}
-}
-return nil
+    var lowerBound = 0
+    var upperBound = a.count
+    while lowerBound < upperBound {
+        let midIndex = lowerBound + (upperBound - lowerBound) / 2
+        if a[midIndex] == key {
+            return midIndex
+        } else if a[midIndex] < key {
+            lowerBound = midIndex + 1
+        } else {
+            upperBound = midIndex
+        }
+    }
+    return nil
 }
 ```
 

From 232c92f1760601e35e8e9f3fe87df6706e6ccb6a Mon Sep 17 00:00:00 2001
From: lenli <leonard.li@gmail.com>
Date: Fri, 19 Aug 2016 18:19:55 -0400
Subject: [PATCH 0458/1679] Fix array midpoint figures in Binary Search readme

---
 Binary Search/README.markdown | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 0faa46128..0aa039254 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -102,7 +102,7 @@ It might be useful to look at how the algorithm works in detail.
 
 The array from the above example consists of 19 numbers and looks like this when sorted:
 
-[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+	[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
 
 We're trying to determine if the number `43` is in this array.
 
@@ -116,8 +116,8 @@ Initially, the range has `lowerBound = 0` and `upperBound = 19`. Filling in thes
 
 In the next figure, the `*` shows the middle item. As you can see, the number of items on each side is the same, so we're split right down the middle.
 
-[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
-*
+	[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+                                      *
 
 Now binary search will determine which half to use. The relevant section from the code is:
 
@@ -135,35 +135,35 @@ In this case, `a[midIndex] = 29`. That's less than the search key, so we can saf
 
 Now we can simply repeat the binary search, but on the array interval from `midIndex + 1` to `range.upperBound`:
 
-[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
 
 Since we no longer need to concern ourselves with the left half of the array, I've marked that with `x`'s. From now on we'll only look at the right half, which starts at array index 10.
 
 We calculate the index of the new middle element: `midIndex = 10 + (19 - 10)/2 = 14`, and split the array down the middle again.
 
-[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
-*
+	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43, 47, 53, 59, 61, 67 ]
+	                                                 *
 
 As you can see, `a[14]` is indeed the middle element of the array's right half.
 
 Is the search key greater or smaller than `a[14]`? It's smaller because `43 < 47`. This time we're taking the left half and ignore the larger numbers on the right:
 
-[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
+	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
 
 The new `midIndex` is here:
 
-[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
-*
+	[ x, x, x, x, x, x, x, x, x, x | 31, 37, 41, 43 | x, x, x, x, x ]
+	                                     *
 
 The search key is greater than `37`, so continue with the right side:
 
-[ x, x, x, x, x, x, x, x, x, x | x, x | 41, 43 | x, x, x, x, x ]
-*
+	[ x, x, x, x, x, x, x, x, x, x | x, x | 41, 43 | x, x, x, x, x ]
+	                                        *
 
 Again, the search key is greater, so split once more and take the right side:
 
-[ x, x, x, x, x, x, x, x, x, x | x, x | x | 43 | x, x, x, x, x ]
-*
+	[ x, x, x, x, x, x, x, x, x, x | x, x | x | 43 | x, x, x, x, x ]
+	                                            *
 
 And now we're done. The search key equals the array element we're looking at, so we've finally found what we were searching for: number `43` is at array index `13`. w00t!
 

From 19cc32e3d6d0ccd9c9e507b2f52a9679c44823a9 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 20 Aug 2016 20:47:51 +1200
Subject: [PATCH 0459/1679] Enabling binary search tree tests. Removed unused
 xcodeproj file.

---
 .travis.yml                                   |  2 +-
 .../project.pbxproj                           | 20 ++++++++--------
 .../contents.xcworkspacedata                  |  0
 .../xcshareddata/xcschemes/Tests.xcscheme     | 24 +++++++++----------
 4 files changed, 23 insertions(+), 23 deletions(-)
 rename Binary Search/Tests/{BinarySearchTests.xcodeproj => Tests.xcodeproj}/project.pbxproj (92%)
 rename Binary Search/Tests/{BinarySearchTests.xcodeproj => Tests.xcodeproj}/project.xcworkspace/contents.xcworkspacedata (100%)
 rename Binary Search/Tests/{BinarySearchTests.xcodeproj => Tests.xcodeproj}/xcshareddata/xcschemes/Tests.xcscheme (78%)

diff --git a/.travis.yml b/.travis.yml
index 970f85aa8..0ed853d81 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,7 +11,7 @@ script:
 # - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
 # - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Binary Search/Tests/BinarySearchTests.xcodeproj/project.pbxproj b/Binary Search/Tests/Tests.xcodeproj/project.pbxproj
similarity index 92%
rename from Binary Search/Tests/BinarySearchTests.xcodeproj/project.pbxproj
rename to Binary Search/Tests/Tests.xcodeproj/project.pbxproj
index 2db8ac5b6..6e29252ec 100644
--- a/Binary Search/Tests/BinarySearchTests.xcodeproj/project.pbxproj	
+++ b/Binary Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -12,7 +12,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* BinarySearchTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = BinarySearchTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BinarySearchTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BinarySearchTests.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3CF1C77A263003CECC7 /* BinarySearch.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearch.swift; path = ../BinarySearch.swift; sourceTree = SOURCE_ROOT; };
@@ -40,7 +40,7 @@
 		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC801C779D720067B71D /* BinarySearchTests.xctest */,
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -59,9 +59,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* BinarySearchTests */ = {
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "BinarySearchTests" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
 			buildPhases = (
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
@@ -71,9 +71,9 @@
 			);
 			dependencies = (
 			);
-			name = BinarySearchTests;
+			name = Tests;
 			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* BinarySearchTests.xctest */;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -92,7 +92,7 @@
 					};
 				};
 			};
-			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "BinarySearchTests" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -105,7 +105,7 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				7B2BBC7F1C779D720067B71D /* BinarySearchTests */,
+				7B2BBC7F1C779D720067B71D /* Tests */,
 			);
 		};
 /* End PBXProject section */
@@ -245,7 +245,7 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "BinarySearchTests" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC871C779D720067B71D /* Debug */,
@@ -254,7 +254,7 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "BinarySearchTests" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC8D1C779D720067B71D /* Debug */,
diff --git a/Binary Search/Tests/BinarySearchTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Binary Search/Tests/BinarySearchTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Binary Search/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/Binary Search/Tests/BinarySearchTests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 78%
rename from Binary Search/Tests/BinarySearchTests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index d6cd9152b..14f27f777 100644
--- a/Binary Search/Tests/BinarySearchTests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -15,9 +15,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "BinarySearchTests.xctest"
-               BlueprintName = "BinarySearchTests"
-               ReferencedContainer = "container:BinarySearchTests.xcodeproj">
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
             </BuildableReference>
          </BuildActionEntry>
       </BuildActionEntries>
@@ -33,9 +33,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "BinarySearchTests.xctest"
-               BlueprintName = "BinarySearchTests"
-               ReferencedContainer = "container:BinarySearchTests.xcodeproj">
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
             </BuildableReference>
          </TestableReference>
       </Testables>
@@ -56,9 +56,9 @@
          <BuildableReference
             BuildableIdentifier = "primary"
             BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "BinarySearchTests.xctest"
-            BlueprintName = "BinarySearchTests"
-            ReferencedContainer = "container:BinarySearchTests.xcodeproj">
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
          </BuildableReference>
       </MacroExpansion>
       <AdditionalOptions>
@@ -74,9 +74,9 @@
          <BuildableReference
             BuildableIdentifier = "primary"
             BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "BinarySearchTests.xctest"
-            BlueprintName = "BinarySearchTests"
-            ReferencedContainer = "container:BinarySearchTests.xcodeproj">
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
          </BuildableReference>
       </MacroExpansion>
    </ProfileAction>

From 20236b26099c0a4041f1043e26aa46281c229ca4 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Sat, 20 Aug 2016 20:55:31 +1200
Subject: [PATCH 0460/1679] Removing "a" label from binarySearch method in
 playground so it matches BinarySearch.swift. Applying same change to readme.

---
 .../BinarySearch.playground/Contents.swift       | 16 ++++++++--------
 .../Sources/BinarySearch.swift                   |  8 ++++----
 Binary Search/README.markdown                    |  8 ++++----
 3 files changed, 16 insertions(+), 16 deletions(-)

diff --git a/Binary Search/BinarySearch.playground/Contents.swift b/Binary Search/BinarySearch.playground/Contents.swift
index cccf9f8ac..f673f25c4 100644
--- a/Binary Search/BinarySearch.playground/Contents.swift	
+++ b/Binary Search/BinarySearch.playground/Contents.swift	
@@ -7,13 +7,13 @@ let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 4
 let sorted = numbers.sorted()
 
 // Using recursive solution
-binarySearch(a: sorted, key: 2, range: 0 ..< sorted.count)   // gives 0
-binarySearch(a: sorted, key: 67, range: 0 ..< sorted.count)  // gives 18
-binarySearch(a: sorted, key: 43, range: 0 ..< sorted.count)  // gives 13
-binarySearch(a: sorted, key: 42, range: 0 ..< sorted.count)  // nil
+binarySearch(sorted, key: 2, range: 0 ..< sorted.count)   // gives 0
+binarySearch(sorted, key: 67, range: 0 ..< sorted.count)  // gives 18
+binarySearch(sorted, key: 43, range: 0 ..< sorted.count)  // gives 13
+binarySearch(sorted, key: 42, range: 0 ..< sorted.count)  // nil
 
 // Using iterative solution
-binarySearch(a: sorted, key: 2)   // gives 0
-binarySearch(a: sorted, key: 67)  // gives 18
-binarySearch(a: sorted, key: 43)  // gives 13
-binarySearch(a: sorted, key: 42)  // nil
+binarySearch(sorted, key: 2)   // gives 0
+binarySearch(sorted, key: 67)  // gives 18
+binarySearch(sorted, key: 43)  // gives 13
+binarySearch(sorted, key: 42)  // nil
diff --git a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift b/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
index a7a24bd3a..d6623e355 100644
--- a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift	
+++ b/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift	
@@ -13,15 +13,15 @@ import Foundation
 
 // The recursive version of binary search.
 
-public func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> Int? {
+public func binarySearch<T: Comparable>(_ a: [T], key: T, range: Range<Int>) -> Int? {
     if range.lowerBound >= range.upperBound {
         return nil
     } else {
         let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
         if a[midIndex] > key {
-            return binarySearch(a: a, key: key, range: range.lowerBound ..< midIndex)
+            return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
         } else if a[midIndex] < key {
-            return binarySearch(a: a, key: key, range: midIndex + 1 ..< range.upperBound)
+            return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
         } else {
             return midIndex
         }
@@ -35,7 +35,7 @@ public func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> In
  uses a while loop, while the other calls itself recursively.
  **/
 
-public func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
+public func binarySearch<T: Comparable>(_ a: [T], key: T) -> Int? {
     var lowerBound = 0
     var upperBound = a.count
     while lowerBound < upperBound {
diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 0aa039254..c65d0b5fd 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -15,7 +15,7 @@ numbers.indexOf(43)  // returns 15
 The built-in `indexOf()` function performs a [linear search](../Linear Search/). In code that looks something like this:
 
 ```swift
-func linearSearch<T: Equatable>(a: [T], _ key: T) -> Int? {
+func linearSearch<T: Equatable>(_ a: [T], _ key: T) -> Int? {
     for i in 0 ..< a.count {
         if a[i] == key {
             return i
@@ -45,7 +45,7 @@ Sounds great, but there is a downside to using binary search: the array must be
 
 Here's how binary search works:
 
-- Split the array in half and determine whether the thing you're looking for, known as the *search key*, is in the left half or in the right half. 
+- Split the array in half and determine whether the thing you're looking for, known as the *search key*, is in the left half or in the right half.
 - How do you determine in which half the search key is? This is why you sorted the array first, so you can do a simple `<` or `>` comparison.
 - If the search key is in the left half, you repeat the process there: split the left half into two even smaller pieces and look in which piece the search key must lie. (Likewise for when it's the right half.)
 - This repeats until the search key is found. If the array cannot be split up any further, you must regrettably conclude that the search key is not present in the array.
@@ -57,7 +57,7 @@ Now you know why it's called a "binary" search: in every step it splits the arra
 Here is a recursive implementation of binary search in Swift:
 
 ```swift
-func binarySearch<T: Comparable>(a: [T], key: T, range: Range<Int>) -> Int? {
+func binarySearch<T: Comparable>(_ a: [T], key: T, range: Range<Int>) -> Int? {
     if range.lowerBound >= range.upperBound {
         // If we get here, then the search key is not present in the array.
         return nil
@@ -180,7 +180,7 @@ Binary search is recursive in nature because you apply the same logic over and o
 Here is an iterative implementation of binary search in Swift:
 
 ```swift
-func binarySearch<T: Comparable>(a: [T], key: T) -> Int? {
+func binarySearch<T: Comparable>(_ a: [T], key: T) -> Int? {
     var lowerBound = 0
     var upperBound = a.count
     while lowerBound < upperBound {

From 6e77eba6b8c242c09093a160d90dee5ee3e92828 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Sat, 20 Aug 2016 22:57:42 -0600
Subject: [PATCH 0461/1679] Updated Bubble Sort description

Added the runtime, memory and a better description of bubble sort. The implementation was not added but it is good to know the concept.
---
 Bubble Sort/README.markdown | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index 1c3d89798..8660d6d54 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,4 +1,13 @@
 # Bubble Sort
 
-This is a horrible algorithm. There is no reason why you should have to know it.
+Bubble sort is a sorting algorthim that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparision is then moved onto the next pair and so on and so forth. This is done until the the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
 
+Runtime:
+- Average: O(N^2) 
+- Worst: O(N^2)
+
+Memory: 
+- O(1)
+
+Implementation: 
+The implemenatation will not be shown because as you can see from the average and worst runtimes this is a very inefficent algorithm but having a grasp of the concept will help in getting to know the basics of simple sorting algorthims.

From 68f581965f060a2725446bb95c3cbaaa4344b1f6 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Sat, 20 Aug 2016 23:09:03 -0600
Subject: [PATCH 0462/1679] Updated formatting and grammar errors

---
 Bubble Sort/README.markdown | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index 8660d6d54..ceb2a98cb 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,13 +1,14 @@
 # Bubble Sort
 
-Bubble sort is a sorting algorthim that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparision is then moved onto the next pair and so on and so forth. This is done until the the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
+Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
 
-Runtime:
+##### Runtime:
 - Average: O(N^2) 
 - Worst: O(N^2)
 
-Memory: 
+##### Memory: 
 - O(1)
 
-Implementation: 
-The implemenatation will not be shown because as you can see from the average and worst runtimes this is a very inefficent algorithm but having a grasp of the concept will help in getting to know the basics of simple sorting algorthims.
+### Implementation:
+
+The implementation will not be shown because as you can see from the average and worst runtimes this is a very inefficient algorithm but having a grasp of the concept will help in getting to know the basics of simple sorting algorithms.

From a5411848ff096e8da74e7d8cc9ba3e35f3069ee7 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Sun, 21 Aug 2016 19:10:44 +0200
Subject: [PATCH 0463/1679] Add SkipList

---
 Skip-List/SkipList.swift | 266 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 266 insertions(+)
 create mode 100644 Skip-List/SkipList.swift

diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
new file mode 100644
index 000000000..b07cd98c8
--- /dev/null
+++ b/Skip-List/SkipList.swift
@@ -0,0 +1,266 @@
+// The MIT License (MIT)
+
+// Copyright (c) 2016 Mike Taghavi (mitghi[at]me.com)
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+
+import Foundation
+
+
+// Stack from : https://github.com/raywenderlich/swift-algorithm-club/tree/master/Stack
+public struct Stack<T> {
+    private var array = [T]()
+
+    public var isEmpty: Bool {
+        return array.isEmpty
+    }
+
+    public var count: Int {
+        return array.count
+    }
+
+    public mutating func push(element: T) {
+        array.append(element)
+    }
+
+    public mutating func pop() -> T? {
+        return array.popLast()
+    }
+
+    public func peek() -> T? {
+        return array.last
+    }
+}
+
+extension Stack: SequenceType {
+    public func generate() -> AnyGenerator<T> {
+        var curr = self
+        return AnyGenerator {
+                   _ -> T? in
+                   return curr.pop()
+            }
+    }
+}
+
+
+func random() -> Bool {
+    #if os(Linux)
+        return random() % 2 == 0
+    #elseif os(OSX)
+        return arc4random_uniform(2) == 1
+    #endif
+}
+
+
+
+class DataNode<Key: Comparable, Payload>{
+    internal typealias Node = DataNode<Key,Payload>
+    
+    internal var key   : Key?
+    internal var data  : Payload?
+    internal var _next : Node?
+    internal var _down : Node?
+
+    internal var next: Node? {
+        get        { return self._next  }
+        set(value) { self._next = value }        
+    }
+
+    internal var down:Node? {
+        get        { return self._down  }
+        set(value) { self._down = value }
+    }
+    
+    init(key:Key, data:Payload){
+        self.key  = key
+        self.data = data
+    }
+
+    init(header: Bool){        
+    }
+    
+}
+
+
+class SkipList<Key: Comparable, Payload>{
+    internal typealias Node = DataNode<Key, Payload>
+    internal var head: Node?
+
+    private func find_head(key:Key) -> Node? {
+        var current     = self.head
+        var found: Bool = false
+
+        while !found {
+            if let curr = current {
+                if curr.next == nil { current = curr.down }
+                else {
+                    if curr.next!.key == key { found = true }
+                    else {                        
+                        if key < curr.next!.key{ current = curr.down }
+                        else { current = curr.next }
+                    }
+                }
+            } else {
+                break
+            }
+        }
+
+        if found {
+            return current
+        } else {
+            return nil
+        }        
+    }
+    
+
+    private func insert_head(key:Key, data:Payload) -> Void {
+        
+        self.head       = Node(header: true)
+        var temp        = Node(key:key, data:data)
+        self.head!.next = temp
+        var top         = temp
+
+        while random() {
+            let newhead  = Node(header: true)
+            temp         = Node(key:key, data:data)
+            temp.down    = top
+            newhead.next = temp
+            newhead.down = self.head
+            self.head    = newhead
+            top          = temp                
+        }
+    }
+
+    private func insert_rest(key:Key, data:Payload) -> Void {
+        var stack = Stack<Node>()
+        var current_head: Node? = self.head
+
+        while current_head != nil {
+
+            if let next = current_head!._next {
+                if next.key > key {
+                    stack.push(current_head!)
+                    current_head = next
+                } else {
+                    current_head = next
+                }
+                
+            } else {
+                stack.push(current_head!)
+                current_head = current_head!.down                    
+            }
+            
+        }            
+
+        let lowest   = stack.pop()
+        var temp     = Node(key:key, data:data)
+        temp.next    = lowest!.next
+        lowest!.next = temp
+        var top      = temp
+
+        while random() {
+            if stack.isEmpty {
+                let newhead  = Node(header: true)
+                temp         = Node(key:key, data:data)
+                temp.down    = top
+                newhead.next = temp
+                newhead.down = self.head
+                self.head    = newhead
+                top          = temp
+            } else {
+                let next   = stack.pop()
+                temp       = Node(key:key, data:data)
+                temp.down  = top
+                temp.next  = next!.next
+                next!.next = temp
+                top        = temp
+            }
+        }        
+    }
+    
+    func search(key:Key) -> Payload? {
+        guard let item = self.find_head(key) else {
+            return nil
+        }
+
+        return item.next!.data        
+    }
+    
+    func remove(key:Key) -> Void {
+        guard let item = self.find_head(key) else {
+            return
+        }
+        
+        var curr = Optional(item)
+        
+        while curr != nil {
+            let node      = curr!.next
+            
+            if node!.key != key { curr = node ; continue }
+
+            let node_next = node!.next            
+            curr!.next    = node_next
+            curr          = curr!.down
+            
+        }
+        
+    }
+    
+    func insert(key: Key, data:Payload){
+        if self.head != nil{
+            if let node = self.find_head(key) {
+                
+                var curr = node.next                
+                while curr != nil && curr!.key == key{
+                    curr!.data = data
+                    curr       = curr!.down
+                }
+                
+            } else {                        
+                self.insert_rest(key, data:data)
+            }
+            
+        } else {
+            self.insert_head(key, data:data)
+        }
+    }
+
+}
+
+
+class Map<Key: Comparable, Payload>{    
+    var collection: SkipList<Key, Payload>
+
+    init(){
+        self.collection = SkipList<Key, Payload>()
+    }
+    
+    func insert(key:Key, data: Payload){
+        self.collection.insert(key, data:data)
+    }
+
+    func get(key:Key) -> Payload?{
+        return self.collection.search(key)
+    }
+    
+    func remove(key:Key) -> Void {
+        return self.collection.remove(key)
+    }
+}

From 28df4f3ab785436bf08b1b6f1751f865bc59660c Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Sun, 21 Aug 2016 19:25:31 +0200
Subject: [PATCH 0464/1679] Update README.md

---
 Skip-List/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 8b1378917..ca1dce7ae 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -1 +1,3 @@
+# Skip List
 
+> Skip lists are a probabilistic data structure that seem likely to supplant balanced trees as the implementation method of choice for many applications. Skip list algorithms have the same asymptotic expected time bounds as balanced trees and are simpler, faster and use less space.  -**[William Pugh](https://en.wikipedia.org/wiki/William_Pugh)**

From 96f58f76902b7ce30142dfa4a1853642b0869ec4 Mon Sep 17 00:00:00 2001
From: Mark Baxter <baxter.mark@yahoo.com>
Date: Fri, 26 Aug 2016 08:59:23 -0700
Subject: [PATCH 0465/1679] Swift 3

---
 .../Palindromes.playground/Contents.swift     | 22 +++++++++----------
 Palindromes/Palindromes.swift                 |  8 +++----
 Palindromes/README.markdown                   | 12 +++++-----
 3 files changed, 21 insertions(+), 21 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index b548182af..0df899937 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -2,7 +2,7 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.stringByTrimmingCharactersInSet(.whitespaceCharacterSet()).lowercaseString
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces())
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {
@@ -11,9 +11,9 @@ public func palindromeCheck (text: String?) -> Bool {
     
     if length == 1 {
       return true
-    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.endIndex.predecessor()] {
-      let range = Range<String.Index>(mutableText.startIndex.successor()..<mutableText.endIndex.predecessor())
-      return palindromeCheck(mutableText.substringWithRange(range))
+    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
+      let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
+      return palindromeCheck(text: mutableText.substring(with: range))
     }
   }
   
@@ -21,16 +21,16 @@ public func palindromeCheck (text: String?) -> Bool {
 }
 
 // Test to check that non-palindromes are handled correctly:
-palindromeCheck("owls")
+palindromeCheck(text: "owls")
 
 // Test to check that palindromes are accurately found (regardless of case and whitespace:
-palindromeCheck("lol")
-palindromeCheck("race car")
-palindromeCheck("Race fast Safe car")
+palindromeCheck(text: "lol")
+palindromeCheck(text: "race car")
+palindromeCheck(text: "Race fast Safe car")
 
 // Test to check that palindromes are found regardless of case:
-palindromeCheck("HelloLLEH")
+palindromeCheck(text: "HelloLLEH")
 
 // Test that nil and empty Strings return false:
-palindromeCheck("")
-palindromeCheck(nil)
+palindromeCheck(text: "")
+palindromeCheck(text: nil)
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 61e7740ab..1e61cc1ca 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -2,7 +2,7 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.stringByTrimmingCharactersInSet(.whitespaceCharacterSet()).lowercaseString
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces())
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {
@@ -11,9 +11,9 @@ public func palindromeCheck (text: String?) -> Bool {
     
     if length == 1 {
       return true
-    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.endIndex.predecessor()] {
-      let range = Range<String.Index>(mutableText.startIndex.successor()..<mutableText.endIndex.predecessor())
-      return palindromeCheck(mutableText.substringWithRange(range))
+    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
+      let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
+      return palindromeCheck(text: mutableText.substring(with: range))
     }
   }
   
diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 3df775e31..6d0ff8ef7 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -28,18 +28,18 @@ Here is a recursive implementation of this in Swift:
 ```swift
 func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.stringByTrimmingCharactersInSet(.whitespaceCharacterSet()).lowercaseString
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces())
     let length: Int = mutableText.characters.count
     
-    guard length >= 1 {
+    guard length >= 1 else {
       return false
     }
 
     if length == 1 {
       return true
-    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.endIndex.predecessor()] {
-      let range = Range<String.Index>(mutableText.startIndex.successor()..<mutableText.endIndex.predecessor())
-      return palindromeCheck(mutableText.substringWithRange(range))
+    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
+      let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
+      return palindromeCheck(text: mutableText.substring(with: range))
     }
   }
 
@@ -51,7 +51,7 @@ func palindromeCheck (text: String?) -> Bool {
 This code can be tested in a playground using the following: 
 
 ```swift
-palindromeCheck("Race car")
+palindromeCheck(text: "Race car")
 ```
 
 Since the phrase "Race car" is a palindrome, this will return true. 

From 5f1b0715d5181b89e600fa8c64e74ff91f8c35cc Mon Sep 17 00:00:00 2001
From: Mark Baxter <baxter.mark@yahoo.com>
Date: Fri, 26 Aug 2016 09:11:30 -0700
Subject: [PATCH 0466/1679] Swift 3

---
 Palindromes/Palindromes.playground/Contents.swift | 2 +-
 Palindromes/Palindromes.swift                     | 2 +-
 Palindromes/README.markdown                       | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index 0df899937..f1a85c073 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -2,7 +2,7 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces())
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces()).lowercased()
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 1e61cc1ca..2082dbb4d 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -2,7 +2,7 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces())
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces()).lowercased()
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {
diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 6d0ff8ef7..12f868251 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -28,7 +28,7 @@ Here is a recursive implementation of this in Swift:
 ```swift
 func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces())
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces()).lowercased()
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {

From be653b21e366c8225c07f7bc19ae790abb381b86 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nvlahovic@razor.rs>
Date: Mon, 29 Aug 2016 11:08:07 +0200
Subject: [PATCH 0467/1679] Migrate Array2D algorithm to Swift 3

---
 Array2D/Array2D.playground/Contents.swift     | 4 ++--
 Array2D/Array2D.swift                         | 4 ++--
 Array2D/Tests/Array2DTests.swift              | 4 ++--
 Array2D/Tests/Tests.xcodeproj/project.pbxproj | 3 +++
 4 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 0bcb7b5b9..7064de59c 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -6,12 +6,12 @@
 public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
-  private var array: [T]
+  fileprivate var array: [T]
 
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = .init(count: rows*columns, repeatedValue: initialValue)
+    array = .init(repeatElement(initialValue, count: rows*columns))
   }
 
   public subscript(column: Int, row: Int) -> T {
diff --git a/Array2D/Array2D.swift b/Array2D/Array2D.swift
index 6177974d7..6d6c01902 100644
--- a/Array2D/Array2D.swift
+++ b/Array2D/Array2D.swift
@@ -6,12 +6,12 @@
 public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
-  private var array: [T]
+  fileprivate var array: [T]
 
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = .init(count: rows*columns, repeatedValue: initialValue)
+    array = .init(repeating: initialValue, count: rows*columns)
   }
 
   public subscript(column: Int, row: Int) -> T {
diff --git a/Array2D/Tests/Array2DTests.swift b/Array2D/Tests/Array2DTests.swift
index f4019a03a..b30769ac4 100644
--- a/Array2D/Tests/Array2DTests.swift
+++ b/Array2D/Tests/Array2DTests.swift
@@ -43,7 +43,7 @@ class Array2DTest: XCTestCase {
   }
 
   func testPerformanceOnSmallArray() {
-    self.measureBlock {
+    self.measure {
       self.printArrayWith(columns: 2, rows: 2, inititalValue: 1)
     }
   }
@@ -54,7 +54,7 @@ class Array2DTest: XCTestCase {
   //        }
   //    }
 
-  private func printArrayWith(columns columns: Int, rows: Int, inititalValue: Int) {
+  fileprivate func printArrayWith(columns: Int, rows: Int, inititalValue: Int) {
     let array = Array2D(columns: columns, rows: rows, initialValue: 4)
     for r in 0..<array.rows {
       for c in 0..<array.columns {
diff --git a/Array2D/Tests/Tests.xcodeproj/project.pbxproj b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
index 8618e7530..acacd28ea 100644
--- a/Array2D/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
@@ -88,6 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -220,6 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 677f2c23660a9064a27216e6640b72e65cbb90f3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nvlahovic@razor.rs>
Date: Mon, 29 Aug 2016 11:18:20 +0200
Subject: [PATCH 0468/1679] Uncomment Array2D in .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 0ed853d81..1eba40123 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,7 +9,7 @@ install:
 script:
 
 # - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-# - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests

From 99c00720289b9396b45c9045fea67ee983fbacf5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Mon, 29 Aug 2016 14:36:12 +0200
Subject: [PATCH 0469/1679] Migrate Stack to Swift 3

---
 Stack/Stack.playground/Contents.swift       |  6 +++---
 Stack/Stack.swift                           | 10 +++++-----
 Stack/Tests/Tests.xcodeproj/project.pbxproj |  3 +++
 3 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 4f4f826f2..24b5e7176 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -12,7 +12,7 @@
 */
 
 public struct Stack<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var count: Int {
     return array.count
@@ -36,10 +36,10 @@ public struct Stack<T> {
 }
 
 // Create a stack and put some elements on it already.
-var stackOfNames = Stack(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
+var stackOfNames = Stack(array:["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
 // Add an element to the top of the stack.
-stackOfNames.push("Mike")
+stackOfNames.push(element: "Mike")
 
 // The stack is now ["Carl", "Lisa", "Stephanie", "Jeff", "Wade", "Mike"]
 print(stackOfNames.array)
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 454b66fa0..49edaf4cb 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -4,7 +4,7 @@
   Push and pop are O(1) operations.
 */
 public struct Stack<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -14,7 +14,7 @@ public struct Stack<T> {
     return array.count
   }
 
-  public mutating func push(element: T) {
+  public mutating func push(_ element: T) {
     array.append(element)
   }
 
@@ -27,10 +27,10 @@ public struct Stack<T> {
   }
 }
 
-extension Stack: SequenceType {
-    public func generate() -> AnyGenerator<T> {
+extension Stack: Sequence {
+    public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyGenerator {
+        return AnyIterator {
             _ -> T? in
             return curr.pop()
         }
diff --git a/Stack/Tests/Tests.xcodeproj/project.pbxproj b/Stack/Tests/Tests.xcodeproj/project.pbxproj
index a36d7c51d..5ec8dc987 100644
--- a/Stack/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Stack/Tests/Tests.xcodeproj/project.pbxproj
@@ -88,6 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -220,6 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 9ecfd88d02fff6d73a70e4e63ad41c6ed5931051 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Mon, 29 Aug 2016 14:40:44 +0200
Subject: [PATCH 0470/1679] Revert "Migrate Stack to Swift 3"

This reverts commit 99c00720289b9396b45c9045fea67ee983fbacf5.
---
 Stack/Stack.playground/Contents.swift       |  6 +++---
 Stack/Stack.swift                           | 10 +++++-----
 Stack/Tests/Tests.xcodeproj/project.pbxproj |  3 ---
 3 files changed, 8 insertions(+), 11 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 24b5e7176..4f4f826f2 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -12,7 +12,7 @@
 */
 
 public struct Stack<T> {
-  fileprivate var array = [T]()
+  private var array = [T]()
 
   public var count: Int {
     return array.count
@@ -36,10 +36,10 @@ public struct Stack<T> {
 }
 
 // Create a stack and put some elements on it already.
-var stackOfNames = Stack(array:["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
+var stackOfNames = Stack(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
 // Add an element to the top of the stack.
-stackOfNames.push(element: "Mike")
+stackOfNames.push("Mike")
 
 // The stack is now ["Carl", "Lisa", "Stephanie", "Jeff", "Wade", "Mike"]
 print(stackOfNames.array)
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 49edaf4cb..454b66fa0 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -4,7 +4,7 @@
   Push and pop are O(1) operations.
 */
 public struct Stack<T> {
-  fileprivate var array = [T]()
+  private var array = [T]()
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -14,7 +14,7 @@ public struct Stack<T> {
     return array.count
   }
 
-  public mutating func push(_ element: T) {
+  public mutating func push(element: T) {
     array.append(element)
   }
 
@@ -27,10 +27,10 @@ public struct Stack<T> {
   }
 }
 
-extension Stack: Sequence {
-    public func makeIterator() -> AnyIterator<T> {
+extension Stack: SequenceType {
+    public func generate() -> AnyGenerator<T> {
         var curr = self
-        return AnyIterator {
+        return AnyGenerator {
             _ -> T? in
             return curr.pop()
         }
diff --git a/Stack/Tests/Tests.xcodeproj/project.pbxproj b/Stack/Tests/Tests.xcodeproj/project.pbxproj
index 5ec8dc987..a36d7c51d 100644
--- a/Stack/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Stack/Tests/Tests.xcodeproj/project.pbxproj
@@ -88,7 +88,6 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -221,7 +220,6 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -233,7 +231,6 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From d6378f859dbf0d0fe65cfd1c69d90cc49f37714c Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 12:15:29 +1200
Subject: [PATCH 0471/1679] Fixed warning when opening array 2d test project

---
 Array2D/Tests/Tests.xcodeproj/project.pbxproj              | 7 ++++++-
 .../Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme  | 2 +-
 2 files changed, 7 insertions(+), 2 deletions(-)

diff --git a/Array2D/Tests/Tests.xcodeproj/project.pbxproj b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
index acacd28ea..a0fb1480b 100644
--- a/Array2D/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,7 +83,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -146,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -190,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
diff --git a/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Array2D/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 7e4f2e0f0c4f5c7a37508965d981da9223ca4c40 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 12:38:14 +1200
Subject: [PATCH 0472/1679] Fixing NSCharacterSet.whitespaces() warning

---
 Palindromes/Palindromes.playground/Contents.swift | 4 ++--
 Palindromes/Palindromes.swift                     | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index f1a85c073..20df10ee4 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -1,8 +1,8 @@
 import Cocoa
 
-public func palindromeCheck (text: String?) -> Bool {
+public func palindromeCheck(text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces()).lowercased()
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 2082dbb4d..b873af3b0 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -2,7 +2,7 @@ import Cocoa
 
 public func palindromeCheck (text: String?) -> Bool {
   if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces()).lowercased()
+    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
     let length: Int = mutableText.characters.count
     
     guard length >= 1 else {

From 9646535ec738fa6a72f2202ecd363a0ac7a1a434 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 12:39:07 +1200
Subject: [PATCH 0473/1679] Spacing

---
 Palindromes/Palindromes.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index b873af3b0..036ce3d34 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -1,6 +1,6 @@
 import Cocoa
 
-public func palindromeCheck (text: String?) -> Bool {
+public func palindromeCheck(text: String?) -> Bool {
   if let text = text {
     let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
     let length: Int = mutableText.characters.count

From 93e1eeab430ff108e44182963f8fc053331e4501 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 13:16:39 +1200
Subject: [PATCH 0474/1679] Updating to Swift 3

---
 Union-Find/README.markdown                    | 22 +++++++++----------
 .../UnionFind.playground/Contents.swift       | 14 ++++++------
 Union-Find/UnionFind.swift                    | 14 ++++++------
 3 files changed, 25 insertions(+), 25 deletions(-)

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 1d674e965..5102f6b89 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -9,7 +9,7 @@ What do we mean by this? For example, the Union-Find data structure could be kee
 	[ g, d, c ]
 	[ i, j ]
 
-These sets are disjoint because they have no members in common. 
+These sets are disjoint because they have no members in common.
 
 Union-Find supports three basic operations:
 
@@ -41,9 +41,9 @@ Example: If `parent` looks like this,
 
 	parent [ 1, 1, 1, 0, 2, 0, 6, 6, 6 ]
 	     i   0  1  2  3  4  5  6  7  8
-	
+
 then the tree structure looks like:
-	
+
 	      1              6
 	    /   \           / \
 	  0       2        7   8
@@ -63,7 +63,7 @@ Note that the `parent[]` of a root node points to itself. So `parent[1] = 1` and
 Let's look at the implementation of these basic operations, starting with adding a new set.
 
 ```swift
-public mutating func addSetWith(element: T) {
+public mutating func addSetWith(_ element: T) {
   index[element] = parent.count  // 1
   parent.append(parent.count)    // 2
   size.append(1)                 // 3
@@ -83,7 +83,7 @@ When you add a new element, this actually adds a new subset containing just that
 Often we want to determine whether we already have a set that contains a given element. That's what the **Find** operation does. In our `UnionFind` data structure it is called `setOf()`:
 
 ```swift
-public mutating func setOf(element: T) -> Int? {
+public mutating func setOf(_ element: T) -> Int? {
   if let indexOfElement = index[element] {
     return setByIndex(indexOfElement)
   } else {
@@ -95,7 +95,7 @@ public mutating func setOf(element: T) -> Int? {
 This looks up the element's index in the `index` dictionary and then uses a helper method to find the set that this element belongs to:
 
 ```swift
-private mutating func setByIndex(index: Int) -> Int {
+private mutating func setByIndex(_ index: Int) -> Int {
   if parent[index] == index {  // 1
     return index
   } else {
@@ -109,7 +109,7 @@ Because we're dealing with a tree structure, this is a recursive method.
 
 Recall that each set is represented by a tree and that the index of the root node serves as the number that identifies the set. We're going to find the root node of the tree that the element we're searching for belongs to, and return its index.
 
-1. First, we check if the given index represents a root node (i.e. a node whose `parent` points back to the node itself). If so, we're done. 
+1. First, we check if the given index represents a root node (i.e. a node whose `parent` points back to the node itself). If so, we're done.
 
 2. Otherwise we recursively call this method on the parent of the current node. And then we do a **very important thing**: we overwrite the parent of the current node with the index of root node, in effect reconnecting the node directly to the root of the tree. The next time we call this method, it will execute faster because the path to the root of the tree is now much shorter. Without that optimization, this method's complexity is **O(n)** but now in combination with the size optimization (covered in the Union section) it is almost **O(1)**.
 
@@ -130,8 +130,8 @@ Now if we need to call `setOf(4)` again, we no longer have to go through node `2
 There is also a helper method to check that two elements are in the same set:
 
 ```swift
-public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
-  if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+  if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
     return firstSet == secondSet
   } else {
     return false
@@ -146,8 +146,8 @@ Since this calls `setOf()` it also optimizes the tree.
 The final operation is **Union**, which combines two sets into one larger set.
 
 ```swift
-public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
-  if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {  // 1
+public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+  if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {  // 1
     if firstSet != secondSet {               // 2
       if size[firstSet] < size[secondSet] {  // 3
         parent[firstSet] = secondSet         // 4
diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 5747b15b5..09649b938 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -5,13 +5,13 @@ public struct UnionFind<T: Hashable> {
   private var parent = [Int]()
   private var size = [Int]()
 
-  public mutating func addSetWith(element: T) {
+  public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
 
-  private mutating func setByIndex(index: Int) -> Int {
+  private mutating func setByIndex(_ index: Int) -> Int {
     if parent[index] == index {
       return index
     } else {
@@ -20,7 +20,7 @@ public struct UnionFind<T: Hashable> {
     }
   }
 
-  public mutating func setOf(element: T) -> Int? {
+  public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
     } else {
@@ -28,8 +28,8 @@ public struct UnionFind<T: Hashable> {
     }
   }
 
-  public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
-    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
         if size[firstSet] < size[secondSet] {
           parent[firstSet] = secondSet
@@ -42,8 +42,8 @@ public struct UnionFind<T: Hashable> {
     }
   }
 
-  public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
-    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
     } else {
       return false
diff --git a/Union-Find/UnionFind.swift b/Union-Find/UnionFind.swift
index 4323b80d4..506cdc1fe 100644
--- a/Union-Find/UnionFind.swift
+++ b/Union-Find/UnionFind.swift
@@ -12,13 +12,13 @@ public struct UnionFind<T: Hashable> {
   private var parent = [Int]()
   private var size = [Int]()
 
-  public mutating func addSetWith(element: T) {
+  public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
 
-  private mutating func setByIndex(index: Int) -> Int {
+  private mutating func setByIndex(_ index: Int) -> Int {
     if parent[index] == index {
       return index
     } else {
@@ -27,7 +27,7 @@ public struct UnionFind<T: Hashable> {
     }
   }
 
-  public mutating func setOf(element: T) -> Int? {
+  public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
     } else {
@@ -35,8 +35,8 @@ public struct UnionFind<T: Hashable> {
     }
   }
 
-  public mutating func unionSetsContaining(firstElement: T, and secondElement: T) {
-    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
         if size[firstSet] < size[secondSet] {
           parent[firstSet] = secondSet
@@ -49,8 +49,8 @@ public struct UnionFind<T: Hashable> {
     }
   }
 
-  public mutating func inSameSet(firstElement: T, and secondElement: T) -> Bool {
-    if let firstSet = setOf(firstElement), secondSet = setOf(secondElement) {
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
     } else {
       return false

From 310f110de8614fc65589158422bc671519a275bb Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 13:30:51 +1200
Subject: [PATCH 0475/1679] Updating tree to Swift3

---
 Tree/README.markdown                | 12 ++++++------
 Tree/Tree.playground/Contents.swift |  6 +++---
 Tree/Tree.swift                     |  6 +++---
 3 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/Tree/README.markdown b/Tree/README.markdown
index 52a46c597..5cf3e6beb 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -10,7 +10,7 @@ Nodes have links to their children and usually to their parent as well. The chil
 
 ![A tree](Images/ParentChildren.png)
 
-A node without a parent is the *root* node. A node without children is a *leaf* node. 
+A node without a parent is the *root* node. A node without children is a *leaf* node.
 
 The pointers in a tree do not form cycles. This is not a tree:
 
@@ -25,15 +25,15 @@ Here's a basic implementation in Swift:
 ```swift
 public class TreeNode<T> {
   public var value: T
-  
+
   public var parent: TreeNode?
   public var children = [TreeNode<T>]()
 
   public init(value: T) {
     self.value = value
   }
-  
-  public func addChild(node: TreeNode<T>) {
+
+  public func addChild(_ node: TreeNode<T>) {
     children.append(node)
     node.parent = self
   }
@@ -49,7 +49,7 @@ extension TreeNode: CustomStringConvertible {
   public var description: String {
     var s = "\(value)"
     if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joinWithSeparator(", ") + "}"
+      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
     }
     return s
   }
@@ -129,7 +129,7 @@ Here's the code:
 
 ```swift
 extension TreeNode where T: Equatable {
-  func search(value: T) -> TreeNode? {
+  func search(_ value: T) -> TreeNode? {
     if value == self.value {
       return self
     }
diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index c8ee8fe71..7b3c97005 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -10,7 +10,7 @@ public class TreeNode<T> {
     self.value = value
   }
 
-  public func addChild(node: TreeNode<T>) {
+  public func addChild(_ node: TreeNode<T>) {
     children.append(node)
     node.parent = self
   }
@@ -20,7 +20,7 @@ extension TreeNode: CustomStringConvertible {
   public var description: String {
     var s = "\(value)"
     if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joinWithSeparator(", ") + "}"
+      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
     }
     return s
   }
@@ -71,7 +71,7 @@ teaNode.parent
 teaNode.parent!.parent
 
 extension TreeNode where T: Equatable {
-  func search(value: T) -> TreeNode? {
+  func search(_ value: T) -> TreeNode? {
     if value == self.value {
       return self
     }
diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index 39d1f3df5..00119c963 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -8,7 +8,7 @@ public class TreeNode<T> {
     self.value = value
   }
 
-  public func addChild(node: TreeNode<T>) {
+  public func addChild(_ node: TreeNode<T>) {
     children.append(node)
     node.parent = self
   }
@@ -18,14 +18,14 @@ extension TreeNode: CustomStringConvertible {
   public var description: String {
     var s = "\(value)"
     if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joinWithSeparator(", ") + "}"
+      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
     }
     return s
   }
 }
 
 extension TreeNode where T: Equatable {
-  public func search(value: T) -> TreeNode? {
+  public func search(_ value: T) -> TreeNode? {
     if value == self.value {
       return self
     }

From 8680a97bc576c937d13cb9156c59662e636ce6de Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 17:59:17 +1200
Subject: [PATCH 0476/1679] Updating to Swift3

---
 .../BitSet.playground/Sources/BitSet.swift    | 22 +++++-----
 Bit Set/BitSet.swift                          | 22 +++++-----
 Bit Set/README.markdown                       | 44 +++++++++----------
 3 files changed, 44 insertions(+), 44 deletions(-)

diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index 46f51dbba..d8985bd13 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -11,7 +11,7 @@ public struct BitSet {
   */
   private let N = 64
   public typealias Word = UInt64
-  private(set) public var words: [Word]
+  fileprivate(set) public var words: [Word]
 
   private let allOnes = ~Word()
 
@@ -22,11 +22,11 @@ public struct BitSet {
 
     // Round up the count to the next multiple of 64.
     let n = (size + (N-1)) / N
-    words = .init(count: n, repeatedValue: 0)
+    words = [Word](repeating: 0, count: n)
   }
 
   /* Converts a bit index into an array index and a mask inside the word. */
-  private func indexOf(i: Int) -> (Int, Word) {
+  private func indexOf(_ i: Int) -> (Int, Word) {
     precondition(i >= 0)
     precondition(i < size)
     let o = i / N
@@ -52,7 +52,7 @@ public struct BitSet {
     that we're not using, or bitwise operations between two differently sized
     BitSets will go wrong.
   */
-  private mutating func clearUnusedBits() {
+  fileprivate mutating func clearUnusedBits() {
     words[words.count - 1] &= lastWordMask()
   }
 
@@ -63,7 +63,7 @@ public struct BitSet {
   }
 
   /* Sets the bit at the specified index to 1. */
-  public mutating func set(i: Int) {
+  public mutating func set(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] |= m
   }
@@ -77,7 +77,7 @@ public struct BitSet {
   }
 
   /* Sets the bit at the specified index to 0. */
-  public mutating func clear(i: Int) {
+  public mutating func clear(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] &= ~m
   }
@@ -90,14 +90,14 @@ public struct BitSet {
   }
 
   /* Changes 0 into 1 and 1 into 0. Returns the new value of the bit. */
-  public mutating func flip(i: Int) -> Bool {
+  public mutating func flip(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     words[j] ^= m
     return (words[j] & m) != 0
   }
 
   /* Determines whether the bit at the specific index is 1 (true) or 0 (false). */
-  public func isSet(i: Int) -> Bool {
+  public func isSet(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     return (words[j] & m) != 0
   }
@@ -158,7 +158,7 @@ extension BitSet: Hashable {
   /* Based on the hashing code from Java's BitSet. */
   public var hashValue: Int {
     var h = Word(1234)
-    for i in words.count.stride(to: 0, by: -1) {
+    for i in stride(from: words.count, to: 0, by: -1) {
       h ^= words[i - 1] &* Word(i)
     }
     return Int((h >> 32) ^ h)
@@ -167,13 +167,13 @@ extension BitSet: Hashable {
 
 // MARK: - Bitwise operations
 
-extension BitSet: BitwiseOperationsType {
+extension BitSet: BitwiseOperations {
   public static var allZeros: BitSet {
     return BitSet(size: 64)
   }
 }
 
-private func copyLargest(lhs: BitSet, _ rhs: BitSet) -> BitSet {
+private func copyLargest(_ lhs: BitSet, _ rhs: BitSet) -> BitSet {
   return (lhs.words.count > rhs.words.count) ? lhs : rhs
 }
 
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index 46f51dbba..d8985bd13 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -11,7 +11,7 @@ public struct BitSet {
   */
   private let N = 64
   public typealias Word = UInt64
-  private(set) public var words: [Word]
+  fileprivate(set) public var words: [Word]
 
   private let allOnes = ~Word()
 
@@ -22,11 +22,11 @@ public struct BitSet {
 
     // Round up the count to the next multiple of 64.
     let n = (size + (N-1)) / N
-    words = .init(count: n, repeatedValue: 0)
+    words = [Word](repeating: 0, count: n)
   }
 
   /* Converts a bit index into an array index and a mask inside the word. */
-  private func indexOf(i: Int) -> (Int, Word) {
+  private func indexOf(_ i: Int) -> (Int, Word) {
     precondition(i >= 0)
     precondition(i < size)
     let o = i / N
@@ -52,7 +52,7 @@ public struct BitSet {
     that we're not using, or bitwise operations between two differently sized
     BitSets will go wrong.
   */
-  private mutating func clearUnusedBits() {
+  fileprivate mutating func clearUnusedBits() {
     words[words.count - 1] &= lastWordMask()
   }
 
@@ -63,7 +63,7 @@ public struct BitSet {
   }
 
   /* Sets the bit at the specified index to 1. */
-  public mutating func set(i: Int) {
+  public mutating func set(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] |= m
   }
@@ -77,7 +77,7 @@ public struct BitSet {
   }
 
   /* Sets the bit at the specified index to 0. */
-  public mutating func clear(i: Int) {
+  public mutating func clear(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] &= ~m
   }
@@ -90,14 +90,14 @@ public struct BitSet {
   }
 
   /* Changes 0 into 1 and 1 into 0. Returns the new value of the bit. */
-  public mutating func flip(i: Int) -> Bool {
+  public mutating func flip(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     words[j] ^= m
     return (words[j] & m) != 0
   }
 
   /* Determines whether the bit at the specific index is 1 (true) or 0 (false). */
-  public func isSet(i: Int) -> Bool {
+  public func isSet(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     return (words[j] & m) != 0
   }
@@ -158,7 +158,7 @@ extension BitSet: Hashable {
   /* Based on the hashing code from Java's BitSet. */
   public var hashValue: Int {
     var h = Word(1234)
-    for i in words.count.stride(to: 0, by: -1) {
+    for i in stride(from: words.count, to: 0, by: -1) {
       h ^= words[i - 1] &* Word(i)
     }
     return Int((h >> 32) ^ h)
@@ -167,13 +167,13 @@ extension BitSet: Hashable {
 
 // MARK: - Bitwise operations
 
-extension BitSet: BitwiseOperationsType {
+extension BitSet: BitwiseOperations {
   public static var allZeros: BitSet {
     return BitSet(size: 64)
   }
 }
 
-private func copyLargest(lhs: BitSet, _ rhs: BitSet) -> BitSet {
+private func copyLargest(_ lhs: BitSet, _ rhs: BitSet) -> BitSet {
   return (lhs.words.count > rhs.words.count) ? lhs : rhs
 }
 
diff --git a/Bit Set/README.markdown b/Bit Set/README.markdown
index 85d55e06e..6bb6e7c89 100644
--- a/Bit Set/README.markdown	
+++ b/Bit Set/README.markdown	
@@ -18,7 +18,7 @@ public struct BitSet {
 
   private let N = 64
   public typealias Word = UInt64
-  private(set) public var words: [Word]
+  fileprivate(set) public var words: [Word]
 
   public init(size: Int) {
     precondition(size > 0)
@@ -26,7 +26,7 @@ public struct BitSet {
 
     // Round up the count to the next multiple of 64.
     let n = (size + (N-1)) / N
-    words = .init(count: n, repeatedValue: 0)
+    words = [Word](repeating: 0, count: n)
   }
 ```
 
@@ -47,7 +47,7 @@ then the `BitSet` allocates an array of three words. Each word has 64 bits and t
 Most of the operations on `BitSet` take the index of the bit as a parameter, so it's useful to have a way to find which word contains that bit.
 
 ```swift
-  private func indexOf(i: Int) -> (Int, Word) {
+  private func indexOf(_ i: Int) -> (Int, Word) {
     precondition(i >= 0)
     precondition(i < size)
     let o = i / N
@@ -77,7 +77,7 @@ Note that the mask is always 64 bits because we look at the data one word at a t
 Now that we know where to find a bit, setting it to 1 is easy:
 
 ```swift
-  public mutating func set(i: Int) {
+  public mutating func set(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] |= m
   }
@@ -88,7 +88,7 @@ This looks up the word index and the mask, then performs a bitwise OR between th
 Clearing the bit -- i.e. changing it to 0 -- is just as easy:
 
 ```swift
-  public mutating func clear(i: Int) {
+  public mutating func clear(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] &= ~m
   }
@@ -99,7 +99,7 @@ Instead of a bitwise OR we now do a bitwise AND with the inverse of the mask. So
 To see if a bit is set we also use the bitwise AND but without inverting:
 
 ```swift
-  public func isSet(i: Int) -> Bool {
+  public func isSet(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     return (words[j] & m) != 0
   }
@@ -127,15 +127,15 @@ print(bits)
 This will print the three words that the 140-bit `BitSet` uses to store everything:
 
 ```swift
-0010000000000000000000000000000000000000000000000000000000000000 
-0000000000000000000000000000000000010000000000000000000000000000 
-1000000000000000000000000000000000000000000000000000000000000000 
+0010000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000010000000000000000000000000000
+1000000000000000000000000000000000000000000000000000000000000000
 ```
 
 Something else that's fun to do with bits is flipping them. This changes 0 into 1 and 1 into 0. Here's `flip()`:
 
 ```swift
-  public mutating func flip(i: Int) -> Bool {
+  public mutating func flip(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     words[j] ^= m
     return (words[j] & m) != 0
@@ -170,17 +170,17 @@ There is also `setAll()` to make all the bits 1. However, this has to deal with
 First, we copy ones into all the words in our array. The array is now:
 
 ```swift
-1111111111111111111111111111111111111111111111111111111111111111 
-1111111111111111111111111111111111111111111111111111111111111111 
-1111111111111111111111111111111111111111111111111111111111111111 
+1111111111111111111111111111111111111111111111111111111111111111
+1111111111111111111111111111111111111111111111111111111111111111
+1111111111111111111111111111111111111111111111111111111111111111
 ```
 
 But this is incorrect... Since we don't use most of the last word, we should leave those bits at 0:
 
 ```swift
-1111111111111111111111111111111111111111111111111111111111111111 
-1111111111111111111111111111111111111111111111111111111111111111 
-1111111111110000000000000000000000000000000000000000000000000000 
+1111111111111111111111111111111111111111111111111111111111111111
+1111111111111111111111111111111111111111111111111111111111111111
+1111111111110000000000000000000000000000000000000000000000000000
 ```
 
 Instead of 192 one-bits we now have only 140 one-bits. The fact that the last word may not be completely filled up means that we always have to treat this last word specially.
@@ -189,7 +189,7 @@ Setting those "leftover" bits to 0 is what the `clearUnusedBits()` helper functi
 
 This uses some advanced bit manipulation, so pay close attention:
 
-```swift 
+```swift
   private func lastWordMask() -> Word {
     let diff = words.count*N - size       // 1
     if diff > 0 {
@@ -199,7 +199,7 @@ This uses some advanced bit manipulation, so pay close attention:
       return ~Word()
     }
   }
-  
+
   private mutating func clearUnusedBits() {
     words[words.count - 1] &= lastWordMask()   // 4
   }  
@@ -211,15 +211,15 @@ Here's what it does, step-by-step:
 
 2) Create a mask that is all 0's, except the highest bit that's still valid is a 1. In our example, that would be:
 
-	0000000000010000000000000000000000000000000000000000000000000000 
+	0000000000010000000000000000000000000000000000000000000000000000
 
 3) Subtract 1 to turn it into:
 
-	1111111111100000000000000000000000000000000000000000000000000000 
+	1111111111100000000000000000000000000000000000000000000000000000
 
 and add the high bit back in to get:
 
-	1111111111110000000000000000000000000000000000000000000000000000 
+	1111111111110000000000000000000000000000000000000000000000000000
 
 There are now 12 one-bits in this word because `140 - 2*64 = 12`.
 
@@ -236,7 +236,7 @@ The first one only uses the first 4 bits; the second one uses 8 bits. The first
 	00100011  
 	-------- OR
 	10101111
-	
+
 That is wrong since two of those 1-bits aren't supposed to be here. The correct way to do it is:
 
 	10000000       unused bits set to 0 first!

From e6cfec424571c1c5afed292fb4159b5e8b766df9 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 30 Aug 2016 18:27:49 +1200
Subject: [PATCH 0477/1679] Updating to Swift3

---
 .travis.yml                                   |  2 +-
 .../BloomFilter.playground/Contents.swift     | 18 ++--
 Bloom Filter/BloomFilter.swift                | 16 ++--
 Bloom Filter/README.markdown                  | 16 ++--
 Bloom Filter/Tests/BloomFilterTests.swift     | 88 +++++++++----------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 7 files changed, 80 insertions(+), 72 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 1eba40123..5b31c3085 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -13,7 +13,7 @@ script:
  - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index ce59eecaa..d5e7d2dc6 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -1,31 +1,31 @@
 //: Playground - noun: a place where people can play
 
 public class BloomFilter<T> {
-  private var array: [Bool]
-  private var hashFunctions: [T -> Int]
+  fileprivate var array: [Bool]
+  private var hashFunctions: [(T) -> Int]
 
-  public init(size: Int = 1024, hashFunctions: [T -> Int]) {
-    self.array = .init(count: size, repeatedValue: false)
+  public init(size: Int = 1024, hashFunctions: [(T) -> Int]) {
+    self.array = [Bool](repeating: false, count: size)
     self.hashFunctions = hashFunctions
   }
 
-  private func computeHashes(value: T) -> [Int] {
+  private func computeHashes(_ value: T) -> [Int] {
     return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
   }
 
-  public func insert(element: T) {
+  public func insert(_ element: T) {
     for hashValue in computeHashes(element) {
       array[hashValue] = true
     }
   }
 
-  public func insert(values: [T]) {
+  public func insert(_ values: [T]) {
     for value in values {
       insert(value)
     }
   }
 
-  public func query(value: T) -> Bool {
+  public func query(_ value: T) -> Bool {
     let hashValues = computeHashes(value)
 
     // Map hashes to indices in the Bloom Filter
@@ -37,7 +37,7 @@ public class BloomFilter<T> {
     // only that it may be. If the query returns false, however,
     // you can be certain that the value was not added.
 
-    let exists = results.reduce(true, combine: { $0 && $1 })
+    let exists = results.reduce(true, { $0 && $1 })
     return exists
   }
 
diff --git a/Bloom Filter/BloomFilter.swift b/Bloom Filter/BloomFilter.swift
index 97a982f48..03b5333f1 100644
--- a/Bloom Filter/BloomFilter.swift	
+++ b/Bloom Filter/BloomFilter.swift	
@@ -1,29 +1,29 @@
 public class BloomFilter<T> {
   private var array: [Bool]
-  private var hashFunctions: [T -> Int]
+  private var hashFunctions: [(T) -> Int]
 
-  public init(size: Int = 1024, hashFunctions: [T -> Int]) {
-    self.array = .init(count: size, repeatedValue: false)
+  public init(size: Int = 1024, hashFunctions: [(T) -> Int]) {
+    self.array = [Bool](repeating: false, count: size)
     self.hashFunctions = hashFunctions
   }
 
-  private func computeHashes(value: T) -> [Int] {
+  private func computeHashes(_ value: T) -> [Int] {
     return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
   }
 
-  public func insert(element: T) {
+  public func insert(_ element: T) {
     for hashValue in computeHashes(element) {
       array[hashValue] = true
     }
   }
 
-  public func insert(values: [T]) {
+  public func insert(_ values: [T]) {
     for value in values {
       insert(value)
     }
   }
 
-  public func query(value: T) -> Bool {
+  public func query(_ value: T) -> Bool {
     let hashValues = computeHashes(value)
 
     // Map hashes to indices in the Bloom Filter
@@ -35,7 +35,7 @@ public class BloomFilter<T> {
     // only that it may be. If the query returns false, however,
     // you can be certain that the value was not added.
 
-    let exists = results.reduce(true, combine: { $0 && $1 })
+    let exists = results.reduce(true, { $0 && $1 })
     return exists
   }
 
diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index 3e37ee50b..a85d71be4 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -58,11 +58,11 @@ Performance of a Bloom Filter is **O(k)** where **k** is the number of hashing f
 
 ## The code
 
-The code is quite straightforward. The internal bit array is set to a fixed length on initialization, which cannot be mutated once it is initialized. 
+The code is quite straightforward. The internal bit array is set to a fixed length on initialization, which cannot be mutated once it is initialized.
 
 ```swift
-public init(size: Int = 1024, hashFunctions: [T -> Int]) {
-  self.array = .init(count: size, repeatedValue: false)
+public init(size: Int = 1024, hashFunctions: [(T) -> Int]) {
+	self.array = [Bool](repeating: false, count: size)
   self.hashFunctions = hashFunctions
 }
 ```
@@ -72,7 +72,7 @@ Several hash functions should be specified at initialization. Which hash functio
 Insertion just flips the required bits to `true`:
 
 ```swift
-public func insert(element: T) {
+public func insert(_ element: T) {
   for hashValue in computeHashes(element) {
     array[hashValue] = true
   }
@@ -82,7 +82,7 @@ public func insert(element: T) {
 This uses the `computeHashes()` function, which loops through the specified `hashFunctions` and returns an array of indices:
 
 ```swift
-private func computeHashes(value: T) -> [Int] {
+private func computeHashes(_ value: T) -> [Int] {
   return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
 }
 ```
@@ -90,14 +90,14 @@ private func computeHashes(value: T) -> [Int] {
 And querying checks to make sure the bits at the hashed values are `true`:
 
 ```swift
-public func query(value: T) -> Bool {
+public func query(_ value: T) -> Bool {
   let hashValues = computeHashes(value)
   let results = hashValues.map() { hashValue in array[hashValue] }
-  let exists = results.reduce(true, combine: { $0 && $1 })
+	let exists = results.reduce(true, { $0 && $1 })
   return exists
 }
 ```
 
-If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop. 
+If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop.
 
 *Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans.*
diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index ffac8192d..82bf4fb8f 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -1,76 +1,76 @@
 import XCTest
 
 /* Two hash functions, adapted from
-    http://www.cse.yorku.ca/~oz/hash.html */
+ http://www.cse.yorku.ca/~oz/hash.html */
 
-func djb2(x: String) -> Int {
-    var hash = 5381
+func djb2(_ x: String) -> Int {
+  var hash = 5381
 
-    for char in x.characters {
-        hash = ((hash << 5) &+ hash) &+ char.hashValue
-    }
+  for char in x.characters {
+    hash = ((hash << 5) &+ hash) &+ char.hashValue
+  }
 
-    return Int(hash)
+  return Int(hash)
 }
 
-func sdbm(x: String) -> Int {
-    var hash = 0
+func sdbm(_ x: String) -> Int {
+  var hash = 0
 
-    for char in x.characters {
-        hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
-    }
+  for char in x.characters {
+    hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
+  }
 
-    return Int(hash)
+  return Int(hash)
 }
 
 
 class BloomFilterTests: XCTestCase {
 
-    func testSingleHashFunction() {
-        let bloom = BloomFilter<String>(hashFunctions: [djb2])
+  func testSingleHashFunction() {
+    let bloom = BloomFilter<String>(hashFunctions: [djb2])
 
-        bloom.insert("Hello world!")
+    bloom.insert("Hello world!")
 
-        let result_good = bloom.query("Hello world!")
-        let result_bad = bloom.query("Hello world")
+    let result_good = bloom.query("Hello world!")
+    let result_bad = bloom.query("Hello world")
 
-        XCTAssertTrue(result_good)
-        XCTAssertFalse(result_bad)
-    }
+    XCTAssertTrue(result_good)
+    XCTAssertFalse(result_bad)
+  }
 
-    func testEmptyFilter() {
-        let bloom = BloomFilter<String>(hashFunctions: [djb2])
+  func testEmptyFilter() {
+    let bloom = BloomFilter<String>(hashFunctions: [djb2])
 
-        let empty = bloom.isEmpty()
+    let empty = bloom.isEmpty()
 
-        XCTAssertTrue(empty)
-    }
+    XCTAssertTrue(empty)
+  }
 
-    func testMultipleHashFunctions() {
-        let bloom = BloomFilter<String>(hashFunctions: [djb2, sdbm])
+  func testMultipleHashFunctions() {
+    let bloom = BloomFilter<String>(hashFunctions: [djb2, sdbm])
 
-        bloom.insert("Hello world!")
+    bloom.insert("Hello world!")
 
-        let result_good = bloom.query("Hello world!")
-        let result_bad = bloom.query("Hello world")
+    let result_good = bloom.query("Hello world!")
+    let result_bad = bloom.query("Hello world")
 
-        XCTAssertTrue(result_good)
-        XCTAssertFalse(result_bad)
-    }
+    XCTAssertTrue(result_good)
+    XCTAssertFalse(result_bad)
+  }
 
-    func testFalsePositive() {
-        let bloom = BloomFilter<String>(size: 5, hashFunctions: [djb2, sdbm])
+  func testFalsePositive() {
+    let bloom = BloomFilter<String>(size: 5, hashFunctions: [djb2, sdbm])
 
-        bloom.insert(["hello", "elloh", "llohe", "lohel", "ohell"])
+    bloom.insert(["hello", "elloh", "llohe", "lohel", "ohell"])
 
-        print("Inserted")
+    print("Inserted")
 
-        let query = bloom.query("This wasn't inserted!")
+    let query = bloom.query("This wasn't inserted!")
 
-        // This is true even though we did not insert the value in the Bloom filter;
-        // the Bloom filter is capable of producing false positives but NOT
-        // false negatives.
+    // This is true even though we did not insert the value in the Bloom filter;
+    // the Bloom filter is capable of producing false positives but NOT
+    // false negatives.
 
-        XCTAssertTrue(query)
-    }
+    XCTAssertTrue(query)
+  }
 }
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj
index d413110c9..20998a80e 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,11 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -145,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -189,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -220,6 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 66da2bc7bd13cb8722476c74699e0c8a935c3b76 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 11:33:34 +0200
Subject: [PATCH 0478/1679] Updating Stack to Swift 3

---
 Stack/Stack.playground/Contents.swift       |  4 ++--
 Stack/Stack.swift                           | 10 +++++-----
 Stack/Tests/Tests.xcodeproj/project.pbxproj |  3 +++
 3 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 4f4f826f2..12c29faa0 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -12,7 +12,7 @@
 */
 
 public struct Stack<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var count: Int {
     return array.count
@@ -39,7 +39,7 @@ public struct Stack<T> {
 var stackOfNames = Stack(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
 // Add an element to the top of the stack.
-stackOfNames.push("Mike")
+stackOfNames.push(element: "Mike")
 
 // The stack is now ["Carl", "Lisa", "Stephanie", "Jeff", "Wade", "Mike"]
 print(stackOfNames.array)
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 454b66fa0..49edaf4cb 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -4,7 +4,7 @@
   Push and pop are O(1) operations.
 */
 public struct Stack<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -14,7 +14,7 @@ public struct Stack<T> {
     return array.count
   }
 
-  public mutating func push(element: T) {
+  public mutating func push(_ element: T) {
     array.append(element)
   }
 
@@ -27,10 +27,10 @@ public struct Stack<T> {
   }
 }
 
-extension Stack: SequenceType {
-    public func generate() -> AnyGenerator<T> {
+extension Stack: Sequence {
+    public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyGenerator {
+        return AnyIterator {
             _ -> T? in
             return curr.pop()
         }
diff --git a/Stack/Tests/Tests.xcodeproj/project.pbxproj b/Stack/Tests/Tests.xcodeproj/project.pbxproj
index a36d7c51d..5ec8dc987 100644
--- a/Stack/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Stack/Tests/Tests.xcodeproj/project.pbxproj
@@ -88,6 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -220,6 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 8d4636648f751297d9b99e66f2170c564aed246b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 11:38:23 +0200
Subject: [PATCH 0479/1679] Uncomment Stack tests

---
 .travis.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 1eba40123..f430659e0 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,7 +9,7 @@ install:
 script:
 
 # - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
- - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
  - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
@@ -37,5 +37,5 @@ script:
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-# - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+  - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From adf2f61a6403d60ac0915bc234e29b6cc6712245 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 11:46:19 +0200
Subject: [PATCH 0480/1679] Fix .travis.yml

---
 .travis.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index f430659e0..2be5210c4 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -10,8 +10,8 @@ script:
 
 # - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
 # - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
- - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
- - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests

From 5ad3bb022e98b21b7a3a1d11d6cb32d5b4eff26c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 14:04:52 +0200
Subject: [PATCH 0481/1679] Update push method, update to recommended settings

---
 .travis.yml                                                | 6 +++---
 Stack/README.markdown                                      | 4 ++--
 Stack/Stack.playground/Contents.swift                      | 4 ++--
 Stack/Tests/Tests.xcodeproj/project.pbxproj                | 7 ++++++-
 .../Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme  | 2 +-
 5 files changed, 14 insertions(+), 9 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 2be5210c4..7ac58cd33 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,9 +9,9 @@ install:
 script:
 
 # - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-# - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+  - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+  - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+  - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Stack/README.markdown b/Stack/README.markdown
index 17770643b..9d157f290 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -42,7 +42,7 @@ A stack is easy to create in Swift. It's just a wrapper around an array that jus
 
 ```swift
 public struct Stack<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -52,7 +52,7 @@ public struct Stack<T> {
     return array.count
   }
 
-  public mutating func push(element: T) {
+  public mutating func push(_ element: T) {
     array.append(element)
   }
 
diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 12c29faa0..f086ca817 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -22,7 +22,7 @@ public struct Stack<T> {
     return array.isEmpty
   }
 
-  public mutating func push(element: T) {
+  public mutating func push(_ element: T) {
     array.append(element)
   }
 
@@ -39,7 +39,7 @@ public struct Stack<T> {
 var stackOfNames = Stack(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
 // Add an element to the top of the stack.
-stackOfNames.push(element: "Mike")
+stackOfNames.push("Mike")
 
 // The stack is now ["Carl", "Lisa", "Stephanie", "Jeff", "Wade", "Mike"]
 print(stackOfNames.array)
diff --git a/Stack/Tests/Tests.xcodeproj/project.pbxproj b/Stack/Tests/Tests.xcodeproj/project.pbxproj
index 5ec8dc987..8924fc935 100644
--- a/Stack/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Stack/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,7 +83,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -146,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -190,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
diff --git a/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 3c2d60b7bbfaf63991cdb62aa2a4ff82917d7b74 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 15:15:28 +0200
Subject: [PATCH 0482/1679] Update Queue to Swift 3

---
 .travis.yml                                            |  2 +-
 Queue/Queue-Optimized.swift                            |  6 +++---
 Queue/Queue-Simple.swift                               |  4 ++--
 Queue/Queue.playground/Contents.swift                  |  4 ++--
 Queue/README.markdown                                  | 10 +++++-----
 Queue/Tests/Tests.xcodeproj/project.pbxproj            | 10 +++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme              |  2 +-
 7 files changed, 23 insertions(+), 15 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 1eba40123..ff451b26e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -29,7 +29,7 @@ script:
 # - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
+  - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index 5a9d04394..ad6999295 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -7,8 +7,8 @@
   Enqueuing and dequeuing are O(1) operations.
 */
 public struct Queue<T> {
-  private var array = [T?]()
-  private var head = 0
+  fileprivate var array = [T?]()
+  fileprivate var head = 0
 
   public var isEmpty: Bool {
     return count == 0
@@ -18,7 +18,7 @@ public struct Queue<T> {
     return array.count - head
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Queue/Queue-Simple.swift b/Queue/Queue-Simple.swift
index 6d3c197ee..27fbdee4d 100644
--- a/Queue/Queue-Simple.swift
+++ b/Queue/Queue-Simple.swift
@@ -8,7 +8,7 @@
   implemented with a linked list, then both would be O(1).
 */
 public struct Queue<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var count: Int {
     return array.count
@@ -18,7 +18,7 @@ public struct Queue<T> {
     return array.isEmpty
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 0c48afd5b..6b771ccd1 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -12,7 +12,7 @@
 */
 
 public struct Queue<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -22,7 +22,7 @@ public struct Queue<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Queue/README.markdown b/Queue/README.markdown
index 92118d37b..f7779aa69 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -46,7 +46,7 @@ Here is a very simplistic implementation of a queue in Swift. It's just a wrappe
 
 ```swift
 public struct Queue<T> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -56,7 +56,7 @@ public struct Queue<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
   
@@ -136,8 +136,8 @@ Here is how you could implement this version of `Queue`:
 
 ```swift
 public struct Queue<T> {
-  private var array = [T?]()
-  private var head = 0
+  fileprivate var array = [T?]()
+  fileprivate var head = 0
   
   public var isEmpty: Bool {
     return count == 0
@@ -147,7 +147,7 @@ public struct Queue<T> {
     return array.count - head
   }
   
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
   
diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
index ac23063a5..a554fd16e 100644
--- a/Queue/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,11 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -145,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -189,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -220,6 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From e6ed6399344692ece56808d853c2cedf31599651 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 15:18:15 +0200
Subject: [PATCH 0483/1679] Fix .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index ff451b26e..278aba883 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -37,5 +37,5 @@ script:
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-# - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+  - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 8527a528c451b04d6e9c8a2ed4f54c77dfa9b831 Mon Sep 17 00:00:00 2001
From: Nemanja Vlahovic <nemanja@nemanjavlahovic.com>
Date: Tue, 30 Aug 2016 22:21:21 +0200
Subject: [PATCH 0484/1679] Fix spaces in .travis.yml

---
 .travis.yml | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 278aba883..c2ac363d1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,9 +9,9 @@ install:
 script:
 
 # - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
- - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
- - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
- - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
@@ -29,7 +29,7 @@ script:
 # - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-  - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
@@ -37,5 +37,5 @@ script:
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-  - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 7d1c4a3a3b11ba5583df7d14bcc1e43ba48fdfc4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nvlahovic@razor.rs>
Date: Wed, 31 Aug 2016 09:56:45 +0200
Subject: [PATCH 0485/1679] Update Insertion Sort to Swift 3

---
 .../InsertionSort.playground/Contents.swift   |  4 +--
 Insertion Sort/InsertionSort.swift            |  2 +-
 Insertion Sort/README.markdown                |  6 ++--
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 +++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 Quicksort/Tests/SortingTestHelpers.swift      | 34 +++++++++----------
 6 files changed, 33 insertions(+), 25 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 867feb190..b25916b23 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -1,6 +1,6 @@
 //: Playground - noun: a place where people can play
 
-func insertionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   var a = array
   for x in 1..<a.count {
     var y = x
@@ -16,4 +16,4 @@ func insertionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 insertionSort(list, <)
-insertionSort(list, >)
+insertionSort(list, >)
\ No newline at end of file
diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 886054e53..5d8a9565b 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -1,4 +1,4 @@
-func insertionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   guard array.count > 1 else { return array }
 
   var a = array
diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index b67541669..286d92ed1 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -90,7 +90,7 @@ This was a description of the inner loop of the insertion sort algorithm, which
 Here is an implementation of insertion sort in Swift:
 
 ```swift
-func insertionSort(array: [Int]) -> [Int] {
+func insertionSort(_ array: [Int]) -> [Int] {
   var a = array                             // 1
   for x in 1..<a.count {                    // 2
     var y = x
@@ -151,7 +151,7 @@ Instead of swapping with each of the previous elements, we can just shift all th
 In code that looks like this:
 
 ```swift
-func insertionSort(array: [Int]) -> [Int] {
+func insertionSort(_ array: [Int]) -> [Int] {
   var a = array
   for x in 1..<a.count {
     var y = x
@@ -175,7 +175,7 @@ It would be nice to sort other things than just numbers. We can make the datatyp
 The function signature becomes:
 
 ```swift
-func insertionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 ```
 
 The array has type `[T]` where `T` is the placeholder type for the generics. Now `insertionSort()` will accept any kind of array, whether it contains numbers, strings, or something else.
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj
index f8c23899c..ee3ca1cae 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,11 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -149,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -224,6 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Quicksort/Tests/SortingTestHelpers.swift b/Quicksort/Tests/SortingTestHelpers.swift
index 3b56d3c3e..d699ec1e4 100644
--- a/Quicksort/Tests/SortingTestHelpers.swift
+++ b/Quicksort/Tests/SortingTestHelpers.swift
@@ -1,7 +1,7 @@
 import Foundation
 import XCTest
 
-func randomArray(size: Int) -> [Int] {
+func randomArray(_ size: Int) -> [Int] {
   var a = [Int]()
   for _ in 1...size {
     a.append(Int(arc4random_uniform(1000)))
@@ -9,16 +9,16 @@ func randomArray(size: Int) -> [Int] {
   return a
 }
 
-func arrayIsSortedLowToHigh(a: [Int]) -> Bool {
+func arrayIsSortedLowToHigh(_ a: [Int]) -> Bool {
   for x in 1..<a.count {
     if a[x - 1] > a[x] { return false }
   }
   return true
 }
 
-typealias SortFunction = [Int] -> [Int]
+typealias SortFunction = ([Int]) -> [Int]
 
-func checkSortingRandomArray(sortFunction: SortFunction) {
+func checkSortingRandomArray(_ sortFunction: SortFunction) {
   let numberOfIterations = 100
   for _ in 1...numberOfIterations {
     let a = randomArray(Int(arc4random_uniform(100)) + 1)
@@ -28,73 +28,73 @@ func checkSortingRandomArray(sortFunction: SortFunction) {
   }
 }
 
-func checkSortingEmptyArray(sortFunction: SortFunction) {
+func checkSortingEmptyArray(_ sortFunction: SortFunction) {
   let a = [Int]()
   let s = sortFunction(a)
   XCTAssertEqual(s.count, 0)
 }
 
-func checkSortingArrayOneElement(sortFunction: SortFunction) {
+func checkSortingArrayOneElement(_ sortFunction: SortFunction) {
   let a = [123]
   let s = sortFunction(a)
   XCTAssertEqual(s, [123])
 }
 
-func checkSortingArrayTwoElementsInOrder(sortFunction: SortFunction) {
+func checkSortingArrayTwoElementsInOrder(_ sortFunction: SortFunction) {
   let a = [123, 456]
   let s = sortFunction(a)
   XCTAssertEqual(s, [123, 456])
 }
 
-func checkSortingArrayTwoElementsOutOfOrder(sortFunction: SortFunction) {
+func checkSortingArrayTwoElementsOutOfOrder(_ sortFunction: SortFunction) {
   let a = [456, 123]
   let s = sortFunction(a)
   XCTAssertEqual(s, [123, 456])
 }
 
-func checkSortingArrayTwoEqualElements(sortFunction: SortFunction) {
+func checkSortingArrayTwoEqualElements(_ sortFunction: SortFunction) {
   let a = [123, 123]
   let s = sortFunction(a)
   XCTAssertEqual(s, [123, 123])
 }
 
-func checkSortingArrayThreeElementsABC(sortFunction: SortFunction) {
+func checkSortingArrayThreeElementsABC(_ sortFunction: SortFunction) {
   let a = [2, 4, 6]
   let s = sortFunction(a)
   XCTAssertEqual(s, [2, 4, 6])
 }
 
-func checkSortingArrayThreeElementsACB(sortFunction: SortFunction) {
+func checkSortingArrayThreeElementsACB(_ sortFunction: SortFunction) {
   let a = [2, 6, 4]
   let s = sortFunction(a)
   XCTAssertEqual(s, [2, 4, 6])
 }
 
-func checkSortingArrayThreeElementsBAC(sortFunction: SortFunction) {
+func checkSortingArrayThreeElementsBAC(_ sortFunction: SortFunction) {
   let a = [4, 2, 6]
   let s = sortFunction(a)
   XCTAssertEqual(s, [2, 4, 6])
 }
 
-func checkSortingArrayThreeElementsBCA(sortFunction: SortFunction) {
+func checkSortingArrayThreeElementsBCA(_ sortFunction: SortFunction) {
   let a = [4, 6, 2]
   let s = sortFunction(a)
   XCTAssertEqual(s, [2, 4, 6])
 }
 
-func checkSortingArrayThreeElementsCAB(sortFunction: SortFunction) {
+func checkSortingArrayThreeElementsCAB(_ sortFunction: SortFunction) {
   let a = [6, 2, 4]
   let s = sortFunction(a)
   XCTAssertEqual(s, [2, 4, 6])
 }
 
-func checkSortingArrayThreeElementsCBA(sortFunction: SortFunction) {
+func checkSortingArrayThreeElementsCBA(_ sortFunction: SortFunction) {
   let a = [6, 4, 2]
   let s = sortFunction(a)
   XCTAssertEqual(s, [2, 4, 6])
 }
 
-func checkSortAlgorithm(sortFunction: SortFunction) {
+func checkSortAlgorithm(_ sortFunction: SortFunction) {
   checkSortingEmptyArray(sortFunction)
   checkSortingArrayOneElement(sortFunction)
   checkSortingArrayTwoElementsInOrder(sortFunction)
@@ -109,6 +109,6 @@ func checkSortAlgorithm(sortFunction: SortFunction) {
   checkSortingRandomArray(sortFunction)
 }
 
-func checkSortAlgorithm(sortFunction: ([Int], (Int, Int) -> Bool) -> [Int]) {
+func checkSortAlgorithm(_ sortFunction: @escaping ([Int], (Int, Int) -> Bool) -> [Int]) {
   checkSortAlgorithm { a in sortFunction(a, <) }
 }

From a50e2879edd581fcc3c8b8388dde19dc4877e114 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nvlahovic@razor.rs>
Date: Wed, 31 Aug 2016 10:01:20 +0200
Subject: [PATCH 0486/1679] Update travis.yml

---
 .travis.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 1eba40123..6b1fe2dff 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -23,7 +23,7 @@ script:
 # - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
 # - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
@@ -37,5 +37,5 @@ script:
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-# - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
+ - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 8f0447566427f089789a29e01dbdc60e97bf2d01 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 31 Aug 2016 21:18:13 +1200
Subject: [PATCH 0487/1679] Update .travis.yml

Removed space before insertion sort tests.
---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 32f43c129..8cf0b486b 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -23,7 +23,7 @@ script:
 # - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
 # - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
- - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests

From 283ba84440385e36965943aa0581e6b81d917d13 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nvlahovic@razor.rs>
Date: Wed, 31 Aug 2016 13:27:13 +0200
Subject: [PATCH 0488/1679] Update Merge Sort to Swift 3

---
 Merge Sort/MergeSort.playground/Contents.swift | 6 +++---
 Merge Sort/MergeSort.swift                     | 6 +++---
 Merge Sort/README.markdown                     | 6 +++---
 3 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index a71a90136..ac166131e 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -1,6 +1,6 @@
 /* Top-down recursive version */
 
-func mergeSort(array: [Int]) -> [Int] {
+func mergeSort(_ array: [Int]) -> [Int] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
   let leftArray = mergeSort(Array(array[0..<middleIndex]))
@@ -8,7 +8,7 @@ func mergeSort(array: [Int]) -> [Int] {
   return merge(leftPile: leftArray, rightPile: rightArray)
 }
 
-func merge(leftPile leftPile: [Int], rightPile: [Int]) -> [Int] {
+func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
   var leftIndex = 0
   var rightIndex = 0
   var orderedPile = [Int]()
@@ -48,7 +48,7 @@ let sortedArray = mergeSort(array)
 
 /* Bottom-up iterative version */
 
-func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   let n = a.count
   var z = [a, a]   // the two working arrays
   var d = 0        // z[d] is used for reading, z[1 - d] for writing
diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index 968484dd1..20316663f 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -6,7 +6,7 @@
 //
 //
 
-func mergeSort(array: [Int]) -> [Int] {
+func mergeSort(_ array: [Int]) -> [Int] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
   let leftArray = mergeSort(Array(array[0..<middleIndex]))
@@ -14,7 +14,7 @@ func mergeSort(array: [Int]) -> [Int] {
   return merge(leftPile: leftArray, rightPile: rightArray)
 }
 
-func merge(leftPile leftPile: [Int], rightPile: [Int]) -> [Int] {
+func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
   var leftIndex = 0
   var rightIndex = 0
   var orderedPile = [Int]()
@@ -59,7 +59,7 @@ func merge(leftPile leftPile: [Int], rightPile: [Int]) -> [Int] {
   To avoid allocating many temporary array objects, it uses double-buffering with
   just two arrays.
 */
-func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   let n = a.count
   var z = [a, a]   // the two working arrays
   var d = 0        // z[d] is used for reading, z[1 - d] for writing
diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index a24c71f2f..3ff69fdd5 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -42,7 +42,7 @@ You're left with only two piles and `[9]` finally gets its chance to merge, resu
 Here's what merge sort may look like in Swift:
 
 ```swift
-func mergeSort(array: [Int]) -> [Int] {
+func mergeSort(_ array: [Int]) -> [Int] {
   guard array.count > 1 else { return array }    // 1
 
   let middleIndex = array.count / 2              // 2
@@ -70,7 +70,7 @@ A step-by-step explanation of how the code works:
 Here's the merging algorithm:
 
 ```swift
-func merge(leftPile leftPile: [Int], rightPile: [Int]) -> [Int] {
+func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
   // 1
   var leftIndex = 0
   var rightIndex = 0
@@ -162,7 +162,7 @@ The implementation of merge sort you've seen so far is called "top-down" because
 Time to step up the game a little. :-) Here is a complete bottom-up implementation in Swift:
 
 ```swift
-func mergeSortBottomUp<T>(a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   let n = a.count
 
   var z = [a, a]      // 1

From 33b6e653c03765fbaad06423bd2122de4199686e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nvlahovic@razor.rs>
Date: Wed, 31 Aug 2016 13:46:09 +0200
Subject: [PATCH 0489/1679] Update Linear Search to Swift 3

---
 Linear Search/LinearSearch.playground/Contents.swift | 4 ++--
 Linear Search/LinearSearch.swift                     | 4 ++--
 Linear Search/README.markdown                        | 4 ++--
 3 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 02fb6e940..34e859fa3 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,7 +1,7 @@
 //: Playground - noun: a place where people can play
 
-func linearSearch<T: Equatable>(array: [T], _ object: T) -> Int? {
-  for (index, obj) in array.enumerate() where obj == object {
+func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
+  for (index, obj) in array.enumerated() where obj == object {
     return index
   }
   return nil
diff --git a/Linear Search/LinearSearch.swift b/Linear Search/LinearSearch.swift
index fe64ef24e..882795180 100644
--- a/Linear Search/LinearSearch.swift	
+++ b/Linear Search/LinearSearch.swift	
@@ -1,5 +1,5 @@
-func linearSearch<T: Equatable>(array: [T], _ object: T) -> Int? {
-  for (index, obj) in array.enumerate() where obj == object {
+func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
+  for (index, obj) in array.enumerated() where obj == object {
     return index
   }
   return nil
diff --git a/Linear Search/README.markdown b/Linear Search/README.markdown
index 115dd7ee2..4649f4fc4 100644
--- a/Linear Search/README.markdown	
+++ b/Linear Search/README.markdown	
@@ -17,8 +17,8 @@ We compare the number `2` from the array to our number `2` and notice they are e
 Here is a simple implementation of linear search in Swift:
 
 ```swift
-func linearSearch<T: Equatable>(array: [T], _ object: T) -> Int? {
-  for (index, obj) in array.enumerate() where obj == object {
+func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
+  for (index, obj) in array.enumerated() where obj == object {
     return index
   }
   return nil

From 7f627a21b2beb5cf9f72c77eccb151ef66231d25 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nemanja=20Vlahovic=CC=81?= <nemanja@nemanjavlahovic.com>
Date: Wed, 31 Aug 2016 14:02:17 +0200
Subject: [PATCH 0490/1679] Update Count Occurrences to Swift 3

---
 Count Occurrences/CountOccurrences.playground/Contents.swift | 4 ++--
 Count Occurrences/CountOccurrences.swift                     | 2 +-
 Count Occurrences/README.markdown                            | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index b90ba12ce..cbb43c868 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,6 +1,6 @@
 //: Playground - noun: a place where people can play
 
-func countOccurrencesOfKey(key: Int, inArray a: [Int]) -> Int {
+func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {
     var low = 0
     var high = a.count
@@ -53,7 +53,7 @@ func createArray() -> [Int] {
       }
     }
   }
-  return a.sort(<)
+  return a.sorted()
 }
 
 for _ in 0..<10 {
diff --git a/Count Occurrences/CountOccurrences.swift b/Count Occurrences/CountOccurrences.swift
index 57c75c735..10dd12c4f 100644
--- a/Count Occurrences/CountOccurrences.swift	
+++ b/Count Occurrences/CountOccurrences.swift	
@@ -2,7 +2,7 @@
   Counts the number of times a value appears in an array in O(lg n) time.
   The array must be sorted from low to high.
 */
-func countOccurrencesOfKey(key: Int, inArray a: [Int]) -> Int {
+func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {
     var low = 0
     var high = a.count
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index be8c2061e..90a9ec2f3 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,7 +22,7 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrencesOfKey(key: Int, inArray a: [Int]) -> Int {
+func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {
     var low = 0
     var high = a.count

From ecae2cc08805bc2be1a22d4482a9d97e86d1776a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Simk=C3=B3?= <aqviktor@gmail.com>
Date: Thu, 1 Sep 2016 10:53:51 +0200
Subject: [PATCH 0491/1679] migrated to Swift 3

---
 B-Tree/BTree.swift                            | 419 +++++++++++-------
 B-Tree/Tests/Tests.xcodeproj/project.pbxproj  |  10 +-
 .../xcshareddata/xcschemes/Tests.xcscheme     |   2 +-
 B-Tree/Tests/Tests/BTreeNodeTests.swift       |  16 +-
 B-Tree/Tests/Tests/BTreeTests.swift           |  36 +-
 5 files changed, 303 insertions(+), 180 deletions(-)

diff --git a/B-Tree/BTree.swift b/B-Tree/BTree.swift
index 16c4eabe4..f5638ea4e 100644
--- a/B-Tree/BTree.swift
+++ b/B-Tree/BTree.swift
@@ -21,17 +21,17 @@
 // SOFTWARE.
 
 /*
- B-Tree
-	
- A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
+ *  B-Tree
+ *
+ *  A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
  */
 
 // MARK: - BTreeNode class
 
 class BTreeNode<Key: Comparable, Value> {
-  unowned var ownerTree: BTree<Key, Value>
+  unowned var owner: BTree<Key, Value>
   
-  private var keys = [Key]()
+  fileprivate var keys = [Key]()
   var values = [Value]()
   var children: [BTreeNode]?
   
@@ -43,13 +43,13 @@ class BTreeNode<Key: Comparable, Value> {
     return keys.count
   }
   
-  init(ownerTree: BTree<Key, Value>) {
-    self.ownerTree = ownerTree
+  init(owner: BTree<Key, Value>) {
+    self.owner = owner
   }
   
-  convenience init(ownerTree: BTree<Key, Value>, keys: [Key],
+  convenience init(owner: BTree<Key, Value>, keys: [Key],
                    values: [Value], children: [BTreeNode]? = nil) {
-    self.init(ownerTree: ownerTree)
+    self.init(owner: owner)
     self.keys += keys
     self.values += values
     self.children = children
@@ -59,19 +59,26 @@ class BTreeNode<Key: Comparable, Value> {
 // MARK: BTreeNode extesnion: Searching
 
 extension BTreeNode {
- func valueForKey(key: Key) -> Value? {
+  
+  /**
+   *  Returns the value for a given `key`, returns nil if the `key` is not found.
+   *  
+   *  - Parameters:
+   *    - key: the key of the value to be returned
+   */
+  func value(for key: Key) -> Value? {
     var index = keys.startIndex
     
-    while index.successor() < keys.endIndex && keys[index] < key {
-      index = index.successor()
+    while (index + 1) < keys.endIndex && keys[index] < key {
+      index = (index + 1)
     }
     
     if key == keys[index] {
       return values[index]
     } else if key < keys[index] {
-      return children?[index].valueForKey(key)
+      return children?[index].value(for: key)
     } else {
-      return children?[index.successor()].valueForKey(key)
+      return children?[(index + 1)].value(for: key)
     }
   }
 }
@@ -79,7 +86,14 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Travelsals
 
 extension BTreeNode {
-  func traverseKeysInOrder(@noescape process: Key -> Void) {
+  
+  /**
+   *  Traverses the keys in order, executes `process` for every key.
+   * 
+   *  - Parameters:
+   *    - process: the closure to be executed for every key
+   */
+  func traverseKeysInOrder(_ process: (Key) -> Void) {
     for i in 0..<numberOfKeys {
       children?[i].traverseKeysInOrder(process)
       process(keys[i])
@@ -92,11 +106,19 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Insertion
 
 extension BTreeNode {
-  func insertValue(value: Value, forKey key: Key) {
+  
+  /**
+   *  Inserts `value` for `key` to the node, or to one if its descendants.
+   *  
+   *  - Parameters:
+   *    - value: the value to be inserted for `key`
+   *    - key: the key for the `value`
+   */
+  func insert(_ value: Value, for key: Key) {
     var index = keys.startIndex
     
     while index < keys.endIndex && keys[index] < key {
-      index = index.successor()
+      index = (index + 1)
     }
     
     if index < keys.endIndex && keys[index] == key {
@@ -105,52 +127,68 @@ extension BTreeNode {
     }
     
     if isLeaf {
-      keys.insert(key, atIndex: index)
-      values.insert(value, atIndex: index)
-      ownerTree.numberOfKeys += 1
+      keys.insert(key, at: index)
+      values.insert(value, at: index)
+      owner.numberOfKeys += 1
     } else {
-      children![index].insertValue(value, forKey: key)
-      if children![index].numberOfKeys > ownerTree.order * 2 {
-        splitChild(children![index], atIndex: index)
+      children![index].insert(value, for: key)
+      if children![index].numberOfKeys > owner.order * 2 {
+        split(children![index], at: index)
       }
     }
   }
   
-  private func splitChild(child: BTreeNode, atIndex index: Int) {
+  /**
+   *  Splits `child` at `index`.
+   *  The key-value pair at `index` gets moved up to the parent node,
+   *  or if there is not an parent node, then a new parent node is created.
+   *  
+   *  - Parameters:
+   *    - child: the child to be split
+   *    - index: the index of the key, which will be moved up to the parent
+   */
+  fileprivate func split(_ child: BTreeNode, at index: Int) {
     let middleIndex = child.numberOfKeys / 2
-    keys.insert(child.keys[middleIndex], atIndex: index)
-    values.insert(child.values[middleIndex], atIndex: index)
-    child.keys.removeAtIndex(middleIndex)
-    child.values.removeAtIndex(middleIndex)
+    keys.insert(child.keys[middleIndex], at: index)
+    values.insert(child.values[middleIndex], at: index)
+    child.keys.remove(at: middleIndex)
+    child.values.remove(at: middleIndex)
     
     let rightSibling = BTreeNode(
-      ownerTree: ownerTree,
-      keys: Array(child.keys[middleIndex..<child.keys.endIndex]),
-      values: Array(child.values[middleIndex..<child.values.endIndex])
+      owner: owner,
+      keys: Array(child.keys[child.keys.indices.suffix(from: middleIndex)]),
+      values: Array(child.values[child.values.indices.suffix(from: middleIndex)])
     )
-    child.keys.removeRange(middleIndex..<child.keys.endIndex)
-    child.values.removeRange(middleIndex..<child.values.endIndex)
+    child.keys.removeSubrange(child.keys.indices.suffix(from: middleIndex))
+    child.values.removeSubrange(child.values.indices.suffix(from: middleIndex))
     
-    children!.insert(rightSibling, atIndex: index.successor())
+    children!.insert(rightSibling, at: (index + 1))
     
     if child.children != nil {
       rightSibling.children = Array(
-        child.children![middleIndex.successor()..<child.children!.endIndex]
+        child.children![child.children!.indices.suffix(from: (middleIndex + 1))]
       )
-      child.children!.removeRange(middleIndex.successor()..<child.children!.endIndex)
+      child.children!.removeSubrange(child.children!.indices.suffix(from: (middleIndex + 1)))
     }
   }
 }
 
 // MARK: BTreeNode extension: Removal
 
+/**
+ *  An enumeration to indicate a node's position according to another node.
+ *  
+ *  Possible values:
+ *    - left
+ *    - right
+ */
 private enum BTreeNodePosition {
-  case Left
-  case Right
+  case left
+  case right
 }
 
 extension BTreeNode {
-  private var inorderPredecessor: BTreeNode {
+  fileprivate var inorderPredecessor: BTreeNode {
     if isLeaf {
       return self
     } else {
@@ -158,34 +196,41 @@ extension BTreeNode {
     }
   }
   
-  func removeKey(key: Key) {
+  /**
+   *  Removes `key` and the value associated with it from the node
+   *  or one of its descendants.
+   *  
+   *  - Parameters:
+   *    - key: the key to be removed
+   */
+  func remove(_ key: Key) {
     var index = keys.startIndex
     
-    while index.successor() < keys.endIndex && keys[index] < key {
-      index = index.successor()
+    while (index + 1) < keys.endIndex && keys[index] < key {
+      index = (index + 1)
     }
     
     if keys[index] == key {
       if isLeaf {
-        keys.removeAtIndex(index)
-        values.removeAtIndex(index)
-        ownerTree.numberOfKeys -= 1
+        keys.remove(at: index)
+        values.remove(at: index)
+        owner.numberOfKeys -= 1
       } else {
         let predecessor = children![index].inorderPredecessor
         keys[index] = predecessor.keys.last!
         values[index] = predecessor.values.last!
-        children![index].removeKey(keys[index])
-        if children![index].numberOfKeys < ownerTree.order {
-          fixChildWithLessNodesThanOrder(children![index], atIndex: index)
+        children![index].remove(keys[index])
+        if children![index].numberOfKeys < owner.order {
+          fix(children![index], at: index)
         }
       }
     } else if key < keys[index] {
       // We should go to left child...
       
       if let leftChild = children?[index] {
-        leftChild.removeKey(key)
-        if leftChild.numberOfKeys < ownerTree.order {
-          fixChildWithLessNodesThanOrder(leftChild, atIndex: index)
+        leftChild.remove(key)
+        if leftChild.numberOfKeys < owner.order {
+          fix(leftChild, at: index)
         }
       } else {
         print("The key:\(key) is not in the tree.")
@@ -193,10 +238,10 @@ extension BTreeNode {
     } else {
       // We should go to right child...
       
-      if let rightChild = children?[index.successor()] {
-        rightChild.removeKey(key)
-        if rightChild.numberOfKeys < ownerTree.order {
-          fixChildWithLessNodesThanOrder(rightChild, atIndex: index.successor())
+      if let rightChild = children?[(index + 1)] {
+        rightChild.remove(key)
+        if rightChild.numberOfKeys < owner.order {
+          fix(rightChild, at: (index + 1))
         }
       } else {
         print("The key:\(key) is not in the tree")
@@ -204,112 +249,136 @@ extension BTreeNode {
     }
   }
   
-  private func fixChildWithLessNodesThanOrder(child: BTreeNode, atIndex index: Int) {
+  /**
+   *  Fixes the `child` at `index`.
+   *  If `child` contains too many children then it moves a child to one of 
+   *  `child`'s neighbouring nodes.
+   *  If `child` contains too few children then it merges it with one of its neighbours.
+   *
+   *  - Parameters:
+   *    - child: the child to be fixed
+   *    - index: the index of the child to be fixed in the current node
+   */
+  fileprivate func fix(_ child: BTreeNode, at index: Int) {
     
-    if index.predecessor() >= 0 &&
-       children![index.predecessor()].numberOfKeys > ownerTree.order {
-      
-      moveKeyAtIndex(index.predecessor(), toNode: child,
-                     fromNode: children![index.predecessor()], atPosition: .Left)
-      
-    } else if index.successor() < children!.count &&
-              children![index.successor()].numberOfKeys > ownerTree.order {
-      
-      moveKeyAtIndex(index, toNode: child,
-                     fromNode: children![index.successor()], atPosition: .Right)
-      
-    } else if index.predecessor() >= 0 {
-      mergeChild(child, withIndex: index, toNodeAtPosition: .Left)
+    if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
+      move(keyAt: (index - 1), to: child, from: children![(index - 1)], at: .left)
+    } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
+      move(keyAt: index, to: child, from: children![(index + 1)], at: .right)
+    } else if (index - 1) >= 0 {
+      merge(child, at: index, to: .left)
     } else {
-      mergeChild(child, withIndex: index, toNodeAtPosition: .Right)
+      merge(child, at: index, to: .right)
     }
   }
   
-  private func moveKeyAtIndex(keyIndex: Int, toNode targetNode: BTreeNode,
-                             fromNode: BTreeNode, atPosition position: BTreeNodePosition) {
+  /**
+   *  Moves the key at the specified `index` from `node` to
+   *  the `targetNode` at `position`
+   *  
+   *  - Parameters:
+   *    - index: the index of the key to be moved in `node`
+   *    - targetNode: the node to move the key into
+   *    - node: the node to move the key from
+   *    - position: the position of the from node relative to the targetNode
+   */
+  fileprivate func move(keyAt index: Int, to targetNode: BTreeNode,
+                                  from node: BTreeNode, at position: BTreeNodePosition) {
     switch position {
-    case .Left:
-      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.startIndex)
-      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.startIndex)
-      keys[keyIndex] = fromNode.keys.last!
-      values[keyIndex] = fromNode.values.last!
-      fromNode.keys.removeLast()
-      fromNode.values.removeLast()
+    case .left:
+      targetNode.keys.insert(keys[index], at: targetNode.keys.startIndex)
+      targetNode.values.insert(values[index], at: targetNode.values.startIndex)
+      keys[index] = node.keys.last!
+      values[index] = node.values.last!
+      node.keys.removeLast()
+      node.values.removeLast()
       if !targetNode.isLeaf {
-        targetNode.children!.insert(fromNode.children!.last!,
-                                    atIndex: targetNode.children!.startIndex)
-        fromNode.children!.removeLast()
+        targetNode.children!.insert(node.children!.last!,
+                                    at: targetNode.children!.startIndex)
+        node.children!.removeLast()
       }
       
-    case .Right:
-      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.endIndex)
-      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.endIndex)
-      keys[keyIndex] = fromNode.keys.first!
-      values[keyIndex] = fromNode.values.first!
-      fromNode.keys.removeFirst()
-      fromNode.values.removeFirst()
+    case .right:
+      targetNode.keys.insert(keys[index], at: targetNode.keys.endIndex)
+      targetNode.values.insert(values[index], at: targetNode.values.endIndex)
+      keys[index] = node.keys.first!
+      values[index] = node.values.first!
+      node.keys.removeFirst()
+      node.values.removeFirst()
       if !targetNode.isLeaf {
-        targetNode.children!.insert(fromNode.children!.first!,
-                                    atIndex: targetNode.children!.endIndex)
-        fromNode.children!.removeFirst()
+        targetNode.children!.insert(node.children!.first!,
+                                    at: targetNode.children!.endIndex)
+        node.children!.removeFirst()
       }
     }
   }
   
-  private func mergeChild(child: BTreeNode, withIndex index: Int, toNodeAtPosition position: BTreeNodePosition) {
+  /**
+   *  Merges `child` at `position` to the node at the `position`.
+   *  
+   *  - Parameters:
+   *    - child: the child to be merged
+   *    - index: the index of the child in the current node
+   *    - position: the position of the node to merge into
+   */
+  fileprivate func merge(_ child: BTreeNode, at index: Int, to position: BTreeNodePosition) {
     switch position {
-    case .Left:
+    case .left:
       // We can merge to the left sibling
       
-      children![index.predecessor()].keys = children![index.predecessor()].keys +
-        [keys[index.predecessor()]] + child.keys
+      children![(index - 1)].keys = children![(index - 1)].keys +
+        [keys[(index - 1)]] + child.keys
       
-      children![index.predecessor()].values = children![index.predecessor()].values +
-        [values[index.predecessor()]] + child.values
+      children![(index - 1)].values = children![(index - 1)].values +
+        [values[(index - 1)]] + child.values
       
-      keys.removeAtIndex(index.predecessor())
-      values.removeAtIndex(index.predecessor())
+      keys.remove(at: (index - 1))
+      values.remove(at: (index - 1))
       
       if !child.isLeaf {
-        children![index.predecessor()].children =
-          children![index.predecessor()].children! + child.children!
+        children![(index - 1)].children =
+          children![(index - 1)].children! + child.children!
       }
       
-    case .Right:
+    case .right:
       // We should merge to the right sibling
       
-      children![index.successor()].keys = child.keys + [keys[index]] +
-        children![index.successor()].keys
+      children![(index + 1)].keys = child.keys + [keys[index]] +
+        children![(index + 1)].keys
       
-      children![index.successor()].values = child.values + [values[index]] +
-        children![index.successor()].values
+      children![(index + 1)].values = child.values + [values[index]] +
+        children![(index + 1)].values
       
-      keys.removeAtIndex(index)
-      values.removeAtIndex(index)
+      keys.remove(at: index)
+      values.remove(at: index)
       
       if !child.isLeaf {
-        children![index.successor()].children =
-          child.children! + children![index.successor()].children!
+        children![(index + 1)].children =
+          child.children! + children![(index + 1)].children!
       }
     }
-    children!.removeAtIndex(index)
+    children!.remove(at: index)
   }
 }
 
 // MARK: BTreeNode extension: Conversion
 
 extension BTreeNode {
-  func inorderArrayFromKeys() -> [Key] {
+  /**
+   *  Returns an array which contains the keys from the current node
+   *  and its descendants in order.
+   */
+  var inorderArrayFromKeys: [Key] {
     var array = [Key] ()
     
     for i in 0..<numberOfKeys {
-      if let returnedArray = children?[i].inorderArrayFromKeys() {
+      if let returnedArray = children?[i].inorderArrayFromKeys {
         array += returnedArray
       }
       array += [keys[i]]
     }
     
-    if let returnedArray = children?.last?.inorderArrayFromKeys() {
+    if let returnedArray = children?.last?.inorderArrayFromKeys {
       array += returnedArray
     }
     
@@ -320,6 +389,9 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Description
 
 extension BTreeNode: CustomStringConvertible {
+  /**
+   *  Returns a String containing the preorder representation of the nodes.
+   */
   var description: String {
     var str = "\(keys)"
     
@@ -335,26 +407,27 @@ extension BTreeNode: CustomStringConvertible {
 
 // MARK: - BTree class
 
-public class BTree<Key: Comparable, Value> {
-  
+open class BTree<Key: Comparable, Value> {
   /**
-   The order of the B-Tree
-   
-   The number of keys in every node should be in the [order, 2*order] range,
-   except the root node which is allowed to contain less keys than the value of order.
+   *  The order of the B-Tree
+   *
+   *  The number of keys in every node should be in the [order, 2*order] range,
+   *  except the root node which is allowed to contain less keys than the value of order.
    */
-  public let order: Int
+  open let order: Int
   
-  /// The root node of the tree
+  /** 
+   *  The root node of the tree
+   */
   var rootNode: BTreeNode<Key, Value>!
   
-  private(set) public var numberOfKeys = 0
+  fileprivate(set) open var numberOfKeys = 0
   
   /**
-   Designated initializer for the tree
-   
-   - parameters:
-   - order: The order of the tree.
+   *  Designated initializer for the tree
+   *
+   *  - Parameters:
+   *    - order: The order of the tree.
    */
   public init?(order: Int) {
     guard order > 0 else {
@@ -362,14 +435,20 @@ public class BTree<Key: Comparable, Value> {
       return nil
     }
     self.order = order
-    rootNode = BTreeNode<Key, Value>(ownerTree: self)
+    rootNode = BTreeNode<Key, Value>(owner: self)
   }
 }
 
 // MARK: BTree extension: Travelsals
 
 extension BTree {
-  public func traverseKeysInOrder(@noescape process: Key -> Void) {
+  /**
+   *  Traverses the keys in order, executes `process` for every key.
+   *
+   *  - Parameters:
+   *    - process: the closure to be executed for every key
+   */
+  public func traverseKeysInOrder(_ process: (Key) -> Void) {
     rootNode.traverseKeysInOrder(process)
   }
 }
@@ -377,6 +456,12 @@ extension BTree {
 // MARK: BTree extension: Subscript
 
 extension BTree {
+  /**
+   *  Returns the value for a given `key`, returns nil if the `key` is not found.
+   *
+   *  - Parameters:
+   *    - key: the key of the value to be returned
+   */
   public subscript (key: Key) -> Value? {
     return valueForKey(key)
   }
@@ -385,52 +470,71 @@ extension BTree {
 // MARK: BTree extension: Value for Key
 
 extension BTree {
-  public func valueForKey(key: Key) -> Value? {
+  /**
+   *  Returns the value for a given `key`, returns nil if the `key` is not found.
+   *
+   *  - Parameters:
+   *    - key: the key of the value to be returned
+   */
+  public func valueForKey(_ key: Key) -> Value? {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
     
-    return rootNode.valueForKey(key)
+    return rootNode.value(for: key)
   }
 }
 
 // MARK: BTree extension: Insertion
 
 extension BTree {
-  public func insertValue(value: Value, forKey key: Key) {
-    rootNode.insertValue(value, forKey: key)
+  /**
+   *  Inserts the `value` for the `key` into the tree.
+   *
+   *  - Parameters:
+   *    - value: the value to be inserted for `key`
+   *    - key: the key for the `value`
+   */
+  public func insert(_ value: Value, for key: Key) {
+    rootNode.insert(value, for: key)
     
     if rootNode.numberOfKeys > order * 2 {
       splitRoot()
     }
   }
   
-  private func splitRoot() {
+  /**
+   *  Splits the root node of the tree.
+   *  
+   *  - Precondition:
+   *    The root node of the tree contains `order` * 2 keys.
+   */
+  fileprivate func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
     
     let newRoot = BTreeNode<Key, Value>(
-      ownerTree: self,
+      owner: self,
       keys: [rootNode.keys[middleIndexOfOldRoot]],
       values: [rootNode.values[middleIndexOfOldRoot]],
       children: [rootNode]
     )
-    rootNode.keys.removeAtIndex(middleIndexOfOldRoot)
-    rootNode.values.removeAtIndex(middleIndexOfOldRoot)
+    rootNode.keys.remove(at: middleIndexOfOldRoot)
+    rootNode.values.remove(at: middleIndexOfOldRoot)
     
     let newRightChild = BTreeNode<Key, Value>(
-      ownerTree: self,
-      keys: Array(rootNode.keys[middleIndexOfOldRoot..<rootNode.keys.endIndex]),
-      values: Array(rootNode.values[middleIndexOfOldRoot..<rootNode.values.endIndex])
+      owner: self,
+      keys: Array(rootNode.keys[rootNode.keys.indices.suffix(from: middleIndexOfOldRoot)]),
+      values: Array(rootNode.values[rootNode.values.indices.suffix(from: middleIndexOfOldRoot)])
     )
-    rootNode.keys.removeRange(middleIndexOfOldRoot..<rootNode.keys.endIndex)
-    rootNode.values.removeRange(middleIndexOfOldRoot..<rootNode.values.endIndex)
+    rootNode.keys.removeSubrange(rootNode.keys.indices.suffix(from: middleIndexOfOldRoot))
+    rootNode.values.removeSubrange(rootNode.values.indices.suffix(from: middleIndexOfOldRoot))
     
     if rootNode.children != nil {
       newRightChild.children = Array(
-        rootNode.children![middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex]
+        rootNode.children![rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))]
       )
-      rootNode.children!.removeRange(
-        middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex
+      rootNode.children!.removeSubrange(
+        rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))
       )
     }
     
@@ -442,12 +546,18 @@ extension BTree {
 // MARK: BTree extension: Removal
 
 extension BTree {
-  public func removeKey(key: Key) {
+  /**
+   *  Removes `key` and the value associated with it from the tree.
+   *  
+   *  - Parameters:
+   *    - key: the key to remove
+   */
+  public func removeKey(_ key: Key) {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
     
-    rootNode.removeKey(key)
+    rootNode.remove(key)
     
     if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
       rootNode = rootNode.children!.first!
@@ -458,15 +568,20 @@ extension BTree {
 // MARK: BTree extension: Conversion
 
 extension BTree {
-  public func inorderArrayFromKeys() -> [Key] {
-    return rootNode.inorderArrayFromKeys()
+  /**
+   *  The keys of the tree in order.
+   */
+  public var inorderArrayFromKeys: [Key] {
+    return rootNode.inorderArrayFromKeys
   }
 }
 
 // MARK: BTree extension: Decription
 
 extension BTree: CustomStringConvertible {
-  // Returns a String containing the preorder representation of the nodes
+  /** 
+   *  Returns a String containing the preorder representation of the nodes.
+   */
   public var description: String {
     return rootNode.description
   }
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
index 0780f04c8..79552bbe5 100644
--- a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
+++ b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,11 +85,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0730;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Viktor Szilárd Simkó";
 				TargetAttributes = {
 					C66702771D0EEE25008CD769 = {
 						CreatedOnToolsVersion = 7.3.1;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -148,8 +149,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -226,6 +232,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -238,6 +245,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index d9200547d..9d6c542ae 100644
--- a/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index 07457d937..da6ebe9f6 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -10,7 +10,7 @@ import XCTest
 
 class BTreeNodeTests: XCTestCase {
   
-  let ownerTree = BTree<Int, Int>(order: 2)!
+  let owner = BTree<Int, Int>(order: 2)!
   var root: BTreeNode<Int, Int>!
   var leftChild: BTreeNode<Int, Int>!
   var rightChild: BTreeNode<Int, Int>!
@@ -18,11 +18,11 @@ class BTreeNodeTests: XCTestCase {
   override func setUp() {
     super.setUp()
     
-    root = BTreeNode(ownerTree: ownerTree)
-    leftChild = BTreeNode(ownerTree: ownerTree)
-    rightChild = BTreeNode(ownerTree: ownerTree)
+    root = BTreeNode(owner: owner)
+    leftChild = BTreeNode(owner: owner)
+    rightChild = BTreeNode(owner: owner)
     
-    root.insertValue(1, forKey: 1)
+    root.insert(1, for: 1)
     root.children = [leftChild, rightChild]
   }
   
@@ -36,9 +36,9 @@ class BTreeNodeTests: XCTestCase {
   }
   
   func testOwner() {
-    XCTAssert(root.ownerTree === ownerTree)
-    XCTAssert(leftChild.ownerTree === ownerTree)
-    XCTAssert(rightChild.ownerTree === ownerTree)
+    XCTAssert(root.owner === owner)
+    XCTAssert(leftChild.owner === owner)
+    XCTAssert(rightChild.owner === owner)
   }
   
   func testNumberOfKeys() {
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index 947781478..231a423e2 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -45,7 +45,7 @@ class BTreeTests: XCTestCase {
   }
   
   func testInsertToEmptyTree() {
-    bTree.insertValue(1, forKey: 1)
+    bTree.insert(1, for: 1)
     
     XCTAssertEqual(bTree[1]!, 1)
   }
@@ -56,7 +56,7 @@ class BTreeTests: XCTestCase {
   }
   
   func testInorderArrayFromEmptyTree() {
-    XCTAssertEqual(bTree.inorderArrayFromKeys(), [Int]())
+    XCTAssertEqual(bTree.inorderArrayFromKeys, [Int]())
   }
   
   func testDescriptionOfEmptyTree() {
@@ -67,7 +67,7 @@ class BTreeTests: XCTestCase {
   
   func testInorderTravelsal() {
     for i in 1...20 {
-      bTree.insertValue(i, forKey: i)
+      bTree.insert(i, for: i)
     }
     
     var j = 1
@@ -82,7 +82,7 @@ class BTreeTests: XCTestCase {
   
   func testSearchForMaximum() {
     for i in 1...20 {
-      bTree.insertValue(i, forKey: i)
+      bTree.insert(i, for: i)
     }
     
     XCTAssertEqual(bTree.valueForKey(20)!, 20)
@@ -90,7 +90,7 @@ class BTreeTests: XCTestCase {
   
   func testSearchForMinimum() {
     for i in 1...20 {
-      bTree.insertValue(i, forKey: i)
+      bTree.insert(i, for: i)
     }
     
     XCTAssertEqual(bTree.valueForKey(1)!, 1)
@@ -118,7 +118,7 @@ class BTreeTests: XCTestCase {
   
   func testRemoveMaximum() {
     for i in 1...20 {
-      bTree.insertValue(i, forKey: i)
+      bTree.insert(i, for: i)
     }
     
     bTree.removeKey(20)
@@ -184,7 +184,7 @@ class BTreeTests: XCTestCase {
     
     XCTAssertEqual(bTree.numberOfKeys, 20)
     
-    for i in (1...20).reverse() {
+    for i in (1...20).reversed() {
       bTree.removeKey(i)
     }
     
@@ -202,24 +202,24 @@ class BTreeTests: XCTestCase {
 	func testInorderArray() {
     bTree.insertKeysUpTo(20)
 		
-		let returnedArray = bTree.inorderArrayFromKeys()
+		let returnedArray = bTree.inorderArrayFromKeys
 		let targetArray = Array<Int>(1...20)
 		
 		XCTAssertEqual(returnedArray, targetArray)
 	}
 }
 
-enum BTreeError: ErrorType {
-  case TooManyNodes
-  case TooFewNodes
+enum BTreeError: Error {
+  case tooManyNodes
+  case tooFewNodes
 }
 
 extension BTreeNode {
   func checkBalanced(isRoot root: Bool) throws {
-    if numberOfKeys > ownerTree.order * 2 {
-      throw BTreeError.TooManyNodes
-    } else if !root && numberOfKeys < ownerTree.order {
-      throw BTreeError.TooFewNodes
+    if numberOfKeys > owner.order * 2 {
+      throw BTreeError.tooManyNodes
+    } else if !root && numberOfKeys < owner.order {
+      throw BTreeError.tooFewNodes
     }
     
     if !isLeaf {
@@ -230,13 +230,13 @@ extension BTreeNode {
   }
 }
 
-extension BTree where Key: SignedIntegerType, Value: SignedIntegerType {
-  func insertKeysUpTo(to: Int) {
+extension BTree where Key: SignedInteger, Value: SignedInteger {
+  func insertKeysUpTo(_ to: Int) {
     var k: Key = 1
     var v: Value = 1
     
     for _ in 1...to {
-      insertValue(v, forKey: k)
+      insert(v, for: k)
       k = k + 1
       v = v + 1
     }

From 9b3458e6fb974d2e1c02a4df6790a54e7c435975 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Simk=C3=B3?= <aqviktor@gmail.com>
Date: Thu, 1 Sep 2016 10:56:05 +0200
Subject: [PATCH 0492/1679] updated .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 8cf0b486b..edfe5e624 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -17,7 +17,7 @@ script:
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests

From 7f71ac77f17565f94444843d0c854c345aaa5298 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Simk=C3=B3?= <aqviktor@gmail.com>
Date: Thu, 1 Sep 2016 12:16:42 +0200
Subject: [PATCH 0493/1679] corrected method naming

---
 B-Tree/BTree.swift                  | 45 +++++++++++++++--------------
 B-Tree/Tests/Tests/BTreeTests.swift | 22 +++++++-------
 2 files changed, 35 insertions(+), 32 deletions(-)

diff --git a/B-Tree/BTree.swift b/B-Tree/BTree.swift
index f5638ea4e..e6494af0a 100644
--- a/B-Tree/BTree.swift
+++ b/B-Tree/BTree.swift
@@ -29,10 +29,13 @@
 // MARK: - BTreeNode class
 
 class BTreeNode<Key: Comparable, Value> {
+  /**
+   * The tree that owns the node.
+   */
   unowned var owner: BTree<Key, Value>
   
   fileprivate var keys = [Key]()
-  var values = [Value]()
+  fileprivate var values = [Value]()
   var children: [BTreeNode]?
   
   var isLeaf: Bool {
@@ -147,7 +150,7 @@ extension BTreeNode {
    *    - child: the child to be split
    *    - index: the index of the key, which will be moved up to the parent
    */
-  fileprivate func split(_ child: BTreeNode, at index: Int) {
+  private func split(_ child: BTreeNode, at index: Int) {
     let middleIndex = child.numberOfKeys / 2
     keys.insert(child.keys[middleIndex], at: index)
     values.insert(child.values[middleIndex], at: index)
@@ -188,7 +191,7 @@ private enum BTreeNodePosition {
 }
 
 extension BTreeNode {
-  fileprivate var inorderPredecessor: BTreeNode {
+  private var inorderPredecessor: BTreeNode {
     if isLeaf {
       return self
     } else {
@@ -221,7 +224,7 @@ extension BTreeNode {
         values[index] = predecessor.values.last!
         children![index].remove(keys[index])
         if children![index].numberOfKeys < owner.order {
-          fix(children![index], at: index)
+          fix(child: children![index], at: index)
         }
       }
     } else if key < keys[index] {
@@ -230,7 +233,7 @@ extension BTreeNode {
       if let leftChild = children?[index] {
         leftChild.remove(key)
         if leftChild.numberOfKeys < owner.order {
-          fix(leftChild, at: index)
+          fix(child: leftChild, at: index)
         }
       } else {
         print("The key:\(key) is not in the tree.")
@@ -241,7 +244,7 @@ extension BTreeNode {
       if let rightChild = children?[(index + 1)] {
         rightChild.remove(key)
         if rightChild.numberOfKeys < owner.order {
-          fix(rightChild, at: (index + 1))
+          fix(child: rightChild, at: (index + 1))
         }
       } else {
         print("The key:\(key) is not in the tree")
@@ -259,16 +262,16 @@ extension BTreeNode {
    *    - child: the child to be fixed
    *    - index: the index of the child to be fixed in the current node
    */
-  fileprivate func fix(_ child: BTreeNode, at index: Int) {
+  private func fix(child: BTreeNode, at index: Int) {
     
     if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
-      move(keyAt: (index - 1), to: child, from: children![(index - 1)], at: .left)
+      move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
     } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
-      move(keyAt: index, to: child, from: children![(index + 1)], at: .right)
+      move(keyAtIndex: index, to: child, from: children![(index + 1)], at: .right)
     } else if (index - 1) >= 0 {
-      merge(child, at: index, to: .left)
+      merge(child: child, atIndex: index, to: .left)
     } else {
-      merge(child, at: index, to: .right)
+      merge(child: child, atIndex: index, to: .right)
     }
   }
   
@@ -282,7 +285,7 @@ extension BTreeNode {
    *    - node: the node to move the key from
    *    - position: the position of the from node relative to the targetNode
    */
-  fileprivate func move(keyAt index: Int, to targetNode: BTreeNode,
+  private func move(keyAtIndex index: Int, to targetNode: BTreeNode,
                                   from node: BTreeNode, at position: BTreeNodePosition) {
     switch position {
     case .left:
@@ -321,7 +324,7 @@ extension BTreeNode {
    *    - index: the index of the child in the current node
    *    - position: the position of the node to merge into
    */
-  fileprivate func merge(_ child: BTreeNode, at index: Int, to position: BTreeNodePosition) {
+  private func merge(child: BTreeNode, atIndex index: Int, to position: BTreeNodePosition) {
     switch position {
     case .left:
       // We can merge to the left sibling
@@ -407,21 +410,21 @@ extension BTreeNode: CustomStringConvertible {
 
 // MARK: - BTree class
 
-open class BTree<Key: Comparable, Value> {
+public class BTree<Key: Comparable, Value> {
   /**
    *  The order of the B-Tree
    *
    *  The number of keys in every node should be in the [order, 2*order] range,
    *  except the root node which is allowed to contain less keys than the value of order.
    */
-  open let order: Int
+  public let order: Int
   
-  /** 
+  /**
    *  The root node of the tree
    */
   var rootNode: BTreeNode<Key, Value>!
   
-  fileprivate(set) open var numberOfKeys = 0
+  fileprivate(set) public var numberOfKeys = 0
   
   /**
    *  Designated initializer for the tree
@@ -463,7 +466,7 @@ extension BTree {
    *    - key: the key of the value to be returned
    */
   public subscript (key: Key) -> Value? {
-    return valueForKey(key)
+    return value(for: key)
   }
 }
 
@@ -476,7 +479,7 @@ extension BTree {
    *  - Parameters:
    *    - key: the key of the value to be returned
    */
-  public func valueForKey(_ key: Key) -> Value? {
+  public func value(for key: Key) -> Value? {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
@@ -509,7 +512,7 @@ extension BTree {
    *  - Precondition:
    *    The root node of the tree contains `order` * 2 keys.
    */
-  fileprivate func splitRoot() {
+  private func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
     
     let newRoot = BTreeNode<Key, Value>(
@@ -552,7 +555,7 @@ extension BTree {
    *  - Parameters:
    *    - key: the key to remove
    */
-  public func removeKey(_ key: Key) {
+  public func remove(_ key: Key) {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index 231a423e2..f81016ae7 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -41,7 +41,7 @@ class BTreeTests: XCTestCase {
   }
   
   func testSearchEmptyTree() {
-    XCTAssertEqual(bTree.valueForKey(1), nil)
+    XCTAssertEqual(bTree.value(for: 1), nil)
   }
   
   func testInsertToEmptyTree() {
@@ -51,7 +51,7 @@ class BTreeTests: XCTestCase {
   }
   
   func testRemoveFromEmptyTree() {
-    bTree.removeKey(1)
+    bTree.remove(1)
     XCTAssertEqual(bTree.description, "[]")
   }
   
@@ -85,7 +85,7 @@ class BTreeTests: XCTestCase {
       bTree.insert(i, for: i)
     }
     
-    XCTAssertEqual(bTree.valueForKey(20)!, 20)
+    XCTAssertEqual(bTree.value(for: 20)!, 20)
   }
   
   func testSearchForMinimum() {
@@ -93,7 +93,7 @@ class BTreeTests: XCTestCase {
       bTree.insert(i, for: i)
     }
     
-    XCTAssertEqual(bTree.valueForKey(1)!, 1)
+    XCTAssertEqual(bTree.value(for: 1)!, 1)
   }
   
   // MARK: - Insertion
@@ -121,7 +121,7 @@ class BTreeTests: XCTestCase {
       bTree.insert(i, for: i)
     }
     
-    bTree.removeKey(20)
+    bTree.remove(20)
     
     XCTAssertNil(bTree[20])
     
@@ -135,7 +135,7 @@ class BTreeTests: XCTestCase {
   func testRemoveMinimum() {
     bTree.insertKeysUpTo(20)
     
-    bTree.removeKey(1)
+    bTree.remove(1)
     
     XCTAssertNil(bTree[1])
     
@@ -149,8 +149,8 @@ class BTreeTests: XCTestCase {
   func testRemoveSome() {
     bTree.insertKeysUpTo(20)
     
-    bTree.removeKey(6)
-    bTree.removeKey(9)
+    bTree.remove(6)
+    bTree.remove(9)
     
     XCTAssertNil(bTree[6])
     XCTAssertNil(bTree[9])
@@ -166,8 +166,8 @@ class BTreeTests: XCTestCase {
     bTree = BTree<Int, Int>(order: 2)!
     bTree.insertKeysUpTo(20)
     
-    bTree.removeKey(6)
-    bTree.removeKey(9)
+    bTree.remove(6)
+    bTree.remove(9)
     
     XCTAssertNil(bTree[6])
     XCTAssertNil(bTree[9])
@@ -185,7 +185,7 @@ class BTreeTests: XCTestCase {
     XCTAssertEqual(bTree.numberOfKeys, 20)
     
     for i in (1...20).reversed() {
-      bTree.removeKey(i)
+      bTree.remove(i)
     }
     
     do {

From 26b9b64d66b693ee83346c470aefc9f68ae94bb6 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Thu, 1 Sep 2016 17:05:20 +0200
Subject: [PATCH 0494/1679] Update README.md

---
 Skip-List/README.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index ca1dce7ae..1722e1fe6 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -1,3 +1,8 @@
 # Skip List
 
-> Skip lists are a probabilistic data structure that seem likely to supplant balanced trees as the implementation method of choice for many applications. Skip list algorithms have the same asymptotic expected time bounds as balanced trees and are simpler, faster and use less space.  -**[William Pugh](https://en.wikipedia.org/wiki/William_Pugh)**
+Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. Fast searching is possible by building a hierarchy of sorted linked-lists acting as an express lane to the layer underneath. Layers are created on top of the base layer ( regular sorted linked-list ) probablisticly by coin-flipping.
+
+A layer consists of a Head node, holding reference to the next and the node below. Each node has also same references similar to the Head node.
+
+#TODO
+ - finish readme

From 568ae3cded5c0530d50926136f916ec6b499c4ce Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Thu, 1 Sep 2016 17:05:56 +0200
Subject: [PATCH 0495/1679] Images folder

---
 Skip-List/Images/base | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Skip-List/Images/base

diff --git a/Skip-List/Images/base b/Skip-List/Images/base
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/Skip-List/Images/base
@@ -0,0 +1 @@
+

From afec24cba04b3d084f463c3f5185c7b4af5fee6a Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Thu, 1 Sep 2016 17:06:06 +0200
Subject: [PATCH 0496/1679] Delete base

---
 Skip-List/Images/base | 1 -
 1 file changed, 1 deletion(-)
 delete mode 100644 Skip-List/Images/base

diff --git a/Skip-List/Images/base b/Skip-List/Images/base
deleted file mode 100644
index 8b1378917..000000000
--- a/Skip-List/Images/base
+++ /dev/null
@@ -1 +0,0 @@
-

From 6db2dd7758a6f0bcadab6be316489887a7814b79 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Szil=C3=A1rd=20Simk=C3=B3?= <aqviktor@gmail.com>
Date: Thu, 1 Sep 2016 19:28:19 +0200
Subject: [PATCH 0497/1679] updated README.md

---
 B-Tree/README.md | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/B-Tree/README.md b/B-Tree/README.md
index 28b617ca1..493fdedfb 100644
--- a/B-Tree/README.md
+++ b/B-Tree/README.md
@@ -20,9 +20,9 @@ A second order B-Tree with keys from 1 to 20 looks like this:
 
 ```swift
 class BTreeNode<Key: Comparable, Value> {
-  unowned var ownerTree: BTree<Key, Value>
+  unowned var owner: BTree<Key, Value>
   
-  private var keys = [Key]()
+  fileprivate var keys = [Key]()
   var children: [BTreeNode]?
   
   ...
@@ -55,7 +55,7 @@ This is necessary because nodes have to know the order of the tree.
 
 ### The code
 
-`valueForKey(_:)` method searches for the given key and if it's in the tree,  
+`value(for:)` method searches for the given key and if it's in the tree,  
 it returns the value associated with it, else it returns `nil`.
 
 ## Insertion
@@ -72,7 +72,7 @@ Keys can only be inserted to leaf nodes.
 After insertion we should check if the number of keys in the node is in the correct range.  
 If there are more keys in the node than `order*2`, we need to split the node.
 
-####Splitting a node
+#### Splitting a node
 
 1. Move up the middle key of the node we want to split, to its parent (if it has one).  
 2. If it hasn't got a parent(it is the root), then create a new root and insert to it.  
@@ -90,9 +90,9 @@ An insertion to a first order tree looks like this:
 
 ### The code
 
-The method `insertValue(_:forKey:)` does the insertion.
+The method `insert(_:for:)` does the insertion.
 After it has inserted a key, as the recursion goes up every node checks the number of keys in its child.  
-if a node has too many keys, its parent calls the `splitChild(_:atIndex:)` method on it.
+if a node has too many keys, its parent calls the `split(child:atIndex:)` method on it.
 
 The root node is checked by the tree itself.  
 If the root has too many nodes after the insertion the tree calls the `splitRoot()` method.
@@ -112,7 +112,7 @@ After a key have been removed from a node we should check that the node has enou
 If a node has fewer keys than the order of the tree, then we should move a key to it,  
 or merge it with one of its siblings.
 
-####Moving a key to the child
+#### Moving a key to the child
 
 If the problematic node has a nearest sibling that has more keys than the order of the tree,  
 we should perform this operation on the tree, else we should merge the node with one of its siblings.
@@ -156,13 +156,13 @@ so in the worst case merging also can go up to the root, in which case the heigh
 
 ### The code
 
-- `removeKey(_:)` method removes the given key from the tree. After a key has been deleted,  
+- `remove(_:)` method removes the given key from the tree. After a key has been deleted,  
   every node checks the number of keys in its child. If a child has less nodes than the order of the tree,
-  it calls the `fixChildWithLessNodesThanOrder(_:atIndex:)` method.  
+  it calls the `fix(childWithTooFewKeys:atIndex:)` method.  
 
-- `fixChildWithLessNodesThanOrder(_:atIndex:)` method decides which way to fix the child (by moving a key to it,
-  or by merging it), then calls `moveKeyAtIndex(keyIndex:toNode:fromNode:atPosition:)` or 
-  `mergeChild(_:withIndex:toNodeAtPosition:)` method according to its choice.
+- `fix(childWithTooFewKeys:atIndex:)` method decides which way to fix the child (by moving a key to it,
+  or by merging it), then calls `move(keyAtIndex:to:from:at:)` or 
+  `merge(child:atIndex:to:)` method according to its choice.
 
 ## See also
 

From 3bc80955f527274fc3ab4a9f4dedf71198b77e54 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Simk=C3=B3?= <aqviktor@gmail.com>
Date: Thu, 1 Sep 2016 19:31:15 +0200
Subject: [PATCH 0498/1679] corrected comments, tweaked method naming

---
 B-Tree/BTree.swift                  | 21 +++++++++++----------
 B-Tree/Tests/Tests/BTreeTests.swift | 20 ++++++++++----------
 2 files changed, 21 insertions(+), 20 deletions(-)

diff --git a/B-Tree/BTree.swift b/B-Tree/BTree.swift
index e6494af0a..52cda4e43 100644
--- a/B-Tree/BTree.swift
+++ b/B-Tree/BTree.swift
@@ -136,7 +136,7 @@ extension BTreeNode {
     } else {
       children![index].insert(value, for: key)
       if children![index].numberOfKeys > owner.order * 2 {
-        split(children![index], at: index)
+        split(child: children![index], atIndex: index)
       }
     }
   }
@@ -150,7 +150,7 @@ extension BTreeNode {
    *    - child: the child to be split
    *    - index: the index of the key, which will be moved up to the parent
    */
-  private func split(_ child: BTreeNode, at index: Int) {
+  private func split(child: BTreeNode, atIndex index: Int) {
     let middleIndex = child.numberOfKeys / 2
     keys.insert(child.keys[middleIndex], at: index)
     values.insert(child.values[middleIndex], at: index)
@@ -224,7 +224,7 @@ extension BTreeNode {
         values[index] = predecessor.values.last!
         children![index].remove(keys[index])
         if children![index].numberOfKeys < owner.order {
-          fix(child: children![index], at: index)
+          fix(childWithTooFewKeys: children![index], atIndex: index)
         }
       }
     } else if key < keys[index] {
@@ -233,7 +233,7 @@ extension BTreeNode {
       if let leftChild = children?[index] {
         leftChild.remove(key)
         if leftChild.numberOfKeys < owner.order {
-          fix(child: leftChild, at: index)
+          fix(childWithTooFewKeys: leftChild, atIndex: index)
         }
       } else {
         print("The key:\(key) is not in the tree.")
@@ -244,7 +244,7 @@ extension BTreeNode {
       if let rightChild = children?[(index + 1)] {
         rightChild.remove(key)
         if rightChild.numberOfKeys < owner.order {
-          fix(child: rightChild, at: (index + 1))
+          fix(childWithTooFewKeys: rightChild, atIndex: (index + 1))
         }
       } else {
         print("The key:\(key) is not in the tree")
@@ -253,16 +253,17 @@ extension BTreeNode {
   }
   
   /**
-   *  Fixes the `child` at `index`.
-   *  If `child` contains too many children then it moves a child to one of 
-   *  `child`'s neighbouring nodes.
-   *  If `child` contains too few children then it merges it with one of its neighbours.
+   *  Fixes `childWithTooFewKeys` by either moving a key to it from 
+   *  one of its neighbouring nodes, or by merging.
+   *
+   *  - Precondition:
+   *    `childWithTooFewKeys` must have less keys than the order of the tree.
    *
    *  - Parameters:
    *    - child: the child to be fixed
    *    - index: the index of the child to be fixed in the current node
    */
-  private func fix(child: BTreeNode, at index: Int) {
+  private func fix(childWithTooFewKeys child: BTreeNode, atIndex index: Int) {
     
     if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
       move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index f81016ae7..c8db17fa3 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -108,7 +108,7 @@ class BTreeTests: XCTestCase {
     }
     
     do {
-      try bTree.checkBalanced()
+      try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
@@ -126,7 +126,7 @@ class BTreeTests: XCTestCase {
     XCTAssertNil(bTree[20])
     
     do {
-      try bTree.checkBalanced()
+      try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
@@ -140,7 +140,7 @@ class BTreeTests: XCTestCase {
     XCTAssertNil(bTree[1])
     
     do {
-      try bTree.checkBalanced()
+      try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
@@ -156,7 +156,7 @@ class BTreeTests: XCTestCase {
     XCTAssertNil(bTree[9])
     
     do {
-      try bTree.checkBalanced()
+      try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
@@ -173,7 +173,7 @@ class BTreeTests: XCTestCase {
     XCTAssertNil(bTree[9])
     
     do {
-      try bTree.checkBalanced()
+      try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
@@ -189,7 +189,7 @@ class BTreeTests: XCTestCase {
     }
     
     do {
-      try bTree.checkBalanced()
+      try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
@@ -215,7 +215,7 @@ enum BTreeError: Error {
 }
 
 extension BTreeNode {
-  func checkBalanced(isRoot root: Bool) throws {
+  func checkBalance(isRoot root: Bool) throws {
     if numberOfKeys > owner.order * 2 {
       throw BTreeError.tooManyNodes
     } else if !root && numberOfKeys < owner.order {
@@ -224,7 +224,7 @@ extension BTreeNode {
     
     if !isLeaf {
       for child in children! {
-        try child.checkBalanced(isRoot: false)
+        try child.checkBalance(isRoot: false)
       }
     }
   }
@@ -242,7 +242,7 @@ extension BTree where Key: SignedInteger, Value: SignedInteger {
     }
   }
   
-  func checkBalanced() throws {
-    try rootNode.checkBalanced(isRoot: true)
+  func checkBalance() throws {
+    try rootNode.checkBalance(isRoot: true)
   }
 }

From 25a82a8b9769805fc413a592441726c326a14258 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Fri, 2 Sep 2016 09:20:39 +0200
Subject: [PATCH 0499/1679] Update README.md

---
 Skip-List/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 1722e1fe6..fc98a4768 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -2,7 +2,7 @@
 
 Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. Fast searching is possible by building a hierarchy of sorted linked-lists acting as an express lane to the layer underneath. Layers are created on top of the base layer ( regular sorted linked-list ) probablisticly by coin-flipping.
 
-A layer consists of a Head node, holding reference to the next and the node below. Each node has also same references similar to the Head node.
+A layer consists of a Head node, holding reference to the next and the node below. Each node also holds references similar to the Head node.
 
 #TODO
  - finish readme

From c20c4dec42a0281d930fb800134ba48c4bb0d33a Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Fri, 2 Sep 2016 09:41:01 +0200
Subject: [PATCH 0500/1679] Update README.md

---
 Skip-List/README.md | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index fc98a4768..7c6ca754f 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -1,8 +1,6 @@
 # Skip List
 
-Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. Fast searching is possible by building a hierarchy of sorted linked-lists acting as an express lane to the layer underneath. Layers are created on top of the base layer ( regular sorted linked-list ) probablisticly by coin-flipping.
-
-A layer consists of a Head node, holding reference to the next and the node below. Each node also holds references similar to the Head node.
+Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. The building blocks are hierarchy of layers (regular sorted linked-lists), created probablisticly by coin flipping, each acting as an express lane to the layer underneath, therefore making fast O(log n) search possible by skipping lanes. A layer consists of a Head node, holding reference to the subsequent and the node below. Each node also holds similar references as the Head node.
 
 #TODO
  - finish readme

From e1ab353a76d48e18915013edfa8d3303996254ce Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Fri, 2 Sep 2016 09:43:08 +0200
Subject: [PATCH 0501/1679] Add schematic image

---
 Skip-List/Intro.png | Bin 0 -> 21910 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Skip-List/Intro.png

diff --git a/Skip-List/Intro.png b/Skip-List/Intro.png
new file mode 100644
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From 587aa152ff1d0f8c477a2ad9a5547b1cec756b90 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Fri, 2 Sep 2016 09:44:37 +0200
Subject: [PATCH 0502/1679] Add schematic image

---
 Skip-List/Intro.png | Bin 21910 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Skip-List/Intro.png

diff --git a/Skip-List/Intro.png b/Skip-List/Intro.png
deleted file mode 100644
index 0bb64865d5d93747e5d2700376b2969b21f8aa9e..0000000000000000000000000000000000000000
GIT binary patch
literal 0
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From 5a0c71e2be157476105e9c833c9f2e719c64a30c Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Fri, 2 Sep 2016 09:45:13 +0200
Subject: [PATCH 0503/1679] Add schematic image

---
 Skip-List/Images/Intro.png | Bin 0 -> 21910 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Skip-List/Images/Intro.png

diff --git a/Skip-List/Images/Intro.png b/Skip-List/Images/Intro.png
new file mode 100644
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HcmV?d00001


From 78048a69052819b0affc90ebc5e1f5f34bc0e68e Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Fri, 2 Sep 2016 09:46:56 +0200
Subject: [PATCH 0504/1679] Update README.md

---
 Skip-List/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 7c6ca754f..5b2607b96 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -2,5 +2,7 @@
 
 Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. The building blocks are hierarchy of layers (regular sorted linked-lists), created probablisticly by coin flipping, each acting as an express lane to the layer underneath, therefore making fast O(log n) search possible by skipping lanes. A layer consists of a Head node, holding reference to the subsequent and the node below. Each node also holds similar references as the Head node.
 
+![Schematic view](Images/Intro.png
+)
 #TODO
  - finish readme

From 3f66f8413845b22653f91e1326a92ba0c01ea739 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Fri, 2 Sep 2016 17:32:02 +0200
Subject: [PATCH 0505/1679] Update README.md

---
 Skip-List/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 5b2607b96..f65609fb2 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -1,6 +1,6 @@
 # Skip List
 
-Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. The building blocks are hierarchy of layers (regular sorted linked-lists), created probablisticly by coin flipping, each acting as an express lane to the layer underneath, therefore making fast O(log n) search possible by skipping lanes. A layer consists of a Head node, holding reference to the subsequent and the node below. Each node also holds similar references as the Head node.
+Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. The building blocks are hierarchy of layers (regular sorted linked-lists), created probablisticly by coin flipping, each acting as an express lane to the layer underneath, therefore making fast O(log n) search possible by skipping lanes and reducing travel distance. A layer consists of a Head node, holding reference to the subsequent and the node below. Each node also holds similar references as the Head node.
 
 ![Schematic view](Images/Intro.png
 )

From 297f9c25e638d9c760c5756ac7a4f1a00ecdf259 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Fri, 2 Sep 2016 18:13:11 +0200
Subject: [PATCH 0506/1679] New Images

---
 Skip-List/Images/Insert1.png  | Bin 0 -> 8064 bytes
 Skip-List/Images/Insert10.png | Bin 0 -> 11662 bytes
 Skip-List/Images/Insert11.png | Bin 0 -> 11517 bytes
 Skip-List/Images/Insert12.png | Bin 0 -> 18755 bytes
 Skip-List/Images/Insert2.png  | Bin 0 -> 11545 bytes
 Skip-List/Images/Insert3.png  | Bin 0 -> 7420 bytes
 Skip-List/Images/Insert4.png  | Bin 0 -> 7550 bytes
 Skip-List/Images/Insert5.png  | Bin 0 -> 11124 bytes
 Skip-List/Images/Insert6.png  | Bin 0 -> 11045 bytes
 Skip-List/Images/Insert8.png  | Bin 0 -> 10902 bytes
 Skip-List/Images/Insert9.png  | Bin 0 -> 11692 bytes
 Skip-List/Images/Search1.png  | Bin 0 -> 18947 bytes
 Skip-List/Images/insert7.png  | Bin 0 -> 11052 bytes
 13 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Skip-List/Images/Insert1.png
 create mode 100644 Skip-List/Images/Insert10.png
 create mode 100644 Skip-List/Images/Insert11.png
 create mode 100644 Skip-List/Images/Insert12.png
 create mode 100644 Skip-List/Images/Insert2.png
 create mode 100644 Skip-List/Images/Insert3.png
 create mode 100644 Skip-List/Images/Insert4.png
 create mode 100644 Skip-List/Images/Insert5.png
 create mode 100644 Skip-List/Images/Insert6.png
 create mode 100644 Skip-List/Images/Insert8.png
 create mode 100644 Skip-List/Images/Insert9.png
 create mode 100644 Skip-List/Images/Search1.png
 create mode 100644 Skip-List/Images/insert7.png

diff --git a/Skip-List/Images/Insert1.png b/Skip-List/Images/Insert1.png
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HcmV?d00001


From 1a880aad0336b13a46c987bd15bdb6257c09d681 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Fri, 2 Sep 2016 18:38:55 +0200
Subject: [PATCH 0507/1679] Update README.md

---
 Skip-List/README.md | 40 ++++++++++++++++++++++++++++++++++++++--
 1 file changed, 38 insertions(+), 2 deletions(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index f65609fb2..64f221a23 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -4,5 +4,41 @@ Skip List is a probablistic data-structure with same efficiency as AVL tree or R
 
 ![Schematic view](Images/Intro.png
 )
-#TODO
- - finish readme
+
+
+#Inserting
+
+1. Inserting a new element in initial state where no prior layer is created yet begins by construction of a Head node with a reference to data node (just like regular lists). After this operation coin-flipping starts to determine wether a new layer must be created. When positive, a new layer containing Head and data node ( similar to previous layer ) is created and head is updated to reference the new layer and the head node underneath. Subsequently data node is also updated to reference the node below; until coin-flip function return a negative value to terminate this process.
+
+2. After initial state, we start at top most layer to find a node where its value is less than the new value and its next node value is greater-equal/nil than new value. Then we use this node to travel to layer underneath until we reach the layer 0 where the element must be inserted first, after this node. Node references must be updated accordingly by back tracing the path to the top. If the first element in the layer does not meet the criteria, same procedure is used to travel to the layer below using the head node.
+
+
+**Example**
+
+
+1 - Inserting 10 in initial state with coin flips (0)
+
+![Inserting first element](Images/Insert1.png)
+
+
+2 - 12 inserted with coin flips (1,1,0)
+
+
+3 - Inserting 13. with coin flips (0)
+
+![Inserting first element](Images/Insert5.png)
+![Inserting first element](Images/Insert6.png)
+![Inserting first element](Images/insert7.png)
+![Inserting first element](Images/Insert8.png)
+![Inserting first element](Images/Insert9.png)
+
+
+#Searching
+
+TODO
+
+#See also
+
+[Skip List on Wikipedia](https://en.wikipedia.org/wiki/Skip_list) 
+
+Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi)

From c8cfb08c8a6165a9c887d0c424de49ca66685ce4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Viktor=20Simk=C3=B3?= <aqviktor@gmail.com>
Date: Sat, 3 Sep 2016 16:20:47 +0200
Subject: [PATCH 0508/1679] updated playground

---
 B-Tree/BTree.playground/Contents.swift      |  14 +-
 B-Tree/BTree.playground/Sources/BTree.swift | 419 +++++++++++++-------
 2 files changed, 276 insertions(+), 157 deletions(-)

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index 186718bbd..8238fe5a5 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -4,15 +4,15 @@ import Foundation
 
 let bTree = BTree<Int, Int>(order: 1)!
 
-bTree.insertValue(1, forKey: 1)
-bTree.insertValue(2, forKey: 2)
-bTree.insertValue(3, forKey: 3)
-bTree.insertValue(4, forKey: 4)
+bTree.insert(1, for: 1)
+bTree.insert(2, for: 2)
+bTree.insert(3, for: 3)
+bTree.insert(4, for: 4)
 
-bTree.valueForKey(3)
+bTree.value(for: 3)
 bTree[3]
 
-bTree.removeKey(2)
+bTree.remove(2)
 
 bTree.traverseKeysInOrder {
   key in
@@ -23,4 +23,4 @@ bTree.numberOfKeys
 
 bTree.order
 
-bTree.inorderArrayFromKeys()
\ No newline at end of file
+bTree.inorderArrayFromKeys
diff --git a/B-Tree/BTree.playground/Sources/BTree.swift b/B-Tree/BTree.playground/Sources/BTree.swift
index 16c4eabe4..52cda4e43 100644
--- a/B-Tree/BTree.playground/Sources/BTree.swift
+++ b/B-Tree/BTree.playground/Sources/BTree.swift
@@ -21,18 +21,21 @@
 // SOFTWARE.
 
 /*
- B-Tree
-	
- A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
+ *  B-Tree
+ *
+ *  A B-Tree is a self-balancing search tree, in which nodes can have more than two children.
  */
 
 // MARK: - BTreeNode class
 
 class BTreeNode<Key: Comparable, Value> {
-  unowned var ownerTree: BTree<Key, Value>
+  /**
+   * The tree that owns the node.
+   */
+  unowned var owner: BTree<Key, Value>
   
-  private var keys = [Key]()
-  var values = [Value]()
+  fileprivate var keys = [Key]()
+  fileprivate var values = [Value]()
   var children: [BTreeNode]?
   
   var isLeaf: Bool {
@@ -43,13 +46,13 @@ class BTreeNode<Key: Comparable, Value> {
     return keys.count
   }
   
-  init(ownerTree: BTree<Key, Value>) {
-    self.ownerTree = ownerTree
+  init(owner: BTree<Key, Value>) {
+    self.owner = owner
   }
   
-  convenience init(ownerTree: BTree<Key, Value>, keys: [Key],
+  convenience init(owner: BTree<Key, Value>, keys: [Key],
                    values: [Value], children: [BTreeNode]? = nil) {
-    self.init(ownerTree: ownerTree)
+    self.init(owner: owner)
     self.keys += keys
     self.values += values
     self.children = children
@@ -59,19 +62,26 @@ class BTreeNode<Key: Comparable, Value> {
 // MARK: BTreeNode extesnion: Searching
 
 extension BTreeNode {
- func valueForKey(key: Key) -> Value? {
+  
+  /**
+   *  Returns the value for a given `key`, returns nil if the `key` is not found.
+   *  
+   *  - Parameters:
+   *    - key: the key of the value to be returned
+   */
+  func value(for key: Key) -> Value? {
     var index = keys.startIndex
     
-    while index.successor() < keys.endIndex && keys[index] < key {
-      index = index.successor()
+    while (index + 1) < keys.endIndex && keys[index] < key {
+      index = (index + 1)
     }
     
     if key == keys[index] {
       return values[index]
     } else if key < keys[index] {
-      return children?[index].valueForKey(key)
+      return children?[index].value(for: key)
     } else {
-      return children?[index.successor()].valueForKey(key)
+      return children?[(index + 1)].value(for: key)
     }
   }
 }
@@ -79,7 +89,14 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Travelsals
 
 extension BTreeNode {
-  func traverseKeysInOrder(@noescape process: Key -> Void) {
+  
+  /**
+   *  Traverses the keys in order, executes `process` for every key.
+   * 
+   *  - Parameters:
+   *    - process: the closure to be executed for every key
+   */
+  func traverseKeysInOrder(_ process: (Key) -> Void) {
     for i in 0..<numberOfKeys {
       children?[i].traverseKeysInOrder(process)
       process(keys[i])
@@ -92,11 +109,19 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Insertion
 
 extension BTreeNode {
-  func insertValue(value: Value, forKey key: Key) {
+  
+  /**
+   *  Inserts `value` for `key` to the node, or to one if its descendants.
+   *  
+   *  - Parameters:
+   *    - value: the value to be inserted for `key`
+   *    - key: the key for the `value`
+   */
+  func insert(_ value: Value, for key: Key) {
     var index = keys.startIndex
     
     while index < keys.endIndex && keys[index] < key {
-      index = index.successor()
+      index = (index + 1)
     }
     
     if index < keys.endIndex && keys[index] == key {
@@ -105,48 +130,64 @@ extension BTreeNode {
     }
     
     if isLeaf {
-      keys.insert(key, atIndex: index)
-      values.insert(value, atIndex: index)
-      ownerTree.numberOfKeys += 1
+      keys.insert(key, at: index)
+      values.insert(value, at: index)
+      owner.numberOfKeys += 1
     } else {
-      children![index].insertValue(value, forKey: key)
-      if children![index].numberOfKeys > ownerTree.order * 2 {
-        splitChild(children![index], atIndex: index)
+      children![index].insert(value, for: key)
+      if children![index].numberOfKeys > owner.order * 2 {
+        split(child: children![index], atIndex: index)
       }
     }
   }
   
-  private func splitChild(child: BTreeNode, atIndex index: Int) {
+  /**
+   *  Splits `child` at `index`.
+   *  The key-value pair at `index` gets moved up to the parent node,
+   *  or if there is not an parent node, then a new parent node is created.
+   *  
+   *  - Parameters:
+   *    - child: the child to be split
+   *    - index: the index of the key, which will be moved up to the parent
+   */
+  private func split(child: BTreeNode, atIndex index: Int) {
     let middleIndex = child.numberOfKeys / 2
-    keys.insert(child.keys[middleIndex], atIndex: index)
-    values.insert(child.values[middleIndex], atIndex: index)
-    child.keys.removeAtIndex(middleIndex)
-    child.values.removeAtIndex(middleIndex)
+    keys.insert(child.keys[middleIndex], at: index)
+    values.insert(child.values[middleIndex], at: index)
+    child.keys.remove(at: middleIndex)
+    child.values.remove(at: middleIndex)
     
     let rightSibling = BTreeNode(
-      ownerTree: ownerTree,
-      keys: Array(child.keys[middleIndex..<child.keys.endIndex]),
-      values: Array(child.values[middleIndex..<child.values.endIndex])
+      owner: owner,
+      keys: Array(child.keys[child.keys.indices.suffix(from: middleIndex)]),
+      values: Array(child.values[child.values.indices.suffix(from: middleIndex)])
     )
-    child.keys.removeRange(middleIndex..<child.keys.endIndex)
-    child.values.removeRange(middleIndex..<child.values.endIndex)
+    child.keys.removeSubrange(child.keys.indices.suffix(from: middleIndex))
+    child.values.removeSubrange(child.values.indices.suffix(from: middleIndex))
     
-    children!.insert(rightSibling, atIndex: index.successor())
+    children!.insert(rightSibling, at: (index + 1))
     
     if child.children != nil {
       rightSibling.children = Array(
-        child.children![middleIndex.successor()..<child.children!.endIndex]
+        child.children![child.children!.indices.suffix(from: (middleIndex + 1))]
       )
-      child.children!.removeRange(middleIndex.successor()..<child.children!.endIndex)
+      child.children!.removeSubrange(child.children!.indices.suffix(from: (middleIndex + 1)))
     }
   }
 }
 
 // MARK: BTreeNode extension: Removal
 
+/**
+ *  An enumeration to indicate a node's position according to another node.
+ *  
+ *  Possible values:
+ *    - left
+ *    - right
+ */
 private enum BTreeNodePosition {
-  case Left
-  case Right
+  case left
+  case right
 }
 
 extension BTreeNode {
@@ -158,34 +199,41 @@ extension BTreeNode {
     }
   }
   
-  func removeKey(key: Key) {
+  /**
+   *  Removes `key` and the value associated with it from the node
+   *  or one of its descendants.
+   *  
+   *  - Parameters:
+   *    - key: the key to be removed
+   */
+  func remove(_ key: Key) {
     var index = keys.startIndex
     
-    while index.successor() < keys.endIndex && keys[index] < key {
-      index = index.successor()
+    while (index + 1) < keys.endIndex && keys[index] < key {
+      index = (index + 1)
     }
     
     if keys[index] == key {
       if isLeaf {
-        keys.removeAtIndex(index)
-        values.removeAtIndex(index)
-        ownerTree.numberOfKeys -= 1
+        keys.remove(at: index)
+        values.remove(at: index)
+        owner.numberOfKeys -= 1
       } else {
         let predecessor = children![index].inorderPredecessor
         keys[index] = predecessor.keys.last!
         values[index] = predecessor.values.last!
-        children![index].removeKey(keys[index])
-        if children![index].numberOfKeys < ownerTree.order {
-          fixChildWithLessNodesThanOrder(children![index], atIndex: index)
+        children![index].remove(keys[index])
+        if children![index].numberOfKeys < owner.order {
+          fix(childWithTooFewKeys: children![index], atIndex: index)
         }
       }
     } else if key < keys[index] {
       // We should go to left child...
       
       if let leftChild = children?[index] {
-        leftChild.removeKey(key)
-        if leftChild.numberOfKeys < ownerTree.order {
-          fixChildWithLessNodesThanOrder(leftChild, atIndex: index)
+        leftChild.remove(key)
+        if leftChild.numberOfKeys < owner.order {
+          fix(childWithTooFewKeys: leftChild, atIndex: index)
         }
       } else {
         print("The key:\(key) is not in the tree.")
@@ -193,10 +241,10 @@ extension BTreeNode {
     } else {
       // We should go to right child...
       
-      if let rightChild = children?[index.successor()] {
-        rightChild.removeKey(key)
-        if rightChild.numberOfKeys < ownerTree.order {
-          fixChildWithLessNodesThanOrder(rightChild, atIndex: index.successor())
+      if let rightChild = children?[(index + 1)] {
+        rightChild.remove(key)
+        if rightChild.numberOfKeys < owner.order {
+          fix(childWithTooFewKeys: rightChild, atIndex: (index + 1))
         }
       } else {
         print("The key:\(key) is not in the tree")
@@ -204,112 +252,137 @@ extension BTreeNode {
     }
   }
   
-  private func fixChildWithLessNodesThanOrder(child: BTreeNode, atIndex index: Int) {
+  /**
+   *  Fixes `childWithTooFewKeys` by either moving a key to it from 
+   *  one of its neighbouring nodes, or by merging.
+   *
+   *  - Precondition:
+   *    `childWithTooFewKeys` must have less keys than the order of the tree.
+   *
+   *  - Parameters:
+   *    - child: the child to be fixed
+   *    - index: the index of the child to be fixed in the current node
+   */
+  private func fix(childWithTooFewKeys child: BTreeNode, atIndex index: Int) {
     
-    if index.predecessor() >= 0 &&
-       children![index.predecessor()].numberOfKeys > ownerTree.order {
-      
-      moveKeyAtIndex(index.predecessor(), toNode: child,
-                     fromNode: children![index.predecessor()], atPosition: .Left)
-      
-    } else if index.successor() < children!.count &&
-              children![index.successor()].numberOfKeys > ownerTree.order {
-      
-      moveKeyAtIndex(index, toNode: child,
-                     fromNode: children![index.successor()], atPosition: .Right)
-      
-    } else if index.predecessor() >= 0 {
-      mergeChild(child, withIndex: index, toNodeAtPosition: .Left)
+    if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
+      move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
+    } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
+      move(keyAtIndex: index, to: child, from: children![(index + 1)], at: .right)
+    } else if (index - 1) >= 0 {
+      merge(child: child, atIndex: index, to: .left)
     } else {
-      mergeChild(child, withIndex: index, toNodeAtPosition: .Right)
+      merge(child: child, atIndex: index, to: .right)
     }
   }
   
-  private func moveKeyAtIndex(keyIndex: Int, toNode targetNode: BTreeNode,
-                             fromNode: BTreeNode, atPosition position: BTreeNodePosition) {
+  /**
+   *  Moves the key at the specified `index` from `node` to
+   *  the `targetNode` at `position`
+   *  
+   *  - Parameters:
+   *    - index: the index of the key to be moved in `node`
+   *    - targetNode: the node to move the key into
+   *    - node: the node to move the key from
+   *    - position: the position of the from node relative to the targetNode
+   */
+  private func move(keyAtIndex index: Int, to targetNode: BTreeNode,
+                                  from node: BTreeNode, at position: BTreeNodePosition) {
     switch position {
-    case .Left:
-      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.startIndex)
-      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.startIndex)
-      keys[keyIndex] = fromNode.keys.last!
-      values[keyIndex] = fromNode.values.last!
-      fromNode.keys.removeLast()
-      fromNode.values.removeLast()
+    case .left:
+      targetNode.keys.insert(keys[index], at: targetNode.keys.startIndex)
+      targetNode.values.insert(values[index], at: targetNode.values.startIndex)
+      keys[index] = node.keys.last!
+      values[index] = node.values.last!
+      node.keys.removeLast()
+      node.values.removeLast()
       if !targetNode.isLeaf {
-        targetNode.children!.insert(fromNode.children!.last!,
-                                    atIndex: targetNode.children!.startIndex)
-        fromNode.children!.removeLast()
+        targetNode.children!.insert(node.children!.last!,
+                                    at: targetNode.children!.startIndex)
+        node.children!.removeLast()
       }
       
-    case .Right:
-      targetNode.keys.insert(keys[keyIndex], atIndex: targetNode.keys.endIndex)
-      targetNode.values.insert(values[keyIndex], atIndex: targetNode.values.endIndex)
-      keys[keyIndex] = fromNode.keys.first!
-      values[keyIndex] = fromNode.values.first!
-      fromNode.keys.removeFirst()
-      fromNode.values.removeFirst()
+    case .right:
+      targetNode.keys.insert(keys[index], at: targetNode.keys.endIndex)
+      targetNode.values.insert(values[index], at: targetNode.values.endIndex)
+      keys[index] = node.keys.first!
+      values[index] = node.values.first!
+      node.keys.removeFirst()
+      node.values.removeFirst()
       if !targetNode.isLeaf {
-        targetNode.children!.insert(fromNode.children!.first!,
-                                    atIndex: targetNode.children!.endIndex)
-        fromNode.children!.removeFirst()
+        targetNode.children!.insert(node.children!.first!,
+                                    at: targetNode.children!.endIndex)
+        node.children!.removeFirst()
       }
     }
   }
   
-  private func mergeChild(child: BTreeNode, withIndex index: Int, toNodeAtPosition position: BTreeNodePosition) {
+  /**
+   *  Merges `child` at `position` to the node at the `position`.
+   *  
+   *  - Parameters:
+   *    - child: the child to be merged
+   *    - index: the index of the child in the current node
+   *    - position: the position of the node to merge into
+   */
+  private func merge(child: BTreeNode, atIndex index: Int, to position: BTreeNodePosition) {
     switch position {
-    case .Left:
+    case .left:
       // We can merge to the left sibling
       
-      children![index.predecessor()].keys = children![index.predecessor()].keys +
-        [keys[index.predecessor()]] + child.keys
+      children![(index - 1)].keys = children![(index - 1)].keys +
+        [keys[(index - 1)]] + child.keys
       
-      children![index.predecessor()].values = children![index.predecessor()].values +
-        [values[index.predecessor()]] + child.values
+      children![(index - 1)].values = children![(index - 1)].values +
+        [values[(index - 1)]] + child.values
       
-      keys.removeAtIndex(index.predecessor())
-      values.removeAtIndex(index.predecessor())
+      keys.remove(at: (index - 1))
+      values.remove(at: (index - 1))
       
       if !child.isLeaf {
-        children![index.predecessor()].children =
-          children![index.predecessor()].children! + child.children!
+        children![(index - 1)].children =
+          children![(index - 1)].children! + child.children!
       }
       
-    case .Right:
+    case .right:
       // We should merge to the right sibling
       
-      children![index.successor()].keys = child.keys + [keys[index]] +
-        children![index.successor()].keys
+      children![(index + 1)].keys = child.keys + [keys[index]] +
+        children![(index + 1)].keys
       
-      children![index.successor()].values = child.values + [values[index]] +
-        children![index.successor()].values
+      children![(index + 1)].values = child.values + [values[index]] +
+        children![(index + 1)].values
       
-      keys.removeAtIndex(index)
-      values.removeAtIndex(index)
+      keys.remove(at: index)
+      values.remove(at: index)
       
       if !child.isLeaf {
-        children![index.successor()].children =
-          child.children! + children![index.successor()].children!
+        children![(index + 1)].children =
+          child.children! + children![(index + 1)].children!
       }
     }
-    children!.removeAtIndex(index)
+    children!.remove(at: index)
   }
 }
 
 // MARK: BTreeNode extension: Conversion
 
 extension BTreeNode {
-  func inorderArrayFromKeys() -> [Key] {
+  /**
+   *  Returns an array which contains the keys from the current node
+   *  and its descendants in order.
+   */
+  var inorderArrayFromKeys: [Key] {
     var array = [Key] ()
     
     for i in 0..<numberOfKeys {
-      if let returnedArray = children?[i].inorderArrayFromKeys() {
+      if let returnedArray = children?[i].inorderArrayFromKeys {
         array += returnedArray
       }
       array += [keys[i]]
     }
     
-    if let returnedArray = children?.last?.inorderArrayFromKeys() {
+    if let returnedArray = children?.last?.inorderArrayFromKeys {
       array += returnedArray
     }
     
@@ -320,6 +393,9 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Description
 
 extension BTreeNode: CustomStringConvertible {
+  /**
+   *  Returns a String containing the preorder representation of the nodes.
+   */
   var description: String {
     var str = "\(keys)"
     
@@ -336,25 +412,26 @@ extension BTreeNode: CustomStringConvertible {
 // MARK: - BTree class
 
 public class BTree<Key: Comparable, Value> {
-  
   /**
-   The order of the B-Tree
-   
-   The number of keys in every node should be in the [order, 2*order] range,
-   except the root node which is allowed to contain less keys than the value of order.
+   *  The order of the B-Tree
+   *
+   *  The number of keys in every node should be in the [order, 2*order] range,
+   *  except the root node which is allowed to contain less keys than the value of order.
    */
   public let order: Int
   
-  /// The root node of the tree
+  /**
+   *  The root node of the tree
+   */
   var rootNode: BTreeNode<Key, Value>!
   
-  private(set) public var numberOfKeys = 0
+  fileprivate(set) public var numberOfKeys = 0
   
   /**
-   Designated initializer for the tree
-   
-   - parameters:
-   - order: The order of the tree.
+   *  Designated initializer for the tree
+   *
+   *  - Parameters:
+   *    - order: The order of the tree.
    */
   public init?(order: Int) {
     guard order > 0 else {
@@ -362,14 +439,20 @@ public class BTree<Key: Comparable, Value> {
       return nil
     }
     self.order = order
-    rootNode = BTreeNode<Key, Value>(ownerTree: self)
+    rootNode = BTreeNode<Key, Value>(owner: self)
   }
 }
 
 // MARK: BTree extension: Travelsals
 
 extension BTree {
-  public func traverseKeysInOrder(@noescape process: Key -> Void) {
+  /**
+   *  Traverses the keys in order, executes `process` for every key.
+   *
+   *  - Parameters:
+   *    - process: the closure to be executed for every key
+   */
+  public func traverseKeysInOrder(_ process: (Key) -> Void) {
     rootNode.traverseKeysInOrder(process)
   }
 }
@@ -377,60 +460,85 @@ extension BTree {
 // MARK: BTree extension: Subscript
 
 extension BTree {
+  /**
+   *  Returns the value for a given `key`, returns nil if the `key` is not found.
+   *
+   *  - Parameters:
+   *    - key: the key of the value to be returned
+   */
   public subscript (key: Key) -> Value? {
-    return valueForKey(key)
+    return value(for: key)
   }
 }
 
 // MARK: BTree extension: Value for Key
 
 extension BTree {
-  public func valueForKey(key: Key) -> Value? {
+  /**
+   *  Returns the value for a given `key`, returns nil if the `key` is not found.
+   *
+   *  - Parameters:
+   *    - key: the key of the value to be returned
+   */
+  public func value(for key: Key) -> Value? {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
     
-    return rootNode.valueForKey(key)
+    return rootNode.value(for: key)
   }
 }
 
 // MARK: BTree extension: Insertion
 
 extension BTree {
-  public func insertValue(value: Value, forKey key: Key) {
-    rootNode.insertValue(value, forKey: key)
+  /**
+   *  Inserts the `value` for the `key` into the tree.
+   *
+   *  - Parameters:
+   *    - value: the value to be inserted for `key`
+   *    - key: the key for the `value`
+   */
+  public func insert(_ value: Value, for key: Key) {
+    rootNode.insert(value, for: key)
     
     if rootNode.numberOfKeys > order * 2 {
       splitRoot()
     }
   }
   
+  /**
+   *  Splits the root node of the tree.
+   *  
+   *  - Precondition:
+   *    The root node of the tree contains `order` * 2 keys.
+   */
   private func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
     
     let newRoot = BTreeNode<Key, Value>(
-      ownerTree: self,
+      owner: self,
       keys: [rootNode.keys[middleIndexOfOldRoot]],
       values: [rootNode.values[middleIndexOfOldRoot]],
       children: [rootNode]
     )
-    rootNode.keys.removeAtIndex(middleIndexOfOldRoot)
-    rootNode.values.removeAtIndex(middleIndexOfOldRoot)
+    rootNode.keys.remove(at: middleIndexOfOldRoot)
+    rootNode.values.remove(at: middleIndexOfOldRoot)
     
     let newRightChild = BTreeNode<Key, Value>(
-      ownerTree: self,
-      keys: Array(rootNode.keys[middleIndexOfOldRoot..<rootNode.keys.endIndex]),
-      values: Array(rootNode.values[middleIndexOfOldRoot..<rootNode.values.endIndex])
+      owner: self,
+      keys: Array(rootNode.keys[rootNode.keys.indices.suffix(from: middleIndexOfOldRoot)]),
+      values: Array(rootNode.values[rootNode.values.indices.suffix(from: middleIndexOfOldRoot)])
     )
-    rootNode.keys.removeRange(middleIndexOfOldRoot..<rootNode.keys.endIndex)
-    rootNode.values.removeRange(middleIndexOfOldRoot..<rootNode.values.endIndex)
+    rootNode.keys.removeSubrange(rootNode.keys.indices.suffix(from: middleIndexOfOldRoot))
+    rootNode.values.removeSubrange(rootNode.values.indices.suffix(from: middleIndexOfOldRoot))
     
     if rootNode.children != nil {
       newRightChild.children = Array(
-        rootNode.children![middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex]
+        rootNode.children![rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))]
       )
-      rootNode.children!.removeRange(
-        middleIndexOfOldRoot.successor()..<rootNode.children!.endIndex
+      rootNode.children!.removeSubrange(
+        rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))
       )
     }
     
@@ -442,12 +550,18 @@ extension BTree {
 // MARK: BTree extension: Removal
 
 extension BTree {
-  public func removeKey(key: Key) {
+  /**
+   *  Removes `key` and the value associated with it from the tree.
+   *  
+   *  - Parameters:
+   *    - key: the key to remove
+   */
+  public func remove(_ key: Key) {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
     
-    rootNode.removeKey(key)
+    rootNode.remove(key)
     
     if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
       rootNode = rootNode.children!.first!
@@ -458,15 +572,20 @@ extension BTree {
 // MARK: BTree extension: Conversion
 
 extension BTree {
-  public func inorderArrayFromKeys() -> [Key] {
-    return rootNode.inorderArrayFromKeys()
+  /**
+   *  The keys of the tree in order.
+   */
+  public var inorderArrayFromKeys: [Key] {
+    return rootNode.inorderArrayFromKeys
   }
 }
 
 // MARK: BTree extension: Decription
 
 extension BTree: CustomStringConvertible {
-  // Returns a String containing the preorder representation of the nodes
+  /** 
+   *  Returns a String containing the preorder representation of the nodes.
+   */
   public var description: String {
     return rootNode.description
   }

From 9035cddfca64d7814e774ab86dab36259338eea0 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Tue, 6 Sep 2016 21:24:02 +1200
Subject: [PATCH 0509/1679] Update .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 76799365d..d0f565651 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -13,7 +13,7 @@ script:
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
- - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 3945383d306ac027f779461789d6b0deddca4348 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 7 Sep 2016 05:01:56 -0700
Subject: [PATCH 0510/1679] Migrated over to Swift 3

---
 Heap/Heap.swift                               | 56 +++++++++----------
 Heap/README.markdown                          |  4 +-
 Heap/Tests/HeapTests.swift                    | 42 +++++++-------
 Heap/Tests/Tests.xcodeproj/project.pbxproj    | 10 +++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 5 files changed, 61 insertions(+), 53 deletions(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index bf7031abe..eba7ca1cf 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -8,14 +8,14 @@ public struct Heap<T> {
   var elements = [T]()
 
   /** Determines whether this is a max-heap (>) or min-heap (<). */
-  private var isOrderedBefore: (T, T) -> Bool
+  fileprivate var isOrderedBefore: (T, T) -> Bool
 
   /**
    * Creates an empty heap.
    * The sort function determines whether this is a min-heap or max-heap.
    * For integers, > makes a max-heap, < makes a min-heap.
    */
-  public init(sort: (T, T) -> Bool) {
+  public init(sort: @escaping (T, T) -> Bool) {
     self.isOrderedBefore = sort
   }
 
@@ -24,9 +24,9 @@ public struct Heap<T> {
    * the elements are inserted into the heap in the order determined by the
    * sort function.
    */
-  public init(array: [T], sort: (T, T) -> Bool) {
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
     self.isOrderedBefore = sort
-    buildHeap(array)
+    buildHeap(fromArray: array)
   }
 
   /*
@@ -43,9 +43,9 @@ public struct Heap<T> {
    * Converts an array to a max-heap or min-heap in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
    */
-  private mutating func buildHeap(array: [T]) {
+  fileprivate mutating func buildHeap(fromArray array: [T]) {
     elements = array
-    for i in (elements.count/2 - 1).stride(through: 0, by: -1) {
+    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
       shiftDown(index: i, heapSize: elements.count)
     }
   }
@@ -62,7 +62,7 @@ public struct Heap<T> {
    * Returns the index of the parent of the element at index i.
    * The element at index 0 is the root of the tree and has no parent.
    */
-  @inline(__always) func indexOfParent(i: Int) -> Int {
+  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
     return (i - 1) / 2
   }
 
@@ -71,7 +71,7 @@ public struct Heap<T> {
    * Note that this index can be greater than the heap size, in which case
    * there is no left child.
    */
-  @inline(__always) func indexOfLeftChild(i: Int) -> Int {
+  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
     return 2*i + 1
   }
 
@@ -80,7 +80,7 @@ public struct Heap<T> {
    * Note that this index can be greater than the heap size, in which case
    * there is no right child.
    */
-  @inline(__always) func indexOfRightChild(i: Int) -> Int {
+  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
     return 2*i + 2
   }
 
@@ -96,12 +96,12 @@ public struct Heap<T> {
    * Adds a new value to the heap. This reorders the heap so that the max-heap
    * or min-heap property still holds. Performance: O(log n).
    */
-  public mutating func insert(value: T) {
+  public mutating func insert(_ value: T) {
     elements.append(value)
     shiftUp(index: elements.count - 1)
   }
 
-  public mutating func insert<S: SequenceType where S.Generator.Element == T>(sequence: S) {
+  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
     for value in sequence {
       insert(value)
     }
@@ -123,7 +123,7 @@ public struct Heap<T> {
    * Removes the root node from the heap. For a max-heap, this is the maximum
    * value; for a min-heap it is the minimum value. Performance: O(log n).
    */
-  public mutating func remove() -> T? {
+  @discardableResult public mutating func remove() -> T? {
     if elements.isEmpty {
       return nil
     } else if elements.count == 1 {
@@ -142,14 +142,14 @@ public struct Heap<T> {
    * Removes an arbitrary node from the heap. Performance: O(log n). You need
    * to know the node's index, which may actually take O(n) steps to find.
    */
-  public mutating func removeAtIndex(i: Int) -> T? {
-    guard i < elements.count else { return nil }
+  public mutating func removeAt(index: Int) -> T? {
+    guard index < elements.count else { return nil }
     
     let size = elements.count - 1
-    if i != size {
-      swap(&elements[i], &elements[size])
-      shiftDown(index: i, heapSize: size)
-      shiftUp(index: i)
+    if index != size {
+      swap(&elements[index], &elements[size])
+      shiftDown(index: index, heapSize: size)
+      shiftUp(index: index)
     }
     return elements.removeLast()
   }
@@ -158,15 +158,15 @@ public struct Heap<T> {
    * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
-  mutating func shiftUp(index index: Int) {
+  mutating func shiftUp(index: Int) {
     var childIndex = index
     let child = elements[childIndex]
-    var parentIndex = indexOfParent(childIndex)
+    var parentIndex = self.parentIndex(ofIndex: childIndex)
 
     while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
       elements[childIndex] = elements[parentIndex]
       childIndex = parentIndex
-      parentIndex = indexOfParent(childIndex)
+      parentIndex = self.parentIndex(ofIndex: childIndex)
     }
 
     elements[childIndex] = child
@@ -180,11 +180,11 @@ public struct Heap<T> {
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  mutating func shiftDown(index index: Int, heapSize: Int) {
+  mutating func shiftDown(index: Int, heapSize: Int) {
     var parentIndex = index
 
     while true {
-      let leftChildIndex = indexOfLeftChild(parentIndex)
+      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
       let rightChildIndex = leftChildIndex + 1
 
       // Figure out which comes first if we order them by the sort function:
@@ -212,16 +212,16 @@ extension Heap where T: Equatable {
   /**
    * Searches the heap for the given element. Performance: O(n).
    */
-  public func indexOf(element: T) -> Int? {
-    return indexOf(element, 0)
+  public func index(of element: T) -> Int? {
+    return index(of: element, 0)
   }
 
-  private func indexOf(element: T, _ i: Int) -> Int? {
+  fileprivate func index(of element: T, _ i: Int) -> Int? {
     if i >= count { return nil }
     if isOrderedBefore(element, elements[i]) { return nil }
     if element == elements[i] { return i }
-    if let j = indexOf(element, indexOfLeftChild(i)) { return j }
-    if let j = indexOf(element, indexOfRightChild(i)) { return j }
+    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
     return nil
   }
 }
diff --git a/Heap/README.markdown b/Heap/README.markdown
index fb5092fe3..88ea25eeb 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -260,7 +260,7 @@ It can be convenient to convert an array into a heap. This just shuffles the arr
 In code it would look like this:
 
 ```swift
-  private mutating func buildHeap(array: [T]) {
+  private mutating func buildHeap(fromArray array: [T]) {
     for value in array {
       insert(value)
     }
@@ -274,7 +274,7 @@ If you didn't gloss over the math section, you'd have seen that for any heap the
 In code:
 
 ```swift
-  private mutating func buildHeap(array: [T]) {
+  private mutating func buildHeap(fromArray array: [T]) {
     elements = array
     for i in (elements.count/2 - 1).stride(through: 0, by: -1) {
       shiftDown(index: i, heapSize: elements.count)
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 6178a8094..c5b479f14 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -7,11 +7,11 @@ import XCTest
 
 class HeapTests: XCTestCase {
 
-  private func verifyMaxHeap(h: Heap<Int>) -> Bool {
+  fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
     for i in 0..<h.count {
-      let left = h.indexOfLeftChild(i)
-      let right = h.indexOfRightChild(i)
-      let parent = h.indexOfParent(i)
+      let left = h.leftChildIndex(ofIndex: i)
+      let right = h.rightChildIndex(ofIndex: i)
+      let parent = h.parentIndex(ofIndex: i)
       if left < h.count && h.elements[i] < h.elements[left] { return false }
       if right < h.count && h.elements[i] < h.elements[right] { return false }
       if i > 0 && h.elements[parent] < h.elements[i] { return false }
@@ -19,11 +19,11 @@ class HeapTests: XCTestCase {
     return true
   }
 
-  private func verifyMinHeap(h: Heap<Int>) -> Bool {
+  fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
     for i in 0..<h.count {
-      let left = h.indexOfLeftChild(i)
-      let right = h.indexOfRightChild(i)
-      let parent = h.indexOfParent(i)
+      let left = h.leftChildIndex(ofIndex: i)
+      let right = h.rightChildIndex(ofIndex: i)
+      let parent = h.parentIndex(ofIndex: i)
       if left < h.count && h.elements[i] > h.elements[left] { return false }
       if right < h.count && h.elements[i] > h.elements[right] { return false }
       if i > 0 && h.elements[parent] > h.elements[i] { return false }
@@ -31,14 +31,14 @@ class HeapTests: XCTestCase {
     return true
   }
 
-  private func isPermutation(array1: [Int], _ array2: [Int]) -> Bool {
+  fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
     var a1 = array1
     var a2 = array2
     if a1.count != a2.count { return false }
     while a1.count > 0 {
-      if let i = a2.indexOf(a1[0]) {
-        a1.removeAtIndex(0)
-        a2.removeAtIndex(i)
+      if let i = a2.index(of: a1[0]) {
+        a1.remove(at: 0)
+        a2.remove(at: i)
       } else {
         return false
       }
@@ -161,7 +161,7 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
   }
 
-  private func randomArray(n: Int) -> [Int] {
+  fileprivate func randomArray(_ n: Int) -> [Int] {
     var a = [Int]()
     for _ in 0..<n {
       a.append(Int(arc4random()))
@@ -197,27 +197,27 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
 
     //test index out of bounds
-    let v = h.removeAtIndex(10)
+    let v = h.removeAt(index: 10)
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
     
-    let v1 = h.removeAtIndex(5)
+    let v1 = h.removeAt(index: 5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
 
-    let v2 = h.removeAtIndex(4)
+    let v2 = h.removeAt(index: 4)
     XCTAssertEqual(v2, 20)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
 
-    let v3 = h.removeAtIndex(4)
+    let v3 = h.removeAt(index: 4)
     XCTAssertEqual(v3, 50)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 65, 70, 10])
 
-    let v4 = h.removeAtIndex(0)
+    let v4 = h.removeAt(index: 0)
     XCTAssertEqual(v4, 100)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [70, 65, 10])
@@ -270,9 +270,9 @@ class HeapTests: XCTestCase {
       let m = (n + 1)/2
       for k in 1...m {
         let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        let v = h.removeAtIndex(i)!
-        let j = a.indexOf(v)!
-        a.removeAtIndex(j)
+        let v = h.removeAt(index: i)!
+        let j = a.index(of: v)!
+        a.remove(at: j)
 
         XCTAssertTrue(verifyMaxHeap(h))
         XCTAssertEqual(h.count, a.count)
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
index a2302e38b..9319e2089 100644
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,11 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -145,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -189,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -220,6 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 6ee811901e79b860c443f8bd8ea3ccfecd9f08ba Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 8 Sep 2016 07:55:54 -0700
Subject: [PATCH 0511/1679] Updated playground to Swift 3

---
 .../Contents.swift                            | 30 +++++-----
 .../Sources/BinarySearchTree.swift            | 56 +++++++++----------
 2 files changed, 43 insertions(+), 43 deletions(-)

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 4c2a6c358..6d73585b5 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,21 +1,21 @@
 //: Playground - noun: a place where people can play
 
 let tree = BinarySearchTree<Int>(value: 7)
-tree.insert(2)
-tree.insert(5)
-tree.insert(10)
-tree.insert(9)
-tree.insert(1)
+tree.insert(value: 2)
+tree.insert(value: 5)
+tree.insert(value: 10)
+tree.insert(value: 9)
+tree.insert(value: 1)
 
 tree
 tree.debugDescription
 
 let tree2 = BinarySearchTree<Int>(array: [7, 2, 5, 10, 9, 1])
 
-tree.search(5)
-tree.search(2)
-tree.search(7)
-tree.search(6)
+tree.search(value: 5)
+tree.search(value: 2)
+tree.search(value: 7)
+tree.search(value: 6)
 
 tree.traverseInOrder { value in print(value) }
 
@@ -24,7 +24,7 @@ tree.toArray()
 tree.minimum()
 tree.maximum()
 
-if let node2 = tree.search(2) {
+if let node2 = tree.search(value: 2) {
   node2.remove()
   node2
   print(tree)
@@ -34,25 +34,25 @@ tree.height()
 tree.predecessor()
 tree.successor()
 
-if let node10 = tree.search(10) {
+if let node10 = tree.search(value: 10) {
   node10.depth()        // 1
   node10.height()       // 1
   node10.predecessor()
   node10.successor()    // nil
 }
 
-if let node9 = tree.search(9) {
+if let node9 = tree.search(value: 9) {
   node9.depth()        // 2
   node9.height()       // 0
   node9.predecessor()
   node9.successor()
 }
 
-if let node1 = tree.search(1) {
+if let node1 = tree.search(value: 1) {
   // This makes it an invalid binary search tree because 100 is greater
   // than the root, 7, and so must be in the right branch not in the left.
   tree.isBST(minValue: Int.min, maxValue: Int.max)  // true
-  node1.insert(100)
-  tree.search(100)                                  // nil
+  node1.insert(value: 100)
+  tree.search(value: 100)                                  // nil
   tree.isBST(minValue: Int.min, maxValue: Int.max)  // false
 }
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index a58ac075a..f4960380e 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -10,10 +10,10 @@
   you should insert new values in randomized order, not in sorted order.
 */
 public class BinarySearchTree<T: Comparable> {
-  private(set) public var value: T
-  private(set) public var parent: BinarySearchTree?
-  private(set) public var left: BinarySearchTree?
-  private(set) public var right: BinarySearchTree?
+  fileprivate(set) public var value: T
+  fileprivate(set) public var parent: BinarySearchTree?
+  fileprivate(set) public var left: BinarySearchTree?
+  fileprivate(set) public var right: BinarySearchTree?
 
   public init(value: T) {
     self.value = value
@@ -22,8 +22,8 @@ public class BinarySearchTree<T: Comparable> {
   public convenience init(array: [T]) {
     precondition(array.count > 0)
     self.init(value: array.first!)
-    for v in array.dropFirst() {
-      insert(v, parent: self)
+    for v in array.dropFirst() { 
+      insert(value: v, parent: self)
     }
   }
 
@@ -74,20 +74,20 @@ extension BinarySearchTree {
     Performance: runs in O(h) time, where h is the height of the tree.
   */
   public func insert(value: T) {
-    insert(value, parent: self)
+    insert(value: value, parent: self)
   }
 
-  private func insert(value: T, parent: BinarySearchTree) {
+  fileprivate func insert(value: T, parent: BinarySearchTree) {
     if value < self.value {
       if let left = left {
-        left.insert(value, parent: left)
+        left.insert(value: value, parent: left)
       } else {
         left = BinarySearchTree(value: value)
         left?.parent = parent
       }
     } else {
       if let right = right {
-        right.insert(value, parent: right)
+        right.insert(value: value, parent: right)
       } else {
         right = BinarySearchTree(value: value)
         right?.parent = parent
@@ -108,7 +108,7 @@ extension BinarySearchTree {
 
     Performance: runs in O(h) time, where h is the height of the tree.
   */
-  public func remove() -> BinarySearchTree? {
+  @discardableResult public func remove() -> BinarySearchTree? {
     let replacement: BinarySearchTree?
 
     if let left = left {
@@ -126,7 +126,7 @@ extension BinarySearchTree {
       replacement = nil
     }
 
-    reconnectParentToNode(replacement)
+    reconnectParentTo(node: replacement)
 
     // The current node is no longer part of the tree, so clean it up.
     parent = nil
@@ -136,7 +136,7 @@ extension BinarySearchTree {
     return replacement
   }
 
-  private func removeNodeWithTwoChildren(left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
+  private func removeNodeWithTwoChildren(_ left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
     // This node has two children. It must be replaced by the smallest
     // child that is larger than this node's value, which is the leftmost
     // descendent of the right child.
@@ -164,7 +164,7 @@ extension BinarySearchTree {
     return successor
   }
 
-  private func reconnectParentToNode(node: BinarySearchTree?) {
+  private func reconnectParentTo(node: BinarySearchTree?) {
     if let parent = parent {
       if isLeftChild {
         parent.left = node
@@ -211,7 +211,7 @@ extension BinarySearchTree {
   */
 
   public func contains(value: T) -> Bool {
-    return search(value) != nil
+    return search(value: value) != nil
   }
 
   /*
@@ -298,32 +298,32 @@ extension BinarySearchTree {
 // MARK: - Traversal
 
 extension BinarySearchTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
-    left?.traverseInOrder(process)
+  public func traverseInOrder(process: (T) -> Void) {
+    left?.traverseInOrder(process: process)
     process(value)
-    right?.traverseInOrder(process)
+    right?.traverseInOrder(process: process)
   }
 
-  public func traversePreOrder(@noescape process: T -> Void) {
+  public func traversePreOrder(process: (T) -> Void) {
     process(value)
-    left?.traversePreOrder(process)
-    right?.traversePreOrder(process)
+    left?.traversePreOrder(process: process)
+    right?.traversePreOrder(process: process)
   }
 
-  public func traversePostOrder(@noescape process: T -> Void) {
-    left?.traversePostOrder(process)
-    right?.traversePostOrder(process)
+  public func traversePostOrder(process: (T) -> Void) {
+    left?.traversePostOrder(process: process)
+    right?.traversePostOrder(process: process)
     process(value)
   }
 
   /*
     Performs an in-order traversal and collects the results in an array.
   */
-  public func map(@noescape formula: T -> T) -> [T] {
+  public func map(formula: (T) -> T) -> [T] {
     var a = [T]()
-    if let left = left { a += left.map(formula) }
+    if let left = left { a += left.map(formula: formula) }
     a.append(formula(value))
-    if let right = right { a += right.map(formula) }
+    if let right = right { a += right.map(formula: formula) }
     return a
   }
 }
@@ -332,7 +332,7 @@ extension BinarySearchTree {
   Is this binary tree a valid binary search tree?
 */
 extension BinarySearchTree {
-  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
+  public func isBST(minValue: T, maxValue: T) -> Bool {
     if value < minValue || value > maxValue { return false }
     let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
     let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true

From b502621861aa6bef64ba755736a0de3f509985fc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 8 Sep 2016 07:59:12 -0700
Subject: [PATCH 0512/1679] Migration to Swift 3

---
 .../BinarySearchTree.playground/Contents.swift | 18 ++++++++++--------
 .../Sources/BinarySearchTree.swift             | 10 +++++-----
 2 files changed, 15 insertions(+), 13 deletions(-)

diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 217cb489e..12fbba81d 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -2,13 +2,15 @@
 
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.Leaf(7)
-tree = tree.insert(2)
-tree = tree.insert(5)
-tree = tree.insert(10)
-tree = tree.insert(9)
-tree = tree.insert(1)
+tree = tree.insert(newValue: 2)
+tree = tree.insert(newValue: 5)
+tree = tree.insert(newValue: 10)
+tree = tree.insert(newValue: 9)
+tree = tree.insert(newValue: 1)
 print(tree)
 
-tree.search(10)
-tree.search(1)
-tree.search(11)
+tree.search(x: 10)
+tree.search(x: 1)
+tree.search(x: 11)
+
+
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index ce2868bbf..b692efdc4 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -44,9 +44,9 @@ public enum BinarySearchTree<T: Comparable> {
 
     case .Node(let left, let value, let right):
       if newValue < value {
-        return .Node(left.insert(newValue), value, right)
+        return .Node(left.insert(newValue: newValue), value, right)
       } else {
-        return .Node(left, value, right.insert(newValue))
+        return .Node(left, value, right.insert(newValue: newValue))
       }
     }
   }
@@ -63,9 +63,9 @@ public enum BinarySearchTree<T: Comparable> {
       return (x == y) ? self : nil
     case let .Node(left, y, right):
       if x < y {
-        return left.search(x)
+        return left.search(x: x)
       } else if y < x {
-        return right.search(x)
+        return right.search(x: x)
       } else {
         return self
       }
@@ -73,7 +73,7 @@ public enum BinarySearchTree<T: Comparable> {
   }
 
   public func contains(x: T) -> Bool {
-    return search(x) != nil
+    return search(x: x) != nil
   }
 
   /*

From b88fb4d7bb422e81981b6ddfaef52a2f07fe649b Mon Sep 17 00:00:00 2001
From: Nemanja Vlahovic <nemanja@nemanjavlahovic.com>
Date: Sat, 10 Sep 2016 19:22:35 +0200
Subject: [PATCH 0513/1679] Update Selection Sort to Swift 3

---
 Selection Sort/README.markdown                         |  2 +-
 Selection Sort/SelectionSort.playground/Contents.swift |  2 +-
 Selection Sort/SelectionSort.swift                     |  2 +-
 Selection Sort/Tests/Tests.xcodeproj/project.pbxproj   | 10 +++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme              |  2 +-
 5 files changed, 13 insertions(+), 5 deletions(-)

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index 6eb019ab1..c583b47ea 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -59,7 +59,7 @@ As you can see, selection sort is an *in-place* sort because everything happens
 Here is an implementation of selection sort in Swift:
 
 ```swift
-func selectionSort(array: [Int]) -> [Int] {
+func selectionSort(_ array: [Int]) -> [Int] {
   guard array.count > 1 else { return array }  // 1
 
   var a = array                    // 2
diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index dd57e9c3a..bd8c7cccf 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -1,6 +1,6 @@
 //: Playground - noun: a place where people can play
 
-func selectionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func selectionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   guard array.count > 1 else { return array }
   var a = array
   for x in 0 ..< a.count - 1 {
diff --git a/Selection Sort/SelectionSort.swift b/Selection Sort/SelectionSort.swift
index 9d7b45ad8..e02c87259 100644
--- a/Selection Sort/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.swift	
@@ -1,4 +1,4 @@
-func selectionSort<T>(array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+func selectionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   guard array.count > 1 else { return array }
 
   var a = array
diff --git a/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj b/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj
index 11aefac3c..a42f3dc3f 100644
--- a/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Selection Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,11 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -149,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -224,6 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Selection Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 19a2eb980c1d2d70ab532f9d04609197959f31b3 Mon Sep 17 00:00:00 2001
From: Nemanja Vlahovic <nemanja@nemanjavlahovic.com>
Date: Sat, 10 Sep 2016 19:30:13 +0200
Subject: [PATCH 0514/1679] Uncomment selection sort tests

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 8cf0b486b..bdda5eb7d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -33,7 +33,7 @@ script:
 # - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests

From 7480ea45bf0091251a86e9d2ddd7264d6047284a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 10 Sep 2016 16:00:30 -0700
Subject: [PATCH 0515/1679] Marking the Swift file to read that it is currently
 undergoing refactoring

---
 Trie/trie.swift | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Trie/trie.swift b/Trie/trie.swift
index 9ebfba8bc..8227d0243 100644
--- a/Trie/trie.swift
+++ b/Trie/trie.swift
@@ -1,3 +1,5 @@
+/// TODO: - Undergoing refactoring.
+
 /*
   Queue implementation (taken from repository, needed for findPrefix())
 */

From 8a679ffae71e2dd0e1999d1abee43de74426e1ef Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 10 Sep 2016 16:39:06 -0700
Subject: [PATCH 0516/1679] Adds a playground with the first step of
 refactoring the implementation.

---
 Trie/Trie.playground/Contents.swift           |   0
 Trie/Trie.playground/Sources/Node.swift       |  64 ++++++
 Trie/Trie.playground/Sources/Queue.swift      |  31 +++
 Trie/Trie.playground/Sources/Trie.swift       | 212 ++++++++++++++++++
 Trie/Trie.playground/contents.xcplayground    |   4 +
 .../contents.xcworkspacedata                  |   7 +
 6 files changed, 318 insertions(+)
 create mode 100644 Trie/Trie.playground/Contents.swift
 create mode 100644 Trie/Trie.playground/Sources/Node.swift
 create mode 100644 Trie/Trie.playground/Sources/Queue.swift
 create mode 100644 Trie/Trie.playground/Sources/Trie.swift
 create mode 100644 Trie/Trie.playground/contents.xcplayground
 create mode 100644 Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Trie/Trie.playground/Contents.swift b/Trie/Trie.playground/Contents.swift
new file mode 100644
index 000000000..e69de29bb
diff --git a/Trie/Trie.playground/Sources/Node.swift b/Trie/Trie.playground/Sources/Node.swift
new file mode 100644
index 000000000..72600af2f
--- /dev/null
+++ b/Trie/Trie.playground/Sources/Node.swift
@@ -0,0 +1,64 @@
+/// A Trie (prefix tree)
+///
+/// Some of the functionality of the trie makes use of the Queue implementation for this project
+///
+/// Every node in the Trie stores a bit of information pertaining to what it references:
+///   -Character (letter of an inserted word)
+///   -Parent (Letter that comes before the current letter in some word)
+///   -Children (Words that have more letters than available in the prefix)
+///   -isAWord (Does the current letter mark the end of a known inserted word?)
+///   -visited (Mainly for the findPrefix() function)
+public class Node {
+  public var character: String
+  public var parent: Node?
+  public var children: [String: Node]
+  public var isAWord: Bool
+  public var visited: Bool // only for findPrefix
+  
+  init(character: String, parent: Node?) {
+    self.character = character
+    self.children = [:]
+    self.isAWord = false
+    self.parent = parent
+    self.visited = false
+  }
+  
+  /// Returns `true` if the node is a leaf node, false otherwise.
+  var isLeaf: Bool {
+    return children.count == 0
+  }
+  
+  /// Changes the parent of the current node to the passed in node.
+  ///
+  /// - parameter node: A `Node` object.
+  func setParent(node: Node) {
+    parent = node
+  }
+  
+  /// Returns the child node that holds the specific passed letter.
+  ///
+  /// - parameter character: A `String`
+  ///
+  /// - returns: The `Node` object that contains the `character`.
+  func getChildAt(character: String) -> Node {
+    return children[character]!
+  }
+  
+  /// Returns whether or not the current node marks the end of a valid word.
+  var isValidWord: Bool {
+    return isAWord
+  }
+  
+  
+  /// Returns whether or not the current node is the root of the trie.
+  var isRoot: Bool {
+    return character == ""
+  }
+}
+
+// MARK: - CustomStringConvertible
+extension Node: CustomStringConvertible {
+  public var description: String {
+    return ""
+  }
+}
diff --git a/Trie/Trie.playground/Sources/Queue.swift b/Trie/Trie.playground/Sources/Queue.swift
new file mode 100644
index 000000000..81bde190a
--- /dev/null
+++ b/Trie/Trie.playground/Sources/Queue.swift
@@ -0,0 +1,31 @@
+/// Queue implementation taken from the repository.
+public struct Queue<T> {
+  private var array: [T?] = []
+  private var head = 0
+  
+  public var isEmpty: Bool {
+    return count == 0
+  }
+  
+  public var count: Int {
+    return array.count - head
+  }
+  
+  public mutating func enqueue(element: T) {
+    array.append(element)
+  }
+  
+  public mutating func dequeue() -> T? {
+    guard head < array.count, let element = array[head] else { return nil }
+    array[head] = nil
+    head += 1
+    
+    let percentage = Double(head) / Double(array.count)
+    if array.count > 50 && percentage > 0.25 {
+      array.removeFirst(head)
+      head = 0
+    }
+    
+    return element
+  }
+}
diff --git a/Trie/Trie.playground/Sources/Trie.swift b/Trie/Trie.playground/Sources/Trie.swift
new file mode 100644
index 000000000..053bd7113
--- /dev/null
+++ b/Trie/Trie.playground/Sources/Trie.swift
@@ -0,0 +1,212 @@
+/// The Trie class has the following attributes:
+///   -root (the root of the trie)
+///   -wordList (the words that currently exist in the trie)
+///   -wordCount (the number of words in the trie)
+public class Trie {
+  private var root = Node(character: "", parent: nil)
+  private(set) var wordList: [String] = []
+  private(set) var wordCount = 0
+  
+  init(words: Set<String>) {
+    words.forEach { insert(word: $0) }
+  }
+  
+  /// Merge two `Trie` objects into one and returns the merged `Trie`
+  ///
+  /// - parameter other: Another `Trie`
+  ///
+  /// - returns: The newly unioned `Trie`.
+  func merge(other: Trie) -> Trie {
+    let newWordList = Set(wordList + other.wordList)
+    return Trie(words: newWordList)
+  }
+  
+  /// Looks for a specific key and returns a tuple that has a reference to the node (if found) and true/false depending on if it was found.
+  ///
+  /// - parameter key: A `String` that you would like to find.
+  ///
+  /// - returns: A tuple containing the an optional `Node`. If the key is found, it will return a non-nil `Node`. The second part of the tuple contains a bool indicating whether it was found or not.
+  func find(key: String) -> (node: Node?, found: Bool) {
+    var currentNode = root
+    
+    for character in key.characters {
+      if currentNode.children["\(character)"] == nil {
+        return (nil, false)
+      }
+      currentNode = currentNode.children["\(character)"]!
+    }
+    return (currentNode, currentNode.isValidWord)
+  }
+  
+  /// Returns true if the `Trie` is empty, false otherwise.
+  var isEmpty: Bool {
+    return wordCount == 0
+  }
+  
+  /// Checks if the a word is currently in the `Trie`.
+  ///
+  /// - parameter word: A `String` you want to check.
+  ///
+  /// - returns: Returns `true` if the word exists in the `Trie`. False otherwise.
+  func contains(word: String) -> Bool {
+    return find(key: word.lowercased()).found
+  }
+  
+  func isPrefix(_ prefix: String) -> (node: Node?, found: Bool) {
+    let prefix = prefix.lowercased()
+    var currentNode = root
+    
+    for character in prefix.characters {
+      if currentNode.children["\(character)"] == nil {
+        return (nil, false)
+      }
+      
+      currentNode = currentNode.children["\(character)"]!
+    }
+    
+    if currentNode.children.count > 0 {
+      return (currentNode, true)
+    }
+    
+    return (nil, false)
+  }
+  
+  /// Inserts a word into the trie. Returns a tuple containing the word attempted to tbe added, and true/false depending on whether or not the insertion was successful.
+  ///
+  /// - parameter word: A `String`.
+  ///
+  /// - returns: A tuple containing the word attempted to be added, and whether it was successful.
+  @discardableResult func insert(word: String) -> (word: String, inserted: Bool) {
+    let word = word.lowercased()
+    guard !contains(word: word), !word.isEmpty else { return (word, false) }
+    
+    var currentNode = root
+    var length = word.characters.count
+    
+    var index = 0
+    var character = word.characters.first!
+    
+    while let child = currentNode.children["\(character)"] {
+      currentNode = child
+      length -= 1
+      index += 1
+      
+      if length == 0 {
+        currentNode.isAWord = true
+        wordList.append(word)
+        wordCount += 1
+        return (word, true)
+      }
+      
+      character = Array(word.characters)[index]
+    }
+    
+    let remainingCharacters = String(word.characters.suffix(length))
+    for character in remainingCharacters.characters {
+      currentNode.children["\(character)"] = Node(character: "\(character)", parent: currentNode)
+      currentNode = currentNode.children["\(character)"]!
+    }
+    
+    currentNode.isAWord = true
+    wordList.append(word)
+    wordCount += 1
+    return (word, true)
+  }
+  
+  /// Attempts to insert all words from input array. Returns a tuple containing the input array and true if some of the words were successfully added, false if none were added.
+  ///
+  /// - parameter words: An array of `String` objects.
+  ///
+  /// - returns: A tuple stating whether all the words were inserted.
+  func insert(words: [String]) -> (wordList: [String], inserted: Bool) {
+    var successful: Bool = false
+    for word in wordList {
+      successful = insert(word: word).inserted || successful
+    }
+    
+    return (wordList, successful)
+  }
+  
+  /// Removes the specified key from the `Trie` if it exists, returns tuple containing the word attempted to be removed and true/false if the removal was successful.
+  ///
+  /// - parameter word: A `String` to be removed.
+  ///
+  /// - returns: A tuple containing the word to be removed, and a `Bool` indicating whether removal was successful or not.
+  @discardableResult func remove(word: String) -> (word: String, removed: Bool) {
+    let word = word.lowercased()
+    
+    guard contains(word: word) else { return (word, false) }
+    var currentNode = root
+    
+    for character in word.characters {
+      currentNode = currentNode.getChildAt(character: "\(character)")
+    }
+    
+    if currentNode.children.count > 0 {
+      currentNode.isAWord = false
+    } else {
+      var character = currentNode.character
+      while currentNode.children.count == 0 && !currentNode.isRoot {
+        currentNode = currentNode.parent!
+        currentNode.children[character]!.parent = nil
+        character = currentNode.character
+      }
+    }
+    
+    wordCount -= 1
+    
+    var index = 0
+    for item in wordList {
+      if item == word {
+        wordList.remove(at: index)
+      }
+      index += 1
+    }
+    
+    return (word, true)
+  }
+  
+  func find(prefix: String) -> [String] {
+    guard isPrefix(prefix).found else { return [] }
+    var queue = Queue<Node>()
+    let node = isPrefix(prefix).node!
+    
+    var wordsWithPrefix: [String] = []
+    let word = prefix
+    var tmp = ""
+    queue.enqueue(element: node)
+    
+    while let current = queue.dequeue() {
+      for (_, child) in current.children {
+        if !child.visited {
+          queue.enqueue(element: child)
+          child.visited = true
+          if child.isValidWord {
+            var currentNode = child
+            while currentNode !== node {
+              tmp += currentNode.character
+              currentNode = currentNode.parent!
+            }
+            tmp = "\(tmp.characters.reversed())"
+            wordsWithPrefix.append(word + tmp)
+            tmp = ""
+          }
+        }
+      }
+    }
+    
+    return wordsWithPrefix
+  }
+  
+  func removeAll() {
+    for word in wordList {
+      remove(word: word)
+    }
+  }
+}
+
+extension Trie: CustomStringConvertible {
+  public var description: String {
+    return ""
+  }
+}
diff --git a/Trie/Trie.playground/contents.xcplayground b/Trie/Trie.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Trie/Trie.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata b/Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 1da1118e1ff00d21ae02025c5a222631925d2e55 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Mon, 12 Sep 2016 08:28:58 -0700
Subject: [PATCH 0517/1679] Refactored implementation of Trie. Leaving the old
 implementation in a folder for future reference.

---
 Trie/{ => Old Implementation}/trie.swift |   0
 Trie/Trie.playground/Contents.swift      |  16 ++
 Trie/Trie.playground/Sources/Node.swift  |  71 ++-----
 Trie/Trie.playground/Sources/Queue.swift |  31 ---
 Trie/Trie.playground/Sources/Trie.swift  | 229 +++++------------------
 5 files changed, 80 insertions(+), 267 deletions(-)
 rename Trie/{ => Old Implementation}/trie.swift (100%)
 delete mode 100644 Trie/Trie.playground/Sources/Queue.swift

diff --git a/Trie/trie.swift b/Trie/Old Implementation/trie.swift
similarity index 100%
rename from Trie/trie.swift
rename to Trie/Old Implementation/trie.swift
diff --git a/Trie/Trie.playground/Contents.swift b/Trie/Trie.playground/Contents.swift
index e69de29bb..89a160c8d 100644
--- a/Trie/Trie.playground/Contents.swift
+++ b/Trie/Trie.playground/Contents.swift
@@ -0,0 +1,16 @@
+let trie = Trie()
+
+trie.insert(word: "apple")
+trie.insert(word: "ap")
+trie.insert(word: "a")
+
+trie.contains(word: "apple")
+trie.contains(word: "ap")
+trie.contains(word: "a")
+
+trie.remove(word: "apple")
+trie.contains(word: "a")
+trie.contains(word: "apple")
+
+trie.insert(word: "apple")
+trie.contains(word: "apple")
diff --git a/Trie/Trie.playground/Sources/Node.swift b/Trie/Trie.playground/Sources/Node.swift
index 72600af2f..56faed3e5 100644
--- a/Trie/Trie.playground/Sources/Node.swift
+++ b/Trie/Trie.playground/Sources/Node.swift
@@ -1,64 +1,21 @@
-/// A Trie (prefix tree)
-///
-/// Some of the functionality of the trie makes use of the Queue implementation for this project
-///
-/// Every node in the Trie stores a bit of information pertaining to what it references:
-///   -Character (letter of an inserted word)
-///   -Parent (Letter that comes before the current letter in some word)
-///   -Children (Words that have more letters than available in the prefix)
-///   -isAWord (Does the current letter mark the end of a known inserted word?)
-///   -visited (Mainly for the findPrefix() function)
-public class Node {
-  public var character: String
-  public var parent: Node?
-  public var children: [String: Node]
-  public var isAWord: Bool
-  public var visited: Bool // only for findPrefix
+public final class TrieNode<T: Hashable> {
+  public var value: T?
+  public weak var parent: TrieNode?
+  public var children: [T: TrieNode] = [:]
+  public var isTerminating = false
   
-  init(character: String, parent: Node?) {
-    self.character = character
-    self.children = [:]
-    self.isAWord = false
-    self.parent = parent
-    self.visited = false
-  }
-  
-  /// Returns `true` if the node is a leaf node, false otherwise.
-  var isLeaf: Bool {
-    return children.count == 0
-  }
-  
-  /// Changes the parent of the current node to the passed in node.
-  ///
-  /// - parameter node: A `Node` object.
-  func setParent(node: Node) {
-    parent = node
-  }
+  init() {}
   
-  /// Returns the child node that holds the specific passed letter.
-  ///
-  /// - parameter character: A `String`
-  ///
-  /// - returns: The `Node` object that contains the `character`.
-  func getChildAt(character: String) -> Node {
-    return children[character]!
-  }
-  
-  /// Returns whether or not the current node marks the end of a valid word.
-  var isValidWord: Bool {
-    return isAWord
-  }
-  
-  
-  /// Returns whether or not the current node is the root of the trie.
-  var isRoot: Bool {
-    return character == ""
+  init(value: T, parent: TrieNode? = nil) {
+    self.value = value
+    self.parent = parent
   }
 }
 
-// MARK: - CustomStringConvertible
-extension Node: CustomStringConvertible {
-  public var description: String {
-    return ""
+// MARK: - Insertion
+public extension TrieNode {
+  func add(child: T) {
+    guard children[child] == nil else { return }
+    children[child] = TrieNode(value: child, parent: self)
   }
 }
diff --git a/Trie/Trie.playground/Sources/Queue.swift b/Trie/Trie.playground/Sources/Queue.swift
deleted file mode 100644
index 81bde190a..000000000
--- a/Trie/Trie.playground/Sources/Queue.swift
+++ /dev/null
@@ -1,31 +0,0 @@
-/// Queue implementation taken from the repository.
-public struct Queue<T> {
-  private var array: [T?] = []
-  private var head = 0
-  
-  public var isEmpty: Bool {
-    return count == 0
-  }
-  
-  public var count: Int {
-    return array.count - head
-  }
-  
-  public mutating func enqueue(element: T) {
-    array.append(element)
-  }
-  
-  public mutating func dequeue() -> T? {
-    guard head < array.count, let element = array[head] else { return nil }
-    array[head] = nil
-    head += 1
-    
-    let percentage = Double(head) / Double(array.count)
-    if array.count > 50 && percentage > 0.25 {
-      array.removeFirst(head)
-      head = 0
-    }
-    
-    return element
-  }
-}
diff --git a/Trie/Trie.playground/Sources/Trie.swift b/Trie/Trie.playground/Sources/Trie.swift
index 053bd7113..ddce0ba84 100644
--- a/Trie/Trie.playground/Sources/Trie.swift
+++ b/Trie/Trie.playground/Sources/Trie.swift
@@ -2,211 +2,82 @@
 ///   -root (the root of the trie)
 ///   -wordList (the words that currently exist in the trie)
 ///   -wordCount (the number of words in the trie)
-public class Trie {
-  private var root = Node(character: "", parent: nil)
-  private(set) var wordList: [String] = []
-  private(set) var wordCount = 0
+public final class Trie {
+  typealias Node = TrieNode<Character>
+  fileprivate let root: Node
   
-  init(words: Set<String>) {
-    words.forEach { insert(word: $0) }
+  public init() {
+    root = TrieNode<Character>()
   }
-  
-  /// Merge two `Trie` objects into one and returns the merged `Trie`
-  ///
-  /// - parameter other: Another `Trie`
-  ///
-  /// - returns: The newly unioned `Trie`.
-  func merge(other: Trie) -> Trie {
-    let newWordList = Set(wordList + other.wordList)
-    return Trie(words: newWordList)
-  }
-  
-  /// Looks for a specific key and returns a tuple that has a reference to the node (if found) and true/false depending on if it was found.
-  ///
-  /// - parameter key: A `String` that you would like to find.
-  ///
-  /// - returns: A tuple containing the an optional `Node`. If the key is found, it will return a non-nil `Node`. The second part of the tuple contains a bool indicating whether it was found or not.
-  func find(key: String) -> (node: Node?, found: Bool) {
+}
+
+// MARK: - Basic Methods
+public extension Trie {
+  func insert(word: String) {
+    guard !word.isEmpty else { return }
     var currentNode = root
     
-    for character in key.characters {
-      if currentNode.children["\(character)"] == nil {
-        return (nil, false)
-      }
-      currentNode = currentNode.children["\(character)"]!
-    }
-    return (currentNode, currentNode.isValidWord)
-  }
-  
-  /// Returns true if the `Trie` is empty, false otherwise.
-  var isEmpty: Bool {
-    return wordCount == 0
-  }
-  
-  /// Checks if the a word is currently in the `Trie`.
-  ///
-  /// - parameter word: A `String` you want to check.
-  ///
-  /// - returns: Returns `true` if the word exists in the `Trie`. False otherwise.
-  func contains(word: String) -> Bool {
-    return find(key: word.lowercased()).found
-  }
-  
-  func isPrefix(_ prefix: String) -> (node: Node?, found: Bool) {
-    let prefix = prefix.lowercased()
-    var currentNode = root
+    var characters = Array(word.lowercased().characters)
+    var currentIndex = 0
     
-    for character in prefix.characters {
-      if currentNode.children["\(character)"] == nil {
-        return (nil, false)
+    while currentIndex < characters.count {
+      let character = characters[currentIndex]
+      if let child = currentNode.children[character] {
+        currentNode = child
+      } else {
+        currentNode.add(child: character)
+        currentNode = currentNode.children[character]!
       }
       
-      currentNode = currentNode.children["\(character)"]!
-    }
-    
-    if currentNode.children.count > 0 {
-      return (currentNode, true)
+      currentIndex += 1
+      if currentIndex == characters.count {
+        currentNode.isTerminating = true
+      }
     }
-    
-    return (nil, false)
   }
   
-  /// Inserts a word into the trie. Returns a tuple containing the word attempted to tbe added, and true/false depending on whether or not the insertion was successful.
-  ///
-  /// - parameter word: A `String`.
-  ///
-  /// - returns: A tuple containing the word attempted to be added, and whether it was successful.
-  @discardableResult func insert(word: String) -> (word: String, inserted: Bool) {
-    let word = word.lowercased()
-    guard !contains(word: word), !word.isEmpty else { return (word, false) }
-    
+  func contains(word: String) -> Bool {
+    guard !word.isEmpty else { return false }
     var currentNode = root
-    var length = word.characters.count
     
-    var index = 0
-    var character = word.characters.first!
+    var characters = Array(word.lowercased().characters)
+    var currentIndex = 0
     
-    while let child = currentNode.children["\(character)"] {
+    while currentIndex < characters.count, let child = currentNode.children[characters[currentIndex]] {
       currentNode = child
-      length -= 1
-      index += 1
-      
-      if length == 0 {
-        currentNode.isAWord = true
-        wordList.append(word)
-        wordCount += 1
-        return (word, true)
-      }
-      
-      character = Array(word.characters)[index]
-    }
-    
-    let remainingCharacters = String(word.characters.suffix(length))
-    for character in remainingCharacters.characters {
-      currentNode.children["\(character)"] = Node(character: "\(character)", parent: currentNode)
-      currentNode = currentNode.children["\(character)"]!
+      currentIndex += 1
     }
     
-    currentNode.isAWord = true
-    wordList.append(word)
-    wordCount += 1
-    return (word, true)
-  }
-  
-  /// Attempts to insert all words from input array. Returns a tuple containing the input array and true if some of the words were successfully added, false if none were added.
-  ///
-  /// - parameter words: An array of `String` objects.
-  ///
-  /// - returns: A tuple stating whether all the words were inserted.
-  func insert(words: [String]) -> (wordList: [String], inserted: Bool) {
-    var successful: Bool = false
-    for word in wordList {
-      successful = insert(word: word).inserted || successful
+    if currentIndex == characters.count && currentNode.isTerminating {
+      return true
+    } else {
+      return false
     }
-    
-    return (wordList, successful)
   }
   
-  /// Removes the specified key from the `Trie` if it exists, returns tuple containing the word attempted to be removed and true/false if the removal was successful.
-  ///
-  /// - parameter word: A `String` to be removed.
-  ///
-  /// - returns: A tuple containing the word to be removed, and a `Bool` indicating whether removal was successful or not.
-  @discardableResult func remove(word: String) -> (word: String, removed: Bool) {
-    let word = word.lowercased()
-    
-    guard contains(word: word) else { return (word, false) }
+  func remove(word: String) {
+    guard !word.isEmpty else { return }
     var currentNode = root
     
-    for character in word.characters {
-      currentNode = currentNode.getChildAt(character: "\(character)")
+    var characters = Array(word.lowercased().characters)
+    var currentIndex = 0
+    
+    while currentIndex < characters.count {
+      let character = characters[currentIndex]
+      guard let child = currentNode.children[character] else { return }
+      currentNode = child
+      currentIndex += 1
     }
     
     if currentNode.children.count > 0 {
-      currentNode.isAWord = false
+      currentNode.isTerminating = false
     } else {
-      var character = currentNode.character
-      while currentNode.children.count == 0 && !currentNode.isRoot {
-        currentNode = currentNode.parent!
-        currentNode.children[character]!.parent = nil
-        character = currentNode.character
-      }
-    }
-    
-    wordCount -= 1
-    
-    var index = 0
-    for item in wordList {
-      if item == word {
-        wordList.remove(at: index)
-      }
-      index += 1
-    }
-    
-    return (word, true)
-  }
-  
-  func find(prefix: String) -> [String] {
-    guard isPrefix(prefix).found else { return [] }
-    var queue = Queue<Node>()
-    let node = isPrefix(prefix).node!
-    
-    var wordsWithPrefix: [String] = []
-    let word = prefix
-    var tmp = ""
-    queue.enqueue(element: node)
-    
-    while let current = queue.dequeue() {
-      for (_, child) in current.children {
-        if !child.visited {
-          queue.enqueue(element: child)
-          child.visited = true
-          if child.isValidWord {
-            var currentNode = child
-            while currentNode !== node {
-              tmp += currentNode.character
-              currentNode = currentNode.parent!
-            }
-            tmp = "\(tmp.characters.reversed())"
-            wordsWithPrefix.append(word + tmp)
-            tmp = ""
-          }
-        }
+      var character = currentNode.value
+      while currentNode.children.count == 0, let parent = currentNode.parent, !parent.isTerminating {
+        currentNode = parent
+        currentNode.children[character!] = nil
+        character = currentNode.value
       }
     }
-    
-    return wordsWithPrefix
-  }
-  
-  func removeAll() {
-    for word in wordList {
-      remove(word: word)
-    }
-  }
-}
-
-extension Trie: CustomStringConvertible {
-  public var description: String {
-    return ""
   }
 }

From 931e85bfb6d6fee122451840ea7cd044dd895763 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Mon, 12 Sep 2016 13:48:25 -0700
Subject: [PATCH 0518/1679] Refactored README fileg

---
 Trie/ReadMe.md       | 294 ++++++++++++++++++-------------------------
 Trie/images/trie.png | Bin 0 -> 174737 bytes
 2 files changed, 119 insertions(+), 175 deletions(-)
 create mode 100644 Trie/images/trie.png

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 844eb1df0..a1cd7757b 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,220 +1,164 @@
 # Trie
 
-##What is a Trie?
-A trie (also known as a prefix tree, or radix tree in some other (but different) implementations) is a special type of tree used to store associative data structures where the key item is normally of type String.  Each node in the trie is typically not associated with a value containing strictly itself, but more so is linked to some common prefix that precedes it in levels above it.  Oftentimes, true key-value pairs are associated with the leaves of the trie, but they are not limited to this.
+## What is a Trie?
 
-##Why a Trie?
-Tries are very useful simply for the fact that it has some advantages over other data structures, like the binary tree or a hash map.  These advantages include:
-* Looking up keys is typically faster in the worst case when compared to other data structures.
-* Unlike a hash map, a trie need not worry about key collisions
-* No need for hasing, as each key will have a unique path in the trie
-* Tries, by implementation, can be by default alphabetically ordered.
+A `Trie`, (also known as a prefix tree, or radix tree in some other implementations) is a special type of tree used to store associative data structures. A `Trie` for a dictionary might look like this:
 
+![A Trie](Images/trie.png)
 
-##Common Algorithms
+Storing the English language is a primary use case for a `Trie`. Each node in the `Trie` would representing a single character of a word. A series of nodes then make up a word.
 
-###Find (or any general lookup function)
-Tries make looking up keys a trivial task, as all one has to do is walk over the nodes until we either hit a null reference or we find the key in question.
+## Why a Trie?
 
-The algorithm would be as follows:
-```
-  let node be the root of the trie
-  
-  for each character in the key
-    if the child of node with value character is null
-      return false (key doesn't exist in trie)
-    else
-      node = child of node with value character  (move to the next node)
-  return true (key exists in trie and was found
-```
+Tries are very useful for certain situations. Here are some of the advantages:
 
-And in swift:
-```swift
-func find(key: String) -> (node: Node?, found: Bool) {
-    var currentNode = self.root
-
-    for c in key.characters {
-      if currentNode.children[String(c)] == nil {
-        return(nil, false)
-      }
-      currentNode = currentNode.children[String(c)]!
-    }
+* Looking up values typically have a better worst-case time complexity.
+* Unlike a hash map, a `Trie` does not need to worry about key collisions.
+* Doesn't utilize hashing to guarantee a unique path to elements.
+* `Trie` structures can be alphabetically ordered by default.
 
-    return(currentNode, currentNode.isValidWord())
-  }
-```
+## Common Algorithms
 
-###Insertion
-Insertion is also a trivial task with a Trie, as all one needs to do is walk over the nodes until we either halt on a node that we must mark as a key, or we reach a point where we need to add extra nodes to represent it.
+### Contains (or any general lookup method)
 
-Let's walk through the algorithm:
+`Trie` structures are great for lookup operations. For `Trie` structures that model the English language, finding a particular word is a matter of a few pointer traversals:
 
-```
-  let S be the root node of our tree
-  let word be the input key
-  let length be the length of the key
-  
+```swift
+func contains(word: String) -> Bool {
+	guard !word.isEmpty else { return false }
+
+	// 1
+	var currentNode = root
   
-  find(word)
-  if the word was found
-    return false
-  else
-    
-    for each character in word
-      if child node with value character does not exist
-        break
-      else
-        node = child node with value character
-        decrement length
-      
-    if length != 0
-      let suffix be the remaining characters in the key defined by the shortened length
-      
-      for each character in suffix
-        create a new node with value character and let it be the child of node
-        node = newly created child now
-      mark node as a valid key
-    else
-      mark node as valid key
+  // 2
+	var characters = Array(word.lowercased().characters)
+	var currentIndex = 0
+ 
+  // 3
+	while currentIndex < characters.count, 
+	  let child = currentNode.children[character[currentIndex]] {
+
+	  currentNode = child
+	  currentIndex += 1
+	}
+
+  // 4
+	if currentIndex == characters.count && currentNode.isTerminating {
+	  return true
+	} else {
+		return false
+	}
+}
 ```
 
-And the corresponding swift code:
+The `contains` method is fairly straightforward:
 
-```swift
-  func insert(w: String) -> (word: String, inserted: Bool) {
-
-    let word = w.lowercaseString
-    var currentNode = self.root
-    var length = word.characters.count
+1. Create a reference to the `root`. This reference will allow you to walk down a chain of nodes.
+2. Keep track of the characters of the word you're trying to match.
+3. Walk the pointer down the nodes.
+4. `isTerminating` is a boolean flag for whether or not this node is the end of a word. If this `if` condition is satisfied, it means you are able to find the word in the `trie`.
 
-    if self.contains(word) {
-      return (w, false)
-    }
+### Insertion
 
-    var index = 0
-    var c = Array(word.characters)[index]
+Insertion into a `Trie` requires you to walk over the nodes until you either halt on a node that must be marked as `terminating`, or reach a point where you need to add extra nodes.
 
-    while let child = currentNode.children[String(c)] {
-      currentNode = child
-      length -= 1
-      index += 1
+```swift
+func insert(word: String) {
+  guard !word.isEmpty else { return }
 
-      if(length == 0) {
-        currentNode.isWord()
-        wordList.append(w)
-        wordCount += 1
-        return (w, true)
-      }
+  // 1
+  var currentNode = root
+  
+  // 2
+  var characters = Array(word.lowercased().characters)
+  var currentIndex = 0
+  
+  // 3
+  while currentIndex < characters.count {
+    let character = characters[currentIndex]
 
-      c = Array(word.characters)[index]
+    // 4
+    if let child = currentNode.children[character] {
+      currentNode = child
+    } else {
+      currentNode.add(child: character)
+      currentNode = currentNode.children[character]!
     }
+    
+    currentIndex += 1
 
-    let remainingChars = String(word.characters.suffix(length))
-    for c in remainingChars.characters {
-      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
-      currentNode = currentNode.children[String(c)]!
+    // 5
+    if currentIndex == characters.count {
+      currentNode.isTerminating = true
     }
-
-    currentNode.isWord()
-    wordList.append(w)
-    wordCount += 1
-    return (w, true)
   }
-
+}
 ```
 
-###Removal
-Removing keys from the trie is a little more tricky, as there a few more cases that we have to take into account the fact that keys may exist that are actually sub-strings of other valid keys.  That being said, it isn't as simple a process to just delete the nodes for a specific key, as we could be deleting references/nodes necessary for already exisitng keys!
+1. Once again, you create a reference to the root node. You'll move this reference down a chain of nodes.
+2. Keep track of the word you want to insert.
+3. Begin walking through your word letter by letter
+4. Sometimes, the required node to insert already exists. That is the case for two words inside the `Trie` that shares letters (i.e "Apple", "App"). If a letter already exists, you'll reuse it, and simply traverse deeper down the chain. Otherwise, you'll create a new node representing the letter.
+5. Once you get to the end, you mark `isTerminating` to true to mark that specific node as the end of a word.
 
-The algorithm would be as follows:
-
-```
-  
-  let word be the key to remove
-  let node be the root of the trie
-  
-  find(word)
-  if word was not found
-    return false
-  else
-  
-    for each character in word
-      node = child node with value character
-      
-      if node has more than just 1 child node
-        Mark node as an invalid key, since removing it would remove nodes still in use
-      else
-        while node has no valid children and node is not the root node
-          let character = node's value
-          node = the parent of node
-          delete node's child node with value character
-        return true
-```
+### Removal
 
+Removing keys from the trie is a little tricky, as there are a few more cases you'll need to take into account. Nodes in a `Trie` may be shared between different words. Consider the two words "Apple" and "App". Inside a `Trie`, the chain of nodes representing "App" is shared with "Apple". 
 
-
-and the corresponding swift code:
+If you'd like to remove "Apple", you'll need to take care to leave the "App" chain in tact.
 
 ```swift
-  func remove(w: String) -> (word: String, removed: Bool){
-    let word = w.lowercaseString
-
-    if(!self.contains(w)) {
-      return (w, false)
-    }
-    var currentNode = self.root
+func remove(word: String) {
+  guard !word.isEmpty else { return }
 
-    for c in word.characters {
-      currentNode = currentNode.getChildAt(String(c))
-    }
-
-    if currentNode.numChildren() > 0 {
-      currentNode.isNotWord()
-    } else {
-      var character = currentNode.char()
-      while(currentNode.numChildren() == 0 && !currentNode.isRoot()) {
-        currentNode = currentNode.getParent()
-        currentNode.children[character]!.setParent(nil)
-        currentNode.children[character]!.update(nil)
-        currentNode.children[character] = nil
-        character = currentNode.char()
-      }
-    }
-
-    wordCount -= 1
-
-    var index = 0
-    for item in wordList{
-      if item == w {
-        wordList.removeAtIndex(index)
-      }
-      index += 1
+  // 1
+  var currentNode = root
+  
+  // 2
+  var characters = Array(word.lowercased().characters)
+  var currentIndex = 0
+  
+  // 3
+  while currentIndex < characters.count {
+    let character = characters[currentIndex]
+    guard let child = currentNode.children[character] else { return }
+    currentNode = child
+    currentIndex += 1
+  }
+  
+  // 4
+  if currentNode.children.count > 0 {
+    currentNode.isTerminating = false
+  } else {
+    var character = currentNode.value
+    while currentNode.children.count == 0, let parent = currentNode.parent, !parent.isTerminating {
+      currentNode = parent
+      currentNode.children[character!] = nil
+      character = currentNode.value
     }
-
-    return (w, true)
   }
-
+}
 ```
 
+1. Once again, you create a reference to the root node.
+2. Keep track of the word you want to remove.
+3. Attempt to walk to the terminating node of the word. The `guard` statement will return if it can't find one of the letters; It's possible to call `remove` on a non-existant entry.
+4. If you reach the node representing the last letter of the word you want to remove, you'll have 2 cases to deal with. Either it's a leaf node, or it has more children. If it has more children, it means the node is used for other words. In that case, you'll just mark `isTerminating` to false. In the other case, you'll delete the nodes.
 
-###Running Times
+### Time Complexity
 
-Let n be the length of some key in the trie
+Let n be the length of some value in the `Trie`.
 
-* Find(...) : In the Worst case O(n)
-* Insert(...) :  O(n)
-* Remove(...) :  O(n)
+* `contains` - Worst case O(n)
+* `insert` - O(n)
+* `remove` - O(n)
 
-###Other Notable Operations
+### Other Notable Operations
 
-* Count:  Returns the number of keys in the trie ( O(1) )
-* getWords:  Returns a list containing all keys in the trie ( *O(1) )
-* isEmpty:  Returns true f the trie is empty, false otherwise ( *O(1) )
-* contains:  Returns true if the trie has a given key, false otherwise ( O(n) )
-
-`* denotes that running time may vary depending on implementation
+* `count`: Returns the number of keys in the `Trie` - O(1)
+* `words`: Returns a list containing all the keys in the `Trie` - O(1)
+* `isEmpty`: Returns `true` if the `Trie` is empty, `false` otherwise - O(1)
 
 See also [Wikipedia entry for Trie](https://en.wikipedia.org/wiki/Trie).
 
-*Written for the Swift Algorithm Club by Christian Encarnacion*
-
+*Written for the Swift Algorithm Club by Christian Encarnacion. Refactored by Kelvin Lau*
diff --git a/Trie/images/trie.png b/Trie/images/trie.png
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zgkA>`_^NjUE$+SLqLA}Vq`1RVBM!a}FnYA$soGpfamn%YFK0FK`50dwr2;S0&r6Xr
z$FEpc3Jh2Ri5~%*iX`s=55l0T6N>Zbv`g`g$*vkam<)VP<B?r4s!1vS6Uh4yZTD_y
zY?MhDRJwVc+-TpFY>WOWZK3`{)4TqzKIr$rb#Vztli}`)`ysj5MBzK+*P#_paS#9-
zI}TTl#8d(ES4Th5=~?$?85FVIZn3or>B1Ji8i|r&YhF-@O;(z+FOKgj$+B3WcIH_7
z_th7Zf>&QPE!`WJ3jH7zCan(Iw+<tXQyxSuWaYrccIs_t+=`rf3#)4_$CFy)yuu{+
z%(s}0OaD;p@Z36xKdwv_SXdD5l>LC;FdH>Tw@)DT3xGAelO@(KReH0P<Hn+#=spY$
zb!J5^=^H@?%Y>g*%QI2%sh->z2e|zSucrfwH$zz8sn6Zt9>|<da!pYQdHwnx+9k*K
znUYgSd)A#cDV3k|0kM$E*WB{R_L+FDl-!yBfp-V4xl&Ks)%U66?rEQxaIYztxoET|
zGptYu(mowhNvtTjJ$ru7=5ArAyN%(2fkCjn&1JTZxroY~zwV!~0bs>3i&(wIt&d4q
z!%Q#HJ~n<S@nEjkDq?2Uv;gK1h_rLj5&OQkNH%@toaWyzpj#{HbltC3`^N1`R|4n^
z*8W*-8HNE(0C@De+h~2zgYvc+7WoCCwq&y7ax&fZp!Chh_wWCGE%>CV-vo9&Ix4z7
zLg|9+n7jn;$qikOb22oUOzl;sMdynEx_TE9VuGBQ5%tG^Tp~TE6tj8#@ZWWsFDV?o
zIMaZ@Q`_&v)_Q1cFS$!95(O;0*JsEe?*L;U10Z{(L9JK`q?|8@N9wmhvYl%aj(}Ul
zw0c5&9rp=Unrl@mbF3z$f(5XqjFt|(4?+%8tJ?mNd&xOEvqF@Jv!ihy2%vnR!x2et
zt)2LI`JZD(e;AU%-Qy2&L`FA1n9QugxLP05O*2pjBU9xh0-<1PLo1b_-k0EFI)iIY
z{-kRP4fq#^R~xn_XaJwFhc!*KqrL%_>Aok6QQGWCv6n6VZkSQ1oC9`d?fw<@#{sLP
zG-G{n<ezu69KEA^V)$?m_Kiewiiyg^B7|&JAh~qRJF?G<1t-wC00z+MLjsaEO@$w9
z@>4|pxW}}Etx{eC+#{)HwMgv9*?uwHr*6v!>NY*(&J{ozX*jJ|vxo`>AnV#^UFjfd
zp5a!#?*8Wo;a(NtdBosxdSH*M+vwv64{@ju|84=B(8!NWh6mrwW}avH>jcuX!sW}~
zi;~~Id}vBdgv|P$sI>`#M-VbRRk-<~X;s2bEszR#61JZ#1vT8k*whAQ+^2C2zJY-c
zk+s2#7kk;{Bg906&hqd~9{#fZTXt@mS2Wac7pxv`Gd@q#T!Lw5&^?&&zHy9}{^vR4
zxmm#J3B`DE@AR@nyOInLbd6Yh+{{I9c2jBnQzS+{fiIBk&^?2r83F?iadr`;2zZNF
z%x+a2=D2g;|KEVk??%ux--|TE5J(U_3S0opBkSs_ZTfl*(FWBN1iXR1j>x(!4)L|8
z+5#b?Rgdd_d`L7m_By3<lQ+!@mhz!dQz`W0=>NZ4p1$PrgU9$k?FIj(4S{z8Y(HeH
ztbCZ`&d>S4{gTM7Ne3-Z$@1xL`a6g)i^_rrb2r#3_{>5bE)(#GU<BIxW^M8Vh{7Z7
z42jh>ci7#~5`4f9U_7_h^8<4ZSRtqGfm7dF_SN#p!D0rQWE_AVWH8JGUM7m%4@L^E
zQqXda@Ar(0aVTJDWB{sQKC%Qgp&?9QXuJY!ANk*{K7R(S+kvo=Nd(v|5tzITA%eyV
z3J2C(rSENx(U!#{2EI4~fGQk(W;r3*jN&N|P#JJ#?|10@8H(I!V4#IJFrSR33`9y&
caA^F`e#~HF)@`jl{0u<g>FVdQ&MBb@07dCJ3;+NC

literal 0
HcmV?d00001


From b563b932f903c732790f2e363a7e294483e4665b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Mon, 12 Sep 2016 13:51:20 -0700
Subject: [PATCH 0519/1679] Fixed spacing

---
 Trie/ReadMe.md | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index a1cd7757b..ee101a0a9 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -30,11 +30,11 @@ func contains(word: String) -> Bool {
 	// 1
 	var currentNode = root
   
-  // 2
+	// 2
 	var characters = Array(word.lowercased().characters)
 	var currentIndex = 0
  
-  // 3
+	// 3
 	while currentIndex < characters.count, 
 	  let child = currentNode.children[character[currentIndex]] {
 
@@ -42,7 +42,7 @@ func contains(word: String) -> Bool {
 	  currentIndex += 1
 	}
 
-  // 4
+	// 4
 	if currentIndex == characters.count && currentNode.isTerminating {
 	  return true
 	} else {
@@ -69,15 +69,15 @@ func insert(word: String) {
   // 1
   var currentNode = root
   
-  // 2
+	// 2
   var characters = Array(word.lowercased().characters)
   var currentIndex = 0
   
-  // 3
+	// 3
   while currentIndex < characters.count {
     let character = characters[currentIndex]
 
-    // 4
+		// 4
     if let child = currentNode.children[character] {
       currentNode = child
     } else {
@@ -87,7 +87,7 @@ func insert(word: String) {
     
     currentIndex += 1
 
-    // 5
+		// 5
     if currentIndex == characters.count {
       currentNode.isTerminating = true
     }
@@ -111,14 +111,14 @@ If you'd like to remove "Apple", you'll need to take care to leave the "App" cha
 func remove(word: String) {
   guard !word.isEmpty else { return }
 
-  // 1
+	// 1
   var currentNode = root
   
-  // 2
+	// 2
   var characters = Array(word.lowercased().characters)
   var currentIndex = 0
   
-  // 3
+	// 3
   while currentIndex < characters.count {
     let character = characters[currentIndex]
     guard let child = currentNode.children[character] else { return }
@@ -126,7 +126,7 @@ func remove(word: String) {
     currentIndex += 1
   }
   
-  // 4
+	// 4
   if currentNode.children.count > 0 {
     currentNode.isTerminating = false
   } else {

From 0faf88a574d5ea8c923819c63cd394eb503eeecb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Mon, 12 Sep 2016 13:51:49 -0700
Subject: [PATCH 0520/1679] Fixed a typo.

---
 Trie/ReadMe.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index ee101a0a9..3e3dad3a6 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -4,7 +4,7 @@
 
 A `Trie`, (also known as a prefix tree, or radix tree in some other implementations) is a special type of tree used to store associative data structures. A `Trie` for a dictionary might look like this:
 
-![A Trie](Images/trie.png)
+![A Trie](images/trie.png)
 
 Storing the English language is a primary use case for a `Trie`. Each node in the `Trie` would representing a single character of a word. A series of nodes then make up a word.
 

From 8035d8dccf919099ae581ef899ed5558fce938b1 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Mon, 12 Sep 2016 18:03:20 -0700
Subject: [PATCH 0521/1679] Init & Claim Karatsuba Multiplication Algorithm

---
 Karatsuba Multiplication/KaratsubaMultiplication.swift | 9 +++++++++
 Karatsuba Multiplication/README.markdown               | 8 ++++++++
 2 files changed, 17 insertions(+)
 create mode 100644 Karatsuba Multiplication/KaratsubaMultiplication.swift
 create mode 100644 Karatsuba Multiplication/README.markdown

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
new file mode 100644
index 000000000..725b87939
--- /dev/null
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -0,0 +1,9 @@
+//
+//  KaratsubaMultiplication.swift
+//  
+//
+//  Created by Richard Ash on 9/12/16.
+//
+//
+
+import Foundation
diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
new file mode 100644
index 000000000..0afd91b0c
--- /dev/null
+++ b/Karatsuba Multiplication/README.markdown	
@@ -0,0 +1,8 @@
+# Karatsuba Multiplication
+
+TODO: Explanation/Examples
+
+
+
+
+*Written for Swift Algorithm Club by Richard Ash*

From b6c05be12875e17e1734b4438eb9e72869aeb228 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Mon, 12 Sep 2016 18:04:23 -0700
Subject: [PATCH 0522/1679] Added implmentation for the Karatsuba Algorithm

---
 .../Contents.swift                            | 57 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 .../contents.xcworkspacedata                  |  7 +++
 .../KaratsubaMultiplication.swift             | 25 ++++++++
 4 files changed, 93 insertions(+)
 create mode 100644 Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
 create mode 100644 Karatsuba Multiplication/KaratsubaMultiplication.playground/contents.xcplayground
 create mode 100644 Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
new file mode 100644
index 000000000..bf4454956
--- /dev/null
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -0,0 +1,57 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+infix operator ^^ { associativity left precedence 160 }
+func ^^ (radix: Int, power: Int) -> Int {
+  return Int(pow(Double(radix), Double(power)))
+}
+
+// Long Multiplication - O(n^2)
+func multiply(num1: Int, _ num2: Int, base: Int = 10) -> Int {
+  let num1Array = String(num1).characters.reverse().map{ Int(String($0))! }
+  let num2Array = String(num2).characters.reverse().map{ Int(String($0))! }
+  
+  var product = Array(count: num1Array.count + num2Array.count, repeatedValue: 0)
+
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
+    }
+    product[i + num2Array.count] += carry
+  }
+  
+  return Int(product.reverse().map{ String($0) }.reduce("", combine: +))!
+}
+
+// Karatsuba Multiplication - O(nlogn)
+func karatsuba(num1: Int, _ num2: Int) -> Int {
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return multiply(num1, num2)
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, c)
+  let bd = karatsuba(b, d)
+  let adPluscd = karatsuba(a+b, c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
+  
+  return product
+}
+
+print(multiply(236742342, 1231234224))
+print(karatsuba(236742342, 1231234224))
\ No newline at end of file
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/contents.xcplayground b/Karatsuba Multiplication/KaratsubaMultiplication.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata b/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index 725b87939..a315d7494 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -7,3 +7,28 @@
 //
 
 import Foundation
+
+func karatsuba(num1: Int, _ num2: Int) -> Int {
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return num1 * num2
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, c)
+  let bd = karatsuba(b, d)
+  let adPluscd = karatsuba(a+b, c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
+  
+  return product
+}
\ No newline at end of file

From 8d03fea237fb50ab1420dcd1614dfb903e5629e7 Mon Sep 17 00:00:00 2001
From: Tulio Troncoso <tuliot@live.com>
Date: Tue, 13 Sep 2016 16:33:55 -0400
Subject: [PATCH 0523/1679] Updated Linked List playground to swift 3

---
 .../LinkedList.playground/Contents.swift      | 40 +++++++++----------
 1 file changed, 20 insertions(+), 20 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index cc7ed3d59..5c05c1a3e 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -13,7 +13,7 @@ public class LinkedListNode<T> {
 public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
-  private var head: Node?
+  fileprivate var head: Node?
 
   public var isEmpty: Bool {
     return head == nil
@@ -61,7 +61,7 @@ public class LinkedList<T> {
   }
 
   public subscript(index: Int) -> T {
-    let node = nodeAtIndex(index)
+    let node = nodeAtIndex(index: index)
     assert(node != nil)
     return node!.value
   }
@@ -94,7 +94,7 @@ public class LinkedList<T> {
   }
 
   public func insert(value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index)
+    let (prev, next) = nodesBeforeAndAfter(index: index)
 
     let newNode = Node(value: value)
     newNode.previous = prev
@@ -129,13 +129,13 @@ public class LinkedList<T> {
 
   public func removeLast() -> T {
     assert(!isEmpty)
-    return removeNode(last!)
+    return removeNode(node: last!)
   }
 
   public func removeAtIndex(index: Int) -> T {
-    let node = nodeAtIndex(index)
+    let node = nodeAtIndex(index: index)
     assert(node != nil)
-    return removeNode(node!)
+    return removeNode(node: node!)
   }
 }
 
@@ -164,22 +164,22 @@ extension LinkedList {
 }
 
 extension LinkedList {
-  public func map<U>(transform: T -> U) -> LinkedList<U> {
+  public func map<U>(transform: (T) -> U) -> LinkedList<U> {
     let result = LinkedList<U>()
     var node = head
     while node != nil {
-      result.append(transform(node!.value))
+      result.append(value: transform(node!.value))
       node = node!.next
     }
     return result
   }
 
-  public func filter(predicate: T -> Bool) -> LinkedList<T> {
+  public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
     while node != nil {
       if predicate(node!.value) {
-        result.append(node!.value)
+        result.append(value: node!.value)
       }
       node = node!.next
     }
@@ -195,13 +195,13 @@ list.isEmpty                  // true
 list.first                    // nil
 list.last                     // nil
 
-list.append("Hello")
+list.append(value: "Hello")
 list.isEmpty
 list.first!.value             // "Hello"
 list.last!.value              // "Hello"
 list.count                    // 1
 
-list.append("World")
+list.append(value: "World")
 list.first!.value             // "Hello"
 list.last!.value              // "World"
 list.count                    // 2
@@ -211,15 +211,15 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.nodeAtIndex(0)!.value    // "Hello"
-list.nodeAtIndex(1)!.value    // "World"
-list.nodeAtIndex(2)           // nil
+list.nodeAtIndex(index: 0)!.value    // "Hello"
+list.nodeAtIndex(index: 1)!.value    // "World"
+list.nodeAtIndex(index: 2)           // nil
 
 list[0]     // "Hello"
 list[1]     // "World"
 //list[2]   // crash!
 
-list.insert("Swift", atIndex: 1)
+list.insert(value: "Swift", atIndex: 1)
 list[0]
 list[1]
 list[2]
@@ -227,8 +227,8 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.nodeAtIndex(0)!.value = "Universe"
-list.nodeAtIndex(1)!.value = "Swifty"
+list.nodeAtIndex(index: 0)!.value = "Universe"
+list.nodeAtIndex(index: 1)!.value = "Swifty"
 let m = list.map { s in s.characters.count }
 m    // [8, 6, 5]
 let f = list.filter { s in s.characters.count > 5 }
@@ -237,7 +237,7 @@ f    // [Universe, Swifty]
 //list.removeAll()
 //list.isEmpty
 
-list.removeNode(list.first!)   // "Hello"
+list.removeNode(node: list.first!)   // "Hello"
 list.count                     // 2
 list[0]                        // "Swift"
 list[1]                        // "World"
@@ -246,5 +246,5 @@ list.removeLast()              // "World"
 list.count                     // 1
 list[0]                        // "Swift"
 
-list.removeAtIndex(0)          // "Swift"
+list.removeAtIndex(index: 0)          // "Swift"
 list.count                     // 0

From 900811288a73e20e1c17c5b80d852f0c120b56f3 Mon Sep 17 00:00:00 2001
From: Tulio Troncoso <tuliot@live.com>
Date: Tue, 13 Sep 2016 16:48:40 -0400
Subject: [PATCH 0524/1679] Updated LinkedList.swift for Swift 3

---
 .../Sources/LinkedList.swift                  | 191 ++++++++++++++++++
 Linked List/LinkedList.swift                  |  20 +-
 2 files changed, 201 insertions(+), 10 deletions(-)
 create mode 100755 Linked List/LinkedList.playground/Sources/LinkedList.swift

diff --git a/Linked List/LinkedList.playground/Sources/LinkedList.swift b/Linked List/LinkedList.playground/Sources/LinkedList.swift
new file mode 100755
index 000000000..ef95a0b58
--- /dev/null
+++ b/Linked List/LinkedList.playground/Sources/LinkedList.swift	
@@ -0,0 +1,191 @@
+/*
+  Doubly-linked list
+
+  Most operations on the linked list have complexity O(n).
+*/
+public class LinkedListNode<T> {
+  var value: T
+  var next: LinkedListNode?
+  weak var previous: LinkedListNode?
+
+  public init(value: T) {
+    self.value = value
+  }
+}
+
+public class LinkedList<T> {
+  public typealias Node = LinkedListNode<T>
+
+  private var head: Node?
+
+  public var isEmpty: Bool {
+    return head == nil
+  }
+
+  public var first: Node? {
+    return head
+  }
+
+  public var last: Node? {
+    if var node = head {
+      while case let next? = node.next {
+        node = next
+      }
+      return node
+    } else {
+      return nil
+    }
+  }
+
+  public var count: Int {
+    if var node = head {
+      var c = 1
+      while case let next? = node.next {
+        node = next
+        c += 1
+      }
+      return c
+    } else {
+      return 0
+    }
+  }
+
+  public func nodeAtIndex(index: Int) -> Node? {
+    if index >= 0 {
+      var node = head
+      var i = index
+      while node != nil {
+        if i == 0 { return node }
+        i -= 1
+        node = node!.next
+      }
+    }
+    return nil
+  }
+
+  public subscript(index: Int) -> T {
+    let node = nodeAtIndex(index)
+    assert(node != nil)
+    return node!.value
+  }
+
+  public func append(value: T) {
+    let newNode = Node(value: value)
+    if let lastNode = last {
+      newNode.previous = lastNode
+      lastNode.next = newNode
+    } else {
+      head = newNode
+    }
+  }
+
+  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
+    assert(index >= 0)
+
+    var i = index
+    var next = head
+    var prev: Node?
+
+    while next != nil && i > 0 {
+      i -= 1
+      prev = next
+      next = next!.next
+    }
+    assert(i == 0)  // if > 0, then specified index was too large
+
+    return (prev, next)
+  }
+
+  public func insert(value: T, atIndex index: Int) {
+    let (prev, next) = nodesBeforeAndAfter(index)
+
+    let newNode = Node(value: value)
+    newNode.previous = prev
+    newNode.next = next
+    prev?.next = newNode
+    next?.previous = newNode
+
+    if prev == nil {
+      head = newNode
+    }
+  }
+
+  public func removeAll() {
+    head = nil
+  }
+
+  public func removeNode(node: Node) -> T {
+    let prev = node.previous
+    let next = node.next
+
+    if let prev = prev {
+      prev.next = next
+    } else {
+      head = next
+    }
+    next?.previous = prev
+
+    node.previous = nil
+    node.next = nil
+    return node.value
+  }
+
+  public func removeLast() -> T {
+    assert(!isEmpty)
+    return removeNode(last!)
+  }
+
+  public func removeAtIndex(index: Int) -> T {
+    let node = nodeAtIndex(index)
+    assert(node != nil)
+    return removeNode(node!)
+  }
+}
+
+extension LinkedList: CustomStringConvertible {
+  public var description: String {
+    var s = "["
+    var node = head
+    while node != nil {
+      s += "\(node!.value)"
+      node = node!.next
+      if node != nil { s += ", " }
+    }
+    return s + "]"
+  }
+}
+
+extension LinkedList {
+  public func reverse() {
+    var node = head
+    while let currentNode = node {
+      node = currentNode.next
+      swap(&currentNode.next, &currentNode.previous)
+      head = currentNode
+    }
+  }
+}
+
+extension LinkedList {
+  public func map<U>(transform: T -> U) -> LinkedList<U> {
+    let result = LinkedList<U>()
+    var node = head
+    while node != nil {
+      result.append(transform(node!.value))
+      node = node!.next
+    }
+    return result
+  }
+
+  public func filter(predicate: T -> Bool) -> LinkedList<T> {
+    let result = LinkedList<T>()
+    var node = head
+    while node != nil {
+      if predicate(node!.value) {
+        result.append(node!.value)
+      }
+      node = node!.next
+    }
+    return result
+  }
+}
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index ef95a0b58..336775c3c 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -16,7 +16,7 @@ public class LinkedListNode<T> {
 public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
-  private var head: Node?
+  fileprivate var head: Node?
 
   public var isEmpty: Bool {
     return head == nil
@@ -64,7 +64,7 @@ public class LinkedList<T> {
   }
 
   public subscript(index: Int) -> T {
-    let node = nodeAtIndex(index)
+    let node = nodeAtIndex(index: index)
     assert(node != nil)
     return node!.value
   }
@@ -97,7 +97,7 @@ public class LinkedList<T> {
   }
 
   public func insert(value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index)
+    let (prev, next) = nodesBeforeAndAfter(index: index)
 
     let newNode = Node(value: value)
     newNode.previous = prev
@@ -132,13 +132,13 @@ public class LinkedList<T> {
 
   public func removeLast() -> T {
     assert(!isEmpty)
-    return removeNode(last!)
+    return removeNode(node: last!)
   }
 
   public func removeAtIndex(index: Int) -> T {
-    let node = nodeAtIndex(index)
+    let node = nodeAtIndex(index: index)
     assert(node != nil)
-    return removeNode(node!)
+    return removeNode(node: node!)
   }
 }
 
@@ -167,22 +167,22 @@ extension LinkedList {
 }
 
 extension LinkedList {
-  public func map<U>(transform: T -> U) -> LinkedList<U> {
+  public func map<U>(transform: (T)-> U) -> LinkedList<U> {
     let result = LinkedList<U>()
     var node = head
     while node != nil {
-      result.append(transform(node!.value))
+        result.append(value: transform(node!.value))
       node = node!.next
     }
     return result
   }
 
-  public func filter(predicate: T -> Bool) -> LinkedList<T> {
+  public func filter(predicate: (T)-> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
     while node != nil {
       if predicate(node!.value) {
-        result.append(node!.value)
+        result.append(value: node!.value)
       }
       node = node!.next
     }

From bd5b4c0fbcf18adb32f698fcd0f68afee1a8232e Mon Sep 17 00:00:00 2001
From: Tulio Troncoso <tuliot@live.com>
Date: Tue, 13 Sep 2016 16:50:29 -0400
Subject: [PATCH 0525/1679] Removed LinkedList.swift from playground

It was added by mistake
---
 .../Sources/LinkedList.swift                  | 191 ------------------
 1 file changed, 191 deletions(-)
 delete mode 100755 Linked List/LinkedList.playground/Sources/LinkedList.swift

diff --git a/Linked List/LinkedList.playground/Sources/LinkedList.swift b/Linked List/LinkedList.playground/Sources/LinkedList.swift
deleted file mode 100755
index ef95a0b58..000000000
--- a/Linked List/LinkedList.playground/Sources/LinkedList.swift	
+++ /dev/null
@@ -1,191 +0,0 @@
-/*
-  Doubly-linked list
-
-  Most operations on the linked list have complexity O(n).
-*/
-public class LinkedListNode<T> {
-  var value: T
-  var next: LinkedListNode?
-  weak var previous: LinkedListNode?
-
-  public init(value: T) {
-    self.value = value
-  }
-}
-
-public class LinkedList<T> {
-  public typealias Node = LinkedListNode<T>
-
-  private var head: Node?
-
-  public var isEmpty: Bool {
-    return head == nil
-  }
-
-  public var first: Node? {
-    return head
-  }
-
-  public var last: Node? {
-    if var node = head {
-      while case let next? = node.next {
-        node = next
-      }
-      return node
-    } else {
-      return nil
-    }
-  }
-
-  public var count: Int {
-    if var node = head {
-      var c = 1
-      while case let next? = node.next {
-        node = next
-        c += 1
-      }
-      return c
-    } else {
-      return 0
-    }
-  }
-
-  public func nodeAtIndex(index: Int) -> Node? {
-    if index >= 0 {
-      var node = head
-      var i = index
-      while node != nil {
-        if i == 0 { return node }
-        i -= 1
-        node = node!.next
-      }
-    }
-    return nil
-  }
-
-  public subscript(index: Int) -> T {
-    let node = nodeAtIndex(index)
-    assert(node != nil)
-    return node!.value
-  }
-
-  public func append(value: T) {
-    let newNode = Node(value: value)
-    if let lastNode = last {
-      newNode.previous = lastNode
-      lastNode.next = newNode
-    } else {
-      head = newNode
-    }
-  }
-
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-    assert(index >= 0)
-
-    var i = index
-    var next = head
-    var prev: Node?
-
-    while next != nil && i > 0 {
-      i -= 1
-      prev = next
-      next = next!.next
-    }
-    assert(i == 0)  // if > 0, then specified index was too large
-
-    return (prev, next)
-  }
-
-  public func insert(value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index)
-
-    let newNode = Node(value: value)
-    newNode.previous = prev
-    newNode.next = next
-    prev?.next = newNode
-    next?.previous = newNode
-
-    if prev == nil {
-      head = newNode
-    }
-  }
-
-  public func removeAll() {
-    head = nil
-  }
-
-  public func removeNode(node: Node) -> T {
-    let prev = node.previous
-    let next = node.next
-
-    if let prev = prev {
-      prev.next = next
-    } else {
-      head = next
-    }
-    next?.previous = prev
-
-    node.previous = nil
-    node.next = nil
-    return node.value
-  }
-
-  public func removeLast() -> T {
-    assert(!isEmpty)
-    return removeNode(last!)
-  }
-
-  public func removeAtIndex(index: Int) -> T {
-    let node = nodeAtIndex(index)
-    assert(node != nil)
-    return removeNode(node!)
-  }
-}
-
-extension LinkedList: CustomStringConvertible {
-  public var description: String {
-    var s = "["
-    var node = head
-    while node != nil {
-      s += "\(node!.value)"
-      node = node!.next
-      if node != nil { s += ", " }
-    }
-    return s + "]"
-  }
-}
-
-extension LinkedList {
-  public func reverse() {
-    var node = head
-    while let currentNode = node {
-      node = currentNode.next
-      swap(&currentNode.next, &currentNode.previous)
-      head = currentNode
-    }
-  }
-}
-
-extension LinkedList {
-  public func map<U>(transform: T -> U) -> LinkedList<U> {
-    let result = LinkedList<U>()
-    var node = head
-    while node != nil {
-      result.append(transform(node!.value))
-      node = node!.next
-    }
-    return result
-  }
-
-  public func filter(predicate: T -> Bool) -> LinkedList<T> {
-    let result = LinkedList<T>()
-    var node = head
-    while node != nil {
-      if predicate(node!.value) {
-        result.append(node!.value)
-      }
-      node = node!.next
-    }
-    return result
-  }
-}

From b2fe7f39ccfedaf816d4a9c69ac3455ebd7db67b Mon Sep 17 00:00:00 2001
From: Tulio Troncoso <tuliot@live.com>
Date: Tue, 13 Sep 2016 16:56:45 -0400
Subject: [PATCH 0526/1679] Changed naming of functions to fit the Swift 3
 style

Functions like nodeAtIndex(index: Int) are now nodeAt(index: Int)
---
 .../LinkedList.playground/Contents.swift      | 28 +++++++++----------
 Linked List/LinkedList.swift                  | 14 +++++-----
 2 files changed, 21 insertions(+), 21 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 5c05c1a3e..2078c0baf 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -47,7 +47,7 @@ public class LinkedList<T> {
     }
   }
 
-  public func nodeAtIndex(index: Int) -> Node? {
+  public func nodeAt(index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -61,7 +61,7 @@ public class LinkedList<T> {
   }
 
   public subscript(index: Int) -> T {
-    let node = nodeAtIndex(index: index)
+    let node = nodeAt(index: index)
     assert(node != nil)
     return node!.value
   }
@@ -111,7 +111,7 @@ public class LinkedList<T> {
     head = nil
   }
 
-  public func removeNode(node: Node) -> T {
+  public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
 
@@ -129,13 +129,13 @@ public class LinkedList<T> {
 
   public func removeLast() -> T {
     assert(!isEmpty)
-    return removeNode(node: last!)
+    return remove(node: last!)
   }
 
-  public func removeAtIndex(index: Int) -> T {
-    let node = nodeAtIndex(index: index)
+  public func removeAt(index: Int) -> T {
+    let node = nodeAt(index: index)
     assert(node != nil)
-    return removeNode(node: node!)
+    return remove(node: node!)
   }
 }
 
@@ -211,9 +211,9 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.nodeAtIndex(index: 0)!.value    // "Hello"
-list.nodeAtIndex(index: 1)!.value    // "World"
-list.nodeAtIndex(index: 2)           // nil
+list.nodeAt(index: 0)!.value    // "Hello"
+list.nodeAt(index: 1)!.value    // "World"
+list.nodeAt(index: 2)           // nil
 
 list[0]     // "Hello"
 list[1]     // "World"
@@ -227,8 +227,8 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.nodeAtIndex(index: 0)!.value = "Universe"
-list.nodeAtIndex(index: 1)!.value = "Swifty"
+list.nodeAt(index: 0)!.value = "Universe"
+list.nodeAt(index: 1)!.value = "Swifty"
 let m = list.map { s in s.characters.count }
 m    // [8, 6, 5]
 let f = list.filter { s in s.characters.count > 5 }
@@ -237,7 +237,7 @@ f    // [Universe, Swifty]
 //list.removeAll()
 //list.isEmpty
 
-list.removeNode(node: list.first!)   // "Hello"
+list.remove(node: list.first!)   // "Hello"
 list.count                     // 2
 list[0]                        // "Swift"
 list[1]                        // "World"
@@ -246,5 +246,5 @@ list.removeLast()              // "World"
 list.count                     // 1
 list[0]                        // "Swift"
 
-list.removeAtIndex(index: 0)          // "Swift"
+list.removeAt(index: 0)          // "Swift"
 list.count                     // 0
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 336775c3c..8d95c4ac1 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -50,7 +50,7 @@ public class LinkedList<T> {
     }
   }
 
-  public func nodeAtIndex(index: Int) -> Node? {
+  public func nodeAt(index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -64,7 +64,7 @@ public class LinkedList<T> {
   }
 
   public subscript(index: Int) -> T {
-    let node = nodeAtIndex(index: index)
+    let node = nodeAt(index: index)
     assert(node != nil)
     return node!.value
   }
@@ -114,7 +114,7 @@ public class LinkedList<T> {
     head = nil
   }
 
-  public func removeNode(node: Node) -> T {
+  public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
 
@@ -132,13 +132,13 @@ public class LinkedList<T> {
 
   public func removeLast() -> T {
     assert(!isEmpty)
-    return removeNode(node: last!)
+    return remove(node: last!)
   }
 
-  public func removeAtIndex(index: Int) -> T {
-    let node = nodeAtIndex(index: index)
+  public func removeAt(index: Int) -> T {
+    let node = nodeAt(index: index)
     assert(node != nil)
-    return removeNode(node: node!)
+    return remove(node: node!)
   }
 }
 

From b0baae91b1681c187fe7f8df37e296b733a1988e Mon Sep 17 00:00:00 2001
From: Tulio Troncoso <tuliot@live.com>
Date: Tue, 13 Sep 2016 17:19:59 -0400
Subject: [PATCH 0527/1679] Updated tests to swift 3 and fixed playground

There was a better way to do the naming. Instead of doing
nodeAt(index: Int), I changed it to nodeAt(_ index: Int)
which allows you to call nodeAt(3) instead of nodeAt(index: 3)
---
 .../LinkedList.playground/Contents.swift      | 20 ++++----
 Linked List/LinkedList.swift                  | 48 +++++++++----------
 Linked List/Tests/LinkedListTests.swift       | 34 ++++++-------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  3 ++
 4 files changed, 54 insertions(+), 51 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 2078c0baf..72dcffe02 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -47,7 +47,7 @@ public class LinkedList<T> {
     }
   }
 
-  public func nodeAt(index: Int) -> Node? {
+  public func nodeAt(_ index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -61,7 +61,7 @@ public class LinkedList<T> {
   }
 
   public subscript(index: Int) -> T {
-    let node = nodeAt(index: index)
+    let node = nodeAt(index)
     assert(node != nil)
     return node!.value
   }
@@ -132,8 +132,8 @@ public class LinkedList<T> {
     return remove(node: last!)
   }
 
-  public func removeAt(index: Int) -> T {
-    let node = nodeAt(index: index)
+  public func removeAt(_ index: Int) -> T {
+    let node = nodeAt(index)
     assert(node != nil)
     return remove(node: node!)
   }
@@ -211,9 +211,9 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.nodeAt(index: 0)!.value    // "Hello"
-list.nodeAt(index: 1)!.value    // "World"
-list.nodeAt(index: 2)           // nil
+list.nodeAt(0)!.value    // "Hello"
+list.nodeAt(1)!.value    // "World"
+list.nodeAt(2)           // nil
 
 list[0]     // "Hello"
 list[1]     // "World"
@@ -227,8 +227,8 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.nodeAt(index: 0)!.value = "Universe"
-list.nodeAt(index: 1)!.value = "Swifty"
+list.nodeAt(0)!.value = "Universe"
+list.nodeAt(1)!.value = "Swifty"
 let m = list.map { s in s.characters.count }
 m    // [8, 6, 5]
 let f = list.filter { s in s.characters.count > 5 }
@@ -246,5 +246,5 @@ list.removeLast()              // "World"
 list.count                     // 1
 list[0]                        // "Swift"
 
-list.removeAt(index: 0)          // "Swift"
+list.removeAt(0)          // "Swift"
 list.count                     // 0
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 8d95c4ac1..306743354 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -3,7 +3,7 @@
 
   Most operations on the linked list have complexity O(n).
 */
-public class LinkedListNode<T> {
+open class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
   weak var previous: LinkedListNode?
@@ -13,20 +13,20 @@ public class LinkedListNode<T> {
   }
 }
 
-public class LinkedList<T> {
+open class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
   fileprivate var head: Node?
 
-  public var isEmpty: Bool {
+  open var isEmpty: Bool {
     return head == nil
   }
 
-  public var first: Node? {
+  open var first: Node? {
     return head
   }
 
-  public var last: Node? {
+  open var last: Node? {
     if var node = head {
       while case let next? = node.next {
         node = next
@@ -37,7 +37,7 @@ public class LinkedList<T> {
     }
   }
 
-  public var count: Int {
+  open var count: Int {
     if var node = head {
       var c = 1
       while case let next? = node.next {
@@ -50,7 +50,7 @@ public class LinkedList<T> {
     }
   }
 
-  public func nodeAt(index: Int) -> Node? {
+  open func nodeAt(_ index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -63,13 +63,13 @@ public class LinkedList<T> {
     return nil
   }
 
-  public subscript(index: Int) -> T {
-    let node = nodeAt(index: index)
+  open subscript(index: Int) -> T {
+    let node = nodeAt(index)
     assert(node != nil)
     return node!.value
   }
 
-  public func append(value: T) {
+  open func append(_ value: T) {
     let newNode = Node(value: value)
     if let lastNode = last {
       newNode.previous = lastNode
@@ -79,7 +79,7 @@ public class LinkedList<T> {
     }
   }
 
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
+  fileprivate func nodesBeforeAndAfter(_ index: Int) -> (Node?, Node?) {
     assert(index >= 0)
 
     var i = index
@@ -96,8 +96,8 @@ public class LinkedList<T> {
     return (prev, next)
   }
 
-  public func insert(value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index: index)
+  open func insert(_ value: T, atIndex index: Int) {
+    let (prev, next) = nodesBeforeAndAfter(index)
 
     let newNode = Node(value: value)
     newNode.previous = prev
@@ -110,11 +110,11 @@ public class LinkedList<T> {
     }
   }
 
-  public func removeAll() {
+  open func removeAll() {
     head = nil
   }
 
-  public func remove(node: Node) -> T {
+  open func remove(_ node: Node) -> T {
     let prev = node.previous
     let next = node.next
 
@@ -130,15 +130,15 @@ public class LinkedList<T> {
     return node.value
   }
 
-  public func removeLast() -> T {
+  open func removeLast() -> T {
     assert(!isEmpty)
-    return remove(node: last!)
+    return remove(last!)
   }
 
-  public func removeAt(index: Int) -> T {
-    let node = nodeAt(index: index)
+  open func removeAt(_ index: Int) -> T {
+    let node = nodeAt(index)
     assert(node != nil)
-    return remove(node: node!)
+    return remove(node!)
   }
 }
 
@@ -167,22 +167,22 @@ extension LinkedList {
 }
 
 extension LinkedList {
-  public func map<U>(transform: (T)-> U) -> LinkedList<U> {
+  public func map<U>(_ transform: (T)-> U) -> LinkedList<U> {
     let result = LinkedList<U>()
     var node = head
     while node != nil {
-        result.append(value: transform(node!.value))
+        result.append(transform(node!.value))
       node = node!.next
     }
     return result
   }
 
-  public func filter(predicate: (T)-> Bool) -> LinkedList<T> {
+  public func filter(_ predicate: (T)-> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
     while node != nil {
       if predicate(node!.value) {
-        result.append(value: node!.value)
+        result.append(node!.value)
       }
       node = node!.next
     }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 4bdc0adae..beba84299 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -3,7 +3,7 @@ import XCTest
 class LinkedListTest: XCTestCase {
   let numbers = [8, 2, 10, 9, 7, 5]
 
-  private func buildList() -> LinkedList<Int> {
+  fileprivate func buildList() -> LinkedList<Int> {
     let list = LinkedList<Int>()
     for number in numbers {
       list.append(number)
@@ -88,7 +88,7 @@ class LinkedListTest: XCTestCase {
 
   func testNodeAtIndexInEmptyList() {
     let list = LinkedList<Int>()
-    let node = list.nodeAtIndex(0)
+    let node = list.nodeAt(0)
     XCTAssertNil(node)
   }
 
@@ -96,7 +96,7 @@ class LinkedListTest: XCTestCase {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let node = list.nodeAtIndex(0)
+    let node = list.nodeAt(0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node!.value, 123)
     XCTAssertTrue(node === list.first)
@@ -108,21 +108,21 @@ class LinkedListTest: XCTestCase {
     let nodeCount = list.count
     XCTAssertEqual(nodeCount, numbers.count)
 
-    XCTAssertNil(list.nodeAtIndex(-1))
-    XCTAssertNil(list.nodeAtIndex(nodeCount))
+    XCTAssertNil(list.nodeAt(-1))
+    XCTAssertNil(list.nodeAt(nodeCount))
 
-    let first = list.nodeAtIndex(0)
+    let first = list.nodeAt(0)
     XCTAssertNotNil(first)
     XCTAssertTrue(first === list.first)
     XCTAssertEqual(first!.value, numbers[0])
 
-    let last = list.nodeAtIndex(nodeCount - 1)
+    let last = list.nodeAt(nodeCount - 1)
     XCTAssertNotNil(last)
     XCTAssertTrue(last === list.last)
     XCTAssertEqual(last!.value, numbers[nodeCount - 1])
 
     for i in 0..<nodeCount {
-      let node = list.nodeAtIndex(i)
+      let node = list.nodeAt(i)
       XCTAssertNotNil(node)
       XCTAssertEqual(node!.value, numbers[i])
     }
@@ -142,20 +142,20 @@ class LinkedListTest: XCTestCase {
     XCTAssertFalse(list.isEmpty)
     XCTAssertEqual(list.count, 1)
 
-    let node = list.nodeAtIndex(0)
+    let node = list.nodeAt(0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node!.value, 123)
   }
 
   func testInsertAtIndex() {
     let list = buildList()
-    let prev = list.nodeAtIndex(2)
-    let next = list.nodeAtIndex(3)
+    let prev = list.nodeAt(2)
+    let next = list.nodeAt(3)
     let nodeCount = list.count
 
     list.insert(444, atIndex: 3)
 
-    let node = list.nodeAtIndex(3)
+    let node = list.nodeAt(3)
     XCTAssertNotNil(node)
     XCTAssertEqual(node!.value, 444)
     XCTAssertEqual(nodeCount + 1, list.count)
@@ -170,7 +170,7 @@ class LinkedListTest: XCTestCase {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let value = list.removeAtIndex(0)
+    let value = list.removeAt(0)
     XCTAssertEqual(value, 123)
 
     XCTAssertTrue(list.isEmpty)
@@ -181,16 +181,16 @@ class LinkedListTest: XCTestCase {
 
   func testRemoveAtIndex() {
     let list = buildList()
-    let prev = list.nodeAtIndex(2)
-    let next = list.nodeAtIndex(3)
+    let prev = list.nodeAt(2)
+    let next = list.nodeAt(3)
     let nodeCount = list.count
 
     list.insert(444, atIndex: 3)
 
-    let value = list.removeAtIndex(3)
+    let value = list.removeAt(3)
     XCTAssertEqual(value, 444)
 
-    let node = list.nodeAtIndex(3)
+    let node = list.nodeAt(3)
     XCTAssertTrue(next === node)
     XCTAssertTrue(prev!.next === node)
     XCTAssertTrue(node!.previous === prev)
diff --git a/Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Linked List/Tests/Tests.xcodeproj/project.pbxproj
index 7c6a2020a..3a29f5677 100644
--- a/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -88,6 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -220,6 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 9857da6a63ddfdc22d1246d199a1030bbdfab662 Mon Sep 17 00:00:00 2001
From: Tulio Troncoso <tuliot@live.com>
Date: Tue, 13 Sep 2016 17:28:12 -0400
Subject: [PATCH 0528/1679] Updated README.md

---
 Linked List/README.markdown | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index e78735350..7b2ec0c0d 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -216,7 +216,7 @@ It loops through the list in the same manner but this time increments a counter
 What if we wanted to find the node at a specific index in the list? With an array we can just write `array[index]` and it's an **O(1)** operation. It's a bit more involved with linked lists, but again the code follows a similar pattern:
 
 ```swift
-  public func nodeAtIndex(index: Int) -> Node? {
+  public func nodeAt(_ index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -235,16 +235,16 @@ The loop looks a little different but it does the same thing: it starts at `head
 Try it out:
 
 ```swift
-list.nodeAtIndex(0)!.value    // "Hello"
-list.nodeAtIndex(1)!.value    // "World"
-list.nodeAtIndex(2)           // nil
+list.nodeAt(0)!.value    // "Hello"
+list.nodeAt(1)!.value    // "World"
+list.nodeAt(2)           // nil
 ```
 
 For fun we can implement a `subscript` method too:
 
 ```swift
   public subscript(index: Int) -> T {
-    let node = nodeAtIndex(index)
+    let node = nodeAt(index)
     assert(node != nil)
     return node!.value
   }
@@ -367,7 +367,7 @@ If you had a tail pointer, you'd set it to `nil` here too.
 Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first. 
 
 ```swift
-  public func removeNode(node: Node) -> T {
+  public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
     
@@ -391,24 +391,24 @@ Don't forget the `head` pointer! If this was the first node in the list then `he
 Try it out:
 
 ```swift
-list.removeNode(list.first!)   // "Hello"
+list.remove(list.first!)   // "Hello"
 list.count                     // 2
 list[0]                        // "Swift"
 list[1]                        // "World"
 ```
 
-If you don't have a reference to the node, you can use `removeLast()` or `removeAtIndex()`:
+If you don't have a reference to the node, you can use `removeLast()` or `removeAt()`:
 
 ```swift
   public func removeLast() -> T {
     assert(!isEmpty)
-    return removeNode(last!)
+    return remove(node: last!)
   }
 
-  public func removeAtIndex(index: Int) -> T {
-    let node = nodeAtIndex(index)
+  public func removeAt(_ index: Int) -> T {
+    let node = nodeAt(index)
     assert(node != nil)
-    return removeNode(node!)
+    return remove(node: node!)
   }
 ```
 
@@ -419,7 +419,7 @@ list.removeLast()              // "World"
 list.count                     // 1
 list[0]                        // "Swift"
 
-list.removeAtIndex(0)          // "Swift"
+list.removeAt(0)          // "Swift"
 list.count                     // 0
 ```
 

From 5fbcd67b80b1f3295456341e857660e8db160ed8 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Thu, 15 Sep 2016 18:08:04 -0700
Subject: [PATCH 0529/1679] Converted playground and fixed README for swift 3.

---
 .../BinaryTree.playground/Contents.swift       | 18 +++++++++---------
 Binary Tree/README.markdown                    | 18 +++++++++---------
 2 files changed, 18 insertions(+), 18 deletions(-)

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index b953b6a71..b35e90c27 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -53,26 +53,26 @@ tree.count  // 12
 
 
 extension BinaryTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
+  public func traverseInOrder(process: (T) -> Void) {
     if case let .Node(left, value, right) = self {
-      left.traverseInOrder(process)
+      left.traverseInOrder(process: process)
       process(value)
-      right.traverseInOrder(process)
+      right.traverseInOrder(process: process)
     }
   }
 
-  public func traversePreOrder(@noescape process: T -> Void) {
+  public func traversePreOrder(process: (T) -> Void) {
     if case let .Node(left, value, right) = self {
       process(value)
-      left.traversePreOrder(process)
-      right.traversePreOrder(process)
+      left.traversePreOrder(process: process)
+      right.traversePreOrder(process: process)
     }
   }
 
-  public func traversePostOrder(@noescape process: T -> Void) {
+  public func traversePostOrder(process: (T) -> Void) {
     if case let .Node(left, value, right) = self {
-      left.traversePostOrder(process)
-      right.traversePostOrder(process)
+      left.traversePostOrder(process: process)
+      right.traversePostOrder(process: process)
       process(value)
     }
   }
diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 24498b035..4b5fe7180 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -111,26 +111,26 @@ Something you often need to do with trees is traverse them, i.e. look at all the
 Here is how you'd implement that:
 
 ```swift
-  public func traverseInOrder(@noescape process: T -> Void) {
+  public func traverseInOrder(process: (T) -> Void) {
     if case let .Node(left, value, right) = self {
-      left.traverseInOrder(process)
+      left.traverseInOrder(process: process)
       process(value)
-      right.traverseInOrder(process)
+      right.traverseInOrder(process: process)
     }
   }
   
-  public func traversePreOrder(@noescape process: T -> Void) {
+  public func traversePreOrder(process: (T) -> Void) {
     if case let .Node(left, value, right) = self {
       process(value)
-      left.traversePreOrder(process)
-      right.traversePreOrder(process)
+      left.traversePreOrder(process: process)
+      right.traversePreOrder(process: process)
     }
   }
   
-  public func traversePostOrder(@noescape process: T -> Void) {
+  public func traversePostOrder(process: (T) -> Void) {
     if case let .Node(left, value, right) = self {
-      left.traversePostOrder(process)
-      right.traversePostOrder(process)
+      left.traversePostOrder(process: process)
+      right.traversePostOrder(process: process)
       process(value)
     }
   }

From 68be8b845f00c5c8eb284b46a534e448f69a630a Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Fri, 16 Sep 2016 14:08:30 +0200
Subject: [PATCH 0530/1679] rbtree implementation

---
 Red-Black Tree 2/RBTree.swift                 | Bin 0 -> 1104 bytes
 Red-Black Tree 2/README.markdown              |  10 +
 .../Contents.swift                            |   9 +
 .../Sources/RBTree.swift                      | 486 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 6 files changed, 516 insertions(+)
 create mode 100644 Red-Black Tree 2/RBTree.swift
 create mode 100644 Red-Black Tree 2/README.markdown
 create mode 100644 Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift
 create mode 100644 Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift
 create mode 100644 Red-Black Tree 2/Red-Black Tree 2.playground/contents.xcplayground
 create mode 100644 Red-Black Tree 2/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Red-Black Tree 2/RBTree.swift b/Red-Black Tree 2/RBTree.swift
new file mode 100644
index 0000000000000000000000000000000000000000..0ed831f72932e9675aa57dc32405330ef33285a7
GIT binary patch
literal 1104
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z)CqN9U}QjuKY*bdv??1TBNDJNBGCbupyB(RyQD_qN#DEAd-weAr|Z7I$zTmDi2E5Z
zDVL^bIzw#`<`);fw9>iV{WAG$k!BsGFbW<RKm!;=rznioLLP+OQ0y;SR*Ujztl~TT
ztl;p0OJ%%uKX9XshGu*1I!#7-%iPfn&$2hwYQVWVdHz4~iI!(=tp|R)>9ErxXT@&^
zHV@gb{KlXf6Y+E^#ZECs^AL|iwAU)+K~JF<&=8cyzOq-5e8PYDIO+d6h>xe2|8D0v
zkzaU{^k-it{kebqdEu+5LhJmD{u}fg8pgR?fX1PDXbGZq(%F~yce8WA9Hii0FcjNG
zFq!O$6<n0OH_DTH?e45U_EXeX&fvaXkI&}wd3mOHE!%BIez>9DGUfL;xnFcoy*0i0
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z{+!@@E4Ae%)3@6V-i&TLXxufI2Y2{Ze=i3(hZ5zZcbaY;*gGR)Y4nE4;>U6W)^+1n
z#k|LzPKVY&HU`n(u@`%I|KL?Im;pZ%ya3)2Tm`=sTsy({!FwW}QW=ZHy$yoDig*V6
zLvR*+MdXZthXjv;bAnZHRd4|;>nn$hy_a>s7>aG=kg<;<u6*d{XTbDc$i|Mk{|E6U
O@M}?jJH@tN3H}S0xrV#|

literal 0
HcmV?d00001

diff --git a/Red-Black Tree 2/README.markdown b/Red-Black Tree 2/README.markdown
new file mode 100644
index 000000000..abb1c2f55
--- /dev/null
+++ b/Red-Black Tree 2/README.markdown	
@@ -0,0 +1,10 @@
+# Red-Black Tree
+
+Used info from
+
+https://en.wikipedia.org/wiki/Red–black_tree
+http://www.geeksforgeeks.org/red-black-tree-set-1-introduction-2/
+http://www.geeksforgeeks.org/red-black-tree-set-2-insert/
+http://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/
+
+Important to note is that the last one doesn't mention a few important details about deletion cases which can be found in the code itself.
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift
new file mode 100644
index 000000000..b4fadff92
--- /dev/null
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift	
@@ -0,0 +1,9 @@
+//: Playground - noun: a place where people can play
+
+let array = [6,78,89,4]
+var tree = RBTree<Int>(withArray: array)
+tree.insert(5)
+tree.insert(8)
+tree.insert(2)
+tree.delete(6)
+tree.delete(8)
\ No newline at end of file
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift
new file mode 100644
index 000000000..c5bcd0a3e
--- /dev/null
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -0,0 +1,486 @@
+
+private enum RBTColor {
+    case Red
+    case Black
+    case DoubleBlack
+}
+
+public class RBTNode<T: Comparable> {
+    fileprivate var color: RBTColor = .Red
+    public var value: T! = nil
+    public var right:  RBTNode<T>!
+    public var left:  RBTNode<T>!
+    public var parent:  RBTNode<T>!
+    
+    init(tree: RBTree<T>) {
+        right = tree.nullLeaf
+        left = tree.nullLeaf
+        parent = tree.nullLeaf
+    }
+    
+    init() {
+        //This method is here to support the creation of a nullLeaf
+    }
+    
+    public var isLeftChild: Bool {
+        return self.parent.left === self
+    }
+    
+    public var isRightChild: Bool {
+        return self.parent.right === self
+    }
+    
+    public var grandparent: RBTNode<T> {
+        return parent.parent
+    }
+    
+    public var sibling: RBTNode<T>! {
+        if isLeftChild {
+            return self.parent.right
+        } else if isRightChild {
+            return self.parent.left
+        } else {
+            return nil
+        }
+    }
+    
+    public var uncle: RBTNode<T> {
+        return parent.sibling
+    }
+    
+    fileprivate var isRed: Bool {
+        return color == .Red
+    }
+    
+    fileprivate var isBlack: Bool {
+        return color == .Black
+    }
+    
+    fileprivate var isDoubleBlack: Bool {
+        return color == .DoubleBlack
+    }
+}
+
+public class RBTree<T: Comparable> {
+    public var root: RBTNode<T>
+    fileprivate let nullLeaf: RBTNode<T>
+    
+    public init() {
+        nullLeaf = RBTNode<T>()
+        nullLeaf.color = .Black
+        root = nullLeaf
+    }
+    
+    public convenience init(withValue value: T) {
+        self.init()
+        insert(value)
+    }
+    
+    public convenience init(withArray array: [T]) {
+        self.init()
+        insert(array)
+    }
+    
+    public func insert(_ value: T) {
+        let newNode = RBTNode<T>(tree: self)
+        newNode.value = value
+        insertNode(n: newNode)
+    }
+    
+    public func insert(_ values: [T]) {
+        for value in values {
+            print(value)
+            insert(value)
+        }
+    }
+    
+    public func delete(_ value: T) {
+        let nodeToDelete = find(value)
+        if nodeToDelete !== nullLeaf {
+            deleteNode(n: nodeToDelete)
+        }
+    }
+    
+    public func find(_ value: T) -> RBTNode<T> {
+        let foundNode = findNode(rootNode: root, value: value)
+        return foundNode
+    }
+    
+    public func minimum(n: RBTNode<T>) -> RBTNode<T> {
+        var min = n
+        if n.left !== nullLeaf {
+            min = minimum(n: n.left)
+        }
+        
+        return min
+    }
+    
+    public func maximum(n: RBTNode<T>) -> RBTNode<T> {
+        var max = n
+        if n.right !== nullLeaf {
+            max = maximum(n: n.right)
+        }
+        
+        return max
+    }
+    
+    public func verify() {
+        if self.root === nullLeaf {
+            print("The tree is empty")
+            return
+        }
+        property1()
+        property2(n: self.root)
+        property3()
+    }
+    
+    private func findNode(rootNode: RBTNode<T>, value: T) -> RBTNode<T> {
+        var nextNode = rootNode
+        if rootNode !== nullLeaf && value != rootNode.value {
+            if value < rootNode.value {
+                nextNode = findNode(rootNode: rootNode.left, value: value)
+            } else {
+                nextNode = findNode(rootNode: rootNode.right, value: value)
+            }
+        }
+        
+        return nextNode
+    }
+    
+    private func insertNode(n: RBTNode<T>) {
+        BSTInsertNode(n: n, parent: root)
+        insertCase1(n: n)
+    }
+    
+    private func BSTInsertNode(n: RBTNode<T>, parent: RBTNode<T>) {
+        if parent === nullLeaf {
+            self.root = n
+        } else if n.value < parent.value {
+            if parent.left !== nullLeaf {
+                BSTInsertNode(n: n, parent: parent.left)
+            } else {
+                parent.left = n
+                parent.left.parent = parent
+            }
+        } else {
+            if parent.right !== nullLeaf {
+                BSTInsertNode(n: n, parent: parent.right)
+            } else {
+                parent.right = n
+                parent.right.parent = parent
+            }
+        }
+    }
+    
+    // if node is root change color to black, else move on
+    private func insertCase1(n: RBTNode<T>) {
+        if n === root {
+            n.color = .Black
+        } else {
+            insertCase2(n: n)
+        }
+    }
+    
+    // if parent of node is not black, and node is not root move on
+    private func insertCase2(n: RBTNode<T>) {
+        if !n.parent.isBlack {
+            insertCase3(n: n)
+        }
+    }
+    
+    // if uncle is red do stuff otherwise move to 4
+    private func insertCase3(n: RBTNode<T>) {
+        if n.uncle.isRed { // node must have grandparent as children of root have a black parent
+            // both parent and uncle are red, so grandparent must be black.
+            n.parent.color = .Black
+            n.uncle.color = .Black
+            n.grandparent.color = .Red
+            // now both parent and uncle are black and grandparent is red.
+            // we repeat for the grandparent
+            insertCase1(n: n.grandparent)
+        } else {
+            insertCase4(n: n)
+        }
+    }
+    
+    // parent is red, grandparent is black, uncle is black
+    // There are 4 cases left:
+    // - left left
+    // - left right
+    // - right right
+    // - right left
+    
+    // the cases "left right" and "right left" can be rotated into the other two
+    // so if either of the two is detected we apply a rotation and then move on to
+    // deal with the final two cases, if neither is detected we move on to those cases anyway
+    private func insertCase4(n: RBTNode<T>) {
+        if n.parent.isLeftChild && n.isRightChild { // left right case
+            leftRotate(n: n.parent)
+            insertCase5(n: n.left)
+        } else if n.parent.isRightChild && n.isLeftChild { // right left case
+            rightRotate(n: n.parent)
+            insertCase5(n: n.right)
+        }
+    }
+    
+    private func insertCase5(n: RBTNode<T>) {
+        // swap color of parent and grandparent
+        // parent is red grandparent is black
+        n.parent.color = .Black
+        n.grandparent.color = .Red
+        
+        if n.isLeftChild { // left left case
+            rightRotate(n: n.grandparent)
+        } else { // right right case
+            leftRotate(n: n.grandparent)
+        }
+    }
+    
+    private func deleteNode(n: RBTNode<T>) {
+        var toDel = n
+        
+        if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.parent === nullLeaf {
+            self.root = nullLeaf
+            return
+        }
+        
+        if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.isRed {
+            if toDel.isLeftChild {
+                toDel.parent.left = nullLeaf
+            } else {
+                toDel.parent.right = nullLeaf
+            }
+            return
+        }
+        
+        if toDel.left !== nullLeaf && toDel.right !== nullLeaf {
+            let pred = maximum(n: toDel.left)
+            toDel.value = pred.value
+            toDel = pred
+        }
+        
+        // from here toDel has at most 1 non nullLeaf child
+        
+        var child: RBTNode<T>
+        if toDel.left !== nullLeaf {
+            child = toDel.left
+        } else {
+            child = toDel.right
+        }
+        
+        if toDel.isRed || child.isRed {
+            child.color = .Black
+            
+            if toDel.isLeftChild {
+                toDel.parent.left = child
+            } else {
+                toDel.parent.right = child
+            }
+            
+            if child !== nullLeaf {
+                child.parent = toDel.parent
+            }
+        } else { // both toDel and child are black
+            
+            var sibling = toDel.sibling
+            
+            if toDel.isLeftChild {
+                toDel.parent.left = child
+            } else {
+                toDel.parent.right = child
+            }
+            if child !== nullLeaf {
+                child.parent = toDel.parent
+            }
+            child.color = .DoubleBlack
+            
+            while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
+                if sibling!.isBlack {
+                    
+                    var leftRedChild: RBTNode<T>! = nil
+                    if sibling!.left.isRed {
+                        leftRedChild = sibling!.left
+                    }
+                    var rightRedChild: RBTNode<T>! = nil
+                    if sibling!.right.isRed {
+                        rightRedChild = sibling!.right
+                    }
+                    
+                    if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
+                        child.color = .Black
+                        if sibling!.isLeftChild {
+                            if leftRedChild != nil { // left left case
+                                sibling!.left.color = .Black
+                                let tempColor = sibling!.parent.color
+                                sibling!.parent.color = sibling!.color
+                                sibling!.color = tempColor
+                                rightRotate(n: sibling!.parent)
+                            } else { // left right case
+                                if sibling!.parent.isRed {
+                                    sibling!.parent.color = .Black
+                                } else {
+                                    sibling!.right.color = .Black
+                                }
+                                leftRotate(n: sibling!)
+                                rightRotate(n: sibling!.grandparent)
+                            }
+                        } else {
+                            if rightRedChild != nil { // right right case
+                                sibling!.right.color = .Black
+                                let tempColor = sibling!.parent.color
+                                sibling!.parent.color = sibling!.color
+                                sibling!.color = tempColor
+                                leftRotate(n: sibling!.parent)
+                            } else { // right left case
+                                if sibling!.parent.isRed {
+                                    sibling!.parent.color = .Black
+                                } else {
+                                    sibling!.left.color = .Black
+                                }
+                                rightRotate(n: sibling!)
+                                leftRotate(n: sibling!.grandparent)
+                            }
+                        }
+                        break
+                    } else { // both sibling's children are black
+                        child.color = .Black
+                        sibling!.color = .Red
+                        if sibling!.parent.isRed {
+                            sibling!.parent.color = .Black
+                            break
+                        }
+                        sibling!.parent.color = .DoubleBlack
+                        child = sibling!.parent
+                        sibling = child.sibling
+                    }
+                } else { // sibling is red
+                    sibling!.color = .Black
+                    
+                    if sibling!.isLeftChild { // left case
+                        rightRotate(n: sibling!.parent)
+                        sibling = sibling!.right.left
+                        sibling!.parent.color = .Red
+                    } else { // right case
+                        leftRotate(n: sibling!.parent)
+                        sibling = sibling!.left.right
+                        sibling!.parent.color = .Red
+                    }
+                }
+                
+                // sibling check is here for when child is a nullLeaf and thus does not have a parent.
+                // child is here as sibling can become nil when child is the root
+                if (sibling != nil && sibling!.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
+                    child.color = .Black
+                }
+            }
+        }
+    }
+    
+    private func property1() {
+        
+        if self.root.isRed {
+            print("Root is not black")
+        }
+    }
+    
+    private func property2(n: RBTNode<T>) {
+        if n === nullLeaf {
+            return
+        }
+        if n.isRed {
+            if n.left !== nullLeaf && n.left.isRed {
+                print("Red node: \(n.value), has red left child")
+            } else if n.right !== nullLeaf && n.right.isRed {
+                print("Red node: \(n.value), has red right child")
+            }
+        }
+        property2(n: n.left)
+        property2(n: n.right)
+    }
+    
+    private func property3() {
+        let bDepth = blackDepth(root: self.root)
+        
+        let leaves:[RBTNode<T>] = getLeaves(n: self.root)
+        
+        for leaflet in leaves {
+            var leaf = leaflet
+            var i = 0
+            
+            while leaf !== nullLeaf {
+                if leaf.isBlack {
+                    i = i + 1
+                }
+                leaf = leaf.parent
+            }
+            
+            if i != bDepth {
+                print("black depth: \(bDepth), is not equal (depth: \(i)) for leaf with value: \(leaflet.value)")
+            }
+        }
+        
+    }
+    
+    private func getLeaves(n: RBTNode<T>) -> [RBTNode<T>] {
+        var leaves = [RBTNode<T>]()
+        
+        if n !== nullLeaf {
+            if n.left === nullLeaf && n.right === nullLeaf {
+                leaves.append(n)
+            } else {
+                let leftLeaves = getLeaves(n: n.left)
+                let rightLeaves = getLeaves(n: n.right)
+                
+                leaves.append(contentsOf: leftLeaves)
+                leaves.append(contentsOf: rightLeaves)
+            }
+        }
+        
+        return leaves
+    }
+    
+    private func blackDepth(root: RBTNode<T>) -> Int {
+        if root === nullLeaf {
+            return 0
+        } else {
+            let returnValue = root.isBlack ? 1 : 0
+            return returnValue + (max(blackDepth(root: root.left), blackDepth(root: root.right)))
+        }
+    }
+    
+    private func leftRotate(n: RBTNode<T>) {
+        let newRoot = n.right!
+        n.right = newRoot.left!
+        if newRoot.left !== nullLeaf {
+            newRoot.left.parent = n
+        }
+        newRoot.parent = n.parent
+        if n.parent === nullLeaf {
+            self.root = newRoot
+        } else if n.isLeftChild {
+            n.parent.left = newRoot
+        } else {
+            n.parent.right = newRoot
+        }
+        newRoot.left = n
+        n.parent = newRoot
+    }
+    
+    private func rightRotate(n: RBTNode<T>) {
+        let newRoot = n.left!
+        n.left = newRoot.right!
+        if newRoot.right !== nullLeaf {
+            newRoot.right.parent = n
+        }
+        newRoot.parent = n.parent
+        if n.parent === nullLeaf {
+            self.root = newRoot
+        } else if n.isRightChild {
+            n.parent.right = newRoot
+        } else {
+            n.parent.left = newRoot
+        }
+        newRoot.right = n
+        n.parent = newRoot
+    }
+}
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/contents.xcplayground b/Red-Black Tree 2/Red-Black Tree 2.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata b/Red-Black Tree 2/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 7f94c350ab439aeeaecec3eabe365b3d127934df Mon Sep 17 00:00:00 2001
From: "Glenn R. Fisher" <glennrfisher@gmail.com>
Date: Sat, 17 Sep 2016 11:54:48 -0500
Subject: [PATCH 0531/1679] Update hash table for Swift 3.0

---
 .../HashTable.playground/Contents.swift       | 115 ++-----------
 .../Sources/HashTable.swift                   | 153 +++++++++++++++++
 .../HashTable.playground/timeline.xctimeline  |   6 -
 Hash Table/HashTable.swift                    | 159 ------------------
 Hash Table/README.markdown                    |  41 +++--
 .../contents.xcworkspacedata                  |   3 -
 6 files changed, 182 insertions(+), 295 deletions(-)
 create mode 100644 Hash Table/HashTable.playground/Sources/HashTable.swift
 delete mode 100644 Hash Table/HashTable.playground/timeline.xctimeline
 delete mode 100644 Hash Table/HashTable.swift

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index cda0919de..121fb6032 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,129 +1,34 @@
 //: Playground - noun: a place where people can play
 
-public struct HashTable<Key: Hashable, Value> {
-  private typealias Element = (key: Key, value: Value)
-  private typealias Bucket = [Element]
-
-  private var buckets: [Bucket]
-  private(set) var count = 0
-
-  public init(capacity: Int) {
-    assert(capacity > 0)
-    buckets = .init(count: capacity, repeatedValue: [])
-  }
-
-  public var isEmpty: Bool {
-    return count == 0
-  }
-
-  private func indexForKey(key: Key) -> Int {
-    return abs(key.hashValue) % buckets.count
-  }
-}
-
-extension HashTable {
-  public subscript(key: Key) -> Value? {
-    get {
-      return valueForKey(key)
-    }
-    set {
-      if let value = newValue {
-        updateValue(value, forKey: key)
-      } else {
-        removeValueForKey(key)
-      }
-    }
-  }
-
-  public func valueForKey(key: Key) -> Value? {
-    let index = indexForKey(key)
-
-    for element in buckets[index] {
-      if element.key == key {
-        return element.value
-      }
-    }
-    return nil  // key not in hash table
-  }
-
-  public mutating func updateValue(value: Value, forKey key: Key) -> Value? {
-    let index = indexForKey(key)
-
-    // Do we already have this key in the bucket?
-    for (i, element) in buckets[index].enumerate() {
-      if element.key == key {
-        let oldValue = element.value
-        buckets[index][i].value = value
-        return oldValue
-      }
-    }
-
-    // This key isn't in the bucket yet; add it to the chain.
-    buckets[index].append((key: key, value: value))
-    count += 1
-    return nil
-  }
-
-  public mutating func removeValueForKey(key: Key) -> Value? {
-    let index = indexForKey(key)
-
-    // Find the element in the bucket's chain and remove it.
-    for (i, element) in buckets[index].enumerate() {
-      if element.key == key {
-        buckets[index].removeAtIndex(i)
-        count -= 1
-        return element.value
-      }
-    }
-    return nil  // key not in hash table
-  }
-
-  public mutating func removeAll() {
-    buckets = .init(count: buckets.count, repeatedValue: [])
-    count = 0
-  }
-}
-
-extension HashTable: CustomStringConvertible {
-  public var description: String {
-    return buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }.joinWithSeparator(", ")
-  }
-}
-
-extension HashTable: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = ""
-    for (i, bucket) in buckets.enumerate() {
-      s += "bucket \(i): " + bucket.map { e in "\(e.key) = \(e.value)" }.joinWithSeparator(", ") + "\n"
-    }
-    return s
-  }
-}
-
-
-
 // Playing with hash values
+
 "firstName".hashValue
 abs("firstName".hashValue) % 5
+
 "lastName".hashValue
 abs("lastName".hashValue) % 5
+
 "hobbies".hashValue
 abs("hobbies".hashValue) % 5
 
-
-
 // Playing with the hash table
+
 var hashTable = HashTable<String, String>(capacity: 5)
 
 hashTable["firstName"] = "Steve"
 hashTable["lastName"] = "Jobs"
 hashTable["hobbies"] = "Programming Swift"
 
-hashTable.description
+print(hashTable)
 print(hashTable.debugDescription)
 
 let x = hashTable["firstName"]
 hashTable["firstName"] = "Tim"
+
 let y = hashTable["firstName"]
 hashTable["firstName"] = nil
+
 let z = hashTable["firstName"]
+
+print(hashTable)
+print(hashTable.debugDescription)
diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
new file mode 100644
index 000000000..947737c32
--- /dev/null
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -0,0 +1,153 @@
+/*
+ Hash Table: A symbol table of generic key-value pairs.
+ 
+ The key must be `Hashable`, which means it can be transformed into a fairly
+ unique integer value. The more unique the hash value, the better.
+ 
+ Hash tables use an internal array of buckets to store key-value pairs. The
+ hash table's capacity is determined by the number of buckets. This
+ implementation has a fixed capacity--it does not resize the array as more
+ key-value pairs are inserted.
+ 
+ To insert or locate a particular key-value pair, a hash function transforms the
+ key into an array index. An ideal hash function would guarantee that different
+ keys map to different indices. In practice, however, this is difficult to
+ achieve.
+ 
+ Since different keys can map to the same array index, all hash tables implement
+ a collision resolution strategy. This implementation uses a strategy called
+ separate chaining, where key-value pairs that hash to the same index are
+ "chained together" in a list. For good performance, the capacity of the hash
+ table should be sufficiently large so that the lists are small.
+ 
+ A well-sized hash table provides very good average performance. In the
+ worst-case, however, all keys map to the same bucket, resulting in a list that
+ that requires O(n) time to traverse.
+ 
+        Average Worst-Case
+ Space:   O(n)     O(n)
+ Search:  O(1)     O(n)
+ Insert:  O(1)     O(n)
+ Delete:  O(1)     O(n)
+ */
+public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
+    private typealias Element = (key: Key, value: Value)
+    private typealias Bucket = [Element]
+    private var buckets: [Bucket]
+    
+    /// The number of key-value pairs in the hash table.
+    private(set) public var count = 0
+    
+    /// A Boolean value that indicates whether the hash table is empty.
+    public var isEmpty: Bool { return count == 0 }
+    
+    /// A string that represents the contents of the hash table.
+    public var description: String {
+        let pairs = buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }
+        return pairs.joined(separator: ", ")
+    }
+    
+    /// A string that represents the contents of
+    /// the hash table, suitable for debugging.
+    public var debugDescription: String {
+        var str = ""
+        for (i, bucket) in buckets.enumerated() {
+            let pairs = bucket.map { e in "\(e.key) = \(e.value)" }
+            str += "bucket \(i): " + pairs.joined(separator: ", ") + "\n"
+        }
+        return str
+    }
+    
+    /**
+     Create a hash table with the given capacity.
+     */
+    public init(capacity: Int) {
+        assert(capacity > 0)
+        buckets = Array<Bucket>(repeatElement([], count: capacity))
+    }
+    
+    /**
+     Accesses the value associated with
+     the given key for reading and writing.
+     */
+    public subscript(key: Key) -> Value? {
+        get {
+            return value(forKey: key)
+        }
+        set {
+            if let value = newValue {
+                updateValue(value, forKey: key)
+            } else {
+                removeValue(forKey: key)
+            }
+        }
+    }
+    
+    /**
+     Returns the value for the given key.
+     */
+    public func value(forKey key: Key) -> Value? {
+        let index = self.index(forKey: key)
+        for element in buckets[index] {
+            if element.key == key {
+                return element.value
+            }
+        }
+        return nil  // key not in hash table
+    }
+    
+    /**
+     Updates the value stored in the hash table for the given key,
+     or adds a new key-value pair if the key does not exist.
+     */
+    @discardableResult public mutating func updateValue(_ value: Value, forKey key: Key) -> Value? {
+        let index = self.index(forKey: key)
+        
+        // Do we already have this key in the bucket?
+        for (i, element) in buckets[index].enumerated() {
+            if element.key == key {
+                let oldValue = element.value
+                buckets[index][i].value = value
+                return oldValue
+            }
+        }
+        
+        // This key isn't in the bucket yet; add it to the chain.
+        buckets[index].append((key: key, value: value))
+        count += 1
+        return nil
+    }
+    
+    /**
+     Removes the given key and its
+     associated value from the hash table.
+     */
+    @discardableResult public mutating func removeValue(forKey key: Key) -> Value? {
+        let index = self.index(forKey: key)
+        
+        // Find the element in the bucket's chain and remove it.
+        for (i, element) in buckets[index].enumerated() {
+            if element.key == key {
+                buckets[index].remove(at: i)
+                count -= 1
+                return element.value
+            }
+        }
+        return nil  // key not in hash table
+    }
+    
+    /**
+     Removes all key-value pairs from the hash table.
+     */
+    public mutating func removeAll() {
+        buckets = Array<Bucket>(repeatElement([], count: buckets.count))
+        count = 0
+    }
+    
+    /**
+     Returns the given key's array index.
+     */
+    private func index(forKey key: Key) -> Int {
+        return abs(key.hashValue) % buckets.count
+    }
+}
diff --git a/Hash Table/HashTable.playground/timeline.xctimeline b/Hash Table/HashTable.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Hash Table/HashTable.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Hash Table/HashTable.swift b/Hash Table/HashTable.swift
deleted file mode 100644
index 46c73e284..000000000
--- a/Hash Table/HashTable.swift	
+++ /dev/null
@@ -1,159 +0,0 @@
-/*
-  Hash table
-
-  Allows you to store and retrieve objects by a "key".
-
-  The key must be Hashable, which means it can be converted into a fairly
-  unique Int that represents the key as a number. The more unique the hash
-  value, the better.
-
-  The hashed version of the key is used to calculate an index into the array
-  of "buckets". The capacity of the hash table is how many of these buckets
-  it has. Ideally, the number of buckets is the same as the maximum number of
-  items you'll be storing in the HashTable, and each hash value maps to its
-  own bucket. In practice that is hard to achieve.
-
-  When there is more than one hash value that maps to the same bucket index
-  -- a "collision" -- they are chained together, using an array. (Note that
-  more clever ways exist for dealing with the chaining issue.)
-
-  While there are free buckets, inserting/retrieving/removing are O(1).
-  But when the buckets are full and the chains are long, using the hash table
-  becomes an O(n) operation.
-
-  Counting the size of the hash table is O(1) because we're caching the count.
-
-  The order of the elements in the hash table is undefined.
-
-  This implementation has a fixed capacity; it does not resize when the table
-  gets too full. (To do that, you'd allocate a larger array of buckets and then
-  insert each of the elements into that new array; this is necessary because
-  the hash values will now map to different bucket indexes.)
-*/
-public struct HashTable<Key: Hashable, Value> {
-  private typealias Element = (key: Key, value: Value)
-  private typealias Bucket = [Element]
-
-  private var buckets: [Bucket]
-  private(set) var count = 0
-
-  public init(capacity: Int) {
-    assert(capacity > 0)
-    buckets = .init(count: capacity, repeatedValue: [])
-  }
-
-  public var isEmpty: Bool {
-    return count == 0
-  }
-
-  private func indexForKey(key: Key) -> Int {
-    return abs(key.hashValue) % buckets.count
-  }
-}
-
-// MARK: - Basic operations
-
-extension HashTable {
-  public subscript(key: Key) -> Value? {
-    get {
-      return valueForKey(key)
-    }
-    set {
-      if let value = newValue {
-        updateValue(value, forKey: key)
-      } else {
-        removeValueForKey(key)
-      }
-    }
-  }
-
-  public func valueForKey(key: Key) -> Value? {
-    let index = indexForKey(key)
-
-    for element in buckets[index] {
-      if element.key == key {
-        return element.value
-      }
-    }
-    return nil  // key not in hash table
-  }
-
-  public mutating func updateValue(value: Value, forKey key: Key) -> Value? {
-    let index = indexForKey(key)
-
-    // Do we already have this key in the bucket?
-    for (i, element) in buckets[index].enumerate() {
-      if element.key == key {
-        let oldValue = element.value
-        buckets[index][i].value = value
-        return oldValue
-      }
-    }
-
-    // This key isn't in the bucket yet; add it to the chain.
-    buckets[index].append((key: key, value: value))
-    count += 1
-    return nil
-  }
-
-  public mutating func removeValueForKey(key: Key) -> Value? {
-    let index = indexForKey(key)
-
-    // Find the element in the bucket's chain and remove it.
-    for (i, element) in buckets[index].enumerate() {
-      if element.key == key {
-        buckets[index].removeAtIndex(i)
-        count -= 1
-        return element.value
-      }
-    }
-    return nil  // key not in hash table
-  }
-
-  public mutating func removeAll() {
-    buckets = .init(count: buckets.count, repeatedValue: [])
-    count = 0
-  }
-}
-
-// MARK: - Helper methods for inspecting the hash table
-
-extension HashTable {
-  public var keys: [Key] {
-    var a = [Key]()
-    for bucket in buckets {
-      for element in bucket {
-        a.append(element.key)
-      }
-    }
-    return a
-  }
-
-  public var values: [Value] {
-    var a = [Value]()
-    for bucket in buckets {
-      for element in bucket {
-        a.append(element.value)
-      }
-    }
-    return a
-  }
-}
-
-// MARK: - For debugging
-
-extension HashTable: CustomStringConvertible {
-  public var description: String {
-    return buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }.joinWithSeparator(", ")
-  }
-}
-
-extension HashTable: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = ""
-    for (i, bucket) in buckets.enumerate() {
-      s += "bucket \(i): " + bucket.map { e in "\(e.key) = \(e.value)" }.joinWithSeparator(", ") + "\n"
-    }
-    return s
-  }
-}
diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 02a2c9578..4399b0f86 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -115,17 +115,15 @@ Let's look at a basic implementation of a hash table in Swift. We'll build it up
 public struct HashTable<Key: Hashable, Value> {
   private typealias Element = (key: Key, value: Value)
   private typealias Bucket = [Element]
-  
   private var buckets: [Bucket]
-  private(set) var count = 0
+
+  private(set) public var count = 0
   
+  public var isEmpty: Bool { return count == 0 }
+
   public init(capacity: Int) {
     assert(capacity > 0)
-    buckets = .init(count: capacity, repeatedValue: [])
-  }
-  
-  public var isEmpty: Bool {
-    return count == 0
+    buckets = Array<Bucket>(repeatElement([], count: capacity))
   }
 ```
 
@@ -142,7 +140,7 @@ var hashTable = HashTable<String, String>(capacity: 5)
 Currently the hash table doesn't do anything yet, so let's add the remaining functionality. First, add a helper method that calculates the array index for a given key:
 
 ```swift
-  private func indexForKey(key: Key) -> Int {
+  private func index(forKey key: Key) -> Int {
     return abs(key.hashValue) % buckets.count
   }
 ```
@@ -170,24 +168,23 @@ We can do all these things with a `subscript` function:
 ```swift
   public subscript(key: Key) -> Value? {
     get {
-      return valueForKey(key)
+      return value(forKey: key)
     }
     set {
       if let value = newValue {
         updateValue(value, forKey: key)
       } else {
-        removeValueForKey(key)
+        removeValue(forKey: key)
       }
     }
   }
 ```
 
-This calls three helper functions to do the actual work. Let's take a look at `valueForKey()` first, which retrieves an object from the hash table.
+This calls three helper functions to do the actual work. Let's take a look at `value(forKey:)` first, which retrieves an object from the hash table.
 
 ```swift
-  public func valueForKey(key: Key) -> Value? {
-    let index = indexForKey(key)
-
+  public func value(forKey key: Key) -> Value? {
+    let index = self.index(forKey: key)
     for element in buckets[index] {
       if element.key == key {
         return element.value
@@ -197,13 +194,13 @@ This calls three helper functions to do the actual work. Let's take a look at `v
   }
 ```
 
-First it calls `indexForKey()` to convert the key into an array index. That gives us the bucket number, but if there were collisions this bucket may be used by more than one key. So `valueForKey()` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
+First it calls `index(forKey:)` to convert the key into an array index. That gives us the bucket number, but if there were collisions this bucket may be used by more than one key. So `value(forKey:)` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
 
-The code to insert a new element or update an existing element lives in `updateValue(forKey)`. It's a little bit more complicated:
+The code to insert a new element or update an existing element lives in `updateValue(_:forKey:)`. It's a little bit more complicated:
 
 ```swift
-  public mutating func updateValue(value: Value, forKey key: Key) -> Value? {
-    let index = indexForKey(key)
+  public mutating func updateValue(_ value: Value, forKey key: Key) -> Value? {
+    let index = self.index(forKey: key)
     
     // Do we already have this key in the bucket?
     for (i, element) in buckets[index].enumerate() {
@@ -228,13 +225,13 @@ As you can see, it's important that chains are kept short (by making the hash ta
 Removing is similar in that again it loops through the chain:
 
 ```swift
-  public mutating func removeValueForKey(key: Key) -> Value? {
-    let index = indexForKey(key)
+  public mutating func removeValue(forKey key: Key) -> Value? {
+    let index = self.index(forKey: key)
 
     // Find the element in the bucket's chain and remove it.
-    for (i, element) in buckets[index].enumerate() {
+    for (i, element) in buckets[index].enumerated() {
       if element.key == key {
-        buckets[index].removeAtIndex(i)
+        buckets[index].remove(at: i)
         count -= 1
         return element.value
       }
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4e0f19dc2..e7288f299 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -868,9 +868,6 @@
       <FileRef
          location = "group:HashTable.playground">
       </FileRef>
-      <FileRef
-         location = "group:HashTable.swift">
-      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From 8aeacb054d85a3024675fb0985e369a1e01add86 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Sat, 17 Sep 2016 23:55:39 +0200
Subject: [PATCH 0532/1679] New style / Broken down into extensions

---
 Skip-List/SkipList.swift | 409 +++++++++++++++++++++------------------
 1 file changed, 218 insertions(+), 191 deletions(-)

diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index b07cd98c8..31b4e9144 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -26,241 +26,268 @@ import Foundation
 
 // Stack from : https://github.com/raywenderlich/swift-algorithm-club/tree/master/Stack
 public struct Stack<T> {
-    private var array = [T]()
+  fileprivate var array = [T]()
 
-    public var isEmpty: Bool {
-        return array.isEmpty
-    }
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
 
-    public var count: Int {
-        return array.count
-    }
+  public var count: Int {
+    return array.count
+  }
 
-    public mutating func push(element: T) {
-        array.append(element)
-    }
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
 
-    public mutating func pop() -> T? {
-        return array.popLast()
-    }
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
 
-    public func peek() -> T? {
-        return array.last
-    }
+  public func peek() -> T? {
+    return array.last
+  }
 }
 
-extension Stack: SequenceType {
-    public func generate() -> AnyGenerator<T> {
-        var curr = self
-        return AnyGenerator {
-                   _ -> T? in
-                   return curr.pop()
-            }
-    }
+extension Stack: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator {
+             _ -> T? in
+             return curr.pop()
+      }
+  }
 }
 
 
-func random() -> Bool {
-    #if os(Linux)
-        return random() % 2 == 0
-    #elseif os(OSX)
-        return arc4random_uniform(2) == 1
-    #endif
+private func coinFlip() -> Bool {
+  #if os(Linux)
+   return random() % 2 == 0
+  #elseif os(OSX)
+   return arc4random_uniform(2) == 1
+  #endif
 }
 
 
+// MARK: - Node
+
+public class DataNode<Key: Comparable, Payload> {
+  public typealias Node = DataNode<Key, Payload>
+  
+  var data            : Payload?  
+  fileprivate var key : Key?
+  internal var next   : Node?
+  internal var down   : Node?
+  
+  public init(key: Key, data: Payload) {
+    self.key  = key
+    self.data = data
+  }
+
+  public init(asHead head: Bool){
+  }
+  
+}
 
-class DataNode<Key: Comparable, Payload>{
-    internal typealias Node = DataNode<Key,Payload>
-    
-    internal var key   : Key?
-    internal var data  : Payload?
-    internal var _next : Node?
-    internal var _down : Node?
-
-    internal var next: Node? {
-        get        { return self._next  }
-        set(value) { self._next = value }        
-    }
 
-    internal var down:Node? {
-        get        { return self._down  }
-        set(value) { self._down = value }
-    }
-    
-    init(key:Key, data:Payload){
-        self.key  = key
-        self.data = data
-    }
+// MARK: - Skip List
 
-    init(header: Bool){        
-    }
-    
+open class SkipList<Key: Comparable, Payload> {
+  public typealias Node = DataNode<Key, Payload>
+  
+  fileprivate(set) var head: Node?
+
+  public init() { }
+  
 }
 
 
-class SkipList<Key: Comparable, Payload>{
-    internal typealias Node = DataNode<Key, Payload>
-    internal var head: Node?
-
-    private func find_head(key:Key) -> Node? {
-        var current     = self.head
-        var found: Bool = false
-
-        while !found {
-            if let curr = current {
-                if curr.next == nil { current = curr.down }
-                else {
-                    if curr.next!.key == key { found = true }
-                    else {                        
-                        if key < curr.next!.key{ current = curr.down }
-                        else { current = curr.next }
-                    }
-                }
+
+// MARK: - Searching
+
+extension SkipList {
+  
+  internal func findNode(key: Key) -> Node? {
+    var currentNode : Node? = self.head
+    var isFound     : Bool  = false
+
+    while !isFound {
+      if let node = currentNode {
+        
+        switch node.next {
+        case .none:
+          
+          currentNode = node.down
+        case .some(let value) where value.key != nil:
+
+          if value.key == key {
+            isFound = true
+            break
+          }
+          else {
+            if key < value.key! {
+              currentNode = node.down
             } else {
-                break
-            }
+              currentNode = node.next
+            }            
+          }
+          
+        default:
+          continue
         }
+        
+      } else { 
+        break
+      }
+    }
 
-        if found {
-            return current
-        } else {
-            return nil
-        }        
+    if isFound {
+      return currentNode
+    } else {
+      return nil
     }
     
+  }
 
-    private func insert_head(key:Key, data:Payload) -> Void {
-        
-        self.head       = Node(header: true)
-        var temp        = Node(key:key, data:data)
-        self.head!.next = temp
-        var top         = temp
-
-        while random() {
-            let newhead  = Node(header: true)
-            temp         = Node(key:key, data:data)
-            temp.down    = top
-            newhead.next = temp
-            newhead.down = self.head
-            self.head    = newhead
-            top          = temp                
-        }
+  internal func search(key: Key) -> Payload? {
+    guard let node = self.findNode(key: key) else {
+      return nil
     }
 
-    private func insert_rest(key:Key, data:Payload) -> Void {
-        var stack = Stack<Node>()
-        var current_head: Node? = self.head
+    return node.next!.data    
+  }    
+ 
+}
+
 
-        while current_head != nil {
 
-            if let next = current_head!._next {
-                if next.key > key {
-                    stack.push(current_head!)
-                    current_head = next
-                } else {
-                    current_head = next
-                }
-                
-            } else {
-                stack.push(current_head!)
-                current_head = current_head!.down                    
-            }
-            
-        }            
-
-        let lowest   = stack.pop()
-        var temp     = Node(key:key, data:data)
-        temp.next    = lowest!.next
-        lowest!.next = temp
-        var top      = temp
-
-        while random() {
-            if stack.isEmpty {
-                let newhead  = Node(header: true)
-                temp         = Node(key:key, data:data)
-                temp.down    = top
-                newhead.next = temp
-                newhead.down = self.head
-                self.head    = newhead
-                top          = temp
-            } else {
-                let next   = stack.pop()
-                temp       = Node(key:key, data:data)
-                temp.down  = top
-                temp.next  = next!.next
-                next!.next = temp
-                top        = temp
-            }
-        }        
-    }
-    
-    func search(key:Key) -> Payload? {
-        guard let item = self.find_head(key) else {
-            return nil
-        }
+// MARK: - Inserting
+
+extension SkipList {
+  private func bootstrapBaseLayer(key: Key, data: Payload) -> Void {    
+    self.head          = Node(asHead: true)    
+    var node           = Node(key: key, data: data)
 
-        return item.next!.data        
+    self.head!.next    = node
+    
+    var currentTopNode = node
+
+    while coinFlip() {
+      let newHead    = Node(asHead: true)
+      node           = Node(key: key, data: data)
+      node.down      = currentTopNode
+      newHead.next   = node
+      newHead.down   = self.head
+      self.head      = newHead
+      currentTopNode = node
     }
     
-    func remove(key:Key) -> Void {
-        guard let item = self.find_head(key) else {
-            return
+  }
+
+
+  private func insertItem(key: Key, data: Payload) -> Void {
+    var stack              = Stack<Node>()
+    var currentNode: Node? = self.head
+
+    while currentNode != nil {
+
+      if let nextNode = currentNode!.next {
+        if nextNode.key! > key {
+          stack.push(currentNode!)
+          currentNode = currentNode!.down
+        } else {
+          currentNode = nextNode
         }
         
-        var curr = Optional(item)
+      } else {
+        stack.push(currentNode!)
+        currentNode = currentNode!.down           
+      }
+      
+    }       
+
+    let itemAtLayer    = stack.pop()
+    var node           = Node(key: key, data: data)
+    node.next          = itemAtLayer!.next
+    itemAtLayer!.next  = node
+    var currentTopNode = node
+
+    while coinFlip() {
+      if stack.isEmpty {
+        let newHead    = Node(asHead: true)
         
-        while curr != nil {
-            let node      = curr!.next
-            
-            if node!.key != key { curr = node ; continue }
-
-            let node_next = node!.next            
-            curr!.next    = node_next
-            curr          = curr!.down
-            
-        }
+        node           = Node(key: key, data: data)
+        node.down      = currentTopNode
+        newHead.next   = node
+        newHead.down   = self.head
+        self.head      = newHead
+        currentTopNode = node
         
-    }
-    
-    func insert(key: Key, data:Payload){
-        if self.head != nil{
-            if let node = self.find_head(key) {
-                
-                var curr = node.next                
-                while curr != nil && curr!.key == key{
-                    curr!.data = data
-                    curr       = curr!.down
-                }
-                
-            } else {                        
-                self.insert_rest(key, data:data)
-            }
-            
-        } else {
-            self.insert_head(key, data:data)
+      } else {        
+        let nextNode  = stack.pop()
+        
+        node           = Node(key: key, data: data)
+        node.down      = currentTopNode
+        node.next      = nextNode!.next
+        nextNode!.next = node
+        currentTopNode = node
+      }
+    }     
+  }
+
+
+  internal func insert(key: Key, data: Payload) {
+    if self.head != nil {
+      if let node = self.findNode(key: key) {
+        // replace in case key already exists
+        var currentNode = node.next        
+        while currentNode != nil && currentNode!.key == key {
+          currentNode!.data = data
+          currentNode       = currentNode!.down
         }
+      } else {
+        self.insertItem(key: key, data: data)
+      }
+      
+    } else {
+      self.bootstrapBaseLayer(key: key, data: data)
     }
-
+  }
+  
 }
 
 
-class Map<Key: Comparable, Payload>{    
-    var collection: SkipList<Key, Payload>
+// MARK: - Removing
 
-    init(){
-        self.collection = SkipList<Key, Payload>()
+extension SkipList {
+  public func remove(key: Key) -> Void {
+    guard let item = self.findNode(key: key) else {
+      return
     }
     
-    func insert(key:Key, data: Payload){
-        self.collection.insert(key, data:data)
-    }
-
-    func get(key:Key) -> Payload?{
-        return self.collection.search(key)
-    }
+    var currentNode = Optional(item)
     
-    func remove(key:Key) -> Void {
-        return self.collection.remove(key)
+    while currentNode != nil {
+      let node   = currentNode!.next
+      
+      if node!.key != key {
+        currentNode = node
+        continue
+      }
+
+      let nextNode      = node!.next
+      
+      currentNode!.next = nextNode
+      currentNode       = currentNode!.down
+      
     }
+    
+  }  
+}
+
+extension SkipList {
+  
+  public func get(key:Key) -> Payload?{
+    return self.search(key: key)
+  }
 }

From e9ce16b8e3328671537daf3c93e7510fb56458ab Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 17 Sep 2016 18:00:29 -0700
Subject: [PATCH 0533/1679] Fixes syntax in playground for Swift3.

---
 Quicksort/Quicksort.playground/Contents.swift | 20 +++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 0894ae61b..da02b69ce 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -5,7 +5,7 @@ import Foundation
 
 // *** Simple but inefficient version of quicksort ***
 
-func quicksort<T: Comparable>(a: [T]) -> [T] {
+func quicksort<T: Comparable>(_ a: [T]) -> [T] {
   guard a.count > 1 else { return a }
 
   let pivot = a[a.count/2]
@@ -34,7 +34,7 @@ quicksort(list1)
   partition is [low...p-1]; the right partition is [p+1...high], where p is the
   return value.
 */
-func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[high]
 
   var i = low
@@ -53,7 +53,7 @@ var list2 = [ 10, 0, 3, 9, 2, 14, 26, 27, 1, 5, 8, -1, 8 ]
 partitionLomuto(&list2, low: 0, high: list2.count - 1)
 list2
 
-func quicksortLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let p = partitionLomuto(&a, low: low, high: high)
     quicksortLomuto(&a, low: low, high: p - 1)
@@ -75,7 +75,7 @@ quicksortLomuto(&list2, low: 0, high: list2.count - 1)
   where p is the return value. The pivot value is placed somewhere inside one
   of the two partitions, but the algorithm doesn't tell you which one or where.
 */
-func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[low]
   var i = low - 1
   var j = high + 1
@@ -96,7 +96,7 @@ var list3 = [ 8, 0, 3, 9, 2, 14, 10, 27, 1, 5, 8, -1, 26 ]
 partitionHoare(&list3, low: 0, high: list3.count - 1)
 list3
 
-func quicksortHoare<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let p = partitionHoare(&a, low: low, high: high)
     quicksortHoare(&a, low: low, high: p)
@@ -111,12 +111,12 @@ quicksortHoare(&list3, low: 0, high: list3.count - 1)
 // *** Randomized sorting ***
 
 /* Returns a random integer in the range min...max, inclusive. */
-public func random(min min: Int, max: Int) -> Int {
+public func random(min: Int, max: Int) -> Int {
   assert(min < max)
   return min + Int(arc4random_uniform(UInt32(max - min + 1)))
 }
 
-func quicksortRandom<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortRandom<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let pivotIndex = random(min: low, max: high)
     (a[pivotIndex], a[high]) = (a[high], a[pivotIndex])
@@ -139,7 +139,7 @@ list4
   Swift's swap() doesn't like it if the items you're trying to swap refer to
   the same memory location. This little wrapper simply ignores such swaps.
 */
-public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
+public func swap<T>(_ a: inout [T], _ i: Int, _ j: Int) {
   if i != j {
     swap(&a[i], &a[j])
   }
@@ -149,7 +149,7 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
   Dutch national flag partitioning.
   Returns a tuple with the start and end index of the middle area.
 */
-func partitionDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
+func partitionDutchFlag<T: Comparable>(_ a: inout [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
   let pivot = a[pivotIndex]
 
   var smaller = low
@@ -175,7 +175,7 @@ var list5 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 partitionDutchFlag(&list5, low: 0, high: list5.count - 1, pivotIndex: 10)
 list5
 
-func quicksortDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortDutchFlag<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let pivotIndex = random(min: low, max: high)
     let (p, q) = partitionDutchFlag(&a, low: low, high: high, pivotIndex: pivotIndex)

From 35cca84d481a6b20dacbc196b68e0db0d7925594 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 17 Sep 2016 18:04:17 -0700
Subject: [PATCH 0534/1679] Changed README to reflect Swift 3 migration.

---
 Quicksort/README.markdown | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index 936f9f44c..e3d284333 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -7,7 +7,7 @@ Quicksort is one of the most famous algorithms in history. It was invented way b
 Here's an implementation in Swift that should be easy to understand:
 
 ```swift
-func quicksort<T: Comparable>(a: [T]) -> [T] {
+func quicksort<T: Comparable>(_ a: [T]) -> [T] {
   guard a.count > 1 else { return a }
 
   let pivot = a[a.count/2]
@@ -131,7 +131,7 @@ In the first example of quicksort I showed you, partitioning was done by calling
 Here's an implementation of Lomuto's partitioning scheme in Swift:
 
 ```swift
-func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[high]
   
   var i = low
@@ -250,7 +250,7 @@ And we return `i`, the index of the pivot element.
 Let's use this partitioning scheme to build quicksort. Here's the code:
 
 ```swift
-func quicksortLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let p = partitionLomuto(&a, low: low, high: high)
     quicksortLomuto(&a, low: low, high: p - 1)
@@ -277,7 +277,7 @@ This partitioning scheme is by Hoare, the inventor of quicksort.
 Here is the code:
 
 ```Swift
-func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[low]
   var i = low - 1
   var j = high + 1
@@ -318,7 +318,7 @@ The pivot is placed somewhere inside one of the two partitions, but the algorith
 Because of these differences, the implementation of Hoare's quicksort is slightly different:
 
 ```swift
-func quicksortHoare<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let p = partitionHoare(&a, low: low, high: high)
     quicksortHoare(&a, low: low, high: p)
@@ -380,7 +380,7 @@ Another common solution is to choose the pivot randomly. Sometimes this may resu
 Here is how you can do quicksort with a randomly chosen pivot:
 
 ```swift
-func quicksortRandom<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortRandom<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let pivotIndex = random(min: low, max: high)         // 1
 
@@ -412,7 +412,7 @@ But as you've seen with the Lomuto partitioning scheme, if the pivot occurs more
 The code for this scheme is:
 
 ```swift
-func partitionDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
+func partitionDutchFlag<T: Comparable>(_ a: inout [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
   let pivot = a[pivotIndex]
 
   var smaller = low
@@ -461,7 +461,7 @@ Notice how the two `8`s are in the middle now. The return value from `partitionD
 Here is how you would use it in quicksort:
 
 ```swift
-func quicksortDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortDutchFlag<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let pivotIndex = random(min: low, max: high)
     let (p, q) = partitionDutchFlag(&a, low: low, high: high, pivotIndex: pivotIndex)

From 6f14d9e9c739769b9b756c8d0fbd6ba81031e4c7 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 17 Sep 2016 18:11:28 -0700
Subject: [PATCH 0535/1679] Revised playground code to compile in Swift3.

---
 .../Sources/BoundedPriorityQueue.swift                 | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift
index 58dc5034e..fc399811d 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
@@ -12,7 +12,7 @@ public class BoundedPriorityQueue<T: Comparable> {
   private typealias Node = LinkedListNode<T>
 
   private(set) public var count = 0
-  private var head: Node?
+  fileprivate var head: Node?
   private var tail: Node?
   private var maxElements: Int
 
@@ -28,7 +28,7 @@ public class BoundedPriorityQueue<T: Comparable> {
     return head?.value
   }
 
-  public func enqueue(value: T) {
+  public func enqueue(_ value: T) {
     if let node = insert(value, after: findInsertionPoint(value)) {
       // If the newly inserted node is the last one in the list, then update
       // the tail pointer.
@@ -44,7 +44,7 @@ public class BoundedPriorityQueue<T: Comparable> {
     }
   }
 
-  private func insert(value: T, after: Node?) -> Node? {
+  private func insert(_ value: T, after: Node?) -> Node? {
     if let previous = after {
 
       // If the queue is full and we have to insert at the end of the list,
@@ -78,11 +78,11 @@ public class BoundedPriorityQueue<T: Comparable> {
 
   /* Find the node after which to insert the new value. If this returns nil,
      the new value should be inserted at the head of the list. */
-  private func findInsertionPoint(value: T) -> Node? {
+  private func findInsertionPoint(_ value: T) -> Node? {
     var node = head
     var prev: Node? = nil
 
-    while let current = node where value < current.value {
+    while let current = node, value < current.value {
       prev = node
       node = current.next
     }

From 6e2f5c199b67469988b452a3266aa1b9ab26da34 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 17 Sep 2016 18:13:20 -0700
Subject: [PATCH 0536/1679] Fixes README file for Swift3.

---
 Bounded Priority Queue/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
index 8d6ea1804..8d47adefb 100644
--- a/Bounded Priority Queue/README.markdown	
+++ b/Bounded Priority Queue/README.markdown	
@@ -35,7 +35,7 @@ public class BoundedPriorityQueue<T: Comparable> {
   private typealias Node = LinkedListNode<T>
 
   private(set) public var count = 0
-  private var head: Node?
+  fileprivate var head: Node?
   private var tail: Node?
   private var maxElements: Int
 
@@ -55,7 +55,7 @@ public class BoundedPriorityQueue<T: Comparable> {
 The `BoundedPriorityQueue` class contains a doubly linked list of `LinkedListNode` objects. Nothing special here yet. The fun stuff happens in the `enqueue()` method:
 
 ```swift
-public func enqueue(value: T) {
+public func enqueue(_ value: T) {
   if let node = insert(value, after: findInsertionPoint(value)) {
     // If the newly inserted node is the last one in the list, then update
     // the tail pointer.
@@ -71,7 +71,7 @@ public func enqueue(value: T) {
   }
 }
 
-private func insert(value: T, after: Node?) -> Node? {
+private func insert(_ value: T, after: Node?) -> Node? {
   if let previous = after {
 
     // If the queue is full and we have to insert at the end of the list,
@@ -105,7 +105,7 @@ private func insert(value: T, after: Node?) -> Node? {
 
 /* Find the node after which to insert the new value. If this returns nil,
    the new value should be inserted at the head of the list. */
-private func findInsertionPoint(value: T) -> Node? {
+private func findInsertionPoint(_ value: T) -> Node? {
   var node = head
   var prev: Node? = nil
 

From 562c85c1b0d717c73e4a04d1a0913a5e83732cea Mon Sep 17 00:00:00 2001
From: FarzadShbfn <farzad.shbfn@gmail.com>
Date: Sun, 18 Sep 2016 15:34:10 +0430
Subject: [PATCH 0537/1679] Upgrade to Swift3

---
 GCD/GCD.playground/Contents.swift | 4 ++--
 GCD/GCD.swift                     | 6 +++---
 GCD/README.markdown               | 6 +++---
 3 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index dedf6e293..2e264be93 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,7 +1,7 @@
 //: Playground - noun: a place where people can play
 
 // Recursive version
-func gcd(a: Int, _ b: Int) -> Int {
+func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b
   if r != 0 {
     return gcd(b, r)
@@ -26,7 +26,7 @@ func gcd(m: Int, _ n: Int) -> Int {
 }
 */
 
-func lcm(m: Int, _ n: Int) -> Int {
+func lcm(_ m: Int, _ n: Int) -> Int {
   return m*n / gcd(m, n)
 }
 
diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index dc473ccd4..ce7e7fa78 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -1,7 +1,7 @@
 /*
   Euclid's algorithm for finding the greatest common divisor
 */
-func gcd(m: Int, _ n: Int) -> Int {
+func gcd(_ m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
   var r = min(m, n)
@@ -16,7 +16,7 @@ func gcd(m: Int, _ n: Int) -> Int {
 
 /*
 // Recursive version
-func gcd(a: Int, _ b: Int) -> Int {
+func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b
   if r != 0 {
     return gcd(b, r)
@@ -29,6 +29,6 @@ func gcd(a: Int, _ b: Int) -> Int {
 /*
   Returns the least common multiple of two numbers.
 */
-func lcm(m: Int, _ n: Int) -> Int {
+func lcm(_ m: Int, _ n: Int) -> Int {
   return m*n / gcd(m, n)
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index 1d20fb9cb..07d2de1ca 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -17,7 +17,7 @@ where `a % b` calculates the remainder of `a` divided by `b`.
 Here is an implementation of this idea in Swift:
 
 ```swift
-func gcd(a: Int, _ b: Int) -> Int {
+func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b
   if r != 0 {
     return gcd(b, r)
@@ -68,7 +68,7 @@ gcd(841, 299)     // 1
 Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop.
 
 ```swift
-func gcd(m: Int, _ n: Int) -> Int {
+func gcd(_ m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
   var r = min(m, n)
@@ -101,7 +101,7 @@ We can calculate the LCM using Euclid's algorithm too:
 In code:
 
 ```swift
-func lcm(m: Int, _ n: Int) -> Int {
+func lcm(_ m: Int, _ n: Int) -> Int {
   return m*n / gcd(m, n)
 }
 ```

From ab02cf521de7eca87ff67f5001b0f546844d5593 Mon Sep 17 00:00:00 2001
From: FarzadShbfn <farzad.shbfn@gmail.com>
Date: Sun, 18 Sep 2016 15:54:01 +0430
Subject: [PATCH 0538/1679] Update to Swift3

---
 .../SegmentTree.playground/Contents.swift     | 192 +++++++++---------
 .../contents.xcplayground                     |   2 +-
 .../timeline.xctimeline                       |   6 -
 Segment Tree/SegmentTree.swift                | 116 +++++------
 4 files changed, 155 insertions(+), 161 deletions(-)
 delete mode 100644 Segment Tree/SegmentTree.playground/timeline.xctimeline

diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 14b7f57cf..6b33b2f44 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -1,64 +1,64 @@
 //: Playground - noun: a place where people can play
 
 public class SegmentTree<T> {
-
-  private var value: T
-  private var function: (T, T) -> T
-  private var leftBound: Int
-  private var rightBound: Int
-  private var leftChild: SegmentTree<T>?
-  private var rightChild: SegmentTree<T>?
-
-  public init(array: [T], leftBound: Int, rightBound: Int, function: (T, T) -> T) {
-    self.leftBound = leftBound
-    self.rightBound = rightBound
-    self.function = function
-
-    if leftBound == rightBound {
-      value = array[leftBound]
-    } else {
-      let middle = (leftBound + rightBound) / 2
-      leftChild = SegmentTree<T>(array: array, leftBound: leftBound, rightBound: middle, function: function)
-      rightChild = SegmentTree<T>(array: array, leftBound: middle+1, rightBound: rightBound, function: function)
-      value = function(leftChild!.value, rightChild!.value)
-    }
-  }
-
-  public convenience init(array: [T], function: (T, T) -> T) {
-    self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
-  }
-
-  public func queryWithLeftBound(leftBound: Int, rightBound: Int) -> T {
-    if self.leftBound == leftBound && self.rightBound == rightBound {
-      return self.value
-    }
-
-    guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
-    guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-
-    if leftChild.rightBound < leftBound {
-      return rightChild.queryWithLeftBound(leftBound, rightBound: rightBound)
-    } else if rightChild.leftBound > rightBound {
-      return leftChild.queryWithLeftBound(leftBound, rightBound: rightBound)
-    } else {
-      let leftResult = leftChild.queryWithLeftBound(leftBound, rightBound: leftChild.rightBound)
-      let rightResult = rightChild.queryWithLeftBound(rightChild.leftBound, rightBound: rightBound)
-      return function(leftResult, rightResult)
-    }
-  }
-
-  public func replaceItemAtIndex(index: Int, withItem item: T) {
-    if leftBound == rightBound {
-      value = item
-    } else if let leftChild = leftChild, rightChild = rightChild {
-      if leftChild.rightBound >= index {
-        leftChild.replaceItemAtIndex(index, withItem: item)
-      } else {
-        rightChild.replaceItemAtIndex(index, withItem: item)
-      }
-      value = function(leftChild.value, rightChild.value)
-    }
-  }
+	
+	private var value: T
+	private var function: (T, T) -> T
+	private var leftBound: Int
+	private var rightBound: Int
+	private var leftChild: SegmentTree<T>?
+	private var rightChild: SegmentTree<T>?
+	
+	public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
+		self.leftBound = leftBound
+		self.rightBound = rightBound
+		self.function = function
+		
+		if leftBound == rightBound {
+			value = array[leftBound]
+		} else {
+			let middle = (leftBound + rightBound) / 2
+			leftChild = SegmentTree<T>(array: array, leftBound: leftBound, rightBound: middle, function: function)
+			rightChild = SegmentTree<T>(array: array, leftBound: middle+1, rightBound: rightBound, function: function)
+			value = function(leftChild!.value, rightChild!.value)
+		}
+	}
+	
+	public convenience init(array: [T], function: @escaping (T, T) -> T) {
+		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
+	}
+	
+	public func query(withLeftBound: Int, rightBound: Int) -> T {
+		if self.leftBound == leftBound && self.rightBound == rightBound {
+			return self.value
+		}
+		
+		guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
+		guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+		
+		if leftChild.rightBound < leftBound {
+			return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
+		} else if rightChild.leftBound > rightBound {
+			return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
+		} else {
+			let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
+			let rightResult = rightChild.query(withLeftBound:rightChild.leftBound, rightBound: rightBound)
+			return function(leftResult, rightResult)
+		}
+	}
+	
+	public func replaceItem(at index: Int, withItem item: T) {
+		if leftBound == rightBound {
+			value = item
+		} else if let leftChild = leftChild, let rightChild = rightChild {
+			if leftChild.rightBound >= index {
+				leftChild.replaceItem(at: index, withItem: item)
+			} else {
+				rightChild.replaceItem(at: index, withItem: item)
+			}
+			value = function(leftChild.value, rightChild.value)
+		}
+	}
 }
 
 
@@ -68,42 +68,42 @@ let array = [1, 2, 3, 4]
 
 let sumSegmentTree = SegmentTree(array: array, function: +)
 
-print(sumSegmentTree.queryWithLeftBound(0, rightBound: 3)) // 1 + 2 + 3 + 4 = 10
-print(sumSegmentTree.queryWithLeftBound(1, rightBound: 2)) // 2 + 3 = 5
-print(sumSegmentTree.queryWithLeftBound(0, rightBound: 0)) // 1 = 1
+print(sumSegmentTree.query(withLeftBound: 0, rightBound: 3)) // 1 + 2 + 3 + 4 = 10
+print(sumSegmentTree.query(withLeftBound: 1, rightBound: 2)) // 2 + 3 = 5
+print(sumSegmentTree.query(withLeftBound: 0, rightBound: 0)) // 1 = 1
 
-sumSegmentTree.replaceItemAtIndex(0, withItem: 2) //our array now is [2, 2, 3, 4]
+sumSegmentTree.replaceItem(at: 0, withItem: 2) //our array now is [2, 2, 3, 4]
 
-print(sumSegmentTree.queryWithLeftBound(0, rightBound: 0)) // 2 = 2
-print(sumSegmentTree.queryWithLeftBound(0, rightBound: 1)) // 2 + 2 = 4
+print(sumSegmentTree.query(withLeftBound: 0, rightBound: 0)) // 2 = 2
+print(sumSegmentTree.query(withLeftBound: 0, rightBound: 1)) // 2 + 2 = 4
 
 
 //you can use any associative function (i.e (a+b)+c == a+(b+c)) as function for segment tree
-func gcd(m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
-
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+func gcd(_ m: Int, _ n: Int) -> Int {
+	var a = 0
+	var b = max(m, n)
+	var r = min(m, n)
+	
+	while r != 0 {
+		a = b
+		b = r
+		r = a % b
+	}
+	return b
 }
 
 let gcdArray = [2, 4, 6, 3, 5]
 
 let gcdSegmentTree = SegmentTree(array: gcdArray, function: gcd)
 
-print(gcdSegmentTree.queryWithLeftBound(0, rightBound: 1)) // gcd(2, 4) = 2
-print(gcdSegmentTree.queryWithLeftBound(2, rightBound: 3)) // gcd(6, 3) = 3
-print(gcdSegmentTree.queryWithLeftBound(1, rightBound: 3)) // gcd(4, 6, 3) = 1
-print(gcdSegmentTree.queryWithLeftBound(0, rightBound: 4)) // gcd(2, 4, 6, 3, 5) = 1
+print(gcdSegmentTree.query(withLeftBound: 0, rightBound: 1)) // gcd(2, 4) = 2
+print(gcdSegmentTree.query(withLeftBound: 2, rightBound: 3)) // gcd(6, 3) = 3
+print(gcdSegmentTree.query(withLeftBound: 1, rightBound: 3)) // gcd(4, 6, 3) = 1
+print(gcdSegmentTree.query(withLeftBound: 0, rightBound: 4)) // gcd(2, 4, 6, 3, 5) = 1
 
-gcdSegmentTree.replaceItemAtIndex(3, withItem: 10) //gcdArray now is [2, 4, 6, 10, 5]
+gcdSegmentTree.replaceItem(at: 3, withItem: 10) //gcdArray now is [2, 4, 6, 10, 5]
 
-print(gcdSegmentTree.queryWithLeftBound(3, rightBound: 4)) // gcd(10, 5) = 5
+print(gcdSegmentTree.query(withLeftBound: 3, rightBound: 4)) // gcd(10, 5) = 5
 
 
 //example of segment tree which finds minimum on given range
@@ -111,12 +111,12 @@ let minArray = [2, 4, 1, 5, 3]
 
 let minSegmentTree = SegmentTree(array: minArray, function: min)
 
-print(minSegmentTree.queryWithLeftBound(0, rightBound: 4)) // min(2, 4, 1, 5, 3) = 1
-print(minSegmentTree.queryWithLeftBound(0, rightBound: 1)) // min(2, 4) = 2
+print(minSegmentTree.query(withLeftBound: 0, rightBound: 4)) // min(2, 4, 1, 5, 3) = 1
+print(minSegmentTree.query(withLeftBound: 0, rightBound: 1)) // min(2, 4) = 2
 
-minSegmentTree.replaceItemAtIndex(2, withItem: 10) // minArray now is [2, 4, 10, 5, 3]
+minSegmentTree.replaceItem(at: 2, withItem: 10) // minArray now is [2, 4, 10, 5, 3]
 
-print(minSegmentTree.queryWithLeftBound(0, rightBound: 4)) // min(2, 4, 10, 5, 3) = 2
+print(minSegmentTree.query(withLeftBound: 0, rightBound: 4)) // min(2, 4, 10, 5, 3) = 2
 
 
 //type of elements in array can be any type which has some associative function
@@ -124,16 +124,16 @@ let stringArray = ["a", "b", "c", "A", "B", "C"]
 
 let stringSegmentTree = SegmentTree(array: stringArray, function: +)
 
-print(stringSegmentTree.queryWithLeftBound(0, rightBound: 1)) // "a"+"b" = "ab"
-print(stringSegmentTree.queryWithLeftBound(2, rightBound: 3)) // "c"+"A" = "cA"
-print(stringSegmentTree.queryWithLeftBound(1, rightBound: 3)) // "b"+"c"+"A" = "bcA"
-print(stringSegmentTree.queryWithLeftBound(0, rightBound: 5)) // "a"+"b"+"c"+"A"+"B"+"C" = "abcABC"
+print(stringSegmentTree.query(withLeftBound: 0, rightBound: 1)) // "a"+"b" = "ab"
+print(stringSegmentTree.query(withLeftBound: 2, rightBound: 3)) // "c"+"A" = "cA"
+print(stringSegmentTree.query(withLeftBound: 1, rightBound: 3)) // "b"+"c"+"A" = "bcA"
+print(stringSegmentTree.query(withLeftBound: 0, rightBound: 5)) // "a"+"b"+"c"+"A"+"B"+"C" = "abcABC"
 
-stringSegmentTree.replaceItemAtIndex(0, withItem: "I")
-stringSegmentTree.replaceItemAtIndex(1, withItem: " like")
-stringSegmentTree.replaceItemAtIndex(2, withItem: " algorithms")
-stringSegmentTree.replaceItemAtIndex(3, withItem: " and")
-stringSegmentTree.replaceItemAtIndex(4, withItem: " swift")
-stringSegmentTree.replaceItemAtIndex(5, withItem: "!")
+stringSegmentTree.replaceItem(at: 0, withItem: "I")
+stringSegmentTree.replaceItem(at: 1, withItem: " like")
+stringSegmentTree.replaceItem(at: 2, withItem: " algorithms")
+stringSegmentTree.replaceItem(at: 3, withItem: " and")
+stringSegmentTree.replaceItem(at: 4, withItem: " swift")
+stringSegmentTree.replaceItem(at: 5, withItem: "!")
 
-print(stringSegmentTree.queryWithLeftBound(0, rightBound: 5))
+print(stringSegmentTree.query(withLeftBound: 0, rightBound: 5))
diff --git a/Segment Tree/SegmentTree.playground/contents.xcplayground b/Segment Tree/SegmentTree.playground/contents.xcplayground
index 06828af92..16f9952aa 100644
--- a/Segment Tree/SegmentTree.playground/contents.xcplayground	
+++ b/Segment Tree/SegmentTree.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='0800'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Segment Tree/SegmentTree.playground/timeline.xctimeline b/Segment Tree/SegmentTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Segment Tree/SegmentTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Segment Tree/SegmentTree.swift b/Segment Tree/SegmentTree.swift
index 608d5151a..b360d409a 100644
--- a/Segment Tree/SegmentTree.swift	
+++ b/Segment Tree/SegmentTree.swift	
@@ -8,62 +8,62 @@
 */
 
 public class SegmentTree<T> {
-
-  private var value: T
-  private var function: (T, T) -> T
-  private var leftBound: Int
-  private var rightBound: Int
-  private var leftChild: SegmentTree<T>?
-  private var rightChild: SegmentTree<T>?
-
-  public init(array: [T], leftBound: Int, rightBound: Int, function: (T, T) -> T) {
-    self.leftBound = leftBound
-    self.rightBound = rightBound
-    self.function = function
-
-    if leftBound == rightBound {
-      value = array[leftBound]
-    } else {
-      let middle = (leftBound + rightBound) / 2
-      leftChild = SegmentTree<T>(array: array, leftBound: leftBound, rightBound: middle, function: function)
-      rightChild = SegmentTree<T>(array: array, leftBound: middle+1, rightBound: rightBound, function: function)
-      value = function(leftChild!.value, rightChild!.value)
-    }
-  }
-
-  public convenience init(array: [T], function: (T, T) -> T) {
-    self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
-  }
-
-  public func queryWithLeftBound(leftBound: Int, rightBound: Int) -> T {
-    if self.leftBound == leftBound && self.rightBound == rightBound {
-      return self.value
-    }
-
-    guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
-    guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-
-    if leftChild.rightBound < leftBound {
-      return rightChild.queryWithLeftBound(leftBound, rightBound: rightBound)
-    } else if rightChild.leftBound > rightBound {
-      return leftChild.queryWithLeftBound(leftBound, rightBound: rightBound)
-    } else {
-      let leftResult = leftChild.queryWithLeftBound(leftBound, rightBound: leftChild.rightBound)
-      let rightResult = rightChild.queryWithLeftBound(rightChild.leftBound, rightBound: rightBound)
-      return function(leftResult, rightResult)
-    }
-  }
-
-  public func replaceItemAtIndex(index: Int, withItem item: T) {
-    if leftBound == rightBound {
-      value = item
-    } else if let leftChild = leftChild, rightChild = rightChild {
-      if leftChild.rightBound >= index {
-        leftChild.replaceItemAtIndex(index, withItem: item)
-      } else {
-        rightChild.replaceItemAtIndex(index, withItem: item)
-      }
-      value = function(leftChild.value, rightChild.value)
-    }
-  }
+	
+	private var value: T
+	private var function: (T, T) -> T
+	private var leftBound: Int
+	private var rightBound: Int
+	private var leftChild: SegmentTree<T>?
+	private var rightChild: SegmentTree<T>?
+	
+	public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
+		self.leftBound = leftBound
+		self.rightBound = rightBound
+		self.function = function
+		
+		if leftBound == rightBound {
+			value = array[leftBound]
+		} else {
+			let middle = (leftBound + rightBound) / 2
+			leftChild = SegmentTree<T>(array: array, leftBound: leftBound, rightBound: middle, function: function)
+			rightChild = SegmentTree<T>(array: array, leftBound: middle+1, rightBound: rightBound, function: function)
+			value = function(leftChild!.value, rightChild!.value)
+		}
+	}
+	
+	public convenience init(array: [T], function: @escaping (T, T) -> T) {
+		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
+	}
+	
+	public func query(withLeftBound: Int, rightBound: Int) -> T {
+		if self.leftBound == leftBound && self.rightBound == rightBound {
+			return self.value
+		}
+		
+		guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
+		guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+		
+		if leftChild.rightBound < leftBound {
+			return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
+		} else if rightChild.leftBound > rightBound {
+			return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
+		} else {
+			let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
+			let rightResult = rightChild.query(withLeftBound:rightChild.leftBound, rightBound: rightBound)
+			return function(leftResult, rightResult)
+		}
+	}
+	
+	public func replaceItem(at index: Int, withItem item: T) {
+		if leftBound == rightBound {
+			value = item
+		} else if let leftChild = leftChild, let rightChild = rightChild {
+			if leftChild.rightBound >= index {
+				leftChild.replaceItem(at: index, withItem: item)
+			} else {
+				rightChild.replaceItem(at: index, withItem: item)
+			}
+			value = function(leftChild.value, rightChild.value)
+		}
+	}
 }

From f7ecb1ae4a886a8983670ce77e5bed3e6cde0890 Mon Sep 17 00:00:00 2001
From: FarzadShbfn <farzad.shbfn@gmail.com>
Date: Sun, 18 Sep 2016 16:08:19 +0430
Subject: [PATCH 0539/1679] Updated ReadMe for Swift3

---
 Segment Tree/README.markdown | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 0bb6d8da5..15b1a3227 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -73,7 +73,7 @@ The `leftBound` and `rightBound` of each node are marked in red.
 Here's how we create a node of the segment tree:
 
 ```swift
-public init(array: [T], leftBound: Int, rightBound: Int, function: (T, T) -> T) {
+public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
     self.leftBound = leftBound
     self.rightBound = rightBound
     self.function = function
@@ -111,7 +111,7 @@ We go through all this trouble so we can efficiently query the tree.
 Here's the code:
 
 ```swift
-  public func queryWithLeftBound(leftBound: Int, rightBound: Int) -> T {
+  public func query(withLeftBound: leftBound: Int, rightBound: Int) -> T {
     // 1
     if self.leftBound == leftBound && self.rightBound == rightBound {
       return self.value
@@ -122,16 +122,16 @@ Here's the code:
     
     // 2
     if leftChild.rightBound < leftBound {
-      return rightChild.queryWithLeftBound(leftBound, rightBound: rightBound)
+      return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
       
     // 3
     } else if rightChild.leftBound > rightBound {
-      return leftChild.queryWithLeftBound(leftBound, rightBound: rightBound)
+      return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
       
     // 4
     } else {
-      let leftResult = leftChild.queryWithLeftBound(leftBound, rightBound: leftChild.rightBound)
-      let rightResult = rightChild.queryWithLeftBound(rightChild.leftBound, rightBound: rightBound)
+      let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
+      let rightResult = rightChild.query(withLeftBound: rightChild.leftBound, rightBound: rightBound)
       return function(leftResult, rightResult)
     }
   }
@@ -162,10 +162,10 @@ let array = [1, 2, 3, 4]
 
 let sumSegmentTree = SegmentTree(array: array, function: +)
 
-sumSegmentTree.queryWithLeftBound(0, rightBound: 3)  // 1 + 2 + 3 + 4 = 10
-sumSegmentTree.queryWithLeftBound(1, rightBound: 2)  // 2 + 3 = 5
-sumSegmentTree.queryWithLeftBound(0, rightBound: 0)  // just 1
-sumSegmentTree.queryWithLeftBound(3, rightBound: 3)  // just 4
+sumSegmentTree.query(withLeftBound: 0, rightBound: 3)  // 1 + 2 + 3 + 4 = 10
+sumSegmentTree.query(withLeftBound: 1, rightBound: 2)  // 2 + 3 = 5
+sumSegmentTree.query(withLeftBound: 0, rightBound: 0)  // just 1
+sumSegmentTree.query(withLeftBound: 3, rightBound: 3)  // just 4
 ```
 
 Querying the tree takes **O(log n)** time.
@@ -177,21 +177,21 @@ The value of a node in the segment tree depends on the nodes below it. So if we
 Here is the code:
 
 ```swift
-  public func replaceItemAtIndex(index: Int, withItem item: T) {
+  public func replaceItem(at index: Int, withItem item: T) {
     if leftBound == rightBound {
       value = item
     } else if let leftChild = leftChild, rightChild = rightChild {
       if leftChild.rightBound >= index {
-        leftChild.replaceItemAtIndex(index, withItem: item)
+        leftChild.replaceItem(at: index, withItem: item)
       } else {
-        rightChild.replaceItemAtIndex(index, withItem: item)
+        rightChild.replaceItem(at: index, withItem: item)
       }
       value = function(leftChild.value, rightChild.value)
     }
   }
 ```
 
-As usual, this works with recursion. If the node is a leaf, we just change its value. If the node is not a leaf, then we recursively call `replaceItemAtIndex()` to update its children. After that, we recalculate the node's own value so that it is up-to-date again.
+As usual, this works with recursion. If the node is a leaf, we just change its value. If the node is not a leaf, then we recursively call `replaceItem(at: )` to update its children. After that, we recalculate the node's own value so that it is up-to-date again.
 
 Replacing an item takes **O(log n)** time.
 

From a03d083365ba342e16ca44d2a5695f31e1cd22c6 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Mon, 19 Sep 2016 00:13:14 +0200
Subject: [PATCH 0540/1679] update documentation

---
 Skip-List/README.md | 96 +++++++++++++++++++++++++++++++++++++++------
 1 file changed, 85 insertions(+), 11 deletions(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 64f221a23..5c569e177 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -1,30 +1,95 @@
 # Skip List
 
-Skip List is a probablistic data-structure with same efficiency as AVL tree or Red-Black tree. The building blocks are hierarchy of layers (regular sorted linked-lists), created probablisticly by coin flipping, each acting as an express lane to the layer underneath, therefore making fast O(log n) search possible by skipping lanes and reducing travel distance. A layer consists of a Head node, holding reference to the subsequent and the node below. Each node also holds similar references as the Head node.
+Skip List is a probablistic data-structure  with same logarithmic time bound and
+efficiency  as AVL/  or  Red-Black  tree and  provides  a  clever compromise  to
+efficiently support  search and update  operations and is relatively  simpler to
+implement compared to other map data structures.
 
-![Schematic view](Images/Intro.png
-)
+A skip  list *S*  consists of  series of  sorted linked  lists *{L0,  ..., Ln}*,
+layered hierarchicaly and each layer *L* stores  a subset of items in layer *L0*
+in incremental order.  The items in layers  *{L1, ... Ln}* are  chosen at random
+based on a coin flipping function  with probability 1/2 .  For traversing, every
+item in  a layer  hold references  to the node  below and  the next  node.  This
+layers serve as  express lanes to the layer underneath  them, effectively making
+fast O(log n) searching possible by  skipping lanes and reducing travel distance
+and in worse case  searching degrades to O (n), as  expected with regular linked
+list.
 
+For a skip list *S*:
+
+1. List *L0* contains every inserted item.
+2.  For lists *{L1, ..., Ln}*, *Li*  contains a randomly generated subset of the
+   items in *Li-1*
+3. Height is determined by coin-flipping.
+
+![Schematic view](Images/Intro.png)
+Figure 1
+
+
+#Searching
+
+Searching for  element *N* starts by  traversing from top most  layer *Ln* until
+*L0*.
+
+Our objective  is to find an  element *K* such  that its value at  the rightmost
+position of current layer, is less-than  target item and its subsequent node has
+a greater-equal  value or nil (  * K.key < N.key  <= (K.next.key or nil)*  ). if
+value of *K.next* is equal to *N*,  search is terminated and we return *K.next*,
+otherwise drop underneath using *K.down* to the node below ( at layer Ln-1 ) and
+repeat the process until *L0* where *K.down* is `nil` which indicates that level
+is *L0* and item doesn't exists.
+
+
+###Example:
+
+![Inserting first element](Images/Insert5.png)
 
 #Inserting
 
-1. Inserting a new element in initial state where no prior layer is created yet begins by construction of a Head node with a reference to data node (just like regular lists). After this operation coin-flipping starts to determine wether a new layer must be created. When positive, a new layer containing Head and data node ( similar to previous layer ) is created and head is updated to reference the new layer and the head node underneath. Subsequently data node is also updated to reference the node below; until coin-flip function return a negative value to terminate this process.
+Inserting  element  *N*  has  a  similar process  as  searching.  It  starts  by
+traversing from  top most layer *Ln*  until *L0*. We  need to keep track  of our
+traversal path  using a  stack. It  helps us  to traverse  the path  upward when
+coin-flipping starts, so we can insert  our new element and update references to
+it.
 
-2. After initial state, we start at top most layer to find a node where its value is less than the new value and its next node value is greater-equal/nil than new value. Then we use this node to travel to layer underneath until we reach the layer 0 where the element must be inserted first, after this node. Node references must be updated accordingly by back tracing the path to the top. If the first element in the layer does not meet the criteria, same procedure is used to travel to the layer below using the head node.
+Our objective  is to find  a element  *K* such that  its value at  the rightmost
+position of  layer *Ln*,  is less-than new  item and its  subsequent node  has a
+greater-equal value  or nil (  * K.key  < N.key <  (K.next.key or nil)*  ). Push
+element *K*  to the stack and  with element *K*,  go down using *K.down*  to the
+node below  ( at layer Ln-1  ) and repeat the  process ( forward searching  ) up
+until  *L0* where  *K.down* is  `nil`  which indicates  that level  is *L0*.  We
+terminate the process when *K.down* is nil.
 
+At *L0*, *N* can be inserted after *K*.
 
-**Example**
+Here is the  interesting part. We use coin flipping  function to randomly create
+layers.
 
+When  coin flip  function returns  0,  the whole  process is  finished but  when
+returns 1, there are two possibilities:
 
-1 - Inserting 10 in initial state with coin flips (0)
+1. Stack is empty ( Level is *L0* / -*Ln* or at uninitialized stage)
+2. Stack has items ( traversing upward is possible )
 
-![Inserting first element](Images/Insert1.png)
+In case 1:
 
+A new layer M*  is created with a head node *NM* referencing  head node of layer
+below  and *NM.next*  referencing new  element *N*.  New element  *N* referecing
+element *N* at previous layer.
 
-2 - 12 inserted with coin flips (1,1,0)
+In case 2:
 
+repeat until stack is empty Pop an item *F* from stack and update the references
+accordingly.  *F.next* will be *K.next* and *K.next* will be *F*
+	
+when  stack  is  empty Create  a  new  layer  consisintg  of a  head  node  *NM*
+referencing  head node  of layer  below  and *NM.next*  referencing new  element
+*N*. New element *N* referencing element *N* at previous layer.
+		 
 
-3 - Inserting 13. with coin flips (0)
+###Example:
+
+Inserting 13. with coin flips (0)
 
 ![Inserting first element](Images/Insert5.png)
 ![Inserting first element](Images/Insert6.png)
@@ -33,7 +98,16 @@ Skip List is a probablistic data-structure with same efficiency as AVL tree or R
 ![Inserting first element](Images/Insert9.png)
 
 
-#Searching
+
+Inserting 20. with 4 times coin flips (1) 
+![Inserting first element](Images/Insert9.png)
+![Inserting first element](Images/Insert10.png)
+![Inserting first element](Images/insert11.png)
+![Inserting first element](Images/Insert12.png)
+
+#Removing
+
+Removing works similar to insert procedure.
 
 TODO
 

From 23e776b334b69f3ede8a98282c2cd0726118870e Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 19 Sep 2016 00:16:04 +0200
Subject: [PATCH 0541/1679] Update README.md

---
 Skip-List/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 5c569e177..575005ddc 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -102,7 +102,7 @@ Inserting 13. with coin flips (0)
 Inserting 20. with 4 times coin flips (1) 
 ![Inserting first element](Images/Insert9.png)
 ![Inserting first element](Images/Insert10.png)
-![Inserting first element](Images/insert11.png)
+![Inserting first element](Images/Insert11.png)
 ![Inserting first element](Images/Insert12.png)
 
 #Removing

From 8519c48d9f7f235f52a92b22f8fdb4a904e1f2e8 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 19 Sep 2016 00:18:53 +0200
Subject: [PATCH 0542/1679] Update README.md

---
 Skip-List/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 575005ddc..664684621 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -22,7 +22,7 @@ For a skip list *S*:
    items in *Li-1*
 3. Height is determined by coin-flipping.
 
-![Schematic view](Images/Intro.png)
+![Schematic view](Images/Search.png)
 Figure 1
 
 

From 512b603a7acf860b4af0aac124ecfa5794a8ecd8 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 19 Sep 2016 00:19:13 +0200
Subject: [PATCH 0543/1679] Update README.md

---
 Skip-List/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 664684621..6d47f05df 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -22,7 +22,7 @@ For a skip list *S*:
    items in *Li-1*
 3. Height is determined by coin-flipping.
 
-![Schematic view](Images/Search.png)
+![Schematic view](Images/Search1.png)
 Figure 1
 
 

From 87d81428ad852ee84f82a0e5f9583da9134c25c3 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 19 Sep 2016 00:19:36 +0200
Subject: [PATCH 0544/1679] Update README.md

---
 Skip-List/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 6d47f05df..5c39e3db8 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -22,7 +22,7 @@ For a skip list *S*:
    items in *Li-1*
 3. Height is determined by coin-flipping.
 
-![Schematic view](Images/Search1.png)
+![Schematic view](Images/Intro.png)
 Figure 1
 
 
@@ -42,7 +42,7 @@ is *L0* and item doesn't exists.
 
 ###Example:
 
-![Inserting first element](Images/Insert5.png)
+![Inserting first element](Images/Search1.png)
 
 #Inserting
 

From 5891a6b4b9d26d97b837d2fcfe2b93e50043fcb4 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 19 Sep 2016 00:20:59 +0200
Subject: [PATCH 0545/1679] Update README.md

---
 Skip-List/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Skip-List/README.md b/Skip-List/README.md
index 5c39e3db8..d3824952b 100644
--- a/Skip-List/README.md
+++ b/Skip-List/README.md
@@ -33,7 +33,7 @@ Searching for  element *N* starts by  traversing from top most  layer *Ln* until
 
 Our objective  is to find an  element *K* such  that its value at  the rightmost
 position of current layer, is less-than  target item and its subsequent node has
-a greater-equal  value or nil (  * K.key < N.key  <= (K.next.key or nil)*  ). if
+a greater-equal  value or nil (  *K.key < N.key  <= (K.next.key or nil)*  ). if
 value of *K.next* is equal to *N*,  search is terminated and we return *K.next*,
 otherwise drop underneath using *K.down* to the node below ( at layer Ln-1 ) and
 repeat the process until *L0* where *K.down* is `nil` which indicates that level
@@ -54,7 +54,7 @@ it.
 
 Our objective  is to find  a element  *K* such that  its value at  the rightmost
 position of  layer *Ln*,  is less-than new  item and its  subsequent node  has a
-greater-equal value  or nil (  * K.key  < N.key <  (K.next.key or nil)*  ). Push
+greater-equal value  or nil (  *K.key  < N.key <  (K.next.key or nil)*  ). Push
 element *K*  to the stack and  with element *K*,  go down using *K.down*  to the
 node below  ( at layer Ln-1  ) and repeat the  process ( forward searching  ) up
 until  *L0* where  *K.down* is  `nil`  which indicates  that level  is *L0*.  We
@@ -68,7 +68,7 @@ layers.
 When  coin flip  function returns  0,  the whole  process is  finished but  when
 returns 1, there are two possibilities:
 
-1. Stack is empty ( Level is *L0* / -*Ln* or at uninitialized stage)
+1. Stack is empty ( Level is *L0* /- *Ln* or at uninitialized stage)
 2. Stack has items ( traversing upward is possible )
 
 In case 1:

From a8b5ef93d12b8399586427624dac24cecb760e42 Mon Sep 17 00:00:00 2001
From: Kauserali Hafizji <ali.hafizji@gmail.com>
Date: Mon, 19 Sep 2016 21:20:22 +0530
Subject: [PATCH 0546/1679] Palindromes now work with strings with even length

---
 Palindromes/Palindromes.playground/Contents.swift | 8 +++-----
 Palindromes/Palindromes.swift                     | 6 +-----
 2 files changed, 4 insertions(+), 10 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index 20df10ee4..bb666ee9a 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -5,11 +5,7 @@ public func palindromeCheck(text: String?) -> Bool {
     let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
     let length: Int = mutableText.characters.count
     
-    guard length >= 1 else {
-      return false
-    }
-    
-    if length == 1 {
+    if length == 1 || length == 0 {
       return true
     } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
       let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
@@ -31,6 +27,8 @@ palindromeCheck(text: "Race fast Safe car")
 // Test to check that palindromes are found regardless of case:
 palindromeCheck(text: "HelloLLEH")
 
+palindromeCheck(text: "moom")
+
 // Test that nil and empty Strings return false:
 palindromeCheck(text: "")
 palindromeCheck(text: nil)
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 036ce3d34..889ff357e 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -5,11 +5,7 @@ public func palindromeCheck(text: String?) -> Bool {
     let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
     let length: Int = mutableText.characters.count
     
-    guard length >= 1 else {
-      return false
-    }
-    
-    if length == 1 {
+    if length == 1 || length == 0 {
       return true
     } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
       let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))

From 1be7dec130c5193d8b9427fa94783195bb42c312 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Mon, 19 Sep 2016 20:03:12 +0200
Subject: [PATCH 0547/1679] made enums lowerCamelCase

---
 .../Sources/RBTree.swift                      | 62 +++++++++----------
 1 file changed, 31 insertions(+), 31 deletions(-)

diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift
index c5bcd0a3e..9649a2175 100644
--- a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -1,12 +1,12 @@
 
 private enum RBTColor {
-    case Red
-    case Black
-    case DoubleBlack
+    case red
+    case black
+    case doubleBlack
 }
 
 public class RBTNode<T: Comparable> {
-    fileprivate var color: RBTColor = .Red
+    fileprivate var color: RBTColor = .red
     public var value: T! = nil
     public var right:  RBTNode<T>!
     public var left:  RBTNode<T>!
@@ -49,15 +49,15 @@ public class RBTNode<T: Comparable> {
     }
     
     fileprivate var isRed: Bool {
-        return color == .Red
+        return color == .red
     }
     
     fileprivate var isBlack: Bool {
-        return color == .Black
+        return color == .black
     }
     
     fileprivate var isDoubleBlack: Bool {
-        return color == .DoubleBlack
+        return color == .doubleBlack
     }
 }
 
@@ -67,7 +67,7 @@ public class RBTree<T: Comparable> {
     
     public init() {
         nullLeaf = RBTNode<T>()
-        nullLeaf.color = .Black
+        nullLeaf.color = .black
         root = nullLeaf
     }
     
@@ -175,7 +175,7 @@ public class RBTree<T: Comparable> {
     // if node is root change color to black, else move on
     private func insertCase1(n: RBTNode<T>) {
         if n === root {
-            n.color = .Black
+            n.color = .black
         } else {
             insertCase2(n: n)
         }
@@ -192,9 +192,9 @@ public class RBTree<T: Comparable> {
     private func insertCase3(n: RBTNode<T>) {
         if n.uncle.isRed { // node must have grandparent as children of root have a black parent
             // both parent and uncle are red, so grandparent must be black.
-            n.parent.color = .Black
-            n.uncle.color = .Black
-            n.grandparent.color = .Red
+            n.parent.color = .black
+            n.uncle.color = .black
+            n.grandparent.color = .red
             // now both parent and uncle are black and grandparent is red.
             // we repeat for the grandparent
             insertCase1(n: n.grandparent)
@@ -226,8 +226,8 @@ public class RBTree<T: Comparable> {
     private func insertCase5(n: RBTNode<T>) {
         // swap color of parent and grandparent
         // parent is red grandparent is black
-        n.parent.color = .Black
-        n.grandparent.color = .Red
+        n.parent.color = .black
+        n.grandparent.color = .red
         
         if n.isLeftChild { // left left case
             rightRotate(n: n.grandparent)
@@ -269,7 +269,7 @@ public class RBTree<T: Comparable> {
         }
         
         if toDel.isRed || child.isRed {
-            child.color = .Black
+            child.color = .black
             
             if toDel.isLeftChild {
                 toDel.parent.left = child
@@ -292,7 +292,7 @@ public class RBTree<T: Comparable> {
             if child !== nullLeaf {
                 child.parent = toDel.parent
             }
-            child.color = .DoubleBlack
+            child.color = .doubleBlack
             
             while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
                 if sibling!.isBlack {
@@ -307,35 +307,35 @@ public class RBTree<T: Comparable> {
                     }
                     
                     if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
-                        child.color = .Black
+                        child.color = .black
                         if sibling!.isLeftChild {
                             if leftRedChild != nil { // left left case
-                                sibling!.left.color = .Black
+                                sibling!.left.color = .black
                                 let tempColor = sibling!.parent.color
                                 sibling!.parent.color = sibling!.color
                                 sibling!.color = tempColor
                                 rightRotate(n: sibling!.parent)
                             } else { // left right case
                                 if sibling!.parent.isRed {
-                                    sibling!.parent.color = .Black
+                                    sibling!.parent.color = .black
                                 } else {
-                                    sibling!.right.color = .Black
+                                    sibling!.right.color = .black
                                 }
                                 leftRotate(n: sibling!)
                                 rightRotate(n: sibling!.grandparent)
                             }
                         } else {
                             if rightRedChild != nil { // right right case
-                                sibling!.right.color = .Black
+                                sibling!.right.color = .black
                                 let tempColor = sibling!.parent.color
                                 sibling!.parent.color = sibling!.color
                                 sibling!.color = tempColor
                                 leftRotate(n: sibling!.parent)
                             } else { // right left case
                                 if sibling!.parent.isRed {
-                                    sibling!.parent.color = .Black
+                                    sibling!.parent.color = .black
                                 } else {
-                                    sibling!.left.color = .Black
+                                    sibling!.left.color = .black
                                 }
                                 rightRotate(n: sibling!)
                                 leftRotate(n: sibling!.grandparent)
@@ -343,34 +343,34 @@ public class RBTree<T: Comparable> {
                         }
                         break
                     } else { // both sibling's children are black
-                        child.color = .Black
-                        sibling!.color = .Red
+                        child.color = .black
+                        sibling!.color = .red
                         if sibling!.parent.isRed {
-                            sibling!.parent.color = .Black
+                            sibling!.parent.color = .black
                             break
                         }
-                        sibling!.parent.color = .DoubleBlack
+                        sibling!.parent.color = .doubleBlack
                         child = sibling!.parent
                         sibling = child.sibling
                     }
                 } else { // sibling is red
-                    sibling!.color = .Black
+                    sibling!.color = .black
                     
                     if sibling!.isLeftChild { // left case
                         rightRotate(n: sibling!.parent)
                         sibling = sibling!.right.left
-                        sibling!.parent.color = .Red
+                        sibling!.parent.color = .red
                     } else { // right case
                         leftRotate(n: sibling!.parent)
                         sibling = sibling!.left.right
-                        sibling!.parent.color = .Red
+                        sibling!.parent.color = .red
                     }
                 }
                 
                 // sibling check is here for when child is a nullLeaf and thus does not have a parent.
                 // child is here as sibling can become nil when child is the root
                 if (sibling != nil && sibling!.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
-                    child.color = .Black
+                    child.color = .black
                 }
             }
         }

From a5397bbe7fd3ed678665980abaffb0ec00e92667 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Mon, 19 Sep 2016 20:51:36 +0200
Subject: [PATCH 0548/1679] adopted CustomStringConvertible protocol

---
 .../Sources/RBTree.swift                      | 29 +++++++++++++++++--
 1 file changed, 27 insertions(+), 2 deletions(-)

diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift
index 9649a2175..adfd38216 100644
--- a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -5,13 +5,34 @@ private enum RBTColor {
     case doubleBlack
 }
 
-public class RBTNode<T: Comparable> {
+public class RBTNode<T: Comparable>: CustomStringConvertible {
     fileprivate var color: RBTColor = .red
     public var value: T! = nil
     public var right:  RBTNode<T>!
     public var left:  RBTNode<T>!
     public var parent:  RBTNode<T>!
     
+    public var description: String {
+        if self.value == nil {
+            return "null"
+        } else {
+            var nodeValue: String
+            
+            // If the value is encapsulated by parentheses it is red
+            // If the value is encapsulated by pipes it is black
+            // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
+            if self.isRed {
+                nodeValue = "(\(self.value!))"
+            } else if self.isBlack{
+                nodeValue = "|\(self.value!)|"
+            } else {
+                nodeValue = "||\(self.value!)||"
+            }
+            
+            return "(\(self.left.description)<-\(nodeValue)->\(self.right.description))"
+        }
+    }
+    
     init(tree: RBTree<T>) {
         right = tree.nullLeaf
         left = tree.nullLeaf
@@ -61,10 +82,14 @@ public class RBTNode<T: Comparable> {
     }
 }
 
-public class RBTree<T: Comparable> {
+public class RBTree<T: Comparable>: CustomStringConvertible {
     public var root: RBTNode<T>
     fileprivate let nullLeaf: RBTNode<T>
     
+    public var description: String {
+        return root.description
+    }
+    
     public init() {
         nullLeaf = RBTNode<T>()
         nullLeaf.color = .black

From d663d5dfe909b3bde9e3c3391dca3239ebc8d920 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 20 Sep 2016 00:30:39 +0200
Subject: [PATCH 0549/1679] changed sibling property to be non optional and
 fixed insertion bug

---
 .../Contents.swift                            | 25 +++--
 .../Sources/RBTree.swift                      | 98 ++++++++++---------
 2 files changed, 72 insertions(+), 51 deletions(-)

diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift
index b4fadff92..d55c153d5 100644
--- a/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift	
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift	
@@ -1,9 +1,20 @@
 //: Playground - noun: a place where people can play
+import Foundation
 
-let array = [6,78,89,4]
-var tree = RBTree<Int>(withArray: array)
-tree.insert(5)
-tree.insert(8)
-tree.insert(2)
-tree.delete(6)
-tree.delete(8)
\ No newline at end of file
+let tree = RBTree<Double>()
+let randomMax = Double(0x100000000)
+var values = [Double]()
+for _ in 0..<1000 {
+    let value = Double(arc4random()) / randomMax
+    values.append(value)
+    tree.insert(value)
+}
+tree.verify()
+ 
+for _ in 0..<1000 {
+    let rand = arc4random_uniform(UInt32(values.count))
+    let index = Int(rand)
+    let value = values.remove(at: index)
+    tree.delete(value)
+}
+tree.verify()
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift
index adfd38216..1735798d5 100644
--- a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -55,13 +55,11 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
         return parent.parent
     }
     
-    public var sibling: RBTNode<T>! {
+    public var sibling: RBTNode<T> {
         if isLeftChild {
             return self.parent.right
-        } else if isRightChild {
-            return self.parent.left
         } else {
-            return nil
+            return self.parent.left
         }
     }
     
@@ -245,6 +243,8 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         } else if n.parent.isRightChild && n.isLeftChild { // right left case
             rightRotate(n: n.parent)
             insertCase5(n: n.right)
+        } else {
+            insertCase5(n: n)
         }
     }
     
@@ -320,81 +320,91 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             child.color = .doubleBlack
             
             while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
-                if sibling!.isBlack {
+                if sibling.isBlack {
                     
                     var leftRedChild: RBTNode<T>! = nil
-                    if sibling!.left.isRed {
-                        leftRedChild = sibling!.left
+                    if sibling.left.isRed {
+                        leftRedChild = sibling.left
                     }
                     var rightRedChild: RBTNode<T>! = nil
-                    if sibling!.right.isRed {
-                        rightRedChild = sibling!.right
+                    if sibling.right.isRed {
+                        rightRedChild = sibling.right
                     }
                     
                     if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
                         child.color = .black
-                        if sibling!.isLeftChild {
+                        if sibling.isLeftChild {
                             if leftRedChild != nil { // left left case
-                                sibling!.left.color = .black
-                                let tempColor = sibling!.parent.color
-                                sibling!.parent.color = sibling!.color
-                                sibling!.color = tempColor
-                                rightRotate(n: sibling!.parent)
+                                sibling.left.color = .black
+                                let tempColor = sibling.parent.color
+                                sibling.parent.color = sibling.color
+                                sibling.color = tempColor
+                                rightRotate(n: sibling.parent)
                             } else { // left right case
-                                if sibling!.parent.isRed {
-                                    sibling!.parent.color = .black
+                                if sibling.parent.isRed {
+                                    sibling.parent.color = .black
                                 } else {
-                                    sibling!.right.color = .black
+                                    sibling.right.color = .black
                                 }
-                                leftRotate(n: sibling!)
-                                rightRotate(n: sibling!.grandparent)
+                                leftRotate(n: sibling)
+                                rightRotate(n: sibling.grandparent)
                             }
                         } else {
                             if rightRedChild != nil { // right right case
-                                sibling!.right.color = .black
-                                let tempColor = sibling!.parent.color
-                                sibling!.parent.color = sibling!.color
-                                sibling!.color = tempColor
-                                leftRotate(n: sibling!.parent)
+                                sibling.right.color = .black
+                                let tempColor = sibling.parent.color
+                                sibling.parent.color = sibling.color
+                                sibling.color = tempColor
+                                leftRotate(n: sibling.parent)
                             } else { // right left case
-                                if sibling!.parent.isRed {
-                                    sibling!.parent.color = .black
+                                if sibling.parent.isRed {
+                                    sibling.parent.color = .black
                                 } else {
-                                    sibling!.left.color = .black
+                                    sibling.left.color = .black
                                 }
-                                rightRotate(n: sibling!)
-                                leftRotate(n: sibling!.grandparent)
+                                rightRotate(n: sibling)
+                                leftRotate(n: sibling.grandparent)
                             }
                         }
                         break
                     } else { // both sibling's children are black
                         child.color = .black
-                        sibling!.color = .red
-                        if sibling!.parent.isRed {
-                            sibling!.parent.color = .black
+                        sibling.color = .red
+                        if sibling.parent.isRed {
+                            sibling.parent.color = .black
                             break
                         }
-                        sibling!.parent.color = .doubleBlack
-                        child = sibling!.parent
+                        /*
+                        sibling.parent.color = .doubleBlack
+                        child = sibling.parent
                         sibling = child.sibling
+                        */
+                        if sibling.parent.parent === nullLeaf { // parent of child is root
+                            break
+                        } else {
+                            sibling.parent.color = .doubleBlack
+                            child = sibling.parent
+                            sibling = child.sibling // can become nill if child is root as parent is nullLeaf
+                        }
+                        //---------------
                     }
                 } else { // sibling is red
-                    sibling!.color = .black
+                    sibling.color = .black
                     
-                    if sibling!.isLeftChild { // left case
-                        rightRotate(n: sibling!.parent)
-                        sibling = sibling!.right.left
-                        sibling!.parent.color = .red
+                    if sibling.isLeftChild { // left case
+                        rightRotate(n: sibling.parent)
+                        sibling = sibling.right.left
+                        sibling.parent.color = .red
                     } else { // right case
-                        leftRotate(n: sibling!.parent)
-                        sibling = sibling!.left.right
-                        sibling!.parent.color = .red
+                        leftRotate(n: sibling.parent)
+                        sibling = sibling.left.right
+                        sibling.parent.color = .red
                     }
                 }
                 
                 // sibling check is here for when child is a nullLeaf and thus does not have a parent.
                 // child is here as sibling can become nil when child is the root
-                if (sibling != nil && sibling!.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
+                if (sibling.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
                     child.color = .black
                 }
             }

From 4800819588174de53542fc9a4b791d931e035541 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 20 Sep 2016 02:04:02 +0200
Subject: [PATCH 0550/1679] Updated readme

---
 Red-Black Tree 2/README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Red-Black Tree 2/README.markdown b/Red-Black Tree 2/README.markdown
index abb1c2f55..47fc6a08f 100644
--- a/Red-Black Tree 2/README.markdown	
+++ b/Red-Black Tree 2/README.markdown	
@@ -8,3 +8,5 @@ http://www.geeksforgeeks.org/red-black-tree-set-2-insert/
 http://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/
 
 Important to note is that the last one doesn't mention a few important details about deletion cases which can be found in the code itself.
+
+*Written for Swift Algorithm Club by Jaap Wijnen*

From 64f93cf4945fadde007756e040dbef4eb0d92ec9 Mon Sep 17 00:00:00 2001
From: Dee <dee@Dee-2.local>
Date: Tue, 20 Sep 2016 13:35:59 +0800
Subject: [PATCH 0551/1679] make some conversion

---
 .../kthLargest.playground/Contents.swift      | 34 +++++++++----------
 .../xcshareddata/kthLargest.xcscmblueprint    | 30 ++++++++++++++++
 .../kthLargest.playground/timeline.xctimeline |  6 ----
 3 files changed, 47 insertions(+), 23 deletions(-)
 create mode 100644 Kth Largest Element/kthLargest.playground/playground.xcworkspace/xcshareddata/kthLargest.xcscmblueprint
 delete mode 100644 Kth Largest Element/kthLargest.playground/timeline.xctimeline

diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 628892d9c..9fba2b483 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -1,9 +1,9 @@
 //: Playground - noun: a place where people can play
 
-func kthLargest(a: [Int], k: Int) -> Int? {
+func kthLargest(_ a: [Int], _ k: Int) -> Int? {
   let len = a.count
   if k > 0 && k <= len {
-    let sorted = a.sort()
+    let sorted = a.sorted()
     return sorted[len - k]
   } else {
     return nil
@@ -12,15 +12,15 @@ func kthLargest(a: [Int], k: Int) -> Int? {
 
 let a = [5, 1, 3, 2, 7, 6, 4]
 
-kthLargest(a, k: 0)
-kthLargest(a, k: 1)
-kthLargest(a, k: 2)
-kthLargest(a, k: 3)
-kthLargest(a, k: 4)
-kthLargest(a, k: 5)
-kthLargest(a, k: 6)
-kthLargest(a, k: 7)
-kthLargest(a, k: 8)
+kthLargest(a, 0)
+kthLargest(a, 1)
+kthLargest(a, 2)
+kthLargest(a, 3)
+kthLargest(a, 4)
+kthLargest(a, 5)
+kthLargest(a, 6)
+kthLargest(a, 7)
+kthLargest(a, 8)
 
 
 
@@ -28,7 +28,7 @@ kthLargest(a, k: 8)
 import Foundation
 
 /* Returns a random integer in the range min...max, inclusive. */
-public func random(min min: Int, max: Int) -> Int {
+public func random( min: Int, max: Int) -> Int {
   assert(min < max)
   return min + Int(arc4random_uniform(UInt32(max - min + 1)))
 }
@@ -37,22 +37,22 @@ public func random(min min: Int, max: Int) -> Int {
   Swift's swap() doesn't like it if the items you're trying to swap refer to
   the same memory location. This little wrapper simply ignores such swaps.
 */
-public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
+public func swap<T>(_ a:inout [T], _ i: Int, _ j: Int) {
   if i != j {
     swap(&a[i], &a[j])
   }
 }
 
-public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
+public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
-  func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
+  func randomPivot<T: Comparable>(_ a: inout[T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
     swap(&a, pivotIndex, high)
     return a[high]
   }
 
-  func randomizedPartition<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> Int {
+  func randomizedPartition<T: Comparable>(_ a: inout[T], _ low: Int, _ high: Int) -> Int {
     let pivot = randomPivot(&a, low, high)
     var i = low
     for j in low..<high {
@@ -65,7 +65,7 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
     return i
   }
 
-  func randomizedSelect<T: Comparable>(inout a: [T], _ low: Int, _ high: Int, _ k: Int) -> T {
+  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
     if low < high {
       let p = randomizedPartition(&a, low, high)
       if k == p {
diff --git a/Kth Largest Element/kthLargest.playground/playground.xcworkspace/xcshareddata/kthLargest.xcscmblueprint b/Kth Largest Element/kthLargest.playground/playground.xcworkspace/xcshareddata/kthLargest.xcscmblueprint
new file mode 100644
index 000000000..c747b8a38
--- /dev/null
+++ b/Kth Largest Element/kthLargest.playground/playground.xcworkspace/xcshareddata/kthLargest.xcscmblueprint	
@@ -0,0 +1,30 @@
+{
+  "DVTSourceControlWorkspaceBlueprintPrimaryRemoteRepositoryKey" : "CF309AABC690F91A443043D5C69EECB0069B5411",
+  "DVTSourceControlWorkspaceBlueprintWorkingCopyRepositoryLocationsKey" : {
+
+  },
+  "DVTSourceControlWorkspaceBlueprintWorkingCopyStatesKey" : {
+    "CF309AABC690F91A443043D5C69EECB0069B5411" : 9223372036854775807,
+    "FA0506A44181383605977F2A9C8020B861F7CE04" : 9223372036854775807
+  },
+  "DVTSourceControlWorkspaceBlueprintIdentifierKey" : "6CCD70DA-EE44-4E31-98F0-6DA8B083772A",
+  "DVTSourceControlWorkspaceBlueprintWorkingCopyPathsKey" : {
+    "CF309AABC690F91A443043D5C69EECB0069B5411" : "swift-algorithm-club\/",
+    "FA0506A44181383605977F2A9C8020B861F7CE04" : ""
+  },
+  "DVTSourceControlWorkspaceBlueprintNameKey" : "kthLargest",
+  "DVTSourceControlWorkspaceBlueprintVersion" : 204,
+  "DVTSourceControlWorkspaceBlueprintRelativePathToProjectKey" : "Kth Largest Element\/kthLargest.playground",
+  "DVTSourceControlWorkspaceBlueprintRemoteRepositoriesKey" : [
+    {
+      "DVTSourceControlWorkspaceBlueprintRemoteRepositoryURLKey" : "https:\/\/github.com\/Deeer\/swift-algorithm-club.git",
+      "DVTSourceControlWorkspaceBlueprintRemoteRepositorySystemKey" : "com.apple.dt.Xcode.sourcecontrol.Git",
+      "DVTSourceControlWorkspaceBlueprintRemoteRepositoryIdentifierKey" : "CF309AABC690F91A443043D5C69EECB0069B5411"
+    },
+    {
+      "DVTSourceControlWorkspaceBlueprintRemoteRepositoryURLKey" : "https:\/\/github.com\/Deeer\/CuteSticker.git",
+      "DVTSourceControlWorkspaceBlueprintRemoteRepositorySystemKey" : "com.apple.dt.Xcode.sourcecontrol.Git",
+      "DVTSourceControlWorkspaceBlueprintRemoteRepositoryIdentifierKey" : "FA0506A44181383605977F2A9C8020B861F7CE04"
+    }
+  ]
+}
\ No newline at end of file
diff --git a/Kth Largest Element/kthLargest.playground/timeline.xctimeline b/Kth Largest Element/kthLargest.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Kth Largest Element/kthLargest.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From b4b572f4dcf580d550f5757f547e761db78a30b1 Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Tue, 20 Sep 2016 22:30:03 +0800
Subject: [PATCH 0552/1679] updated fizzBuzz to swift3

---
 Fizz Buzz/FizzBuzz.playground/Contents.swift               | 2 +-
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 +++++++
 Fizz Buzz/FizzBuzz.playground/timeline.xctimeline          | 6 ------
 Fizz Buzz/FizzBuzz.swift                                   | 2 +-
 Fizz Buzz/README.markdown                                  | 2 +-
 5 files changed, 10 insertions(+), 9 deletions(-)
 create mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/timeline.xctimeline

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index 9d7a974fa..ba2f83b15 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,4 +1,4 @@
-func fizzBuzz(numberOfTurns: Int) {
+func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
     var result = ""
 
diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Fizz Buzz/FizzBuzz.playground/timeline.xctimeline b/Fizz Buzz/FizzBuzz.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Fizz Buzz/FizzBuzz.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index a801f34ee..b6bb410e7 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,4 +1,4 @@
-func fizzBuzz(numberOfTurns: Int) {
+func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
     var result = ""
 
diff --git a/Fizz Buzz/README.markdown b/Fizz Buzz/README.markdown
index e4cf485ff..8c250da27 100644
--- a/Fizz Buzz/README.markdown	
+++ b/Fizz Buzz/README.markdown	
@@ -58,7 +58,7 @@ Finding numbers divisible by five:
 Here is a simple implementation in Swift:
 
 ```swift
-func fizzBuzz(numberOfTurns: Int) {
+func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
     var result = ""
 

From 3e6623179d8809e27fc9b151a3fd9d1ede4f503d Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 20 Sep 2016 17:58:01 +0200
Subject: [PATCH 0553/1679] updated readme

---
 Red-Black Tree 2/README.markdown | 119 +++++++++++++++++++++++++++++--
 1 file changed, 113 insertions(+), 6 deletions(-)

diff --git a/Red-Black Tree 2/README.markdown b/Red-Black Tree 2/README.markdown
index 47fc6a08f..9496e6318 100644
--- a/Red-Black Tree 2/README.markdown	
+++ b/Red-Black Tree 2/README.markdown	
@@ -1,12 +1,119 @@
 # Red-Black Tree
 
-Used info from
+A Red-Black tree is a special version of a [Binary Search  Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Search%20Tree). Binary search trees(BSTs) can become unbalanced after a lot of insertions/deletions. The only difference between a node from a BST and a Red-Black Tree(RBT) is that RBT nodes have a color property added to them which can either be red or black. A RBT rebalances itself by making sure the following properties hold:
 
-https://en.wikipedia.org/wiki/Red–black_tree
-http://www.geeksforgeeks.org/red-black-tree-set-1-introduction-2/
-http://www.geeksforgeeks.org/red-black-tree-set-2-insert/
-http://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/
+## Properties
+1. A node is either red or black
+2. The root is always black
+3. All leaves are black
+4. If a node is red, both of its children are black
+5. Every path to a leaf contains the same number of black nodes (The amount of black nodes met when going down a RBT is called the black-depth of the tree.)
 
-Important to note is that the last one doesn't mention a few important details about deletion cases which can be found in the code itself.
+## Methods
+* `insert(_ value: T)` inserts the value into the tree
+* `insert(_ values: [T])` inserts an array of values into the tree
+* `delete(_ value: T)` deletes the value from the tree
+* `find(_ value: T) -> RBTNode<T>` looks for a node in the tree with given value and returns it
+* `minimum(n: RBTNode<T>) -> RBTNode<T>` looks for the maximum value of a subtree starting at the given node
+* `maximum(n: RBTNode<T>) -> RBTNode<T>` looks for the minimum value of a subtree starting at the given node
+* `func verify()` verifies if the tree is still valid. Prints warning messages if this is not the case
+
+## Rotation
+
+In order to rebalance their nodes RBTs use an operation known as rotation. You can either left or right rotate a node and its child. Rotating a node and its child swaps the nodes and interchanges their subtrees. Left rotation swaps the parent node with its right child. while right rotation swaps the parent node with its left child.
+
+Left rotation:
+```
+before left rotating p       after left rotating p  
+     p                         b
+   /   \                     /   \
+  a     b          ->       p     n
+ / \   / \                 / \   
+n   n  n  n               a   n
+                         / \
+                        n   n
+```
+Right rotation:
+```
+before right rotating p       after right rotating p  
+     p                         a
+   /   \                     /   \
+  a     b          ->       n     p
+ / \   / \                       / \   
+n   n  n  n                     n   b
+                                   / \
+                                  n   n
+```
+
+## Insertion
+
+We create a new node with the value to be inserted into the tree. The color of this new node is always red.
+We perform a standard BST insert with this node. Now the three might not be a valid RBT anymore.
+We now go through several insertion steps in order to make the tree valid again. We call the just inserted node n.
+1. We check if n is the rootNode, if so we paint it black and we are done. If not we go to step 2.
+
+We now know that n at least has a parent as it is not the rootNode.
+
+2. We check if the parent of n is black if so we are done. If not we go to step 3.
+
+We now know the parent is also not the root node as the parent is red. Thus n also has a grandparent and thus also an uncle as every node has two children. This uncle may however be a nullLeaf
+
+3. We check if n's uncle is red. If not we go to 4. If n's uncle is indeed red we recolor uncle and parent to black and n's grandparent to red. We now go back to step 1 performing the same logic on n's grandparent.
+
+From here there are four cases:
+- **The left left case.** n's parent is the left child of its parent and n is the left child of its parent.
+- **The left right case** n's parent is the left child of its parent and n is the right child of its parent.
+- **The right right case** n's parent is the right child of its parent and n is the right child of its parent.
+- **The right left case** n's parent is the right child of its parent and n is the left child of its parent.
+
+4. Step 4 checks if either the **left right** case or the **right left** case applies to the current situation.
+  - If we find the **left right case**, we left rotate n's parent and go to step 5 while setting n to n's parent. (This transforms the **left right** case into the **left left** case)
+  - If we find the **right left case**, we right rotate n's parent and go to step 5 while setting n to n's parent. (This transforms the **right left** case into the **right right** case)
+  - If we find neither of these two we proceed to step 5.
+
+n's parent is now red, while n's grandparent is black.
+
+5. We swap the colors of n's parent and grandparent.
+  - We either right rotate n's grandparent in case of the **left left** case
+  - Or we left rotate n's grandparent in case of the **right right** case
+
+Reaching the end we have successfully made the tree valid again.
+
+# Deletion
+
+Deletion is a little more complicated than insertion. In the following we call del the node to be deleted.
+First we try and find the node to be deleted using find()
+we send the result of find to del.
+We now go through the following steps in order to delete the node del.
+
+First we do a few checks:
+- Is del the rootNode if so set the root to a nullLeaf and we are done.
+- If del has 2 nullLeaf children and is red. We check if del is either a left or a right child and set del's parent left or right to a nullLeaf.
+- If del has two non nullLeaf children we look for the maximum value in del's left subtree. We set del's value to this maximum value and continue to instead delete this maximum node. Which we will now call del.
+
+Because of these checks we now know that del has at most 1 non nullLeaf child. It has either two nullLeaf children or one nullLeaf and one regular red child. (The child is red otherwise the black-depth wouldn't be the same for every leaf)
+
+We now call the non nullLeaf child of del, child. If del has two nullLeaf children child will be a nullLeaf. This means child can either be a nullLeaf or a red node.
+
+We now have three options
+
+- If del is red its child is a nullLeaf and we can just delete it as it doesn't change the black-depth of the tree. We are done
+
+- If child is red we recolor it black and child's parent to del's parent. del is now deleted and we are done.
+
+- Both del and child are black we go through
+
+If both del and child are black we introduce a new variable sibling. Which is del's sibling. We also replace del with child and recolor it doubleBlack. del is now deleted and child and sibling are siblings.
+
+We now have to go through a lot of steps in order to remove this doubleBlack color. Which are hard to explain in text without just writing the full code in text. This is due the many possible combination of nodes and colors. The code is commented, but if you don't quite understand please leave me a message. Also part of the deletion is described by the final link in the Also See section.
+
+## Also see
+
+* [Wikipedia](https://en.wikipedia.org/wiki/Red–black_tree)
+* [GeeksforGeeks - introduction](http://www.geeksforgeeks.org/red-black-tree-set-1-introduction-2/)
+* [GeeksforGeeks - insertion](http://www.geeksforgeeks.org/red-black-tree-set-2-insert/)
+* [GeeksforGeeks - deletion](http://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/)
+
+Important to note is that GeeksforGeeks doesn't mention a few deletion cases that do occur. The code however does implement these.
 
 *Written for Swift Algorithm Club by Jaap Wijnen*

From 551fd6dec6f3490046d31a9ec726a8395c3245a0 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 20 Sep 2016 18:10:37 +0200
Subject: [PATCH 0554/1679] replaced old RBTree with new implementation

---
 Red-Black Tree 2/RBTree.swift                 | Bin 1104 -> 0 bytes
 Red-Black Tree/RBTree.swift                   | Bin 13367 -> 1104 bytes
 .../README.markdown                           |   0
 Red-Black Tree/README.md                      |  69 ------------------
 .../Contents.swift                            |   0
 .../Sources/RBTree.swift                      |   0
 .../contents.xcplayground                     |   0
 .../contents.xcworkspacedata                  |   0
 Red-Black Tree/files/fig1.png                 | Bin 24455 -> 0 bytes
 Red-Black Tree/files/fig2.png                 | Bin 40534 -> 0 bytes
 10 files changed, 69 deletions(-)
 delete mode 100644 Red-Black Tree 2/RBTree.swift
 rename {Red-Black Tree 2 => Red-Black Tree}/README.markdown (100%)
 delete mode 100644 Red-Black Tree/README.md
 rename {Red-Black Tree 2 => Red-Black Tree}/Red-Black Tree 2.playground/Contents.swift (100%)
 rename {Red-Black Tree 2 => Red-Black Tree}/Red-Black Tree 2.playground/Sources/RBTree.swift (100%)
 rename {Red-Black Tree 2 => Red-Black Tree}/Red-Black Tree 2.playground/contents.xcplayground (100%)
 rename {Red-Black Tree 2 => Red-Black Tree}/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata (100%)
 delete mode 100644 Red-Black Tree/files/fig1.png
 delete mode 100644 Red-Black Tree/files/fig2.png

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diff --git a/Red-Black Tree 2/README.markdown b/Red-Black Tree/README.markdown
similarity index 100%
rename from Red-Black Tree 2/README.markdown
rename to Red-Black Tree/README.markdown
diff --git a/Red-Black Tree/README.md b/Red-Black Tree/README.md
deleted file mode 100644
index e1b887c3a..000000000
--- a/Red-Black Tree/README.md	
+++ /dev/null
@@ -1,69 +0,0 @@
-# Red Black Tree
-![fig1](files/fig1.png)  
-Red-black trees are an evolution of binary search trees that aim to keep the tree balanced without affecting the complexity of the primitive operations. This is done by coloring each node in the tree with either red or black and preserving a set of properties that guarantee that the deepest path in the tree is not longer than twice the shortest one.  
-## Motivation:
-* We want a balanced binary search tree    
-* Height of the tree is O(log n)  
-* Red-Black Tree is an implementation of a balanced binary search tree
-
-
-## Invariants:  
-1. Every node is colored either red or black
-2. All leaf (nil) nodes are colored with black; if a node’s child is missing then we will assume that it has a nil child in that place and this nil child is always colored black.
-3. Both children of a red node must be black nodes.
-4. Every path from a node n to a descendent leaf has the same number of black nodes (not counting node n).   
-
-## Methods:
-
-Since the red-black tree is a balanced BST, it supports the functions:
-  * find(key)
-  * Predecessor(key)
-  * Successor(key)
-  * Minimum(key)
-  * maximum(key)
-  * insert(key)
-  * delete(key)    
-
-Since an insertion or deletion may violate one of the invariant's of the red-black tree we must either change colors, or perform rotation actions.  
-
-#Rotation  
-To ensure that its color scheme and properties don’t get thrown off, red-black trees employ a key operation known as rotation. Rotation is a binary operation, between a parent node and one of its children, that swaps nodes and modifys their pointers while preserving the inorder traversal of the tree (so that elements are still sorted). There are two types of rotations: left rotation and right rotation. Left rotation swaps the parent node with its right child, while right rotation swaps the parent node with its left child.
-![fig2](files/fig2.png)
-###Left-Rotation:  
-```c++
-y ← x->right 
-x->right ← y->left 
-y->left->p ← x 
-y->p ← x->p 
-if 	x->p = Null 
-	then   T->root ← y 
-	else if x = x->p->left  
-		then x->p->left ← y 
-		else  x->p->right ← y 
-y->left ← x 
-x->p ← y 
-```
-###Right-Rotation:
-```c++
-y ← x->left 
-x->left ← y->right 
-y->right->p ← x 
-y->p ← x->p 
-if 	x->p = Null 
-	then T->root ← y 
-	else if x = x->p->right  
-		then x->p->right ← y 
-		else  x->p->left ← y 
-y->right ← x 
-x->p ← y 
-```  
-###Insertion:
-When adding a new node to a binary search tree, note that the new node will always be a leaf in the tree. To insert a new node, all we will do is navigate the BST starting from the root. If the new node value is smaller than the current node value, we go left – if it is larger, we go right. When we reach a leaf node, the last step is to attach the new node as a child to this leaf node in a way that preserves the BST constraint. We must recheck the RBTree invariants to see if any were violated  
-
-###Deletion:
-The same concept behind red-black tree insertions applies here. Removing a node from a red-black tree makes use of the BST deletion procedure and then restores the red-black tree properties in O(log n). The total running time for the deletion process takes O(log n) time, then, which meets the complexity requirements for the primitive operations.  
-
-See also [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree).  
-
-*Written for the Swift Algorithm Club by Ashwin Raghuraman*
-
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
similarity index 100%
rename from Red-Black Tree 2/Red-Black Tree 2.playground/Contents.swift
rename to Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
similarity index 100%
rename from Red-Black Tree 2/Red-Black Tree 2.playground/Sources/RBTree.swift
rename to Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/contents.xcplayground b/Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground
similarity index 100%
rename from Red-Black Tree 2/Red-Black Tree 2.playground/contents.xcplayground
rename to Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground
diff --git a/Red-Black Tree 2/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata b/Red-Black Tree/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Red-Black Tree 2/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Red-Black Tree/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata
diff --git a/Red-Black Tree/files/fig1.png b/Red-Black Tree/files/fig1.png
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From 52a29a16b2efb745a796017236acecf904474f8b Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 20 Sep 2016 18:12:34 +0200
Subject: [PATCH 0555/1679] removed bad alias

---
 Red-Black Tree/RBTree.swift | Bin 1104 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Red-Black Tree/RBTree.swift

diff --git a/Red-Black Tree/RBTree.swift b/Red-Black Tree/RBTree.swift
deleted file mode 100644
index 0ed831f72932e9675aa57dc32405330ef33285a7..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

literal 1104
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O@M}?jJH@tN3H}S0xrV#|


From 4cc91449780d96c13b7071e119d2889816343227 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Tue, 20 Sep 2016 14:02:16 -0700
Subject: [PATCH 0556/1679] Added credit to previous author.

---
 Red-Black Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 9496e6318..d4e86a095 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -116,4 +116,4 @@ We now have to go through a lot of steps in order to remove this doubleBlack col
 
 Important to note is that GeeksforGeeks doesn't mention a few deletion cases that do occur. The code however does implement these.
 
-*Written for Swift Algorithm Club by Jaap Wijnen*
+*Written for Swift Algorithm Club by Jaap Wijnen. Updated from Ashwin Raghuraman's contribution.*

From c4a4c89d644476cbf01cde349156f4223c7280ab Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Wed, 21 Sep 2016 12:06:09 +0800
Subject: [PATCH 0557/1679] deque update to swift 3

updated readme
---
 Deque/Deque-Optimized.swift                |  6 +++---
 Deque/Deque-Simple.swift                   |  4 ++--
 Deque/Deque.playground/Contents.swift      |  6 +++---
 Deque/Deque.playground/timeline.xctimeline |  6 ------
 Deque/README.markdown                      | 10 +++++-----
 5 files changed, 13 insertions(+), 19 deletions(-)
 delete mode 100644 Deque/Deque.playground/timeline.xctimeline

diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index ea68059c0..17ff89e68 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -8,7 +8,7 @@ public struct Deque<T> {
   private var head: Int
   private var capacity: Int
 
-  public init(capacity: Int = 10) {
+  public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
     array = .init(count: capacity, repeatedValue: nil)
     head = capacity
@@ -22,11 +22,11 @@ public struct Deque<T> {
     return array.count - head
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
-  public mutating func enqueueFront(element: T) {
+  public mutating func enqueueFront(_ element: T) {
     if head == 0 {
       capacity *= 2
       let emptySpace = [T?](count: capacity, repeatedValue: nil)
diff --git a/Deque/Deque-Simple.swift b/Deque/Deque-Simple.swift
index 0ccba0caa..f4f5f0409 100644
--- a/Deque/Deque-Simple.swift
+++ b/Deque/Deque-Simple.swift
@@ -16,11 +16,11 @@ public struct Deque<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
-  public mutating func enqueueFront(element: T) {
+  public mutating func enqueueFront(_ element: T) {
     array.insert(element, atIndex: 0)
   }
 
diff --git a/Deque/Deque.playground/Contents.swift b/Deque/Deque.playground/Contents.swift
index 15bf1ee07..9e7b22c02 100644
--- a/Deque/Deque.playground/Contents.swift
+++ b/Deque/Deque.playground/Contents.swift
@@ -11,12 +11,12 @@ public struct Deque<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
-  public mutating func enqueueFront(element: T) {
-    array.insert(element, atIndex: 0)
+  public mutating func enqueueFront(_ element: T) {
+    array.insert(element, at: 0)
   }
 
   public mutating func dequeue() -> T? {
diff --git a/Deque/Deque.playground/timeline.xctimeline b/Deque/Deque.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Deque/Deque.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 3329adca0..7671555dc 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -18,11 +18,11 @@ public struct Deque<T> {
     return array.count
   }
   
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
   
-  public mutating func enqueueFront(element: T) {
+  public mutating func enqueueFront(_ element: T) {
     array.insert(element, atIndex: 0)
   }
   
@@ -120,7 +120,7 @@ public struct Deque<T> {
   private var head: Int
   private var capacity: Int
   
-  public init(capacity: Int = 10) {
+  public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
     array = .init(count: capacity, repeatedValue: nil)
     head = capacity
@@ -134,11 +134,11 @@ public struct Deque<T> {
     return array.count - head
   }
   
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
   
-  public mutating func enqueueFront(element: T) {
+  public mutating func enqueueFront(_ element: T) {
     // this is explained below
   }
 

From 4efac1614da03629229c2913da7896ce27199ec0 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 22 Sep 2016 02:00:24 +0200
Subject: [PATCH 0558/1679] Updated OrderedArray to Swift 3

---
 .../OrderedArray.playground/Contents.swift    | 36 ++++++++++---------
 1 file changed, 19 insertions(+), 17 deletions(-)

diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index aae146ca2..dfbf67fcb 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -1,10 +1,10 @@
 //: Playground - noun: a place where people can play
 
 public struct OrderedArray<T: Comparable> {
-  private var array = [T]()
+  fileprivate var array = [T]()
 
   public init(array: [T]) {
-    self.array = array.sort()
+    self.array = array.sorted()
   }
 
   public var isEmpty: Bool {
@@ -20,16 +20,16 @@ public struct OrderedArray<T: Comparable> {
   }
 
   public mutating func removeAtIndex(index: Int) -> T {
-    return array.removeAtIndex(index)
+    return array.remove(at: index)
   }
 
   public mutating func removeAll() {
     array.removeAll()
   }
 
-  public mutating func insert(newElement: T) -> Int {
-    let i = findInsertionPoint(newElement)
-    array.insert(newElement, atIndex: i)
+  public mutating func insert(_ newElement: T) -> Int {
+    let i = findInsertionPoint(newElement: newElement)
+    array.insert(newElement, at: i)
     return i
   }
 
@@ -47,18 +47,20 @@ public struct OrderedArray<T: Comparable> {
 
   // Fast version that uses a binary search.
   private func findInsertionPoint(newElement: T) -> Int {
-    var range = 0..<array.count
-    while range.startIndex < range.endIndex {
-      let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-      if array[midIndex] == newElement {
-        return midIndex
-      } else if array[midIndex] < newElement {
-        range.startIndex = midIndex + 1
-      } else {
-        range.endIndex = midIndex
-      }
+    var startIndex = 0
+    var endIndex = array.count
+    
+    while startIndex < endIndex {
+        let midIndex = startIndex + (endIndex - startIndex) / 2
+        if array[midIndex] == newElement {
+            return midIndex
+        } else if array[midIndex] < newElement {
+            startIndex = midIndex + 1
+        } else {
+            endIndex = midIndex
+        }
     }
-    return range.startIndex
+    return startIndex
   }
 }
 

From 3011410b20ca84287f8fdddc17470876037ae2f2 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 22 Sep 2016 02:09:38 +0200
Subject: [PATCH 0559/1679] updated readme

---
 .../OrderedArray.playground/Contents.swift    |  4 +-
 Ordered Array/README.markdown                 | 52 ++++++++++---------
 2 files changed, 29 insertions(+), 27 deletions(-)

diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index dfbf67fcb..1a0320a65 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -28,7 +28,7 @@ public struct OrderedArray<T: Comparable> {
   }
 
   public mutating func insert(_ newElement: T) -> Int {
-    let i = findInsertionPoint(newElement: newElement)
+    let i = findInsertionPoint(newElement)
     array.insert(newElement, at: i)
     return i
   }
@@ -46,7 +46,7 @@ public struct OrderedArray<T: Comparable> {
   */
 
   // Fast version that uses a binary search.
-  private func findInsertionPoint(newElement: T) -> Int {
+  private func findInsertionPoint(_ newElement: T) -> Int {
     var startIndex = 0
     var endIndex = array.count
     
diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index f64e55057..ca088c325 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -8,28 +8,28 @@ The implementation is quite basic. It's simply a wrapper around Swift's built-in
 
 ```swift
 public struct OrderedArray<T: Comparable> {
-  private var array = [T]()
-  
+  fileprivate var array = [T]()
+
   public init(array: [T]) {
-    self.array = array.sort()
+    self.array = array.sorted()
   }
 
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public subscript(index: Int) -> T {
     return array[index]
   }
-  
+
   public mutating func removeAtIndex(index: Int) -> T {
-    return array.removeAtIndex(index)
+    return array.remove(at: index)
   }
-  
+
   public mutating func removeAll() {
     array.removeAll()
   }
@@ -47,13 +47,13 @@ As you can see, all these methods simply call the corresponding method on the in
 What remains is the `insert()` function. Here is an initial stab at it:
 
 ```swift
-  public mutating func insert(newElement: T) -> Int {
+  public mutating func insert(_ newElement: T) -> Int {
     let i = findInsertionPoint(newElement)
-    array.insert(newElement, atIndex: i)
+    array.insert(newElement, at: i)
     return i
   }
 
-  private func findInsertionPoint(newElement: T) -> Int {
+  private func findInsertionPoint(_ newElement: T) -> Int {
     for i in 0..<array.count {
       if newElement <= array[i] {
         return i
@@ -63,7 +63,7 @@ What remains is the `insert()` function. Here is an initial stab at it:
   }
 ```
 
-The helper function `findInsertionPoint()` simply iterates through the entire array, looking for the right place to insert the new element. 
+The helper function `findInsertionPoint()` simply iterates through the entire array, looking for the right place to insert the new element.
 
 > **Note:** Quite conveniently, `array.insert(... atIndex: array.count)` adds the new object to the end of the array, so if no suitable insertion point was found we can simply return `array.count` as the index.
 
@@ -81,26 +81,28 @@ a.insert(10)   // inserted at index 8
 a              // [-2, -1, 1, 3, 4, 5, 7, 9, 10]
 ```
 
-The array's contents will always be sorted from low to high, now matter what. 
+The array's contents will always be sorted from low to high, now matter what.
 
 Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array. We can speed this up by using a [binary search](../Binary Search) to find the insertion point.
 
 Here is the new version:
 
 ```swift
-  private func findInsertionPoint(newElement: T) -> Int {
-    var range = 0..<array.count
-    while range.startIndex < range.endIndex {
-      let midIndex = range.startIndex + (range.endIndex - range.startIndex) / 2
-      if array[midIndex] == newElement {
-        return midIndex
-      } else if array[midIndex] < newElement {
-        range.startIndex = midIndex + 1
-      } else {
-        range.endIndex = midIndex
-      }
+  private func findInsertionPoint(_ newElement: T) -> Int {
+    var startIndex = 0
+    var endIndex = array.count
+
+    while startIndex < endIndex {
+        let midIndex = startIndex + (endIndex - startIndex) / 2
+        if array[midIndex] == newElement {
+            return midIndex
+        } else if array[midIndex] < newElement {
+            startIndex = midIndex + 1
+        } else {
+            endIndex = midIndex
+        }
     }
-    return range.startIndex
+    return startIndex
   }
 ```
 

From 9cb0ca2ecffdda661fb4286bf077660c5775b326 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 22 Sep 2016 02:19:54 +0200
Subject: [PATCH 0560/1679] updated Priority Queue to swift 3

---
 Priority Queue/PriorityQueue.swift                     | 10 +++++-----
 Priority Queue/README.markdown                         |  4 ++--
 Priority Queue/Tests/Tests.xcodeproj/project.pbxproj   | 10 +++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme              |  2 +-
 4 files changed, 17 insertions(+), 9 deletions(-)

diff --git a/Priority Queue/PriorityQueue.swift b/Priority Queue/PriorityQueue.swift
index 757a6c539..92f7b6d3f 100644
--- a/Priority Queue/PriorityQueue.swift	
+++ b/Priority Queue/PriorityQueue.swift	
@@ -11,13 +11,13 @@
   queue (largest element first) or a min-priority queue (smallest element first).
 */
 public struct PriorityQueue<T> {
-  private var heap: Heap<T>
+  fileprivate var heap: Heap<T>
 
   /*
     To create a max-priority queue, supply a > sort function. For a min-priority
     queue, use <.
   */
-  public init(sort: (T, T) -> Bool) {
+  public init(sort: @escaping (T, T) -> Bool) {
     heap = Heap(sort: sort)
   }
 
@@ -33,7 +33,7 @@ public struct PriorityQueue<T> {
     return heap.peek()
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     heap.insert(element)
   }
 
@@ -52,7 +52,7 @@ public struct PriorityQueue<T> {
 }
 
 extension PriorityQueue where T: Equatable {
-  public func indexOf(element: T) -> Int? {
-    return heap.indexOf(element)
+  public func index(of element: T) -> Int? {
+    return heap.index(of: element)
   }
 }
diff --git a/Priority Queue/README.markdown b/Priority Queue/README.markdown
index 0c04e7445..8308ec16f 100644
--- a/Priority Queue/README.markdown	
+++ b/Priority Queue/README.markdown	
@@ -8,7 +8,7 @@ The queue can be a *max-priority* queue (largest element first) or a *min-priori
 
 Priority queues are useful for algorithms that need to process a (large) number of items and where you repeatedly need to identify which one is now the biggest or smallest -- or however you define "most important".
 
-Examples of algorithms that can benefit from a priority queue: 
+Examples of algorithms that can benefit from a priority queue:
 
 - Event-driven simulations. Each event is given a timestamp and you want events to be performed in order of their timestamps. The priority queue makes it easy to find the next event that needs to be simulated.
 - Dijkstra's algorithm for graph searching uses a priority queue to calculate the minimum cost.
@@ -39,7 +39,7 @@ Here's a Swift priority queue based on a heap:
 
 ```swift
 public struct PriorityQueue<T> {
-  private var heap: Heap<T>
+  fileprivate var heap: Heap<T>
 
   public init(sort: (T, T) -> Bool) {
     heap = Heap(sort: sort)
diff --git a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 5c6a20355..77423c57a 100644
--- a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,11 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -149,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -224,6 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From a6bff78fb65cc50f56b53c4bd3018b5fd4e78708 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 22 Sep 2016 02:52:40 +0200
Subject: [PATCH 0561/1679] updated Ordered Set to swift 3

---
 .../Example 1.xcplaygroundpage/Contents.swift |  2 +-
 .../timeline.xctimeline                       | 21 ++++++++++
 .../Example 2.xcplaygroundpage/Contents.swift |  2 +-
 .../Example 3.xcplaygroundpage/Contents.swift |  6 +--
 .../timeline.xctimeline                       |  6 +++
 .../Sources/OrderedSet.swift                  | 24 +++++------
 .../Sources/Player.swift                      |  2 +-
 .../Sources/Random.swift                      |  2 +-
 Ordered Set/README.markdown                   | 40 +++++++++----------
 9 files changed, 66 insertions(+), 39 deletions(-)
 create mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline

diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index c1fe6fe11..2420019fc 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -4,7 +4,7 @@ var mySet = OrderedSet<Int>()
 
 // Insert random numbers into the set
 for _ in 0..<50 {
-  mySet.insert(random(50, max: 500))
+  mySet.insert(random(min: 50, max: 500))
 }
 
 print(mySet)
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
new file mode 100644
index 000000000..454d1011b
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
@@ -0,0 +1,21 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=21&amp;CharacterRangeLoc=288&amp;EndingColumnNumber=22&amp;EndingLineNumber=18&amp;StartingColumnNumber=1&amp;StartingLineNumber=18&amp;Timestamp=496197876.557751"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=24&amp;CharacterRangeLoc=329&amp;EndingColumnNumber=27&amp;EndingLineNumber=20&amp;StartingColumnNumber=3&amp;StartingLineNumber=20&amp;Timestamp=496197876.557751"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=25&amp;CharacterRangeLoc=428&amp;EndingColumnNumber=28&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=26&amp;Timestamp=496197876.557751"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
index 6fc1f66ed..c30260fff 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
@@ -23,7 +23,7 @@ print(playerSet.max())
 print(playerSet.min())
 
 // We'll find our player now:
-let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
+let level = playerSet.count - playerSet.index(of: anotherPlayer)!
 print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
 
 //: [Next](@next)
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
index 872b5aeb4..52f154c05 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
@@ -17,6 +17,6 @@ repeatedSet.insert(Player(name: "Player 9", points: 25))
 print(repeatedSet)
 //debugPrint(repeatedSet)
 
-print(repeatedSet.indexOf(Player(name: "Player 5", points: 100)))
-print(repeatedSet.indexOf(Player(name: "Random Player", points: 100)))
-print(repeatedSet.indexOf(Player(name: "Player 5", points: 1000)))
+print(repeatedSet.index(of: Player(name: "Player 5", points: 100)))
+print(repeatedSet.index(of: Player(name: "Random Player", points: 100)))
+print(repeatedSet.index(of: Player(name: "Player 5", points: 1000)))
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
index a8b3b0966..8490a3320 100644
--- a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
@@ -14,7 +14,7 @@ public struct OrderedSet<T: Comparable> {
   }
 
   // Inserts an item. Performance: O(n)
-  public mutating func insert(item: T) {
+  public mutating func insert(_ item: T) {
     if exists(item) {
       return  // don't add an item if it already exists
     }
@@ -22,7 +22,7 @@ public struct OrderedSet<T: Comparable> {
     // Insert new the item just before the one that is larger.
     for i in 0..<count {
       if internalSet[i] > item {
-        internalSet.insert(item, atIndex: i)
+        internalSet.insert(item, at: i)
         return
       }
     }
@@ -32,19 +32,19 @@ public struct OrderedSet<T: Comparable> {
   }
 
   // Removes an item if it exists. Performance: O(n)
-  public mutating func remove(item: T) {
-    if let index = indexOf(item) {
-      internalSet.removeAtIndex(index)
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
     }
   }
 
   // Returns true if and only if the item exists somewhere in the set.
-  public func exists(item: T) -> Bool {
-    return indexOf(item) != nil
+  public func exists(_ item: T) -> Bool {
+    return index(of: item) != nil
   }
 
   // Returns the index of an item if it exists, or -1 otherwise.
-  public func indexOf(item: T) -> Int? {
+  public func index(of item: T) -> Int? {
     var leftBound = 0
     var rightBound = count - 1
 
@@ -64,7 +64,7 @@ public struct OrderedSet<T: Comparable> {
         // and to the left in order to find an exact match.
 
         // Check to the right.
-        for j in mid.stride(to: count - 1, by: 1) {
+        for j in stride(from: mid, to: count - 1, by: 1) {
           if internalSet[j + 1] == item {
             return j + 1
           } else if internalSet[j] < internalSet[j + 1] {
@@ -73,7 +73,7 @@ public struct OrderedSet<T: Comparable> {
         }
 
         // Check to the left.
-        for j in mid.stride(to: 0, by: -1) {
+        for j in stride(from: mid, to: 0, by: -1) {
           if internalSet[j - 1] == item {
             return j - 1
           } else if internalSet[j] > internalSet[j - 1] {
@@ -105,13 +105,13 @@ public struct OrderedSet<T: Comparable> {
 
   // Returns the k-th largest element in the set, if k is in the range
   // [1, count]. Returns nil otherwise.
-  public func kLargest(k: Int) -> T? {
+  public func kLargest(_ k: Int) -> T? {
     return k > count || k <= 0 ? nil : internalSet[count - k]
   }
 
   // Returns the k-th smallest element in the set, if k is in the range
   // [1, count]. Returns nil otherwise.
-  public func kSmallest(k: Int) -> T? {
+  public func kSmallest(_ k: Int) -> T? {
     return k > count || k <= 0 ? nil : internalSet[k - 1]
   }
 }
diff --git a/Ordered Set/OrderedSet.playground/Sources/Player.swift b/Ordered Set/OrderedSet.playground/Sources/Player.swift
index 9357744db..26835b0a8 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Player.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/Player.swift	
@@ -6,7 +6,7 @@ public struct Player: Comparable {
 
   public init() {
     self.name = String.random()
-    self.points = random(0, max: 5000)
+    self.points = random(min: 0, max: 5000)
   }
 
   public init(name: String, points: Int) {
diff --git a/Ordered Set/OrderedSet.playground/Sources/Random.swift b/Ordered Set/OrderedSet.playground/Sources/Random.swift
index b6e1f7736..eccd65df6 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Random.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/Random.swift	
@@ -13,7 +13,7 @@ extension String {
 
     for _ in 0..<length {
       let randomValue = arc4random_uniform(UInt32(base.characters.count))
-      randomString += "\(base[base.startIndex.advancedBy(Int(randomValue))])"
+      randomString += "\(base[base.index(base.startIndex, offsetBy: Int(randomValue))])"
     }
     return randomString
   }
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index b2e4e737c..0525a31ed 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -1,6 +1,6 @@
 # Ordered Set
 
-An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest. 
+An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
 
 The Ordered Set data type is a hybrid of:
 
@@ -11,7 +11,7 @@ It's important to keep in mind that two items can have the same *value* but stil
 
 ## Why use an ordered set?
 
-Ordered Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Ordered Set are **O(1)**. 
+Ordered Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Ordered Set are **O(1)**.
 
 A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below).
 
@@ -55,7 +55,7 @@ public struct OrderedSet<T: Comparable> {
 Lets take a look at the `insert()` function first. This first checks if the item already exists in the collection. If so, it returns and does not insert the item.  Otherwise, it will insert the item through straightforward iteration.
 
 ```swift
-  public mutating func insert(item: T){
+  public mutating func insert(_ item: T){
     if exists(item) {
       return  // don't add an item if it already exists
     }
@@ -63,7 +63,7 @@ Lets take a look at the `insert()` function first. This first checks if the item
     // Insert new the item just before the one that is larger.
     for i in 0..<count {
       if internalSet[i] > item {
-        internalSet.insert(item, atIndex: i)
+        internalSet.insert(item, at: i)
         return
       }
     }
@@ -82,19 +82,19 @@ The total performance of the `insert()` function is therefore **O(n)**.
 Next up is the `remove()` function:
 
 ```swift
-  public mutating func remove(item: T) {
-    if let index = indexOf(item) {
-      internalSet.removeAtIndex(index)
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
     }
   }
 ```
 
 First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n)**.
 
-The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item. 
+The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item.
 
 ```swift
-  public func indexOf(item: T) -> Int? {
+  public func index(of item: T) -> Int? {
     var leftBound = 0
     var rightBound = count - 1
 
@@ -115,9 +115,9 @@ The next function is `indexOf()`, which takes in an object of type `T` and retur
   }
 ```
 
-> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary Search). 
+> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary Search).
 
-However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item. 
+However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item.
 
 For example, consider this ordered set of `Player` objects. Each `Player` has a name and a number of points:
 
@@ -147,13 +147,13 @@ Therefore, we also need to check the items with the same value to the right and
             break
           }
         }
-        
+
         return nil
 ```
 
 These loops start at the current `mid` value and then look at the neighboring values until we've found the correct object.
 
-The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for. 
+The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for.
 
 Since the set is sorted, the following operations are all **O(1)**:
 
@@ -168,15 +168,15 @@ Since the set is sorted, the following operations are all **O(1)**:
     return count == 0 ? nil : internalSet[0]
   }
 
-  // Returns the k-th largest element in the set, if k is in the range 
+  // Returns the k-th largest element in the set, if k is in the range
   // [1, count]. Returns nil otherwise.
-  public func kLargest(k: Int) -> T? {
+  public func kLargest(_ k: Int) -> T? {
     return k > count || k <= 0 ? nil : internalSet[count - k]
   }
 
   // Returns the k-th smallest element in the set, if k is in the range
   // [1, count]. Returns nil otherwise.
-  public func kSmallest(k: Int) -> T? {
+  public func kSmallest(_ k: Int) -> T? {
     return k > count || k <= 0 ? nil : internalSet[k - 1]
   }
 ```
@@ -228,7 +228,7 @@ public struct Player: Comparable {
 The `Player` also gets its own `==` and `<` operators. The `<` operator is used to determine the sort order of the set, while `==` determines whether two objects are really equal.
 
 Note that `==` compares both the name and the points:  
-  
+
 ```swifr
 func ==(x: Player, y: Player) -> Bool {
   return x.name == y.name && x.points == y.points
@@ -272,7 +272,7 @@ print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.po
 
 ### Example 3
 
-The final example demonstrates the need to look for the right item even after the binary search has completed. 
+The final example demonstrates the need to look for the right item even after the binary search has completed.
 
 We insert 9 players into the set:
 
@@ -299,7 +299,7 @@ The set looks something like this:
 The next line looks for `Player 2`:
 
 ```swift
-print(repeatedSet.indexOf(Player(name: "Player 2", points: 100)))
+print(repeatedSet.index(of: Player(name: "Player 2", points: 100)))
 ```
 
 After the binary search finishes, the value of `mid` is at index 5:
@@ -312,7 +312,7 @@ However, this is not `Player 2`. Both `Player 4` and `Player 2` have the same po
 But we do know that `Player 2` must be either to the immediate left or the right of `Player 4`, so we check both sides of `mid`. We only need to look at the objects with the same value as `Player 4`. The others are replaced by `X`:
 
 	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                                       mid 
+	                                       mid
 
 The code then first checks on the right of `mid` (where the `*` is):
 

From 8e4dbdb2721d8171f7ab95dfa0d478c6b9607691 Mon Sep 17 00:00:00 2001
From: ssarber <ssarber@gmail.com>
Date: Fri, 23 Sep 2016 10:57:21 -0700
Subject: [PATCH 0562/1679] Convert to Swift 3 syntax to get rid of Xcode 8
 errors

---
 Counting Sort/CountingSort.playground/Contents.swift | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 67d416f2f..2d85347ef 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,6 +1,6 @@
 //: Playground - noun: a place where people can play
 
-enum CountingSortError: ErrorType {
+enum CountingSortError: Error {
   case ArrayEmpty
 }
 
@@ -11,9 +11,9 @@ func countingSort(array: [Int]) throws -> [Int] {
 
   // Step 1
   // Create an array to store the count of each element
-  let maxElement = array.maxElement() ?? 0
+  let maxElement = array.max() ?? 0
 
-  var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
+  var countArray = [Int](repeating: 0, count: Int(maxElement + 1))
   for element in array {
     countArray[element] += 1
   }
@@ -29,7 +29,7 @@ func countingSort(array: [Int]) throws -> [Int] {
 
   // Step 3
   // Place the element in the final array as per the number of elements before it
-  var sortedArray = [Int](count: array.count, repeatedValue: 0)
+  var sortedArray = [Int](repeating: 0, count: array.count)
   for element in array {
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
@@ -38,4 +38,4 @@ func countingSort(array: [Int]) throws -> [Int] {
 }
 
 
-try countingSort([10, 9, 8, 7, 1, 2, 7, 3])
+try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
\ No newline at end of file

From 17887c35c322a1361c82b8f40b36f636c780101d Mon Sep 17 00:00:00 2001
From: ssarber <ssarber@gmail.com>
Date: Fri, 23 Sep 2016 12:16:23 -0700
Subject: [PATCH 0563/1679] Update readme

---
 Counting Sort/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Counting Sort/README.markdown b/Counting Sort/README.markdown
index 55b60104f..959becc8c 100644
--- a/Counting Sort/README.markdown	
+++ b/Counting Sort/README.markdown	
@@ -20,9 +20,9 @@ Count 0 1 1 1 0 0 0 2 1 1 1
 Here is the code to accomplish this:
 
 ```swift
-  let maxElement = array.maxElement() ?? 0
-  
-  var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
+  let maxElement = array.max() ?? 0
+
+  var countArray = [Int](repeating: 0, count: Int(maxElement + 1))
   for element in array {
     countArray[element] += 1
   }
@@ -62,7 +62,7 @@ Output 1 2 3 7 7 8 9 10
 Here is the code for this final step:
 
 ```swift
-  var sortedArray = [Int](count: array.count, repeatedValue: 0)
+  var sortedArray = [Int](repeating: 0, count: array.count)
   for element in array {
     countArray[element] -= 1
     sortedArray[countArray[element]] = element

From 4470e09fd636ddfad61848dc99ed26e07e6a37f3 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Sat, 24 Sep 2016 14:04:23 +0200
Subject: [PATCH 0564/1679] first commit: added Knuth-Morris-Pratt and Z
 algorithms for string search

---
 .../Contents.swift                            | 122 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../timeline.xctimeline                       |   6 +
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     |  65 ++++++++++
 Z-Algorithm/ZAlgorithm.swift                  |  66 ++++++++++
 .../ZetaAlgorithm.playground/Contents.swift   |  95 ++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../timeline.xctimeline                       |   6 +
 Z-Algorithm/ZetaAlgorithm.swift               |  32 +++++
 11 files changed, 414 insertions(+)
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.swift
 create mode 100644 Z-Algorithm/ZAlgorithm.swift
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
 create mode 100644 Z-Algorithm/ZetaAlgorithm.swift

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
new file mode 100644
index 000000000..147477c80
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -0,0 +1,122 @@
+//: Playground - noun: a place where people can play
+
+
+func ZetaAlgorithm(ptnr: String) -> [Int]? {
+
+    let pattern = Array(ptnr.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength {
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength {
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
+
+extension String {
+
+    func indexesOf(ptnr: String) -> [Int]? {
+
+        let text = Array(self.characters)
+        let pattern = Array(ptnr.characters)
+
+        let textLength: Int = text.count
+        let patternLength: Int = pattern.count
+
+        guard patternLength > 0 else {
+            return nil
+        }
+
+        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
+        var textIndex: Int = 0
+        var patternIndex: Int = 0
+        var indexes: [Int] = [Int]()
+
+        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+        let zeta = ZetaAlgorithm(ptnr)
+
+        for patternIndex in (1 ..< patternLength).reverse() {
+            textIndex = patternIndex + zeta![patternIndex] - 1
+            suffixPrefix[textIndex] = zeta![patternIndex]
+        }
+
+        /* Search stage: scanning the text for pattern matching */
+        textIndex = 0
+        patternIndex = 0
+
+        while textIndex + (patternLength - patternIndex - 1) < textLength {
+
+            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+                textIndex = textIndex + 1
+                patternIndex = patternIndex + 1
+            }
+
+            if patternIndex == patternLength {
+                indexes.append(textIndex - patternIndex)
+            }
+
+            if patternIndex == 0 {
+                textIndex = textIndex + 1
+            } else {
+                patternIndex = suffixPrefix[patternIndex - 1]
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+        return indexes
+    }
+}
+
+/* Examples */
+
+let dna = "ACCCGGTTTTAAAGAACCACCATAAGATATAGACAGATATAGGACAGATATAGAGACAAAACCCCATACCCCAATATTTTTTTGGGGAGAAAAACACCACAGATAGATACACAGACTACACGAGATACGACATACAGCAGCATAACGACAACAGCAGATAGACGATCATAACAGCAATCAGACCGAGCGCAGCAGCTTTTAAGCACCAGCCCCACAAAAAACGACAATFATCATCATATACAGACGACGACACGACATATCACACGACAGCATA"
+dna.indexesOf("CATA")   // [20, 64, 130, 140, 166, 234, 255, 270]
+
+let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
+concert.indexesOf("🎻🎷")   // [6]
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
new file mode 100644
index 000000000..5cce1556f
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -0,0 +1,65 @@
+/*  Knuth-Morris-Pratt algorithm for pattern/string matching
+
+    The code is based on the book:
+    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+    by Dan Gusfield
+    Cambridge University Press, 1997
+*/
+
+import Foundation
+
+extension String {
+
+    func indexesOf(ptnr: String) -> [Int]? {
+
+        let text = Array(self.characters)
+        let pattern = Array(ptnr.characters)
+
+        let textLength: Int = text.count
+        let patternLength: Int = pattern.count
+
+        guard patternLength > 0 else {
+            return nil
+        }
+
+        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
+        var textIndex: Int = 0
+        var patternIndex: Int = 0
+        var indexes: [Int] = [Int]()
+
+        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+        let zeta = ZetaAlgorithm(ptnr)
+
+        for patternIndex in (1 ..< patternLength).reverse() {
+            textIndex = patternIndex + zeta![patternIndex] - 1
+            suffixPrefix[textIndex] = zeta![patternIndex]
+        }
+
+        /* Search stage: scanning the text for pattern matching */
+        textIndex = 0
+        patternIndex = 0
+
+        while textIndex + (patternLength - patternIndex - 1) < textLength {
+
+            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+                textIndex = textIndex + 1
+                patternIndex = patternIndex + 1
+            }
+
+            if patternIndex == patternLength {
+                indexes.append(textIndex - patternIndex)
+            }
+
+            if patternIndex == 0 {
+                textIndex = textIndex + 1
+            } else {
+                patternIndex = suffixPrefix[patternIndex - 1]
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+        return indexes
+    }
+}
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
new file mode 100644
index 000000000..3b6d34908
--- /dev/null
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -0,0 +1,66 @@
+/*  Z-Algorithm for pattern/string pre-processing
+
+    The code is based on the book:
+    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+    by Dan Gusfield
+    Cambridge University Press, 1997
+*/
+
+import Foundation
+
+func ZetaAlgorithm(ptrn: String) -> [Int]? {
+
+    let pattern = Array(ptrn.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength {
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength {
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
new file mode 100644
index 000000000..dfe24ddf6
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -0,0 +1,95 @@
+//: Playground - noun: a place where people can play
+
+
+func ZetaAlgorithm(ptrn: String) -> [Int]? {
+
+    let pattern = Array(ptrn.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength {
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength {
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
+
+
+extension String {
+
+    func indexesOf(pattern: String) -> [Int]? {
+        let patternLength: Int = pattern.characters.count
+        let zeta = ZetaAlgorithm(pattern + "💲" + self)
+
+        guard zeta != nil else {
+            return nil
+        }
+
+        var indexes: [Int] = [Int]()
+
+        /* Scan the zeta array to find matched patterns */
+        for i in 0 ..< zeta!.count {
+            if zeta![i] == patternLength {
+                indexes.append(i - patternLength - 1)
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+
+        return indexes
+    }
+}
+
+/* Examples */
+
+let str = "Hello, playground!"
+str.indexesOf("ground")   // [11]
+
+let traffic = "🚗🚙🚌🚕🚑🚐🚗🚒🚚🚎🚛🚐🏎🚜🚗🏍🚒🚲🚕🚓🚌🚑"
+traffic.indexesOf("🚑") // [4, 21]
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground b/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata b/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline b/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
new file mode 100644
index 000000000..c31e27c66
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -0,0 +1,32 @@
+/*  Z-Algorithm based algorithm for pattern/string matching
+
+    The code is based on the book:
+    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+    by Dan Gusfield
+    Cambridge University Press, 1997
+*/
+
+import Foundation
+
+extension String {
+
+    func indexesOf(pattern: String) -> [Int]? {
+        let patternLength: Int = pattern.characters.count
+        let zeta = ZetaAlgorithm(pattern + "💲" + self)
+
+        var indexes: [Int] = [Int]()
+
+        /* Scan the zeta array to find matched patterns */
+        for index in indexes {
+            if index == patternLength {
+                indexes.append(index)
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+
+        return indexes
+    }
+}

From 6230a2bbc54bb08b9815764bcfc7909d471131c2 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Sat, 24 Sep 2016 14:31:50 +0200
Subject: [PATCH 0565/1679] removed directories

---
 .../Contents.swift                            | 122 ------------------
 .../contents.xcplayground                     |   4 -
 .../contents.xcworkspacedata                  |   7 -
 .../timeline.xctimeline                       |   6 -
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     |  65 ----------
 Z-Algorithm/ZAlgorithm.swift                  |  66 ----------
 .../ZetaAlgorithm.playground/Contents.swift   |  95 --------------
 .../contents.xcplayground                     |   4 -
 .../contents.xcworkspacedata                  |   7 -
 .../timeline.xctimeline                       |   6 -
 Z-Algorithm/ZetaAlgorithm.swift               |  32 -----
 11 files changed, 414 deletions(-)
 delete mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
 delete mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
 delete mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
 delete mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
 delete mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.swift
 delete mode 100644 Z-Algorithm/ZAlgorithm.swift
 delete mode 100644 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
 delete mode 100644 Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
 delete mode 100644 Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
 delete mode 100644 Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
 delete mode 100644 Z-Algorithm/ZetaAlgorithm.swift

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
deleted file mode 100644
index 147477c80..000000000
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ /dev/null
@@ -1,122 +0,0 @@
-//: Playground - noun: a place where people can play
-
-
-func ZetaAlgorithm(ptnr: String) -> [Int]? {
-
-    let pattern = Array(ptnr.characters)
-    let patternLength: Int = pattern.count
-
-    guard patternLength > 0 else {
-        return nil
-    }
-
-    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
-
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
-    var textIndex: Int = 0
-    var patternIndex: Int = 0
-
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
-            }
-
-            zeta[k] = patternIndex
-
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
-        }
-    }
-    return zeta
-}
-
-extension String {
-
-    func indexesOf(ptnr: String) -> [Int]? {
-
-        let text = Array(self.characters)
-        let pattern = Array(ptnr.characters)
-
-        let textLength: Int = text.count
-        let patternLength: Int = pattern.count
-
-        guard patternLength > 0 else {
-            return nil
-        }
-
-        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
-        var textIndex: Int = 0
-        var patternIndex: Int = 0
-        var indexes: [Int] = [Int]()
-
-        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr)
-
-        for patternIndex in (1 ..< patternLength).reverse() {
-            textIndex = patternIndex + zeta![patternIndex] - 1
-            suffixPrefix[textIndex] = zeta![patternIndex]
-        }
-
-        /* Search stage: scanning the text for pattern matching */
-        textIndex = 0
-        patternIndex = 0
-
-        while textIndex + (patternLength - patternIndex - 1) < textLength {
-
-            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
-                textIndex = textIndex + 1
-                patternIndex = patternIndex + 1
-            }
-
-            if patternIndex == patternLength {
-                indexes.append(textIndex - patternIndex)
-            }
-
-            if patternIndex == 0 {
-                textIndex = textIndex + 1
-            } else {
-                patternIndex = suffixPrefix[patternIndex - 1]
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        return indexes
-    }
-}
-
-/* Examples */
-
-let dna = "ACCCGGTTTTAAAGAACCACCATAAGATATAGACAGATATAGGACAGATATAGAGACAAAACCCCATACCCCAATATTTTTTTGGGGAGAAAAACACCACAGATAGATACACAGACTACACGAGATACGACATACAGCAGCATAACGACAACAGCAGATAGACGATCATAACAGCAATCAGACCGAGCGCAGCAGCTTTTAAGCACCAGCCCCACAAAAAACGACAATFATCATCATATACAGACGACGACACGACATATCACACGACAGCATA"
-dna.indexesOf("CATA")   // [20, 64, 130, 140, 166, 234, 255, 270]
-
-let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
-concert.indexesOf("🎻🎷")   // [6]
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
deleted file mode 100644
index 06828af92..000000000
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
deleted file mode 100644
index 5cce1556f..000000000
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ /dev/null
@@ -1,65 +0,0 @@
-/*  Knuth-Morris-Pratt algorithm for pattern/string matching
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
-
-import Foundation
-
-extension String {
-
-    func indexesOf(ptnr: String) -> [Int]? {
-
-        let text = Array(self.characters)
-        let pattern = Array(ptnr.characters)
-
-        let textLength: Int = text.count
-        let patternLength: Int = pattern.count
-
-        guard patternLength > 0 else {
-            return nil
-        }
-
-        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
-        var textIndex: Int = 0
-        var patternIndex: Int = 0
-        var indexes: [Int] = [Int]()
-
-        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr)
-
-        for patternIndex in (1 ..< patternLength).reverse() {
-            textIndex = patternIndex + zeta![patternIndex] - 1
-            suffixPrefix[textIndex] = zeta![patternIndex]
-        }
-
-        /* Search stage: scanning the text for pattern matching */
-        textIndex = 0
-        patternIndex = 0
-
-        while textIndex + (patternLength - patternIndex - 1) < textLength {
-
-            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
-                textIndex = textIndex + 1
-                patternIndex = patternIndex + 1
-            }
-
-            if patternIndex == patternLength {
-                indexes.append(textIndex - patternIndex)
-            }
-
-            if patternIndex == 0 {
-                textIndex = textIndex + 1
-            } else {
-                patternIndex = suffixPrefix[patternIndex - 1]
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        return indexes
-    }
-}
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
deleted file mode 100644
index 3b6d34908..000000000
--- a/Z-Algorithm/ZAlgorithm.swift
+++ /dev/null
@@ -1,66 +0,0 @@
-/*  Z-Algorithm for pattern/string pre-processing
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
-
-import Foundation
-
-func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-    let pattern = Array(ptrn.characters)
-    let patternLength: Int = pattern.count
-
-    guard patternLength > 0 else {
-        return nil
-    }
-
-    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
-
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
-    var textIndex: Int = 0
-    var patternIndex: Int = 0
-
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
-            }
-
-            zeta[k] = patternIndex
-
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
-        }
-    }
-    return zeta
-}
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
deleted file mode 100644
index dfe24ddf6..000000000
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ /dev/null
@@ -1,95 +0,0 @@
-//: Playground - noun: a place where people can play
-
-
-func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-    let pattern = Array(ptrn.characters)
-    let patternLength: Int = pattern.count
-
-    guard patternLength > 0 else {
-        return nil
-    }
-
-    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
-
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
-    var textIndex: Int = 0
-    var patternIndex: Int = 0
-
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
-            }
-
-            zeta[k] = patternIndex
-
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
-        }
-    }
-    return zeta
-}
-
-
-extension String {
-
-    func indexesOf(pattern: String) -> [Int]? {
-        let patternLength: Int = pattern.characters.count
-        let zeta = ZetaAlgorithm(pattern + "💲" + self)
-
-        guard zeta != nil else {
-            return nil
-        }
-
-        var indexes: [Int] = [Int]()
-
-        /* Scan the zeta array to find matched patterns */
-        for i in 0 ..< zeta!.count {
-            if zeta![i] == patternLength {
-                indexes.append(i - patternLength - 1)
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-
-        return indexes
-    }
-}
-
-/* Examples */
-
-let str = "Hello, playground!"
-str.indexesOf("ground")   // [11]
-
-let traffic = "🚗🚙🚌🚕🚑🚐🚗🚒🚚🚎🚛🚐🏎🚜🚗🏍🚒🚲🚕🚓🚌🚑"
-traffic.indexesOf("🚑") // [4, 21]
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground b/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
deleted file mode 100644
index 06828af92..000000000
--- a/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata b/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline b/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
deleted file mode 100644
index c31e27c66..000000000
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ /dev/null
@@ -1,32 +0,0 @@
-/*  Z-Algorithm based algorithm for pattern/string matching
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
-
-import Foundation
-
-extension String {
-
-    func indexesOf(pattern: String) -> [Int]? {
-        let patternLength: Int = pattern.characters.count
-        let zeta = ZetaAlgorithm(pattern + "💲" + self)
-
-        var indexes: [Int] = [Int]()
-
-        /* Scan the zeta array to find matched patterns */
-        for index in indexes {
-            if index == patternLength {
-                indexes.append(index)
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-
-        return indexes
-    }
-}

From c416818dc12878181d8c5a0e54b78be72f68c665 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Sat, 24 Sep 2016 14:41:37 +0200
Subject: [PATCH 0566/1679] first commit: added Knuth-Morris-Pratt and Z
 algorithms implementation

---
 .../Contents.swift                            | 122 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../timeline.xctimeline                       |   6 +
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     |  65 ++++++++++
 Z-Algorithm/ZAlgorithm.swift                  |  66 ++++++++++
 .../ZetaAlgorithm.playground/Contents.swift   |  95 ++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../timeline.xctimeline                       |   6 +
 Z-Algorithm/ZetaAlgorithm.swift               |  32 +++++
 11 files changed, 414 insertions(+)
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
 create mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.swift
 create mode 100644 Z-Algorithm/ZAlgorithm.swift
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
 create mode 100644 Z-Algorithm/ZetaAlgorithm.swift

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
new file mode 100644
index 000000000..147477c80
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -0,0 +1,122 @@
+//: Playground - noun: a place where people can play
+
+
+func ZetaAlgorithm(ptnr: String) -> [Int]? {
+
+    let pattern = Array(ptnr.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength {
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength {
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
+
+extension String {
+
+    func indexesOf(ptnr: String) -> [Int]? {
+
+        let text = Array(self.characters)
+        let pattern = Array(ptnr.characters)
+
+        let textLength: Int = text.count
+        let patternLength: Int = pattern.count
+
+        guard patternLength > 0 else {
+            return nil
+        }
+
+        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
+        var textIndex: Int = 0
+        var patternIndex: Int = 0
+        var indexes: [Int] = [Int]()
+
+        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+        let zeta = ZetaAlgorithm(ptnr)
+
+        for patternIndex in (1 ..< patternLength).reverse() {
+            textIndex = patternIndex + zeta![patternIndex] - 1
+            suffixPrefix[textIndex] = zeta![patternIndex]
+        }
+
+        /* Search stage: scanning the text for pattern matching */
+        textIndex = 0
+        patternIndex = 0
+
+        while textIndex + (patternLength - patternIndex - 1) < textLength {
+
+            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+                textIndex = textIndex + 1
+                patternIndex = patternIndex + 1
+            }
+
+            if patternIndex == patternLength {
+                indexes.append(textIndex - patternIndex)
+            }
+
+            if patternIndex == 0 {
+                textIndex = textIndex + 1
+            } else {
+                patternIndex = suffixPrefix[patternIndex - 1]
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+        return indexes
+    }
+}
+
+/* Examples */
+
+let dna = "ACCCGGTTTTAAAGAACCACCATAAGATATAGACAGATATAGGACAGATATAGAGACAAAACCCCATACCCCAATATTTTTTTGGGGAGAAAAACACCACAGATAGATACACAGACTACACGAGATACGACATACAGCAGCATAACGACAACAGCAGATAGACGATCATAACAGCAATCAGACCGAGCGCAGCAGCTTTTAAGCACCAGCCCCACAAAAAACGACAATFATCATCATATACAGACGACGACACGACATATCACACGACAGCATA"
+dna.indexesOf("CATA")   // [20, 64, 130, 140, 166, 234, 255, 270]
+
+let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
+concert.indexesOf("🎻🎷")   // [6]
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
new file mode 100644
index 000000000..5cce1556f
--- /dev/null
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -0,0 +1,65 @@
+/*  Knuth-Morris-Pratt algorithm for pattern/string matching
+
+    The code is based on the book:
+    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+    by Dan Gusfield
+    Cambridge University Press, 1997
+*/
+
+import Foundation
+
+extension String {
+
+    func indexesOf(ptnr: String) -> [Int]? {
+
+        let text = Array(self.characters)
+        let pattern = Array(ptnr.characters)
+
+        let textLength: Int = text.count
+        let patternLength: Int = pattern.count
+
+        guard patternLength > 0 else {
+            return nil
+        }
+
+        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
+        var textIndex: Int = 0
+        var patternIndex: Int = 0
+        var indexes: [Int] = [Int]()
+
+        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+        let zeta = ZetaAlgorithm(ptnr)
+
+        for patternIndex in (1 ..< patternLength).reverse() {
+            textIndex = patternIndex + zeta![patternIndex] - 1
+            suffixPrefix[textIndex] = zeta![patternIndex]
+        }
+
+        /* Search stage: scanning the text for pattern matching */
+        textIndex = 0
+        patternIndex = 0
+
+        while textIndex + (patternLength - patternIndex - 1) < textLength {
+
+            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+                textIndex = textIndex + 1
+                patternIndex = patternIndex + 1
+            }
+
+            if patternIndex == patternLength {
+                indexes.append(textIndex - patternIndex)
+            }
+
+            if patternIndex == 0 {
+                textIndex = textIndex + 1
+            } else {
+                patternIndex = suffixPrefix[patternIndex - 1]
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+        return indexes
+    }
+}
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
new file mode 100644
index 000000000..3b6d34908
--- /dev/null
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -0,0 +1,66 @@
+/*  Z-Algorithm for pattern/string pre-processing
+
+    The code is based on the book:
+    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+    by Dan Gusfield
+    Cambridge University Press, 1997
+*/
+
+import Foundation
+
+func ZetaAlgorithm(ptrn: String) -> [Int]? {
+
+    let pattern = Array(ptrn.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength {
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength {
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
new file mode 100644
index 000000000..dfe24ddf6
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -0,0 +1,95 @@
+//: Playground - noun: a place where people can play
+
+
+func ZetaAlgorithm(ptrn: String) -> [Int]? {
+
+    let pattern = Array(ptrn.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength {
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength {
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
+
+
+extension String {
+
+    func indexesOf(pattern: String) -> [Int]? {
+        let patternLength: Int = pattern.characters.count
+        let zeta = ZetaAlgorithm(pattern + "💲" + self)
+
+        guard zeta != nil else {
+            return nil
+        }
+
+        var indexes: [Int] = [Int]()
+
+        /* Scan the zeta array to find matched patterns */
+        for i in 0 ..< zeta!.count {
+            if zeta![i] == patternLength {
+                indexes.append(i - patternLength - 1)
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+
+        return indexes
+    }
+}
+
+/* Examples */
+
+let str = "Hello, playground!"
+str.indexesOf("ground")   // [11]
+
+let traffic = "🚗🚙🚌🚕🚑🚐🚗🚒🚚🚎🚛🚐🏎🚜🚗🏍🚒🚲🚕🚓🚌🚑"
+traffic.indexesOf("🚑") // [4, 21]
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground b/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
new file mode 100644
index 000000000..06828af92
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata b/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline b/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
new file mode 100644
index 000000000..c31e27c66
--- /dev/null
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -0,0 +1,32 @@
+/*  Z-Algorithm based algorithm for pattern/string matching
+
+    The code is based on the book:
+    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+    by Dan Gusfield
+    Cambridge University Press, 1997
+*/
+
+import Foundation
+
+extension String {
+
+    func indexesOf(pattern: String) -> [Int]? {
+        let patternLength: Int = pattern.characters.count
+        let zeta = ZetaAlgorithm(pattern + "💲" + self)
+
+        var indexes: [Int] = [Int]()
+
+        /* Scan the zeta array to find matched patterns */
+        for index in indexes {
+            if index == patternLength {
+                indexes.append(index)
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+
+        return indexes
+    }
+}

From e3967dfdd69b3a04243760d4ce73fd83576fef15 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Sat, 24 Sep 2016 21:15:04 +0200
Subject: [PATCH 0567/1679] swift 3 fix

---
 .../Contents.swift                            | 12 +++----
 .../timeline.xctimeline                       |  6 ----
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     | 32 +++++++++----------
 Z-Algorithm/ZAlgorithm.swift                  | 26 +++++++--------
 .../ZetaAlgorithm.playground/Contents.swift   |  8 ++---
 .../timeline.xctimeline                       |  6 ----
 Z-Algorithm/ZetaAlgorithm.swift               | 22 +++++++------
 7 files changed, 52 insertions(+), 60 deletions(-)
 delete mode 100644 Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
 delete mode 100644 Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index 147477c80..35fb27ff8 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -10,7 +10,7 @@ func ZetaAlgorithm(ptnr: String) -> [Int]? {
         return nil
     }
 
-    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
 
     var left: Int = 0
     var right: Int = 0
@@ -71,15 +71,15 @@ extension String {
             return nil
         }
 
-        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
+        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
         var textIndex: Int = 0
         var patternIndex: Int = 0
         var indexes: [Int] = [Int]()
 
         /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr)
+        let zeta = ZetaAlgorithm(ptnr: ptnr)
 
-        for patternIndex in (1 ..< patternLength).reverse() {
+        for patternIndex in (1 ..< patternLength).reversed() {
             textIndex = patternIndex + zeta![patternIndex] - 1
             suffixPrefix[textIndex] = zeta![patternIndex]
         }
@@ -116,7 +116,7 @@ extension String {
 /* Examples */
 
 let dna = "ACCCGGTTTTAAAGAACCACCATAAGATATAGACAGATATAGGACAGATATAGAGACAAAACCCCATACCCCAATATTTTTTTGGGGAGAAAAACACCACAGATAGATACACAGACTACACGAGATACGACATACAGCAGCATAACGACAACAGCAGATAGACGATCATAACAGCAATCAGACCGAGCGCAGCAGCTTTTAAGCACCAGCCCCACAAAAAACGACAATFATCATCATATACAGACGACGACACGACATATCACACGACAGCATA"
-dna.indexesOf("CATA")   // [20, 64, 130, 140, 166, 234, 255, 270]
+dna.indexesOf(ptnr: "CATA")   // [20, 64, 130, 140, 166, 234, 255, 270]
 
 let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
-concert.indexesOf("🎻🎷")   // [6]
+concert.indexesOf(ptnr: "🎻🎷")   // [6]
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 5cce1556f..46a88c134 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -9,54 +9,54 @@
 import Foundation
 
 extension String {
-
+    
     func indexesOf(ptnr: String) -> [Int]? {
-
+        
         let text = Array(self.characters)
         let pattern = Array(ptnr.characters)
-
+        
         let textLength: Int = text.count
         let patternLength: Int = pattern.count
-
+        
         guard patternLength > 0 else {
             return nil
         }
-
-        var suffixPrefix: [Int] = [Int](count: patternLength, repeatedValue: 0)
+        
+        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
         var textIndex: Int = 0
         var patternIndex: Int = 0
         var indexes: [Int] = [Int]()
-
+        
         /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr)
-
-        for patternIndex in (1 ..< patternLength).reverse() {
+        let zeta = ZetaAlgorithm(ptnr: ptnr)
+        
+        for patternIndex in (1 ..< patternLength).reversed() {
             textIndex = patternIndex + zeta![patternIndex] - 1
             suffixPrefix[textIndex] = zeta![patternIndex]
         }
-
+        
         /* Search stage: scanning the text for pattern matching */
         textIndex = 0
         patternIndex = 0
-
+        
         while textIndex + (patternLength - patternIndex - 1) < textLength {
-
+            
             while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
                 textIndex = textIndex + 1
                 patternIndex = patternIndex + 1
             }
-
+            
             if patternIndex == patternLength {
                 indexes.append(textIndex - patternIndex)
             }
-
+            
             if patternIndex == 0 {
                 textIndex = textIndex + 1
             } else {
                 patternIndex = suffixPrefix[patternIndex - 1]
             }
         }
-
+        
         guard !indexes.isEmpty else {
             return nil
         }
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
index 3b6d34908..c9d7de876 100644
--- a/Z-Algorithm/ZAlgorithm.swift
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -9,34 +9,34 @@
 import Foundation
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
+    
     let pattern = Array(ptrn.characters)
     let patternLength: Int = pattern.count
-
+    
     guard patternLength > 0 else {
         return nil
     }
-
-    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
-
+    
+    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
+    
     var left: Int = 0
     var right: Int = 0
     var k_1: Int = 0
     var betaLength: Int = 0
     var textIndex: Int = 0
     var patternIndex: Int = 0
-
+    
     for k in 1 ..< patternLength {
         if k > right {
             patternIndex = 0
-
+            
             while k + patternIndex < patternLength  &&
                 pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
+                    patternIndex = patternIndex + 1
             }
-
+            
             zeta[k] = patternIndex
-
+            
             if zeta[k] > 0 {
                 left = k
                 right = k + zeta[k] - 1
@@ -44,18 +44,18 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
         } else {
             k_1 = k - left + 1
             betaLength = right - k + 1
-
+            
             if zeta[k_1 - 1] < betaLength {
                 zeta[k] = zeta[k_1 - 1]
             } else if zeta[k_1 - 1] >= betaLength {
                 textIndex = betaLength
                 patternIndex = right + 1
-
+                
                 while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
                     textIndex = textIndex + 1
                     patternIndex = patternIndex + 1
                 }
-
+                
                 zeta[k] = patternIndex - k
                 left = k
                 right = patternIndex - 1
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index dfe24ddf6..c9d942149 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -10,7 +10,7 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
         return nil
     }
 
-    var zeta: [Int] = [Int](count: patternLength, repeatedValue: 0)
+    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
 
     var left: Int = 0
     var right: Int = 0
@@ -63,7 +63,7 @@ extension String {
 
     func indexesOf(pattern: String) -> [Int]? {
         let patternLength: Int = pattern.characters.count
-        let zeta = ZetaAlgorithm(pattern + "💲" + self)
+        let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
         guard zeta != nil else {
             return nil
@@ -89,7 +89,7 @@ extension String {
 /* Examples */
 
 let str = "Hello, playground!"
-str.indexesOf("ground")   // [11]
+str.indexesOf(pattern: "ground")   // [11]
 
 let traffic = "🚗🚙🚌🚕🚑🚐🚗🚒🚚🚎🚛🚐🏎🚜🚗🏍🚒🚲🚕🚓🚌🚑"
-traffic.indexesOf("🚑") // [4, 21]
+traffic.indexesOf(pattern: "🚑") // [4, 21]
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline b/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Z-Algorithm/ZetaAlgorithm.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
index c31e27c66..4d80aa665 100644
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -9,24 +9,28 @@
 import Foundation
 
 extension String {
-
+    
     func indexesOf(pattern: String) -> [Int]? {
         let patternLength: Int = pattern.characters.count
-        let zeta = ZetaAlgorithm(pattern + "💲" + self)
-
+        let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
+        
+        guard zeta != nil else {
+            return nil
+        }
+        
         var indexes: [Int] = [Int]()
-
+        
         /* Scan the zeta array to find matched patterns */
-        for index in indexes {
-            if index == patternLength {
-                indexes.append(index)
+        for i in 0 ..< zeta!.count {
+            if zeta![i] == patternLength {
+                indexes.append(i - patternLength - 1)
             }
         }
-
+        
         guard !indexes.isEmpty else {
             return nil
         }
-
+        
         return indexes
     }
 }

From aeaa72a741e2213cfaf3e55bb8f915fb5176f3e8 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sat, 24 Sep 2016 15:29:51 -0700
Subject: [PATCH 0568/1679] Updated syntax to Swift 3

---
 .../Contents.swift                            | 30 +++++++++++--------
 .../KaratsubaMultiplication.swift             | 21 +++++++++----
 2 files changed, 33 insertions(+), 18 deletions(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index bf4454956..53980ac1e 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -2,17 +2,23 @@
 
 import Foundation
 
-infix operator ^^ { associativity left precedence 160 }
+precedencegroup ExponentiativePrecedence {
+  higherThan: MultiplicationPrecedence
+  lowerThan: BitwiseShiftPrecedence
+  associativity: left
+}
+
+infix operator ^^: ExponentiativePrecedence
 func ^^ (radix: Int, power: Int) -> Int {
   return Int(pow(Double(radix), Double(power)))
 }
 
 // Long Multiplication - O(n^2)
-func multiply(num1: Int, _ num2: Int, base: Int = 10) -> Int {
-  let num1Array = String(num1).characters.reverse().map{ Int(String($0))! }
-  let num2Array = String(num2).characters.reverse().map{ Int(String($0))! }
+func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
+  let num1Array = String(num1).characters.reversed().map{ Int(String($0))! }
+  let num2Array = String(num2).characters.reversed().map{ Int(String($0))! }
   
-  var product = Array(count: num1Array.count + num2Array.count, repeatedValue: 0)
+  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
 
   for i in num1Array.indices {
     var carry = 0
@@ -24,16 +30,16 @@ func multiply(num1: Int, _ num2: Int, base: Int = 10) -> Int {
     product[i + num2Array.count] += carry
   }
   
-  return Int(product.reverse().map{ String($0) }.reduce("", combine: +))!
+  return Int(product.reversed().map{ String($0) }.reduce("", +))!
 }
 
 // Karatsuba Multiplication - O(nlogn)
-func karatsuba(num1: Int, _ num2: Int) -> Int {
+func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters
   
   guard num1Array.count > 1 && num2Array.count > 1 else {
-    return multiply(num1, num2)
+    return multiply(num1, by: num2)
   }
   
   let n = max(num1Array.count, num2Array.count)
@@ -44,14 +50,12 @@ func karatsuba(num1: Int, _ num2: Int) -> Int {
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
   
-  let ac = karatsuba(a, c)
-  let bd = karatsuba(b, d)
-  let adPluscd = karatsuba(a+b, c+d) - ac - bd
+  let ac = karatsuba(a, by: c)
+  let bd = karatsuba(b, by: d)
+  let adPluscd = karatsuba(a+b, by: c+d) - ac - bd
   
   let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
   
   return product
 }
 
-print(multiply(236742342, 1231234224))
-print(karatsuba(236742342, 1231234224))
\ No newline at end of file
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index a315d7494..7837e3f3c 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -8,7 +8,18 @@
 
 import Foundation
 
-func karatsuba(num1: Int, _ num2: Int) -> Int {
+precedencegroup ExponentiativePrecedence {
+  higherThan: MultiplicationPrecedence
+  lowerThan: BitwiseShiftPrecedence
+  associativity: left
+}
+
+infix operator ^^: ExponentiativePrecedence
+func ^^ (radix: Int, power: Int) -> Int {
+  return Int(pow(Double(radix), Double(power)))
+}
+
+func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters
   
@@ -24,11 +35,11 @@ func karatsuba(num1: Int, _ num2: Int) -> Int {
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
   
-  let ac = karatsuba(a, c)
-  let bd = karatsuba(b, d)
-  let adPluscd = karatsuba(a+b, c+d) - ac - bd
+  let ac = karatsuba(a, by: c)
+  let bd = karatsuba(b, by: d)
+  let adPluscd = karatsuba(a+b, by: c+d) - ac - bd
   
   let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
   
   return product
-}
\ No newline at end of file
+}

From 215ca9352840b52be84fc171954613ddde6f7a5e Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Mon, 26 Sep 2016 17:00:03 +0800
Subject: [PATCH 0569/1679] migrating dfs to swift3

---
 .../Simple Example.xcplaygroundpage/Contents.swift   |  2 +-
 .../timeline.xctimeline                              |  6 ------
 .../DepthFirstSearch.playground/Sources/Edge.swift   |  4 ++--
 .../DepthFirstSearch.playground/Sources/Graph.swift  | 12 ++++++------
 .../DepthFirstSearch.playground/Sources/Node.swift   |  8 ++++----
 Depth-First Search/DepthFirstSearch.swift            |  2 +-
 Depth-First Search/README.markdown                   |  2 +-
 7 files changed, 15 insertions(+), 21 deletions(-)
 delete mode 100644 Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 770712bfb..b1d8494d6 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,4 +1,4 @@
-func depthFirstSearch(graph: Graph, source: Node) -> [String] {
+func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
 
diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift
index 9a58a1f96..7c841be30 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
@@ -1,11 +1,11 @@
 public class Edge: Equatable {
   public var neighbor: Node
 
-  public init(neighbor: Node) {
+  public init(_ neighbor: Node) {
     self.neighbor = neighbor
   }
 }
 
-public func == (lhs: Edge, rhs: Edge) -> Bool {
+public func == (_ lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index 8cfb2a09c..87e21897c 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -5,14 +5,14 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(label: String) -> Node {
-    let node = Node(label: label)
+  public func addNode(_ label: String) -> Node {
+    let node = Node(label)
     nodes.append(node)
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
-    let edge = Edge(neighbor: neighbor)
+  public func addEdge(_ source: Node, neighbor: Node) {
+    let edge = Edge(neighbor)
     source.neighbors.append(edge)
   }
 
@@ -27,7 +27,7 @@ public class Graph: CustomStringConvertible, Equatable {
     return description
   }
 
-  public func findNodeWithLabel(label: String) -> Node {
+  public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
 
@@ -50,6 +50,6 @@ public class Graph: CustomStringConvertible, Equatable {
   }
 }
 
-public func == (lhs: Graph, rhs: Graph) -> Bool {
+public func == (_ lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift
index 37a3b3fdf..48fc952e3 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
@@ -5,7 +5,7 @@ public class Node: CustomStringConvertible, Equatable {
   public var distance: Int?
   public var visited: Bool
 
-  public init(label: String) {
+  public init(_ label: String) {
     self.label = label
     neighbors = []
     visited = false
@@ -22,11 +22,11 @@ public class Node: CustomStringConvertible, Equatable {
     return distance != nil
   }
 
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+  public func remove(_ edge: Edge) {
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
-public func == (lhs: Node, rhs: Node) -> Bool {
+public func == (_ lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Depth-First Search/DepthFirstSearch.swift b/Depth-First Search/DepthFirstSearch.swift
index 4393ac864..04e84cb66 100644
--- a/Depth-First Search/DepthFirstSearch.swift	
+++ b/Depth-First Search/DepthFirstSearch.swift	
@@ -1,4 +1,4 @@
-func depthFirstSearch(graph: Graph, source: Node) -> [String] {
+func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
 
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index a44ae8163..9e1a5112d 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -27,7 +27,7 @@ The parent of a node is the one that "discovered" that node. The root of the tre
 Simple recursive implementation of depth-first search:
 
 ```swift
-func depthFirstSearch(graph: Graph, source: Node) -> [String] {
+func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
 

From ef081622f899131b7ba45c863637a9049f962d8d Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Mon, 26 Sep 2016 17:04:03 +0800
Subject: [PATCH 0570/1679] migrating bfs to swift3

---
 .../Simple example.xcplaygroundpage/Contents.swift   |  2 +-
 .../timeline.xctimeline                              |  6 ------
 .../BreadthFirstSearch.playground/Sources/Edge.swift |  4 ++--
 .../Sources/Graph.swift                              | 12 ++++++------
 .../BreadthFirstSearch.playground/Sources/Node.swift |  8 ++++----
 .../Sources/Queue.swift                              |  2 +-
 Breadth-First Search/BreadthFirstSearch.swift        |  2 +-
 Breadth-First Search/README.markdown                 |  2 +-
 8 files changed, 16 insertions(+), 22 deletions(-)
 delete mode 100644 Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 93aa6b337..0fb98e1c8 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,4 +1,4 @@
-func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
+func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
 
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift
index 9a58a1f96..7c841be30 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Edge.swift	
@@ -1,11 +1,11 @@
 public class Edge: Equatable {
   public var neighbor: Node
 
-  public init(neighbor: Node) {
+  public init(_ neighbor: Node) {
     self.neighbor = neighbor
   }
 }
 
-public func == (lhs: Edge, rhs: Edge) -> Bool {
+public func == (_ lhs: Edge, rhs: Edge) -> Bool {
   return lhs.neighbor == rhs.neighbor
 }
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
index 8cfb2a09c..87e21897c 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -5,14 +5,14 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(label: String) -> Node {
-    let node = Node(label: label)
+  public func addNode(_ label: String) -> Node {
+    let node = Node(label)
     nodes.append(node)
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
-    let edge = Edge(neighbor: neighbor)
+  public func addEdge(_ source: Node, neighbor: Node) {
+    let edge = Edge(neighbor)
     source.neighbors.append(edge)
   }
 
@@ -27,7 +27,7 @@ public class Graph: CustomStringConvertible, Equatable {
     return description
   }
 
-  public func findNodeWithLabel(label: String) -> Node {
+  public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
 
@@ -50,6 +50,6 @@ public class Graph: CustomStringConvertible, Equatable {
   }
 }
 
-public func == (lhs: Graph, rhs: Graph) -> Bool {
+public func == (_ lhs: Graph, rhs: Graph) -> Bool {
   return lhs.nodes == rhs.nodes
 }
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift
index 37a3b3fdf..48fc952e3 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Node.swift	
@@ -5,7 +5,7 @@ public class Node: CustomStringConvertible, Equatable {
   public var distance: Int?
   public var visited: Bool
 
-  public init(label: String) {
+  public init(_ label: String) {
     self.label = label
     neighbors = []
     visited = false
@@ -22,11 +22,11 @@ public class Node: CustomStringConvertible, Equatable {
     return distance != nil
   }
 
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+  public func remove(_ edge: Edge) {
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
-public func == (lhs: Node, rhs: Node) -> Bool {
+public func == (_ lhs: Node, rhs: Node) -> Bool {
   return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift
index bf462bbdd..3d98f801c 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Queue.swift	
@@ -13,7 +13,7 @@ public struct Queue<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Breadth-First Search/BreadthFirstSearch.swift b/Breadth-First Search/BreadthFirstSearch.swift
index aa396ac7b..75508682a 100644
--- a/Breadth-First Search/BreadthFirstSearch.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.swift	
@@ -1,4 +1,4 @@
-func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
+func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
 
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 12e906532..23edf6da5 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -90,7 +90,7 @@ For an unweighted graph, this tree defines a shortest path from the starting nod
 Simple implementation of breadth-first search using a queue:
 
 ```swift
-func breadthFirstSearch(graph: Graph, source: Node) -> [String] {
+func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)
 

From a2bdc50e9e2307c11ad232f37acca34d944ff211 Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Mon, 26 Sep 2016 17:26:34 +0800
Subject: [PATCH 0571/1679] Migrating Brute Force String Search to Swift3

---
 .../Contents.swift                            | 11 ++++----
 .../timeline.xctimeline                       |  6 ----
 .../BruteForceStringSearch.swift              | 28 +++++++++----------
 Brute-Force String Search/README.markdown     | 28 +++++++++----------
 4 files changed, 34 insertions(+), 39 deletions(-)
 delete mode 100644 Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline

diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index 57f2b2090..61064c698 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -1,16 +1,17 @@
 //: Playground - noun: a place where people can play
 
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    for i in self.startIndex ..< self.endIndex {
+  func indexOf(_ pattern: String) -> String.Index? {
+    
+    for i in self.characters.indices {
       var j = i
       var found = true
-      for p in pattern.startIndex ..< pattern.endIndex {
-        if j == self.endIndex || self[j] != pattern[p] {
+      for p in pattern.characters.indices{
+        if j == self.characters.endIndex || self[j] != pattern[p] {
           found = false
           break
         } else {
-          j = j.successor()
+            j = self.characters.index(after: j)
         }
       }
       if found {
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline b/Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Brute-Force String Search/BruteForceStringSearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Brute-Force String Search/BruteForceStringSearch.swift b/Brute-Force String Search/BruteForceStringSearch.swift
index 431677a4a..03a2dff13 100644
--- a/Brute-Force String Search/BruteForceStringSearch.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.swift	
@@ -2,21 +2,21 @@
   Brute-force string search
 */
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    for i in self.startIndex ..< self.endIndex {
-      var j = i
-      var found = true
-      for p in pattern.startIndex ..< pattern.endIndex {
-        if j == self.endIndex || self[j] != pattern[p] {
-          found = false
-          break
-        } else {
-          j = j.successor()
+  func indexOf(_ pattern: String) -> String.Index? {
+    for i in self.characters.indices {
+        var j = i
+        var found = true
+        for p in pattern.characters.indices{
+            if j == self.characters.endIndex || self[j] != pattern[p] {
+                found = false
+                break
+            } else {
+                j = self.characters.index(after: j)
+            }
+        }
+        if found {
+            return i
         }
-      }
-      if found {
-        return i
-      }
     }
     return nil
   }
diff --git a/Brute-Force String Search/README.markdown b/Brute-Force String Search/README.markdown
index 748be872f..4e967bcfb 100644
--- a/Brute-Force String Search/README.markdown	
+++ b/Brute-Force String Search/README.markdown	
@@ -28,21 +28,21 @@ Here is a brute-force solution:
 
 ```swift
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    for i in self.startIndex ..< self.endIndex {
-      var j = i
-      var found = true
-      for p in pattern.startIndex ..< pattern.endIndex {
-        if j == self.endIndex || self[j] != pattern[p] {
-          found = false
-          break
-        } else {
-          j = j.successor()
+  func indexOf(_ pattern: String) -> String.Index? {
+    for i in self.characters.indices {
+        var j = i
+        var found = true
+        for p in pattern.characters.indices{
+            if j == self.characters.endIndex || self[j] != pattern[p] {
+                found = false
+                break
+            } else {
+                j = self.characters.index(after: j)
+            }
+        }
+        if found {
+            return i
         }
-      }
-      if found {
-        return i
-      }
     }
     return nil
   }

From 183cfcf5e26c35f68a2f7ec0d075c11dcf597e55 Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Tue, 27 Sep 2016 12:08:19 +0800
Subject: [PATCH 0572/1679] migrating montyhall to swift 3

---
 Monty Hall Problem/MontyHall.playground/Contents.swift      | 2 +-
 Monty Hall Problem/MontyHall.playground/timeline.xctimeline | 6 ------
 2 files changed, 1 insertion(+), 7 deletions(-)
 delete mode 100644 Monty Hall Problem/MontyHall.playground/timeline.xctimeline

diff --git a/Monty Hall Problem/MontyHall.playground/Contents.swift b/Monty Hall Problem/MontyHall.playground/Contents.swift
index 930dad714..bcdafd137 100644
--- a/Monty Hall Problem/MontyHall.playground/Contents.swift	
+++ b/Monty Hall Problem/MontyHall.playground/Contents.swift	
@@ -2,7 +2,7 @@
 
 import Foundation
 
-func random(n: Int) -> Int {
+func random(_ n: Int) -> Int {
   return Int(arc4random_uniform(UInt32(n)))
 }
 
diff --git a/Monty Hall Problem/MontyHall.playground/timeline.xctimeline b/Monty Hall Problem/MontyHall.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Monty Hall Problem/MontyHall.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From ecbcfeaa8f41d8bc2fde76933d2bf664c958cf3c Mon Sep 17 00:00:00 2001
From: SendilKumar N <sendilkumarn@live.com>
Date: Tue, 27 Sep 2016 12:41:55 +0800
Subject: [PATCH 0573/1679] migrating radix-sort to swift3

---
 .../Sources/RadixTree.swift                   |  38 +-
 Radix Tree/RadixTree.swift                    | 730 +++++++++---------
 2 files changed, 384 insertions(+), 384 deletions(-)

diff --git a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift
index 3cba5254a..1914f57bc 100644
--- a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
+++ b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
@@ -85,7 +85,7 @@ public class Edge: Root {
 			// For each child, erase it, then remove it from the children array.
 			for _ in 0...children.count-1 {
 				children[0].erase()
-				children.removeAtIndex(0)
+				children.remove(at: 0)
 			}
 		}
 	}
@@ -137,7 +137,7 @@ public class RadixTree {
 	}
 
 	// Inserts a string into the tree.
-	public func insert(str: String) -> Bool {
+	public func insert(_ str: String) -> Bool {
 		//Account for a blank input. The empty string is already in the tree.
 		if str == "" {
 			return false
@@ -182,9 +182,9 @@ public class RadixTree {
 					currEdge = e
 					var tempIndex = searchStr.startIndex
 					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
+						tempIndex = searchStr.characters.index(after: tempIndex)
 					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
+                    searchStr = searchStr.substring(from: tempIndex)
 					found = true
 					break
 				}
@@ -197,13 +197,13 @@ public class RadixTree {
 
 					// Create index objects and move them to after the shared prefix
 					for _ in 1...shared.characters.count {
-						index = index.successor()
-						labelIndex = labelIndex.successor()
+                        index = searchStr.characters.index(after: index)
+						labelIndex = e.label.characters.index(after: labelIndex)
 					}
 
 					// Substring both the search string and the label from the shared prefix
-					searchStr = searchStr.substringFromIndex(index)
-					e.label = e.label.substringFromIndex(labelIndex)
+                    searchStr = searchStr.substring(from: index)
+                    e.label = e.label.substring(from: labelIndex)
 
 					// Create 2 new edges and update parent/children values
 					let newEdge = Edge(e.label)
@@ -236,7 +236,7 @@ public class RadixTree {
 	}
 
 	// Tells you if a string is in the tree
-	public func find(str: String) -> Bool {
+	public func find(_ str: String) -> Bool {
 		// A radix tree always contains the empty string
 		if str == "" {
 			return true
@@ -267,9 +267,9 @@ public class RadixTree {
 					currEdge = c
 					var tempIndex = searchStr.startIndex
 					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
+						tempIndex = searchStr.characters.index(after: tempIndex)
 					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
+					searchStr = searchStr.substring(from: tempIndex)
 					found = true
 					break
 				}
@@ -300,12 +300,12 @@ public class RadixTree {
 	}
 
 	// Removes a string from the tree
-	public func remove(str: String) -> Bool {
+	public func remove(_ str: String) -> Bool {
 		// Removing the empty string removes everything in the tree
 		if str == "" {
 			for c in root.children {
 				c.erase()
-				root.children.removeAtIndex(0)
+				root.children.remove(at: 0)
 			}
 			return true
 		}
@@ -329,7 +329,7 @@ public class RadixTree {
 				// and everything below it in the tree
 				if currEdge.children[c].label == searchStr {
 					currEdge.children[c].erase()
-					currEdge.children.removeAtIndex(c)
+					currEdge.children.remove(at: c)
 					return true
 				}
 
@@ -341,9 +341,9 @@ public class RadixTree {
 					currEdge = currEdge.children[c]
 					var tempIndex = searchStr.startIndex
 					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
+						tempIndex = searchStr.characters.index(after: tempIndex)
 					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
+					searchStr = searchStr.substring(from: tempIndex)
 					found = true
 					break
 				}
@@ -364,15 +364,15 @@ public class RadixTree {
 
 // Returns the prefix that is shared between the two input strings
 // i.e. sharedPrefix("court", "coral") -> "co"
-public func sharedPrefix(str1: String, _ str2: String) -> String {
+public func sharedPrefix(_ str1: String, _ str2: String) -> String {
 	var temp = ""
 	var c1 = str1.characters.startIndex
 	var c2 = str2.characters.startIndex
 	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
 		if str1[c1] == str2[c2] {
 			temp.append( str1[c1] )
-			c1 = c1.successor()
-			c2 = c2.successor()
+            c1 = str1.characters.index(after:c1)
+            c2 = str2.characters.index(after:c2)
 		} else {
 			return temp
 		}
diff --git a/Radix Tree/RadixTree.swift b/Radix Tree/RadixTree.swift
index 3cba5254a..5badf0810 100644
--- a/Radix Tree/RadixTree.swift	
+++ b/Radix Tree/RadixTree.swift	
@@ -2,380 +2,380 @@ import Foundation
 
 // The root is the top of the Radix Tree
 public class Root {
-	var children: [Edge]
-
-	public init() {
-		children = [Edge]()
-	}
-
-	// Returns the length (in number of edges) of the longest traversal down the tree.
-	public func height() -> Int {
-		// Base case: no children: the tree has a height of 1
-		if children.count == 0 {
-			return 1
-		}
-		// Recursion: find the max height of a root's child and return 1 + that max
-		else {
-			var max = 1
-			for c in children {
-				if c.height() > max {
-					max = c.height()
-				}
-			}
-			return 1 + max
-		}
-	}
-
-	// Returns how far down in the tree a Root/Edge is.
-	// A root's level is always 0.
-	public func level() -> Int {
-		return 0
-	}
-
-	// Prints the tree for debugging/visualization purposes.
-	public func printRoot() {
-		// Print the first half of the children
-		if children.count > 1 {
-			for c in 0...children.count/2-1 {
-				children[c].printEdge()
-				print("|")
-			}
-		} else if children.count > 0 {
-			children[0].printEdge()
-		}
-		// Then print the root
-		print("ROOT")
-		// Print the second half of the children
-		if children.count > 1 {
-			for c in children.count/2...children.count-1 {
-				children[c].printEdge()
-				print("|")
-			}
-		}
-		print()
-	}
+    var children: [Edge]
+    
+    public init() {
+        children = [Edge]()
+    }
+    
+    // Returns the length (in number of edges) of the longest traversal down the tree.
+    public func height() -> Int {
+        // Base case: no children: the tree has a height of 1
+        if children.count == 0 {
+            return 1
+        }
+            // Recursion: find the max height of a root's child and return 1 + that max
+        else {
+            var max = 1
+            for c in children {
+                if c.height() > max {
+                    max = c.height()
+                }
+            }
+            return 1 + max
+        }
+    }
+    
+    // Returns how far down in the tree a Root/Edge is.
+    // A root's level is always 0.
+    public func level() -> Int {
+        return 0
+    }
+    
+    // Prints the tree for debugging/visualization purposes.
+    public func printRoot() {
+        // Print the first half of the children
+        if children.count > 1 {
+            for c in 0...children.count/2-1 {
+                children[c].printEdge()
+                print("|")
+            }
+        } else if children.count > 0 {
+            children[0].printEdge()
+        }
+        // Then print the root
+        print("ROOT")
+        // Print the second half of the children
+        if children.count > 1 {
+            for c in children.count/2...children.count-1 {
+                children[c].printEdge()
+                print("|")
+            }
+        }
+        print()
+    }
 }
 
 // Edges are what actually store the Strings in the tree
 public class Edge: Root {
-	var parent: Root?
-	var label: String
-
-	public init(_ label: String) {
-		self.label = label
-		super.init()
-	}
-
-	public override func level() -> Int {
-		// Recurse up the tree incrementing level by one until the root is reached
-		if parent != nil {
-			return 1 + parent!.level()
-		}
-		// If an edge has no parent, it's level is one
-		// NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
-		else {
-			return 1
-		}
-	}
-
-	// Erases a specific edge (and all edges below it in the tree).
-	public func erase() {
-		self.parent = nil
-		if children.count > 0 {
-			// For each child, erase it, then remove it from the children array.
-			for _ in 0...children.count-1 {
-				children[0].erase()
-				children.removeAtIndex(0)
-			}
-		}
-	}
-
-	// Prints the tree for debugging/visualization purposes.
-	public func printEdge() {
-		// Print the first half of the edge's children
-		if children.count > 1 {
-			for c in 0...children.count/2-1 {
-				children[c].printEdge()
-			}
-		} else if children.count > 0 {
-			children[0].printEdge()
-		}
-		// Tab over once up to the edge's level
-		for x in 1...level() {
-			if x == level() {
-				print("|------>", terminator: "")
-			} else {
-				print("|       ", terminator: "")
-			}
-		}
-		print(label)
-		// Print the second half of the edge's children
-		if children.count == 0 {
-			for _ in 1...level() {
-				print("|       ", terminator: "")
-			}
-			print()
-		}
-		if children.count > 1 {
-			for c in children.count/2...children.count-1 {
-				children[c].printEdge()
-			}
-		}
-	}
+    var parent: Root?
+    var label: String
+    
+    public init(_ label: String) {
+        self.label = label
+        super.init()
+    }
+    
+    public override func level() -> Int {
+        // Recurse up the tree incrementing level by one until the root is reached
+        if parent != nil {
+            return 1 + parent!.level()
+        }
+            // If an edge has no parent, it's level is one
+            // NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
+        else {
+            return 1
+        }
+    }
+    
+    // Erases a specific edge (and all edges below it in the tree).
+    public func erase() {
+        self.parent = nil
+        if children.count > 0 {
+            // For each child, erase it, then remove it from the children array.
+            for _ in 0...children.count-1 {
+                children[0].erase()
+                children.remove(at: 0)
+            }
+        }
+    }
+    
+    // Prints the tree for debugging/visualization purposes.
+    public func printEdge() {
+        // Print the first half of the edge's children
+        if children.count > 1 {
+            for c in 0...children.count/2-1 {
+                children[c].printEdge()
+            }
+        } else if children.count > 0 {
+            children[0].printEdge()
+        }
+        // Tab over once up to the edge's level
+        for x in 1...level() {
+            if x == level() {
+                print("|------>", terminator: "")
+            } else {
+                print("|       ", terminator: "")
+            }
+        }
+        print(label)
+        // Print the second half of the edge's children
+        if children.count == 0 {
+            for _ in 1...level() {
+                print("|       ", terminator: "")
+            }
+            print()
+        }
+        if children.count > 1 {
+            for c in children.count/2...children.count-1 {
+                children[c].printEdge()
+            }
+        }
+    }
 }
 
 public class RadixTree {
-	var root: Root
-
-	public init() {
-		root = Root()
-	}
-
-	// Returns the height of the tree by calling the root's height function.
-	public func height() -> Int {
-		return root.height() - 1
-	}
-
-	// Inserts a string into the tree.
-	public func insert(str: String) -> Bool {
-		//Account for a blank input. The empty string is already in the tree.
-		if str == "" {
-			return false
-		}
-
-		// searchStr is the parameter of the function
-		// it will be substringed as the function traverses down the tree
-		var searchStr = str
-
-		// currEdge is the current Edge (or Root) in question
-		var currEdge = root
-
-		while true {
-			var found = false
-
-			// If the current Edge has no children then the remaining searchStr is
-			// created as a child
-			if currEdge.children.count == 0 {
-				let newEdge = Edge(searchStr)
-				currEdge.children.append(newEdge)
-				newEdge.parent = currEdge
-				return true
-			}
-
-			// Loop through all of the children
-			for e in currEdge.children {
-				// Get the shared prefix between the child in question and the
-				// search string
-				let shared = sharedPrefix(searchStr, e.label)
-				var index  = shared.startIndex
-
-				// If the search string is equal to the shared string,
-				// the string already exists in the tree
-				if searchStr == shared {
-					return false
-				}
-
-				// If the child's label is equal to the shared string, you have to
-				// traverse another level down the tree, so substring the search
-				// string, break the loop, and run it back
-				else if shared == e.label {
-					currEdge = e
-					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
-					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
-					found = true
-					break
-				}
-
-				// If the child's label and the search string share a partial prefix,
-				// then both the label and the search string need to be substringed
-				// and a new branch needs to be created
-				else if shared.characters.count > 0 {
-					var labelIndex = e.label.characters.startIndex
-
-					// Create index objects and move them to after the shared prefix
-					for _ in 1...shared.characters.count {
-						index = index.successor()
-						labelIndex = labelIndex.successor()
-					}
-
-					// Substring both the search string and the label from the shared prefix
-					searchStr = searchStr.substringFromIndex(index)
-					e.label = e.label.substringFromIndex(labelIndex)
-
-					// Create 2 new edges and update parent/children values
-					let newEdge = Edge(e.label)
-					e.label = shared
-					for ec in e.children {
-						newEdge.children.append(ec)
-					}
-					newEdge.parent = e
-					e.children.removeAll()
-					for nec in newEdge.children {
-						nec.parent = newEdge
-					}
-					e.children.append(newEdge)
-					let newEdge2 = Edge(searchStr)
-					newEdge2.parent = e
-					e.children.append(newEdge2)
-					return true
-				}
-				// If they don't share a prefix, go to next child
-			}
-
-			// If none of the children share a prefix, you have to create a new child
-			if !found {
-				let newEdge = Edge(searchStr)
-				currEdge.children.append(newEdge)
-				newEdge.parent = currEdge
-				return true
-			}
-		}
-	}
-
-	// Tells you if a string is in the tree
-	public func find(str: String) -> Bool {
-		// A radix tree always contains the empty string
-		if str == "" {
-			return true
-		}
-		// If there are no children then the string cannot be in the tree
-		else if root.children.count == 0 {
-			return false
-		}
-		var searchStr = str
-		var currEdge = root
-		while true {
-			var found = false
-			// Loop through currEdge's children
-			for c in currEdge.children {
-				// First check if the search string and the child's label are equal
-				// if so the string is in the tree, return true
-				if searchStr == c.label {
-					return true
-				}
-
-				// If that is not true, find the shared string b/t the search string
-				// and the label
-				let shared = sharedPrefix(searchStr, c.label)
-
-				// If the shared string is equal to the label, update the curent node,
-				// break the loop, and run it back
-				if shared == c.label {
-					currEdge = c
-					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
-					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
-					found = true
-					break
-				}
-
-				// If the shared string is empty, go to the next child
-				else if shared.characters.count == 0 {
-					continue
-				}
-
-				// If the shared string matches the search string, return true
-				else if shared == searchStr {
-					return true
-				}
-
-				// If the search string and the child's label only share some characters,
-				// the string is not in the tree, return false
-				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-				  shared.characters.count < c.label.characters.count {
-				  	return false
-				}
-			}
-
-			// If nothing was found, return false
-			if !found {
-				return false
-			}
-		}
-	}
-
-	// Removes a string from the tree
-	public func remove(str: String) -> Bool {
-		// Removing the empty string removes everything in the tree
-		if str == "" {
-			for c in root.children {
-				c.erase()
-				root.children.removeAtIndex(0)
-			}
-			return true
-		}
-		// If the tree is empty, you cannot remove anything
-		else if root.children.count == 0 {
-			return false
-		}
-
-		var searchStr = str
-		var currEdge = root
-		while true {
-			var found = false
-			// If currEdge has no children, then the searchStr is not in the tree
-			if currEdge.children.count == 0 {
-				return false
-			}
-
-			// Loop through the children
-			for c in 0...currEdge.children.count-1 {
-				// If the child's label matches the search string, remove that child
-				// and everything below it in the tree
-				if currEdge.children[c].label == searchStr {
-					currEdge.children[c].erase()
-					currEdge.children.removeAtIndex(c)
-					return true
-				}
-
-				// Find the shared string
-				let shared = sharedPrefix(searchStr, currEdge.children[c].label)
-
-				// If the shared string is equal to the child's string, go down a level
-				if shared == currEdge.children[c].label {
-					currEdge = currEdge.children[c]
-					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = tempIndex.successor()
-					}
-					searchStr = searchStr.substringFromIndex(tempIndex)
-					found = true
-					break
-				}
-			}
-
-			// If there is no match, then the searchStr is not in the tree
-			if !found {
-				return false
-			}
-		}
-	}
-
-	// Prints the tree by calling the root's print function
-	public func printTree() {
-		root.printRoot()
-	}
+    var root: Root
+    
+    public init() {
+        root = Root()
+    }
+    
+    // Returns the height of the tree by calling the root's height function.
+    public func height() -> Int {
+        return root.height() - 1
+    }
+    
+    // Inserts a string into the tree.
+    public func insert(_ str: String) -> Bool {
+        //Account for a blank input. The empty string is already in the tree.
+        if str == "" {
+            return false
+        }
+        
+        // searchStr is the parameter of the function
+        // it will be substringed as the function traverses down the tree
+        var searchStr = str
+        
+        // currEdge is the current Edge (or Root) in question
+        var currEdge = root
+        
+        while true {
+            var found = false
+            
+            // If the current Edge has no children then the remaining searchStr is
+            // created as a child
+            if currEdge.children.count == 0 {
+                let newEdge = Edge(searchStr)
+                currEdge.children.append(newEdge)
+                newEdge.parent = currEdge
+                return true
+            }
+            
+            // Loop through all of the children
+            for e in currEdge.children {
+                // Get the shared prefix between the child in question and the
+                // search string
+                let shared = sharedPrefix(searchStr, e.label)
+                var index  = shared.startIndex
+                
+                // If the search string is equal to the shared string,
+                // the string already exists in the tree
+                if searchStr == shared {
+                    return false
+                }
+                    
+                    // If the child's label is equal to the shared string, you have to
+                    // traverse another level down the tree, so substring the search
+                    // string, break the loop, and run it back
+                else if shared == e.label {
+                    currEdge = e
+                    var tempIndex = searchStr.startIndex
+                    for _ in 1...shared.characters.count {
+                        tempIndex = searchStr.characters.index(after: tempIndex)
+                    }
+                    searchStr = searchStr.substring(from: tempIndex)
+                    found = true
+                    break
+                }
+                    
+                    // If the child's label and the search string share a partial prefix,
+                    // then both the label and the search string need to be substringed
+                    // and a new branch needs to be created
+                else if shared.characters.count > 0 {
+                    var labelIndex = e.label.characters.startIndex
+                    
+                    // Create index objects and move them to after the shared prefix
+                    for _ in 1...shared.characters.count {
+                        index = searchStr.characters.index(after: index)
+                        labelIndex = e.label.characters.index(after: labelIndex)
+                    }
+                    
+                    // Substring both the search string and the label from the shared prefix
+                    searchStr = searchStr.substring(from: index)
+                    e.label = e.label.substring(from: labelIndex)
+                    
+                    // Create 2 new edges and update parent/children values
+                    let newEdge = Edge(e.label)
+                    e.label = shared
+                    for ec in e.children {
+                        newEdge.children.append(ec)
+                    }
+                    newEdge.parent = e
+                    e.children.removeAll()
+                    for nec in newEdge.children {
+                        nec.parent = newEdge
+                    }
+                    e.children.append(newEdge)
+                    let newEdge2 = Edge(searchStr)
+                    newEdge2.parent = e
+                    e.children.append(newEdge2)
+                    return true
+                }
+                // If they don't share a prefix, go to next child
+            }
+            
+            // If none of the children share a prefix, you have to create a new child
+            if !found {
+                let newEdge = Edge(searchStr)
+                currEdge.children.append(newEdge)
+                newEdge.parent = currEdge
+                return true
+            }
+        }
+    }
+    
+    // Tells you if a string is in the tree
+    public func find(_ str: String) -> Bool {
+        // A radix tree always contains the empty string
+        if str == "" {
+            return true
+        }
+            // If there are no children then the string cannot be in the tree
+        else if root.children.count == 0 {
+            return false
+        }
+        var searchStr = str
+        var currEdge = root
+        while true {
+            var found = false
+            // Loop through currEdge's children
+            for c in currEdge.children {
+                // First check if the search string and the child's label are equal
+                // if so the string is in the tree, return true
+                if searchStr == c.label {
+                    return true
+                }
+                
+                // If that is not true, find the shared string b/t the search string
+                // and the label
+                let shared = sharedPrefix(searchStr, c.label)
+                
+                // If the shared string is equal to the label, update the curent node,
+                // break the loop, and run it back
+                if shared == c.label {
+                    currEdge = c
+                    var tempIndex = searchStr.startIndex
+                    for _ in 1...shared.characters.count {
+                        tempIndex = searchStr.characters.index(after: tempIndex)
+                    }
+                    searchStr = searchStr.substring(from: tempIndex)
+                    found = true
+                    break
+                }
+                    
+                    // If the shared string is empty, go to the next child
+                else if shared.characters.count == 0 {
+                    continue
+                }
+                    
+                    // If the shared string matches the search string, return true
+                else if shared == searchStr {
+                    return true
+                }
+                    
+                    // If the search string and the child's label only share some characters,
+                    // the string is not in the tree, return false
+                else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
+                    shared.characters.count < c.label.characters.count {
+                    return false
+                }
+            }
+            
+            // If nothing was found, return false
+            if !found {
+                return false
+            }
+        }
+    }
+    
+    // Removes a string from the tree
+    public func remove(_ str: String) -> Bool {
+        // Removing the empty string removes everything in the tree
+        if str == "" {
+            for c in root.children {
+                c.erase()
+                root.children.remove(at: 0)
+            }
+            return true
+        }
+            // If the tree is empty, you cannot remove anything
+        else if root.children.count == 0 {
+            return false
+        }
+        
+        var searchStr = str
+        var currEdge = root
+        while true {
+            var found = false
+            // If currEdge has no children, then the searchStr is not in the tree
+            if currEdge.children.count == 0 {
+                return false
+            }
+            
+            // Loop through the children
+            for c in 0...currEdge.children.count-1 {
+                // If the child's label matches the search string, remove that child
+                // and everything below it in the tree
+                if currEdge.children[c].label == searchStr {
+                    currEdge.children[c].erase()
+                    currEdge.children.remove(at: c)
+                    return true
+                }
+                
+                // Find the shared string
+                let shared = sharedPrefix(searchStr, currEdge.children[c].label)
+                
+                // If the shared string is equal to the child's string, go down a level
+                if shared == currEdge.children[c].label {
+                    currEdge = currEdge.children[c]
+                    var tempIndex = searchStr.startIndex
+                    for _ in 1...shared.characters.count {
+                        tempIndex = searchStr.characters.index(after: tempIndex)
+                    }
+                    searchStr = searchStr.substring(from: tempIndex)
+                    found = true
+                    break
+                }
+            }
+            
+            // If there is no match, then the searchStr is not in the tree
+            if !found {
+                return false
+            }
+        }
+    }
+    
+    // Prints the tree by calling the root's print function
+    public func printTree() {
+        root.printRoot()
+    }
 }
 
 // Returns the prefix that is shared between the two input strings
 // i.e. sharedPrefix("court", "coral") -> "co"
-public func sharedPrefix(str1: String, _ str2: String) -> String {
-	var temp = ""
-	var c1 = str1.characters.startIndex
-	var c2 = str2.characters.startIndex
-	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
-		if str1[c1] == str2[c2] {
-			temp.append( str1[c1] )
-			c1 = c1.successor()
-			c2 = c2.successor()
-		} else {
-			return temp
-		}
-	}
-	return temp
+public func sharedPrefix(_ str1: String, _ str2: String) -> String {
+    var temp = ""
+    var c1 = str1.characters.startIndex
+    var c2 = str2.characters.startIndex
+    for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+        if str1[c1] == str2[c2] {
+            temp.append( str1[c1] )
+            c1 = str1.characters.index(after:c1)
+            c2 = str2.characters.index(after:c2)
+        } else {
+            return temp
+        }
+    }
+    return temp
 }

From b2c302faf26a78e0eafceaf0496cd7262b9305b2 Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Tue, 27 Sep 2016 21:10:24 -0700
Subject: [PATCH 0574/1679] Migrate LCS to Swift 3.0

---
 .travis.yml                                   |  2 +-
 .../Contents.swift                            | 18 ++++----
 .../contents.xcplayground                     |  2 +-
 .../LongestCommonSubsequence.swift            | 19 +++++----
 Longest Common Subsequence/README.markdown    | 31 +++++++-------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 41 ++++++++++++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 7 files changed, 77 insertions(+), 38 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index a04a2e742..949fc759f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -26,7 +26,7 @@ script:
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index bb6fa7c2a..0fc9ec325 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,11 +1,11 @@
 extension String {
-  public func longestCommonSubsequence(other: String) -> String {
+  public func longestCommonSubsequence(_ other: String) -> String {
 
-    func lcsLength(other: String) -> [[Int]] {
-      var matrix = [[Int]](count: self.characters.count+1, repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
+    func lcsLength(_ other: String) -> [[Int]] {
+      var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.characters.count+1), count: self.characters.count+1)
 
-      for (i, selfChar) in self.characters.enumerate() {
-        for (j, otherChar) in other.characters.enumerate() {
+      for (i, selfChar) in self.characters.enumerated() {
+        for (j, otherChar) in other.characters.enumerated() {
           if otherChar == selfChar {
             matrix[i+1][j+1] = matrix[i][j] + 1
           } else {
@@ -16,7 +16,7 @@ extension String {
       return matrix
     }
 
-    func backtrack(matrix: [[Int]]) -> String {
+    func backtrack(_ matrix: [[Int]]) -> String {
       var i = self.characters.count
       var j = other.characters.count
       var charInSequence = self.endIndex
@@ -28,15 +28,15 @@ extension String {
           j -= 1
         } else if matrix[i][j] == matrix[i - 1][j] {
           i -= 1
-          charInSequence = charInSequence.predecessor()
+          charInSequence = self.index(before: charInSequence)
         } else {
           i -= 1
           j -= 1
-          charInSequence = charInSequence.predecessor()
+          charInSequence = self.index(before: charInSequence)
           lcs.append(self[charInSequence])
         }
       }
-      return String(lcs.characters.reverse())
+      return String(lcs.characters.reversed())
     }
 
     return backtrack(lcsLength(other))
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground
index 5da2641c9..9f5f2f40c 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.swift b/Longest Common Subsequence/LongestCommonSubsequence.swift
index 23d191102..b6834279d 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.swift	
@@ -1,17 +1,17 @@
 extension String {
-  public func longestCommonSubsequence(other: String) -> String {
+  public func longestCommonSubsequence(_ other: String) -> String {
 
     // Computes the length of the lcs using dynamic programming.
     // Output is a matrix of size (n+1)x(m+1), where matrix[x][y] is the length
     // of lcs between substring (0, x-1) of self and substring (0, y-1) of other.
-    func lcsLength(other: String) -> [[Int]] {
+    func lcsLength(_ other: String) -> [[Int]] {
 
       // Create matrix of size (n+1)x(m+1). The algorithm needs first row and
       // first column to be filled with 0.
-      var matrix = [[Int]](count: self.characters.count+1, repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
+      var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.characters.count+1), count: self.characters.count+1)
 
-      for (i, selfChar) in self.characters.enumerate() {
-        for (j, otherChar) in other.characters.enumerate() {
+      for (i, selfChar) in self.characters.enumerated() {
+        for (j, otherChar) in other.characters.enumerated() {
           if otherChar == selfChar {
             // Common char found, add 1 to highest lcs found so far.
             matrix[i+1][j+1] = matrix[i][j] + 1
@@ -28,7 +28,7 @@ extension String {
 
     // Backtracks from matrix[n][m] to matrix[1][1] looking for chars that are
     // common to both strings.
-    func backtrack(matrix: [[Int]]) -> String {
+    func backtrack(_ matrix: [[Int]]) -> String {
       var i = self.characters.count
       var j = other.characters.count
 
@@ -46,21 +46,22 @@ extension String {
         else if matrix[i][j] == matrix[i - 1][j] {
           i -= 1
           // As i was decremented, move back charInSequence.
-          charInSequence = charInSequence.predecessor()
+          charInSequence = self.index(before: charInSequence)
         }
         // Value on the left and above are different than current cell.
         // This means 1 was added to lcs length (line 17).
         else {
           i -= 1
           j -= 1
-          charInSequence = charInSequence.predecessor()
+            charInSequence = self.index(before: charInSequence)
+
           lcs.append(self[charInSequence])
         }
       }
 
       // Due to backtrack, chars were added in reverse order: reverse it back.
       // Append and reverse is faster than inserting at index 0.
-      return String(lcs.characters.reverse())
+      return String(lcs.characters.reversed())
     }
 
     // Combine dynamic programming approach with backtrack to find the lcs.
diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index 64d3988c6..ba514728a 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -18,9 +18,9 @@ To determine the length of the LCS between all combinations of substrings of `a`
 
 > **Note:** During the following explanation, `n` is the length of string `a`, and `m` is the length of string `b`.
 
-To find the lengths of all possible subsequences, we use a helper function, `lcsLength()`. This creates a matrix of size `(n+1)` by `(m+1)`, where `matrix[x][y]` is the length of the LCS between the substrings `a[0...x-1]` and `b[0...y-1]`.
+To find the lengths of all possible subsequences, we use a helper function, `lcsLength(_:)`. This creates a matrix of size `(n+1)` by `(m+1)`, where `matrix[x][y]` is the length of the LCS between the substrings `a[0...x-1]` and `b[0...y-1]`.
 
-Given strings `"ABCBX"` and `"ABDCAB"`, the output matrix of `lcsLength()` is the following:
+Given strings `"ABCBX"` and `"ABDCAB"`, the output matrix of `lcsLength(_:)` is the following:
 
 ```
 |   | Ø | A | B | D | C | A | B |
@@ -34,16 +34,15 @@ Given strings `"ABCBX"` and `"ABDCAB"`, the output matrix of `lcsLength()` is th
 
 In this example, if we look at `matrix[3][4]` we find the value `3`. This means the length of the LCS between `a[0...2]` and `b[0...3]`, or between `"ABC"` and `"ABDC"`, is 3. That is correct, because these two substrings have the subsequence `ABC` in common. (Note: the first row and column of the matrix are always filled with zeros.)
 
-Here is the source code for `lcsLength()`; this lives in an extension on `String`:
+Here is the source code for `lcsLength(_:)`; this lives in an extension on `String`:
 
 ```swift
-func lcsLength(other: String) -> [[Int]] {
+func lcsLength(_ other: String) -> [[Int]] {
 
-  var matrix = [[Int]](count: self.characters.count+1, 
-                       repeatedValue: [Int](count: other.characters.count+1, repeatedValue: 0))
+  var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.characters.count+1), count: self.characters.count+1)
 
-  for (i, selfChar) in self.characters.enumerate() {
-	for (j, otherChar) in other.characters.enumerate() {
+  for (i, selfChar) in self.characters.enumerated() {
+	for (j, otherChar) in other.characters.enumerated() {
 	  if otherChar == selfChar {
 		// Common char found, add 1 to highest lcs found so far.
 		matrix[i+1][j+1] = matrix[i][j] + 1
@@ -96,7 +95,7 @@ Now we compare `C` with `C`. These are equal, and we increment the length to `3`
 | X | 0 |   |   |   |   |   |   |
 ```
 
-And so on... this is how `lcsLength()` fills in the entire matrix.
+And so on... this is how `lcsLength(_:)` fills in the entire matrix.
 
 ## Backtracking to find the actual subsequence
 
@@ -125,7 +124,7 @@ One thing to notice is, as it's running backwards, the LCS is built in reverse o
 Here is the backtracking code:
 
 ```swift
-func backtrack(matrix: [[Int]]) -> String {
+func backtrack(_ matrix: [[Int]]) -> String {
   var i = self.characters.count
   var j = other.characters.count
   
@@ -141,14 +140,14 @@ func backtrack(matrix: [[Int]]) -> String {
 	// Indicates propagation without change: no new char was added to lcs.
 	else if matrix[i][j] == matrix[i - 1][j] {
 	  i -= 1
-	  charInSequence = charInSequence.predecessor()
+	  charInSequence = self.index(before: charInSequence)
 	}
 	// Value on the left and above are different than current cell.
 	// This means 1 was added to lcs length.
 	else {
 	  i -= 1
 	  j -= 1
-	  charInSequence = charInSequence.predecessor()
+	  charInSequence = self.index(before: charInSequence)
 	  lcs.append(self[charInSequence])
 	}
   }
@@ -165,17 +164,17 @@ Due to backtracking, characters are added in reverse order, so at the end of the
 
 ## Putting it all together
 
-To find the LCS between two strings, we first call `lcsLength()` and then `backtrack()`:
+To find the LCS between two strings, we first call `lcsLength(_:)` and then `backtrack(_:)`:
 
 ```swift
 extension String {
-  public func longestCommonSubsequence(other: String) -> String {
+  public func longestCommonSubsequence(_ other: String) -> String {
 
-    func lcsLength(other: String) -> [[Int]] {
+    func lcsLength(_ other: String) -> [[Int]] {
       ...
     }
     
-    func backtrack(matrix: [[Int]]) -> String {
+    func backtrack(_ matrix: [[Int]]) -> String {
       ...
     }
 
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj
index abf3084dd..bf9c18fd3 100644
--- a/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/project.pbxproj	
@@ -82,7 +82,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				TargetAttributes = {
 					4716C7A61C93750500F6C1C0 = {
 						CreatedOnToolsVersion = 7.2.1;
@@ -132,12 +132,49 @@
 		4716C7861C936DCB00F6C1C0 /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				ONLY_ACTIVE_ARCH = YES;
 			};
 			name = Debug;
 		};
 		4716C7871C936DCB00F6C1C0 /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -187,6 +224,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -228,6 +266,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = me.pedrovereza.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 3d7f342b3..0b0682c43 100644
--- a/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Longest Common Subsequence/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From a172311433bc1c9cbd86f21cc284731ff04a9510 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Wed, 28 Sep 2016 14:14:24 +0200
Subject: [PATCH 0575/1679] added Z-Algorithm README

---
 Z-Algorithm/README.markdown | 176 ++++++++++++++++++++++++++++++++++++
 1 file changed, 176 insertions(+)
 create mode 100644 Z-Algorithm/README.markdown

diff --git a/Z-Algorithm/README.markdown b/Z-Algorithm/README.markdown
new file mode 100644
index 000000000..7fbb9b48b
--- /dev/null
+++ b/Z-Algorithm/README.markdown
@@ -0,0 +1,176 @@
+# Z-Algorithm String Search
+
+Goal: Write a simple linear-time string matching algorithm in Swift that returns the indexes of all the occurrencies of a given pattern. 
+ 
+In other words, we want to implement an `indexesOf(pattern: String)` extension on `String` that returns an array `[Int]` of integers, representing all occurrences' indexes of the search pattern, or `nil` if the pattern could not be found inside the string.
+ 
+For example:
+
+```swift
+let str = "Hello, playground!"
+str.indexesOf(pattern: "ground")   // Output: [11]
+
+let traffic = "🚗🚙🚌🚕🚑🚐🚗🚒🚚🚎🚛🚐🏎🚜🚗🏍🚒🚲🚕🚓🚌🚑"
+traffic.indexesOf(pattern: "🚑") // Output: [4, 21]
+```
+
+Many string search algorithms use a pre-processing function to compute a table that will be used in successive stage. This table can save some time during the pattern search stage because it allows to avoid un-needed characters comparisons. The [Z-Algorithm]() is one of these functions. It borns as a pattern pre-processing function (this is its role in the [Knuth-Morris-Pratt algorithm](../Knuth-Morris-Pratt/) and others) but, just like we will show here, it can be used also as a single string search algorithm.
+
+### Z-Algorithm as pattern pre-processor
+
+As we said, the Z-Algorithm is foremost an algorithm that process a pattern in order to calculate a skip-comparisons-table.
+The computation of the Z-Algorithm over a pattern `P` produces an array (called `Z` in the literature) of integers in which each element, call it `Z[i]`, represents the length of the longest substring of `P` that starts at `i` and matches a prefix of `P`. In simpler words, `Z[i]` records the longest prefix of `P[i...|P|]` that matches a prefix of `P`. As an example, let's consider `P = "ffgtrhghhffgtggfredg"`. We have that `Z[5] = 0 (f...h...)`, `Z[9] = 4 (ffgtr...ffgtg...)` and `Z[15] = 1 (ff...fr...)`.
+
+But how do we compute `Z`? Before we describe the algorithm we must indroduce the concept of Z-box. A Z-box is a pair `(left, right)` used during the computation that records the substring of maximal length that occurs also as a prefix of `P`. The two indices `left` and `right` represent, respectively, the left-end index and the right-end index of this substring. 
+The definition of the Z-Algorithm is inductive and it computes the elements of the array for every position `k` in the pattern, starting from `k = 1`. The following values (`Z[k + 1]`, `Z[k + 2]`, ...) are computed after `Z[k]`. The idea behind the algorithm is that previously computed values can speed up the calculus of `Z[k + 1]`, avoiding some character comparisons that were already done before. Consider this example: suppose we are at iteration `k = 100`, so we are analyzing position `100` of the pattern. All the values between `Z[1]` and `Z[99]` were correctly computed and `left = 70` and `right = 120`. This means that there is a substring of length `51` starting at position `70` and ending at position `120` that matches the prefix of the pattern/string we are considering. Reasoning on it a little bit we can say that the substring of length `21` starting at position `100` matches the substring of length `21` starting at position `30` of the pattern (because we are inside a substring that matches a prefix of the pattern). So we can use `Z[30]` to compute `Z[100]` without additional character comparisons.
+This a simple description of the idea that is behind this algorithm. There are a few cases to manage when the use of pre-computed values cannot be directly applied and some comparisons are to be made.
+
+Here is the code of the function that computes the Z-array:
+```
+swift
+func ZetaAlgorithm(ptrn: String) -> [Int]? {
+
+    let pattern = Array(ptrn.characters)
+    let patternLength: Int = pattern.count
+
+    guard patternLength > 0 else {
+        return nil
+    }
+
+    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
+
+    var left: Int = 0
+    var right: Int = 0
+    var k_1: Int = 0
+    var betaLength: Int = 0
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+
+    for k in 1 ..< patternLength {
+        if k > right {  // Outside a Z-box: compare the characters until mismatch
+            patternIndex = 0
+
+            while k + patternIndex < patternLength  &&
+                pattern[k + patternIndex] == pattern[patternIndex] {
+                patternIndex = patternIndex + 1
+            }
+
+            zeta[k] = patternIndex
+
+            if zeta[k] > 0 {
+                left = k
+                right = k + zeta[k] - 1
+            }
+        } else {  // Inside a Z-box
+            k_1 = k - left + 1
+            betaLength = right - k + 1
+
+            if zeta[k_1 - 1] < betaLength { // Entirely inside a Z-box: we can use the values computed before
+                zeta[k] = zeta[k_1 - 1]
+            } else if zeta[k_1 - 1] >= betaLength { // Not entirely inside a Z-box: we must proceed with comparisons too
+                textIndex = betaLength
+                patternIndex = right + 1
+
+                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+                    textIndex = textIndex + 1
+                    patternIndex = patternIndex + 1
+                }
+
+                zeta[k] = patternIndex - k
+                left = k
+                right = patternIndex - 1
+            }
+        }
+    }
+    return zeta
+}
+```
+
+Let's make an example reasoning with the code above. Let's consider the string `P = “abababab"`. The algorithm begins with `k = 1`, `left = right = 0`. So, no Z-box is "active" and thus, because `k > right` we start with the character comparisons beetwen `P[1]` and `P[0]`.
+  
+    
+       01234567
+    k:  x
+       abababbb
+       x
+    Z: 00000000
+    left:  0
+    right: 0
+
+We have a mismatch at the first comparison and so the substring starting at `P[1]` does not match a prefix of `P`. So, we put `Z[1] = 0` and let `left` and `right` untouched. We begin another iteration with `k = 2`, we have `2 > 0` and again we start comparing characters `P[2]` with `P[0]`. This time the characters match and so we continue the comparisons until a mismatch occurs. It happens at position `6`. The characters matched are `4`, so we put `Z[2] = 4` and set `left = k = 2` and `right = k + Z[k] - 1 = 5`. We have our first Z-box that is the substring `"abab"` (notice that it matches a prefix of `P`) starting at position `left = 2`.
+
+       01234567
+    k:   x
+       abababbb
+       x
+    Z: 00400000
+    left:  2
+    right: 5
+
+We then proceed with `k = 3`. We have `3 <= 5`. We are inside the Z-box previously found and inside a prefix of `P`. So we can look for a position that has a previously computed value. We calculate `k_1 = k - left = 1` that is the index of the prefix's character equal to `P[k]`. We check `Z[1] = 0` and `0 < (right - k + 1 = 3)` and we find that we are exactly inside the Z-box. We can use the previously computed value, so we put `Z[3] = Z[1] = 0`, `left` and `right` remain unchanged.
+At iteration `k = 4` we initially execute the `else` branch of the outer `if`. Then in the inner `if` we have that `k_1 = 2` and `(Z[2] = 4) >= 5 - 4 + 1`. So, the substring `P[k...r]` matches for `right - k + 1 = 2` chars the prefix of `P` but it could not for the following characters. We must then compare the characters starting at `r + 1 = 6` with those starting at `right - k + 1 = 2`. We have `P[6] != P[2]` and so we have to set `Z[k] = 6 - 4 = 2`, `left = 4` and `right = 5`.
+
+       01234567
+    k:     x
+       abababbb
+       x
+    Z: 00402000
+    left:  4
+    right: 5
+
+With iteration `k = 5` we have `k <= right` and then `(Z[k_1] = 0) < (right - k + 1 = 1)` and so we set `z[k] = 0`. In iteration `6` and `7` we execute the first branch of the outer `if` but we only have mismatches, so the algorithms terminates returning the Z-array as `Z = [0, 0, 4, 0, 2, 0, 0, 0]`.
+
+The Z-Algorithm runs in linear time. More specifically, the Z-Algorithm for a string `P` of size `n` has a running time of `O(n)`.
+
+The implementation of Z-Algorithm as string pre-processor is contained in the [ZAlgorithm.swift](./ZAlgorithm.swift) file.
+
+### Z-Algorithm as string search algorithm 
+
+The Z-Algorithm discussed above leads to the simplest linear-time string matching algorithm. To obtain it, we have to simply concatenate the pattern `P` and text `T` in a string `S = P$T` where `$` is a character that does not appear neither in `P` nor `T`. Then we run the algorithm on `S` obtaining the Z-array. All we have to do now is scan the Z-array looking for elements equal to `n` (which is the pattern length). When we find such value we can report an occurrence.
+
+```swift
+extension String {
+
+    func indexesOf(pattern: String) -> [Int]? {
+        let patternLength: Int = pattern.characters.count
+        /* Let's calculate the Z-Algorithm on the concatenation of pattern and text */
+        let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
+
+        guard zeta != nil else {
+            return nil
+        }
+
+        var indexes: [Int] = [Int]()
+
+        /* Scan the zeta array to find matched patterns */
+        for i in 0 ..< zeta!.count {
+            if zeta![i] == patternLength {
+                indexes.append(i - patternLength - 1)
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+
+        return indexes
+    }
+}
+```
+
+Let's make an example. Let `P = “CATA“` and `T = "GAGAACATACATGACCAT"` be the pattern and the text. Let's concatenate them with the character `$`. We have the string `S = "CATA$GAGAACATACATGACCAT"`. After computing the Z-Algorithm on `S` we obtain:
+
+                1         2
+      01234567890123456789012
+      CATA$GAGAACATACATGACCAT
+    Z 00000000004000300001300
+                ^
+
+We scan the Z-array and at position `10` we find `Z[10] = 4 = n`. So we can report a match occuring at text position `10 - n - 1 = 5`.
+
+As said before, the complexity of this algorithm is linear. Defining `n` and `m` as pattern and text lengths, the final complexity we obtain is `O(n + m + 1) = O(n + m)`.
+
+
+Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"]() by Dan Gusfield, Cambridge University Press, 1997. 
+
+*Written for Swift Algorithm Club by Matteo Dunnhofer*

From 41712e0275fbc50e63f32580d402ca12d1648888 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Wed, 28 Sep 2016 14:20:58 +0200
Subject: [PATCH 0576/1679] edited Z-Algorithm README

---
 Z-Algorithm/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Z-Algorithm/README.markdown b/Z-Algorithm/README.markdown
index 7fbb9b48b..c6c50a23b 100644
--- a/Z-Algorithm/README.markdown
+++ b/Z-Algorithm/README.markdown
@@ -86,7 +86,7 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
 }
 ```
 
-Let's make an example reasoning with the code above. Let's consider the string `P = “abababab"`. The algorithm begins with `k = 1`, `left = right = 0`. So, no Z-box is "active" and thus, because `k > right` we start with the character comparisons beetwen `P[1]` and `P[0]`.
+Let's make an example reasoning with the code above. Let's consider the string `P = “abababbb"`. The algorithm begins with `k = 1`, `left = right = 0`. So, no Z-box is "active" and thus, because `k > right` we start with the character comparisons beetwen `P[1]` and `P[0]`.
   
     
        01234567
@@ -171,6 +171,6 @@ We scan the Z-array and at position `10` we find `Z[10] = 4 = n`. So we can repo
 As said before, the complexity of this algorithm is linear. Defining `n` and `m` as pattern and text lengths, the final complexity we obtain is `O(n + m + 1) = O(n + m)`.
 
 
-Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"]() by Dan Gusfield, Cambridge University Press, 1997. 
+Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"](https://books.google.it/books/about/Algorithms_on_Strings_Trees_and_Sequence.html?id=Ofw5w1yuD8kC&redir_esc=y) by Dan Gusfield, Cambridge University Press, 1997. 
 
 *Written for Swift Algorithm Club by Matteo Dunnhofer*

From 72ee49b05218ce4ca627caabaa9b2960154a9dde Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Wed, 28 Sep 2016 16:32:15 +0200
Subject: [PATCH 0577/1679] edited Z-Algorithm README

---
 Z-Algorithm/README.markdown | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Z-Algorithm/README.markdown b/Z-Algorithm/README.markdown
index c6c50a23b..8b84c28bf 100644
--- a/Z-Algorithm/README.markdown
+++ b/Z-Algorithm/README.markdown
@@ -26,8 +26,7 @@ The definition of the Z-Algorithm is inductive and it computes the elements of t
 This a simple description of the idea that is behind this algorithm. There are a few cases to manage when the use of pre-computed values cannot be directly applied and some comparisons are to be made.
 
 Here is the code of the function that computes the Z-array:
-```
-swift
+```swift
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
     let pattern = Array(ptrn.characters)

From 69758422a5fade80fda9c550818ad0056dc0634b Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Wed, 28 Sep 2016 16:49:22 -0700
Subject: [PATCH 0578/1679] Fixed a typo in the Karatsuba algorithm

---
 .../KaratsubaMultiplication.playground/Contents.swift         | 4 ++--
 Karatsuba Multiplication/KaratsubaMultiplication.swift        | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 53980ac1e..95a498322 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -52,9 +52,9 @@ func karatsuba(_ num1: Int, by num2: Int) -> Int {
   
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
-  let adPluscd = karatsuba(a+b, by: c+d) - ac - bd
+  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
   
-  let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
+  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
   
   return product
 }
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index 7837e3f3c..fb20a667d 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -37,9 +37,9 @@ func karatsuba(_ num1: Int, by num2: Int) -> Int {
   
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
-  let adPluscd = karatsuba(a+b, by: c+d) - ac - bd
+  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
   
-  let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
+  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
   
   return product
 }

From ab2949e77658260df2153e95f32f525bff68b785 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Wed, 28 Sep 2016 16:50:12 -0700
Subject: [PATCH 0579/1679] Added an explanation and examples to the README

---
 Karatsuba Multiplication/README.markdown | 123 ++++++++++++++++++++++-
 1 file changed, 122 insertions(+), 1 deletion(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index 0afd91b0c..af3392612 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -1,8 +1,129 @@
 # Karatsuba Multiplication
 
-TODO: Explanation/Examples
+Goal: To quickly multiply two numbers together
 
+## Long Multiplication
 
+In grade school we all learned how to multiply two numbers together via Long Multiplication. So let's try that first!
 
+Example 1: Multiply 1234 by 5678 using Long Multiplication
+
+	    5678
+	   *1234
+	  ------
+	   22712
+	  17034-
+	 11356--
+	 5678---
+	--------
+	 7006652
+
+So what's the problem with long multiplication? Speed. Long Multiplication runs in **O(n^2)**. 
+
+You can see where the **O(n^2)** comes from in the implementation for Long Multiplication:
+
+```swift
+// Long Multiplication
+func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
+  let num1Array = String(num1).characters.reversed().map{ Int(String($0))! }
+  let num2Array = String(num2).characters.reversed().map{ Int(String($0))! }
+  
+  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
+    }
+    product[i + num2Array.count] += carry
+  }
+  
+  return Int(product.reversed().map{ String($0) }.reduce("", +))!
+}
+```
+
+The double for loop is the culprit! So Long Multiplication might not be the best algorithm after all. Can we do better?
+
+## Karatsuba Multiplication
+
+The Karatsuba Algorithm was discovered by Anatoly Karatsuba and published in 1962. Karatsuba discovered that you could compute the product of two large numbers using three smaller products and some addition and subtraction.
+
+For two numbers x, y, where m <= n:
+
+	x = a*10^m + b
+	y = c*10^m + d
+
+Now, we can say:
+
+	x*y = a*c*10^(2m) + (a*d + b*c)*10^(m) + b*d
+
+We can compute this function recursively, and that's what makes Karatsuba Multiplication fast.
+
+```swift
+let ac = karatsuba(a, by: c)
+let bd = karatsuba(b, by: d)
+let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
+```
+
+The last recursion is interesting. Normally, you'd think we would have to run four recursions to find the product `x*y` (`a*c`, `a*d`, `b*c`, `b*d`). However, Karatsuba realized that you only need three recursions, and some addition and subtraction. Here's the math:
+
+	(a+b)*(c+d) - a*c - b*c  = (a*c + a*d + b*c + b*d) - a*c - b*c
+		    		 = (a*d + b*c)
+
+Pretty cool, huh?
+
+Here's the full implementation
+
+```swift
+// Karatsuba Multiplication
+func karatsuba(_ num1: Int, by num2: Int) -> Int {
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return num1*num2
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, by: c)
+  let bd = karatsuba(b, by: d)
+  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
+  
+  return product
+}
+```
+
+The run time for this algorithm is about **O(n^1.56)** which is better than the **O(n^2)** for Long Multiplication. 
+
+Example 2: Multiply 1234 by 5678 using Karatsuba Multiplication
+
+	m = 2
+	x = 1234 = a*10^2 + b = 12*10^2 + 34
+	y = 5678 = c*10^2 + d = 56*10^2 + 78
+
+	a*c = 672
+	b*d = 2652
+	(a*d + b*c) = 2840
+	
+	x*y = 672*10^4 + 2840*10^2 + 2652
+	    = 6720000 + 284000 + 2652
+	    = 7006652	
+ 
+## Resources
+
+[Wikipedia] (https://en.wikipedia.org/wiki/Karatsuba_algorithm)
+
+[WolframMathWorld] (http://mathworld.wolfram.com/KaratsubaMultiplication.html) 
 
 *Written for Swift Algorithm Club by Richard Ash*

From b8ea4fd9b63ac20c3ae521d3a1ff018500a587d3 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Sat, 1 Oct 2016 23:02:12 +0200
Subject: [PATCH 0580/1679] added Knuth-Morris-Pratt README

---
 Knuth-Morris-Pratt/README.markdown | 157 +++++++++++++++++++++++++++++
 1 file changed, 157 insertions(+)
 create mode 100644 Knuth-Morris-Pratt/README.markdown

diff --git a/Knuth-Morris-Pratt/README.markdown b/Knuth-Morris-Pratt/README.markdown
new file mode 100644
index 000000000..ab8e78cdc
--- /dev/null
+++ b/Knuth-Morris-Pratt/README.markdown
@@ -0,0 +1,157 @@
+# Knuth-Morris-Pratt String Search
+
+Goal: Write a linear-time string matching algorithm in Swift that returns the indexes of all the occurrencies of a given pattern. 
+ 
+In other words, we want to implement an `indexesOf(pattern: String)` extension on `String` that returns an array `[Int]` of integers, representing all occurrences' indexes of the search pattern, or `nil` if the pattern could not be found inside the string.
+ 
+For example:
+
+```swift
+let dna = "ACCCGGTTTTAAAGAACCACCATAAGATATAGACAGATATAGGACAGATATAGAGACAAAACCCCATACCCCAATATTTTTTTGGGGAGAAAAACACCACAGATAGATACACAGACTACACGAGATACGACATACAGCAGCATAACGACAACAGCAGATAGACGATCATAACAGCAATCAGACCGAGCGCAGCAGCTTTTAAGCACCAGCCCCACAAAAAACGACAATFATCATCATATACAGACGACGACACGACATATCACACGACAGCATA"
+dna.indexesOf(ptnr: "CATA")   // Output: [20, 64, 130, 140, 166, 234, 255, 270]
+
+let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
+concert.indexesOf(ptnr: "🎻🎷")   // Output: [6]
+```
+
+The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm) is considered one of the best algorithms for solving the pattern matching problem. Although in practice [Boyer-Moore](../Boyer-Moore/) is usually preferred, the algorithm that we will introduce is simpler, and has the same (linear) running time.
+
+The idea behind the algorithm is not too different from the [naive string search](../Brute-Force String Search/) procedure. As it, Knuth-Morris-Pratt aligns the text with the pattern and goes with character comparisons from left to right. But, instead of making a shift of one character when a mismatch occurs, it uses a more intelligent way to move the pattern along the text. In fact, the algorithm features a pattern pre-processing stage where it acquires all the informations that will make the algorithm skip redundant comparisons, resulting in larger shifts.
+
+The pre-processing stage produces an array (called `suffixPrefix` in the code) of integers in which every element `suffixPrefix[i]` records the length of the longest proper suffix of `P[0...i]` (where `P` is the pattern) that matches a prefix of `P`. In other words, `suffixPrefix[i]` is the longest proper substring of `P` that ends at position `i` and that is a prefix of `P`. Just a quick example. Consider `P = "abadfryaabsabadffg", then `suffixPrefix[4] = 0`, `suffixPrefix[9] = 2`, `suffixPrefix[14] = 4`.
+There are different ways to obtain the values of `SuffixPrefix` array. We will use the method based on the [Z-Algorithm](../Z-Algorithm/). This function takes in input the pattern and produces an array of integers. Each element represents the length of the longest substring starting at position `i` of `P` and that matches a prefix of `P`. You can notice that the two arrays are similar, they record the same informations but on the different places. We only have to find a method to map `Z[i]` to `suffixPrefix[j]`. It is not that difficult and this is the code that will do for us:
+
+```swift
+for patternIndex in (1 ..< patternLength).reversed() {
+    textIndex = patternIndex + zeta![patternIndex] - 1
+    suffixPrefix[textIndex] = zeta![patternIndex]
+}
+```
+
+We are simply computing the index of the end of the substring starting at position `i` (as we know matches a prefix of `P`). The element of `suffixPrefix` at that index then it will be set with the length of the substring.
+
+Once the shift-array `suffixPrefix` is ready we can begin with pattern search stage. The algorithm first attempts to compare the characters of the text with those of the pattern. If it succeeds, it goes on until a mismatch occurs. When it happens, it checks if an occurrence of the pattern is present (and reports it). Otherwise, if no comparisons are made then the text cursor is moved forward, else the pattern is shifted to the right. The shift's amount is based on the `suffixPrefix` array, and it guarantees that the prefix `P[0...suffixPrefix[i]]` will match its opposing substring in the text. In this way, shifts of more than one character are often made and lot of comparisons can be avoided, saving a lot of time.
+
+Here is the code of the Knuth-Morris-Pratt algorithm:
+
+```swift
+extension String {
+
+    func indexesOf(ptnr: String) -> [Int]? {
+
+        let text = Array(self.characters)
+        let pattern = Array(ptnr.characters)
+
+        let textLength: Int = text.count
+        let patternLength: Int = pattern.count
+
+        guard patternLength > 0 else {
+            return nil
+        }
+
+        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
+        var textIndex: Int = 0
+        var patternIndex: Int = 0
+        var indexes: [Int] = [Int]()
+
+        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+        let zeta = ZetaAlgorithm(ptnr: ptnr)
+
+        for patternIndex in (1 ..< patternLength).reversed() {
+            textIndex = patternIndex + zeta![patternIndex] - 1
+            suffixPrefix[textIndex] = zeta![patternIndex]
+        }
+
+        /* Search stage: scanning the text for pattern matching */
+        textIndex = 0
+        patternIndex = 0
+
+        while textIndex + (patternLength - patternIndex - 1) < textLength {
+
+            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+                textIndex = textIndex + 1
+                patternIndex = patternIndex + 1
+            }
+
+            if patternIndex == patternLength {
+                indexes.append(textIndex - patternIndex)
+            }
+
+            if patternIndex == 0 {
+                textIndex = textIndex + 1
+            } else {
+                patternIndex = suffixPrefix[patternIndex - 1]
+            }
+        }
+
+        guard !indexes.isEmpty else {
+            return nil
+        }
+        return indexes
+    }
+}
+```
+
+Let's make an example reasoning with the code above. Let's consider the string `P = ACTGACTA"`, the consequentially obtained `suffixPrefix` array equal to `[0, 0, 0, 0, 0, 0, 3, 1]`, and the text `T = "GCACTGACTGACTGACTAG"`. The algorithm begins with the text and the pattern aligned like below. We have to compare `T[0]` with `P[0]`.  
+  
+                              1       
+                    0123456789012345678
+    text:           GCACTGACTGACTGACTAG 
+    textIndex:      ^
+    pattern:        ACTGACTA
+    patternIndex:   ^
+                    x
+    suffixPrefix:   00000031
+
+We have a mismatch and we move on comparing `T[1]` and `P[0]`. We have to check if a pattern occurrence is present but there is not. So, we have to shift the pattern right and by doing so we have to check `suffixPrefix[1 - 1]`. Its value is `0` and we restart by comparing `T[1]` with `P[0]`. Again a mismath occurs, so we go on with `T[2]` and `P[0]`.
+  
+                              1      
+                    0123456789012345678
+    text:           GCACTGACTGACTGACTAG
+    textIndex:        ^ 
+    pattern:          ACTGACTA
+    patternIndex:     ^
+    suffixPrefix:     00000031
+
+This time we have a match. And it continues until position `8`. Unfortunately the length of the match is not equal to the pattern length, we cannot report an occurrence. But we are still lucky because we can use the values computed in the `suffixPrefix` array now. In fact, the length of the match is `7`, and if we look at the element `suffixPrefix[7 - 1]` we discover that is `3`. This information tell us that that the prefix of `P` matches the suffix of the susbtring `T[0...8]`. So the `suffixPrefix` array guarantees us that the two substring match and that we do not have to compare their characters, so we can shift right the pattern for more than one character!
+The comparisons restart from `T[9]` and `P[3]`.  
+      
+                              1       
+                    0123456789012345678
+    text:           GCACTGACTGACTGACTAG 
+    textIndex:               ^
+    pattern:              ACTGACTA
+    patternIndex:            ^
+    suffixPrefix:         00000031
+
+They match so we continue the compares until position `13` where a misatch occurs beetwen charcter `G` and `A`. Just like before, we are lucky and we can use the `suffixPrefix` array to shift right the pattern.
+      
+                              1       
+                    0123456789012345678
+    text:           GCACTGACTGACTGACTAG 
+    textIndex:                   ^
+    pattern:                  ACTGACTA
+    patternIndex:                ^
+    suffixPrefix:             00000031
+
+Again, we have to compare. But this time the comparisons finally take us to an occurrence, at position `17 - 7 = 10`.
+      
+                              1       
+                    0123456789012345678
+    text:           GCACTGACTGACTGACTAG 
+    textIndex:                       ^
+    pattern:                  ACTGACTA
+    patternIndex:                    ^
+    suffixPrefix:             00000031
+
+The algorithm than tries to compare `T[18]` with `P[1]` (because we used the element `suffixPrefix[8 - 1] = 1`) but it fails and at the next iteration it ends its work.
+ 
+
+The pre-processing stage involves only the pattern. The running time of the Z-Algorithm is linear and takes `O(n)`, where `n` is the length of the pattern `P`. After that, the search stage does not "overshoot" the length of the text `T` (call it `m`). It can be be proved that number of comparisons of the search stage is bounded by `2 * m`. The final running time of the Knuth-Morris-Pratt algorithm is `O(n + m)`.
+
+
+> **Note:** To execute the code in the [KnuthMorrisPratt.swift](./KnuthMorrisPratt.swift) you have to copy the [ZAlgorithm.swift](../Z-Algorithm/ZAlgorithm.swift) file contained in the [Z-Algorithm](../Z-Algorithm/) folder. The [KnuthMorrisPratt.playground](./KnuthMorrisPratt.playground) already includes the definition of the `Zeta` function.
+
+Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"](https://books.google.it/books/about/Algorithms_on_Strings_Trees_and_Sequence.html?id=Ofw5w1yuD8kC&redir_esc=y) by Dan Gusfield, Cambridge University Press, 1997. 
+
+*Written for Swift Algorithm Club by Matteo Dunnhofer*

From 5423763065c6844d2c573b76435623662670b947 Mon Sep 17 00:00:00 2001
From: dontfollowmeimcrazy <mattdunnhofer@gmail.com>
Date: Sat, 1 Oct 2016 23:05:50 +0200
Subject: [PATCH 0581/1679] edited Knuth-Morris-Pratt README

---
 Knuth-Morris-Pratt/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Knuth-Morris-Pratt/README.markdown b/Knuth-Morris-Pratt/README.markdown
index ab8e78cdc..f01b87b3d 100644
--- a/Knuth-Morris-Pratt/README.markdown
+++ b/Knuth-Morris-Pratt/README.markdown
@@ -18,7 +18,7 @@ The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris
 
 The idea behind the algorithm is not too different from the [naive string search](../Brute-Force String Search/) procedure. As it, Knuth-Morris-Pratt aligns the text with the pattern and goes with character comparisons from left to right. But, instead of making a shift of one character when a mismatch occurs, it uses a more intelligent way to move the pattern along the text. In fact, the algorithm features a pattern pre-processing stage where it acquires all the informations that will make the algorithm skip redundant comparisons, resulting in larger shifts.
 
-The pre-processing stage produces an array (called `suffixPrefix` in the code) of integers in which every element `suffixPrefix[i]` records the length of the longest proper suffix of `P[0...i]` (where `P` is the pattern) that matches a prefix of `P`. In other words, `suffixPrefix[i]` is the longest proper substring of `P` that ends at position `i` and that is a prefix of `P`. Just a quick example. Consider `P = "abadfryaabsabadffg", then `suffixPrefix[4] = 0`, `suffixPrefix[9] = 2`, `suffixPrefix[14] = 4`.
+The pre-processing stage produces an array (called `suffixPrefix` in the code) of integers in which every element `suffixPrefix[i]` records the length of the longest proper suffix of `P[0...i]` (where `P` is the pattern) that matches a prefix of `P`. In other words, `suffixPrefix[i]` is the longest proper substring of `P` that ends at position `i` and that is a prefix of `P`. Just a quick example. Consider `P = "abadfryaabsabadffg"`, then `suffixPrefix[4] = 0`, `suffixPrefix[9] = 2`, `suffixPrefix[14] = 4`.
 There are different ways to obtain the values of `SuffixPrefix` array. We will use the method based on the [Z-Algorithm](../Z-Algorithm/). This function takes in input the pattern and produces an array of integers. Each element represents the length of the longest substring starting at position `i` of `P` and that matches a prefix of `P`. You can notice that the two arrays are similar, they record the same informations but on the different places. We only have to find a method to map `Z[i]` to `suffixPrefix[j]`. It is not that difficult and this is the code that will do for us:
 
 ```swift

From f4dc41feb8b66fe9c02d78627d2caafd3bd4f1fa Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Tue, 4 Oct 2016 22:21:13 -0500
Subject: [PATCH 0582/1679] began convert to swift3

---
 .../BoyerMoore.playground/Contents.swift       | 18 +++++++++---------
 .../BoyerMoore.playground/timeline.xctimeline  |  6 ------
 2 files changed, 9 insertions(+), 15 deletions(-)
 delete mode 100644 Boyer-Moore/BoyerMoore.playground/timeline.xctimeline

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 433935133..631b0d43a 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -7,20 +7,20 @@ extension String {
     assert(patternLength <= self.characters.count)
 
     var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerate() {
+    for (i, c) in pattern.characters.enumerated() {
       skipTable[c] = patternLength - i - 1
     }
 
-    let p = pattern.endIndex.predecessor()
+    let p = pattern.index(before: endIndex)
     let lastChar = pattern[p]
-    var i = self.startIndex.advancedBy(patternLength - 1)
+    var i = self.index(startIndex, offsetBy: patternLength - 1)
 
     func backwards() -> String.Index? {
       var q = p
       var j = i
       while q > pattern.startIndex {
-        j = j.predecessor()
-        q = q.predecessor()
+        j = index(before: j)
+        q = index(before: q)
         if self[j] != pattern[q] { return nil }
       }
       return j
@@ -30,9 +30,9 @@ extension String {
       let c = self[i]
       if c == lastChar {
         if let k = backwards() { return k }
-        i = i.successor()
+          i = index(after: i)
       } else {
-        i = i.advancedBy(skipTable[c] ?? patternLength)
+        i = index(i, offsetBy: skipTable[c] ?? patternLength)
       }
     }
     return nil
@@ -44,7 +44,7 @@ extension String {
 // A few simple tests
 
 let s = "Hello, World"
-s.indexOf("World")  // 7
+s.indexOf(pattern: "World")  // 7
 
 let animals = "🐶🐔🐷🐮🐱"
-animals.indexOf("🐮")  // 6
+animals.indexOf(pattern: "🐮")  // 6
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From c79d699b5e31206341ee623b642c7181943e7928 Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Tue, 4 Oct 2016 22:39:54 -0500
Subject: [PATCH 0583/1679] fixed bug with end index

---
 .../BoyerMoore.playground/Contents.swift      |  6 ++----
 .../BoyerMoore.playground/timeline.xctimeline | 21 +++++++++++++++++++
 2 files changed, 23 insertions(+), 4 deletions(-)
 create mode 100644 Boyer-Moore/BoyerMoore.playground/timeline.xctimeline

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 631b0d43a..59cc85b86 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -11,7 +11,7 @@ extension String {
       skipTable[c] = patternLength - i - 1
     }
 
-    let p = pattern.index(before: endIndex)
+    let p = pattern.index(before: pattern.endIndex)
     let lastChar = pattern[p]
     var i = self.index(startIndex, offsetBy: patternLength - 1)
 
@@ -39,12 +39,10 @@ extension String {
   }
 }
 
-
-
 // A few simple tests
 
 let s = "Hello, World"
 s.indexOf(pattern: "World")  // 7
 
 let animals = "🐶🐔🐷🐮🐱"
-animals.indexOf(pattern: "🐮")  // 6
+//animals.indexOf(pattern: "🐮")  // 6
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
new file mode 100644
index 000000000..623552dab
--- /dev/null
+++ b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
@@ -0,0 +1,21 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497331454.819397"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497331454.819493"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497331454.819555"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>

From e53faf4fced5aa86e0bfb3f97bc98b1bd76557d2 Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Tue, 4 Oct 2016 22:53:37 -0500
Subject: [PATCH 0584/1679] uncomment test

---
 Boyer-Moore/BoyerMoore.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 59cc85b86..6203d36e7 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -45,4 +45,4 @@ let s = "Hello, World"
 s.indexOf(pattern: "World")  // 7
 
 let animals = "🐶🐔🐷🐮🐱"
-//animals.indexOf(pattern: "🐮")  // 6
+animals.indexOf(pattern: "🐮")  // 6

From df1cc1e4d16e488ff3ed35d3c0b5b1df3d59d4fe Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Tue, 4 Oct 2016 22:56:33 -0500
Subject: [PATCH 0585/1679] formatting

---
 Boyer-Moore/BoyerMoore.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 6203d36e7..9a3d619dc 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -30,7 +30,7 @@ extension String {
       let c = self[i]
       if c == lastChar {
         if let k = backwards() { return k }
-          i = index(after: i)
+        i = index(after: i)
       } else {
         i = index(i, offsetBy: skipTable[c] ?? patternLength)
       }

From 2e9e887c07f42306d80ac1d102e0253ecc1a9f06 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 5 Oct 2016 21:40:45 +1300
Subject: [PATCH 0586/1679] LCS - Restoring executeOnSourceChanges to default

---
 .../LongestCommonSubsequence.playground/contents.xcplayground | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground
index 9f5f2f40c..fc5b4ab70 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+<playground version='5.0' target-platform='ios'>
     <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
+</playground>

From bf9ba314510af9a5dd15eaa0eb8d0f1dc789eb60 Mon Sep 17 00:00:00 2001
From: Chris Pilcher <nzchrisp@gmail.com>
Date: Wed, 5 Oct 2016 21:55:24 +1300
Subject: [PATCH 0587/1679] Radix tree re-indent to use two spaces

---
 Radix Tree/RadixTree.swift | 684 ++++++++++++++++++-------------------
 1 file changed, 342 insertions(+), 342 deletions(-)

diff --git a/Radix Tree/RadixTree.swift b/Radix Tree/RadixTree.swift
index 5badf0810..958ffb4e6 100644
--- a/Radix Tree/RadixTree.swift	
+++ b/Radix Tree/RadixTree.swift	
@@ -2,380 +2,380 @@ import Foundation
 
 // The root is the top of the Radix Tree
 public class Root {
-    var children: [Edge]
-    
-    public init() {
-        children = [Edge]()
+  var children: [Edge]
+
+  public init() {
+    children = [Edge]()
+  }
+
+  // Returns the length (in number of edges) of the longest traversal down the tree.
+  public func height() -> Int {
+    // Base case: no children: the tree has a height of 1
+    if children.count == 0 {
+      return 1
     }
-    
-    // Returns the length (in number of edges) of the longest traversal down the tree.
-    public func height() -> Int {
-        // Base case: no children: the tree has a height of 1
-        if children.count == 0 {
-            return 1
-        }
-            // Recursion: find the max height of a root's child and return 1 + that max
-        else {
-            var max = 1
-            for c in children {
-                if c.height() > max {
-                    max = c.height()
-                }
-            }
-            return 1 + max
+      // Recursion: find the max height of a root's child and return 1 + that max
+    else {
+      var max = 1
+      for c in children {
+        if c.height() > max {
+          max = c.height()
         }
+      }
+      return 1 + max
     }
-    
-    // Returns how far down in the tree a Root/Edge is.
-    // A root's level is always 0.
-    public func level() -> Int {
-        return 0
+  }
+
+  // Returns how far down in the tree a Root/Edge is.
+  // A root's level is always 0.
+  public func level() -> Int {
+    return 0
+  }
+
+  // Prints the tree for debugging/visualization purposes.
+  public func printRoot() {
+    // Print the first half of the children
+    if children.count > 1 {
+      for c in 0...children.count/2-1 {
+        children[c].printEdge()
+        print("|")
+      }
+    } else if children.count > 0 {
+      children[0].printEdge()
     }
-    
-    // Prints the tree for debugging/visualization purposes.
-    public func printRoot() {
-        // Print the first half of the children
-        if children.count > 1 {
-            for c in 0...children.count/2-1 {
-                children[c].printEdge()
-                print("|")
-            }
-        } else if children.count > 0 {
-            children[0].printEdge()
-        }
-        // Then print the root
-        print("ROOT")
-        // Print the second half of the children
-        if children.count > 1 {
-            for c in children.count/2...children.count-1 {
-                children[c].printEdge()
-                print("|")
-            }
-        }
-        print()
+    // Then print the root
+    print("ROOT")
+    // Print the second half of the children
+    if children.count > 1 {
+      for c in children.count/2...children.count-1 {
+        children[c].printEdge()
+        print("|")
+      }
     }
+    print()
+  }
 }
 
 // Edges are what actually store the Strings in the tree
 public class Edge: Root {
-    var parent: Root?
-    var label: String
-    
-    public init(_ label: String) {
-        self.label = label
-        super.init()
+  var parent: Root?
+  var label: String
+
+  public init(_ label: String) {
+    self.label = label
+    super.init()
+  }
+
+  public override func level() -> Int {
+    // Recurse up the tree incrementing level by one until the root is reached
+    if parent != nil {
+      return 1 + parent!.level()
     }
-    
-    public override func level() -> Int {
-        // Recurse up the tree incrementing level by one until the root is reached
-        if parent != nil {
-            return 1 + parent!.level()
-        }
-            // If an edge has no parent, it's level is one
-            // NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
-        else {
-            return 1
-        }
+      // If an edge has no parent, it's level is one
+      // NOTE: THIS SHOULD NEVER HAPPEN AS THE ROOT IS ALWAYS THE TOP OF THE TREE
+    else {
+      return 1
     }
-    
-    // Erases a specific edge (and all edges below it in the tree).
-    public func erase() {
-        self.parent = nil
-        if children.count > 0 {
-            // For each child, erase it, then remove it from the children array.
-            for _ in 0...children.count-1 {
-                children[0].erase()
-                children.remove(at: 0)
-            }
-        }
+  }
+
+  // Erases a specific edge (and all edges below it in the tree).
+  public func erase() {
+    self.parent = nil
+    if children.count > 0 {
+      // For each child, erase it, then remove it from the children array.
+      for _ in 0...children.count-1 {
+        children[0].erase()
+        children.remove(at: 0)
+      }
     }
-    
-    // Prints the tree for debugging/visualization purposes.
-    public func printEdge() {
-        // Print the first half of the edge's children
-        if children.count > 1 {
-            for c in 0...children.count/2-1 {
-                children[c].printEdge()
-            }
-        } else if children.count > 0 {
-            children[0].printEdge()
-        }
-        // Tab over once up to the edge's level
-        for x in 1...level() {
-            if x == level() {
-                print("|------>", terminator: "")
-            } else {
-                print("|       ", terminator: "")
-            }
+  }
+
+  // Prints the tree for debugging/visualization purposes.
+  public func printEdge() {
+    // Print the first half of the edge's children
+    if children.count > 1 {
+      for c in 0...children.count/2-1 {
+        children[c].printEdge()
+      }
+    } else if children.count > 0 {
+      children[0].printEdge()
+    }
+    // Tab over once up to the edge's level
+    for x in 1...level() {
+      if x == level() {
+        print("|------>", terminator: "")
+      } else {
+        print("|       ", terminator: "")
+      }
+    }
+    print(label)
+    // Print the second half of the edge's children
+    if children.count == 0 {
+      for _ in 1...level() {
+        print("|       ", terminator: "")
+      }
+      print()
+    }
+    if children.count > 1 {
+      for c in children.count/2...children.count-1 {
+        children[c].printEdge()
+      }
+    }
+  }
+}
+
+public class RadixTree {
+  var root: Root
+
+  public init() {
+    root = Root()
+  }
+
+  // Returns the height of the tree by calling the root's height function.
+  public func height() -> Int {
+    return root.height() - 1
+  }
+
+  // Inserts a string into the tree.
+  public func insert(_ str: String) -> Bool {
+    //Account for a blank input. The empty string is already in the tree.
+    if str == "" {
+      return false
+    }
+
+    // searchStr is the parameter of the function
+    // it will be substringed as the function traverses down the tree
+    var searchStr = str
+
+    // currEdge is the current Edge (or Root) in question
+    var currEdge = root
+
+    while true {
+      var found = false
+
+      // If the current Edge has no children then the remaining searchStr is
+      // created as a child
+      if currEdge.children.count == 0 {
+        let newEdge = Edge(searchStr)
+        currEdge.children.append(newEdge)
+        newEdge.parent = currEdge
+        return true
+      }
+
+      // Loop through all of the children
+      for e in currEdge.children {
+        // Get the shared prefix between the child in question and the
+        // search string
+        let shared = sharedPrefix(searchStr, e.label)
+        var index  = shared.startIndex
+
+        // If the search string is equal to the shared string,
+        // the string already exists in the tree
+        if searchStr == shared {
+          return false
         }
-        print(label)
-        // Print the second half of the edge's children
-        if children.count == 0 {
-            for _ in 1...level() {
-                print("|       ", terminator: "")
-            }
-            print()
+
+          // If the child's label is equal to the shared string, you have to
+          // traverse another level down the tree, so substring the search
+          // string, break the loop, and run it back
+        else if shared == e.label {
+          currEdge = e
+          var tempIndex = searchStr.startIndex
+          for _ in 1...shared.characters.count {
+            tempIndex = searchStr.characters.index(after: tempIndex)
+          }
+          searchStr = searchStr.substring(from: tempIndex)
+          found = true
+          break
         }
-        if children.count > 1 {
-            for c in children.count/2...children.count-1 {
-                children[c].printEdge()
-            }
+
+          // If the child's label and the search string share a partial prefix,
+          // then both the label and the search string need to be substringed
+          // and a new branch needs to be created
+        else if shared.characters.count > 0 {
+          var labelIndex = e.label.characters.startIndex
+
+          // Create index objects and move them to after the shared prefix
+          for _ in 1...shared.characters.count {
+            index = searchStr.characters.index(after: index)
+            labelIndex = e.label.characters.index(after: labelIndex)
+          }
+
+          // Substring both the search string and the label from the shared prefix
+          searchStr = searchStr.substring(from: index)
+          e.label = e.label.substring(from: labelIndex)
+
+          // Create 2 new edges and update parent/children values
+          let newEdge = Edge(e.label)
+          e.label = shared
+          for ec in e.children {
+            newEdge.children.append(ec)
+          }
+          newEdge.parent = e
+          e.children.removeAll()
+          for nec in newEdge.children {
+            nec.parent = newEdge
+          }
+          e.children.append(newEdge)
+          let newEdge2 = Edge(searchStr)
+          newEdge2.parent = e
+          e.children.append(newEdge2)
+          return true
         }
+        // If they don't share a prefix, go to next child
+      }
+
+      // If none of the children share a prefix, you have to create a new child
+      if !found {
+        let newEdge = Edge(searchStr)
+        currEdge.children.append(newEdge)
+        newEdge.parent = currEdge
+        return true
+      }
     }
-}
+  }
 
-public class RadixTree {
-    var root: Root
-    
-    public init() {
-        root = Root()
+  // Tells you if a string is in the tree
+  public func find(_ str: String) -> Bool {
+    // A radix tree always contains the empty string
+    if str == "" {
+      return true
     }
-    
-    // Returns the height of the tree by calling the root's height function.
-    public func height() -> Int {
-        return root.height() - 1
+      // If there are no children then the string cannot be in the tree
+    else if root.children.count == 0 {
+      return false
     }
-    
-    // Inserts a string into the tree.
-    public func insert(_ str: String) -> Bool {
-        //Account for a blank input. The empty string is already in the tree.
-        if str == "" {
-            return false
+    var searchStr = str
+    var currEdge = root
+    while true {
+      var found = false
+      // Loop through currEdge's children
+      for c in currEdge.children {
+        // First check if the search string and the child's label are equal
+        // if so the string is in the tree, return true
+        if searchStr == c.label {
+          return true
         }
-        
-        // searchStr is the parameter of the function
-        // it will be substringed as the function traverses down the tree
-        var searchStr = str
-        
-        // currEdge is the current Edge (or Root) in question
-        var currEdge = root
-        
-        while true {
-            var found = false
-            
-            // If the current Edge has no children then the remaining searchStr is
-            // created as a child
-            if currEdge.children.count == 0 {
-                let newEdge = Edge(searchStr)
-                currEdge.children.append(newEdge)
-                newEdge.parent = currEdge
-                return true
-            }
-            
-            // Loop through all of the children
-            for e in currEdge.children {
-                // Get the shared prefix between the child in question and the
-                // search string
-                let shared = sharedPrefix(searchStr, e.label)
-                var index  = shared.startIndex
-                
-                // If the search string is equal to the shared string,
-                // the string already exists in the tree
-                if searchStr == shared {
-                    return false
-                }
-                    
-                    // If the child's label is equal to the shared string, you have to
-                    // traverse another level down the tree, so substring the search
-                    // string, break the loop, and run it back
-                else if shared == e.label {
-                    currEdge = e
-                    var tempIndex = searchStr.startIndex
-                    for _ in 1...shared.characters.count {
-                        tempIndex = searchStr.characters.index(after: tempIndex)
-                    }
-                    searchStr = searchStr.substring(from: tempIndex)
-                    found = true
-                    break
-                }
-                    
-                    // If the child's label and the search string share a partial prefix,
-                    // then both the label and the search string need to be substringed
-                    // and a new branch needs to be created
-                else if shared.characters.count > 0 {
-                    var labelIndex = e.label.characters.startIndex
-                    
-                    // Create index objects and move them to after the shared prefix
-                    for _ in 1...shared.characters.count {
-                        index = searchStr.characters.index(after: index)
-                        labelIndex = e.label.characters.index(after: labelIndex)
-                    }
-                    
-                    // Substring both the search string and the label from the shared prefix
-                    searchStr = searchStr.substring(from: index)
-                    e.label = e.label.substring(from: labelIndex)
-                    
-                    // Create 2 new edges and update parent/children values
-                    let newEdge = Edge(e.label)
-                    e.label = shared
-                    for ec in e.children {
-                        newEdge.children.append(ec)
-                    }
-                    newEdge.parent = e
-                    e.children.removeAll()
-                    for nec in newEdge.children {
-                        nec.parent = newEdge
-                    }
-                    e.children.append(newEdge)
-                    let newEdge2 = Edge(searchStr)
-                    newEdge2.parent = e
-                    e.children.append(newEdge2)
-                    return true
-                }
-                // If they don't share a prefix, go to next child
-            }
-            
-            // If none of the children share a prefix, you have to create a new child
-            if !found {
-                let newEdge = Edge(searchStr)
-                currEdge.children.append(newEdge)
-                newEdge.parent = currEdge
-                return true
-            }
+
+        // If that is not true, find the shared string b/t the search string
+        // and the label
+        let shared = sharedPrefix(searchStr, c.label)
+
+        // If the shared string is equal to the label, update the curent node,
+        // break the loop, and run it back
+        if shared == c.label {
+          currEdge = c
+          var tempIndex = searchStr.startIndex
+          for _ in 1...shared.characters.count {
+            tempIndex = searchStr.characters.index(after: tempIndex)
+          }
+          searchStr = searchStr.substring(from: tempIndex)
+          found = true
+          break
         }
-    }
-    
-    // Tells you if a string is in the tree
-    public func find(_ str: String) -> Bool {
-        // A radix tree always contains the empty string
-        if str == "" {
-            return true
+
+          // If the shared string is empty, go to the next child
+        else if shared.characters.count == 0 {
+          continue
         }
-            // If there are no children then the string cannot be in the tree
-        else if root.children.count == 0 {
-            return false
+
+          // If the shared string matches the search string, return true
+        else if shared == searchStr {
+          return true
         }
-        var searchStr = str
-        var currEdge = root
-        while true {
-            var found = false
-            // Loop through currEdge's children
-            for c in currEdge.children {
-                // First check if the search string and the child's label are equal
-                // if so the string is in the tree, return true
-                if searchStr == c.label {
-                    return true
-                }
-                
-                // If that is not true, find the shared string b/t the search string
-                // and the label
-                let shared = sharedPrefix(searchStr, c.label)
-                
-                // If the shared string is equal to the label, update the curent node,
-                // break the loop, and run it back
-                if shared == c.label {
-                    currEdge = c
-                    var tempIndex = searchStr.startIndex
-                    for _ in 1...shared.characters.count {
-                        tempIndex = searchStr.characters.index(after: tempIndex)
-                    }
-                    searchStr = searchStr.substring(from: tempIndex)
-                    found = true
-                    break
-                }
-                    
-                    // If the shared string is empty, go to the next child
-                else if shared.characters.count == 0 {
-                    continue
-                }
-                    
-                    // If the shared string matches the search string, return true
-                else if shared == searchStr {
-                    return true
-                }
-                    
-                    // If the search string and the child's label only share some characters,
-                    // the string is not in the tree, return false
-                else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-                    shared.characters.count < c.label.characters.count {
-                    return false
-                }
-            }
-            
-            // If nothing was found, return false
-            if !found {
-                return false
-            }
+
+          // If the search string and the child's label only share some characters,
+          // the string is not in the tree, return false
+        else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
+          shared.characters.count < c.label.characters.count {
+          return false
         }
+      }
+
+      // If nothing was found, return false
+      if !found {
+        return false
+      }
     }
-    
-    // Removes a string from the tree
-    public func remove(_ str: String) -> Bool {
-        // Removing the empty string removes everything in the tree
-        if str == "" {
-            for c in root.children {
-                c.erase()
-                root.children.remove(at: 0)
-            }
-            return true
-        }
-            // If the tree is empty, you cannot remove anything
-        else if root.children.count == 0 {
-            return false
+  }
+
+  // Removes a string from the tree
+  public func remove(_ str: String) -> Bool {
+    // Removing the empty string removes everything in the tree
+    if str == "" {
+      for c in root.children {
+        c.erase()
+        root.children.remove(at: 0)
+      }
+      return true
+    }
+      // If the tree is empty, you cannot remove anything
+    else if root.children.count == 0 {
+      return false
+    }
+
+    var searchStr = str
+    var currEdge = root
+    while true {
+      var found = false
+      // If currEdge has no children, then the searchStr is not in the tree
+      if currEdge.children.count == 0 {
+        return false
+      }
+
+      // Loop through the children
+      for c in 0...currEdge.children.count-1 {
+        // If the child's label matches the search string, remove that child
+        // and everything below it in the tree
+        if currEdge.children[c].label == searchStr {
+          currEdge.children[c].erase()
+          currEdge.children.remove(at: c)
+          return true
         }
-        
-        var searchStr = str
-        var currEdge = root
-        while true {
-            var found = false
-            // If currEdge has no children, then the searchStr is not in the tree
-            if currEdge.children.count == 0 {
-                return false
-            }
-            
-            // Loop through the children
-            for c in 0...currEdge.children.count-1 {
-                // If the child's label matches the search string, remove that child
-                // and everything below it in the tree
-                if currEdge.children[c].label == searchStr {
-                    currEdge.children[c].erase()
-                    currEdge.children.remove(at: c)
-                    return true
-                }
-                
-                // Find the shared string
-                let shared = sharedPrefix(searchStr, currEdge.children[c].label)
-                
-                // If the shared string is equal to the child's string, go down a level
-                if shared == currEdge.children[c].label {
-                    currEdge = currEdge.children[c]
-                    var tempIndex = searchStr.startIndex
-                    for _ in 1...shared.characters.count {
-                        tempIndex = searchStr.characters.index(after: tempIndex)
-                    }
-                    searchStr = searchStr.substring(from: tempIndex)
-                    found = true
-                    break
-                }
-            }
-            
-            // If there is no match, then the searchStr is not in the tree
-            if !found {
-                return false
-            }
+
+        // Find the shared string
+        let shared = sharedPrefix(searchStr, currEdge.children[c].label)
+
+        // If the shared string is equal to the child's string, go down a level
+        if shared == currEdge.children[c].label {
+          currEdge = currEdge.children[c]
+          var tempIndex = searchStr.startIndex
+          for _ in 1...shared.characters.count {
+            tempIndex = searchStr.characters.index(after: tempIndex)
+          }
+          searchStr = searchStr.substring(from: tempIndex)
+          found = true
+          break
         }
+      }
+
+      // If there is no match, then the searchStr is not in the tree
+      if !found {
+        return false
+      }
     }
-    
-    // Prints the tree by calling the root's print function
-    public func printTree() {
-        root.printRoot()
-    }
+  }
+
+  // Prints the tree by calling the root's print function
+  public func printTree() {
+    root.printRoot()
+  }
 }
 
 // Returns the prefix that is shared between the two input strings
 // i.e. sharedPrefix("court", "coral") -> "co"
 public func sharedPrefix(_ str1: String, _ str2: String) -> String {
-    var temp = ""
-    var c1 = str1.characters.startIndex
-    var c2 = str2.characters.startIndex
-    for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
-        if str1[c1] == str2[c2] {
-            temp.append( str1[c1] )
-            c1 = str1.characters.index(after:c1)
-            c2 = str2.characters.index(after:c2)
-        } else {
-            return temp
-        }
+  var temp = ""
+  var c1 = str1.characters.startIndex
+  var c2 = str2.characters.startIndex
+  for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+    if str1[c1] == str2[c2] {
+      temp.append( str1[c1] )
+      c1 = str1.characters.index(after:c1)
+      c2 = str2.characters.index(after:c2)
+    } else {
+      return temp
     }
-    return temp
+  }
+  return temp
 }

From 00c6b720b984928f3ea3d3ab9f679c0d49cf8087 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Thu, 6 Oct 2016 22:19:50 -0700
Subject: [PATCH 0588/1679] Updated README

---
 Karatsuba Multiplication/README.markdown | 35 ++++++++++--------------
 1 file changed, 15 insertions(+), 20 deletions(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index af3392612..d4c99ec2d 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -4,9 +4,9 @@ Goal: To quickly multiply two numbers together
 
 ## Long Multiplication
 
-In grade school we all learned how to multiply two numbers together via Long Multiplication. So let's try that first!
+In grade school we learned how to multiply two numbers together via Long Multiplication. Let's try that first!
 
-Example 1: Multiply 1234 by 5678 using Long Multiplication
+### Example 1: Multiply 1234 by 5678 using Long Multiplication
 
 	    5678
 	   *1234
@@ -18,9 +18,9 @@ Example 1: Multiply 1234 by 5678 using Long Multiplication
 	--------
 	 7006652
 
-So what's the problem with long multiplication? Speed. Long Multiplication runs in **O(n^2)**. 
+So what's the problem with Long Multiplication? Well remember the first part of our goal. To *quickly* multiply two numbers together. Long Multiplication is slow! (**O(n^2)**) 
 
-You can see where the **O(n^2)** comes from in the implementation for Long Multiplication:
+You can see where the **O(n^2)** comes from in the implementation of Long Multiplication:
 
 ```swift
 // Long Multiplication
@@ -44,7 +44,7 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
 }
 ```
 
-The double for loop is the culprit! So Long Multiplication might not be the best algorithm after all. Can we do better?
+The double for loop is the culprit! By comparing each of the digits (as is necessary!) we set ourselves up for an **O(n^2)** running time. So Long Multiplication might not be the best algorithm after all. Can we do better?
 
 ## Karatsuba Multiplication
 
@@ -57,24 +57,17 @@ For two numbers x, y, where m <= n:
 
 Now, we can say:
 
-	x*y = a*c*10^(2m) + (a*d + b*c)*10^(m) + b*d
+	x*y = (a*10^m + b) * (c*10^m + d)
+	    = a*c*10^(2m) + (a*d + b*c)*10^(m) + b*d
 
-We can compute this function recursively, and that's what makes Karatsuba Multiplication fast.
+This had been know since the 19th century. The problem is that the method requires 4 multiplications (`a*c`, `a*d`, `b*c`, `b*d`). Karatsuba's insight was that you only need three! (`a*c`, `b*d`, `(a+b)*(c+d)`). Now a perfectly valid question right now would be "How is that possible!?!" Here's the math:
 
-```swift
-let ac = karatsuba(a, by: c)
-let bd = karatsuba(b, by: d)
-let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-```
-
-The last recursion is interesting. Normally, you'd think we would have to run four recursions to find the product `x*y` (`a*c`, `a*d`, `b*c`, `b*d`). However, Karatsuba realized that you only need three recursions, and some addition and subtraction. Here's the math:
-
-	(a+b)*(c+d) - a*c - b*c  = (a*c + a*d + b*c + b*d) - a*c - b*c
-		    		 = (a*d + b*c)
+        (a+b)*(c+d) - a*c - b*c  = (a*c + a*d + b*c + b*d) - a*c - b*c
+                                 = (a*d + b*c)
 
 Pretty cool, huh?
 
-Here's the full implementation
+Here's the full implementation. Note that the recursive algorithm is most efficient at m = n/2.
 
 ```swift
 // Karatsuba Multiplication
@@ -104,9 +97,9 @@ func karatsuba(_ num1: Int, by num2: Int) -> Int {
 }
 ```
 
-The run time for this algorithm is about **O(n^1.56)** which is better than the **O(n^2)** for Long Multiplication. 
+What about the running time of this algorithm? Is all this extra work worth it? We can use the Master Theorem to answer this question. This leads us to `T(n) = 3*T(n/2) + c*n + d` where c & d are some constants. It follows (because 3 > 2^1) that the running time is **O(n^log2(3))** which is roughly **O(n^1.56)**. Much better! 
 
-Example 2: Multiply 1234 by 5678 using Karatsuba Multiplication
+### Example 2: Multiply 1234 by 5678 using Karatsuba Multiplication
 
 	m = 2
 	x = 1234 = a*10^2 + b = 12*10^2 + 34
@@ -126,4 +119,6 @@ Example 2: Multiply 1234 by 5678 using Karatsuba Multiplication
 
 [WolframMathWorld] (http://mathworld.wolfram.com/KaratsubaMultiplication.html) 
 
+[Master Theorem] (https://en.wikipedia.org/wiki/Master_theorem)
+
 *Written for Swift Algorithm Club by Richard Ash*

From d0da5de44f445e2d651e9e08eeb8854b16c52a99 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Thu, 6 Oct 2016 23:03:27 -0700
Subject: [PATCH 0589/1679] Fixed a typo

---
 .../KaratsubaMultiplication.playground/Contents.swift           | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 95a498322..075f75098 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -33,7 +33,7 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
   return Int(product.reversed().map{ String($0) }.reduce("", +))!
 }
 
-// Karatsuba Multiplication - O(nlogn)
+// Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters

From 3d26e9258de7d82a494806019919f93150bc9e8d Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Fri, 7 Oct 2016 20:18:22 -0500
Subject: [PATCH 0590/1679] updated readme

---
 .../BoyerMoore.playground/Contents.swift      |  3 +
 .../BoyerMoore.playground/timeline.xctimeline |  6 +-
 Boyer-Moore/README.markdown                   | 81 ++++++++++---------
 3 files changed, 47 insertions(+), 43 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 9a3d619dc..4b2bad42c 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -46,3 +46,6 @@ s.indexOf(pattern: "World")  // 7
 
 let animals = "🐶🐔🐷🐮🐱"
 animals.indexOf(pattern: "🐮")  // 6
+
+
+
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
index 623552dab..59d8c8667 100644
--- a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
+++ b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497331454.819397"
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497453081.589625"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497331454.819493"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497453081.589795"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497331454.819555"
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497453081.589932"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index ad1d3bc73..4d98f5a28 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -9,14 +9,14 @@ For example:
 ```swift
 // Input: 
 let s = "Hello, World"
-s.indexOf("World")
+s.indexOf(pattern: "World")
 
 // Output:
 <String.Index?> 7
 
 // Input:
 let animals = "🐶🐔🐷🐮🐱"
-animals.indexOf("🐮")
+animals.indexOf(pattern: "🐮")
 
 // Output:
 <String.Index?> 6
@@ -32,67 +32,68 @@ Here's how you could write it in Swift:
 
 ```swift
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    // Cache the length of the search pattern because we're going to
-    // use it a few times and it's expensive to calculate.
+func indexOf(pattern: String) -> String.Index? {
+// Cache the length of the search pattern because we're going to
+// use it a few times and it's expensive to calculate.
     let patternLength = pattern.characters.count
-    assert(patternLength > 0)
-    assert(patternLength <= self.characters.count)
+        assert(patternLength > 0)
+        assert(patternLength <= self.characters.count)
 
-    // Make the skip table. This table determines how far we skip ahead
-    // when a character from the pattern is found.
+// Make the skip table. This table determines how far we skip ahead
+// when a character from the pattern is found.
     var skipTable = [Character: Int]()
     for (i, c) in pattern.characters.enumerate() {
-      skipTable[c] = patternLength - i - 1
+        skipTable[c] = patternLength - i - 1
     }
 
-    // This points at the last character in the pattern.
+// This points at the last character in the pattern.
     let p = pattern.endIndex.predecessor()
     let lastChar = pattern[p]
 
-    // The pattern is scanned right-to-left, so skip ahead in the string by
-    // the length of the pattern. (Minus 1 because startIndex already points
-    // at the first character in the source string.)
+// The pattern is scanned right-to-left, so skip ahead in the string by
+// the length of the pattern. (Minus 1 because startIndex already points
+// at the first character in the source string.)
     var i = self.startIndex.advancedBy(patternLength - 1)
 
-    // This is a helper function that steps backwards through both strings 
-    // until we find a character that doesn’t match, or until we’ve reached
-    // the beginning of the pattern.
+// This is a helper function that steps backwards through both strings 
+// until we find a character that doesn’t match, or until we’ve reached
+// the beginning of the pattern.
     func backwards() -> String.Index? {
-      var q = p
-      var j = i
-      while q > pattern.startIndex {
-        j = j.predecessor()
-        q = q.predecessor()
-        if self[j] != pattern[q] { return nil }
-      }
-      return j
+        var q = p
+        var j = i
+        while q > pattern.startIndex {
+            j = j.predecessor()
+            q = q.predecessor()
+            if self[j] != pattern[q] { return nil }
+        }
+        return j
     }
 
-    // The main loop. Keep going until the end of the string is reached.
+// The main loop. Keep going until the end of the string is reached.
     while i < self.endIndex {
-      let c = self[i]
+        let c = self[i]
 
-      // Does the current character match the last character from the pattern?
-      if c == lastChar {
+// Does the current character match the last character from the pattern?
+        if c == lastChar {
 
-        // There is a possible match. Do a brute-force search backwards.
+// There is a possible match. Do a brute-force search backwards.
         if let k = backwards() { return k }
 
-        // If no match, we can only safely skip one character ahead.
+// If no match, we can only safely skip one character ahead.
         i = i.successor()
-      } else {
-        // The characters are not equal, so skip ahead. The amount to skip is
-        // determined by the skip table. If the character is not present in the
-        // pattern, we can skip ahead by the full pattern length. However, if
-        // the character *is* present in the pattern, there may be a match up
-        // ahead and we can't skip as far.
+        } else {
+// The characters are not equal, so skip ahead. The amount to skip is
+// determined by the skip table. If the character is not present in the
+// pattern, we can skip ahead by the full pattern length. However, if
+// the character *is* present in the pattern, there may be a match up
+// ahead and we can't skip as far.
         i = i.advancedBy(skipTable[c] ?? patternLength)
-      }
+        }
     }
-    return nil
-  }
+        return nil
+        }
 }
+
 ```
 
 The algorithm works as follows. You line up the search pattern with the source string and see what character from the string matches the *last* character of the search pattern:

From a2892beff7f3769087ecc20c00a868e6b99f5628 Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Fri, 7 Oct 2016 20:36:43 -0500
Subject: [PATCH 0591/1679] formatting

---
 .../BoyerMoore.playground/Contents.swift      |  1 +
 .../BoyerMoore.playground/timeline.xctimeline |  6 +-
 Boyer-Moore/README.markdown                   | 92 +++++++++----------
 3 files changed, 50 insertions(+), 49 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 4b2bad42c..14447f495 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -39,6 +39,7 @@ extension String {
   }
 }
 
+
 // A few simple tests
 
 let s = "Hello, World"
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
index 59d8c8667..7e38effd2 100644
--- a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
+++ b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497453081.589625"
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497583231.982889"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497453081.589795"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497583231.983042"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497453081.589932"
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497583231.983159"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 4d98f5a28..dc40413ec 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -33,65 +33,65 @@ Here's how you could write it in Swift:
 ```swift
 extension String {
 func indexOf(pattern: String) -> String.Index? {
-// Cache the length of the search pattern because we're going to
-// use it a few times and it's expensive to calculate.
+    // Cache the length of the search pattern because we're going to
+    // use it a few times and it's expensive to calculate.
     let patternLength = pattern.characters.count
-        assert(patternLength > 0)
-        assert(patternLength <= self.characters.count)
+    assert(patternLength > 0)
+    assert(patternLength <= self.characters.count)
 
-// Make the skip table. This table determines how far we skip ahead
-// when a character from the pattern is found.
+    // Make the skip table. This table determines how far we skip ahead
+    // when a character from the pattern is found.
     var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerate() {
-        skipTable[c] = patternLength - i - 1
+    for (i, c) in pattern.characters.enumerated() {
+    skipTable[c] = patternLength - i - 1
     }
 
-// This points at the last character in the pattern.
-    let p = pattern.endIndex.predecessor()
+    // This points at the last character in the pattern.
+    let p = index(before: pattern.endIndex)
     let lastChar = pattern[p]
 
-// The pattern is scanned right-to-left, so skip ahead in the string by
-// the length of the pattern. (Minus 1 because startIndex already points
-// at the first character in the source string.)
-    var i = self.startIndex.advancedBy(patternLength - 1)
+    // The pattern is scanned right-to-left, so skip ahead in the string by
+    // the length of the pattern. (Minus 1 because startIndex already points
+    // at the first character in the source string.)
+    var i = index(self.startIndex, offsetBy: patternLength - 1)
 
-// This is a helper function that steps backwards through both strings 
-// until we find a character that doesn’t match, or until we’ve reached
-// the beginning of the pattern.
+    // This is a helper function that steps backwards through both strings
+    // until we find a character that doesn’t match, or until we’ve reached
+    // the beginning of the pattern.
     func backwards() -> String.Index? {
-        var q = p
-        var j = i
-        while q > pattern.startIndex {
-            j = j.predecessor()
-            q = q.predecessor()
-            if self[j] != pattern[q] { return nil }
-        }
-        return j
+    var q = p
+    var j = i
+    while q > pattern.startIndex {
+    j = index(before: j)
+    q = index(before: q)
+    if self[j] != pattern[q] { return nil }
+    }
+    return j
     }
 
-// The main loop. Keep going until the end of the string is reached.
+    // The main loop. Keep going until the end of the string is reached.
     while i < self.endIndex {
-        let c = self[i]
-
-// Does the current character match the last character from the pattern?
-        if c == lastChar {
-
-// There is a possible match. Do a brute-force search backwards.
-        if let k = backwards() { return k }
-
-// If no match, we can only safely skip one character ahead.
-        i = i.successor()
-        } else {
-// The characters are not equal, so skip ahead. The amount to skip is
-// determined by the skip table. If the character is not present in the
-// pattern, we can skip ahead by the full pattern length. However, if
-// the character *is* present in the pattern, there may be a match up
-// ahead and we can't skip as far.
-        i = i.advancedBy(skipTable[c] ?? patternLength)
-        }
+    let c = self[i]
+
+    // Does the current character match the last character from the pattern?
+    if c == lastChar {
+
+    // There is a possible match. Do a brute-force search backwards.
+    if let k = backwards() { return k }
+
+    // If no match, we can only safely skip one character ahead.
+    i = index(after: i)
+    } else {
+    // The characters are not equal, so skip ahead. The amount to skip is
+    // determined by the skip table. If the character is not present in the
+    // pattern, we can skip ahead by the full pattern length. However, if
+    // the character *is* present in the pattern, there may be a match up
+    // ahead and we can't skip as far.
+    i = index(i, offsetBy: skipTable[c] ?? patternLength)
+    }
+    }
+    return nil
     }
-        return nil
-        }
 }
 
 ```

From f09b42be3e59052a5ec5937fc645f71467aa0677 Mon Sep 17 00:00:00 2001
From: Kevin Taniguchi <kv.taniguchi@gmail.com>
Date: Fri, 7 Oct 2016 21:16:05 -0500
Subject: [PATCH 0592/1679] updated readme

---
 .../BoyerMoore.playground/Contents.swift      |  4 --
 .../BoyerMoore.playground/timeline.xctimeline |  6 +--
 Boyer-Moore/README.markdown                   | 42 +++++++++++--------
 3 files changed, 28 insertions(+), 24 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 14447f495..9a3d619dc 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -39,7 +39,6 @@ extension String {
   }
 }
 
-
 // A few simple tests
 
 let s = "Hello, World"
@@ -47,6 +46,3 @@ s.indexOf(pattern: "World")  // 7
 
 let animals = "🐶🐔🐷🐮🐱"
 animals.indexOf(pattern: "🐮")  // 6
-
-
-
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
index 7e38effd2..a15b8d6e0 100644
--- a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
+++ b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497583231.982889"
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497585369.829471"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497583231.983042"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497585369.82964"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497583231.983159"
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497585369.82978"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index dc40413ec..4acc1ffb3 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -150,34 +150,42 @@ Here's an implementation of the Boyer-Moore-Horspool algorithm:
 
 ```swift
 extension String {
-  public func indexOf(pattern: String) -> String.Index? {
+    func indexOf(pattern: String) -> String.Index? {
     let patternLength = pattern.characters.count
     assert(patternLength > 0)
     assert(patternLength <= self.characters.count)
 
     var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.dropLast().enumerate() {
-      skipTable[c] = patternLength - i - 1
+    for (i, c) in pattern.characters.enumerated() {
+    skipTable[c] = patternLength - i - 1
     }
 
-    var index = self.startIndex.advancedBy(patternLength - 1)
-
-    while index < self.endIndex {
-      var i = index
-      var p = pattern.endIndex.predecessor()
-
-      while self[i] == pattern[p] {
-        if p == pattern.startIndex { return i }
-        i = i.predecessor()
-        p = p.predecessor()
-      }
+    let p = pattern.index(before: pattern.endIndex)
+    let lastChar = pattern[p]
+    var i = self.index(startIndex, offsetBy: patternLength - 1)
 
-      let advance = skipTable[self[index]] ?? patternLength
-      index = index.advancedBy(advance)
+    func backwards() -> String.Index? {
+    var q = p
+    var j = i
+    while q > pattern.startIndex {
+    j = index(before: j)
+    q = index(before: q)
+    if self[j] != pattern[q] { return nil }
+    }
+    return j
     }
 
+    while i < self.endIndex {
+    let c = self[i]
+    if c == lastChar {
+    if let k = backwards() { return k }
+    i = index(after: i)
+    } else {
+    i = index(i, offsetBy: skipTable[c] ?? patternLength)
+    }
+    }
     return nil
-  }
+    }
 }
 ```
 

From 0fa26236edb993696d77e00e47e7eebec07fe2d0 Mon Sep 17 00:00:00 2001
From: Peter Ivanics <peter.ivanics@reslink.fi>
Date: Sat, 8 Oct 2016 22:31:46 +0300
Subject: [PATCH 0593/1679] Migrate Linked List to Swift 3.0

---
 .../LinkedList.playground/Contents.swift      | 39 ++++----
 Linked List/LinkedList.swift                  | 97 +++++++++----------
 Linked List/Tests/LinkedListTests.swift       | 32 +++---
 3 files changed, 80 insertions(+), 88 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 72dcffe02..e73f89518 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -47,7 +47,7 @@ public class LinkedList<T> {
     }
   }
 
-  public func nodeAt(_ index: Int) -> Node? {
+  public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -61,12 +61,12 @@ public class LinkedList<T> {
   }
 
   public subscript(index: Int) -> T {
-    let node = nodeAt(index)
+    let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
 
-  public func append(value: T) {
+  public func append(_ value: T) {
     let newNode = Node(value: value)
     if let lastNode = last {
       newNode.previous = lastNode
@@ -93,7 +93,7 @@ public class LinkedList<T> {
     return (prev, next)
   }
 
-  public func insert(value: T, atIndex index: Int) {
+  public func insert(_ value: T, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index: index)
 
     let newNode = Node(value: value)
@@ -132,8 +132,8 @@ public class LinkedList<T> {
     return remove(node: last!)
   }
 
-  public func removeAt(_ index: Int) -> T {
-    let node = nodeAt(index)
+  public func remove(atIndex index: Int) -> T {
+    let node = self.node(atIndex: index)
     assert(node != nil)
     return remove(node: node!)
   }
@@ -168,7 +168,7 @@ extension LinkedList {
     let result = LinkedList<U>()
     var node = head
     while node != nil {
-      result.append(value: transform(node!.value))
+      result.append(transform(node!.value))
       node = node!.next
     }
     return result
@@ -179,7 +179,7 @@ extension LinkedList {
     var node = head
     while node != nil {
       if predicate(node!.value) {
-        result.append(value: node!.value)
+        result.append(node!.value)
       }
       node = node!.next
     }
@@ -187,21 +187,18 @@ extension LinkedList {
   }
 }
 
-
-
-
 let list = LinkedList<String>()
 list.isEmpty                  // true
 list.first                    // nil
 list.last                     // nil
 
-list.append(value: "Hello")
+list.append("Hello")
 list.isEmpty
 list.first!.value             // "Hello"
 list.last!.value              // "Hello"
 list.count                    // 1
 
-list.append(value: "World")
+list.append("World")
 list.first!.value             // "Hello"
 list.last!.value              // "World"
 list.count                    // 2
@@ -211,15 +208,15 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.nodeAt(0)!.value    // "Hello"
-list.nodeAt(1)!.value    // "World"
-list.nodeAt(2)           // nil
+list.node(atIndex: 0)!.value    // "Hello"
+list.node(atIndex: 1)!.value    // "World"
+list.node(atIndex: 2)           // nil
 
 list[0]     // "Hello"
 list[1]     // "World"
 //list[2]   // crash!
 
-list.insert(value: "Swift", atIndex: 1)
+list.insert("Swift", atIndex: 1)
 list[0]
 list[1]
 list[2]
@@ -227,8 +224,8 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.nodeAt(0)!.value = "Universe"
-list.nodeAt(1)!.value = "Swifty"
+list.node(atIndex: 0)!.value = "Universe"
+list.node(atIndex: 1)!.value = "Swifty"
 let m = list.map { s in s.characters.count }
 m    // [8, 6, 5]
 let f = list.filter { s in s.characters.count > 5 }
@@ -237,7 +234,7 @@ f    // [Universe, Swifty]
 //list.removeAll()
 //list.isEmpty
 
-list.remove(node: list.first!)   // "Hello"
+list.remove(node: list.first!) // "Hello"
 list.count                     // 2
 list[0]                        // "Swift"
 list[1]                        // "World"
@@ -246,5 +243,5 @@ list.removeLast()              // "World"
 list.count                     // 1
 list[0]                        // "Swift"
 
-list.removeAt(0)          // "Swift"
+list.remove(atIndex: 0)        // "Swift"
 list.count                     // 0
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 306743354..49f1c0915 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,32 +1,27 @@
-/*
-  Doubly-linked list
-
-  Most operations on the linked list have complexity O(n).
-*/
-open class LinkedListNode<T> {
+public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
   weak var previous: LinkedListNode?
-
+  
   public init(value: T) {
     self.value = value
   }
 }
 
-open class LinkedList<T> {
+public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
-
+  
   fileprivate var head: Node?
-
-  open var isEmpty: Bool {
+  
+  public var isEmpty: Bool {
     return head == nil
   }
-
-  open var first: Node? {
+  
+  public var first: Node? {
     return head
   }
-
-  open var last: Node? {
+  
+  public var last: Node? {
     if var node = head {
       while case let next? = node.next {
         node = next
@@ -36,8 +31,8 @@ open class LinkedList<T> {
       return nil
     }
   }
-
-  open var count: Int {
+  
+  public var count: Int {
     if var node = head {
       var c = 1
       while case let next? = node.next {
@@ -49,8 +44,8 @@ open class LinkedList<T> {
       return 0
     }
   }
-
-  open func nodeAt(_ index: Int) -> Node? {
+  
+  public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
       var i = index
@@ -62,14 +57,14 @@ open class LinkedList<T> {
     }
     return nil
   }
-
-  open subscript(index: Int) -> T {
-    let node = nodeAt(index)
+  
+  public subscript(index: Int) -> T {
+    let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
-
-  open func append(_ value: T) {
+  
+  public func append(_ value: T) {
     let newNode = Node(value: value)
     if let lastNode = last {
       newNode.previous = lastNode
@@ -78,67 +73,67 @@ open class LinkedList<T> {
       head = newNode
     }
   }
-
-  fileprivate func nodesBeforeAndAfter(_ index: Int) -> (Node?, Node?) {
+  
+  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-
+    
     var i = index
     var next = head
     var prev: Node?
-
+    
     while next != nil && i > 0 {
       i -= 1
       prev = next
       next = next!.next
     }
     assert(i == 0)  // if > 0, then specified index was too large
-
+    
     return (prev, next)
   }
-
-  open func insert(_ value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index)
-
+  
+  public func insert(_ value: T, atIndex index: Int) {
+    let (prev, next) = nodesBeforeAndAfter(index: index)
+    
     let newNode = Node(value: value)
     newNode.previous = prev
     newNode.next = next
     prev?.next = newNode
     next?.previous = newNode
-
+    
     if prev == nil {
       head = newNode
     }
   }
-
-  open func removeAll() {
+  
+  public func removeAll() {
     head = nil
   }
-
-  open func remove(_ node: Node) -> T {
+  
+  public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
-
+    
     if let prev = prev {
       prev.next = next
     } else {
       head = next
     }
     next?.previous = prev
-
+    
     node.previous = nil
     node.next = nil
     return node.value
   }
-
-  open func removeLast() -> T {
+  
+  public func removeLast() -> T {
     assert(!isEmpty)
-    return remove(last!)
+    return remove(node: last!)
   }
-
-  open func removeAt(_ index: Int) -> T {
-    let node = nodeAt(index)
+  
+  public func remove(atIndex index: Int) -> T {
+    let node = self.node(atIndex: index)
     assert(node != nil)
-    return remove(node!)
+    return remove(node: node!)
   }
 }
 
@@ -167,17 +162,17 @@ extension LinkedList {
 }
 
 extension LinkedList {
-  public func map<U>(_ transform: (T)-> U) -> LinkedList<U> {
+  public func map<U>(transform: (T) -> U) -> LinkedList<U> {
     let result = LinkedList<U>()
     var node = head
     while node != nil {
-        result.append(transform(node!.value))
+      result.append(transform(node!.value))
       node = node!.next
     }
     return result
   }
-
-  public func filter(_ predicate: (T)-> Bool) -> LinkedList<T> {
+  
+  public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
     while node != nil {
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index beba84299..367ec8c6b 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -88,7 +88,7 @@ class LinkedListTest: XCTestCase {
 
   func testNodeAtIndexInEmptyList() {
     let list = LinkedList<Int>()
-    let node = list.nodeAt(0)
+    let node = list.node(atIndex: 0)
     XCTAssertNil(node)
   }
 
@@ -96,7 +96,7 @@ class LinkedListTest: XCTestCase {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let node = list.nodeAt(0)
+    let node = list.node(atIndex: 0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node!.value, 123)
     XCTAssertTrue(node === list.first)
@@ -108,21 +108,21 @@ class LinkedListTest: XCTestCase {
     let nodeCount = list.count
     XCTAssertEqual(nodeCount, numbers.count)
 
-    XCTAssertNil(list.nodeAt(-1))
-    XCTAssertNil(list.nodeAt(nodeCount))
+    XCTAssertNil(list.node(atIndex: -1))
+    XCTAssertNil(list.node(atIndex: nodeCount))
 
-    let first = list.nodeAt(0)
+    let first = list.node(atIndex: 0)
     XCTAssertNotNil(first)
     XCTAssertTrue(first === list.first)
     XCTAssertEqual(first!.value, numbers[0])
 
-    let last = list.nodeAt(nodeCount - 1)
+    let last = list.node(atIndex: nodeCount - 1)
     XCTAssertNotNil(last)
     XCTAssertTrue(last === list.last)
     XCTAssertEqual(last!.value, numbers[nodeCount - 1])
 
     for i in 0..<nodeCount {
-      let node = list.nodeAt(i)
+      let node = list.node(atIndex: i)
       XCTAssertNotNil(node)
       XCTAssertEqual(node!.value, numbers[i])
     }
@@ -142,20 +142,20 @@ class LinkedListTest: XCTestCase {
     XCTAssertFalse(list.isEmpty)
     XCTAssertEqual(list.count, 1)
 
-    let node = list.nodeAt(0)
+    let node = list.node(atIndex: 0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node!.value, 123)
   }
 
   func testInsertAtIndex() {
     let list = buildList()
-    let prev = list.nodeAt(2)
-    let next = list.nodeAt(3)
+    let prev = list.node(atIndex: 2)
+    let next = list.node(atIndex: 3)
     let nodeCount = list.count
 
     list.insert(444, atIndex: 3)
 
-    let node = list.nodeAt(3)
+    let node = list.node(atIndex: 3)
     XCTAssertNotNil(node)
     XCTAssertEqual(node!.value, 444)
     XCTAssertEqual(nodeCount + 1, list.count)
@@ -170,7 +170,7 @@ class LinkedListTest: XCTestCase {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let value = list.removeAt(0)
+    let value = list.remove(atIndex: 0)
     XCTAssertEqual(value, 123)
 
     XCTAssertTrue(list.isEmpty)
@@ -181,16 +181,16 @@ class LinkedListTest: XCTestCase {
 
   func testRemoveAtIndex() {
     let list = buildList()
-    let prev = list.nodeAt(2)
-    let next = list.nodeAt(3)
+    let prev = list.node(atIndex: 2)
+    let next = list.node(atIndex: 3)
     let nodeCount = list.count
 
     list.insert(444, atIndex: 3)
 
-    let value = list.removeAt(3)
+    let value = list.remove(atIndex: 3)
     XCTAssertEqual(value, 444)
 
-    let node = list.nodeAt(3)
+    let node = list.node(atIndex: 3)
     XCTAssertTrue(next === node)
     XCTAssertTrue(prev!.next === node)
     XCTAssertTrue(node!.previous === prev)

From 4f5565d15ef94ba1cc2a6f2f08c2cebc96baa058 Mon Sep 17 00:00:00 2001
From: Artur <artu-antonov@yandex.ru>
Date: Sat, 8 Oct 2016 23:58:07 +0300
Subject: [PATCH 0594/1679] Migrate treap to swift 3

---
 .travis.yml                                   |   1 +
 Treap/Treap.swift                             | 253 ++++---
 Treap/Treap/Treap.xcodeproj/project.pbxproj   | 162 +----
 .../xcshareddata/WorkspaceSettings.xcsettings |   8 +
 .../xcshareddata/xcschemes/Tests.xcscheme     |  33 +-
 .../xcshareddata/xcschemes/Treap.xcscheme     | 101 ---
 Treap/Treap/Treap/AppDelegate.swift           |  43 --
 .../AppIcon.appiconset/Contents.json          |  58 --
 Treap/Treap/Treap/Base.lproj/MainMenu.xib     | 681 ------------------
 Treap/Treap/TreapTests/TreapTests.swift       |  83 ++-
 Treap/TreapCollectionType.swift               | 138 ++--
 Treap/TreapMergeSplit.swift                   | 156 ++--
 12 files changed, 375 insertions(+), 1342 deletions(-)
 create mode 100644 Treap/Treap/Treap.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
 delete mode 100644 Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme
 delete mode 100644 Treap/Treap/Treap/AppDelegate.swift
 delete mode 100644 Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 Treap/Treap/Treap/Base.lproj/MainMenu.xib

diff --git a/.travis.yml b/.travis.yml
index 949fc759f..35bcf6199 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -39,3 +39,4 @@ script:
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index e1d1d4892..478f248df 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -25,146 +25,145 @@ THE SOFTWARE.*/
 import Foundation
 
 public indirect enum Treap<Key: Comparable, Element> {
-    case Empty
-    case Node(key: Key, val: Element, p: Int, left: Treap, right: Treap)
-
-    public init() {
-        self = .Empty
-    }
-
-    internal func get(key: Key) -> Element? {
-        switch self {
-        case .Empty:
-            return nil
-        case let .Node(treeKey, val, _, _, _) where treeKey == key:
-            return val
-        case let .Node(treeKey, _, _, left, _) where key < treeKey:
-            return left.get(key)
-        case let .Node(treeKey, _, _, _, right) where key > treeKey:
-            return right.get(key)
-        default:
-            return nil
-        }
+  case empty
+  case node(key: Key, val: Element, p: Int, left: Treap, right: Treap)
+  
+  public init() {
+    self = .empty
+  }
+  
+  internal func get(_ key: Key) -> Element? {
+    switch self {
+    case .empty:
+      return nil
+    case let .node(treeKey, val, _, _, _) where treeKey == key:
+      return val
+    case let .node(treeKey, _, _, left, _) where key < treeKey:
+      return left.get(key)
+    case let .node(treeKey, _, _, _, right) where key > treeKey:
+      return right.get(key)
+    default:
+      return nil
     }
-
-    public func contains(key: Key) -> Bool {
-        switch self {
-        case .Empty:
-            return false
-        case let .Node(treeKey, _, _, _, _) where treeKey == key:
-            return true
-        case let .Node(treeKey, _, _, left, _) where key < treeKey:
-            return left.contains(key)
-        case let .Node(treeKey, _, _, _, right) where key > treeKey:
-            return right.contains(key)
-        default:
-            return false
-        }
+  }
+  
+  public func contains(_ key: Key) -> Bool {
+    switch self {
+    case .empty:
+      return false
+    case let .node(treeKey, _, _, _, _) where treeKey == key:
+      return true
+    case let .node(treeKey, _, _, left, _) where key < treeKey:
+      return left.contains(key)
+    case let .node(treeKey, _, _, _, right) where key > treeKey:
+      return right.contains(key)
+    default:
+      return false
     }
-
-    public var depth: Int {
-        get {
-            switch self {
-            case .Empty:
-                return 0
-            case let .Node(_, _, _, left, .Empty):
-                return 1 + left.depth
-            case let .Node(_, _, _, .Empty, right):
-                return 1 + right.depth
-            case let .Node(_, _, _, left, right):
-                let leftDepth = left.depth
-                let rightDepth = right.depth
-                return 1 + max(leftDepth, rightDepth)
-            }
-
-        }
+  }
+  
+  public var depth: Int {
+    get {
+      switch self {
+      case .empty:
+        return 0
+      case let .node(_, _, _, left, .empty):
+        return 1 + left.depth
+      case let .node(_, _, _, .empty, right):
+        return 1 + right.depth
+      case let .node(_, _, _, left, right):
+        let leftDepth = left.depth
+        let rightDepth = right.depth
+        return 1 + leftDepth > rightDepth ? leftDepth : rightDepth
+      }
+      
     }
-
-    public var count: Int {
-        get {
-            return Treap.countHelper(self)
-        }
+  }
+  
+  public var count: Int {
+    get {
+      return Treap.countHelper(self)
     }
-
-    private static func countHelper(treap: Treap<Key, Element>) -> Int {
-        if case let .Node(_, _, _, left, right) = treap {
-            return countHelper(left) + 1 + countHelper(right)
-        }
-
-        return 0
+  }
+  
+  fileprivate static func countHelper(_ treap: Treap<Key, Element>) -> Int {
+    if case let .node(_, _, _, left, right) = treap {
+      return countHelper(left) + 1 + countHelper(right)
     }
+    
+    return 0
+  }
 }
 
-internal func leftRotate<Key: Comparable, Element>(tree: Treap<Key, Element>) -> Treap<Key, Element> {
-    if case let .Node(key, val, p, .Node(leftKey, leftVal, leftP, leftLeft, leftRight), right) = tree {
-        return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft,
-                     right: Treap.Node(key: key, val: val, p: p, left: leftRight, right: right))
-    } else {
-        return .Empty
-    }
+internal func leftRotate<Key: Comparable, Element>(_ tree: Treap<Key, Element>) -> Treap<Key, Element> {
+  if case let .node(key, val, p, .node(leftKey, leftVal, leftP, leftLeft, leftRight), right) = tree {
+    return .node(key: leftKey, val: leftVal, p: leftP, left: leftLeft,
+                 right: Treap.node(key: key, val: val, p: p, left: leftRight, right: right))
+  } else {
+    return .empty
+  }
 }
 
-internal func rightRotate<Key: Comparable, Element>(tree: Treap<Key, Element>) -> Treap<Key, Element> {
-    if case let .Node(key, val, p, left, .Node(rightKey, rightVal, rightP, rightLeft, rightRight)) = tree {
-        return .Node(key: rightKey, val: rightVal, p: rightP,
-                     left: Treap.Node(key: key, val: val, p: p, left: left, right: rightLeft), right: rightRight)
-    } else {
-        return .Empty
-    }
+internal func rightRotate<Key: Comparable, Element>(_ tree: Treap<Key, Element>) -> Treap<Key, Element> {
+  if case let .node(key, val, p, left, .node(rightKey, rightVal, rightP, rightLeft, rightRight)) = tree {
+    return .node(key: rightKey, val: rightVal, p: rightP,
+                 left: Treap.node(key: key, val: val, p: p, left: left, right: rightLeft), right: rightRight)
+  } else {
+    return .empty
+  }
 }
 
 public extension Treap {
-    internal func set(key: Key, val: Element, p: Int = Int(arc4random())) -> Treap {
-        switch self {
-        case .Empty:
-            return .Node(key: key, val: val, p: p, left: .Empty, right: .Empty)
-        case let .Node(nodeKey, nodeVal, nodeP, left, right) where key != nodeKey:
-            return insertAndBalance(nodeKey, nodeVal, nodeP, left, right, key, val, p)
-        case let .Node(nodeKey, _, nodeP, left, right) where key == nodeKey:
-            return .Node(key: key, val: val, p: nodeP, left: left, right: right)
-        default: // should never happen
-            return .Empty
-        }
-
+  internal func set(key: Key, val: Element, p: Int = Int(arc4random())) -> Treap {
+    switch self {
+    case .empty:
+      return .node(key: key, val: val, p: p, left: .empty, right: .empty)
+    case let .node(nodeKey, nodeVal, nodeP, left, right) where key != nodeKey:
+      return insertAndBalance(nodeKey, nodeVal, nodeP, left, right, key, val, p)
+    case let .node(nodeKey, _, nodeP, left, right) where key == nodeKey:
+      return .node(key: key, val: val, p: nodeP, left: left, right: right)
+    default: // should never happen
+      return .empty
     }
-
-    private func insertAndBalance(nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap,
-                                  _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
-        let newChild: Treap<Key, Element>
-        let newNode: Treap<Key, Element>
-        let rotate: (Treap) -> Treap
-        if key < nodeKey {
-            newChild = left.set(key, val: val, p: p)
-            newNode = .Node(key: nodeKey, val: nodeVal, p: nodeP, left: newChild, right: right)
-            rotate = leftRotate
-        } else if key > nodeKey {
-            newChild = right.set(key, val: val, p: p)
-            newNode = .Node(key: nodeKey, val: nodeVal, p: nodeP, left: left, right: newChild)
-            rotate = rightRotate
-        } else {
-            // It should be impossible to reach here
-            newChild = .Empty
-            newNode = .Empty
-            return newNode
-        }
-
-        if case let .Node(_, _, newChildP, _, _) = newChild where newChildP < nodeP {
-            return rotate(newNode)
-        } else {
-            return newNode
-        }
+  }
+  
+  fileprivate func insertAndBalance(_ nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap,
+                                    _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
+    let newChild: Treap<Key, Element>
+    let newNode: Treap<Key, Element>
+    let rotate: (Treap) -> Treap
+    if key < nodeKey {
+      newChild = left.set(key: key, val: val, p: p)
+      newNode = .node(key: nodeKey, val: nodeVal, p: nodeP, left: newChild, right: right)
+      rotate = leftRotate
+    } else if key > nodeKey {
+      newChild = right.set(key: key, val: val, p: p)
+      newNode = .node(key: nodeKey, val: nodeVal, p: nodeP, left: left, right: newChild)
+      rotate = rightRotate
+    } else {
+      // It should be impossible to reach here
+      newChild = .empty
+      newNode = .empty
+      return newNode
     }
-
-    internal func delete(key: Key) throws -> Treap {
-        switch self {
-        case .Empty:
-            throw NSError(domain: "com.wta.treap.errorDomain", code: -1, userInfo: nil)
-        case let .Node(nodeKey, val, p, left, right) where key < nodeKey:
-                return try Treap.Node(key: nodeKey, val: val, p: p, left: left.delete(key), right: right)
-        case let .Node(nodeKey, val, p, left, right) where key > nodeKey:
-                return try Treap.Node(key: nodeKey, val: val, p: p, left: left, right: right.delete(key))
-        case let .Node(_, _, _, left, right):
-                return merge(left, right: right)
-        }
+    
+    if case let .node(_, _, newChildP, _, _) = newChild , newChildP < nodeP {
+      return rotate(newNode)
+    } else {
+      return newNode
+    }
+  }
+  
+  internal func delete(key: Key) throws -> Treap {
+    switch self {
+    case .empty:
+      throw NSError(domain: "com.wta.treap.errorDomain", code: -1, userInfo: nil)
+    case let .node(nodeKey, val, p, left, right) where key < nodeKey:
+      return try Treap.node(key: nodeKey, val: val, p: p, left: left.delete(key: key), right: right)
+    case let .node(nodeKey, val, p, left, right) where key > nodeKey:
+      return try Treap.node(key: nodeKey, val: val, p: p, left: left, right: right.delete(key: key))
+    case let .node(_, _, _, left, right):
+      return merge(left, right: right)
     }
+  }
 }
diff --git a/Treap/Treap/Treap.xcodeproj/project.pbxproj b/Treap/Treap/Treap.xcodeproj/project.pbxproj
index 319a22f37..df9a0d6ee 100644
--- a/Treap/Treap/Treap.xcodeproj/project.pbxproj
+++ b/Treap/Treap/Treap.xcodeproj/project.pbxproj
@@ -7,32 +7,15 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		E1E34DC71C7670240023AF4D /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DC61C7670240023AF4D /* AppDelegate.swift */; };
-		E1E34DC91C7670240023AF4D /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = E1E34DC81C7670240023AF4D /* Assets.xcassets */; };
-		E1E34DCC1C7670240023AF4D /* MainMenu.xib in Resources */ = {isa = PBXBuildFile; fileRef = E1E34DCA1C7670240023AF4D /* MainMenu.xib */; };
+		750439C01DA9924E0045C660 /* Treap.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE11C7670350023AF4D /* Treap.swift */; };
+		750439C11DA992510045C660 /* TreapMergeSplit.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE21C7670350023AF4D /* TreapMergeSplit.swift */; };
+		750439C21DA992530045C660 /* TreapCollectionType.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE91C7671200023AF4D /* TreapCollectionType.swift */; };
 		E1E34DD71C7670250023AF4D /* TreapTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DD61C7670250023AF4D /* TreapTests.swift */; };
-		E1E34DE31C7670350023AF4D /* Treap.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE11C7670350023AF4D /* Treap.swift */; };
-		E1E34DE41C7670350023AF4D /* TreapMergeSplit.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE21C7670350023AF4D /* TreapMergeSplit.swift */; };
-		E1E34DEA1C7671200023AF4D /* TreapCollectionType.swift in Sources */ = {isa = PBXBuildFile; fileRef = E1E34DE91C7671200023AF4D /* TreapCollectionType.swift */; };
 /* End PBXBuildFile section */
 
-/* Begin PBXContainerItemProxy section */
-		E1E34DD31C7670250023AF4D /* PBXContainerItemProxy */ = {
-			isa = PBXContainerItemProxy;
-			containerPortal = E1E34DBB1C7670240023AF4D /* Project object */;
-			proxyType = 1;
-			remoteGlobalIDString = E1E34DC21C7670240023AF4D;
-			remoteInfo = Treap;
-		};
-/* End PBXContainerItemProxy section */
-
 /* Begin PBXFileReference section */
-		E1E34DC31C7670240023AF4D /* Treap.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = Treap.app; sourceTree = BUILT_PRODUCTS_DIR; };
-		E1E34DC61C7670240023AF4D /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
-		E1E34DC81C7670240023AF4D /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
-		E1E34DCB1C7670240023AF4D /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.xib; name = Base; path = Base.lproj/MainMenu.xib; sourceTree = "<group>"; };
 		E1E34DCD1C7670240023AF4D /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
-		E1E34DD21C7670250023AF4D /* TreapTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = TreapTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		E1E34DD21C7670250023AF4D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		E1E34DD61C7670250023AF4D /* TreapTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = TreapTests.swift; sourceTree = "<group>"; };
 		E1E34DD81C7670250023AF4D /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		E1E34DE11C7670350023AF4D /* Treap.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Treap.swift; path = ../../Treap.swift; sourceTree = "<group>"; };
@@ -41,13 +24,6 @@
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
-		E1E34DC01C7670240023AF4D /* Frameworks */ = {
-			isa = PBXFrameworksBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
 		E1E34DCF1C7670250023AF4D /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
@@ -70,8 +46,7 @@
 		E1E34DC41C7670240023AF4D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				E1E34DC31C7670240023AF4D /* Treap.app */,
-				E1E34DD21C7670250023AF4D /* TreapTests.xctest */,
+				E1E34DD21C7670250023AF4D /* Tests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -79,9 +54,6 @@
 		E1E34DC51C7670240023AF4D /* Treap */ = {
 			isa = PBXGroup;
 			children = (
-				E1E34DC61C7670240023AF4D /* AppDelegate.swift */,
-				E1E34DC81C7670240023AF4D /* Assets.xcassets */,
-				E1E34DCA1C7670240023AF4D /* MainMenu.xib */,
 				E1E34DE11C7670350023AF4D /* Treap.swift */,
 				E1E34DE21C7670350023AF4D /* TreapMergeSplit.swift */,
 				E1E34DE91C7671200023AF4D /* TreapCollectionType.swift */,
@@ -102,26 +74,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		E1E34DC21C7670240023AF4D /* Treap */ = {
+		E1E34DD11C7670250023AF4D /* Tests */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = E1E34DDB1C7670250023AF4D /* Build configuration list for PBXNativeTarget "Treap" */;
-			buildPhases = (
-				E1E34DBF1C7670240023AF4D /* Sources */,
-				E1E34DC01C7670240023AF4D /* Frameworks */,
-				E1E34DC11C7670240023AF4D /* Resources */,
-			);
-			buildRules = (
-			);
-			dependencies = (
-			);
-			name = Treap;
-			productName = Treap;
-			productReference = E1E34DC31C7670240023AF4D /* Treap.app */;
-			productType = "com.apple.product-type.application";
-		};
-		E1E34DD11C7670250023AF4D /* TreapTests */ = {
-			isa = PBXNativeTarget;
-			buildConfigurationList = E1E34DDE1C7670250023AF4D /* Build configuration list for PBXNativeTarget "TreapTests" */;
+			buildConfigurationList = E1E34DDE1C7670250023AF4D /* Build configuration list for PBXNativeTarget "Tests" */;
 			buildPhases = (
 				E1E34DCE1C7670250023AF4D /* Sources */,
 				E1E34DCF1C7670250023AF4D /* Frameworks */,
@@ -130,11 +85,10 @@
 			buildRules = (
 			);
 			dependencies = (
-				E1E34DD41C7670250023AF4D /* PBXTargetDependency */,
 			);
-			name = TreapTests;
+			name = Tests;
 			productName = TreapTests;
-			productReference = E1E34DD21C7670250023AF4D /* TreapTests.xctest */;
+			productReference = E1E34DD21C7670250023AF4D /* Tests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -144,15 +98,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "WillowTree, Inc.";
 				TargetAttributes = {
-					E1E34DC21C7670240023AF4D = {
-						CreatedOnToolsVersion = 7.2.1;
-					};
 					E1E34DD11C7670250023AF4D = {
 						CreatedOnToolsVersion = 7.2.1;
-						TestTargetID = E1E34DC21C7670240023AF4D;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -169,22 +120,12 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				E1E34DC21C7670240023AF4D /* Treap */,
-				E1E34DD11C7670250023AF4D /* TreapTests */,
+				E1E34DD11C7670250023AF4D /* Tests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
-		E1E34DC11C7670240023AF4D /* Resources */ = {
-			isa = PBXResourcesBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-				E1E34DC91C7670240023AF4D /* Assets.xcassets in Resources */,
-				E1E34DCC1C7670240023AF4D /* MainMenu.xib in Resources */,
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
 		E1E34DD01C7670250023AF4D /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
@@ -195,46 +136,19 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
-		E1E34DBF1C7670240023AF4D /* Sources */ = {
-			isa = PBXSourcesBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-				E1E34DEA1C7671200023AF4D /* TreapCollectionType.swift in Sources */,
-				E1E34DE31C7670350023AF4D /* Treap.swift in Sources */,
-				E1E34DC71C7670240023AF4D /* AppDelegate.swift in Sources */,
-				E1E34DE41C7670350023AF4D /* TreapMergeSplit.swift in Sources */,
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
 		E1E34DCE1C7670250023AF4D /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				750439C01DA9924E0045C660 /* Treap.swift in Sources */,
 				E1E34DD71C7670250023AF4D /* TreapTests.swift in Sources */,
+				750439C21DA992530045C660 /* TreapCollectionType.swift in Sources */,
+				750439C11DA992510045C660 /* TreapMergeSplit.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
 /* End PBXSourcesBuildPhase section */
 
-/* Begin PBXTargetDependency section */
-		E1E34DD41C7670250023AF4D /* PBXTargetDependency */ = {
-			isa = PBXTargetDependency;
-			target = E1E34DC21C7670240023AF4D /* Treap */;
-			targetProxy = E1E34DD31C7670250023AF4D /* PBXContainerItemProxy */;
-		};
-/* End PBXTargetDependency section */
-
-/* Begin PBXVariantGroup section */
-		E1E34DCA1C7670240023AF4D /* MainMenu.xib */ = {
-			isa = PBXVariantGroup;
-			children = (
-				E1E34DCB1C7670240023AF4D /* Base */,
-			);
-			name = MainMenu.xib;
-			sourceTree = "<group>";
-		};
-/* End PBXVariantGroup section */
-
 /* Begin XCBuildConfiguration section */
 		E1E34DD91C7670250023AF4D /* Debug */ = {
 			isa = XCBuildConfiguration;
@@ -249,8 +163,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -293,8 +209,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -313,56 +231,31 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-			};
-			name = Release;
-		};
-		E1E34DDC1C7670250023AF4D /* Debug */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = Treap/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.Treap;
-				PRODUCT_NAME = "$(TARGET_NAME)";
-			};
-			name = Debug;
-		};
-		E1E34DDD1C7670250023AF4D /* Release */ = {
-			isa = XCBuildConfiguration;
-			buildSettings = {
-				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				COMBINE_HIDPI_IMAGES = YES;
-				INFOPLIST_FILE = Treap/Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.Treap;
-				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
 		E1E34DDF1C7670250023AF4D /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = TreapTests/Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Treap.app/Contents/MacOS/Treap";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
 		E1E34DE01C7670250023AF4D /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
-				BUNDLE_LOADER = "$(TEST_HOST)";
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = TreapTests/Info.plist;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Treap.app/Contents/MacOS/Treap";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
@@ -378,21 +271,14 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		E1E34DDB1C7670250023AF4D /* Build configuration list for PBXNativeTarget "Treap" */ = {
-			isa = XCConfigurationList;
-			buildConfigurations = (
-				E1E34DDC1C7670250023AF4D /* Debug */,
-				E1E34DDD1C7670250023AF4D /* Release */,
-			);
-			defaultConfigurationIsVisible = 0;
-		};
-		E1E34DDE1C7670250023AF4D /* Build configuration list for PBXNativeTarget "TreapTests" */ = {
+		E1E34DDE1C7670250023AF4D /* Build configuration list for PBXNativeTarget "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				E1E34DDF1C7670250023AF4D /* Debug */,
 				E1E34DE01C7670250023AF4D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/Treap/Treap/Treap.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Treap/Treap/Treap.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Treap/Treap/Treap.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>
diff --git a/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 3eb165e19..fa2508008 100644
--- a/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,7 +1,7 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
-   version = "1.3">
+   LastUpgradeVersion = "0800"
+   version = "1.7">
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
@@ -15,8 +15,8 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
-               BuildableName = "TreapTests.xctest"
-               BlueprintName = "TreapTests"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
                ReferencedContainer = "container:Treap.xcodeproj">
             </BuildableReference>
          </BuildActionEntry>
@@ -33,12 +33,25 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
-               BuildableName = "TreapTests.xctest"
-               BlueprintName = "TreapTests"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
                ReferencedContainer = "container:Treap.xcodeproj">
             </BuildableReference>
+            <LocationScenarioReference
+               identifier = "com.apple.dt.IDEFoundation.CurrentLocationScenarioIdentifier"
+               referenceType = "1">
+            </LocationScenarioReference>
          </TestableReference>
       </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Treap.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </TestAction>
@@ -56,8 +69,8 @@
          <BuildableReference
             BuildableIdentifier = "primary"
             BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
-            BuildableName = "TreapTests.xctest"
-            BlueprintName = "TreapTests"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
             ReferencedContainer = "container:Treap.xcodeproj">
          </BuildableReference>
       </MacroExpansion>
@@ -74,8 +87,8 @@
          <BuildableReference
             BuildableIdentifier = "primary"
             BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
-            BuildableName = "TreapTests.xctest"
-            BlueprintName = "TreapTests"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
             ReferencedContainer = "container:Treap.xcodeproj">
          </BuildableReference>
       </MacroExpansion>
diff --git a/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme b/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme
deleted file mode 100644
index 566c370e1..000000000
--- a/Treap/Treap/Treap.xcodeproj/xcshareddata/xcschemes/Treap.xcscheme
+++ /dev/null
@@ -1,101 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Scheme
-   LastUpgradeVersion = "0730"
-   version = "1.3">
-   <BuildAction
-      parallelizeBuildables = "YES"
-      buildImplicitDependencies = "YES">
-      <BuildActionEntries>
-         <BuildActionEntry
-            buildForTesting = "YES"
-            buildForRunning = "YES"
-            buildForProfiling = "YES"
-            buildForArchiving = "YES"
-            buildForAnalyzing = "YES">
-            <BuildableReference
-               BuildableIdentifier = "primary"
-               BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
-               BuildableName = "Treap.app"
-               BlueprintName = "Treap"
-               ReferencedContainer = "container:Treap.xcodeproj">
-            </BuildableReference>
-         </BuildActionEntry>
-      </BuildActionEntries>
-   </BuildAction>
-   <TestAction
-      buildConfiguration = "Debug"
-      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
-      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      shouldUseLaunchSchemeArgsEnv = "YES">
-      <Testables>
-         <TestableReference
-            skipped = "NO">
-            <BuildableReference
-               BuildableIdentifier = "primary"
-               BlueprintIdentifier = "E1E34DD11C7670250023AF4D"
-               BuildableName = "TreapTests.xctest"
-               BlueprintName = "TreapTests"
-               ReferencedContainer = "container:Treap.xcodeproj">
-            </BuildableReference>
-         </TestableReference>
-      </Testables>
-      <MacroExpansion>
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
-            BuildableName = "Treap.app"
-            BlueprintName = "Treap"
-            ReferencedContainer = "container:Treap.xcodeproj">
-         </BuildableReference>
-      </MacroExpansion>
-      <AdditionalOptions>
-      </AdditionalOptions>
-   </TestAction>
-   <LaunchAction
-      buildConfiguration = "Debug"
-      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
-      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      launchStyle = "0"
-      useCustomWorkingDirectory = "NO"
-      ignoresPersistentStateOnLaunch = "NO"
-      debugDocumentVersioning = "YES"
-      debugServiceExtension = "internal"
-      allowLocationSimulation = "YES">
-      <BuildableProductRunnable
-         runnableDebuggingMode = "0">
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
-            BuildableName = "Treap.app"
-            BlueprintName = "Treap"
-            ReferencedContainer = "container:Treap.xcodeproj">
-         </BuildableReference>
-      </BuildableProductRunnable>
-      <AdditionalOptions>
-      </AdditionalOptions>
-   </LaunchAction>
-   <ProfileAction
-      buildConfiguration = "Release"
-      shouldUseLaunchSchemeArgsEnv = "YES"
-      savedToolIdentifier = ""
-      useCustomWorkingDirectory = "NO"
-      debugDocumentVersioning = "YES">
-      <BuildableProductRunnable
-         runnableDebuggingMode = "0">
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "E1E34DC21C7670240023AF4D"
-            BuildableName = "Treap.app"
-            BlueprintName = "Treap"
-            ReferencedContainer = "container:Treap.xcodeproj">
-         </BuildableReference>
-      </BuildableProductRunnable>
-   </ProfileAction>
-   <AnalyzeAction
-      buildConfiguration = "Debug">
-   </AnalyzeAction>
-   <ArchiveAction
-      buildConfiguration = "Release"
-      revealArchiveInOrganizer = "YES">
-   </ArchiveAction>
-</Scheme>
diff --git a/Treap/Treap/Treap/AppDelegate.swift b/Treap/Treap/Treap/AppDelegate.swift
deleted file mode 100644
index a6a68a40c..000000000
--- a/Treap/Treap/Treap/AppDelegate.swift
+++ /dev/null
@@ -1,43 +0,0 @@
-//
-//  AppDelegate.swift
-//  Treap
-//
-//  Created by Robert Thompson on 2/18/16.
-//  Copyright © 2016 Robert Thompson
-/* Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in
-all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-THE SOFTWARE.*/
-//
-
-import Cocoa
-
-@NSApplicationMain
-class AppDelegate: NSObject, NSApplicationDelegate {
-
-    @IBOutlet weak var window: NSWindow!
-
-
-    func applicationDidFinishLaunching(aNotification: NSNotification) {
-        // Insert code here to initialize your application
-    }
-
-    func applicationWillTerminate(aNotification: NSNotification) {
-        // Insert code here to tear down your application
-    }
-
-
-}
diff --git a/Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json b/Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 2db2b1c7c..000000000
--- a/Treap/Treap/Treap/Assets.xcassets/AppIcon.appiconset/Contents.json
+++ /dev/null
@@ -1,58 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "16x16",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "32x32",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "128x128",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "256x256",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "mac",
-      "size" : "512x512",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Treap/Treap/Treap/Base.lproj/MainMenu.xib b/Treap/Treap/Treap/Base.lproj/MainMenu.xib
deleted file mode 100644
index 8955ad822..000000000
--- a/Treap/Treap/Treap/Base.lproj/MainMenu.xib
+++ /dev/null
@@ -1,681 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.Cocoa.XIB" version="3.0" toolsVersion="9532" systemVersion="15E39c" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" customObjectInstantitationMethod="direct">
-    <dependencies>
-        <deployment identifier="macosx"/>
-        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="9532"/>
-    </dependencies>
-    <objects>
-        <customObject id="-2" userLabel="File's Owner" customClass="NSApplication">
-            <connections>
-                <outlet property="delegate" destination="Voe-Tx-rLC" id="GzC-gU-4Uq"/>
-            </connections>
-        </customObject>
-        <customObject id="-1" userLabel="First Responder" customClass="FirstResponder"/>
-        <customObject id="-3" userLabel="Application" customClass="NSObject"/>
-        <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModule="Treap" customModuleProvider="target">
-            <connections>
-                <outlet property="window" destination="QvC-M9-y7g" id="gIp-Ho-8D9"/>
-            </connections>
-        </customObject>
-        <customObject id="YLy-65-1bz" customClass="NSFontManager"/>
-        <menu title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
-            <items>
-                <menuItem title="Treap" id="1Xt-HY-uBw">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Treap" systemMenu="apple" id="uQy-DD-JDr">
-                        <items>
-                            <menuItem title="About Treap" id="5kV-Vb-QxS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="orderFrontStandardAboutPanel:" target="-1" id="Exp-CZ-Vem"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
-                            <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
-                            <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
-                            <menuItem title="Services" id="NMo-om-nkz">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
-                            <menuItem title="Hide Treap" keyEquivalent="h" id="Olw-nP-bQN">
-                                <connections>
-                                    <action selector="hide:" target="-1" id="PnN-Uc-m68"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="hideOtherApplications:" target="-1" id="VT4-aY-XCT"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Show All" id="Kd2-mp-pUS">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="unhideAllApplications:" target="-1" id="Dhg-Le-xox"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
-                            <menuItem title="Quit Treap" keyEquivalent="q" id="4sb-4s-VLi">
-                                <connections>
-                                    <action selector="terminate:" target="-1" id="Te7-pn-YzF"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="File" id="dMs-cI-mzQ">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="File" id="bib-Uj-vzu">
-                        <items>
-                            <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
-                                <connections>
-                                    <action selector="newDocument:" target="-1" id="4Si-XN-c54"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
-                                <connections>
-                                    <action selector="openDocument:" target="-1" id="bVn-NM-KNZ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Open Recent" id="tXI-mr-wws">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
-                                    <items>
-                                        <menuItem title="Clear Menu" id="vNY-rz-j42">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="clearRecentDocuments:" target="-1" id="Daa-9d-B3U"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
-                            <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
-                                <connections>
-                                    <action selector="performClose:" target="-1" id="HmO-Ls-i7Q"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
-                                <connections>
-                                    <action selector="saveDocument:" target="-1" id="teZ-XB-qJY"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
-                                <connections>
-                                    <action selector="saveDocumentAs:" target="-1" id="mDf-zr-I0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Revert to Saved" id="KaW-ft-85H">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="revertDocumentToSaved:" target="-1" id="iJ3-Pv-kwq"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
-                            <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
-                                <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
-                                <connections>
-                                    <action selector="runPageLayout:" target="-1" id="Din-rz-gC5"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
-                                <connections>
-                                    <action selector="print:" target="-1" id="qaZ-4w-aoO"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Edit" id="5QF-Oa-p0T">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Edit" id="W48-6f-4Dl">
-                        <items>
-                            <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
-                                <connections>
-                                    <action selector="undo:" target="-1" id="M6e-cu-g7V"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
-                                <connections>
-                                    <action selector="redo:" target="-1" id="oIA-Rs-6OD"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
-                            <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
-                                <connections>
-                                    <action selector="cut:" target="-1" id="YJe-68-I9s"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
-                                <connections>
-                                    <action selector="copy:" target="-1" id="G1f-GL-Joy"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
-                                <connections>
-                                    <action selector="paste:" target="-1" id="UvS-8e-Qdg"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="pasteAsPlainText:" target="-1" id="cEh-KX-wJQ"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Delete" id="pa3-QI-u2k">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="delete:" target="-1" id="0Mk-Ml-PaM"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
-                                <connections>
-                                    <action selector="selectAll:" target="-1" id="VNm-Mi-diN"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
-                            <menuItem title="Find" id="4EN-yA-p0u">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Find" id="1b7-l0-nxx">
-                                    <items>
-                                        <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="cD7-Qs-BN4"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="WD3-Gg-5AJ"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="NDo-RZ-v9R"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="HOh-sY-3ay"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
-                                            <connections>
-                                                <action selector="performFindPanelAction:" target="-1" id="U76-nv-p5D"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
-                                            <connections>
-                                                <action selector="centerSelectionInVisibleArea:" target="-1" id="IOG-6D-g5B"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
-                                    <items>
-                                        <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
-                                            <connections>
-                                                <action selector="showGuessPanel:" target="-1" id="vFj-Ks-hy3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
-                                            <connections>
-                                                <action selector="checkSpelling:" target="-1" id="fz7-VC-reM"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
-                                        <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleContinuousSpellChecking:" target="-1" id="7w6-Qz-0kB"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleGrammarChecking:" target="-1" id="muD-Qn-j4w"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticSpellingCorrection:" target="-1" id="2lM-Qi-WAP"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Substitutions" id="9ic-FL-obx">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
-                                    <items>
-                                        <menuItem title="Show Substitutions" id="z6F-FW-3nz">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="orderFrontSubstitutionsPanel:" target="-1" id="oku-mr-iSq"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
-                                        <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleSmartInsertDelete:" target="-1" id="3IJ-Se-DZD"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Quotes" id="hQb-2v-fYv">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticQuoteSubstitution:" target="-1" id="ptq-xd-QOA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Dashes" id="rgM-f4-ycn">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDashSubstitution:" target="-1" id="oCt-pO-9gS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smart Links" id="cwL-P1-jid">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticLinkDetection:" target="-1" id="Gip-E3-Fov"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Data Detectors" id="tRr-pd-1PS">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticDataDetection:" target="-1" id="R1I-Nq-Kbl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Text Replacement" id="HFQ-gK-NFA">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleAutomaticTextReplacement:" target="-1" id="DvP-Fe-Py6"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Transformations" id="2oI-Rn-ZJC">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
-                                    <items>
-                                        <menuItem title="Make Upper Case" id="vmV-6d-7jI">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="uppercaseWord:" target="-1" id="sPh-Tk-edu"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Make Lower Case" id="d9M-CD-aMd">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="lowercaseWord:" target="-1" id="iUZ-b5-hil"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Capitalize" id="UEZ-Bs-lqG">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="capitalizeWord:" target="-1" id="26H-TL-nsh"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Speech" id="xrE-MZ-jX0">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
-                                    <items>
-                                        <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="startSpeaking:" target="-1" id="654-Ng-kyl"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="stopSpeaking:" target="-1" id="dX8-6p-jy9"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Format" id="jxT-CU-nIS">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Format" id="GEO-Iw-cKr">
-                        <items>
-                            <menuItem title="Font" id="Gi5-1S-RQB">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
-                                    <items>
-                                        <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq">
-                                            <connections>
-                                                <action selector="orderFrontFontPanel:" target="YLy-65-1bz" id="WHr-nq-2xA"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="hqk-hr-sYV"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq">
-                                            <connections>
-                                                <action selector="addFontTrait:" target="YLy-65-1bz" id="IHV-OB-c03"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
-                                            <connections>
-                                                <action selector="underline:" target="-1" id="FYS-2b-JAY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
-                                        <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="Uc7-di-UnL"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST">
-                                            <connections>
-                                                <action selector="modifyFont:" target="YLy-65-1bz" id="HcX-Lf-eNd"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
-                                        <menuItem title="Kern" id="jBQ-r6-VK2">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
-                                                <items>
-                                                    <menuItem title="Use Default" id="GUa-eO-cwY">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardKerning:" target="-1" id="6dk-9l-Ckg"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="cDB-IK-hbR">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffKerning:" target="-1" id="U8a-gz-Maa"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Tighten" id="46P-cB-AYj">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="tightenKerning:" target="-1" id="hr7-Nz-8ro"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Loosen" id="ogc-rX-tC1">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="loosenKerning:" target="-1" id="8i4-f9-FKE"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Ligatures" id="o6e-r0-MWq">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
-                                                <items>
-                                                    <menuItem title="Use Default" id="agt-UL-0e3">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useStandardLigatures:" target="-1" id="7uR-wd-Dx6"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use None" id="J7y-lM-qPV">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="turnOffLigatures:" target="-1" id="iX2-gA-Ilz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Use All" id="xQD-1f-W4t">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="useAllLigatures:" target="-1" id="KcB-kA-TuK"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem title="Baseline" id="OaQ-X3-Vso">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Baseline" id="ijk-EB-dga">
-                                                <items>
-                                                    <menuItem title="Use Default" id="3Om-Ey-2VK">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="unscript:" target="-1" id="0vZ-95-Ywn"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Superscript" id="Rqc-34-cIF">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="superscript:" target="-1" id="3qV-fo-wpU"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Subscript" id="I0S-gh-46l">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="subscript:" target="-1" id="Q6W-4W-IGz"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Raise" id="2h7-ER-AoG">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="raiseBaseline:" target="-1" id="4sk-31-7Q9"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem title="Lower" id="1tx-W0-xDw">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="lowerBaseline:" target="-1" id="OF1-bc-KW4"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
-                                        <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
-                                            <connections>
-                                                <action selector="orderFrontColorPanel:" target="-1" id="mSX-Xz-DV3"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
-                                        <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyFont:" target="-1" id="GJO-xA-L4q"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
-                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteFont:" target="-1" id="JfD-CL-leO"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                            <menuItem title="Text" id="Fal-I4-PZk">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <menu key="submenu" title="Text" id="d9c-me-L2H">
-                                    <items>
-                                        <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
-                                            <connections>
-                                                <action selector="alignLeft:" target="-1" id="zUv-R1-uAa"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
-                                            <connections>
-                                                <action selector="alignCenter:" target="-1" id="spX-mk-kcS"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Justify" id="J5U-5w-g23">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="alignJustified:" target="-1" id="ljL-7U-jND"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
-                                            <connections>
-                                                <action selector="alignRight:" target="-1" id="r48-bG-YeY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
-                                        <menuItem title="Writing Direction" id="H1b-Si-o9J">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
-                                                <items>
-                                                    <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="YGs-j5-SAR">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionNatural:" target="-1" id="qtV-5e-UBP"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="Lbh-J2-qVU">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionLeftToRight:" target="-1" id="S0X-9S-QSf"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="jFq-tB-4Kx">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeBaseWritingDirectionRightToLeft:" target="-1" id="5fk-qB-AqJ"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
-                                                    <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                    </menuItem>
-                                                    <menuItem id="Nop-cj-93Q">
-                                                        <string key="title">	Default</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionNatural:" target="-1" id="lPI-Se-ZHp"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="BgM-ve-c93">
-                                                        <string key="title">	Left to Right</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionLeftToRight:" target="-1" id="caW-Bv-w94"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                    <menuItem id="RB4-Sm-HuC">
-                                                        <string key="title">	Right to Left</string>
-                                                        <modifierMask key="keyEquivalentModifierMask"/>
-                                                        <connections>
-                                                            <action selector="makeTextWritingDirectionRightToLeft:" target="-1" id="EXD-6r-ZUu"/>
-                                                        </connections>
-                                                    </menuItem>
-                                                </items>
-                                            </menu>
-                                        </menuItem>
-                                        <menuItem isSeparatorItem="YES" id="fKy-g9-1gm"/>
-                                        <menuItem title="Show Ruler" id="vLm-3I-IUL">
-                                            <modifierMask key="keyEquivalentModifierMask"/>
-                                            <connections>
-                                                <action selector="toggleRuler:" target="-1" id="FOx-HJ-KwY"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Copy Ruler" keyEquivalent="c" id="MkV-Pr-PK5">
-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="copyRuler:" target="-1" id="71i-fW-3W2"/>
-                                            </connections>
-                                        </menuItem>
-                                        <menuItem title="Paste Ruler" keyEquivalent="v" id="LVM-kO-fVI">
-                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
-                                            <connections>
-                                                <action selector="pasteRuler:" target="-1" id="cSh-wd-qM2"/>
-                                            </connections>
-                                        </menuItem>
-                                    </items>
-                                </menu>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="View" id="H8h-7b-M4v">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="View" id="HyV-fh-RgO">
-                        <items>
-                            <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
-                                <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
-                                <connections>
-                                    <action selector="toggleToolbarShown:" target="-1" id="BXY-wc-z0C"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="runToolbarCustomizationPalette:" target="-1" id="pQI-g3-MTW"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Window" id="aUF-d1-5bR">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
-                        <items>
-                            <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
-                                <connections>
-                                    <action selector="performMiniaturize:" target="-1" id="VwT-WD-YPe"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem title="Zoom" id="R4o-n2-Eq4">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="performZoom:" target="-1" id="DIl-cC-cCs"/>
-                                </connections>
-                            </menuItem>
-                            <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
-                            <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
-                                <modifierMask key="keyEquivalentModifierMask"/>
-                                <connections>
-                                    <action selector="arrangeInFront:" target="-1" id="DRN-fu-gQh"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-                <menuItem title="Help" id="wpr-3q-Mcd">
-                    <modifierMask key="keyEquivalentModifierMask"/>
-                    <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
-                        <items>
-                            <menuItem title="Treap Help" keyEquivalent="?" id="FKE-Sm-Kum">
-                                <connections>
-                                    <action selector="showHelp:" target="-1" id="y7X-2Q-9no"/>
-                                </connections>
-                            </menuItem>
-                        </items>
-                    </menu>
-                </menuItem>
-            </items>
-        </menu>
-        <window title="Treap" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" releasedWhenClosed="NO" animationBehavior="default" id="QvC-M9-y7g">
-            <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
-            <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
-            <rect key="contentRect" x="335" y="390" width="480" height="360"/>
-            <rect key="screenRect" x="0.0" y="0.0" width="1920" height="1057"/>
-            <view key="contentView" id="EiT-Mj-1SZ">
-                <rect key="frame" x="0.0" y="0.0" width="480" height="360"/>
-                <autoresizingMask key="autoresizingMask"/>
-            </view>
-        </window>
-    </objects>
-</document>
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index 5f43a376f..f349e6ab8 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -25,50 +25,49 @@ THE SOFTWARE.*/
 // swiftlint:disable force_try
 
 import XCTest
-@testable import Treap
 
 class TreapTests: XCTestCase {
-
-    override func setUp() {
-        super.setUp()
-        // Put setup code here. This method is called before the invocation of each test method in the class.
+  
+  override func setUp() {
+    super.setUp()
+    // Put setup code here. This method is called before the invocation of each test method in the class.
+  }
+  
+  override func tearDown() {
+    // Put teardown code here. This method is called after the invocation of each test method in the class.
+    super.tearDown()
+  }
+  
+  func testSanity() {
+    var treap = Treap<Int, String>.empty
+    treap = treap.set(key: 5, val: "a").set(key: 7, val: "b")
+    XCTAssert(treap.get(5) == "a")
+    XCTAssert(treap.get(7) == "b")
+    treap = treap.set(key: 2, val: "c")
+    XCTAssert(treap.get(2) == "c")
+    treap = treap.set(key: 2, val: "d")
+    XCTAssert(treap.get(2) == "d")
+    treap = try! treap.delete(key: 5)
+    XCTAssert(!treap.contains(5))
+    XCTAssert(treap.contains(7))
+  }
+  
+  func testFairlyBalanced() {
+    var treap = Treap<Int, Int?>.empty
+    for i in 0..<1000 {
+      treap = treap.set(key: i, val: nil)
     }
-
-    override func tearDown() {
-        // Put teardown code here. This method is called after the invocation of each test method in the class.
-        super.tearDown()
+    let depth = treap.depth
+    XCTAssert(depth < 30, "treap.depth was \(depth)")
+  }
+  
+  func testFairlyBalancedCollection() {
+    var treap = Treap<Int, Int?>()
+    for i in 0..<1000 {
+      treap[i] = Optional<Int>.none
     }
-
-    func testSanity() {
-        var treap = Treap<Int, String>.Empty
-        treap = treap.set(5, val: "a").set(7, val: "b")
-        XCTAssert(treap.get(5) == "a")
-        XCTAssert(treap.get(7) == "b")
-        treap = treap.set(2, val: "c")
-        XCTAssert(treap.get(2) == "c")
-        treap = treap.set(2, val: "d")
-        XCTAssert(treap.get(2) == "d")
-        treap = try! treap.delete(5)
-        XCTAssert(!treap.contains(5))
-        XCTAssert(treap.contains(7))
-    }
-
-    func testFairlyBalanced() {
-        var treap = Treap<Int, Int?>.Empty
-        for i in 0..<1000 {
-            treap = treap.set(i, val: nil)
-        }
-        let depth = treap.depth
-        XCTAssert(depth < 30, "treap.depth was \(depth)")
-    }
-
-    func testFairlyBalancedCollection() {
-        var treap = Treap<Int, Int?>()
-        for i in 0..<1000 {
-            treap[i] = Optional<Int>.None
-        }
-        let depth = treap.depth
-        XCTAssert(depth > 0 && depth < 30)
-    }
-
+    let depth = treap.depth
+    XCTAssert(depth > 0 && depth < 30)
+  }
+  
 }
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index 36d02eaac..de40464d1 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -24,78 +24,88 @@ THE SOFTWARE.*/
 
 import Foundation
 
-extension Treap: MutableCollectionType {
-    public typealias Index = TreapIndex<Key>
-
-    public subscript(index: TreapIndex<Key>) -> Element {
-        get {
-            guard let result = self.get(index.keys[index.keyIndex]) else {
-                fatalError("Invalid index!")
-            }
-
-            return result
-        }
-
-        mutating set {
-            let key = index.keys[index.keyIndex]
-            self = self.set(key, val: newValue)
-        }
+extension Treap: MutableCollection {
+  
+  public typealias Index = TreapIndex<Key>
+  
+  public subscript(index: TreapIndex<Key>) -> Element {
+    get {
+      guard let result = self.get(index.keys[index.keyIndex]) else {
+        fatalError("Invalid index!")
+      }
+      
+      return result
     }
-
-    public subscript(key: Key) -> Element? {
-        get {
-            return self.get(key)
-        }
-
-        mutating set {
-            guard let value = newValue else {
-                let _ = try? self.delete(key)
-                return
-            }
-
-            self = self.set(key, val: value)
-        }
+    
+    mutating set {
+      let key = index.keys[index.keyIndex]
+      self = self.set(key: key, val: newValue)
     }
-
-    public var startIndex: TreapIndex<Key> {
-        return TreapIndex<Key>(keys: keys, keyIndex: 0)
+  }
+  
+  public subscript(key: Key) -> Element? {
+    get {
+      return self.get(key)
     }
-
-    public var endIndex: TreapIndex<Key> {
-        let keys = self.keys
-        return TreapIndex<Key>(keys: keys, keyIndex: keys.count)
+    
+    mutating set {
+      guard let value = newValue else {
+        let _ = try? self.delete(key: key)
+        return
+      }
+      
+      self = self.set(key: key, val: value)
     }
-
-    private var keys: [Key] {
-        var results: [Key] = []
-        if case let .Node(key, _, _, left, right) = self {
-            results.appendContentsOf(left.keys)
-            results.append(key)
-            results.appendContentsOf(right.keys)
-        }
-
-        return results
+  }
+  
+  public var startIndex: TreapIndex<Key> {
+    return TreapIndex<Key>(keys: keys, keyIndex: 0)
+  }
+  
+  public var endIndex: TreapIndex<Key> {
+    let keys = self.keys
+    return TreapIndex<Key>(keys: keys, keyIndex: keys.count)
+  }
+  
+  public func index(after i: TreapIndex<Key>) -> TreapIndex<Key> {
+    return i.successor()
+  }
+  
+  fileprivate var keys: [Key] {
+    var results: [Key] = []
+    if case let .node(key, _, _, left, right) = self {
+      results.append(contentsOf: left.keys)
+      results.append(key)
+      results.append(contentsOf: right.keys)
     }
+    
+    return results
+  }
 }
 
-public struct TreapIndex<Key: Comparable>: BidirectionalIndexType {
-    private let keys: [Key]
-    private let keyIndex: Int
-
-    public func successor() -> TreapIndex {
-        return TreapIndex(keys: keys, keyIndex: keyIndex + 1)
-    }
-
-    public func predecessor() -> TreapIndex {
-        return TreapIndex(keys: keys, keyIndex: keyIndex - 1)
-    }
-
-    private init(keys: [Key] = [], keyIndex: Int = 0) {
-        self.keys = keys
-        self.keyIndex = keyIndex
-    }
+public struct TreapIndex<Key: Comparable>: Comparable {
+  
+  public static func <(lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
+    return lhs.keyIndex < rhs.keyIndex
+  }
+  
+  fileprivate let keys: [Key]
+  fileprivate let keyIndex: Int
+  
+  public func successor() -> TreapIndex {
+    return TreapIndex(keys: keys, keyIndex: keyIndex + 1)
+  }
+  
+  public func predecessor() -> TreapIndex {
+    return TreapIndex(keys: keys, keyIndex: keyIndex - 1)
+  }
+  
+  fileprivate init(keys: [Key] = [], keyIndex: Int = 0) {
+    self.keys = keys
+    self.keyIndex = keyIndex
+  }
 }
 
 public func ==<Key: Comparable>(lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
-    return lhs.keys == rhs.keys && lhs.keyIndex == rhs.keyIndex
+  return lhs.keys == rhs.keys && lhs.keyIndex == rhs.keyIndex
 }
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index 277cb40b7..660bd4932 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -24,93 +24,93 @@ THE SOFTWARE.*/
 
 import Foundation
 public extension Treap {
-    internal func split(key: Key) -> (left: Treap, right: Treap) {
-        var current = self
-        let val: Element
-        if let newVal = self.get(key) {
-          // swiftlint:disable force_try
-            current = try! current.delete(key)
-          // swiftlint:enable force_try
-            val = newVal
-        } else if case let .Node(_, newVal, _, _, _) = self {
-            val = newVal
-        } else {
-            fatalError("No values in treap")
-        }
-
-        switch self {
-        case .Node:
-            if case let .Node(_, _, _, left, right) = current.set(key, val: val, p: -1) {
-                return (left: left, right: right)
-            } else {
-                return (left: .Empty, right: .Empty)
-            }
-        default:
-            return (left: .Empty, right: .Empty)
-        }
+  internal func split(_ key: Key) -> (left: Treap, right: Treap) {
+    var current = self
+    let val: Element
+    if let newVal = self.get(key) {
+      // swiftlint:disable force_try
+      current = try! current.delete(key: key)
+      // swiftlint:enable force_try
+      val = newVal
+    } else if case let .node(_, newVal, _, _, _) = self {
+      val = newVal
+    } else {
+      fatalError("No values in treap")
     }
-
-    internal var leastKey: Key? {
-        switch self {
-        case .Empty:
-            return nil
-        case let .Node(key, _, _, .Empty, _):
-            return key
-        case let .Node(_, _, _, left, _):
-            return left.leastKey
-        }
+    
+    switch self {
+    case .node:
+      if case let .node(_, _, _, left, right) = current.set(key: key, val: val, p: -1) {
+        return (left: left, right: right)
+      } else {
+        return (left: .empty, right: .empty)
+      }
+    default:
+      return (left: .empty, right: .empty)
     }
-
-    internal var mostKey: Key? {
-        switch self {
-        case .Empty:
-            return nil
-        case let .Node(key, _, _, _, .Empty):
-            return key
-        case let .Node(_, _, _, _, right):
-            return right.mostKey
-        }
+  }
+  
+  internal var leastKey: Key? {
+    switch self {
+    case .empty:
+      return nil
+    case let .node(key, _, _, .empty, _):
+      return key
+    case let .node(_, _, _, left, _):
+      return left.leastKey
+    }
+  }
+  
+  internal var mostKey: Key? {
+    switch self {
+    case .empty:
+      return nil
+    case let .node(key, _, _, _, .empty):
+      return key
+    case let .node(_, _, _, _, right):
+      return right.mostKey
     }
+  }
 }
 
-internal func merge<Key: Comparable, Element>(left: Treap<Key, Element>, right: Treap<Key, Element>) -> Treap<Key, Element> {
-    switch (left, right) {
-    case (.Empty, _):
-        return right
-    case (_, .Empty):
-        return left
-
-    case let (.Node(leftKey, leftVal, leftP, leftLeft, leftRight), .Node(rightKey, rightVal, rightP, rightLeft, rightRight)):
-        if leftP < rightP {
-            return .Node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: merge(leftRight, right: right))
-        } else {
-            return .Node(key: rightKey, val: rightVal, p: rightP, left: merge(rightLeft, right: left), right: rightRight)
-        }
-    default:
-        break
+internal func merge<Key: Comparable, Element>(_ left: Treap<Key, Element>, right: Treap<Key, Element>) -> Treap<Key, Element> {
+  switch (left, right) {
+  case (.empty, _):
+    return right
+  case (_, .empty):
+    return left
+    
+  case let (.node(leftKey, leftVal, leftP, leftLeft, leftRight), .node(rightKey, rightVal, rightP, rightLeft, rightRight)):
+    if leftP < rightP {
+      return .node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: merge(leftRight, right: right))
+    } else {
+      return .node(key: rightKey, val: rightVal, p: rightP, left: merge(rightLeft, right: left), right: rightRight)
     }
-    return .Empty
+  default:
+    break
+  }
+  return .empty
 }
 
 extension Treap: CustomStringConvertible {
-    public var description: String {
-        get {
-            return Treap.descHelper(self, indent: 0)
-        }
+  public var description: String {
+    get {
+      return Treap.descHelper(self, indent: 0)
     }
-
-    private static func descHelper(treap: Treap<Key, Element>, indent: Int) -> String {
-        if case let .Node(key, value, priority, left, right) = treap {
-            var result = ""
-            let tabs = String(count: indent, repeatedValue: Character("\t"))
-
-            result += descHelper(left, indent: indent + 1)
-            result += "\n" + tabs + "\(key), \(value), \(priority)\n"
-            result += descHelper(right, indent: indent + 1)
-
-            return result
-        } else {
-            return ""
-        }
+  }
+  
+  fileprivate static func descHelper(_ treap: Treap<Key, Element>, indent: Int) -> String {
+    if case let .node(key, value, priority, left, right) = treap {
+      var result = ""
+      let tabs = String(repeating: "\t", count: indent)
+      
+      result += descHelper(left, indent: indent + 1)
+      result += "\n" + tabs + "\(key), \(value), \(priority)\n"
+      result += descHelper(right, indent: indent + 1)
+      
+      return result
+    } else {
+      return ""
     }
+  }
 }

From 18c33157976e6d2f010460004ed2a8866243b4f6 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 11 Oct 2016 23:21:10 +0200
Subject: [PATCH 0595/1679] Haversine Distance

---
 .../Contents.swift                            | 31 +++++++++++++++++++
 .../contents.xcplayground                     |  4 +++
 .../contents.xcworkspacedata                  |  7 +++++
 HaversineDistance/README.md                   | 23 ++++++++++++++
 4 files changed, 65 insertions(+)
 create mode 100644 HaversineDistance/HaversineDistance.playground/Contents.swift
 create mode 100644 HaversineDistance/HaversineDistance.playground/contents.xcplayground
 create mode 100644 HaversineDistance/HaversineDistance.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 HaversineDistance/README.md

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
new file mode 100644
index 000000000..f46d7c394
--- /dev/null
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -0,0 +1,31 @@
+
+import UIKit
+
+func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
+    
+    let haversin = { (angle: Double) -> Double in
+        return (1 - cos(angle))/2
+    }
+    
+    let ahaversin = { (angle: Double) -> Double in
+        return 2*asin(sqrt(angle))
+    }
+    
+    // Converts from degrees to radians
+    let dToR = { (angle: Double) -> Double in
+        return (angle / 360) * 2 * M_PI
+    }
+    
+    let lat1 = dToR(la1)
+    let lon1 = dToR(lo1)
+    let lat2 = dToR(la2)
+    let lon2 = dToR(lo2)
+    
+    return radius * ahaversin(haversin(lat2 - lat1) + cos(lat1) * cos(lat2) * haversin(lon2 - lon1))
+}
+
+let amsterdam = (52.3702, 4.8952)
+let newYork = (40.7128, -74.0059)
+
+// Google says it's 5857 km so our result is only off by 2km which could be due to all kinds of things, not sure how google calculates the distance or which latitude and longitude google uses to calculate the distance.
+haversineDinstance(la1: amsterdam.0, lo1: amsterdam.1, la2: newYork.0, lo2: newYork.1)
diff --git a/HaversineDistance/HaversineDistance.playground/contents.xcplayground b/HaversineDistance/HaversineDistance.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/HaversineDistance/HaversineDistance.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/HaversineDistance/HaversineDistance.playground/playground.xcworkspace/contents.xcworkspacedata b/HaversineDistance/HaversineDistance.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/HaversineDistance/HaversineDistance.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/HaversineDistance/README.md b/HaversineDistance/README.md
new file mode 100644
index 000000000..84030cbff
--- /dev/null
+++ b/HaversineDistance/README.md
@@ -0,0 +1,23 @@
+# Haversine Distance
+
+Calculates the distance on a sphere between two points given in latitude and longitude using the haversine formula.
+
+The haversine formula can be found on [Wikipedia](https://en.wikipedia.org/wiki/Haversine_formula)
+
+The Haversine Distance is implemented as a function as a class would be kind of overkill.
+
+`haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double`
+
+- `la1` is the latitude of point 1 in degrees.
+- `lo1` is the longitude of point 1 in degrees.
+- `la2` is the latitude of point 2 in degrees.
+- `lo2` is the longitude of point 2 in degrees.
+- `radius` is the radius of the sphere considered in meters, which defaults to the mean radius of the earth (from [WolframAlpha](http://www.wolframalpha.com/input/?i=earth+radius)).
+
+The function contains 3 closures in order to make the code more readable and comparable to the Haversine formula given by the Wikipedia page mentioned above.
+
+1. `haversine` implements the haversine, a trigonometric function.
+2. `ahaversine` the inverse function of the haversine.
+3. `dToR` a closure converting degrees to radians.
+
+The result of `haversineDistance` is returned in meters.

From 08b9778deb23187d71c7221f04d57a4ba4a1a61d Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 11 Oct 2016 23:23:56 +0200
Subject: [PATCH 0596/1679] update readme

---
 HaversineDistance/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/HaversineDistance/README.md b/HaversineDistance/README.md
index 84030cbff..4d5f20e6a 100644
--- a/HaversineDistance/README.md
+++ b/HaversineDistance/README.md
@@ -21,3 +21,5 @@ The function contains 3 closures in order to make the code more readable and com
 3. `dToR` a closure converting degrees to radians.
 
 The result of `haversineDistance` is returned in meters.
+
+*Written for Swift Algorithm Club by Jaap Wijnen.*

From 5dc980eec227665710b452013dee0599e278d248 Mon Sep 17 00:00:00 2001
From: Michael Vilabrera <m.vilabrera@gmail.com>
Date: Thu, 13 Oct 2016 23:24:39 -0400
Subject: [PATCH 0597/1679] Added Swift Structures to repository list

---
 README.markdown | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/README.markdown b/README.markdown
index 28a56dfd3..6b9f15a6c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -10,7 +10,7 @@ The goal of this project is to **explain how algorithms work**. The focus is on
 
 All code is compatible with **Xcode 7.3** and **Swift 2.2**. We'll keep this updated with the latest version of Swift.
 
-This is a work in progress. More algorithms will be added soon. :-) 
+This is a work in progress. More algorithms will be added soon. :-)
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 
@@ -26,7 +26,7 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 [How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
 
-[Under construction](Under Construction.markdown). Algorithms that are under construction. 
+[Under construction](Under Construction.markdown). Algorithms that are under construction.
 
 ## Where to start?
 
@@ -210,6 +210,7 @@ Other algorithm repositories:
 - [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
 - [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
 - [AlgorithmVisualizer](http://jasonpark.me/AlgorithmVisualizer/). Visualize algorithms on your browser.
+- [Swift Structures](https://github.com/waynewbishop/SwiftStructures) Data Structures with directions on how to use them [here](http://waynewbishop.com/swift)
 
 ## Credits
 

From d15c1b824ebdbe33b0d415b72ef193b337fbc01a Mon Sep 17 00:00:00 2001
From: Keita Ito <keitaitok@gmail.com>
Date: Fri, 14 Oct 2016 11:59:41 -0700
Subject: [PATCH 0598/1679] Fix method name from reverse() to reversed() in
 README.markdown

---
 Longest Common Subsequence/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index ba514728a..4cd2c2fcb 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -152,7 +152,7 @@ func backtrack(_ matrix: [[Int]]) -> String {
 	}
   }
   
-  return String(lcs.characters.reverse())
+  return String(lcs.characters.reversed())
 }
 ```  
 
@@ -160,7 +160,7 @@ This backtracks from `matrix[n+1][m+1]` (bottom-right corner) to `matrix[1][1]`
 
 The `charInSequence` variable is an index into the string given by `self`. Initially this points to the last character of the string. Each time we decrement `i`, we also move back `charInSequence`. When the two characters are found to be equal, we add the character at `self[charInSequence]` to the new `lcs` string. (We can't just write `self[i]` because `i` may not map to the current position inside the Swift string.)
 
-Due to backtracking, characters are added in reverse order, so at the end of the function we call `reverse()` to put the string in the right order. (Appending new characters to the end of the string and then reversing it once is faster than always inserting the characters at the front of the string.)
+Due to backtracking, characters are added in reverse order, so at the end of the function we call `reversed()` to put the string in the right order. (Appending new characters to the end of the string and then reversing it once is faster than always inserting the characters at the front of the string.)
 
 ## Putting it all together
 

From 67a2659ac972779ff7d410bcb0783375699cc5d9 Mon Sep 17 00:00:00 2001
From: Eric Yulianto <eric.yulianto.ang@gmail.com>
Date: Sun, 16 Oct 2016 01:58:14 +0800
Subject: [PATCH 0599/1679] Migrated Topological Sort to Swift 3

---
 .travis.yml                                            |  2 +-
 Topological Sort/Graph.swift                           |  2 +-
 Topological Sort/Tests/Tests.xcodeproj/project.pbxproj | 10 +++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme              |  2 +-
 Topological Sort/Tests/TopologicalSortTests.swift      | 10 +++++-----
 .../Topological Sort.playground/Sources/Graph.swift    |  2 +-
 .../Sources/TopologicalSort1.swift                     |  4 ++--
 .../Sources/TopologicalSort3.swift                     |  8 ++++----
 Topological Sort/TopologicalSort1.swift                |  4 ++--
 Topological Sort/TopologicalSort3.swift                |  8 ++++----
 10 files changed, 30 insertions(+), 22 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 949fc759f..a495ecde6 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -38,4 +38,4 @@ script:
 # - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Topological Sort/Graph.swift b/Topological Sort/Graph.swift
index 173676537..1e1be6919 100644
--- a/Topological Sort/Graph.swift	
+++ b/Topological Sort/Graph.swift	
@@ -7,7 +7,7 @@ public class Graph: CustomStringConvertible {
     adjacencyLists = [Node : [Node]]()
   }
 
-  public func addNode(value: Node) -> Node {
+  public func addNode(_ value: Node) -> Node {
     adjacencyLists[value] = []
     return value
   }
diff --git a/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj b/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj
index 83c59dbab..f97ffdc69 100644
--- a/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Topological Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -92,11 +92,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -157,8 +158,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -201,8 +204,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -221,6 +226,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -232,6 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -243,6 +250,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..14f27f777 100644
--- a/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Topological Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Topological Sort/Tests/TopologicalSortTests.swift b/Topological Sort/Tests/TopologicalSortTests.swift
index 5acdcf2ae..939f15fae 100644
--- a/Topological Sort/Tests/TopologicalSortTests.swift	
+++ b/Topological Sort/Tests/TopologicalSortTests.swift	
@@ -2,9 +2,9 @@ import Foundation
 import XCTest
 
 extension Graph {
-  public func loadEdgeList(lines: [String]) {
+  public func loadEdgeList(_ lines: [String]) {
     for line in lines {
-      let items = line.componentsSeparatedByString(" ").filter { s in !s.isEmpty }
+      let items = line.components(separatedBy: " ").filter { s in !s.isEmpty }
       if adjacencyList(forNode: items[0]) == nil {
         addNode(items[0])
       }
@@ -20,10 +20,10 @@ class TopologicalSort: XCTestCase {
 
   // The topological sort is valid if a node does not have any of its
   // predecessors in its adjacency list.
-  func checkIsValidTopologicalSort(graph: Graph, _ a: [Graph.Node]) {
-    for i in (a.count - 1).stride(to: 0, by: -1) {
+  func checkIsValidTopologicalSort(_ graph: Graph, _ a: [Graph.Node]) {
+    for i in stride(from: (a.count - 1), to: 0, by: -1) {
       if let neighbors = graph.adjacencyList(forNode: a[i]) {
-        for j in (i - 1).stride(through: 0, by: -1) {
+        for j in stride(from: (i - 1), through: 0, by: -1) {
           XCTAssertFalse(neighbors.contains(a[j]), "\(a) is not a valid topological sort")
         }
       }
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index 173676537..1e1be6919 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -7,7 +7,7 @@ public class Graph: CustomStringConvertible {
     adjacencyLists = [Node : [Node]]()
   }
 
-  public func addNode(value: Node) -> Node {
+  public func addNode(_ value: Node) -> Node {
     adjacencyLists[value] = []
     return value
   }
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index 7f1aca5e7..0f9566f6a 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -1,10 +1,10 @@
 extension Graph {
-  private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
+  private func depthFirstSearch(_ source: Node, visited: inout [Node : Bool]) -> [Node] {
     var result = [Node]()
 
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
-        if let seen = visited[nodeInAdjacencyList] where !seen {
+        if let seen = visited[nodeInAdjacencyList], !seen {
           result = depthFirstSearch(nodeInAdjacencyList, visited: &visited) + result
         }
       }
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift
index cdc479b41..3d4a2bbbc 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort3.swift	
@@ -12,10 +12,10 @@ extension Graph {
       visited[node] = false
     }
 
-    func depthFirstSearch(source: Node) {
+    func depthFirstSearch(_ source: Node) {
       if let adjacencyList = adjacencyList(forNode: source) {
         for neighbor in adjacencyList {
-          if let seen = visited[neighbor] where !seen {
+          if let seen = visited[neighbor], !seen {
             depthFirstSearch(neighbor)
           }
         }
@@ -25,11 +25,11 @@ extension Graph {
     }
 
     for (node, _) in visited {
-      if let seen = visited[node] where !seen {
+      if let seen = visited[node], !seen {
         depthFirstSearch(node)
       }
     }
 
-    return stack.reverse()
+    return stack.reversed()
   }
 }
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 7f1aca5e7..0f9566f6a 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -1,10 +1,10 @@
 extension Graph {
-  private func depthFirstSearch(source: Node, inout visited: [Node : Bool]) -> [Node] {
+  private func depthFirstSearch(_ source: Node, visited: inout [Node : Bool]) -> [Node] {
     var result = [Node]()
 
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
-        if let seen = visited[nodeInAdjacencyList] where !seen {
+        if let seen = visited[nodeInAdjacencyList], !seen {
           result = depthFirstSearch(nodeInAdjacencyList, visited: &visited) + result
         }
       }
diff --git a/Topological Sort/TopologicalSort3.swift b/Topological Sort/TopologicalSort3.swift
index cdc479b41..3d4a2bbbc 100644
--- a/Topological Sort/TopologicalSort3.swift	
+++ b/Topological Sort/TopologicalSort3.swift	
@@ -12,10 +12,10 @@ extension Graph {
       visited[node] = false
     }
 
-    func depthFirstSearch(source: Node) {
+    func depthFirstSearch(_ source: Node) {
       if let adjacencyList = adjacencyList(forNode: source) {
         for neighbor in adjacencyList {
-          if let seen = visited[neighbor] where !seen {
+          if let seen = visited[neighbor], !seen {
             depthFirstSearch(neighbor)
           }
         }
@@ -25,11 +25,11 @@ extension Graph {
     }
 
     for (node, _) in visited {
-      if let seen = visited[node] where !seen {
+      if let seen = visited[node], !seen {
         depthFirstSearch(node)
       }
     }
 
-    return stack.reverse()
+    return stack.reversed()
   }
 }

From dc2b5ba3c19d9733efa3f97eb450d86fc9fea4ca Mon Sep 17 00:00:00 2001
From: Steven Chen <Chen.steven.yu@gmail.com>
Date: Mon, 17 Oct 2016 15:03:11 -0500
Subject: [PATCH 0600/1679] Update to Swift 3.0

---
 Shell Sort/Tests/Tests.xcodeproj/project.pbxproj | 3 +++
 Shell Sort/shellsort.swift                       | 6 +++---
 2 files changed, 6 insertions(+), 3 deletions(-)

diff --git a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj
index 9f7f4391e..1de1c7213 100644
--- a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -91,6 +91,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
 					};
 				};
 			};
@@ -224,6 +225,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +237,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Shell Sort/shellsort.swift b/Shell Sort/shellsort.swift
index 489a92ebc..0740272fc 100644
--- a/Shell Sort/shellsort.swift	
+++ b/Shell Sort/shellsort.swift	
@@ -20,8 +20,8 @@
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.
 
-public func insertionSort(inout list: [Int], start: Int, gap: Int) {
-  for i in (start + gap).stride(to: list.count, by: gap) {
+public func insertionSort(_ list: inout [Int], start: Int, gap: Int) {
+  for i in stride(from: (start + gap), to: list.count, by: gap) {
     let currentValue = list[i]
     var pos = i
     while pos >= gap && list[pos - gap] > currentValue {
@@ -32,7 +32,7 @@ public func insertionSort(inout list: [Int], start: Int, gap: Int) {
   }
 }
 
-public func shellSort(inout list: [Int]) {
+public func shellSort(_ list: inout [Int]) {
   var sublistCount = list.count / 2
   while sublistCount > 0 {
     for pos in 0..<sublistCount {

From 4e46a8b1d99865c75cad255b7e5d2a571f5bf0db Mon Sep 17 00:00:00 2001
From: Janie Clayton <janie.k.clayton@gmail.com>
Date: Mon, 17 Oct 2016 19:58:29 -0500
Subject: [PATCH 0601/1679] Added public init and array init

I added a public init so this can be used in a Playground. I also added
an extension to create a linked list from an array of values.
---
 Linked List/LinkedList.playground/Contents.swift | 10 ++++++++++
 Linked List/LinkedList.swift                     | 14 +++++++++++++-
 2 files changed, 23 insertions(+), 1 deletion(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index e73f89518..a90b7180c 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -187,6 +187,16 @@ extension LinkedList {
   }
 }
 
+extension LinkedList {
+  convenience init(array: Array<T>) {
+    self.init()
+        
+    for element in array {
+      self.append(element)
+    }
+  }
+}
+
 let list = LinkedList<String>()
 list.isEmpty                  // true
 list.first                    // nil
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 49f1c0915..86d2bca9b 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -12,7 +12,9 @@ public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
   
   fileprivate var head: Node?
-  
+    
+  public init() {}
+    
   public var isEmpty: Bool {
     return head == nil
   }
@@ -184,3 +186,13 @@ extension LinkedList {
     return result
   }
 }
+
+extension LinkedList {
+  convenience init(array: Array<T>) {
+    self.init()
+        
+    for element in array {
+      self.append(element)
+    }
+  }
+}

From 133f2d85b0fa188da954c837381570efd263a5ec Mon Sep 17 00:00:00 2001
From: Sahn Cha <schalin@gmail.com>
Date: Tue, 18 Oct 2016 23:35:15 +0900
Subject: [PATCH 0602/1679] Miller-Rabin primality test: probabilistic version

---
 Miller-Rabin Primality Test/MRPrimality.swift | 61 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  7 +++
 2 files changed, 68 insertions(+)
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.swift

diff --git a/Miller-Rabin Primality Test/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.swift
new file mode 100644
index 000000000..8be5ab00d
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.swift	
@@ -0,0 +1,61 @@
+//
+//  MRPrimality.swift
+//  
+//
+//  Created by Sahn Cha on 2016. 10. 18..
+//
+//
+
+import Foundation
+
+public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
+  guard n > 2 && n % 2 == 1 else { return false }
+  
+  var d = n - 1
+  var s = 0
+  
+  while d % 2 == 0 {
+    d /= 2
+    s += 1
+  }
+  
+  let range = UInt64.max - UInt64.max % (n - 2)
+  var r: UInt64 = 0
+  
+  repeat {
+    arc4random_buf(&r, MemoryLayout.size(ofValue: r))
+  } while r >= range
+  
+  r = r % (n - 2) + 2
+  
+  for _ in 1 ... k {
+    var x = modpow64(r, d, n)
+    if x == 1 || x == n - 1 { continue }
+    
+    for _ in 1 ... s - 1 {
+      x = modpow64(x, 2, n)
+      if x == 1 { return false }
+      if x == n - 1 { break }
+    }
+    
+    if x != n - 1 { return false }
+  }
+  return true
+}
+
+private func modpow64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
+  if m == 1 { return 0 }
+  
+  var result: UInt64 = 1
+  var b = base % m
+  var e = exp
+  
+  while e > 0 {
+    if e % 2 == 1 {
+      result = (result * b) % m
+    }
+    e >>= 1
+    b = (b * b) % m
+  }
+  return result
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index e7288f299..fb2aeda4b 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -25,6 +25,13 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "group:Miller-Rabin Primality Test"
+      name = "Miller-Rabin Primality Test">
+      <FileRef
+         location = "group:MRPrimality.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:All-Pairs Shortest Paths"
       name = "All-Pairs Shortest Paths">

From 902e6f6a4a9ec8780029e1c9f8277f9b86841948 Mon Sep 17 00:00:00 2001
From: Sahn Cha <schalin@gmail.com>
Date: Thu, 20 Oct 2016 02:09:45 +0900
Subject: [PATCH 0603/1679] Now with playground, comments and pesticide

---
 .../MRPrimality.playground/Contents.swift     |  24 ++++
 .../Sources/MRPrimality.swift                 | 111 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 Miller-Rabin Primality Test/MRPrimality.swift |  66 +++++++++--
 .../contents.xcworkspacedata                  |   3 +
 5 files changed, 200 insertions(+), 8 deletions(-)
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/contents.xcplayground

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
new file mode 100644
index 000000000..8d97dc409
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -0,0 +1,24 @@
+//: Playground - noun: a place where people can play
+
+// Real primes
+mrPrimalityTest(5)
+mrPrimalityTest(439)
+mrPrimalityTest(1201)
+mrPrimalityTest(143477)
+mrPrimalityTest(1299869)
+mrPrimalityTest(15487361)
+mrPrimalityTest(179426363)
+mrPrimalityTest(32416187747)
+
+// Fake primes
+mrPrimalityTest(15)
+mrPrimalityTest(435)
+mrPrimalityTest(1207)
+mrPrimalityTest(143473)
+mrPrimalityTest(1291869)
+mrPrimalityTest(15487161)
+mrPrimalityTest(178426363)
+mrPrimalityTest(32415187747)
+
+// With iteration
+mrPrimalityTest(32416190071, iteration: 10)
\ No newline at end of file
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
new file mode 100644
index 000000000..9dca23996
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
@@ -0,0 +1,111 @@
+//
+//  MRPrimality.swift
+//  
+//
+//  Created by Sahn Cha on 2016. 10. 18..
+//
+//
+
+import Foundation
+
+/*
+  Miller-Rabin Primality Test.
+  One of the most used algorithms for primality testing.
+  Since this is a probabilistic algorithm, it needs to be executed multiple times to increase accuracy.
+  
+  Inputs:
+    n: UInt64 { target integer to be tested for primality }
+    k: Int    { optional. number of iterations }
+ 
+  Outputs:
+    true      { probably prime }
+    false     { composite }
+ */
+public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
+  guard n > 2 && n % 2 == 1 else { return false }
+  
+  var d = n - 1
+  var s = 0
+  
+  while d % 2 == 0 {
+    d /= 2
+    s += 1
+  }
+  
+  let range = UInt64.max - UInt64.max % (n - 2)
+  var r: UInt64 = 0
+  repeat {
+    arc4random_buf(&r, MemoryLayout.size(ofValue: r))
+  } while r >= range
+  
+  r = r % (n - 2) + 2
+  
+  for _ in 1 ... k {
+    var x = powmod64(r, d, n)
+    if x == 1 || x == n - 1 { continue }
+    
+    if s == 1 { s = 2 }
+    
+    for _ in 1 ... s - 1 {
+      x = powmod64(x, 2, n)
+      if x == 1 { return false }
+      if x == n - 1 { break }
+    }
+    
+    if x != n - 1 { return false }
+  }
+  
+  return true
+}
+
+/*
+  Calculates (base^exp) mod m.
+ 
+  Inputs:
+    base: UInt64  { base }
+    exp: UInt64   { exponent }
+    m: UInt64     { modulus }
+ 
+  Outputs:
+    the result
+ */
+private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
+  if m == 1 { return 0 }
+  
+  var result: UInt64 = 1
+  var b = base % m
+  var e = exp
+  
+  while e > 0 {
+    if e % 2 == 1 { result = mulmod64(result, b, m) }
+    b = mulmod64(b, b, m)
+    e >>= 1
+  }
+  
+  return result
+}
+
+/*
+  Calculates (first * second) mod m, hopefully without overflow. :]
+ 
+  Inputs:
+    first: UInt64   { first integer }
+    second: UInt64  { second integer }
+    m: UInt64       { modulus }
+ 
+  Outputs:
+    the result
+ */
+private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64 {
+  var result: UInt64 = 0
+  var a = first
+  var b = second
+  
+  while a != 0 {
+    if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
+    a >>= 1
+    b = (b << 1) % m
+  }
+  
+  return result
+}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/contents.xcplayground b/Miller-Rabin Primality Test/MRPrimality.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Miller-Rabin Primality Test/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.swift
index 8be5ab00d..9dca23996 100644
--- a/Miller-Rabin Primality Test/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.swift	
@@ -8,6 +8,19 @@
 
 import Foundation
 
+/*
+  Miller-Rabin Primality Test.
+  One of the most used algorithms for primality testing.
+  Since this is a probabilistic algorithm, it needs to be executed multiple times to increase accuracy.
+  
+  Inputs:
+    n: UInt64 { target integer to be tested for primality }
+    k: Int    { optional. number of iterations }
+ 
+  Outputs:
+    true      { probably prime }
+    false     { composite }
+ */
 public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
   guard n > 2 && n % 2 == 1 else { return false }
   
@@ -21,7 +34,6 @@ public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
   
   let range = UInt64.max - UInt64.max % (n - 2)
   var r: UInt64 = 0
-  
   repeat {
     arc4random_buf(&r, MemoryLayout.size(ofValue: r))
   } while r >= range
@@ -29,21 +41,35 @@ public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
   r = r % (n - 2) + 2
   
   for _ in 1 ... k {
-    var x = modpow64(r, d, n)
+    var x = powmod64(r, d, n)
     if x == 1 || x == n - 1 { continue }
     
+    if s == 1 { s = 2 }
+    
     for _ in 1 ... s - 1 {
-      x = modpow64(x, 2, n)
+      x = powmod64(x, 2, n)
       if x == 1 { return false }
       if x == n - 1 { break }
     }
     
     if x != n - 1 { return false }
   }
+  
   return true
 }
 
-private func modpow64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
+/*
+  Calculates (base^exp) mod m.
+ 
+  Inputs:
+    base: UInt64  { base }
+    exp: UInt64   { exponent }
+    m: UInt64     { modulus }
+ 
+  Outputs:
+    the result
+ */
+private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
   if m == 1 { return 0 }
   
   var result: UInt64 = 1
@@ -51,11 +77,35 @@ private func modpow64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
   var e = exp
   
   while e > 0 {
-    if e % 2 == 1 {
-      result = (result * b) % m
-    }
+    if e % 2 == 1 { result = mulmod64(result, b, m) }
+    b = mulmod64(b, b, m)
     e >>= 1
-    b = (b * b) % m
   }
+  
+  return result
+}
+
+/*
+  Calculates (first * second) mod m, hopefully without overflow. :]
+ 
+  Inputs:
+    first: UInt64   { first integer }
+    second: UInt64  { second integer }
+    m: UInt64       { modulus }
+ 
+  Outputs:
+    the result
+ */
+private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64 {
+  var result: UInt64 = 0
+  var a = first
+  var b = second
+  
+  while a != 0 {
+    if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
+    a >>= 1
+    b = (b << 1) % m
+  }
+  
   return result
 }
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index fb2aeda4b..dd0c6b668 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -31,6 +31,9 @@
       <FileRef
          location = "group:MRPrimality.swift">
       </FileRef>
+      <FileRef
+         location = "group:MRPrimality.playground">
+      </FileRef>
    </Group>
    <Group
       location = "group:All-Pairs Shortest Paths"

From 26cb9d12d544e3efe506dcec8c680ba90927c01c Mon Sep 17 00:00:00 2001
From: Bill Barbour <bill.barbour@oracle.com>
Date: Thu, 20 Oct 2016 10:03:44 -0400
Subject: [PATCH 0604/1679] Switched to Double to handle large prime multiplier

---
 README.markdown                               |   2 +-
 Rabin-Karp/README.markdown                    |  79 ++++++++++++++
 .../Rabin-Karp.playground/Contents.swift      |  85 +++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 ++
 Rabin-Karp/rabin-karp.swift                   | 103 ++++++++++++++++++
 6 files changed, 279 insertions(+), 1 deletion(-)
 create mode 100644 Rabin-Karp/README.markdown
 create mode 100644 Rabin-Karp/Rabin-Karp.playground/Contents.swift
 create mode 100644 Rabin-Karp/Rabin-Karp.playground/contents.xcplayground
 create mode 100644 Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Rabin-Karp/rabin-karp.swift

diff --git a/README.markdown b/README.markdown
index 28a56dfd3..1bf9e7e6a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -56,7 +56,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Brute-Force String Search](Brute-Force String Search/). A naive method.
 - [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
 - Knuth-Morris-Pratt
-- Rabin-Karp
+- [Rabin-Karp](Rabin-Karp/)  Faster search by using hashing.
 - [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
 
 ### Sorting
diff --git a/Rabin-Karp/README.markdown b/Rabin-Karp/README.markdown
new file mode 100644
index 000000000..0c3d0b1be
--- /dev/null
+++ b/Rabin-Karp/README.markdown
@@ -0,0 +1,79 @@
+# Rabin-Karp string search algorithm
+
+The Rabin-Karp string search alogrithm is used to search text for a pattern.
+
+Algorithms that check for palindromes are a common programming interview question.
+
+## Example
+
+Given a text of "The big dog jumped over the fox" and a search pattern of "ump" this will return 13.
+It starts by hashing "ump" then hashing "The".  If hashed don't match then it slides the window a character
+at a time (e.g. "he ") and subtracts out the previous hash from the "T".
+
+## Algorithm
+
+The Rabin-Karp alogrithm uses a sliding window the size of the search pattern.  It starts by hashing the search pattern, then
+hashing the first x characters of the text string where x is the length of the search pattern.  It then slides the window one character over and uses
+the previous hash value to calculate the new hash faster.  Only when it finds a hash that matches the hash of the search pattern will it compare
+the two strings it see if they are the same (prevent a hash collision from producing a false positive)
+
+## The code
+
+The major search method is next.  More implementation details are in rabin-karp.swift
+
+```swift
+public func search(text: String , pattern: String) -> Int {
+    // convert to array of ints
+    let patternArray = pattern.characters.flatMap { $0.asInt }
+    let textArray = text.characters.flatMap { $0.asInt }
+
+    if textArray.count < patternArray.count {
+        return -1
+    }
+
+    let patternHash = hash(array: patternArray)
+    var endIdx = patternArray.count - 1
+    let firstChars = Array(textArray[0...endIdx])
+    let firstHash = hash(array: firstChars)
+
+    if (patternHash == firstHash) {
+        // Verify this was not a hash collison
+        if firstChars == patternArray {
+            return 0
+        }
+    }
+
+    var prevHash = firstHash
+    // Now slide the window across the text to be searched
+    for idx in 1...(textArray.count - patternArray.count) {
+        endIdx = idx + (patternArray.count - 1)
+        let window = Array(textArray[idx...endIdx])
+        let windowHash = nextHash(prevHash: prevHash, dropped: textArray[idx - 1], added: textArray[endIdx], patternSize: patternArray.count - 1)
+
+        if windowHash == patternHash {
+            if patternArray == window {
+                return idx
+            }
+        }
+
+        prevHash = windowHash
+    }
+
+    return -1
+}
+```
+
+This code can be tested in a playground using the following:
+
+```swift
+  search(text: "The big dog jumped"", "ump")
+```
+
+This will return 13 since ump is in the 13 position of the zero based string.
+
+## Additional Resources
+
+[Rabin-Karp Wikipedia](https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm)
+
+
+*Written by [Bill Barbour](https://github.com/brbatwork)*
\ No newline at end of file
diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
new file mode 100644
index 000000000..f9c8c1919
--- /dev/null
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -0,0 +1,85 @@
+//: Taking our rabin-karp algorithm for a walk
+
+import UIKit
+
+struct Constants {
+    static let hashMultiplier = 69069
+}
+
+precedencegroup PowerPrecedence { higherThan: MultiplicationPrecedence }
+infix operator ** : PowerPrecedence
+func ** (radix: Int, power: Int) -> Int {
+    return Int(pow(Double(radix), Double(power)))
+}
+func ** (radix: Double, power: Int) -> Double {
+    return pow(radix, Double(power))
+}
+
+extension Character {
+    var asInt:Int {
+        let s = String(self).unicodeScalars
+        return Int(s[s.startIndex].value)
+    }
+}
+
+// Find first position of pattern in the text using Rabin Karp algorithm
+public func search(text: String , pattern: String) -> Int {
+    // convert to array of ints
+    let patternArray = pattern.characters.flatMap { $0.asInt }
+    let textArray = text.characters.flatMap { $0.asInt }
+    
+    if textArray.count < patternArray.count {
+        return -1
+    }
+    
+    let patternHash = hash(array: patternArray)
+    var endIdx = patternArray.count - 1
+    let firstChars = Array(textArray[0...endIdx])
+    let firstHash = hash(array: firstChars)
+    
+    if (patternHash == firstHash) {
+        // Verify this was not a hash collison
+        if firstChars == patternArray {
+            return 0
+        }
+    }
+    
+    var prevHash = firstHash
+    // Now slide the window across the text to be searched
+    for idx in 1...(textArray.count - patternArray.count) {
+        endIdx = idx + (patternArray.count - 1)
+        let window = Array(textArray[idx...endIdx])
+        let windowHash = nextHash(prevHash: prevHash, dropped: textArray[idx - 1], added: textArray[endIdx], patternSize: patternArray.count - 1)
+        
+        if windowHash == patternHash {
+            if patternArray == window {
+                return idx
+            }
+        }
+        
+        prevHash = windowHash
+    }
+    
+    return -1
+}
+
+public func hash(array: Array<Int>) -> Double {
+    var total : Double = 0
+    var exponent = array.count - 1
+    for i in array {
+        total += Double(i) * (Double(Constants.hashMultiplier) ** exponent)
+        exponent -= 1
+    }
+    
+    return Double(total)
+}
+
+public func nextHash(prevHash: Double, dropped: Int, added: Int, patternSize: Int) -> Double {
+    let oldHash = prevHash - (Double(dropped) * (Double(Constants.hashMultiplier) ** patternSize))
+    return Double(Constants.hashMultiplier) * oldHash + Double(added)
+}
+
+// TESTS
+assert(search(text:"The big dog jumped over the fox", pattern:"ump") == 13, "Invalid index returned")
+assert(search(text:"The big dog jumped over the fox", pattern:"missed") == Int(-1), "Invalid index returned")
+assert(search(text:"The big dog jumped over the fox", pattern:"T") == 0, "Invalid index returned")
diff --git a/Rabin-Karp/Rabin-Karp.playground/contents.xcplayground b/Rabin-Karp/Rabin-Karp.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Rabin-Karp/Rabin-Karp.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/contents.xcworkspacedata b/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Rabin-Karp/rabin-karp.swift b/Rabin-Karp/rabin-karp.swift
new file mode 100644
index 000000000..54ef24fce
--- /dev/null
+++ b/Rabin-Karp/rabin-karp.swift
@@ -0,0 +1,103 @@
+// The MIT License (MIT)
+
+// Copyright (c) 2016 Bill Barbour (brbatwork[at]gmail.com)
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+struct Constants {
+    static let hashMultiplier = 69069
+}
+
+precedencegroup PowerPrecedence { higherThan: MultiplicationPrecedence }
+infix operator ** : PowerPrecedence
+func ** (radix: Int, power: Int) -> Int {
+    return Int(pow(Double(radix), Double(power)))
+}
+func ** (radix: Double, power: Int) -> Double {
+    return pow(radix, Double(power))
+}
+
+extension Character {
+    var asInt:Int {
+        let s = String(self).unicodeScalars
+        return Int(s[s.startIndex].value)
+    }
+}
+
+// Find first position of pattern in the text using Rabin Karp algorithm
+public func search(text: String , pattern: String) -> Int {
+    // convert to array of ints
+    let patternArray = pattern.characters.flatMap { $0.asInt }
+    let textArray = text.characters.flatMap { $0.asInt }
+
+    if textArray.count < patternArray.count {
+        return -1
+    }
+
+    let patternHash = hash(array: patternArray)
+    var endIdx = patternArray.count - 1
+    let firstChars = Array(textArray[0...endIdx])
+    let firstHash = hash(array: firstChars)
+
+    if (patternHash == firstHash) {
+        // Verify this was not a hash collison
+        if firstChars == patternArray {
+            return 0
+        }
+    }
+
+    var prevHash = firstHash
+    // Now slide the window across the text to be searched
+    for idx in 1...(textArray.count - patternArray.count) {
+        endIdx = idx + (patternArray.count - 1)
+        let window = Array(textArray[idx...endIdx])
+        let windowHash = nextHash(prevHash: prevHash, dropped: textArray[idx - 1], added: textArray[endIdx], patternSize: patternArray.count - 1)
+
+        if windowHash == patternHash {
+            if patternArray == window {
+                return idx
+            }
+        }
+
+        prevHash = windowHash
+    }
+
+    return -1
+}
+
+public func hash(array: Array<Int>) -> Double {
+    var total : Double = 0
+    var exponent = array.count - 1
+    for i in array {
+        total += Double(i) * (Double(Constants.hashMultiplier) ** exponent)
+        exponent -= 1
+    }
+
+    return Double(total)
+}
+
+public func nextHash(prevHash: Double, dropped: Int, added: Int, patternSize: Int) -> Double {
+    let oldHash = prevHash - (Double(dropped) * (Double(Constants.hashMultiplier) ** patternSize))
+    return Double(Constants.hashMultiplier) * oldHash + Double(added)
+}
+
+// TESTS
+assert(search(text:"The big dog jumped over the fox", pattern:"ump") == 13, "Invalid index returned")
+assert(search(text:"The big dog jumped over the fox", pattern:"missed") == -1, "Invalid index returned")
+assert(search(text:"The big dog jumped over the fox", pattern:"T") == 0, "Invalid index returned")
\ No newline at end of file

From 4813ee12dcd26489ab10176694829a6c1d98c669 Mon Sep 17 00:00:00 2001
From: billbarbour <bill@barbour.us>
Date: Thu, 20 Oct 2016 11:27:13 -0400
Subject: [PATCH 0605/1679] Corrected copy pasta

---
 Rabin-Karp/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Rabin-Karp/README.markdown b/Rabin-Karp/README.markdown
index 0c3d0b1be..79699caa8 100644
--- a/Rabin-Karp/README.markdown
+++ b/Rabin-Karp/README.markdown
@@ -2,7 +2,7 @@
 
 The Rabin-Karp string search alogrithm is used to search text for a pattern.
 
-Algorithms that check for palindromes are a common programming interview question.
+A practical application of the algorithm is detecting plagiarism. Given source material, the algorithm can rapidly search through a paper for instances of sentences from the source material, ignoring details such as case and punctuation. Because of the abundance of the sought strings, single-string searching algorithms are impractical.
 
 ## Example
 

From 663f902de3b1066c9c8bfc93bdbc05836d05fb02 Mon Sep 17 00:00:00 2001
From: billbarbour <bill@barbour.us>
Date: Thu, 20 Oct 2016 11:56:09 -0400
Subject: [PATCH 0606/1679] linter cleanup

---
 .../Rabin-Karp.playground/Contents.swift      | 45 ++++++++++++-------
 Rabin-Karp/rabin-karp.swift                   | 29 ++++++++----
 2 files changed, 48 insertions(+), 26 deletions(-)

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index f9c8c1919..4956fabe3 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -16,70 +16,81 @@ func ** (radix: Double, power: Int) -> Double {
 }
 
 extension Character {
-    var asInt:Int {
+    var asInt: Int {
         let s = String(self).unicodeScalars
         return Int(s[s.startIndex].value)
     }
 }
 
 // Find first position of pattern in the text using Rabin Karp algorithm
-public func search(text: String , pattern: String) -> Int {
+public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
     let patternArray = pattern.characters.flatMap { $0.asInt }
     let textArray = text.characters.flatMap { $0.asInt }
-    
+
     if textArray.count < patternArray.count {
         return -1
     }
-    
+
     let patternHash = hash(array: patternArray)
     var endIdx = patternArray.count - 1
     let firstChars = Array(textArray[0...endIdx])
     let firstHash = hash(array: firstChars)
-    
-    if (patternHash == firstHash) {
+
+    if patternHash == firstHash {
         // Verify this was not a hash collison
         if firstChars == patternArray {
             return 0
         }
     }
-    
+
     var prevHash = firstHash
     // Now slide the window across the text to be searched
     for idx in 1...(textArray.count - patternArray.count) {
         endIdx = idx + (patternArray.count - 1)
         let window = Array(textArray[idx...endIdx])
-        let windowHash = nextHash(prevHash: prevHash, dropped: textArray[idx - 1], added: textArray[endIdx], patternSize: patternArray.count - 1)
-        
+        let windowHash = nextHash(
+          prevHash: prevHash,
+          dropped: textArray[idx - 1],
+          added: textArray[endIdx],
+          patternSize: patternArray.count - 1
+        )
+
         if windowHash == patternHash {
             if patternArray == window {
                 return idx
             }
         }
-        
+
         prevHash = windowHash
     }
-    
+
     return -1
 }
 
 public func hash(array: Array<Int>) -> Double {
-    var total : Double = 0
+    var total: Double = 0
     var exponent = array.count - 1
     for i in array {
         total += Double(i) * (Double(Constants.hashMultiplier) ** exponent)
         exponent -= 1
     }
-    
+
     return Double(total)
 }
 
 public func nextHash(prevHash: Double, dropped: Int, added: Int, patternSize: Int) -> Double {
-    let oldHash = prevHash - (Double(dropped) * (Double(Constants.hashMultiplier) ** patternSize))
+    let oldHash = prevHash - (Double(dropped) *
+      (Double(Constants.hashMultiplier) ** patternSize))
     return Double(Constants.hashMultiplier) * oldHash + Double(added)
 }
 
 // TESTS
-assert(search(text:"The big dog jumped over the fox", pattern:"ump") == 13, "Invalid index returned")
-assert(search(text:"The big dog jumped over the fox", pattern:"missed") == Int(-1), "Invalid index returned")
-assert(search(text:"The big dog jumped over the fox", pattern:"T") == 0, "Invalid index returned")
+assert(search(text:"The big dog jumped over the fox",
+  pattern:"ump") == 13, "Invalid index returned")
+
+assert(search(text:"The big dog jumped over the fox",
+  pattern:"missed") == -1, "Invalid index returned")
+
+assert(search(text:"The big dog jumped over the fox",
+  pattern:"T") == 0, "Invalid index returned")
diff --git a/Rabin-Karp/rabin-karp.swift b/Rabin-Karp/rabin-karp.swift
index 54ef24fce..c337de1a7 100644
--- a/Rabin-Karp/rabin-karp.swift
+++ b/Rabin-Karp/rabin-karp.swift
@@ -34,14 +34,14 @@ func ** (radix: Double, power: Int) -> Double {
 }
 
 extension Character {
-    var asInt:Int {
+    var asInt: Int {
         let s = String(self).unicodeScalars
         return Int(s[s.startIndex].value)
     }
 }
 
 // Find first position of pattern in the text using Rabin Karp algorithm
-public func search(text: String , pattern: String) -> Int {
+public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
     let patternArray = pattern.characters.flatMap { $0.asInt }
     let textArray = text.characters.flatMap { $0.asInt }
@@ -55,7 +55,7 @@ public func search(text: String , pattern: String) -> Int {
     let firstChars = Array(textArray[0...endIdx])
     let firstHash = hash(array: firstChars)
 
-    if (patternHash == firstHash) {
+    if patternHash == firstHash {
         // Verify this was not a hash collison
         if firstChars == patternArray {
             return 0
@@ -67,7 +67,12 @@ public func search(text: String , pattern: String) -> Int {
     for idx in 1...(textArray.count - patternArray.count) {
         endIdx = idx + (patternArray.count - 1)
         let window = Array(textArray[idx...endIdx])
-        let windowHash = nextHash(prevHash: prevHash, dropped: textArray[idx - 1], added: textArray[endIdx], patternSize: patternArray.count - 1)
+        let windowHash = nextHash(
+          prevHash: prevHash,
+          dropped: textArray[idx - 1],
+          added: textArray[endIdx],
+          patternSize: patternArray.count - 1
+        )
 
         if windowHash == patternHash {
             if patternArray == window {
@@ -82,7 +87,7 @@ public func search(text: String , pattern: String) -> Int {
 }
 
 public func hash(array: Array<Int>) -> Double {
-    var total : Double = 0
+    var total: Double = 0
     var exponent = array.count - 1
     for i in array {
         total += Double(i) * (Double(Constants.hashMultiplier) ** exponent)
@@ -93,11 +98,17 @@ public func hash(array: Array<Int>) -> Double {
 }
 
 public func nextHash(prevHash: Double, dropped: Int, added: Int, patternSize: Int) -> Double {
-    let oldHash = prevHash - (Double(dropped) * (Double(Constants.hashMultiplier) ** patternSize))
+    let oldHash = prevHash - (Double(dropped) *
+      (Double(Constants.hashMultiplier) ** patternSize))
     return Double(Constants.hashMultiplier) * oldHash + Double(added)
 }
 
 // TESTS
-assert(search(text:"The big dog jumped over the fox", pattern:"ump") == 13, "Invalid index returned")
-assert(search(text:"The big dog jumped over the fox", pattern:"missed") == -1, "Invalid index returned")
-assert(search(text:"The big dog jumped over the fox", pattern:"T") == 0, "Invalid index returned")
\ No newline at end of file
+assert(search(text:"The big dog jumped over the fox",
+  pattern:"ump") == 13, "Invalid index returned")
+
+assert(search(text:"The big dog jumped over the fox",
+  pattern:"missed") == -1, "Invalid index returned")
+
+assert(search(text:"The big dog jumped over the fox",
+  pattern:"T") == 0, "Invalid index returned")

From 182e51b1434ea3b8ecc3e94a1c6b5a7d2f21d0fe Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Fri, 21 Oct 2016 01:11:51 -0700
Subject: [PATCH 0607/1679] Updated README to show Slow sort, Karatsuba
 Manipulation, and Haversine Distance.

---
 .../KaratsubaMultiplication.playground/Contents.swift           | 1 -
 README.markdown                                                 | 2 ++
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 075f75098..bde8fd9f9 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -58,4 +58,3 @@ func karatsuba(_ num1: Int, by num2: Int) -> Int {
   
   return product
 }
-
diff --git a/README.markdown b/README.markdown
index 28a56dfd3..2acedd0fa 100644
--- a/README.markdown
+++ b/README.markdown
@@ -84,6 +84,7 @@ Special-purpose sorts:
 Bad sorting algorithms (don't use these!):
 
 - [Bubble Sort](Bubble Sort/)
+- [Slow Sort](Slow Sort/)
 
 ### Compression
 
@@ -101,6 +102,7 @@ Bad sorting algorithms (don't use these!):
 - [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
 - [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
 - Statistics
+- [Karatsuba Multiplication](Karatsuba Multiplication/). Another take on elementary multiplication.
 
 ### Machine learning
 

From 3947c6bff451b6d8724739ec9d3e157e481249bd Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Fri, 21 Oct 2016 13:38:55 +0200
Subject: [PATCH 0608/1679] migrate ring buffer to swift 3

---
 Ring Buffer/RingBuffer.playground/Contents.swift   | 14 +++++++-------
 .../RingBuffer.playground/timeline.xctimeline      |  6 ------
 2 files changed, 7 insertions(+), 13 deletions(-)
 delete mode 100644 Ring Buffer/RingBuffer.playground/timeline.xctimeline

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index a7522c366..29b9917a0 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -1,15 +1,15 @@
 //: Playground - noun: a place where people can play
 
 public struct RingBuffer<T> {
-  private var array: [T?]
-  private var readIndex = 0
-  private var writeIndex = 0
+  fileprivate var array: [T?]
+  fileprivate var readIndex = 0
+  fileprivate var writeIndex = 0
 
   public init(count: Int) {
-    array = [T?](count: count, repeatedValue: nil)
+    array = [T?](repeating: nil, count: count)
   }
 
-  public mutating func write(element: T) -> Bool {
+  public mutating func write(_ element: T) -> Bool {
     if !isFull {
       array[writeIndex % array.count] = element
       writeIndex += 1
@@ -29,7 +29,7 @@ public struct RingBuffer<T> {
     }
   }
 
-  private var availableSpaceForReading: Int {
+  fileprivate var availableSpaceForReading: Int {
     return writeIndex - readIndex
   }
 
@@ -37,7 +37,7 @@ public struct RingBuffer<T> {
     return availableSpaceForReading == 0
   }
 
-  private var availableSpaceForWriting: Int {
+  fileprivate var availableSpaceForWriting: Int {
     return array.count - availableSpaceForReading
   }
 
diff --git a/Ring Buffer/RingBuffer.playground/timeline.xctimeline b/Ring Buffer/RingBuffer.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ring Buffer/RingBuffer.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 8cb4917968ad3e70bf7f67aca78908f22ecc97cd Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Fri, 21 Oct 2016 13:45:33 +0200
Subject: [PATCH 0609/1679] migrate two sum problem to swift 3

---
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift   | 2 +-
 .../Solution 1/2Sum.playground/timeline.xctimeline          | 6 ------
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift   | 6 +++---
 3 files changed, 4 insertions(+), 10 deletions(-)
 delete mode 100644 Two-Sum Problem/Solution 1/2Sum.playground/timeline.xctimeline

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 11c95b96c..00ce05136 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,6 +1,6 @@
 //: Playground - noun: a place where people can play
 
-func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
+func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
 
   for i in 0 ..< a.count {
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/timeline.xctimeline b/Two-Sum Problem/Solution 1/2Sum.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Two-Sum Problem/Solution 1/2Sum.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index 1d6b0a9c8..9a555f0eb 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,6 +1,6 @@
 //: Playground - noun: a place where people can play
 
-func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
+func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
   var j = a.count - 1
 
@@ -9,9 +9,9 @@ func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
     if sum == k {
       return (i, j)
     } else if sum < k {
-      ++i
+      i += 1
     } else {
-      --j
+      j -= 1
     }
   }
   return nil

From 56a5fa6f0273efd3959292977db3d092f0d42524 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Fri, 21 Oct 2016 13:46:43 +0200
Subject: [PATCH 0610/1679] Removed duplicate swift files as these were already
 in the playground itself

---
 Two-Sum Problem/Solution 1/2Sum.swift | 22 ----------------------
 Two-Sum Problem/Solution 2/2Sum.swift | 21 ---------------------
 2 files changed, 43 deletions(-)
 delete mode 100644 Two-Sum Problem/Solution 1/2Sum.swift
 delete mode 100644 Two-Sum Problem/Solution 2/2Sum.swift

diff --git a/Two-Sum Problem/Solution 1/2Sum.swift b/Two-Sum Problem/Solution 1/2Sum.swift
deleted file mode 100644
index b3ef54790..000000000
--- a/Two-Sum Problem/Solution 1/2Sum.swift	
+++ /dev/null
@@ -1,22 +0,0 @@
-/*
-  Determines if there are any entries a[i] + a[j] == k in the array.
-  Returns a tuple with the indices of the first pair of elements that sum to k.
-
-  Uses a dictionary to store differences between the target and each element.
-  If any value in the dictionary equals an element in the array, they sum to k.
-
-  This is an O(n) solution.
-*/
-func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
-  var map = [Int: Int]()
-
-  for i in 0 ..< a.count {
-    if let newK = map[a[i]] {
-      return (newK, i)
-    } else {
-      map[k - a[i]] =  i
-    }
-  }
-
-  return nil  // if empty array or no entries sum to target k
-}
diff --git a/Two-Sum Problem/Solution 2/2Sum.swift b/Two-Sum Problem/Solution 2/2Sum.swift
deleted file mode 100644
index 184e23800..000000000
--- a/Two-Sum Problem/Solution 2/2Sum.swift	
+++ /dev/null
@@ -1,21 +0,0 @@
-/*
-  Determines if there are any entries a[i] + a[j] == k in the array.
-  This is an O(n) solution.
-  The array must be sorted for this to work!
-*/
-func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
-  var i = 0
-  var j = a.count - 1
-
-  while i < j {
-    let sum = a[i] + a[j]
-    if sum == k {
-      return (i, j)
-    } else if sum < k {
-      ++i
-    } else {
-      --j
-    }
-  }
-  return nil
-}

From 0227ee1a5ffaec264238cfb1ae21d0779ec12f57 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Fri, 21 Oct 2016 13:49:11 +0200
Subject: [PATCH 0611/1679] update readme

---
 Two-Sum Problem/README.markdown | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index e2e15d4c0..a20666efd 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -8,10 +8,10 @@ There are a variety of solutions to this problem (some better than others). The
 
 This solution uses a dictionary to store differences between each element in the array and the sum `k` that we're looking for. The dictionary also stores the indices of each element.
 
-With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum to `k`. 
+With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum to `k`.
 
 ```swift
-func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
+func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var dict = [Int: Int]()
 
   for i in 0 ..< a.count {
@@ -69,7 +69,7 @@ The running time of this algorithm is **O(n)** because it potentially may need t
 Here is the code in Swift:
 
 ```swift
-func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
+func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
   var j = a.count - 1
 
@@ -78,9 +78,9 @@ func twoSumProblem(a: [Int], k: Int) -> ((Int, Int))? {
     if sum == k {
       return (i, j)
     } else if sum < k {
-      ++i
+      i += 1
     } else {
-      --j
+      j -= 1
     }
   }
   return nil

From 6e281b957a2cee068ee55390dc7baad1f38779c5 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Fri, 21 Oct 2016 14:34:50 +0200
Subject: [PATCH 0612/1679] Migrate Graph to Swift3

---
 Graph/Graph.playground/Contents.swift         |  8 ++---
 Graph/Graph.playground/timeline.xctimeline    | 11 ++++++
 Graph/Graph.xcodeproj/project.pbxproj         | 12 ++++++-
 .../xcshareddata/xcschemes/Graph.xcscheme     |  2 +-
 .../xcschemes/GraphTests.xcscheme             |  2 +-
 Graph/Graph/AdjacencyListGraph.swift          | 36 ++++++++++---------
 Graph/Graph/AdjacencyMatrixGraph.swift        | 26 +++++++-------
 Graph/Graph/Edge.swift                        |  4 +--
 Graph/Graph/Graph.swift                       | 18 +++++-----
 Graph/Graph/Vertex.swift                      |  2 +-
 10 files changed, 70 insertions(+), 51 deletions(-)
 create mode 100644 Graph/Graph.playground/timeline.xctimeline

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index 4e6d98a11..77de8484b 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,11 +1,7 @@
 import Graph
 
-// Create the vertices
-var adjacencyMatrixGraph = AdjacencyMatrixGraph<Int>()
-var adjacencyListGraph = AdjacencyListGraph<Int>()
-
-for graph in [ adjacencyMatrixGraph, adjacencyListGraph ] {
-
+for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
+    
   let v1 = graph.createVertex(1)
   let v2 = graph.createVertex(2)
   let v3 = graph.createVertex(3)
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph.playground/timeline.xctimeline
new file mode 100644
index 000000000..688276d32
--- /dev/null
+++ b/Graph/Graph.playground/timeline.xctimeline
@@ -0,0 +1,11 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=12&amp;CharacterRangeLoc=1238&amp;EndingColumnNumber=15&amp;EndingLineNumber=38&amp;StartingColumnNumber=3&amp;StartingLineNumber=38&amp;Timestamp=498745868.545441"
+         selectedRepresentationIndex = "1"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>
diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index 0157eb377..82a5f2377 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -158,11 +158,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0730;
+				LastUpgradeCheck = 0800;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					49BFA2FC1CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
+						LastSwiftMigration = 0800;
 					};
 					49BFA3061CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
@@ -250,8 +251,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -298,8 +301,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -319,6 +324,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -328,6 +334,7 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				CLANG_ENABLE_MODULES = YES;
+				CODE_SIGN_IDENTITY = "";
 				COMBINE_HIDPI_IMAGES = YES;
 				DEFINES_MODULE = YES;
 				DYLIB_COMPATIBILITY_VERSION = 1;
@@ -341,6 +348,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -348,6 +356,7 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				CLANG_ENABLE_MODULES = YES;
+				CODE_SIGN_IDENTITY = "";
 				COMBINE_HIDPI_IMAGES = YES;
 				DEFINES_MODULE = YES;
 				DYLIB_COMPATIBILITY_VERSION = 1;
@@ -360,6 +369,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.Graph";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index a8ce1124d..c4750d846 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index b5a957429..42c83c5ad 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0800"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 562a48514..e5e9fc2db 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -7,7 +7,9 @@
 
 import Foundation
 
-private class EdgeList<T where T: Equatable, T: Hashable> {
+
+
+private class EdgeList<T> where T: Equatable, T: Hashable {
 
   var vertex: Vertex<T>
   var edges: [Edge<T>]? = nil
@@ -16,15 +18,15 @@ private class EdgeList<T where T: Equatable, T: Hashable> {
     self.vertex = vertex
   }
 
-  func addEdge(edge: Edge<T>) {
+  func addEdge(_ edge: Edge<T>) {
     edges?.append(edge)
   }
 
 }
 
-public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGraph<T> {
+open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashable {
 
-  private var adjacencyList: [EdgeList<T>] = []
+  fileprivate var adjacencyList: [EdgeList<T>] = []
 
   public required init() {
     super.init()
@@ -34,7 +36,7 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
     super.init(fromGraph: graph)
   }
 
-  public override var vertices: [Vertex<T>] {
+  open override var vertices: [Vertex<T>] {
     get {
       var vertices = [Vertex<T>]()
       for edgeList in adjacencyList {
@@ -44,7 +46,7 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
     }
   }
 
-  public override var edges: [Edge<T>] {
+  open override var edges: [Edge<T>] {
     get {
       var allEdges = Set<Edge<T>>()
       for edgeList in adjacencyList {
@@ -60,7 +62,7 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
     }
   }
 
-  public override func createVertex(data: T) -> Vertex<T> {
+  open override func createVertex(_ data: T) -> Vertex<T> {
     // check if the vertex already exists
     let matchingVertices = vertices.filter() { vertex in
       return vertex.data == data
@@ -76,24 +78,24 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
     return vertex
   }
 
-  public override func addDirectedEdge(from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
+  open override func addDirectedEdge(_ from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
     // works
     let edge = Edge(from: from, to: to, weight: weight)
     let edgeList = adjacencyList[from.index]
-    if edgeList.edges?.count > 0 {
-      edgeList.addEdge(edge)
+    if let _ = edgeList.edges {
+        edgeList.addEdge(edge)
     } else {
-      edgeList.edges = [edge]
+        edgeList.edges = [edge]
     }
   }
 
-  public override func addUndirectedEdge(vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
+  open override func addUndirectedEdge(_ vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
     addDirectedEdge(vertices.0, to: vertices.1, withWeight: weight)
     addDirectedEdge(vertices.1, to: vertices.0, withWeight: weight)
   }
 
 
-  public override func weightFrom(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
+  open override func weightFrom(_ sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
     guard let edges = adjacencyList[sourceVertex.index].edges else {
       return nil
     }
@@ -107,11 +109,11 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
     return nil
   }
 
-  public override func edgesFrom(sourceVertex: Vertex<T>) -> [Edge<T>] {
+  open override func edgesFrom(_ sourceVertex: Vertex<T>) -> [Edge<T>] {
     return adjacencyList[sourceVertex.index].edges ?? []
   }
 
-  public override var description: String {
+  open override var description: String {
     get {
       var rows = [String]()
       for edgeList in adjacencyList {
@@ -129,10 +131,10 @@ public class AdjacencyListGraph<T where T: Equatable, T: Hashable>: AbstractGrap
           row.append(value)
         }
 
-        rows.append("\(edgeList.vertex.data) -> [\(row.joinWithSeparator(", "))]")
+        rows.append("\(edgeList.vertex.data) -> [\(row.joined(separator: ", "))]")
       }
 
-      return rows.joinWithSeparator("\n")
+      return rows.joined(separator: "\n")
     }
   }
 }
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index 6b19bcfcc..8f357bc8c 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -7,12 +7,12 @@
 
 import Foundation
 
-public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGraph<T> {
+open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashable {
 
   // If adjacencyMatrix[i][j] is not nil, then there is an edge from
   // vertex i to vertex j.
-  private var adjacencyMatrix: [[Double?]] = []
-  private var _vertices: [Vertex<T>] = []
+  fileprivate var adjacencyMatrix: [[Double?]] = []
+  fileprivate var _vertices: [Vertex<T>] = []
 
   public required init() {
     super.init()
@@ -22,13 +22,13 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
     super.init(fromGraph: graph)
   }
 
-  public override var vertices: [Vertex<T>] {
+  open override var vertices: [Vertex<T>] {
     get {
       return _vertices
     }
   }
 
-  public override var edges: [Edge<T>] {
+  open override var edges: [Edge<T>] {
     get {
       var edges = [Edge<T>]()
       for row in 0 ..< adjacencyMatrix.count {
@@ -44,7 +44,7 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
 
   // Adds a new vertex to the matrix.
   // Performance: possibly O(n^2) because of the resizing of the matrix.
-  public override func createVertex(data: T) -> Vertex<T> {
+  open override func createVertex(_ data: T) -> Vertex<T> {
     // check if the vertex already exists
     let matchingVertices = vertices.filter() { vertex in
       return vertex.data == data
@@ -63,7 +63,7 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
     }
 
     // Add one new row at the bottom.
-    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
+    let newRow = [Double?](repeating: nil, count: adjacencyMatrix.count + 1)
     adjacencyMatrix.append(newRow)
 
     _vertices.append(vertex)
@@ -71,20 +71,20 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
     return vertex
   }
 
-  public override func addDirectedEdge(from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
+  open override func addDirectedEdge(_ from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
     adjacencyMatrix[from.index][to.index] = weight
   }
 
-  public override func addUndirectedEdge(vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
+  open override func addUndirectedEdge(_ vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
     addDirectedEdge(vertices.0, to: vertices.1, withWeight: weight)
     addDirectedEdge(vertices.1, to: vertices.0, withWeight: weight)
   }
 
-  public override func weightFrom(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
+  open override func weightFrom(_ sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
     return adjacencyMatrix[sourceVertex.index][destinationVertex.index]
   }
 
-  public override func edgesFrom(sourceVertex: Vertex<T>) -> [Edge<T>] {
+  open override func edgesFrom(_ sourceVertex: Vertex<T>) -> [Edge<T>] {
     var outEdges = [Edge<T>]()
     let fromIndex = sourceVertex.index
     for column in 0..<adjacencyMatrix.count {
@@ -95,7 +95,7 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
     return outEdges
   }
 
-  public override var description: String {
+  open override var description: String {
     get {
       var grid = [String]()
       let n = self.adjacencyMatrix.count
@@ -111,7 +111,7 @@ public class AdjacencyMatrixGraph<T where T: Equatable, T: Hashable>: AbstractGr
         }
         grid.append(row)
       }
-      return (grid as NSArray).componentsJoinedByString("\n")
+      return (grid as NSArray).componentsJoined(by: "\n")
     }
   }
 
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index a867e164a..03518da83 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public struct Edge<T where T: Equatable, T: Hashable>: Equatable {
+public struct Edge<T>: Equatable where T: Equatable, T: Hashable {
 
   public let from: Vertex<T>
   public let to: Vertex<T>
@@ -35,7 +35,7 @@ extension Edge: Hashable {
     get {
       var string = "\(from.description)\(to.description)"
       if weight != nil {
-        string.appendContentsOf("\(weight!)")
+        string.append("\(weight!)")
       }
       return string.hashValue
     }
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
index 75b4bddec..2ad91608b 100644
--- a/Graph/Graph/Graph.swift
+++ b/Graph/Graph/Graph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public class AbstractGraph<T where T: Equatable, T: Hashable>: CustomStringConvertible {
+open class AbstractGraph<T>: CustomStringConvertible where T: Equatable, T: Hashable {
 
   public required init() {}
 
@@ -20,19 +20,19 @@ public class AbstractGraph<T where T: Equatable, T: Hashable>: CustomStringConve
     }
   }
 
-  public var description: String {
+  open var description: String {
     get {
       fatalError("abstract property accessed")
     }
   }
 
-  public var vertices: [Vertex<T>] {
+  open var vertices: [Vertex<T>] {
     get {
       fatalError("abstract property accessed")
     }
   }
 
-  public var edges: [Edge<T>] {
+  open var edges: [Edge<T>] {
     get {
       fatalError("abstract property accessed")
     }
@@ -40,23 +40,23 @@ public class AbstractGraph<T where T: Equatable, T: Hashable>: CustomStringConve
 
   // Adds a new vertex to the matrix.
   // Performance: possibly O(n^2) because of the resizing of the matrix.
-  public func createVertex(data: T) -> Vertex<T> {
+  open func createVertex(_ data: T) -> Vertex<T> {
     fatalError("abstract function called")
   }
 
-  public func addDirectedEdge(from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
+  open func addDirectedEdge(_ from: Vertex<T>, to: Vertex<T>, withWeight weight: Double?) {
     fatalError("abstract function called")
   }
 
-  public func addUndirectedEdge(vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
+  open func addUndirectedEdge(_ vertices: (Vertex<T>, Vertex<T>), withWeight weight: Double?) {
     fatalError("abstract function called")
   }
 
-  public func weightFrom(sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
+  open func weightFrom(_ sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
     fatalError("abstract function called")
   }
 
-  public func edgesFrom(sourceVertex: Vertex<T>) -> [Edge<T>] {
+  open func edgesFrom(_ sourceVertex: Vertex<T>) -> [Edge<T>] {
     fatalError("abstract function called")
   }
 }
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 1223eb116..43cabcd1f 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public struct Vertex<T where T: Equatable, T: Hashable>: Equatable {
+public struct Vertex<T>: Equatable where T: Equatable, T: Hashable {
 
   public var data: T
   public let index: Int

From 263faef2847eb2249e650138984df56dcb5cb702 Mon Sep 17 00:00:00 2001
From: Sahn Cha <schalin@gmail.com>
Date: Fri, 21 Oct 2016 23:18:42 +0900
Subject: [PATCH 0613/1679] README ready.

---
 .../Images/img_pseudo.png                     | Bin 0 -> 149885 bytes
 Miller-Rabin Primality Test/README.markdown   |  43 ++++++++++++++++++
 .../contents.xcworkspacedata                  |  12 ++++-
 3 files changed, 54 insertions(+), 1 deletion(-)
 create mode 100644 Miller-Rabin Primality Test/Images/img_pseudo.png
 create mode 100644 Miller-Rabin Primality Test/README.markdown

diff --git a/Miller-Rabin Primality Test/Images/img_pseudo.png b/Miller-Rabin Primality Test/Images/img_pseudo.png
new file mode 100644
index 0000000000000000000000000000000000000000..1a06d151aa90ae0d81fd6c413426357f907d2ae1
GIT binary patch
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diff --git a/Miller-Rabin Primality Test/README.markdown b/Miller-Rabin Primality Test/README.markdown
new file mode 100644
index 000000000..9fa849836
--- /dev/null
+++ b/Miller-Rabin Primality Test/README.markdown	
@@ -0,0 +1,43 @@
+# Miller-Rabin Primality Test
+
+In 1976, Gray Miller introduced an algorithm, through his ph.d thesis[1], which determines a primality of the given number. The original algorithm was deterministic under the Extended Reimann Hypothesis, which is yet to be proven. After four years, Michael O. Rabin improved the algorithm[2] by using probabilistic approach and it no longer assumes the unproven hypothesis.
+
+## Probabilistic
+
+The result of the test is simply a boolean. However, `true` does not implicate *the number is prime*. In fact, it means *the number is **probably** prime*. But `false` does mean *the number is composite*.
+
+In order to increase the accuracy of the test, it needs to be iterated few times. If it returns `true` in every single iteration, than we can say with confidence that *the number is pro......bably prime*.
+
+## Algorithm
+
+Let `n` be the given number, and write `n-1` as `2^s·d`, where d is odd. And choose a random number `a` within the range from `2` to `n - 1`.
+
+Now make a sequence, in modulo `n`, as following:
+
+> a^d, a^(2·d), a^(4·d), ... , a^((2^(s-1))·d), a^((2^s)·d) = a^(n-1)
+
+And we say the number `n` passes the test, *probably prime*, if 1) `a^d` is congruence to `1` in modulo `n`, or 2) `a^((2^k)·d)` is congruence to `-1` for some `k = 1, 2, ..., s-1`.
+
+### Pseudo Code
+
+The following pseudo code is excerpted from Wikipedia[3]:
+
+![Image of Pseudocode](./Images/img_pseudo.png)
+
+## Usage
+
+```swift
+mrPrimalityTest(7)                      // test if 7 is prime. (default iteration = 1)
+mrPrimalityTest(7, iteration: 10)       // test if 7 is prime & iterate 10 times.
+```
+
+## Reference
+1. G. L. Miller, "Riemann's Hypothesis and Tests for Primality". *J. Comput. System Sci.* 13 (1976), 300-317.
+2. M. O. Rabin, "Probabilistic algorithm for testing primality". *Journal of Number Theory.* 12 (1980), 128-138.
+3. Miller–Rabin primality test - Wikipedia, the free encyclopedia
+
+*Written for Swift Algorithm Club by **Sahn Cha**, @scha00*
+
+[1]: https://cs.uwaterloo.ca/research/tr/1975/CS-75-27.pdf
+[2]: http://www.sciencedirect.com/science/article/pii/0022314X80900840
+[3]: https://en.wikipedia.org/wiki/Miller–Rabin_primality_test
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index dd0c6b668..75a941c3f 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -28,11 +28,21 @@
    <Group
       location = "group:Miller-Rabin Primality Test"
       name = "Miller-Rabin Primality Test">
+      <Group
+         location = "container:Miller-Rabin Primality Test/Images"
+         name = "Images">
+         <FileRef
+            location = "group:img_pseudo.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:MRPrimality.playground">
+      </FileRef>
       <FileRef
          location = "group:MRPrimality.swift">
       </FileRef>
       <FileRef
-         location = "group:MRPrimality.playground">
+         location = "group:README.markdown">
       </FileRef>
    </Group>
    <Group

From 00947395376a7192f12bf15e3da19999cfe13c52 Mon Sep 17 00:00:00 2001
From: Sahn Cha <schalin@gmail.com>
Date: Fri, 21 Oct 2016 23:25:01 +0900
Subject: [PATCH 0614/1679] Update README.markdown

---
 Miller-Rabin Primality Test/README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Miller-Rabin Primality Test/README.markdown b/Miller-Rabin Primality Test/README.markdown
index 9fa849836..84020a9ec 100644
--- a/Miller-Rabin Primality Test/README.markdown	
+++ b/Miller-Rabin Primality Test/README.markdown	
@@ -4,9 +4,9 @@ In 1976, Gray Miller introduced an algorithm, through his ph.d thesis[1], which
 
 ## Probabilistic
 
-The result of the test is simply a boolean. However, `true` does not implicate *the number is prime*. In fact, it means *the number is **probably** prime*. But `false` does mean *the number is composite*.
+The result of the test is simply a boolean. However, `true` does not implicate _the number is prime_. In fact, it means _the number is **probably** prime_. But `false` does mean _the number is composite_.
 
-In order to increase the accuracy of the test, it needs to be iterated few times. If it returns `true` in every single iteration, than we can say with confidence that *the number is pro......bably prime*.
+In order to increase the accuracy of the test, it needs to be iterated few times. If it returns `true` in every single iteration, than we can say with confidence that _the number is pro......bably prime_.
 
 ## Algorithm
 
@@ -16,7 +16,7 @@ Now make a sequence, in modulo `n`, as following:
 
 > a^d, a^(2·d), a^(4·d), ... , a^((2^(s-1))·d), a^((2^s)·d) = a^(n-1)
 
-And we say the number `n` passes the test, *probably prime*, if 1) `a^d` is congruence to `1` in modulo `n`, or 2) `a^((2^k)·d)` is congruence to `-1` for some `k = 1, 2, ..., s-1`.
+And we say the number `n` passes the test, _probably prime_, if 1) `a^d` is congruence to `1` in modulo `n`, or 2) `a^((2^k)·d)` is congruence to `-1` for some `k = 1, 2, ..., s-1`.
 
 ### Pseudo Code
 
@@ -32,11 +32,11 @@ mrPrimalityTest(7, iteration: 10)       // test if 7 is prime & iterate 10 times
 ```
 
 ## Reference
-1. G. L. Miller, "Riemann's Hypothesis and Tests for Primality". *J. Comput. System Sci.* 13 (1976), 300-317.
-2. M. O. Rabin, "Probabilistic algorithm for testing primality". *Journal of Number Theory.* 12 (1980), 128-138.
+1. G. L. Miller, "Riemann's Hypothesis and Tests for Primality". _J. Comput. System Sci._ 13 (1976), 300-317.
+2. M. O. Rabin, "Probabilistic algorithm for testing primality". _Journal of Number Theory._ 12 (1980), 128-138.
 3. Miller–Rabin primality test - Wikipedia, the free encyclopedia
 
-*Written for Swift Algorithm Club by **Sahn Cha**, @scha00*
+_Written for Swift Algorithm Club by **Sahn Cha**, @scha00_
 
 [1]: https://cs.uwaterloo.ca/research/tr/1975/CS-75-27.pdf
 [2]: http://www.sciencedirect.com/science/article/pii/0022314X80900840

From a2fa24d380496152dc83eb81c8ec6a10b600878c Mon Sep 17 00:00:00 2001
From: Sahn Cha <schalin@gmail.com>
Date: Fri, 21 Oct 2016 23:34:08 +0900
Subject: [PATCH 0615/1679] typo.

---
 Miller-Rabin Primality Test/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Miller-Rabin Primality Test/README.markdown b/Miller-Rabin Primality Test/README.markdown
index 84020a9ec..07acb9e18 100644
--- a/Miller-Rabin Primality Test/README.markdown	
+++ b/Miller-Rabin Primality Test/README.markdown	
@@ -6,11 +6,11 @@ In 1976, Gray Miller introduced an algorithm, through his ph.d thesis[1], which
 
 The result of the test is simply a boolean. However, `true` does not implicate _the number is prime_. In fact, it means _the number is **probably** prime_. But `false` does mean _the number is composite_.
 
-In order to increase the accuracy of the test, it needs to be iterated few times. If it returns `true` in every single iteration, than we can say with confidence that _the number is pro......bably prime_.
+In order to increase the accuracy of the test, it needs to be iterated few times. If it returns `true` in every single iteration, then we can say with confidence that _the number is pro......bably prime_.
 
 ## Algorithm
 
-Let `n` be the given number, and write `n-1` as `2^s·d`, where d is odd. And choose a random number `a` within the range from `2` to `n - 1`.
+Let `n` be the given number, and write `n-1` as `2^s·d`, where `d` is odd. And choose a random number `a` within the range from `2` to `n - 1`.
 
 Now make a sequence, in modulo `n`, as following:
 
@@ -28,7 +28,7 @@ The following pseudo code is excerpted from Wikipedia[3]:
 
 ```swift
 mrPrimalityTest(7)                      // test if 7 is prime. (default iteration = 1)
-mrPrimalityTest(7, iteration: 10)       // test if 7 is prime & iterate 10 times.
+mrPrimalityTest(7, iteration: 10)       // test if 7 is prime && iterate 10 times.
 ```
 
 ## Reference

From 4c19e5f9091112090b3ec6ce10a0376e1b41abf3 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Sat, 22 Oct 2016 10:43:38 +0200
Subject: [PATCH 0616/1679] Clean up

---
 Skip-List/SkipList.swift | 78 ++++++++++++++++++++--------------------
 1 file changed, 38 insertions(+), 40 deletions(-)

diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 31b4e9144..5fc61bf8e 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -26,7 +26,7 @@ import Foundation
 
 // Stack from : https://github.com/raywenderlich/swift-algorithm-club/tree/master/Stack
 public struct Stack<T> {
-  fileprivate var array = [T]()
+  fileprivate var array: [T] = []
 
   public var isEmpty: Bool {
     return array.isEmpty
@@ -62,53 +62,48 @@ extension Stack: Sequence {
 
 private func coinFlip() -> Bool {
   #if os(Linux)
-   return random() % 2 == 0
+      return random() % 2 == 0
   #elseif os(OSX)
-   return arc4random_uniform(2) == 1
+      return arc4random_uniform(2) == 1
   #endif
 }
 
 
-// MARK: - Node
-
 public class DataNode<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
   
   var data            : Payload?  
   fileprivate var key : Key?
-  internal var next   : Node?
-  internal var down   : Node?
+  var next            : Node?
+  var down            : Node?
   
   public init(key: Key, data: Payload) {
     self.key  = key
     self.data = data
   }
 
-  public init(asHead head: Bool){
-  }
+  public init(asHead head: Bool){}
   
 }
 
 
-// MARK: - Skip List
-
 open class SkipList<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
   
   fileprivate(set) var head: Node?
 
-  public init() { }
+  public init() {}
   
 }
 
 
 
-// MARK: - Searching
+// MARK: - Search lanes for a node with a given key
 
 extension SkipList {
   
-  internal func findNode(key: Key) -> Node? {
-    var currentNode : Node? = self.head
+  func findNode(key: Key) -> Node? {
+    var currentNode : Node? = head
     var isFound     : Bool  = false
 
     while !isFound {
@@ -117,7 +112,7 @@ extension SkipList {
         switch node.next {
         case .none:
           
-          currentNode = node.down
+          currentNode = node.down          
         case .some(let value) where value.key != nil:
 
           if value.key == key {
@@ -149,26 +144,26 @@ extension SkipList {
     
   }
 
-  internal func search(key: Key) -> Payload? {
-    guard let node = self.findNode(key: key) else {
+  func search(key: Key) -> Payload? {
+    guard let node = findNode(key: key) else {
       return nil
     }
 
     return node.next!.data    
   }    
- 
+  
 }
 
 
 
-// MARK: - Inserting
+// MARK: - Insert a node into lanes depending on skip list status ( bootstrap base-layer if head is empty / start insertion from current head ).
 
 extension SkipList {
-  private func bootstrapBaseLayer(key: Key, data: Payload) -> Void {    
-    self.head          = Node(asHead: true)    
-    var node           = Node(key: key, data: data)
+  private func bootstrapBaseLayer(key: Key, data: Payload) {    
+    head       = Node(asHead: true)    
+    var node   = Node(key: key, data: data)
 
-    self.head!.next    = node
+    head!.next = node
     
     var currentTopNode = node
 
@@ -177,17 +172,17 @@ extension SkipList {
       node           = Node(key: key, data: data)
       node.down      = currentTopNode
       newHead.next   = node
-      newHead.down   = self.head
-      self.head      = newHead
+      newHead.down   = head
+      head           = newHead
       currentTopNode = node
     }
     
   }
 
 
-  private func insertItem(key: Key, data: Payload) -> Void {
+  private func insertItem(key: Key, data: Payload) {
     var stack              = Stack<Node>()
-    var currentNode: Node? = self.head
+    var currentNode: Node? = head
 
     while currentNode != nil {
 
@@ -219,8 +214,8 @@ extension SkipList {
         node           = Node(key: key, data: data)
         node.down      = currentTopNode
         newHead.next   = node
-        newHead.down   = self.head
-        self.head      = newHead
+        newHead.down   = head
+        head           = newHead
         currentTopNode = node
         
       } else {        
@@ -236,32 +231,32 @@ extension SkipList {
   }
 
 
-  internal func insert(key: Key, data: Payload) {
-    if self.head != nil {
-      if let node = self.findNode(key: key) {
-        // replace in case key already exists
+  func insert(key: Key, data: Payload) {
+    if head != nil {
+      if let node = findNode(key: key) {
+        // replace, in case of key already exists. 
         var currentNode = node.next        
         while currentNode != nil && currentNode!.key == key {
           currentNode!.data = data
           currentNode       = currentNode!.down
         }
       } else {
-        self.insertItem(key: key, data: data)
+        insertItem(key: key, data: data)
       }
       
     } else {
-      self.bootstrapBaseLayer(key: key, data: data)
+      bootstrapBaseLayer(key: key, data: data)
     }
   }
   
 }
 
 
-// MARK: - Removing
+// MARK: - Remove a node with a given key. First, find its position in layers at the top, then remove it from each lane by traversing down to the base layer.
 
 extension SkipList {
-  public func remove(key: Key) -> Void {
-    guard let item = self.findNode(key: key) else {
+  public func remove(key: Key) {
+    guard let item = findNode(key: key) else {
       return
     }
     
@@ -285,9 +280,12 @@ extension SkipList {
   }  
 }
 
+
+// MARK: - Get associated payload from a node with a given key.
+
 extension SkipList {
   
   public func get(key:Key) -> Payload?{
-    return self.search(key: key)
+    return search(key: key)
   }
 }

From 1de177535f8facdd188464df0c98e50cc5148504 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Mon, 24 Oct 2016 18:33:25 -0700
Subject: [PATCH 0617/1679] Init & claim of Strassen's Matrix Multiplication
 Algorithm

---
 Strassen Matrix Multiplication/README.markdown | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Strassen Matrix Multiplication/README.markdown

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
new file mode 100644
index 000000000..d07004bad
--- /dev/null
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -0,0 +1 @@
+## TODO: Examples & Explanation

From 95069fd26cd6c0f5c60f9c980411df72c61ce379 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Wed, 26 Oct 2016 14:12:39 -0700
Subject: [PATCH 0618/1679] Implementation for Strassen Matrix Multiplication
 Algorithm

---
 .../Contents.swift                            | 316 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 3 files changed, 327 insertions(+)
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
new file mode 100644
index 000000000..d4b4d8330
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -0,0 +1,316 @@
+//: Playground - noun: a place where people can play
+// Reference - http://mathworld.wolfram.com/StrassenFormulas.html
+
+
+import UIKit
+
+enum RowOrColumn {
+  case row, column
+}
+
+protocol Number: Multipliable, Addable {
+  static var zero: Self { get }
+}
+
+protocol Addable {
+  static func +(lhs: Self, rhs: Self) -> Self
+  static func -(lhs: Self, rhs: Self) -> Self
+}
+
+protocol Multipliable {
+  static func *(lhs: Self, rhs: Self) -> Self
+}
+
+extension Int: Number {
+  static var zero: Int {
+    return 0
+  }
+}
+
+extension Double: Number {
+  static var zero: Double {
+    return 0.0
+  }
+}
+
+extension Float: Number {
+  static var zero: Float {
+    return 0.0
+  }
+}
+
+
+extension Array where Element: Number {
+  func dot(_ b: Array<Element>) -> Element {
+    let a = self
+    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
+    let c = a.indices.map{ a[$0] * b[$0] }
+    return c.reduce(Element.zero, { $0 + $1 })
+  }
+}
+
+struct MatrixSize: Equatable {
+  let rows: Int
+  let columns: Int
+  
+  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try? body(row, column)
+      }
+    }
+  }
+}
+
+func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+}
+
+
+struct Matrix<T: Number> {
+  
+  // MARK: - Variables
+  
+  let rows: Int, columns: Int
+  var grid: [T]
+  
+  var isSquare: Bool {
+    return rows == columns
+  }
+  
+  var size: MatrixSize {
+    return MatrixSize(rows: rows, columns: columns)
+  }
+  
+  // MARK: - Init
+  
+  init(rows: Int, columns: Int, initialValue: T = T.zero) {
+    self.rows = rows
+    self.columns = columns
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  init(size: Int, initialValue: T = T.zero) {
+    self.rows = size
+    self.columns = size
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  // MARK: - Subscript
+  
+  subscript(row: Int, column: Int) -> T {
+    get {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      return grid[(row * columns) + column]
+    }
+    set {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      grid[(row * columns) + column] = newValue
+    }
+  }
+  
+  subscript(type: RowOrColumn, value: Int) -> [T] {
+    get {
+      switch type {
+      case .row:
+        assert(indexIsValid(row: value, column: 0), "Index out of range")
+        return Array(grid[(value * columns)..<(value * columns) + columns])
+      case .column:
+        assert(indexIsValid(row: 0, column: value), "Index out of range")
+        var columns: [T] = []
+        for row in 0..<rows {
+          for column in 0..<self.columns {
+            if column == value {
+              columns.append(grid[(row * self.columns) + value])
+            }
+          }
+        }
+        return columns
+      }
+    } set {
+      switch type {
+      case .row:
+        assert(newValue.count == columns)
+        for (column, element) in newValue.enumerated() {
+          grid[(value * columns) + column] = element
+        }
+      case .column:
+        assert(newValue.count == rows)
+        for (row, element) in newValue.enumerated() {
+          grid[(row * columns) + value] = element
+        }
+      }
+    }
+  }
+  
+  // MARK: - Private Functions
+  
+  private func indexIsValid(row: Int, column: Int) -> Bool {
+    return row >= 0 && row < rows && column >= 0 && column < columns
+  }
+  
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
+    guard A.rows > 1 && B.rows > 1 else { return A * B }
+    
+    let n    = A.rows
+    let nBy2 = n / 2
+    
+    var a11 = Matrix(size: nBy2)
+    var a12 = Matrix(size: nBy2)
+    var a21 = Matrix(size: nBy2)
+    var a22 = Matrix(size: nBy2)
+    var b11 = Matrix(size: nBy2)
+    var b12 = Matrix(size: nBy2)
+    var b21 = Matrix(size: nBy2)
+    var b22 = Matrix(size: nBy2)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        a11[i,j] = A[i,j]
+        a12[i,j] = A[i, j+nBy2]
+        a21[i,j] = A[i+nBy2, j]
+        a22[i,j] = A[i+nBy2, j+nBy2]
+        b11[i,j] = B[i,j]
+        b12[i,j] = B[i, j+nBy2]
+        b21[i,j] = B[i+nBy2, j]
+        b22[i,j] = B[i+nBy2, j+nBy2]
+      }
+    }
+    
+    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
+    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
+    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
+    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
+    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
+    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
+    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
+    
+    let c11 = q1 + q4 - q5 + q7
+    let c12 = q3 + q5
+    let c21 = q2 + q4
+    let c22 = q1 + q3 - q2 + q6
+    var C   = Matrix(size: n)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        C[i, j]           = c11[i,j]
+        C[i, j+nBy2]      = c12[i,j]
+        C[i+nBy2, j]      = c21[i,j]
+        C[i+nBy2, j+nBy2] = c22[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func nextPowerOfTwo(of n: Int) -> Int {
+    return Int(pow(2, ceil(log2(Double(n)))))
+  }
+  
+  // MARK: - Functions
+  
+  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(of: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.size.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.size.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    return C
+  }
+  
+  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+var A = Matrix(rows: 2, columns: 4, initialValue: 0)
+A[.row, 0] = [2, 3, -1, 0]
+A[.row, 1] = [-7, 2, 1, 10]
+
+var B = Matrix(rows: 4, columns: 2, initialValue: 0)
+B[.column, 0] = [3, 2, -1, 2]
+B[.column, 1] = [4, 1, 2, 7]
+
+let C = A.matrixMultiply(by: B)
+let D = A.strassenMatrixMultiply(by: B)
+let E = B.matrixMultiply(by: A)
+let F = B.strassenMatrixMultiply(by: A)
+print(C)
+print(D)
+print(E)
+print(F)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 87c23249e572ed9b32191df58cf93d549072463e Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 27 Oct 2016 10:47:09 +0200
Subject: [PATCH 0619/1679] update readme

---
 Ring Buffer/README.markdown | 36 +++++++++++++++++-------------------
 1 file changed, 17 insertions(+), 19 deletions(-)

diff --git a/Ring Buffer/README.markdown b/Ring Buffer/README.markdown
index 70e0ad108..0652ff548 100644
--- a/Ring Buffer/README.markdown	
+++ b/Ring Buffer/README.markdown	
@@ -17,7 +17,7 @@ Initially, the array is empty and the read (`r`) and write (`w`) pointers are at
 Let's add some data to this array. We'll write, or "enqueue", the number `123`:
 
 	[ 123,    ,    ,    ,     ]
-	  r 
+	  r
 	  ---> w
 
 Each time we add data, the write pointer moves one step forward. Let's add a few more elements:
@@ -46,7 +46,7 @@ Whoops, the write pointer has reached the end of the array, so there is no more
 	[ 555, 456, 789, 666, 333 ]
 	  ---> w         r        
 
-We can now read the remaining three items, `666`, `333`, and `555`. 
+We can now read the remaining three items, `666`, `333`, and `555`.
 
 	[ 555, 456, 789, 666, 333 ]
 	       w         --------> r        
@@ -63,16 +63,15 @@ Here is a very basic implementation in Swift:
 
 ```swift
 public struct RingBuffer<T> {
-  private var array: [T?]
-  private var readIndex = 0
-  private var writeIndex = 0
-  
+  fileprivate var array: [T?]
+  fileprivate var readIndex = 0
+  fileprivate var writeIndex = 0
+
   public init(count: Int) {
-    array = [T?](count: count, repeatedValue: nil)
+    array = [T?](repeating: nil, count: count)
   }
-  
-  /* Returns false if out of space. */
-  public mutating func write(element: T) -> Bool {
+
+  public mutating func write(_ element: T) -> Bool {
     if !isFull {
       array[writeIndex % array.count] = element
       writeIndex += 1
@@ -81,8 +80,7 @@ public struct RingBuffer<T> {
       return false
     }
   }
-  
-  /* Returns nil if the buffer is empty. */
+
   public mutating func read() -> T? {
     if !isEmpty {
       let element = array[readIndex % array.count]
@@ -92,19 +90,19 @@ public struct RingBuffer<T> {
       return nil
     }
   }
-  
-  private var availableSpaceForReading: Int {
+
+  fileprivate var availableSpaceForReading: Int {
     return writeIndex - readIndex
   }
-  
+
   public var isEmpty: Bool {
     return availableSpaceForReading == 0
   }
-  
-  private var availableSpaceForWriting: Int {
+
+  fileprivate var availableSpaceForWriting: Int {
     return array.count - availableSpaceForReading
   }
-  
+
   public var isFull: Bool {
     return availableSpaceForWriting == 0
   }
@@ -130,7 +128,7 @@ In other words, we take the modulo (or the remainder) of the read index and writ
 The reason this is a bit controversial is that `writeIndex` and `readIndex` always increment, so in theory these values could become too large to fit into an integer and the app will crash. However, a quick back-of-the-napkin calculation should take away those fears.
 
 Both `writeIndex` and `readIndex` are 64-bit integers. If we assume that they are incremented 1000 times per second, which is a lot, then doing this continuously for one year requires `ceil(log_2(365 * 24 * 60 * 60 * 1000)) = 35` bits. That leaves 28 bits to spare, so that should give you about 2^28 years before running into problems. That's a long time. :-)
-  
+
 To play with this ring buffer, copy the code to a playground and do the following to mimic the example above:
 
 ```swift

From e0547e96c4e11f436b1a4f2a9c6c9cbe2de1fbb5 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 27 Oct 2016 10:55:53 +0200
Subject: [PATCH 0620/1679] update readme

---
 Graph/README.markdown | 94 +++++++++++++++++++++----------------------
 1 file changed, 46 insertions(+), 48 deletions(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index 349add81a..1ff1a82ac 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -42,7 +42,7 @@ Like a tree this does not have any cycles in it (no matter where you start, ther
 
 Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that graphs are an extremely useful data structure.
 
-If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First Search/) or [depth-first search](../Depth-First Search) to find a solution. 
+If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First Search/) or [depth-first search](../Depth-First Search) to find a solution.
 
 For example, let's say you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
 
@@ -110,12 +110,13 @@ We'll show you sample implementations of both adjacency list and adjacency matri
 The adjacency list for each vertex consists of `Edge` objects:
 
 ```swift
-public struct Edge<T where T: Equatable, T: Hashable>: Equatable {
-  
+public struct Edge<T>: Equatable where T: Equatable, T: Hashable {
+
   public let from: Vertex<T>
   public let to: Vertex<T>
 
   public let weight: Double?
+
 }
 ```
 
@@ -124,7 +125,7 @@ This struct describes the "from" and "to" vertices and a weight value. Note that
 The `Vertex` looks like this:
 
 ```swift
-public struct Vertex<T where T: Equatable, T: Hashable>: Equatable {
+public struct Vertex<T>: Equatable where T: Equatable, T: Hashable {
 
   public var data: T
   public let index: Int
@@ -147,10 +148,7 @@ We can represent it as an adjacency matrix or adjacency list. The classes implem
 Let's create some directed, weighted graphs, using each representation, to store the example:
 
 ```swift
-var adjacencyMatrixGraph = AdjacencyMatrixGraph<Int>()
-var adjacencyListGraph = AdjacencyListGraph<Int>()
-
-for graph in [ adjacencyMatrixGraph, adjacencyListGraph ] {
+for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 
   let v1 = graph.createVertex(1)
   let v2 = graph.createVertex(2)
@@ -163,8 +161,8 @@ for graph in [ adjacencyMatrixGraph, adjacencyListGraph ] {
   graph.addDirectedEdge(v3, to: v4, withWeight: 4.5)
   graph.addDirectedEdge(v4, to: v1, withWeight: 2.8)
   graph.addDirectedEdge(v2, to: v5, withWeight: 3.2)
-}
 
+}
 ```
 
 As mentioned earlier, to create an undirected edge you need to make two directed edges. If we wanted undirected graphs, we'd call this method instead, which takes care of that work for us:
@@ -184,7 +182,7 @@ We could provide `nil` as the values for the `withWeight` parameter in either ca
 To maintain the adjacency list, there is a class that maps a list of edges to a vertex. The graph simply maintains an array of such objects and modifies them as necessary.
 
 ```swift
-private class EdgeList<T where T: Equatable, T: Hashable> {
+private class EdgeList<T> where T: Equatable, T: Hashable {
 
   var vertex: Vertex<T>
   var edges: [Edge<T>]? = nil
@@ -193,34 +191,34 @@ private class EdgeList<T where T: Equatable, T: Hashable> {
     self.vertex = vertex
   }
 
-  func addEdge(edge: Edge<T>) {
+  func addEdge(_ edge: Edge<T>) {
     edges?.append(edge)
   }
 
 }
-``` 
+```
 
 They are implemented as a class as opposed to structs so we can modify them by reference, in place, like when adding an edge to a new vertex, where the source vertex already has an edge list:
 
 ```swift
-  public override func createVertex(data: T) -> Vertex<T> {
-    // check if the vertex already exists
-    let matchingVertices = vertices.filter() { vertex in
-      return vertex.data == data
-    }
-
-    if matchingVertices.count > 0 {
-      return matchingVertices.last!
-    }
-
-    // if the vertex doesn't exist, create a new one
-    let vertex = Vertex(data: data, index: adjacencyList.count)
-    adjacencyList.append(EdgeList(vertex: vertex))
-    return vertex
+open override func createVertex(_ data: T) -> Vertex<T> {
+  // check if the vertex already exists
+  let matchingVertices = vertices.filter() { vertex in
+    return vertex.data == data
+  }
+
+  if matchingVertices.count > 0 {
+    return matchingVertices.last!
   }
+
+  // if the vertex doesn't exist, create a new one
+  let vertex = Vertex(data: data, index: adjacencyList.count)
+  adjacencyList.append(EdgeList(vertex: vertex))
+  return vertex
+}
 ```
 
-The adjacency list for the example looks like this: 
+The adjacency list for the example looks like this:
 
 ```
 v1 -> [(v2: 1.0)]
@@ -238,32 +236,32 @@ We'll keep track of the adjacency matrix in a two-dimensional `[[Double?]]` arra
 To index into the matrix using vertices, we use the `index` property in `Vertex`, which is assigned when creating the vertex through the graph object. When creating a new vertex, the graph must resize the matrix:
 
 ```swift
-  public override func createVertex(data: T) -> Vertex<T> {
-    // check if the vertex already exists
-    let matchingVertices = vertices.filter() { vertex in
-      return vertex.data == data
-    }
+open override func createVertex(_ data: T) -> Vertex<T> {
+  // check if the vertex already exists
+  let matchingVertices = vertices.filter() { vertex in
+    return vertex.data == data
+  }
 
-    if matchingVertices.count > 0 {
-      return matchingVertices.last!
-    }
+  if matchingVertices.count > 0 {
+    return matchingVertices.last!
+  }
 
-    // if the vertex doesn't exist, create a new one
-    let vertex = Vertex(data: data, index: adjacencyMatrix.count)
+  // if the vertex doesn't exist, create a new one
+  let vertex = Vertex(data: data, index: adjacencyMatrix.count)
 
-    // Expand each existing row to the right one column.
-    for i in 0 ..< adjacencyMatrix.count {
-      adjacencyMatrix[i].append(nil)
-    }
+  // Expand each existing row to the right one column.
+  for i in 0 ..< adjacencyMatrix.count {
+    adjacencyMatrix[i].append(nil)
+  }
 
-    // Add one new row at the bottom.
-    let newRow = [Double?](count: adjacencyMatrix.count + 1, repeatedValue: nil)
-    adjacencyMatrix.append(newRow)
+  // Add one new row at the bottom.
+  let newRow = [Double?](repeating: nil, count: adjacencyMatrix.count + 1)
+  adjacencyMatrix.append(newRow)
 
-    _vertices.append(vertex)
+  _vertices.append(vertex)
 
-    return vertex
-  }
+  return vertex
+}
 ```
 
 Then the adjacency matrix looks like this:
@@ -273,7 +271,7 @@ Then the adjacency matrix looks like this:
 	 [nil, nil, nil, 4.5, nil]    v3
 	 [2.8, nil, nil, nil, nil]    v4
 	 [nil, nil, nil, nil, nil]]   v5
-	 
+
 	  v1   v2   v3   v4   v5
 
 

From 2b64b05087ab0b2014fd0a30fa8bda42f3b32a64 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 27 Oct 2016 16:15:44 +0200
Subject: [PATCH 0621/1679] migrate combinatorics to swift3

---
 .../Combinatorics.playground/Contents.swift   |  32 ++---
 .../timeline.xctimeline                       |   6 +
 Combinatorics/Combinatorics.swift             | 121 ------------------
 Combinatorics/README.markdown                 |  36 +++---
 4 files changed, 40 insertions(+), 155 deletions(-)
 create mode 100644 Combinatorics/Combinatorics.playground/timeline.xctimeline
 delete mode 100644 Combinatorics/Combinatorics.swift

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 5cb91967e..94951810f 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -1,7 +1,7 @@
 //: Playground - noun: a place where people can play
 
 /* Calculates n! */
-func factorial(n: Int) -> Int {
+func factorial(_ n: Int) -> Int {
   var n = n
   var result = 1
   while n > 1 {
@@ -20,7 +20,7 @@ factorial(20)
  Calculates P(n, k), the number of permutations of n distinct symbols
  in groups of size k.
  */
-func permutations(n: Int, _ k: Int) -> Int {
+func permutations(_ n: Int, _ k: Int) -> Int {
   var n = n
   var answer = n
   for _ in 1..<k {
@@ -41,7 +41,7 @@ permutations(9, 4)
  Original algorithm by Niklaus Wirth.
  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
  */
-func permuteWirth<T>(a: [T], _ n: Int) {
+func permuteWirth<T>(_ a: [T], _ n: Int) {
   if n == 0 {
     print(a)   // display the current permutation
   } else {
@@ -75,7 +75,7 @@ permuteWirth(xyz, 2)
  Original algorithm by Robert Sedgewick.
  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
  */
-func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
+func permuteSedgewick(_ a: [Int], _ n: Int, _ pos: inout Int) {
   var a = a
   pos += 1
   a[n] = pos
@@ -103,16 +103,16 @@ permuteSedgewick(numbers, 0, &pos)
  Calculates C(n, k), or "n-choose-k", i.e. how many different selections
  of size k out of a total number of distinct elements (n) you can make.
  */
-func combinations(n: Int, _ k: Int) -> Int {
+func combinations(_ n: Int, choose k: Int) -> Int {
   return permutations(n, k) / factorial(k)
 }
 
-combinations(3, 2)
-combinations(28, 5)
+combinations(3, choose: 2)
+combinations(28, choose: 5)
 
 print("\nCombinations:")
 for i in 1...20 {
-  print("\(20)-choose-\(i) = \(combinations(20, i))")
+    print("\(20)-choose-\(i) = \(combinations(20, choose: i))")
 }
 
 
@@ -121,7 +121,7 @@ for i in 1...20 {
  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
  k things out of n possibilities.
  */
-func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+func quickBinomialCoefficient(_ n: Int, choose k: Int) -> Int {
   var result = 1
 
   for i in 0..<k {
@@ -131,8 +131,8 @@ func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
   return result
 }
 
-quickBinomialCoefficient(8, 2)
-quickBinomialCoefficient(30, 15)
+quickBinomialCoefficient(8, choose: 2)
+quickBinomialCoefficient(30, choose: 15)
 
 
 
@@ -145,7 +145,7 @@ struct Array2D<T> {
   init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = .init(count: rows*columns, repeatedValue: initialValue)
+    array = Array(repeating: initialValue, count: rows*columns)
   }
 
   subscript(column: Int, row: Int) -> T {
@@ -163,8 +163,8 @@ struct Array2D<T> {
  space for the cached values.
  */
 
-func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+func binomialCoefficient(_ n: Int, choose k: Int) -> Int {
+  var bc = Array(repeating: Array(repeating: 0, count: n + 1), count: n + 1)
 
   for i in 0...n {
     bc[i][0] = 1
@@ -182,5 +182,5 @@ func binomialCoefficient(n: Int, _ k: Int) -> Int {
   return bc[n][k]
 }
 
-binomialCoefficient(30, 15)
-binomialCoefficient(66, 33)
+binomialCoefficient(30, choose: 15)
+binomialCoefficient(66, choose: 33)
diff --git a/Combinatorics/Combinatorics.playground/timeline.xctimeline b/Combinatorics/Combinatorics.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Combinatorics/Combinatorics.playground/timeline.xctimeline
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/Combinatorics/Combinatorics.swift b/Combinatorics/Combinatorics.swift
deleted file mode 100644
index 04ef98765..000000000
--- a/Combinatorics/Combinatorics.swift
+++ /dev/null
@@ -1,121 +0,0 @@
-/* Calculates n! */
-func factorial(n: Int) -> Int {
-  var n = n
-  var result = 1
-  while n > 1 {
-    result *= n
-    n -= 1
-  }
-  return result
-}
-
-/*
- Calculates P(n, k), the number of permutations of n distinct symbols
- in groups of size k.
- */
-func permutations(n: Int, _ k: Int) -> Int {
-  var n = n
-  var answer = n
-  for _ in 1..<k {
-    n -= 1
-    answer *= n
-  }
-  return answer
-}
-
-/*
- Prints out all the permutations of the given array.
- Original algorithm by Niklaus Wirth.
- See also Dr.Dobb's Magazine June 1993, Algorithm Alley
- */
-func permuteWirth<T>(a: [T], _ n: Int) {
-  if n == 0 {
-    print(a)   // display the current permutation
-  } else {
-    var a = a
-    permuteWirth(a, n - 1)
-    for i in 0..<n {
-      swap(&a[i], &a[n])
-      permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
-    }
-  }
-}
-
-/*
- Prints out all the permutations of an n-element collection.
-
- The initial array must be initialized with all zeros. The algorithm
- uses 0 as a flag that indicates more work to be done on each level
- of the recursion.
-
- Original algorithm by Robert Sedgewick.
- See also Dr.Dobb's Magazine June 1993, Algorithm Alley
- */
-func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
-  var a = a
-  pos += 1
-  a[n] = pos
-  if pos == a.count - 1 {
-    print(a)              // display the current permutation
-  } else {
-    for i in 0..<a.count {
-      if a[i] == 0 {
-        permuteSedgewick(a, i, &pos)
-      }
-    }
-  }
-  pos -= 1
-  a[n] = 0
-}
-
-/*
- Calculates C(n, k), or "n-choose-k", i.e. how many different selections
- of size k out of a total number of distinct elements (n) you can make.
- Doesn't work very well for large numbers.
- */
-func combinations(n: Int, _ k: Int) -> Int {
-  return permutations(n, k) / factorial(k)
-}
-
-/*
- Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
- k things out of n possibilities.
- */
-func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
-  var result = 1
-
-  for i in 0..<k {
-    result *= (n - i)
-    result /= (i + 1)
-  }
-  return result
-}
-
-/*
- Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
- k things out of n possibilities.
-
- Thanks to the dynamic programming, this algorithm from Skiena allows for
- the calculation of much larger numbers, at the cost of temporary storage
- space for the cached values.
- */
-
-func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
-
-  for i in 0...n {
-    bc[i][0] = 1
-    bc[i][i] = 1
-  }
-
-  if n > 0 {
-    for i in 1...n {
-      for j in 1..<i {
-        bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
-      }
-    }
-  }
-
-  return bc[n][k]
-}
diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index 81a56261e..b365b389b 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -3,7 +3,7 @@
 A *permutation* is a certain arrangement of the objects from a collection. For example, if we have the first five letters from the alphabet, then this is a permutation:
 
 	a, b, c, d, e
-	
+
 This is another permutation:
 
 	b, e, d, a, c
@@ -28,7 +28,7 @@ After picking the second letter, there are only three letters left to choose fro
 To calculate the factorial in Swift:
 
 ```swift
-func factorial(n: Int) -> Int {
+func factorial(_ n: Int) -> Int {
   var n = n
   var result = 1
   while n > 1 {
@@ -62,7 +62,7 @@ You could implement this in terms of the `factorial()` function from earlier, bu
 Here is an algorithm that can deal with larger numbers:
 
 ```swift
-func permutations(n: Int, _ k: Int) -> Int {
+func permutations(_ n: Int, _ k: Int) -> Int {
   var n = n
   var answer = n
   for _ in 1..<k {
@@ -98,7 +98,7 @@ So far we've counted how many permutations exist for a given collection, but how
 Here's a recursive algorithm by Niklaus Wirth:
 
 ```swift
-func permuteWirth<T>(a: [T], _ n: Int) {
+func permuteWirth<T>(_ a: [T], _ n: Int) {
   if n == 0 {
     print(a)   // display the current permutation
   } else {
@@ -216,7 +216,7 @@ If the above is still not entirely clear, then I suggest you give it a go in the
 For fun, here is an alternative algorithm, by Robert Sedgewick:
 
 ```swift
-func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
+func permuteSedgewick(_ a: [Int], _ n: Int, _ pos: inout Int) {
   var a = a
   pos += 1
   a[n] = pos
@@ -282,7 +282,7 @@ The formula for `C(n, k)` is:
 
 As you can see, you can derive it from the formula for `P(n, k)`. There are always more permutations than combinations. You divide the number of permutations by `k!` because a total of `k!` of these permutations give the same combination.
 
-Above I showed that the number of permutations of `k` `l` `m` is 6, but if you pick only two of those letters the number of combinations is 3. If we use the formula we should get the same answer. We want to calculate `C(3, 2)` because we choose 2 letters out of a collection of 3. 
+Above I showed that the number of permutations of `k` `l` `m` is 6, but if you pick only two of those letters the number of combinations is 3. If we use the formula we should get the same answer. We want to calculate `C(3, 2)` because we choose 2 letters out of a collection of 3.
 
 	          3 * 2 * 1    6
 	C(3, 2) = --------- = --- = 3
@@ -291,7 +291,7 @@ Above I showed that the number of permutations of `k` `l` `m` is 6, but if you p
 Here's a simple function to calculate `C(n, k)`:
 
 ```swift
-func combinations(n: Int, _ k: Int) -> Int {
+func combinations(_ n: Int, choose k: Int) -> Int {
   return permutations(n, k) / factorial(k)
 }
 ```
@@ -299,7 +299,7 @@ func combinations(n: Int, _ k: Int) -> Int {
 Use it like this:
 
 ```swift
-combinations(28, 5)    // prints 98280
+combinations(28, choose: 5)    // prints 98280
 ```
 
 Because this uses the `permutations()` and `factorial()` functions under the hood, you're still limited by how large these numbers can get. For example, `combinations(30, 15)` is "only" `155,117,520` but because the intermediate results don't fit into a 64-bit integer, you can't calculate it with the given function.
@@ -319,7 +319,7 @@ After the reduction of fractions, we get the following formula:
 We can implement this formula as follows:
 
 ```swift
-func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
+func quickBinomialCoefficient(_ n: Int, choose k: Int) -> Int {
   var result = 1
   for i in 0..<k {
     result *= (n - i)
@@ -334,8 +334,8 @@ This algorithm can create larger numbers than the previous method. Instead of ca
 Here's how you can use this improved algorithm:
 
 ```swift
-quickBinomialCoefficient(8, 2)     // prints 28
-quickBinomialCoefficient(30, 15)   // prints 155117520
+quickBinomialCoefficient(8, choose: 2)     // prints 28
+quickBinomialCoefficient(30, choose: 15)   // prints 155117520
 ```
 
 This new method is quite fast but you're still limited in how large the numbers can get. You can calculate `C(30, 15)` without any problems, but something like `C(66, 33)` will still cause integer overflow in the numerator.
@@ -345,10 +345,10 @@ Here is an algorithm that uses dynamic programming to overcome the need for calc
 	0:               1
 	1:             1   1
 	2:           1   2   1
-	3:         1   3   3   1 
-	4:       1   4   6   4   1 
-	5:     1   5  10   10  5   1 
-	6:   1   6  15  20   15  6   1 
+	3:         1   3   3   1
+	4:       1   4   6   4   1
+	5:     1   5  10   10  5   1
+	6:   1   6  15  20   15  6   1
 
 Each number in the next row is made up by adding two numbers from the previous row. For example in row 6, the number 15 is made by adding the 5 and 10 from row 5. These numbers are called the binomial coefficients and as it happens they are the same as `C(n, k)`.
 
@@ -365,8 +365,8 @@ For example, for row 6:
 The following code calculates Pascal's triangle in order to find the `C(n, k)` you're looking for:
 
 ```swift
-func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+func binomialCoefficient(_ n: Int, choose k: Int) -> Int {
+  var bc = Array(repeating: Array(repeating: 0, count: n + 1), count: n + 1)
 
   for i in 0...n {
     bc[i][0] = 1
@@ -390,7 +390,7 @@ The algorithm itself is quite simple: the first loop fills in the 1s at the oute
 Now you can calculate `C(66, 33)` without any problems:
 
 ```swift
-binomialCoefficient(66, 33)   // prints a very large number
+binomialCoefficient(66, choose: 33)   // prints a very large number
 ```
 
 You may wonder what the point is in calculating these permutations and combinations, but many algorithm problems are really combinatorics problems in disguise. Often you may need to look at all possible combinations of your data to see which one gives the right solution. If that means you need to search through `n!` potential solutions, you may want to consider a different approach -- as you've seen, these numbers become huge very quickly!

From b15b38396a262291bee0b5db407d09eba3833148 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Thu, 27 Oct 2016 16:38:11 +0200
Subject: [PATCH 0622/1679] migrate fixedsizearray to swift3

---
 .../FixedSizeArray.playground/Contents.swift  | 56 ++++++++++++++
 .../contents.xcplayground                     |  4 +
 .../contents.xcworkspacedata                  |  7 ++
 .../timeline.xctimeline                       | 16 ++++
 Fixed Size Array/FixedSizeArray.swift         | 46 -----------
 Fixed Size Array/README.markdown              | 77 ++++++++++---------
 6 files changed, 125 insertions(+), 81 deletions(-)
 create mode 100644 Fixed Size Array/FixedSizeArray.playground/Contents.swift
 create mode 100644 Fixed Size Array/FixedSizeArray.playground/contents.xcplayground
 create mode 100644 Fixed Size Array/FixedSizeArray.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline
 delete mode 100644 Fixed Size Array/FixedSizeArray.swift

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
new file mode 100644
index 000000000..663050d31
--- /dev/null
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -0,0 +1,56 @@
+//: Playground - noun: a place where people can play
+
+/*
+ An unordered array with a maximum size.
+ 
+ Performance is always O(1).
+ */
+struct FixedSizeArray<T> {
+    private var maxSize: Int
+    private var defaultValue: T
+    private var array: [T]
+    private (set) var count = 0
+    
+    init(maxSize: Int, defaultValue: T) {
+        self.maxSize = maxSize
+        self.defaultValue = defaultValue
+        self.array = [T](repeating: defaultValue, count: maxSize)
+    }
+    
+    subscript(index: Int) -> T {
+        assert(index >= 0)
+        assert(index < count)
+        return array[index]
+    }
+    
+    mutating func append(newElement: T) {
+        assert(count < maxSize)
+        array[count] = newElement
+        count += 1
+    }
+    
+    mutating func removeAtIndex(index: Int) -> T {
+        assert(index >= 0)
+        assert(index < count)
+        count -= 1
+        let result = array[index]
+        array[index] = array[count]
+        array[count] = defaultValue
+        return result
+    }
+    
+    mutating func removeAll() {
+        for i in 0..<count {
+            array[i] = defaultValue
+        }
+        count = 0
+    }
+}
+
+var array = FixedSizeArray(maxSize: 5, defaultValue: 0)
+array.append(newElement: 4)
+array.append(newElement: 2)
+array[1]
+array.removeAtIndex(index: 0)
+array.removeAll()
+
diff --git a/Fixed Size Array/FixedSizeArray.playground/contents.xcplayground b/Fixed Size Array/FixedSizeArray.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Fixed Size Array/FixedSizeArray.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Fixed Size Array/FixedSizeArray.playground/playground.xcworkspace/contents.xcworkspacedata b/Fixed Size Array/FixedSizeArray.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Fixed Size Array/FixedSizeArray.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline b/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline
new file mode 100644
index 000000000..def6161e4
--- /dev/null
+++ b/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline	
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1228&amp;EndingColumnNumber=6&amp;EndingLineNumber=52&amp;StartingColumnNumber=1&amp;StartingLineNumber=52&amp;Timestamp=499271741.074357"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1295&amp;EndingColumnNumber=6&amp;EndingLineNumber=54&amp;StartingColumnNumber=1&amp;StartingLineNumber=54&amp;Timestamp=499271760.916283"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>
diff --git a/Fixed Size Array/FixedSizeArray.swift b/Fixed Size Array/FixedSizeArray.swift
deleted file mode 100644
index 270222230..000000000
--- a/Fixed Size Array/FixedSizeArray.swift	
+++ /dev/null
@@ -1,46 +0,0 @@
-/*
-  An unordered array with a maximum size.
-
-  Performance is always O(1).
-*/
-struct FixedSizeArray<T> {
-  private var maxSize: Int
-  private var defaultValue: T
-  private var array: [T]
-  private (set) var count = 0
-
-  init(maxSize: Int, defaultValue: T) {
-    self.maxSize = maxSize
-    self.defaultValue = defaultValue
-    self.array = [T](count: maxSize, repeatedValue: defaultValue)
-  }
-
-  subscript(index: Int) -> T {
-    assert(index >= 0)
-    assert(index < count)
-    return array[index]
-  }
-
-  mutating func append(newElement: T) {
-    assert(count < maxSize)
-    array[count] = newElement
-    count += 1
-  }
-
-  mutating func removeAtIndex(index: Int) -> T {
-    assert(index >= 0)
-    assert(index < count)
-    count -= 1
-    let result = array[index]
-    array[index] = array[count]
-    array[count] = defaultValue
-    return result
-  }
-
-  mutating func removeAll() {
-    for i in 0..<count {
-      array[i] = defaultValue
-    }
-    count = 0
-  }
-}
diff --git a/Fixed Size Array/README.markdown b/Fixed Size Array/README.markdown
index 8a87f077c..efacda710 100644
--- a/Fixed Size Array/README.markdown	
+++ b/Fixed Size Array/README.markdown	
@@ -1,11 +1,11 @@
 # Fixed-Size Arrays
 
-Early programming languages didn't have very fancy arrays. You'd create the array with a specific size and from that moment on it would never grow or shrink. Even the standard arrays in C and Objective-C are still of this type. 
+Early programming languages didn't have very fancy arrays. You'd create the array with a specific size and from that moment on it would never grow or shrink. Even the standard arrays in C and Objective-C are still of this type.
 
 When you define an array like so,
 
 	int myArray[10];
-	
+
 the compiler allocates one contiguous block of memory that can hold 40 bytes (assuming an `int` is 4 bytes):
 
 ![An array with room for 10 elements](Images/array.png)
@@ -42,7 +42,7 @@ The expensive operations are inserting and deleting. When you insert an element
 
 ![Insert requires a memory copy](Images/insert.png)
 
-If your code was using any indexes into the array beyond the insertion point, these indexes are now referring to the wrong objects. 
+If your code was using any indexes into the array beyond the insertion point, these indexes are now referring to the wrong objects.
 
 Deleting requires a copy the other way around:
 
@@ -95,38 +95,45 @@ Here is an implementation in Swift:
 
 ```swift
 struct FixedSizeArray<T> {
-  private var maxSize: Int
-  private var defaultValue: T
-  private var array: [T]
-  private (set) var count = 0
-
-  init(maxSize: Int, defaultValue: T) {
-    self.maxSize = maxSize
-    self.defaultValue = defaultValue
-    self.array = [T](count: maxSize, repeatedValue: defaultValue)
-  }
-
-  subscript(index: Int) -> T {
-    assert(index >= 0)
-    assert(index < count)
-    return array[index]
-  }
-
-  mutating func append(newElement: T) {
-    assert(count < maxSize)
-    array[count] = newElement
-    count += 1
-  }
-
-  mutating func removeAtIndex(index: Int) -> T {
-    assert(index >= 0)
-    assert(index < count)
-    count -= 1
-    let result = array[index]
-    array[index] = array[count]
-    array[count] = defaultValue
-    return result
-  }
+    private var maxSize: Int
+    private var defaultValue: T
+    private var array: [T]
+    private (set) var count = 0
+
+    init(maxSize: Int, defaultValue: T) {
+        self.maxSize = maxSize
+        self.defaultValue = defaultValue
+        self.array = [T](repeating: defaultValue, count: maxSize)
+    }
+
+    subscript(index: Int) -> T {
+        assert(index >= 0)
+        assert(index < count)
+        return array[index]
+    }
+
+    mutating func append(newElement: T) {
+        assert(count < maxSize)
+        array[count] = newElement
+        count += 1
+    }
+
+    mutating func removeAtIndex(index: Int) -> T {
+        assert(index >= 0)
+        assert(index < count)
+        count -= 1
+        let result = array[index]
+        array[index] = array[count]
+        array[count] = defaultValue
+        return result
+    }
+
+    mutating func removeAll() {
+        for i in 0..<count {
+            array[i] = defaultValue
+        }
+        count = 0
+    }
 }
 ```
 

From 7295526436fa7e8a6dfd16f76f78aaf3a6b72a85 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Fri, 28 Oct 2016 12:44:05 -0700
Subject: [PATCH 0623/1679] Added File implementations

---
 Strassen Matrix Multiplication/Matrix.swift     | 9 +++++++++
 Strassen Matrix Multiplication/MatrixSize.swift | 9 +++++++++
 Strassen Matrix Multiplication/Number.swift     | 9 +++++++++
 3 files changed, 27 insertions(+)
 create mode 100644 Strassen Matrix Multiplication/Matrix.swift
 create mode 100644 Strassen Matrix Multiplication/MatrixSize.swift
 create mode 100644 Strassen Matrix Multiplication/Number.swift

diff --git a/Strassen Matrix Multiplication/Matrix.swift b/Strassen Matrix Multiplication/Matrix.swift
new file mode 100644
index 000000000..493e27e06
--- /dev/null
+++ b/Strassen Matrix Multiplication/Matrix.swift	
@@ -0,0 +1,9 @@
+//
+//  Matrix.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation
diff --git a/Strassen Matrix Multiplication/MatrixSize.swift b/Strassen Matrix Multiplication/MatrixSize.swift
new file mode 100644
index 000000000..a01123f3c
--- /dev/null
+++ b/Strassen Matrix Multiplication/MatrixSize.swift	
@@ -0,0 +1,9 @@
+//
+//  MatrixSize.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation
diff --git a/Strassen Matrix Multiplication/Number.swift b/Strassen Matrix Multiplication/Number.swift
new file mode 100644
index 000000000..1bd6cf634
--- /dev/null
+++ b/Strassen Matrix Multiplication/Number.swift	
@@ -0,0 +1,9 @@
+//
+//  Number.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation

From bf24ad0267c3cc6371f61450a9ada56aee1076cc Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Fri, 28 Oct 2016 23:33:46 -0700
Subject: [PATCH 0624/1679] fix for Swift 3

---
 Shuffle/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index e0be6c1e4..ced138572 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -12,7 +12,7 @@ extension Array {
     var temp = [Element]()
     while !isEmpty {
       let i = random(count)
-      let obj = removeAtIndex(i)
+      let obj = remove(at: i)
       temp.append(obj)
     }
     self = temp
@@ -44,7 +44,7 @@ Here is a much improved version of the shuffle algorithm:
 ```swift
 extension Array {
   public mutating func shuffle() {
-    for i in (count - 1).stride(through: 1, by: -1) {
+    for i in stride(from: count - 1, through: 1, by: -1) {
       let j = random(i + 1)
       if i != j {
         swap(&self[i], &self[j])
@@ -96,8 +96,8 @@ There is a slight variation on this algorithm that is useful for when you want t
 Here is the code:
 
 ```swift
-public func shuffledArray(n: Int) -> [Int] {
-  var a = [Int](count: n, repeatedValue: 0)
+public func shuffledArray(_ n: Int) -> [Int] {
+  var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
     let j = random(i + 1)
     if i != j {

From d244ba5fddf47059e0691fde9c182ad3e670971a Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Fri, 28 Oct 2016 23:38:01 -0700
Subject: [PATCH 0625/1679] fix for Swift 3

---
 Shuffle/Shuffle.playground/Contents.swift | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index a12086548..e6d4f000d 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -3,7 +3,7 @@
 import Foundation
 
 /* Returns a random integer between 0 and n-1. */
-public func random(n: Int) -> Int {
+public func random(_ n: Int) -> Int {
   return Int(arc4random_uniform(UInt32(n)))
 }
 
@@ -12,7 +12,7 @@ public func random(n: Int) -> Int {
 /* Fisher-Yates / Knuth shuffle */
 extension Array {
   public mutating func shuffle() {
-    for i in (count - 1).stride(through: 1, by: -1) {
+    for i in stride(from: count - 1, through: 1, by: -1) {
       let j = random(i + 1)
       if i != j {
         swap(&self[i], &self[j])
@@ -29,8 +29,8 @@ list.shuffle()
 
 
 /* Create a new array of numbers that is already shuffled. */
-public func shuffledArray(n: Int) -> [Int] {
-  var a = [Int](count: n, repeatedValue: 0)
+public func shuffledArray(_ n: Int) -> [Int] {
+  var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
     let j = random(i + 1)
     if i != j {

From 22ffeb2bcfa2a4fac261dc7a65ede2bc52a786c1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Mon, 31 Oct 2016 00:29:56 -0700
Subject: [PATCH 0626/1679] Added HaversineDistance to front page.

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 2acedd0fa..bc0dbf21d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -103,6 +103,7 @@ Bad sorting algorithms (don't use these!):
 - [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
 - Statistics
 - [Karatsuba Multiplication](Karatsuba Multiplication/). Another take on elementary multiplication.
+- [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
 
 ### Machine learning
 

From 8328491307b7850c1fd6eb6d50a279fc195ed075 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Mon, 31 Oct 2016 20:34:34 +0100
Subject: [PATCH 0627/1679] migratehashsetswift3

---
 Hash Set/HashSet.playground/Contents.swift    |  72 ------------
 .../HashSet.playground/Sources/HashSet.swift  |  76 +++++++++++++
 Hash Set/README.markdown                      | 104 +++++++++---------
 3 files changed, 130 insertions(+), 122 deletions(-)
 create mode 100644 Hash Set/HashSet.playground/Sources/HashSet.swift

diff --git a/Hash Set/HashSet.playground/Contents.swift b/Hash Set/HashSet.playground/Contents.swift
index 636d4d925..551c6dc86 100644
--- a/Hash Set/HashSet.playground/Contents.swift	
+++ b/Hash Set/HashSet.playground/Contents.swift	
@@ -1,33 +1,5 @@
 //: Playground - noun: a place where people can play
 
-public struct HashSet<T: Hashable> {
-  private var dictionary = Dictionary<T, Bool>()
-
-  public mutating func insert(element: T) {
-    dictionary[element] = true
-  }
-
-  public mutating func remove(element: T) {
-    dictionary[element] = nil
-  }
-
-  public func contains(element: T) -> Bool {
-    return dictionary[element] != nil
-  }
-
-  public func allElements() -> [T] {
-    return Array(dictionary.keys)
-  }
-
-  public var count: Int {
-    return dictionary.count
-  }
-
-  public var isEmpty: Bool {
-    return dictionary.isEmpty
-  }
-}
-
 var set = HashSet<String>()
 
 set.insert("one")
@@ -43,24 +15,8 @@ set.remove("one")
 set.allElements()
 set.contains("one")
 
-
-
 /* Union */
 
-extension HashSet {
-  public func union(otherSet: HashSet<T>) -> HashSet<T> {
-    var combined = HashSet<T>()
-    for obj in dictionary.keys {
-      combined.insert(obj)
-    }
-    for obj in otherSet.dictionary.keys {
-      combined.insert(obj)
-    }
-    return combined
-  }
-}
-
-
 var setA = HashSet<Int>()
 setA.insert(1)
 setA.insert(2)
@@ -76,41 +32,13 @@ setB.insert(6)
 let union = setA.union(setB)
 union.allElements()          // [5, 6, 2, 3, 1, 4]
 
-
-
 /* Intersection */
 
-extension HashSet {
-  public func intersect(otherSet: HashSet<T>) -> HashSet<T> {
-    var common = HashSet<T>()
-    for obj in dictionary.keys {
-      if otherSet.contains(obj) {
-        common.insert(obj)
-      }
-    }
-    return common
-  }
-}
-
 let intersection = setA.intersect(setB)
 intersection.allElements()               // [3, 4]
 
-
-
 /* Difference */
 
-extension HashSet {
-  public func difference(otherSet: HashSet<T>) -> HashSet<T> {
-    var diff = HashSet<T>()
-    for obj in dictionary.keys {
-      if !otherSet.contains(obj) {
-        diff.insert(obj)
-      }
-    }
-    return diff
-  }
-}
-
 let difference1 = setA.difference(setB)
 difference1.allElements()                // [2, 1]
 
diff --git a/Hash Set/HashSet.playground/Sources/HashSet.swift b/Hash Set/HashSet.playground/Sources/HashSet.swift
new file mode 100644
index 000000000..c3365110b
--- /dev/null
+++ b/Hash Set/HashSet.playground/Sources/HashSet.swift	
@@ -0,0 +1,76 @@
+//: Playground - noun: a place where people can play
+
+public struct HashSet<T: Hashable> {
+    fileprivate var dictionary = Dictionary<T, Bool>()
+    
+    public init() {
+        
+    }
+    
+    public mutating func insert(_ element: T) {
+        dictionary[element] = true
+    }
+    
+    public mutating func remove(_ element: T) {
+        dictionary[element] = nil
+    }
+    
+    public func contains(_ element: T) -> Bool {
+        return dictionary[element] != nil
+    }
+    
+    public func allElements() -> [T] {
+        return Array(dictionary.keys)
+    }
+    
+    public var count: Int {
+        return dictionary.count
+    }
+    
+    public var isEmpty: Bool {
+        return dictionary.isEmpty
+    }
+}
+
+/* Union */
+
+extension HashSet {
+    public func union(_ otherSet: HashSet<T>) -> HashSet<T> {
+        var combined = HashSet<T>()
+        for obj in self.dictionary.keys {
+            combined.insert(obj)
+        }
+        for obj in otherSet.dictionary.keys {
+            combined.insert(obj)
+        }
+        return combined
+    }
+}
+
+/* Intersection */
+
+extension HashSet {
+    public func intersect(_ otherSet: HashSet<T>) -> HashSet<T> {
+        var common = HashSet<T>()
+        for obj in dictionary.keys {
+            if otherSet.contains(obj) {
+                common.insert(obj)
+            }
+        }
+        return common
+    }
+}
+
+/* Difference */
+
+extension HashSet {
+    public func difference(_ otherSet: HashSet<T>) -> HashSet<T> {
+        var diff = HashSet<T>()
+        for obj in dictionary.keys {
+            if !otherSet.contains(obj) {
+                diff.insert(obj)
+            }
+        }
+        return diff
+    }
+}
diff --git a/Hash Set/README.markdown b/Hash Set/README.markdown
index c6616fb42..368920a1c 100644
--- a/Hash Set/README.markdown	
+++ b/Hash Set/README.markdown	
@@ -38,31 +38,35 @@ Here are the beginnings of `HashSet` in Swift:
 
 ```swift
 public struct HashSet<T: Hashable> {
-  private var dictionary = Dictionary<T, Bool>()
-  
-  public mutating func insert(element: T) {
-    dictionary[element] = true
-  }
-  
-  public mutating func remove(element: T) {
-    dictionary[element] = nil
-  }
-  
-  public func contains(element: T) -> Bool {
-    return dictionary[element] != nil
-  }
-  
-  public func allElements() -> [T] {
-    return Array(dictionary.keys)
-  }
-  
-  public var count: Int {
-    return dictionary.count
-  }
-  
-  public var isEmpty: Bool {
-    return dictionary.isEmpty
-  }
+    fileprivate var dictionary = Dictionary<T, Bool>()
+
+    public init() {
+
+    }
+
+    public mutating func insert(_ element: T) {
+        dictionary[element] = true
+    }
+
+    public mutating func remove(_ element: T) {
+        dictionary[element] = nil
+    }
+
+    public func contains(_ element: T) -> Bool {
+        return dictionary[element] != nil
+    }
+
+    public func allElements() -> [T] {
+        return Array(dictionary.keys)
+    }
+
+    public var count: Int {
+        return dictionary.count
+    }
+
+    public var isEmpty: Bool {
+        return dictionary.isEmpty
+    }
 }
 ```
 
@@ -101,16 +105,16 @@ Here is the code for the union operation:
 
 ```swift
 extension HashSet {
-  public func union(otherSet: HashSet<T>) -> HashSet<T> {
-    var combined = HashSet<T>()
-    for obj in dictionary.keys {
-      combined.insert(obj)
-    }
-    for obj in otherSet.dictionary.keys {
-      combined.insert(obj)
+    public func union(_ otherSet: HashSet<T>) -> HashSet<T> {
+        var combined = HashSet<T>()
+        for obj in self.dictionary.keys {
+            combined.insert(obj)
+        }
+        for obj in otherSet.dictionary.keys {
+            combined.insert(obj)
+        }
+        return combined
     }
-    return combined
-  }
 }
 ```
 
@@ -141,15 +145,15 @@ The *intersection* of two sets contains only the elements that they have in comm
 
 ```swift
 extension HashSet {
-  public func intersect(otherSet: HashSet<T>) -> HashSet<T> {
-    var common = HashSet<T>()
-    for obj in dictionary.keys {
-      if otherSet.contains(obj) {
-        common.insert(obj)
-      }
+    public func intersect(_ otherSet: HashSet<T>) -> HashSet<T> {
+        var common = HashSet<T>()
+        for obj in dictionary.keys {
+            if otherSet.contains(obj) {
+                common.insert(obj)
+            }
+        }
+        return common
     }
-    return common
-  }
 }
 ```
 
@@ -166,15 +170,15 @@ Finally, the *difference* between two sets removes the elements they have in com
 
 ```swift
 extension HashSet {
-  public func difference(otherSet: HashSet<T>) -> HashSet<T> {
-    var diff = HashSet<T>()
-    for obj in dictionary.keys {
-      if !otherSet.contains(obj) {
-        diff.insert(obj)
-      }
+    public func difference(_ otherSet: HashSet<T>) -> HashSet<T> {
+        var diff = HashSet<T>()
+        for obj in dictionary.keys {
+            if !otherSet.contains(obj) {
+                diff.insert(obj)
+            }
+        }
+        return diff
     }
-    return diff
-  }
 }
 ```
 

From 3fe357f6fd4123fc063f39d5eec8607529a1f617 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Tue, 1 Nov 2016 04:06:30 -0700
Subject: [PATCH 0628/1679] Removed an argument label for the append method in
 an effort to keep consistent with native collection types. Changed a method
 name to be more Swift like.

---
 .../FixedSizeArray.playground/Contents.swift           | 10 +++++-----
 .../FixedSizeArray.playground/timeline.xctimeline      |  4 ++--
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 663050d31..afe666a31 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -23,13 +23,13 @@ struct FixedSizeArray<T> {
         return array[index]
     }
     
-    mutating func append(newElement: T) {
+    mutating func append(_ newElement: T) {
         assert(count < maxSize)
         array[count] = newElement
         count += 1
     }
     
-    mutating func removeAtIndex(index: Int) -> T {
+    mutating func removeAt(index: Int) -> T {
         assert(index >= 0)
         assert(index < count)
         count -= 1
@@ -48,9 +48,9 @@ struct FixedSizeArray<T> {
 }
 
 var array = FixedSizeArray(maxSize: 5, defaultValue: 0)
-array.append(newElement: 4)
-array.append(newElement: 2)
+array.append(4)
+array.append(2)
 array[1]
-array.removeAtIndex(index: 0)
+array.removeAt(index: 0)
 array.removeAll()
 
diff --git a/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline b/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline
index def6161e4..d95db1553 100644
--- a/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline	
+++ b/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1228&amp;EndingColumnNumber=6&amp;EndingLineNumber=52&amp;StartingColumnNumber=1&amp;StartingLineNumber=52&amp;Timestamp=499271741.074357"
+         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1213&amp;EndingColumnNumber=6&amp;EndingLineNumber=52&amp;StartingColumnNumber=1&amp;StartingLineNumber=52&amp;Timestamp=499691083.961245"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1295&amp;EndingColumnNumber=6&amp;EndingLineNumber=54&amp;StartingColumnNumber=1&amp;StartingLineNumber=54&amp;Timestamp=499271760.916283"
+         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1263&amp;EndingColumnNumber=6&amp;EndingLineNumber=54&amp;StartingColumnNumber=1&amp;StartingLineNumber=54&amp;Timestamp=499691083.961359"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>

From b2bc31b7e8e1764f7431d07cbfacccccf7733518 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Tue, 1 Nov 2016 04:10:58 -0700
Subject: [PATCH 0629/1679] Changed tabs from 4 spaces to 2 spaces. Updated
 README file to reflect the updated syntax.

---
 .../FixedSizeArray.playground/Contents.swift  | 76 ++++++++---------
 .../timeline.xctimeline                       |  4 +-
 Fixed Size Array/README.markdown              | 84 +++++++++----------
 3 files changed, 82 insertions(+), 82 deletions(-)

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index afe666a31..f1bc63315 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -6,45 +6,45 @@
  Performance is always O(1).
  */
 struct FixedSizeArray<T> {
-    private var maxSize: Int
-    private var defaultValue: T
-    private var array: [T]
-    private (set) var count = 0
-    
-    init(maxSize: Int, defaultValue: T) {
-        self.maxSize = maxSize
-        self.defaultValue = defaultValue
-        self.array = [T](repeating: defaultValue, count: maxSize)
-    }
-    
-    subscript(index: Int) -> T {
-        assert(index >= 0)
-        assert(index < count)
-        return array[index]
-    }
-    
-    mutating func append(_ newElement: T) {
-        assert(count < maxSize)
-        array[count] = newElement
-        count += 1
-    }
-    
-    mutating func removeAt(index: Int) -> T {
-        assert(index >= 0)
-        assert(index < count)
-        count -= 1
-        let result = array[index]
-        array[index] = array[count]
-        array[count] = defaultValue
-        return result
-    }
-    
-    mutating func removeAll() {
-        for i in 0..<count {
-            array[i] = defaultValue
-        }
-        count = 0
+  private var maxSize: Int
+  private var defaultValue: T
+  private var array: [T]
+  private (set) var count = 0
+  
+  init(maxSize: Int, defaultValue: T) {
+    self.maxSize = maxSize
+    self.defaultValue = defaultValue
+    self.array = [T](repeating: defaultValue, count: maxSize)
+  }
+  
+  subscript(index: Int) -> T {
+    assert(index >= 0)
+    assert(index < count)
+    return array[index]
+  }
+  
+  mutating func append(_ newElement: T) {
+    assert(count < maxSize)
+    array[count] = newElement
+    count += 1
+  }
+  
+  mutating func removeAt(index: Int) -> T {
+    assert(index >= 0)
+    assert(index < count)
+    count -= 1
+    let result = array[index]
+    array[index] = array[count]
+    array[count] = defaultValue
+    return result
+  }
+  
+  mutating func removeAll() {
+    for i in 0..<count {
+      array[i] = defaultValue
     }
+    count = 0
+  }
 }
 
 var array = FixedSizeArray(maxSize: 5, defaultValue: 0)
diff --git a/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline b/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline
index d95db1553..31fc7c826 100644
--- a/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline	
+++ b/Fixed Size Array/FixedSizeArray.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1213&amp;EndingColumnNumber=6&amp;EndingLineNumber=52&amp;StartingColumnNumber=1&amp;StartingLineNumber=52&amp;Timestamp=499691083.961245"
+         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1093&amp;EndingColumnNumber=6&amp;EndingLineNumber=52&amp;StartingColumnNumber=1&amp;StartingLineNumber=52&amp;Timestamp=499691409.537369"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1263&amp;EndingColumnNumber=6&amp;EndingLineNumber=54&amp;StartingColumnNumber=1&amp;StartingLineNumber=54&amp;Timestamp=499691083.961359"
+         documentLocation = "#CharacterRangeLen=5&amp;CharacterRangeLoc=1143&amp;EndingColumnNumber=6&amp;EndingLineNumber=54&amp;StartingColumnNumber=1&amp;StartingLineNumber=54&amp;Timestamp=499691409.537492"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Fixed Size Array/README.markdown b/Fixed Size Array/README.markdown
index efacda710..e9eade140 100644
--- a/Fixed Size Array/README.markdown	
+++ b/Fixed Size Array/README.markdown	
@@ -55,12 +55,12 @@ Fixed-size arrays are a good solution when:
 1. You know beforehand the maximum number of elements you'll need. In a game this could be the number of sprites that can be active at a time. It's not unreasonable to put a limit on this. (For games it's a good idea to allocate all the objects you need in advance anyway.)
 2. It is not necessary to have a sorted version of the array, i.e. the order of the elements does not matter.
 
-If the array does not need to be sorted, then an `insertAtIndex()` operation is not needed. You can simply append any new elements to the end, until the array is full.
+If the array does not need to be sorted, then an `insertAt(index)` operation is not needed. You can simply append any new elements to the end, until the array is full.
 
 The code for adding an element becomes:
 
 ```swift
-func append(newElement) {
+func append(_ newElement: T) {
   if count < maxSize {
     array[count] = newElement
     count += 1
@@ -75,7 +75,7 @@ Determining the number of elements in the array is just a matter of reading the
 The code for removing an element is equally simple:
 
 ```swift
-func removeAtIndex(index) {
+func removeAt(index: Int) {
   count -= 1
   array[index] = array[count]
 }
@@ -95,45 +95,45 @@ Here is an implementation in Swift:
 
 ```swift
 struct FixedSizeArray<T> {
-    private var maxSize: Int
-    private var defaultValue: T
-    private var array: [T]
-    private (set) var count = 0
-
-    init(maxSize: Int, defaultValue: T) {
-        self.maxSize = maxSize
-        self.defaultValue = defaultValue
-        self.array = [T](repeating: defaultValue, count: maxSize)
-    }
-
-    subscript(index: Int) -> T {
-        assert(index >= 0)
-        assert(index < count)
-        return array[index]
-    }
-
-    mutating func append(newElement: T) {
-        assert(count < maxSize)
-        array[count] = newElement
-        count += 1
-    }
-
-    mutating func removeAtIndex(index: Int) -> T {
-        assert(index >= 0)
-        assert(index < count)
-        count -= 1
-        let result = array[index]
-        array[index] = array[count]
-        array[count] = defaultValue
-        return result
-    }
-
-    mutating func removeAll() {
-        for i in 0..<count {
-            array[i] = defaultValue
-        }
-        count = 0
+  private var maxSize: Int
+  private var defaultValue: T
+  private var array: [T]
+  private (set) var count = 0
+  
+  init(maxSize: Int, defaultValue: T) {
+    self.maxSize = maxSize
+    self.defaultValue = defaultValue
+    self.array = [T](repeating: defaultValue, count: maxSize)
+  }
+  
+  subscript(index: Int) -> T {
+    assert(index >= 0)
+    assert(index < count)
+    return array[index]
+  }
+  
+  mutating func append(_ newElement: T) {
+    assert(count < maxSize)
+    array[count] = newElement
+    count += 1
+  }
+  
+  mutating func removeAt(index: Int) -> T {
+    assert(index >= 0)
+    assert(index < count)
+    count -= 1
+    let result = array[index]
+    array[index] = array[count]
+    array[count] = defaultValue
+    return result
+  }
+  
+  mutating func removeAll() {
+    for i in 0..<count {
+      array[i] = defaultValue
     }
+    count = 0
+  }
 }
 ```
 
@@ -143,6 +143,6 @@ When creating the array, you specify the maximum size and a default value:
 var a = FixedSizeArray(maxSize: 10, defaultValue: 0)
 ```
 
-Note that `removeAtIndex()` overwrites the last element with this `defaultValue` to clean up the "junk" object that gets left behind. Normally it wouldn't matter to leave that duplicate object in the array, but if it's a class or a struct it may have strong references to other objects and it's good boyscout practice to zero those out.
+Note that `removeAt(index: Int)` overwrites the last element with this `defaultValue` to clean up the "junk" object that gets left behind. Normally it wouldn't matter to leave that duplicate object in the array, but if it's a class or a struct it may have strong references to other objects and it's good boyscout practice to zero those out.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 5238f222705c9005605cee40c94d944db87c1350 Mon Sep 17 00:00:00 2001
From: Beth Knight <bethknight1234@gmail.com>
Date: Tue, 1 Nov 2016 18:54:39 -0500
Subject: [PATCH 0630/1679] took off an extra min

---
 .../SelectionSampling.playground/Contents.swift             | 3 +--
 .../SelectionSampling.playground/timeline.xctimeline        | 6 ------
 2 files changed, 1 insertion(+), 8 deletions(-)
 delete mode 100644 Selection Sampling/SelectionSampling.playground/timeline.xctimeline

diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index f6032137b..df1bb2e32 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -3,7 +3,7 @@
 import Foundation
 
 /* Returns a random integer in the range min...max, inclusive. */
-public func random(min min: Int, max: Int) -> Int {
+public func random(min: Int, max: Int) -> Int {
   assert(min < max)
   return min + Int(arc4random_uniform(UInt32(max - min + 1)))
 }
@@ -45,7 +45,6 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
 }
 
 
-
 let poem = [
   "there", "once", "was", "a", "man", "from", "nantucket",
   "who", "kept", "all", "of", "his", "cash", "in", "a", "bucket",
diff --git a/Selection Sampling/SelectionSampling.playground/timeline.xctimeline b/Selection Sampling/SelectionSampling.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Selection Sampling/SelectionSampling.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From f0c17d5aeedf8d78c5449fa326e91152dc3cc5dc Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <Jacopo.Mangiavacchi@uk.ibm.com>
Date: Wed, 2 Nov 2016 12:12:45 +0000
Subject: [PATCH 0631/1679] Dining Philosophers Problem Algorithm

---
 .../project.pbxproj                           | 250 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcschemes/DiningPhilosophers.xcscheme     |  71 +++++
 .../xcschemes/xcschememanagement.plist        |  12 +
 DiningPhilosophers/LICENSE                    | 201 ++++++++++++++
 DiningPhilosophers/Package.swift              |   5 +
 DiningPhilosophers/README.md                  |  13 +
 DiningPhilosophers/Sources/main.swift         | 107 ++++++++
 8 files changed, 666 insertions(+)
 create mode 100755 DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
 create mode 100755 DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100755 DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/DiningPhilosophers.xcscheme
 create mode 100755 DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/xcschememanagement.plist
 create mode 100755 DiningPhilosophers/LICENSE
 create mode 100755 DiningPhilosophers/Package.swift
 create mode 100755 DiningPhilosophers/README.md
 create mode 100755 DiningPhilosophers/Sources/main.swift

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
new file mode 100755
index 000000000..9743ff7d1
--- /dev/null
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -0,0 +1,250 @@
+// !$*UTF8*$!
+{
+   archiveVersion = "1";
+   objectVersion = "46";
+   objects = {
+      OBJ_1 = {
+         isa = "PBXProject";
+         attributes = {
+            LastUpgradeCheck = "9999";
+         };
+         buildConfigurationList = OBJ_2;
+         compatibilityVersion = "Xcode 3.2";
+         developmentRegion = "English";
+         hasScannedForEncodings = "0";
+         knownRegions = (
+            "en",
+         );
+         mainGroup = OBJ_5;
+         productRefGroup = OBJ_11;
+         projectDirPath = ".";
+         targets = (
+            OBJ_13,
+         );
+      };
+      OBJ_10 = {
+         isa = "PBXGroup";
+         children = (
+         );
+         path = "Tests";
+         sourceTree = "<group>";
+      };
+      OBJ_11 = {
+         isa = "PBXGroup";
+         children = (
+            OBJ_12,
+         );
+         name = "Products";
+         path = "";
+         sourceTree = "BUILT_PRODUCTS_DIR";
+      };
+      OBJ_12 = {
+         isa = "PBXFileReference";
+         path = "DiningPhilosophers";
+         sourceTree = "BUILT_PRODUCTS_DIR";
+      };
+      OBJ_13 = {
+         isa = "PBXNativeTarget";
+         buildConfigurationList = OBJ_14;
+         buildPhases = (
+            OBJ_17,
+            OBJ_19,
+         );
+         dependencies = (
+         );
+         name = "DiningPhilosophers";
+         productName = "DiningPhilosophers";
+         productReference = OBJ_12;
+         productType = "com.apple.product-type.tool";
+      };
+      OBJ_14 = {
+         isa = "XCConfigurationList";
+         buildConfigurations = (
+            OBJ_15,
+            OBJ_16,
+         );
+         defaultConfigurationIsVisible = "0";
+         defaultConfigurationName = "Debug";
+      };
+      OBJ_15 = {
+         isa = "XCBuildConfiguration";
+         buildSettings = {
+            FRAMEWORK_SEARCH_PATHS = (
+               "$(PLATFORM_DIR)/Developer/Library/Frameworks",
+            );
+            HEADER_SEARCH_PATHS = (
+            );
+            INFOPLIST_FILE = "DiningPhilosophers.xcodeproj/DiningPhilosophers_Info.plist";
+            LD_RUNPATH_SEARCH_PATHS = (
+               "$(TOOLCHAIN_DIR)/usr/lib/swift/macosx",
+               "@executable_path",
+            );
+            OTHER_LDFLAGS = (
+               "$(inherited)",
+            );
+            OTHER_SWIFT_FLAGS = (
+               "$(inherited)",
+            );
+            SUPPORTED_PLATFORMS = (
+               "macosx",
+            );
+            SWIFT_ACTIVE_COMPILATION_CONDITIONS = "SWIFT_PACKAGE";
+            SWIFT_FORCE_DYNAMIC_LINK_STDLIB = "YES";
+            SWIFT_FORCE_STATIC_LINK_STDLIB = "NO";
+            SWIFT_VERSION = "3.0";
+            TARGET_NAME = "DiningPhilosophers";
+         };
+         name = "Debug";
+      };
+      OBJ_16 = {
+         isa = "XCBuildConfiguration";
+         buildSettings = {
+            FRAMEWORK_SEARCH_PATHS = (
+               "$(PLATFORM_DIR)/Developer/Library/Frameworks",
+            );
+            HEADER_SEARCH_PATHS = (
+            );
+            INFOPLIST_FILE = "DiningPhilosophers.xcodeproj/DiningPhilosophers_Info.plist";
+            LD_RUNPATH_SEARCH_PATHS = (
+               "$(TOOLCHAIN_DIR)/usr/lib/swift/macosx",
+               "@executable_path",
+            );
+            OTHER_LDFLAGS = (
+               "$(inherited)",
+            );
+            OTHER_SWIFT_FLAGS = (
+               "$(inherited)",
+            );
+            SUPPORTED_PLATFORMS = (
+               "macosx",
+            );
+            SWIFT_ACTIVE_COMPILATION_CONDITIONS = "SWIFT_PACKAGE";
+            SWIFT_FORCE_DYNAMIC_LINK_STDLIB = "YES";
+            SWIFT_FORCE_STATIC_LINK_STDLIB = "NO";
+            SWIFT_VERSION = "3.0";
+            TARGET_NAME = "DiningPhilosophers";
+         };
+         name = "Release";
+      };
+      OBJ_17 = {
+         isa = "PBXSourcesBuildPhase";
+         files = (
+            OBJ_18,
+         );
+      };
+      OBJ_18 = {
+         isa = "PBXBuildFile";
+         fileRef = OBJ_9;
+      };
+      OBJ_19 = {
+         isa = "PBXFrameworksBuildPhase";
+         files = (
+         );
+      };
+      OBJ_2 = {
+         isa = "XCConfigurationList";
+         buildConfigurations = (
+            OBJ_3,
+            OBJ_4,
+         );
+         defaultConfigurationIsVisible = "0";
+         defaultConfigurationName = "Debug";
+      };
+      OBJ_3 = {
+         isa = "XCBuildConfiguration";
+         buildSettings = {
+            COMBINE_HIDPI_IMAGES = "YES";
+            COPY_PHASE_STRIP = "NO";
+            DEBUG_INFORMATION_FORMAT = "dwarf";
+            DYLIB_INSTALL_NAME_BASE = "@rpath";
+            ENABLE_NS_ASSERTIONS = "YES";
+            GCC_OPTIMIZATION_LEVEL = "0";
+            MACOSX_DEPLOYMENT_TARGET = "10.10";
+            ONLY_ACTIVE_ARCH = "YES";
+            OTHER_SWIFT_FLAGS = (
+               "-DXcode",
+            );
+            PRODUCT_NAME = "$(TARGET_NAME)";
+            SUPPORTED_PLATFORMS = (
+               "macosx",
+               "iphoneos",
+               "iphonesimulator",
+               "appletvos",
+               "appletvsimulator",
+               "watchos",
+               "watchsimulator",
+            );
+            SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+            USE_HEADERMAP = "NO";
+         };
+         name = "Debug";
+      };
+      OBJ_4 = {
+         isa = "XCBuildConfiguration";
+         buildSettings = {
+            COMBINE_HIDPI_IMAGES = "YES";
+            COPY_PHASE_STRIP = "YES";
+            DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+            DYLIB_INSTALL_NAME_BASE = "@rpath";
+            GCC_OPTIMIZATION_LEVEL = "s";
+            MACOSX_DEPLOYMENT_TARGET = "10.10";
+            OTHER_SWIFT_FLAGS = (
+               "-DXcode",
+            );
+            PRODUCT_NAME = "$(TARGET_NAME)";
+            SUPPORTED_PLATFORMS = (
+               "macosx",
+               "iphoneos",
+               "iphonesimulator",
+               "appletvos",
+               "appletvsimulator",
+               "watchos",
+               "watchsimulator",
+            );
+            SWIFT_OPTIMIZATION_LEVEL = "-O";
+            USE_HEADERMAP = "NO";
+         };
+         name = "Release";
+      };
+      OBJ_5 = {
+         isa = "PBXGroup";
+         children = (
+            OBJ_6,
+            OBJ_7,
+            OBJ_10,
+            OBJ_11,
+         );
+         path = "";
+         sourceTree = "<group>";
+      };
+      OBJ_6 = {
+         isa = "PBXFileReference";
+         explicitFileType = "sourcecode.swift";
+         path = "Package.swift";
+         sourceTree = "<group>";
+      };
+      OBJ_7 = {
+         isa = "PBXGroup";
+         children = (
+            OBJ_8,
+         );
+         path = "Sources";
+         sourceTree = "<group>";
+      };
+      OBJ_8 = {
+         isa = "PBXGroup";
+         children = (
+            OBJ_9,
+         );
+         name = "DiningPhilosophers";
+         path = "Sources";
+         sourceTree = "SOURCE_ROOT";
+      };
+      OBJ_9 = {
+         isa = "PBXFileReference";
+         path = "main.swift";
+         sourceTree = "<group>";
+      };
+   };
+   rootObject = OBJ_1;
+}
diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100755
index 000000000..919434a62
--- /dev/null
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/DiningPhilosophers.xcscheme b/DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/DiningPhilosophers.xcscheme
new file mode 100755
index 000000000..3c17791b7
--- /dev/null
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/DiningPhilosophers.xcscheme
@@ -0,0 +1,71 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "9999"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "OBJ_13"
+               BuildableName = "DiningPhilosophers"
+               BlueprintName = "DiningPhilosophers"
+               ReferencedContainer = "container:DiningPhilosophers.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "OBJ_13"
+            BuildableName = "DiningPhilosophers"
+            BlueprintName = "DiningPhilosophers"
+            ReferencedContainer = "container:DiningPhilosophers.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/xcschememanagement.plist b/DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/xcschememanagement.plist
new file mode 100755
index 000000000..4cd3e1d66
--- /dev/null
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/xcshareddata/xcschemes/xcschememanagement.plist
@@ -0,0 +1,12 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<plist version="1.0">
+<dict>
+  <key>SchemeUserState</key>
+  <dict>
+    <key>DiningPhilosophers.xcscheme</key>
+    <dict></dict>
+  </dict>
+  <key>SuppressBuildableAutocreation</key>
+  <dict></dict>
+</dict>
+</plist>
diff --git a/DiningPhilosophers/LICENSE b/DiningPhilosophers/LICENSE
new file mode 100755
index 000000000..8dada3eda
--- /dev/null
+++ b/DiningPhilosophers/LICENSE
@@ -0,0 +1,201 @@
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+
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diff --git a/DiningPhilosophers/Package.swift b/DiningPhilosophers/Package.swift
new file mode 100755
index 000000000..c7e5efd4f
--- /dev/null
+++ b/DiningPhilosophers/Package.swift
@@ -0,0 +1,5 @@
+import PackageDescription
+
+let package = Package(
+    name: "DiningPhilosophers"
+)
diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
new file mode 100755
index 000000000..06302cf2a
--- /dev/null
+++ b/DiningPhilosophers/README.md
@@ -0,0 +1,13 @@
+# SwiftDiningPhilosophers
+Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using GCD and Semaphore in Swift)
+
+Written by Jacopo Mangiavacchi
+
+
+# from https://en.wikipedia.org/wiki/Dining_philosophers_problem
+
+In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
+
+It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.
+
+This Swift implementation is based on the Chandy/Misra solution and it use GCD Dispatch and Semaphone on Swift cross platform
diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
new file mode 100755
index 000000000..dfde40773
--- /dev/null
+++ b/DiningPhilosophers/Sources/main.swift
@@ -0,0 +1,107 @@
+//
+//  Swift Dining philosophers problem Algorithm
+//  https://en.wikipedia.org/wiki/Dining_philosophers_problem
+//
+//  Created by Jacopo Mangiavacchi on 11/02/16.
+//
+//
+
+
+import Foundation
+import Dispatch
+
+let numberOfPhilosophers = 4
+
+class ForkPair {
+    static let forksSemaphore:[DispatchSemaphore] = Array(repeating: DispatchSemaphore(value: 1), count: numberOfPhilosophers)
+    
+    let leftFork: DispatchSemaphore
+    let rightFork: DispatchSemaphore
+    
+    init(leftIndex: Int, rightIndex: Int) {
+        //Order forks by index to prevent deadlock
+        if leftIndex > rightIndex {
+            leftFork = ForkPair.forksSemaphore[leftIndex]
+            rightFork = ForkPair.forksSemaphore[rightIndex]
+        }
+        else {
+            leftFork = ForkPair.forksSemaphore[rightIndex]
+            rightFork = ForkPair.forksSemaphore[leftIndex]
+        }
+    }
+
+    func pickUp() {
+        //Acquire by starting with the lower index
+        leftFork.wait()
+        rightFork.wait()
+    }
+    
+    func putDown() {
+        //The order does not matter here
+        leftFork.signal()
+        rightFork.signal()
+    }
+}
+
+
+class Philosophers {
+    let forkPair: ForkPair
+    let philosopherIndex: Int
+    
+    var leftIndex = -1
+    var rightIndex = -1
+    
+    init(philosopherIndex: Int) {
+        leftIndex = philosopherIndex
+        rightIndex = philosopherIndex - 1
+        
+        if rightIndex < 0 {
+            rightIndex += numberOfPhilosophers
+        }
+
+        self.forkPair = ForkPair(leftIndex: leftIndex, rightIndex: rightIndex)
+        self.philosopherIndex = philosopherIndex
+        
+        print("Philosopher: \(philosopherIndex)  left: \(leftIndex)  right: \(rightIndex)")
+    }
+    
+    func run() {
+        while true {
+            print("Acquiring lock for Philosofer: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
+            forkPair.pickUp()
+            print("Start Eating Philosopher: \(philosopherIndex)")
+            //sleep(1000)
+            print("Releasing lock for Philosofer: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
+            forkPair.putDown()
+        }
+    }
+}
+
+
+// Layout of the table (P = philosopher, f = fork) for 4 Philosopher
+//          P0
+//       f3    f0
+//     P3        P1
+//       f2    f1
+//          P2
+
+let globalSem = DispatchSemaphore(value: 0)
+
+for i in 0..<numberOfPhilosophers {
+    DispatchQueue.global(qos: .background).async {
+        let p = Philosophers(philosopherIndex: i)
+        
+        p.run()
+    }
+}
+
+//start the thread signaling the semaphore
+for i in 0..<numberOfPhilosophers {
+    ForkPair.forksSemaphore[i].signal()
+}
+
+
+//wait forever
+globalSem.wait()
+
+

From ee38a5a6055c12f823f3e2fc2852a299e8a04357 Mon Sep 17 00:00:00 2001
From: Vladimir Zamyatin <boba@opendsp.com>
Date: Wed, 2 Nov 2016 15:23:31 +0100
Subject: [PATCH 0632/1679] Fix a bug in SegmentTree

---
 .../SegmentTree.playground/Contents.swift     | 46 +++++++++----------
 Segment Tree/SegmentTree.swift                | 10 ++--
 2 files changed, 28 insertions(+), 28 deletions(-)

diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 6b33b2f44..5bba56cc0 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -28,7 +28,7 @@ public class SegmentTree<T> {
 		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
 	}
 	
-	public func query(withLeftBound: Int, rightBound: Int) -> T {
+	public func query(leftBound: Int, rightBound: Int) -> T {
 		if self.leftBound == leftBound && self.rightBound == rightBound {
 			return self.value
 		}
@@ -37,12 +37,12 @@ public class SegmentTree<T> {
 		guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
 		
 		if leftChild.rightBound < leftBound {
-			return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
+			return rightChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else if rightChild.leftBound > rightBound {
-			return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
+			return leftChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else {
-			let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
-			let rightResult = rightChild.query(withLeftBound:rightChild.leftBound, rightBound: rightBound)
+			let leftResult = leftChild.query(leftBound: leftBound, rightBound: leftChild.rightBound)
+			let rightResult = rightChild.query(leftBound:rightChild.leftBound, rightBound: rightBound)
 			return function(leftResult, rightResult)
 		}
 	}
@@ -68,14 +68,14 @@ let array = [1, 2, 3, 4]
 
 let sumSegmentTree = SegmentTree(array: array, function: +)
 
-print(sumSegmentTree.query(withLeftBound: 0, rightBound: 3)) // 1 + 2 + 3 + 4 = 10
-print(sumSegmentTree.query(withLeftBound: 1, rightBound: 2)) // 2 + 3 = 5
-print(sumSegmentTree.query(withLeftBound: 0, rightBound: 0)) // 1 = 1
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 1 + 2 + 3 + 4 = 10
+print(sumSegmentTree.query(leftBound: 1, rightBound: 2)) // 2 + 3 = 5
+print(sumSegmentTree.query(leftBound: 0, rightBound: 0)) // 1 = 1
 
 sumSegmentTree.replaceItem(at: 0, withItem: 2) //our array now is [2, 2, 3, 4]
 
-print(sumSegmentTree.query(withLeftBound: 0, rightBound: 0)) // 2 = 2
-print(sumSegmentTree.query(withLeftBound: 0, rightBound: 1)) // 2 + 2 = 4
+print(sumSegmentTree.query(leftBound: 0, rightBound: 0)) // 2 = 2
+print(sumSegmentTree.query(leftBound: 0, rightBound: 1)) // 2 + 2 = 4
 
 
 //you can use any associative function (i.e (a+b)+c == a+(b+c)) as function for segment tree
@@ -96,14 +96,14 @@ let gcdArray = [2, 4, 6, 3, 5]
 
 let gcdSegmentTree = SegmentTree(array: gcdArray, function: gcd)
 
-print(gcdSegmentTree.query(withLeftBound: 0, rightBound: 1)) // gcd(2, 4) = 2
-print(gcdSegmentTree.query(withLeftBound: 2, rightBound: 3)) // gcd(6, 3) = 3
-print(gcdSegmentTree.query(withLeftBound: 1, rightBound: 3)) // gcd(4, 6, 3) = 1
-print(gcdSegmentTree.query(withLeftBound: 0, rightBound: 4)) // gcd(2, 4, 6, 3, 5) = 1
+print(gcdSegmentTree.query(leftBound: 0, rightBound: 1)) // gcd(2, 4) = 2
+print(gcdSegmentTree.query(leftBound: 2, rightBound: 3)) // gcd(6, 3) = 3
+print(gcdSegmentTree.query(leftBound: 1, rightBound: 3)) // gcd(4, 6, 3) = 1
+print(gcdSegmentTree.query(leftBound: 0, rightBound: 4)) // gcd(2, 4, 6, 3, 5) = 1
 
 gcdSegmentTree.replaceItem(at: 3, withItem: 10) //gcdArray now is [2, 4, 6, 10, 5]
 
-print(gcdSegmentTree.query(withLeftBound: 3, rightBound: 4)) // gcd(10, 5) = 5
+print(gcdSegmentTree.query(leftBound: 3, rightBound: 4)) // gcd(10, 5) = 5
 
 
 //example of segment tree which finds minimum on given range
@@ -111,12 +111,12 @@ let minArray = [2, 4, 1, 5, 3]
 
 let minSegmentTree = SegmentTree(array: minArray, function: min)
 
-print(minSegmentTree.query(withLeftBound: 0, rightBound: 4)) // min(2, 4, 1, 5, 3) = 1
-print(minSegmentTree.query(withLeftBound: 0, rightBound: 1)) // min(2, 4) = 2
+print(minSegmentTree.query(leftBound: 0, rightBound: 4)) // min(2, 4, 1, 5, 3) = 1
+print(minSegmentTree.query(leftBound: 0, rightBound: 1)) // min(2, 4) = 2
 
 minSegmentTree.replaceItem(at: 2, withItem: 10) // minArray now is [2, 4, 10, 5, 3]
 
-print(minSegmentTree.query(withLeftBound: 0, rightBound: 4)) // min(2, 4, 10, 5, 3) = 2
+print(minSegmentTree.query(leftBound: 0, rightBound: 4)) // min(2, 4, 10, 5, 3) = 2
 
 
 //type of elements in array can be any type which has some associative function
@@ -124,10 +124,10 @@ let stringArray = ["a", "b", "c", "A", "B", "C"]
 
 let stringSegmentTree = SegmentTree(array: stringArray, function: +)
 
-print(stringSegmentTree.query(withLeftBound: 0, rightBound: 1)) // "a"+"b" = "ab"
-print(stringSegmentTree.query(withLeftBound: 2, rightBound: 3)) // "c"+"A" = "cA"
-print(stringSegmentTree.query(withLeftBound: 1, rightBound: 3)) // "b"+"c"+"A" = "bcA"
-print(stringSegmentTree.query(withLeftBound: 0, rightBound: 5)) // "a"+"b"+"c"+"A"+"B"+"C" = "abcABC"
+print(stringSegmentTree.query(leftBound: 0, rightBound: 1)) // "a"+"b" = "ab"
+print(stringSegmentTree.query(leftBound: 2, rightBound: 3)) // "c"+"A" = "cA"
+print(stringSegmentTree.query(leftBound: 1, rightBound: 3)) // "b"+"c"+"A" = "bcA"
+print(stringSegmentTree.query(leftBound: 0, rightBound: 5)) // "a"+"b"+"c"+"A"+"B"+"C" = "abcABC"
 
 stringSegmentTree.replaceItem(at: 0, withItem: "I")
 stringSegmentTree.replaceItem(at: 1, withItem: " like")
@@ -136,4 +136,4 @@ stringSegmentTree.replaceItem(at: 3, withItem: " and")
 stringSegmentTree.replaceItem(at: 4, withItem: " swift")
 stringSegmentTree.replaceItem(at: 5, withItem: "!")
 
-print(stringSegmentTree.query(withLeftBound: 0, rightBound: 5))
+print(stringSegmentTree.query(leftBound: 0, rightBound: 5))
diff --git a/Segment Tree/SegmentTree.swift b/Segment Tree/SegmentTree.swift
index b360d409a..a3ec8b1bf 100644
--- a/Segment Tree/SegmentTree.swift	
+++ b/Segment Tree/SegmentTree.swift	
@@ -35,7 +35,7 @@ public class SegmentTree<T> {
 		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
 	}
 	
-	public func query(withLeftBound: Int, rightBound: Int) -> T {
+	public func query(leftBound: Int, rightBound: Int) -> T {
 		if self.leftBound == leftBound && self.rightBound == rightBound {
 			return self.value
 		}
@@ -44,12 +44,12 @@ public class SegmentTree<T> {
 		guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
 		
 		if leftChild.rightBound < leftBound {
-			return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
+			return rightChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else if rightChild.leftBound > rightBound {
-			return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
+			return leftChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else {
-			let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
-			let rightResult = rightChild.query(withLeftBound:rightChild.leftBound, rightBound: rightBound)
+			let leftResult = leftChild.query(leftBound: leftBound, rightBound: leftChild.rightBound)
+			let rightResult = rightChild.query(leftBound:rightChild.leftBound, rightBound: rightBound)
 			return function(leftResult, rightResult)
 		}
 	}

From ea634305e542a2d9601ca560ced4d4b84796f8cd Mon Sep 17 00:00:00 2001
From: Chris Amanse <chris@chrisamanse.xyz>
Date: Fri, 4 Nov 2016 23:37:20 -0700
Subject: [PATCH 0633/1679] Fix memory leak in Tree implementation

- caused by retain cycle between parent and child (parent has a strong
  reference to child, and child has a strong reference to parent)
---
 Tree/Tree.playground/Contents.swift | 2 +-
 Tree/Tree.swift                     | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 7b3c97005..77e8fd22e 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -3,7 +3,7 @@
 public class TreeNode<T> {
   public var value: T
 
-  public var parent: TreeNode?
+  public weak var parent: TreeNode?
   public var children = [TreeNode<T>]()
 
   public init(value: T) {
diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index 00119c963..fa49f25e9 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -1,7 +1,7 @@
 public class TreeNode<T> {
   public var value: T
 
-  public var parent: TreeNode?
+  public weak var parent: TreeNode?
   public var children = [TreeNode<T>]()
 
   public init(value: T) {

From b23ad94b1758cf572dc814966b3260fbedb8a8c1 Mon Sep 17 00:00:00 2001
From: Chris Amanse <chris@chrisamanse.xyz>
Date: Fri, 4 Nov 2016 23:41:44 -0700
Subject: [PATCH 0634/1679] Fix code in Tree docs (set parent to weak)

---
 Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Tree/README.markdown b/Tree/README.markdown
index 5cf3e6beb..529a68cf1 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -26,7 +26,7 @@ Here's a basic implementation in Swift:
 public class TreeNode<T> {
   public var value: T
 
-  public var parent: TreeNode?
+  public weak var parent: TreeNode?
   public var children = [TreeNode<T>]()
 
   public init(value: T) {

From f77809c0476c7ed1d8701cb54d0eeb01fed36198 Mon Sep 17 00:00:00 2001
From: Divyendu Singh <divyendu.z@gmail.com>
Date: Tue, 8 Nov 2016 01:58:40 +0530
Subject: [PATCH 0635/1679] typo fix and claim commit

---
 Bucket Sort/README.markdown | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index f6e318c1f..f572fc9a1 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -9,16 +9,16 @@ Bucket Sort, also known as Bin Sort, is a distributed sorting algorithm, which s
 See the algorithm in action [here](https://www.cs.usfca.edu/~galles/visualization/BucketSort.html) and [here](http://www.algostructure.com/sorting/bucketsort.php).
 
 The performance for execution time is:  
-  
+
 | Case  | Performance |
 |:-------------: |:---------------:|
 | Worst       |  O(n^2) |
 | Best      | 	Omega(n + k)        |
-|  Average | 	Theta(n + k)       | 
-  
+|  Average | 	Theta(n + k)       |
+
 Where **n** = the number of elements and **k** is the number of buckets.
 
-In the *best case*, the algorithm distributes the elements uniformily between buckets, a few elements are placed on each bucket and sorting the buckets is **O(1)**. Rearranging the elements is one more run through the initial list.  
+In the *best case*, the algorithm distributes the elements uniformly between buckets, a few elements are placed on each bucket and sorting the buckets is **O(1)**. Rearranging the elements is one more run through the initial list.  
 
 In the *worst case*, the elements are sent all to the same bucket, making the process take **O(n^2)**.
 
@@ -63,11 +63,11 @@ So the buckets are:
 Now we need to choose a distribution function.  
 
 `bucketNumber = (elementValue / totalNumberOfBuckets) + 1`  
-   
+
 Such that by applying that function we distribute all the elements in the buckets.  
 
 In our example it is like the following:  
-  
+
 1. Apply the distribution function to `2`. `bucketNumber = (2 / 10) + 1 = 1`
 2. Apply the distribution function to `56`. `bucketNumber = (56 / 10) + 1 = 6`
 3. Apply the distribution function to `4`. `bucketNumber = (4 / 10) + 1 = 1`
@@ -91,12 +91,12 @@ Our buckets will be filled now:
 
 We can choose to insert the elements in every bucket in order, or sort every bucket after distributing all the elements.  
 
-### Put the elements back in the list 
+### Put the elements back in the list
 
 Finally we go through all the buckets and put the elements back in the list:  
-  
+
   `[2,  4,  26,  55,  56,  77,  98]`  
-  
+
 
 ## Swift implementation
 
@@ -109,9 +109,9 @@ Here is a diagram that shows the functions, data structures and protocols for ou
 `bucketSort()` is a generic function that can apply the algorithm to any element of type `T`, as long as `T` is `Sortable`.
 
 ```swift
-public func bucketSort<T:Sortable>(elements: [T], 
-                                distributor: Distributor, 
-                                     sorter: Sorter, 
+public func bucketSort<T:Sortable>(elements: [T],
+                                distributor: Distributor,
+                                     sorter: Sorter,
                                     buckets: [Bucket<T>]) -> [T] {
 	precondition(allPositiveNumbers(elements))
 	precondition(enoughSpaceInBuckets(buckets, elements: elements))
@@ -201,11 +201,11 @@ public struct InsertionSorter: Sorter {
 		for i in 0 ..< results.count {
 			var j = i
 			while ( j > 0 && results[j-1] > results[j]) {
-			
+
 				let auxiliar = results[j-1]
 				results[j-1] = results[j]
 				results[j] = auxiliar
-			
+
 				j -= 1
 			}
 		}
@@ -236,7 +236,7 @@ public struct RangeDistributor: Distributor {
 	 public func distribute<T:Sortable>(element: T, inout buckets: [Bucket<T>]) {
 	 let value = element.toInt()
 	 let bucketCapacity = buckets.first!.capacity
-	
+
 	 let bucketIndex = value / bucketCapacity
 	 buckets[bucketIndex].add(element)
 	}

From 3132f5d75780fafe146258d934f4b4a5e5ff9463 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Mon, 7 Nov 2016 16:57:54 -0500
Subject: [PATCH 0636/1679] Initial commit and claim

---
 Rootish Array Stack/README.md | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Rootish Array Stack/README.md

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
new file mode 100644
index 000000000..e69de29bb

From 6c9e3a86f9a564cff15170e5a22d088e9d381cd9 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:46:21 -0500
Subject: [PATCH 0637/1679] Update to Swift 3.0

---
 .../LinearRegression.playground/Contents.swift   | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 585471487..ae2e4fc14 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -19,26 +19,26 @@ let alpha = 0.0001
 
 for n in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
-        let difference = carPrice[i] - predictedCarPrice(carAge[i])
+        let difference = carPrice[i] - predictedCarPrice(carAge: carAge[i])
         intercept += alpha * difference
         slope += alpha * difference * carAge[i]
     }
 }
 
-print("A car age of 4 years is predicted to be worth £\(Int(predictedCarPrice(4)))")
+print("A car age of 4 years is predicted to be worth £\(Int(predictedCarPrice(carAge: 4)))")
 
 // A closed form solution
 
-func average(input: [Double]) -> Double {
-    return input.reduce(0, combine: +) / Double(input.count)
+func average(_ input: [Double]) -> Double {
+    return input.reduce(0, +) / Double(input.count)
 }
 
-func multiply(input1: [Double], _ input2: [Double]) -> [Double] {
-    return input1.enumerate().map({ (index, element) in return element*input2[index] })
+func multiply(_ input1: [Double], _ input2: [Double]) -> [Double] {
+    return input1.enumerated().map({ (index, element) in return element*input2[index] })
 }
 
-func linearRegression(xVariable: [Double], _ yVariable: [Double]) -> (Double -> Double) {
-    let sum1 = average(multiply(xVariable, yVariable)) - average(xVariable) * average(yVariable)
+func linearRegression(_ xVariable: [Double], _ yVariable: [Double]) -> ((Double) -> Double) {
+    let sum1 = average(multiply(yVariable, xVariable)) - average(xVariable) * average(yVariable)
     let sum2 = average(multiply(xVariable, xVariable)) - pow(average(xVariable), 2)
     let slope = sum1 / sum2
     let intercept = average(yVariable) - slope * average(xVariable)

From 087dc18fdf9dac0429540ee353d8696ded901b2a Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:48:35 -0500
Subject: [PATCH 0638/1679] Make multiply(_:_:) function more elegant

---
 Linear Regression/LinearRegression.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index ae2e4fc14..32d2cc195 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -34,7 +34,7 @@ func average(_ input: [Double]) -> Double {
 }
 
 func multiply(_ input1: [Double], _ input2: [Double]) -> [Double] {
-    return input1.enumerated().map({ (index, element) in return element*input2[index] })
+    return zip(input1, input2).map { $0.0 * $0.1 }
 }
 
 func linearRegression(_ xVariable: [Double], _ yVariable: [Double]) -> ((Double) -> Double) {

From dda0d7957da6dadc9edab569c79ccd11e1d702af Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:49:43 -0500
Subject: [PATCH 0639/1679] Make multiply(_:_:) function even more elegant

---
 Linear Regression/LinearRegression.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 32d2cc195..fd711849a 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -33,8 +33,8 @@ func average(_ input: [Double]) -> Double {
     return input.reduce(0, +) / Double(input.count)
 }
 
-func multiply(_ input1: [Double], _ input2: [Double]) -> [Double] {
-    return zip(input1, input2).map { $0.0 * $0.1 }
+func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
+    return zip(a,b).map { $0.0 * $0.1 }
 }
 
 func linearRegression(_ xVariable: [Double], _ yVariable: [Double]) -> ((Double) -> Double) {

From 95efaec8dc8bf00dd6d1da6702855c49d6a5fe87 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:50:52 -0500
Subject: [PATCH 0640/1679] Rename (xVariable, yVariable) -> (xs, ys)

---
 .../LinearRegression.playground/Contents.swift            | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index fd711849a..f50bdefbc 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -37,11 +37,11 @@ func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
     return zip(a,b).map { $0.0 * $0.1 }
 }
 
-func linearRegression(_ xVariable: [Double], _ yVariable: [Double]) -> ((Double) -> Double) {
-    let sum1 = average(multiply(yVariable, xVariable)) - average(xVariable) * average(yVariable)
-    let sum2 = average(multiply(xVariable, xVariable)) - pow(average(xVariable), 2)
+func linearRegression(_ xs: [Double], _ ys: [Double]) -> ((Double) -> Double) {
+    let sum1 = average(multiply(ys, xs)) - average(xs) * average(ys)
+    let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2
-    let intercept = average(yVariable) - slope * average(xVariable)
+    let intercept = average(ys) - slope * average(xs)
     return { intercept + slope * $0 }
 }
 

From 58a7f1c9a8aaba7a527261a67cbdca3fc6c9c9d3 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:52:54 -0500
Subject: [PATCH 0641/1679] Update multiply(_:_:) in README.md

---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index c04e3b3dc..4c98b8995 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -113,8 +113,8 @@ We are using the ```reduce``` Swift function to sum up all the elements of the a
 We also need to be able to multiply each element in an array by the corresponding element in another array, to create a new array. Here is a function which will do this:
 
 ```swift
-func multiply(input1: [Double], _ input2: [Double]) -> [Double] {
-    return input1.enumerate().map({ (index, element) in return element*input2[index] })
+func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
+    return zip(a,b).map { $0.0 * $0.1 }
 }
 ```
 

From f7ec3c45d920155ea47c5c41869f5c984c98f8f9 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:54:18 -0500
Subject: [PATCH 0642/1679] Update linearRegression(_:_:) in README.md

---
 Linear Regression/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 4c98b8995..fde04ed2d 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -123,11 +123,11 @@ We are using the ```map``` function to multiply each element.
 Finally, the function which fits the line to the data:
 
 ```swift
-func linearRegression(xVariable: [Double], _ yVariable: [Double]) -> (Double -> Double) {
-    let sum1 = average(multiply(xVariable, yVariable)) - average(xVariable) * average(yVariable)
-    let sum2 = average(multiply(xVariable, xVariable)) - pow(average(xVariable), 2)
+func linearRegression(xs: [Double], _ ys: [Double]) -> (Double -> Double) {
+    let sum1 = average(multiply(xs, ys)) - average(xs) * average(ys)
+    let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2
-    let intercept = average(yVariable) - slope * average(xVariable)
+    let intercept = average(ys) - slope * average(xs)
     return { intercept + slope * $0 }
 }
 ```

From 1c09008e5a4394d0058941debef9bba2c1798570 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:55:16 -0500
Subject: [PATCH 0643/1679] Update README.md

---
 Linear Regression/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index fde04ed2d..9e61888ed 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -104,8 +104,8 @@ There is another way we can calculate the line of best fit, without having to do
 First we need some helper functions. This one calculates the average (the mean) of an array of Doubles:
 
 ```swift
-func average(input: [Double]) -> Double {
-    return input.reduce(0, combine: +) / Double(input.count)
+func average(_ input: [Double]) -> Double {
+    return input.reduce(0, +) / Double(input.count)
 }
 ```
 We are using the ```reduce``` Swift function to sum up all the elements of the array, and then divide that by the number of elements. This gives us the mean value.
@@ -123,7 +123,7 @@ We are using the ```map``` function to multiply each element.
 Finally, the function which fits the line to the data:
 
 ```swift
-func linearRegression(xs: [Double], _ ys: [Double]) -> (Double -> Double) {
+func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double -> Double) {
     let sum1 = average(multiply(xs, ys)) - average(xs) * average(ys)
     let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2

From 40d074807f83eba87d433b3b092afb7587f75660 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:56:17 -0500
Subject: [PATCH 0644/1679] Make x variable explicit in closure

---
 Linear Regression/LinearRegression.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index f50bdefbc..2d882314a 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -42,7 +42,7 @@ func linearRegression(_ xs: [Double], _ ys: [Double]) -> ((Double) -> Double) {
     let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2
     let intercept = average(ys) - slope * average(xs)
-    return { intercept + slope * $0 }
+    return { x in intercept + slope * x }
 }
 
 let result = linearRegression(carAge, carPrice)(4)

From f2564ce7bf38177b1c233a258795652ff8c7dacc Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 20:56:39 -0500
Subject: [PATCH 0645/1679] Update README.md

---
 Linear Regression/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 9e61888ed..f50f4fd66 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -123,12 +123,12 @@ We are using the ```map``` function to multiply each element.
 Finally, the function which fits the line to the data:
 
 ```swift
-func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double -> Double) {
-    let sum1 = average(multiply(xs, ys)) - average(xs) * average(ys)
+func linearRegression(_ xs: [Double], _ ys: [Double]) -> ((Double) -> Double) {
+    let sum1 = average(multiply(ys, xs)) - average(xs) * average(ys)
     let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2
     let intercept = average(ys) - slope * average(xs)
-    return { intercept + slope * $0 }
+    return { x in intercept + slope * x }
 }
 ```
 This function takes as arguments two arrays of Doubles, and returns a function which is the line of best fit. The formulas to calculate the slope and the intercept can be derived from our definition of the function J. Let's see how the output from this line fits our data:

From ba0d7558187b118c390bd9cf5b475aaa9697bacf Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:01:40 -0500
Subject: [PATCH 0646/1679] Remove parens Xcode convinced me I needed

---
 Linear Regression/LinearRegression.playground/Contents.swift | 2 +-
 Linear Regression/README.markdown                            | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 2d882314a..648868971 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -37,7 +37,7 @@ func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
     return zip(a,b).map { $0.0 * $0.1 }
 }
 
-func linearRegression(_ xs: [Double], _ ys: [Double]) -> ((Double) -> Double) {
+func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
     let sum1 = average(multiply(ys, xs)) - average(xs) * average(ys)
     let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2
diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index f50f4fd66..b7a5b5ba0 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -123,7 +123,7 @@ We are using the ```map``` function to multiply each element.
 Finally, the function which fits the line to the data:
 
 ```swift
-func linearRegression(_ xs: [Double], _ ys: [Double]) -> ((Double) -> Double) {
+func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
     let sum1 = average(multiply(ys, xs)) - average(xs) * average(ys)
     let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2

From c505f184d0cde36e7372fb1bfa3cd046213d7835 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:03:24 -0500
Subject: [PATCH 0647/1679] Ensure README looks like code

---
 Linear Regression/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index b7a5b5ba0..3e132b013 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -58,12 +58,12 @@ Now for the code which will perform the iterations:
 
 ```swift
 let numberOfCarAdvertsWeSaw = carPrice.count
-let iterations = 2000
+let numberOfIterations = 100
 let alpha = 0.0001
 
-for n in 1...iterations {
+for n in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
-        let difference = carPrice[i] - predictedCarPrice(carAge[i])
+        let difference = carPrice[i] - predictedCarPrice(carAge: carAge[i])
         intercept += alpha * difference
         slope += alpha * difference * carAge[i]
     }

From 7b10055227d729c7e11fdd57c8854ba5beaff341 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:06:21 -0500
Subject: [PATCH 0648/1679] Revert labeling of argument

---
 .../LinearRegression.playground/Contents.swift              | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 648868971..4f18b7add 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -7,7 +7,7 @@ let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
 var intercept = 0.0
 var slope = 0.0
 
-func predictedCarPrice(carAge: Double) -> Double {
+func predictedCarPrice(_ carAge: Double) -> Double {
     return intercept + slope * carAge
 }
 
@@ -19,13 +19,13 @@ let alpha = 0.0001
 
 for n in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
-        let difference = carPrice[i] - predictedCarPrice(carAge: carAge[i])
+        let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference
         slope += alpha * difference * carAge[i]
     }
 }
 
-print("A car age of 4 years is predicted to be worth £\(Int(predictedCarPrice(carAge: 4)))")
+print("A car age of 4 years is predicted to be worth £\(Int(predictedCarPrice(4)))")
 
 // A closed form solution
 

From 7a5f58c32e7ee7f412e2cd6530868460357614db Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:07:29 -0500
Subject: [PATCH 0649/1679] Update README

---
 Linear Regression/README.markdown | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 3e132b013..89f81842a 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -50,9 +50,10 @@ This is how we can represent our straight line:
 ```swift
 var intercept = 0.0
 var slope = 0.0
-func predictedCarPrice(carAge: Double) -> Double {
+func predictedCarPrice(_ carAge: Double) -> Double {
     return intercept + slope * carAge
 }
+
 ```
 Now for the code which will perform the iterations:
 
@@ -63,7 +64,7 @@ let alpha = 0.0001
 
 for n in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
-        let difference = carPrice[i] - predictedCarPrice(carAge: carAge[i])
+        let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference
         slope += alpha * difference * carAge[i]
     }

From 9e715c3b85a90be768a39384cf4bea230b8c1c22 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:09:13 -0500
Subject: [PATCH 0650/1679] Add code formatting to distinguish equations

---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 89f81842a..41af0169e 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -30,7 +30,7 @@ We can describe the straight line in terms of two variables:
 
 This is the equation for our line:
 
-carPrice = slope * carAge + intercept 
+`carPrice = slope * carAge + intercept`
 
 
 How can we find the best values for the intercept and the slope? Let's look at two different ways to do this.
@@ -75,7 +75,7 @@ for n in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimse the square of the distance between the line and the points. We define a function J which represents this distance - for simplicity we consider only one point here. This function J is proprotional to  ((slope.carAge+intercept) - carPrice))^2
+We want to minimse the square of the distance between the line and the points. We define a function J which represents this distance - for simplicity we consider only one point here. This function J is proprotional to `((slope.carAge+intercept) - carPrice))^2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 

From be2167c6c071952b05ee53e88ef4c690cf363453 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:13:00 -0500
Subject: [PATCH 0651/1679] Add code formatting to distinguish function name

---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 41af0169e..94ee6aa28 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -75,7 +75,7 @@ for n in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimse the square of the distance between the line and the points. We define a function J which represents this distance - for simplicity we consider only one point here. This function J is proprotional to `((slope.carAge+intercept) - carPrice))^2`.
+We want to minimse the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proprotional to `((slope.carAge+intercept) - carPrice))^2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 
@@ -132,7 +132,7 @@ func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
     return { x in intercept + slope * x }
 }
 ```
-This function takes as arguments two arrays of Doubles, and returns a function which is the line of best fit. The formulas to calculate the slope and the intercept can be derived from our definition of the function J. Let's see how the output from this line fits our data:
+This function takes as arguments two arrays of Doubles, and returns a function which is the line of best fit. The formulas to calculate the slope and the intercept can be derived from our definition of the function `J`. Let's see how the output from this line fits our data:
 
 ![graph3](Images/graph3.png)
 

From ad9f78d936d7e2c15271d2aa854a22d9c24c7d4f Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:14:13 -0500
Subject: [PATCH 0652/1679] Give some breathing room

---
 Linear Regression/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 94ee6aa28..de233fae1 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -75,7 +75,7 @@ for n in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimse the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proprotional to `((slope.carAge+intercept) - carPrice))^2`.
+We want to minimse the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proprotional to `((slope.carAge + intercept) - carPrice)) ^ 2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 

From 75c0102bcfb7544c4464cb8090ffa1bfa17fa5a7 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Tue, 8 Nov 2016 21:31:27 -0500
Subject: [PATCH 0653/1679] Put xs back before ys

---
 Linear Regression/LinearRegression.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 4f18b7add..f265c3c5f 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -38,7 +38,7 @@ func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
 }
 
 func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
-    let sum1 = average(multiply(ys, xs)) - average(xs) * average(ys)
+    let sum1 = average(multiply(xs, ys)) - average(xs) * average(ys)
     let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
     let slope = sum1 / sum2
     let intercept = average(ys) - slope * average(xs)

From 7513bc03d8df99ba5b117420922e2f90c7a1c562 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Wed, 9 Nov 2016 17:48:33 -0500
Subject: [PATCH 0654/1679] Make multiply(_:_:) even even more elegant

---
 Linear Regression/LinearRegression.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index f265c3c5f..8b579b3c1 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -34,7 +34,7 @@ func average(_ input: [Double]) -> Double {
 }
 
 func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
-    return zip(a,b).map { $0.0 * $0.1 }
+    return zip(a,b).map(*)
 }
 
 func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {

From b5bda5b6453e13f1eae0623d4d06b260a4fecd2c Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Wed, 9 Nov 2016 17:49:03 -0500
Subject: [PATCH 0655/1679] Update README

---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index de233fae1..1a1a1eb8b 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -115,7 +115,7 @@ We also need to be able to multiply each element in an array by the correspondin
 
 ```swift
 func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
-    return zip(a,b).map { $0.0 * $0.1 }
+    return zip(a,b).map(*)
 }
 ```
 
@@ -146,4 +146,4 @@ Well, the line we've found doesn't fit the data perfectly. For one thing, the gr
 
 It turns out that in some of these more complicated models, the iterative approach is the only viable or efficient approach. This can also occur when the arrays of data are very large and may be sparsely populated with data values.
 
-*Written for Swift Algorithm Club by James Harrop*
\ No newline at end of file
+*Written for Swift Algorithm Club by James Harrop*

From 8a5c49af0b15d0e61b7606ad6ac0cad8bb5672e6 Mon Sep 17 00:00:00 2001
From: Kenny Batista <kennybatista7@gmail.com>
Date: Fri, 11 Nov 2016 11:11:13 -0800
Subject: [PATCH 0656/1679] Update ReadMe.md

---
 Trie/ReadMe.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 3e3dad3a6..30082a450 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -6,7 +6,7 @@ A `Trie`, (also known as a prefix tree, or radix tree in some other implementati
 
 ![A Trie](images/trie.png)
 
-Storing the English language is a primary use case for a `Trie`. Each node in the `Trie` would representing a single character of a word. A series of nodes then make up a word.
+Storing the English language is a primary use case for a `Trie`. Each node in the `Trie` would represent a single character of a word. A series of nodes then make up a word.
 
 ## Why a Trie?
 

From b40c3d6873caa252b4b63666642f3128e74bf891 Mon Sep 17 00:00:00 2001
From: Raul Ferreira <raulmendesferreira@gmail.com>
Date: Sat, 12 Nov 2016 16:37:40 +0000
Subject: [PATCH 0657/1679] Fix mistake in the formula that simplifies to (a*d
 + b*c)

(a+b)*(c+d) - a*c - b*c  = (a*c + a*d + b*c + b*d) - a*c - b*c

should be

(a+b)*(c+d) - a*c - b*d  = (a*c + a*d + b*c + b*d) - a*c - b*d
---
 Karatsuba Multiplication/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index d4c99ec2d..c86f69831 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -62,7 +62,7 @@ Now, we can say:
 
 This had been know since the 19th century. The problem is that the method requires 4 multiplications (`a*c`, `a*d`, `b*c`, `b*d`). Karatsuba's insight was that you only need three! (`a*c`, `b*d`, `(a+b)*(c+d)`). Now a perfectly valid question right now would be "How is that possible!?!" Here's the math:
 
-        (a+b)*(c+d) - a*c - b*c  = (a*c + a*d + b*c + b*d) - a*c - b*c
+        (a+b)*(c+d) - a*c - b*d  = (a*c + a*d + b*c + b*d) - a*c - b*d
                                  = (a*d + b*c)
 
 Pretty cool, huh?

From 16eb36c653007865a199e0d9fa1fc9cf5f2515ce Mon Sep 17 00:00:00 2001
From: Robin Malhotra <malhotra.robin@icloud.com>
Date: Thu, 17 Nov 2016 20:03:50 +0530
Subject: [PATCH 0658/1679] Update Contents.swift

IMHO, making peek a computed variable feels _swiftier_
---
 Queue/Queue.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 6b771ccd1..a8be21b08 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -34,7 +34,7 @@ public struct Queue<T> {
     }
   }
 
-  public func peek() -> T? {
+  public var peek: T? {
     return array.first
   }
 }
@@ -56,7 +56,7 @@ queueOfNames.dequeue()
 
 // Return the first element in the queue.
 // Returns "Lisa" since "Carl" was dequeued on the previous line.
-queueOfNames.peek()
+queueOfNames.peek
 
 // Check to see if the queue is empty.
 // Returns "false" since the queue still has elements in it.

From d7267e911efa8ba6d7b3c26da6c8cef59d82b9c7 Mon Sep 17 00:00:00 2001
From: jsbean <jbean46@gmail.com>
Date: Wed, 23 Nov 2016 23:32:37 -0500
Subject: [PATCH 0659/1679] Update code and README for Swift 3.0

---
 .../Contents.swift}                           | 28 ++++++++-------
 .../contents.xcplayground                     |  4 +++
 .../contents.xcworkspacedata                  |  7 ++++
 Minimum Edit Distance/README.markdown         | 35 +++++++++----------
 4 files changed, 43 insertions(+), 31 deletions(-)
 rename Minimum Edit Distance/{MinimumEditDistance.swift => MinimumEditDistance.playground/Contents.swift} (53%)
 mode change 100644 => 100755
 create mode 100755 Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground
 create mode 100755 Minimum Edit Distance/MinimumEditDistance.playground/playground.xcworkspace/contents.xcworkspacedata
 mode change 100644 => 100755 Minimum Edit Distance/README.markdown

diff --git a/Minimum Edit Distance/MinimumEditDistance.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
old mode 100644
new mode 100755
similarity index 53%
rename from Minimum Edit Distance/MinimumEditDistance.swift
rename to Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
index a128b2dab..d651ddf2e
--- a/Minimum Edit Distance/MinimumEditDistance.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,34 +1,36 @@
 extension String {
-
+    
     public func minimumEditDistance(other: String) -> Int {
         let m = self.characters.count
         let n = other.characters.count
-        var matrix = [[Int]](count: m+1, repeatedValue: [Int](count: n+1, repeatedValue: 0))
-
-
+        var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
+        
         // initialize matrix
         for index in 1...m {
             // the distance of any first string to an empty second string
-            matrix[index][0]=index
+            matrix[index][0] = index
         }
+        
         for index in 1...n {
             // the distance of any second string to an empty first string
-            matrix[0][index]=index
+            matrix[0][index] = index
         }
-
+        
         // compute Levenshtein distance
-        for (i, selfChar) in self.characters.enumerate() {
-            for (j, otherChar) in other.characters.enumerate() {
+        for (i, selfChar) in self.characters.enumerated() {
+            for (j, otherChar) in other.characters.enumerated() {
                 if otherChar == selfChar {
                     // substitution of equal symbols with cost 0
-                    matrix[i+1][j+1] = matrix[i][j]
+                    matrix[i + 1][j + 1] = matrix[i][j]
                 } else {
-                    // minimum of the cost of insertion, deletion, or substitution added to the already computed costs in the corresponding cells
-                    matrix[i+1][j+1] = min(matrix[i][j]+1, matrix[i+1][j]+1, matrix[i][j+1]+1)
+                    // minimum of the cost of insertion, deletion, or substitution 
+                    // added to the already computed costs in the corresponding cells
+                    matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
                 }
-
             }
         }
         return matrix[m][n]
     }
 }
+
+"Door".minimumEditDistance(other: "Dolls")
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground b/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground
new file mode 100755
index 000000000..5da2641c9
--- /dev/null
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/playground.xcworkspace/contents.xcworkspacedata b/Minimum Edit Distance/MinimumEditDistance.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100755
index 000000000..919434a62
--- /dev/null
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Minimum Edit Distance/README.markdown b/Minimum Edit Distance/README.markdown
old mode 100644
new mode 100755
index d72e0dbda..905b358ae
--- a/Minimum Edit Distance/README.markdown	
+++ b/Minimum Edit Distance/README.markdown	
@@ -6,7 +6,7 @@ The minimum edit distance is a possibility to measure the similarity of two stri
 
 A common distance measure is given by the *Levenshtein distance*, which allows the following three transformation operations:
 
-* **Inseration** (*ε→x*) of a single symbol *x* with **cost 1**,
+* **Insertion** (*ε→x*) of a single symbol *x* with **cost 1**,
 * **Deletion** (*x→ε*) of a single symbol *x* with **cost 1**, and
 * **Substitution** (*x→y*) of two single symbols *x, y* with **cost 1** if *x≠y* and with **cost 0** otherwise.
 
@@ -15,7 +15,7 @@ When transforming a string by a sequence of operations, the costs of the single
 To avoid exponential time complexity, the minimum edit distance of two strings in the usual is computed using *dynamic programming*. For this in a matrix
 
 ```swift
-var matrix = [[Int]](count: m+1, repeatedValue: [Int](count: n+1, repeatedValue: 0))
+var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
 ```
 
 already computed minimal edit distances of prefixes of *w* and *u* (of length *m* and *n*, respectively) are used to fill the matrix. In a first step the matrix is initialized by filling the first row and the first column as follows:
@@ -23,29 +23,30 @@ already computed minimal edit distances of prefixes of *w* and *u* (of length *m
 ```swift
 // initialize matrix
 for index in 1...m {
-    // the distance of any prefix of the first string to an empty second string
-    matrix[index][0]=index
+    // the distance of any first string to an empty second string
+    matrix[index][0] = index
 }
+
 for index in 1...n {
-    // the distance of any prefix of the second string to an empty first string
-    matrix[0][index]=index
+    // the distance of any second string to an empty first string
+    matrix[0][index] = index
 }
 ```
+
 Then in each cell the minimum of the cost of insertion, deletion, or substitution added to the already computed costs in the corresponding cells is chosen. In this way the matrix is filled iteratively:
 
 ```swift
 // compute Levenshtein distance
-for (i, selfChar) in self.characters.enumerate() {
-    for (j, otherChar) in other.characters.enumerate() {
+for (i, selfChar) in self.characters.enumerated() {
+    for (j, otherChar) in other.characters.enumerated() {
         if otherChar == selfChar {
             // substitution of equal symbols with cost 0
-            matrix[i+1][j+1] = matrix[i][j]
+            matrix[i + 1][j + 1] = matrix[i][j]
         } else {
-            // minimum of the cost of insertion, deletion, or substitution added 
-            // to the already computed costs in the corresponing cells
-            matrix[i+1][j+1] = min(matrix[i][j]+1, matrix[i+1][j]+1, matrix[i][j+1]+1)
-        }
-                
+            // minimum of the cost of insertion, deletion, or substitution 
+            // added to the already computed costs in the corresponding cells
+            matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+        } 
     }
 }
 ```
@@ -58,8 +59,6 @@ return matrix[m][n]
 
 This algorithm has a time complexity of Θ(*mn*).
 
-### Other distance measures
-
-**todo**
+**TODO**: Other distance measures.
 
-*Written for Swift Algorithm Club by Luisa Herrmann*
\ No newline at end of file
+*Written for Swift Algorithm Club by Luisa Herrmann*

From 38dc9eefedf61e5edc838fcb034657df2a22dcc6 Mon Sep 17 00:00:00 2001
From: Joe <jihd@dream1024.com>
Date: Thu, 24 Nov 2016 15:36:22 +0800
Subject: [PATCH 0660/1679] update Array2D, Deque to swift3.0

update Array2D, Deque to swift3.0
---
 Array2D/README.markdown     | 6 +++---
 Deque/Deque-Optimized.swift | 4 ++--
 Deque/README.markdown       | 6 +++---
 3 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index e73d453a6..51e77435e 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -30,14 +30,14 @@ let myCookie = cookies[3][6]
 Actually, you could create the array in a single line of code, like so:
 
 ```swift
-var cookies = [[Int]](count: 9, repeatedValue: [Int](count: 7, repeatedValue: 0))
+var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 ```
 
 but that's just ugly. To be fair, you can hide the ugliness in a helper function:
 
 ```swift
 func dim<T>(count: Int, _ value: T) -> [T] {
-  return [T](count: count, repeatedValue: value)
+  return [T](repeating: value, count: count)
 }
 ```
 
@@ -72,7 +72,7 @@ public struct Array2D<T> {
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = .init(count: rows*columns, repeatedValue: initialValue)
+    array = .init(repeating: initialValue, count: rows*columns)
   }
 
   public subscript(column: Int, row: Int) -> T {
diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index 17ff89e68..6326b457b 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -10,7 +10,7 @@ public struct Deque<T> {
 
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
-    array = .init(count: capacity, repeatedValue: nil)
+    array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
 
@@ -29,7 +29,7 @@ public struct Deque<T> {
   public mutating func enqueueFront(_ element: T) {
     if head == 0 {
       capacity *= 2
-      let emptySpace = [T?](count: capacity, repeatedValue: nil)
+      let emptySpace = [T?](repeating: nil, count: capacity)
       array.insertContentsOf(emptySpace, at: 0)
       head = capacity
     }
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 7671555dc..5858f3e6d 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -122,7 +122,7 @@ public struct Deque<T> {
   
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
-    array = .init(count: capacity, repeatedValue: nil)
+    array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
   
@@ -238,8 +238,8 @@ There is one tiny problem... If you enqueue a lot of objects at the front, you'r
   public mutating func enqueueFront(element: T) {
     if head == 0 {
       capacity *= 2
-      let emptySpace = [T?](count: capacity, repeatedValue: nil)
-      array.insertContentsOf(emptySpace, at: 0)
+      let emptySpace = [T?](repeating: nil, count: capacity)
+      array.insert(contentsOf: emptySpace, at: 0)
       head = capacity
     }
 

From 653452a37c4a491e60ba66ff2d79f76b66c39014 Mon Sep 17 00:00:00 2001
From: JJ <jeremiah.oligario@gmail.com>
Date: Fri, 25 Nov 2016 21:33:24 -0500
Subject: [PATCH 0661/1679] Fix for #246: Invalid tree in MinimumMaximum.png
 and update README.markdown to match.

---
 Binary Search Tree/Images/MinimumMaximum.png | Bin 12151 -> 11913 bytes
 Binary Search Tree/README.markdown           |   8 ++++----
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Binary Search Tree/Images/MinimumMaximum.png b/Binary Search Tree/Images/MinimumMaximum.png
index 70fe4ea7b2cee1bd641a785981e0015815f3a594..10b4e635291d25cc899f659679dafdf8c8985b1a 100644
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diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 483e75a58..bacb1ffe1 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -412,7 +412,7 @@ To see how this works, take the following tree:
 
 ![Example](Images/MinimumMaximum.png)
 
-For example, if we look at node `10`, its leftmost descendent is `6`. We get there by following all the `left` pointers until there are no more left children to look at. The leftmost descendent of the root node `7` is `1`. Therefore, `1` is the minimum value in the entire tree.
+For example, if we look at node `10`, its leftmost descendent is `7`. We get there by following all the `left` pointers until there are no more left children to look at. The leftmost descendent of the root node `6` is `1`. Therefore, `1` is the minimum value in the entire tree.
 
 We won't need it for deleting, but for completeness' sake, here is the opposite of `minimum()`:
 
@@ -426,7 +426,7 @@ We won't need it for deleting, but for completeness' sake, here is the opposite
   }
 ```
 
-It returns the rightmost descendent of the node. We find it by following `right` pointers until we get to the end. In the above example, the rightmost descendent of node `2` is `5`. The maximum value in the entire tree is `11`, because that is the rightmost descendent of the root node `7`.
+It returns the rightmost descendent of the node. We find it by following `right` pointers until we get to the end. In the above example, the rightmost descendent of node `2` is `5`. The maximum value in the entire tree is `11`, because that is the rightmost descendent of the root node `6`.
 
 Finally, we can write the code that removes a node from the tree:
 
@@ -500,11 +500,11 @@ if let node2 = tree.search(2) {
 
 First you find the node that you want to remove with `search()` and then you call `remove()` on that object. Before the removal, the tree printed like this:
 
-	((1) <- 2 -> (5)) <- 7 -> ((9) <- 10)
+	((1) <- 2 -> (5)) <- 6 -> ((9) <- 10)
 
 But after `remove()` you get:
 
-	((1) <- 5) <- 7 -> ((9) <- 10)
+	((1) <- 5) <- 6 -> ((9) <- 10)
 
 As you can see, node `5` has taken the place of `2`.
 

From e9eeab8c00c7a1674ba8b0f5ac7f1b51356ef925 Mon Sep 17 00:00:00 2001
From: Divyendu Singh <divyendu.z@gmail.com>
Date: Sun, 27 Nov 2016 18:34:47 +0530
Subject: [PATCH 0662/1679] Migration of code to swift 3 style

This includes
1. Correct location for inout keyword
2. Correct function calls
---
 Bucket Sort/BucketSort.playground/Contents.swift  |  7 ++-----
 .../Sources/BucketSort.swift                      | 15 +++++++--------
 2 files changed, 9 insertions(+), 13 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Contents.swift b/Bucket Sort/BucketSort.playground/Contents.swift
index f7383746c..c111c3961 100644
--- a/Bucket Sort/BucketSort.playground/Contents.swift	
+++ b/Bucket Sort/BucketSort.playground/Contents.swift	
@@ -20,9 +20,6 @@
 //
 //
 
-
-
-
 //////////////////////////////////////
 // MARK: Extensions
 //////////////////////////////////////
@@ -38,8 +35,8 @@ extension Int: IntConvertible, Sortable {
 //////////////////////////////////////
 
 let input = [1, 2, 4, 6, 10]
-let buckets = [Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15)]
+var buckets = [Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15)]
 
-let sortedElements = bucketSort(input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
+let sortedElements = bucketSort(elements: input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: &buckets)
 
 print(sortedElements)
diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index c93b96cb2..e510e51b4 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -27,16 +27,15 @@ import Foundation
 //////////////////////////////////////
 
 
-public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
-  var bucketsCopy = buckets
+public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: inout [Bucket<T>]) -> [T] {
   for elem in elements {
-    distributor.distribute(elem, buckets: &bucketsCopy)
+    distributor.distribute(element: elem, buckets: &buckets)
   }
 
   var results = [T]()
 
   for bucket in buckets {
-    results += bucket.sort(sorter)
+    results += bucket.sort(algorithm: sorter)
   }
 
   return results
@@ -48,7 +47,7 @@ public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sor
 
 
 public protocol Distributor {
-  func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
+  func distribute<T: Sortable>(element: T, buckets: inout [Bucket<T>])
 }
 
 /*
@@ -70,12 +69,12 @@ public struct RangeDistributor: Distributor {
 
   public init() {}
 
-  public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
+  public func distribute<T: Sortable>(element: T, buckets: inout [Bucket<T>]) {
     let value = element.toInt()
     let bucketCapacity = buckets.first!.capacity
 
     let bucketIndex = value / bucketCapacity
-    buckets[bucketIndex].add(element)
+    buckets[bucketIndex].add(item: element)
   }
 }
 
@@ -139,6 +138,6 @@ public struct Bucket<T:Sortable> {
   }
 
   public func sort(algorithm: Sorter) -> [T] {
-    return algorithm.sort(elements)
+    return algorithm.sort(items: elements)
   }
 }

From 2245c950594c4e9d7bde2383f0890c1fa95305d5 Mon Sep 17 00:00:00 2001
From: Divyendu Singh <divyendu.z@gmail.com>
Date: Sun, 27 Nov 2016 19:44:26 +0530
Subject: [PATCH 0663/1679] uncomment bucket sort in travis.yml file

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 45f0d4beb..17655c21e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -16,7 +16,7 @@ script:
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests

From 30dd3a043e44e63a0ba11bcfda2c6be26cbf1298 Mon Sep 17 00:00:00 2001
From: Divyendu Singh <divyendu.z@gmail.com>
Date: Sun, 27 Nov 2016 20:00:31 +0530
Subject: [PATCH 0664/1679] move the text cases to swift 3 syntax

---
 Bucket Sort/BucketSort.swift                  | 44 ++++++++++++++-----
 Bucket Sort/Tests/Tests.swift                 |  8 ++--
 .../Tests/Tests.xcodeproj/project.pbxproj     |  3 ++
 3 files changed, 41 insertions(+), 14 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 8363fd867..ef72c67dc 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -21,6 +21,30 @@
 //
 
 import Foundation
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func < <T : Comparable>(lhs: T?, rhs: T?) -> Bool {
+  switch (lhs, rhs) {
+  case let (l?, r?):
+    return l < r
+  case (nil, _?):
+    return true
+  default:
+    return false
+  }
+}
+
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func >= <T : Comparable>(lhs: T?, rhs: T?) -> Bool {
+  switch (lhs, rhs) {
+  case let (l?, r?):
+    return l >= r
+  default:
+    return !(lhs < rhs)
+  }
+}
+
 
 //////////////////////////////////////
 // MARK: Main algorithm
@@ -39,7 +63,7 @@ import Foundation
     - Returns: A new array with sorted elements
  */
 
-public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+public func bucketSort<T: Sortable>(_ elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
     precondition(allPositiveNumbers(elements))
     precondition(enoughSpaceInBuckets(buckets, elements: elements))
 
@@ -57,12 +81,12 @@ public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sor
     return results
 }
 
-private func allPositiveNumbers<T: Sortable>(array: [T]) -> Bool {
+private func allPositiveNumbers<T: Sortable>(_ array: [T]) -> Bool {
     return array.filter { $0.toInt() >= 0 }.count > 0
 }
 
-private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [T]) -> Bool {
-    let maximumValue = elements.maxElement()?.toInt()
+private func enoughSpaceInBuckets<T: Sortable>(_ buckets: [Bucket<T>], elements: [T]) -> Bool {
+    let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
 
     return totalCapacity >= maximumValue
@@ -74,7 +98,7 @@ private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [
 
 
 public protocol Distributor {
-    func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
+    func distribute<T: Sortable>(_ element: T, buckets: inout [Bucket<T>])
 }
 
 /*
@@ -96,7 +120,7 @@ public struct RangeDistributor: Distributor {
 
     public init() {}
 
-    public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
+    public func distribute<T: Sortable>(_ element: T, buckets: inout [Bucket<T>]) {
         let value = element.toInt()
         let bucketCapacity = buckets.first!.capacity
 
@@ -121,14 +145,14 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-    func sort<T: Sortable>(items: [T]) -> [T]
+    func sort<T: Sortable>(_ items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
 
     public init() {}
 
-    public func sort<T: Sortable>(items: [T]) -> [T] {
+    public func sort<T: Sortable>(_ items: [T]) -> [T] {
         var results = items
         for i in 0 ..< results.count {
             var j = i
@@ -158,13 +182,13 @@ public struct Bucket<T:Sortable> {
         elements = [T]()
     }
 
-    public mutating func add(item: T) {
+    public mutating func add(_ item: T) {
         if elements.count < capacity {
             elements.append(item)
         }
     }
 
-    public func sort(algorithm: Sorter) -> [T] {
+    public func sort(_ algorithm: Sorter) -> [T] {
         return algorithm.sort(elements)
     }
 }
diff --git a/Bucket Sort/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
index 22ac751de..b50789ed0 100644
--- a/Bucket Sort/Tests/Tests.swift	
+++ b/Bucket Sort/Tests/Tests.swift	
@@ -25,7 +25,7 @@ class TestTests: XCTestCase {
 
         largeArray = [Int]()
         for _ in 0..<total {
-            largeArray!.append( random() % maximum )
+            largeArray!.append( Int(arc4random_uniform( UInt32( maximum ) ) ) )
         }
 
         sparsedArray = [Int]()
@@ -57,9 +57,9 @@ class TestTests: XCTestCase {
 
     // MARK: Private functions
 
-    private func performBucketSort(elements: [Int], totalBuckets: Int) -> [Int] {
+    fileprivate func performBucketSort(_ elements: [Int], totalBuckets: Int) -> [Int] {
 
-        let value = (elements.maxElement()?.toInt())! + 1
+        let value = (elements.max()?.toInt())! + 1
         let capacityRequired = Int( ceil( Double(value) / Double(totalBuckets) ) )
 
         var buckets = [Bucket<Int>]()
@@ -71,7 +71,7 @@ class TestTests: XCTestCase {
         return results
     }
 
-    func isSorted(array: [Int]) -> Bool {
+    func isSorted(_ array: [Int]) -> Bool {
 
         var index = 0
         var sorted = true
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 9a42afa4b..64eb170b0 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -88,6 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0810;
 					};
 				};
 			};
@@ -222,6 +223,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -234,6 +236,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 187f9236924896710b945d879c426370bfb130d7 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Mon, 7 Nov 2016 22:38:03 -0500
Subject: [PATCH 0665/1679] Added implementation

---
 Rootish Array Stack/README.md                 |  19 +++
 Rootish Array Stack/RootishArrayStack.swift   | 115 ++++++++++++++++++
 .../images/RootishArrayStackExample.png       | Bin 0 -> 152134 bytes
 .../images/RootishArrayStackIntro.png         | Bin 0 -> 72856 bytes
 .../contents.xcworkspacedata                  |  10 ++
 5 files changed, 144 insertions(+)
 create mode 100644 Rootish Array Stack/RootishArrayStack.swift
 create mode 100644 Rootish Array Stack/images/RootishArrayStackExample.png
 create mode 100644 Rootish Array Stack/images/RootishArrayStackIntro.png

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index e69de29bb..842439a0c 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -0,0 +1,19 @@
+# Rootish Array Stack
+
+A *Rootish Array Stack* is an ordered array based structure that minimizes wasted space (based on [Gauss's summation technique](https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/)). A *Rootish Array Stack* consists of an array holding many fixed size arrays in ascending size.  
+
+![Rootish Array Stack Intro](/images/RootishArrayStackIntro.png)
+<!-- ![Rootish Array Stack Intro](https://github.com/raywenderlich/swift-algorithm-club/blob/master/Rootish%20Array%20Stack/images/RootishArrayStackIntro.png) -->
+
+A resizable array holds references to blocks (arrays of fixed size). A block's capacity is the same as it's index in the resizable array. Blocks don't grow/shrink like regular Swift arrays. Instead, when their capacity is reached, a new slightly larger block is created. When a block is emptied the last block is freed. This is a great improvement on what a swift array does in terms of wasted space.
+
+![Rootish Array Stack Intro](/images/RootishArrayStackExample.png)
+
+Here you can see how insert/remove operations would behave (very similar to how a Swift array handles such operations).
+
+### How indices map:
+| Subscript index | Indices of Blocks|
+| :------------- | :------------- |
+| `[0]`       | `blocks[0][0]`       |
+
+## A Mathematical Explanation
diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
new file mode 100644
index 000000000..f17f9620e
--- /dev/null
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -0,0 +1,115 @@
+//
+//  main.swift
+//  RootishArrayStack
+//
+//  Created by Benjamin Emdon on 2016-11-07.
+//
+
+import Darwin
+
+public struct RootishArrayStack<T> {
+	fileprivate var blocks = [Array<T?>]()
+	fileprivate var internalCount = 0
+
+	public init() { }
+
+	var count: Int {
+		return internalCount
+	}
+
+	var capacity: Int {
+		return blocks.count * (blocks.count + 1) / 2
+	}
+
+	fileprivate static func toBlock(index: Int) -> Int {
+		let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
+		return block
+	}
+
+	fileprivate mutating func grow() {
+		let newArray = [T?](repeating: nil, count: blocks.count + 1)
+		blocks.append(newArray)
+	}
+
+	fileprivate mutating func shrink() {
+		var numberOfBlocks = blocks.count
+		while numberOfBlocks > 0 && (numberOfBlocks - 2) * (numberOfBlocks - 1) / 2 >= count {
+			blocks.remove(at: blocks.count - 1)
+			numberOfBlocks -= 1
+		}
+	}
+
+	public subscript(index: Int) -> T {
+		get {
+			let block = RootishArrayStack.toBlock(index: index)
+			let blockIndex = index - block * (block + 1) / 2
+			return blocks[block][blockIndex]!
+		}
+		set(newValue) {
+			let block = RootishArrayStack.toBlock(index: index)
+			let blockIndex = index - block * (block + 1) / 2
+			blocks[block][blockIndex] = newValue
+		}
+	}
+
+	public mutating func insert(element: T, atIndex index: Int) {
+		if capacity < count + 1 {
+			grow()
+		}
+		internalCount += 1
+		var i = count - 1
+		while i > index {
+			self[i] = self[i - 1]
+			i -= 1
+		}
+		self[index] = element
+	}
+
+	public mutating func append(element: T) {
+		insert(element: element, atIndex: count)
+	}
+
+	fileprivate mutating func makeNil(atIndex index: Int) {
+		let block = RootishArrayStack.toBlock(index: index)
+		let blockIndex = index - block * (block + 1) / 2
+		blocks[block][blockIndex] = nil
+	}
+
+	public mutating func remove(atIndex index: Int) -> T {
+		let element = self[index]
+		for i in index..<count - 1 {
+			self[i] = self[i + 1]
+		}
+		internalCount -= 1
+		makeNil(atIndex: count)
+		if capacity >= count {
+			shrink()
+		}
+		return element
+	}
+
+	public var memoryDescription: String {
+		var s = "{\n"
+		for i in blocks {
+			s += "\t["
+			for j in i {
+				s += "\(j), "
+			}
+			s += "]\n"
+		}
+		return s + "}"
+	}
+}
+
+extension RootishArrayStack: CustomStringConvertible {
+	public var description: String {
+		var s = "["
+		for index in 0..<count {
+			s += "\(self[index])"
+			if index + 1 != count {
+				s += ", "
+			}
+		}
+		return s + "]"
+	}
+}
diff --git a/Rootish Array Stack/images/RootishArrayStackExample.png b/Rootish Array Stack/images/RootishArrayStackExample.png
new file mode 100644
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zFz2@TZt@tLt4il%ii8YZx&b(h-QUu%RKC+Ii3J~N@s1;jxkJLwfDxel$4_sbn)YCs
z;)=8&2j!D)U&^d&`0TI#>wg$-vEB#XqhzPK=66Re_*i%1j0&B~AH#gNB_Xst77w4v
zBA&IpNj(1!eva@MZLSO+Hp!$rf)cQo`|H8K%p1d56GgN1I7vnSKi}*3pShkIDY`?-
zp5y-YxS#WQX$Q9bzhD2orT<;J?}GGSvHAacWbTvq*-^<(4{3gSybJuODQRCVy?o=r
F{{XywOS}L8

literal 0
HcmV?d00001

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5f2c83aee..ac3a79be9 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1520,6 +1520,16 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Rootish Array Stack"
+      name = "Rootish Array Stack">
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:RootishArrayStack.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Segment Tree"
       name = "Segment Tree">

From dbc751f344f64648c175d83444f8dc0bcb6033ca Mon Sep 17 00:00:00 2001
From: Marcio Klepacz <marcioklepacz@gmail.com>
Date: Mon, 28 Nov 2016 22:09:59 -0500
Subject: [PATCH 0666/1679] Fix link to Minimum Spanning Tree (Unweighted)

---
 Breadth-First Search/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 23edf6da5..084f4611a 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -149,6 +149,6 @@ This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
 Breadth-first search can be used to solve many problems. A small selection:
 
 * Computing the [shortest path](../Shortest Path/) between a source node and each of the other nodes (only for unweighted graphs).
-* Calculating the [minimum spanning tree](../Minimum Spanning Tree/) on an unweighted graph.
+* Calculating the [minimum spanning tree](../Minimum Spanning Tree (Unweighted)/) on an unweighted graph.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*

From e0f13280433d5fe91855d3e133a145a1eaa2446f Mon Sep 17 00:00:00 2001
From: ViktorSimko <aqviktor@gmail.com>
Date: Sun, 4 Dec 2016 12:51:16 +0100
Subject: [PATCH 0667/1679] fixed typos in B-Tree README

---
 B-Tree/README.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/B-Tree/README.md b/B-Tree/README.md
index 493fdedfb..f6924aadc 100644
--- a/B-Tree/README.md
+++ b/B-Tree/README.md
@@ -123,13 +123,13 @@ If the child `c2` at index `i-1` has more keys than the order of the tree:
 
 1. We move the key at index `i-1` from the parent node to the child `c1`'s keys array at index `0`.
 2. We move the last key from `c2` to the parent's keys array at index `i-1`.
-3. (If `c1` is non-leaf) We move the last children from `c1` to `c2`'s children array at index 0.
+3. (If `c1` is non-leaf) We move the last child from `c2` to `c1`'s children array at index 0.
 
 Else:  
 
 1. We move the key at index `i` from the parent node to the end of child `c1`'s keys array.
 2. We move the first key from `c2` to the parent's keys array at index `i`.
-3. (If `c1` isn't a leaf) We move the first children from `c2` to the end of `c1`'s children array. 
+3. (If `c1` isn't a leaf) We move the first child from `c2` to the end of `c1`'s children array. 
 
 ![Moving Key](Images/MovingKey.png)
 
@@ -141,13 +141,13 @@ If `c1` has a left sibling `c2`:
 
 1. We move the key from the parent at index `i-1` to the end of `c2`'s keys array.
 2. We move the keys and the children(if it's a non-leaf) from `c1` to the end of `c2`'s keys and children array.
-3. We remove the children at index `i` from the parent node.
+3. We remove the child at index `i-1` from the parent node.
 
 Else if `c1` only has a right sibling `c2`:
 
 1. We move the key from the parent at index `i` to the beginning of `c2`'s keys array.
 2. We move the keys and the children(if it's a non-leaf) from `c1` to the beginning of `c2`'s keys and children array.
-3. We remove the children at index `i` from the parent node.
+3. We remove the child at index `i` from the parent node.
 
 After merging it is possible that now the parent node contains too few keys,  
 so in the worst case merging also can go up to the root, in which case the height of the tree decreases.

From 4072983c1fb4725fa21a52421897d82e3040c459 Mon Sep 17 00:00:00 2001
From: Dannel Albert <cuebix@MacBookBro.local>
Date: Wed, 7 Dec 2016 00:25:05 -0500
Subject: [PATCH 0668/1679] + methods to append, insert, remove node objects

Useful for manipulating linked lists and you already have node objects
---
 Linked List/LinkedList.swift | 366 ++++++++++++++++++-----------------
 1 file changed, 187 insertions(+), 179 deletions(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 86d2bca9b..83f898f6c 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,198 +1,206 @@
 public class LinkedListNode<T> {
-  var value: T
-  var next: LinkedListNode?
-  weak var previous: LinkedListNode?
-  
-  public init(value: T) {
-    self.value = value
-  }
+    var value: T
+    var next: LinkedListNode?
+    weak var previous: LinkedListNode?
+    
+    public init(value: T) {
+        self.value = value
+    }
 }
 
 public class LinkedList<T> {
-  public typealias Node = LinkedListNode<T>
-  
-  fileprivate var head: Node?
-    
-  public init() {}
-    
-  public var isEmpty: Bool {
-    return head == nil
-  }
-  
-  public var first: Node? {
-    return head
-  }
-  
-  public var last: Node? {
-    if var node = head {
-      while case let next? = node.next {
-        node = next
-      }
-      return node
-    } else {
-      return nil
-    }
-  }
-  
-  public var count: Int {
-    if var node = head {
-      var c = 1
-      while case let next? = node.next {
-        node = next
-        c += 1
-      }
-      return c
-    } else {
-      return 0
-    }
-  }
-  
-  public func node(atIndex index: Int) -> Node? {
-    if index >= 0 {
-      var node = head
-      var i = index
-      while node != nil {
-        if i == 0 { return node }
-        i -= 1
-        node = node!.next
-      }
-    }
-    return nil
-  }
-  
-  public subscript(index: Int) -> T {
-    let node = self.node(atIndex: index)
-    assert(node != nil)
-    return node!.value
-  }
-  
-  public func append(_ value: T) {
-    let newNode = Node(value: value)
-    if let lastNode = last {
-      newNode.previous = lastNode
-      lastNode.next = newNode
-    } else {
-      head = newNode
-    }
-  }
-  
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-    assert(index >= 0)
-    
-    var i = index
-    var next = head
-    var prev: Node?
-    
-    while next != nil && i > 0 {
-      i -= 1
-      prev = next
-      next = next!.next
-    }
-    assert(i == 0)  // if > 0, then specified index was too large
-    
-    return (prev, next)
-  }
-  
-  public func insert(_ value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index: index)
-    
-    let newNode = Node(value: value)
-    newNode.previous = prev
-    newNode.next = next
-    prev?.next = newNode
-    next?.previous = newNode
-    
-    if prev == nil {
-      head = newNode
-    }
-  }
-  
-  public func removeAll() {
-    head = nil
-  }
-  
-  public func remove(node: Node) -> T {
-    let prev = node.previous
-    let next = node.next
-    
-    if let prev = prev {
-      prev.next = next
-    } else {
-      head = next
-    }
-    next?.previous = prev
-    
-    node.previous = nil
-    node.next = nil
-    return node.value
-  }
-  
-  public func removeLast() -> T {
-    assert(!isEmpty)
-    return remove(node: last!)
-  }
-  
-  public func remove(atIndex index: Int) -> T {
-    let node = self.node(atIndex: index)
-    assert(node != nil)
-    return remove(node: node!)
-  }
+    public typealias Node = LinkedListNode<T>
+    
+    fileprivate var head: Node?
+    
+    public init() {}
+    
+    public var isEmpty: Bool {
+        return head == nil
+    }
+    
+    public var first: Node? {
+        return head
+    }
+    
+    public var last: Node? {
+        if var node = head {
+            while case let next? = node.next {
+                node = next
+            }
+            return node
+        } else {
+            return nil
+        }
+    }
+    
+    public var count: Int {
+        if var node = head {
+            var c = 1
+            while case let next? = node.next {
+                node = next
+                c += 1
+            }
+            return c
+        } else {
+            return 0
+        }
+    }
+    
+    public func node(atIndex index: Int) -> Node? {
+        if index >= 0 {
+            var node = head
+            var i = index
+            while node != nil {
+                if i == 0 { return node }
+                i -= 1
+                node = node!.next
+            }
+        }
+        return nil
+    }
+    
+    public subscript(index: Int) -> T {
+        let node = self.node(atIndex: index)
+        assert(node != nil)
+        return node!.value
+    }
+    
+    public func append(_ value: T) {
+        let newNode = Node(value: value)
+        self.append(newNode)
+    }
+    
+    public func append(_ newNode: Node) {
+        if let lastNode = last {
+            newNode.previous = lastNode
+            lastNode.next = newNode
+        } else {
+            head = newNode
+        }
+    }
+    
+    private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
+        assert(index >= 0)
+        
+        var i = index
+        var next = head
+        var prev: Node?
+        
+        while next != nil && i > 0 {
+            i -= 1
+            prev = next
+            next = next!.next
+        }
+        assert(i == 0)  // if > 0, then specified index was too large
+        
+        return (prev, next)
+    }
+    
+    public func insert(_ value: T, atIndex index: Int) {
+        let newNode = Node(value: value)
+        self.insert(newNode, atIndex: index)
+    }
+    
+    public func insert(_ newNode: Node, atIndex index: Int) {
+        let (prev, next) = nodesBeforeAndAfter(index: index)
+        
+        newNode.previous = prev
+        newNode.next = next
+        prev?.next = newNode
+        next?.previous = newNode
+        
+        if prev == nil {
+            head = newNode
+        }
+    }
+    
+    public func removeAll() {
+        head = nil
+    }
+    
+    @discardableResult public func remove(node: Node) -> T {
+        let prev = node.previous
+        let next = node.next
+        
+        if let prev = prev {
+            prev.next = next
+        } else {
+            head = next
+        }
+        next?.previous = prev
+        
+        node.previous = nil
+        node.next = nil
+        return node.value
+    }
+    
+    @discardableResult public func removeLast() -> T {
+        assert(!isEmpty)
+        return remove(node: last!)
+    }
+    
+    @discardableResult public func remove(atIndex index: Int) -> T {
+        let node = self.node(atIndex: index)
+        assert(node != nil)
+        return remove(node: node!)
+    }
 }
 
 extension LinkedList: CustomStringConvertible {
-  public var description: String {
-    var s = "["
-    var node = head
-    while node != nil {
-      s += "\(node!.value)"
-      node = node!.next
-      if node != nil { s += ", " }
-    }
-    return s + "]"
-  }
+    public var description: String {
+        var s = "["
+        var node = head
+        while node != nil {
+            s += "\(node!.value)"
+            node = node!.next
+            if node != nil { s += ", " }
+        }
+        return s + "]"
+    }
 }
 
 extension LinkedList {
-  public func reverse() {
-    var node = head
-    while let currentNode = node {
-      node = currentNode.next
-      swap(&currentNode.next, &currentNode.previous)
-      head = currentNode
-    }
-  }
+    public func reverse() {
+        var node = head
+        while let currentNode = node {
+            node = currentNode.next
+            swap(&currentNode.next, &currentNode.previous)
+            head = currentNode
+        }
+    }
 }
 
 extension LinkedList {
-  public func map<U>(transform: (T) -> U) -> LinkedList<U> {
-    let result = LinkedList<U>()
-    var node = head
-    while node != nil {
-      result.append(transform(node!.value))
-      node = node!.next
-    }
-    return result
-  }
-  
-  public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
-    let result = LinkedList<T>()
-    var node = head
-    while node != nil {
-      if predicate(node!.value) {
-        result.append(node!.value)
-      }
-      node = node!.next
-    }
-    return result
-  }
+    public func map<U>(transform: (T) -> U) -> LinkedList<U> {
+        let result = LinkedList<U>()
+        var node = head
+        while node != nil {
+            result.append(transform(node!.value))
+            node = node!.next
+        }
+        return result
+    }
+    
+    public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
+        let result = LinkedList<T>()
+        var node = head
+        while node != nil {
+            if predicate(node!.value) {
+                result.append(node!.value)
+            }
+            node = node!.next
+        }
+        return result
+    }
 }
 
 extension LinkedList {
-  convenience init(array: Array<T>) {
-    self.init()
+    convenience init(array: Array<T>) {
+        self.init()
         
-    for element in array {
-      self.append(element)
+        for element in array {
+            self.append(element)
+        }
     }
-  }
 }

From cf5ca9cb198437b589f7c4ffcd47bcefe7e4b12a Mon Sep 17 00:00:00 2001
From: Andreas <developer@anerma.de>
Date: Mon, 12 Dec 2016 10:13:35 +0100
Subject: [PATCH 0669/1679] Updated to Swift 3.
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Updated to Swift 3 Syntax.
The .swift file wasn’t converted yet. Additionally, I fixed a bug in
there.
---
 .../BoyerMoore.playground/Contents.swift      |  94 ++++++----
 .../BoyerMoore.playground/timeline.xctimeline |   6 +-
 Boyer-Moore/BoyerMoore.swift                  | 118 ++++++------
 Boyer-Moore/README.markdown                   | 169 +++++++++---------
 4 files changed, 209 insertions(+), 178 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 9a3d619dc..362a298f9 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -1,42 +1,66 @@
 //: Playground - noun: a place where people can play
 
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    let patternLength = pattern.characters.count
-    assert(patternLength > 0)
-    assert(patternLength <= self.characters.count)
-
-    var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerated() {
-      skipTable[c] = patternLength - i - 1
-    }
-
-    let p = pattern.index(before: pattern.endIndex)
-    let lastChar = pattern[p]
-    var i = self.index(startIndex, offsetBy: patternLength - 1)
-
-    func backwards() -> String.Index? {
-      var q = p
-      var j = i
-      while q > pattern.startIndex {
-        j = index(before: j)
-        q = index(before: q)
-        if self[j] != pattern[q] { return nil }
-      }
-      return j
-    }
-
-    while i < self.endIndex {
-      let c = self[i]
-      if c == lastChar {
-        if let k = backwards() { return k }
-        i = index(after: i)
-      } else {
-        i = index(i, offsetBy: skipTable[c] ?? patternLength)
-      }
+    func indexOf(pattern: String) -> String.Index? {
+        // Cache the length of the search pattern because we're going to
+        // use it a few times and it's expensive to calculate.
+        let patternLength = pattern.characters.count
+        assert(patternLength > 0)
+        assert(patternLength <= self.characters.count)
+        
+        // Make the skip table. This table determines how far we skip ahead
+        // when a character from the pattern is found.
+        var skipTable = [Character: Int]()
+        for (i, c) in pattern.characters.enumerated() {
+            skipTable[c] = patternLength - i - 1
+        }
+        
+        // This points at the last character in the pattern.
+        let p = pattern.index(before: pattern.endIndex)
+        let lastChar = pattern[p]
+        
+        // The pattern is scanned right-to-left, so skip ahead in the string by
+        // the length of the pattern. (Minus 1 because startIndex already points
+        // at the first character in the source string.)
+        var i = self.index(startIndex, offsetBy: patternLength - 1)
+        
+        // This is a helper function that steps backwards through both strings
+        // until we find a character that doesn’t match, or until we’ve reached
+        // the beginning of the pattern.
+        func backwards() -> String.Index? {
+            var q = p
+            var j = i
+            while q > pattern.startIndex {
+                j = index(before: j)
+                q = index(before: q)
+                if self[j] != pattern[q] { return nil }
+            }
+            return j
+        }
+        
+        // The main loop. Keep going until the end of the string is reached.
+        while i < self.endIndex {
+            let c = self[i]
+            
+            // Does the current character match the last character from the pattern?
+            if c == lastChar {
+                
+                // There is a possible match. Do a brute-force search backwards.
+                if let k = backwards() { return k }
+                
+                // If no match, we can only safely skip one character ahead.
+                i = index(after: i)
+            } else {
+                // The characters are not equal, so skip ahead. The amount to skip is
+                // determined by the skip table. If the character is not present in the
+                // pattern, we can skip ahead by the full pattern length. However, if
+                // the character *is* present in the pattern, there may be a match up
+                // ahead and we can't skip as far.
+                i = self.index(i, offsetBy: skipTable[c] ?? patternLength)
+            }
+        }
+        return nil
     }
-    return nil
-  }
 }
 
 // A few simple tests
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
index a15b8d6e0..89bc76f90 100644
--- a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
+++ b/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=37&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497585369.829471"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=37&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616217"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=26&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497585369.82964"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=26&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.61657"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=345&amp;EndingColumnNumber=25&amp;EndingLineNumber=9&amp;StartingColumnNumber=9&amp;StartingLineNumber=9&amp;Timestamp=497585369.82978"
+         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=25&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616725"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore/BoyerMoore.swift
index 12a1d86c1..4d7660ec3 100644
--- a/Boyer-Moore/BoyerMoore.swift
+++ b/Boyer-Moore/BoyerMoore.swift
@@ -6,64 +6,64 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    // Cache the length of the search pattern because we're going to
-    // use it a few times and it's expensive to calculate.
-    let patternLength = pattern.characters.count
-    assert(patternLength > 0)
-    assert(patternLength <= self.characters.count)
-
-    // Make the skip table. This table determines how far we skip ahead
-    // when a character from the pattern is found.
-    var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerate() {
-      skipTable[c] = patternLength - i - 1
-    }
-
-    // This points at the last character in the pattern.
-    let p = pattern.endIndex.predecessor()
-    let lastChar = pattern[p]
-
-    // The pattern is scanned right-to-left, so skip ahead in the string by
-    // the length of the pattern. (Minus 1 because startIndex already points
-    // at the first character in the source string.)
-    var i = self.startIndex.advancedBy(patternLength - 1)
-
-    // This is a helper function that steps backwards through both strings
-    // until we find a character that doesn’t match, or until we’ve reached
-    // the beginning of the pattern.
-    func backwards() -> String.Index? {
-      var q = p
-      var j = i
-      while q > pattern.startIndex {
-        j = j.predecessor()
-        q = q.predecessor()
-        if self[j] != pattern[q] { return nil }
-      }
-      return j
-    }
-
-    // The main loop. Keep going until the end of the string is reached.
-    while i < self.endIndex {
-      let c = self[i]
-
-      // Does the current character match the last character from the pattern?
-      if c == lastChar {
-
-        // There is a possible match. Do a brute-force search backwards.
-        if let k = backwards() { return k }
-
-        // If no match, we can only safely skip one character ahead.
-        i = i.successor()
-      } else {
-        // The characters are not equal, so skip ahead. The amount to skip is
-        // determined by the skip table. If the character is not present in the
-        // pattern, we can skip ahead by the full pattern length. However, if
-        // the character *is* present in the pattern, there may be a match up
-        // ahead and we can't skip as far.
-        i = i.advancedBy(skipTable[c] ?? patternLength)
-      }
+    func indexOf(pattern: String) -> String.Index? {
+        // Cache the length of the search pattern because we're going to
+        // use it a few times and it's expensive to calculate.
+        let patternLength = pattern.characters.count
+        assert(patternLength > 0)
+        assert(patternLength <= self.characters.count)
+        
+        // Make the skip table. This table determines how far we skip ahead
+        // when a character from the pattern is found.
+        var skipTable = [Character: Int]()
+        for (i, c) in pattern.characters.enumerated() {
+            skipTable[c] = patternLength - i - 1
+        }
+        
+        // This points at the last character in the pattern.
+        let p = pattern.index(before: pattern.endIndex)
+        let lastChar = pattern[p]
+        
+        // The pattern is scanned right-to-left, so skip ahead in the string by
+        // the length of the pattern. (Minus 1 because startIndex already points
+        // at the first character in the source string.)
+        var i = self.index(startIndex, offsetBy: patternLength - 1)
+        
+        // This is a helper function that steps backwards through both strings
+        // until we find a character that doesn’t match, or until we’ve reached
+        // the beginning of the pattern.
+        func backwards() -> String.Index? {
+            var q = p
+            var j = i
+            while q > pattern.startIndex {
+                j = index(before: j)
+                q = index(before: q)
+                if self[j] != pattern[q] { return nil }
+            }
+            return j
+        }
+        
+        // The main loop. Keep going until the end of the string is reached.
+        while i < self.endIndex {
+            let c = self[i]
+            
+            // Does the current character match the last character from the pattern?
+            if c == lastChar {
+                
+                // There is a possible match. Do a brute-force search backwards.
+                if let k = backwards() { return k }
+                
+                // If no match, we can only safely skip one character ahead.
+                i = index(after: i)
+            } else {
+                // The characters are not equal, so skip ahead. The amount to skip is
+                // determined by the skip table. If the character is not present in the
+                // pattern, we can skip ahead by the full pattern length. However, if
+                // the character *is* present in the pattern, there may be a match up
+                // ahead and we can't skip as far.
+                i = self.index(i, offsetBy: skipTable[c] ?? patternLength)
+            }
+        }
+        return nil
     }
-    return nil
-  }
 }
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 4acc1ffb3..576f6d17b 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -1,13 +1,13 @@
 # Boyer-Moore String Search
 
-Goal: Write a string search algorithm in pure Swift without importing Foundation or using `NSString`'s `rangeOfString()` method. 
- 
+Goal: Write a string search algorithm in pure Swift without importing Foundation or using `NSString`'s `rangeOfString()` method.
+
 In other words, we want to implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
- 
+
 For example:
 
 ```swift
-// Input: 
+// Input:
 let s = "Hello, World"
 s.indexOf(pattern: "World")
 
@@ -24,7 +24,7 @@ animals.indexOf(pattern: "🐮")
 
 > **Note:** The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
 
-The [brute-force approach](../Brute-Force String Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at *every* character from the source string -- you can often skip ahead multiple characters.
+The [brute-force approach](../Brute-Force String Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at _every_ character from the source string -- you can often skip ahead multiple characters.
 
 The skip-ahead algorithm is called [Boyer-Moore](https://en.wikipedia.org/wiki/Boyer–Moore_string_search_algorithm) and it has been around for a long time. It is considered the benchmark for all string search algorithms.
 
@@ -32,75 +32,76 @@ Here's how you could write it in Swift:
 
 ```swift
 extension String {
-func indexOf(pattern: String) -> String.Index? {
-    // Cache the length of the search pattern because we're going to
-    // use it a few times and it's expensive to calculate.
-    let patternLength = pattern.characters.count
-    assert(patternLength > 0)
-    assert(patternLength <= self.characters.count)
-
-    // Make the skip table. This table determines how far we skip ahead
-    // when a character from the pattern is found.
-    var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerated() {
-    skipTable[c] = patternLength - i - 1
-    }
-
-    // This points at the last character in the pattern.
-    let p = index(before: pattern.endIndex)
-    let lastChar = pattern[p]
-
-    // The pattern is scanned right-to-left, so skip ahead in the string by
-    // the length of the pattern. (Minus 1 because startIndex already points
-    // at the first character in the source string.)
-    var i = index(self.startIndex, offsetBy: patternLength - 1)
-
-    // This is a helper function that steps backwards through both strings
-    // until we find a character that doesn’t match, or until we’ve reached
-    // the beginning of the pattern.
-    func backwards() -> String.Index? {
-    var q = p
-    var j = i
-    while q > pattern.startIndex {
-    j = index(before: j)
-    q = index(before: q)
-    if self[j] != pattern[q] { return nil }
-    }
-    return j
-    }
-
-    // The main loop. Keep going until the end of the string is reached.
-    while i < self.endIndex {
-    let c = self[i]
-
-    // Does the current character match the last character from the pattern?
-    if c == lastChar {
-
-    // There is a possible match. Do a brute-force search backwards.
-    if let k = backwards() { return k }
-
-    // If no match, we can only safely skip one character ahead.
-    i = index(after: i)
-    } else {
-    // The characters are not equal, so skip ahead. The amount to skip is
-    // determined by the skip table. If the character is not present in the
-    // pattern, we can skip ahead by the full pattern length. However, if
-    // the character *is* present in the pattern, there may be a match up
-    // ahead and we can't skip as far.
-    i = index(i, offsetBy: skipTable[c] ?? patternLength)
-    }
-    }
-    return nil
+    func indexOf(pattern: String) -> String.Index? {
+        // Cache the length of the search pattern because we're going to
+        // use it a few times and it's expensive to calculate.
+        let patternLength = pattern.characters.count
+        assert(patternLength > 0)
+        assert(patternLength <= self.characters.count)
+
+        // Make the skip table. This table determines how far we skip ahead
+        // when a character from the pattern is found.
+        var skipTable = [Character: Int]()
+        for (i, c) in pattern.characters.enumerated() {
+            skipTable[c] = patternLength - i - 1
+        }
+
+        // This points at the last character in the pattern.
+        let p = pattern.index(before: pattern.endIndex)
+        let lastChar = pattern[p]
+
+        // The pattern is scanned right-to-left, so skip ahead in the string by
+        // the length of the pattern. (Minus 1 because startIndex already points
+        // at the first character in the source string.)
+        var i = self.index(startIndex, offsetBy: patternLength - 1)
+
+        // This is a helper function that steps backwards through both strings
+        // until we find a character that doesn’t match, or until we’ve reached
+        // the beginning of the pattern.
+        func backwards() -> String.Index? {
+            var q = p
+            var j = i
+            while q > pattern.startIndex {
+                j = index(before: j)
+                q = index(before: q)
+                if self[j] != pattern[q] { return nil }
+            }
+            return j
+        }
+
+        // The main loop. Keep going until the end of the string is reached.
+        while i < self.endIndex {
+            let c = self[i]
+
+            // Does the current character match the last character from the pattern?
+            if c == lastChar {
+
+                // There is a possible match. Do a brute-force search backwards.
+                if let k = backwards() { return k }
+
+                // If no match, we can only safely skip one character ahead.
+                i = index(after: i)
+            } else {
+                // The characters are not equal, so skip ahead. The amount to skip is
+                // determined by the skip table. If the character is not present in the
+                // pattern, we can skip ahead by the full pattern length. However, if
+                // the character *is* present in the pattern, there may be a match up
+                // ahead and we can't skip as far.
+                i = self.index(i, offsetBy: skipTable[c] ?? patternLength)
+            }
+        }
+        return nil
     }
 }
-
 ```
 
-The algorithm works as follows. You line up the search pattern with the source string and see what character from the string matches the *last* character of the search pattern:
+The algorithm works as follows. You line up the search pattern with the source string and see what character from the string matches the _last_ character of the search pattern:
 
-	source string:  Hello, World
-	search pattern: World
-	                    ^
+```
+source string:  Hello, World
+search pattern: World
+                    ^
+```
 
 There are three possibilities:
 
@@ -112,25 +113,31 @@ There are three possibilities:
 
 In the example, the characters `o` and `d` do not match, but `o` does appear in the search pattern. That means we can skip ahead several positions:
 
-	source string:  Hello, World
-	search pattern:    World
-	                       ^
+```
+source string:  Hello, World
+search pattern:    World
+                       ^
+```
 
 Note how the two `o` characters line up now. Again you compare the last character of the search pattern with the search text: `W` vs `d`. These are not equal but the `W` does appear in the pattern. So skip ahead again to line up those two `W` characters:
 
-	source string:  Hello, World
-	search pattern:        World
-	                           ^
+```
+source string:  Hello, World
+search pattern:        World
+                           ^
+```
 
 This time the two characters are equal and there is a possible match. To verify the match you do a brute-force search, but backwards, from the end of the search pattern to the beginning. And that's all there is to it.
 
 The amount to skip ahead at any given time is determined by the "skip table", which is a dictionary of all the characters in the search pattern and the amount to skip by. The skip table in the example looks like:
 
-	W: 4
-	o: 3
-	r: 2
-	l: 1
-	d: 0
+```
+W: 4
+o: 3
+r: 2
+l: 1
+d: 0
+```
 
 The closer a character is to the end of the pattern, the smaller the skip amount. If a character appears more than once in the pattern, the one nearest to the end of the pattern determines the skip value for that character.
 
@@ -193,4 +200,4 @@ In practice, the Horspool version of the algorithm tends to perform a little bet
 
 Credits: This code is based on the paper: [R. N. Horspool (1980). "Practical fast searching in strings". Software - Practice & Experience 10 (6): 501–506.](http://www.cin.br/~paguso/courses/if767/bib/Horspool_1980.pdf)
 
-*Written for Swift Algorithm Club by Matthijs Hollemans*
+_Written for Swift Algorithm Club by Matthijs Hollemans, updated by Andreas Neusüß_

From 24fa81839a45e24a6d5600c774fce3b730eb4de1 Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Mon, 12 Dec 2016 15:42:21 -0500
Subject: [PATCH 0670/1679] I created an Xcode project with my changes.  It
 makes it easier to test and the playground was crashing!

---
 Trie/ReadMe.md                                |     10 +
 Trie/Trie/Trie.xcodeproj/project.pbxproj      |    531 +
 .../contents.xcworkspacedata                  |      7 +
 Trie/Trie/Trie/AppDelegate.swift              |     26 +
 .../AppIcon.appiconset/Contents.json          |     58 +
 Trie/Trie/Trie/Base.lproj/Main.storyboard     |    693 +
 Trie/Trie/Trie/Info.plist                     |     32 +
 Trie/Trie/Trie/Trie.swift                     |    207 +
 Trie/Trie/Trie/ViewController.swift           |     27 +
 Trie/Trie/Trie/dictionary.txt                 | 162825 +++++++++++++++
 Trie/Trie/TrieTests/Info.plist                |     22 +
 Trie/Trie/TrieTests/TrieTests.swift           |    162 +
 Trie/Trie/TrieUITests/Info.plist              |     22 +
 Trie/Trie/TrieUITests/TrieUITests.swift       |     36 +
 14 files changed, 164658 insertions(+)
 create mode 100644 Trie/Trie/Trie.xcodeproj/project.pbxproj
 create mode 100644 Trie/Trie/Trie.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Trie/Trie/Trie/AppDelegate.swift
 create mode 100644 Trie/Trie/Trie/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Trie/Trie/Trie/Base.lproj/Main.storyboard
 create mode 100644 Trie/Trie/Trie/Info.plist
 create mode 100644 Trie/Trie/Trie/Trie.swift
 create mode 100644 Trie/Trie/Trie/ViewController.swift
 create mode 100644 Trie/Trie/Trie/dictionary.txt
 create mode 100644 Trie/Trie/TrieTests/Info.plist
 create mode 100644 Trie/Trie/TrieTests/TrieTests.swift
 create mode 100644 Trie/Trie/TrieUITests/Info.plist
 create mode 100644 Trie/Trie/TrieUITests/TrieUITests.swift

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 30082a450..6b28dd189 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -162,3 +162,13 @@ Let n be the length of some value in the `Trie`.
 See also [Wikipedia entry for Trie](https://en.wikipedia.org/wiki/Trie).
 
 *Written for the Swift Algorithm Club by Christian Encarnacion. Refactored by Kelvin Lau*
+
+# Changes by Rick Zaccone
+
+* Added comments to all methods
+* Refactored the `remove` method
+* Renamed some variables.  I have mixed feelings about the way Swift infers types.  It's not always apparent what type a variable will have.  To address this, I made changes such as renaming `parent` to `parentNode` to emphasize that it is a node and not the value contained within the node.
+* Added a `words` property that recursively traverses the trie and constructs an array containing all of the words in the trie.
+* Added a `isLeaf` property to `TrieNode` for readability.
+* Implemented `count` and `isEmpty` properties for the trie.
+* I tried stress testing the trie by adding 162,825 words.  The playground was very slow while adding the words and eventually crashed.  To fix this problem, I moved everything into a project and wrote `XCTest` tests that test the trie.  There are also several performance tests.  Everything passes.
diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..70a0626da
--- /dev/null
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -0,0 +1,531 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		EB798DFE1DFEF79900F0628D /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798DFD1DFEF79900F0628D /* AppDelegate.swift */; };
+		EB798E001DFEF79900F0628D /* ViewController.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798DFF1DFEF79900F0628D /* ViewController.swift */; };
+		EB798E021DFEF79900F0628D /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = EB798E011DFEF79900F0628D /* Assets.xcassets */; };
+		EB798E051DFEF79900F0628D /* Main.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = EB798E031DFEF79900F0628D /* Main.storyboard */; };
+		EB798E101DFEF79900F0628D /* TrieTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798E0F1DFEF79900F0628D /* TrieTests.swift */; };
+		EB798E1B1DFEF79900F0628D /* TrieUITests.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798E1A1DFEF79900F0628D /* TrieUITests.swift */; };
+		EB798E291DFEF81400F0628D /* Trie.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798E281DFEF81400F0628D /* Trie.swift */; };
+		EB798E2A1DFEF81400F0628D /* Trie.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798E281DFEF81400F0628D /* Trie.swift */; };
+		EB798E2C1DFEF90B00F0628D /* dictionary.txt in Resources */ = {isa = PBXBuildFile; fileRef = EB798E2B1DFEF90B00F0628D /* dictionary.txt */; };
+		EB798E2D1DFEF90B00F0628D /* dictionary.txt in Resources */ = {isa = PBXBuildFile; fileRef = EB798E2B1DFEF90B00F0628D /* dictionary.txt */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
+		EB798E0C1DFEF79900F0628D /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = EB798DF21DFEF79900F0628D /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = EB798DF91DFEF79900F0628D;
+			remoteInfo = Trie;
+		};
+		EB798E171DFEF79900F0628D /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = EB798DF21DFEF79900F0628D /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = EB798DF91DFEF79900F0628D;
+			remoteInfo = Trie;
+		};
+/* End PBXContainerItemProxy section */
+
+/* Begin PBXFileReference section */
+		EB798DFA1DFEF79900F0628D /* Trie.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = Trie.app; sourceTree = BUILT_PRODUCTS_DIR; };
+		EB798DFD1DFEF79900F0628D /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
+		EB798DFF1DFEF79900F0628D /* ViewController.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = ViewController.swift; sourceTree = "<group>"; };
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+	rootObject = EB798DF21DFEF79900F0628D /* Project object */;
+}
diff --git a/Trie/Trie/Trie.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Trie/Trie/Trie.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..cd768f89b
--- /dev/null
+++ b/Trie/Trie/Trie.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Trie.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
new file mode 100644
index 000000000..4da9dc345
--- /dev/null
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -0,0 +1,26 @@
+//
+//  AppDelegate.swift
+//  Trie
+//
+//  Created by Rick Zaccone on 2016-12-12.
+//  Copyright © 2016 Rick Zaccone. All rights reserved.
+//
+
+import Cocoa
+
+@NSApplicationMain
+class AppDelegate: NSObject, NSApplicationDelegate {
+
+
+
+    func applicationDidFinishLaunching(_ aNotification: Notification) {
+        // Insert code here to initialize your application
+    }
+
+    func applicationWillTerminate(_ aNotification: Notification) {
+        // Insert code here to tear down your application
+    }
+
+
+}
+
diff --git a/Trie/Trie/Trie/Assets.xcassets/AppIcon.appiconset/Contents.json b/Trie/Trie/Trie/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..2db2b1c7c
--- /dev/null
+++ b/Trie/Trie/Trie/Assets.xcassets/AppIcon.appiconset/Contents.json
@@ -0,0 +1,58 @@
+{
+  "images" : [
+    {
+      "idiom" : "mac",
+      "size" : "16x16",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "16x16",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "32x32",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "32x32",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "128x128",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "128x128",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "256x256",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "256x256",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "512x512",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "mac",
+      "size" : "512x512",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Trie/Trie/Trie/Base.lproj/Main.storyboard b/Trie/Trie/Trie/Base.lproj/Main.storyboard
new file mode 100644
index 000000000..64d3d90d8
--- /dev/null
+++ b/Trie/Trie/Trie/Base.lproj/Main.storyboard
@@ -0,0 +1,693 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.Cocoa.Storyboard.XIB" version="3.0" toolsVersion="11134" systemVersion="15F34" targetRuntime="MacOSX.Cocoa" propertyAccessControl="none" useAutolayout="YES" initialViewController="B8D-0N-5wS">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.CocoaPlugin" version="11134"/>
+    </dependencies>
+    <scenes>
+        <!--Application-->
+        <scene sceneID="JPo-4y-FX3">
+            <objects>
+                <application id="hnw-xV-0zn" sceneMemberID="viewController">
+                    <menu key="mainMenu" title="Main Menu" systemMenu="main" id="AYu-sK-qS6">
+                        <items>
+                            <menuItem title="Trie" id="1Xt-HY-uBw">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Trie" systemMenu="apple" id="uQy-DD-JDr">
+                                    <items>
+                                        <menuItem title="About Trie" id="5kV-Vb-QxS">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="orderFrontStandardAboutPanel:" target="Ady-hI-5gd" id="Exp-CZ-Vem"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="VOq-y0-SEH"/>
+                                        <menuItem title="Preferences…" keyEquivalent="," id="BOF-NM-1cW"/>
+                                        <menuItem isSeparatorItem="YES" id="wFC-TO-SCJ"/>
+                                        <menuItem title="Services" id="NMo-om-nkz">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Services" systemMenu="services" id="hz9-B4-Xy5"/>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="4je-JR-u6R"/>
+                                        <menuItem title="Hide Trie" keyEquivalent="h" id="Olw-nP-bQN">
+                                            <connections>
+                                                <action selector="hide:" target="Ady-hI-5gd" id="PnN-Uc-m68"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Hide Others" keyEquivalent="h" id="Vdr-fp-XzO">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="hideOtherApplications:" target="Ady-hI-5gd" id="VT4-aY-XCT"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Show All" id="Kd2-mp-pUS">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="unhideAllApplications:" target="Ady-hI-5gd" id="Dhg-Le-xox"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="kCx-OE-vgT"/>
+                                        <menuItem title="Quit Trie" keyEquivalent="q" id="4sb-4s-VLi">
+                                            <connections>
+                                                <action selector="terminate:" target="Ady-hI-5gd" id="Te7-pn-YzF"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="File" id="dMs-cI-mzQ">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="File" id="bib-Uj-vzu">
+                                    <items>
+                                        <menuItem title="New" keyEquivalent="n" id="Was-JA-tGl">
+                                            <connections>
+                                                <action selector="newDocument:" target="Ady-hI-5gd" id="4Si-XN-c54"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Open…" keyEquivalent="o" id="IAo-SY-fd9">
+                                            <connections>
+                                                <action selector="openDocument:" target="Ady-hI-5gd" id="bVn-NM-KNZ"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Open Recent" id="tXI-mr-wws">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Open Recent" systemMenu="recentDocuments" id="oas-Oc-fiZ">
+                                                <items>
+                                                    <menuItem title="Clear Menu" id="vNY-rz-j42">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="clearRecentDocuments:" target="Ady-hI-5gd" id="Daa-9d-B3U"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="m54-Is-iLE"/>
+                                        <menuItem title="Close" keyEquivalent="w" id="DVo-aG-piG">
+                                            <connections>
+                                                <action selector="performClose:" target="Ady-hI-5gd" id="HmO-Ls-i7Q"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Save…" keyEquivalent="s" id="pxx-59-PXV">
+                                            <connections>
+                                                <action selector="saveDocument:" target="Ady-hI-5gd" id="teZ-XB-qJY"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Save As…" keyEquivalent="S" id="Bw7-FT-i3A">
+                                            <connections>
+                                                <action selector="saveDocumentAs:" target="Ady-hI-5gd" id="mDf-zr-I0C"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Revert to Saved" keyEquivalent="r" id="KaW-ft-85H">
+                                            <connections>
+                                                <action selector="revertDocumentToSaved:" target="Ady-hI-5gd" id="iJ3-Pv-kwq"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="aJh-i4-bef"/>
+                                        <menuItem title="Page Setup…" keyEquivalent="P" id="qIS-W8-SiK">
+                                            <modifierMask key="keyEquivalentModifierMask" shift="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="runPageLayout:" target="Ady-hI-5gd" id="Din-rz-gC5"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Print…" keyEquivalent="p" id="aTl-1u-JFS">
+                                            <connections>
+                                                <action selector="print:" target="Ady-hI-5gd" id="qaZ-4w-aoO"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Edit" id="5QF-Oa-p0T">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Edit" id="W48-6f-4Dl">
+                                    <items>
+                                        <menuItem title="Undo" keyEquivalent="z" id="dRJ-4n-Yzg">
+                                            <connections>
+                                                <action selector="undo:" target="Ady-hI-5gd" id="M6e-cu-g7V"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Redo" keyEquivalent="Z" id="6dh-zS-Vam">
+                                            <connections>
+                                                <action selector="redo:" target="Ady-hI-5gd" id="oIA-Rs-6OD"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="WRV-NI-Exz"/>
+                                        <menuItem title="Cut" keyEquivalent="x" id="uRl-iY-unG">
+                                            <connections>
+                                                <action selector="cut:" target="Ady-hI-5gd" id="YJe-68-I9s"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Copy" keyEquivalent="c" id="x3v-GG-iWU">
+                                            <connections>
+                                                <action selector="copy:" target="Ady-hI-5gd" id="G1f-GL-Joy"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Paste" keyEquivalent="v" id="gVA-U4-sdL">
+                                            <connections>
+                                                <action selector="paste:" target="Ady-hI-5gd" id="UvS-8e-Qdg"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Paste and Match Style" keyEquivalent="V" id="WeT-3V-zwk">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="pasteAsPlainText:" target="Ady-hI-5gd" id="cEh-KX-wJQ"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Delete" id="pa3-QI-u2k">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="delete:" target="Ady-hI-5gd" id="0Mk-Ml-PaM"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Select All" keyEquivalent="a" id="Ruw-6m-B2m">
+                                            <connections>
+                                                <action selector="selectAll:" target="Ady-hI-5gd" id="VNm-Mi-diN"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="uyl-h8-XO2"/>
+                                        <menuItem title="Find" id="4EN-yA-p0u">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Find" id="1b7-l0-nxx">
+                                                <items>
+                                                    <menuItem title="Find…" tag="1" keyEquivalent="f" id="Xz5-n4-O0W">
+                                                        <connections>
+                                                            <action selector="performFindPanelAction:" target="Ady-hI-5gd" id="cD7-Qs-BN4"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Find and Replace…" tag="12" keyEquivalent="f" id="YEy-JH-Tfz">
+                                                        <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                                        <connections>
+                                                            <action selector="performFindPanelAction:" target="Ady-hI-5gd" id="WD3-Gg-5AJ"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Find Next" tag="2" keyEquivalent="g" id="q09-fT-Sye">
+                                                        <connections>
+                                                            <action selector="performFindPanelAction:" target="Ady-hI-5gd" id="NDo-RZ-v9R"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Find Previous" tag="3" keyEquivalent="G" id="OwM-mh-QMV">
+                                                        <connections>
+                                                            <action selector="performFindPanelAction:" target="Ady-hI-5gd" id="HOh-sY-3ay"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Use Selection for Find" tag="7" keyEquivalent="e" id="buJ-ug-pKt">
+                                                        <connections>
+                                                            <action selector="performFindPanelAction:" target="Ady-hI-5gd" id="U76-nv-p5D"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Jump to Selection" keyEquivalent="j" id="S0p-oC-mLd">
+                                                        <connections>
+                                                            <action selector="centerSelectionInVisibleArea:" target="Ady-hI-5gd" id="IOG-6D-g5B"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Spelling and Grammar" id="Dv1-io-Yv7">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Spelling" id="3IN-sU-3Bg">
+                                                <items>
+                                                    <menuItem title="Show Spelling and Grammar" keyEquivalent=":" id="HFo-cy-zxI">
+                                                        <connections>
+                                                            <action selector="showGuessPanel:" target="Ady-hI-5gd" id="vFj-Ks-hy3"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Check Document Now" keyEquivalent=";" id="hz2-CU-CR7">
+                                                        <connections>
+                                                            <action selector="checkSpelling:" target="Ady-hI-5gd" id="fz7-VC-reM"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="bNw-od-mp5"/>
+                                                    <menuItem title="Check Spelling While Typing" id="rbD-Rh-wIN">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleContinuousSpellChecking:" target="Ady-hI-5gd" id="7w6-Qz-0kB"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Check Grammar With Spelling" id="mK6-2p-4JG">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleGrammarChecking:" target="Ady-hI-5gd" id="muD-Qn-j4w"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Correct Spelling Automatically" id="78Y-hA-62v">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleAutomaticSpellingCorrection:" target="Ady-hI-5gd" id="2lM-Qi-WAP"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Substitutions" id="9ic-FL-obx">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Substitutions" id="FeM-D8-WVr">
+                                                <items>
+                                                    <menuItem title="Show Substitutions" id="z6F-FW-3nz">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="orderFrontSubstitutionsPanel:" target="Ady-hI-5gd" id="oku-mr-iSq"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="gPx-C9-uUO"/>
+                                                    <menuItem title="Smart Copy/Paste" id="9yt-4B-nSM">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleSmartInsertDelete:" target="Ady-hI-5gd" id="3IJ-Se-DZD"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Smart Quotes" id="hQb-2v-fYv">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleAutomaticQuoteSubstitution:" target="Ady-hI-5gd" id="ptq-xd-QOA"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Smart Dashes" id="rgM-f4-ycn">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleAutomaticDashSubstitution:" target="Ady-hI-5gd" id="oCt-pO-9gS"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Smart Links" id="cwL-P1-jid">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleAutomaticLinkDetection:" target="Ady-hI-5gd" id="Gip-E3-Fov"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Data Detectors" id="tRr-pd-1PS">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleAutomaticDataDetection:" target="Ady-hI-5gd" id="R1I-Nq-Kbl"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Text Replacement" id="HFQ-gK-NFA">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleAutomaticTextReplacement:" target="Ady-hI-5gd" id="DvP-Fe-Py6"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Transformations" id="2oI-Rn-ZJC">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Transformations" id="c8a-y6-VQd">
+                                                <items>
+                                                    <menuItem title="Make Upper Case" id="vmV-6d-7jI">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="uppercaseWord:" target="Ady-hI-5gd" id="sPh-Tk-edu"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Make Lower Case" id="d9M-CD-aMd">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="lowercaseWord:" target="Ady-hI-5gd" id="iUZ-b5-hil"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Capitalize" id="UEZ-Bs-lqG">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="capitalizeWord:" target="Ady-hI-5gd" id="26H-TL-nsh"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Speech" id="xrE-MZ-jX0">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Speech" id="3rS-ZA-NoH">
+                                                <items>
+                                                    <menuItem title="Start Speaking" id="Ynk-f8-cLZ">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="startSpeaking:" target="Ady-hI-5gd" id="654-Ng-kyl"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Stop Speaking" id="Oyz-dy-DGm">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="stopSpeaking:" target="Ady-hI-5gd" id="dX8-6p-jy9"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Format" id="jxT-CU-nIS">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Format" id="GEO-Iw-cKr">
+                                    <items>
+                                        <menuItem title="Font" id="Gi5-1S-RQB">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Font" systemMenu="font" id="aXa-aM-Jaq">
+                                                <items>
+                                                    <menuItem title="Show Fonts" keyEquivalent="t" id="Q5e-8K-NDq"/>
+                                                    <menuItem title="Bold" tag="2" keyEquivalent="b" id="GB9-OM-e27"/>
+                                                    <menuItem title="Italic" tag="1" keyEquivalent="i" id="Vjx-xi-njq"/>
+                                                    <menuItem title="Underline" keyEquivalent="u" id="WRG-CD-K1S">
+                                                        <connections>
+                                                            <action selector="underline:" target="Ady-hI-5gd" id="FYS-2b-JAY"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="5gT-KC-WSO"/>
+                                                    <menuItem title="Bigger" tag="3" keyEquivalent="+" id="Ptp-SP-VEL"/>
+                                                    <menuItem title="Smaller" tag="4" keyEquivalent="-" id="i1d-Er-qST"/>
+                                                    <menuItem isSeparatorItem="YES" id="kx3-Dk-x3B"/>
+                                                    <menuItem title="Kern" id="jBQ-r6-VK2">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <menu key="submenu" title="Kern" id="tlD-Oa-oAM">
+                                                            <items>
+                                                                <menuItem title="Use Default" id="GUa-eO-cwY">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="useStandardKerning:" target="Ady-hI-5gd" id="6dk-9l-Ckg"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Use None" id="cDB-IK-hbR">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="turnOffKerning:" target="Ady-hI-5gd" id="U8a-gz-Maa"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Tighten" id="46P-cB-AYj">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="tightenKerning:" target="Ady-hI-5gd" id="hr7-Nz-8ro"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Loosen" id="ogc-rX-tC1">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="loosenKerning:" target="Ady-hI-5gd" id="8i4-f9-FKE"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                            </items>
+                                                        </menu>
+                                                    </menuItem>
+                                                    <menuItem title="Ligatures" id="o6e-r0-MWq">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <menu key="submenu" title="Ligatures" id="w0m-vy-SC9">
+                                                            <items>
+                                                                <menuItem title="Use Default" id="agt-UL-0e3">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="useStandardLigatures:" target="Ady-hI-5gd" id="7uR-wd-Dx6"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Use None" id="J7y-lM-qPV">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="turnOffLigatures:" target="Ady-hI-5gd" id="iX2-gA-Ilz"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Use All" id="xQD-1f-W4t">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="useAllLigatures:" target="Ady-hI-5gd" id="KcB-kA-TuK"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                            </items>
+                                                        </menu>
+                                                    </menuItem>
+                                                    <menuItem title="Baseline" id="OaQ-X3-Vso">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <menu key="submenu" title="Baseline" id="ijk-EB-dga">
+                                                            <items>
+                                                                <menuItem title="Use Default" id="3Om-Ey-2VK">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="unscript:" target="Ady-hI-5gd" id="0vZ-95-Ywn"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Superscript" id="Rqc-34-cIF">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="superscript:" target="Ady-hI-5gd" id="3qV-fo-wpU"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Subscript" id="I0S-gh-46l">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="subscript:" target="Ady-hI-5gd" id="Q6W-4W-IGz"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Raise" id="2h7-ER-AoG">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="raiseBaseline:" target="Ady-hI-5gd" id="4sk-31-7Q9"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem title="Lower" id="1tx-W0-xDw">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="lowerBaseline:" target="Ady-hI-5gd" id="OF1-bc-KW4"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                            </items>
+                                                        </menu>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="Ndw-q3-faq"/>
+                                                    <menuItem title="Show Colors" keyEquivalent="C" id="bgn-CT-cEk">
+                                                        <connections>
+                                                            <action selector="orderFrontColorPanel:" target="Ady-hI-5gd" id="mSX-Xz-DV3"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="iMs-zA-UFJ"/>
+                                                    <menuItem title="Copy Style" keyEquivalent="c" id="5Vv-lz-BsD">
+                                                        <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                                        <connections>
+                                                            <action selector="copyFont:" target="Ady-hI-5gd" id="GJO-xA-L4q"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Paste Style" keyEquivalent="v" id="vKC-jM-MkH">
+                                                        <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                                        <connections>
+                                                            <action selector="pasteFont:" target="Ady-hI-5gd" id="JfD-CL-leO"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                        <menuItem title="Text" id="Fal-I4-PZk">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <menu key="submenu" title="Text" id="d9c-me-L2H">
+                                                <items>
+                                                    <menuItem title="Align Left" keyEquivalent="{" id="ZM1-6Q-yy1">
+                                                        <connections>
+                                                            <action selector="alignLeft:" target="Ady-hI-5gd" id="zUv-R1-uAa"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Center" keyEquivalent="|" id="VIY-Ag-zcb">
+                                                        <connections>
+                                                            <action selector="alignCenter:" target="Ady-hI-5gd" id="spX-mk-kcS"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Justify" id="J5U-5w-g23">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="alignJustified:" target="Ady-hI-5gd" id="ljL-7U-jND"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Align Right" keyEquivalent="}" id="wb2-vD-lq4">
+                                                        <connections>
+                                                            <action selector="alignRight:" target="Ady-hI-5gd" id="r48-bG-YeY"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="4s2-GY-VfK"/>
+                                                    <menuItem title="Writing Direction" id="H1b-Si-o9J">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <menu key="submenu" title="Writing Direction" id="8mr-sm-Yjd">
+                                                            <items>
+                                                                <menuItem title="Paragraph" enabled="NO" id="ZvO-Gk-QUH">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                </menuItem>
+                                                                <menuItem id="YGs-j5-SAR">
+                                                                    <string key="title">	Default</string>
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="makeBaseWritingDirectionNatural:" target="Ady-hI-5gd" id="qtV-5e-UBP"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem id="Lbh-J2-qVU">
+                                                                    <string key="title">	Left to Right</string>
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="makeBaseWritingDirectionLeftToRight:" target="Ady-hI-5gd" id="S0X-9S-QSf"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem id="jFq-tB-4Kx">
+                                                                    <string key="title">	Right to Left</string>
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="makeBaseWritingDirectionRightToLeft:" target="Ady-hI-5gd" id="5fk-qB-AqJ"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem isSeparatorItem="YES" id="swp-gr-a21"/>
+                                                                <menuItem title="Selection" enabled="NO" id="cqv-fj-IhA">
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                </menuItem>
+                                                                <menuItem id="Nop-cj-93Q">
+                                                                    <string key="title">	Default</string>
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="makeTextWritingDirectionNatural:" target="Ady-hI-5gd" id="lPI-Se-ZHp"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem id="BgM-ve-c93">
+                                                                    <string key="title">	Left to Right</string>
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="makeTextWritingDirectionLeftToRight:" target="Ady-hI-5gd" id="caW-Bv-w94"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                                <menuItem id="RB4-Sm-HuC">
+                                                                    <string key="title">	Right to Left</string>
+                                                                    <modifierMask key="keyEquivalentModifierMask"/>
+                                                                    <connections>
+                                                                        <action selector="makeTextWritingDirectionRightToLeft:" target="Ady-hI-5gd" id="EXD-6r-ZUu"/>
+                                                                    </connections>
+                                                                </menuItem>
+                                                            </items>
+                                                        </menu>
+                                                    </menuItem>
+                                                    <menuItem isSeparatorItem="YES" id="fKy-g9-1gm"/>
+                                                    <menuItem title="Show Ruler" id="vLm-3I-IUL">
+                                                        <modifierMask key="keyEquivalentModifierMask"/>
+                                                        <connections>
+                                                            <action selector="toggleRuler:" target="Ady-hI-5gd" id="FOx-HJ-KwY"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Copy Ruler" keyEquivalent="c" id="MkV-Pr-PK5">
+                                                        <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                                        <connections>
+                                                            <action selector="copyRuler:" target="Ady-hI-5gd" id="71i-fW-3W2"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                    <menuItem title="Paste Ruler" keyEquivalent="v" id="LVM-kO-fVI">
+                                                        <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                                        <connections>
+                                                            <action selector="pasteRuler:" target="Ady-hI-5gd" id="cSh-wd-qM2"/>
+                                                        </connections>
+                                                    </menuItem>
+                                                </items>
+                                            </menu>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="View" id="H8h-7b-M4v">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="View" id="HyV-fh-RgO">
+                                    <items>
+                                        <menuItem title="Show Toolbar" keyEquivalent="t" id="snW-S8-Cw5">
+                                            <modifierMask key="keyEquivalentModifierMask" option="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="toggleToolbarShown:" target="Ady-hI-5gd" id="BXY-wc-z0C"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Customize Toolbar…" id="1UK-8n-QPP">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="runToolbarCustomizationPalette:" target="Ady-hI-5gd" id="pQI-g3-MTW"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="hB3-LF-h0Y"/>
+                                        <menuItem title="Show Sidebar" keyEquivalent="s" id="kIP-vf-haE">
+                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="toggleSourceList:" target="Ady-hI-5gd" id="iwa-gc-5KM"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Enter Full Screen" keyEquivalent="f" id="4J7-dP-txa">
+                                            <modifierMask key="keyEquivalentModifierMask" control="YES" command="YES"/>
+                                            <connections>
+                                                <action selector="toggleFullScreen:" target="Ady-hI-5gd" id="dU3-MA-1Rq"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Window" id="aUF-d1-5bR">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Window" systemMenu="window" id="Td7-aD-5lo">
+                                    <items>
+                                        <menuItem title="Minimize" keyEquivalent="m" id="OY7-WF-poV">
+                                            <connections>
+                                                <action selector="performMiniaturize:" target="Ady-hI-5gd" id="VwT-WD-YPe"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem title="Zoom" id="R4o-n2-Eq4">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="performZoom:" target="Ady-hI-5gd" id="DIl-cC-cCs"/>
+                                            </connections>
+                                        </menuItem>
+                                        <menuItem isSeparatorItem="YES" id="eu3-7i-yIM"/>
+                                        <menuItem title="Bring All to Front" id="LE2-aR-0XJ">
+                                            <modifierMask key="keyEquivalentModifierMask"/>
+                                            <connections>
+                                                <action selector="arrangeInFront:" target="Ady-hI-5gd" id="DRN-fu-gQh"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                            <menuItem title="Help" id="wpr-3q-Mcd">
+                                <modifierMask key="keyEquivalentModifierMask"/>
+                                <menu key="submenu" title="Help" systemMenu="help" id="F2S-fz-NVQ">
+                                    <items>
+                                        <menuItem title="Trie Help" keyEquivalent="?" id="FKE-Sm-Kum">
+                                            <connections>
+                                                <action selector="showHelp:" target="Ady-hI-5gd" id="y7X-2Q-9no"/>
+                                            </connections>
+                                        </menuItem>
+                                    </items>
+                                </menu>
+                            </menuItem>
+                        </items>
+                    </menu>
+                    <connections>
+                        <outlet property="delegate" destination="Voe-Tx-rLC" id="PrD-fu-P6m"/>
+                    </connections>
+                </application>
+                <customObject id="Voe-Tx-rLC" customClass="AppDelegate" customModuleProvider="target"/>
+                <customObject id="Ady-hI-5gd" userLabel="First Responder" customClass="NSResponder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="75" y="0.0"/>
+        </scene>
+        <!--Window Controller-->
+        <scene sceneID="R2V-B0-nI4">
+            <objects>
+                <windowController id="B8D-0N-5wS" sceneMemberID="viewController">
+                    <window key="window" title="Window" allowsToolTipsWhenApplicationIsInactive="NO" autorecalculatesKeyViewLoop="NO" oneShot="NO" releasedWhenClosed="NO" showsToolbarButton="NO" visibleAtLaunch="NO" animationBehavior="default" id="IQv-IB-iLA">
+                        <windowStyleMask key="styleMask" titled="YES" closable="YES" miniaturizable="YES" resizable="YES"/>
+                        <windowPositionMask key="initialPositionMask" leftStrut="YES" rightStrut="YES" topStrut="YES" bottomStrut="YES"/>
+                        <rect key="contentRect" x="196" y="240" width="480" height="270"/>
+                        <rect key="screenRect" x="0.0" y="0.0" width="1680" height="1027"/>
+                    </window>
+                    <connections>
+                        <segue destination="XfG-lQ-9wD" kind="relationship" relationship="window.shadowedContentViewController" id="cq2-FE-JQM"/>
+                    </connections>
+                </windowController>
+                <customObject id="Oky-zY-oP4" userLabel="First Responder" customClass="NSResponder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="75" y="250"/>
+        </scene>
+        <!--View Controller-->
+        <scene sceneID="hIz-AP-VOD">
+            <objects>
+                <viewController id="XfG-lQ-9wD" customClass="ViewController" customModuleProvider="target" sceneMemberID="viewController">
+                    <view key="view" wantsLayer="YES" id="m2S-Jp-Qdl">
+                        <rect key="frame" x="0.0" y="0.0" width="480" height="270"/>
+                        <autoresizingMask key="autoresizingMask"/>
+                    </view>
+                </viewController>
+                <customObject id="rPt-NT-nkU" userLabel="First Responder" customClass="NSResponder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="75" y="655"/>
+        </scene>
+    </scenes>
+</document>
diff --git a/Trie/Trie/Trie/Info.plist b/Trie/Trie/Trie/Info.plist
new file mode 100644
index 000000000..ed3668788
--- /dev/null
+++ b/Trie/Trie/Trie/Info.plist
@@ -0,0 +1,32 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIconFile</key>
+	<string></string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSMinimumSystemVersion</key>
+	<string>$(MACOSX_DEPLOYMENT_TARGET)</string>
+	<key>NSHumanReadableCopyright</key>
+	<string>Copyright © 2016 Rick Zaccone. All rights reserved.</string>
+	<key>NSMainStoryboardFile</key>
+	<string>Main</string>
+	<key>NSPrincipalClass</key>
+	<string>NSApplication</string>
+</dict>
+</plist>
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
new file mode 100644
index 000000000..bd1abc538
--- /dev/null
+++ b/Trie/Trie/Trie/Trie.swift
@@ -0,0 +1,207 @@
+//
+//  Trie.swift
+//  Trie
+//
+//  Created by Rick Zaccone on 2016-12-12.
+//  Copyright © 2016 Rick Zaccone. All rights reserved.
+//
+
+import Foundation
+
+
+/// A node in the trie
+class TrieNode<T: Hashable> {
+    var value: T?
+    weak var parentNode: TrieNode?
+    var children: [T: TrieNode] = [:]
+    var isTerminating = false
+    var isLeaf: Bool {
+        get {
+            return children.count == 0
+        }
+    }
+
+    /// Initializes a node.
+    ///
+    /// - Parameters:
+    ///   - value: The value that goes into the node
+    ///   - parentNode: A reference to this node's parent
+    init(value: T? = nil, parentNode: TrieNode? = nil) {
+        self.value = value
+        self.parentNode = parentNode
+    }
+
+    /// Adds a child node to self.  If the child is already present,
+    /// do nothing.
+    ///
+    /// - Parameter value: The item to be added to this node.
+    func add(value: T) {
+        guard children[value] == nil else {
+            return
+        }
+        children[value] = TrieNode(value: value, parentNode: self)
+    }
+}
+
+/// A trie data structure containing words.  Each node is a single
+/// character of a word.
+class Trie {
+    typealias Node = TrieNode<Character>
+    /// The number of words in the trie
+    public var count: Int {
+        return wordCount
+    }
+    /// Is the trie empty?
+    public var isEmpty: Bool {
+        return wordCount == 0
+    }
+    /// All words currently in the trie
+    public var words: [String] {
+        return wordsInSubtrie(rootNode: root, partialWord: "")
+    }
+    fileprivate let root: Node
+    fileprivate var wordCount: Int
+
+    /// Creats an empty trie.
+    init() {
+        root = Node()
+        wordCount = 0
+    }
+}
+
+// MARK: - Adds methods: insert, remove, contains
+extension Trie {
+
+    /// Inserts a word into the trie.  If the word is already present,
+    /// there is no change.
+    ///
+    /// - Parameter word: the word to be inserted.
+    func insert(word: String) {
+        guard !word.isEmpty else {
+            return
+        }
+        var currentNode = root
+        let charactersInWord = Array(word.lowercased().characters)
+        var index = 0
+        while index < charactersInWord.count {
+            let character = charactersInWord[index]
+            if let childNode = currentNode.children[character] {
+                currentNode = childNode
+            } else {
+                currentNode.add(value: character)
+                currentNode = currentNode.children[character]!
+            }
+            index += 1
+        }
+        // Word already present?
+        guard !currentNode.isTerminating else {
+            return
+        }
+        self.wordCount += 1
+        currentNode.isTerminating = true
+    }
+
+    /// Determines whether a word is in the trie.
+    ///
+    /// - Parameter word: the word to check for
+    /// - Returns: true if the word is present, false otherwise.
+    func contains(word: String) -> Bool {
+        guard !word.isEmpty else {
+            return false
+        }
+        var currentNode = root
+        let charactersInWord = Array(word.lowercased().characters)
+        var index = 0
+        while index < charactersInWord.count, let childNode = currentNode.children[charactersInWord[index]] {
+            index += 1
+            currentNode = childNode
+        }
+        return index == charactersInWord.count && currentNode.isTerminating
+    }
+
+    /// Attempts to walk to the terminating node of a word.  The
+    /// search will fail if the word is not present.
+    ///
+    /// - Parameter word: the word in question
+    /// - Returns: the node where the search ended, nil if the
+    /// search failed.
+    private func findTerminalNodeOf(word: String) -> Node? {
+        var currentNode = root
+        var charactersInWord = Array(word.lowercased().characters)
+        var index = 0
+        while index < charactersInWord.count {
+            let character = charactersInWord[index]
+            guard let childNode = currentNode.children[character] else {
+                return nil
+            }
+            currentNode = childNode
+            index += 1
+        }
+        return currentNode.isTerminating ? currentNode : nil
+    }
+
+
+    /// Deletes a word from the trie by starting with the last letter
+    /// and moving back, deleting nodes until either a non-leaf or a
+    /// terminating node is found.
+    ///
+    /// - Parameter terminalNode: the node representing the last node
+    /// of a word
+    private func deleteNodesForWordEndingWith(terminalNode: Node) {
+        var lastNode = terminalNode
+        var character = lastNode.value
+        while lastNode.isLeaf, let parentNode = lastNode.parentNode {
+            lastNode = parentNode
+            lastNode.children[character!] = nil
+            character = lastNode.value
+            if lastNode.isTerminating {
+                break
+            }
+        }
+    }
+
+    /// Removes a word from the trie.  If the word is not present or
+    /// it is empty, just ignore it.  If the last node is a leaf,
+    /// delete that node and higher nodes that are leaves until a
+    /// terminating node or non-leaf is found.  If the last node of
+    /// the word has more children, the word is part of other words.
+    /// Mark the last node as non-terminating.
+    ///
+    /// - Parameter word: the word to be removed
+    func remove(word: String) {
+        guard !word.isEmpty else {
+            return
+        }
+        guard let terminalNode = findTerminalNodeOf(word: word) else {
+            return
+        }
+        if terminalNode.isLeaf {
+            deleteNodesForWordEndingWith(terminalNode: terminalNode)
+        } else {
+            terminalNode.isTerminating = false
+        }
+        self.wordCount -= 1
+    }
+
+    /// Returns an array of words in a subtrie of the trie
+    ///
+    /// - Parameters:
+    ///   - rootNode: the root node of the subtrie
+    ///   - partialWord: the letters collected by traversing to this node
+    /// - Returns: the words in the subtrie
+    func wordsInSubtrie(rootNode: Node, partialWord: String) -> [String] {
+        var subtrieWords = [String]()
+        var previousLetters = partialWord
+        if let value = rootNode.value {
+            previousLetters.append(value)
+        }
+        if rootNode.isTerminating {
+            subtrieWords.append(previousLetters)
+        }
+        for (_, childNode) in rootNode.children {
+            let childWords = wordsInSubtrie(rootNode: childNode, partialWord: previousLetters)
+            subtrieWords += childWords
+        }
+        return subtrieWords
+    }
+}
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
new file mode 100644
index 000000000..b2e9d9105
--- /dev/null
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -0,0 +1,27 @@
+//
+//  ViewController.swift
+//  Trie
+//
+//  Created by Rick Zaccone on 2016-12-12.
+//  Copyright © 2016 Rick Zaccone. All rights reserved.
+//
+
+import Cocoa
+
+class ViewController: NSViewController {
+
+    override func viewDidLoad() {
+        super.viewDidLoad()
+
+        // Do any additional setup after loading the view.
+    }
+
+    override var representedObject: Any? {
+        didSet {
+        // Update the view, if already loaded.
+        }
+    }
+
+
+}
+
diff --git a/Trie/Trie/Trie/dictionary.txt b/Trie/Trie/Trie/dictionary.txt
new file mode 100644
index 000000000..4e5bcd075
--- /dev/null
+++ b/Trie/Trie/Trie/dictionary.txt
@@ -0,0 +1,162825 @@
+10s
+10th
+11th
+12th
+13th
+14th
+15th
+16th
+17th
+1800s
+1890s
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+1910s
+1920s
+1930s
+1940s
+1950s
+1960s
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+1980s
+1990s
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+à
+âge
+åland
+ångstrom
+ångstroms
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+éclaircissement
+éclairs
+éclat
+éclats
+école
+écoles
+écorché
+écrasez
+écu
+écus
+élan
+élans
+élite
+élites
+élitism
+élitist
+élitists
+émigré
+émigrés
+éminence
+éminences
+époque
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+épéeist
+épéeists
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+öland
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+øresund
+œil
+œuvre
\ No newline at end of file
diff --git a/Trie/Trie/TrieTests/Info.plist b/Trie/Trie/TrieTests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Trie/Trie/TrieTests/Info.plist
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
new file mode 100644
index 000000000..236908ece
--- /dev/null
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -0,0 +1,162 @@
+//
+//  TrieTests.swift
+//  TrieTests
+//
+//  Created by Rick Zaccone on 2016-12-12.
+//  Copyright © 2016 Rick Zaccone. All rights reserved.
+//
+
+import XCTest
+@testable import Trie
+
+class TrieTests: XCTestCase {
+    var wordArray: [String]?
+    var trie = Trie()
+    
+    /// Makes sure that the wordArray and trie are initialized before each test.
+    override func setUp() {
+        super.setUp()
+        createWordArray()
+        insertWordsIntoTrie()
+    }
+    
+    /// Don't need to do anything here because the wordArrayu and trie should
+    /// stay around.
+    override func tearDown() {
+        super.tearDown()
+    }
+    
+    /// Reads words from the dictionary file and inserts them into an array.  If
+    /// the word array already has words, do nothing.  This allows running all
+    /// tests without repeatedly filling the array with the same values.
+    func createWordArray() {
+        guard wordArray == nil else {
+            return
+        }
+        let resourcePath = Bundle.main.resourcePath! as NSString
+        let fileName = "dictionary.txt"
+        let filePath = resourcePath.appendingPathComponent(fileName)
+        
+        var data: String?
+        do {
+            data = try String(contentsOfFile: filePath, encoding: String.Encoding.utf8)
+        } catch let error as NSError {
+            XCTAssertNil(error)
+        }
+        XCTAssertNotNil(data)
+        let dictionarySize = 162825
+        wordArray = data!.components(separatedBy: "\n")
+        XCTAssertEqual(wordArray!.count, dictionarySize)
+    }
+    
+    /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
+    func insertWordsIntoTrie() {
+        guard trie.count == 0 else {
+            return
+        }
+        let numberOfWordsToInsert = wordArray!.count
+        for i in 0..<numberOfWordsToInsert {
+            trie.insert(word: wordArray![i])
+        }
+    }
+    
+    /// Tests that a newly created trie has zero words.
+    func testCreate() {
+        let trie = Trie()
+        XCTAssertEqual(trie.count, 0)
+    }
+    
+    /// Tests the insert method
+    func testInsert() {
+        let trie = Trie()
+        trie.insert(word: "cute")
+        trie.insert(word: "cutie")
+        trie.insert(word: "fred")
+        XCTAssertTrue(trie.contains(word: "cute"))
+        XCTAssertFalse(trie.contains(word: "cut"))
+        trie.insert(word: "cut")
+        XCTAssertTrue(trie.contains(word: "cut"))
+        XCTAssertEqual(trie.count, 4)
+    }
+    
+    /// Tests the remove method
+    func testRemove() {
+        let trie = Trie()
+        trie.insert(word: "cute")
+        trie.insert(word: "cut")
+        XCTAssertEqual(trie.count, 2)
+        trie.remove(word: "cute")
+        XCTAssertTrue(trie.contains(word: "cut"))
+        XCTAssertFalse(trie.contains(word: "cute"))
+        XCTAssertEqual(trie.count, 1)
+    }
+    
+    /// Tests the words property
+    func testWords() {
+        let trie = Trie()
+        var words = trie.words
+        XCTAssertEqual(words.count, 0)
+        trie.insert(word: "foobar")
+        words = trie.words
+        XCTAssertEqual(words[0], "foobar")
+        XCTAssertEqual(words.count, 1)
+    }
+    
+    /// Tests the performance of the insert method.
+    func testInsertPerformance() {
+        let trie = Trie()
+        self.measure() {
+            let numberOfWordsToInsert = self.wordArray!.count
+            for i in 0..<numberOfWordsToInsert {
+                trie.insert(word: self.wordArray![i])
+            }
+        }
+        XCTAssertGreaterThan(trie.count, 0)
+        XCTAssertEqual(trie.count, wordArray?.count)
+    }
+    
+    /// Tests the performance of the insert method when the words are already
+    /// present.
+    func testInsertAgainPerformance() {
+        self.measure() {
+            let numberOfWordsToInsert = self.wordArray!.count
+            for i in 0..<numberOfWordsToInsert {
+                self.trie.insert(word: self.wordArray![i])
+            }
+        }
+    }
+    
+    /// Tests the performance of the contains method.
+    func testContainsPerformance() {
+        self.measure() {
+            for i in 0..<self.wordArray!.count {
+                XCTAssertTrue(self.trie.contains(word: self.wordArray![i]))
+            }
+            
+        }
+    }
+    
+    /// Tests the performance of the remove method.
+    func testRemovePerformance() {
+        self.measure() {
+            let numberOfWordsToRemove = self.wordArray!.count
+            for i in 0..<numberOfWordsToRemove {
+                self.trie.remove(word: self.wordArray![i])
+            }
+        }
+        XCTAssertEqual(trie.count, 0)
+    }
+    
+    /// Tests the performance of the words computed property.  Also tests to see
+    /// if it worked properly.
+    func testWordsPerformance() {
+        var words: [String]?
+        self.measure {
+            words = self.trie.words
+        }
+        XCTAssertEqual(words?.count, trie.count)
+        for word in words! {
+            XCTAssertTrue(self.trie.contains(word: word))
+        }
+    }
+}
diff --git a/Trie/Trie/TrieUITests/Info.plist b/Trie/Trie/TrieUITests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Trie/Trie/TrieUITests/Info.plist
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Trie/Trie/TrieUITests/TrieUITests.swift b/Trie/Trie/TrieUITests/TrieUITests.swift
new file mode 100644
index 000000000..f3da2a67f
--- /dev/null
+++ b/Trie/Trie/TrieUITests/TrieUITests.swift
@@ -0,0 +1,36 @@
+//
+//  TrieUITests.swift
+//  TrieUITests
+//
+//  Created by Rick Zaccone on 2016-12-12.
+//  Copyright © 2016 Rick Zaccone. All rights reserved.
+//
+
+import XCTest
+
+class TrieUITests: XCTestCase {
+        
+    override func setUp() {
+        super.setUp()
+        
+        // Put setup code here. This method is called before the invocation of each test method in the class.
+        
+        // In UI tests it is usually best to stop immediately when a failure occurs.
+        continueAfterFailure = false
+        // UI tests must launch the application that they test. Doing this in setup will make sure it happens for each test method.
+        XCUIApplication().launch()
+
+        // In UI tests it’s important to set the initial state - such as interface orientation - required for your tests before they run. The setUp method is a good place to do this.
+    }
+    
+    override func tearDown() {
+        // Put teardown code here. This method is called after the invocation of each test method in the class.
+        super.tearDown()
+    }
+    
+    func testExample() {
+        // Use recording to get started writing UI tests.
+        // Use XCTAssert and related functions to verify your tests produce the correct results.
+    }
+    
+}

From 1e23b7f859ed83e21dd37941113102af0d8c4d28 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Tue, 13 Dec 2016 14:30:07 -0800
Subject: [PATCH 0671/1679] Code updates

---
 Strassen Matrix Multiplication/Matrix.swift   | 237 ++++++++++++++++++
 .../MatrixSize.swift                          |  17 ++
 Strassen Matrix Multiplication/Number.swift   |  41 +++
 3 files changed, 295 insertions(+)

diff --git a/Strassen Matrix Multiplication/Matrix.swift b/Strassen Matrix Multiplication/Matrix.swift
index 493e27e06..657cf3c80 100644
--- a/Strassen Matrix Multiplication/Matrix.swift	
+++ b/Strassen Matrix Multiplication/Matrix.swift	
@@ -7,3 +7,240 @@
 //
 
 import Foundation
+
+enum RowOrColumn {
+  case row, column
+}
+
+struct Matrix<T: Number> {
+  
+  // MARK: - Variables
+  
+  let rows: Int, columns: Int
+  var grid: [T]
+  
+  var isSquare: Bool {
+    return rows == columns
+  }
+  
+  var size: MatrixSize {
+    return MatrixSize(rows: rows, columns: columns)
+  }
+  
+  // MARK: - Init
+  
+  init(rows: Int, columns: Int, initialValue: T = T.zero) {
+    self.rows = rows
+    self.columns = columns
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  init(size: Int, initialValue: T = T.zero) {
+    self.rows = size
+    self.columns = size
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  // MARK: - Subscript
+  
+  subscript(row: Int, column: Int) -> T {
+    get {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      return grid[(row * columns) + column]
+    }
+    set {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      grid[(row * columns) + column] = newValue
+    }
+  }
+  
+  subscript(type: RowOrColumn, value: Int) -> [T] {
+    get {
+      switch type {
+      case .row:
+        assert(indexIsValid(row: value, column: 0), "Index out of range")
+        return Array(grid[(value * columns)..<(value * columns) + columns])
+      case .column:
+        assert(indexIsValid(row: 0, column: value), "Index out of range")
+        var columns: [T] = []
+        for row in 0..<rows {
+          for column in 0..<self.columns {
+            if column == value {
+              columns.append(grid[(row * self.columns) + value])
+            }
+          }
+        }
+        return columns
+      }
+    } set {
+      switch type {
+      case .row:
+        assert(newValue.count == columns)
+        for (column, element) in newValue.enumerated() {
+          grid[(value * columns) + column] = element
+        }
+      case .column:
+        assert(newValue.count == rows)
+        for (row, element) in newValue.enumerated() {
+          grid[(row * columns) + value] = element
+        }
+      }
+    }
+  }
+  
+  // MARK: - Private Functions
+  
+  private func indexIsValid(row: Int, column: Int) -> Bool {
+    return row >= 0 && row < rows && column >= 0 && column < columns
+  }
+  
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
+    guard A.rows > 1 && B.rows > 1 else { return A * B }
+    
+    let n    = A.rows
+    let nBy2 = n / 2
+    
+    var a11 = Matrix(size: nBy2)
+    var a12 = Matrix(size: nBy2)
+    var a21 = Matrix(size: nBy2)
+    var a22 = Matrix(size: nBy2)
+    var b11 = Matrix(size: nBy2)
+    var b12 = Matrix(size: nBy2)
+    var b21 = Matrix(size: nBy2)
+    var b22 = Matrix(size: nBy2)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        a11[i,j] = A[i,j]
+        a12[i,j] = A[i, j+nBy2]
+        a21[i,j] = A[i+nBy2, j]
+        a22[i,j] = A[i+nBy2, j+nBy2]
+        b11[i,j] = B[i,j]
+        b12[i,j] = B[i, j+nBy2]
+        b21[i,j] = B[i+nBy2, j]
+        b22[i,j] = B[i+nBy2, j+nBy2]
+      }
+    }
+    
+    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
+    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
+    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
+    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
+    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
+    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
+    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
+    
+    let c11 = q1 + q4 - q5 + q7
+    let c12 = q3 + q5
+    let c21 = q2 + q4
+    let c22 = q1 + q3 - q2 + q6
+    var C   = Matrix(size: n)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        C[i, j]           = c11[i,j]
+        C[i, j+nBy2]      = c12[i,j]
+        C[i+nBy2, j]      = c21[i,j]
+        C[i+nBy2, j+nBy2] = c22[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func nextPowerOfTwo(of n: Int) -> Int {
+    return Int(pow(2, ceil(log2(Double(n)))))
+  }
+  
+  // MARK: - Functions
+  
+  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(of: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.size.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.size.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    return C
+  }
+  
+  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+// Term-by-term Matrix Math
+
+func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+    }
+  }
+  return newMatrix
+}
diff --git a/Strassen Matrix Multiplication/MatrixSize.swift b/Strassen Matrix Multiplication/MatrixSize.swift
index a01123f3c..f1eada931 100644
--- a/Strassen Matrix Multiplication/MatrixSize.swift	
+++ b/Strassen Matrix Multiplication/MatrixSize.swift	
@@ -7,3 +7,20 @@
 //
 
 import Foundation
+
+struct MatrixSize: Equatable {
+  let rows: Int
+  let columns: Int
+  
+  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try? body(row, column)
+      }
+    }
+  }
+}
+
+func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+}
diff --git a/Strassen Matrix Multiplication/Number.swift b/Strassen Matrix Multiplication/Number.swift
index 1bd6cf634..34c6d5308 100644
--- a/Strassen Matrix Multiplication/Number.swift	
+++ b/Strassen Matrix Multiplication/Number.swift	
@@ -7,3 +7,44 @@
 //
 
 import Foundation
+
+protocol Number: Multipliable, Addable {
+  static var zero: Self { get }
+}
+
+protocol Addable {
+  static func +(lhs: Self, rhs: Self) -> Self
+  static func -(lhs: Self, rhs: Self) -> Self
+}
+
+protocol Multipliable {
+  static func *(lhs: Self, rhs: Self) -> Self
+}
+
+extension Int: Number {
+  static var zero: Int {
+    return 0
+  }
+}
+
+extension Double: Number {
+  static var zero: Double {
+    return 0.0
+  }
+}
+
+extension Float: Number {
+  static var zero: Float {
+    return 0.0
+  }
+}
+
+
+extension Array where Element: Number {
+  func dot(_ b: Array<Element>) -> Element {
+    let a = self
+    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
+    let c = a.indices.map{ a[$0] * b[$0] }
+    return c.reduce(Element.zero, { $0 + $1 })
+  }
+}

From 31bc4c3159ea7574ee557ad46dbb65be33987395 Mon Sep 17 00:00:00 2001
From: Nagasawa Hiroki <civokjots10.pico@gmail.com>
Date: Thu, 15 Dec 2016 08:52:41 +0900
Subject: [PATCH 0672/1679] Use lower camel case in enum case

---
 .../BinaryTree.playground/Contents.swift      | 42 +++++++++----------
 Binary Tree/BinaryTree.swift                  | 24 +++++------
 2 files changed, 33 insertions(+), 33 deletions(-)

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index b35e90c27..b4d65ec1f 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -1,14 +1,14 @@
 //: Playground - noun: a place where people can play
 
 public indirect enum BinaryTree<T> {
-  case Node(BinaryTree<T>, T, BinaryTree<T>)
-  case Empty
+  case node(BinaryTree<T>, T, BinaryTree<T>)
+  case empty
 
   public var count: Int {
     switch self {
-    case let .Node(left, _, right):
+    case let .node(left, _, right):
       return left.count + 1 + right.count
-    case .Empty:
+    case .empty:
       return 0
     }
   }
@@ -17,9 +17,9 @@ public indirect enum BinaryTree<T> {
 extension BinaryTree: CustomStringConvertible {
   public var description: String {
     switch self {
-    case let .Node(left, value, right):
+    case let .node(left, value, right):
       return "value: \(value), left = [" + left.description + "], right = [" + right.description + "]"
-    case .Empty:
+    case .empty:
       return ""
     }
   }
@@ -28,24 +28,24 @@ extension BinaryTree: CustomStringConvertible {
 
 
 // leaf nodes
-let node5 = BinaryTree.Node(.Empty, "5", .Empty)
-let nodeA = BinaryTree.Node(.Empty, "a", .Empty)
-let node10 = BinaryTree.Node(.Empty, "10", .Empty)
-let node4 = BinaryTree.Node(.Empty, "4", .Empty)
-let node3 = BinaryTree.Node(.Empty, "3", .Empty)
-let nodeB = BinaryTree.Node(.Empty, "b", .Empty)
+let node5 = BinaryTree.node(.empty, "5", .empty)
+let nodeA = BinaryTree.node(.empty, "a", .empty)
+let node10 = BinaryTree.node(.empty, "10", .empty)
+let node4 = BinaryTree.node(.empty, "4", .empty)
+let node3 = BinaryTree.node(.empty, "3", .empty)
+let nodeB = BinaryTree.node(.empty, "b", .empty)
 
 // intermediate nodes on the left
-let aMinus10 = BinaryTree.Node(nodeA, "-", node10)
-let timesLeft = BinaryTree.Node(node5, "*", aMinus10)
+let aMinus10 = BinaryTree.node(nodeA, "-", node10)
+let timesLeft = BinaryTree.node(node5, "*", aMinus10)
 
 // intermediate nodes on the right
-let minus4 = BinaryTree.Node(.Empty, "-", node4)
-let divide3andB = BinaryTree.Node(node3, "/", nodeB)
-let timesRight = BinaryTree.Node(minus4, "*", divide3andB)
+let minus4 = BinaryTree.node(.empty, "-", node4)
+let divide3andB = BinaryTree.node(node3, "/", nodeB)
+let timesRight = BinaryTree.node(minus4, "*", divide3andB)
 
 // root node
-let tree = BinaryTree.Node(timesLeft, "+", timesRight)
+let tree = BinaryTree.node(timesLeft, "+", timesRight)
 
 print(tree)
 tree.count  // 12
@@ -54,7 +54,7 @@ tree.count  // 12
 
 extension BinaryTree {
   public func traverseInOrder(process: (T) -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       left.traverseInOrder(process: process)
       process(value)
       right.traverseInOrder(process: process)
@@ -62,7 +62,7 @@ extension BinaryTree {
   }
 
   public func traversePreOrder(process: (T) -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       process(value)
       left.traversePreOrder(process: process)
       right.traversePreOrder(process: process)
@@ -70,7 +70,7 @@ extension BinaryTree {
   }
 
   public func traversePostOrder(process: (T) -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       left.traversePostOrder(process: process)
       right.traversePostOrder(process: process)
       process(value)
diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index 0c55af20e..ad5fcfd13 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -4,14 +4,14 @@
   Nodes don't have a reference to their parent.
 */
 public indirect enum BinaryTree<T> {
-  case Node(BinaryTree<T>, T, BinaryTree<T>)
-  case Empty
+  case node(BinaryTree<T>, T, BinaryTree<T>)
+  case empty
 
   public var count: Int {
     switch self {
-    case let .Node(left, _, right):
+    case let .node(left, _, right):
       return left.count + 1 + right.count
-    case .Empty:
+    case .empty:
       return 0
     }
   }
@@ -20,9 +20,9 @@ public indirect enum BinaryTree<T> {
 extension BinaryTree: CustomStringConvertible {
   public var description: String {
     switch self {
-    case let .Node(left, value, right):
+    case let .node(left, value, right):
       return "value: \(value), left = [" + left.description + "], right = [" + right.description + "]"
-    case .Empty:
+    case .empty:
       return ""
     }
   }
@@ -30,7 +30,7 @@ extension BinaryTree: CustomStringConvertible {
 
 extension BinaryTree {
   public func traverseInOrder(@noescape process: T -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       left.traverseInOrder(process)
       process(value)
       right.traverseInOrder(process)
@@ -38,7 +38,7 @@ extension BinaryTree {
   }
 
   public func traversePreOrder(@noescape process: T -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       process(value)
       left.traversePreOrder(process)
       right.traversePreOrder(process)
@@ -46,7 +46,7 @@ extension BinaryTree {
   }
 
   public func traversePostOrder(@noescape process: T -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       left.traversePostOrder(process)
       right.traversePostOrder(process)
       process(value)
@@ -56,10 +56,10 @@ extension BinaryTree {
 
 extension BinaryTree {
   func invert() -> BinaryTree {
-    if case let .Node(left, value, right) = self {
-      return .Node(right.invert(), value, left.invert())
+    if case let .node(left, value, right) = self {
+      return .node(right.invert(), value, left.invert())
     } else {
-      return .Empty
+      return .empty
     }
   }
 }

From 95cd7732290fd1b9c100adebe2d52dc96ef12f17 Mon Sep 17 00:00:00 2001
From: Nagasawa Hiroki <civokjots10.pico@gmail.com>
Date: Thu, 15 Dec 2016 08:57:32 +0900
Subject: [PATCH 0673/1679] Update README in Binary Tree

---
 Binary Tree/README.markdown | 42 ++++++++++++++++++-------------------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 4b5fe7180..52089b8e7 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -20,8 +20,8 @@ Here's how you could implement a general-purpose binary tree in Swift:
 
 ```swift
 public indirect enum BinaryTree<T> {
-  case Node(BinaryTree<T>, T, BinaryTree<T>)
-  case Empty
+  case node(BinaryTree<T>, T, BinaryTree<T>)
+  case empty
 }
 ```
 
@@ -29,24 +29,24 @@ As an example of how to use this, let's build that tree of arithmetic operations
 
 ```swift
 // leaf nodes
-let node5 = BinaryTree.Node(.Empty, "5", .Empty)
-let nodeA = BinaryTree.Node(.Empty, "a", .Empty)
-let node10 = BinaryTree.Node(.Empty, "10", .Empty)
-let node4 = BinaryTree.Node(.Empty, "4", .Empty)
-let node3 = BinaryTree.Node(.Empty, "3", .Empty)
-let nodeB = BinaryTree.Node(.Empty, "b", .Empty)
+let node5 = BinaryTree.node(.empty, "5", .empty)
+let nodeA = BinaryTree.node(.empty, "a", .empty)
+let node10 = BinaryTree.node(.empty, "10", .empty)
+let node4 = BinaryTree.node(.empty, "4", .empty)
+let node3 = BinaryTree.node(.empty, "3", .empty)
+let nodeB = BinaryTree.node(.empty, "b", .empty)
 
 // intermediate nodes on the left
-let Aminus10 = BinaryTree.Node(nodeA, "-", node10)
-let timesLeft = BinaryTree.Node(node5, "*", Aminus10)
+let Aminus10 = BinaryTree.node(nodeA, "-", node10)
+let timesLeft = BinaryTree.node(node5, "*", Aminus10)
 
 // intermediate nodes on the right
-let minus4 = BinaryTree.Node(.Empty, "-", node4)
-let divide3andB = BinaryTree.Node(node3, "/", nodeB)
-let timesRight = BinaryTree.Node(minus4, "*", divide3andB)
+let minus4 = BinaryTree.node(.empty, "-", node4)
+let divide3andB = BinaryTree.node(node3, "/", nodeB)
+let timesRight = BinaryTree.node(minus4, "*", divide3andB)
 
 // root node
-let tree = BinaryTree.Node(timesLeft, "+", timesRight)
+let tree = BinaryTree.node(timesLeft, "+", timesRight)
 ```
 
 You need to build up the tree in reverse, starting with the leaf nodes and working your way up to the top.
@@ -57,10 +57,10 @@ It will be useful to add a `description` method so you can print the tree:
 extension BinaryTree: CustomStringConvertible {
   public var description: String {
     switch self {
-    case let .Node(left, value, right):
+    case let .node(left, value, right):
       return "value: \(value), left = [" + left.description + "], right = [" 
                                          + right.description + "]"
-    case .Empty:
+    case .empty:
       return ""
     }
   }
@@ -92,9 +92,9 @@ Another useful method is counting the number of nodes in the tree:
 ```swift
   public var count: Int {
     switch self {
-    case let .Node(left, _, right):
+    case let .node(left, _, right):
       return left.count + 1 + right.count
-    case .Empty:
+    case .empty:
       return 0
     }
   }
@@ -112,7 +112,7 @@ Here is how you'd implement that:
 
 ```swift
   public func traverseInOrder(process: (T) -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       left.traverseInOrder(process: process)
       process(value)
       right.traverseInOrder(process: process)
@@ -120,7 +120,7 @@ Here is how you'd implement that:
   }
   
   public func traversePreOrder(process: (T) -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       process(value)
       left.traversePreOrder(process: process)
       right.traversePreOrder(process: process)
@@ -128,7 +128,7 @@ Here is how you'd implement that:
   }
   
   public func traversePostOrder(process: (T) -> Void) {
-    if case let .Node(left, value, right) = self {
+    if case let .node(left, value, right) = self {
       left.traversePostOrder(process: process)
       right.traversePostOrder(process: process)
       process(value)

From 733487f53eadf59a7c702cb8f4db04297db64a0b Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Wed, 14 Dec 2016 18:58:09 -0500
Subject: [PATCH 0674/1679] Made improvements suggested by others.  These
 changes cause things to be done in a more Swift-like manner.  Also updated
 the project to Xcode 8.2.

---
 Trie/Trie/Trie.xcodeproj/project.pbxproj |  7 +++++-
 Trie/Trie/Trie/Trie.swift                | 29 ++++++++----------------
 2 files changed, 16 insertions(+), 20 deletions(-)

diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 70a0626da..8d3611b6d 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -193,7 +193,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0810;
-				LastUpgradeCheck = 0810;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Rick Zaccone";
 				TargetAttributes = {
 					EB798DF91DFEF79900F0628D = {
@@ -333,6 +333,7 @@
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_SUSPICIOUS_MOVES = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -382,6 +383,7 @@
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_SUSPICIOUS_MOVES = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -508,6 +510,7 @@
 				EB798E211DFEF79900F0628D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 		EB798E221DFEF79900F0628D /* Build configuration list for PBXNativeTarget "TrieTests" */ = {
 			isa = XCConfigurationList;
@@ -516,6 +519,7 @@
 				EB798E241DFEF79900F0628D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 		EB798E251DFEF79900F0628D /* Build configuration list for PBXNativeTarget "TrieUITests" */ = {
 			isa = XCConfigurationList;
@@ -524,6 +528,7 @@
 				EB798E271DFEF79900F0628D /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index bd1abc538..ad4e9f2e7 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -81,23 +81,19 @@ extension Trie {
             return
         }
         var currentNode = root
-        let charactersInWord = Array(word.lowercased().characters)
-        var index = 0
-        while index < charactersInWord.count {
-            let character = charactersInWord[index]
+        for character in word.lowercased().characters {
             if let childNode = currentNode.children[character] {
                 currentNode = childNode
             } else {
                 currentNode.add(value: character)
                 currentNode = currentNode.children[character]!
             }
-            index += 1
         }
         // Word already present?
         guard !currentNode.isTerminating else {
             return
         }
-        self.wordCount += 1
+        wordCount += 1
         currentNode.isTerminating = true
     }
 
@@ -110,13 +106,13 @@ extension Trie {
             return false
         }
         var currentNode = root
-        let charactersInWord = Array(word.lowercased().characters)
-        var index = 0
-        while index < charactersInWord.count, let childNode = currentNode.children[charactersInWord[index]] {
-            index += 1
+        for character in word.lowercased().characters {
+            guard let childNode = currentNode.children[character] else {
+                return false
+            }
             currentNode = childNode
         }
-        return index == charactersInWord.count && currentNode.isTerminating
+        return currentNode.isTerminating
     }
 
     /// Attempts to walk to the terminating node of a word.  The
@@ -127,20 +123,15 @@ extension Trie {
     /// search failed.
     private func findTerminalNodeOf(word: String) -> Node? {
         var currentNode = root
-        var charactersInWord = Array(word.lowercased().characters)
-        var index = 0
-        while index < charactersInWord.count {
-            let character = charactersInWord[index]
+        for character in word.lowercased().characters {
             guard let childNode = currentNode.children[character] else {
                 return nil
             }
             currentNode = childNode
-            index += 1
         }
         return currentNode.isTerminating ? currentNode : nil
     }
 
-
     /// Deletes a word from the trie by starting with the last letter
     /// and moving back, deleting nodes until either a non-leaf or a
     /// terminating node is found.
@@ -180,7 +171,7 @@ extension Trie {
         } else {
             terminalNode.isTerminating = false
         }
-        self.wordCount -= 1
+        wordCount -= 1
     }
 
     /// Returns an array of words in a subtrie of the trie
@@ -198,7 +189,7 @@ extension Trie {
         if rootNode.isTerminating {
             subtrieWords.append(previousLetters)
         }
-        for (_, childNode) in rootNode.children {
+        for childNode in rootNode.children.values {
             let childWords = wordsInSubtrie(rootNode: childNode, partialWord: previousLetters)
             subtrieWords += childWords
         }

From f27c4aa6073bf35191d651d6d02459c7b38776cc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Fri, 16 Dec 2016 03:47:34 -0800
Subject: [PATCH 0675/1679] Removes old implementation. Updated README to
 reflect the new code changes.

---
 Trie/Old Implementation/trie.swift            | 523 ------------------
 Trie/ReadMe.md                                |  86 ++-
 Trie/Trie.playground/Contents.swift           |  16 -
 Trie/Trie.playground/Sources/Node.swift       |  21 -
 Trie/Trie.playground/Sources/Trie.swift       |  83 ---
 Trie/Trie.playground/contents.xcplayground    |   4 -
 .../contents.xcworkspacedata                  |   7 -
 Trie/Trie/Trie/Trie.swift                     | 334 +++++------
 8 files changed, 201 insertions(+), 873 deletions(-)
 delete mode 100644 Trie/Old Implementation/trie.swift
 delete mode 100644 Trie/Trie.playground/Contents.swift
 delete mode 100644 Trie/Trie.playground/Sources/Node.swift
 delete mode 100644 Trie/Trie.playground/Sources/Trie.swift
 delete mode 100644 Trie/Trie.playground/contents.xcplayground
 delete mode 100644 Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Trie/Old Implementation/trie.swift b/Trie/Old Implementation/trie.swift
deleted file mode 100644
index 8227d0243..000000000
--- a/Trie/Old Implementation/trie.swift	
+++ /dev/null
@@ -1,523 +0,0 @@
-/// TODO: - Undergoing refactoring.
-
-/*
-  Queue implementation (taken from repository, needed for findPrefix())
-*/
-public struct Queue<T> {
-  private var array = [T?]()
-  private var head = 0
-
-  public var isEmpty: Bool {
-    return count == 0
-  }
-
-  public var count: Int {
-    return array.count - head
-  }
-
-  public mutating func enqueue(element: T) {
-    array.append(element)
-  }
-
-  public mutating func dequeue() -> T? {
-    guard head < array.count, let element = array[head] else { return nil }
-
-    array[head] = nil
-    head += 1
-
-    let percentage = Double(head)/Double(array.count)
-    if array.count > 50 && percentage > 0.25 {
-      array.removeFirst(head)
-      head = 0
-    }
-
-    return element
-  }
-}
-/*
-  A Trie (Pre-fix Tree)
-
-  Some of the functionality of the trie makes use of the Queue implementation for this project.
-
-
-  Every node in the Trie stores a bit of information pertainining to what it references:
-    -Character (letter of an inserted word)
-    -Parent  (Letter that comes before the current letter in some word)
-    -Children (Words that have more letters than available in the prefix)
-    -isAWord (Does the current letter mark the end of a known inserted word?)
-    -visited (Mainly for the findPrefix() function)
-*/
-public class Node {
-  private var character: String?
-  private var parent: Node?
-  private var children: [String:Node]
-  private var isAWord: Bool
-  private var visited: Bool  //only for findPrefix
-
-  init(c: String?, p: Node?) {
-    self.character = c
-    self.children = [String:Node]()
-    self.isAWord = false
-    self.parent = p
-    self.visited = false
-    }
-
-  /*
-    Function Name:  char()
-    Input:  N/A
-    Output:  String
-    Functionality: Returns the associated value of the node
-  */
-  func char() -> String {
-    return self.character!
-  }
-
-  /*
-    Function Name:  update
-    Input: String
-    Output: N/A
-    Functionality: Updates the associated value of the node
-  */
-  func update(c: String?) {
-    self.character = c
-  }
-
-  /*
-    Function Name:  isLeaf
-    Input:  N/A
-    Output:  Bool
-    Functionality: Returns true if the node is a leaf node, false otherwise
-  */
-  func isLeaf() -> Bool {
-    return self.children.count == 0
-  }
-
-  /*
-    Function Name:  getParent
-    Input:  N/A
-    Output:  Node
-    Functionality: Returns the parent node of the current node
-  */
-  func getParent() -> Node {
-    return parent!
-  }
-
-  /*
-    Function Name:  setParent
-    Input:  Node
-    Output:  N/A
-    Functionality: Changes the parent of the current node to the passed node
-  */
-
-  func setParent(node: Node?) {
-    self.parent = node
-  }
-
-  /*
-    Function Name:  getChildAt
-    Input:  String
-    Output:  Node
-    Functionality:  returns the child node that holds the specific passed letter
-  */
-  func getChildAt(s: String) -> Node {
-    return self.children[s]!
-  }
-
-  /*
-    Function Name:  isValidWord
-    Input:  N/A
-    Output:  Bool
-    Functionality: Returns whether or not the current node marks the end of a valid word
-  */
-  func isValidWord() -> Bool {
-    return self.isAWord
-  }
-
-  /*
-    Function Name:  isWord
-    Input:  N/A
-    Output:  N/A
-    Functionality:  the current node is indeed a word
-  */
-  func isWord() {
-    self.isAWord = true
-  }
-
-  /*
-    Function Name: isNotWord
-    Input:  N/A
-    Output:  N/A
-    Functionality:  marks the current node as not a word
-  */
-  func isNotWord() {
-    self.isAWord = false
-  }
-
-  /*
-    Function Name:  isRoot
-    Input: N/A
-    Output: Bool
-    Functionality:  Returns whether or not the current node is the root of the trie
-  */
-  func isRoot() -> Bool {
-    return self.character == ""
-  }
-
-  /*
-    Function Name:  numChildren
-    Input:  N/A
-    Output:  Int
-    Functionality:  Returns the number of immediate letters that follow the current node
-  */
-  func numChildren() -> Int {
-    return self.children.count
-  }
-
-  /*
-    Function Name:  getChildren
-    Input:  N/A
-    Output:  [String: Node]
-    Functionality:  Returns the letters that immediately follow the current node's value for possible word segments that follow
-  */
-  func getChildren() -> [String: Node] {
-    return self.children
-  }
-
-
-  /*
-    Function Name:  printNode
-    Input:  String, Bool
-    Output:  N/A
-    Functionality:  prints to the console a string representation of the current node in the trie
-  */
-  func printNode(var indent: String, leaf: Bool) {
-
-    print(indent, terminator: "")
-    if leaf {
-      print("\\-", terminator: "")
-      indent += " "
-    } else {
-      print("|-", terminator: "")
-      indent += "| "
-    }
-
-    print(self.char())
-
-    var i = 0
-    for (_, node) in self.children {
-      node.printNode(indent, leaf: i == self.getChildren().count-1)
-      i+=1
-    }
-
-  }
-
-}
-
-
-/*
-  The Trie class has the following attributes:
-    -root (the root of the trie)
-    -wordList (the words that currently exist in the trie)
-    -wordCount (the number of words in the trie)
-*/
-public class Trie {
-  private var root: Node
-  private var wordList: [String]
-  private var wordCount = 0
-
-  init() {
-    self.root = Node(c: "", p: nil)
-    self.wordList = []
-  }
-
-  init(wordList: Set<String>) {
-
-    self.root = Node(c: "", p: nil)
-    self.wordList = []
-
-    for word in wordList {
-      self.insert(word)
-    }
-  }
-
-  /*
-    Function Name: merge
-    Input:  Trie
-    Output:  Trie
-    Functionality:  Merges two tries into one and returns the merged trie
-  */
-  func merge(other: Trie) -> Trie {
-    let newWordList = Set(self.getWords() + other.getWords())
-    return Trie(wordList: newWordList)
-  }
-
-  /*
-    Function Name:  find
-    Input:  String
-    Output:  (Node?, Bool)
-    Functionality:  Looks for a specific key and returns a tuple that
-                    has a reference to the node(if found) and true/false
-                    depending on if it was found
-  */
-  func find(key: String) -> (node: Node?, found: Bool) {
-    var currentNode = self.root
-
-    for c in key.characters {
-      if currentNode.children[String(c)] == nil {
-        return(nil, false)
-      }
-      currentNode = currentNode.children[String(c)]!
-    }
-
-    return(currentNode, currentNode.isValidWord())
-  }
-
-  /*
-    Function Name: isEmpty
-    Input:  N/A
-    Output:  Bool
-    Functionality:  returns true if the trie is empty, false otherwise
-  */
-  func isEmpty() -> Bool {
-    return wordCount == 0
-  }
-
-  /*
-    Function Name:  count
-    Input:  N/A
-    Output:  Int
-    Functionality:  returns the number of words in the trie
-  */
-  func count() -> Int {
-    return wordCount
-  }
-
-  /*
-    Function Name:  getWords
-    Input:  N/A
-    Output:  [String]
-    Functionality:  returns the list of words that exist in the trie
-  */
-  func getWords() -> [String] {
-    return wordList
-  }
-
-  /*
-    Function Name:  contains
-    Input:  String
-    Output:  Bool
-    Functionality:  returns true if the tries has the word passed, false otherwise
-  */
-  func contains(w: String) -> Bool {
-    return find(w.lowercaseString).found
-  }
-
-  /*
-    Function Name:  isPrefix
-    Input:  String
-    Output: (Node?, Bool)
-    Functionality:  returns a tuple containing a reference to the final
-                    node in the prefix (if it exists) and true/false
-                    depending on whether or not the prefix exists in the trie
-  */
-  func isPrefix(p: String) -> (node: Node?, found: Bool) {
-    let prefixP = p.lowercaseString
-
-    var currentNode = self.root
-
-    for c in prefixP.characters {
-      if currentNode.children[String(c)] == nil {
-        return (nil, false)
-      }
-
-      currentNode = currentNode.children[String(c)]!
-    }
-
-    if currentNode.numChildren() > 0 {
-      return (currentNode, true)
-    }
-
-    return (nil, false)
-  }
-
-  /*
-    Function Name:  insert
-    Input:  String
-    Output:  (String, Bool)
-    Functionality:  Inserts a word int othe trie.  Returns a tuple containing
-                    the word attempted to be added, and true/false depending on
-                    whether or not the insertion was successful
-  */
-  func insert(w: String) -> (word: String, inserted: Bool) {
-
-    let word = w.lowercaseString
-    var currentNode = self.root
-    var length = word.characters.count
-
-    if self.contains(word) {
-      return (w, false)
-    }
-
-    var index = 0
-    var c = Array(word.characters)[index]
-
-    while let child = currentNode.children[String(c)] {
-      currentNode = child
-      length -= 1
-      index += 1
-
-      if length == 0 {
-        currentNode.isWord()
-        wordList.append(w)
-        wordCount += 1
-        return (w, true)
-      }
-
-      c = Array(word.characters)[index]
-    }
-
-    let remainingChars = String(word.characters.suffix(length))
-    for c in remainingChars.characters {
-      currentNode.children[String(c)] = Node(c: String(c), p: currentNode)
-      currentNode = currentNode.children[String(c)]!
-    }
-
-    currentNode.isWord()
-    wordList.append(w)
-    wordCount += 1
-    return (w, true)
-  }
-
-  /*
-    Function Name:  insertWords
-    Input:  [String]
-    Output:  ([String], Bool)
-    Functionality:  attempts to insert all words from input array.  returns a tuple
-                    containing the input array and true if some of the words were
-                    succesffuly added, false if none were added
-  */
-
-  func insertWords(wordList: [String]) -> (wordList: [String], inserted: Bool) {
-
-    var succesful: Bool = false
-    for word in wordList {
-      succesful = self.insert(word).inserted || succesful
-    }
-
-    return(wordList, succesful)
-  }
-
-  /*
-    Function Name:  remove
-    Input:  String
-    Output:  (String, Bool)
-    Functionality:  Removes the specified key from the trie if it exists, returns
-                    tuple containing the word attempted to be removed and true/false
-                    if the removal was succesful
-  */
-  func remove(w: String) -> (word: String, removed: Bool) {
-    let word = w.lowercaseString
-
-    if !self.contains(w) {
-      return (w, false)
-    }
-    var currentNode = self.root
-
-    for c in word.characters {
-      currentNode = currentNode.getChildAt(String(c))
-    }
-
-    if currentNode.numChildren() > 0 {
-      currentNode.isNotWord()
-    } else {
-      var character = currentNode.char()
-      while currentNode.numChildren() == 0 && !currentNode.isRoot() {
-        currentNode = currentNode.getParent()
-        currentNode.children[character]!.setParent(nil)
-        currentNode.children[character]!.update(nil)
-        currentNode.children[character] = nil
-        character = currentNode.char()
-      }
-    }
-
-    wordCount -= 1
-
-    var index = 0
-    for item in wordList {
-      if item == w {
-        wordList.removeAtIndex(index)
-      }
-      index += 1
-    }
-
-    return (w, true)
-  }
-
-  /*
-    Function Name: findPrefix
-    Input:  String
-    Output:  [String]
-    Functionality:  returns a list containing all words in the trie that have the specified prefix
-  */
-  func findPrefix(p: String) -> [String] {
-
-    if !self.isPrefix(p).found {
-      return []
-    }
-
-    var q: Queue = Queue<Node>()
-    var n: Node = self.isPrefix(p).node!
-
-    var wordsWithPrefix: [String] = []
-    var word = p
-    var tmp = ""
-    q.enqueue(n)
-
-    while let current = q.dequeue() {
-      for (char, child) in current.getChildren() {
-        if !child.visited {
-          q.enqueue(child)
-          child.visited = true
-          if child.isValidWord() {
-            var currentNode = child
-            while currentNode !== n {
-              tmp += currentNode.char()
-              currentNode = currentNode.getParent()
-            }
-            tmp = String(tmp.characters.reverse())
-            wordsWithPrefix.append(word + tmp)
-            tmp = ""
-          }
-        }
-      }
-    }
-
-
-    return wordsWithPrefix
-  }
-
-
-  /*
-    Function Name:  removeAll
-    Input:  N/A
-    Output:  N/A
-    Functionality:  removes all nodes in the trie using remove as a subroutine
-  */
-  func removeAll() {
-    for word in wordList {
-      self.remove(word)
-    }
-  }
-
-
-  /*
-    Function Name:  printTrie
-    Input:  N/A
-    Output:  N/A
-    Functionality:  prints all the nodes of the trie to console in a nice and easy to understand format
-  */
-  func printTrie() {
-    self.root.printNode("", leaf: true)
-  }
-
-}
diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 6b28dd189..172ff4750 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -64,42 +64,38 @@ Insertion into a `Trie` requires you to walk over the nodes until you either hal
 
 ```swift
 func insert(word: String) {
-  guard !word.isEmpty else { return }
+  guard !word.isEmpty else {
+    return
+  }
 
   // 1
   var currentNode = root
-  
-	// 2
-  var characters = Array(word.lowercased().characters)
-  var currentIndex = 0
-  
-	// 3
-  while currentIndex < characters.count {
-    let character = characters[currentIndex]
 
-		// 4
-    if let child = currentNode.children[character] {
-      currentNode = child
+  // 2
+  for character in word.lowercased().characters {
+    // 3
+    if let childNode = currentNode.children[character] {
+      currentNode = childNode
     } else {
-      currentNode.add(child: character)
+      currentNode.add(value: character)
       currentNode = currentNode.children[character]!
     }
-    
-    currentIndex += 1
-
-		// 5
-    if currentIndex == characters.count {
-      currentNode.isTerminating = true
-    }
   }
+  // Word already present?
+  guard !currentNode.isTerminating else {
+    return
+  }
+
+  // 4
+  wordCount += 1
+  currentNode.isTerminating = true
 }
 ```
 
 1. Once again, you create a reference to the root node. You'll move this reference down a chain of nodes.
-2. Keep track of the word you want to insert.
-3. Begin walking through your word letter by letter
-4. Sometimes, the required node to insert already exists. That is the case for two words inside the `Trie` that shares letters (i.e "Apple", "App"). If a letter already exists, you'll reuse it, and simply traverse deeper down the chain. Otherwise, you'll create a new node representing the letter.
-5. Once you get to the end, you mark `isTerminating` to true to mark that specific node as the end of a word.
+2. Begin walking through your word letter by letter
+3. Sometimes, the required node to insert already exists. That is the case for two words inside the `Trie` that shares letters (i.e "Apple", "App"). If a letter already exists, you'll reuse it, and simply traverse deeper down the chain. Otherwise, you'll create a new node representing the letter.
+4. Once you get to the end, you mark `isTerminating` to true to mark that specific node as the end of a word.
 
 ### Removal
 
@@ -109,41 +105,27 @@ If you'd like to remove "Apple", you'll need to take care to leave the "App" cha
 
 ```swift
 func remove(word: String) {
-  guard !word.isEmpty else { return }
+  guard !word.isEmpty else {
+    return
+  }
 
-	// 1
-  var currentNode = root
-  
-	// 2
-  var characters = Array(word.lowercased().characters)
-  var currentIndex = 0
-  
-	// 3
-  while currentIndex < characters.count {
-    let character = characters[currentIndex]
-    guard let child = currentNode.children[character] else { return }
-    currentNode = child
-    currentIndex += 1
+  // 1
+  guard let terminalNode = findTerminalNodeOf(word: word) else {
+    return
   }
-  
-	// 4
-  if currentNode.children.count > 0 {
-    currentNode.isTerminating = false
+
+  // 2
+  if terminalNode.isLeaf {
+    deleteNodesForWordEndingWith(terminalNode: terminalNode)
   } else {
-    var character = currentNode.value
-    while currentNode.children.count == 0, let parent = currentNode.parent, !parent.isTerminating {
-      currentNode = parent
-      currentNode.children[character!] = nil
-      character = currentNode.value
-    }
+    terminalNode.isTerminating = false
   }
+  wordCount -= 1
 }
 ```
 
-1. Once again, you create a reference to the root node.
-2. Keep track of the word you want to remove.
-3. Attempt to walk to the terminating node of the word. The `guard` statement will return if it can't find one of the letters; It's possible to call `remove` on a non-existant entry.
-4. If you reach the node representing the last letter of the word you want to remove, you'll have 2 cases to deal with. Either it's a leaf node, or it has more children. If it has more children, it means the node is used for other words. In that case, you'll just mark `isTerminating` to false. In the other case, you'll delete the nodes.
+1. `findTerminalNodeOf` traverses through the Trie to find the last node that represents the `word`. If it is unable to traverse through the chain of characters, it returns `nil`.
+2. `deleteNodesForWordEndingWith` traverse backwords, deleting the nodes represented by the `word`.
 
 ### Time Complexity
 
diff --git a/Trie/Trie.playground/Contents.swift b/Trie/Trie.playground/Contents.swift
deleted file mode 100644
index 89a160c8d..000000000
--- a/Trie/Trie.playground/Contents.swift
+++ /dev/null
@@ -1,16 +0,0 @@
-let trie = Trie()
-
-trie.insert(word: "apple")
-trie.insert(word: "ap")
-trie.insert(word: "a")
-
-trie.contains(word: "apple")
-trie.contains(word: "ap")
-trie.contains(word: "a")
-
-trie.remove(word: "apple")
-trie.contains(word: "a")
-trie.contains(word: "apple")
-
-trie.insert(word: "apple")
-trie.contains(word: "apple")
diff --git a/Trie/Trie.playground/Sources/Node.swift b/Trie/Trie.playground/Sources/Node.swift
deleted file mode 100644
index 56faed3e5..000000000
--- a/Trie/Trie.playground/Sources/Node.swift
+++ /dev/null
@@ -1,21 +0,0 @@
-public final class TrieNode<T: Hashable> {
-  public var value: T?
-  public weak var parent: TrieNode?
-  public var children: [T: TrieNode] = [:]
-  public var isTerminating = false
-  
-  init() {}
-  
-  init(value: T, parent: TrieNode? = nil) {
-    self.value = value
-    self.parent = parent
-  }
-}
-
-// MARK: - Insertion
-public extension TrieNode {
-  func add(child: T) {
-    guard children[child] == nil else { return }
-    children[child] = TrieNode(value: child, parent: self)
-  }
-}
diff --git a/Trie/Trie.playground/Sources/Trie.swift b/Trie/Trie.playground/Sources/Trie.swift
deleted file mode 100644
index ddce0ba84..000000000
--- a/Trie/Trie.playground/Sources/Trie.swift
+++ /dev/null
@@ -1,83 +0,0 @@
-/// The Trie class has the following attributes:
-///   -root (the root of the trie)
-///   -wordList (the words that currently exist in the trie)
-///   -wordCount (the number of words in the trie)
-public final class Trie {
-  typealias Node = TrieNode<Character>
-  fileprivate let root: Node
-  
-  public init() {
-    root = TrieNode<Character>()
-  }
-}
-
-// MARK: - Basic Methods
-public extension Trie {
-  func insert(word: String) {
-    guard !word.isEmpty else { return }
-    var currentNode = root
-    
-    var characters = Array(word.lowercased().characters)
-    var currentIndex = 0
-    
-    while currentIndex < characters.count {
-      let character = characters[currentIndex]
-      if let child = currentNode.children[character] {
-        currentNode = child
-      } else {
-        currentNode.add(child: character)
-        currentNode = currentNode.children[character]!
-      }
-      
-      currentIndex += 1
-      if currentIndex == characters.count {
-        currentNode.isTerminating = true
-      }
-    }
-  }
-  
-  func contains(word: String) -> Bool {
-    guard !word.isEmpty else { return false }
-    var currentNode = root
-    
-    var characters = Array(word.lowercased().characters)
-    var currentIndex = 0
-    
-    while currentIndex < characters.count, let child = currentNode.children[characters[currentIndex]] {
-      currentNode = child
-      currentIndex += 1
-    }
-    
-    if currentIndex == characters.count && currentNode.isTerminating {
-      return true
-    } else {
-      return false
-    }
-  }
-  
-  func remove(word: String) {
-    guard !word.isEmpty else { return }
-    var currentNode = root
-    
-    var characters = Array(word.lowercased().characters)
-    var currentIndex = 0
-    
-    while currentIndex < characters.count {
-      let character = characters[currentIndex]
-      guard let child = currentNode.children[character] else { return }
-      currentNode = child
-      currentIndex += 1
-    }
-    
-    if currentNode.children.count > 0 {
-      currentNode.isTerminating = false
-    } else {
-      var character = currentNode.value
-      while currentNode.children.count == 0, let parent = currentNode.parent, !parent.isTerminating {
-        currentNode = parent
-        currentNode.children[character!] = nil
-        character = currentNode.value
-      }
-    }
-  }
-}
diff --git a/Trie/Trie.playground/contents.xcplayground b/Trie/Trie.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Trie/Trie.playground/contents.xcplayground
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata b/Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Trie/Trie.playground/playground.xcworkspace/contents.xcworkspacedata
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index ad4e9f2e7..d9b3bbed9 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -11,188 +11,188 @@ import Foundation
 
 /// A node in the trie
 class TrieNode<T: Hashable> {
-    var value: T?
-    weak var parentNode: TrieNode?
-    var children: [T: TrieNode] = [:]
-    var isTerminating = false
-    var isLeaf: Bool {
-        get {
-            return children.count == 0
-        }
+  var value: T?
+  weak var parentNode: TrieNode?
+  var children: [T: TrieNode] = [:]
+  var isTerminating = false
+  var isLeaf: Bool {
+    get {
+      return children.count == 0
     }
-
-    /// Initializes a node.
-    ///
-    /// - Parameters:
-    ///   - value: The value that goes into the node
-    ///   - parentNode: A reference to this node's parent
-    init(value: T? = nil, parentNode: TrieNode? = nil) {
-        self.value = value
-        self.parentNode = parentNode
-    }
-
-    /// Adds a child node to self.  If the child is already present,
-    /// do nothing.
-    ///
-    /// - Parameter value: The item to be added to this node.
-    func add(value: T) {
-        guard children[value] == nil else {
-            return
-        }
-        children[value] = TrieNode(value: value, parentNode: self)
+  }
+  
+  /// Initializes a node.
+  ///
+  /// - Parameters:
+  ///   - value: The value that goes into the node
+  ///   - parentNode: A reference to this node's parent
+  init(value: T? = nil, parentNode: TrieNode? = nil) {
+    self.value = value
+    self.parentNode = parentNode
+  }
+  
+  /// Adds a child node to self.  If the child is already present,
+  /// do nothing.
+  ///
+  /// - Parameter value: The item to be added to this node.
+  func add(value: T) {
+    guard children[value] == nil else {
+      return
     }
+    children[value] = TrieNode(value: value, parentNode: self)
+  }
 }
 
 /// A trie data structure containing words.  Each node is a single
 /// character of a word.
 class Trie {
-    typealias Node = TrieNode<Character>
-    /// The number of words in the trie
-    public var count: Int {
-        return wordCount
-    }
-    /// Is the trie empty?
-    public var isEmpty: Bool {
-        return wordCount == 0
-    }
-    /// All words currently in the trie
-    public var words: [String] {
-        return wordsInSubtrie(rootNode: root, partialWord: "")
-    }
-    fileprivate let root: Node
-    fileprivate var wordCount: Int
-
-    /// Creats an empty trie.
-    init() {
-        root = Node()
-        wordCount = 0
-    }
+  typealias Node = TrieNode<Character>
+  /// The number of words in the trie
+  public var count: Int {
+    return wordCount
+  }
+  /// Is the trie empty?
+  public var isEmpty: Bool {
+    return wordCount == 0
+  }
+  /// All words currently in the trie
+  public var words: [String] {
+    return wordsInSubtrie(rootNode: root, partialWord: "")
+  }
+  fileprivate let root: Node
+  fileprivate var wordCount: Int
+  
+  /// Creats an empty trie.
+  init() {
+    root = Node()
+    wordCount = 0
+  }
 }
 
 // MARK: - Adds methods: insert, remove, contains
 extension Trie {
-
-    /// Inserts a word into the trie.  If the word is already present,
-    /// there is no change.
-    ///
-    /// - Parameter word: the word to be inserted.
-    func insert(word: String) {
-        guard !word.isEmpty else {
-            return
-        }
-        var currentNode = root
-        for character in word.lowercased().characters {
-            if let childNode = currentNode.children[character] {
-                currentNode = childNode
-            } else {
-                currentNode.add(value: character)
-                currentNode = currentNode.children[character]!
-            }
-        }
-        // Word already present?
-        guard !currentNode.isTerminating else {
-            return
-        }
-        wordCount += 1
-        currentNode.isTerminating = true
+  
+  /// Inserts a word into the trie.  If the word is already present,
+  /// there is no change.
+  ///
+  /// - Parameter word: the word to be inserted.
+  func insert(word: String) {
+    guard !word.isEmpty else {
+      return
     }
-
-    /// Determines whether a word is in the trie.
-    ///
-    /// - Parameter word: the word to check for
-    /// - Returns: true if the word is present, false otherwise.
-    func contains(word: String) -> Bool {
-        guard !word.isEmpty else {
-            return false
-        }
-        var currentNode = root
-        for character in word.lowercased().characters {
-            guard let childNode = currentNode.children[character] else {
-                return false
-            }
-            currentNode = childNode
-        }
-        return currentNode.isTerminating
+    var currentNode = root
+    for character in word.lowercased().characters {
+      if let childNode = currentNode.children[character] {
+        currentNode = childNode
+      } else {
+        currentNode.add(value: character)
+        currentNode = currentNode.children[character]!
+      }
     }
-
-    /// Attempts to walk to the terminating node of a word.  The
-    /// search will fail if the word is not present.
-    ///
-    /// - Parameter word: the word in question
-    /// - Returns: the node where the search ended, nil if the
-    /// search failed.
-    private func findTerminalNodeOf(word: String) -> Node? {
-        var currentNode = root
-        for character in word.lowercased().characters {
-            guard let childNode = currentNode.children[character] else {
-                return nil
-            }
-            currentNode = childNode
-        }
-        return currentNode.isTerminating ? currentNode : nil
+    // Word already present?
+    guard !currentNode.isTerminating else {
+      return
     }
-
-    /// Deletes a word from the trie by starting with the last letter
-    /// and moving back, deleting nodes until either a non-leaf or a
-    /// terminating node is found.
-    ///
-    /// - Parameter terminalNode: the node representing the last node
-    /// of a word
-    private func deleteNodesForWordEndingWith(terminalNode: Node) {
-        var lastNode = terminalNode
-        var character = lastNode.value
-        while lastNode.isLeaf, let parentNode = lastNode.parentNode {
-            lastNode = parentNode
-            lastNode.children[character!] = nil
-            character = lastNode.value
-            if lastNode.isTerminating {
-                break
-            }
-        }
+    wordCount += 1
+    currentNode.isTerminating = true
+  }
+  
+  /// Determines whether a word is in the trie.
+  ///
+  /// - Parameter word: the word to check for
+  /// - Returns: true if the word is present, false otherwise.
+  func contains(word: String) -> Bool {
+    guard !word.isEmpty else {
+      return false
     }
-
-    /// Removes a word from the trie.  If the word is not present or
-    /// it is empty, just ignore it.  If the last node is a leaf,
-    /// delete that node and higher nodes that are leaves until a
-    /// terminating node or non-leaf is found.  If the last node of
-    /// the word has more children, the word is part of other words.
-    /// Mark the last node as non-terminating.
-    ///
-    /// - Parameter word: the word to be removed
-    func remove(word: String) {
-        guard !word.isEmpty else {
-            return
-        }
-        guard let terminalNode = findTerminalNodeOf(word: word) else {
-            return
-        }
-        if terminalNode.isLeaf {
-            deleteNodesForWordEndingWith(terminalNode: terminalNode)
-        } else {
-            terminalNode.isTerminating = false
-        }
-        wordCount -= 1
+    var currentNode = root
+    for character in word.lowercased().characters {
+      guard let childNode = currentNode.children[character] else {
+        return false
+      }
+      currentNode = childNode
     }
-
-    /// Returns an array of words in a subtrie of the trie
-    ///
-    /// - Parameters:
-    ///   - rootNode: the root node of the subtrie
-    ///   - partialWord: the letters collected by traversing to this node
-    /// - Returns: the words in the subtrie
-    func wordsInSubtrie(rootNode: Node, partialWord: String) -> [String] {
-        var subtrieWords = [String]()
-        var previousLetters = partialWord
-        if let value = rootNode.value {
-            previousLetters.append(value)
-        }
-        if rootNode.isTerminating {
-            subtrieWords.append(previousLetters)
-        }
-        for childNode in rootNode.children.values {
-            let childWords = wordsInSubtrie(rootNode: childNode, partialWord: previousLetters)
-            subtrieWords += childWords
-        }
-        return subtrieWords
+    return currentNode.isTerminating
+  }
+  
+  /// Attempts to walk to the terminating node of a word.  The
+  /// search will fail if the word is not present.
+  ///
+  /// - Parameter word: the word in question
+  /// - Returns: the node where the search ended, nil if the
+  /// search failed.
+  private func findTerminalNodeOf(word: String) -> Node? {
+    var currentNode = root
+    for character in word.lowercased().characters {
+      guard let childNode = currentNode.children[character] else {
+        return nil
+      }
+      currentNode = childNode
+    }
+    return currentNode.isTerminating ? currentNode : nil
+  }
+  
+  /// Deletes a word from the trie by starting with the last letter
+  /// and moving back, deleting nodes until either a non-leaf or a
+  /// terminating node is found.
+  ///
+  /// - Parameter terminalNode: the node representing the last node
+  /// of a word
+  private func deleteNodesForWordEndingWith(terminalNode: Node) {
+    var lastNode = terminalNode
+    var character = lastNode.value
+    while lastNode.isLeaf, let parentNode = lastNode.parentNode {
+      lastNode = parentNode
+      lastNode.children[character!] = nil
+      character = lastNode.value
+      if lastNode.isTerminating {
+        break
+      }
+    }
+  }
+  
+  /// Removes a word from the trie.  If the word is not present or
+  /// it is empty, just ignore it.  If the last node is a leaf,
+  /// delete that node and higher nodes that are leaves until a
+  /// terminating node or non-leaf is found.  If the last node of
+  /// the word has more children, the word is part of other words.
+  /// Mark the last node as non-terminating.
+  ///
+  /// - Parameter word: the word to be removed
+  func remove(word: String) {
+    guard !word.isEmpty else {
+      return
+    }
+    guard let terminalNode = findTerminalNodeOf(word: word) else {
+      return
+    }
+    if terminalNode.isLeaf {
+      deleteNodesForWordEndingWith(terminalNode: terminalNode)
+    } else {
+      terminalNode.isTerminating = false
+    }
+    wordCount -= 1
+  }
+  
+  /// Returns an array of words in a subtrie of the trie
+  ///
+  /// - Parameters:
+  ///   - rootNode: the root node of the subtrie
+  ///   - partialWord: the letters collected by traversing to this node
+  /// - Returns: the words in the subtrie
+  func wordsInSubtrie(rootNode: Node, partialWord: String) -> [String] {
+    var subtrieWords = [String]()
+    var previousLetters = partialWord
+    if let value = rootNode.value {
+      previousLetters.append(value)
+    }
+    if rootNode.isTerminating {
+      subtrieWords.append(previousLetters)
+    }
+    for childNode in rootNode.children.values {
+      let childWords = wordsInSubtrie(rootNode: childNode, partialWord: previousLetters)
+      subtrieWords += childWords
     }
+    return subtrieWords
+  }
 }

From e7bc36cf645d11539cac9e2c9ffe098457488ad6 Mon Sep 17 00:00:00 2001
From: Anton <Antondomashnev@gmail.com>
Date: Sat, 17 Dec 2016 19:41:31 +0100
Subject: [PATCH 0676/1679] Fix Skip-List link in readme

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 4c812b0f3..7ac170a65 100644
--- a/README.markdown
+++ b/README.markdown
@@ -142,7 +142,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 ### Lists
 
 - [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
-- Skip List
+- [Skip-List](Skip-List/). Skip List is a probablistic data-structure with same logarithmic time bound and efficiency as AVL/ or Red-Black tree and provides a clever compromise to efficiently support search and update operations.
 
 ### Trees
 

From a277fed473caf69108eae0aa3276d7a78f01fa90 Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Sat, 17 Dec 2016 21:35:42 +0100
Subject: [PATCH 0677/1679] Add AVL tree rotation example image;

Update image;

Update image;
---
 AVL Tree/Images/Rotation.jpg | Bin 0 -> 35153 bytes
 AVL Tree/README.markdown     |   5 +++--
 2 files changed, 3 insertions(+), 2 deletions(-)
 create mode 100644 AVL Tree/Images/Rotation.jpg

diff --git a/AVL Tree/Images/Rotation.jpg b/AVL Tree/Images/Rotation.jpg
new file mode 100644
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HcmV?d00001

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 159f9e1dc..22ea99f53 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -46,7 +46,8 @@ If after an insertion or deletion the balance factor becomes greater than 1, the
 
 Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.
 
-TODO: describe with pictures how these rotations work
+Example of balancing the unbalanced tree using rotation:
+![Rotation](Images/Rotation.jpg)
 
 Insertion never needs more than 2 rotations. Removal might require up to *log(n)* rotations.
 
@@ -56,7 +57,7 @@ Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary searc
 
 > **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary Search Tree/). It will make the rest of the AVL tree easier to understand.
 
-The interesting bits are in the `balance()` method which is called after inserting or deleting a node. 
+The interesting bits are in the `balance()` method which is called after inserting or deleting a node.
 
 ## See also
 

From 7050669ebf695f1f5b029812fffbff38b83540e8 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 20 Dec 2016 02:02:10 -0800
Subject: [PATCH 0678/1679] Modified the queue's peek property name to front
 per naming design guidelines. Computed properties should not imply action.
 Also checks out on Knuth's Fundamental Algorithms book page 241 where front
 and rear is the choice for his wording.

---
 Queue/Queue.playground/Contents.swift      |  4 ++--
 Queue/Queue.playground/timeline.xctimeline |  6 ------
 Queue/README.markdown                      | 10 +++-------
 3 files changed, 5 insertions(+), 15 deletions(-)
 delete mode 100644 Queue/Queue.playground/timeline.xctimeline

diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index a8be21b08..a90fa647e 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -34,7 +34,7 @@ public struct Queue<T> {
     }
   }
 
-  public var peek: T? {
+  public var front: T? {
     return array.first
   }
 }
@@ -56,7 +56,7 @@ queueOfNames.dequeue()
 
 // Return the first element in the queue.
 // Returns "Lisa" since "Carl" was dequeued on the previous line.
-queueOfNames.peek
+queueOfNames.front
 
 // Check to see if the queue is empty.
 // Returns "false" since the queue still has elements in it.
diff --git a/Queue/Queue.playground/timeline.xctimeline b/Queue/Queue.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Queue/Queue.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Queue/README.markdown b/Queue/README.markdown
index f7779aa69..25d6205f8 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -68,7 +68,7 @@ public struct Queue<T> {
     }
   }
   
-  public func peek() -> T? {
+  public var front: T? {
     return array.first
   }
 }
@@ -166,12 +166,8 @@ public struct Queue<T> {
     return element
   }
   
-  public func peek() -> T? {
-    if isEmpty {
-      return nil
-    } else {
-      return array[head]
-    }
+  public var front: T? {
+    return array.first
   }
 }
 ```

From 6a66252ad17ae92b068d8e27356b54a526bb7865 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 20 Dec 2016 02:11:41 -0800
Subject: [PATCH 0679/1679] Updated the peek function of the stack to a
 computed property instead. This change is inspired by the Swift naming
 conventions guide and Knuth's fundamental algorithms book page 242 where he
 states the element at the top of the stack may be denoted by top(A) where A
 is the stack.

---
 Stack/README.markdown                 | 6 +++---
 Stack/Stack.playground/Contents.swift | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Stack/README.markdown b/Stack/README.markdown
index 9d157f290..a79e2c261 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -38,7 +38,7 @@ stack.pop()
 
 This returns `3`, and so on. If the stack is empty, popping returns `nil` or in some implementations it gives an error message ("stack underflow").
 
-A stack is easy to create in Swift. It's just a wrapper around an array that just lets you push, pop, and peek:
+A stack is easy to create in Swift. It's just a wrapper around an array that just lets you push, pop, and look at the top element of the stack:
 
 ```swift
 public struct Stack<T> {
@@ -60,8 +60,8 @@ public struct Stack<T> {
     return array.popLast()
   }
 
-  public func peek() -> T? {
-    return array.last
+  public var top: T? {
+  	return array.last
   }
 }
 ```
diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index f086ca817..1eb705f20 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -30,7 +30,7 @@ public struct Stack<T> {
     return array.popLast()
   }
 
-  public func peek() -> T? {
+  public var top: T? {
     return array.last
   }
 }
@@ -49,7 +49,7 @@ stackOfNames.pop()
 
 // Look at the first element from the stack.
 // Returns "Wade" since "Mike" was popped on the previous line.
-stackOfNames.peek()
+stackOfNames.top
 
 // Check to see if the stack is empty.
 // Returns "false" since the stack still has elements in it.

From bfeac916bedcaba9555f49f982d96a1e84ce157a Mon Sep 17 00:00:00 2001
From: Anton <Antondomashnev@gmail.com>
Date: Tue, 20 Dec 2016 23:40:39 +0100
Subject: [PATCH 0680/1679] Add rotation steps description;

---
 AVL Tree/README.markdown | 25 ++++++++++++++++++++++---
 1 file changed, 22 insertions(+), 3 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 22ea99f53..bcbbbabbc 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -43,13 +43,32 @@ The difference between the heights of the left and right subtrees is called the
 If after an insertion or deletion the balance factor becomes greater than 1, then we need to re-balance this part of the AVL tree. And that is done with rotations.
 
 ## Rotations
-
 Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.
 
-Example of balancing the unbalanced tree using rotation:
+Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation :
 ![Rotation](Images/Rotation.jpg)
 
-Insertion never needs more than 2 rotations. Removal might require up to *log(n)* rotations.
+Let's dig into rotation algorithm in detail using the terminology:
+* *Root* - the parent not of the subtrees that will be rotated;
+* *Pivot* - the node that will become parent (basically will be on the *Root*'s position) after rotation;
+* *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
+* *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation
+
+The steps of rotation on the example image could be described by following:
+* Select the *Pivot* as `D` and hence the *Root* as `F`;
+* Assign the *RotationSubtree* as a new *OppositeSubtree* for the *Root*;
+* Assign the *Root* as a new *RotationSubtree* for the *Pivot*;
+* Check the final result
+
+In pseudocode the algorithm above could be written as follows:
+```
+Root.OS = Pivot.RS
+Pivot.RS = Root
+Root = Pivot
+```
+
+This is a constant time operation - __O(1)__
+Insertion never needs more than 2 rotations. Removal might require up to __log(n)__ rotations.
 
 ## The code
 

From 45b5619710d40c5602cc3f70b2e5fdb3300e22ac Mon Sep 17 00:00:00 2001
From: Antonio081014 <antonio081014@antonio081014.com>
Date: Tue, 20 Dec 2016 16:40:49 -0800
Subject: [PATCH 0681/1679] Add missing link for Trie in README.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 7ac170a65..5c769688a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -156,7 +156,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
-- Trie
+- [Trie](Trie/). A special type of tree used to store associative data structures.
 - [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
 
 ### Hashing

From 09b74c41364723dbb9b3752765913b13dcb1c6b7 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sat, 26 Nov 2016 17:58:21 -0500
Subject: [PATCH 0682/1679] Mathimatical explination

---
 Rootish Array Stack/README.md                 |  90 ++++++++++++++++--
 .../images/RootishArrayStackExample2.png      | Bin 0 -> 81023 bytes
 2 files changed, 82 insertions(+), 8 deletions(-)
 create mode 100644 Rootish Array Stack/images/RootishArrayStackExample2.png

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index 842439a0c..285f39b14 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -2,18 +2,92 @@
 
 A *Rootish Array Stack* is an ordered array based structure that minimizes wasted space (based on [Gauss's summation technique](https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/)). A *Rootish Array Stack* consists of an array holding many fixed size arrays in ascending size.  
 
-![Rootish Array Stack Intro](/images/RootishArrayStackIntro.png)
-<!-- ![Rootish Array Stack Intro](https://github.com/raywenderlich/swift-algorithm-club/blob/master/Rootish%20Array%20Stack/images/RootishArrayStackIntro.png) -->
+![Rootish Array Stack Intro](images/RootishArrayStackIntro.png)
 
 A resizable array holds references to blocks (arrays of fixed size). A block's capacity is the same as it's index in the resizable array. Blocks don't grow/shrink like regular Swift arrays. Instead, when their capacity is reached, a new slightly larger block is created. When a block is emptied the last block is freed. This is a great improvement on what a swift array does in terms of wasted space.
 
-![Rootish Array Stack Intro](/images/RootishArrayStackExample.png)
+![Rootish Array Stack Intro](images/RootishArrayStackExample.png)
 
 Here you can see how insert/remove operations would behave (very similar to how a Swift array handles such operations).
 
-### How indices map:
-| Subscript index | Indices of Blocks|
-| :------------- | :------------- |
-| `[0]`       | `blocks[0][0]`       |
+## The Math
+The data structure is based on Gauss's summation technique:
+```
+sum from 1...n = n * (n + 1) / 2
+```
+To understand this imagine `n` blocks where `x` represents `1` unit. In this example let `n` be `5`:
+```
+blocks:     [x] [x x] [x x x] [x x x x] [x x x x x]
+# of x's:    1    2      3        4          5
+```
+_Block `1` has 1 `x`, block `2` as 2 `x`s, block `3` has 3 `x`s, etc..._
 
-## A Mathematical Explanation
+If you wanted to take the sum of all the blocks from `1` to `n` you could go through and count them _one by one_. This is okay, but for a large sequence of blocks that could take a long time! Instead you could arrange the blocks to look like a _half pyramid_:
+```
+# |  blocks
+--|-------------
+1 |  x
+2 |  x x
+3 |  x x x
+4 |  x x x x
+5 |  x x x x x
+
+```
+Then we mirror the _half pyramid_ and rearrange the image so that it fits with the original _half pyramid_ in a rectangular shape:
+```
+x                  o      x o o o o o
+x x              o o      x x o o o o
+x x x          o o o  =>  x x x o o o
+x x x x      o o o o      x x x x o o
+x x x x x  o o o o o      x x x x x o
+```
+Here we have `n` rows and `n + 1` columns of units. _5 rows and 6 columns_.
+
+We could calculate sum just as we would an area! Lets also express width and hight in terms of `n`:
+```
+area of a rectangle = height * width = n * (n + 1)
+```
+But we only want to calculate the amount of `x`s, not the amount of `o`s. Since there's a 1:1 ratio between `x`s and `o`s we and just divide our area by 2!
+```
+area of only x = n * (n + 1) / 2
+```
+And voila! We have an interesting new way to arrange our data!
+
+## Get/Set with Speed
+Next we want to find an efficient way to access a random index. For example which block does `rootishArrayStack[12]` point to? To answer this we will need MORE MATH!
+Determining the inner block `index` turns out to be easy. If `index` is in some `block` then:
+```
+inner block index = index - block * (block + 1) / 2
+```
+
+More difficult is determining which `block` an index points to. The number of elements that have indices less than or equal to the the requested `index` is: `index + 1` elements. The number of elements in blocks `0...block` is `(block + 1) * (block + 2) / 2`. Therefore, `block` is the smaller integer such that:
+```
+(block + 1) * (block + 2) / 2 >= index + 1
+```
+This can be rewritten as:
+```
+(block)^2 + (3 * block) - (2 * index) >= 0
+```
+Using the quadratic formula we can get:
+```
+block = (-3 ± √(9 + 8 * index)) / 2
+```
+A negative block doesn't make sense so we take the positive root instead. In general this solution is not an integer but going back to our inequality, we want the smallest block such that `b => (-3 + √(9 + 8 * index)) / 2`. So we take the ceiling of the result:
+```
+block = ⌈(-3 + √(9 + 8 * index)) / 2⌉
+```
+
+Now we can figure out that `rootishArrayStack[12]` would point to the block at index `4` and at inner block index `2`.
+![Rootish Array Stack Intro](images/RootishArrayStackExample2.png)
+
+# The Code
+
+To get the `capacity` of the structure we can use the equation we figured out above:
+```swift
+var capacity: Int {
+  return blocks.count * (blocks.count + 1) / 2
+}
+```
+Since Swift arrays check `count` in `O(1)` time, this capacity lookup is also `O(1)`.
+
+To solve the problem of which block holds the block holds the element we are looking for we need
diff --git a/Rootish Array Stack/images/RootishArrayStackExample2.png b/Rootish Array Stack/images/RootishArrayStackExample2.png
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From df6e54a0c0eadb4edba616430f247edb54b60d32 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sun, 27 Nov 2016 22:32:12 -0500
Subject: [PATCH 0683/1679] Added 'Code' segment

---
 Rootish Array Stack/README.md | 41 +++++++++++++++++++++++++++++------
 1 file changed, 34 insertions(+), 7 deletions(-)

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index 285f39b14..3f154629f 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -10,8 +10,9 @@ A resizable array holds references to blocks (arrays of fixed size). A block's c
 
 Here you can see how insert/remove operations would behave (very similar to how a Swift array handles such operations).
 
-## The Math
-The data structure is based on Gauss's summation technique:
+## Gauss's Summation Trick
+<!-- TODO: Gaussian flavour text -->
+This data structure is based on Gauss's summation technique:
 ```
 sum from 1...n = n * (n + 1) / 2
 ```
@@ -51,10 +52,10 @@ But we only want to calculate the amount of `x`s, not the amount of `o`s. Since
 ```
 area of only x = n * (n + 1) / 2
 ```
-And voila! We have an interesting new way to arrange our data!
+And voila! A super fast way to take a sum of all the blocks! This equation is useful for deriving fast `block` and `inner block index` equations.
 
 ## Get/Set with Speed
-Next we want to find an efficient way to access a random index. For example which block does `rootishArrayStack[12]` point to? To answer this we will need MORE MATH!
+Next we want to find an efficient and accurate way to access an element at a random index. For example which block does `rootishArrayStack[12]` point to? To answer this we will need more math!
 Determining the inner block `index` turns out to be easy. If `index` is in some `block` then:
 ```
 inner block index = index - block * (block + 1) / 2
@@ -81,13 +82,39 @@ Now we can figure out that `rootishArrayStack[12]` would point to the block at i
 ![Rootish Array Stack Intro](images/RootishArrayStackExample2.png)
 
 # The Code
+Lets start with instance variables and struct declaration:
+```swift
+import Darwin
+
+public struct RootishArrayStack<T> {
+	fileprivate var blocks = [Array<T?>]()
+	fileprivate var internalCount = 0
+
+	public init() { }
 
-To get the `capacity` of the structure we can use the equation we figured out above:
+	var count: Int {
+		return internalCount
+	}
+
+
+```
+The elements are of generic type `T`, so data of any kind can be stored in the list. `blocks` will be a resizable array to hold fixed sized arrays that take type `T?`.
+> The reason for the fixed size arrays taking type `T?` is so that references to elements aren't retained after they've been removed. Eg: if you remove the last element, the last index must be set to `nil` to prevent the last element being held in memory at an inaccessible index.
+
+`internalCount` is an internal mutable counter that keeps track of the number of elements. `count` is a read only variables that gives the `internalCount` value. `Darwin` is imported here to provide simple math functions such as `ceil()` and `sqrt()`.
+
+The `capacity` of the structure is simply the Gaussian summation trick:
 ```swift
 var capacity: Int {
   return blocks.count * (blocks.count + 1) / 2
 }
 ```
-Since Swift arrays check `count` in `O(1)` time, this capacity lookup is also `O(1)`.
 
-To solve the problem of which block holds the block holds the element we are looking for we need
+To determine which block an index map to:
+```swift
+fileprivate static func toBlock(index: Int) -> Int {
+  let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
+  return block
+}
+```
+This comes straight from the equations derived earlier. As mentioned `sqrt()`, and `ceil()` were imported from `Darwin`.

From 1d16285c873b4b7e7d31d6a7de611cdc838ecbc2 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Mon, 28 Nov 2016 00:32:17 -0500
Subject: [PATCH 0684/1679] Preventing thrashing

---
 Rootish Array Stack/README.md               | 19 ++++++--
 Rootish Array Stack/RootishArrayStack.swift | 53 +++++++++++----------
 2 files changed, 45 insertions(+), 27 deletions(-)

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index 3f154629f..f6d55b03a 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -110,11 +110,24 @@ var capacity: Int {
 }
 ```
 
-To determine which block an index map to:
+Next lets build what we need to get/set elements:
 ```swift
-fileprivate static func toBlock(index: Int) -> Int {
+fileprivate func toBlock(index: Int) -> Int {
   let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
   return block
 }
+
+public subscript(index: Int) -> T {
+  get {
+    let block = toBlock(index: index)
+    let blockIndex = index - block * (block + 1) / 2
+    return blocks[block][blockIndex]!
+  }
+  set(newValue) {
+    let block = toBlock(index: index)
+    let blockIndex = index - block * (block + 1) / 2
+    blocks[block][blockIndex] = newValue
+  }
+}
 ```
-This comes straight from the equations derived earlier. As mentioned `sqrt()`, and `ceil()` were imported from `Darwin`.
+`toBlock` is really just wrapping the `block` equation derived earlier. `superscript` lets us have `get/set` access to the structure with the familiar `[index]` syntax.
diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index f17f9620e..6cb1cff06 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -21,11 +21,24 @@ public struct RootishArrayStack<T> {
 		return blocks.count * (blocks.count + 1) / 2
 	}
 
-	fileprivate static func toBlock(index: Int) -> Int {
+	fileprivate func toBlock(index: Int) -> Int {
 		let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
 		return block
 	}
 
+	public subscript(index: Int) -> T {
+		get {
+			let block = toBlock(index: index)
+			let blockIndex = index - block * (block + 1) / 2
+			return blocks[block][blockIndex]!
+		}
+		set(newValue) {
+			let block = toBlock(index: index)
+			let blockIndex = index - block * (block + 1) / 2
+			blocks[block][blockIndex] = newValue
+		}
+	}
+
 	fileprivate mutating func grow() {
 		let newArray = [T?](repeating: nil, count: blocks.count + 1)
 		blocks.append(newArray)
@@ -39,21 +52,8 @@ public struct RootishArrayStack<T> {
 		}
 	}
 
-	public subscript(index: Int) -> T {
-		get {
-			let block = RootishArrayStack.toBlock(index: index)
-			let blockIndex = index - block * (block + 1) / 2
-			return blocks[block][blockIndex]!
-		}
-		set(newValue) {
-			let block = RootishArrayStack.toBlock(index: index)
-			let blockIndex = index - block * (block + 1) / 2
-			blocks[block][blockIndex] = newValue
-		}
-	}
-
 	public mutating func insert(element: T, atIndex index: Int) {
-		if capacity < count + 1 {
+		if capacity - blocks.count < count + 1 {
 			grow()
 		}
 		internalCount += 1
@@ -70,7 +70,7 @@ public struct RootishArrayStack<T> {
 	}
 
 	fileprivate mutating func makeNil(atIndex index: Int) {
-		let block = RootishArrayStack.toBlock(index: index)
+		let block = toBlock(index: index)
 		let blockIndex = index - block * (block + 1) / 2
 		blocks[block][blockIndex] = nil
 	}
@@ -82,22 +82,22 @@ public struct RootishArrayStack<T> {
 		}
 		internalCount -= 1
 		makeNil(atIndex: count)
-		if capacity >= count {
+		if capacity + blocks.count >= count {
 			shrink()
 		}
 		return element
 	}
 
 	public var memoryDescription: String {
-		var s = "{\n"
-		for i in blocks {
-			s += "\t["
-			for j in i {
-				s += "\(j), "
+		var description = "{\n"
+		for block in blocks {
+			description += "\t["
+			for rawElement in block {
+				description += "\(rawElement), "
 			}
-			s += "]\n"
+			description += "]\n"
 		}
-		return s + "}"
+		return description + "}"
 	}
 }
 
@@ -113,3 +113,8 @@ extension RootishArrayStack: CustomStringConvertible {
 		return s + "]"
 	}
 }
+
+var list = RootishArrayStack<Int>()
+for i in 0...10 {
+	list.append(element: i)
+}

From c3d03b9b2d56b17bd66eed450e64b58ef2a469c6 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Mon, 28 Nov 2016 22:04:34 -0500
Subject: [PATCH 0685/1679] Finished implementation explination

---
 Rootish Array Stack/README.md               | 69 ++++++++++++++++++++-
 Rootish Array Stack/RootishArrayStack.swift | 43 ++++++-------
 2 files changed, 86 insertions(+), 26 deletions(-)

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index f6d55b03a..790eea6da 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -96,6 +96,9 @@ public struct RootishArrayStack<T> {
 		return internalCount
 	}
 
+	...
+
+}
 
 ```
 The elements are of generic type `T`, so data of any kind can be stored in the list. `blocks` will be a resizable array to hold fixed sized arrays that take type `T?`.
@@ -110,7 +113,7 @@ var capacity: Int {
 }
 ```
 
-Next lets build what we need to get/set elements:
+Next lets look at we would `get` and `set` elements:
 ```swift
 fileprivate func toBlock(index: Int) -> Int {
   let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
@@ -130,4 +133,66 @@ public subscript(index: Int) -> T {
   }
 }
 ```
-`toBlock` is really just wrapping the `block` equation derived earlier. `superscript` lets us have `get/set` access to the structure with the familiar `[index]` syntax.
+`toBlock(index:)` is really just wrapping the `block` equation derived earlier to return the block that an index maps to. `superscript` lets us have `get` and `set` access to the structure with the familiar `[index:]` syntax. For both `get` and `set` in superscript we use the same logic:
+ 	1. determine the block that the index points to
+	2. determine the inner block index
+	3. `get`/`set` the value
+
+Next lets look at how we would `growIfNeeded()` and `shrinkIfNeeded()` the structure.
+```swift
+fileprivate mutating func growIfNeeded() {
+	if capacity - blocks.count < count + 1 {
+		let newArray = [T?](repeating: nil, count: blocks.count + 1)
+		blocks.append(newArray)
+	}
+}
+
+fileprivate mutating func shrinkIfNeeded() {
+	if capacity + blocks.count >= count {
+		var numberOfBlocks = blocks.count
+		while numberOfBlocks > 0 && (numberOfBlocks - 2) * (numberOfBlocks - 1) / 2 >= count {
+			blocks.remove(at: blocks.count - 1)
+			numberOfBlocks -= 1
+		}
+	}
+}
+```
+If our data set grows or shrinks in size, we want our data structure to accommodate the change.
+Just like a Swift array when a capacity threshold is met we will `grow` or `shrink` the size of our structure. For the Rootish Array Stack we want to `grow` if the second last block is full on an `insert` operation, and `shrink` if the two last blocks are empty.
+
+Now to the more familiar Swift array behaviour.  
+```swift
+public mutating func insert(element: T, atIndex index: Int) {
+	growIfNeeded()
+	internalCount += 1
+	var i = count - 1
+	while i > index {
+		self[i] = self[i - 1]
+		i -= 1
+	}
+	self[index] = element
+}
+
+public mutating func append(element: T) {
+	insert(element: element, atIndex: count)
+}
+
+public mutating func remove(atIndex index: Int) -> T {
+	let element = self[index]
+	for i in index..<count - 1 {
+		self[i] = self[i + 1]
+	}
+	internalCount -= 1
+	makeNil(atIndex: count)
+	shrinkIfNeeded()
+	return element
+}
+
+fileprivate mutating func makeNil(atIndex index: Int) {
+	let block = toBlock(index: index)
+	let blockIndex = index - block * (block + 1) / 2
+	blocks[block][blockIndex] = nil
+}
+```
+To `insert(element:, atIndex:)` we move all elements after the `index` to the right by 1. After space has been made for the element we set the value using the `subscript` convenience. `append(element:)` is just a convenience method to add to the end. To `remove(atIndex:)` we move all the elements after the `index` to the left by 1. After the removed value is covered by it's proceeding value, we set the last value in the structure to `nil`. `makeNil(atIndex:)` uses the same logic as our `subscript` method but is used to set the root optional at a particular index to `nil` (because setting it's wrapped value to `nil` is something only the user of the data structure should do).
+> Setting a optionals value to `nil` is different than setting it's wrapped value to `nil`. An optionals wrapped value is an embedded type within the optional reference. This means that a `nil` wrapped value is actually `.some(.none)` wheres setting the root reference to `nil` is `.none`. To better understand Swift optionals I recommend checking out @SebastianBoldt's article [Swift! Optionals?](https://medium.com/ios-os-x-development/swift-optionals-78dafaa53f3#.rvjobhuzs).
diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index 6cb1cff06..4edc58b2f 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -26,6 +26,23 @@ public struct RootishArrayStack<T> {
 		return block
 	}
 
+	fileprivate mutating func growIfNeeded() {
+		if capacity - blocks.count < count + 1 {
+			let newArray = [T?](repeating: nil, count: blocks.count + 1)
+			blocks.append(newArray)
+		}
+	}
+
+	fileprivate mutating func shrinkIfNeeded() {
+		if capacity + blocks.count >= count {
+			var numberOfBlocks = blocks.count
+			while numberOfBlocks > 0 && (numberOfBlocks - 2) * (numberOfBlocks - 1) / 2 >= count {
+				blocks.remove(at: blocks.count - 1)
+				numberOfBlocks -= 1
+			}
+		}
+	}
+
 	public subscript(index: Int) -> T {
 		get {
 			let block = toBlock(index: index)
@@ -39,23 +56,8 @@ public struct RootishArrayStack<T> {
 		}
 	}
 
-	fileprivate mutating func grow() {
-		let newArray = [T?](repeating: nil, count: blocks.count + 1)
-		blocks.append(newArray)
-	}
-
-	fileprivate mutating func shrink() {
-		var numberOfBlocks = blocks.count
-		while numberOfBlocks > 0 && (numberOfBlocks - 2) * (numberOfBlocks - 1) / 2 >= count {
-			blocks.remove(at: blocks.count - 1)
-			numberOfBlocks -= 1
-		}
-	}
-
 	public mutating func insert(element: T, atIndex index: Int) {
-		if capacity - blocks.count < count + 1 {
-			grow()
-		}
+		growIfNeeded()
 		internalCount += 1
 		var i = count - 1
 		while i > index {
@@ -82,9 +84,7 @@ public struct RootishArrayStack<T> {
 		}
 		internalCount -= 1
 		makeNil(atIndex: count)
-		if capacity + blocks.count >= count {
-			shrink()
-		}
+		shrinkIfNeeded()
 		return element
 	}
 
@@ -113,8 +113,3 @@ extension RootishArrayStack: CustomStringConvertible {
 		return s + "]"
 	}
 }
-
-var list = RootishArrayStack<Int>()
-for i in 0...10 {
-	list.append(element: i)
-}

From 72c12e92485f49b24c30b61522ae9aff9035cdaf Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Mon, 28 Nov 2016 22:32:23 -0500
Subject: [PATCH 0686/1679] Added Gauss' legend

Polished example
---
 Rootish Array Stack/README.md               | 36 +++++++++++++++------
 Rootish Array Stack/RootishArrayStack.swift |  4 +--
 2 files changed, 27 insertions(+), 13 deletions(-)

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index 790eea6da..5f62cec2c 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -10,9 +10,8 @@ A resizable array holds references to blocks (arrays of fixed size). A block's c
 
 Here you can see how insert/remove operations would behave (very similar to how a Swift array handles such operations).
 
-## Gauss's Summation Trick
-<!-- TODO: Gaussian flavour text -->
-This data structure is based on Gauss's summation technique:
+## Gauss' Summation Trick
+One of the most well known legends about famous mathematician [Carl Friedrich Gauss](https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss) goes back to when he was in primary school. One day Gauss' teacher asked his class to add up all the numbers from 1 to 100, hoping that the task would take long enough for the teacher to step out for a smoke break. The teacher was shocked when young Gauss had his hand up with the answer `5050`. So soon? The teacher suspected a cheat, but no. Gauss had found a formula to sidestep the problem of manual adding up all the number 1 by 1. His formula:
 ```
 sum from 1...n = n * (n + 1) / 2
 ```
@@ -42,9 +41,9 @@ x x x          o o o  =>  x x x o o o
 x x x x      o o o o      x x x x o o
 x x x x x  o o o o o      x x x x x o
 ```
-Here we have `n` rows and `n + 1` columns of units. _5 rows and 6 columns_.
+Here we have `n` rows and `n + 1` columns. _5 rows and 6 columns_.
 
-We could calculate sum just as we would an area! Lets also express width and hight in terms of `n`:
+We could calculate sum just as we would an area! Lets also express the width and hight in terms of `n`:
 ```
 area of a rectangle = height * width = n * (n + 1)
 ```
@@ -78,10 +77,26 @@ A negative block doesn't make sense so we take the positive root instead. In gen
 block = ⌈(-3 + √(9 + 8 * index)) / 2⌉
 ```
 
-Now we can figure out that `rootishArrayStack[12]` would point to the block at index `4` and at inner block index `2`.
+Now we can figure out that `rootishArrayStack[12]` points to! First lets see which block the `12` points to:
+```
+block = ⌈(-3 + √(9 + 8 * (12))) / 2⌉
+block = ⌈(-3 + √105) / 2⌉
+block = ⌈(-3 + (10.246950766)) / 2⌉
+block = ⌈(7.246950766) / 2⌉
+block = ⌈3.623475383⌉
+block = 4
+```
+Next lets see which `innerBlockIndex` `12` points to:
+```
+inner block index = (12) - (4) * ((4) + 1) / 2
+inner block index = (12) - (4) * (5) / 2
+inner block index = (12) - 10
+inner block index = 2
+```
+Therefore `rootishArrayStack[12]` points to the block at index `4` and at inner block index `2`.
 ![Rootish Array Stack Intro](images/RootishArrayStackExample2.png)
 
-# The Code
+# Implementation Details
 Lets start with instance variables and struct declaration:
 ```swift
 import Darwin
@@ -149,10 +164,8 @@ fileprivate mutating func growIfNeeded() {
 
 fileprivate mutating func shrinkIfNeeded() {
 	if capacity + blocks.count >= count {
-		var numberOfBlocks = blocks.count
-		while numberOfBlocks > 0 && (numberOfBlocks - 2) * (numberOfBlocks - 1) / 2 >= count {
+		while blocks.count > 0 && (blocks.count - 2) * (blocks.count - 1) / 2 >= count {
 			blocks.remove(at: blocks.count - 1)
-			numberOfBlocks -= 1
 		}
 	}
 }
@@ -196,3 +209,6 @@ fileprivate mutating func makeNil(atIndex index: Int) {
 ```
 To `insert(element:, atIndex:)` we move all elements after the `index` to the right by 1. After space has been made for the element we set the value using the `subscript` convenience. `append(element:)` is just a convenience method to add to the end. To `remove(atIndex:)` we move all the elements after the `index` to the left by 1. After the removed value is covered by it's proceeding value, we set the last value in the structure to `nil`. `makeNil(atIndex:)` uses the same logic as our `subscript` method but is used to set the root optional at a particular index to `nil` (because setting it's wrapped value to `nil` is something only the user of the data structure should do).
 > Setting a optionals value to `nil` is different than setting it's wrapped value to `nil`. An optionals wrapped value is an embedded type within the optional reference. This means that a `nil` wrapped value is actually `.some(.none)` wheres setting the root reference to `nil` is `.none`. To better understand Swift optionals I recommend checking out @SebastianBoldt's article [Swift! Optionals?](https://medium.com/ios-os-x-development/swift-optionals-78dafaa53f3#.rvjobhuzs).
+
+# Runtime Analysis
+<!-- TODO: fin runtime explanation -->
diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index 4edc58b2f..66a681f97 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -35,10 +35,8 @@ public struct RootishArrayStack<T> {
 
 	fileprivate mutating func shrinkIfNeeded() {
 		if capacity + blocks.count >= count {
-			var numberOfBlocks = blocks.count
-			while numberOfBlocks > 0 && (numberOfBlocks - 2) * (numberOfBlocks - 1) / 2 >= count {
+			while blocks.count > 0 && (blocks.count - 2) * (blocks.count - 1) / 2 >= count {
 				blocks.remove(at: blocks.count - 1)
-				numberOfBlocks -= 1
 			}
 		}
 	}

From cb673314ee570504f655c3d6d992fe90d3c2425e Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Thu, 8 Dec 2016 22:15:14 -0500
Subject: [PATCH 0687/1679] Added performance explination + cleaned up some
 implementation details

---
 Rootish Array Stack/README.md               | 27 +++++++++++++--------
 Rootish Array Stack/RootishArrayStack.swift | 24 ++++++++++--------
 2 files changed, 31 insertions(+), 20 deletions(-)

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index 5f62cec2c..ee2351d4d 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -102,16 +102,17 @@ Lets start with instance variables and struct declaration:
 import Darwin
 
 public struct RootishArrayStack<T> {
-	fileprivate var blocks = [Array<T?>]()
-	fileprivate var internalCount = 0
 
-	public init() { }
+  fileprivate var blocks = [Array<T?>]()
+  fileprivate var internalCount = 0
 
-	var count: Int {
-		return internalCount
-	}
+    public init() { }
+
+    var count: Int {
+  	return internalCount
+  }
 
-	...
+  ...
 
 }
 
@@ -149,7 +150,7 @@ public subscript(index: Int) -> T {
 }
 ```
 `toBlock(index:)` is really just wrapping the `block` equation derived earlier to return the block that an index maps to. `superscript` lets us have `get` and `set` access to the structure with the familiar `[index:]` syntax. For both `get` and `set` in superscript we use the same logic:
- 	1. determine the block that the index points to
+	1. determine the block that the index points to
 	2. determine the inner block index
 	3. `get`/`set` the value
 
@@ -210,5 +211,11 @@ fileprivate mutating func makeNil(atIndex index: Int) {
 To `insert(element:, atIndex:)` we move all elements after the `index` to the right by 1. After space has been made for the element we set the value using the `subscript` convenience. `append(element:)` is just a convenience method to add to the end. To `remove(atIndex:)` we move all the elements after the `index` to the left by 1. After the removed value is covered by it's proceeding value, we set the last value in the structure to `nil`. `makeNil(atIndex:)` uses the same logic as our `subscript` method but is used to set the root optional at a particular index to `nil` (because setting it's wrapped value to `nil` is something only the user of the data structure should do).
 > Setting a optionals value to `nil` is different than setting it's wrapped value to `nil`. An optionals wrapped value is an embedded type within the optional reference. This means that a `nil` wrapped value is actually `.some(.none)` wheres setting the root reference to `nil` is `.none`. To better understand Swift optionals I recommend checking out @SebastianBoldt's article [Swift! Optionals?](https://medium.com/ios-os-x-development/swift-optionals-78dafaa53f3#.rvjobhuzs).
 
-# Runtime Analysis
-<!-- TODO: fin runtime explanation -->
+# Performance
+* An internal counter keeps track of the number of elements in the structure. `count` is executed in **O(1)** time.
+
+* `capacity` can be calculated using Gauss' summation trick in an equation which takes **O(1)** time to execute.
+
+* Since `subcript[index:]` uses the `block` and `inner block index` equations, which can be executed in **O(1)** time, all get and set operations take **O(1)**.
+
+* Ignoring the time cost to `grow()` and `shrink()`, `insert()` and `remove()` operations shift all elements right of the specified index resulting in **O(n)** time.
diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index 66a681f97..842e34f72 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -21,11 +21,15 @@ public struct RootishArrayStack<T> {
 		return blocks.count * (blocks.count + 1) / 2
 	}
 
-	fileprivate func toBlock(index: Int) -> Int {
+	fileprivate func block(fromIndex index: Int) -> Int {
 		let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
 		return block
 	}
 
+	fileprivate func innerBlockIndex(fromIndex index: Int, fromBlock block: Int) -> Int {
+		return index - block * (block + 1) / 2
+	}
+
 	fileprivate mutating func growIfNeeded() {
 		if capacity - blocks.count < count + 1 {
 			let newArray = [T?](repeating: nil, count: blocks.count + 1)
@@ -43,14 +47,14 @@ public struct RootishArrayStack<T> {
 
 	public subscript(index: Int) -> T {
 		get {
-			let block = toBlock(index: index)
-			let blockIndex = index - block * (block + 1) / 2
-			return blocks[block][blockIndex]!
+			let block = self.block(fromIndex: index)
+			let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+			return blocks[block][innerBlockIndex]!
 		}
 		set(newValue) {
-			let block = toBlock(index: index)
-			let blockIndex = index - block * (block + 1) / 2
-			blocks[block][blockIndex] = newValue
+			let block = self.block(fromIndex: index)
+			let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+			blocks[block][innerBlockIndex] = newValue
 		}
 	}
 
@@ -70,9 +74,9 @@ public struct RootishArrayStack<T> {
 	}
 
 	fileprivate mutating func makeNil(atIndex index: Int) {
-		let block = toBlock(index: index)
-		let blockIndex = index - block * (block + 1) / 2
-		blocks[block][blockIndex] = nil
+		let block = self.block(fromIndex: index)
+		let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+		blocks[block][innerBlockIndex] = nil
 	}
 
 	public mutating func remove(atIndex index: Int) -> T {

From b8f87bfe07d5268b37ad7e4fb5f2319a94d7d060 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sat, 10 Dec 2016 23:14:15 -0500
Subject: [PATCH 0688/1679] Added performance analysis

---
 Rootish Array Stack/README.md | 68 ++++++++++++++++++++++-------------
 1 file changed, 43 insertions(+), 25 deletions(-)

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index ee2351d4d..c00061082 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -11,7 +11,7 @@ A resizable array holds references to blocks (arrays of fixed size). A block's c
 Here you can see how insert/remove operations would behave (very similar to how a Swift array handles such operations).
 
 ## Gauss' Summation Trick
-One of the most well known legends about famous mathematician [Carl Friedrich Gauss](https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss) goes back to when he was in primary school. One day Gauss' teacher asked his class to add up all the numbers from 1 to 100, hoping that the task would take long enough for the teacher to step out for a smoke break. The teacher was shocked when young Gauss had his hand up with the answer `5050`. So soon? The teacher suspected a cheat, but no. Gauss had found a formula to sidestep the problem of manual adding up all the number 1 by 1. His formula:
+One of the most well known legends about famous mathematician [Carl Friedrich Gauss](https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss) goes back to when he was in primary school. One day Gauss' teacher asked his class to add up all the numbers from 1 to 100, hoping that the task would take long enough for the teacher to step out for a smoke break. The teacher was shocked when young Gauss had his hand up with the answer `5050`. So soon? The teacher suspected a cheat, but no. Gauss had found a formula to sidestep the problem of manually adding up all the numbers 1 by 1. His formula:
 ```
 sum from 1...n = n * (n + 1) / 2
 ```
@@ -96,6 +96,9 @@ inner block index = 2
 Therefore `rootishArrayStack[12]` points to the block at index `4` and at inner block index `2`.
 ![Rootish Array Stack Intro](images/RootishArrayStackExample2.png)
 
+### Interesting Discovery
+Using the `block` equation we can see that the number of `blocks` is proportional to the square root of the number of elements: **O(blocks) = O(√n)**.
+
 # Implementation Details
 Lets start with instance variables and struct declaration:
 ```swift
@@ -106,10 +109,10 @@ public struct RootishArrayStack<T> {
   fileprivate var blocks = [Array<T?>]()
   fileprivate var internalCount = 0
 
-    public init() { }
+  public init() { }
 
-    var count: Int {
-  	return internalCount
+  var count: Int {
+    return internalCount
   }
 
   ...
@@ -131,25 +134,29 @@ var capacity: Int {
 
 Next lets look at we would `get` and `set` elements:
 ```swift
-fileprivate func toBlock(index: Int) -> Int {
+fileprivate func block(fromIndex: Int) -> Int {
   let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
   return block
 }
 
+fileprivate func innerBlockIndex(fromIndex index: Int, fromBlock block: Int) -> Int {
+  return index - block * (block + 1) / 2
+}
+
 public subscript(index: Int) -> T {
   get {
-    let block = toBlock(index: index)
-    let blockIndex = index - block * (block + 1) / 2
-    return blocks[block][blockIndex]!
+    let block = self.block(fromIndex: index)
+    let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+    return blocks[block][innerBlockIndex]!
   }
   set(newValue) {
-    let block = toBlock(index: index)
-    let blockIndex = index - block * (block + 1) / 2
-    blocks[block][blockIndex] = newValue
+    let block = self.block(fromIndex: index)
+    let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+    blocks[block][innerBlockIndex] = newValue
   }
 }
 ```
-`toBlock(index:)` is really just wrapping the `block` equation derived earlier to return the block that an index maps to. `superscript` lets us have `get` and `set` access to the structure with the familiar `[index:]` syntax. For both `get` and `set` in superscript we use the same logic:
+`block(fromIndex:)` and `innerBlockIndex(fromIndex:, fromBlock:)` are wrapping the `block` and `inner block index` equations derived earlier. `superscript` lets us have `get` and `set` access to the structure with the familiar `[index:]` syntax. For both `get` and `set` in superscript we use the same logic:
 	1. determine the block that the index points to
 	2. determine the inner block index
 	3. `get`/`set` the value
@@ -157,18 +164,18 @@ public subscript(index: Int) -> T {
 Next lets look at how we would `growIfNeeded()` and `shrinkIfNeeded()` the structure.
 ```swift
 fileprivate mutating func growIfNeeded() {
-	if capacity - blocks.count < count + 1 {
-		let newArray = [T?](repeating: nil, count: blocks.count + 1)
-		blocks.append(newArray)
-	}
+  if capacity - blocks.count < count + 1 {
+    let newArray = [T?](repeating: nil, count: blocks.count + 1)
+    blocks.append(newArray)
+  }
 }
 
 fileprivate mutating func shrinkIfNeeded() {
-	if capacity + blocks.count >= count {
-		while blocks.count > 0 && (blocks.count - 2) * (blocks.count - 1) / 2 >= count {
-			blocks.remove(at: blocks.count - 1)
-		}
-	}
+  if capacity + blocks.count >= count {
+    while blocks.count > 0 && (blocks.count - 2) * (blocks.count - 1) / 2 >    count {
+      blocks.remove(at: blocks.count - 1)
+    }
+  }
 }
 ```
 If our data set grows or shrinks in size, we want our data structure to accommodate the change.
@@ -203,9 +210,9 @@ public mutating func remove(atIndex index: Int) -> T {
 }
 
 fileprivate mutating func makeNil(atIndex index: Int) {
-	let block = toBlock(index: index)
-	let blockIndex = index - block * (block + 1) / 2
-	blocks[block][blockIndex] = nil
+  let block = self.block(fromIndex: index)
+  let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+  blocks[block][innerBlockIndex] = nil
 }
 ```
 To `insert(element:, atIndex:)` we move all elements after the `index` to the right by 1. After space has been made for the element we set the value using the `subscript` convenience. `append(element:)` is just a convenience method to add to the end. To `remove(atIndex:)` we move all the elements after the `index` to the left by 1. After the removed value is covered by it's proceeding value, we set the last value in the structure to `nil`. `makeNil(atIndex:)` uses the same logic as our `subscript` method but is used to set the root optional at a particular index to `nil` (because setting it's wrapped value to `nil` is something only the user of the data structure should do).
@@ -218,4 +225,15 @@ To `insert(element:, atIndex:)` we move all elements after the `index` to the ri
 
 * Since `subcript[index:]` uses the `block` and `inner block index` equations, which can be executed in **O(1)** time, all get and set operations take **O(1)**.
 
-* Ignoring the time cost to `grow()` and `shrink()`, `insert()` and `remove()` operations shift all elements right of the specified index resulting in **O(n)** time.
+* Ignoring the time cost to `grow` and `shrink`, `insert(atIndex:)` and `remove(atIndex:)` operations shift all elements right of the specified index resulting in **O(n)** time.
+
+# Analysis of Growing and Shrinking
+The performance analysis doesn't account for the cost to `grow` and `shrink`. Unlike a regular Swift array, `grow` and `shrink` operations don't copy all the elements into a backing array. They only allocate or free an array proportional to the number of `blocks`. The number of `blocks` is proportional to the  square root of the number of elements. Growing and shrinking only cost **O(√n)**.
+
+# Wasted Space
+Wasted space is how much memory with respect to the number of elements `n` is unused. The Rootish Array Stack never has more than 2 empty blocks and it never has less than 1 empty block. The last two blocks are proportional to the number of blocks which is proportional to the square root of the number of elements. The number of references needed to point to each block is the same as the number of blocks. Therefore, the amount of wasted space with respect to the number of elements is **O(√n)**.
+
+
+_Written for Swift Algorithm Club by @BenEmdon_
+
+_With help from [OpenDataStructures.org](http://opendatastructures.org)_

From 0879118bfdffa6ec3d9f426322b3b751e87e6b85 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sat, 10 Dec 2016 23:44:08 -0500
Subject: [PATCH 0689/1679] Marks in swift file

---
 Rootish Array Stack/RootishArrayStack.swift | 40 +++++++++++++--------
 1 file changed, 26 insertions(+), 14 deletions(-)

diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index 842e34f72..0d2b15c3c 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -1,18 +1,24 @@
 //
-//  main.swift
 //  RootishArrayStack
 //
-//  Created by Benjamin Emdon on 2016-11-07.
+//  Created by @BenEmdon on 2016-11-07.
 //
 
 import Darwin
 
 public struct RootishArrayStack<T> {
+
+	// MARK: - Instance variables
+
 	fileprivate var blocks = [Array<T?>]()
 	fileprivate var internalCount = 0
 
+	// MARK: - Init
+
 	public init() { }
 
+	// MARK: - Calculated variables
+
 	var count: Int {
 		return internalCount
 	}
@@ -21,6 +27,8 @@ public struct RootishArrayStack<T> {
 		return blocks.count * (blocks.count + 1) / 2
 	}
 
+	// MARK: - Equations
+
 	fileprivate func block(fromIndex index: Int) -> Int {
 		let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
 		return block
@@ -30,6 +38,8 @@ public struct RootishArrayStack<T> {
 		return index - block * (block + 1) / 2
 	}
 
+	// MARK: - Behavior
+
 	fileprivate mutating func growIfNeeded() {
 		if capacity - blocks.count < count + 1 {
 			let newArray = [T?](repeating: nil, count: blocks.count + 1)
@@ -89,20 +99,10 @@ public struct RootishArrayStack<T> {
 		shrinkIfNeeded()
 		return element
 	}
-
-	public var memoryDescription: String {
-		var description = "{\n"
-		for block in blocks {
-			description += "\t["
-			for rawElement in block {
-				description += "\(rawElement), "
-			}
-			description += "]\n"
-		}
-		return description + "}"
-	}
 }
 
+// MARK: - Struct to string
+
 extension RootishArrayStack: CustomStringConvertible {
 	public var description: String {
 		var s = "["
@@ -114,4 +114,16 @@ extension RootishArrayStack: CustomStringConvertible {
 		}
 		return s + "]"
 	}
+
+	public var memoryDescription: String {
+		var description = "{\n"
+		for block in blocks {
+			description += "\t["
+			for rawElement in block {
+				description += "\(rawElement), "
+			}
+			description += "]\n"
+		}
+		return description + "}"
+	}
 }

From e5dfe6637980b9f425371c0dbe82dedae1100d3e Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sun, 11 Dec 2016 00:25:58 -0500
Subject: [PATCH 0690/1679] Added isEmpty, first, last

---
 Rootish Array Stack/RootishArrayStack.swift      | 16 ++++++++++++++++
 .../contents.xcworkspacedata                     |  3 +++
 2 files changed, 19 insertions(+)

diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index 0d2b15c3c..4033d75f6 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -27,6 +27,22 @@ public struct RootishArrayStack<T> {
 		return blocks.count * (blocks.count + 1) / 2
 	}
 
+	var isEmpty: Bool {
+		return blocks.count == 0
+	}
+
+	var first: T? {
+		guard capacity > 0 else { return nil }
+		return blocks[0][0]
+	}
+
+	var last: T? {
+		guard capacity > 0 else { return nil }
+		let block = self.block(fromIndex: count - 1)
+		let innerBlockIndex = self.innerBlockIndex(fromIndex: count - 1, fromBlock: block)
+		return blocks[block][innerBlockIndex]
+	}
+
 	// MARK: - Equations
 
 	fileprivate func block(fromIndex index: Int) -> Int {
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ac3a79be9..c2ae29f70 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1529,6 +1529,9 @@
       <FileRef
          location = "group:RootishArrayStack.swift">
       </FileRef>
+      <FileRef
+         location = "group:RootishArrayStack.playground">
+      </FileRef>
    </Group>
    <Group
       location = "group:Segment Tree"

From 4225b7f26adc13dbe93b6269de9f478f23b1bb19 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sun, 11 Dec 2016 00:32:20 -0500
Subject: [PATCH 0691/1679] Added playground

Finished playground
---
 Rootish Array Stack/README.md                 |  58 ++---
 .../Contents.swift                            | 219 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 Rootish Array Stack/RootishArrayStack.swift   |  35 +--
 4 files changed, 273 insertions(+), 43 deletions(-)
 create mode 100644 Rootish Array Stack/RootishArrayStack.playground/Contents.swift
 create mode 100644 Rootish Array Stack/RootishArrayStack.playground/contents.xcplayground

diff --git a/Rootish Array Stack/README.md b/Rootish Array Stack/README.md
index c00061082..6a45b262a 100644
--- a/Rootish Array Stack/README.md	
+++ b/Rootish Array Stack/README.md	
@@ -4,14 +4,14 @@ A *Rootish Array Stack* is an ordered array based structure that minimizes waste
 
 ![Rootish Array Stack Intro](images/RootishArrayStackIntro.png)
 
-A resizable array holds references to blocks (arrays of fixed size). A block's capacity is the same as it's index in the resizable array. Blocks don't grow/shrink like regular Swift arrays. Instead, when their capacity is reached, a new slightly larger block is created. When a block is emptied the last block is freed. This is a great improvement on what a swift array does in terms of wasted space.
+A resizable array holds references to blocks (arrays of fixed size). A block's capacity is the same as it's index in the resizable array. Blocks don't grow/shrink like regular Swift arrays. Instead, when their capacity is reached, a new slightly larger block is created. When a block is emptied the last block is freed. This is a great improvement on what Swift arrays do in terms of wasted space.
 
 ![Rootish Array Stack Intro](images/RootishArrayStackExample.png)
 
 Here you can see how insert/remove operations would behave (very similar to how a Swift array handles such operations).
 
 ## Gauss' Summation Trick
-One of the most well known legends about famous mathematician [Carl Friedrich Gauss](https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss) goes back to when he was in primary school. One day Gauss' teacher asked his class to add up all the numbers from 1 to 100, hoping that the task would take long enough for the teacher to step out for a smoke break. The teacher was shocked when young Gauss had his hand up with the answer `5050`. So soon? The teacher suspected a cheat, but no. Gauss had found a formula to sidestep the problem of manually adding up all the numbers 1 by 1. His formula:
+One of the most well known legends about famous mathematician [Carl Friedrich Gauss](https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss) goes back to when he was in primary school. One day, Gauss' teacher asked his class to add up all the numbers from 1 to 100, hoping that the task would take long enough for him to step out for a smoke break. The teacher was shocked when young Gauss had his hand up with the answer `5050`. So soon? The teacher suspected a cheat, but no. Gauss had found a formula to sidestep the problem of manually adding up all the numbers 1 by 1. His formula:
 ```
 sum from 1...n = n * (n + 1) / 2
 ```
@@ -22,7 +22,7 @@ blocks:     [x] [x x] [x x x] [x x x x] [x x x x x]
 ```
 _Block `1` has 1 `x`, block `2` as 2 `x`s, block `3` has 3 `x`s, etc..._
 
-If you wanted to take the sum of all the blocks from `1` to `n` you could go through and count them _one by one_. This is okay, but for a large sequence of blocks that could take a long time! Instead you could arrange the blocks to look like a _half pyramid_:
+If you wanted to take the sum of all the blocks from `1` to `n`, you could go through and count them _one by one_. This is okay, but for a large sequence of blocks that could take a long time! Instead, you could arrange the blocks to look like a _half pyramid_:
 ```
 # |  blocks
 --|-------------
@@ -43,24 +43,24 @@ x x x x x  o o o o o      x x x x x o
 ```
 Here we have `n` rows and `n + 1` columns. _5 rows and 6 columns_.
 
-We could calculate sum just as we would an area! Lets also express the width and hight in terms of `n`:
+We can calculate the sum just as we would an area! Let's also express the width and height in terms of `n`:
 ```
 area of a rectangle = height * width = n * (n + 1)
 ```
-But we only want to calculate the amount of `x`s, not the amount of `o`s. Since there's a 1:1 ratio between `x`s and `o`s we and just divide our area by 2!
+We only want to calculate the amount of `x`s, not the amount of `o`s. Since there's a 1:1 ratio between `x`s and `o`s we can just divide our area by 2!
 ```
 area of only x = n * (n + 1) / 2
 ```
-And voila! A super fast way to take a sum of all the blocks! This equation is useful for deriving fast `block` and `inner block index` equations.
+Voila! A super fast way to take a sum of all the blocks! This equation is useful for deriving fast `block` and `inner block index` equations.
+<!-- TODO: Define block and innerBlockIndex -->
 
 ## Get/Set with Speed
-Next we want to find an efficient and accurate way to access an element at a random index. For example which block does `rootishArrayStack[12]` point to? To answer this we will need more math!
+Next, we want to find an efficient and accurate way to access an element at a random index. For example, which block does `rootishArrayStack[12]` point to? To answer this we will need more math!
 Determining the inner block `index` turns out to be easy. If `index` is in some `block` then:
 ```
 inner block index = index - block * (block + 1) / 2
 ```
-
-More difficult is determining which `block` an index points to. The number of elements that have indices less than or equal to the the requested `index` is: `index + 1` elements. The number of elements in blocks `0...block` is `(block + 1) * (block + 2) / 2`. Therefore, `block` is the smaller integer such that:
+Determining which `block` an index points to is more difficult. The number of elements up to and including the element requested is: `index + 1` elements. The number of elements in blocks `0...block` is `(block + 1) * (block + 2) / 2` (equation derived above). The relationship between the `block` and the `index` is as follows:
 ```
 (block + 1) * (block + 2) / 2 >= index + 1
 ```
@@ -68,16 +68,16 @@ This can be rewritten as:
 ```
 (block)^2 + (3 * block) - (2 * index) >= 0
 ```
-Using the quadratic formula we can get:
+Using the quadratic formula we get:
 ```
 block = (-3 ± √(9 + 8 * index)) / 2
 ```
-A negative block doesn't make sense so we take the positive root instead. In general this solution is not an integer but going back to our inequality, we want the smallest block such that `b => (-3 + √(9 + 8 * index)) / 2`. So we take the ceiling of the result:
+A negative block doesn't make sense, so we take the positive root instead. In general, this solution is not an integer. However, going back to our inequality, we want the smallest block such that `block => (-3 + √(9 + 8 * index)) / 2`. Next, we take the ceiling of the result:
 ```
 block = ⌈(-3 + √(9 + 8 * index)) / 2⌉
 ```
 
-Now we can figure out that `rootishArrayStack[12]` points to! First lets see which block the `12` points to:
+Now we can figure out what `rootishArrayStack[12]` points to! First, let's see which block the `12` points to:
 ```
 block = ⌈(-3 + √(9 + 8 * (12))) / 2⌉
 block = ⌈(-3 + √105) / 2⌉
@@ -93,14 +93,14 @@ inner block index = (12) - (4) * (5) / 2
 inner block index = (12) - 10
 inner block index = 2
 ```
-Therefore `rootishArrayStack[12]` points to the block at index `4` and at inner block index `2`.
+Therefore, `rootishArrayStack[12]` points to the block at index `4` and at inner block index `2`.
 ![Rootish Array Stack Intro](images/RootishArrayStackExample2.png)
 
 ### Interesting Discovery
-Using the `block` equation we can see that the number of `blocks` is proportional to the square root of the number of elements: **O(blocks) = O(√n)**.
+Using the `block` equation, we can see that the number of `blocks` is proportional to the square root of the number of elements: **O(blocks) = O(√n)**.
 
 # Implementation Details
-Lets start with instance variables and struct declaration:
+Let's start with instance variables and struct declaration:
 ```swift
 import Darwin
 
@@ -123,7 +123,7 @@ public struct RootishArrayStack<T> {
 The elements are of generic type `T`, so data of any kind can be stored in the list. `blocks` will be a resizable array to hold fixed sized arrays that take type `T?`.
 > The reason for the fixed size arrays taking type `T?` is so that references to elements aren't retained after they've been removed. Eg: if you remove the last element, the last index must be set to `nil` to prevent the last element being held in memory at an inaccessible index.
 
-`internalCount` is an internal mutable counter that keeps track of the number of elements. `count` is a read only variables that gives the `internalCount` value. `Darwin` is imported here to provide simple math functions such as `ceil()` and `sqrt()`.
+`internalCount` is an internal mutable counter that keeps track of the number of elements. `count` is a read only variable that returns the `internalCount` value. `Darwin` is imported here to provide simple math functions such as `ceil()` and `sqrt()`.
 
 The `capacity` of the structure is simply the Gaussian summation trick:
 ```swift
@@ -132,7 +132,7 @@ var capacity: Int {
 }
 ```
 
-Next lets look at we would `get` and `set` elements:
+Next, let's look at how we would `get` and `set` elements:
 ```swift
 fileprivate func block(fromIndex: Int) -> Int {
   let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
@@ -156,12 +156,13 @@ public subscript(index: Int) -> T {
   }
 }
 ```
-`block(fromIndex:)` and `innerBlockIndex(fromIndex:, fromBlock:)` are wrapping the `block` and `inner block index` equations derived earlier. `superscript` lets us have `get` and `set` access to the structure with the familiar `[index:]` syntax. For both `get` and `set` in superscript we use the same logic:
-	1. determine the block that the index points to
-	2. determine the inner block index
-	3. `get`/`set` the value
+`block(fromIndex:)` and `innerBlockIndex(fromIndex:, fromBlock:)` are wrapping the `block` and `inner block index` equations we derived earlier. `superscript` lets us have `get` and `set` access to the structure with the familiar `[index:]` syntax. For both `get` and `set` in `superscript` we use the same logic:
+
+1. determine the block that the index points to
+2. determine the inner block index
+3. `get`/`set` the value
 
-Next lets look at how we would `growIfNeeded()` and `shrinkIfNeeded()` the structure.
+Next, let's look at how we would `growIfNeeded()` and `shrinkIfNeeded()`.
 ```swift
 fileprivate mutating func growIfNeeded() {
   if capacity - blocks.count < count + 1 {
@@ -179,7 +180,7 @@ fileprivate mutating func shrinkIfNeeded() {
 }
 ```
 If our data set grows or shrinks in size, we want our data structure to accommodate the change.
-Just like a Swift array when a capacity threshold is met we will `grow` or `shrink` the size of our structure. For the Rootish Array Stack we want to `grow` if the second last block is full on an `insert` operation, and `shrink` if the two last blocks are empty.
+Just like a Swift array, when a capacity threshold is met we will `grow` or `shrink` the size of our structure. For the Rootish Array Stack we want to `grow` if the second last block is full on an `insert` operation, and `shrink` if the two last blocks are empty.
 
 Now to the more familiar Swift array behaviour.  
 ```swift
@@ -215,8 +216,11 @@ fileprivate mutating func makeNil(atIndex index: Int) {
   blocks[block][innerBlockIndex] = nil
 }
 ```
-To `insert(element:, atIndex:)` we move all elements after the `index` to the right by 1. After space has been made for the element we set the value using the `subscript` convenience. `append(element:)` is just a convenience method to add to the end. To `remove(atIndex:)` we move all the elements after the `index` to the left by 1. After the removed value is covered by it's proceeding value, we set the last value in the structure to `nil`. `makeNil(atIndex:)` uses the same logic as our `subscript` method but is used to set the root optional at a particular index to `nil` (because setting it's wrapped value to `nil` is something only the user of the data structure should do).
-> Setting a optionals value to `nil` is different than setting it's wrapped value to `nil`. An optionals wrapped value is an embedded type within the optional reference. This means that a `nil` wrapped value is actually `.some(.none)` wheres setting the root reference to `nil` is `.none`. To better understand Swift optionals I recommend checking out @SebastianBoldt's article [Swift! Optionals?](https://medium.com/ios-os-x-development/swift-optionals-78dafaa53f3#.rvjobhuzs).
+To `insert(element:, atIndex:)` we move all elements after the `index` to the right by 1. After space has been made for the element, we set the value using the `subscript` convenience method.
+`append(element:)` is just a convenience method to `insert` to the end.
+To `remove(atIndex:)` we move all the elements after the `index` to the left by 1. After the removed value is covered by it's proceeding value, we set the last value in the structure to `nil`.
+`makeNil(atIndex:)` uses the same logic as our `subscript` method but is used to set the root optional at a particular index to `nil` (because setting it's wrapped value to `nil` is something only the user of the data structure should do).
+> Setting a optionals value to `nil` is different than setting it's wrapped value to `nil`. An optionals wrapped value is an embedded type within the optional reference. This means that a `nil` wrapped value is actually `.some(.none)` whereas setting the root reference to `nil` is `.none`. To better understand Swift optionals I recommend checking out @SebastianBoldt's article [Swift! Optionals?](https://medium.com/ios-os-x-development/swift-optionals-78dafaa53f3#.rvjobhuzs).
 
 # Performance
 * An internal counter keeps track of the number of elements in the structure. `count` is executed in **O(1)** time.
@@ -228,10 +232,10 @@ To `insert(element:, atIndex:)` we move all elements after the `index` to the ri
 * Ignoring the time cost to `grow` and `shrink`, `insert(atIndex:)` and `remove(atIndex:)` operations shift all elements right of the specified index resulting in **O(n)** time.
 
 # Analysis of Growing and Shrinking
-The performance analysis doesn't account for the cost to `grow` and `shrink`. Unlike a regular Swift array, `grow` and `shrink` operations don't copy all the elements into a backing array. They only allocate or free an array proportional to the number of `blocks`. The number of `blocks` is proportional to the  square root of the number of elements. Growing and shrinking only cost **O(√n)**.
+The performance analysis doesn't account for the cost to `grow` and `shrink`. Unlike a regular Swift array, `grow` and `shrink` operations don't copy all the elements into a backing array. They only allocate or free an array proportional to the number of `blocks`. The number of `blocks` is proportional to the  square root of the number of elements. Growing and shrinking only costs **O(√n)**.
 
 # Wasted Space
-Wasted space is how much memory with respect to the number of elements `n` is unused. The Rootish Array Stack never has more than 2 empty blocks and it never has less than 1 empty block. The last two blocks are proportional to the number of blocks which is proportional to the square root of the number of elements. The number of references needed to point to each block is the same as the number of blocks. Therefore, the amount of wasted space with respect to the number of elements is **O(√n)**.
+Wasted space is how much memory with respect to the number of elements `n` is unused. The Rootish Array Stack never has more than 2 empty blocks and it never has less than 1 empty block. The last two blocks are proportional to the number of blocks, which is proportional to the square root of the number of elements. The number of references needed to point to each block is the same as the number of blocks. Therefore, the amount of wasted space with respect to the number of elements is **O(√n)**.
 
 
 _Written for Swift Algorithm Club by @BenEmdon_
diff --git a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift
new file mode 100644
index 000000000..401c773d6
--- /dev/null
+++ b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
@@ -0,0 +1,219 @@
+//: Playground - noun: a place where people can play
+
+import Darwin
+
+public struct RootishArrayStack<T> {
+
+	// MARK: - Instance variables
+
+	fileprivate var blocks = [Array<T?>]()
+	fileprivate var internalCount = 0
+
+	// MARK: - Init
+
+	public init() { }
+
+	// MARK: - Calculated variables
+
+	var count: Int {
+		return internalCount
+	}
+
+	var capacity: Int {
+		return blocks.count * (blocks.count + 1) / 2
+	}
+
+	var isEmpty: Bool {
+		return blocks.count == 0
+	}
+
+	var first: T? {
+		guard capacity > 0 else { return nil }
+		return blocks[0][0]
+	}
+
+	var last: T? {
+		guard capacity > 0 else { return nil }
+		let block = self.block(fromIndex: count - 1)
+		let innerBlockIndex = self.innerBlockIndex(fromIndex: count - 1, fromBlock: block)
+		return blocks[block][innerBlockIndex]
+	}
+
+	// MARK: - Equations
+
+	fileprivate func block(fromIndex index: Int) -> Int {
+		let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
+		return block
+	}
+
+	fileprivate func innerBlockIndex(fromIndex index: Int, fromBlock block: Int) -> Int {
+		return index - block * (block + 1) / 2
+	}
+
+	// MARK: - Behavior
+
+	fileprivate mutating func growIfNeeded() {
+		if capacity - blocks.count < count + 1 {
+			let newArray = [T?](repeating: nil, count: blocks.count + 1)
+			blocks.append(newArray)
+		}
+	}
+
+	fileprivate mutating func shrinkIfNeeded() {
+		if capacity + blocks.count >= count {
+			while blocks.count > 0 && (blocks.count - 2) * (blocks.count - 1) / 2 >= count {
+				blocks.remove(at: blocks.count - 1)
+			}
+		}
+	}
+
+	public subscript(index: Int) -> T {
+		get {
+			let block = self.block(fromIndex: index)
+			let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+			return blocks[block][innerBlockIndex]!
+		}
+		set(newValue) {
+			let block = self.block(fromIndex: index)
+			let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+			blocks[block][innerBlockIndex] = newValue
+		}
+	}
+
+	public mutating func insert(element: T, atIndex index: Int) {
+		growIfNeeded()
+		internalCount += 1
+		var i = count - 1
+		while i > index {
+			self[i] = self[i - 1]
+			i -= 1
+		}
+		self[index] = element
+	}
+
+	public mutating func append(element: T) {
+		insert(element: element, atIndex: count)
+	}
+
+	fileprivate mutating func makeNil(atIndex index: Int) {
+		let block = self.block(fromIndex: index)
+		let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+		blocks[block][innerBlockIndex] = nil
+	}
+
+	public mutating func remove(atIndex index: Int) -> T {
+		let element = self[index]
+		for i in index..<count - 1 {
+			self[i] = self[i + 1]
+		}
+		internalCount -= 1
+		makeNil(atIndex: count)
+		shrinkIfNeeded()
+		return element
+	}
+
+	// MARK: - Struct to string
+
+	public var memoryDescription: String {
+		var description = "{\n"
+		for block in blocks {
+			description += "\t["
+			for index in 0..<block.count {
+				description += "\(block[index])"
+				if index + 1 != block.count {
+					description += ", "
+				}
+			}
+			description += "]\n"
+		}
+		return description + "}"
+	}
+}
+
+extension RootishArrayStack: CustomStringConvertible {
+	public var description: String {
+		var description = "["
+		for index in 0..<count {
+			description += "\(self[index])"
+			if index + 1 != count {
+				description += ", "
+			}
+		}
+		return description + "]"
+	}
+}
+
+var list = RootishArrayStack<String>()
+list.isEmpty								// true
+list.first									// nil
+list.last										// nil
+list.count									// 0
+list.capacity								// 0
+
+list.memoryDescription
+//	{
+//	}
+
+list.append(element: "Hello")
+list.isEmpty								// false
+list.first									// "Hello"
+list.last										// "hello"
+list.count									// 1
+list.capacity								// 1
+
+list.memoryDescription
+//	{
+//		[Optional("Hello")]
+//	}
+
+list.append(element: "World")
+list.isEmpty								// false
+list.first									// "Hello"
+list.last										// "World"
+list.count									// 2
+list.capacity								// 3
+
+list[0]											// "Hello"
+list[1]											// "World"
+//list[2]										// crash!
+
+
+list.memoryDescription
+//	{
+//		[Optional("Hello")]
+//		[Optional("World"), nil]
+//	}
+
+
+list.insert(element: "Swift", atIndex: 1)
+list.isEmpty								// false
+list.first									// "Hello"
+list.last										// "World"
+list.count									// 3
+list.capacity								// 6
+
+list[0]											// "Hello"
+list[1]											// "Swift"
+list[2]											// "World"
+
+list.memoryDescription
+//	{
+//		[Optional("Hello")]
+//		[Optional("Swift"), Optional("World")]
+//		[nil, nil, nil]
+//	}
+
+list.remove(atIndex: 2)			// "World"
+list.isEmpty								// false
+list.first									// "Hello"
+list.last										// "Swift"
+list.count									// 2
+list.capacity								// 3
+
+list[0]											// "Hello"
+list[1]											// "Swift"
+//list[2]										// crash!
+
+list[0] = list[1]
+list[1] = "is awesome"
+list												// ["Swift", "is awesome"]
diff --git a/Rootish Array Stack/RootishArrayStack.playground/contents.xcplayground b/Rootish Array Stack/RootishArrayStack.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Rootish Array Stack/RootishArrayStack.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Rootish Array Stack/RootishArrayStack.swift b/Rootish Array Stack/RootishArrayStack.swift
index 4033d75f6..af95a4316 100644
--- a/Rootish Array Stack/RootishArrayStack.swift	
+++ b/Rootish Array Stack/RootishArrayStack.swift	
@@ -115,31 +115,34 @@ public struct RootishArrayStack<T> {
 		shrinkIfNeeded()
 		return element
 	}
-}
-
-// MARK: - Struct to string
 
-extension RootishArrayStack: CustomStringConvertible {
-	public var description: String {
-		var s = "["
-		for index in 0..<count {
-			s += "\(self[index])"
-			if index + 1 != count {
-				s += ", "
-			}
-		}
-		return s + "]"
-	}
+	// MARK: - Struct to string
 
 	public var memoryDescription: String {
 		var description = "{\n"
 		for block in blocks {
 			description += "\t["
-			for rawElement in block {
-				description += "\(rawElement), "
+			for index in 0..<block.count {
+				description += "\(block[index])"
+				if index + 1 != block.count {
+					description += ", "
+				}
 			}
 			description += "]\n"
 		}
 		return description + "}"
 	}
 }
+
+extension RootishArrayStack: CustomStringConvertible {
+	public var description: String {
+		var description = "["
+		for index in 0..<count {
+			description += "\(self[index])"
+			if index + 1 != count {
+				description += ", "
+			}
+		}
+		return description + "]"
+	}
+}

From 82b8c829d3a02ba7154bc9cb26f06156995b3dba Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sun, 18 Dec 2016 16:57:29 -0500
Subject: [PATCH 0692/1679] Added tests template

---
 Rootish Array Stack/Tests/Info.plist          |  24 ++
 .../Tests/RootishArrayStack.swift             | 148 ++++++++++
 .../Tests/RootishArrayStackTests.swift        | 251 +++++++++++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 264 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     |  90 ++++++
 6 files changed, 784 insertions(+)
 create mode 100644 Rootish Array Stack/Tests/Info.plist
 create mode 100644 Rootish Array Stack/Tests/RootishArrayStack.swift
 create mode 100755 Rootish Array Stack/Tests/RootishArrayStackTests.swift
 create mode 100644 Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Rootish Array Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Rootish Array Stack/Tests/Info.plist b/Rootish Array Stack/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Rootish Array Stack/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Rootish Array Stack/Tests/RootishArrayStack.swift b/Rootish Array Stack/Tests/RootishArrayStack.swift
new file mode 100644
index 000000000..af95a4316
--- /dev/null
+++ b/Rootish Array Stack/Tests/RootishArrayStack.swift	
@@ -0,0 +1,148 @@
+//
+//  RootishArrayStack
+//
+//  Created by @BenEmdon on 2016-11-07.
+//
+
+import Darwin
+
+public struct RootishArrayStack<T> {
+
+	// MARK: - Instance variables
+
+	fileprivate var blocks = [Array<T?>]()
+	fileprivate var internalCount = 0
+
+	// MARK: - Init
+
+	public init() { }
+
+	// MARK: - Calculated variables
+
+	var count: Int {
+		return internalCount
+	}
+
+	var capacity: Int {
+		return blocks.count * (blocks.count + 1) / 2
+	}
+
+	var isEmpty: Bool {
+		return blocks.count == 0
+	}
+
+	var first: T? {
+		guard capacity > 0 else { return nil }
+		return blocks[0][0]
+	}
+
+	var last: T? {
+		guard capacity > 0 else { return nil }
+		let block = self.block(fromIndex: count - 1)
+		let innerBlockIndex = self.innerBlockIndex(fromIndex: count - 1, fromBlock: block)
+		return blocks[block][innerBlockIndex]
+	}
+
+	// MARK: - Equations
+
+	fileprivate func block(fromIndex index: Int) -> Int {
+		let block = Int(ceil((-3.0 + sqrt(9.0 + 8.0 * Double(index))) / 2))
+		return block
+	}
+
+	fileprivate func innerBlockIndex(fromIndex index: Int, fromBlock block: Int) -> Int {
+		return index - block * (block + 1) / 2
+	}
+
+	// MARK: - Behavior
+
+	fileprivate mutating func growIfNeeded() {
+		if capacity - blocks.count < count + 1 {
+			let newArray = [T?](repeating: nil, count: blocks.count + 1)
+			blocks.append(newArray)
+		}
+	}
+
+	fileprivate mutating func shrinkIfNeeded() {
+		if capacity + blocks.count >= count {
+			while blocks.count > 0 && (blocks.count - 2) * (blocks.count - 1) / 2 >= count {
+				blocks.remove(at: blocks.count - 1)
+			}
+		}
+	}
+
+	public subscript(index: Int) -> T {
+		get {
+			let block = self.block(fromIndex: index)
+			let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+			return blocks[block][innerBlockIndex]!
+		}
+		set(newValue) {
+			let block = self.block(fromIndex: index)
+			let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+			blocks[block][innerBlockIndex] = newValue
+		}
+	}
+
+	public mutating func insert(element: T, atIndex index: Int) {
+		growIfNeeded()
+		internalCount += 1
+		var i = count - 1
+		while i > index {
+			self[i] = self[i - 1]
+			i -= 1
+		}
+		self[index] = element
+	}
+
+	public mutating func append(element: T) {
+		insert(element: element, atIndex: count)
+	}
+
+	fileprivate mutating func makeNil(atIndex index: Int) {
+		let block = self.block(fromIndex: index)
+		let innerBlockIndex = self.innerBlockIndex(fromIndex: index, fromBlock: block)
+		blocks[block][innerBlockIndex] = nil
+	}
+
+	public mutating func remove(atIndex index: Int) -> T {
+		let element = self[index]
+		for i in index..<count - 1 {
+			self[i] = self[i + 1]
+		}
+		internalCount -= 1
+		makeNil(atIndex: count)
+		shrinkIfNeeded()
+		return element
+	}
+
+	// MARK: - Struct to string
+
+	public var memoryDescription: String {
+		var description = "{\n"
+		for block in blocks {
+			description += "\t["
+			for index in 0..<block.count {
+				description += "\(block[index])"
+				if index + 1 != block.count {
+					description += ", "
+				}
+			}
+			description += "]\n"
+		}
+		return description + "}"
+	}
+}
+
+extension RootishArrayStack: CustomStringConvertible {
+	public var description: String {
+		var description = "["
+		for index in 0..<count {
+			description += "\(self[index])"
+			if index + 1 != count {
+				description += ", "
+			}
+		}
+		return description + "]"
+	}
+}
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
new file mode 100755
index 000000000..7fa420cb2
--- /dev/null
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -0,0 +1,251 @@
+import XCTest
+
+class RootishArrayStackTests: XCTestCase {
+  let numbers = [8, 2, 10, 9, 7, 5]
+
+  fileprivate func buildList() -> LinkedList<Int> {
+    let list = LinkedList<Int>()
+    for number in numbers {
+      list.append(number)
+    }
+    return list
+  }
+
+  func testEmptyList() {
+    let list = LinkedList<Int>()
+    XCTAssertTrue(list.isEmpty)
+    XCTAssertEqual(list.count, 0)
+    XCTAssertNil(list.first)
+    XCTAssertNil(list.last)
+  }
+
+  func testListWithOneElement() {
+    let list = LinkedList<Int>()
+    list.append(123)
+
+    XCTAssertFalse(list.isEmpty)
+    XCTAssertEqual(list.count, 1)
+
+    XCTAssertNotNil(list.first)
+    XCTAssertNil(list.first!.previous)
+    XCTAssertNil(list.first!.next)
+    XCTAssertEqual(list.first!.value, 123)
+
+    XCTAssertNotNil(list.last)
+    XCTAssertNil(list.last!.previous)
+    XCTAssertNil(list.last!.next)
+    XCTAssertEqual(list.last!.value, 123)
+
+    XCTAssertTrue(list.first === list.last)
+  }
+
+  func testListWithTwoElements() {
+    let list = LinkedList<Int>()
+    list.append(123)
+    list.append(456)
+
+    XCTAssertEqual(list.count, 2)
+
+    XCTAssertNotNil(list.first)
+    XCTAssertEqual(list.first!.value, 123)
+
+    XCTAssertNotNil(list.last)
+    XCTAssertEqual(list.last!.value, 456)
+
+    XCTAssertTrue(list.first !== list.last)
+
+    XCTAssertNil(list.first!.previous)
+    XCTAssertTrue(list.first!.next === list.last)
+    XCTAssertTrue(list.last!.previous === list.first)
+    XCTAssertNil(list.last!.next)
+  }
+
+  func testListWithThreeElements() {
+    let list = LinkedList<Int>()
+    list.append(123)
+    list.append(456)
+    list.append(789)
+
+    XCTAssertEqual(list.count, 3)
+
+    XCTAssertNotNil(list.first)
+    XCTAssertEqual(list.first!.value, 123)
+
+    let second = list.first!.next
+    XCTAssertNotNil(second)
+    XCTAssertEqual(second!.value, 456)
+
+    XCTAssertNotNil(list.last)
+    XCTAssertEqual(list.last!.value, 789)
+
+    XCTAssertNil(list.first!.previous)
+    XCTAssertTrue(list.first!.next === second)
+    XCTAssertTrue(second!.previous === list.first)
+    XCTAssertTrue(second!.next === list.last)
+    XCTAssertTrue(list.last!.previous === second)
+    XCTAssertNil(list.last!.next)
+  }
+
+  func testNodeAtIndexInEmptyList() {
+    let list = LinkedList<Int>()
+    let node = list.node(atIndex: 0)
+    XCTAssertNil(node)
+  }
+
+  func testNodeAtIndexInListWithOneElement() {
+    let list = LinkedList<Int>()
+    list.append(123)
+
+    let node = list.node(atIndex: 0)
+    XCTAssertNotNil(node)
+    XCTAssertEqual(node!.value, 123)
+    XCTAssertTrue(node === list.first)
+  }
+
+  func testNodeAtIndex() {
+    let list = buildList()
+
+    let nodeCount = list.count
+    XCTAssertEqual(nodeCount, numbers.count)
+
+    XCTAssertNil(list.node(atIndex: -1))
+    XCTAssertNil(list.node(atIndex: nodeCount))
+
+    let first = list.node(atIndex: 0)
+    XCTAssertNotNil(first)
+    XCTAssertTrue(first === list.first)
+    XCTAssertEqual(first!.value, numbers[0])
+
+    let last = list.node(atIndex: nodeCount - 1)
+    XCTAssertNotNil(last)
+    XCTAssertTrue(last === list.last)
+    XCTAssertEqual(last!.value, numbers[nodeCount - 1])
+
+    for i in 0..<nodeCount {
+      let node = list.node(atIndex: i)
+      XCTAssertNotNil(node)
+      XCTAssertEqual(node!.value, numbers[i])
+    }
+  }
+
+  func testSubscript() {
+    let list = buildList()
+    for i in 0 ..< list.count {
+      XCTAssertEqual(list[i], numbers[i])
+    }
+  }
+
+  func testInsertAtIndexInEmptyList() {
+    let list = LinkedList<Int>()
+    list.insert(123, atIndex: 0)
+
+    XCTAssertFalse(list.isEmpty)
+    XCTAssertEqual(list.count, 1)
+
+    let node = list.node(atIndex: 0)
+    XCTAssertNotNil(node)
+    XCTAssertEqual(node!.value, 123)
+  }
+
+  func testInsertAtIndex() {
+    let list = buildList()
+    let prev = list.node(atIndex: 2)
+    let next = list.node(atIndex: 3)
+    let nodeCount = list.count
+
+    list.insert(444, atIndex: 3)
+
+    let node = list.node(atIndex: 3)
+    XCTAssertNotNil(node)
+    XCTAssertEqual(node!.value, 444)
+    XCTAssertEqual(nodeCount + 1, list.count)
+
+    XCTAssertFalse(prev === node)
+    XCTAssertFalse(next === node)
+    XCTAssertTrue(prev!.next === node)
+    XCTAssertTrue(next!.previous === node)
+  }
+
+  func testRemoveAtIndexOnListWithOneElement() {
+    let list = LinkedList<Int>()
+    list.append(123)
+
+    let value = list.remove(atIndex: 0)
+    XCTAssertEqual(value, 123)
+
+    XCTAssertTrue(list.isEmpty)
+    XCTAssertEqual(list.count, 0)
+    XCTAssertNil(list.first)
+    XCTAssertNil(list.last)
+  }
+
+  func testRemoveAtIndex() {
+    let list = buildList()
+    let prev = list.node(atIndex: 2)
+    let next = list.node(atIndex: 3)
+    let nodeCount = list.count
+
+    list.insert(444, atIndex: 3)
+
+    let value = list.remove(atIndex: 3)
+    XCTAssertEqual(value, 444)
+
+    let node = list.node(atIndex: 3)
+    XCTAssertTrue(next === node)
+    XCTAssertTrue(prev!.next === node)
+    XCTAssertTrue(node!.previous === prev)
+    XCTAssertEqual(nodeCount, list.count)
+  }
+
+  func testRemoveLastOnListWithOneElement() {
+    let list = LinkedList<Int>()
+    list.append(123)
+
+    let value = list.removeLast()
+    XCTAssertEqual(value, 123)
+
+    XCTAssertTrue(list.isEmpty)
+    XCTAssertEqual(list.count, 0)
+    XCTAssertNil(list.first)
+    XCTAssertNil(list.last)
+  }
+
+  func testRemoveLast() {
+    let list = buildList()
+    let last = list.last
+    let prev = last!.previous
+    let nodeCount = list.count
+
+    let value = list.removeLast()
+    XCTAssertEqual(value, 5)
+
+    XCTAssertNil(last!.previous)
+    XCTAssertNil(last!.next)
+
+    XCTAssertNil(prev!.next)
+    XCTAssertTrue(list.last === prev)
+    XCTAssertEqual(nodeCount - 1, list.count)
+  }
+
+  func testRemoveAll() {
+    let list = buildList()
+    list.removeAll()
+    XCTAssertTrue(list.isEmpty)
+    XCTAssertEqual(list.count, 0)
+    XCTAssertNil(list.first)
+    XCTAssertNil(list.last)
+  }
+
+  func testReverseLinkedList() {
+    let list = buildList()
+    let first = list.first
+    let last = list.last
+    let nodeCount = list.count
+
+    list.reverse()
+
+    XCTAssertTrue(first === list.last)
+    XCTAssertTrue(last === list.first)
+    XCTAssertEqual(nodeCount, list.count)
+  }
+}
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..d6fb62c9d
--- /dev/null
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,264 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		1D059BB21E073CED00391DD1 /* RootishArrayStack.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1D059BB11E073CED00391DD1 /* RootishArrayStack.swift */; };
+		7B80C3FA1C77A61E003CECC7 /* RootishArrayStackTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3F91C77A61E003CECC7 /* RootishArrayStackTests.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		1D059BB11E073CED00391DD1 /* RootishArrayStack.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = RootishArrayStack.swift; path = ../RootishArrayStack.swift; sourceTree = "<group>"; };
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C3F91C77A61E003CECC7 /* RootishArrayStackTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = RootishArrayStackTests.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				1D059BB11E073CED00391DD1 /* RootishArrayStack.swift */,
+				7B80C3F91C77A61E003CECC7 /* RootishArrayStackTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0720;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C3FA1C77A61E003CECC7 /* RootishArrayStackTests.swift in Sources */,
+				1D059BB21E073CED00391DD1 /* RootishArrayStack.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Rootish Array Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..8ef8d8581
--- /dev/null
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0720"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From f709ee8d52dbef684e02e6350bd5110c2ffb313b Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Sun, 18 Dec 2016 17:31:52 -0500
Subject: [PATCH 0693/1679] added test scheme to travis

---
 .travis.yml                                   |   1 +
 .../contents.xcworkspacedata                  |   7 +
 .../Tests/RootishArrayStackTests.swift        | 492 +++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |   9 +-
 .../xcshareddata/xcschemes/Tests.xcscheme     |   2 +-
 .../contents.xcworkspacedata                  |  29 ++
 6 files changed, 293 insertions(+), 247 deletions(-)
 create mode 100644 Rootish Array Stack/RootishArrayStack.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/.travis.yml b/.travis.yml
index 45f0d4beb..695c702c2 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -31,6 +31,7 @@ script:
 # - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Rootish Array Stack/RootishArrayStack.playground/playground.xcworkspace/contents.xcworkspacedata b/Rootish Array Stack/RootishArrayStack.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Rootish Array Stack/RootishArrayStack.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index 7fa420cb2..8292f3d30 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -1,251 +1,255 @@
 import XCTest
 
 class RootishArrayStackTests: XCTestCase {
-  let numbers = [8, 2, 10, 9, 7, 5]
-
-  fileprivate func buildList() -> LinkedList<Int> {
-    let list = LinkedList<Int>()
-    for number in numbers {
-      list.append(number)
-    }
+//  let randomNumbers = [8, 2, 10, 9, 7, 5]
+
+	func buildList(withNumbers numbers: [Int]? = nil) -> RootishArrayStack<Int> {
+    var list = RootishArrayStack<Int>()
+		if let numbers = numbers {
+			for number in numbers {
+				list.append(element: number)
+			}
+		}
     return list
   }
 
-  func testEmptyList() {
-    let list = LinkedList<Int>()
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    XCTAssertFalse(list.isEmpty)
-    XCTAssertEqual(list.count, 1)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertNil(list.first!.previous)
-    XCTAssertNil(list.first!.next)
-    XCTAssertEqual(list.first!.value, 123)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertNil(list.last!.previous)
-    XCTAssertNil(list.last!.next)
-    XCTAssertEqual(list.last!.value, 123)
-
-    XCTAssertTrue(list.first === list.last)
-  }
-
-  func testListWithTwoElements() {
-    let list = LinkedList<Int>()
-    list.append(123)
-    list.append(456)
-
-    XCTAssertEqual(list.count, 2)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertEqual(list.first!.value, 123)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertEqual(list.last!.value, 456)
-
-    XCTAssertTrue(list.first !== list.last)
-
-    XCTAssertNil(list.first!.previous)
-    XCTAssertTrue(list.first!.next === list.last)
-    XCTAssertTrue(list.last!.previous === list.first)
-    XCTAssertNil(list.last!.next)
-  }
-
-  func testListWithThreeElements() {
-    let list = LinkedList<Int>()
-    list.append(123)
-    list.append(456)
-    list.append(789)
-
-    XCTAssertEqual(list.count, 3)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertEqual(list.first!.value, 123)
-
-    let second = list.first!.next
-    XCTAssertNotNil(second)
-    XCTAssertEqual(second!.value, 456)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertEqual(list.last!.value, 789)
-
-    XCTAssertNil(list.first!.previous)
-    XCTAssertTrue(list.first!.next === second)
-    XCTAssertTrue(second!.previous === list.first)
-    XCTAssertTrue(second!.next === list.last)
-    XCTAssertTrue(list.last!.previous === second)
-    XCTAssertNil(list.last!.next)
-  }
-
-  func testNodeAtIndexInEmptyList() {
-    let list = LinkedList<Int>()
-    let node = list.node(atIndex: 0)
-    XCTAssertNil(node)
-  }
-
-  func testNodeAtIndexInListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let node = list.node(atIndex: 0)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 123)
-    XCTAssertTrue(node === list.first)
-  }
-
-  func testNodeAtIndex() {
-    let list = buildList()
-
-    let nodeCount = list.count
-    XCTAssertEqual(nodeCount, numbers.count)
-
-    XCTAssertNil(list.node(atIndex: -1))
-    XCTAssertNil(list.node(atIndex: nodeCount))
-
-    let first = list.node(atIndex: 0)
-    XCTAssertNotNil(first)
-    XCTAssertTrue(first === list.first)
-    XCTAssertEqual(first!.value, numbers[0])
-
-    let last = list.node(atIndex: nodeCount - 1)
-    XCTAssertNotNil(last)
-    XCTAssertTrue(last === list.last)
-    XCTAssertEqual(last!.value, numbers[nodeCount - 1])
-
-    for i in 0..<nodeCount {
-      let node = list.node(atIndex: i)
-      XCTAssertNotNil(node)
-      XCTAssertEqual(node!.value, numbers[i])
-    }
-  }
-
-  func testSubscript() {
-    let list = buildList()
-    for i in 0 ..< list.count {
-      XCTAssertEqual(list[i], numbers[i])
-    }
-  }
-
-  func testInsertAtIndexInEmptyList() {
-    let list = LinkedList<Int>()
-    list.insert(123, atIndex: 0)
-
-    XCTAssertFalse(list.isEmpty)
-    XCTAssertEqual(list.count, 1)
-
-    let node = list.node(atIndex: 0)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 123)
-  }
-
-  func testInsertAtIndex() {
-    let list = buildList()
-    let prev = list.node(atIndex: 2)
-    let next = list.node(atIndex: 3)
-    let nodeCount = list.count
-
-    list.insert(444, atIndex: 3)
-
-    let node = list.node(atIndex: 3)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 444)
-    XCTAssertEqual(nodeCount + 1, list.count)
-
-    XCTAssertFalse(prev === node)
-    XCTAssertFalse(next === node)
-    XCTAssertTrue(prev!.next === node)
-    XCTAssertTrue(next!.previous === node)
-  }
-
-  func testRemoveAtIndexOnListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let value = list.remove(atIndex: 0)
-    XCTAssertEqual(value, 123)
-
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testRemoveAtIndex() {
-    let list = buildList()
-    let prev = list.node(atIndex: 2)
-    let next = list.node(atIndex: 3)
-    let nodeCount = list.count
-
-    list.insert(444, atIndex: 3)
-
-    let value = list.remove(atIndex: 3)
-    XCTAssertEqual(value, 444)
-
-    let node = list.node(atIndex: 3)
-    XCTAssertTrue(next === node)
-    XCTAssertTrue(prev!.next === node)
-    XCTAssertTrue(node!.previous === prev)
-    XCTAssertEqual(nodeCount, list.count)
-  }
-
-  func testRemoveLastOnListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let value = list.removeLast()
-    XCTAssertEqual(value, 123)
-
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testRemoveLast() {
-    let list = buildList()
-    let last = list.last
-    let prev = last!.previous
-    let nodeCount = list.count
-
-    let value = list.removeLast()
-    XCTAssertEqual(value, 5)
-
-    XCTAssertNil(last!.previous)
-    XCTAssertNil(last!.next)
-
-    XCTAssertNil(prev!.next)
-    XCTAssertTrue(list.last === prev)
-    XCTAssertEqual(nodeCount - 1, list.count)
-  }
-
-  func testRemoveAll() {
-    let list = buildList()
-    list.removeAll()
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testReverseLinkedList() {
-    let list = buildList()
-    let first = list.first
-    let last = list.last
-    let nodeCount = list.count
-
-    list.reverse()
-
-    XCTAssertTrue(first === list.last)
-    XCTAssertTrue(last === list.first)
-    XCTAssertEqual(nodeCount, list.count)
-  }
+	func testEmptyList() {
+		let list = buildList()
+		XCTAssertTrue(list.isEmpty)
+		XCTAssertEqual(list.count, 0)
+		XCTAssertEqual(list.capacity, 0)
+		XCTAssertNil(list.first)
+		XCTAssertNil(list.last)
+	}
+
+	func testListWithOneElement() {
+		let list = buildList(withNumbers: [1])
+		XCTAssertFalse(list.isEmpty)
+		XCTAssertEqual(list.count, 1)
+		XCTAssertEqual(list.capacity, 1)
+		XCTAssertEqual(list.first, 1)
+		XCTAssertEqual(list.last, 1)
+		XCTAssertEqual(list.first, list.last)
+	}
+
+	func testListWithTwoElements() {
+		let list = buildList(withNumbers: [1, 2])
+		XCTAssertFalse(list.isEmpty)
+		XCTAssertEqual(list.count, 2)
+		XCTAssertEqual(list.capacity, 3)
+		XCTAssertEqual(list.first, 1)
+		XCTAssertEqual(list.last, 2)
+		XCTAssertNotEqual(list.first, list.last)
+	}
+
+//
+//  func testListWithTwoElements() {
+//    var list = RootishArrayStack<Int>()
+//    list.append(123)
+//    list.append(456)
+//
+//    XCTAssertEqual(list.count, 2)
+//
+//    XCTAssertNotNil(list.first)
+//    XCTAssertEqual(list.first!.value, 123)
+//
+//    XCTAssertNotNil(list.last)
+//    XCTAssertEqual(list.last!.value, 456)
+//
+//    XCTAssertTrue(list.first !== list.last)
+//
+//    XCTAssertNil(list.first!.previous)
+//    XCTAssertTrue(list.first!.next === list.last)
+//    XCTAssertTrue(list.last!.previous === list.first)
+//    XCTAssertNil(list.last!.next)
+//  }
+//
+//  func testListWithThreeElements() {
+//    var list = RootishArrayStack<Int>()
+//    list.append(123)
+//    list.append(456)
+//    list.append(789)
+//
+//    XCTAssertEqual(list.count, 3)
+//
+//    XCTAssertNotNil(list.first)
+//    XCTAssertEqual(list.first!.value, 123)
+//
+//    let second = list.first!.next
+//    XCTAssertNotNil(second)
+//    XCTAssertEqual(second!.value, 456)
+//
+//    XCTAssertNotNil(list.last)
+//    XCTAssertEqual(list.last!.value, 789)
+//
+//    XCTAssertNil(list.first!.previous)
+//    XCTAssertTrue(list.first!.next === second)
+//    XCTAssertTrue(second!.previous === list.first)
+//    XCTAssertTrue(second!.next === list.last)
+//    XCTAssertTrue(list.last!.previous === second)
+//    XCTAssertNil(list.last!.next)
+//  }
+//
+//  func testNodeAtIndexInEmptyList() {
+//    var list = RootishArrayStack<Int>()
+//    let node = list.node(atIndex: 0)
+//    XCTAssertNil(node)
+//  }
+//
+//  func testNodeAtIndexInListWithOneElement() {
+//    let list = RootishArrayStack<Int>()
+//    list.append(123)
+//
+//    let node = list.node(atIndex: 0)
+//    XCTAssertNotNil(node)
+//    XCTAssertEqual(node!.value, 123)
+//    XCTAssertTrue(node === list.first)
+//  }
+//
+//  func testNodeAtIndex() {
+//    let list = buildList()
+//
+//    let nodeCount = list.count
+//    XCTAssertEqual(nodeCount, numbers.count)
+//
+//    XCTAssertNil(list.node(atIndex: -1))
+//    XCTAssertNil(list.node(atIndex: nodeCount))
+//
+//    let first = list.node(atIndex: 0)
+//    XCTAssertNotNil(first)
+//    XCTAssertTrue(first === list.first)
+//    XCTAssertEqual(first!.value, numbers[0])
+//
+//    let last = list.node(atIndex: nodeCount - 1)
+//    XCTAssertNotNil(last)
+//    XCTAssertTrue(last === list.last)
+//    XCTAssertEqual(last!.value, numbers[nodeCount - 1])
+//
+//    for i in 0..<nodeCount {
+//      let node = list.node(atIndex: i)
+//      XCTAssertNotNil(node)
+//      XCTAssertEqual(node!.value, numbers[i])
+//    }
+//  }
+//
+//  func testSubscript() {
+//    let list = buildList()
+//    for i in 0 ..< list.count {
+//      XCTAssertEqual(list[i], numbers[i])
+//    }
+//  }
+//
+//  func testInsertAtIndexInEmptyList() {
+//    let list = RootishArrayStack<Int>()
+//    list.insert(123, atIndex: 0)
+//
+//    XCTAssertFalse(list.isEmpty)
+//    XCTAssertEqual(list.count, 1)
+//
+//    let node = list.node(atIndex: 0)
+//    XCTAssertNotNil(node)
+//    XCTAssertEqual(node!.value, 123)
+//  }
+//
+//  func testInsertAtIndex() {
+//    let list = buildList()
+//    let prev = list.node(atIndex: 2)
+//    let next = list.node(atIndex: 3)
+//    let nodeCount = list.count
+//
+//    list.insert(444, atIndex: 3)
+//
+//    let node = list.node(atIndex: 3)
+//    XCTAssertNotNil(node)
+//    XCTAssertEqual(node!.value, 444)
+//    XCTAssertEqual(nodeCount + 1, list.count)
+//
+//    XCTAssertFalse(prev === node)
+//    XCTAssertFalse(next === node)
+//    XCTAssertTrue(prev!.next === node)
+//    XCTAssertTrue(next!.previous === node)
+//  }
+//
+//  func testRemoveAtIndexOnListWithOneElement() {
+//    let list = LinkedList<Int>()
+//    list.append(123)
+//
+//    let value = list.remove(atIndex: 0)
+//    XCTAssertEqual(value, 123)
+//
+//    XCTAssertTrue(list.isEmpty)
+//    XCTAssertEqual(list.count, 0)
+//    XCTAssertNil(list.first)
+//    XCTAssertNil(list.last)
+//  }
+//
+//  func testRemoveAtIndex() {
+//    let list = buildList()
+//    let prev = list.node(atIndex: 2)
+//    let next = list.node(atIndex: 3)
+//    let nodeCount = list.count
+//
+//    list.insert(444, atIndex: 3)
+//
+//    let value = list.remove(atIndex: 3)
+//    XCTAssertEqual(value, 444)
+//
+//    let node = list.node(atIndex: 3)
+//    XCTAssertTrue(next === node)
+//    XCTAssertTrue(prev!.next === node)
+//    XCTAssertTrue(node!.previous === prev)
+//    XCTAssertEqual(nodeCount, list.count)
+//  }
+//
+//  func testRemoveLastOnListWithOneElement() {
+//    let list = LinkedList<Int>()
+//    list.append(123)
+//
+//    let value = list.removeLast()
+//    XCTAssertEqual(value, 123)
+//
+//    XCTAssertTrue(list.isEmpty)
+//    XCTAssertEqual(list.count, 0)
+//    XCTAssertNil(list.first)
+//    XCTAssertNil(list.last)
+//  }
+//
+//  func testRemoveLast() {
+//    let list = buildList()
+//    let last = list.last
+//    let prev = last!.previous
+//    let nodeCount = list.count
+//
+//    let value = list.removeLast()
+//    XCTAssertEqual(value, 5)
+//
+//    XCTAssertNil(last!.previous)
+//    XCTAssertNil(last!.next)
+//
+//    XCTAssertNil(prev!.next)
+//    XCTAssertTrue(list.last === prev)
+//    XCTAssertEqual(nodeCount - 1, list.count)
+//  }
+//
+//  func testRemoveAll() {
+//    let list = buildList()
+//    list.removeAll()
+//    XCTAssertTrue(list.isEmpty)
+//    XCTAssertEqual(list.count, 0)
+//    XCTAssertNil(list.first)
+//    XCTAssertNil(list.last)
+//  }
+//
+//  func testReverseLinkedList() {
+//    let list = buildList()
+//    let first = list.first
+//    let last = list.last
+//    let nodeCount = list.count
+//
+//    list.reverse()
+//
+//    XCTAssertTrue(first === list.last)
+//    XCTAssertTrue(last === list.first)
+//    XCTAssertEqual(nodeCount, list.count)
+//  }
 }
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj
index d6fb62c9d..cdfd35f71 100644
--- a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -146,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -190,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..dfcf6de42 100644
--- a/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index c2ae29f70..2cea625d1 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1523,6 +1523,35 @@
    <Group
       location = "group:Rootish Array Stack"
       name = "Rootish Array Stack">
+      <Group
+         location = "group:images"
+         name = "images">
+         <FileRef
+            location = "group:RootishArrayStackExample.png">
+         </FileRef>
+         <FileRef
+            location = "group:RootishArrayStackExample2.png">
+         </FileRef>
+         <FileRef
+            location = "group:RootishArrayStackIntro.png">
+         </FileRef>
+      </Group>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:RootishArrayStack.swift">
+         </FileRef>
+         <FileRef
+            location = "group:RootishArrayStackTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
       <FileRef
          location = "group:README.md">
       </FileRef>

From 3a44c0b3c948f43856f0135167934d6ccc6c3077 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Mon, 19 Dec 2016 11:27:18 -0500
Subject: [PATCH 0694/1679] Added tests

---
 .../Tests/RootishArrayStackTests.swift        | 382 ++++++++----------
 .../contents.xcworkspacedata                  |   4 +-
 2 files changed, 170 insertions(+), 216 deletions(-)

diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index 8292f3d30..f73857d0f 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -1,10 +1,22 @@
 import XCTest
 
+fileprivate extension RootishArrayStack {
+	func equal(toArray array: Array<Int>) -> Bool{
+		for index in 0..<count {
+			guard let integerElement = self[index] as? Int else { return false }
+			if (array[index] != integerElement) {
+				return false
+			}
+		}
+		return true
+	}
+}
+
 class RootishArrayStackTests: XCTestCase {
-//  let randomNumbers = [8, 2, 10, 9, 7, 5]
 
-	func buildList(withNumbers numbers: [Int]? = nil) -> RootishArrayStack<Int> {
+	private func buildList(withNumbers numbers: [Int]? = nil) -> RootishArrayStack<Int> {
     var list = RootishArrayStack<Int>()
+
 		if let numbers = numbers {
 			for number in numbers {
 				list.append(element: number)
@@ -14,242 +26,184 @@ class RootishArrayStackTests: XCTestCase {
   }
 
 	func testEmptyList() {
+		let emptyArray = [Int]()
 		let list = buildList()
+
 		XCTAssertTrue(list.isEmpty)
 		XCTAssertEqual(list.count, 0)
 		XCTAssertEqual(list.capacity, 0)
 		XCTAssertNil(list.first)
 		XCTAssertNil(list.last)
+		XCTAssertTrue(list.equal(toArray: emptyArray))
 	}
 
 	func testListWithOneElement() {
-		let list = buildList(withNumbers: [1])
+		let array = [1]
+		let list = buildList(withNumbers: array)
+
 		XCTAssertFalse(list.isEmpty)
 		XCTAssertEqual(list.count, 1)
 		XCTAssertEqual(list.capacity, 1)
 		XCTAssertEqual(list.first, 1)
 		XCTAssertEqual(list.last, 1)
 		XCTAssertEqual(list.first, list.last)
+		XCTAssertTrue(list.equal(toArray: array))
 	}
 
 	func testListWithTwoElements() {
-		let list = buildList(withNumbers: [1, 2])
+		let array = [1, 2]
+		let list = buildList(withNumbers: array)
+
 		XCTAssertFalse(list.isEmpty)
 		XCTAssertEqual(list.count, 2)
 		XCTAssertEqual(list.capacity, 3)
 		XCTAssertEqual(list.first, 1)
 		XCTAssertEqual(list.last, 2)
 		XCTAssertNotEqual(list.first, list.last)
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+	func testListWithThreeElements() {
+		let array = [1, 2, 3]
+		let list = buildList(withNumbers: array)
+
+		XCTAssertFalse(list.isEmpty)
+		XCTAssertEqual(list.count, 3)
+		XCTAssertEqual(list.capacity, 6)
+		XCTAssertEqual(list.first, 1)
+		XCTAssertEqual(list.last, 3)
+		XCTAssertNotEqual(list.first, list.last)
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+	func testFillThenEmpty() {
+		let array = [Int](0..<100)
+		let emptyArray = [Int]()
+		var list = buildList(withNumbers: array)
+
+		XCTAssertTrue(list.equal(toArray: array))
+
+		for _ in 0..<100 {
+			list.remove(atIndex: list.count - 1)
+		}
+
+		XCTAssertEqual(list.count, 0)
+		XCTAssertEqual(list.capacity, 0)
+		XCTAssertTrue(list.equal(toArray: emptyArray))
+	}
+
+	func testInsertFront() {
+		var array = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+		var list = buildList(withNumbers: array)
+
+		XCTAssertEqual(list.count, 10)
+		XCTAssertEqual(list.capacity, 15)
+		XCTAssertEqual(list.first, 1)
+		XCTAssertTrue(list.equal(toArray: array))
+
+		let newElement = 0
+		list.insert(element: newElement, atIndex: 0)
+		array.insert(newElement, at: 0)
+
+		XCTAssertEqual(list.count, 11)
+		XCTAssertEqual(list.capacity, 21)
+		XCTAssertEqual(list.first, newElement)
+		XCTAssertTrue(list.equal(toArray: array))
 	}
 
-//
-//  func testListWithTwoElements() {
-//    var list = RootishArrayStack<Int>()
-//    list.append(123)
-//    list.append(456)
-//
-//    XCTAssertEqual(list.count, 2)
-//
-//    XCTAssertNotNil(list.first)
-//    XCTAssertEqual(list.first!.value, 123)
-//
-//    XCTAssertNotNil(list.last)
-//    XCTAssertEqual(list.last!.value, 456)
-//
-//    XCTAssertTrue(list.first !== list.last)
-//
-//    XCTAssertNil(list.first!.previous)
-//    XCTAssertTrue(list.first!.next === list.last)
-//    XCTAssertTrue(list.last!.previous === list.first)
-//    XCTAssertNil(list.last!.next)
-//  }
-//
-//  func testListWithThreeElements() {
-//    var list = RootishArrayStack<Int>()
-//    list.append(123)
-//    list.append(456)
-//    list.append(789)
-//
-//    XCTAssertEqual(list.count, 3)
-//
-//    XCTAssertNotNil(list.first)
-//    XCTAssertEqual(list.first!.value, 123)
-//
-//    let second = list.first!.next
-//    XCTAssertNotNil(second)
-//    XCTAssertEqual(second!.value, 456)
-//
-//    XCTAssertNotNil(list.last)
-//    XCTAssertEqual(list.last!.value, 789)
-//
-//    XCTAssertNil(list.first!.previous)
-//    XCTAssertTrue(list.first!.next === second)
-//    XCTAssertTrue(second!.previous === list.first)
-//    XCTAssertTrue(second!.next === list.last)
-//    XCTAssertTrue(list.last!.previous === second)
-//    XCTAssertNil(list.last!.next)
-//  }
-//
-//  func testNodeAtIndexInEmptyList() {
-//    var list = RootishArrayStack<Int>()
-//    let node = list.node(atIndex: 0)
-//    XCTAssertNil(node)
-//  }
-//
-//  func testNodeAtIndexInListWithOneElement() {
-//    let list = RootishArrayStack<Int>()
-//    list.append(123)
-//
-//    let node = list.node(atIndex: 0)
-//    XCTAssertNotNil(node)
-//    XCTAssertEqual(node!.value, 123)
-//    XCTAssertTrue(node === list.first)
-//  }
-//
-//  func testNodeAtIndex() {
-//    let list = buildList()
-//
-//    let nodeCount = list.count
-//    XCTAssertEqual(nodeCount, numbers.count)
-//
-//    XCTAssertNil(list.node(atIndex: -1))
-//    XCTAssertNil(list.node(atIndex: nodeCount))
-//
-//    let first = list.node(atIndex: 0)
-//    XCTAssertNotNil(first)
-//    XCTAssertTrue(first === list.first)
-//    XCTAssertEqual(first!.value, numbers[0])
-//
-//    let last = list.node(atIndex: nodeCount - 1)
-//    XCTAssertNotNil(last)
-//    XCTAssertTrue(last === list.last)
-//    XCTAssertEqual(last!.value, numbers[nodeCount - 1])
-//
-//    for i in 0..<nodeCount {
-//      let node = list.node(atIndex: i)
-//      XCTAssertNotNil(node)
-//      XCTAssertEqual(node!.value, numbers[i])
-//    }
-//  }
-//
-//  func testSubscript() {
-//    let list = buildList()
-//    for i in 0 ..< list.count {
-//      XCTAssertEqual(list[i], numbers[i])
-//    }
-//  }
-//
-//  func testInsertAtIndexInEmptyList() {
-//    let list = RootishArrayStack<Int>()
-//    list.insert(123, atIndex: 0)
-//
-//    XCTAssertFalse(list.isEmpty)
-//    XCTAssertEqual(list.count, 1)
-//
-//    let node = list.node(atIndex: 0)
-//    XCTAssertNotNil(node)
-//    XCTAssertEqual(node!.value, 123)
-//  }
-//
-//  func testInsertAtIndex() {
-//    let list = buildList()
-//    let prev = list.node(atIndex: 2)
-//    let next = list.node(atIndex: 3)
-//    let nodeCount = list.count
-//
-//    list.insert(444, atIndex: 3)
-//
-//    let node = list.node(atIndex: 3)
-//    XCTAssertNotNil(node)
-//    XCTAssertEqual(node!.value, 444)
-//    XCTAssertEqual(nodeCount + 1, list.count)
-//
-//    XCTAssertFalse(prev === node)
-//    XCTAssertFalse(next === node)
-//    XCTAssertTrue(prev!.next === node)
-//    XCTAssertTrue(next!.previous === node)
-//  }
-//
-//  func testRemoveAtIndexOnListWithOneElement() {
-//    let list = LinkedList<Int>()
-//    list.append(123)
-//
-//    let value = list.remove(atIndex: 0)
-//    XCTAssertEqual(value, 123)
-//
-//    XCTAssertTrue(list.isEmpty)
-//    XCTAssertEqual(list.count, 0)
-//    XCTAssertNil(list.first)
-//    XCTAssertNil(list.last)
-//  }
-//
-//  func testRemoveAtIndex() {
-//    let list = buildList()
-//    let prev = list.node(atIndex: 2)
-//    let next = list.node(atIndex: 3)
-//    let nodeCount = list.count
-//
-//    list.insert(444, atIndex: 3)
-//
-//    let value = list.remove(atIndex: 3)
-//    XCTAssertEqual(value, 444)
-//
-//    let node = list.node(atIndex: 3)
-//    XCTAssertTrue(next === node)
-//    XCTAssertTrue(prev!.next === node)
-//    XCTAssertTrue(node!.previous === prev)
-//    XCTAssertEqual(nodeCount, list.count)
-//  }
-//
-//  func testRemoveLastOnListWithOneElement() {
-//    let list = LinkedList<Int>()
-//    list.append(123)
-//
-//    let value = list.removeLast()
-//    XCTAssertEqual(value, 123)
-//
-//    XCTAssertTrue(list.isEmpty)
-//    XCTAssertEqual(list.count, 0)
-//    XCTAssertNil(list.first)
-//    XCTAssertNil(list.last)
-//  }
-//
-//  func testRemoveLast() {
-//    let list = buildList()
-//    let last = list.last
-//    let prev = last!.previous
-//    let nodeCount = list.count
-//
-//    let value = list.removeLast()
-//    XCTAssertEqual(value, 5)
-//
-//    XCTAssertNil(last!.previous)
-//    XCTAssertNil(last!.next)
-//
-//    XCTAssertNil(prev!.next)
-//    XCTAssertTrue(list.last === prev)
-//    XCTAssertEqual(nodeCount - 1, list.count)
-//  }
-//
-//  func testRemoveAll() {
-//    let list = buildList()
-//    list.removeAll()
-//    XCTAssertTrue(list.isEmpty)
-//    XCTAssertEqual(list.count, 0)
-//    XCTAssertNil(list.first)
-//    XCTAssertNil(list.last)
-//  }
-//
-//  func testReverseLinkedList() {
-//    let list = buildList()
-//    let first = list.first
-//    let last = list.last
-//    let nodeCount = list.count
-//
-//    list.reverse()
-//
-//    XCTAssertTrue(first === list.last)
-//    XCTAssertTrue(last === list.first)
-//    XCTAssertEqual(nodeCount, list.count)
-//  }
+	func testInsertMiddle() {
+		var array = [0, 2, 3]
+		var list = buildList(withNumbers: array)
+
+		XCTAssertEqual(list.count, 3)
+		XCTAssertEqual(list.capacity, 6)
+		XCTAssertTrue(list.equal(toArray: array))
+
+		let newElement = 1
+		list.insert(element: newElement, atIndex: 1)
+		array.insert(newElement, at: 1)
+
+		XCTAssertEqual(list.count, 4)
+		XCTAssertEqual(list.capacity, 10)
+		XCTAssertEqual(list[1], newElement)
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+	func testSubscriptGet() {
+		let array = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+		let list = buildList(withNumbers: array)
+		for index in 0...9 {
+			XCTAssertEqual(list[index], index)
+		}
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+	func testSubscriptSet() {
+		var array = [Int](0..<10)
+		var list = buildList(withNumbers: array)
+
+		list[1] = 100
+		list[5] = 500
+		list[8] = 800
+		array[1] = 100
+		array[5] = 500
+		array[8] = 800
+
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+	func testRemoveFirst() {
+		var array = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+		var list = buildList(withNumbers: array)
+
+		XCTAssertEqual(list.count, 10)
+		XCTAssertEqual(list.capacity, 15)
+		XCTAssertEqual(list.first, 1)
+		XCTAssertTrue(list.equal(toArray: array))
+
+		list.remove(atIndex: 0)
+		array.remove(at: 0)
+
+		XCTAssertEqual(list.count, 9)
+		XCTAssertEqual(list.capacity, 15)
+		XCTAssertEqual(list.first, 2)
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+
+	func testRemoveMiddle() {
+		var array = [0, 1, 2, 3]
+		var list = buildList(withNumbers: array)
+
+		XCTAssertEqual(list.count, 4)
+		XCTAssertEqual(list.capacity, 10)
+		XCTAssertEqual(list.first, 0)
+		XCTAssertTrue(list.equal(toArray: array))
+
+		list.remove(atIndex: 2)
+		array.remove(at: 2)
+
+		XCTAssertEqual(list.count, 3)
+		XCTAssertEqual(list.capacity, 6)
+		XCTAssertEqual(list.first, 0)
+		XCTAssertTrue(list.equal(toArray: array))
+	}
+
+	func testRemoveLast() {
+		var array = [0, 1, 2, 3]
+		var list = buildList(withNumbers: array)
+
+		XCTAssertEqual(list.count, 4)
+		XCTAssertEqual(list.capacity, 10)
+		XCTAssertEqual(list.first, 0)
+		XCTAssertTrue(list.equal(toArray: array))
+
+		list.remove(atIndex: 3)
+		array.remove(at: 3)
+
+		XCTAssertEqual(list.count, 3)
+		XCTAssertEqual(list.capacity, 6)
+		XCTAssertEqual(list.first, 0)
+		XCTAssertTrue(list.equal(toArray: array))
+	}
 }
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 2cea625d1..194c0ae79 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1543,10 +1543,10 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:RootishArrayStack.swift">
+            location = "group:RootishArrayStackTests.swift">
          </FileRef>
          <FileRef
-            location = "group:RootishArrayStackTests.swift">
+            location = "group:RootishArrayStack.swift">
          </FileRef>
          <FileRef
             location = "group:Tests.xcodeproj">

From 3b5a508c8d16bbbfbff3ea5b1028b286464d22d5 Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Tue, 20 Dec 2016 20:46:30 -0500
Subject: [PATCH 0695/1679] Added Rootish Array Stack to Readme

---
 README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.markdown b/README.markdown
index 4c812b0f3..d4637f7c0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -130,6 +130,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Bit Set](Bit Set/). A fixed-size sequence of *n* bits.
 - [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
 - [Ordered Array](Ordered Array/). An array that is always sorted.
+- [Rootish Array Stack](Rootish Array Stack/). A space and time efficient variation on Swift arrays.
 
 ### Queues
 
@@ -205,6 +206,7 @@ The following books are available for free online:
 - [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
 - [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
 - Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
+- [Open Data Structures](http://opendatastructures.org) by Pat Morin
 - [Wikibooks: Algorithms and Implementations](https://en.wikibooks.org/wiki/Algorithm_Implementation)
 
 Other algorithm repositories:

From 0ffeb21dc6ec1e2a2146a43800b3c058c403a435 Mon Sep 17 00:00:00 2001
From: Stefan Cimander <stefan.cimander@me.com>
Date: Wed, 21 Dec 2016 18:20:18 +0100
Subject: [PATCH 0696/1679] Fix typo in ReadMe

---
 Trie/ReadMe.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 172ff4750..7caa927a7 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -36,7 +36,7 @@ func contains(word: String) -> Bool {
  
 	// 3
 	while currentIndex < characters.count, 
-	  let child = currentNode.children[character[currentIndex]] {
+	  let child = currentNode.children[characters[currentIndex]] {
 
 	  currentNode = child
 	  currentIndex += 1

From 22675cf8d18407a6618909a0d3bb916dbe69762f Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:03:18 +0100
Subject: [PATCH 0697/1679] Add new images;

---
 AVL Tree/Images/Rotation.jpg      | Bin 35153 -> 0 bytes
 AVL Tree/Images/RotationStep0.jpg | Bin 0 -> 22802 bytes
 AVL Tree/Images/RotationStep1.jpg | Bin 0 -> 18406 bytes
 AVL Tree/Images/RotationStep2.jpg | Bin 0 -> 18836 bytes
 AVL Tree/Images/RotationStep3.jpg | Bin 0 -> 18108 bytes
 5 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 AVL Tree/Images/Rotation.jpg
 create mode 100644 AVL Tree/Images/RotationStep0.jpg
 create mode 100644 AVL Tree/Images/RotationStep1.jpg
 create mode 100644 AVL Tree/Images/RotationStep2.jpg
 create mode 100644 AVL Tree/Images/RotationStep3.jpg

diff --git a/AVL Tree/Images/Rotation.jpg b/AVL Tree/Images/Rotation.jpg
deleted file mode 100644
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From 5cc12cd45f6a386788d9cb98065953c448130e19 Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:08:24 +0100
Subject: [PATCH 0698/1679] Update images;

---
 AVL Tree/Images/RotationStep0.jpg | Bin 22802 -> 9159 bytes
 AVL Tree/Images/RotationStep1.jpg | Bin 18406 -> 8046 bytes
 AVL Tree/Images/RotationStep2.jpg | Bin 18836 -> 8277 bytes
 AVL Tree/Images/RotationStep3.jpg | Bin 18108 -> 7430 bytes
 4 files changed, 0 insertions(+), 0 deletions(-)

diff --git a/AVL Tree/Images/RotationStep0.jpg b/AVL Tree/Images/RotationStep0.jpg
index 156b18062e84cd5bd05a5557c80404ee6aa9636f..99b69d3e0f58e0faf7d98ecd0a0daf30e2e48640 100644
GIT binary patch
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From 2f8f348816ee0b9ef8bf52a23cc60883a7486e79 Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:13:05 +0100
Subject: [PATCH 0699/1679] Update readme;

---
 AVL Tree/README.markdown | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index bcbbbabbc..9deea5649 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -45,20 +45,21 @@ If after an insertion or deletion the balance factor becomes greater than 1, the
 ## Rotations
 Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.
 
-Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation :
-![Rotation](Images/Rotation.jpg)
+Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation:
+![Rotation0](Images/RotationStep0.jpg)
 
-Let's dig into rotation algorithm in detail using the terminology:
+For the rotation we're using the terminology:
 * *Root* - the parent not of the subtrees that will be rotated;
 * *Pivot* - the node that will become parent (basically will be on the *Root*'s position) after rotation;
 * *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
 * *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation
 
+![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)
+
 The steps of rotation on the example image could be described by following:
-* Select the *Pivot* as `D` and hence the *Root* as `F`;
-* Assign the *RotationSubtree* as a new *OppositeSubtree* for the *Root*;
-* Assign the *Root* as a new *RotationSubtree* for the *Pivot*;
-* Check the final result
+1. Assign the *RotationSubtree* as a new *OppositeSubtree* for the *Root*;
+2. Assign the *Root* as a new *RotationSubtree* for the *Pivot*;
+3. Check the final result
 
 In pseudocode the algorithm above could be written as follows:
 ```

From 341c504c3508ef0ffd3dd111c06e4eb128106d46 Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:14:46 +0100
Subject: [PATCH 0700/1679] Update readme;

---
 AVL Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 9deea5649..25073f260 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -45,7 +45,7 @@ If after an insertion or deletion the balance factor becomes greater than 1, the
 ## Rotations
 Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.
 
-Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation:
+Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation:  
 ![Rotation0](Images/RotationStep0.jpg)
 
 For the rotation we're using the terminology:

From 047de8fdfe7221aaca2d0ad3a39be58ed5e11f25 Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:20:47 +0100
Subject: [PATCH 0701/1679] Update readme;

---
 AVL Tree/Images/RotationStep0.jpg | Bin 9159 -> 22246 bytes
 AVL Tree/Images/RotationStep1.jpg | Bin 8046 -> 18235 bytes
 AVL Tree/Images/RotationStep2.jpg | Bin 8277 -> 18777 bytes
 AVL Tree/Images/RotationStep3.jpg | Bin 7430 -> 18265 bytes
 AVL Tree/README.markdown          |   2 +-
 5 files changed, 1 insertion(+), 1 deletion(-)

diff --git a/AVL Tree/Images/RotationStep0.jpg b/AVL Tree/Images/RotationStep0.jpg
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diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 25073f260..9254ffedf 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -56,7 +56,7 @@ For the rotation we're using the terminology:
 
 ![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)
 
-The steps of rotation on the example image could be described by following:
+The steps of rotation on the example image could be described by following:  
 1. Assign the *RotationSubtree* as a new *OppositeSubtree* for the *Root*;
 2. Assign the *Root* as a new *RotationSubtree* for the *Pivot*;
 3. Check the final result

From 3f30747694400904d889588aec00133dcfef45b0 Mon Sep 17 00:00:00 2001
From: Anton Domashnev <antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:25:58 +0100
Subject: [PATCH 0702/1679] Update readme;

---
 AVL Tree/Images/RotationStep1.jpg | Bin 18235 -> 13059 bytes
 AVL Tree/Images/RotationStep2.jpg | Bin 18777 -> 13357 bytes
 AVL Tree/Images/RotationStep3.jpg | Bin 18265 -> 12998 bytes
 3 files changed, 0 insertions(+), 0 deletions(-)

diff --git a/AVL Tree/Images/RotationStep1.jpg b/AVL Tree/Images/RotationStep1.jpg
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z{J@5H*bJ7>S~hGIfUDo2hp)$Ur8dK^e$fx?&zF1Ulg~Z;qG`k4`Gbkpa8rki|H6?e
zp$w)tHMcCU4vST!C-zZjLA`fJ;8B`ns!hhN)-m^-#cSg~fMQ;qYTCBzYS^|6tzs{`
z9((T-M)@VXIFqYB0498%yD)~9u>#E8gibXk-rytzXYTGRkow|WAlFKLonDStviKv1
zw*F+%O@@b%c1q=YqeF)NJhT5;<!S$aC9eB22_OKDFrvSCOD{wSavSwd1}*3762C27
zCS^S-`3sIX`Qd380XJte8039MIDhiiTUSZ+JJi!ZixG1BfS8SMfnJXEtiCzZ4LN@I
zZnkx63^jZNZdH0|L(Va@E{!$q%9T+uUCMK;$LIylbLwhs@6kYMTy#8KbSz{L84GSy
zy-(vMRn@V(kG8p=6Ku*Jm5eo?=+4u%GwD=*W=+m?4j;bM?+HRg+g|stx&7hMscILG
zlpFs?y?acX{UQWdv8=}!!a3_;`|$v?05JJ_lW6t&ADH}}Y;%IiADCSEa@9HvlmpsJ
z_!9|Nfba4Ef$)uy;=fR|z{s~gQ)WDWp=cNGhFHFEPWpqQZLh4!@FzbAix7iPcGZQT
z1Q;XW<^=U843V!;JUg1-rGWC1Qed0hfISXvdXj`&Zc<NdSKxg5X|T*yPN?jqU=!)%
z$ei&$2XTggeT3$ru$fX^i2WALBXC^;)vW5=8t08^?)J7L{O5-sf^>j&H|gdIK#kbH
z7v29ZSp2gj97t{GG)T%&7Kt-|QXBrPGm)k?WBxzTQOGf|x_rPtWpgCG$INFzh}K$}
zQnx6Ue^PTZS=?TN6Kb6j?9soM;@q1D`tRD~pWCnkL9#jl#qN_eCqm3B@GtRgGLvm?
ztdGAPBPStve(^{Jy2Gv6=N~1yf2&?Q-DXTk<)&aRe;`gJ22&&Lt=f$wdaJ)%>hZr>
zMTtMk%>J5W-@T3OR0R^dmb#WjH2L9k*F#l@eTJJd11uvKZr8$Oez($I?V&I}uX%C|
zxEOulI(r~rY`viV2+!RH<cn{vyDi#|?aaUeOQm*j>xu>HG;SO^`#)LYt@0C@1fXrH
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zx@hfkg$XvNsS+(>E86a}-h{ZFacZz(>#+Op%#asFgDT7zfYhU_fl^pDxYnQKr&DcW
zvZ?i$KLPy;IR<@~562L-{q|k|ZT<VfKNV8{Z2`ys#`d3U7XLTy`L}x<{8Me#-~RvK
T*#5mb;Xh%Z|G)P?nErnNyi*J7


From 2c7fd0cf36b8b398a1a5eef679f484224a4294da Mon Sep 17 00:00:00 2001
From: Anton <Antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:27:41 +0100
Subject: [PATCH 0703/1679] Update README.markdown

---
 AVL Tree/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 9254ffedf..eaa4aa3c3 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -57,6 +57,7 @@ For the rotation we're using the terminology:
 ![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)
 
 The steps of rotation on the example image could be described by following:  
+
 1. Assign the *RotationSubtree* as a new *OppositeSubtree* for the *Root*;
 2. Assign the *Root* as a new *RotationSubtree* for the *Pivot*;
 3. Check the final result

From 39ac2ec3c36cf0cdf239d2b9b279258bd0f96dbb Mon Sep 17 00:00:00 2001
From: Anton <Antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:30:49 +0100
Subject: [PATCH 0704/1679] Update README.markdown

---
 AVL Tree/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index eaa4aa3c3..8358fde9c 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -62,6 +62,7 @@ The steps of rotation on the example image could be described by following:
 2. Assign the *Root* as a new *RotationSubtree* for the *Pivot*;
 3. Check the final result
 
+
 In pseudocode the algorithm above could be written as follows:
 ```
 Root.OS = Pivot.RS

From 9ecd211c61cfd4baab2665b10dc7c79547f5ec4b Mon Sep 17 00:00:00 2001
From: Anton <Antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:31:44 +0100
Subject: [PATCH 0705/1679] Update README.markdown

---
 AVL Tree/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 8358fde9c..86b631ae8 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -45,7 +45,8 @@ If after an insertion or deletion the balance factor becomes greater than 1, the
 ## Rotations
 Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.
 
-Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation:  
+Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation: 
+
 ![Rotation0](Images/RotationStep0.jpg)
 
 For the rotation we're using the terminology:

From bd645f33bc3640586c992e6b2c54728b4e50bccb Mon Sep 17 00:00:00 2001
From: Anton <Antondomashnev@gmail.com>
Date: Wed, 21 Dec 2016 23:33:22 +0100
Subject: [PATCH 0706/1679] Update README.markdown

---
 AVL Tree/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 86b631ae8..355204587 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -45,8 +45,6 @@ If after an insertion or deletion the balance factor becomes greater than 1, the
 ## Rotations
 Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.
 
-Example of balancing the unbalanced tree using *Right* (clockwise direction) rotation: 
-
 ![Rotation0](Images/RotationStep0.jpg)
 
 For the rotation we're using the terminology:
@@ -55,9 +53,11 @@ For the rotation we're using the terminology:
 * *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
 * *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation
 
+Let take an example of balancing the unbalanced tree using *Right* (clockwise direction) rotation: 
+
 ![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)
 
-The steps of rotation on the example image could be described by following:  
+The steps of rotation could be described by following:  
 
 1. Assign the *RotationSubtree* as a new *OppositeSubtree* for the *Root*;
 2. Assign the *Root* as a new *RotationSubtree* for the *Pivot*;

From b64df56ea624b77b126cbc64d42ab7d687f05e1e Mon Sep 17 00:00:00 2001
From: BenEmdon <benjaminemdon@gmail.com>
Date: Thu, 22 Dec 2016 00:35:37 -0500
Subject: [PATCH 0707/1679] Fixed comment spacing in playground

---
 .../Contents.swift                            | 72 +++++++++----------
 1 file changed, 36 insertions(+), 36 deletions(-)

diff --git a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift
index 401c773d6..68ec0a53e 100644
--- a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
+++ b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
@@ -144,22 +144,22 @@ extension RootishArrayStack: CustomStringConvertible {
 }
 
 var list = RootishArrayStack<String>()
-list.isEmpty								// true
-list.first									// nil
-list.last										// nil
-list.count									// 0
-list.capacity								// 0
+list.isEmpty   // true
+list.first     // nil
+list.last      // nil
+list.count     // 0
+list.capacity  // 0
 
 list.memoryDescription
 //	{
 //	}
 
 list.append(element: "Hello")
-list.isEmpty								// false
-list.first									// "Hello"
-list.last										// "hello"
-list.count									// 1
-list.capacity								// 1
+list.isEmpty  // false
+list.first    // "Hello"
+list.last     // "hello"
+list.count    // 1
+list.capacity // 1
 
 list.memoryDescription
 //	{
@@ -167,15 +167,15 @@ list.memoryDescription
 //	}
 
 list.append(element: "World")
-list.isEmpty								// false
-list.first									// "Hello"
-list.last										// "World"
-list.count									// 2
-list.capacity								// 3
+list.isEmpty  // false
+list.first    // "Hello"
+list.last     // "World"
+list.count    // 2
+list.capacity // 3
 
-list[0]											// "Hello"
-list[1]											// "World"
-//list[2]										// crash!
+list[0]       // "Hello"
+list[1]       // "World"
+//list[2]     // crash!
 
 
 list.memoryDescription
@@ -186,15 +186,15 @@ list.memoryDescription
 
 
 list.insert(element: "Swift", atIndex: 1)
-list.isEmpty								// false
-list.first									// "Hello"
-list.last										// "World"
-list.count									// 3
-list.capacity								// 6
+list.isEmpty  // false
+list.first    // "Hello"
+list.last     // "World"
+list.count    // 3
+list.capacity // 6
 
-list[0]											// "Hello"
-list[1]											// "Swift"
-list[2]											// "World"
+list[0]  // "Hello"
+list[1]  // "Swift"
+list[2]  // "World"
 
 list.memoryDescription
 //	{
@@ -203,17 +203,17 @@ list.memoryDescription
 //		[nil, nil, nil]
 //	}
 
-list.remove(atIndex: 2)			// "World"
-list.isEmpty								// false
-list.first									// "Hello"
-list.last										// "Swift"
-list.count									// 2
-list.capacity								// 3
+list.remove(atIndex: 2)  // "World"
+list.isEmpty  // false
+list.first    // "Hello"
+list.last     // "Swift"
+list.count    // 2
+list.capacity // 3
 
-list[0]											// "Hello"
-list[1]											// "Swift"
-//list[2]										// crash!
+list[0]    // "Hello"
+list[1]    // "Swift"
+//list[2]  // crash!
 
 list[0] = list[1]
 list[1] = "is awesome"
-list												// ["Swift", "is awesome"]
+list       // ["Swift", "is awesome"]

From 3dd067453818046186792746479bdd4986c3ef7b Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:13:39 -0700
Subject: [PATCH 0708/1679] Update palindrome swift file contents

---
 Palindromes/Palindromes.swift | 35 ++++++++++++++++++++++-------------
 1 file changed, 22 insertions(+), 13 deletions(-)

diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 889ff357e..2760137ca 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -1,17 +1,26 @@
-import Cocoa
+import Foundation
 
-public func palindromeCheck(text: String?) -> Bool {
-  if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
-    let length: Int = mutableText.characters.count
+func isPalindrome(_ str: String) -> Bool {
+    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+    let length = strippedString.characters.count
     
-    if length == 1 || length == 0 {
-      return true
-    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
-      let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
-      return palindromeCheck(text: mutableText.substring(with: range))
+    if length > 1 {
+        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
     }
-  }
-  
-  return false
+    return false
+}
+
+private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
+    if left >= right {
+        return true
+    }
+    
+    let lhs = str[str.index(str.startIndex, offsetBy: left)]
+    let rhs = str[str.index(str.startIndex, offsetBy: right)]
+    
+    if lhs != rhs {
+        return false
+    }
+    
+    return palindrome(str, left: left + 1, right: right - 1)
 }

From fe93184c3899f0ee6aebc23c453ce14fbddf4db8 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:13:57 -0700
Subject: [PATCH 0709/1679] Update palindrome playground

---
 .../Palindromes.playground/Contents.swift     | 81 ++++++++++++-------
 1 file changed, 54 insertions(+), 27 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index bb666ee9a..e8562a367 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -1,34 +1,61 @@
-import Cocoa
+//: Playground - noun: a place where people can play
 
-public func palindromeCheck(text: String?) -> Bool {
-  if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces).lowercased()
-    let length: Int = mutableText.characters.count
+import Foundation
+
+/**
+ Validate that a string is a plaindrome
+ - parameter str: The string to validate
+ - returns: `true` if string is plaindrome, `false` if string is not
+ */
+func isPalindrome(_ str: String) -> Bool {
+    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+    let length = strippedString.characters.count
     
-    if length == 1 || length == 0 {
-      return true
-    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
-      let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
-      return palindromeCheck(text: mutableText.substring(with: range))
+    if length > 1 {
+        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
     }
-  }
-  
-  return false
+    return false
 }
 
-// Test to check that non-palindromes are handled correctly:
-palindromeCheck(text: "owls")
-
-// Test to check that palindromes are accurately found (regardless of case and whitespace:
-palindromeCheck(text: "lol")
-palindromeCheck(text: "race car")
-palindromeCheck(text: "Race fast Safe car")
-
-// Test to check that palindromes are found regardless of case:
-palindromeCheck(text: "HelloLLEH")
+/**
+ Compares a strings left side character against right side character following
+ - parameter str: The string to compare characters of
+ - parameter left: Index of left side to compare, must be less than or equal to right
+ - parameter right: Index of right side to compare, must be greater than or equal to left
+ - returns: `true` if left side and right side have all been compared and they all match, `false` if a left and right aren't equal
+ */
+private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
+    if left >= right {
+        return true
+    }
+    
+    let lhs = str[str.index(str.startIndex, offsetBy: left)]
+    let rhs = str[str.index(str.startIndex, offsetBy: right)]
+    
+    if lhs != rhs {
+        return false
+    }
+    
+    return palindrome(str, left: left + 1, right: right - 1)
+}
 
-palindromeCheck(text: "moom")
+//true
+isPalindrome("A man, a plan, a canal, Panama!")
+isPalindrome("abbcbba")
+isPalindrome("racecar")
+isPalindrome("Madam, I'm Adam")
+isPalindrome("Madam in Eden, I'm Adam")
+isPalindrome("Never odd or even")
+isPalindrome("5885")
+isPalindrome("5 8 8 5")
+isPalindrome("58 85")
+isPalindrome("৯৯")
+isPalindrome("In girum imus nocte et consumimur igni")
 
-// Test that nil and empty Strings return false:
-palindromeCheck(text: "")
-palindromeCheck(text: nil)
+// false
+isPalindrome("\\\\")
+isPalindrome("desserts")
+isPalindrome("😀😀")
+isPalindrome("")
+isPalindrome("a")
+isPalindrome("power")

From 33048487610b59b9c7e09cafb1f33573bda5e252 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:15:07 -0700
Subject: [PATCH 0710/1679] Update the read for palindromes

---
 Palindromes/README.markdown | 101 ++++++++++++++++++++++++------------
 1 file changed, 68 insertions(+), 33 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 12f868251..fe31cf297 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -1,64 +1,99 @@
 # Palindromes
 
-A palindrome is a word or phrase that is spelled the exact same when read forwards or backwards. 
-For this example puzzle, palindromes will not take case into account, meaning that uppercase and
-lowercase text will be treated the same. In addition, spaces will not be considered, allowing 
-for multi-word phrases to constitute palindromes too. 
+A palindrome is a word or phrase that is spelled the exact same when reading it forwards or backward. Palindromes are allowed to be lowercase or uppercase, contain spaces, punctuation, and word dividers.
 
 Algorithms that check for palindromes are a common programming interview question. 
 
 ## Example 
 
-The word "radar" is spelled the exact same both forwards and backwards, and as a result is a palindrome. 
-The phrase "race car" is another common palindrome that is spelled the same forwards and backwards. 
+The word racecar is a valid palindrome, as it is a word spelled the same when backgrounds and forwards. The examples below shows valid cases of the palindrome `racecar`.
+`raceCar`
+`r a c e c a r`
+`r?a?c?e?c?a?r?`
+`RACEcar`
 
 ## Algorithm 
 
-To check for palindromes, the first and last characters of a String must be compared for equality. 
-When the first and last characters are the same, they are removed from the String, resulting in a 
-substring starting with the second character and ending at the second to last character. 
+To check for palindromes, a strings character are compared starting from the beginning and end and moving inward moving to toward the middle of the string and keep the same distance apart in the comparison index.
 
-In this implementation of a palindrome checker, recursion is used to check each substring of the 
-original String. 
+In this implementation of a palindrome algorithm, recursion is used to check each of the characters on the left-hand side and right-hand side moving inward.
 
 ## The code 
 
 Here is a recursive implementation of this in Swift: 
 
 ```swift
-func palindromeCheck (text: String?) -> Bool {
-  if let text = text {
-    let mutableText = text.trimmingCharacters(in: NSCharacterSet.whitespaces()).lowercased()
-    let length: Int = mutableText.characters.count
-    
-    guard length >= 1 else {
-      return false
-    }
-
-    if length == 1 {
-      return true
-    } else if mutableText[mutableText.startIndex] == mutableText[mutableText.index(mutableText.endIndex, offsetBy: -1)] {
-      let range = Range<String.Index>(mutableText.index(mutableText.startIndex, offsetBy: 1)..<mutableText.index(mutableText.endIndex, offsetBy: -1))
-      return palindromeCheck(text: mutableText.substring(with: range))
-    }
-  }
-
-  return false
+func isPalindrome(_ str: String) -> Bool {
+let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+let length = strippedString.characters.count
+
+if length > 1 {
+return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+}
+return false
+}
+
+private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
+if left >= right {
+return true
+}
+
+let lhs = str[str.index(str.startIndex, offsetBy: left)]
+let rhs = str[str.index(str.startIndex, offsetBy: right)]
+
+if lhs != rhs {
+return false
 }
+
+return palindrome(str, left: left + 1, right: right - 1)
+}
+```
+
+This algorithm has a two-step process. 
+1. The first step is to pass the string to validate as a palindrome into the `isPalindrome` method. This method first removes occurrences of non-word pattern matches `\W` [Regex reference](http://regexr.com). It is written with two \\ to escape the \ in the String literal. 
+
+```swift
+let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
 ```
 
+The length of the string is then checked to make sure that the string after being stripped of non-word characters is still in a valid length. It is then passed into the next step after being lowercased.
 
-This code can be tested in a playground using the following: 
+2. The second step is to pass the string in a recursive method. This method takes a string, a left index, and a right index. The method checks the characters of the string using the indexes to compare each character on both sides. The method checks if the left is greater or equal to the right if so the entire string has been run through without returning false so the string is equal on both sides thus returning true. 
+```swift
+if left >= right {
+return true
+}
+```
+If the check doesn't pass it continues to get the characters at the specified indexes and compare each. If they are not the same the method returns false and exits. 
+```swift
+let lhs = str[str.index(str.startIndex, offsetBy: left)]
+let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
+if lhs != rhs {
+return false
+}
+```
+If they are the same the method calls itself again and updates the indexes accordingly to continue to check the rest of the string. 
 ```swift
-palindromeCheck(text: "Race car")
+return palindrome(str, left: left + 1, right: right - 1)
 ```
 
-Since the phrase "Race car" is a palindrome, this will return true. 
+Step 1:
+` race?C ar -> raceCar -> racecar``
+
+Step 2:
+|     |
+racecar -> r == r
+ |   |
+racecar -> a == a
+  | |
+racecar -> c == c
+   |
+racecar -> left index == right index -> return true
 
 ## Additional Resources
 
 [Palindrome Wikipedia](https://en.wikipedia.org/wiki/Palindrome)
 
 
-*Written by [Stephen Rutstein](https://github.com/srutstein21)*
+*Written by [Joshua Alvarado](https://github.com/https://github.com/lostatseajoshua)*

From 0ffeb1fdd0d4568270b4bef42fef73e89fb108d9 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:28:44 -0700
Subject: [PATCH 0711/1679] Update README formatting

---
 Palindromes/README.markdown | 48 ++++++++++++++++++++-----------------
 1 file changed, 26 insertions(+), 22 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index fe31cf297..48420f323 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -7,6 +7,7 @@ Algorithms that check for palindromes are a common programming interview questio
 ## Example 
 
 The word racecar is a valid palindrome, as it is a word spelled the same when backgrounds and forwards. The examples below shows valid cases of the palindrome `racecar`.
+
 `raceCar`
 `r a c e c a r`
 `r?a?c?e?c?a?r?`
@@ -14,9 +15,7 @@ The word racecar is a valid palindrome, as it is a word spelled the same when ba
 
 ## Algorithm 
 
-To check for palindromes, a strings character are compared starting from the beginning and end and moving inward moving to toward the middle of the string and keep the same distance apart in the comparison index.
-
-In this implementation of a palindrome algorithm, recursion is used to check each of the characters on the left-hand side and right-hand side moving inward.
+To check for palindromes, a string's characters are compared starting from the beginning and end then moving inward toward the middle of the string while maintaining the same distance apart. In this implementation of a palindrome algorithm, recursion is used to check each of the characters on the left-hand side and right-hand side moving inward.
 
 ## The code 
 
@@ -24,32 +23,33 @@ Here is a recursive implementation of this in Swift:
 
 ```swift
 func isPalindrome(_ str: String) -> Bool {
-let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-let length = strippedString.characters.count
+  let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+  let length = strippedString.characters.count
 
-if length > 1 {
-return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-}
-return false
+  if length > 1 {
+    return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+  }
+    return false
 }
 
 private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-if left >= right {
-return true
-}
+  if left >= right {
+    return true
+  }
 
-let lhs = str[str.index(str.startIndex, offsetBy: left)]
-let rhs = str[str.index(str.startIndex, offsetBy: right)]
+  let lhs = str[str.index(str.startIndex, offsetBy: left)]
+  let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
-if lhs != rhs {
-return false
-}
+  if lhs != rhs {
+    return false
+  }
 
-return palindrome(str, left: left + 1, right: right - 1)
+  return palindrome(str, left: left + 1, right: right - 1)
 }
 ```
 
-This algorithm has a two-step process. 
+This algorithm has a two-step process.
+
 1. The first step is to pass the string to validate as a palindrome into the `isPalindrome` method. This method first removes occurrences of non-word pattern matches `\W` [Regex reference](http://regexr.com). It is written with two \\ to escape the \ in the String literal. 
 
 ```swift
@@ -61,7 +61,7 @@ The length of the string is then checked to make sure that the string after bein
 2. The second step is to pass the string in a recursive method. This method takes a string, a left index, and a right index. The method checks the characters of the string using the indexes to compare each character on both sides. The method checks if the left is greater or equal to the right if so the entire string has been run through without returning false so the string is equal on both sides thus returning true. 
 ```swift
 if left >= right {
-return true
+  return true
 }
 ```
 If the check doesn't pass it continues to get the characters at the specified indexes and compare each. If they are not the same the method returns false and exits. 
@@ -70,7 +70,7 @@ let lhs = str[str.index(str.startIndex, offsetBy: left)]
 let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
 if lhs != rhs {
-return false
+  return false
 }
 ```
 If they are the same the method calls itself again and updates the indexes accordingly to continue to check the rest of the string. 
@@ -82,14 +82,18 @@ Step 1:
 ` race?C ar -> raceCar -> racecar``
 
 Step 2:
+```
 |     |
 racecar -> r == r
+
  |   |
 racecar -> a == a
+
   | |
 racecar -> c == c
+
    |
-racecar -> left index == right index -> return true
+racecar -> left index == right index -> return true```
 
 ## Additional Resources
 

From e4c2889bc3c8b6ba0f9fa47be0b86bb1f5c663d3 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:30:15 -0700
Subject: [PATCH 0712/1679] Fix code snippet from running to the bottom of the
 page

---
 Palindromes/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 48420f323..53a48225a 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -93,7 +93,8 @@ racecar -> a == a
 racecar -> c == c
 
    |
-racecar -> left index == right index -> return true```
+racecar -> left index == right index -> return true
+```
 
 ## Additional Resources
 

From 8c0117dbe7fa5dace9de1492280110f0d6353ea4 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:34:57 -0700
Subject: [PATCH 0713/1679] Fix spacing on list of palindrome examples

---
 Palindromes/README.markdown | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 53a48225a..85bdfc992 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -8,10 +8,12 @@ Algorithms that check for palindromes are a common programming interview questio
 
 The word racecar is a valid palindrome, as it is a word spelled the same when backgrounds and forwards. The examples below shows valid cases of the palindrome `racecar`.
 
-`raceCar`
-`r a c e c a r`
-`r?a?c?e?c?a?r?`
-`RACEcar`
+```
+raceCar
+r a c e c a r
+r?a?c?e?c?a?r?
+RACEcar
+```
 
 ## Algorithm 
 

From 13de04998d7f940c5c98bedb947ccee52fa0fe9d Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:35:38 -0700
Subject: [PATCH 0714/1679] Improved formatting in code and markdown

---
 Palindromes/README.markdown | 47 +++++++++++++++++++------------------
 1 file changed, 24 insertions(+), 23 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 85bdfc992..ede0af39d 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -25,34 +25,34 @@ Here is a recursive implementation of this in Swift:
 
 ```swift
 func isPalindrome(_ str: String) -> Bool {
-  let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-  let length = strippedString.characters.count
+let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+let length = strippedString.characters.count
 
-  if length > 1 {
-    return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-  }
-    return false
+if length > 1 {
+return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+}
+return false
 }
 
 private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-  if left >= right {
-    return true
-  }
+if left >= right {
+return true
+}
 
-  let lhs = str[str.index(str.startIndex, offsetBy: left)]
-  let rhs = str[str.index(str.startIndex, offsetBy: right)]
+let lhs = str[str.index(str.startIndex, offsetBy: left)]
+let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
-  if lhs != rhs {
-    return false
-  }
+if lhs != rhs {
+return false
+}
 
-  return palindrome(str, left: left + 1, right: right - 1)
+return palindrome(str, left: left + 1, right: right - 1)
 }
 ```
 
 This algorithm has a two-step process.
 
-1. The first step is to pass the string to validate as a palindrome into the `isPalindrome` method. This method first removes occurrences of non-word pattern matches `\W` [Regex reference](http://regexr.com). It is written with two \\ to escape the \ in the String literal. 
+1 - The first step is to pass the string to validate as a palindrome into the `isPalindrome` method. This method first removes occurrences of non-word pattern matches `\W` [Regex reference](http://regexr.com). It is written with two \\ to escape the \ in the String literal. 
 
 ```swift
 let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
@@ -60,10 +60,10 @@ let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .reg
 
 The length of the string is then checked to make sure that the string after being stripped of non-word characters is still in a valid length. It is then passed into the next step after being lowercased.
 
-2. The second step is to pass the string in a recursive method. This method takes a string, a left index, and a right index. The method checks the characters of the string using the indexes to compare each character on both sides. The method checks if the left is greater or equal to the right if so the entire string has been run through without returning false so the string is equal on both sides thus returning true. 
+2 - The second step is to pass the string in a recursive method. This method takes a string, a left index, and a right index. The method checks the characters of the string using the indexes to compare each character on both sides. The method checks if the left is greater or equal to the right if so the entire string has been run through without returning false so the string is equal on both sides thus returning true. 
 ```swift
 if left >= right {
-  return true
+return true
 }
 ```
 If the check doesn't pass it continues to get the characters at the specified indexes and compare each. If they are not the same the method returns false and exits. 
@@ -72,7 +72,7 @@ let lhs = str[str.index(str.startIndex, offsetBy: left)]
 let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
 if lhs != rhs {
-  return false
+return false
 }
 ```
 If they are the same the method calls itself again and updates the indexes accordingly to continue to check the rest of the string. 
@@ -81,20 +81,21 @@ return palindrome(str, left: left + 1, right: right - 1)
 ```
 
 Step 1:
-` race?C ar -> raceCar -> racecar``
+
+`race?C ar -> raceCar -> racecar`
 
 Step 2:
 ```
 |     |
 racecar -> r == r
 
- |   |
+|   |
 racecar -> a == a
 
-  | |
+| |
 racecar -> c == c
 
-   |
+|
 racecar -> left index == right index -> return true
 ```
 

From 6a15d37a61310e7fd05c944f6be947605508b8f1 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:37:31 -0700
Subject: [PATCH 0715/1679] Revert "Improved formatting in code and markdown"

This reverts commit 13de04998d7f940c5c98bedb947ccee52fa0fe9d.
---
 Palindromes/README.markdown | 47 ++++++++++++++++++-------------------
 1 file changed, 23 insertions(+), 24 deletions(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index ede0af39d..85bdfc992 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -25,34 +25,34 @@ Here is a recursive implementation of this in Swift:
 
 ```swift
 func isPalindrome(_ str: String) -> Bool {
-let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-let length = strippedString.characters.count
+  let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+  let length = strippedString.characters.count
 
-if length > 1 {
-return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-}
-return false
+  if length > 1 {
+    return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+  }
+    return false
 }
 
 private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-if left >= right {
-return true
-}
+  if left >= right {
+    return true
+  }
 
-let lhs = str[str.index(str.startIndex, offsetBy: left)]
-let rhs = str[str.index(str.startIndex, offsetBy: right)]
+  let lhs = str[str.index(str.startIndex, offsetBy: left)]
+  let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
-if lhs != rhs {
-return false
-}
+  if lhs != rhs {
+    return false
+  }
 
-return palindrome(str, left: left + 1, right: right - 1)
+  return palindrome(str, left: left + 1, right: right - 1)
 }
 ```
 
 This algorithm has a two-step process.
 
-1 - The first step is to pass the string to validate as a palindrome into the `isPalindrome` method. This method first removes occurrences of non-word pattern matches `\W` [Regex reference](http://regexr.com). It is written with two \\ to escape the \ in the String literal. 
+1. The first step is to pass the string to validate as a palindrome into the `isPalindrome` method. This method first removes occurrences of non-word pattern matches `\W` [Regex reference](http://regexr.com). It is written with two \\ to escape the \ in the String literal. 
 
 ```swift
 let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
@@ -60,10 +60,10 @@ let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .reg
 
 The length of the string is then checked to make sure that the string after being stripped of non-word characters is still in a valid length. It is then passed into the next step after being lowercased.
 
-2 - The second step is to pass the string in a recursive method. This method takes a string, a left index, and a right index. The method checks the characters of the string using the indexes to compare each character on both sides. The method checks if the left is greater or equal to the right if so the entire string has been run through without returning false so the string is equal on both sides thus returning true. 
+2. The second step is to pass the string in a recursive method. This method takes a string, a left index, and a right index. The method checks the characters of the string using the indexes to compare each character on both sides. The method checks if the left is greater or equal to the right if so the entire string has been run through without returning false so the string is equal on both sides thus returning true. 
 ```swift
 if left >= right {
-return true
+  return true
 }
 ```
 If the check doesn't pass it continues to get the characters at the specified indexes and compare each. If they are not the same the method returns false and exits. 
@@ -72,7 +72,7 @@ let lhs = str[str.index(str.startIndex, offsetBy: left)]
 let rhs = str[str.index(str.startIndex, offsetBy: right)]
 
 if lhs != rhs {
-return false
+  return false
 }
 ```
 If they are the same the method calls itself again and updates the indexes accordingly to continue to check the rest of the string. 
@@ -81,21 +81,20 @@ return palindrome(str, left: left + 1, right: right - 1)
 ```
 
 Step 1:
-
-`race?C ar -> raceCar -> racecar`
+` race?C ar -> raceCar -> racecar``
 
 Step 2:
 ```
 |     |
 racecar -> r == r
 
-|   |
+ |   |
 racecar -> a == a
 
-| |
+  | |
 racecar -> c == c
 
-|
+   |
 racecar -> left index == right index -> return true
 ```
 

From f8888192086c2a542fc9550441a1cb41b7b51e90 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:37:59 -0700
Subject: [PATCH 0716/1679] Remove extra character

---
 Palindromes/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 85bdfc992..bb52678e0 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -81,7 +81,7 @@ return palindrome(str, left: left + 1, right: right - 1)
 ```
 
 Step 1:
-` race?C ar -> raceCar -> racecar``
+`race?C ar -> raceCar -> racecar`
 
 Step 2:
 ```

From 3da3a75413cf64aca60fc98e4987e9a804c12e48 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 11:39:18 -0700
Subject: [PATCH 0717/1679] Improved spacing on code snippet

---
 Palindromes/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index bb52678e0..18518adbe 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -31,7 +31,8 @@ func isPalindrome(_ str: String) -> Bool {
   if length > 1 {
     return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
   }
-    return false
+
+  return false
 }
 
 private func palindrome(_ str: String, left: Int, right: Int) -> Bool {

From 9d4f6ea1204d2a6aa475cdbb2f6e412771b6b83b Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Thu, 22 Dec 2016 16:48:58 -0700
Subject: [PATCH 0718/1679] Add tests for Travis CI

---
 .travis.yml                                   |   1 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 413 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 Palindromes/Tests/Tests/AppDelegate.swift     |  46 ++
 .../AppIcon.appiconset/Contents.json          |  68 +++
 .../Tests/Base.lproj/LaunchScreen.storyboard  |  27 ++
 Palindromes/Tests/Tests/Info.plist            |  45 ++
 Palindromes/Tests/Tests/Palindromes.swift     |  26 ++
 Palindromes/Tests/TestsTests/Info.plist       |  22 +
 .../Tests/TestsTests/PalindromeTests.swift    |  70 +++
 10 files changed, 725 insertions(+)
 create mode 100644 Palindromes/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Palindromes/Tests/Tests/AppDelegate.swift
 create mode 100644 Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard
 create mode 100644 Palindromes/Tests/Tests/Info.plist
 create mode 100644 Palindromes/Tests/Tests/Palindromes.swift
 create mode 100644 Palindromes/Tests/TestsTests/Info.plist
 create mode 100644 Palindromes/Tests/TestsTests/PalindromeTests.swift

diff --git a/.travis.yml b/.travis.yml
index 17655c21e..f7231cdfe 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -40,3 +40,4 @@ script:
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
+- xcodebuild test -project ./Palindromes/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Palindromes/Tests/Tests.xcodeproj/project.pbxproj b/Palindromes/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..63b68d316
--- /dev/null
+++ b/Palindromes/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,413 @@
+// !$*UTF8*$!
+{
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+	classes = {
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+	objectVersion = 46;
+	objects = {
+
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+				94D8AF0E1E0C9AB4007D8806 /* AppDelegate.swift */,
+				94D8AF2E1E0C9AE9007D8806 /* Palindromes.swift */,
+				94D8AF151E0C9AB4007D8806 /* Assets.xcassets */,
+				94D8AF171E0C9AB4007D8806 /* LaunchScreen.storyboard */,
+				94D8AF1A1E0C9AB4007D8806 /* Info.plist */,
+			);
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+		};
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+			isa = XCBuildConfiguration;
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+				ALWAYS_EMBED_SWIFT_STANDARD_LIBRARIES = YES;
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+		};
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+			buildSettings = {
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+/* End XCConfigurationList section */
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+}
diff --git a/Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Palindromes/Tests/Tests/AppDelegate.swift b/Palindromes/Tests/Tests/AppDelegate.swift
new file mode 100644
index 000000000..481c72c62
--- /dev/null
+++ b/Palindromes/Tests/Tests/AppDelegate.swift
@@ -0,0 +1,46 @@
+//
+//  AppDelegate.swift
+//  Tests
+//
+//  Created by Joshua Alvarado on 12/22/16.
+//  Copyright © 2016 Joshua Alvarado. All rights reserved.
+//
+
+import UIKit
+
+@UIApplicationMain
+class AppDelegate: UIResponder, UIApplicationDelegate {
+
+    var window: UIWindow?
+
+
+    func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
+        // Override point for customization after application launch.
+        return true
+    }
+
+    func applicationWillResignActive(_ application: UIApplication) {
+        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
+        // Use this method to pause ongoing tasks, disable timers, and invalidate graphics rendering callbacks. Games should use this method to pause the game.
+    }
+
+    func applicationDidEnterBackground(_ application: UIApplication) {
+        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
+        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
+    }
+
+    func applicationWillEnterForeground(_ application: UIApplication) {
+        // Called as part of the transition from the background to the active state; here you can undo many of the changes made on entering the background.
+    }
+
+    func applicationDidBecomeActive(_ application: UIApplication) {
+        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
+    }
+
+    func applicationWillTerminate(_ application: UIApplication) {
+        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
+    }
+
+
+}
+
diff --git a/Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json b/Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..36d2c80d8
--- /dev/null
+++ b/Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json
@@ -0,0 +1,68 @@
+{
+  "images" : [
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard b/Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard
new file mode 100644
index 000000000..fdf3f97d1
--- /dev/null
+++ b/Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard
@@ -0,0 +1,27 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="11134" systemVersion="15F34" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" colorMatched="YES" initialViewController="01J-lp-oVM">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="11106"/>
+        <capability name="documents saved in the Xcode 8 format" minToolsVersion="8.0"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="EHf-IW-A2E">
+            <objects>
+                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
+                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
+                        <rect key="frame" x="0.0" y="0.0" width="375" height="667"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <color key="backgroundColor" red="1" green="1" blue="1" alpha="1" colorSpace="custom" customColorSpace="sRGB"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="53" y="375"/>
+        </scene>
+    </scenes>
+</document>
diff --git a/Palindromes/Tests/Tests/Info.plist b/Palindromes/Tests/Tests/Info.plist
new file mode 100644
index 000000000..f197d509b
--- /dev/null
+++ b/Palindromes/Tests/Tests/Info.plist
@@ -0,0 +1,45 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSRequiresIPhoneOS</key>
+	<true/>
+	<key>UILaunchStoryboardName</key>
+	<string>LaunchScreen</string>
+	<key>UIMainStoryboardFile</key>
+	<string>LaunchScreen</string>
+	<key>UIRequiredDeviceCapabilities</key>
+	<array>
+		<string>armv7</string>
+	</array>
+	<key>UISupportedInterfaceOrientations</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>UISupportedInterfaceOrientations~ipad</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationPortraitUpsideDown</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+</dict>
+</plist>
diff --git a/Palindromes/Tests/Tests/Palindromes.swift b/Palindromes/Tests/Tests/Palindromes.swift
new file mode 100644
index 000000000..2760137ca
--- /dev/null
+++ b/Palindromes/Tests/Tests/Palindromes.swift
@@ -0,0 +1,26 @@
+import Foundation
+
+func isPalindrome(_ str: String) -> Bool {
+    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+    let length = strippedString.characters.count
+    
+    if length > 1 {
+        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+    }
+    return false
+}
+
+private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
+    if left >= right {
+        return true
+    }
+    
+    let lhs = str[str.index(str.startIndex, offsetBy: left)]
+    let rhs = str[str.index(str.startIndex, offsetBy: right)]
+    
+    if lhs != rhs {
+        return false
+    }
+    
+    return palindrome(str, left: left + 1, right: right - 1)
+}
diff --git a/Palindromes/Tests/TestsTests/Info.plist b/Palindromes/Tests/TestsTests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Palindromes/Tests/TestsTests/Info.plist
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Palindromes/Tests/TestsTests/PalindromeTests.swift b/Palindromes/Tests/TestsTests/PalindromeTests.swift
new file mode 100644
index 000000000..27d8f88b0
--- /dev/null
+++ b/Palindromes/Tests/TestsTests/PalindromeTests.swift
@@ -0,0 +1,70 @@
+//
+//  PalindromeTests.swift
+//  Tests
+//
+//  Created by Joshua Alvarado on 12/22/16.
+//  Copyright © 2016 Joshua Alvarado. All rights reserved.
+//
+
+import XCTest
+@testable import Tests
+
+class PalindromeTests: XCTestCase {
+    
+    override func setUp() {
+        super.setUp()
+        // Put setup code here. This method is called before the invocation of each test method in the class.
+    }
+    
+    override func tearDown() {
+        // Put teardown code here. This method is called after the invocation of each test method in the class.
+        super.tearDown()
+    }
+    
+    func testExample() {
+        // This is an example of a functional test case.
+        // Use XCTAssert and related functions to verify your tests produce the correct results.
+    }
+    
+    func testPerformanceExample() {
+        // This is an example of a performance test case.
+        self.measure {
+            // Put the code you want to measure the time of here.
+            let _ = isPalindrome("abbcbba")
+            let _ = isPalindrome("asdkfaksjdfasjkdfhaslkjdfakjsdfhakljsdhflkjasdfhkasdjhfklajsdfhkljasdf")
+            let _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
+        }
+    }
+    
+    func testPalindromeWord() {
+        XCTAssertTrue(isPalindrome("abbcbba"))
+        XCTAssertTrue(isPalindrome("racecar"))
+    }
+    
+    func testPalindromeSentence() {
+        XCTAssertTrue(isPalindrome("A man, a plan, a canal, Panama!"))
+        XCTAssertTrue(isPalindrome("Madam, I'm Adam"))
+        XCTAssertTrue(isPalindrome("Madam in Eden, I'm Adam"))
+        XCTAssertTrue(isPalindrome("In girum imus nocte et consumimur igni"))
+        XCTAssertTrue(isPalindrome("Never odd or even"))
+    }
+
+    func testPalindromeNumber() {
+        XCTAssertTrue(isPalindrome("5885"))
+        XCTAssertTrue(isPalindrome("5 8 8 5"))
+        XCTAssertTrue(isPalindrome("58 85"))
+    }
+
+    func testSpecialCharacters() {
+        XCTAssertTrue(isPalindrome("৯৯"))
+    }
+    
+    func testNonPalindromes() {
+        XCTAssertFalse(isPalindrome("\\\\"))
+        XCTAssertFalse(isPalindrome("desserts"))
+        XCTAssertFalse(isPalindrome("😀😀"))
+        XCTAssertFalse(isPalindrome(""))
+        XCTAssertFalse(isPalindrome("a"))
+        XCTAssertFalse(isPalindrome("power"))
+    }
+}

From 4d4b63d47ca048f58d1c0ddb30bc87648f45956c Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Fri, 23 Dec 2016 10:36:05 -0700
Subject: [PATCH 0719/1679] Update test project to run palindrome tests

---
 .travis.yml                                   |   2 +-
 .../{Tests/Tests => Test}/Palindromes.swift   |   0
 .../Test/Test.xcodeproj/project.pbxproj       | 273 ++++++++++++
 .../contents.xcworkspacedata                  |   2 +-
 .../TestsTests => Test/Test}/Info.plist       |   0
 .../Test/Test.swift}                          |   9 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     | 413 ------------------
 Palindromes/Tests/Tests/AppDelegate.swift     |  46 --
 .../AppIcon.appiconset/Contents.json          |  68 ---
 .../Tests/Base.lproj/LaunchScreen.storyboard  |  27 --
 Palindromes/Tests/Tests/Info.plist            |  45 --
 11 files changed, 279 insertions(+), 606 deletions(-)
 rename Palindromes/{Tests/Tests => Test}/Palindromes.swift (100%)
 create mode 100644 Palindromes/Test/Test.xcodeproj/project.pbxproj
 rename Palindromes/{Tests/Tests.xcodeproj => Test/Test.xcodeproj}/project.xcworkspace/contents.xcworkspacedata (72%)
 rename Palindromes/{Tests/TestsTests => Test/Test}/Info.plist (100%)
 rename Palindromes/{Tests/TestsTests/PalindromeTests.swift => Test/Test/Test.swift} (96%)
 delete mode 100644 Palindromes/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Palindromes/Tests/Tests/AppDelegate.swift
 delete mode 100644 Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json
 delete mode 100644 Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard
 delete mode 100644 Palindromes/Tests/Tests/Info.plist

diff --git a/.travis.yml b/.travis.yml
index f7231cdfe..dc681ccd1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -40,4 +40,4 @@ script:
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
-- xcodebuild test -project ./Palindromes/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test
diff --git a/Palindromes/Tests/Tests/Palindromes.swift b/Palindromes/Test/Palindromes.swift
similarity index 100%
rename from Palindromes/Tests/Tests/Palindromes.swift
rename to Palindromes/Test/Palindromes.swift
diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..07aae3e63
--- /dev/null
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -0,0 +1,273 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		9437D8841E0D960A00A38FB8 /* Test.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8831E0D960A00A38FB8 /* Test.swift */; };
+		9437D88B1E0D969500A38FB8 /* Palindromes.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8791E0D948A00A38FB8 /* Palindromes.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		9437D8791E0D948A00A38FB8 /* Palindromes.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Palindromes.swift; sourceTree = "<group>"; };
+		9437D8811E0D960A00A38FB8 /* Test.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Test.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		9437D8831E0D960A00A38FB8 /* Test.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Test.swift; sourceTree = "<group>"; };
+		9437D8851E0D960A00A38FB8 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		9437D87E1E0D960A00A38FB8 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		9437D8651E0D945200A38FB8 = {
+			isa = PBXGroup;
+			children = (
+				9437D8791E0D948A00A38FB8 /* Palindromes.swift */,
+				9437D8821E0D960A00A38FB8 /* Test */,
+				9437D86F1E0D945200A38FB8 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		9437D86F1E0D945200A38FB8 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				9437D8811E0D960A00A38FB8 /* Test.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		9437D8821E0D960A00A38FB8 /* Test */ = {
+			isa = PBXGroup;
+			children = (
+				9437D8831E0D960A00A38FB8 /* Test.swift */,
+				9437D8851E0D960A00A38FB8 /* Info.plist */,
+			);
+			path = Test;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		9437D8801E0D960A00A38FB8 /* Test */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 9437D8861E0D960A00A38FB8 /* Build configuration list for PBXNativeTarget "Test" */;
+			buildPhases = (
+				9437D87D1E0D960A00A38FB8 /* Sources */,
+				9437D87E1E0D960A00A38FB8 /* Frameworks */,
+				9437D87F1E0D960A00A38FB8 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Test;
+			productName = Test;
+			productReference = 9437D8811E0D960A00A38FB8 /* Test.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		9437D8661E0D945200A38FB8 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0820;
+				LastUpgradeCheck = 0820;
+				ORGANIZATIONNAME = "Joshua Alvarado";
+				TargetAttributes = {
+					9437D8801E0D960A00A38FB8 = {
+						CreatedOnToolsVersion = 8.2;
+						ProvisioningStyle = Automatic;
+					};
+				};
+			};
+			buildConfigurationList = 9437D8691E0D945200A38FB8 /* Build configuration list for PBXProject "Test" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
+			mainGroup = 9437D8651E0D945200A38FB8;
+			productRefGroup = 9437D86F1E0D945200A38FB8 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				9437D8801E0D960A00A38FB8 /* Test */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		9437D87F1E0D960A00A38FB8 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		9437D87D1E0D960A00A38FB8 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				9437D88B1E0D969500A38FB8 /* Palindromes.swift in Sources */,
+				9437D8841E0D960A00A38FB8 /* Test.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		9437D8721E0D945200A38FB8 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+			};
+			name = Debug;
+		};
+		9437D8731E0D945200A38FB8 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+			};
+			name = Release;
+		};
+		9437D8871E0D960A00A38FB8 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Test/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				PRODUCT_BUNDLE_IDENTIFIER = self.edu.Test;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		9437D8881E0D960A00A38FB8 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Test/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				PRODUCT_BUNDLE_IDENTIFIER = self.edu.Test;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		9437D8691E0D945200A38FB8 /* Build configuration list for PBXProject "Test" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				9437D8721E0D945200A38FB8 /* Debug */,
+				9437D8731E0D945200A38FB8 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		9437D8861E0D960A00A38FB8 /* Build configuration list for PBXNativeTarget "Test" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				9437D8871E0D960A00A38FB8 /* Debug */,
+				9437D8881E0D960A00A38FB8 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 9437D8661E0D945200A38FB8 /* Project object */;
+}
diff --git a/Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Palindromes/Test/Test.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 72%
rename from Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Palindromes/Test/Test.xcodeproj/project.xcworkspace/contents.xcworkspacedata
index 6c0ea8493..87cc241f8 100644
--- a/Palindromes/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
+++ b/Palindromes/Test/Test.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -2,6 +2,6 @@
 <Workspace
    version = "1.0">
    <FileRef
-      location = "self:Tests.xcodeproj">
+      location = "self:Test.xcodeproj">
    </FileRef>
 </Workspace>
diff --git a/Palindromes/Tests/TestsTests/Info.plist b/Palindromes/Test/Test/Info.plist
similarity index 100%
rename from Palindromes/Tests/TestsTests/Info.plist
rename to Palindromes/Test/Test/Info.plist
diff --git a/Palindromes/Tests/TestsTests/PalindromeTests.swift b/Palindromes/Test/Test/Test.swift
similarity index 96%
rename from Palindromes/Tests/TestsTests/PalindromeTests.swift
rename to Palindromes/Test/Test/Test.swift
index 27d8f88b0..e86a40cfb 100644
--- a/Palindromes/Tests/TestsTests/PalindromeTests.swift
+++ b/Palindromes/Test/Test/Test.swift
@@ -1,13 +1,12 @@
 //
 //  PalindromeTests.swift
-//  Tests
+//  Test
 //
-//  Created by Joshua Alvarado on 12/22/16.
+//  Created by Joshua Alvarado on 12/23/16.
 //  Copyright © 2016 Joshua Alvarado. All rights reserved.
 //
 
 import XCTest
-@testable import Tests
 
 class PalindromeTests: XCTestCase {
     
@@ -48,13 +47,13 @@ class PalindromeTests: XCTestCase {
         XCTAssertTrue(isPalindrome("In girum imus nocte et consumimur igni"))
         XCTAssertTrue(isPalindrome("Never odd or even"))
     }
-
+    
     func testPalindromeNumber() {
         XCTAssertTrue(isPalindrome("5885"))
         XCTAssertTrue(isPalindrome("5 8 8 5"))
         XCTAssertTrue(isPalindrome("58 85"))
     }
-
+    
     func testSpecialCharacters() {
         XCTAssertTrue(isPalindrome("৯৯"))
     }
diff --git a/Palindromes/Tests/Tests.xcodeproj/project.pbxproj b/Palindromes/Tests/Tests.xcodeproj/project.pbxproj
deleted file mode 100644
index 63b68d316..000000000
--- a/Palindromes/Tests/Tests.xcodeproj/project.pbxproj
+++ /dev/null
@@ -1,413 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
-	classes = {
-	};
-	objectVersion = 46;
-	objects = {
-
-/* Begin PBXBuildFile section */
-		94D8AF0F1E0C9AB4007D8806 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 94D8AF0E1E0C9AB4007D8806 /* AppDelegate.swift */; };
-		94D8AF161E0C9AB4007D8806 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 94D8AF151E0C9AB4007D8806 /* Assets.xcassets */; };
-		94D8AF191E0C9AB4007D8806 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 94D8AF171E0C9AB4007D8806 /* LaunchScreen.storyboard */; };
-		94D8AF2F1E0C9AE9007D8806 /* Palindromes.swift in Sources */ = {isa = PBXBuildFile; fileRef = 94D8AF2E1E0C9AE9007D8806 /* Palindromes.swift */; };
-		94D8AF331E0C9BB2007D8806 /* PalindromeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 94D8AF321E0C9BB2007D8806 /* PalindromeTests.swift */; };
-/* End PBXBuildFile section */
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diff --git a/Palindromes/Tests/Tests/AppDelegate.swift b/Palindromes/Tests/Tests/AppDelegate.swift
deleted file mode 100644
index 481c72c62..000000000
--- a/Palindromes/Tests/Tests/AppDelegate.swift
+++ /dev/null
@@ -1,46 +0,0 @@
-//
-//  AppDelegate.swift
-//  Tests
-//
-//  Created by Joshua Alvarado on 12/22/16.
-//  Copyright © 2016 Joshua Alvarado. All rights reserved.
-//
-
-import UIKit
-
-@UIApplicationMain
-class AppDelegate: UIResponder, UIApplicationDelegate {
-
-    var window: UIWindow?
-
-
-    func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
-        // Override point for customization after application launch.
-        return true
-    }
-
-    func applicationWillResignActive(_ application: UIApplication) {
-        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
-        // Use this method to pause ongoing tasks, disable timers, and invalidate graphics rendering callbacks. Games should use this method to pause the game.
-    }
-
-    func applicationDidEnterBackground(_ application: UIApplication) {
-        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
-        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
-    }
-
-    func applicationWillEnterForeground(_ application: UIApplication) {
-        // Called as part of the transition from the background to the active state; here you can undo many of the changes made on entering the background.
-    }
-
-    func applicationDidBecomeActive(_ application: UIApplication) {
-        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
-    }
-
-    func applicationWillTerminate(_ application: UIApplication) {
-        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
-    }
-
-
-}
-
diff --git a/Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json b/Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json
deleted file mode 100644
index 36d2c80d8..000000000
--- a/Palindromes/Tests/Tests/Assets.xcassets/AppIcon.appiconset/Contents.json
+++ /dev/null
@@ -1,68 +0,0 @@
-{
-  "images" : [
-    {
-      "idiom" : "iphone",
-      "size" : "29x29",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "29x29",
-      "scale" : "3x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "40x40",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "40x40",
-      "scale" : "3x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "60x60",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "iphone",
-      "size" : "60x60",
-      "scale" : "3x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "29x29",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "29x29",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "40x40",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "40x40",
-      "scale" : "2x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "76x76",
-      "scale" : "1x"
-    },
-    {
-      "idiom" : "ipad",
-      "size" : "76x76",
-      "scale" : "2x"
-    }
-  ],
-  "info" : {
-    "version" : 1,
-    "author" : "xcode"
-  }
-}
\ No newline at end of file
diff --git a/Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard b/Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard
deleted file mode 100644
index fdf3f97d1..000000000
--- a/Palindromes/Tests/Tests/Base.lproj/LaunchScreen.storyboard
+++ /dev/null
@@ -1,27 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="11134" systemVersion="15F34" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" colorMatched="YES" initialViewController="01J-lp-oVM">
-    <dependencies>
-        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="11106"/>
-        <capability name="documents saved in the Xcode 8 format" minToolsVersion="8.0"/>
-    </dependencies>
-    <scenes>
-        <!--View Controller-->
-        <scene sceneID="EHf-IW-A2E">
-            <objects>
-                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
-                    <layoutGuides>
-                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
-                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
-                    </layoutGuides>
-                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
-                        <rect key="frame" x="0.0" y="0.0" width="375" height="667"/>
-                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
-                        <color key="backgroundColor" red="1" green="1" blue="1" alpha="1" colorSpace="custom" customColorSpace="sRGB"/>
-                    </view>
-                </viewController>
-                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
-            </objects>
-            <point key="canvasLocation" x="53" y="375"/>
-        </scene>
-    </scenes>
-</document>
diff --git a/Palindromes/Tests/Tests/Info.plist b/Palindromes/Tests/Tests/Info.plist
deleted file mode 100644
index f197d509b..000000000
--- a/Palindromes/Tests/Tests/Info.plist
+++ /dev/null
@@ -1,45 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>APPL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-	<key>LSRequiresIPhoneOS</key>
-	<true/>
-	<key>UILaunchStoryboardName</key>
-	<string>LaunchScreen</string>
-	<key>UIMainStoryboardFile</key>
-	<string>LaunchScreen</string>
-	<key>UIRequiredDeviceCapabilities</key>
-	<array>
-		<string>armv7</string>
-	</array>
-	<key>UISupportedInterfaceOrientations</key>
-	<array>
-		<string>UIInterfaceOrientationPortrait</string>
-		<string>UIInterfaceOrientationLandscapeLeft</string>
-		<string>UIInterfaceOrientationLandscapeRight</string>
-	</array>
-	<key>UISupportedInterfaceOrientations~ipad</key>
-	<array>
-		<string>UIInterfaceOrientationPortrait</string>
-		<string>UIInterfaceOrientationPortraitUpsideDown</string>
-		<string>UIInterfaceOrientationLandscapeLeft</string>
-		<string>UIInterfaceOrientationLandscapeRight</string>
-	</array>
-</dict>
-</plist>

From 9ac2d762802de647082a7b5977bad4bf9e1db8d6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Sat, 24 Dec 2016 03:39:44 -0800
Subject: [PATCH 0720/1679] Fixed up indentation and removed a few self
 references.

---
 .../BoyerMoore.playground/Contents.swift      | 114 +++++++++---------
 1 file changed, 57 insertions(+), 57 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 362a298f9..9bbc7ec19 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -1,66 +1,66 @@
 //: Playground - noun: a place where people can play
 
 extension String {
-    func indexOf(pattern: String) -> String.Index? {
-        // Cache the length of the search pattern because we're going to
-        // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        assert(patternLength > 0)
-        assert(patternLength <= self.characters.count)
-        
-        // Make the skip table. This table determines how far we skip ahead
-        // when a character from the pattern is found.
-        var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
-            skipTable[c] = patternLength - i - 1
-        }
-        
-        // This points at the last character in the pattern.
-        let p = pattern.index(before: pattern.endIndex)
-        let lastChar = pattern[p]
-        
-        // The pattern is scanned right-to-left, so skip ahead in the string by
-        // the length of the pattern. (Minus 1 because startIndex already points
-        // at the first character in the source string.)
-        var i = self.index(startIndex, offsetBy: patternLength - 1)
+  func indexOf(pattern: String) -> String.Index? {
+    // Cache the length of the search pattern because we're going to
+    // use it a few times and it's expensive to calculate.
+    let patternLength = pattern.characters.count
+    assert(patternLength > 0)
+    assert(patternLength <= characters.count)
+    
+    // Make the skip table. This table determines how far we skip ahead
+    // when a character from the pattern is found.
+    var skipTable = [Character: Int]()
+    for (i, c) in pattern.characters.enumerated() {
+      skipTable[c] = patternLength - i - 1
+    }
+    
+    // This points at the last character in the pattern.
+    let p = pattern.index(before: pattern.endIndex)
+    let lastChar = pattern[p]
+    
+    // The pattern is scanned right-to-left, so skip ahead in the string by
+    // the length of the pattern. (Minus 1 because startIndex already points
+    // at the first character in the source string.)
+    var i = index(startIndex, offsetBy: patternLength - 1)
+    
+    // This is a helper function that steps backwards through both strings
+    // until we find a character that doesn’t match, or until we’ve reached
+    // the beginning of the pattern.
+    func backwards() -> String.Index? {
+      var q = p
+      var j = i
+      while q > pattern.startIndex {
+        j = index(before: j)
+        q = index(before: q)
+        if self[j] != pattern[q] { return nil }
+      }
+      return j
+    }
+    
+    // The main loop. Keep going until the end of the string is reached.
+    while i < endIndex {
+      let c = self[i]
+      
+      // Does the current character match the last character from the pattern?
+      if c == lastChar {
         
-        // This is a helper function that steps backwards through both strings
-        // until we find a character that doesn’t match, or until we’ve reached
-        // the beginning of the pattern.
-        func backwards() -> String.Index? {
-            var q = p
-            var j = i
-            while q > pattern.startIndex {
-                j = index(before: j)
-                q = index(before: q)
-                if self[j] != pattern[q] { return nil }
-            }
-            return j
-        }
+        // There is a possible match. Do a brute-force search backwards.
+        if let k = backwards() { return k }
         
-        // The main loop. Keep going until the end of the string is reached.
-        while i < self.endIndex {
-            let c = self[i]
-            
-            // Does the current character match the last character from the pattern?
-            if c == lastChar {
-                
-                // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k }
-                
-                // If no match, we can only safely skip one character ahead.
-                i = index(after: i)
-            } else {
-                // The characters are not equal, so skip ahead. The amount to skip is
-                // determined by the skip table. If the character is not present in the
-                // pattern, we can skip ahead by the full pattern length. However, if
-                // the character *is* present in the pattern, there may be a match up
-                // ahead and we can't skip as far.
-                i = self.index(i, offsetBy: skipTable[c] ?? patternLength)
-            }
-        }
-        return nil
+        // If no match, we can only safely skip one character ahead.
+        i = index(after: i)
+      } else {
+        // The characters are not equal, so skip ahead. The amount to skip is
+        // determined by the skip table. If the character is not present in the
+        // pattern, we can skip ahead by the full pattern length. However, if
+        // the character *is* present in the pattern, there may be a match up
+        // ahead and we can't skip as far.
+        i = index(i, offsetBy: skipTable[c] ?? patternLength)
+      }
     }
+    return nil
+  }
 }
 
 // A few simple tests

From 7a0417e86553dbe67495deba9f16f2ccdf14b3ea Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:18:55 -0300
Subject: [PATCH 0721/1679] Added some tests. There are a failing test in the
 original code.

---
 Boyer-Moore/Tests/BoyerMooreTests.swift       |  67 +++++
 Boyer-Moore/Tests/Info.plist                  |  24 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 269 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     |  90 ++++++
 5 files changed, 457 insertions(+)
 create mode 100755 Boyer-Moore/Tests/BoyerMooreTests.swift
 create mode 100644 Boyer-Moore/Tests/Info.plist
 create mode 100644 Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Boyer-Moore/Tests/BoyerMooreTests.swift b/Boyer-Moore/Tests/BoyerMooreTests.swift
new file mode 100755
index 000000000..6536d1800
--- /dev/null
+++ b/Boyer-Moore/Tests/BoyerMooreTests.swift
@@ -0,0 +1,67 @@
+import Foundation
+import XCTest
+
+class BoyerMooreTest: XCTestCase {
+    override func setUp() {
+        super.setUp()
+    }
+
+    func assert(pattern: String, doesNotExistsIn string: String) {
+        let index = string.indexOf(pattern: pattern)
+        XCTAssertNil(index)
+    }
+
+    func assert(pattern: String, existsIn string: String) {
+        let index = string.indexOf(pattern: pattern)
+        XCTAssertNotNil(index)
+
+        let startIndex = index!
+        let endIndex = string.index(index!, offsetBy: pattern.characters.count)
+        let match = string.substring(with: startIndex..<endIndex)
+        XCTAssertEqual(match, pattern)
+    }
+    
+    func testSearchTheSameString() {
+        let string = "ABCDEF"
+        let pattern = "ABCDEF"
+        assert(pattern: pattern, existsIn: string)
+    }
+    
+    func testSearchAPreffix() {
+        let string = "ABCDEFGHIJK"
+        let pattern = "ABCDEF"
+        assert(pattern: pattern, existsIn: string)
+    }
+    
+    func testSearchASuffix() {
+        let string = "ABCDEFGHIJK"
+        let pattern = "HIJK"
+        assert(pattern: pattern, existsIn: string)
+    }
+    
+    func testSearchAStringFromTheMiddle() {
+        let string = "ABCDEFGHIJK"
+        let pattern = "EFG"
+        assert(pattern: pattern, existsIn: string)
+    }
+    
+    
+    func testSearchInvalidPattern() {
+        let string = "ABCDEFGHIJK"
+        let pattern = "AEF"
+        assert(pattern: pattern, doesNotExistsIn: string)
+    }
+    
+    func testSearchPatternWithDuplicatedCharacter() {
+        let string = "Goal: Write a string search algorithm in pure Swift without importing Foundation or using NSString's rangeOfString() method."
+        let pattern = "NSS"
+        assert(pattern: pattern, existsIn: string)
+    }
+
+    func testSearchInvalidPatternWithDuplicatedCharacter() {
+        let string = "Goal: Write a string search algorithm in pure Swift without importing Foundation or using NSString's rangeOfString() method."
+        let pattern = "nss"
+        assert(pattern: pattern, doesNotExistsIn: string)
+    }
+    
+}
diff --git a/Boyer-Moore/Tests/Info.plist b/Boyer-Moore/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Boyer-Moore/Tests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..ff4f401a1
--- /dev/null
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,269 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */; };
+		9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreTests.swift; sourceTree = SOURCE_ROOT; };
+		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../../BoyerMoore.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */,
+				7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			path = TestsTests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0800;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0800;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */,
+				7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..14f27f777
--- /dev/null
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0800"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 2be65b442aafa1c96456322c50039dca8184a1e0 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:19:58 -0300
Subject: [PATCH 0722/1679] Fix failing test.

---
 Boyer-Moore/BoyerMoore.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore/BoyerMoore.swift
index 4d7660ec3..d8ff4e6d2 100644
--- a/Boyer-Moore/BoyerMoore.swift
+++ b/Boyer-Moore/BoyerMoore.swift
@@ -61,7 +61,7 @@ extension String {
                 // pattern, we can skip ahead by the full pattern length. However, if
                 // the character *is* present in the pattern, there may be a match up
                 // ahead and we can't skip as far.
-                i = self.index(i, offsetBy: skipTable[c] ?? patternLength)
+                i = index(i, offsetBy: skipTable[c] ?? patternLength, limitedBy: endIndex) ?? endIndex
             }
         }
         return nil

From 4ca7ab9fc784afc018f6dde770fc54afc952664a Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:22:59 -0300
Subject: [PATCH 0723/1679] Add Boyer-Moore-Horspool algorithm and tests.

---
 Boyer-Moore/BoyerMoore.swift                      | 14 +++++++++++---
 Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift   | 14 ++++++++++++++
 Boyer-Moore/Tests/BoyerMooreTests.swift           | 14 ++++++++++++--
 Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj |  4 ++++
 4 files changed, 41 insertions(+), 5 deletions(-)
 create mode 100644 Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift

diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore/BoyerMoore.swift
index d8ff4e6d2..24842b59e 100644
--- a/Boyer-Moore/BoyerMoore.swift
+++ b/Boyer-Moore/BoyerMoore.swift
@@ -6,7 +6,7 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func indexOf(pattern: String) -> String.Index? {
+    func indexOf(pattern: String, useHorspoolImprovement: Bool = false) -> String.Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
@@ -53,8 +53,16 @@ extension String {
                 // There is a possible match. Do a brute-force search backwards.
                 if let k = backwards() { return k }
                 
-                // If no match, we can only safely skip one character ahead.
-                i = index(after: i)
+                if !useHorspoolImprovement {
+                    // If no match, we can only safely skip one character ahead.
+                    i = index(after: i)
+                }
+                else {
+                    // Ensure to jump at least one character (this is needed because the first
+                    // character is in the skipTable, and `skipTable[lastChar] = 0`)
+                    let jumpOffset = max(skipTable[c] ?? patternLength, 1)
+                    i = index(i, offsetBy: jumpOffset, limitedBy: endIndex) ?? endIndex
+                }
             } else {
                 // The characters are not equal, so skip ahead. The amount to skip is
                 // determined by the skip table. If the character is not present in the
diff --git a/Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift b/Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift
new file mode 100644
index 000000000..3924494c7
--- /dev/null
+++ b/Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift
@@ -0,0 +1,14 @@
+//
+//  BoyerMooreHorspoolTests.swift
+//  Tests
+//
+//  Created by Matias Mazzei on 12/24/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
+class BoyerMooreHorspoolTests: BoyerMooreTest {
+    override func setUp() {
+        super.setUp()
+        useHorspoolImprovement = false
+    }
+}
diff --git a/Boyer-Moore/Tests/BoyerMooreTests.swift b/Boyer-Moore/Tests/BoyerMooreTests.swift
index 6536d1800..8a2cbdc77 100755
--- a/Boyer-Moore/Tests/BoyerMooreTests.swift
+++ b/Boyer-Moore/Tests/BoyerMooreTests.swift
@@ -1,18 +1,28 @@
+//
+//  BoyerMooreHorspoolTests.swift
+//  Tests
+//
+//  Created by Matias Mazzei on 12/24/16.
+//  Copyright © 2016 Swift Algorithm Club. All rights reserved.
+//
+
 import Foundation
 import XCTest
 
 class BoyerMooreTest: XCTestCase {
+    var useHorspoolImprovement = false
+
     override func setUp() {
         super.setUp()
     }
 
     func assert(pattern: String, doesNotExistsIn string: String) {
-        let index = string.indexOf(pattern: pattern)
+        let index = string.indexOf(pattern: pattern, useHorspoolImprovement: useHorspoolImprovement)
         XCTAssertNil(index)
     }
 
     func assert(pattern: String, existsIn string: String) {
-        let index = string.indexOf(pattern: pattern)
+        let index = string.indexOf(pattern: pattern, useHorspoolImprovement: useHorspoolImprovement)
         XCTAssertNotNil(index)
 
         let startIndex = index!
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
index ff4f401a1..f263d846a 100644
--- a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
@@ -9,6 +9,7 @@
 /* Begin PBXBuildFile section */
 		7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */; };
 		9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */; };
+		9AED56801E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
@@ -16,6 +17,7 @@
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreTests.swift; sourceTree = SOURCE_ROOT; };
 		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../../BoyerMoore.swift; sourceTree = "<group>"; };
+		9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreHorspoolTests.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -51,6 +53,7 @@
 				9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */,
 				7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
+				9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */,
 			);
 			name = Tests;
 			path = TestsTests;
@@ -125,6 +128,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				9AED56801E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift in Sources */,
 				9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */,
 				7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */,
 			);

From 36fba8ac3f4da6595783f5ebd4e72d19d1621c21 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:25:27 -0300
Subject: [PATCH 0724/1679] Add tests to .travis.yml

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 17655c21e..38099490e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -12,6 +12,7 @@ script:
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Boyer-Moore/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests

From c3cad8c13314eda236ca3d98650c5a79c89861e8 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:30:32 -0300
Subject: [PATCH 0725/1679] Updated README: updated algorithms and credits.

---
 Boyer-Moore/README.markdown | 92 ++++++++++++++++++++++++-------------
 1 file changed, 59 insertions(+), 33 deletions(-)

diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 576f6d17b..08347e3e7 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -87,7 +87,7 @@ extension String {
                 // pattern, we can skip ahead by the full pattern length. However, if
                 // the character *is* present in the pattern, there may be a match up
                 // ahead and we can't skip as far.
-                i = self.index(i, offsetBy: skipTable[c] ?? patternLength)
+                i = index(i, offsetBy: skipTable[c] ?? patternLength, limitedBy: endIndex) ?? endIndex
             }
         }
         return nil
@@ -158,40 +158,66 @@ Here's an implementation of the Boyer-Moore-Horspool algorithm:
 ```swift
 extension String {
     func indexOf(pattern: String) -> String.Index? {
-    let patternLength = pattern.characters.count
-    assert(patternLength > 0)
-    assert(patternLength <= self.characters.count)
+        // Cache the length of the search pattern because we're going to
+        // use it a few times and it's expensive to calculate.
+        let patternLength = pattern.characters.count
+        assert(patternLength > 0)
+        assert(patternLength <= self.characters.count)
 
-    var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerated() {
-    skipTable[c] = patternLength - i - 1
-    }
+        // Make the skip table. This table determines how far we skip ahead
+        // when a character from the pattern is found.
+        var skipTable = [Character: Int]()
+        for (i, c) in pattern.characters.enumerated() {
+            skipTable[c] = patternLength - i - 1
+        }
 
-    let p = pattern.index(before: pattern.endIndex)
-    let lastChar = pattern[p]
-    var i = self.index(startIndex, offsetBy: patternLength - 1)
-
-    func backwards() -> String.Index? {
-    var q = p
-    var j = i
-    while q > pattern.startIndex {
-    j = index(before: j)
-    q = index(before: q)
-    if self[j] != pattern[q] { return nil }
-    }
-    return j
-    }
+        // This points at the last character in the pattern.
+        let p = pattern.index(before: pattern.endIndex)
+        let lastChar = pattern[p]
 
-    while i < self.endIndex {
-    let c = self[i]
-    if c == lastChar {
-    if let k = backwards() { return k }
-    i = index(after: i)
-    } else {
-    i = index(i, offsetBy: skipTable[c] ?? patternLength)
-    }
-    }
-    return nil
+        // The pattern is scanned right-to-left, so skip ahead in the string by
+        // the length of the pattern. (Minus 1 because startIndex already points
+        // at the first character in the source string.)
+        var i = self.index(startIndex, offsetBy: patternLength - 1)
+
+        // This is a helper function that steps backwards through both strings
+        // until we find a character that doesn’t match, or until we’ve reached
+        // the beginning of the pattern.
+        func backwards() -> String.Index? {
+            var q = p
+            var j = i
+            while q > pattern.startIndex {
+                j = index(before: j)
+                q = index(before: q)
+                if self[j] != pattern[q] { return nil }
+            }
+            return j
+        }
+
+        // The main loop. Keep going until the end of the string is reached.
+        while i < self.endIndex {
+            let c = self[i]
+
+            // Does the current character match the last character from the pattern?
+            if c == lastChar {
+
+                // There is a possible match. Do a brute-force search backwards.
+                if let k = backwards() { return k }
+
+                // Ensure to jump at least one character (this is needed because the first
+                // character is in the skipTable, and `skipTable[lastChar] = 0`)
+                let jumpOffset = max(skipTable[c] ?? patternLength, 1)
+                i = index(i, offsetBy: jumpOffset, limitedBy: endIndex) ?? endIndex
+            } else {
+                // The characters are not equal, so skip ahead. The amount to skip is
+                // determined by the skip table. If the character is not present in the
+                // pattern, we can skip ahead by the full pattern length. However, if
+                // the character *is* present in the pattern, there may be a match up
+                // ahead and we can't skip as far.
+                i = index(i, offsetBy: skipTable[c] ?? patternLength, limitedBy: endIndex) ?? endIndex
+            }
+        }
+        return nil
     }
 }
 ```
@@ -200,4 +226,4 @@ In practice, the Horspool version of the algorithm tends to perform a little bet
 
 Credits: This code is based on the paper: [R. N. Horspool (1980). "Practical fast searching in strings". Software - Practice & Experience 10 (6): 501–506.](http://www.cin.br/~paguso/courses/if767/bib/Horspool_1980.pdf)
 
-_Written for Swift Algorithm Club by Matthijs Hollemans, updated by Andreas Neusüß_
+_Written for Swift Algorithm Club by Matthijs Hollemans, updated by Andreas Neusüß_, [Matías Mazzei](https://github.com/mmazzei).

From 78e78a4b9e81b57698d95e68d8abbd86c218ef95 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:42:54 -0300
Subject: [PATCH 0726/1679] Fix swiftlint warnings.

---
 Boyer-Moore/Tests/BoyerMooreTests.swift       | 20 +++++++++----------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 17 ++++++++++++++++
 2 files changed, 27 insertions(+), 10 deletions(-)

diff --git a/Boyer-Moore/Tests/BoyerMooreTests.swift b/Boyer-Moore/Tests/BoyerMooreTests.swift
index 8a2cbdc77..f1638afcd 100755
--- a/Boyer-Moore/Tests/BoyerMooreTests.swift
+++ b/Boyer-Moore/Tests/BoyerMooreTests.swift
@@ -30,48 +30,48 @@ class BoyerMooreTest: XCTestCase {
         let match = string.substring(with: startIndex..<endIndex)
         XCTAssertEqual(match, pattern)
     }
-    
+
     func testSearchTheSameString() {
         let string = "ABCDEF"
         let pattern = "ABCDEF"
         assert(pattern: pattern, existsIn: string)
     }
-    
+
     func testSearchAPreffix() {
         let string = "ABCDEFGHIJK"
         let pattern = "ABCDEF"
         assert(pattern: pattern, existsIn: string)
     }
-    
+
     func testSearchASuffix() {
         let string = "ABCDEFGHIJK"
         let pattern = "HIJK"
         assert(pattern: pattern, existsIn: string)
     }
-    
+
     func testSearchAStringFromTheMiddle() {
         let string = "ABCDEFGHIJK"
         let pattern = "EFG"
         assert(pattern: pattern, existsIn: string)
     }
-    
-    
+
     func testSearchInvalidPattern() {
         let string = "ABCDEFGHIJK"
         let pattern = "AEF"
         assert(pattern: pattern, doesNotExistsIn: string)
     }
-    
+
     func testSearchPatternWithDuplicatedCharacter() {
-        let string = "Goal: Write a string search algorithm in pure Swift without importing Foundation or using NSString's rangeOfString() method."
+        let string = "Goal: Write a string search algorithm in pure Swift "
+                     + "without importing Foundation or using NSString's rangeOfString() method."
         let pattern = "NSS"
         assert(pattern: pattern, existsIn: string)
     }
 
     func testSearchInvalidPatternWithDuplicatedCharacter() {
-        let string = "Goal: Write a string search algorithm in pure Swift without importing Foundation or using NSString's rangeOfString() method."
+        let string = "Goal: Write a string search algorithm in pure Swift "
+            + "without importing Foundation or using NSString's rangeOfString() method."
         let pattern = "nss"
         assert(pattern: pattern, doesNotExistsIn: string)
     }
-    
 }
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
index f263d846a..c4a005163 100644
--- a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
@@ -66,6 +66,7 @@
 			isa = PBXNativeTarget;
 			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
 			buildPhases = (
+				9AED56811E0EEA5B00958DCC /* ShellScript */,
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
 				7B2BBC7E1C779D720067B71D /* Resources */,
@@ -123,6 +124,22 @@
 		};
 /* End PBXResourcesBuildPhase section */
 
+/* Begin PBXShellScriptBuildPhase section */
+		9AED56811E0EEA5B00958DCC /* ShellScript */ = {
+			isa = PBXShellScriptBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			inputPaths = (
+			);
+			outputPaths = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+			shellPath = /bin/sh;
+			shellScript = "if which swiftlint >/dev/null; then\nswiftlint\nelse\necho \"warning: SwiftLint not installed, download from https://github.com/realm/SwiftLint\"\nfi";
+		};
+/* End PBXShellScriptBuildPhase section */
+
 /* Begin PBXSourcesBuildPhase section */
 		7B2BBC7C1C779D720067B71D /* Sources */ = {
 			isa = PBXSourcesBuildPhase;

From cd2106a5bb461cbf12ad008a8412e069d0052df1 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sat, 24 Dec 2016 14:47:56 -0300
Subject: [PATCH 0727/1679] Xcode option 'Uncheck Autocreate schemes'
 unchecked.

---
 .../xcshareddata/WorkspaceSettings.xcsettings             | 8 ++++++++
 1 file changed, 8 insertions(+)
 create mode 100644 Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>

From cf45ebd0dd84a842a1d032f7545e70c76b2cbb79 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sun, 25 Dec 2016 15:08:31 -0300
Subject: [PATCH 0728/1679] Update as requested in code review.

---
 .../BoyerMoore.playground/Contents.swift      | 143 ++++++++++--------
 Boyer-Moore/BoyerMoore.swift                  |  35 ++---
 Boyer-Moore/README.markdown                   |  28 ++--
 Boyer-Moore/Tests/BoyerMooreTests.swift       |  22 ++-
 4 files changed, 135 insertions(+), 93 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index 9bbc7ec19..f1ae5018e 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -1,72 +1,91 @@
 //: Playground - noun: a place where people can play
 
+/*
+  Boyer-Moore string search
+
+  This code is based on the article "Faster String Searches" by Costas Menico
+  from Dr Dobb's magazine, July 1989.
+  http://www.drdobbs.com/database/faster-string-searches/184408171
+*/
 extension String {
-  func indexOf(pattern: String) -> String.Index? {
-    // Cache the length of the search pattern because we're going to
-    // use it a few times and it's expensive to calculate.
-    let patternLength = pattern.characters.count
-    assert(patternLength > 0)
-    assert(patternLength <= characters.count)
-    
-    // Make the skip table. This table determines how far we skip ahead
-    // when a character from the pattern is found.
-    var skipTable = [Character: Int]()
-    for (i, c) in pattern.characters.enumerated() {
-      skipTable[c] = patternLength - i - 1
-    }
-    
-    // This points at the last character in the pattern.
-    let p = pattern.index(before: pattern.endIndex)
-    let lastChar = pattern[p]
-    
-    // The pattern is scanned right-to-left, so skip ahead in the string by
-    // the length of the pattern. (Minus 1 because startIndex already points
-    // at the first character in the source string.)
-    var i = index(startIndex, offsetBy: patternLength - 1)
-    
-    // This is a helper function that steps backwards through both strings
-    // until we find a character that doesn’t match, or until we’ve reached
-    // the beginning of the pattern.
-    func backwards() -> String.Index? {
-      var q = p
-      var j = i
-      while q > pattern.startIndex {
-        j = index(before: j)
-        q = index(before: q)
-        if self[j] != pattern[q] { return nil }
-      }
-      return j
-    }
-    
-    // The main loop. Keep going until the end of the string is reached.
-    while i < endIndex {
-      let c = self[i]
-      
-      // Does the current character match the last character from the pattern?
-      if c == lastChar {
-        
-        // There is a possible match. Do a brute-force search backwards.
-        if let k = backwards() { return k }
-        
-        // If no match, we can only safely skip one character ahead.
-        i = index(after: i)
-      } else {
-        // The characters are not equal, so skip ahead. The amount to skip is
-        // determined by the skip table. If the character is not present in the
-        // pattern, we can skip ahead by the full pattern length. However, if
-        // the character *is* present in the pattern, there may be a match up
-        // ahead and we can't skip as far.
-        i = index(i, offsetBy: skipTable[c] ?? patternLength)
-      }
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
+        // There are no possible match in an empty string
+        guard !isEmpty else { return nil }
+
+        // Cache the length of the search pattern because we're going to
+        // use it a few times and it's expensive to calculate.
+        let patternLength = pattern.characters.count
+        guard patternLength > 0, patternLength <= characters.count else { return nil }
+
+        // Make the skip table. This table determines how far we skip ahead
+        // when a character from the pattern is found.
+        var skipTable = [Character: Int]()
+        for (i, c) in pattern.characters.enumerated() {
+            skipTable[c] = patternLength - i - 1
+        }
+
+        // This points at the last character in the pattern.
+        let p = pattern.index(before: pattern.endIndex)
+        let lastChar = pattern[p]
+
+        // The pattern is scanned right-to-left, so skip ahead in the string by
+        // the length of the pattern. (Minus 1 because startIndex already points
+        // at the first character in the source string.)
+        var i = index(startIndex, offsetBy: patternLength - 1)
+
+        // This is a helper function that steps backwards through both strings
+        // until we find a character that doesn’t match, or until we’ve reached
+        // the beginning of the pattern.
+        func backwards() -> Index? {
+            var q = p
+            var j = i
+            while q > pattern.startIndex {
+                j = index(before: j)
+                q = index(before: q)
+                if self[j] != pattern[q] { return nil }
+            }
+            return j
+        }
+
+        // The main loop. Keep going until the end of the string is reached.
+        while i < endIndex {
+            let c = self[i]
+
+            // Does the current character match the last character from the pattern?
+            if c == lastChar {
+
+                // There is a possible match. Do a brute-force search backwards.
+                if let k = backwards() { return k }
+
+                if !usingHorspoolImprovement {
+                    // If no match, we can only safely skip one character ahead.
+                    i = index(after: i)
+                } else {
+                    // Ensure to jump at least one character (this is needed because the first
+                    // character is in the skipTable, and `skipTable[lastChar] = 0`)
+                    let jumpOffset = max(skipTable[c] ?? patternLength, 1)
+                    i = index(i, offsetBy: jumpOffset, limitedBy: endIndex) ?? endIndex
+                }
+            } else {
+                // The characters are not equal, so skip ahead. The amount to skip is
+                // determined by the skip table. If the character is not present in the
+                // pattern, we can skip ahead by the full pattern length. However, if
+                // the character *is* present in the pattern, there may be a match up
+                // ahead and we can't skip as far.
+                i = index(i, offsetBy: skipTable[c] ?? patternLength, limitedBy: endIndex) ?? endIndex
+            }
+        }
+        return nil
     }
-    return nil
-  }
 }
 
 // A few simple tests
 
-let s = "Hello, World"
-s.indexOf(pattern: "World")  // 7
+let str = "Hello, World"
+str.index(of: "World")  // 7
 
 let animals = "🐶🐔🐷🐮🐱"
-animals.indexOf(pattern: "🐮")  // 6
+animals.index(of: "🐮")  // 6
+
+let lorem = "Lorem ipsum dolor sit amet"
+lorem.index(of: "sit", usingHorspoolImprovement: true)  // 18
diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore/BoyerMoore.swift
index 24842b59e..2f6bf1392 100644
--- a/Boyer-Moore/BoyerMoore.swift
+++ b/Boyer-Moore/BoyerMoore.swift
@@ -6,33 +6,35 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func indexOf(pattern: String, useHorspoolImprovement: Bool = false) -> String.Index? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
+        // There are no possible match in an empty string
+        guard !isEmpty else { return nil }
+
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
-        assert(patternLength > 0)
-        assert(patternLength <= self.characters.count)
-        
+        guard patternLength > 0, patternLength <= characters.count else { return nil }
+
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
         for (i, c) in pattern.characters.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
-        
+
         // This points at the last character in the pattern.
         let p = pattern.index(before: pattern.endIndex)
         let lastChar = pattern[p]
-        
+
         // The pattern is scanned right-to-left, so skip ahead in the string by
         // the length of the pattern. (Minus 1 because startIndex already points
         // at the first character in the source string.)
-        var i = self.index(startIndex, offsetBy: patternLength - 1)
-        
+        var i = index(startIndex, offsetBy: patternLength - 1)
+
         // This is a helper function that steps backwards through both strings
         // until we find a character that doesn’t match, or until we’ve reached
         // the beginning of the pattern.
-        func backwards() -> String.Index? {
+        func backwards() -> Index? {
             var q = p
             var j = i
             while q > pattern.startIndex {
@@ -42,22 +44,21 @@ extension String {
             }
             return j
         }
-        
+
         // The main loop. Keep going until the end of the string is reached.
-        while i < self.endIndex {
+        while i < endIndex {
             let c = self[i]
-            
+
             // Does the current character match the last character from the pattern?
             if c == lastChar {
-                
+
                 // There is a possible match. Do a brute-force search backwards.
                 if let k = backwards() { return k }
-                
-                if !useHorspoolImprovement {
+
+                if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.
                     i = index(after: i)
-                }
-                else {
+                } else {
                     // Ensure to jump at least one character (this is needed because the first
                     // character is in the skipTable, and `skipTable[lastChar] = 0`)
                     let jumpOffset = max(skipTable[c] ?? patternLength, 1)
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 08347e3e7..2cb42b0bd 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -32,12 +32,14 @@ Here's how you could write it in Swift:
 
 ```swift
 extension String {
-    func indexOf(pattern: String) -> String.Index? {
+    func index(of pattern: String) -> Index? {
+        // There are no possible match in an empty string
+        guard !isEmpty else { return nil }
+
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
-        assert(patternLength > 0)
-        assert(patternLength <= self.characters.count)
+        guard patternLength > 0, patternLength <= characters.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
@@ -53,12 +55,12 @@ extension String {
         // The pattern is scanned right-to-left, so skip ahead in the string by
         // the length of the pattern. (Minus 1 because startIndex already points
         // at the first character in the source string.)
-        var i = self.index(startIndex, offsetBy: patternLength - 1)
+        var i = index(startIndex, offsetBy: patternLength - 1)
 
         // This is a helper function that steps backwards through both strings
         // until we find a character that doesn’t match, or until we’ve reached
         // the beginning of the pattern.
-        func backwards() -> String.Index? {
+        func backwards() -> Index? {
             var q = p
             var j = i
             while q > pattern.startIndex {
@@ -70,7 +72,7 @@ extension String {
         }
 
         // The main loop. Keep going until the end of the string is reached.
-        while i < self.endIndex {
+        while i < endIndex {
             let c = self[i]
 
             // Does the current character match the last character from the pattern?
@@ -157,12 +159,14 @@ Here's an implementation of the Boyer-Moore-Horspool algorithm:
 
 ```swift
 extension String {
-    func indexOf(pattern: String) -> String.Index? {
+    func index(of pattern: String) -> Index? {
+        // There are no possible match in an empty string
+        guard !isEmpty else { return nil }
+
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
-        assert(patternLength > 0)
-        assert(patternLength <= self.characters.count)
+        guard patternLength > 0, patternLength <= characters.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
@@ -178,12 +182,12 @@ extension String {
         // The pattern is scanned right-to-left, so skip ahead in the string by
         // the length of the pattern. (Minus 1 because startIndex already points
         // at the first character in the source string.)
-        var i = self.index(startIndex, offsetBy: patternLength - 1)
+        var i = index(startIndex, offsetBy: patternLength - 1)
 
         // This is a helper function that steps backwards through both strings
         // until we find a character that doesn’t match, or until we’ve reached
         // the beginning of the pattern.
-        func backwards() -> String.Index? {
+        func backwards() -> Index? {
             var q = p
             var j = i
             while q > pattern.startIndex {
@@ -195,7 +199,7 @@ extension String {
         }
 
         // The main loop. Keep going until the end of the string is reached.
-        while i < self.endIndex {
+        while i < endIndex {
             let c = self[i]
 
             // Does the current character match the last character from the pattern?
diff --git a/Boyer-Moore/Tests/BoyerMooreTests.swift b/Boyer-Moore/Tests/BoyerMooreTests.swift
index f1638afcd..9efe60874 100755
--- a/Boyer-Moore/Tests/BoyerMooreTests.swift
+++ b/Boyer-Moore/Tests/BoyerMooreTests.swift
@@ -17,12 +17,12 @@ class BoyerMooreTest: XCTestCase {
     }
 
     func assert(pattern: String, doesNotExistsIn string: String) {
-        let index = string.indexOf(pattern: pattern, useHorspoolImprovement: useHorspoolImprovement)
+        let index = string.index(of: pattern, usingHorspoolImprovement: useHorspoolImprovement)
         XCTAssertNil(index)
     }
 
     func assert(pattern: String, existsIn string: String) {
-        let index = string.indexOf(pattern: pattern, useHorspoolImprovement: useHorspoolImprovement)
+        let index = string.index(of: pattern, usingHorspoolImprovement: useHorspoolImprovement)
         XCTAssertNotNil(index)
 
         let startIndex = index!
@@ -31,6 +31,24 @@ class BoyerMooreTest: XCTestCase {
         XCTAssertEqual(match, pattern)
     }
 
+    func testSearchPatternInEmptyString() {
+        let string = ""
+        let pattern = "ABCDEF"
+        assert(pattern: pattern, doesNotExistsIn: string)
+    }
+
+    func testSearchEmptyPatternString() {
+        let string = "ABCDEF"
+        let pattern = ""
+        assert(pattern: pattern, doesNotExistsIn: string)
+    }
+
+    func testSearchPatternLongerThanString() {
+        let string = "ABC"
+        let pattern = "ABCDEF"
+        assert(pattern: pattern, doesNotExistsIn: string)
+    }
+
     func testSearchTheSameString() {
         let string = "ABCDEF"
         let pattern = "ABCDEF"

From 960bca13c0207014040b96ba22e586b688279be9 Mon Sep 17 00:00:00 2001
From: mmazzei <matiasmazzei@gmail.com>
Date: Sun, 25 Dec 2016 17:58:00 -0300
Subject: [PATCH 0729/1679] Removed redundant validation.

---
 Boyer-Moore/BoyerMoore.playground/Contents.swift | 3 ---
 Boyer-Moore/BoyerMoore.swift                     | 3 ---
 Boyer-Moore/README.markdown                      | 6 ------
 3 files changed, 12 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index f1ae5018e..f553e1a00 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -9,9 +9,6 @@
 */
 extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
-        // There are no possible match in an empty string
-        guard !isEmpty else { return nil }
-
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore/BoyerMoore.swift
index 2f6bf1392..af8aea9d9 100644
--- a/Boyer-Moore/BoyerMoore.swift
+++ b/Boyer-Moore/BoyerMoore.swift
@@ -7,9 +7,6 @@
 */
 extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
-        // There are no possible match in an empty string
-        guard !isEmpty else { return nil }
-
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index 2cb42b0bd..e821b812e 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -33,9 +33,6 @@ Here's how you could write it in Swift:
 ```swift
 extension String {
     func index(of pattern: String) -> Index? {
-        // There are no possible match in an empty string
-        guard !isEmpty else { return nil }
-
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count
@@ -160,9 +157,6 @@ Here's an implementation of the Boyer-Moore-Horspool algorithm:
 ```swift
 extension String {
     func index(of pattern: String) -> Index? {
-        // There are no possible match in an empty string
-        guard !isEmpty else { return nil }
-
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.characters.count

From f618414c65e8b45f7f11010ad988e733cea23395 Mon Sep 17 00:00:00 2001
From: Joshua Alvarado <alvaradojoshua0@gmail.com>
Date: Mon, 26 Dec 2016 11:31:54 -0700
Subject: [PATCH 0730/1679] Add shared scheme to test Project for tests

---
 .../xcshareddata/xcschemes/Test.xcscheme      | 99 +++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme

diff --git a/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme b/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
new file mode 100644
index 000000000..9a1b39e69
--- /dev/null
+++ b/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
@@ -0,0 +1,99 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0820"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "NO"
+            buildForArchiving = "NO"
+            buildForAnalyzing = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "9437D8801E0D960A00A38FB8"
+               BuildableName = "Test.xctest"
+               BlueprintName = "Test"
+               ReferencedContainer = "container:Test.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "9437D8801E0D960A00A38FB8"
+               BuildableName = "Test.xctest"
+               BlueprintName = "Test"
+               ReferencedContainer = "container:Test.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "9437D8801E0D960A00A38FB8"
+            BuildableName = "Test.xctest"
+            BlueprintName = "Test"
+            ReferencedContainer = "container:Test.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "9437D8801E0D960A00A38FB8"
+            BuildableName = "Test.xctest"
+            BlueprintName = "Test"
+            ReferencedContainer = "container:Test.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "9437D8801E0D960A00A38FB8"
+            BuildableName = "Test.xctest"
+            BlueprintName = "Test"
+            ReferencedContainer = "container:Test.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From d8b96a480aeaefd3ead13c409c6957071ecfc931 Mon Sep 17 00:00:00 2001
From: Nagasawa Hiroki <civokjots10.pico@gmail.com>
Date: Wed, 28 Dec 2016 08:34:51 +0900
Subject: [PATCH 0731/1679] Fix Access Control position in AVLTree

---
 AVL Tree/AVLTree.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index b4b97f0d6..cfcf114c0 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -29,7 +29,7 @@ public class TreeNode<Key: Comparable, Payload> {
   internal var leftChild: Node?
   internal var rightChild: Node?
   fileprivate var height: Int
-  weak fileprivate var parent: Node?
+  fileprivate weak var parent: Node?
 
   public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
     self.key = key

From 03f176083b22b1ba2c40e0fb0f21af8d0451424b Mon Sep 17 00:00:00 2001
From: Nagasawa Hiroki <civokjots10.pico@gmail.com>
Date: Wed, 28 Dec 2016 10:16:36 +0900
Subject: [PATCH 0732/1679] Make each steps clear

---
 Red-Black Tree/README.markdown | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index d4e86a095..05993f016 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -49,16 +49,17 @@ n   n  n  n                     n   b
 
 We create a new node with the value to be inserted into the tree. The color of this new node is always red.
 We perform a standard BST insert with this node. Now the three might not be a valid RBT anymore.
-We now go through several insertion steps in order to make the tree valid again. We call the just inserted node n.
-1. We check if n is the rootNode, if so we paint it black and we are done. If not we go to step 2.
+We now go through several insertion steps in order to make the tree valid again. We call the just inserted node n.  
+
+**Step 1**: We check if n is the rootNode, if so we paint it black and we are done. If not we go to Step 2.
 
 We now know that n at least has a parent as it is not the rootNode.
 
-2. We check if the parent of n is black if so we are done. If not we go to step 3.
+**Step 2**: We check if the parent of n is black if so we are done. If not we go to Step 3.
 
 We now know the parent is also not the root node as the parent is red. Thus n also has a grandparent and thus also an uncle as every node has two children. This uncle may however be a nullLeaf
 
-3. We check if n's uncle is red. If not we go to 4. If n's uncle is indeed red we recolor uncle and parent to black and n's grandparent to red. We now go back to step 1 performing the same logic on n's grandparent.
+**Step 3**: We check if n's uncle is red. If not we go to Step 4. If n's uncle is indeed red we recolor uncle and parent to black and n's grandparent to red. We now go back to step 1 performing the same logic on n's grandparent.
 
 From here there are four cases:
 - **The left left case.** n's parent is the left child of its parent and n is the left child of its parent.
@@ -66,14 +67,14 @@ From here there are four cases:
 - **The right right case** n's parent is the right child of its parent and n is the right child of its parent.
 - **The right left case** n's parent is the right child of its parent and n is the left child of its parent.
 
-4. Step 4 checks if either the **left right** case or the **right left** case applies to the current situation.
-  - If we find the **left right case**, we left rotate n's parent and go to step 5 while setting n to n's parent. (This transforms the **left right** case into the **left left** case)
-  - If we find the **right left case**, we right rotate n's parent and go to step 5 while setting n to n's parent. (This transforms the **right left** case into the **right right** case)
-  - If we find neither of these two we proceed to step 5.
+**Step 4**: checks if either the **left right** case or the **right left** case applies to the current situation.
+  - If we find the **left right case**, we left rotate n's parent and go to Step 5 while setting n to n's parent. (This transforms the **left right** case into the **left left** case)
+  - If we find the **right left case**, we right rotate n's parent and go to Step 5 while setting n to n's parent. (This transforms the **right left** case into the **right right** case)
+  - If we find neither of these two we proceed to Step 5.
 
 n's parent is now red, while n's grandparent is black.
 
-5. We swap the colors of n's parent and grandparent.
+**Step 5**: We swap the colors of n's parent and grandparent.
   - We either right rotate n's grandparent in case of the **left left** case
   - Or we left rotate n's grandparent in case of the **right right** case
 

From f8857406b07e0012c96d862e297669a04aba195a Mon Sep 17 00:00:00 2001
From: Mohamed Emad Hegab <emadhegab@gmail.com>
Date: Wed, 28 Dec 2016 10:55:57 +0100
Subject: [PATCH 0733/1679] swift 3 update

---
 Select Minimum Maximum/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index 5e006f50e..a67f4ec8e 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -89,7 +89,7 @@ The result is a minimum of `3` and a maximum of `9`.
 Here is a simple implementation in Swift:
 
 ```swift
-func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)? {
+func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
   guard !array.isEmpty else {
     return nil
   }

From 411cbd208df10cb6a9bd9516bba3bae66173d7a6 Mon Sep 17 00:00:00 2001
From: mattthousand <matt.buckley@raizlabs.com>
Date: Wed, 28 Dec 2016 13:33:29 -0500
Subject: [PATCH 0734/1679] Convert to swift 3.0 syntax.

---
 Heap Sort/HeapSort.playground/Contents.swift  | 21 +++++++++++++++++++
 Heap Sort/HeapSort.swift                      |  6 +++---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 Heap/Heap.swift                               | 18 ++++++++--------
 5 files changed, 43 insertions(+), 14 deletions(-)
 create mode 100644 Heap Sort/HeapSort.playground/Contents.swift

diff --git a/Heap Sort/HeapSort.playground/Contents.swift b/Heap Sort/HeapSort.playground/Contents.swift
new file mode 100644
index 000000000..5dbe2e14f
--- /dev/null
+++ b/Heap Sort/HeapSort.playground/Contents.swift	
@@ -0,0 +1,21 @@
+//: Playground - noun: a place where people can play
+
+extension Heap {
+    public mutating func sort() -> [T] {
+        for i in (elements.count - 1).stride(through: 1, by: -1) {
+            swap(&elements[0], &elements[i])
+            shiftDown(index: 0, heapSize: i)
+        }
+        return elements
+    }
+}
+
+/*
+ Sorts an array using a heap.
+ Heapsort can be performed in-place, but it is not a stable sort.
+ */
+public func heapsort<T>(a: [T], _ sort: (T, T) -> Bool) -> [T] {
+    let reverseOrder = { i1, i2 in sort(i2, i1) }
+    var h = Heap(array: a, sort: reverseOrder)
+    return h.sort()
+}
diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index ec5b4a478..3fbaab14d 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,8 +1,8 @@
 extension Heap {
   public mutating func sort() -> [T] {
-    for i in (elements.count - 1).stride(through: 1, by: -1) {
+    for i in stride(from: (elements.count - 1), through: 1, by: -1) {
       swap(&elements[0], &elements[i])
-      shiftDown(index: 0, heapSize: i)
+      shiftDown(0, heapSize: i)
     }
     return elements
   }
@@ -12,7 +12,7 @@ extension Heap {
   Sorts an array using a heap.
   Heapsort can be performed in-place, but it is not a stable sort.
 */
-public func heapsort<T>(a: [T], _ sort: (T, T) -> Bool) -> [T] {
+public func heapsort<T>(_ a: [T], _ sort: @escaping (T, T) -> Bool) -> [T] {
   let reverseOrder = { i1, i2 in sort(i2, i1) }
   var h = Heap(array: a, sort: reverseOrder)
   return h.sort()
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index 454222c49..f7f101cd6 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,11 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -149,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -224,6 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..dfcf6de42 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index eba7ca1cf..fa30df362 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -46,7 +46,7 @@ public struct Heap<T> {
   fileprivate mutating func buildHeap(fromArray array: [T]) {
     elements = array
     for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(index: i, heapSize: elements.count)
+      shiftDown(i, heapSize: elements.count)
     }
   }
 
@@ -98,7 +98,7 @@ public struct Heap<T> {
    */
   public mutating func insert(_ value: T) {
     elements.append(value)
-    shiftUp(index: elements.count - 1)
+    shiftUp(elements.count - 1)
   }
 
   public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
@@ -116,7 +116,7 @@ public struct Heap<T> {
     
     assert(isOrderedBefore(value, elements[i]))
     elements[i] = value
-    shiftUp(index: i)
+    shiftUp(i)
   }
 
   /**
@@ -142,14 +142,14 @@ public struct Heap<T> {
    * Removes an arbitrary node from the heap. Performance: O(log n). You need
    * to know the node's index, which may actually take O(n) steps to find.
    */
-  public mutating func removeAt(index: Int) -> T? {
+  public mutating func removeAt(_ index: Int) -> T? {
     guard index < elements.count else { return nil }
     
     let size = elements.count - 1
     if index != size {
       swap(&elements[index], &elements[size])
-      shiftDown(index: index, heapSize: size)
-      shiftUp(index: index)
+      shiftDown(index, heapSize: size)
+      shiftUp(index)
     }
     return elements.removeLast()
   }
@@ -158,7 +158,7 @@ public struct Heap<T> {
    * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
-  mutating func shiftUp(index: Int) {
+  mutating func shiftUp(_ index: Int) {
     var childIndex = index
     let child = elements[childIndex]
     var parentIndex = self.parentIndex(ofIndex: childIndex)
@@ -173,14 +173,14 @@ public struct Heap<T> {
   }
 
   mutating func shiftDown() {
-    shiftDown(index: 0, heapSize: elements.count)
+    shiftDown(0, heapSize: elements.count)
   }
 
   /**
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  mutating func shiftDown(index: Int, heapSize: Int) {
+  mutating func shiftDown(_ index: Int, heapSize: Int) {
     var parentIndex = index
 
     while true {

From 75d866a0b9df43a2803bcad6f25f3151f51b73c2 Mon Sep 17 00:00:00 2001
From: mattthousand <matt.buckley@raizlabs.com>
Date: Wed, 28 Dec 2016 13:35:51 -0500
Subject: [PATCH 0735/1679] Update README.

---
 Heap Sort/README.markdown | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index 3d8b0f394..5f047f82b 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -48,13 +48,13 @@ Here's how you can implement heap sort in Swift:
 
 ```swift
 extension Heap {
-  public mutating func sort() -> [T] {
-    for i in (elements.count - 1).stride(through: 1, by: -1) {
-      swap(&elements[0], &elements[i])
-      shiftDown(index: 0, heapSize: i)
-    }
+    public mutating func sort() -> [T] {
+        for i in stride(from: (elements.count - 1), through: 1, by: -1) {
+            swap(&elements[0], &elements[i])
+            shiftDown(0, heapSize: i)
+        }
     return elements
-  }
+    }
 }
 ```
 
@@ -70,10 +70,10 @@ Because we need a max-heap to sort from low-to-high, you need to give `Heap` the
 We can write a handy helper function for that:
 
 ```swift
-public func heapsort<T>(a: [T], _ sort: (T, T) -> Bool) -> [T] {
-  let reverseOrder = { i1, i2 in sort(i2, i1) }
-  var h = Heap(array: a, sort: reverseOrder)
-  return h.sort()
+public func heapsort<T>(_ a: [T], _ sort: @escaping (T, T) -> Bool) -> [T] {
+    let reverseOrder = { i1, i2 in sort(i2, i1) }
+    var h = Heap(array: a, sort: reverseOrder)
+    return h.sort()
 }
 ```
 

From bb5cbe6e839501edbc6a75d9c99748511b369040 Mon Sep 17 00:00:00 2001
From: mattthousand <matt.buckley@raizlabs.com>
Date: Wed, 28 Dec 2016 13:39:53 -0500
Subject: [PATCH 0736/1679] Uncomment .travis.yml.

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 7b5faffa6..79eb3e051 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -23,7 +23,7 @@ script:
 # - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
 # - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests

From 6a15e73d72369d44d1b5b118c1e2f45f04b504b7 Mon Sep 17 00:00:00 2001
From: mattthousand <matt.buckley@raizlabs.com>
Date: Wed, 28 Dec 2016 13:41:50 -0500
Subject: [PATCH 0737/1679] Remove playground.

---
 Heap Sort/HeapSort.playground/Contents.swift | 21 --------------------
 1 file changed, 21 deletions(-)
 delete mode 100644 Heap Sort/HeapSort.playground/Contents.swift

diff --git a/Heap Sort/HeapSort.playground/Contents.swift b/Heap Sort/HeapSort.playground/Contents.swift
deleted file mode 100644
index 5dbe2e14f..000000000
--- a/Heap Sort/HeapSort.playground/Contents.swift	
+++ /dev/null
@@ -1,21 +0,0 @@
-//: Playground - noun: a place where people can play
-
-extension Heap {
-    public mutating func sort() -> [T] {
-        for i in (elements.count - 1).stride(through: 1, by: -1) {
-            swap(&elements[0], &elements[i])
-            shiftDown(index: 0, heapSize: i)
-        }
-        return elements
-    }
-}
-
-/*
- Sorts an array using a heap.
- Heapsort can be performed in-place, but it is not a stable sort.
- */
-public func heapsort<T>(a: [T], _ sort: (T, T) -> Bool) -> [T] {
-    let reverseOrder = { i1, i2 in sort(i2, i1) }
-    var h = Heap(array: a, sort: reverseOrder)
-    return h.sort()
-}

From 356844c7d61630b4aa09eb9e3d3d785593cf86e2 Mon Sep 17 00:00:00 2001
From: cruisediary <cruzdiary@gmail.com>
Date: Thu, 29 Dec 2016 18:18:14 +0900
Subject: [PATCH 0738/1679] Updating to Swift3 (enum lowercase)

- playground
- README.md
- some.swift file
---
 .../Contents.swift                            |  2 +-
 .../Sources/BinarySearchTree.swift            | 54 ++++++-------
 .../Solution 2/BinarySearchTree.swift         | 54 ++++++-------
 .../CountingSort.playground/Contents.swift    |  6 +-
 Counting Sort/CountingSort.swift              |  4 +-
 Linked List/README.markdown                   |  4 +-
 .../ShuntingYard.playground/Contents.swift    | 78 +++++++++----------
 Shunting Yard/ShuntingYard.swift              | 62 +++++++--------
 8 files changed, 132 insertions(+), 132 deletions(-)

diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 12fbba81d..8df69fb6a 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,7 +1,7 @@
 //: Playground - noun: a place where people can play
 
 // Each time you insert something, you get back a completely new tree.
-var tree = BinarySearchTree.Leaf(7)
+var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
 tree = tree.insert(newValue: 5)
 tree = tree.insert(newValue: 10)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index b692efdc4..5128bb348 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -4,25 +4,25 @@
   The tree is immutable. Any insertions or deletions will create a new tree.
 */
 public enum BinarySearchTree<T: Comparable> {
-  case Empty
-  case Leaf(T)
-  indirect case Node(BinarySearchTree, T, BinarySearchTree)
+  case empty
+  case leaf(T)
+  indirect case node(BinarySearchTree, T, BinarySearchTree)
 
   /* How many nodes are in this subtree. Performance: O(n). */
   public var count: Int {
     switch self {
-    case .Empty: return 0
-    case .Leaf: return 1
-    case let .Node(left, _, right): return left.count + 1 + right.count
+    case .empty: return 0
+    case .leaf: return 1
+    case let .node(left, _, right): return left.count + 1 + right.count
     }
   }
 
   /* Distance of this node to its lowest leaf. Performance: O(n). */
   public var height: Int {
     switch self {
-    case .Empty: return 0
-    case .Leaf: return 1
-    case let .Node(left, _, right): return 1 + max(left.height, right.height)
+    case .empty: return 0
+    case .leaf: return 1
+    case let .node(left, _, right): return 1 + max(left.height, right.height)
     }
   }
 
@@ -32,21 +32,21 @@ public enum BinarySearchTree<T: Comparable> {
   */
   public func insert(newValue: T) -> BinarySearchTree {
     switch self {
-    case .Empty:
-      return .Leaf(newValue)
+    case .empty:
+      return .leaf(newValue)
 
-    case .Leaf(let value):
+    case .leaf(let value):
       if newValue < value {
-        return .Node(.Leaf(newValue), value, .Empty)
+        return .node(.leaf(newValue), value, .empty)
       } else {
-        return .Node(.Empty, value, .Leaf(newValue))
+        return .node(.empty, value, .leaf(newValue))
       }
 
-    case .Node(let left, let value, let right):
+    case .node(let left, let value, let right):
       if newValue < value {
-        return .Node(left.insert(newValue: newValue), value, right)
+        return .node(left.insert(newValue: newValue), value, right)
       } else {
-        return .Node(left, value, right.insert(newValue: newValue))
+        return .node(left, value, right.insert(newValue: newValue))
       }
     }
   }
@@ -57,11 +57,11 @@ public enum BinarySearchTree<T: Comparable> {
   */
   public func search(x: T) -> BinarySearchTree? {
     switch self {
-    case .Empty:
+    case .empty:
       return nil
-    case .Leaf(let y):
+    case .leaf(let y):
       return (x == y) ? self : nil
-    case let .Node(left, y, right):
+    case let .node(left, y, right):
       if x < y {
         return left.search(x: x)
       } else if y < x {
@@ -82,11 +82,11 @@ public enum BinarySearchTree<T: Comparable> {
   public func minimum() -> BinarySearchTree {
     var node = self
     var prev = node
-    while case let .Node(next, _, _) = node {
+    while case let .node(next, _, _) = node {
       prev = node
       node = next
     }
-    if case .Leaf = node {
+    if case .leaf = node {
       return node
     }
     return prev
@@ -98,11 +98,11 @@ public enum BinarySearchTree<T: Comparable> {
   public func maximum() -> BinarySearchTree {
     var node = self
     var prev = node
-    while case let .Node(_, _, next) = node {
+    while case let .node(_, _, next) = node {
       prev = node
       node = next
     }
-    if case .Leaf = node {
+    if case .leaf = node {
       return node
     }
     return prev
@@ -112,9 +112,9 @@ public enum BinarySearchTree<T: Comparable> {
 extension BinarySearchTree: CustomDebugStringConvertible {
   public var debugDescription: String {
     switch self {
-    case .Empty: return "."
-    case .Leaf(let value): return "\(value)"
-    case .Node(let left, let value, let right):
+    case .empty: return "."
+    case .leaf(let value): return "\(value)"
+    case .node(let left, let value, let right):
       return "(\(left.debugDescription) <- \(value) -> \(right.debugDescription))"
     }
   }
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.swift
index ce2868bbf..272b86368 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.swift	
@@ -4,25 +4,25 @@
   The tree is immutable. Any insertions or deletions will create a new tree.
 */
 public enum BinarySearchTree<T: Comparable> {
-  case Empty
-  case Leaf(T)
-  indirect case Node(BinarySearchTree, T, BinarySearchTree)
+  case empty
+  case leaf(T)
+  indirect case node(BinarySearchTree, T, BinarySearchTree)
 
   /* How many nodes are in this subtree. Performance: O(n). */
   public var count: Int {
     switch self {
-    case .Empty: return 0
-    case .Leaf: return 1
-    case let .Node(left, _, right): return left.count + 1 + right.count
+    case .empty: return 0
+    case .leaf: return 1
+    case let .node(left, _, right): return left.count + 1 + right.count
     }
   }
 
   /* Distance of this node to its lowest leaf. Performance: O(n). */
   public var height: Int {
     switch self {
-    case .Empty: return 0
-    case .Leaf: return 1
-    case let .Node(left, _, right): return 1 + max(left.height, right.height)
+    case .empty: return 0
+    case .leaf: return 1
+    case let .node(left, _, right): return 1 + max(left.height, right.height)
     }
   }
 
@@ -32,21 +32,21 @@ public enum BinarySearchTree<T: Comparable> {
   */
   public func insert(newValue: T) -> BinarySearchTree {
     switch self {
-    case .Empty:
-      return .Leaf(newValue)
+    case .empty:
+      return .leaf(newValue)
 
-    case .Leaf(let value):
+    case .leaf(let value):
       if newValue < value {
-        return .Node(.Leaf(newValue), value, .Empty)
+        return .node(.leaf(newValue), value, .empty)
       } else {
-        return .Node(.Empty, value, .Leaf(newValue))
+        return .node(.empty, value, .leaf(newValue))
       }
 
-    case .Node(let left, let value, let right):
+    case .node(let left, let value, let right):
       if newValue < value {
-        return .Node(left.insert(newValue), value, right)
+        return .node(left.insert(newValue), value, right)
       } else {
-        return .Node(left, value, right.insert(newValue))
+        return .node(left, value, right.insert(newValue))
       }
     }
   }
@@ -57,11 +57,11 @@ public enum BinarySearchTree<T: Comparable> {
   */
   public func search(x: T) -> BinarySearchTree? {
     switch self {
-    case .Empty:
+    case .empty:
       return nil
-    case .Leaf(let y):
+    case .leaf(let y):
       return (x == y) ? self : nil
-    case let .Node(left, y, right):
+    case let .node(left, y, right):
       if x < y {
         return left.search(x)
       } else if y < x {
@@ -82,11 +82,11 @@ public enum BinarySearchTree<T: Comparable> {
   public func minimum() -> BinarySearchTree {
     var node = self
     var prev = node
-    while case let .Node(next, _, _) = node {
+    while case let .node(next, _, _) = node {
       prev = node
       node = next
     }
-    if case .Leaf = node {
+    if case .leaf = node {
       return node
     }
     return prev
@@ -98,11 +98,11 @@ public enum BinarySearchTree<T: Comparable> {
   public func maximum() -> BinarySearchTree {
     var node = self
     var prev = node
-    while case let .Node(_, _, next) = node {
+    while case let .node(_, _, next) = node {
       prev = node
       node = next
     }
-    if case .Leaf = node {
+    if case .leaf = node {
       return node
     }
     return prev
@@ -112,9 +112,9 @@ public enum BinarySearchTree<T: Comparable> {
 extension BinarySearchTree: CustomDebugStringConvertible {
   public var debugDescription: String {
     switch self {
-    case .Empty: return "."
-    case .Leaf(let value): return "\(value)"
-    case .Node(let left, let value, let right):
+    case .empty: return "."
+    case .leaf(let value): return "\(value)"
+    case .node(let left, let value, let right):
       return "(\(left.debugDescription) <- \(value) -> \(right.debugDescription))"
     }
   }
diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 2d85347ef..1d84f8132 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,12 +1,12 @@
 //: Playground - noun: a place where people can play
 
 enum CountingSortError: Error {
-  case ArrayEmpty
+  case arrayEmpty
 }
 
 func countingSort(array: [Int]) throws -> [Int] {
   guard array.count > 0 else {
-    throw CountingSortError.ArrayEmpty
+    throw CountingSortError.arrayEmpty
   }
 
   // Step 1
@@ -38,4 +38,4 @@ func countingSort(array: [Int]) throws -> [Int] {
 }
 
 
-try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
\ No newline at end of file
+try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index ec8c5adcb..d37bb2eff 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -7,12 +7,12 @@
 //
 
 enum CountingSortError: ErrorType {
-  case ArrayEmpty
+  case arrayEmpty
 }
 
 func countingSort(array: [Int]) throws -> [Int] {
   guard array.count > 0 else {
-    throw CountingSortError.ArrayEmpty
+    throw CountingSortError.arrayEmpty
   }
 
   // Step 1
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 7b2ec0c0d..1884aeb23 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -526,8 +526,8 @@ It is possible to implement a linked list with value semantics using an enum. Th
 
 ```swift
 enum ListNode<T> {
-  indirect case Node(T, next: ListNode<T>)
-  case End
+  indirect case node(T, next: ListNode<T>)
+  case end
 }
 ```
 
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index 04fed7739..707e2a0a3 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -1,51 +1,51 @@
 //: Playground - noun: a place where people can play
 
 internal enum OperatorAssociativity {
-  case LeftAssociative
-  case RightAssociative
+  case leftAssociative
+  case rightAssociative
 }
 
 public enum OperatorType: CustomStringConvertible {
-  case Add
-  case Subtract
-  case Divide
-  case Multiply
-  case Percent
-  case Exponent
+  case add
+  case subtract
+  case divide
+  case multiply
+  case percent
+  case exponent
 
   public var description: String {
     switch self {
-      case Add:
+      case add:
         return "+"
-      case Subtract:
+      case subtract:
         return "-"
-      case Divide:
+      case divide:
         return "/"
-      case Multiply:
+      case multiply:
         return "*"
-      case Percent:
+      case percent:
         return "%"
-      case Exponent:
+      case exponent:
         return "^"
     }
   }
 }
 
 public enum TokenType: CustomStringConvertible {
-  case OpenBracket
-  case CloseBracket
+  case openBracket
+  case closeBracket
   case Operator(OperatorToken)
-  case Operand(Double)
+  case operand(Double)
 
   public var description: String {
     switch self {
-      case OpenBracket:
+      case openBracket:
         return "("
-      case CloseBracket:
+      case closeBracket:
         return ")"
       case Operator(let operatorToken):
         return operatorToken.description
-      case Operand(let value):
+      case operand(let value):
         return "\(value)"
     }
   }
@@ -60,21 +60,21 @@ public struct OperatorToken: CustomStringConvertible {
 
   var precedence: Int {
     switch operatorType {
-      case .Add, .Subtract:
+      case .add, .subtract:
         return 0
-      case .Divide, .Multiply, .Percent:
+      case .divide, .multiply, .percent:
         return 5
-      case .Exponent:
+      case .exponent:
         return 10
     }
   }
 
   var associativity: OperatorAssociativity {
     switch operatorType {
-      case .Add, .Subtract, .Divide, .Multiply, .Percent:
-        return .LeftAssociative
-      case .Exponent:
-        return .RightAssociative
+      case .add, .subtract, .divide, .multiply, .percent:
+        return .leftAssociative
+      case .exponent:
+        return .rightAssociative
     }
   }
 
@@ -99,7 +99,7 @@ public struct Token: CustomStringConvertible {
   }
 
   init(operand: Double) {
-    tokenType = .Operand(operand)
+    tokenType = .operand(operand)
   }
 
   init(operatorType: OperatorType) {
@@ -108,7 +108,7 @@ public struct Token: CustomStringConvertible {
 
   var isOpenBracket: Bool {
     switch tokenType {
-      case .OpenBracket:
+      case .openBracket:
         return true
       default:
         return false
@@ -175,14 +175,14 @@ public func reversePolishNotation(expression: [Token]) -> String {
 
   for token in expression {
     switch token.tokenType {
-      case .Operand(_):
+      case .operand(_):
         reversePolishNotation.append(token)
 
-      case .OpenBracket:
+      case .openBracket:
         tokenStack.push(token)
 
-      case .CloseBracket:
-        while tokenStack.count > 0, let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+      case .closeBracket:
+        while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
           reversePolishNotation.append(tempToken)
         }
 
@@ -217,19 +217,19 @@ public func reversePolishNotation(expression: [Token]) -> String {
 
 let expr = InfixExpressionBuilder()
   .addOperand(3)
-  .addOperator(.Add)
+  .addOperator(.add)
   .addOperand(4)
-  .addOperator(.Multiply)
+  .addOperator(.multiply)
   .addOperand(2)
-  .addOperator(.Divide)
+  .addOperator(.divide)
   .addOpenBracket()
   .addOperand(1)
-  .addOperator(.Subtract)
+  .addOperator(.subtract)
   .addOperand(5)
   .addCloseBracket()
-  .addOperator(.Exponent)
+  .addOperator(.exponent)
   .addOperand(2)
-  .addOperator(.Exponent)
+  .addOperator(.exponent)
   .addOperand(3)
   .build()
 
diff --git a/Shunting Yard/ShuntingYard.swift b/Shunting Yard/ShuntingYard.swift
index 5159c9172..9d31d5a58 100644
--- a/Shunting Yard/ShuntingYard.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -7,51 +7,51 @@
 //
 
 internal enum OperatorAssociativity {
-  case LeftAssociative
-  case RightAssociative
+  case leftAssociative
+  case rightAssociative
 }
 
 public enum OperatorType: CustomStringConvertible {
-  case Add
-  case Subtract
-  case Divide
-  case Multiply
-  case Percent
-  case Exponent
+  case add
+  case subtract
+  case divide
+  case multiply
+  case percent
+  case exponent
 
   public var description: String {
     switch self {
-      case Add:
+      case add:
         return "+"
-      case Subtract:
+      case subtract:
         return "-"
-      case Divide:
+      case divide:
         return "/"
-      case Multiply:
+      case multiply:
         return "*"
-      case Percent:
+      case percent:
         return "%"
-      case Exponent:
+      case exponent:
         return "^"
     }
   }
 }
 
 public enum TokenType: CustomStringConvertible {
-  case OpenBracket
-  case CloseBracket
+  case openBracket
+  case closeBracket
   case Operator(OperatorToken)
-  case Operand(Double)
+  case operand(Double)
 
   public var description: String {
     switch self {
-      case OpenBracket:
+      case openBracket:
         return "("
-      case CloseBracket:
+      case closeBracket:
         return ")"
       case Operator(let operatorToken):
         return operatorToken.description
-      case Operand(let value):
+      case operand(let value):
         return "\(value)"
     }
   }
@@ -66,20 +66,20 @@ public struct OperatorToken: CustomStringConvertible {
 
   var precedence: Int {
     switch operatorType {
-      case .Add, .Subtract:
+      case .add, .subtract:
         return 0
-      case .Divide, .Multiply, .Percent:
+      case .divide, .multiply, .percent:
         return 5
-      case .Exponent:
+      case .exponent:
         return 10
     }
   }
 
   var associativity: OperatorAssociativity {
     switch operatorType {
-      case .Add, .Subtract, .Divide, .Multiply, .Percent:
+      case .add, .subtract, .divide, .multiply, .percent:
         return .LeftAssociative
-      case .Exponent:
+      case .exponent:
         return .RightAssociative
     }
   }
@@ -105,7 +105,7 @@ public struct Token: CustomStringConvertible {
   }
 
   init(operand: Double) {
-    tokenType = .Operand(operand)
+    tokenType = .operand(operand)
   }
 
   init(operatorType: OperatorType) {
@@ -114,7 +114,7 @@ public struct Token: CustomStringConvertible {
 
   var isOpenBracket: Bool {
     switch tokenType {
-      case .OpenBracket:
+      case .openBracket:
         return true
       default:
         return false
@@ -181,14 +181,14 @@ public func reversePolishNotation(expression: [Token]) -> String {
 
   for token in expression {
     switch token.tokenType {
-      case .Operand(_):
+      case .operand(_):
         reversePolishNotation.append(token)
 
-      case .OpenBracket:
+      case .openBracket:
         tokenStack.push(token)
 
-      case .CloseBracket:
-        while tokenStack.count > 0, let tempToken = tokenStack.pop() where !tempToken.isOpenBracket {
+      case .closeBracket:
+        while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
           reversePolishNotation.append(tempToken)
         }
 

From e1517dc458375a589a4cfd49a3f7c0c16caaffd6 Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Thu, 29 Dec 2016 14:34:48 -0500
Subject: [PATCH 0739/1679] Corrected a spelling error and removed the "get"
 syntax for a property.

---
 Trie/Trie/Trie/Trie.swift | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index ad4e9f2e7..8f3b46123 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -16,9 +16,7 @@ class TrieNode<T: Hashable> {
     var children: [T: TrieNode] = [:]
     var isTerminating = false
     var isLeaf: Bool {
-        get {
-            return children.count == 0
-        }
+        return children.count == 0
     }
 
     /// Initializes a node.
@@ -62,7 +60,7 @@ class Trie {
     fileprivate let root: Node
     fileprivate var wordCount: Int
 
-    /// Creats an empty trie.
+    /// Creates an empty trie.
     init() {
         root = Node()
         wordCount = 0

From 5021bc79cd44f1d8ae8f32780984759d2cc57b5a Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Thu, 29 Dec 2016 16:48:29 -0500
Subject: [PATCH 0740/1679] Added NSCoding conformance.

---
 ...6ABF2F62-9363-4450-8DE1-D20F57026950.plist | 22 ++++++
 .../Info.plist                                | 33 ++++++++
 Trie/Trie/Trie/Trie.swift                     | 25 ++++++-
 Trie/Trie/TrieTests/TrieTests.swift           | 75 +++++++++++--------
 4 files changed, 121 insertions(+), 34 deletions(-)
 create mode 100644 Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist
 create mode 100644 Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/Info.plist

diff --git a/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist b/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist
new file mode 100644
index 000000000..01ff985c8
--- /dev/null
+++ b/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>classNames</key>
+	<dict>
+		<key>TrieTests</key>
+		<dict>
+			<key>testInsertPerformance()</key>
+			<dict>
+				<key>com.apple.XCTPerformanceMetric_WallClockTime</key>
+				<dict>
+					<key>baselineAverage</key>
+					<real>3.0053</real>
+					<key>baselineIntegrationDisplayName</key>
+					<string>Local Baseline</string>
+				</dict>
+			</dict>
+		</dict>
+	</dict>
+</dict>
+</plist>
diff --git a/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/Info.plist b/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/Info.plist
new file mode 100644
index 000000000..3c07f3d6a
--- /dev/null
+++ b/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/Info.plist
@@ -0,0 +1,33 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>runDestinationsByUUID</key>
+	<dict>
+		<key>6ABF2F62-9363-4450-8DE1-D20F57026950</key>
+		<dict>
+			<key>localComputer</key>
+			<dict>
+				<key>busSpeedInMHz</key>
+				<integer>100</integer>
+				<key>cpuCount</key>
+				<integer>1</integer>
+				<key>cpuKind</key>
+				<string>Intel Core i7</string>
+				<key>cpuSpeedInMHz</key>
+				<integer>3300</integer>
+				<key>logicalCPUCoresPerPackage</key>
+				<integer>4</integer>
+				<key>modelCode</key>
+				<string>MacBookPro13,2</string>
+				<key>physicalCPUCoresPerPackage</key>
+				<integer>2</integer>
+				<key>platformIdentifier</key>
+				<string>com.apple.platform.macosx</string>
+			</dict>
+			<key>targetArchitecture</key>
+			<string>x86_64</string>
+		</dict>
+	</dict>
+</dict>
+</plist>
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 8f3b46123..ec3b1c5cc 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -43,7 +43,7 @@ class TrieNode<T: Hashable> {
 
 /// A trie data structure containing words.  Each node is a single
 /// character of a word.
-class Trie {
+class Trie: NSObject, NSCoding {
     typealias Node = TrieNode<Character>
     /// The number of words in the trie
     public var count: Int {
@@ -61,10 +61,31 @@ class Trie {
     fileprivate var wordCount: Int
 
     /// Creates an empty trie.
-    init() {
+    override init() {
         root = Node()
         wordCount = 0
     }
+
+    // MARK: NSCoding
+
+    /// Initializes the trie with words from an archive
+    ///
+    /// - Parameter decoder: Decodes the archive
+    required convenience init?(coder decoder: NSCoder) {
+        self.init()
+        let words = decoder.decodeObject(forKey: "words") as? [String]
+        for word in words! {
+            self.insert(word: word)
+        }
+    }
+
+    /// Encodes the words in the trie by putting them in an array then encoding
+    /// the array.
+    ///
+    /// - Parameter coder: The object that will encode the array
+    func encode(with coder: NSCoder) {
+        coder.encode(self.words, forKey: "words")
+    }
 }
 
 // MARK: - Adds methods: insert, remove, contains
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 236908ece..7ef02553f 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -12,20 +12,20 @@ import XCTest
 class TrieTests: XCTestCase {
     var wordArray: [String]?
     var trie = Trie()
-    
+
     /// Makes sure that the wordArray and trie are initialized before each test.
     override func setUp() {
         super.setUp()
         createWordArray()
         insertWordsIntoTrie()
     }
-    
-    /// Don't need to do anything here because the wordArrayu and trie should
+
+    /// Don't need to do anything here because the wordArray and trie should
     /// stay around.
     override func tearDown() {
         super.tearDown()
     }
-    
+
     /// Reads words from the dictionary file and inserts them into an array.  If
     /// the word array already has words, do nothing.  This allows running all
     /// tests without repeatedly filling the array with the same values.
@@ -36,7 +36,7 @@ class TrieTests: XCTestCase {
         let resourcePath = Bundle.main.resourcePath! as NSString
         let fileName = "dictionary.txt"
         let filePath = resourcePath.appendingPathComponent(fileName)
-        
+
         var data: String?
         do {
             data = try String(contentsOfFile: filePath, encoding: String.Encoding.utf8)
@@ -48,24 +48,23 @@ class TrieTests: XCTestCase {
         wordArray = data!.components(separatedBy: "\n")
         XCTAssertEqual(wordArray!.count, dictionarySize)
     }
-    
+
     /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
     func insertWordsIntoTrie() {
         guard trie.count == 0 else {
             return
         }
-        let numberOfWordsToInsert = wordArray!.count
-        for i in 0..<numberOfWordsToInsert {
-            trie.insert(word: wordArray![i])
+        for word in self.wordArray! {
+            trie.insert(word: word)
         }
     }
-    
+
     /// Tests that a newly created trie has zero words.
     func testCreate() {
         let trie = Trie()
         XCTAssertEqual(trie.count, 0)
     }
-    
+
     /// Tests the insert method
     func testInsert() {
         let trie = Trie()
@@ -78,7 +77,7 @@ class TrieTests: XCTestCase {
         XCTAssertTrue(trie.contains(word: "cut"))
         XCTAssertEqual(trie.count, 4)
     }
-    
+
     /// Tests the remove method
     func testRemove() {
         let trie = Trie()
@@ -90,7 +89,7 @@ class TrieTests: XCTestCase {
         XCTAssertFalse(trie.contains(word: "cute"))
         XCTAssertEqual(trie.count, 1)
     }
-    
+
     /// Tests the words property
     func testWords() {
         let trie = Trie()
@@ -101,52 +100,53 @@ class TrieTests: XCTestCase {
         XCTAssertEqual(words[0], "foobar")
         XCTAssertEqual(words.count, 1)
     }
-    
+
     /// Tests the performance of the insert method.
     func testInsertPerformance() {
-        let trie = Trie()
         self.measure() {
-            let numberOfWordsToInsert = self.wordArray!.count
-            for i in 0..<numberOfWordsToInsert {
-                trie.insert(word: self.wordArray![i])
+            let trie = Trie()
+            for word in self.wordArray! {
+                trie.insert(word: word)
             }
         }
         XCTAssertGreaterThan(trie.count, 0)
         XCTAssertEqual(trie.count, wordArray?.count)
     }
-    
+
     /// Tests the performance of the insert method when the words are already
     /// present.
     func testInsertAgainPerformance() {
         self.measure() {
-            let numberOfWordsToInsert = self.wordArray!.count
-            for i in 0..<numberOfWordsToInsert {
-                self.trie.insert(word: self.wordArray![i])
+            for word in self.wordArray! {
+                self.trie.insert(word: word)
             }
         }
     }
-    
+
     /// Tests the performance of the contains method.
     func testContainsPerformance() {
         self.measure() {
-            for i in 0..<self.wordArray!.count {
-                XCTAssertTrue(self.trie.contains(word: self.wordArray![i]))
+            for word in self.wordArray! {
+                XCTAssertTrue(self.trie.contains(word: word))
             }
-            
         }
     }
-    
-    /// Tests the performance of the remove method.
+
+    /// Tests the performance of the remove method.  Since setup has already put
+    /// words into the trie, remove them before measuring performance.
     func testRemovePerformance() {
+        for word in self.wordArray! {
+            self.trie.remove(word: word)
+        }
         self.measure() {
-            let numberOfWordsToRemove = self.wordArray!.count
-            for i in 0..<numberOfWordsToRemove {
-                self.trie.remove(word: self.wordArray![i])
+            self.insertWordsIntoTrie()
+            for word in self.wordArray! {
+                self.trie.remove(word: word)
             }
         }
         XCTAssertEqual(trie.count, 0)
     }
-    
+
     /// Tests the performance of the words computed property.  Also tests to see
     /// if it worked properly.
     func testWordsPerformance() {
@@ -159,4 +159,15 @@ class TrieTests: XCTestCase {
             XCTAssertTrue(self.trie.contains(word: word))
         }
     }
+
+    /// Tests the archiving and unarchiving of the trie.
+    func testArchiveAndUnarchive() {
+        let resourcePath = Bundle.main.resourcePath! as NSString
+        let fileName = "dictionary-archive"
+        let filePath = resourcePath.appendingPathComponent(fileName)
+        NSKeyedArchiver.archiveRootObject(trie, toFile: filePath)
+        let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as! Trie
+        XCTAssertEqual(trieCopy.count, trie.count)
+
+    }
 }

From 9eac5103085924368c3f822a502b349ff69a9c52 Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Thu, 29 Dec 2016 17:28:41 -0500
Subject: [PATCH 0741/1679] Added a ReadMe file.

---
 Trie/Trie/Trie.xcodeproj/project.pbxproj |  4 +++
 Trie/Trie/Trie/ReadMe.md                 | 33 ++++++++++++++++++++++++
 2 files changed, 37 insertions(+)
 create mode 100644 Trie/Trie/Trie/ReadMe.md

diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 8d3611b6d..055885ee1 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -17,6 +17,7 @@
 		EB798E2A1DFEF81400F0628D /* Trie.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798E281DFEF81400F0628D /* Trie.swift */; };
 		EB798E2C1DFEF90B00F0628D /* dictionary.txt in Resources */ = {isa = PBXBuildFile; fileRef = EB798E2B1DFEF90B00F0628D /* dictionary.txt */; };
 		EB798E2D1DFEF90B00F0628D /* dictionary.txt in Resources */ = {isa = PBXBuildFile; fileRef = EB798E2B1DFEF90B00F0628D /* dictionary.txt */; };
+		EB8369AD1E15C5710003A7F8 /* ReadMe.md in Sources */ = {isa = PBXBuildFile; fileRef = EB8369AC1E15C5710003A7F8 /* ReadMe.md */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
@@ -51,6 +52,7 @@
 		EB798E1C1DFEF79900F0628D /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		EB798E281DFEF81400F0628D /* Trie.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Trie.swift; sourceTree = "<group>"; };
 		EB798E2B1DFEF90B00F0628D /* dictionary.txt */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text; path = dictionary.txt; sourceTree = "<group>"; };
+		EB8369AC1E15C5710003A7F8 /* ReadMe.md */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = net.daringfireball.markdown; path = ReadMe.md; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -101,6 +103,7 @@
 		EB798DFC1DFEF79900F0628D /* Trie */ = {
 			isa = PBXGroup;
 			children = (
+				EB8369AC1E15C5710003A7F8 /* ReadMe.md */,
 				EB798DFD1DFEF79900F0628D /* AppDelegate.swift */,
 				EB798DFF1DFEF79900F0628D /* ViewController.swift */,
 				EB798E011DFEF79900F0628D /* Assets.xcassets */,
@@ -267,6 +270,7 @@
 			files = (
 				EB798E291DFEF81400F0628D /* Trie.swift in Sources */,
 				EB798E001DFEF79900F0628D /* ViewController.swift in Sources */,
+				EB8369AD1E15C5710003A7F8 /* ReadMe.md in Sources */,
 				EB798DFE1DFEF79900F0628D /* AppDelegate.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
diff --git a/Trie/Trie/Trie/ReadMe.md b/Trie/Trie/Trie/ReadMe.md
new file mode 100644
index 000000000..934585a3f
--- /dev/null
+++ b/Trie/Trie/Trie/ReadMe.md
@@ -0,0 +1,33 @@
+# Changes
+
+- Corrected a spelling error in a comment.
+
+- Got rid of the `get` syntax for a read only property as the coding guidelines suggest.
+
+- Changed several tests so that they are more Swift-like.  That is, they now feel like they are using the features of the language better.
+
+- Fixed a problem in the test method `testRemovePerformance`.  The `measure` method runs the block of code 10 times.  Previously, all words would get removed after the first run and the next 9 runs were very fast because there was nothing to do!  That is corrected now.
+
+- Made the `Trie` class a subclass of `NSObject` and had it conform to `NSCoding`.  Added a test to verify that this works.
+
+---
+
+I wasn't able to figure out how to recursively archive the trie.  Instead, I tried Kelvin's suggestion to use the `words` property to create an array of words in the trie, then archiving the array.
+
+There are a couple of nice aspects to this approach.
+
+- The `TrieNode` class can remain generic since it doesn't need to conform to `NSCoding`.
+
+- It doesn't require much new code.
+
+There are several downsides though.
+
+- The size of the archived words is three times the size of the original file of words!  Did I do this right?  The tests pass, so it seems correct.  I question whether archiving is worth the effort if the resulting archive is so much larger than the original file.
+
+- I would expect that archiving the trie would result in a file that was smaller than the original since a trie doesn't repeat leading character sequences when they are the same.
+
+- This requires that the trie get reconstructed when it is unarchived.
+
+- My gut tells me that it would be faster to archive and unarchive the trie itself, but I don't have any hard data to support this.
+
+I would like to see code that recursively archives the trie so we can compare the performance.

From 02ff5694e848fa5f39ab717b2c418e0fbf014190 Mon Sep 17 00:00:00 2001
From: Yohannes Wijaya <readyforservice@icloud.com>
Date: Fri, 30 Dec 2016 09:33:55 +0700
Subject: [PATCH 0742/1679] Added a new algorithms book under "Learn More"

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 5c769688a..6766e7025 100644
--- a/README.markdown
+++ b/README.markdown
@@ -198,6 +198,7 @@ For more information, check out these great books:
 - [The Algorithm Design Manual](http://www.algorist.com) by Skiena
 - [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
 - [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
+- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava 
 
 The following books are available for free online:
 

From 89fb804a5f006f2bcbe9c55f784a277852484581 Mon Sep 17 00:00:00 2001
From: gonini <zhanggoni@gmail.com>
Date: Mon, 2 Jan 2017 23:24:24 +0900
Subject: [PATCH 0743/1679] Updating to Swift3

I upgraded to swift 3 because it did not run as a grammar problem.
---
 .../Contents.swift                            | 24 +++++++++----------
 .../timeline.xctimeline                       |  6 -----
 .../Sources/Graph.swift                       |  8 +++----
 .../Sources/Node.swift                        |  2 +-
 Shortest Path (Unweighted)/ShortestPath.swift |  2 +-
 5 files changed, 18 insertions(+), 24 deletions(-)
 delete mode 100644 Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline

diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index cfc582c49..2380ebb69 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -2,15 +2,15 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
   var queue = Queue<Node>()
-  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
-  queue.enqueue(sourceInShortestPathsGraph)
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(label: source.label)
+  queue.enqueue(element: sourceInShortestPathsGraph)
   sourceInShortestPathsGraph.distance = 0
 
   while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
-        queue.enqueue(neighborNode)
+        queue.enqueue(element: neighborNode)
         neighborNode.distance = current.distance! + 1
       }
     }
@@ -23,14 +23,14 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
 
 let graph = Graph()
 
-let nodeA = graph.addNode("a")
-let nodeB = graph.addNode("b")
-let nodeC = graph.addNode("c")
-let nodeD = graph.addNode("d")
-let nodeE = graph.addNode("e")
-let nodeF = graph.addNode("f")
-let nodeG = graph.addNode("g")
-let nodeH = graph.addNode("h")
+let nodeA = graph.addNode(label: "a")
+let nodeB = graph.addNode(label: "b")
+let nodeC = graph.addNode(label: "c")
+let nodeD = graph.addNode(label: "d")
+let nodeE = graph.addNode(label: "e")
+let nodeF = graph.addNode(label: "f")
+let nodeG = graph.addNode(label: "g")
+let nodeH = graph.addNode(label: "h")
 
 graph.addEdge(nodeA, neighbor: nodeB)
 graph.addEdge(nodeA, neighbor: nodeC)
@@ -40,5 +40,5 @@ graph.addEdge(nodeC, neighbor: nodeF)
 graph.addEdge(nodeC, neighbor: nodeG)
 graph.addEdge(nodeE, neighbor: nodeH)
 
-let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
+let shortestPathGraph = breadthFirstSearchShortestPath(graph: graph, source: nodeA)
 print(shortestPathGraph.nodes)
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift
index 8cfb2a09c..8c3281aa8 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Graph.swift	
@@ -11,7 +11,7 @@ public class Graph: CustomStringConvertible, Equatable {
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
+  public func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
     source.neighbors.append(edge)
   }
@@ -35,13 +35,13 @@ public class Graph: CustomStringConvertible, Equatable {
     let duplicated = Graph()
 
     for node in nodes {
-      duplicated.addNode(node.label)
+      duplicated.addNode(label: node.label)
     }
 
     for node in nodes {
       for edge in node.neighbors {
-        let source = duplicated.findNodeWithLabel(node.label)
-        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
+        let source = duplicated.findNodeWithLabel(label: node.label)
+        let neighbour = duplicated.findNodeWithLabel(label: edge.neighbor.label)
         duplicated.addEdge(source, neighbor: neighbour)
       }
     }
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift
index 37a3b3fdf..ebdb6f4e3 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Sources/Node.swift	
@@ -23,7 +23,7 @@ public class Node: CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
diff --git a/Shortest Path (Unweighted)/ShortestPath.swift b/Shortest Path (Unweighted)/ShortestPath.swift
index 13ed0c080..6aa082a96 100644
--- a/Shortest Path (Unweighted)/ShortestPath.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.swift	
@@ -10,7 +10,7 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
-        queue.enqueue(neighborNode)
+        queue.enqueue(element: neighborNode)
         neighborNode.distance = current.distance! + 1
       }
     }

From 998fc13118dc7d7cefb7f088d3a70719ec5ea5d1 Mon Sep 17 00:00:00 2001
From: Mohamed Emad Hegab <mohamed.hegab@zalando.de>
Date: Mon, 2 Jan 2017 15:44:58 +0100
Subject: [PATCH 0744/1679] Fix for swift 3 on playground and rest of the
 classes

---
 Select Minimum Maximum/Maximum.swift          | 23 ++---
 Select Minimum Maximum/Minimum.swift          | 23 ++---
 .../MinimumMaximumPairs.swift                 | 63 ++++++------
 Select Minimum Maximum/README.markdown        |  7 +-
 .../Contents.swift                            | 99 ++++++++++---------
 .../timeline.xctimeline                       |  6 --
 6 files changed, 112 insertions(+), 109 deletions(-)
 delete mode 100644 Select Minimum Maximum/SelectMinimumMaximum.playground/timeline.xctimeline

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index 8c78ba478..991a0544e 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -1,15 +1,16 @@
 /*
-  Finds the maximum value in an array in O(n) time.
-*/
+ Finds the maximum value in an array in O(n) time.
+ */
 
-func maximum<T: Comparable>(var array: [T]) -> T? {
-  guard !array.isEmpty else {
-    return nil
-  }
+func maximum<T: Comparable>(_ array: [T]) -> T? {
+    var array = array
+    guard !array.isEmpty else {
+        return nil
+    }
 
-  var maximum = array.removeFirst()
-  for element in array {
-    maximum = element > maximum ? element : maximum
-  }
-  return maximum
+    var maximum = array.removeFirst()
+    for element in array {
+        maximum = element > maximum ? element : maximum
+    }
+    return maximum
 }
diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 9b08deb4f..90dfbd54b 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -1,15 +1,16 @@
 /*
-  Finds the minimum value in an array in O(n) time.
-*/
+ Finds the minimum value in an array in O(n) time.
+ */
 
-func minimum<T: Comparable>(var array: [T]) -> T? {
-  guard !array.isEmpty else {
-    return nil
-  }
+func minimum<T: Comparable>(_ array: [T]) -> T? {
+    var array = array
+    guard !array.isEmpty else {
+        return nil
+    }
 
-  var minimum = array.removeFirst()
-  for element in array {
-    minimum = element < minimum ? element : minimum
-  }
-  return minimum
+    var minimum = array.removeFirst()
+    for element in array {
+        minimum = element < minimum ? element : minimum
+    }
+    return minimum
 }
diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index 5798e1f32..b7deb570a 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -1,39 +1,40 @@
 /*
-  Finds the maximum and minimum value in an array in O(n) time.
-*/
+ Finds the maximum and minimum value in an array in O(n) time.
+ */
 
-func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)? {
-  guard !array.isEmpty else {
-    return nil
-  }
+func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
+    var array = array
+    guard !array.isEmpty else {
+        return nil
+    }
 
-  var minimum = array.first!
-  var maximum = array.first!
+    var minimum = array.first!
+    var maximum = array.first!
 
-  let hasOddNumberOfItems = array.count % 2 != 0
-  if hasOddNumberOfItems {
-    array.removeFirst()
-  }
+    let hasOddNumberOfItems = array.count % 2 != 0
+    if hasOddNumberOfItems {
+        array.removeFirst()
+    }
 
-  while !array.isEmpty {
-    let pair = (array.removeFirst(), array.removeFirst())
+    while !array.isEmpty {
+        let pair = (array.removeFirst(), array.removeFirst())
 
-    if pair.0 > pair.1 {
-      if pair.0 > maximum {
-        maximum = pair.0
-      }
-      if pair.1 < minimum {
-        minimum = pair.1
-      }
-    } else {
-      if pair.1 > maximum {
-        maximum = pair.1
-      }
-      if pair.0 < minimum {
-        minimum = pair.0
-      }
+        if pair.0 > pair.1 {
+            if pair.0 > maximum {
+                maximum = pair.0
+            }
+            if pair.1 < minimum {
+                minimum = pair.1
+            }
+        } else {
+            if pair.1 > maximum {
+                maximum = pair.1
+            }
+            if pair.0 < minimum {
+                minimum = pair.0
+            }
+        }
     }
-  }
-
-  return (minimum, maximum)
+    
+    return (minimum, maximum)
 }
diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index a67f4ec8e..09ca97039 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -23,7 +23,8 @@ Repeat this process until the all elements in the list have been processed.
 Here is a simple implementation in Swift:
 
 ```swift
-func minimum<T: Comparable>(var array: [T]) -> T? {
+func minimum<T: Comparable>(_ array: [T]) -> T? {
+  var array = array
   guard !array.isEmpty else {
     return nil
   }
@@ -35,7 +36,8 @@ func minimum<T: Comparable>(var array: [T]) -> T? {
   return minimum
 }
 
-func maximum<T: Comparable>(var array: [T]) -> T? {
+func maximum<T: Comparable>(_ array: [T]) -> T? {
+  var array = array
   guard !array.isEmpty else {
     return nil
   }
@@ -90,6 +92,7 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
+  var array = array
   guard !array.isEmpty else {
     return nil
   }
diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index ef92ac1e6..6076b5246 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -1,64 +1,67 @@
 // Compare each item to find minimum
-func minimum<T: Comparable>(var array: [T]) -> T? {
-  guard !array.isEmpty else {
-    return nil
-  }
+func minimum<T: Comparable>(_ array: [T]) -> T? {
+    var array = array
+    guard !array.isEmpty else {
+        return nil
+    }
 
-  var minimum = array.removeFirst()
-  for element in array {
-    minimum = element < minimum ? element : minimum
-  }
-  return minimum
+    var minimum = array.removeFirst()
+    for element in array {
+        minimum = element < minimum ? element : minimum
+    }
+    return minimum
 }
 
 // Compare each item to find maximum
-func maximum<T: Comparable>(var array: [T]) -> T? {
-  guard !array.isEmpty else {
-    return nil
-  }
+func maximum<T: Comparable>(_ array: [T]) -> T? {
+    var array = array
+    guard !array.isEmpty else {
+        return nil
+    }
 
-  var maximum = array.removeFirst()
-  for element in array {
-    maximum = element > maximum ? element : maximum
-  }
-  return maximum
+    var maximum = array.removeFirst()
+    for element in array {
+        maximum = element > maximum ? element : maximum
+    }
+    return maximum
 }
 
 // Compare in pairs to find minimum and maximum
-func minimumMaximum<T: Comparable>(var array: [T]) -> (minimum: T, maximum: T)? {
-  guard !array.isEmpty else {
-    return nil
-  }
+func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
+    var array = array
+    guard !array.isEmpty else {
+        return nil
+    }
 
-  var minimum = array.first!
-  var maximum = array.first!
+    var minimum = array.first!
+    var maximum = array.first!
 
-  let hasOddNumberOfItems = array.count % 2 != 0
-  if hasOddNumberOfItems {
-    array.removeFirst()
-  }
+    let hasOddNumberOfItems = array.count % 2 != 0
+    if hasOddNumberOfItems {
+        array.removeFirst()
+    }
 
-  while !array.isEmpty {
-    let pair = (array.removeFirst(), array.removeFirst())
+    while !array.isEmpty {
+        let pair = (array.removeFirst(), array.removeFirst())
 
-    if pair.0 > pair.1 {
-      if pair.0 > maximum {
-        maximum = pair.0
-      }
-      if pair.1 < minimum {
-        minimum = pair.1
-      }
-    } else {
-      if pair.1 > maximum {
-        maximum = pair.1
-      }
-      if pair.0 < minimum {
-        minimum = pair.0
-      }
+        if pair.0 > pair.1 {
+            if pair.0 > maximum {
+                maximum = pair.0
+            }
+            if pair.1 < minimum {
+                minimum = pair.1
+            }
+        } else {
+            if pair.1 > maximum {
+                maximum = pair.1
+            }
+            if pair.0 < minimum {
+                minimum = pair.0
+            }
+        }
     }
-  }
 
-  return (minimum, maximum)
+    return (minimum, maximum)
 }
 
 // Test of minimum and maximum functions
@@ -72,5 +75,5 @@ result.minimum
 result.maximum
 
 // Built-in Swift functions
-array.minElement()
-array.maxElement()
+array.min()
+array.max()
diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/timeline.xctimeline b/Select Minimum Maximum/SelectMinimumMaximum.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From dfc27f868b20b5ad6408238f7d97489ff518cd49 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-iMac.local>
Date: Mon, 2 Jan 2017 07:52:15 -0800
Subject: [PATCH 0745/1679] Fixed indentation of the code.

---
 .../Contents.swift                            | 106 +++++++++---------
 1 file changed, 53 insertions(+), 53 deletions(-)

diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index 6076b5246..182060805 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -1,67 +1,67 @@
 // Compare each item to find minimum
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    var array = array
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var minimum = array.removeFirst()
-    for element in array {
-        minimum = element < minimum ? element : minimum
-    }
-    return minimum
+  var array = array
+  guard !array.isEmpty else {
+    return nil
+  }
+  
+  var minimum = array.removeFirst()
+  for element in array {
+    minimum = element < minimum ? element : minimum
+  }
+  return minimum
 }
 
 // Compare each item to find maximum
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-    var array = array
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var maximum = array.removeFirst()
-    for element in array {
-        maximum = element > maximum ? element : maximum
-    }
-    return maximum
+  var array = array
+  guard !array.isEmpty else {
+    return nil
+  }
+  
+  var maximum = array.removeFirst()
+  for element in array {
+    maximum = element > maximum ? element : maximum
+  }
+  return maximum
 }
 
 // Compare in pairs to find minimum and maximum
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-    var array = array
-    guard !array.isEmpty else {
-        return nil
+  var array = array
+  guard !array.isEmpty else {
+    return nil
+  }
+  
+  var minimum = array.first!
+  var maximum = array.first!
+  
+  let hasOddNumberOfItems = array.count % 2 != 0
+  if hasOddNumberOfItems {
+    array.removeFirst()
+  }
+  
+  while !array.isEmpty {
+    let pair = (array.removeFirst(), array.removeFirst())
+    
+    if pair.0 > pair.1 {
+      if pair.0 > maximum {
+        maximum = pair.0
+      }
+      if pair.1 < minimum {
+        minimum = pair.1
+      }
+    } else {
+      if pair.1 > maximum {
+        maximum = pair.1
+      }
+      if pair.0 < minimum {
+        minimum = pair.0
+      }
     }
-
-    var minimum = array.first!
-    var maximum = array.first!
-
-    let hasOddNumberOfItems = array.count % 2 != 0
-    if hasOddNumberOfItems {
-        array.removeFirst()
-    }
-
-    while !array.isEmpty {
-        let pair = (array.removeFirst(), array.removeFirst())
-
-        if pair.0 > pair.1 {
-            if pair.0 > maximum {
-                maximum = pair.0
-            }
-            if pair.1 < minimum {
-                minimum = pair.1
-            }
-        } else {
-            if pair.1 > maximum {
-                maximum = pair.1
-            }
-            if pair.0 < minimum {
-                minimum = pair.0
-            }
-        }
-    }
-
-    return (minimum, maximum)
+  }
+  
+  return (minimum, maximum)
 }
 
 // Test of minimum and maximum functions

From 728d749d535359788d701296ce338b681fa18b1d Mon Sep 17 00:00:00 2001
From: Zhang <zhanggoni@gmail.com>
Date: Tue, 3 Jan 2017 08:54:29 +0900
Subject: [PATCH 0746/1679] Update README.

Convert to swift 3.0 syntax.
---
 Shortest Path (Unweighted)/README.markdown | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Shortest Path (Unweighted)/README.markdown b/Shortest Path (Unweighted)/README.markdown
index 0107964ae..a16519260 100644
--- a/Shortest Path (Unweighted)/README.markdown	
+++ b/Shortest Path (Unweighted)/README.markdown	
@@ -23,7 +23,7 @@ The root of the tree is the node you started the breadth-first search from. To f
 Let's put breadth-first search into practice and calculate the shortest path from `A` to all the other nodes. We start with the source node `A` and add it to a queue with a distance of `0`.
 
 ```swift
-queue.enqueue(A)
+queue.enqueue(element: A)
 A.distance = 0
 ```
 
@@ -31,9 +31,9 @@ The queue is now `[ A ]`. We dequeue `A` and enqueue its two immediate neighbor
 
 ```swift
 queue.dequeue()   // A
-queue.enqueue(B)
+queue.enqueue(element: B)
 B.distance = A.distance + 1   // result: 1
-queue.enqueue(C)
+queue.enqueue(element: C)
 C.distance = A.distance + 1   // result: 1
 ```
 
@@ -41,9 +41,9 @@ The queue is now `[ B, C ]`. Dequeue `B` and enqueue `B`'s neighbor nodes `D` an
 
 ```swift
 queue.dequeue()   // B
-queue.enqueue(D)
+queue.enqueue(element: D)
 D.distance = B.distance + 1   // result: 2
-queue.enqueue(E)
+queue.enqueue(element: E)
 E.distance = B.distance + 1   // result: 2
 ```
 
@@ -51,9 +51,9 @@ The queue is now `[ C, D, E ]`. Dequeue `C` and enqueue `C`'s neighbor nodes `F`
 
 ```swift
 queue.dequeue()   // C
-queue.enqueue(F)
+queue.enqueue(element: F)
 F.distance = C.distance + 1   // result: 2
-queue.enqueue(G)
+queue.enqueue(element: G)
 G.distance = C.distance + 1   // result: 2
 ```
 
@@ -66,15 +66,15 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
   var queue = Queue<Node>()
-  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
-  queue.enqueue(sourceInShortestPathsGraph)
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(label: source.label)
+  queue.enqueue(element: sourceInShortestPathsGraph)
   sourceInShortestPathsGraph.distance = 0
 
   while let current = queue.dequeue() {
     for edge in current.neighbors {
       let neighborNode = edge.neighbor
       if !neighborNode.hasDistance {
-        queue.enqueue(neighborNode)
+        queue.enqueue(element: neighborNode)
         neighborNode.distance = current.distance! + 1
       }
     }
@@ -87,7 +87,7 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
 Put this code in a playground and test it like so:
 
 ```swift
-let shortestPathGraph = breadthFirstSearchShortestPath(graph, source: nodeA)
+let shortestPathGraph = breadthFirstSearchShortestPath(graph: graph, source: nodeA)
 print(shortestPathGraph.nodes)
 ```
 

From b2688ad3cb3a9705aa73aa8fe54773192acd90a2 Mon Sep 17 00:00:00 2001
From: Zhang <zhanggoni@gmail.com>
Date: Tue, 3 Jan 2017 09:26:34 +0900
Subject: [PATCH 0747/1679] Update .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 7b5faffa6..f6c64488d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -36,7 +36,7 @@ script:
 # - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests

From 6aab6200651772d8f6f7c1e7cf641f2242a784fe Mon Sep 17 00:00:00 2001
From: gonini <zhanggoni@gmail.com>
Date: Tue, 3 Jan 2017 09:40:13 +0900
Subject: [PATCH 0748/1679] Updated with XCTest Swift3 syntax for shortest path

---
 Shortest Path (Unweighted)/Tests/Graph.swift  | 159 +++++++++---------
 .../Tests/ShortestPathTests.swift             |  72 ++++----
 2 files changed, 116 insertions(+), 115 deletions(-)

diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index ed71cab7c..0d2a735c2 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -1,106 +1,107 @@
 // MARK: - Edge
 
 public class Edge: Equatable {
-  public var neighbor: Node
-
-  public init(neighbor: Node) {
-    self.neighbor = neighbor
-  }
+    public var neighbor: Node
+    
+    public init(neighbor: Node) {
+        self.neighbor = neighbor
+    }
 }
 
 public func == (lhs: Edge, rhs: Edge) -> Bool {
-  return lhs.neighbor == rhs.neighbor
+    return lhs.neighbor == rhs.neighbor
 }
 
+
 // MARK: - Node
 
 public class Node: CustomStringConvertible, Equatable {
-  public var neighbors: [Edge]
-
-  public private(set) var label: String
-  public var distance: Int?
-  public var visited: Bool
-
-  public init(label: String) {
-    self.label = label
-    neighbors = []
-    visited = false
-  }
-
-  public var description: String {
-    if let distance = distance {
-      return "Node(label: \(label), distance: \(distance))"
+    public var neighbors: [Edge]
+    
+    public private(set) var label: String
+    public var distance: Int?
+    public var visited: Bool
+    
+    public init(label: String) {
+        self.label = label
+        neighbors = []
+        visited = false
+    }
+    
+    public var description: String {
+        if let distance = distance {
+            return "Node(label: \(label), distance: \(distance))"
+        }
+        return "Node(label: \(label), distance: infinity)"
+    }
+    
+    public var hasDistance: Bool {
+        return distance != nil
+    }
+    
+    public func remove(edge: Edge) {
+        neighbors.remove(at: neighbors.index { $0 === edge }!)
     }
-    return "Node(label: \(label), distance: infinity)"
-  }
-
-  public var hasDistance: Bool {
-    return distance != nil
-  }
-
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
-  }
 }
 
 public func == (lhs: Node, rhs: Node) -> Bool {
-  return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
+    return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
 }
 
 // MARK: - Graph
 
 public class Graph: CustomStringConvertible, Equatable {
-  public private(set) var nodes: [Node]
-
-  public init() {
-    self.nodes = []
-  }
-
-  public func addNode(label: String) -> Node {
-    let node = Node(label: label)
-    nodes.append(node)
-    return node
-  }
-
-  public func addEdge(source: Node, neighbor: Node) {
-    let edge = Edge(neighbor: neighbor)
-    source.neighbors.append(edge)
-  }
-
-  public var description: String {
-    var description = ""
-
-    for node in nodes {
-      if !node.neighbors.isEmpty {
-        description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
-      }
+    public private(set) var nodes: [Node]
+    
+    public init() {
+        self.nodes = []
     }
-    return description
-  }
-
-  public func findNodeWithLabel(label: String) -> Node {
-    return nodes.filter { $0.label == label }.first!
-  }
-
-  public func duplicate() -> Graph {
-    let duplicated = Graph()
-
-    for node in nodes {
-      duplicated.addNode(node.label)
+    
+    public func addNode(label: String) -> Node {
+        let node = Node(label: label)
+        nodes.append(node)
+        return node
     }
-
-    for node in nodes {
-      for edge in node.neighbors {
-        let source = duplicated.findNodeWithLabel(node.label)
-        let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
-        duplicated.addEdge(source, neighbor: neighbour)
-      }
+    
+    public func addEdge(_ source: Node, neighbor: Node) {
+        let edge = Edge(neighbor: neighbor)
+        source.neighbors.append(edge)
+    }
+    
+    public var description: String {
+        var description = ""
+        
+        for node in nodes {
+            if !node.neighbors.isEmpty {
+                description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
+            }
+        }
+        return description
+    }
+    
+    public func findNodeWithLabel(label: String) -> Node {
+        return nodes.filter { $0.label == label }.first!
+    }
+    
+    public func duplicate() -> Graph {
+        let duplicated = Graph()
+        
+        for node in nodes {
+            duplicated.addNode(label: node.label)
+        }
+        
+        for node in nodes {
+            for edge in node.neighbors {
+                let source = duplicated.findNodeWithLabel(label: node.label)
+                let neighbour = duplicated.findNodeWithLabel(label: edge.neighbor.label)
+                duplicated.addEdge(source, neighbor: neighbour)
+            }
+        }
+        
+        return duplicated
     }
-
-    return duplicated
-  }
 }
 
 public func == (lhs: Graph, rhs: Graph) -> Bool {
-  return lhs.nodes == rhs.nodes
+    return lhs.nodes == rhs.nodes
 }
diff --git a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift
index 003f3cf20..71b9f88ab 100644
--- a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
+++ b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
@@ -4,14 +4,14 @@ class ShortestPathTests: XCTestCase {
 
   func testShortestPathWhenGivenTree() {
     let tree = Graph()
-    let nodeA = tree.addNode("a")
-    let nodeB = tree.addNode("b")
-    let nodeC = tree.addNode("c")
-    let nodeD = tree.addNode("d")
-    let nodeE = tree.addNode("e")
-    let nodeF = tree.addNode("f")
-    let nodeG = tree.addNode("g")
-    let nodeH = tree.addNode("h")
+    let nodeA = tree.addNode(label: "a")
+    let nodeB = tree.addNode(label: "b")
+    let nodeC = tree.addNode(label: "c")
+    let nodeD = tree.addNode(label: "d")
+    let nodeE = tree.addNode(label: "e")
+    let nodeF = tree.addNode(label: "f")
+    let nodeG = tree.addNode(label: "g")
+    let nodeH = tree.addNode(label: "h")
     tree.addEdge(nodeA, neighbor: nodeB)
     tree.addEdge(nodeA, neighbor: nodeC)
     tree.addEdge(nodeB, neighbor: nodeD)
@@ -20,30 +20,30 @@ class ShortestPathTests: XCTestCase {
     tree.addEdge(nodeC, neighbor: nodeG)
     tree.addEdge(nodeE, neighbor: nodeH)
 
-    let shortestPaths = breadthFirstSearchShortestPath(tree, source: nodeA)
+    let shortestPaths = breadthFirstSearchShortestPath(graph: tree, source: nodeA)
 
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeA.label).distance, 0)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeB.label).distance, 1)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeC.label).distance, 1)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeD.label).distance, 2)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeE.label).distance, 2)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeF.label).distance, 2)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeG.label).distance, 2)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeH.label).distance, 3)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeA.label).distance, 0)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeB.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeC.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeD.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeE.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeF.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeG.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeH.label).distance, 3)
   }
 
   func testShortestPathWhenGivenGraph() {
     let graph = Graph()
 
-    let nodeA = graph.addNode("a")
-    let nodeB = graph.addNode("b")
-    let nodeC = graph.addNode("c")
-    let nodeD = graph.addNode("d")
-    let nodeE = graph.addNode("e")
-    let nodeF = graph.addNode("f")
-    let nodeG = graph.addNode("g")
-    let nodeH = graph.addNode("h")
-    let nodeI = graph.addNode("i")
+    let nodeA = graph.addNode(label:"a")
+    let nodeB = graph.addNode(label:"b")
+    let nodeC = graph.addNode(label:"c")
+    let nodeD = graph.addNode(label:"d")
+    let nodeE = graph.addNode(label:"e")
+    let nodeF = graph.addNode(label:"f")
+    let nodeG = graph.addNode(label:"g")
+    let nodeH = graph.addNode(label:"h")
+    let nodeI = graph.addNode(label:"i")
 
     graph.addEdge(nodeA, neighbor: nodeB)
     graph.addEdge(nodeA, neighbor: nodeH)
@@ -74,16 +74,16 @@ class ShortestPathTests: XCTestCase {
     graph.addEdge(nodeI, neighbor: nodeG)
     graph.addEdge(nodeI, neighbor: nodeH)
 
-    let shortestPaths = breadthFirstSearchShortestPath(graph, source: nodeA)
+    let shortestPaths = breadthFirstSearchShortestPath(graph: graph, source: nodeA)
 
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeA.label).distance, 0)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeB.label).distance, 1)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeC.label).distance, 2)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeD.label).distance, 3)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeE.label).distance, 4)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeF.label).distance, 3)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeG.label).distance, 2)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeH.label).distance, 1)
-    XCTAssertEqual(shortestPaths.findNodeWithLabel(nodeI.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeA.label).distance, 0)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeB.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeC.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeD.label).distance, 3)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeE.label).distance, 4)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeF.label).distance, 3)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeG.label).distance, 2)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeH.label).distance, 1)
+    XCTAssertEqual(shortestPaths.findNodeWithLabel(label: nodeI.label).distance, 2)
   }
 }

From 6eed97951a180899d8887c739bdb493e554e99da Mon Sep 17 00:00:00 2001
From: gonini <zhanggoni@gmail.com>
Date: Tue, 3 Jan 2017 09:51:16 +0900
Subject: [PATCH 0749/1679] Updated with XCTest Swift3 syntax for shortest path

XCTest Success
---
 Shortest Path (Unweighted)/ShortestPath.swift |  4 +--
 Shortest Path (Unweighted)/Tests/Graph.swift  | 34 +++++++++----------
 Shortest Path (Unweighted)/Tests/Queue.swift  |  2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     |  3 ++
 4 files changed, 23 insertions(+), 20 deletions(-)

diff --git a/Shortest Path (Unweighted)/ShortestPath.swift b/Shortest Path (Unweighted)/ShortestPath.swift
index 6aa082a96..555ad893b 100644
--- a/Shortest Path (Unweighted)/ShortestPath.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.swift	
@@ -2,8 +2,8 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
   var queue = Queue<Node>()
-  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(source.label)
-  queue.enqueue(sourceInShortestPathsGraph)
+  let sourceInShortestPathsGraph = shortestPathGraph.findNodeWithLabel(label: source.label)
+  queue.enqueue(element: sourceInShortestPathsGraph)
   sourceInShortestPathsGraph.distance = 0
 
   while let current = queue.dequeue() {
diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index 0d2a735c2..8322ba0a9 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -1,7 +1,7 @@
 // MARK: - Edge
 
-public class Edge: Equatable {
-    public var neighbor: Node
+open class Edge: Equatable {
+    open var neighbor: Node
     
     public init(neighbor: Node) {
         self.neighbor = neighbor
@@ -15,12 +15,12 @@ public func == (lhs: Edge, rhs: Edge) -> Bool {
 
 // MARK: - Node
 
-public class Node: CustomStringConvertible, Equatable {
-    public var neighbors: [Edge]
+open class Node: CustomStringConvertible, Equatable {
+    open var neighbors: [Edge]
     
-    public private(set) var label: String
-    public var distance: Int?
-    public var visited: Bool
+    open fileprivate(set) var label: String
+    open var distance: Int?
+    open var visited: Bool
     
     public init(label: String) {
         self.label = label
@@ -28,18 +28,18 @@ public class Node: CustomStringConvertible, Equatable {
         visited = false
     }
     
-    public var description: String {
+    open var description: String {
         if let distance = distance {
             return "Node(label: \(label), distance: \(distance))"
         }
         return "Node(label: \(label), distance: infinity)"
     }
     
-    public var hasDistance: Bool {
+    open var hasDistance: Bool {
         return distance != nil
     }
     
-    public func remove(edge: Edge) {
+    open func remove(_ edge: Edge) {
         neighbors.remove(at: neighbors.index { $0 === edge }!)
     }
 }
@@ -50,25 +50,25 @@ public func == (lhs: Node, rhs: Node) -> Bool {
 
 // MARK: - Graph
 
-public class Graph: CustomStringConvertible, Equatable {
-    public private(set) var nodes: [Node]
+open class Graph: CustomStringConvertible, Equatable {
+    open fileprivate(set) var nodes: [Node]
     
     public init() {
         self.nodes = []
     }
     
-    public func addNode(label: String) -> Node {
+    open func addNode(label: String) -> Node {
         let node = Node(label: label)
         nodes.append(node)
         return node
     }
     
-    public func addEdge(_ source: Node, neighbor: Node) {
+    open func addEdge(_ source: Node, neighbor: Node) {
         let edge = Edge(neighbor: neighbor)
         source.neighbors.append(edge)
     }
     
-    public var description: String {
+    open var description: String {
         var description = ""
         
         for node in nodes {
@@ -79,11 +79,11 @@ public class Graph: CustomStringConvertible, Equatable {
         return description
     }
     
-    public func findNodeWithLabel(label: String) -> Node {
+    open func findNodeWithLabel(label: String) -> Node {
         return nodes.filter { $0.label == label }.first!
     }
     
-    public func duplicate() -> Graph {
+    open func duplicate() -> Graph {
         let duplicated = Graph()
         
         for node in nodes {
diff --git a/Shortest Path (Unweighted)/Tests/Queue.swift b/Shortest Path (Unweighted)/Tests/Queue.swift
index bf462bbdd..0d8752466 100644
--- a/Shortest Path (Unweighted)/Tests/Queue.swift	
+++ b/Shortest Path (Unweighted)/Tests/Queue.swift	
@@ -1,5 +1,5 @@
 public struct Queue<T> {
-  private var array: [T]
+  fileprivate var array: [T]
 
   public init() {
     array = []
diff --git a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
index 35aeffa54..f1744fcf1 100644
--- a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
@@ -94,6 +94,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -230,6 +231,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -242,6 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From 914441ec8285ae1e8354c22f692a81ae9bb70de7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20B=C3=B8dskov?= <pb@reeltrak.com>
Date: Tue, 3 Jan 2017 14:40:59 +0100
Subject: [PATCH 0750/1679] converts Huffman Coding to Swift 3 syntax

---
 .../Huffman.playground/Contents.swift         |  10 +-
 .../Huffman.playground/Sources/Heap.swift     |  34 +-
 .../Huffman.playground/Sources/Huffman.swift  |  30 +-
 .../Sources/NSData+Bits.swift                 |   8 +-
 .../Sources/PriorityQueue.swift               |   8 +-
 .../Huffman.playground/timeline.xctimeline    |  10 +
 Huffman Coding/Huffman.swift                  | 294 +++++++++---------
 Huffman Coding/NSData+Bits.swift              |  76 ++---
 Huffman Coding/README.markdown                |  52 ++--
 9 files changed, 265 insertions(+), 257 deletions(-)

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index b67f93a6a..017c5baf2 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -3,21 +3,21 @@
 import Foundation
 
 let s1 = "so much words wow many compression"
-if let originalData = s1.dataUsingEncoding(NSUTF8StringEncoding) {
-  print(originalData.length)
+if let originalData = s1.data(using: String.Encoding.utf8) {
+  print(originalData.count)
 
   let huffman1 = Huffman()
-  let compressedData = huffman1.compressData(originalData)
+  let compressedData = huffman1.compressData(data: originalData as NSData)
   print(compressedData.length)
 
   let frequencyTable = huffman1.frequencyTable()
   //print(frequencyTable)
 
   let huffman2 = Huffman()
-  let decompressedData = huffman2.decompressData(compressedData, frequencyTable: frequencyTable)
+  let decompressedData = huffman2.decompressData(data: compressedData, frequencyTable: frequencyTable)
   print(decompressedData.length)
 
-  let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
+  let s2 = String(data: decompressedData as Data, encoding: String.Encoding.utf8)!
   print(s2)
   assert(s1 == s2)
 }
diff --git a/Huffman Coding/Huffman.playground/Sources/Heap.swift b/Huffman Coding/Huffman.playground/Sources/Heap.swift
index 64bd90cd8..5ace98a17 100644
--- a/Huffman Coding/Huffman.playground/Sources/Heap.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/Heap.swift	
@@ -8,14 +8,14 @@ public struct Heap<T> {
   var elements = [T]()
 
   /** Determines whether this is a max-heap (>) or min-heap (<). */
-  private var isOrderedBefore: (T, T) -> Bool
+  fileprivate var isOrderedBefore: (T, T) -> Bool
 
   /**
    * Creates an empty heap.
    * The sort function determines whether this is a min-heap or max-heap.
    * For integers, > makes a max-heap, < makes a min-heap.
    */
-  public init(sort: (T, T) -> Bool) {
+  public init(sort: @escaping (T, T) -> Bool) {
     self.isOrderedBefore = sort
   }
 
@@ -24,9 +24,9 @@ public struct Heap<T> {
    * the elements are inserted into the heap in the order determined by the
    * sort function.
    */
-  public init(array: [T], sort: (T, T) -> Bool) {
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
     self.isOrderedBefore = sort
-    buildHeap(array)
+    buildHeap(array: array)
   }
 
   /*
@@ -45,7 +45,7 @@ public struct Heap<T> {
    */
   private mutating func buildHeap(array: [T]) {
     elements = array
-    for i in (elements.count/2 - 1).stride(through: 0, by: -1) {
+    for i in stride(from: elements.count/2 - 1, to: 0, by: -1) {
       shiftDown(index: i, heapSize: elements.count)
     }
   }
@@ -96,12 +96,12 @@ public struct Heap<T> {
    * Adds a new value to the heap. This reorders the heap so that the max-heap
    * or min-heap property still holds. Performance: O(log n).
    */
-  public mutating func insert(value: T) {
+  public mutating func insert(_ value: T) {
     elements.append(value)
     shiftUp(index: elements.count - 1)
   }
 
-  public mutating func insert<S: SequenceType where S.Generator.Element == T>(sequence: S) {
+  public mutating func insert<S: Sequence>(sequence: S) where S.Iterator.Element == T {
     for value in sequence {
       insert(value)
     }
@@ -154,15 +154,15 @@ public struct Heap<T> {
    * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
-  mutating func shiftUp(index index: Int) {
+  mutating func shiftUp(index: Int) {
     var childIndex = index
     let child = elements[childIndex]
-    var parentIndex = indexOfParent(childIndex)
+    var parentIndex = indexOfParent(i: childIndex)
 
     while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
       elements[childIndex] = elements[parentIndex]
       childIndex = parentIndex
-      parentIndex = indexOfParent(childIndex)
+      parentIndex = indexOfParent(i: childIndex)
     }
 
     elements[childIndex] = child
@@ -176,11 +176,11 @@ public struct Heap<T> {
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  mutating func shiftDown(index index: Int, heapSize: Int) {
+  mutating func shiftDown(index: Int, heapSize: Int) {
     var parentIndex = index
 
     while true {
-      let leftChildIndex = indexOfLeftChild(parentIndex)
+      let leftChildIndex = indexOfLeftChild(i: parentIndex)
       let rightChildIndex = leftChildIndex + 1
 
       // Figure out which comes first if we order them by the sort function:
@@ -208,16 +208,16 @@ extension Heap where T: Equatable {
   /**
    * Searches the heap for the given element. Performance: O(n).
    */
-  public func indexOf(element: T) -> Int? {
-    return indexOf(element, 0)
+  public func index(of element: T) -> Int? {
+    return index(of: element, 0)
   }
 
-  private func indexOf(element: T, _ i: Int) -> Int? {
+  private func index(of element: T, _ i: Int) -> Int? {
     if i >= count { return nil }
     if isOrderedBefore(element, elements[i]) { return nil }
     if element == elements[i] { return i }
-    if let j = indexOf(element, indexOfLeftChild(i)) { return j }
-    if let j = indexOf(element, indexOfRightChild(i)) { return j }
+    if let j = index(of: element, indexOfLeftChild(i: i)) { return j }
+    if let j = index(of: element, indexOfRightChild(i: i)) { return j }
     return nil
   }
 }
diff --git a/Huffman Coding/Huffman.playground/Sources/Huffman.swift b/Huffman Coding/Huffman.playground/Sources/Huffman.swift
index d50b90d82..79b24b09a 100644
--- a/Huffman Coding/Huffman.playground/Sources/Huffman.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/Huffman.swift	
@@ -29,7 +29,7 @@ public class Huffman {
   /* The tree structure. The first 256 entries are for the leaf nodes (not all
      of those may be used, depending on the input). We add additional nodes as
      we build the tree. */
-  var tree = [Node](count: 256, repeatedValue: Node())
+  var tree = [Node](repeating: Node(), count: 256)
 
   /* This is the last node we add to the tree. */
   var root: NodeIndex = -1
@@ -50,10 +50,10 @@ extension Huffman {
      occurs. These counts are stored in the first 256 nodes in the tree, i.e.
      the leaf nodes. The frequency table used by decompression is derived from
      this. */
-  private func countByteFrequency(data: NSData) {
-    var ptr = UnsafePointer<UInt8>(data.bytes)
+  fileprivate func countByteFrequency(inData data: NSData) {
+    var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
     for _ in 0..<data.length {
-      let i = Int(ptr.memory)
+      let i = Int(ptr.pointee)
       tree[i].count += 1
       tree[i].index = i
       ptr = ptr.successor()
@@ -62,7 +62,7 @@ extension Huffman {
 
   /* Takes a frequency table and rebuilds the tree. This is the first step of
      decompression. */
-  private func restoreTree(frequencyTable: [Freq]) {
+    fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
     for freq in frequencyTable {
       let i = Int(freq.byte)
       tree[i].count = freq.count
@@ -85,7 +85,7 @@ extension Huffman {
 
 extension Huffman {
   /* Builds a Huffman tree from a frequency table. */
-  private func buildTree() {
+  fileprivate func buildTree() {
     // Create a min-priority queue and enqueue all used nodes.
     var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
     for node in tree where node.count > 0 {
@@ -123,13 +123,13 @@ extension Huffman {
 extension Huffman {
   /* Compresses the contents of an NSData object. */
   public func compressData(data: NSData) -> NSData {
-    countByteFrequency(data)
+    countByteFrequency(inData: data)
     buildTree()
 
     let writer = BitWriter()
-    var ptr = UnsafePointer<UInt8>(data.bytes)
+    var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
     for _ in 0..<data.length {
-      let c = ptr.memory
+      let c = ptr.pointee
       let i = Int(c)
       traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
       ptr = ptr.successor()
@@ -141,15 +141,15 @@ extension Huffman {
   /* Recursively walks the tree from a leaf node up to the root, and then back
      again. If a child is the right node, we emit a 0 bit; if it's the left node,
      we emit a 1 bit. */
-  private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
+  private func traverseTree(writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
     if tree[h].parent != -1 {
       traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
     }
     if child != -1 {
       if child == tree[h].left {
-        writer.writeBit(true)
+        writer.writeBit(bit: true)
       } else if child == tree[h].right {
-        writer.writeBit(false)
+        writer.writeBit(bit: false)
       }
     }
   }
@@ -158,7 +158,7 @@ extension Huffman {
 extension Huffman {
   /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
   public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
-    restoreTree(frequencyTable)
+    restoreTree(fromTable: frequencyTable)
 
     let reader = BitReader(data: data)
     let outData = NSMutableData()
@@ -167,7 +167,7 @@ extension Huffman {
     var i = 0
     while i < byteCount {
       var b = findLeafNode(reader: reader, nodeIndex: root)
-      outData.appendBytes(&b, length: 1)
+      outData.append(&b, length: 1)
       i += 1
     }
     return outData
@@ -177,7 +177,7 @@ extension Huffman {
      next bit and use that to determine whether to step to the left or right.
      When we get to the leaf node, we simply return its index, which is equal to
      the original byte value. */
-  private func findLeafNode(reader reader: BitReader, nodeIndex: Int) -> UInt8 {
+  private func findLeafNode(reader: BitReader, nodeIndex: Int) -> UInt8 {
     var h = nodeIndex
     while tree[h].right != -1 {
       if reader.readBit() {
diff --git a/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift b/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift
index 0aa821f72..3e5163521 100644
--- a/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/NSData+Bits.swift	
@@ -8,7 +8,7 @@ public class BitWriter {
 
   public func writeBit(bit: Bool) {
     if outCount == 8 {
-      data.appendBytes(&outByte, length: 1)
+      data.append(&outByte, length: 1)
       outCount = 0
     }
     outByte = (outByte << 1) | (bit ? 1 : 0)
@@ -21,7 +21,7 @@ public class BitWriter {
         let diff = UInt8(8 - outCount)
         outByte <<= diff
       }
-      data.appendBytes(&outByte, length: 1)
+      data.append(&outByte, length: 1)
     }
   }
 }
@@ -33,12 +33,12 @@ public class BitReader {
   var inCount = 8
 
   public init(data: NSData) {
-    ptr = UnsafePointer<UInt8>(data.bytes)
+    ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
   }
 
   public func readBit() -> Bool {
     if inCount == 8 {
-      inByte = ptr.memory    // load the next byte
+      inByte = ptr.pointee    // load the next byte
       inCount = 0
       ptr = ptr.successor()
     }
diff --git a/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift b/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift
index 757a6c539..4cc9d15ed 100644
--- a/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/PriorityQueue.swift	
@@ -11,13 +11,13 @@
   queue (largest element first) or a min-priority queue (smallest element first).
 */
 public struct PriorityQueue<T> {
-  private var heap: Heap<T>
+  fileprivate var heap: Heap<T>
 
   /*
     To create a max-priority queue, supply a > sort function. For a min-priority
     queue, use <.
   */
-  public init(sort: (T, T) -> Bool) {
+  public init(sort: @escaping (T, T) -> Bool) {
     heap = Heap(sort: sort)
   }
 
@@ -33,7 +33,7 @@ public struct PriorityQueue<T> {
     return heap.peek()
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     heap.insert(element)
   }
 
@@ -53,6 +53,6 @@ public struct PriorityQueue<T> {
 
 extension PriorityQueue where T: Equatable {
   public func indexOf(element: T) -> Int? {
-    return heap.indexOf(element)
+    return heap.index(of: element)
   }
 }
diff --git a/Huffman Coding/Huffman.playground/timeline.xctimeline b/Huffman Coding/Huffman.playground/timeline.xctimeline
index bf468afec..2b2555bb1 100644
--- a/Huffman Coding/Huffman.playground/timeline.xctimeline	
+++ b/Huffman Coding/Huffman.playground/timeline.xctimeline	
@@ -2,5 +2,15 @@
 <Timeline
    version = "3.0">
    <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/peter/Programming/iOS/Workspace/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=19&amp;CharacterRangeLoc=678&amp;EndingLineNumber=21&amp;StartingLineNumber=21&amp;Timestamp=505135214.929897"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=14&amp;CharacterRangeLoc=350&amp;EndingColumnNumber=21&amp;EndingLineNumber=12&amp;StartingColumnNumber=7&amp;StartingLineNumber=12&amp;Timestamp=505138287.94525"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
    </TimelineItems>
 </Timeline>
diff --git a/Huffman Coding/Huffman.swift b/Huffman Coding/Huffman.swift
index d50b90d82..7e2961a2f 100644
--- a/Huffman Coding/Huffman.swift	
+++ b/Huffman Coding/Huffman.swift	
@@ -1,191 +1,191 @@
 import Foundation
 
 /*
-  Basic implementation of Huffman encoding. It encodes bytes that occur often
-  with a smaller number of bits than bytes that occur less frequently.
-
-  Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February
-  1991 and October 1992.
-
-  Note: This code is not optimized for speed but explanation.
-*/
+ Basic implementation of Huffman encoding. It encodes bytes that occur often
+ with a smaller number of bits than bytes that occur less frequently.
+ 
+ Based on Al Stevens' C Programming column from Dr.Dobb's Magazine, February
+ 1991 and October 1992.
+ 
+ Note: This code is not optimized for speed but explanation.
+ */
 public class Huffman {
-  /* Tree nodes don't use pointers to refer to each other, but simple integer
+    /* Tree nodes don't use pointers to refer to each other, but simple integer
      indices. That allows us to use structs for the nodes. */
-  typealias NodeIndex = Int
-
-  /* A node in the compression tree. Leaf nodes represent the actual bytes that
+    typealias NodeIndex = Int
+    
+    /* A node in the compression tree. Leaf nodes represent the actual bytes that
      are present in the input data. The count of an intermediary node is the sum
      of the counts of all nodes below it. The root node's count is the number of
      bytes in the original, uncompressed input data. */
-  struct Node {
-    var count = 0
-    var index: NodeIndex = -1
-    var parent: NodeIndex = -1
-    var left: NodeIndex = -1
-    var right: NodeIndex = -1
-  }
-
-  /* The tree structure. The first 256 entries are for the leaf nodes (not all
+    struct Node {
+        var count = 0
+        var index: NodeIndex = -1
+        var parent: NodeIndex = -1
+        var left: NodeIndex = -1
+        var right: NodeIndex = -1
+    }
+    
+    /* The tree structure. The first 256 entries are for the leaf nodes (not all
      of those may be used, depending on the input). We add additional nodes as
      we build the tree. */
-  var tree = [Node](count: 256, repeatedValue: Node())
-
-  /* This is the last node we add to the tree. */
-  var root: NodeIndex = -1
-
-  /* The frequency table describes how often a byte occurs in the input data.
+    var tree = [Node](repeating: Node(), count: 256)
+    
+    /* This is the last node we add to the tree. */
+    var root: NodeIndex = -1
+    
+    /* The frequency table describes how often a byte occurs in the input data.
      You need it to decompress the Huffman-encoded data. The frequency table
      should be serialized along with the compressed data. */
-  public struct Freq {
-    var byte: UInt8 = 0
-    var count = 0
-  }
-
-  public init() { }
+    public struct Freq {
+        var byte: UInt8 = 0
+        var count = 0
+    }
+    
+    public init() { }
 }
 
 extension Huffman {
-  /* To compress a block of data, first we need to count how often each byte
+    /* To compress a block of data, first we need to count how often each byte
      occurs. These counts are stored in the first 256 nodes in the tree, i.e.
      the leaf nodes. The frequency table used by decompression is derived from
      this. */
-  private func countByteFrequency(data: NSData) {
-    var ptr = UnsafePointer<UInt8>(data.bytes)
-    for _ in 0..<data.length {
-      let i = Int(ptr.memory)
-      tree[i].count += 1
-      tree[i].index = i
-      ptr = ptr.successor()
+    fileprivate func countByteFrequency(inData data: NSData) {
+        var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
+        for _ in 0..<data.length {
+            let i = Int(ptr.pointee)
+            tree[i].count += 1
+            tree[i].index = i
+            ptr = ptr.successor()
+        }
     }
-  }
-
-  /* Takes a frequency table and rebuilds the tree. This is the first step of
+    
+    /* Takes a frequency table and rebuilds the tree. This is the first step of
      decompression. */
-  private func restoreTree(frequencyTable: [Freq]) {
-    for freq in frequencyTable {
-      let i = Int(freq.byte)
-      tree[i].count = freq.count
-      tree[i].index = i
+    fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
+        for freq in frequencyTable {
+            let i = Int(freq.byte)
+            tree[i].count = freq.count
+            tree[i].index = i
+        }
+        buildTree()
     }
-    buildTree()
-  }
-
-  /* Returns the frequency table. This is the first 256 nodes from the tree but
+    
+    /* Returns the frequency table. This is the first 256 nodes from the tree but
      only those that are actually used, without the parent/left/right pointers.
      You would serialize this along with the compressed file. */
-  public func frequencyTable() -> [Freq] {
-    var a = [Freq]()
-    for i in 0..<256 where tree[i].count > 0 {
-      a.append(Freq(byte: UInt8(i), count: tree[i].count))
+    public func frequencyTable() -> [Freq] {
+        var a = [Freq]()
+        for i in 0..<256 where tree[i].count > 0 {
+            a.append(Freq(byte: UInt8(i), count: tree[i].count))
+        }
+        return a
     }
-    return a
-  }
 }
 
 extension Huffman {
-  /* Builds a Huffman tree from a frequency table. */
-  private func buildTree() {
-    // Create a min-priority queue and enqueue all used nodes.
-    var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
-    for node in tree where node.count > 0 {
-      queue.enqueue(node)
+    /* Builds a Huffman tree from a frequency table. */
+    fileprivate func buildTree() {
+        // Create a min-priority queue and enqueue all used nodes.
+        var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
+        for node in tree where node.count > 0 {
+            queue.enqueue(node)
+        }
+        
+        while queue.count > 1 {
+            // Find the two nodes with the smallest frequencies that do not have
+            // a parent node yet.
+            let node1 = queue.dequeue()!
+            let node2 = queue.dequeue()!
+            
+            // Create a new intermediate node.
+            var parentNode = Node()
+            parentNode.count = node1.count + node2.count
+            parentNode.left = node1.index
+            parentNode.right = node2.index
+            parentNode.index = tree.count
+            tree.append(parentNode)
+            
+            // Link the two nodes into their new parent node.
+            tree[node1.index].parent = parentNode.index
+            tree[node2.index].parent = parentNode.index
+            
+            // Put the intermediate node back into the queue.
+            queue.enqueue(parentNode)
+        }
+        
+        // The final remaining node in the queue becomes the root of the tree.
+        let rootNode = queue.dequeue()!
+        root = rootNode.index
     }
-
-    while queue.count > 1 {
-      // Find the two nodes with the smallest frequencies that do not have
-      // a parent node yet.
-      let node1 = queue.dequeue()!
-      let node2 = queue.dequeue()!
-
-      // Create a new intermediate node.
-      var parentNode = Node()
-      parentNode.count = node1.count + node2.count
-      parentNode.left = node1.index
-      parentNode.right = node2.index
-      parentNode.index = tree.count
-      tree.append(parentNode)
-
-      // Link the two nodes into their new parent node.
-      tree[node1.index].parent = parentNode.index
-      tree[node2.index].parent = parentNode.index
-
-      // Put the intermediate node back into the queue.
-      queue.enqueue(parentNode)
-    }
-
-    // The final remaining node in the queue becomes the root of the tree.
-    let rootNode = queue.dequeue()!
-    root = rootNode.index
-  }
 }
 
 extension Huffman {
-  /* Compresses the contents of an NSData object. */
-  public func compressData(data: NSData) -> NSData {
-    countByteFrequency(data)
-    buildTree()
-
-    let writer = BitWriter()
-    var ptr = UnsafePointer<UInt8>(data.bytes)
-    for _ in 0..<data.length {
-      let c = ptr.memory
-      let i = Int(c)
-      traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
-      ptr = ptr.successor()
+    /* Compresses the contents of an NSData object. */
+    public func compressData(data: NSData) -> NSData {
+        countByteFrequency(inData: data)
+        buildTree()
+        
+        let writer = BitWriter()
+        var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
+        for _ in 0..<data.length {
+            let c = ptr.pointee
+            let i = Int(c)
+            traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
+            ptr = ptr.successor()
+        }
+        writer.flush()
+        return writer.data
     }
-    writer.flush()
-    return writer.data
-  }
-
-  /* Recursively walks the tree from a leaf node up to the root, and then back
+    
+    /* Recursively walks the tree from a leaf node up to the root, and then back
      again. If a child is the right node, we emit a 0 bit; if it's the left node,
      we emit a 1 bit. */
-  private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
-    if tree[h].parent != -1 {
-      traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
-    }
-    if child != -1 {
-      if child == tree[h].left {
-        writer.writeBit(true)
-      } else if child == tree[h].right {
-        writer.writeBit(false)
-      }
+    private func traverseTree(writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
+        if tree[h].parent != -1 {
+            traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
+        }
+        if child != -1 {
+            if child == tree[h].left {
+                writer.writeBit(bit: true)
+            } else if child == tree[h].right {
+                writer.writeBit(bit: false)
+            }
+        }
     }
-  }
 }
 
 extension Huffman {
-  /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
-  public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
-    restoreTree(frequencyTable)
-
-    let reader = BitReader(data: data)
-    let outData = NSMutableData()
-    let byteCount = tree[root].count
-
-    var i = 0
-    while i < byteCount {
-      var b = findLeafNode(reader: reader, nodeIndex: root)
-      outData.appendBytes(&b, length: 1)
-      i += 1
+    /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
+    public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
+        restoreTree(fromTable: frequencyTable)
+        
+        let reader = BitReader(data: data)
+        let outData = NSMutableData()
+        let byteCount = tree[root].count
+        
+        var i = 0
+        while i < byteCount {
+            var b = findLeafNode(reader: reader, nodeIndex: root)
+            outData.append(&b, length: 1)
+            i += 1
+        }
+        return outData
     }
-    return outData
-  }
-
-  /* Walks the tree from the root down to the leaf node. At every node, read the
+    
+    /* Walks the tree from the root down to the leaf node. At every node, read the
      next bit and use that to determine whether to step to the left or right.
      When we get to the leaf node, we simply return its index, which is equal to
      the original byte value. */
-  private func findLeafNode(reader reader: BitReader, nodeIndex: Int) -> UInt8 {
-    var h = nodeIndex
-    while tree[h].right != -1 {
-      if reader.readBit() {
-        h = tree[h].left
-      } else {
-        h = tree[h].right
-      }
+    private func findLeafNode(reader: BitReader, nodeIndex: Int) -> UInt8 {
+        var h = nodeIndex
+        while tree[h].right != -1 {
+            if reader.readBit() {
+                h = tree[h].left
+            } else {
+                h = tree[h].right
+            }
+        }
+        return UInt8(h)
     }
-    return UInt8(h)
-  }
 }
diff --git a/Huffman Coding/NSData+Bits.swift b/Huffman Coding/NSData+Bits.swift
index 0aa821f72..4ae3c5c6d 100644
--- a/Huffman Coding/NSData+Bits.swift	
+++ b/Huffman Coding/NSData+Bits.swift	
@@ -2,49 +2,49 @@ import Foundation
 
 /* Helper class for writing bits to an NSData object. */
 public class BitWriter {
-  public var data = NSMutableData()
-  var outByte: UInt8 = 0
-  var outCount = 0
-
-  public func writeBit(bit: Bool) {
-    if outCount == 8 {
-      data.appendBytes(&outByte, length: 1)
-      outCount = 0
+    public var data = NSMutableData()
+    var outByte: UInt8 = 0
+    var outCount = 0
+    
+    public func writeBit(bit: Bool) {
+        if outCount == 8 {
+            data.append(&outByte, length: 1)
+            outCount = 0
+        }
+        outByte = (outByte << 1) | (bit ? 1 : 0)
+        outCount += 1
     }
-    outByte = (outByte << 1) | (bit ? 1 : 0)
-    outCount += 1
-  }
-
-  public func flush() {
-    if outCount > 0 {
-      if outCount < 8 {
-        let diff = UInt8(8 - outCount)
-        outByte <<= diff
-      }
-      data.appendBytes(&outByte, length: 1)
+    
+    public func flush() {
+        if outCount > 0 {
+            if outCount < 8 {
+                let diff = UInt8(8 - outCount)
+                outByte <<= diff
+            }
+            data.append(&outByte, length: 1)
+        }
     }
-  }
 }
 
 /* Helper class for reading bits from an NSData object. */
 public class BitReader {
-  var ptr: UnsafePointer<UInt8>
-  var inByte: UInt8 = 0
-  var inCount = 8
-
-  public init(data: NSData) {
-    ptr = UnsafePointer<UInt8>(data.bytes)
-  }
-
-  public func readBit() -> Bool {
-    if inCount == 8 {
-      inByte = ptr.memory    // load the next byte
-      inCount = 0
-      ptr = ptr.successor()
+    var ptr: UnsafePointer<UInt8>
+    var inByte: UInt8 = 0
+    var inCount = 8
+    
+    public init(data: NSData) {
+        ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
+    }
+    
+    public func readBit() -> Bool {
+        if inCount == 8 {
+            inByte = ptr.pointee    // load the next byte
+            inCount = 0
+            ptr = ptr.successor()
+        }
+        let bit = inByte & 0x80  // read the next bit
+        inByte <<= 1
+        inCount += 1
+        return bit == 0 ? false : true
     }
-    let bit = inByte & 0x80  // read the next bit
-    inByte <<= 1
-    inCount += 1
-    return bit == 0 ? false : true
-  }
 }
diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 528ba3a1d..6b2c0d245 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -70,10 +70,10 @@ public class BitWriter {
   public var data = NSMutableData()
   var outByte: UInt8 = 0
   var outCount = 0
-  
+
   public func writeBit(bit: Bool) {
     if outCount == 8 {
-      data.appendBytes(&outByte, length: 1)
+      data.append(&outByte, length: 1)
       outCount = 0
     }
     outByte = (outByte << 1) | (bit ? 1 : 0)
@@ -86,7 +86,7 @@ public class BitWriter {
         let diff = UInt8(8 - outCount)
         outByte <<= diff
       }
-      data.appendBytes(&outByte, length: 1)
+      data.append(&outByte, length: 1)
     }
   }
 }
@@ -103,14 +103,14 @@ public class BitReader {
   var ptr: UnsafePointer<UInt8>
   var inByte: UInt8 = 0
   var inCount = 8
-  
+
   public init(data: NSData) {
-    ptr = UnsafePointer<UInt8>(data.bytes)
+    ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
   }
-  
+
   public func readBit() -> Bool {
     if inCount == 8 {
-      inByte = ptr.memory    // load the next byte
+      inByte = ptr.pointee    // load the next byte
       inCount = 0
       ptr = ptr.successor()
     }
@@ -145,8 +145,8 @@ class Huffman {
     var left: NodeIndex = -1
     var right: NodeIndex = -1
   }
-  
-  var tree = [Node](count: 256, repeatedValue: Node())
+
+  var tree = [Node](repeating: Node(), count: 256)
 
   var root: NodeIndex = -1
 }
@@ -159,10 +159,10 @@ Note that `tree` currently has room for 256 entries. These are for the leaf node
 We use the following method to count how often each byte occurs in the input data:
 
 ```swift
-  private func countByteFrequency(data: NSData) {
-    var ptr = UnsafePointer<UInt8>(data.bytes)
+  fileprivate func countByteFrequency(inData data: NSData) {
+    var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
     for _ in 0..<data.length {
-      let i = Int(ptr.memory)
+      let i = Int(ptr.pointee)
       tree[i].count += 1
       tree[i].index = i
       ptr = ptr.successor()
@@ -214,7 +214,7 @@ This is an ideal place to use a [priority queue](../Priority Queue/). A priority
 The function `buildTree()` then becomes:
 
 ```swift
-  private func buildTree() {
+  fileprivate func buildTree() {
     var queue = PriorityQueue<Node>(sort: { $0.count < $1.count })
     for node in tree where node.count > 0 {
       queue.enqueue(node)                            // 1
@@ -252,7 +252,7 @@ Here is how it works step-by-step:
 
 4. Link the two nodes into their new parent node. Now this new intermediate node has become part of the tree.
 
-5. Put the new intermediate node back into the queue. At this point we're done with `node1` and `node2`, but the `parentNode` stills need to be connected to other nodes in the tree.
+5. Put the new intermediate node back into the queue. At this point we're done with `node1` and `node2`, but the `parentNode` still need to be connected to other nodes in the tree.
 
 6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we're done.
 
@@ -269,20 +269,18 @@ The animation shows what the process looks like:
 Now that we know how to build the compression tree from the frequency table, we can use it to compress the contents of an `NSData` object. Here is the code:
 
 ```swift
-  func compressData(data: NSData) -> NSData {
-    countByteFrequency(data)
+  public func compressData(data: NSData) -> NSData {
+    countByteFrequency(inData: data)
     buildTree()
-    
-    let writer = BitWriter()
-    var ptr = UnsafePointer<UInt8>(data.bytes)
 
+    let writer = BitWriter()
+    var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
     for _ in 0..<data.length {
-      let c = ptr.memory
+      let c = ptr.pointee
       let i = Int(c)
       traverseTree(writer: writer, nodeIndex: i, childIndex: -1)
       ptr = ptr.successor()
     }
-
     writer.flush()
     return writer.data
   }
@@ -297,15 +295,15 @@ Then it loops through the entire input and for each byte calls `traverseTree()`.
 The interesting stuff happens in `traverseTree()`. This is a recursive method:
 
 ```swift
-  private func traverseTree(writer writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
+  private func traverseTree(writer: BitWriter, nodeIndex h: Int, childIndex child: Int) {
     if tree[h].parent != -1 {
       traverseTree(writer: writer, nodeIndex: tree[h].parent, childIndex: h)
     }
     if child != -1 {
       if child == tree[h].left {
-        writer.writeBit(true)
+        writer.writeBit(bit: true)
       } else if child == tree[h].right {
-        writer.writeBit(false)
+        writer.writeBit(bit: false)
       }
     }
   }
@@ -339,7 +337,7 @@ Decompression is pretty much compression in reverse. However, the compressed bit
 We first need some way to turn the `[Freq]` array back into a compression tree. Fortunately, this is pretty easy:
 
 ```swift
-  private func restoreTree(frequencyTable: [Freq]) {
+  fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
     for freq in frequencyTable {
       let i = Int(freq.byte)
       tree[i].count = freq.count
@@ -355,7 +353,7 @@ Here is the code for `decompressData()`, which takes an `NSData` object with Huf
 
 ```swift
   func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
-    restoreTree(frequencyTable)
+    restoreTree(fromTable: frequencyTable)
 
     let reader = BitReader(data: data)
     let outData = NSMutableData()
@@ -364,7 +362,7 @@ Here is the code for `decompressData()`, which takes an `NSData` object with Huf
     var i = 0
     while i < byteCount {
       var b = findLeafNode(reader: reader, nodeIndex: root)
-      outData.appendBytes(&b, length: 1)
+      outData.append(&b, length: 1)
       i += 1
     }
     return outData

From 1e9ebe41a2a74c3a7dc4c01a2176ae14e5f63864 Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Tue, 3 Jan 2017 18:21:23 -0500
Subject: [PATCH 0751/1679] Added super.init() to the initializer.

---
 Trie/Trie/Trie.xcodeproj/project.pbxproj | 2 --
 Trie/Trie/Trie/Trie.swift                | 1 +
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 055885ee1..90c5734cc 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -17,7 +17,6 @@
 		EB798E2A1DFEF81400F0628D /* Trie.swift in Sources */ = {isa = PBXBuildFile; fileRef = EB798E281DFEF81400F0628D /* Trie.swift */; };
 		EB798E2C1DFEF90B00F0628D /* dictionary.txt in Resources */ = {isa = PBXBuildFile; fileRef = EB798E2B1DFEF90B00F0628D /* dictionary.txt */; };
 		EB798E2D1DFEF90B00F0628D /* dictionary.txt in Resources */ = {isa = PBXBuildFile; fileRef = EB798E2B1DFEF90B00F0628D /* dictionary.txt */; };
-		EB8369AD1E15C5710003A7F8 /* ReadMe.md in Sources */ = {isa = PBXBuildFile; fileRef = EB8369AC1E15C5710003A7F8 /* ReadMe.md */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
@@ -270,7 +269,6 @@
 			files = (
 				EB798E291DFEF81400F0628D /* Trie.swift in Sources */,
 				EB798E001DFEF79900F0628D /* ViewController.swift in Sources */,
-				EB8369AD1E15C5710003A7F8 /* ReadMe.md in Sources */,
 				EB798DFE1DFEF79900F0628D /* AppDelegate.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index ec3b1c5cc..bf1c7d9c2 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -64,6 +64,7 @@ class Trie: NSObject, NSCoding {
     override init() {
         root = Node()
         wordCount = 0
+        super.init()
     }
 
     // MARK: NSCoding

From b48107ff77ecd007656177914a9bb2860d0f1737 Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Tue, 3 Jan 2017 18:32:52 -0500
Subject: [PATCH 0752/1679] Added a check for wordArray not nil to the guard
 statement in insertWordsIntoTrie.

---
 Trie/Trie/TrieTests/TrieTests.swift | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 7ef02553f..f8e934f0d 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -51,10 +51,8 @@ class TrieTests: XCTestCase {
 
     /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
     func insertWordsIntoTrie() {
-        guard trie.count == 0 else {
-            return
-        }
-        for word in self.wordArray! {
+        guard let wordArray = wordArray, trie.count == 0 else { return }
+        for word in wordArray {
             trie.insert(word: word)
         }
     }

From 947d4f8052bccdb6f8a104ab1d36892d8152d92e Mon Sep 17 00:00:00 2001
From: gonini <zhanggoni@gmail.com>
Date: Wed, 4 Jan 2017 09:46:09 +0900
Subject: [PATCH 0753/1679] Update Minimum Spanning Tree (Unweighted Graph) to
 Swift 3

---
 .../Contents.swift                                     |  2 +-
 .../timeline.xctimeline                                |  6 ------
 .../MinimumSpanningTree.playground/Sources/Graph.swift |  6 +++---
 .../MinimumSpanningTree.playground/Sources/Node.swift  |  4 ++--
 .../MinimumSpanningTree.playground/Sources/Queue.swift |  2 +-
 .../MinimumSpanningTree.swift                          |  2 +-
 Minimum Spanning Tree (Unweighted)/Tests/Graph.swift   | 10 +++++-----
 Minimum Spanning Tree (Unweighted)/Tests/Queue.swift   |  2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj              |  3 +++
 9 files changed, 17 insertions(+), 20 deletions(-)
 delete mode 100644 Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline

diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 088da1d11..86fe27df8 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,4 +1,4 @@
-func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
+func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 
   var queue = Queue<Node>()
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift
index 8cfb2a09c..8f02baf92 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -5,13 +5,13 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(label: String) -> Node {
+  public func addNode(_ label: String) -> Node {
     let node = Node(label: label)
     nodes.append(node)
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
+  public func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
     source.neighbors.append(edge)
   }
@@ -27,7 +27,7 @@ public class Graph: CustomStringConvertible, Equatable {
     return description
   }
 
-  public func findNodeWithLabel(label: String) -> Node {
+  public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
 
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift
index 37a3b3fdf..0aedb6ef9 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Node.swift	
@@ -22,8 +22,8 @@ public class Node: CustomStringConvertible, Equatable {
     return distance != nil
   }
 
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+  public func remove(_ edge: Edge) {
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Queue.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Queue.swift
index bf462bbdd..3d98f801c 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Queue.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Queue.swift	
@@ -13,7 +13,7 @@ public struct Queue<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.swift
index 92d370878..645a41999 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.swift	
@@ -1,4 +1,4 @@
-func breadthFirstSearchMinimumSpanningTree(graph: Graph, source: Node) -> Graph {
+func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 
   var queue = Queue<Node>()
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift
index ed71cab7c..2d4161245 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift	
@@ -38,8 +38,8 @@ public class Node: CustomStringConvertible, Equatable {
     return distance != nil
   }
 
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+  public func remove(_ edge: Edge) {
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
@@ -56,13 +56,13 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(label: String) -> Node {
+  public func addNode(_ label: String) -> Node {
     let node = Node(label: label)
     nodes.append(node)
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
+  public func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
     source.neighbors.append(edge)
   }
@@ -78,7 +78,7 @@ public class Graph: CustomStringConvertible, Equatable {
     return description
   }
 
-  public func findNodeWithLabel(label: String) -> Node {
+  public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
 
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Queue.swift b/Minimum Spanning Tree (Unweighted)/Tests/Queue.swift
index bf462bbdd..3d98f801c 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Queue.swift	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Queue.swift	
@@ -13,7 +13,7 @@ public struct Queue<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
index 659c7e9f2..a066b7a71 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
@@ -94,6 +94,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -230,6 +231,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -242,6 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From fc208c61f96838af6266980bd058f7141b3cac24 Mon Sep 17 00:00:00 2001
From: GongUi <zhanggoni@gmail.com>
Date: Wed, 4 Jan 2017 09:48:04 +0900
Subject: [PATCH 0754/1679] Update .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 4e2918431..4fbf215de 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -28,7 +28,7 @@ script:
 # - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests

From 017351f6bb67368ff273d73cba89e1ee42aa45f2 Mon Sep 17 00:00:00 2001
From: gonini <zhanggoni@gmail.com>
Date: Thu, 5 Jan 2017 08:10:11 +0900
Subject: [PATCH 0755/1679] Warning correction for unused return function

---
 .../MinimumSpanningTree.playground/Sources/Graph.swift          | 2 +-
 Minimum Spanning Tree (Unweighted)/Tests/Graph.swift            | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift
index 8f02baf92..e2bb82677 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -35,7 +35,7 @@ public class Graph: CustomStringConvertible, Equatable {
     let duplicated = Graph()
 
     for node in nodes {
-      duplicated.addNode(node.label)
+        _ = duplicated.addNode(node.label)
     }
 
     for node in nodes {
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift
index 2d4161245..c8cb77ac8 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Graph.swift	
@@ -86,7 +86,7 @@ public class Graph: CustomStringConvertible, Equatable {
     let duplicated = Graph()
 
     for node in nodes {
-      duplicated.addNode(node.label)
+      _ = duplicated.addNode(node.label)
     }
 
     for node in nodes {

From 58058cf6e9f6813ffbde7cf89ebefba07950d18b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20B=C3=B8dskov?= <pb@reeltrak.com>
Date: Thu, 5 Jan 2017 08:02:06 +0100
Subject: [PATCH 0756/1679] aligning with style guidelines

---
 Huffman Coding/Huffman.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index 017c5baf2..2d59908e9 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -3,7 +3,7 @@
 import Foundation
 
 let s1 = "so much words wow many compression"
-if let originalData = s1.data(using: String.Encoding.utf8) {
+if let originalData = s1.data(using: .utf8) {
   print(originalData.count)
 
   let huffman1 = Huffman()
@@ -17,7 +17,7 @@ if let originalData = s1.data(using: String.Encoding.utf8) {
   let decompressedData = huffman2.decompressData(data: compressedData, frequencyTable: frequencyTable)
   print(decompressedData.length)
 
-  let s2 = String(data: decompressedData as Data, encoding: String.Encoding.utf8)!
+  let s2 = String(data: decompressedData as Data, encoding: .utf8)!
   print(s2)
   assert(s1 == s2)
 }

From 07dc70e66a3a3e42a3cec94a2cfa6b884f1af739 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20B=C3=B8dskov?= <pb@reeltrak.com>
Date: Thu, 5 Jan 2017 12:42:42 +0100
Subject: [PATCH 0757/1679] Migrates App-Pairs Shortest Paths to Swift3 syntax

---
 .travis.yml                                   |  2 +-
 .../APSP/APSP.xcodeproj/project.pbxproj       | 13 +++++++++-
 .../xcshareddata/xcschemes/APSP.xcscheme      |  2 +-
 .../xcshareddata/xcschemes/APSPTests.xcscheme |  2 +-
 All-Pairs Shortest Paths/APSP/APSP/APSP.swift |  2 +-
 .../APSP/APSP/FloydWarshall.swift             | 26 +++++++++----------
 .../APSP/APSP/Helpers.swift                   | 11 ++++----
 .../APSP/APSPTests/APSPTests.swift            |  6 ++---
 8 files changed, 38 insertions(+), 26 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 4fbf215de..2417b4b6a 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -8,7 +8,7 @@ install:
 
 script:
 
-# - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
+- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index e7e95bbb7..b2d93ea35 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -187,14 +187,16 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0730;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					493D8DDF1CDD2A1C0089795A = {
 						CreatedOnToolsVersion = 7.3;
+						LastSwiftMigration = 0820;
 					};
 					493D8DF01CDD5B960089795A = {
 						CreatedOnToolsVersion = 7.3;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -305,8 +307,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -350,8 +354,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -370,6 +376,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -381,6 +388,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -392,6 +400,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
@@ -411,6 +420,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
+				SWIFT_VERSION = 3.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -432,6 +442,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
+				SWIFT_VERSION = 3.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme
index 475997aa9..e313c4b88 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme
index cd141a407..5797cbf9c 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift
index 453f738b7..dec7475bd 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/APSP.swift	
@@ -18,7 +18,7 @@ public protocol APSPAlgorithm {
   associatedtype Q: Hashable
   associatedtype P: APSPResult
 
-  static func apply(graph: AbstractGraph<Q>) -> P
+  static func apply(_ graph: AbstractGraph<Q>) -> P
 
 }
 
diff --git a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
index 806c8677c..b1a870f2a 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
@@ -17,7 +17,7 @@ private typealias StepResult = (distances: Distances, predecessors: Predecessors
 
  - note: In all complexity bounds, `V` is the number of vertices in the graph, and `E` is the number of edges.
  */
-public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
+public struct FloydWarshall<T>: APSPAlgorithm where T: Hashable {
 
   public typealias Q = T
   public typealias P = FloydWarshallResult<T>
@@ -29,7 +29,7 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
    - complexity: `Θ(V^3)` time, `Θ(V^2)` space
    - returns a `FloydWarshallResult` struct which can be queried for shortest paths and their total weights
    */
-  public static func apply<T>(graph: AbstractGraph<T>) -> FloydWarshallResult<T> {
+  public static func apply<T>(_ graph: AbstractGraph<T>) -> FloydWarshallResult<T> {
 
     var previousDistance = constructInitialDistanceMatrix(graph)
     var previousPredecessor = constructInitialPredecessorMatrix(previousDistance)
@@ -59,12 +59,12 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
    - returns: a tuple containing the next distance matrix with weights of currently known
    shortest paths and the corresponding predecessor matrix
    */
-  static private func nextStep<T>(intermediateIdx: Int, previousDistances: Distances,
+  static fileprivate func nextStep<T>(_ intermediateIdx: Int, previousDistances: Distances,
                                previousPredecessors: Predecessors, graph: AbstractGraph<T>) -> StepResult {
 
     let vertexCount = graph.vertices.count
-    var nextDistances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
-    var nextPredecessors = Array(count: vertexCount, repeatedValue: Array<Int?>(count: vertexCount, repeatedValue: nil))
+    var nextDistances = Array(repeating: Array(repeating: Double.infinity, count: vertexCount), count: vertexCount)
+    var nextPredecessors = Array(repeating: Array<Int?>(repeating: nil, count: vertexCount), count: vertexCount)
 
     for fromIdx in 0 ..< vertexCount {
       for toIndex in 0 ..< vertexCount {
@@ -97,12 +97,12 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
    - complexity: `Θ(V^2)` time/space
    - returns: weighted adjacency matrix in form ready for processing with Floyd-Warshall
    */
-  static private func constructInitialDistanceMatrix<T>(graph: AbstractGraph<T>) -> Distances {
+  static fileprivate func constructInitialDistanceMatrix<T>(_ graph: AbstractGraph<T>) -> Distances {
 
     let vertices = graph.vertices
 
     let vertexCount = graph.vertices.count
-    var distances = Array(count: vertexCount, repeatedValue: Array(count: vertexCount, repeatedValue: Double.infinity))
+    var distances = Array(repeating: Array(repeating: Double.infinity, count: vertexCount), count: vertexCount)
 
     for row in vertices {
       for col in vertices {
@@ -125,10 +125,10 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
 
    - complexity: `Θ(V^2)` time/space
   */
-  static private func constructInitialPredecessorMatrix(distances: Distances) -> Predecessors {
+  static fileprivate func constructInitialPredecessorMatrix(_ distances: Distances) -> Predecessors {
 
     let vertexCount = distances.count
-    var predecessors = Array(count: vertexCount, repeatedValue: Array<Int?>(count: vertexCount, repeatedValue: nil))
+    var predecessors = Array(repeating: Array<Int?>(repeating: nil, count: vertexCount), count: vertexCount)
 
     for fromIdx in 0 ..< vertexCount {
       for toIdx in 0 ..< vertexCount {
@@ -151,10 +151,10 @@ public struct FloydWarshall<T where T: Hashable>: APSPAlgorithm {
  It conforms to the `APSPResult` procotol which provides methods to retrieve
  distances and paths between given pairs of start and end nodes.
  */
-public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
+public struct FloydWarshallResult<T>: APSPResult where T: Hashable {
 
-  private var weights: Distances
-  private var predecessors: Predecessors
+  fileprivate var weights: Distances
+  fileprivate var predecessors: Predecessors
 
   /**
    - returns: the total weight of the path from a starting vertex to a destination.
@@ -190,7 +190,7 @@ public struct FloydWarshallResult<T where T: Hashable>: APSPResult {
 
    - returns: the list of predecessors discovered so far
    */
-  private func recursePathFrom(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>],
+  fileprivate func recursePathFrom(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, path: [Vertex<T>],
                                           inGraph graph: AbstractGraph<T>) -> [Vertex<T>]? {
 
     if from.index == to.index {
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift
index 644454491..3812b3f58 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
@@ -7,10 +7,11 @@
 
 import Foundation
 
+
 /**
  Print a matrix, optionally specifying only the cells to display with the triplet (i, j, k) -> matrix[i][j], matrix[i][k], matrix[k][j]
  */
-func printMatrix(matrix: [[Double]], i: Int = -1, j: Int = -1, k: Int = -1) {
+func printMatrix(_ matrix: [[Double]], i: Int = -1, j: Int = -1, k: Int = -1) {
 
   if i >= 0 {
     print("  k: \(k); i: \(i); j: \(j)\n")
@@ -31,12 +32,12 @@ func printMatrix(matrix: [[Double]], i: Int = -1, j: Int = -1, k: Int = -1) {
     }
     grid.append(row)
   }
-  print((grid as NSArray).componentsJoinedByString("\n"))
+  print((grid as NSArray).componentsJoined(by: "\n"))
   print(" =======================")
 
 }
 
-func printIntMatrix(matrix: [[Int?]]) {
+func printIntMatrix(_ matrix: [[Int?]]) {
 
   var grid = [String]()
 
@@ -46,14 +47,14 @@ func printIntMatrix(matrix: [[Int?]]) {
     for y in 0..<n {
       if let value = matrix[x][y] {
         let valueString = NSString(format: "%i", value)
-        row += "\(matrix[x][y] >= 0 ? " " : "")\(valueString) "
+        row += "\(value >= 0 ? " " : "")\(valueString) "
       } else {
         row += "  ø  "
       }
     }
     grid.append(row)
   }
-  print((grid as NSArray).componentsJoinedByString("\n"))
+  print((grid as NSArray).componentsJoined(by: "\n"))
   print(" =======================")
 
 }
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
index 52e87758c..9d026f680 100644
--- a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -9,7 +9,7 @@ import APSP
 import Graph
 import XCTest
 
-struct TestCase<T where T: Hashable> {
+struct TestCase<T> where T: Hashable {
 
   var from: Vertex<T>
   var to: Vertex<T>
@@ -71,7 +71,7 @@ class APSPTests: XCTestCase {
 
     for testCase: TestCase<Int> in cases {
       if let computedPath = result.path(fromVertex: testCase.from, toVertex: testCase.to, inGraph: graph),
-              computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
+         let computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
         XCTAssert(computedDistance == testCase.expectedDistance, "expected distance \(testCase.expectedDistance) but got \(computedDistance)")
         XCTAssert(computedPath == testCase.expectedPath, "expected path \(testCase.expectedPath) but got \(computedPath)")
       }
@@ -111,7 +111,7 @@ class APSPTests: XCTestCase {
 
     for testCase: TestCase<Int> in cases {
       if let computedPath = result.path(fromVertex: testCase.from, toVertex: testCase.to, inGraph: graph),
-        computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
+        let computedDistance = result.distance(fromVertex: testCase.from, toVertex: testCase.to) {
         XCTAssert(computedDistance == testCase.expectedDistance, "expected distance \(testCase.expectedDistance) but got \(computedDistance)")
         XCTAssert(computedPath == testCase.expectedPath, "expected path \(testCase.expectedPath) but got \(computedPath)")
       }

From 797a2e9e2bf70911222cac674e05841b80679310 Mon Sep 17 00:00:00 2001
From: iamsimranjot <iamsimranjot@gmail.com>
Date: Fri, 6 Jan 2017 02:56:13 +0530
Subject: [PATCH 0758/1679] Updated Merge Sort (Recursive) to Generic.

---
 .../MergeSort.playground/Contents.swift       |  6 +-
 Merge Sort/MergeSort.swift                    | 72 +++++++++----------
 2 files changed, 39 insertions(+), 39 deletions(-)

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index ac166131e..e76570481 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -1,6 +1,6 @@
 /* Top-down recursive version */
 
-func mergeSort(_ array: [Int]) -> [Int] {
+func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
   let leftArray = mergeSort(Array(array[0..<middleIndex]))
@@ -8,10 +8,10 @@ func mergeSort(_ array: [Int]) -> [Int] {
   return merge(leftPile: leftArray, rightPile: rightArray)
 }
 
-func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
+func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var leftIndex = 0
   var rightIndex = 0
-  var orderedPile = [Int]()
+  var orderedPile = [T]()
 
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
     if leftPile[leftIndex] < rightPile[rightIndex] {
diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index 20316663f..bb89ea4d4 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -6,45 +6,45 @@
 //
 //
 
-func mergeSort(_ array: [Int]) -> [Int] {
-  guard array.count > 1 else { return array }
-  let middleIndex = array.count / 2
-  let leftArray = mergeSort(Array(array[0..<middleIndex]))
-  let rightArray = mergeSort(Array(array[middleIndex..<array.count]))
-  return merge(leftPile: leftArray, rightPile: rightArray)
+func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
+    guard array.count > 1 else { return array }
+    let middleIndex = array.count / 2
+    let leftArray = mergeSort(Array(array[0..<middleIndex]))
+    let rightArray = mergeSort(Array(array[middleIndex..<array.count]))
+    return merge(leftPile: leftArray, rightPile: rightArray)
 }
 
-func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
-  var leftIndex = 0
-  var rightIndex = 0
-  var orderedPile = [Int]()
-
-  while leftIndex < leftPile.count && rightIndex < rightPile.count {
-    if leftPile[leftIndex] < rightPile[rightIndex] {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
-    } else if leftPile[leftIndex] > rightPile[rightIndex] {
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
-    } else {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
+func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
+    var leftIndex = 0
+    var rightIndex = 0
+    var orderedPile = [T]()
+    
+    while leftIndex < leftPile.count && rightIndex < rightPile.count {
+        if leftPile[leftIndex] < rightPile[rightIndex] {
+            orderedPile.append(leftPile[leftIndex])
+            leftIndex += 1
+        } else if leftPile[leftIndex] > rightPile[rightIndex] {
+            orderedPile.append(rightPile[rightIndex])
+            rightIndex += 1
+        } else {
+            orderedPile.append(leftPile[leftIndex])
+            leftIndex += 1
+            orderedPile.append(rightPile[rightIndex])
+            rightIndex += 1
+        }
     }
-  }
-
-  while leftIndex < leftPile.count {
-    orderedPile.append(leftPile[leftIndex])
-    leftIndex += 1
-  }
-
-  while rightIndex < rightPile.count {
-    orderedPile.append(rightPile[rightIndex])
-    rightIndex += 1
-  }
-
-  return orderedPile
+    
+    while leftIndex < leftPile.count {
+        orderedPile.append(leftPile[leftIndex])
+        leftIndex += 1
+    }
+    
+    while rightIndex < rightPile.count {
+        orderedPile.append(rightPile[rightIndex])
+        rightIndex += 1
+    }
+    
+    return orderedPile
 }
 
 /*

From e7b54f7bbb1c48be56f0f85ff433f889e1ddd880 Mon Sep 17 00:00:00 2001
From: iamsimranjot <iamsimranjot@gmail.com>
Date: Fri, 6 Jan 2017 02:58:50 +0530
Subject: [PATCH 0759/1679] Extra Example Added.

---
 Merge Sort/MergeSort.playground/Contents.swift | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index e76570481..2952fc299 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -43,6 +43,8 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
 
 let array = [2, 1, 5, 4, 9]
 let sortedArray = mergeSort(array)
+let array2 = ["Tom", "Harry", "Ron", "Chandler", "Monica"]
+let sortedArray2 = mergeSort(array2)
 
 
 

From 369bff5d3ed3634c140b73c348dbe000ca7df4da Mon Sep 17 00:00:00 2001
From: iamsimranjot <iamsimranjot@gmail.com>
Date: Sun, 8 Jan 2017 03:47:54 +0530
Subject: [PATCH 0760/1679] Code Re-Indented With 2 Space Indentation.

---
 Merge Sort/MergeSort.swift | 70 +++++++++++++++++++-------------------
 1 file changed, 35 insertions(+), 35 deletions(-)

diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index bb89ea4d4..a7677b0bb 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -7,44 +7,44 @@
 //
 
 func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
-    guard array.count > 1 else { return array }
-    let middleIndex = array.count / 2
-    let leftArray = mergeSort(Array(array[0..<middleIndex]))
-    let rightArray = mergeSort(Array(array[middleIndex..<array.count]))
-    return merge(leftPile: leftArray, rightPile: rightArray)
+  guard array.count > 1 else { return array }
+  let middleIndex = array.count / 2
+  let leftArray = mergeSort(Array(array[0..<middleIndex]))
+  let rightArray = mergeSort(Array(array[middleIndex..<array.count]))
+  return merge(leftPile: leftArray, rightPile: rightArray)
 }
 
 func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
-    var leftIndex = 0
-    var rightIndex = 0
-    var orderedPile = [T]()
-    
-    while leftIndex < leftPile.count && rightIndex < rightPile.count {
-        if leftPile[leftIndex] < rightPile[rightIndex] {
-            orderedPile.append(leftPile[leftIndex])
-            leftIndex += 1
-        } else if leftPile[leftIndex] > rightPile[rightIndex] {
-            orderedPile.append(rightPile[rightIndex])
-            rightIndex += 1
-        } else {
-            orderedPile.append(leftPile[leftIndex])
-            leftIndex += 1
-            orderedPile.append(rightPile[rightIndex])
-            rightIndex += 1
-        }
-    }
-    
-    while leftIndex < leftPile.count {
-        orderedPile.append(leftPile[leftIndex])
-        leftIndex += 1
-    }
-    
-    while rightIndex < rightPile.count {
-        orderedPile.append(rightPile[rightIndex])
-        rightIndex += 1
-    }
-    
-    return orderedPile
+  var leftIndex = 0
+  var rightIndex = 0
+  var orderedPile = [T]()
+  
+  while leftIndex < leftPile.count && rightIndex < rightPile.count {
+      if leftPile[leftIndex] < rightPile[rightIndex] {
+          orderedPile.append(leftPile[leftIndex])
+          leftIndex += 1
+      } else if leftPile[leftIndex] > rightPile[rightIndex] {
+          orderedPile.append(rightPile[rightIndex])
+          rightIndex += 1
+      } else {
+          orderedPile.append(leftPile[leftIndex])
+          leftIndex += 1
+          orderedPile.append(rightPile[rightIndex])
+          rightIndex += 1
+      }
+  }
+  
+  while leftIndex < leftPile.count {
+      orderedPile.append(leftPile[leftIndex])
+      leftIndex += 1
+  }
+  
+  while rightIndex < rightPile.count {
+      orderedPile.append(rightPile[rightIndex])
+      rightIndex += 1
+  }
+  
+  return orderedPile
 }
 
 /*

From f9412936fc0656eebf5f7ad1a79a241a5e05c572 Mon Sep 17 00:00:00 2001
From: iamsimranjot <iamsimranjot@gmail.com>
Date: Sun, 8 Jan 2017 03:57:16 +0530
Subject: [PATCH 0761/1679] Code Re Indented with 2 Space Indentation (Part 2)

---
 Merge Sort/MergeSort.swift | 32 ++++++++++++++++----------------
 1 file changed, 16 insertions(+), 16 deletions(-)

diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index a7677b0bb..4332fc44b 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -20,28 +20,28 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var orderedPile = [T]()
   
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
-      if leftPile[leftIndex] < rightPile[rightIndex] {
-          orderedPile.append(leftPile[leftIndex])
-          leftIndex += 1
-      } else if leftPile[leftIndex] > rightPile[rightIndex] {
-          orderedPile.append(rightPile[rightIndex])
-          rightIndex += 1
-      } else {
-          orderedPile.append(leftPile[leftIndex])
-          leftIndex += 1
-          orderedPile.append(rightPile[rightIndex])
-          rightIndex += 1
-      }
+    if leftPile[leftIndex] < rightPile[rightIndex] {
+      orderedPile.append(leftPile[leftIndex])
+      leftIndex += 1
+    } else if leftPile[leftIndex] > rightPile[rightIndex] {
+      orderedPile.append(rightPile[rightIndex])
+      rightIndex += 1
+    } else {
+      orderedPile.append(leftPile[leftIndex])
+      leftIndex += 1
+      orderedPile.append(rightPile[rightIndex])
+      rightIndex += 1
+    }
   }
   
   while leftIndex < leftPile.count {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
+    orderedPile.append(leftPile[leftIndex])
+    leftIndex += 1
   }
   
   while rightIndex < rightPile.count {
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
+    orderedPile.append(rightPile[rightIndex])
+    rightIndex += 1
   }
   
   return orderedPile

From 0e819963fe321021486aa8247776cb20d65d58cf Mon Sep 17 00:00:00 2001
From: Tai Heng <theng@tucali.ca>
Date: Sun, 8 Jan 2017 15:52:39 -0500
Subject: [PATCH 0762/1679] Updated K-Means Tests.xcodeproj to latest settings.
 Updated K-Means code to Swift3 syntax and changes to API.

---
 .travis.yml                                   |  2 +-
 K-Means/KMeans.swift                          | 18 ++++-----
 K-Means/Tests/KMeansTests.swift               |  2 +-
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 40 ++++++++++++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 K-Means/Tests/Vector.swift                    | 12 +++---
 6 files changed, 57 insertions(+), 19 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 727b247a5..b33835565 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -25,7 +25,7 @@ script:
 # - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 972fd7230..4a89a3fae 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -11,11 +11,11 @@ class KMeans<Label: Hashable> {
     self.numCenters = labels.count
   }
 
-  private func indexOfNearestCenter(x: Vector, centers: [Vector]) -> Int {
+  private func indexOfNearestCenter(_ x: Vector, centers: [Vector]) -> Int {
     var nearestDist = DBL_MAX
     var minIndex = 0
 
-    for (idx, center) in centers.enumerate() {
+    for (idx, center) in centers.enumerated() {
       let dist = x.distanceTo(center)
       if dist < nearestDist {
         minIndex = idx
@@ -25,8 +25,8 @@ class KMeans<Label: Hashable> {
     return minIndex
   }
 
-  func trainCenters(points: [Vector], convergeDistance: Double) {
-    let zeroVector = Vector([Double](count: points[0].length, repeatedValue: 0))
+  func trainCenters(_ points: [Vector], convergeDistance: Double) {
+    let zeroVector = Vector([Double](repeating: 0, count: points[0].length))
 
     // Randomly take k objects from the input data to make the initial centroids.
     var centers = reservoirSample(points, k: numCenters)
@@ -34,7 +34,7 @@ class KMeans<Label: Hashable> {
     var centerMoveDist = 0.0
     repeat {
       // This array keeps track of which data points belong to which centroids.
-      var classification: [[Vector]] = .init(count: numCenters, repeatedValue: [])
+      var classification: [[Vector]] = .init(repeating: [], count: numCenters)
 
       // For each data point, find the centroid that it is closest to.
       for p in points {
@@ -45,7 +45,7 @@ class KMeans<Label: Hashable> {
       // Take the average of all the data points that belong to each centroid.
       // This moves the centroid to a new position.
       let newCenters = classification.map { assignedPoints in
-        assignedPoints.reduce(zeroVector, combine: +) / Double(assignedPoints.count)
+        assignedPoints.reduce(zeroVector, +) / Double(assignedPoints.count)
       }
 
       // Find out how far each centroid moved since the last iteration. If it's
@@ -61,14 +61,14 @@ class KMeans<Label: Hashable> {
     centroids = centers
   }
 
-  func fit(point: Vector) -> Label {
+  func fit(_ point: Vector) -> Label {
     assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
 
     let centroidIndex = indexOfNearestCenter(point, centers: centroids)
     return labels[centroidIndex]
   }
 
-  func fit(points: [Vector]) -> [Label] {
+  func fit(_ points: [Vector]) -> [Label] {
     assert(!centroids.isEmpty, "Exception: KMeans tried to fit on a non trained model.")
 
     return points.map(fit)
@@ -76,7 +76,7 @@ class KMeans<Label: Hashable> {
 }
 
 // Pick k random elements from samples
-func reservoirSample<T>(samples: [T], k: Int) -> [T] {
+func reservoirSample<T>(_ samples: [T], k: Int) -> [T] {
   var result = [T]()
 
   // Fill the result array with first k elements
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index 179f9d418..7e0c93004 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,7 +10,7 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
-  func genPoints(numPoints: Int, numDimensions: Int) -> [Vector] {
+  func genPoints(_ numPoints: Int, numDimensions: Int) -> [Vector] {
     var points = [Vector]()
     for _ in 0..<numPoints {
       var data = [Double]()
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 34fe7fd21..08b64a8f9 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,10 +85,11 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0730;
+				LastUpgradeCheck = 0820;
 				TargetAttributes = {
 					B80894DF1C852D100018730E = {
 						CreatedOnToolsVersion = 7.2.1;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -136,7 +137,24 @@
 		B80894D91C852CDC0018730E /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
 				ENABLE_TESTABILITY = YES;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
 				ONLY_ACTIVE_ARCH = YES;
 			};
 			name = Debug;
@@ -144,6 +162,24 @@
 		B80894DA1C852CDC0018730E /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -193,6 +229,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -234,6 +271,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index a563876e7..2b401e86e 100644
--- a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/K-Means/Tests/Vector.swift b/K-Means/Tests/Vector.swift
index 10baf9338..591d2d498 100644
--- a/K-Means/Tests/Vector.swift
+++ b/K-Means/Tests/Vector.swift
@@ -13,7 +13,7 @@ struct Vector: CustomStringConvertible, Equatable {
     return "Vector (\(data)"
   }
 
-  func distanceTo(other: Vector) -> Double {
+  func distanceTo(_ other: Vector) -> Double {
     var result = 0.0
     for idx in 0..<length {
       result += pow(data[idx] - other.data[idx], 2.0)
@@ -39,7 +39,7 @@ func + (left: Vector, right: Vector) -> Vector {
   return Vector(results)
 }
 
-func += (inout left: Vector, right: Vector) {
+func += (left: inout Vector, right: Vector) {
   left = left + right
 }
 
@@ -51,18 +51,18 @@ func - (left: Vector, right: Vector) -> Vector {
   return Vector(results)
 }
 
-func -= (inout left: Vector, right: Vector) {
+func -= (left: inout Vector, right: Vector) {
   left = left - right
 }
 
 func / (left: Vector, right: Double) -> Vector {
-  var results = [Double](count: left.length, repeatedValue: 0)
-  for (idx, value) in left.data.enumerate() {
+  var results = [Double](repeating: 0, count: left.length)
+  for (idx, value) in left.data.enumerated() {
     results[idx] = value / right
   }
   return Vector(results)
 }
 
-func /= (inout left: Vector, right: Double) {
+func /= (left: inout Vector, right: Double) {
   left = left / right
 }

From bf46bb528139e05d41a48bed0a54d78030b420b2 Mon Sep 17 00:00:00 2001
From: Tai Heng <theng@tucali.ca>
Date: Sun, 8 Jan 2017 16:29:16 -0500
Subject: [PATCH 0763/1679] Converted playground and combSort code to Swift 3
 syntax. Changed combSort to use generic type.

---
 Comb Sort/Comb Sort.playground/Contents.swift | 24 +------------
 .../Sources/Comb Sort.swift                   | 36 +++++++++++++++++++
 Comb Sort/Comb Sort.swift                     |  6 ++--
 3 files changed, 40 insertions(+), 26 deletions(-)
 create mode 100644 Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index 2d6155b50..d6add44f5 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -4,34 +4,12 @@
 
 import Cocoa
 
-func combSort (input: [Int]) -> [Int] {
-  var copy = input
-  var gap = copy.count
-  let shrink = 1.3
-
-  while gap > 1 {
-    gap = Int(Double(gap) / shrink)
-    if gap < 1 {
-      gap = 1
-    }
-
-    var index = 0
-    while index + gap < copy.count {
-      if copy[index] > copy[index + gap] {
-        swap(&copy[index], &copy[index + gap])
-      }
-      index += 1
-    }
-  }
-  return copy
-}
-
 // Test Comb Sort with small array of ten values
 let array = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
 combSort(array)
 
 // Test Comb Sort with large array of 1000 random values
-var bigArray = [Int](count: 1000, repeatedValue: 0)
+var bigArray = [Int](repeating: 0, count: 1000)
 var i = 0
 while i < 1000 {
   bigArray[i] = Int(arc4random_uniform(1000) + 1)
diff --git a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift
new file mode 100644
index 000000000..b6e85fa2b
--- /dev/null
+++ b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
@@ -0,0 +1,36 @@
+//  Comb Sort.swift
+//  Comb Sort
+//
+//  Created by Stephen.Rutstein on 7/16/16.
+//  Copyright © 2016 Stephen.Rutstein. All rights reserved.
+//
+
+import Foundation
+
+public func combSort<T: Comparable>(_ input: [T]) -> [T] {
+    var copy: [T] = input
+    var gap = copy.count
+    let shrink = 1.3
+    
+    while gap > 1 {
+        gap = (Int)(Double(gap) / shrink)
+        if gap < 1 {
+            gap = 1
+        }
+        
+        var index = 0
+        while !(index + gap >= copy.count) {
+            if copy[index] > copy[index + gap] {
+                swap(&copy[index], &copy[index + gap])
+            }
+            index += 1
+        }
+    }
+    return copy
+}
+
+fileprivate func swap<T: Comparable>(a: inout T, b: inout T) {
+    let temp = a
+    a = b
+    b = temp
+}
diff --git a/Comb Sort/Comb Sort.swift b/Comb Sort/Comb Sort.swift
index 7abba8c7f..b6e85fa2b 100644
--- a/Comb Sort/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.swift	
@@ -7,8 +7,8 @@
 
 import Foundation
 
-func combSort (input: [Int]) -> [Int] {
-    var copy: [Int] = input
+public func combSort<T: Comparable>(_ input: [T]) -> [T] {
+    var copy: [T] = input
     var gap = copy.count
     let shrink = 1.3
     
@@ -29,7 +29,7 @@ func combSort (input: [Int]) -> [Int] {
     return copy
 }
 
-func swap (inout a: Int, inout b: Int) {
+fileprivate func swap<T: Comparable>(a: inout T, b: inout T) {
     let temp = a
     a = b
     b = temp

From f1dd6b66c4eca5e01b7b363a329fa4ffa5a46d0e Mon Sep 17 00:00:00 2001
From: iamsimranjot <iamsimranjot@gmail.com>
Date: Mon, 9 Jan 2017 03:12:18 +0530
Subject: [PATCH 0764/1679] Removed Extra Spaces.

---
 Merge Sort/MergeSort.swift | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index 4332fc44b..f77d1cd84 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -18,7 +18,7 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var leftIndex = 0
   var rightIndex = 0
   var orderedPile = [T]()
-  
+
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
     if leftPile[leftIndex] < rightPile[rightIndex] {
       orderedPile.append(leftPile[leftIndex])
@@ -33,17 +33,17 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
       rightIndex += 1
     }
   }
-  
+
   while leftIndex < leftPile.count {
     orderedPile.append(leftPile[leftIndex])
     leftIndex += 1
   }
-  
+
   while rightIndex < rightPile.count {
     orderedPile.append(rightPile[rightIndex])
     rightIndex += 1
   }
-  
+
   return orderedPile
 }
 

From af8b44f97392fb8f8cb5704b0799fb0523ee8e31 Mon Sep 17 00:00:00 2001
From: zaccone <zaccone@bucknell.edu>
Date: Mon, 9 Jan 2017 13:50:28 -0500
Subject: [PATCH 0765/1679] Changed the baseline for one of the tests.

---
 .../6ABF2F62-9363-4450-8DE1-D20F57026950.plist                  | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist b/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist
index 01ff985c8..d8e350129 100644
--- a/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist
+++ b/Trie/Trie/Trie.xcodeproj/xcshareddata/xcbaselines/EB798E0A1DFEF79900F0628D.xcbaseline/6ABF2F62-9363-4450-8DE1-D20F57026950.plist
@@ -11,7 +11,7 @@
 				<key>com.apple.XCTPerformanceMetric_WallClockTime</key>
 				<dict>
 					<key>baselineAverage</key>
-					<real>3.0053</real>
+					<real>3.407</real>
 					<key>baselineIntegrationDisplayName</key>
 					<string>Local Baseline</string>
 				</dict>

From f0e83bdea4dce34d5a495fcd7dc3b3f3dec8c178 Mon Sep 17 00:00:00 2001
From: Tai Heng <theng@tucali.ca>
Date: Mon, 9 Jan 2017 22:05:24 -0500
Subject: [PATCH 0766/1679] Added Comb Sort test.

---
 .travis.yml                                   |   1 +
 Comb Sort/Tests/CombSortTests.swift           |  28 ++
 Comb Sort/Tests/Info.plist                    |  22 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 277 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     | 101 +++++++
 6 files changed, 436 insertions(+)
 create mode 100644 Comb Sort/Tests/CombSortTests.swift
 create mode 100644 Comb Sort/Tests/Info.plist
 create mode 100644 Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Comb Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/.travis.yml b/.travis.yml
index 727b247a5..b4691467f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -19,6 +19,7 @@ script:
 # - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
new file mode 100644
index 000000000..1bcc67fd0
--- /dev/null
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -0,0 +1,28 @@
+//
+//  CombSortTests.swift
+//  Tests
+//
+//  Created by theng on 2017-01-09.
+//  Copyright © 2017 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+
+class CombSortTests: XCTestCase {
+    var sequence: [Int]!
+    let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
+
+    override func setUp() {
+        super.setUp()
+        sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
+    }
+    
+    override func tearDown() {
+        super.tearDown()
+    }
+
+    func testCombSort() {
+        let sortedSequence = combSort(sequence)
+        XCTAssertEqual(sortedSequence, expectedSequence)
+    }
+}
diff --git a/Comb Sort/Tests/Info.plist b/Comb Sort/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Comb Sort/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..60039196c
--- /dev/null
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,277 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		056E927E1E24852900B30F52 /* CombSortTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 056E927D1E24852900B30F52 /* CombSortTests.swift */; };
+		056E92841E248A4000B30F52 /* Comb Sort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 056E92831E248A4000B30F52 /* Comb Sort.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		056E92751E2483D300B30F52 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		056E92791E2483D300B30F52 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		056E927D1E24852900B30F52 /* CombSortTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = CombSortTests.swift; sourceTree = "<group>"; };
+		056E92831E248A4000B30F52 /* Comb Sort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = "Comb Sort.swift"; path = "../Comb Sort.swift"; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		056E92721E2483D300B30F52 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		056E92581E24836C00B30F52 = {
+			isa = PBXGroup;
+			children = (
+				056E92761E2483D300B30F52 /* Tests */,
+				056E92621E24836C00B30F52 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		056E92621E24836C00B30F52 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				056E92751E2483D300B30F52 /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		056E92761E2483D300B30F52 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				056E92831E248A4000B30F52 /* Comb Sort.swift */,
+				056E92791E2483D300B30F52 /* Info.plist */,
+				056E927D1E24852900B30F52 /* CombSortTests.swift */,
+			);
+			name = Tests;
+			sourceTree = SOURCE_ROOT;
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		056E92741E2483D300B30F52 /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 056E927A1E2483D300B30F52 /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				056E92711E2483D300B30F52 /* Sources */,
+				056E92721E2483D300B30F52 /* Frameworks */,
+				056E92731E2483D300B30F52 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = Tests;
+			productReference = 056E92751E2483D300B30F52 /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
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+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		056E92591E24836C00B30F52 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
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+				LastUpgradeCheck = 0820;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					056E92741E2483D300B30F52 = {
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+						LastSwiftMigration = 0820;
+						ProvisioningStyle = Automatic;
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+				};
+			};
+			buildConfigurationList = 056E925C1E24836C00B30F52 /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 056E92581E24836C00B30F52;
+			productRefGroup = 056E92621E24836C00B30F52 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				056E92741E2483D300B30F52 /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		056E92731E2483D300B30F52 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		056E92711E2483D300B30F52 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				056E927E1E24852900B30F52 /* CombSortTests.swift in Sources */,
+				056E92841E248A4000B30F52 /* Comb Sort.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		056E926C1E24836C00B30F52 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		056E926D1E24836C00B30F52 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		056E927B1E2483D300B30F52 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		056E927C1E2483D300B30F52 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		056E925C1E24836C00B30F52 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				056E926C1E24836C00B30F52 /* Debug */,
+				056E926D1E24836C00B30F52 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		056E927A1E2483D300B30F52 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				056E927B1E2483D300B30F52 /* Debug */,
+				056E927C1E2483D300B30F52 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 056E92591E24836C00B30F52 /* Project object */;
+}
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Comb Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..55e697ad3
--- /dev/null
+++ b/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,101 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0820"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92741E2483D300B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92741E2483D300B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92741E2483D300B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92741E2483D300B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92741E2483D300B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 6ec92d76ccecd3f0083252d406e1fc5b3a59d57b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 10 Jan 2017 00:12:50 -0800
Subject: [PATCH 0767/1679] Fixes compile error due to missing brace.

---
 Trie/Trie/Trie/Trie.swift | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index d3c845720..0e11a9c61 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -11,15 +11,15 @@ import Foundation
 
 /// A node in the trie
 class TrieNode<T: Hashable> {
-    var value: T?
-    weak var parentNode: TrieNode?
-    var children: [T: TrieNode] = [:]
-    var isTerminating = false
-    var isLeaf: Bool {
-        return children.count == 0
-    }
+  var value: T?
+  weak var parentNode: TrieNode?
+  var children: [T: TrieNode] = [:]
+  var isTerminating = false
+  var isLeaf: Bool {
+    return children.count == 0
   }
   
+  
   /// Initializes a node.
   ///
   /// - Parameters:

From 53b87713a7f3a8083d67053416d4bc633090e68b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20B=C3=B8dskov?= <me@peterbodskov.dk>
Date: Wed, 11 Jan 2017 02:30:24 +0100
Subject: [PATCH 0768/1679] Migrates Ternary Search Tree to Swift 3 syntax
 (#352)

* migrates Ternary Search Tree to Swift 3 syntax

* aligning function names as suggested

* adds unit tests to TernarySearchTree

* adds guards as suggested
---
 .travis.yml                                   |   1 +
 .../TST.playground/Contents.swift             |  30 +-
 .../Sources/TernarySearchTree.swift           |  48 ++--
 .../TST.playground/Sources/Utils.swift        |  30 ++
 .../TST.playground/contents.xcplayground      |   2 +-
 Ternary Search Tree/TernarySearchTree.swift   |  54 ++--
 Ternary Search Tree/Tests/Info.plist          |  22 ++
 .../Tests/TernarySearchTreeTests.swift        |  58 ++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 264 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++++
 Ternary Search Tree/Utils.swift               |  30 ++
 .../contents.xcworkspacedata                  |  10 +
 12 files changed, 529 insertions(+), 76 deletions(-)
 create mode 100644 Ternary Search Tree/TST.playground/Sources/Utils.swift
 create mode 100644 Ternary Search Tree/Tests/Info.plist
 create mode 100644 Ternary Search Tree/Tests/TernarySearchTreeTests.swift
 create mode 100644 Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Ternary Search Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Ternary Search Tree/Utils.swift

diff --git a/.travis.yml b/.travis.yml
index 6812ac32a..117400d97 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -43,3 +43,4 @@ script:
 - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
 - xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test
+- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index 6b1fe3eaa..bacf56aee 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -4,39 +4,23 @@ import Cocoa
 import Foundation
 
 let treeOfStrings = TernarySearchTree<String>()
-let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
-
-//Random string generator from:
-//http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
-func randomAlphaNumericString(length: Int) -> String {
-    let allowedCharsCount = UInt32(allowedChars.characters.count)
-    var randomString = ""
-
-    for _ in (0..<length) {
-        let randomNum = Int(arc4random_uniform(allowedCharsCount))
-        let newCharacter = allowedChars[allowedChars.startIndex.advancedBy(randomNum)]
-        randomString += String(newCharacter)
-    }
-
-    return randomString
-}
 
 var testStrings: [(key: String, data: String)] = []
 let testCount = 30
 for _ in (1...testCount) {
     let randomLength = Int(arc4random_uniform(10))
-    let key = randomAlphaNumericString(randomLength)
-    let data = randomAlphaNumericString(randomLength)
+    let key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+    let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
 //    print("Key: \(key) Data: \(data)")
 
     if key != "" && data != "" {
         testStrings.append((key, data))
-        treeOfStrings.insert(data, withKey: key)
+        treeOfStrings.insert(data: data, withKey: key)
     }
 }
 
 for aTest in testStrings {
-    let data = treeOfStrings.find(aTest.key)
+    let data = treeOfStrings.find(key: aTest.key)
 
     if data == nil {
         print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
@@ -51,16 +35,16 @@ let treeOfInts = TernarySearchTree<Int>()
 for _ in (1...testCount) {
     let randomNum = Int(arc4random_uniform(UInt32.max))
     let randomLength = Int(arc4random_uniform(10))
-    let key = randomAlphaNumericString(randomLength)
+    let key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
 
     if key != "" {
         testNums.append((key, randomNum))
-        treeOfInts.insert(randomNum, withKey: key)
+        treeOfInts.insert(data: randomNum, withKey: key)
     }
 }
 
 for aTest in testNums {
-    let data = treeOfInts.find(aTest.key)
+    let data = treeOfInts.find(key: aTest.key)
     if data == nil {
         print("TEST FAILED. Key: \(aTest.key) Data: \(aTest.data)")
     }
diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index 43c4453e3..fed8f9710 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -18,11 +18,10 @@ public class TernarySearchTree<Element> {
     //MARK: - Insertion
 
     public func insert(data: Element, withKey key: String) -> Bool {
-        return insertNode(&root, withData: data, andKey: key, atIndex: 0)
-
+        return insert(node: &root, withData: data, andKey: key, atIndex: 0)
     }
 
-    private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
+    private func insert(node: inout TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
 
         //sanity check.
         if key.characters.count == 0 {
@@ -30,30 +29,30 @@ public class TernarySearchTree<Element> {
         }
 
         //create a new node if necessary.
-        if aNode == nil {
-            let index = key.startIndex.advancedBy(charIndex)
-            aNode = TSTNode<Element>(key: key[index])
+        if node == nil {
+            let index = key.index(key.startIndex, offsetBy: charIndex)
+            node = TSTNode<Element>(key: key[index])
         }
 
         //if current char is less than the current node's char, go left
-        let index = key.startIndex.advancedBy(charIndex)
-        if key[index] < aNode!.key {
-            return insertNode(&aNode!.left, withData: data, andKey: key, atIndex: charIndex)
+        let index = key.index(key.startIndex, offsetBy: charIndex)
+        if key[index] < node!.key {
+            return insert(node: &node!.left, withData: data, andKey: key, atIndex: charIndex)
         }
             //if it's greater, go right.
-        else if key[index] > aNode!.key {
-            return insertNode(&aNode!.right, withData: data, andKey: key, atIndex: charIndex)
+        else if key[index] > node!.key {
+            return insert(node: &node!.right, withData: data, andKey: key, atIndex: charIndex)
         }
             //current char is equal to the current nodes, go middle
         else {
             //continue down the middle.
             if charIndex + 1 < key.characters.count {
-                return insertNode(&aNode!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
+                return insert(node: &node!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
             }
                 //otherwise, all done.
             else {
-                aNode!.data = data
-                aNode?.hasData = true
+                node!.data = data
+                node?.hasData = true
                 return true
             }
         }
@@ -64,32 +63,31 @@ public class TernarySearchTree<Element> {
 
 
     public func find(key: String) -> Element? {
-        return findNode(root, withKey: key, atIndex: 0)
+        return find(node: root, withKey: key, atIndex: 0)
     }
 
-
-    private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
+    private func find(node: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
 
         //Given key does not exist in tree.
-        if aNode == nil {
+        if node == nil {
             return nil
         }
 
-        let index = key.startIndex.advancedBy(charIndex)
+        let index = key.index(key.startIndex, offsetBy: charIndex)
         //go left
-        if key[index] < aNode!.key {
-            return findNode(aNode!.left, withKey: key, atIndex: charIndex)
+        if key[index] < node!.key {
+            return find(node: node!.left, withKey: key, atIndex: charIndex)
         }
             //go right
-        else if key[index] > aNode!.key {
-            return findNode(aNode!.right, withKey: key, atIndex: charIndex)
+        else if key[index] > node!.key {
+            return find(node: node!.right, withKey: key, atIndex: charIndex)
         }
             //go middle
         else {
             if charIndex + 1 < key.characters.count {
-                return findNode(aNode!.middle, withKey: key, atIndex: charIndex + 1)
+                return find(node: node!.middle, withKey: key, atIndex: charIndex + 1)
             } else {
-                return aNode!.data
+                return node!.data
             }
         }
     }
diff --git a/Ternary Search Tree/TST.playground/Sources/Utils.swift b/Ternary Search Tree/TST.playground/Sources/Utils.swift
new file mode 100644
index 000000000..cabfe1b68
--- /dev/null
+++ b/Ternary Search Tree/TST.playground/Sources/Utils.swift	
@@ -0,0 +1,30 @@
+//
+//  Utils.swift
+//  
+//
+//  Created by Peter Bødskov on 10/01/17.
+//
+//
+
+import Foundation
+
+public struct Utils {
+    
+    public static let shared = Utils()
+    
+    let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
+    //Random string generator from:
+    //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
+    public func randomAlphaNumericString(withLength length: Int) -> String {
+        let allowedCharsCount = UInt32(allowedChars.characters.count)
+        var randomString = ""
+        
+        for _ in (0..<length) {
+            let randomNum = Int(arc4random_uniform(allowedCharsCount))
+            let newCharacter = allowedChars[allowedChars.index(allowedChars.startIndex, offsetBy: randomNum)]
+            randomString += String(newCharacter)
+        }
+        
+        return randomString
+    }
+}
diff --git a/Ternary Search Tree/TST.playground/contents.xcplayground b/Ternary Search Tree/TST.playground/contents.xcplayground
index 06828af92..d210cc097 100644
--- a/Ternary Search Tree/TST.playground/contents.xcplayground	
+++ b/Ternary Search Tree/TST.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='0810'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 2f143bead..c4b51519a 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -33,52 +33,52 @@ public class TernarySearchTree<Element> {
 
     - returns: Value indicating insertion success/failure.
     */
-    public func insert(data: Element, withKey key: String) -> Bool {
-        return insertNode(&root, withData: data, andKey: key, atIndex: 0)
+    @discardableResult public func insert(data: Element, withKey key: String) -> Bool {
+        return insert(node: &root, withData: data, andKey: key, atIndex: 0)
     }
 
     /**
      Helper method for insertion that does the actual legwork. Insertion is performed recursively.
 
-     - parameter aNode:     The current node to insert below.
+     - parameter node:      The current node to insert below.
      - parameter data:      The data being inserted.
      - parameter key:       The key being used to find an insertion location for the given data
      - parameter charIndex: The index of the character in the key string to use to for the next node.
 
      - returns: Value indicating insertion success/failure.
      */
-    private func insertNode(inout aNode: TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
+    private func insert(node: inout TSTNode<Element>?, withData data: Element, andKey key: String, atIndex charIndex: Int) -> Bool {
 
         //sanity check.
-        if key.characters.count == 0 {
+        guard key.characters.count > 0 else {
             return false
         }
 
         //create a new node if necessary.
-        if aNode == nil {
-            let index = key.startIndex.advancedBy(charIndex)
-            aNode = TSTNode<Element>(key: key[index])
+        if node == nil {
+            let index = key.index(key.startIndex, offsetBy: charIndex)
+            node = TSTNode<Element>(key: key[index])
         }
 
         //if current char is less than the current node's char, go left
-        let index = key.startIndex.advancedBy(charIndex)
-        if key[index] < aNode!.key {
-            return insertNode(&aNode!.left, withData: data, andKey: key, atIndex: charIndex)
+        let index = key.index(key.startIndex, offsetBy: charIndex)
+        if key[index] < node!.key {
+            return insert(node: &node!.left, withData: data, andKey: key, atIndex: charIndex)
         }
             //if it's greater, go right.
-        else if key[index] > aNode!.key {
-            return insertNode(&aNode!.right, withData: data, andKey: key, atIndex: charIndex)
+        else if key[index] > node!.key {
+            return insert(node: &node!.right, withData: data, andKey: key, atIndex: charIndex)
         }
             //current char is equal to the current nodes, go middle
         else {
             //continue down the middle.
             if charIndex + 1 < key.characters.count {
-                return insertNode(&aNode!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
+                return insert(node: &node!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
             }
                 //otherwise, all done.
             else {
-                aNode!.data = data
-                aNode?.hasData = true
+                node!.data = data
+                node?.hasData = true
                 return true
             }
         }
@@ -95,40 +95,40 @@ public class TernarySearchTree<Element> {
     - returns: The element, if found. Otherwise, nil.
     */
     public func find(key: String) -> Element? {
-        return findNode(root, withKey: key, atIndex: 0)
+        return find(node: root, withKey: key, atIndex: 0)
     }
 
     /**
      Helper method that performs actual legwork of find operation. Implemented recursively.
 
-     - parameter aNode:     The current node being evaluated.
+     - parameter node:      The current node being evaluated.
      - parameter key:       The key being used for the search.
      - parameter charIndex: The index of the current char in the search key
 
      - returns: The element, if found. Nil otherwise.
      */
-    private func findNode(aNode: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
+    private func find(node: TSTNode<Element>?, withKey key: String, atIndex charIndex: Int) -> Element? {
 
         //Given key does not exist in tree.
-        if aNode == nil {
+        guard let node = node else {
             return nil
         }
 
-        let index = key.startIndex.advancedBy(charIndex)
+        let index = key.index(key.startIndex, offsetBy: charIndex)
         //go left
-        if key[index] < aNode!.key {
-            return findNode(aNode!.left, withKey: key, atIndex: charIndex)
+        if key[index] < node.key {
+            return find(node: node.left, withKey: key, atIndex: charIndex)
         }
             //go right
-        else if key[index] > aNode!.key {
-            return findNode(aNode!.right, withKey: key, atIndex: charIndex)
+        else if key[index] > node.key {
+            return find(node: node.right, withKey: key, atIndex: charIndex)
         }
             //go middle
         else {
             if charIndex + 1 < key.characters.count {
-                return findNode(aNode!.middle, withKey: key, atIndex: charIndex + 1)
+                return find(node: node.middle, withKey: key, atIndex: charIndex + 1)
             } else {
-                return aNode!.data
+                return node.data
             }
         }
     }
diff --git a/Ternary Search Tree/Tests/Info.plist b/Ternary Search Tree/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Ternary Search Tree/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
new file mode 100644
index 000000000..51e7c808c
--- /dev/null
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -0,0 +1,58 @@
+//
+//  Tests.swift
+//  Tests
+//
+//  Created by Peter Bødskov on 10/01/17.
+//  Copyright © 2017 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+
+class TernarySearchTreeTests: XCTestCase {
+    
+    let treeOfStrings = TernarySearchTree<String>()
+    let testCount = 30
+    
+    func testCanFindStringInTree() {
+        var testStrings: [(key: String, data: String)] = []
+        for _ in (1...testCount) {
+            let randomLength = Int(arc4random_uniform(10))
+            let key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            //    print("Key: \(key) Data: \(data)")
+            
+            if key != "" && data != "" {
+                testStrings.append((key, data))
+                treeOfStrings.insert(data: data, withKey: key)
+            }
+        }
+        
+        for aTest in testStrings {
+            let data = treeOfStrings.find(key: aTest.key)
+            
+            XCTAssertNotNil(data)
+            XCTAssertEqual(data, aTest.data)
+        }
+    }
+    
+    func testCanFindNumberInTree() {
+        var testNums: [(key: String, data: Int)] = []
+        let treeOfInts = TernarySearchTree<Int>()
+        for _ in (1...testCount) {
+            let randomNum = Int(arc4random_uniform(UInt32.max))
+            let randomLength = Int(arc4random_uniform(10))
+            let key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            
+            if key != "" {
+                testNums.append((key, randomNum))
+                treeOfInts.insert(data: randomNum, withKey: key)
+            }
+        }
+        
+        for aTest in testNums {
+            let data = treeOfInts.find(key: aTest.key)
+            XCTAssertNotNil(data)
+            XCTAssertEqual(data, aTest.data)
+        }
+    }
+}
diff --git a/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj b/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..7afaca944
--- /dev/null
+++ b/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,264 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		D06C22031E24D02800622925 /* TernarySearchTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = D06C22021E24D02800622925 /* TernarySearchTreeTests.swift */; };
+		D0957B8A1E24D92D00417988 /* TernarySearchTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = D0957B891E24D92D00417988 /* TernarySearchTree.swift */; };
+		D0957B8C1E24D9A300417988 /* Utils.swift in Sources */ = {isa = PBXBuildFile; fileRef = D0957B8B1E24D9A300417988 /* Utils.swift */; };
+		D0957B8E1E24DA0100417988 /* TSTNode.swift in Sources */ = {isa = PBXBuildFile; fileRef = D0957B8D1E24DA0100417988 /* TSTNode.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		D06C22021E24D02800622925 /* TernarySearchTreeTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = TernarySearchTreeTests.swift; sourceTree = "<group>"; };
+		D06C22041E24D02800622925 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		D06C22081E24D16800622925 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		D0957B891E24D92D00417988 /* TernarySearchTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TernarySearchTree.swift; path = ../TernarySearchTree.swift; sourceTree = "<group>"; };
+		D0957B8B1E24D9A300417988 /* Utils.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Utils.swift; path = ../Utils.swift; sourceTree = "<group>"; };
+		D0957B8D1E24DA0100417988 /* TSTNode.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = TSTNode.swift; path = ../TSTNode.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		D06C21FD1E24D02800622925 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
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+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
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+				LastUpgradeCheck = 0810;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
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+			knownRegions = (
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+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
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+			);
+		};
+/* End PBXProject section */
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+/* Begin PBXResourcesBuildPhase section */
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+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
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+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
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+				D0957B8E1E24DA0100417988 /* TSTNode.swift in Sources */,
+				D0957B8A1E24D92D00417988 /* TernarySearchTree.swift in Sources */,
+				D0957B8C1E24D9A300417988 /* Utils.swift in Sources */,
+			);
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+/* End PBXSourcesBuildPhase section */
+
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+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
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+				CLANG_WARN_CONSTANT_CONVERSION = YES;
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+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVES = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
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+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
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+				GCC_PREPROCESSOR_DEFINITIONS = (
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+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
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+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+			};
+			name = Debug;
+		};
+		D06C21C41E24CC9600622925 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
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+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
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+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
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+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
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+			};
+			name = Release;
+		};
+		D06C22061E24D02800622925 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		D06C22071E24D02800622925 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		D06C21BA1E24CC9600622925 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				D06C21C31E24CC9600622925 /* Debug */,
+				D06C21C41E24CC9600622925 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		D06C22051E24D02800622925 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				D06C22061E24D02800622925 /* Debug */,
+				D06C22071E24D02800622925 /* Release */,
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+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = D06C21B71E24CC9600622925 /* Project object */;
+}
diff --git a/Ternary Search Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Ternary Search Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..752b0c7fc
--- /dev/null
+++ b/Ternary Search Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0810"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "D06C21FF1E24D02800622925"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Ternary Search Tree/Utils.swift b/Ternary Search Tree/Utils.swift
new file mode 100644
index 000000000..cabfe1b68
--- /dev/null
+++ b/Ternary Search Tree/Utils.swift	
@@ -0,0 +1,30 @@
+//
+//  Utils.swift
+//  
+//
+//  Created by Peter Bødskov on 10/01/17.
+//
+//
+
+import Foundation
+
+public struct Utils {
+    
+    public static let shared = Utils()
+    
+    let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
+    //Random string generator from:
+    //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
+    public func randomAlphaNumericString(withLength length: Int) -> String {
+        let allowedCharsCount = UInt32(allowedChars.characters.count)
+        var randomString = ""
+        
+        for _ in (0..<length) {
+            let randomNum = Int(arc4random_uniform(allowedCharsCount))
+            let newCharacter = allowedChars[allowedChars.index(allowedChars.startIndex, offsetBy: randomNum)]
+            randomString += String(newCharacter)
+        }
+        
+        return randomString
+    }
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 194c0ae79..b896d1e94 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1859,6 +1859,16 @@
    <Group
       location = "group:Ternary Search Tree"
       name = "Ternary Search Tree">
+      <Group
+         location = "container:Ternary Search Tree/Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From b9b491d98c50a270184204a98e982e1ccc3b07ac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20B=C3=B8dskov?= <me@peterbodskov.dk>
Date: Wed, 11 Jan 2017 16:05:37 +0100
Subject: [PATCH 0769/1679] fixing failing test (#355)

the problem was that the testdata generator could generate keys that was not unique...which caused the `find` method to return the wrong values for keys when the keys were the same.
---
 Ternary Search Tree/TernarySearchTree.swift   |  2 +-
 .../Tests/TernarySearchTreeTests.swift        | 25 ++++++++++++++-----
 2 files changed, 20 insertions(+), 7 deletions(-)

diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index c4b51519a..2e2ca2917 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -75,7 +75,7 @@ public class TernarySearchTree<Element> {
             if charIndex + 1 < key.characters.count {
                 return insert(node: &node!.middle, withData: data, andKey: key, atIndex: charIndex + 1)
             }
-                //otherwise, all done.
+            //otherwise, all done.
             else {
                 node!.data = data
                 node?.hasData = true
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index 51e7c808c..40739c888 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -10,14 +10,23 @@ import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
     
-    let treeOfStrings = TernarySearchTree<String>()
+
     let testCount = 30
     
     func testCanFindStringInTree() {
         var testStrings: [(key: String, data: String)] = []
+        let treeOfStrings = TernarySearchTree<String>()
+
         for _ in (1...testCount) {
-            let randomLength = Int(arc4random_uniform(10))
-            let key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            var randomLength = Int(arc4random_uniform(10))
+            
+            var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            
+            while testStrings.contains(where: { $0.key == key}) {
+                //That key is taken, so we generate a new one with another length
+                randomLength = Int(arc4random_uniform(10))
+                key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            }
             let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
             //    print("Key: \(key) Data: \(data)")
             
@@ -29,7 +38,6 @@ class TernarySearchTreeTests: XCTestCase {
         
         for aTest in testStrings {
             let data = treeOfStrings.find(key: aTest.key)
-            
             XCTAssertNotNil(data)
             XCTAssertEqual(data, aTest.data)
         }
@@ -40,8 +48,13 @@ class TernarySearchTreeTests: XCTestCase {
         let treeOfInts = TernarySearchTree<Int>()
         for _ in (1...testCount) {
             let randomNum = Int(arc4random_uniform(UInt32.max))
-            let randomLength = Int(arc4random_uniform(10))
-            let key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            var randomLength = Int(arc4random_uniform(10))
+            var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            while testNums.contains(where: { $0.key == key}) {
+                //That key is taken, so we generate a new one with another length
+                randomLength = Int(arc4random_uniform(10))
+                key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+            }
             
             if key != "" {
                 testNums.append((key, randomNum))

From bc73299363a92f07b95bd831942985c2daba1d4b Mon Sep 17 00:00:00 2001
From: Keita <keitaitok@gmail.com>
Date: Wed, 11 Jan 2017 16:58:11 -0800
Subject: [PATCH 0770/1679] Update Stack and Queue files to use top and front
 properties (#351)

* Update Stack.swift and StackTests.swift to use top property

- peek() method was replaced with top property. Update Stack.swift and
StackTests.swift to use top property instead of peek() method.
- Fix indentation in Stack/README.markdown.

* Update Queue-Optimized.swift and QueueTests.swift to use front property

- peek() method was replaced with front property. Update
Queue-Optimized.swift and QueueTests.swift to use front property
instead of peek() method.
- Fix front property implementation of Queue-Optimized in
Queue/README.markdown.

* Update Queue-Simple.swift to use front property instead of peek() method
---
 Queue/Queue-Optimized.swift  |  2 +-
 Queue/Queue-Simple.swift     |  2 +-
 Queue/README.markdown        |  6 +++++-
 Queue/Tests/QueueTests.swift | 16 ++++++++--------
 Stack/README.markdown        |  2 +-
 Stack/Stack.swift            |  2 +-
 Stack/Tests/StackTests.swift | 16 ++++++++--------
 7 files changed, 25 insertions(+), 21 deletions(-)

diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index ad6999295..7dff91698 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -37,7 +37,7 @@ public struct Queue<T> {
     return element
   }
 
-  public func peek() -> T? {
+  public var front: T? {
     if isEmpty {
       return nil
     } else {
diff --git a/Queue/Queue-Simple.swift b/Queue/Queue-Simple.swift
index 27fbdee4d..c5e8067c8 100644
--- a/Queue/Queue-Simple.swift
+++ b/Queue/Queue-Simple.swift
@@ -30,7 +30,7 @@ public struct Queue<T> {
     }
   }
 
-  public func peek() -> T? {
+  public var front: T? {
     return array.first
   }
 }
diff --git a/Queue/README.markdown b/Queue/README.markdown
index 25d6205f8..f8259c31c 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -167,7 +167,11 @@ public struct Queue<T> {
   }
   
   public var front: T? {
-    return array.first
+    if isEmpty {
+      return nil
+    } else {
+      return array[head]
+    }
   }
 }
 ```
diff --git a/Queue/Tests/QueueTests.swift b/Queue/Tests/QueueTests.swift
index 7406f8d35..b820ac0d3 100755
--- a/Queue/Tests/QueueTests.swift
+++ b/Queue/Tests/QueueTests.swift
@@ -6,7 +6,7 @@ class QueueTest: XCTestCase {
     var queue = Queue<Int>()
     XCTAssertTrue(queue.isEmpty)
     XCTAssertEqual(queue.count, 0)
-    XCTAssertEqual(queue.peek(), nil)
+    XCTAssertEqual(queue.front, nil)
     XCTAssertNil(queue.dequeue())
   }
 
@@ -16,13 +16,13 @@ class QueueTest: XCTestCase {
     queue.enqueue(123)
     XCTAssertFalse(queue.isEmpty)
     XCTAssertEqual(queue.count, 1)
-    XCTAssertEqual(queue.peek(), 123)
+    XCTAssertEqual(queue.front, 123)
 
     let result = queue.dequeue()
     XCTAssertEqual(result, 123)
     XCTAssertTrue(queue.isEmpty)
     XCTAssertEqual(queue.count, 0)
-    XCTAssertEqual(queue.peek(), nil)
+    XCTAssertEqual(queue.front, nil)
   }
 
   func testTwoElements() {
@@ -32,19 +32,19 @@ class QueueTest: XCTestCase {
     queue.enqueue(456)
     XCTAssertFalse(queue.isEmpty)
     XCTAssertEqual(queue.count, 2)
-    XCTAssertEqual(queue.peek(), 123)
+    XCTAssertEqual(queue.front, 123)
 
     let result1 = queue.dequeue()
     XCTAssertEqual(result1, 123)
     XCTAssertFalse(queue.isEmpty)
     XCTAssertEqual(queue.count, 1)
-    XCTAssertEqual(queue.peek(), 456)
+    XCTAssertEqual(queue.front, 456)
 
     let result2 = queue.dequeue()
     XCTAssertEqual(result2, 456)
     XCTAssertTrue(queue.isEmpty)
     XCTAssertEqual(queue.count, 0)
-    XCTAssertEqual(queue.peek(), nil)
+    XCTAssertEqual(queue.front, nil)
   }
 
   func testMakeEmpty() {
@@ -58,12 +58,12 @@ class QueueTest: XCTestCase {
 
     queue.enqueue(789)
     XCTAssertEqual(queue.count, 1)
-    XCTAssertEqual(queue.peek(), 789)
+    XCTAssertEqual(queue.front, 789)
 
     let result = queue.dequeue()
     XCTAssertEqual(result, 789)
     XCTAssertTrue(queue.isEmpty)
     XCTAssertEqual(queue.count, 0)
-    XCTAssertEqual(queue.peek(), nil)
+    XCTAssertEqual(queue.front, nil)
   }
 }
diff --git a/Stack/README.markdown b/Stack/README.markdown
index a79e2c261..1a3ca2638 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -61,7 +61,7 @@ public struct Stack<T> {
   }
 
   public var top: T? {
-  	return array.last
+    return array.last
   }
 }
 ```
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 49edaf4cb..974d5a443 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -22,7 +22,7 @@ public struct Stack<T> {
     return array.popLast()
   }
 
-  public func peek() -> T? {
+  public var top: T? {
     return array.last
   }
 }
diff --git a/Stack/Tests/StackTests.swift b/Stack/Tests/StackTests.swift
index 62e26b0fa..f4df09a67 100755
--- a/Stack/Tests/StackTests.swift
+++ b/Stack/Tests/StackTests.swift
@@ -6,7 +6,7 @@ class StackTest: XCTestCase {
     var stack = Stack<Int>()
     XCTAssertTrue(stack.isEmpty)
     XCTAssertEqual(stack.count, 0)
-    XCTAssertEqual(stack.peek(), nil)
+    XCTAssertEqual(stack.top, nil)
     XCTAssertNil(stack.pop())
   }
 
@@ -16,13 +16,13 @@ class StackTest: XCTestCase {
     stack.push(123)
     XCTAssertFalse(stack.isEmpty)
     XCTAssertEqual(stack.count, 1)
-    XCTAssertEqual(stack.peek(), 123)
+    XCTAssertEqual(stack.top, 123)
 
     let result = stack.pop()
     XCTAssertEqual(result, 123)
     XCTAssertTrue(stack.isEmpty)
     XCTAssertEqual(stack.count, 0)
-    XCTAssertEqual(stack.peek(), nil)
+    XCTAssertEqual(stack.top, nil)
     XCTAssertNil(stack.pop())
   }
 
@@ -33,19 +33,19 @@ class StackTest: XCTestCase {
     stack.push(456)
     XCTAssertFalse(stack.isEmpty)
     XCTAssertEqual(stack.count, 2)
-    XCTAssertEqual(stack.peek(), 456)
+    XCTAssertEqual(stack.top, 456)
 
     let result1 = stack.pop()
     XCTAssertEqual(result1, 456)
     XCTAssertFalse(stack.isEmpty)
     XCTAssertEqual(stack.count, 1)
-    XCTAssertEqual(stack.peek(), 123)
+    XCTAssertEqual(stack.top, 123)
 
     let result2 = stack.pop()
     XCTAssertEqual(result2, 123)
     XCTAssertTrue(stack.isEmpty)
     XCTAssertEqual(stack.count, 0)
-    XCTAssertEqual(stack.peek(), nil)
+    XCTAssertEqual(stack.top, nil)
     XCTAssertNil(stack.pop())
   }
 
@@ -60,13 +60,13 @@ class StackTest: XCTestCase {
 
     stack.push(789)
     XCTAssertEqual(stack.count, 1)
-    XCTAssertEqual(stack.peek(), 789)
+    XCTAssertEqual(stack.top, 789)
 
     let result = stack.pop()
     XCTAssertEqual(result, 789)
     XCTAssertTrue(stack.isEmpty)
     XCTAssertEqual(stack.count, 0)
-    XCTAssertEqual(stack.peek(), nil)
+    XCTAssertEqual(stack.top, nil)
     XCTAssertNil(stack.pop())
   }
 }

From d3b2496c3b5a3eca4f80fdc8d33159ccd2fa6c2a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Jan 2017 01:43:41 -0800
Subject: [PATCH 0771/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 9e0ae00fa..e5c8f8dae 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-All code is compatible with **Xcode 7.3** and **Swift 2.2**. We'll keep this updated with the latest version of Swift.
+Most code is compatible with **Xcode 8.2** and **Swift 3**. We'll keep this updated with the latest version of Swift.
 
 This is a work in progress. More algorithms will be added soon. :-)
 

From d44abb819f182abc44f86026d211ed1a132ccc88 Mon Sep 17 00:00:00 2001
From: Tai Heng <theng@tucali.ca>
Date: Tue, 10 Jan 2017 21:47:58 -0500
Subject: [PATCH 0772/1679] Updated radixSort argument to swift3 syntax.

---
 Radix Sort/radixSort.swift | 27 +++++++++++++--------------
 1 file changed, 13 insertions(+), 14 deletions(-)

diff --git a/Radix Sort/radixSort.swift b/Radix Sort/radixSort.swift
index 31a783db7..24d4155d7 100644
--- a/Radix Sort/radixSort.swift	
+++ b/Radix Sort/radixSort.swift	
@@ -5,43 +5,42 @@
 */
 
 
-func radixSort(inout arr: [Int] ) {
-
-
+// NOTE: This implementation does not handle negative numbers
+func radixSort(_ array: inout [Int] ) {
   let radix = 10  //Here we define our radix to be 10
   var done = false
   var index: Int
   var digit = 1  //Which digit are we on?
-
-
+  
+  
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
-
+    
     var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
-
+    
     for _ in 1...radix {
       buckets.append([])
     }
-
-
-    for number in arr {
+    
+    
+    for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
       if done && index > 0 {  //If we arent done, continue to finish, otherwise we are done
         done = false
       }
     }
-
+    
     var i = 0
-
+    
     for j in 0..<radix {
       let bucket = buckets[j]
       for number in bucket {
-        arr[i] = number
+        array[i] = number
         i += 1
       }
     }
-
+    
     digit *= radix  //Move to the next digit
   }
 }

From f355bade40d2bc084191f00805e44c2cf343d142 Mon Sep 17 00:00:00 2001
From: Tai Heng <theng@tucali.ca>
Date: Tue, 10 Jan 2017 21:48:55 -0500
Subject: [PATCH 0773/1679] Added playground demonstrating radixSort.

---
 .../RadixSort.playground/Contents.swift       | 16 +++++++
 .../Sources/radixSort.swift                   | 46 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 3 files changed, 66 insertions(+)
 create mode 100644 Radix Sort/RadixSort.playground/Contents.swift
 create mode 100644 Radix Sort/RadixSort.playground/Sources/radixSort.swift
 create mode 100644 Radix Sort/RadixSort.playground/contents.xcplayground

diff --git a/Radix Sort/RadixSort.playground/Contents.swift b/Radix Sort/RadixSort.playground/Contents.swift
new file mode 100644
index 000000000..a4f7e3527
--- /dev/null
+++ b/Radix Sort/RadixSort.playground/Contents.swift	
@@ -0,0 +1,16 @@
+//: Playground - noun: a place where people can play
+
+import Cocoa
+
+// Test Radix Sort with small array of ten values
+var array: [Int] = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
+radixSort(&array)
+
+// Test Radix Sort with large array of 1000 random values
+var bigArray = [Int](repeating: 0, count: 1000)
+var i = 0
+while i < 1000 {
+  bigArray[i] = Int(arc4random_uniform(1000) + 1)
+  i += 1
+}
+radixSort(&bigArray)
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
new file mode 100644
index 000000000..136ede4fd
--- /dev/null
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -0,0 +1,46 @@
+/*
+ 
+ Sorting Algorithm that sorts an input array of integers digit by digit.
+ 
+ */
+import Foundation
+
+// NOTE: This implementation does not handle negative numbers
+public func radixSort(_ array: inout [Int] ) {
+  let radix = 10  //Here we define our radix to be 10
+  var done = false
+  var index: Int
+  var digit = 1  //Which digit are we on?
+  
+  
+  while !done {  //While our  sorting is not completed
+    done = true  //Assume it is done for now
+    
+    var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
+    
+    for _ in 1...radix {
+      buckets.append([])
+    }
+    
+    
+    for number in array {
+      index = number / digit  //Which bucket will we access?
+      buckets[index % radix].append(number)
+      if done && index > 0 {  //If we arent done, continue to finish, otherwise we are done
+        done = false
+      }
+    }
+    
+    var i = 0
+    
+    for j in 0..<radix {
+      let bucket = buckets[j]
+      for number in bucket {
+        array[i] = number
+        i += 1
+      }
+    }
+    
+    digit *= radix  //Move to the next digit
+  }
+}
diff --git a/Radix Sort/RadixSort.playground/contents.xcplayground b/Radix Sort/RadixSort.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Radix Sort/RadixSort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From 021772eee7c6b8da4598fa7d0ecffb817388aa94 Mon Sep 17 00:00:00 2001
From: Tai Heng <theng@tucali.ca>
Date: Tue, 10 Jan 2017 21:49:55 -0500
Subject: [PATCH 0774/1679] Added tests for RadixSort.

---
 .travis.yml                                   |   1 +
 .../contents.xcworkspacedata                  |   7 +
 Radix Sort/Tests/Info.plist                   |  22 ++
 Radix Sort/Tests/RadixSortTests.swift         |  18 ++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 277 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     | 101 +++++++
 7 files changed, 433 insertions(+)
 create mode 100644 Radix Sort/RadixSort.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Radix Sort/Tests/Info.plist
 create mode 100644 Radix Sort/Tests/RadixSortTests.swift
 create mode 100644 Radix Sort/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Radix Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Radix Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/.travis.yml b/.travis.yml
index 9d8c6e346..64c23eb56 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -33,6 +33,7 @@ script:
 # - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Radix Sort/RadixSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Radix Sort/RadixSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Radix Sort/RadixSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Radix Sort/Tests/Info.plist b/Radix Sort/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Radix Sort/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Radix Sort/Tests/RadixSortTests.swift b/Radix Sort/Tests/RadixSortTests.swift
new file mode 100644
index 000000000..688bcdcb8
--- /dev/null
+++ b/Radix Sort/Tests/RadixSortTests.swift	
@@ -0,0 +1,18 @@
+//
+//  RadixSortTests.swift
+//  Tests
+//
+//  Created by theng on 2017-01-10.
+//  Copyright © 2017 Swift Algorithm Club. All rights reserved.
+//
+
+import XCTest
+
+class RadixSortTests: XCTestCase {
+  func testCombSort() {
+    let expectedSequence: [Int] = [2, 9, 19, 32, 55, 67, 89, 101, 912, 4242]
+    var sequence = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
+    radixSort(&sequence)
+    XCTAssertEqual(sequence, expectedSequence)
+  }
+}
diff --git a/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj b/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..4b32f71b5
--- /dev/null
+++ b/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,277 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		056E92AB1E25D0C700B30F52 /* RadixSortTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 056E92AA1E25D0C700B30F52 /* RadixSortTests.swift */; };
+		056E92AF1E25D3D700B30F52 /* radixSort.swift in Sources */ = {isa = PBXBuildFile; fileRef = 056E92AE1E25D3D700B30F52 /* radixSort.swift */; };
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+		056E92AE1E25D3D700B30F52 /* radixSort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = radixSort.swift; path = ../radixSort.swift; sourceTree = "<group>"; };
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+
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+		056E929F1E25D04D00B30F52 /* Frameworks */ = {
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+			);
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+/* End PBXFrameworksBuildPhase section */
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+			sourceTree = "<group>";
+		};
+		056E92A31E25D04D00B30F52 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
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+				056E92AA1E25D0C700B30F52 /* RadixSortTests.swift */,
+			);
+			name = Tests;
+			sourceTree = SOURCE_ROOT;
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+
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+		056E92A11E25D04D00B30F52 /* Tests */ = {
+			isa = PBXNativeTarget;
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+			buildPhases = (
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+			);
+			buildRules = (
+			);
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+			);
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+/* End PBXNativeTarget section */
+
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+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0820;
+				LastUpgradeCheck = 0820;
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+			);
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+/* End PBXProject section */
+
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+			files = (
+			);
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+/* End PBXResourcesBuildPhase section */
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+/* End PBXSourcesBuildPhase section */
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+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
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+				SDKROOT = macosx;
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+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
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+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
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+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
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+				MTL_ENABLE_DEBUG_INFO = NO;
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+			};
+			name = Release;
+		};
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+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		056E92A91E25D04D00B30F52 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		056E92891E25D03300B30F52 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				056E92991E25D03300B30F52 /* Debug */,
+				056E929A1E25D03300B30F52 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		056E92A71E25D04D00B30F52 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				056E92A81E25D04D00B30F52 /* Debug */,
+				056E92A91E25D04D00B30F52 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 056E92861E25D03300B30F52 /* Project object */;
+}
diff --git a/Radix Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Radix Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Radix Sort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Radix Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Radix Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..b3f6d696a
--- /dev/null
+++ b/Radix Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,101 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0820"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 548f11791666bb2df3cae77183efda861171a0d0 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Thu, 12 Jan 2017 20:17:41 -0800
Subject: [PATCH 0775/1679] Code restructuring

- Moved source files Matrix.swift, MatrixSize.swift & Number.swift to the Sources foler in the PLayground
- Restrucutred the code into extensions to make it more organized and readable
- Deleted all the objects from the playground and moved them to the Sources folder
---
 .../MatrixSize.swift                          |  26 --
 .../Contents.swift                            | 297 +-----------------
 .../Sources}/Matrix.swift                     | 183 +++++------
 .../Sources/MatrixSize.swift                  |  33 ++
 .../Sources}/Number.swift                     |  15 +-
 5 files changed, 136 insertions(+), 418 deletions(-)
 delete mode 100644 Strassen Matrix Multiplication/MatrixSize.swift
 rename Strassen Matrix Multiplication/{ => StrassensMatrixMultiplication.playground/Sources}/Matrix.swift (72%)
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
 rename Strassen Matrix Multiplication/{ => StrassensMatrixMultiplication.playground/Sources}/Number.swift (71%)

diff --git a/Strassen Matrix Multiplication/MatrixSize.swift b/Strassen Matrix Multiplication/MatrixSize.swift
deleted file mode 100644
index f1eada931..000000000
--- a/Strassen Matrix Multiplication/MatrixSize.swift	
+++ /dev/null
@@ -1,26 +0,0 @@
-//
-//  MatrixSize.swift
-//  
-//
-//  Created by Richard Ash on 10/28/16.
-//
-//
-
-import Foundation
-
-struct MatrixSize: Equatable {
-  let rows: Int
-  let columns: Int
-  
-  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
-    for row in 0..<rows {
-      for column in 0..<columns {
-        try? body(row, column)
-      }
-    }
-  }
-}
-
-func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
-  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
-}
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index d4b4d8330..50af60a6f 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,302 +1,7 @@
 //: Playground - noun: a place where people can play
 // Reference - http://mathworld.wolfram.com/StrassenFormulas.html
 
-
-import UIKit
-
-enum RowOrColumn {
-  case row, column
-}
-
-protocol Number: Multipliable, Addable {
-  static var zero: Self { get }
-}
-
-protocol Addable {
-  static func +(lhs: Self, rhs: Self) -> Self
-  static func -(lhs: Self, rhs: Self) -> Self
-}
-
-protocol Multipliable {
-  static func *(lhs: Self, rhs: Self) -> Self
-}
-
-extension Int: Number {
-  static var zero: Int {
-    return 0
-  }
-}
-
-extension Double: Number {
-  static var zero: Double {
-    return 0.0
-  }
-}
-
-extension Float: Number {
-  static var zero: Float {
-    return 0.0
-  }
-}
-
-
-extension Array where Element: Number {
-  func dot(_ b: Array<Element>) -> Element {
-    let a = self
-    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
-    let c = a.indices.map{ a[$0] * b[$0] }
-    return c.reduce(Element.zero, { $0 + $1 })
-  }
-}
-
-struct MatrixSize: Equatable {
-  let rows: Int
-  let columns: Int
-  
-  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
-    for row in 0..<rows {
-      for column in 0..<columns {
-        try? body(row, column)
-      }
-    }
-  }
-}
-
-func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
-  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
-}
-
-
-struct Matrix<T: Number> {
-  
-  // MARK: - Variables
-  
-  let rows: Int, columns: Int
-  var grid: [T]
-  
-  var isSquare: Bool {
-    return rows == columns
-  }
-  
-  var size: MatrixSize {
-    return MatrixSize(rows: rows, columns: columns)
-  }
-  
-  // MARK: - Init
-  
-  init(rows: Int, columns: Int, initialValue: T = T.zero) {
-    self.rows = rows
-    self.columns = columns
-    self.grid = Array(repeating: initialValue, count: rows * columns)
-  }
-  
-  init(size: Int, initialValue: T = T.zero) {
-    self.rows = size
-    self.columns = size
-    self.grid = Array(repeating: initialValue, count: rows * columns)
-  }
-  
-  // MARK: - Subscript
-  
-  subscript(row: Int, column: Int) -> T {
-    get {
-      assert(indexIsValid(row: row, column: column), "Index out of range")
-      return grid[(row * columns) + column]
-    }
-    set {
-      assert(indexIsValid(row: row, column: column), "Index out of range")
-      grid[(row * columns) + column] = newValue
-    }
-  }
-  
-  subscript(type: RowOrColumn, value: Int) -> [T] {
-    get {
-      switch type {
-      case .row:
-        assert(indexIsValid(row: value, column: 0), "Index out of range")
-        return Array(grid[(value * columns)..<(value * columns) + columns])
-      case .column:
-        assert(indexIsValid(row: 0, column: value), "Index out of range")
-        var columns: [T] = []
-        for row in 0..<rows {
-          for column in 0..<self.columns {
-            if column == value {
-              columns.append(grid[(row * self.columns) + value])
-            }
-          }
-        }
-        return columns
-      }
-    } set {
-      switch type {
-      case .row:
-        assert(newValue.count == columns)
-        for (column, element) in newValue.enumerated() {
-          grid[(value * columns) + column] = element
-        }
-      case .column:
-        assert(newValue.count == rows)
-        for (row, element) in newValue.enumerated() {
-          grid[(row * columns) + value] = element
-        }
-      }
-    }
-  }
-  
-  // MARK: - Private Functions
-  
-  private func indexIsValid(row: Int, column: Int) -> Bool {
-    return row >= 0 && row < rows && column >= 0 && column < columns
-  }
-  
-  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
-    guard A.rows > 1 && B.rows > 1 else { return A * B }
-    
-    let n    = A.rows
-    let nBy2 = n / 2
-    
-    var a11 = Matrix(size: nBy2)
-    var a12 = Matrix(size: nBy2)
-    var a21 = Matrix(size: nBy2)
-    var a22 = Matrix(size: nBy2)
-    var b11 = Matrix(size: nBy2)
-    var b12 = Matrix(size: nBy2)
-    var b21 = Matrix(size: nBy2)
-    var b22 = Matrix(size: nBy2)
-    
-    for i in 0..<nBy2 {
-      for j in 0..<nBy2 {
-        a11[i,j] = A[i,j]
-        a12[i,j] = A[i, j+nBy2]
-        a21[i,j] = A[i+nBy2, j]
-        a22[i,j] = A[i+nBy2, j+nBy2]
-        b11[i,j] = B[i,j]
-        b12[i,j] = B[i, j+nBy2]
-        b21[i,j] = B[i+nBy2, j]
-        b22[i,j] = B[i+nBy2, j+nBy2]
-      }
-    }
-    
-    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
-    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
-    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
-    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
-    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
-    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
-    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
-    
-    let c11 = q1 + q4 - q5 + q7
-    let c12 = q3 + q5
-    let c21 = q2 + q4
-    let c22 = q1 + q3 - q2 + q6
-    var C   = Matrix(size: n)
-    
-    for i in 0..<nBy2 {
-      for j in 0..<nBy2 {
-        C[i, j]           = c11[i,j]
-        C[i, j+nBy2]      = c12[i,j]
-        C[i+nBy2, j]      = c21[i,j]
-        C[i+nBy2, j+nBy2] = c22[i,j]
-      }
-    }
-    
-    return C
-  }
-  
-  private func nextPowerOfTwo(of n: Int) -> Int {
-    return Int(pow(2, ceil(log2(Double(n)))))
-  }
-  
-  // MARK: - Functions
-  
-  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    let n = max(A.rows, A.columns, B.rows, B.columns)
-    let m = nextPowerOfTwo(of: n)
-    
-    var APrep = Matrix(size: m)
-    var BPrep = Matrix(size: m)
-    
-    A.size.forEach { (i, j) in
-      APrep[i,j] = A[i,j]
-    }
-    
-    B.size.forEach { (i, j) in
-      BPrep[i,j] = B[i,j]
-    }
-    
-    let CPrep = APrep.strassenR(by: BPrep)
-    var C = Matrix(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i,j] = CPrep[i,j]
-      }
-    }
-    return C
-  }
-  
-  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i, j] = A[.row, i].dot(B[.column, j])
-      }
-    }
-    
-    return C
-  }
-}
-
-func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
-    }
-  }
-  return newMatrix
-}
-
-func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
-    }
-  }
-  return newMatrix
-}
-
-func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
-    }
-  }
-  return newMatrix
-}
+import Foundation
 
 var A = Matrix(rows: 2, columns: 4, initialValue: 0)
 A[.row, 0] = [2, 3, -1, 0]
diff --git a/Strassen Matrix Multiplication/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
similarity index 72%
rename from Strassen Matrix Multiplication/Matrix.swift
rename to Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index 657cf3c80..eba49ce9a 100644
--- a/Strassen Matrix Multiplication/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -8,11 +8,11 @@
 
 import Foundation
 
-enum RowOrColumn {
+public enum RowOrColumn {
   case row, column
 }
 
-struct Matrix<T: Number> {
+public struct Matrix<T: Number> {
   
   // MARK: - Variables
   
@@ -29,20 +29,22 @@ struct Matrix<T: Number> {
   
   // MARK: - Init
   
-  init(rows: Int, columns: Int, initialValue: T = T.zero) {
+  public init(rows: Int, columns: Int, initialValue: T = T.zero) {
     self.rows = rows
     self.columns = columns
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
   
-  init(size: Int, initialValue: T = T.zero) {
+  public init(size: Int, initialValue: T = T.zero) {
     self.rows = size
     self.columns = size
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
-  
-  // MARK: - Subscript
-  
+}
+
+// MARK: - Public Functions
+
+public extension Matrix {
   subscript(row: Int, column: Int) -> T {
     get {
       assert(indexIsValid(row: row, column: column), "Index out of range")
@@ -88,13 +90,59 @@ struct Matrix<T: Number> {
     }
   }
   
-  // MARK: - Private Functions
+  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(of: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.size.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.size.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    return C
+  }
   
-  private func indexIsValid(row: Int, column: Int) -> Bool {
+  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+// MARK: - Private Functions
+
+fileprivate extension Matrix {
+  func indexIsValid(row: Int, column: Int) -> Bool {
     return row >= 0 && row < rows && column >= 0 && column < columns
   }
   
-  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+  func strassenR(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.isSquare && B.isSquare, "This function requires square matricies!")
     guard A.rows > 1 && B.rows > 1 else { return A * B }
@@ -150,97 +198,56 @@ struct Matrix<T: Number> {
     return C
   }
   
-  private func nextPowerOfTwo(of n: Int) -> Int {
+  func nextPowerOfTwo(of n: Int) -> Int {
     return Int(pow(2, ceil(log2(Double(n)))))
   }
-  
-  // MARK: - Functions
-  
-  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    let n = max(A.rows, A.columns, B.rows, B.columns)
-    let m = nextPowerOfTwo(of: n)
-    
-    var APrep = Matrix(size: m)
-    var BPrep = Matrix(size: m)
-    
-    A.size.forEach { (i, j) in
-      APrep[i,j] = A[i,j]
-    }
-    
-    B.size.forEach { (i, j) in
-      BPrep[i,j] = B[i,j]
-    }
-    
-    let CPrep = APrep.strassenR(by: BPrep)
-    var C = Matrix(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i,j] = CPrep[i,j]
-      }
-    }
-    return C
-  }
-  
-  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i, j] = A[.row, i].dot(B[.column, j])
-      }
-    }
-    
-    return C
-  }
 }
 
+
 // Term-by-term Matrix Math
 
-func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+extension Matrix: Addable {
+  public static func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+    assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
+    let rows = lhs.rows
+    let columns = lhs.columns
+    
+    var newMatrix = Matrix<T>(rows: rows, columns: columns)
+    for row in 0..<rows {
+      for column in 0..<columns {
+        newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+      }
     }
+    return newMatrix
   }
-  return newMatrix
-}
-
-func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
   
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+  public static func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+    assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
+    let rows = lhs.rows
+    let columns = lhs.columns
+    
+    var newMatrix = Matrix<T>(rows: rows, columns: columns)
+    for row in 0..<rows {
+      for column in 0..<columns {
+        newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+      }
     }
+    return newMatrix
   }
-  return newMatrix
 }
 
-func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+extension Matrix: Multipliable {
+  public static func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+    assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
+    let rows = lhs.rows
+    let columns = lhs.columns
+    
+    var newMatrix = Matrix<T>(rows: rows, columns: columns)
+    for row in 0..<rows {
+      for column in 0..<columns {
+        newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+      }
     }
+    return newMatrix
   }
-  return newMatrix
 }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
new file mode 100644
index 000000000..f4a604ade
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
@@ -0,0 +1,33 @@
+//
+//  MatrixSize.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation
+
+public struct MatrixSize: Equatable {
+  let rows: Int
+  let columns: Int
+  
+  public init(rows: Int, columns: Int) {
+    self.rows = rows
+    self.columns = columns
+  }
+  
+  public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try? body(row, column)
+      }
+    }
+  }
+}
+
+public extension MatrixSize {
+  static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+    return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+  }
+}
diff --git a/Strassen Matrix Multiplication/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
similarity index 71%
rename from Strassen Matrix Multiplication/Number.swift
rename to Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 34c6d5308..9f4c7f4ab 100644
--- a/Strassen Matrix Multiplication/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -8,40 +8,39 @@
 
 import Foundation
 
-protocol Number: Multipliable, Addable {
+public protocol Number: Multipliable, Addable {
   static var zero: Self { get }
 }
 
-protocol Addable {
+public protocol Addable {
   static func +(lhs: Self, rhs: Self) -> Self
   static func -(lhs: Self, rhs: Self) -> Self
 }
 
-protocol Multipliable {
+public protocol Multipliable {
   static func *(lhs: Self, rhs: Self) -> Self
 }
 
 extension Int: Number {
-  static var zero: Int {
+  public static var zero: Int {
     return 0
   }
 }
 
 extension Double: Number {
-  static var zero: Double {
+  public static var zero: Double {
     return 0.0
   }
 }
 
 extension Float: Number {
-  static var zero: Float {
+  public static var zero: Float {
     return 0.0
   }
 }
 
-
 extension Array where Element: Number {
-  func dot(_ b: Array<Element>) -> Element {
+  public func dot(_ b: Array<Element>) -> Element {
     let a = self
     assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
     let c = a.indices.map{ a[$0] * b[$0] }

From c260a3438c5e7103654d3b576b528065089c6972 Mon Sep 17 00:00:00 2001
From: pbodsk <me@peterbodskov.dk>
Date: Fri, 13 Jan 2017 13:31:37 +0100
Subject: [PATCH 0776/1679] migrates Single-Source Shortest Paths to Swift 3
 syntax

---
 .travis.yml                                   |  2 +-
 .../SSSP.playground/Contents.swift            |  2 +-
 .../SSSP.xcodeproj/project.pbxproj            | 13 +++++++++++-
 .../xcshareddata/xcschemes/SSSP.xcscheme      |  2 +-
 .../xcshareddata/xcschemes/SSSPTests.xcscheme |  2 +-
 .../SSSP/BellmanFord.swift                    | 20 +++++++++----------
 .../SSSP/SSSP.swift                           |  2 +-
 .../SSSPTests/SSSPTests.swift                 | 20 +++++++++----------
 8 files changed, 37 insertions(+), 26 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 9d8c6e346..765f07786 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -39,7 +39,7 @@ script:
 - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
+- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift
index ece36a663..652b558b1 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
@@ -25,4 +25,4 @@ graph.addDirectedEdge(z, to: x, withWeight: 7)
 
 let result = BellmanFord<String>.apply(graph, source: s)!
 
-let path = result.path(z, inGraph: graph)
+let path = result.path(to: z, inGraph: graph)
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj
index 55893acfd..0dd67f69c 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
@@ -184,14 +184,16 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0730;
+				LastUpgradeCheck = 0810;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					49BFA2921CDF86E100522D66 = {
 						CreatedOnToolsVersion = 7.3;
+						LastSwiftMigration = 0810;
 					};
 					49BFA29C1CDF86E100522D66 = {
 						CreatedOnToolsVersion = 7.3;
+						LastSwiftMigration = 0810;
 					};
 				};
 			};
@@ -301,8 +303,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -349,8 +353,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -370,6 +376,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -392,6 +399,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -411,6 +419,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
@@ -422,6 +431,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -433,6 +443,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme
index 9d28c18c4..469159bd8 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0810"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme
index 6efceaf20..043f296a5 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0810"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift
index e2114c963..5b6670806 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
@@ -8,7 +8,7 @@
 import Foundation
 import Graph
 
-public struct BellmanFord<T where T: Hashable> {
+public struct BellmanFord<T> where T: Hashable {
   public typealias Q = T
 }
 
@@ -30,12 +30,12 @@ extension BellmanFord: SSSPAlgorithm {
    - returns a `BellmanFordResult` struct which can be queried for
    shortest paths and their total weights, or `nil` if a negative weight cycle exists
  */
-  public static func apply(graph: AbstractGraph<T>, source: Vertex<Q>) -> BellmanFordResult<T>? {
+  public static func apply(_ graph: AbstractGraph<T>, source: Vertex<Q>) -> BellmanFordResult<T>? {
     let vertices = graph.vertices
     let edges = graph.edges
 
-    var predecessors = Array<Int?>(count: vertices.count, repeatedValue: nil)
-    var weights = Array(count: vertices.count, repeatedValue: Double.infinity)
+    var predecessors = Array<Int?>(repeating: nil, count: vertices.count)
+    var weights = Array(repeating: Double.infinity, count: vertices.count)
     predecessors[source.index] = source.index
     weights[source.index] = 0
 
@@ -78,10 +78,10 @@ extension BellmanFord: SSSPAlgorithm {
  It conforms to the `SSSPResult` procotol which provides methods to
  retrieve distances and paths between given pairs of start and end nodes.
  */
-public struct BellmanFordResult<T where T: Hashable> {
+public struct BellmanFordResult<T> where T: Hashable {
 
-  private var predecessors: [Int?]
-  private var weights: [Double]
+  fileprivate var predecessors: [Int?]
+  fileprivate var weights: [Double]
 
 }
 
@@ -112,7 +112,7 @@ extension BellmanFordResult: SSSPResult {
       return nil
     }
 
-    guard let path = recursePath(to, inGraph: graph, path: [to]) else {
+    guard let path = recursePath(to: to, inGraph: graph, path: [to]) else {
       return nil
     }
 
@@ -126,7 +126,7 @@ extension BellmanFordResult: SSSPResult {
 
    - returns: the list of predecessors discovered so far, or `nil` if the next vertex has no predecessor
    */
-  private func recursePath(to: Vertex<T>, inGraph graph: AbstractGraph<T>, path: [Vertex<T>]) -> [Vertex<T>]? {
+  fileprivate func recursePath(to: Vertex<T>, inGraph graph: AbstractGraph<T>, path: [Vertex<T>]) -> [Vertex<T>]? {
     guard let predecessorIdx = predecessors[to.index] else {
       return nil
     }
@@ -136,7 +136,7 @@ extension BellmanFordResult: SSSPResult {
       return [ to ]
     }
 
-    guard let buildPath = recursePath(predecessor, inGraph: graph, path: path) else {
+    guard let buildPath = recursePath(to: predecessor, inGraph: graph, path: path) else {
       return nil
     }
 
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift
index 8e3afc40a..3066f6516 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift	
@@ -18,7 +18,7 @@ protocol SSSPAlgorithm {
   associatedtype Q: Equatable, Hashable
   associatedtype P: SSSPResult
 
-  static func apply(graph: AbstractGraph<Q>, source: Vertex<Q>) -> P?
+  static func apply(_ graph: AbstractGraph<Q>, source: Vertex<Q>) -> P?
 
 }
 
diff --git a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift
index 1bb862b74..04584dfeb 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
@@ -40,11 +40,11 @@ class SSSPTests: XCTestCase {
     let result = BellmanFord<String>.apply(graph, source: s)!
 
     let expectedPath = ["s", "y", "x", "t", "z"]
-    let computedPath = result.path(z, inGraph: graph)!
+    let computedPath = result.path(to: z, inGraph: graph)!
     XCTAssertEqual(expectedPath, computedPath, "expected path of \(expectedPath) but got \(computedPath)")
 
     let expectedWeight = -2.0
-    let computedWeight = result.distance(z)
+    let computedWeight = result.distance(to: z)
     XCTAssertEqual(expectedWeight, computedWeight, "expected weight of \(expectedWeight) but got \(computedWeight)")
   }
 
@@ -71,11 +71,11 @@ class SSSPTests: XCTestCase {
     let result = BellmanFord<String>.apply(graph, source: a)!
 
     let expectedPath = ["a", "b", "c", "e", "d"]
-    let computedPath = result.path(d, inGraph: graph)!
+    let computedPath = result.path(to: d, inGraph: graph)!
     XCTAssertEqual(expectedPath, computedPath, "expected path of \(expectedPath) but got \(computedPath)")
 
     let expectedWeight = 7.0
-    let computedWeight = result.distance(d)
+    let computedWeight = result.distance(to: d)
     XCTAssertEqual(expectedWeight, computedWeight, "expected weight of \(expectedWeight) but got \(computedWeight)")
   }
 
@@ -104,12 +104,12 @@ class SSSPTests: XCTestCase {
 
     let result = BellmanFord<String>.apply(graph, source: a)!
 
-    XCTAssertNil(result.path(b, inGraph: graph), "a path should not be defined from a ~> b")
-    XCTAssertNil(result.distance(b), "a path should not be defined from a ~> b")
-    XCTAssertNotNil(result.path(s, inGraph: graph), "a path should be defined from a ~> s")
-    XCTAssertNotNil(result.distance(s), "a path should be defined from a ~> s")
-    XCTAssertNotNil(result.path(t, inGraph: graph), "a path should be defined from a ~> t")
-    XCTAssertNotNil(result.distance(t), "a path should be defined from a ~> t")
+    XCTAssertNil(result.path(to: b, inGraph: graph), "a path should not be defined from a ~> b")
+    XCTAssertNil(result.distance(to: b), "a path should not be defined from a ~> b")
+    XCTAssertNotNil(result.path(to: s, inGraph: graph), "a path should be defined from a ~> s")
+    XCTAssertNotNil(result.distance(to: s), "a path should be defined from a ~> s")
+    XCTAssertNotNil(result.path(to: t, inGraph: graph), "a path should be defined from a ~> t")
+    XCTAssertNotNil(result.distance(to: t), "a path should be defined from a ~> t")
   }
 
   func testNegativeWeightCycle() {

From 2e5a4a60471ba9d215bfe52975bd563524908637 Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Sat, 14 Jan 2017 12:50:59 +0000
Subject: [PATCH 0777/1679] Update README.md

---
 DiningPhilosophers/README.md | 26 ++++++++++++++++++++++++--
 1 file changed, 24 insertions(+), 2 deletions(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 06302cf2a..5f5d5383d 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -1,13 +1,35 @@
 # SwiftDiningPhilosophers
 Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using GCD and Semaphore in Swift)
 
-Written by Jacopo Mangiavacchi
+Written for Swift Algorithm Club by Jacopo Mangiavacchi
 
 
-# from https://en.wikipedia.org/wiki/Dining_philosophers_problem
+# Introduction
 
 In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
 
 It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.
 
 This Swift implementation is based on the Chandy/Misra solution and it use GCD Dispatch and Semaphone on Swift cross platform
+
+# Problem statement
+
+Five silent philosophers sit at a round table with bowls of spaghetti. Forks are placed between each pair of adjacent philosophers.
+
+Each philosopher must alternately think and eat. However, a philosopher can only eat spaghetti when they have both left and right forks. Each fork can be held by only one philosopher and so a philosopher can use the fork only if it is not being used by another philosopher. After an individual philosopher finishes eating, they need to put down both forks so that the forks become available to others. A philosopher can take the fork on their right or the one on their left as they become available, but cannot start eating before getting both forks.
+
+Eating is not limited by the remaining amounts of spaghetti or stomach space; an infinite supply and an infinite demand are assumed.
+
+The problem is how to design a discipline of behavior (a concurrent algorithm) such that no philosopher will starve; i.e., each can forever continue to alternate between eating and thinking, assuming that no philosopher can know when others may want to eat or think.
+
+This is an illustration of an dinining table:
+
+![Dining Philosophers table](https://upload.wikimedia.org/wikipedia/commons/7/7b/An_illustration_of_the_dining_philosophers_problem.png)
+
+
+
+# See also
+
+Dining Philosophers on Wikipedia https://en.wikipedia.org/wiki/Dining_philosophers_problem
+
+Written for Swift Algorithm Club by Jacopo Mangiavacchi

From 13d1827d697b030de86dcb042a2068b9f26f3f52 Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Sat, 14 Jan 2017 13:00:23 +0000
Subject: [PATCH 0778/1679] Update README.md

---
 DiningPhilosophers/README.md | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 5f5d5383d..22687d2fd 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -27,6 +27,27 @@ This is an illustration of an dinining table:
 ![Dining Philosophers table](https://upload.wikimedia.org/wikipedia/commons/7/7b/An_illustration_of_the_dining_philosophers_problem.png)
 
 
+# Solution
+There are different solutions for this classic algorithm and this Swift implementation is based on the on the Chandy/Misra solution that more generally allows for arbitrary agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
+
+However, it is very important to note here that this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
+
+
+# Description
+For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with the lower ID (n for agent Pn). Each fork can either be dirty or clean. Initially, all forks are dirty.
+When a philosopher wants to use a set of resources (i.e. eat), said philosopher must obtain the forks from their contending neighbors. For all such forks the philosopher does not have, they send a request message.
+When a philosopher with a fork receives a request message, they keep the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, they clean the fork before doing so.
+After a philosopher is done eating, all their forks become dirty. If another philosopher had previously requested one of the forks, the philosopher that has just finished eating cleans the fork and sends it.
+This solution also allows for a large degree of concurrency, and will solve an arbitrarily large problem.
+
+It also solves the starvation problem. The clean / dirty labels act as a way of giving preference to the most "starved" processes, and a disadvantage to processes that have just "eaten". One could compare their solution to one where philosophers are not allowed to eat twice in a row without letting others use the forks in between. Chandy and Misra's solution is more flexible than that, but has an element tending in that direction.
+
+In their analysis they derive a system of preference levels from the distribution of the forks and their clean/dirty states. They show that this system may describe an acyclic graph, and if so, the operations in their protocol cannot turn that graph into a cyclic one. This guarantees that deadlock cannot occur. However, if the system is initialized to a perfectly symmetric state, like all philosophers holding their left side forks, then the graph is cyclic at the outset, and their solution cannot prevent a deadlock. Initializing the system so that philosophers with lower IDs have dirty forks ensures the graph is initially acyclic.
+
+
+# Swift implementation
+
+
 
 # See also
 

From 4daf0d07dedf6f638a494a535b69d63e17bdf53c Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Sat, 14 Jan 2017 13:01:02 +0000
Subject: [PATCH 0779/1679] Update README.md

---
 DiningPhilosophers/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 22687d2fd..3ac5b1343 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -1,4 +1,4 @@
-# SwiftDiningPhilosophers
+# Dining Philosophers
 Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using GCD and Semaphore in Swift)
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi

From 5b3f3c4570b17be37d4f19344e3755523a9bcd21 Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Sat, 14 Jan 2017 13:08:16 +0000
Subject: [PATCH 0780/1679] Update main.swift

---
 DiningPhilosophers/Sources/main.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index dfde40773..deff344b9 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -12,7 +12,7 @@ import Dispatch
 
 let numberOfPhilosophers = 4
 
-class ForkPair {
+struct ForkPair {
     static let forksSemaphore:[DispatchSemaphore] = Array(repeating: DispatchSemaphore(value: 1), count: numberOfPhilosophers)
     
     let leftFork: DispatchSemaphore
@@ -44,7 +44,7 @@ class ForkPair {
 }
 
 
-class Philosophers {
+struct Philosophers {
     let forkPair: ForkPair
     let philosopherIndex: Int
     

From dca7bf14870e3007247344415b9d00e7d5cd8471 Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Sat, 14 Jan 2017 13:23:28 +0000
Subject: [PATCH 0781/1679] Update README.md

---
 DiningPhilosophers/README.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 3ac5b1343..29b5916e9 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -47,7 +47,13 @@ In their analysis they derive a system of preference levels from the distributio
 
 # Swift implementation
 
+This Swift 3.0 implementation of the Chandy/Misra solution is based on GCD and Semaphore tecnique and it could be built on both macOS and Linux.
 
+The code is based on a ForkPair struct used for holding an array of DispatchSemaphore and a Philosopher struct for associate a couple of forks to each Philosopher.
+
+The ForkPair DispatchSemaphore static array is used for waking the neighbour Philosophers any time a fork pair is put down on the table.
+
+A background DispatchQueue is then used to let any Philosopher run asyncrounosly on the background and a global DispatchSemaphore is simply used in order to keep the main thread on wait forever and let the Philosophers contienue forever in their alternate think and eat cycle.
 
 # See also
 

From 671aa3b26f8ec5ea16c2bfdbc567c1f7a2f5819a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Jan 2017 14:57:45 -0800
Subject: [PATCH 0782/1679] Update README.markdown

Added Dining Philosophers link.
---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index e5c8f8dae..ad5f910b4 100644
--- a/README.markdown
+++ b/README.markdown
@@ -190,6 +190,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Fizz Buzz](Fizz Buzz/)
 - [Monty Hall Problem](Monty Hall Problem/)
 - [Finding Palindromes](Palindromes/)
+- [Dining Philosophers](DiningPhilosophers/)
 
 ## Learn more!
 

From 71d8a43149fe3b125ce21b4ae3f0ec8eeb50220c Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Sun, 15 Jan 2017 11:23:42 -0500
Subject: [PATCH 0783/1679] Update Target to Swift 3.0

---
 .../SSSP.xcodeproj/project.pbxproj                              | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj
index 0dd67f69c..fb425a73e 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
@@ -334,6 +334,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -377,6 +378,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 3.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};

From cf0d1b539b2bf628a76e37b33332bab02c9bcc1a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 16 Jan 2017 10:59:20 -0800
Subject: [PATCH 0784/1679] Modified Z-Algorithm to conform to our style guide.

---
 Z-Algorithm/ZAlgorithm.swift                  | 116 +++++++-------
 .../ZetaAlgorithm.playground/Contents.swift   | 150 +++++++++---------
 Z-Algorithm/ZetaAlgorithm.swift               |  56 +++----
 3 files changed, 161 insertions(+), 161 deletions(-)

diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
index c9d7de876..9bef69687 100644
--- a/Z-Algorithm/ZAlgorithm.swift
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -1,66 +1,66 @@
 /*  Z-Algorithm for pattern/string pre-processing
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
+ 
+ The code is based on the book:
+ "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+ by Dan Gusfield
+ Cambridge University Press, 1997
+ */
 
 import Foundation
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-    
-    let pattern = Array(ptrn.characters)
-    let patternLength: Int = pattern.count
-    
-    guard patternLength > 0 else {
-        return nil
-    }
-    
-    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
-    
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
-    var textIndex: Int = 0
-    var patternIndex: Int = 0
-    
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-            
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                    patternIndex = patternIndex + 1
-            }
-            
-            zeta[k] = patternIndex
-            
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-            
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-                
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-                
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
+  
+  let pattern = Array(ptrn.characters)
+  let patternLength = pattern.count
+  
+  guard patternLength > 0 else {
+    return nil
+  }
+  
+  var zeta = [Int](repeating: 0, count: patternLength)
+  
+  var left = 0
+  var right = 0
+  var k_1 = 0
+  var betaLength = 0
+  var textIndex = 0
+  var patternIndex = 0
+  
+  for k in 1 ..< patternLength {
+    if k > right {
+      patternIndex = 0
+      
+      while k + patternIndex < patternLength  &&
+        pattern[k + patternIndex] == pattern[patternIndex] {
+          patternIndex = patternIndex + 1
+      }
+      
+      zeta[k] = patternIndex
+      
+      if zeta[k] > 0 {
+        left = k
+        right = k + zeta[k] - 1
+      }
+    } else {
+      k_1 = k - left + 1
+      betaLength = right - k + 1
+      
+      if zeta[k_1 - 1] < betaLength {
+        zeta[k] = zeta[k_1 - 1]
+      } else if zeta[k_1 - 1] >= betaLength {
+        textIndex = betaLength
+        patternIndex = right + 1
+        
+        while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+          textIndex = textIndex + 1
+          patternIndex = patternIndex + 1
         }
+        
+        zeta[k] = patternIndex - k
+        left = k
+        right = patternIndex - 1
+      }
     }
-    return zeta
+  }
+  return zeta
 }
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index c9d942149..395122af0 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -2,88 +2,88 @@
 
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-    let pattern = Array(ptrn.characters)
-    let patternLength: Int = pattern.count
-
-    guard patternLength > 0 else {
-        return nil
-    }
-
-    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
-
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
-    var textIndex: Int = 0
-    var patternIndex: Int = 0
-
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
-            }
-
-            zeta[k] = patternIndex
-
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
+  
+  let pattern = Array(ptrn.characters)
+  let patternLength = pattern.count
+  
+  guard patternLength > 0 else {
+    return nil
+  }
+  
+  var zeta = [Int](repeating: 0, count: patternLength)
+  
+  var left = 0
+  var right = 0
+  var k_1 = 0
+  var betaLength = 0
+  var textIndex = 0
+  var patternIndex = 0
+  
+  for k in 1 ..< patternLength {
+    if k > right {
+      patternIndex = 0
+      
+      while k + patternIndex < patternLength  &&
+        pattern[k + patternIndex] == pattern[patternIndex] {
+          patternIndex = patternIndex + 1
+      }
+      
+      zeta[k] = patternIndex
+      
+      if zeta[k] > 0 {
+        left = k
+        right = k + zeta[k] - 1
+      }
+    } else {
+      k_1 = k - left + 1
+      betaLength = right - k + 1
+      
+      if zeta[k_1 - 1] < betaLength {
+        zeta[k] = zeta[k_1 - 1]
+      } else if zeta[k_1 - 1] >= betaLength {
+        textIndex = betaLength
+        patternIndex = right + 1
+        
+        while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+          textIndex = textIndex + 1
+          patternIndex = patternIndex + 1
         }
+        
+        zeta[k] = patternIndex - k
+        left = k
+        right = patternIndex - 1
+      }
     }
-    return zeta
+  }
+  return zeta
 }
 
 
 extension String {
-
-    func indexesOf(pattern: String) -> [Int]? {
-        let patternLength: Int = pattern.characters.count
-        let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
-
-        guard zeta != nil else {
-            return nil
-        }
-
-        var indexes: [Int] = [Int]()
-
-        /* Scan the zeta array to find matched patterns */
-        for i in 0 ..< zeta!.count {
-            if zeta![i] == patternLength {
-                indexes.append(i - patternLength - 1)
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-
-        return indexes
+  
+  func indexesOf(pattern: String) -> [Int]? {
+    let patternLength = pattern.characters.count
+    let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
+    
+    guard zeta != nil else {
+      return nil
+    }
+    
+    var indexes: [Int] = []
+    
+    /* Scan the zeta array to find matched patterns */
+    for i in 0 ..< zeta!.count {
+      if zeta![i] == patternLength {
+        indexes.append(i - patternLength - 1)
+      }
+    }
+    
+    guard !indexes.isEmpty else {
+      return nil
     }
+    
+    return indexes
+  }
 }
 
 /* Examples */
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
index 4d80aa665..c35703272 100644
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -1,36 +1,36 @@
 /*  Z-Algorithm based algorithm for pattern/string matching
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
+ 
+ The code is based on the book:
+ "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+ by Dan Gusfield
+ Cambridge University Press, 1997
+ */
 
 import Foundation
 
 extension String {
+  
+  func indexesOf(pattern: String) -> [Int]? {
+    let patternLength = pattern.characters.count
+    let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
+    
+    guard zeta != nil else {
+      return nil
+    }
+    
+    var indexes: [Int] = [Int]()
     
-    func indexesOf(pattern: String) -> [Int]? {
-        let patternLength: Int = pattern.characters.count
-        let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
-        
-        guard zeta != nil else {
-            return nil
-        }
-        
-        var indexes: [Int] = [Int]()
-        
-        /* Scan the zeta array to find matched patterns */
-        for i in 0 ..< zeta!.count {
-            if zeta![i] == patternLength {
-                indexes.append(i - patternLength - 1)
-            }
-        }
-        
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        
-        return indexes
+    /* Scan the zeta array to find matched patterns */
+    for i in 0 ..< zeta!.count {
+      if zeta![i] == patternLength {
+        indexes.append(i - patternLength - 1)
+      }
     }
+    
+    guard !indexes.isEmpty else {
+      return nil
+    }
+    
+    return indexes
+  }
 }

From e5fb825ffa5fb4604ac0dd40782c372b5a5aef20 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 16 Jan 2017 11:01:46 -0800
Subject: [PATCH 0785/1679] Update README.markdown

Added Z-algorithm link.
---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index ad5f910b4..2d7522b1e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -50,6 +50,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
 - [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
 - [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
+- [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
 
 ### String Search
 

From 10abdbc8efa765f6b9700498e9a08ab8de0ffbe1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 16 Jan 2017 11:02:39 -0800
Subject: [PATCH 0786/1679] Update README.markdown

Updated the Z-algorithm link to the String Search section.
---
 README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 2d7522b1e..97b84057b 100644
--- a/README.markdown
+++ b/README.markdown
@@ -50,7 +50,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
 - [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
 - [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
-- [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
+
 
 ### String Search
 
@@ -59,6 +59,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - Knuth-Morris-Pratt
 - Rabin-Karp
 - [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
+- [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
 
 ### Sorting
 

From ca35d57d14073ac99f6a74c5a2057f1ab7f28c60 Mon Sep 17 00:00:00 2001
From: Bo Qian <boqian@bos-2nd-macbook-pro.local>
Date: Wed, 18 Jan 2017 17:25:53 -0800
Subject: [PATCH 0787/1679] Simplify the insert method by removing the
 fileprivate method.  Delete duplicated BinarySearchTree.swift, so that there
 is only one single file.

---
 .../Sources/BinarySearchTree.swift            |  14 +-
 .../Solution 1/BinarySearchTree.swift         | 377 ------------------
 .../Tests/Tests.xcodeproj/project.pbxproj     |   8 +-
 .../contents.xcworkspacedata                  |   3 -
 4 files changed, 9 insertions(+), 393 deletions(-)
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.swift

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index f4960380e..5edbfc48a 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -23,7 +23,7 @@ public class BinarySearchTree<T: Comparable> {
     precondition(array.count > 0)
     self.init(value: array.first!)
     for v in array.dropFirst() { 
-      insert(value: v, parent: self)
+      insert(value: v)
     }
   }
 
@@ -74,23 +74,19 @@ extension BinarySearchTree {
     Performance: runs in O(h) time, where h is the height of the tree.
   */
   public func insert(value: T) {
-    insert(value: value, parent: self)
-  }
-
-  fileprivate func insert(value: T, parent: BinarySearchTree) {
     if value < self.value {
       if let left = left {
-        left.insert(value: value, parent: left)
+        left.insert(value: value)
       } else {
         left = BinarySearchTree(value: value)
-        left?.parent = parent
+        left?.parent = self
       }
     } else {
       if let right = right {
-        right.insert(value: value, parent: right)
+        right.insert(value: value)
       } else {
         right = BinarySearchTree(value: value)
-        right?.parent = parent
+        right?.parent = self
       }
     }
   }
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.swift
deleted file mode 100644
index a58ac075a..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree.swift	
+++ /dev/null
@@ -1,377 +0,0 @@
-/*
-  A binary search tree.
-
-  Each node stores a value and two children. The left child contains a smaller
-  value; the right a larger (or equal) value.
-
-  This tree allows duplicate elements.
-
-  This tree does not automatically balance itself. To make sure it is balanced,
-  you should insert new values in randomized order, not in sorted order.
-*/
-public class BinarySearchTree<T: Comparable> {
-  private(set) public var value: T
-  private(set) public var parent: BinarySearchTree?
-  private(set) public var left: BinarySearchTree?
-  private(set) public var right: BinarySearchTree?
-
-  public init(value: T) {
-    self.value = value
-  }
-
-  public convenience init(array: [T]) {
-    precondition(array.count > 0)
-    self.init(value: array.first!)
-    for v in array.dropFirst() {
-      insert(v, parent: self)
-    }
-  }
-
-  public var isRoot: Bool {
-    return parent == nil
-  }
-
-  public var isLeaf: Bool {
-    return left == nil && right == nil
-  }
-
-  public var isLeftChild: Bool {
-    return parent?.left === self
-  }
-
-  public var isRightChild: Bool {
-    return parent?.right === self
-  }
-
-  public var hasLeftChild: Bool {
-    return left != nil
-  }
-
-  public var hasRightChild: Bool {
-    return right != nil
-  }
-
-  public var hasAnyChild: Bool {
-    return hasLeftChild || hasRightChild
-  }
-
-  public var hasBothChildren: Bool {
-    return hasLeftChild && hasRightChild
-  }
-
-  /* How many nodes are in this subtree. Performance: O(n). */
-  public var count: Int {
-    return (left?.count ?? 0) + 1 + (right?.count ?? 0)
-  }
-}
-
-// MARK: - Adding items
-
-extension BinarySearchTree {
-  /*
-    Inserts a new element into the tree. You should only insert elements
-    at the root, to make to sure this remains a valid binary tree!
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func insert(value: T) {
-    insert(value, parent: self)
-  }
-
-  private func insert(value: T, parent: BinarySearchTree) {
-    if value < self.value {
-      if let left = left {
-        left.insert(value, parent: left)
-      } else {
-        left = BinarySearchTree(value: value)
-        left?.parent = parent
-      }
-    } else {
-      if let right = right {
-        right.insert(value, parent: right)
-      } else {
-        right = BinarySearchTree(value: value)
-        right?.parent = parent
-      }
-    }
-  }
-}
-
-// MARK: - Deleting items
-
-extension BinarySearchTree {
-  /*
-    Deletes a node from the tree.
-
-    Returns the node that has replaced this removed one (or nil if this was a
-    leaf node). That is primarily useful for when you delete the root node, in
-    which case the tree gets a new root.
-
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func remove() -> BinarySearchTree? {
-    let replacement: BinarySearchTree?
-
-    if let left = left {
-      if let right = right {
-        replacement = removeNodeWithTwoChildren(left, right)
-      } else {
-        // This node only has a left child. The left child replaces the node.
-        replacement = left
-      }
-    } else if let right = right {
-      // This node only has a right child. The right child replaces the node.
-      replacement = right
-    } else {
-      // This node has no children. We just disconnect it from its parent.
-      replacement = nil
-    }
-
-    reconnectParentToNode(replacement)
-
-    // The current node is no longer part of the tree, so clean it up.
-    parent = nil
-    left = nil
-    right = nil
-
-    return replacement
-  }
-
-  private func removeNodeWithTwoChildren(left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
-    // This node has two children. It must be replaced by the smallest
-    // child that is larger than this node's value, which is the leftmost
-    // descendent of the right child.
-    let successor = right.minimum()
-
-    // If this in-order successor has a right child of its own (it cannot
-    // have a left child by definition), then that must take its place.
-    successor.remove()
-
-    // Connect our left child with the new node.
-    successor.left = left
-    left.parent = successor
-
-    // Connect our right child with the new node. If the right child does
-    // not have any left children of its own, then the in-order successor
-    // *is* the right child.
-    if right !== successor {
-      successor.right = right
-      right.parent = successor
-    } else {
-      successor.right = nil
-    }
-
-    // And finally, connect the successor node to our parent.
-    return successor
-  }
-
-  private func reconnectParentToNode(node: BinarySearchTree?) {
-    if let parent = parent {
-      if isLeftChild {
-        parent.left = node
-      } else {
-        parent.right = node
-      }
-    }
-    node?.parent = parent
-  }
-}
-
-// MARK: - Searching
-
-extension BinarySearchTree {
-  /*
-    Finds the "highest" node with the specified value.
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func search(value: T) -> BinarySearchTree? {
-    var node: BinarySearchTree? = self
-    while case let n? = node {
-      if value < n.value {
-        node = n.left
-      } else if value > n.value {
-        node = n.right
-      } else {
-        return node
-      }
-    }
-    return nil
-  }
-
-  /*
-  // Recursive version of search
-  public func search(value: T) -> BinarySearchTree? {
-    if value < self.value {
-      return left?.search(value)
-    } else if value > self.value {
-      return right?.search(value)
-    } else {
-      return self  // found it!
-    }
-  }
-  */
-
-  public func contains(value: T) -> Bool {
-    return search(value) != nil
-  }
-
-  /*
-    Returns the leftmost descendent. O(h) time.
-  */
-  public func minimum() -> BinarySearchTree {
-    var node = self
-    while case let next? = node.left {
-      node = next
-    }
-    return node
-  }
-
-  /*
-    Returns the rightmost descendent. O(h) time.
-  */
-  public func maximum() -> BinarySearchTree {
-    var node = self
-    while case let next? = node.right {
-      node = next
-    }
-    return node
-  }
-
-  /*
-    Calculates the depth of this node, i.e. the distance to the root.
-    Takes O(h) time.
-  */
-  public func depth() -> Int {
-    var node = self
-    var edges = 0
-    while case let parent? = node.parent {
-      node = parent
-      edges += 1
-    }
-    return edges
-  }
-
-  /*
-    Calculates the height of this node, i.e. the distance to the lowest leaf.
-    Since this looks at all children of this node, performance is O(n).
-  */
-  public func height() -> Int {
-    if isLeaf {
-      return 0
-    } else {
-      return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
-    }
-  }
-
-  /*
-    Finds the node whose value precedes our value in sorted order.
-  */
-  public func predecessor() -> BinarySearchTree<T>? {
-    if let left = left {
-      return left.maximum()
-    } else {
-      var node = self
-      while case let parent? = node.parent {
-        if parent.value < value { return parent }
-        node = parent
-      }
-      return nil
-    }
-  }
-
-  /*
-    Finds the node whose value succeeds our value in sorted order.
-  */
-  public func successor() -> BinarySearchTree<T>? {
-    if let right = right {
-      return right.minimum()
-    } else {
-      var node = self
-      while case let parent? = node.parent {
-        if parent.value > value { return parent }
-        node = parent
-      }
-      return nil
-    }
-  }
-}
-
-// MARK: - Traversal
-
-extension BinarySearchTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
-    left?.traverseInOrder(process)
-    process(value)
-    right?.traverseInOrder(process)
-  }
-
-  public func traversePreOrder(@noescape process: T -> Void) {
-    process(value)
-    left?.traversePreOrder(process)
-    right?.traversePreOrder(process)
-  }
-
-  public func traversePostOrder(@noescape process: T -> Void) {
-    left?.traversePostOrder(process)
-    right?.traversePostOrder(process)
-    process(value)
-  }
-
-  /*
-    Performs an in-order traversal and collects the results in an array.
-  */
-  public func map(@noescape formula: T -> T) -> [T] {
-    var a = [T]()
-    if let left = left { a += left.map(formula) }
-    a.append(formula(value))
-    if let right = right { a += right.map(formula) }
-    return a
-  }
-}
-
-/*
-  Is this binary tree a valid binary search tree?
-*/
-extension BinarySearchTree {
-  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
-    if value < minValue || value > maxValue { return false }
-    let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
-    let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
-    return leftBST && rightBST
-  }
-}
-
-// MARK: - Debugging
-
-extension BinarySearchTree: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if let left = left {
-      s += "(\(left.description)) <- "
-    }
-    s += "\(value)"
-    if let right = right {
-      s += " -> (\(right.description))"
-    }
-    return s
-  }
-}
-
-extension BinarySearchTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = "value: \(value)"
-    if let parent = parent {
-      s += ", parent: \(parent.value)"
-    }
-    if let left = left {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = right {
-      s += ", right = [" + right.debugDescription + "]"
-    }
-    return s
-  }
-
-  public func toArray() -> [T] {
-    return map { $0 }
-  }
-}
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index c1d6c8029..7ecfe593f 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -7,15 +7,15 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		7B80C3D81C77A313003CECC7 /* BinarySearchTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3D71C77A313003CECC7 /* BinarySearchTree.swift */; };
 		7B80C3DA1C77A323003CECC7 /* BinarySearchTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3D91C77A323003CECC7 /* BinarySearchTreeTests.swift */; };
+		9E5A58B91E304C3100DAB3BB /* BinarySearchTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9E5A58B81E304C3100DAB3BB /* BinarySearchTree.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
-		7B80C3D71C77A313003CECC7 /* BinarySearchTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearchTree.swift; path = ../BinarySearchTree.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3D91C77A323003CECC7 /* BinarySearchTreeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BinarySearchTreeTests.swift; sourceTree = SOURCE_ROOT; };
+		9E5A58B81E304C3100DAB3BB /* BinarySearchTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearchTree.swift; path = ../BinarySearchTree.playground/Sources/BinarySearchTree.swift; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -48,7 +48,7 @@
 		7B2BBC831C779D720067B71D /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				7B80C3D71C77A313003CECC7 /* BinarySearchTree.swift */,
+				9E5A58B81E304C3100DAB3BB /* BinarySearchTree.swift */,
 				7B80C3D91C77A323003CECC7 /* BinarySearchTreeTests.swift */,
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
@@ -125,7 +125,7 @@
 			buildActionMask = 2147483647;
 			files = (
 				7B80C3DA1C77A323003CECC7 /* BinarySearchTreeTests.swift in Sources */,
-				7B80C3D81C77A313003CECC7 /* BinarySearchTree.swift in Sources */,
+				9E5A58B91E304C3100DAB3BB /* BinarySearchTree.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4231528aa..b2ffce836 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -310,9 +310,6 @@
          <FileRef
             location = "group:BinarySearchTree.playground">
          </FileRef>
-         <FileRef
-            location = "group:BinarySearchTree.swift">
-         </FileRef>
          <Group
             location = "group:Tests"
             name = "Tests">

From 942e3b1738d95645e4dc49c483d84e9e094b1ea5 Mon Sep 17 00:00:00 2001
From: Bo Qian <boqian@bos-2nd-macbook-pro.local>
Date: Thu, 19 Jan 2017 18:33:43 -0800
Subject: [PATCH 0788/1679] Simplified the remove().  I feel the new
 implementation is more elegant and conceptually more straightforward.

---
 .../Sources/BinarySearchTree.swift            | 97 +++++++------------
 1 file changed, 34 insertions(+), 63 deletions(-)

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 5edbfc48a..31ae99a2f 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -106,58 +106,30 @@ extension BinarySearchTree {
   */
   @discardableResult public func remove() -> BinarySearchTree? {
     let replacement: BinarySearchTree?
-
+    
+    // Replacement for current node can be either biggest one on the left or
+    // smallest one on the right, whichever is not nil
     if let left = left {
-      if let right = right {
-        replacement = removeNodeWithTwoChildren(left, right)
-      } else {
-        // This node only has a left child. The left child replaces the node.
-        replacement = left
-      }
+      replacement = left.maximum()
     } else if let right = right {
-      // This node only has a right child. The right child replaces the node.
-      replacement = right
+      replacement = right.minimum()
     } else {
-      // This node has no children. We just disconnect it from its parent.
-      replacement = nil
+      replacement = nil;
     }
-
-    reconnectParentTo(node: replacement)
-
+    
+    replacement?.remove();
+
+    // Place the replacement on current node's position
+    replacement?.right = right;
+    replacement?.left = left;
+    reconnectParentTo(node:replacement);
+    
     // The current node is no longer part of the tree, so clean it up.
     parent = nil
     left = nil
     right = nil
-
-    return replacement
-  }
-
-  private func removeNodeWithTwoChildren(_ left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
-    // This node has two children. It must be replaced by the smallest
-    // child that is larger than this node's value, which is the leftmost
-    // descendent of the right child.
-    let successor = right.minimum()
-
-    // If this in-order successor has a right child of its own (it cannot
-    // have a left child by definition), then that must take its place.
-    successor.remove()
-
-    // Connect our left child with the new node.
-    successor.left = left
-    left.parent = successor
-
-    // Connect our right child with the new node. If the right child does
-    // not have any left children of its own, then the in-order successor
-    // *is* the right child.
-    if right !== successor {
-      successor.right = right
-      right.parent = successor
-    } else {
-      successor.right = nil
-    }
-
-    // And finally, connect the successor node to our parent.
-    return successor
+    
+    return replacement;
   }
 
   private func reconnectParentTo(node: BinarySearchTree?) {
@@ -350,24 +322,23 @@ extension BinarySearchTree: CustomStringConvertible {
     }
     return s
   }
-}
-
-extension BinarySearchTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = "value: \(value)"
-    if let parent = parent {
-      s += ", parent: \(parent.value)"
-    }
-    if let left = left {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = right {
-      s += ", right = [" + right.debugDescription + "]"
-    }
-    return s
-  }
+   
+   public func toArray() -> [T] {
+      return map { $0 }
+   }
 
-  public func toArray() -> [T] {
-    return map { $0 }
-  }
 }
+
+//extension BinarySearchTree: CustomDebugStringConvertible {
+//  public var debugDescription: String {
+//   var s = ""
+//   if let left = left {
+//      s += "(\(left.description)) <- "
+//   }
+//   s += "\(value)"
+//   if let right = right {
+//      s += " -> (\(right.description))"
+//   }
+//   return s
+//  }
+//}

From c3ea705cb7623f9d6a9df3babcfcb01c61abcf4e Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Wed, 25 Jan 2017 11:46:55 -0500
Subject: [PATCH 0789/1679] Added license clarification.

---
 How to Contribute.markdown | 2 +-
 README.markdown            | 2 ++
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 9e83b5ed6..258357e8b 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -21,7 +21,7 @@ To keep this a high quality repo, please follow this process when submitting you
 1. Create a pull request to "claim" an algorithm or data structure. Just so multiple people don't work on the same thing.
 2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
 3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
-4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. If you wrote it, you deserve the credit and fame.
+4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
 5. Add a playground and/or unit tests.
 6. Run [SwiftLint](https://github.com/realm/SwiftLint)  
   - [Install](https://github.com/realm/SwiftLint#installation)
diff --git a/README.markdown b/README.markdown
index c6d2e0149..b33a8f8ae 100644
--- a/README.markdown
+++ b/README.markdown
@@ -233,4 +233,6 @@ The Swift Algorithm Club is a collaborative effort from the [most algorithmic me
 
 All content is licensed under the terms of the MIT open source license.
 
+By posting here, or by submitting any pull request through this forum, you agree that all content you submit or create, both code and text, is subject to this license.  Razeware, LLC, and others will have all the rights described in the license regarding this content.  The precise terms of this license may be found [here](https://github.com/raywenderlich/swift-algorithm-club/blob/master/LICENSE.txt).
+
 [![Build Status](https://travis-ci.org/raywenderlich/swift-algorithm-club.svg?branch=master)](https://travis-ci.org/raywenderlich/swift-algorithm-club)

From 40f667cfbb57e51ed5f639c9bfff5bdcc45fa867 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Wed, 25 Jan 2017 11:47:48 -0500
Subject: [PATCH 0790/1679] Added Vincent as maintainer.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index b33a8f8ae..e2d99e2bc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -225,7 +225,7 @@ Other algorithm repositories:
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
 
-It is now maintained by [Chris Pilcher](https://github.com/chris-pilcher) and [Kelvin Lau](https://github.com/kelvinlauKL).
+It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka) and [Kelvin Lau](https://github.com/kelvinlauKL).
 
 The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How to Contribute.markdown)? :]
 

From 1504e605537c2c2b881c8bdbdadac8eabc209bfd Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Sat, 28 Jan 2017 01:10:46 +0100
Subject: [PATCH 0791/1679] migrated to swift 3

---
 Run-Length Encoding/README.markdown           | 121 ++++----
 .../RLE.playground/Contents.swift             | 162 ++++++-----
 .../RLE.playground/Sources/RLE.swift          |  68 +++++
 Run-Length Encoding/RLE.swift                 |  70 -----
 Run-Length Encoding/Tests/Info.plist          |  24 --
 Run-Length Encoding/Tests/RLETests.swift      | 110 --------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 261 ------------------
 .../contents.xcworkspacedata                  |   7 -
 .../xcshareddata/xcschemes/Tests.xcscheme     |  90 ------
 9 files changed, 228 insertions(+), 685 deletions(-)
 create mode 100644 Run-Length Encoding/RLE.playground/Sources/RLE.swift
 delete mode 100644 Run-Length Encoding/RLE.swift
 delete mode 100644 Run-Length Encoding/Tests/Info.plist
 delete mode 100644 Run-Length Encoding/Tests/RLETests.swift
 delete mode 100644 Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj
 delete mode 100644 Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 delete mode 100644 Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Run-Length Encoding/README.markdown b/Run-Length Encoding/README.markdown
index 8371b1227..f7d196161 100644
--- a/Run-Length Encoding/README.markdown	
+++ b/Run-Length Encoding/README.markdown	
@@ -3,14 +3,14 @@
 RLE is probably the simplest way to do compression. Let's say you have data that looks like this:
 
 	aaaaabbbcdeeeeeeef...
-	
+
 then RLE encodes it as follows:
 
 	5a3b1c1d7e1f...
 
 Instead of repeating bytes, you first write how often that byte occurs and then the byte's actual value. So `5a` means `aaaaa`. If the data has a lot of "byte runs", that is lots of repeating bytes, then RLE can save quite a bit of space. It works quite well on images.
 
-There are many different ways you can implement RLE. Here's an extension of `NSData` that does a version of RLE inspired by the old [PCX image file format](https://en.wikipedia.org/wiki/PCX).
+There are many different ways you can implement RLE. Here's an extension of `Data` that does a version of RLE inspired by the old [PCX image file format](https://en.wikipedia.org/wiki/PCX).
 
 The rules are these:
 
@@ -20,44 +20,42 @@ The rules are these:
 
 - A single byte in the range 192 - 255 is represented by two bytes: first the byte 192 (meaning a run of 1 byte), followed by the actual value.
 
-Here is the compression code. It returns a new `NSData` object containing the run-length encoded bytes:
+Here is the compression code. It returns a new `Data` object containing the run-length encoded bytes:
 
 ```swift
-extension NSData {
-  public func compressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
-      
-      while ptr < end {                        // 1
-        var count = 0
-        var byte = ptr.memory
-        var next = byte
-        
-        while next == byte && ptr < end && count < 64 {   // 2
-          ptr = ptr.advancedBy(1)
-          next = ptr.memory
-          count += 1
-        }
-      
-        if count > 1 || byte >= 192 {          // 3
-          var size = 191 + UInt8(count)
-          data.appendBytes(&size, length: 1)
-          data.appendBytes(&byte, length: 1)
-        } else {                               // 4
-          data.appendBytes(&byte, length: 1)
+extension Data {
+    public func compressRLE() -> Data {
+        var data = Data()
+        self.withUnsafeBytes { (uPtr: UnsafePointer<UInt8>) in
+            var ptr = uPtr
+            let end = ptr + count
+            while ptr < end { 						//1
+                var count = 0
+                var byte = ptr.pointee
+                var next = byte
+
+                while next == byte && ptr < end && count < 64 { //2
+                    ptr = ptr.advanced(by: 1)
+                    next = ptr.pointee
+                    count += 1
+                }
+
+                if count > 1 || byte >= 192 {       // 3
+                    var size = 191 + UInt8(count)
+                    data.append(&size, count: 1)
+                    data.append(&byte, count: 1)
+                } else {                            // 4
+                    data.append(&byte, count: 1)
+                }
+            }
         }
-      }
+        return data
     }
-    return data
-  }
-}
 ```
 
 How it works:
 
-1. We use an `UnsafePointer` to step through the bytes of the original `NSData` object.
+1. We use an `UnsafePointer` to step through the bytes of the original `Data` object.
 
 2. At this point we've read the current byte value into the `byte` variable. If the next byte is the same, then we keep reading until we find a byte value that is different, or we reach the end of the data. We also stop if the run is 64 bytes because that's the maximum we can encode.
 
@@ -69,11 +67,11 @@ You can test it like this in a playground:
 
 ```swift
 let originalString = "aaaaabbbcdeeeeeeef"
-let utf8 = originalString.dataUsingEncoding(NSUTF8StringEncoding)!
+let utf8 = originalString.data(using: String.Encoding.utf8)!
 let compressed = utf8.compressRLE()
 ```
 
-The compressed `NSData` object should be `<c461c262 6364c665 66>`. Let's decode that by hand to see what has happened:
+The compressed `Data` object should be `<c461c262 6364c665 66>`. Let's decode that by hand to see what has happened:
 
 	c4    This is 196 in decimal. It means the next byte appears 5 times.
 	61    The data byte "a".
@@ -90,34 +88,38 @@ So that's 9 bytes encoded versus 18 original. That's a savings of 50%. Of course
 Here is the decompression code:
 
 ```swift
-  public func decompressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
-
-      while ptr < end {
-        var byte = ptr.memory                 // 1
-        ptr = ptr.advancedBy(1)
-        
-        if byte < 192 {                       // 2
-          data.appendBytes(&byte, length: 1)
-
-        } else if ptr < end {                 // 3
-          var value = ptr.memory
-          ptr = ptr.advancedBy(1)
-
-          for _ in 0 ..< byte - 191 {
-            data.appendBytes(&value, length: 1)
-          }
+public func decompressRLE() -> Data {
+        var data = Data()
+        self.withUnsafeBytes { (uPtr: UnsafePointer<UInt8>) in
+            var ptr = uPtr
+            let end = ptr + count
+
+            while ptr < end {
+                // Read the next byte. This is either a single value less than 192,
+                // or the start of a byte run.
+                var byte = ptr.pointee							// 1
+                ptr = ptr.advanced(by: 1)
+
+                if byte < 192 {                     // 2
+                    data.append(&byte, count: 1)
+                } else if ptr < end {               // 3
+                    // Read the actual data value.
+                    var value = ptr.pointee
+                    ptr = ptr.advanced(by: 1)
+
+                    // And write it out repeatedly.
+                    for _ in 0 ..< byte - 191 {
+                        data.append(&value, count: 1)
+                    }
+                }
+            }
         }
-      }
+        return data
     }
-    return data
-  }
+
 ```
 
-1. Again this uses an `UnsafePointer` to read the `NSData`. Here we read the next byte; this is either a single value less than 192, or the start of a byte run.
+1. Again this uses an `UnsafePointer` to read the `Data`. Here we read the next byte; this is either a single value less than 192, or the start of a byte run.
 
 2. If it's a single value, then it's just a matter of copying it to the output.
 
@@ -134,6 +136,7 @@ And now `originalString == restoredString` must be true!
 
 Footnote: The original PCX implementation is slightly different. There, a byte value of 192 (0xC0) means that the following byte will be repeated 0 times. This also limits the maximum run size to 63 bytes. Because it makes no sense to store bytes that don't occur, in my implementation 192 means the next byte appears once, and the maximum run length is 64 bytes.
 
-This was probably a trade-off when they designed the PCX format way back when. If you look at it in binary, the upper two bits indicate whether a byte is compressed. (If both bits are set then the byte value is 192 or more.) To get the run length you can simply do `byte & 0x3F`, giving you a value in the range 0 to 63. 
+This was probably a trade-off when they designed the PCX format way back when. If you look at it in binary, the upper two bits indicate whether a byte is compressed. (If both bits are set then the byte value is 192 or more.) To get the run length you can simply do `byte & 0x3F`, giving you a value in the range 0 to 63.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
+*Migrated to Swift3 by Jaap Wijnen*
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 41dcae3b1..62b4ef437 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -2,81 +2,115 @@
 
 import Foundation
 
-extension NSData {
-  /*
-    Compresses the NSData using run-length encoding.
-  */
-  public func compressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
+let originalString = "aaaaabbbcdeeeeeeef"
+let utf8 = originalString.data(using: String.Encoding.utf8)!
+let compressed = utf8.compressRLE()
 
-      while ptr < end {
-        var count = 0
-        var byte = ptr.memory
-        var next = byte
+let decompressed = compressed.decompressRLE()
+let restoredString = String(data: decompressed, encoding: String.Encoding.utf8)
+originalString == restoredString
 
-        // Is the next byte the same? Keep reading until we find a different
-        // value, or we reach the end of the data, or the run is 64 bytes.
-        while next == byte && ptr < end && count < 64 {
-          ptr = ptr.advancedBy(1)
-          next = ptr.memory
-          count += 1
-        }
+func encodeAndDecode(_ bytes: [UInt8]) -> Bool {
+    var bytes = bytes
+    
+    var data1 = Data(bytes: &bytes, count: bytes.count)
+    print("data1 is \(data1.count) bytes")
+    
+    var rleData = data1.compressRLE()
+    print("encoded data is \(rleData.count) bytes")
+    
+    var data2 = rleData.decompressRLE()
+    print("data2 is \(data2.count) bytes")
+    
+    return data1 == data2
+}
 
-        if count > 1 || byte >= 192 {         // byte run of up to 64 repeats
-          var size = 191 + UInt8(count)
-          data.appendBytes(&size, length: 1)
-          data.appendBytes(&byte, length: 1)
-        } else {                              // single byte between 0 and 192
-          data.appendBytes(&byte, length: 1)
-        }
-      }
-    }
-    return data
-  }
+func testEmpty() -> Bool {
+    let bytes: [UInt8] = []
+    return encodeAndDecode(bytes)
+}
 
-  /*
-    Converts a run-length encoded NSData back to the original.
-  */
-  public func decompressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
+func testOneByteWithLowValue() -> Bool {
+    let bytes: [UInt8] = [0x80]
+    return encodeAndDecode(bytes)
+}
 
-      while ptr < end {
-        // Read the next byte. This is either a single value less than 192,
-        // or the start of a byte run.
-        var byte = ptr.memory
-        ptr = ptr.advancedBy(1)
+func testOneByteWithHighValue() -> Bool {
+    let bytes: [UInt8] = [0xD0]
+    return encodeAndDecode(bytes)
+}
 
-        if byte < 192 {                       // single value
-          data.appendBytes(&byte, length: 1)
+func testSimpleCases() -> Bool {
+    let bytes: [UInt8] = [
+        0x00,
+        0x20, 0x20, 0x20, 0x20, 0x20,
+        0x30,
+        0x00, 0x00,
+        0xC0,
+        0xC1,
+        0xC0, 0xC0, 0xC0,
+        0xFF, 0xFF, 0xFF, 0xFF
+    ]
+    return encodeAndDecode(bytes)
+}
 
-        } else if ptr < end {                 // byte run
-          // Read the actual data value.
-          var value = ptr.memory
-          ptr = ptr.advancedBy(1)
+func testBufferWithoutSpans() -> Bool {
+    // There is nothing that can be encoded in this buffer, so the encoded
+    // data ends up being longer.
+    var bytes: [UInt8] = []
+    for i in 0..<1024 {
+        bytes.append(UInt8(i%256))
+    }
+    return encodeAndDecode(bytes)
+}
 
-          // And write it out repeatedly.
-          for _ in 0 ..< byte - 191 {
-            data.appendBytes(&value, length: 1)
-          }
+func testBufferWithSpans(_ spanSize: Int) -> Bool {
+    print("span size \(spanSize)")
+    
+    let length = spanSize * 32
+    var bytes: [UInt8] = Array<UInt8>(repeating: 0, count: length)
+    
+    for t in stride(from: 0, to: length, by: spanSize) {
+        for i in 0..<spanSize {
+            bytes[t + i] = UInt8(t % 256)
         }
-      }
     }
-    return data
-  }
+    return encodeAndDecode(bytes)
 }
 
+func testRandomByte() -> Bool {
+    let length = 1 + Int(arc4random_uniform(2048))
+    var bytes: [UInt8] = []
+    for _ in 0..<length {
+        bytes.append(UInt8(arc4random() % 256))
+    }
+    return encodeAndDecode(bytes)
+}
 
+func runTests() -> Bool {
+    var tests: [Bool] = [
+        testEmpty(),
+        testOneByteWithLowValue(),
+        testOneByteWithHighValue(),
+        testSimpleCases(),
+        testBufferWithoutSpans(),
+        testBufferWithSpans(4),
+        testBufferWithSpans(63),
+        testBufferWithSpans(64),
+        testBufferWithSpans(65),
+        testBufferWithSpans(66),
+        testBufferWithSpans(80)
+    ]
+    for _ in 0..<10 {
+        let result = testRandomByte()
+        tests.append(result)
+    }
+    var result = true
+    for bool in tests {
+        result = result && bool
+    }
+    
+    return result
+}
 
-let originalString = "aaaaabbbcdeeeeeeef"
-let utf8 = originalString.dataUsingEncoding(NSUTF8StringEncoding)!
-let compressed = utf8.compressRLE()
-
-let decompressed = compressed.decompressRLE()
-let restoredString = String(data: decompressed, encoding: NSUTF8StringEncoding)
-originalString == restoredString
+runTests()
\ No newline at end of file
diff --git a/Run-Length Encoding/RLE.playground/Sources/RLE.swift b/Run-Length Encoding/RLE.playground/Sources/RLE.swift
new file mode 100644
index 000000000..5707e3d9d
--- /dev/null
+++ b/Run-Length Encoding/RLE.playground/Sources/RLE.swift	
@@ -0,0 +1,68 @@
+import Foundation
+
+extension Data {
+    /*
+     Compresses the NSData using run-length encoding.
+     */
+    public func compressRLE() -> Data {
+        var data = Data()
+        self.withUnsafeBytes { (uPtr: UnsafePointer<UInt8>) in
+            var ptr = uPtr
+            let end = ptr + count
+            while ptr < end {
+                var count = 0
+                var byte = ptr.pointee
+                var next = byte
+                
+                // Is the next byte the same? Keep reading until we find a different
+                // value, or we reach the end of the data, or the run is 64 bytes.
+                while next == byte && ptr < end && count < 64 {
+                    ptr = ptr.advanced(by: 1)
+                    next = ptr.pointee
+                    count += 1
+                }
+                
+                if count > 1 || byte >= 192 {       // byte run of up to 64 repeats
+                    var size = 191 + UInt8(count)
+                    data.append(&size, count: 1)
+                    data.append(&byte, count: 1)
+                } else {                            // single byte between 0 and 192
+                    data.append(&byte, count: 1)
+                }
+            }
+        }
+        return data
+    }
+    
+    /*
+     Converts a run-length encoded NSData back to the original.
+     */
+    public func decompressRLE() -> Data {
+        var data = Data()
+        self.withUnsafeBytes { (uPtr: UnsafePointer<UInt8>) in
+            var ptr = uPtr
+            let end = ptr + count
+            
+            while ptr < end {
+                // Read the next byte. This is either a single value less than 192,
+                // or the start of a byte run.
+                var byte = ptr.pointee
+                ptr = ptr.advanced(by: 1)
+                
+                if byte < 192 {                     // single value
+                    data.append(&byte, count: 1)
+                } else if ptr < end {               // byte run
+                    // Read the actual data value.
+                    var value = ptr.pointee
+                    ptr = ptr.advanced(by: 1)
+                    
+                    // And write it out repeatedly.
+                    for _ in 0 ..< byte - 191 {
+                        data.append(&value, count: 1)
+                    }
+                }
+            }
+        }
+        return data
+    }
+}
diff --git a/Run-Length Encoding/RLE.swift b/Run-Length Encoding/RLE.swift
deleted file mode 100644
index b62c59c63..000000000
--- a/Run-Length Encoding/RLE.swift	
+++ /dev/null
@@ -1,70 +0,0 @@
-import Foundation
-
-extension NSData {
-  /*
-    Compresses the NSData using run-length encoding.
-  */
-  public func compressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
-
-      while ptr < end {
-        var count = 0
-        var byte = ptr.memory
-        var next = byte
-
-        // Is the next byte the same? Keep reading until we find a different
-        // value, or we reach the end of the data, or the run is 64 bytes.
-        while next == byte && ptr < end && count < 64 {
-          ptr = ptr.advancedBy(1)
-          next = ptr.memory
-          count += 1
-        }
-
-        if count > 1 || byte >= 192 {         // byte run of up to 64 repeats
-          var size = 191 + UInt8(count)
-          data.appendBytes(&size, length: 1)
-          data.appendBytes(&byte, length: 1)
-        } else {                              // single byte between 0 and 192
-          data.appendBytes(&byte, length: 1)
-        }
-      }
-    }
-    return data
-  }
-
-  /*
-    Converts a run-length encoded NSData back to the original.
-  */
-  public func decompressRLE() -> NSData {
-    let data = NSMutableData()
-    if length > 0 {
-      var ptr = UnsafePointer<UInt8>(bytes)
-      let end = ptr + length
-
-      while ptr < end {
-        // Read the next byte. This is either a single value less than 192,
-        // or the start of a byte run.
-        var byte = ptr.memory
-        ptr = ptr.advancedBy(1)
-
-        if byte < 192 {                       // single value
-          data.appendBytes(&byte, length: 1)
-
-        } else if ptr < end {                 // byte run
-          // Read the actual data value.
-          var value = ptr.memory
-          ptr = ptr.advancedBy(1)
-
-          // And write it out repeatedly.
-          for _ in 0 ..< byte - 191 {
-            data.appendBytes(&value, length: 1)
-          }
-        }
-      }
-    }
-    return data
-  }
-}
diff --git a/Run-Length Encoding/Tests/Info.plist b/Run-Length Encoding/Tests/Info.plist
deleted file mode 100644
index ba72822e8..000000000
--- a/Run-Length Encoding/Tests/Info.plist	
+++ /dev/null
@@ -1,24 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>CFBundleDevelopmentRegion</key>
-	<string>en</string>
-	<key>CFBundleExecutable</key>
-	<string>$(EXECUTABLE_NAME)</string>
-	<key>CFBundleIdentifier</key>
-	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
-	<key>CFBundleInfoDictionaryVersion</key>
-	<string>6.0</string>
-	<key>CFBundleName</key>
-	<string>$(PRODUCT_NAME)</string>
-	<key>CFBundlePackageType</key>
-	<string>BNDL</string>
-	<key>CFBundleShortVersionString</key>
-	<string>1.0</string>
-	<key>CFBundleSignature</key>
-	<string>????</string>
-	<key>CFBundleVersion</key>
-	<string>1</string>
-</dict>
-</plist>
diff --git a/Run-Length Encoding/Tests/RLETests.swift b/Run-Length Encoding/Tests/RLETests.swift
deleted file mode 100644
index f4b2f8d7d..000000000
--- a/Run-Length Encoding/Tests/RLETests.swift	
+++ /dev/null
@@ -1,110 +0,0 @@
-import XCTest
-
-class RLETests: XCTestCase {
-  private var showExtraOutput = false
-
-  private func dumpData(data: NSData) {
-    if showExtraOutput {
-      var ptr = UnsafePointer<UInt8>(data.bytes)
-      for _ in 0..<data.length {
-        print(String(format: "%02x", ptr.memory))
-        ptr = ptr.advancedBy(1)
-      }
-    }
-  }
-
-  private func encodeAndDecode(bytes: [UInt8]) {
-    var bytes = bytes
-
-    let data1 = NSMutableData(bytes: &bytes, length: bytes.count)
-    print("data1 is \(data1.length) bytes")
-    dumpData(data1)
-
-    let rleData = data1.compressRLE()
-    print("encoded data is \(rleData.length) bytes")
-    dumpData(rleData)
-
-    let data2 = rleData.decompressRLE()
-    print("data2 is \(data2.length) bytes")
-    dumpData(data2)
-
-    XCTAssertEqual(data1, data2)
-    print("")
-  }
-
-  func testEmpty() {
-    let bytes: [UInt8] = []
-    encodeAndDecode(bytes)
-  }
-
-  func testOneByteWithLowValue() {
-    let bytes: [UInt8] = [ 0x80 ]
-    encodeAndDecode(bytes)
-  }
-
-  func testOneByteWithHighValue() {
-    let bytes: [UInt8] = [ 0xD0 ]
-    encodeAndDecode(bytes)
-  }
-
-  func testSimpleCases() {
-    let bytes: [UInt8] = [
-      0x00,
-      0x20, 0x20, 0x20, 0x20, 0x20,
-      0x30,
-      0x00, 0x00,
-      0xC0,
-      0xC1,
-      0xC0, 0xC0, 0xC0,
-      0xFF, 0xFF, 0xFF, 0xFF
-    ]
-    encodeAndDecode(bytes)
-  }
-
-  func testBufferWithoutSpans() {
-    // There is nothing that can be encoded in this buffer, so the encoded
-    // data ends up being longer.
-
-    var bytes: [UInt8] = []
-    for i in 0..<1024 {
-      bytes.append(UInt8(i % 256))
-    }
-    encodeAndDecode(bytes)
-  }
-
-  func bufferWithSpans(spanSize: Int) {
-    if showExtraOutput {
-      print("span size \(spanSize)")
-    }
-
-    let length = spanSize * 32
-    var bytes: [UInt8] = .init(count: length, repeatedValue: 0)
-
-    for t in 0.stride(to: length, by: spanSize) {
-      for i in 0..<spanSize {
-        bytes[t + i] = UInt8(t % 256)
-      }
-    }
-    encodeAndDecode(bytes)
-  }
-
-  func testBufferWithSpans() {
-    bufferWithSpans(4)
-    bufferWithSpans(63)
-    bufferWithSpans(64)
-    bufferWithSpans(65)
-    bufferWithSpans(66)
-    bufferWithSpans(80)
-  }
-
-  func testRandomBytes() {
-    for _ in 0..<10 {
-      let length = 1 + Int(arc4random_uniform(2048))
-      var bytes: [UInt8] = []
-      for _ in 0..<length {
-        bytes.append(UInt8(arc4random() % 256))
-      }
-      encodeAndDecode(bytes)
-    }
-  }
-}
diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj b/Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj
deleted file mode 100644
index aae67b064..000000000
--- a/Run-Length Encoding/Tests/Tests.xcodeproj/project.pbxproj	
+++ /dev/null
@@ -1,261 +0,0 @@
-// !$*UTF8*$!
-{
-	archiveVersion = 1;
-	classes = {
-	};
-	objectVersion = 46;
-	objects = {
-
-/* Begin PBXBuildFile section */
-		7B80C4181C77A7F3003CECC7 /* RLE.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4171C77A7F3003CECC7 /* RLE.swift */; };
-		7B80C41A1C77A7FA003CECC7 /* RLETests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C4191C77A7FA003CECC7 /* RLETests.swift */; };
-/* End PBXBuildFile section */
-
-/* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
-		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
-		7B80C4171C77A7F3003CECC7 /* RLE.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = RLE.swift; path = ../RLE.swift; sourceTree = SOURCE_ROOT; };
-		7B80C4191C77A7FA003CECC7 /* RLETests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = RLETests.swift; sourceTree = SOURCE_ROOT; };
-/* End PBXFileReference section */
-
-/* Begin PBXFrameworksBuildPhase section */
-		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
-			isa = PBXFrameworksBuildPhase;
-			buildActionMask = 2147483647;
-			files = (
-			);
-			runOnlyForDeploymentPostprocessing = 0;
-		};
-/* End PBXFrameworksBuildPhase section */
-
-/* Begin PBXGroup section */
-		7B2BBC681C779D710067B71D = {
-			isa = PBXGroup;
-			children = (
-				7B2BBC831C779D720067B71D /* Tests */,
-				7B2BBC721C779D710067B71D /* Products */,
-			);
-			sourceTree = "<group>";
-		};
-		7B2BBC721C779D710067B71D /* Products */ = {
-			isa = PBXGroup;
-			children = (
-				7B2BBC801C779D720067B71D /* Tests.xctest */,
-			);
-			name = Products;
-			sourceTree = "<group>";
-		};
-		7B2BBC831C779D720067B71D /* Tests */ = {
-			isa = PBXGroup;
-			children = (
-				7B80C4171C77A7F3003CECC7 /* RLE.swift */,
-				7B80C4191C77A7FA003CECC7 /* RLETests.swift */,
-				7B2BBC941C779E7B0067B71D /* Info.plist */,
-			);
-			name = Tests;
-			path = TestsTests;
-			sourceTree = "<group>";
-		};
-/* End PBXGroup section */
-
-/* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* Tests */ = {
-			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
-			buildPhases = (
-				7B2BBC7C1C779D720067B71D /* Sources */,
-				7B2BBC7D1C779D720067B71D /* Frameworks */,
-				7B2BBC7E1C779D720067B71D /* Resources */,
-			);
-			buildRules = (
-			);
-			dependencies = (
-			);
-			name = Tests;
-			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
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-				7B2BBC881C779D720067B71D /* Release */,
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-		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
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-				7B2BBC8E1C779D720067B71D /* Release */,
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-		};
-/* End XCConfigurationList section */
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diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 6c0ea8493..000000000
--- a/Run-Length Encoding/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:Tests.xcodeproj">
-   </FileRef>
-</Workspace>
diff --git a/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
deleted file mode 100644
index 8ef8d8581..000000000
--- a/Run-Length Encoding/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ /dev/null
@@ -1,90 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Scheme
-   LastUpgradeVersion = "0720"
-   version = "1.3">
-   <BuildAction
-      parallelizeBuildables = "YES"
-      buildImplicitDependencies = "YES">
-      <BuildActionEntries>
-         <BuildActionEntry
-            buildForTesting = "YES"
-            buildForRunning = "YES"
-            buildForProfiling = "NO"
-            buildForArchiving = "NO"
-            buildForAnalyzing = "NO">
-            <BuildableReference
-               BuildableIdentifier = "primary"
-               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
-            </BuildableReference>
-         </BuildActionEntry>
-      </BuildActionEntries>
-   </BuildAction>
-   <TestAction
-      buildConfiguration = "Debug"
-      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
-      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      shouldUseLaunchSchemeArgsEnv = "YES">
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From 2accb9907f434968e8806afe5637eeab69d4a0a9 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Sat, 28 Jan 2017 01:39:29 +0100
Subject: [PATCH 0792/1679] Migrate Shunting Yard to Swift 3

---
 Shunting Yard/README.markdown                 |   5 +-
 .../ShuntingYard.playground/Contents.swift    |  38 +-
 .../Sources/Stack.swift                       |  32 +-
 Shunting Yard/ShuntingYard.swift              | 364 +++++++++---------
 4 files changed, 218 insertions(+), 221 deletions(-)

diff --git a/Shunting Yard/README.markdown b/Shunting Yard/README.markdown
index d2e568d39..72df4d346 100644
--- a/Shunting Yard/README.markdown	
+++ b/Shunting Yard/README.markdown	
@@ -6,7 +6,7 @@ Any mathematics we write is expressed in a notation known as *infix notation*. F
 
 The operator is placed in between the operands, hence the expression is said to be in *infix* form. If you think about it, any expression that you write on a piece of paper will always be in infix form. This is what we humans understand.
 
-Multiplication has higher precedence than addition, so when the above expression is evaluated you would first multiply **B** and **C**, and then add the result to **A**. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator. 
+Multiplication has higher precedence than addition, so when the above expression is evaluated you would first multiply **B** and **C**, and then add the result to **A**. We humans can easily understand the precedence of operators, but a machine needs to be given instructions about each operator.
 
 To change the order of evaluation, we can use parentheses:
 
@@ -108,4 +108,5 @@ We end up with the postfix expression:
 
 [Shunting yard algorithm on Wikipedia](https://en.wikipedia.org/wiki/Shunting-yard_algorithm)
 
-*Written for the Swift Algorithm Club by [Ali Hafizji](http://www.github.com/aliHafizji)*
\ No newline at end of file
+*Written for the Swift Algorithm Club by [Ali Hafizji](http://www.github.com/aliHafizji)*
+*Migrated to Swift 3 by Jaap Wijnen*
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index 707e2a0a3..b341c673b 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -15,17 +15,17 @@ public enum OperatorType: CustomStringConvertible {
 
   public var description: String {
     switch self {
-      case add:
+      case .add:
         return "+"
-      case subtract:
+      case .subtract:
         return "-"
-      case divide:
+      case .divide:
         return "/"
-      case multiply:
+      case .multiply:
         return "*"
-      case percent:
+      case .percent:
         return "%"
-      case exponent:
+      case .exponent:
         return "^"
     }
   }
@@ -39,13 +39,13 @@ public enum TokenType: CustomStringConvertible {
 
   public var description: String {
     switch self {
-      case openBracket:
+      case .openBracket:
         return "("
-      case closeBracket:
+      case .closeBracket:
         return ")"
-      case Operator(let operatorToken):
+      case .Operator(let operatorToken):
         return operatorToken.description
-      case operand(let value):
+      case .operand(let value):
         return "\(value)"
     }
   }
@@ -141,23 +141,23 @@ public struct Token: CustomStringConvertible {
 public class InfixExpressionBuilder {
   private var expression = [Token]()
 
-  public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
+  public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
 
-  public func addOperand(operand: Double) -> InfixExpressionBuilder {
+  public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
 
   public func addOpenBracket() -> InfixExpressionBuilder {
-    expression.append(Token(tokenType: .OpenBracket))
+    expression.append(Token(tokenType: .openBracket))
     return self
   }
 
   public func addCloseBracket() -> InfixExpressionBuilder {
-    expression.append(Token(tokenType: .CloseBracket))
+    expression.append(Token(tokenType: .closeBracket))
     return self
   }
 
@@ -168,7 +168,7 @@ public class InfixExpressionBuilder {
 }
 
 // This returns the result of the shunting yard algorithm
-public func reversePolishNotation(expression: [Token]) -> String {
+public func reversePolishNotation(_ expression: [Token]) -> String {
 
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
@@ -187,14 +187,14 @@ public func reversePolishNotation(expression: [Token]) -> String {
         }
 
       case .Operator(let operatorToken):
-        for tempToken in tokenStack.generate() {
+        for tempToken in tokenStack.makeIterator() {
           if !tempToken.isOperator {
             break
           }
 
           if let tempOperatorToken = tempToken.operatorToken {
-            if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
-                || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
+            if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
+                || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
               reversePolishNotation.append(tokenStack.pop()!)
             } else {
               break
@@ -209,7 +209,7 @@ public func reversePolishNotation(expression: [Token]) -> String {
     reversePolishNotation.append(tokenStack.pop()!)
   }
 
-  return reversePolishNotation.map({token in token.description}).joinWithSeparator(" ")
+  return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
 
 
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index 0df342af5..a67bb9d64 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -1,41 +1,37 @@
 import Foundation
 
 public struct Stack<T> {
-    private var array = [T]()
-
+    fileprivate var array = [T]()
+    
     public init() {
-        array = []
+        
     }
-
+    
     public var isEmpty: Bool {
         return array.isEmpty
     }
-
+    
     public var count: Int {
         return array.count
     }
-
-    public mutating func push(element: T) {
+    
+    public mutating func push(_ element: T) {
         array.append(element)
     }
-
+    
     public mutating func pop() -> T? {
-        if isEmpty {
-            return nil
-        } else {
-            return array.removeLast()
-        }
+        return array.popLast()
     }
-
-    public func peek() -> T? {
+    
+    public var top: T? {
         return array.last
     }
 }
 
-extension Stack: SequenceType {
-    public func generate() -> AnyGenerator<T> {
+extension Stack: Sequence {
+    public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return anyGenerator {
+        return AnyIterator {
             _ -> T? in
             return curr.pop()
         }
diff --git a/Shunting Yard/ShuntingYard.swift b/Shunting Yard/ShuntingYard.swift
index 9d31d5a58..b8f5f8e6b 100644
--- a/Shunting Yard/ShuntingYard.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -7,213 +7,213 @@
 //
 
 internal enum OperatorAssociativity {
-  case leftAssociative
-  case rightAssociative
+    case leftAssociative
+    case rightAssociative
 }
 
 public enum OperatorType: CustomStringConvertible {
-  case add
-  case subtract
-  case divide
-  case multiply
-  case percent
-  case exponent
-
-  public var description: String {
-    switch self {
-      case add:
-        return "+"
-      case subtract:
-        return "-"
-      case divide:
-        return "/"
-      case multiply:
-        return "*"
-      case percent:
-        return "%"
-      case exponent:
-        return "^"
-    }
-  }
+    case add
+    case subtract
+    case divide
+    case multiply
+    case percent
+    case exponent
+    
+    public var description: String {
+        switch self {
+        case .add:
+            return "+"
+        case .subtract:
+            return "-"
+        case .divide:
+            return "/"
+        case .multiply:
+            return "*"
+        case .percent:
+            return "%"
+        case .exponent:
+            return "^"
+        }
+    }
 }
 
 public enum TokenType: CustomStringConvertible {
-  case openBracket
-  case closeBracket
-  case Operator(OperatorToken)
-  case operand(Double)
-
-  public var description: String {
-    switch self {
-      case openBracket:
-        return "("
-      case closeBracket:
-        return ")"
-      case Operator(let operatorToken):
-        return operatorToken.description
-      case operand(let value):
-        return "\(value)"
-    }
-  }
+    case openBracket
+    case closeBracket
+    case Operator(OperatorToken)
+    case operand(Double)
+    
+    public var description: String {
+        switch self {
+        case .openBracket:
+            return "("
+        case .closeBracket:
+            return ")"
+        case .Operator(let operatorToken):
+            return operatorToken.description
+        case .operand(let value):
+            return "\(value)"
+        }
+    }
 }
 
 public struct OperatorToken: CustomStringConvertible {
-  let operatorType: OperatorType
-
-  init(operatorType: OperatorType) {
-    self.operatorType = operatorType
-  }
-
-  var precedence: Int {
-    switch operatorType {
-      case .add, .subtract:
-        return 0
-      case .divide, .multiply, .percent:
-        return 5
-      case .exponent:
-        return 10
-    }
-  }
-
-  var associativity: OperatorAssociativity {
-    switch operatorType {
-      case .add, .subtract, .divide, .multiply, .percent:
-        return .LeftAssociative
-      case .exponent:
-        return .RightAssociative
-    }
-  }
-
-  public var description: String {
-    return operatorType.description
-  }
+    let operatorType: OperatorType
+    
+    init(operatorType: OperatorType) {
+        self.operatorType = operatorType
+    }
+    
+    var precedence: Int {
+        switch operatorType {
+        case .add, .subtract:
+            return 0
+        case .divide, .multiply, .percent:
+            return 5
+        case .exponent:
+            return 10
+        }
+    }
+    
+    var associativity: OperatorAssociativity {
+        switch operatorType {
+        case .add, .subtract, .divide, .multiply, .percent:
+            return .leftAssociative
+        case .exponent:
+            return .rightAssociative
+        }
+    }
+    
+    public var description: String {
+        return operatorType.description
+    }
 }
 
 func <= (left: OperatorToken, right: OperatorToken) -> Bool {
-  return left.precedence <= right.precedence
+    return left.precedence <= right.precedence
 }
 
 func < (left: OperatorToken, right: OperatorToken) -> Bool {
-  return left.precedence < right.precedence
+    return left.precedence < right.precedence
 }
 
 public struct Token: CustomStringConvertible {
-  let tokenType: TokenType
-
-  init(tokenType: TokenType) {
-    self.tokenType = tokenType
-  }
-
-  init(operand: Double) {
-    tokenType = .operand(operand)
-  }
-
-  init(operatorType: OperatorType) {
-    tokenType = .Operator(OperatorToken(operatorType: operatorType))
-  }
-
-  var isOpenBracket: Bool {
-    switch tokenType {
-      case .openBracket:
-        return true
-      default:
-        return false
-    }
-  }
-
-  var isOperator: Bool {
-    switch tokenType {
-      case .Operator(_):
-        return true
-      default:
-        return false
-    }
-  }
-
-  var operatorToken: OperatorToken? {
-    switch tokenType {
-      case .Operator(let operatorToken):
-        return operatorToken
-      default:
-        return nil
-    }
-  }
-
-  public var description: String {
-    return tokenType.description
-  }
+    let tokenType: TokenType
+    
+    init(tokenType: TokenType) {
+        self.tokenType = tokenType
+    }
+    
+    init(operand: Double) {
+        tokenType = .operand(operand)
+    }
+    
+    init(operatorType: OperatorType) {
+        tokenType = .Operator(OperatorToken(operatorType: operatorType))
+    }
+    
+    var isOpenBracket: Bool {
+        switch tokenType {
+        case .openBracket:
+            return true
+        default:
+            return false
+        }
+    }
+    
+    var isOperator: Bool {
+        switch tokenType {
+        case .Operator(_):
+            return true
+        default:
+            return false
+        }
+    }
+    
+    var operatorToken: OperatorToken? {
+        switch tokenType {
+        case .Operator(let operatorToken):
+            return operatorToken
+        default:
+            return nil
+        }
+    }
+    
+    public var description: String {
+        return tokenType.description
+    }
 }
 
 public class InfixExpressionBuilder {
-  private var expression = [Token]()
-
-  public func addOperator(operatorType: OperatorType) -> InfixExpressionBuilder {
-    expression.append(Token(operatorType: operatorType))
-    return self
-  }
-
-  public func addOperand(operand: Double) -> InfixExpressionBuilder {
-    expression.append(Token(operand: operand))
-    return self
-  }
-
-  public func addOpenBracket() -> InfixExpressionBuilder {
-    expression.append(Token(tokenType: .OpenBracket))
-    return self
-  }
-
-  public func addCloseBracket() -> InfixExpressionBuilder {
-    expression.append(Token(tokenType: .CloseBracket))
-    return self
-  }
-
-  public func build() -> [Token] {
-    // Maybe do some validation here
-    return expression
-  }
+    private var expression = [Token]()
+    
+    public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
+        expression.append(Token(operatorType: operatorType))
+        return self
+    }
+    
+    public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
+        expression.append(Token(operand: operand))
+        return self
+    }
+    
+    public func addOpenBracket() -> InfixExpressionBuilder {
+        expression.append(Token(tokenType: .openBracket))
+        return self
+    }
+    
+    public func addCloseBracket() -> InfixExpressionBuilder {
+        expression.append(Token(tokenType: .closeBracket))
+        return self
+    }
+    
+    public func build() -> [Token] {
+        // Maybe do some validation here
+        return expression
+    }
 }
 
 // This returns the result of the shunting yard algorithm
-public func reversePolishNotation(expression: [Token]) -> String {
-
-  var tokenStack = Stack<Token>()
-  var reversePolishNotation = [Token]()
-
-  for token in expression {
-    switch token.tokenType {
-      case .operand(_):
-        reversePolishNotation.append(token)
-
-      case .openBracket:
-        tokenStack.push(token)
-
-      case .closeBracket:
-        while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
-          reversePolishNotation.append(tempToken)
-        }
-
-      case .Operator(let operatorToken):
-        for tempToken in tokenStack.generate() {
-          if !tempToken.isOperator {
-            break
-          }
-
-          if let tempOperatorToken = tempToken.operatorToken {
-            if operatorToken.associativity == .LeftAssociative && operatorToken <= tempOperatorToken
-                || operatorToken.associativity == .RightAssociative && operatorToken < tempOperatorToken {
-              reversePolishNotation.append(tokenStack.pop()!)
-            } else {
-              break
+public func reversePolishNotation(_ expression: [Token]) -> String {
+    
+    var tokenStack = Stack<Token>()
+    var reversePolishNotation = [Token]()
+    
+    for token in expression {
+        switch token.tokenType {
+        case .operand(_):
+            reversePolishNotation.append(token)
+            
+        case .openBracket:
+            tokenStack.push(token)
+            
+        case .closeBracket:
+            while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
+                reversePolishNotation.append(tempToken)
+            }
+            
+        case .Operator(let operatorToken):
+            for tempToken in tokenStack.makeIterator() {
+                if !tempToken.isOperator {
+                    break
+                }
+                
+                if let tempOperatorToken = tempToken.operatorToken {
+                    if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
+                        || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
+                        reversePolishNotation.append(tokenStack.pop()!)
+                    } else {
+                        break
+                    }
+                }
             }
-          }
+            tokenStack.push(token)
         }
-        tokenStack.push(token)
     }
-  }
-
-  while tokenStack.count > 0 {
-    reversePolishNotation.append(tokenStack.pop()!)
-  }
-
-  return reversePolishNotation.map({token in token.description}).joinWithSeparator(" ")
+    
+    while tokenStack.count > 0 {
+        reversePolishNotation.append(tokenStack.pop()!)
+    }
+    
+    return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }

From 9d5c990ea69bd6f0fce8747630358a8391be48c5 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Sat, 28 Jan 2017 01:55:24 +0100
Subject: [PATCH 0793/1679] Set Cover migrated to swift 3

---
 Set Cover (Unweighted)/README.markdown                        | 3 ++-
 .../SetCover.playground/Sources/RandomArrayOfSets.swift       | 2 +-
 .../SetCover.playground/Sources/SetCover.swift                | 4 ++--
 3 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/Set Cover (Unweighted)/README.markdown b/Set Cover (Unweighted)/README.markdown
index fde032438..0b4ddfefe 100644
--- a/Set Cover (Unweighted)/README.markdown	
+++ b/Set Cover (Unweighted)/README.markdown	
@@ -30,4 +30,5 @@ If there is no cover within the group of sets, `cover` returns `nil`.
 
 [Set cover problem on Wikipedia](https://en.wikipedia.org/wiki/Set_cover_problem)
 
-*Written for Swift Algorithm Club by [Michael C. Rael](https://github.com/mrael2)*
\ No newline at end of file
+*Written for Swift Algorithm Club by [Michael C. Rael](https://github.com/mrael2)*
+*Migrated to Swift 3 by Jaap Wijnen*
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift
index b64d8d70e..9454c6383 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
@@ -18,7 +18,7 @@ public func randomArrayOfSets<T>(covering universe: Set<T>,
 
     while true {
       let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
-      for (setIndex, value) in universe.enumerate() {
+      for (setIndex, value) in universe.enumerated() {
         if setIndex == randomUniverseIndex {
           generatedSet.insert(value)
           break
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift
index 8d40e1fda..043cf46a0 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/SetCover.swift	
@@ -8,7 +8,7 @@ public extension Set {
       var largestSet: Set<Element>?
 
       for set in array {
-        let intersectionLength = remainingSet.intersect(set).count
+        let intersectionLength = remainingSet.intersection(set).count
         if intersectionLength > largestIntersectionLength {
           largestIntersectionLength = intersectionLength
           largestSet = set
@@ -21,7 +21,7 @@ public extension Set {
     while !remainingSet.isEmpty {
       guard let largestSet = largestIntersectingSet() else { break }
       result!.append(largestSet)
-      remainingSet = remainingSet.subtract(largestSet)
+      remainingSet = remainingSet.subtracting(largestSet)
     }
 
     if !remainingSet.isEmpty || isEmpty {

From 83dea87c62a44e8d180811e4d1b5c9da211dddeb Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sat, 28 Jan 2017 19:29:21 +0100
Subject: [PATCH 0794/1679] Splay Tree Initial Commit

---
 Splay Tree/readme.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Splay Tree/readme.md

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
new file mode 100644
index 000000000..2282502fa
--- /dev/null
+++ b/Splay Tree/readme.md	
@@ -0,0 +1 @@
+In progress

From dcd1a0a877d72a5285b56401866ea9a9a97e8017 Mon Sep 17 00:00:00 2001
From: Bo Qian <boqian@bos-2nd-macbook-pro.local>
Date: Sat, 28 Jan 2017 18:11:26 -0800
Subject: [PATCH 0795/1679] Updated README.markdown for the new implementation
 of insert and remove.  Added a remove example in BinarySearchTree.playground.

---
 .../Images/DeleteTwoChildren.graffle          | Bin 2912 -> 11233 bytes
 .../Images/DeleteTwoChildren.png              | Bin 13760 -> 33187 bytes
 Binary Search Tree/README.markdown            | 132 ++++--------------
 .../Contents.swift                            |   3 +-
 4 files changed, 31 insertions(+), 104 deletions(-)

diff --git a/Binary Search Tree/Images/DeleteTwoChildren.graffle b/Binary Search Tree/Images/DeleteTwoChildren.graffle
index a03748077e6c23fec83e473e86fd9d71ef5fe97e..a6a09877a55b170f3d9f0938099d6841e93f1af7 100644
GIT binary patch
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diff --git a/Binary Search Tree/Images/DeleteTwoChildren.png b/Binary Search Tree/Images/DeleteTwoChildren.png
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diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index bacb1ffe1..e8d2f58e2 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -69,21 +69,14 @@ If you traverse a binary search tree in-order, it looks at all the nodes as if t
 
 ## Deleting nodes
 
-Removing nodes is kinda tricky. It is easy to remove a leaf node, you just disconnect it from its parent:
-
-![Deleting a leaf node](Images/DeleteLeaf.png)
-
-If the node to remove has only one child, we can link that child to the parent node. So we just pull the node out:
-
-![Deleting a node with one child](Images/DeleteOneChild.png)
-
-The gnarly part is when the node to remove has two children. To keep the tree properly sorted, we must replace this node by the smallest child that is larger than the node:
+Removing nodes is also easy. After removing a node, we replace the node with either its biggest child on the left or its smallest child on the right. That way the tree is still sorted after the removal. In following example, 10 is removed and replaced with either 9 (Figure 2), or 11 (Figure 3).
 
 ![Deleting a node with two children](Images/DeleteTwoChildren.png)
 
-This is always the leftmost descendant in the right subtree. It requires an additional search of at most **O(h)** to find this child.
+Note the replacement needs to happen when the node has at least one child. If it has no child, you just disconnect it from its parent:
+
+![Deleting a leaf node](Images/DeleteLeaf.png)
 
-Most of the other code involving binary search trees is fairly straightforward (if you understand recursion) but deleting nodes is a bit of a headscratcher.
 
 ## The code (solution 1)
 
@@ -158,23 +151,19 @@ A tree node by itself is pretty useless, so here is how you would add new nodes
 
 ```swift
   public func insert(value: T) {
-    insert(value, parent: self)
-  }
-  
-  private func insert(value: T, parent: BinarySearchTree) {
     if value < self.value {
       if let left = left {
-        left.insert(value, parent: left)
+        left.insert(value: value)
       } else {
         left = BinarySearchTree(value: value)
-        left?.parent = parent
+        left?.parent = self
       }
     } else {
       if let right = right {
-        right.insert(value, parent: right)
+        right.insert(value: value)
       } else {
         right = BinarySearchTree(value: value)
-        right?.parent = parent
+        right?.parent = self
       }
     }
   }
@@ -379,7 +368,7 @@ As an exercise for yourself, see if you can implement filter and reduce.
  
 ### Deleting nodes
 
-You've seen that deleting nodes can be tricky. We can make the code much more readable by defining some helper functions.
+We can make the code much more readable by defining some helper functions.
 
 ```swift
   private func reconnectParentToNode(node: BinarySearchTree?) {
@@ -396,7 +385,7 @@ You've seen that deleting nodes can be tricky. We can make the code much more re
 
 Making changes to the tree involves changing a bunch of `parent` and `left` and `right` pointers. This function helps with that. It takes the parent of the current node -- that is `self` -- and connects it to another node. Usually that other node will be one of the children of `self`.
 
-We also need a function that returns the leftmost descendent of a node:
+We also need a function that returns the minimum and maximum of a node:
 
 ```swift
   public func minimum() -> BinarySearchTree {
@@ -406,17 +395,7 @@ We also need a function that returns the leftmost descendent of a node:
     }
     return node
   }
-```
-
-To see how this works, take the following tree:
-
-![Example](Images/MinimumMaximum.png)
-
-For example, if we look at node `10`, its leftmost descendent is `7`. We get there by following all the `left` pointers until there are no more left children to look at. The leftmost descendent of the root node `6` is `1`. Therefore, `1` is the minimum value in the entire tree.
-
-We won't need it for deleting, but for completeness' sake, here is the opposite of `minimum()`:
-
-```swift
+  
   public func maximum() -> BinarySearchTree {
     var node = self
     while case let next? = node.right {
@@ -424,94 +403,41 @@ We won't need it for deleting, but for completeness' sake, here is the opposite
     }
     return node
   }
-```
 
-It returns the rightmost descendent of the node. We find it by following `right` pointers until we get to the end. In the above example, the rightmost descendent of node `2` is `5`. The maximum value in the entire tree is `11`, because that is the rightmost descendent of the root node `6`.
+```
 
-Finally, we can write the code that removes a node from the tree:
+The rest of the code is pretty self-explanatory:
 
 ```swift
-  public func remove() -> BinarySearchTree? {
+  @discardableResult public func remove() -> BinarySearchTree? {
     let replacement: BinarySearchTree?
-
+    
+    // Replacement for current node can be either biggest one on the left or
+    // smallest one on the right, whichever is not nil
     if let left = left {
-      if let right = right {
-        replacement = removeNodeWithTwoChildren(left, right)  // 1
-      } else {
-        replacement = left           // 2
-      }
-    } else if let right = right {    // 3
-      replacement = right
+      replacement = left.maximum()
+    } else if let right = right {
+      replacement = right.minimum()
     } else {
-      replacement = nil              // 4
+      replacement = nil;
     }
     
-    reconnectParentToNode(replacement)
+    replacement?.remove();
 
+    // Place the replacement on current node's position
+    replacement?.right = right;
+    replacement?.left = left;
+    reconnectParentTo(node:replacement);
+    
+    // The current node is no longer part of the tree, so clean it up.
     parent = nil
     left = nil
     right = nil
-
-    return replacement
-  }
-```
-
-It doesn't look so scary after all. ;-) There are four situations to handle:
-
-1. This node has two children. 
-2. This node only has a left child. The left child replaces the node.
-3. This node only has a right child. The right child replaces the node.
-4. This node has no children. We just disconnect it from its parent.
-
-First, we determine which node will replace the one we're removing and then we call `reconnectParentToNode()` to change the `left`, `right`, and `parent` pointers to make that happen. Since the current node is no longer part of the tree, we clean it up by setting its pointers to `nil`. Finally, we return the node that has replaced the removed one (or `nil` if this was a leaf node).
-
-The only tricky situation here is `// 1` and that logic has its own helper method:
-
-```swift
-  private func removeNodeWithTwoChildren(left: BinarySearchTree, _ right: BinarySearchTree) -> BinarySearchTree {
-    let successor = right.minimum()
-    successor.remove()
-    
-    successor.left = left
-    left.parent = successor
-    
-    if right !== successor {
-      successor.right = right
-      right.parent = successor
-    } else {
-      successor.right = nil
-    }
     
-    return successor
+    return replacement;
   }
 ```
 
-If the node to remove has two children, it must be replaced by the smallest child that is larger than this node's value. That always happens to be the leftmost descendent of the right child, i.e. `right.minimum()`. We take that node out of its original position in the tree and put it into the place of the node we're removing.
-
-Try it out:
-
-```swift
-if let node2 = tree.search(2) {
-  print(tree)     // before
-  node2.remove()
-  print(tree)     // after
-}
-```
-
-First you find the node that you want to remove with `search()` and then you call `remove()` on that object. Before the removal, the tree printed like this:
-
-	((1) <- 2 -> (5)) <- 6 -> ((9) <- 10)
-
-But after `remove()` you get:
-
-	((1) <- 5) <- 6 -> ((9) <- 10)
-
-As you can see, node `5` has taken the place of `2`.
-
-> **Note:** What would happen if you deleted the root node? In that case, `remove()` tells you which node has become the new root. Try it out: call `tree.remove()` and see what happens.
-
-Like most binary search tree operations, removing a node runs in **O(h)** time, where **h** is the height of the tree.
-
 ### Depth and height
 
 Recall that the height of a node is the distance to its lowest leaf. We can calculate that with the following function:
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 6d73585b5..ec9902283 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -7,8 +7,9 @@ tree.insert(value: 10)
 tree.insert(value: 9)
 tree.insert(value: 1)
 
+let toDelete = tree.search(value: 1)
+toDelete?.remove()
 tree
-tree.debugDescription
 
 let tree2 = BinarySearchTree<Int>(array: [7, 2, 5, 10, 9, 1])
 

From eb54bc8544f0d482336878e211269ea43da9a7a7 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Mon, 30 Jan 2017 11:38:32 +0100
Subject: [PATCH 0796/1679] Add Simulated annealing

---
 Simulated annealing/README.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Simulated annealing/README.md

diff --git a/Simulated annealing/README.md b/Simulated annealing/README.md
new file mode 100644
index 000000000..bee8ffe94
--- /dev/null
+++ b/Simulated annealing/README.md	
@@ -0,0 +1 @@
+# Simulated annealing

From a6afbc107e25b96bdb86b9186f4a5794046b004b Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Mon, 30 Jan 2017 18:18:50 +0100
Subject: [PATCH 0797/1679] Initial

---
 Simulated annealing/README.md            |  32 ++++
 Simulated annealing/simann.swift         | 105 +++++++++++
 Simulated annealing/simann_example.swift | 222 +++++++++++++++++++++++
 3 files changed, 359 insertions(+)
 create mode 100644 Simulated annealing/simann.swift
 create mode 100644 Simulated annealing/simann_example.swift

diff --git a/Simulated annealing/README.md b/Simulated annealing/README.md
index bee8ffe94..e7fe75778 100644
--- a/Simulated annealing/README.md	
+++ b/Simulated annealing/README.md	
@@ -1 +1,33 @@
 # Simulated annealing
+
+Simulated Annealing is a nature inspired global optimization technique and a metaheuristic to approximate global maxima in a (often discrete)large search space. The name comes from the process of annealing in metallurgy where a material is heated and cooled down under controlled conditions in order to improve its strength and durabilility. The objective is to find a minimum cost solution in the search space by exploiting properties of a thermodynamic system. 
+Unlike hill climbing techniques which usually gets stuck in a local maxima ( downward moves are not allowed ), simulated annealing can escape local maxima. The interesting property of simulated annealing is that probability of allowing downward moves is high at the high temperatures and gradually reduced as it cools down. In other words, high temperature relaxes the acceptance criteria for the search space and triggers chaotic behavior of acceptance function in the algorithm (e.x initial/high temperature stages) which should make it possible to escape from local maxima and cooler temperatures narrows it and focuses on improvements.
+
+Pseucocode
+
+	Input: initial, temperature, coolingRate, acceptance
+	Output: Sbest
+	Scurrent <- CreateInitialSolution(initial)
+	Sbest <- Scurrent
+	while temperature is not minimum:
+		Snew <- FindNewSolution(Scurrent)
+		if acceptance(Energy(Scurrent), Energy(Snew), temperature) > Rand():
+			Scurrent = Snew
+		if Energy(Scurrent) < Energy(Sbest):
+			Sbest = Scurrent
+		temperature = temperature * (1-coolingRate)
+	
+Common acceptance criteria : P(accept) <- exp((e-ne)/T) where 
+	e is the current energy ( current solution ), 
+	ne is new energy ( new solution ),
+	T is current temperature.
+
+
+We use this algorithm to solve a Travelling salesman problem instance with 20 cities. The code is in `simann_example.swift`
+
+#See also
+
+[Simulated annealing on Wikipedia](https://en.wikipedia.org/wiki/Simulated_annealing) 
+[Travelling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem)
+
+Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi)
diff --git a/Simulated annealing/simann.swift b/Simulated annealing/simann.swift
new file mode 100644
index 000000000..8adfbf817
--- /dev/null
+++ b/Simulated annealing/simann.swift	
@@ -0,0 +1,105 @@
+// The MIT License (MIT)
+// Copyright (c) 2017 Mike Taghavi (mitghi[at]me.com)
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#if os(OSX)
+  import Foundation
+#elseif os(Linux)
+  import Glibc
+#endif
+
+public extension Double {  
+  public static func random(_ lower: Double, _ upper: Double) -> Double {
+    #if os(OSX)
+      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #elseif os(Linux)
+      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #endif
+  }
+}
+
+protocol Clonable {
+  init(current: Self)
+}
+
+// MARK: - create a clone from instance
+
+extension Clonable {
+  func clone() -> Self {
+    return Self.init(current: self)
+  }
+}
+
+protocol SAObject: Clonable {
+  var count: Int { get }
+  func randSwap(a: Int, b: Int)
+  func currentEnergy() -> Double
+  func shuffle()
+}
+
+// MARK: - create a new copy of elements
+
+extension Array where Element: Clonable {
+  func clone() -> Array {
+    var newArray = Array<Element>()
+    for elem in self {
+      newArray.append(elem.clone())
+    }
+    
+    return newArray
+  }
+}
+
+typealias AcceptanceFunc = (Double, Double, Double) -> Double
+
+func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRate: Double, acceptance: AcceptanceFunc) -> T {
+  // Step 1:
+  //  Calculate the initial feasible solution based on a random permutation.
+  //  Set best and current solutions to initial solution
+  
+  var temp: Double = temperature
+  var currentSolution = initial.clone()
+  currentSolution.shuffle()
+  var bestSolution = currentSolution.clone()
+
+  // Step 2:
+  //  Repeat while the system is still hot
+  //   Randomly modify the current solution by swapping its elements
+  //   Randomly decide if the new solution ( neighbor ) is acceptable and set current solution accordingly
+  //   Update the best solution *iff* it had improved ( lower energy = improvement )
+  //   Reduce temperature
+  
+  while temp > 1 {    
+    let newSolution: T = currentSolution.clone()
+    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    newSolution.randSwap(a: pos1, b: pos2)
+    let currentEnergy: Double  = currentSolution.currentEnergy()
+    let newEnergy: Double = newSolution.currentEnergy()
+    
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+      currentSolution = newSolution.clone()
+    }
+    if currentSolution.currentEnergy() < bestSolution.currentEnergy() {
+      bestSolution = currentSolution.clone()
+    }
+    
+    temp *= 1-coolingRate
+  }
+  
+  return bestSolution
+}
diff --git a/Simulated annealing/simann_example.swift b/Simulated annealing/simann_example.swift
new file mode 100644
index 000000000..a0dfaa19a
--- /dev/null
+++ b/Simulated annealing/simann_example.swift	
@@ -0,0 +1,222 @@
+// The MIT License (MIT)
+// Copyright (c) 2017 Mike Taghavi (mitghi[at]me.com)
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#if os(OSX)
+  import Foundation
+#elseif os(Linux)
+  import Glibc
+#endif
+
+public extension Double {
+  
+  public static func random(_ lower: Double, _ upper: Double) -> Double {
+    #if os(OSX)
+      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #elseif os(Linux)
+      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #endif
+  }
+}
+
+protocol Clonable {
+  init(current: Self)
+}
+
+extension Clonable {
+  func clone() -> Self {
+    return Self.init(current: self)
+  }
+}
+
+protocol SAObject: Clonable {
+  var count: Int { get }
+  func randSwap(a: Int, b: Int)
+  func currentEnergy() -> Double
+  func shuffle()
+}
+
+// MARK: - create a new copy of elements
+
+extension Array where Element: Clonable {
+  func clone() -> Array {
+    var newArray = Array<Element>()
+    for elem in self {
+      newArray.append(elem.clone())
+    }
+    
+    return newArray
+  }
+}
+
+typealias Points = [Point]
+typealias AcceptanceFunc = (Double, Double, Double) -> Double
+
+class Point: Clonable {
+  var x: Int
+  var y: Int
+  
+  init(x: Int, y: Int) {
+    self.x = x
+    self.y = y
+  }
+  
+  required init(current: Point){
+    self.x = current.x
+    self.y = current.y
+  }
+}
+
+// MARK: - string representation
+
+extension Point: CustomStringConvertible {
+  public var description: String {
+    return "Point(\(x), \(y))"
+  }
+}
+
+// MARK: - return distance between two points using operator '<->'
+
+infix operator <->: AdditionPrecedence
+extension Point {
+  static func <-> (left: Point, right: Point) -> Double {
+    let xDistance = (left.x - right.x)
+    let yDistance = (left.y - right.y)
+    
+    return Double(sqrt(Double((xDistance * xDistance) + (yDistance * yDistance))))
+  }
+}
+
+
+class Tour: SAObject {
+  var tour: Points
+  var energy: Double = 0.0
+  var count: Int {
+    get {
+      return self.tour.count
+    }
+  }
+  
+  init(points: Points){
+    self.tour = points.clone()
+  }
+  
+  required init(current: Tour) {
+    self.tour = current.tour.clone()
+  }
+}
+
+// MARK: - calculate current tour distance ( energy ).
+
+extension Tour {
+  func randSwap(a: Int, b: Int) -> Void {
+    let (cpos1, cpos2) = (self[a], self[b])
+    self[a] = cpos2
+    self[b] = cpos1
+  }
+  
+  func shuffle() {
+    for i in stride(from:  self.count - 1, through: 1, by: -1) {
+      let j = Int(arc4random()) % (i + 1)
+      if i != j {
+        swap(&self.tour[i], &self.tour[j])
+      }
+    }
+  }
+
+  func currentEnergy() -> Double {
+    if self.energy == 0 {
+      var tourEnergy: Double = 0.0
+      for i in 0..<self.count {
+        let fromCity = self[i]
+        var destCity = self[0]
+        if i+1 < self.count {
+          destCity = self[i+1]
+        }
+        let e = fromCity<->destCity
+        tourEnergy = tourEnergy + e
+        
+      }
+      self.energy = tourEnergy
+    }
+    return self.energy
+  }
+  
+}
+
+// MARK: - subscript to manipulate elements of Tour.
+
+extension Tour {
+  subscript(index: Int) -> Point {
+    get {
+      return self.tour[index]
+    }
+    set(newValue) {
+      self.tour[index] = newValue
+    }
+  }
+}
+
+func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRate: Double, acceptance: AcceptanceFunc) -> T {
+  var temp: Double = temperature
+  var currentSolution = initial.clone()
+  currentSolution.shuffle()
+  var bestSolution = currentSolution.clone()
+  print("Initial solution: ", bestSolution.currentEnergy())
+  
+  while temp > 1 {
+    let newSolution: T = currentSolution.clone()
+    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    newSolution.randSwap(a: pos1, b: pos2)
+    let currentEnergy: Double  = currentSolution.currentEnergy()
+    let newEnergy: Double = newSolution.currentEnergy()
+    
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+      currentSolution = newSolution.clone()
+    }
+    if currentSolution.currentEnergy() < bestSolution.currentEnergy() {
+      bestSolution = currentSolution.clone()
+    }
+    
+    temp *= 1-coolingRate
+  }
+  
+  print("Best solution: ", bestSolution.currentEnergy())
+  return bestSolution
+}
+
+let points: [Point] = [
+  (60 , 200), (180, 200), (80 , 180), (140, 180),
+  (20 , 160), (100, 160), (200, 160), (140, 140),
+  (40 , 120), (100, 120), (180, 100), (60 , 80) ,
+  (120, 80) , (180, 60) , (20 , 40) , (100, 40) ,
+  (200, 40) , (20 , 20) , (60 , 20) , (160, 20) ,
+  ].map{ Point(x: $0.0, y: $0.1) }
+
+let acceptance : AcceptanceFunc = {
+  (e: Double, ne: Double, te: Double) -> Double in
+  if ne < e {
+    return 1.0
+  }
+  return exp((e - ne) / te)
+}
+
+let result: Tour = SimulatedAnnealing(initial     : Tour(points: points),
+                                      temperature : 100000.0,
+                                      coolingRate : 0.003,
+                                      acceptance  : acceptance)

From a794dec1522cd0df09b96a2d8744b261b8185f2a Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 30 Jan 2017 18:23:23 +0100
Subject: [PATCH 0798/1679] Update README.md

---
 Simulated annealing/README.md | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/Simulated annealing/README.md b/Simulated annealing/README.md
index e7fe75778..3a36464d7 100644
--- a/Simulated annealing/README.md	
+++ b/Simulated annealing/README.md	
@@ -17,10 +17,12 @@ Pseucocode
 			Sbest = Scurrent
 		temperature = temperature * (1-coolingRate)
 	
-Common acceptance criteria : P(accept) <- exp((e-ne)/T) where 
-	e is the current energy ( current solution ), 
-	ne is new energy ( new solution ),
-	T is current temperature.
+Common acceptance criteria : 
+
+	P(accept) <- exp((e-ne)/T) where 
+		e is the current energy ( current solution ), 
+		ne is new energy ( new solution ),
+		T is current temperature.
 
 
 We use this algorithm to solve a Travelling salesman problem instance with 20 cities. The code is in `simann_example.swift`
@@ -28,6 +30,7 @@ We use this algorithm to solve a Travelling salesman problem instance with 20 ci
 #See also
 
 [Simulated annealing on Wikipedia](https://en.wikipedia.org/wiki/Simulated_annealing) 
+
 [Travelling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem)
 
 Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi)

From 717794dcb7cfaba84bc5f2dbbe3f316e5b7f57f7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Micha=C3=ABl=20Azevedo?= <mazevedo@prynel.com>
Date: Wed, 1 Feb 2017 16:05:06 +0100
Subject: [PATCH 0799/1679] Fixed the trimming of deques

---
 Deque/Deque-Optimized.swift |  6 ++++--
 Deque/README.markdown       | 12 ++++++++----
 2 files changed, 12 insertions(+), 6 deletions(-)

diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index 6326b457b..f565458c7 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -7,9 +7,11 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
+  private let originalCapacity:Int
 
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
+    originalCapacity = self.capacity
     array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
@@ -30,7 +32,7 @@ public struct Deque<T> {
     if head == 0 {
       capacity *= 2
       let emptySpace = [T?](repeating: nil, count: capacity)
-      array.insertContentsOf(emptySpace, at: 0)
+      array.insert(contentsOf: emptySpace, at: 0)
       head = capacity
     }
 
@@ -44,7 +46,7 @@ public struct Deque<T> {
     array[head] = nil
     head += 1
 
-    if capacity > 10 && head >= capacity*2 {
+    if capacity >= originalCapacity && head >= capacity*2 {
       let amountToRemove = capacity + capacity/2
       array.removeFirst(amountToRemove)
       head -= amountToRemove
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 5858f3e6d..d156f9d97 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -119,9 +119,11 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
+  private let originalCapacity:Int
   
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
+    originalCapacity = self.capacity
     array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
@@ -267,7 +269,7 @@ Those empty spots at the front only get used when you call `enqueueFront()`. But
     array[head] = nil
     head += 1
 
-    if capacity > 10 && head >= capacity*2 {
+    if capacity >= originalCapacity && head >= capacity*2 {
       let amountToRemove = capacity + capacity/2
       array.removeFirst(amountToRemove)
       head -= amountToRemove
@@ -279,6 +281,8 @@ Those empty spots at the front only get used when you call `enqueueFront()`. But
 
 Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off a bunch of these empty spots. We reduce it to about 25%.
 
+> **Note:**  he deque will keep at least its original capacity by comparing `capacity` to `originalCapacity`.
+
 For example, this:
 
 	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
@@ -288,9 +292,9 @@ For example, this:
 becomes after trimming:
 
 	[ x, x, x, x, x, 1, 2, 3 ]
-	              |
-	              head
-	              capacity
+	                 |
+	                 head
+	                 capacity
 
 This way we can strike a balance between fast enqueuing and dequeuing at the front and keeping the memory requirements reasonable.
 

From 096eca30aa4a686f4d0839321dd99089d63c6c5a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Micha=C3=ABl=20Azevedo?= <mazevedo@prynel.com>
Date: Wed, 1 Feb 2017 16:07:50 +0100
Subject: [PATCH 0800/1679] Typo fixed

---
 Deque/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Deque/README.markdown b/Deque/README.markdown
index d156f9d97..67a734576 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -281,7 +281,7 @@ Those empty spots at the front only get used when you call `enqueueFront()`. But
 
 Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off a bunch of these empty spots. We reduce it to about 25%.
 
-> **Note:**  he deque will keep at least its original capacity by comparing `capacity` to `originalCapacity`.
+> **Note:**  The deque will keep at least its original capacity by comparing `capacity` to `originalCapacity`.
 
 For example, this:
 

From 74bbb2105111797bad57ddc795b2b44cb494bb22 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Wed, 1 Feb 2017 19:09:34 -0800
Subject: [PATCH 0801/1679] Update README.markdown

Hello,
My name is Parvaneh. I am taking a writing course in the field of Computer Science. For an assignment, I need to edit some relevant documents and share the result. I hope you like my revisions.
---
 Merge Sort/README.markdown | 72 +++++++++++++++++++-------------------
 1 file changed, 36 insertions(+), 36 deletions(-)

diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 3ff69fdd5..05b90f166 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -2,40 +2,40 @@
 
 Goal: Sort an array from low to high (or high to low)
 
-Invented in 1945 by John von Neumann, merge sort is a fairly efficient sorting algorithm with a best, worst, and average time complexity of **O(n log n)**.
+Invented in 1945 by John von Neumann, merge-sort is an efficient algorithm with a best, worst, and average time complexity of **O(n log n)**.
 
-The idea behind merge sort is to **divide and conquer**: to divide a big problem into smaller problems and solving many small problems instead of solving a big one. I think of merge sort as **split first** and **merge after**. 
+The merge-sort algorithm uses the **divide and conquer** approach which is to divide a big problem into smaller problems and solve them. I think of the merge-sort algorithm as **split first** and **merge after**. 
 
-Assume you're given an array of *n* numbers and you need to put them in the right order. The merge sort algorithm works as follows:
+Assume you need to sort an array of *n* numbers in the right order. The merge-sort algorithm works as follows:
 
-- Put the numbers in a pile. The pile is unsorted.
-- Split the pile into 2. Now you have **two unsorted piles** of numbers.
-- Keep splitting the resulting piles until you can't split anymore. In the end, you will have *n* piles with 1 number in each pile.
-- Begin to **merge** the piles together by sequentially pairing a pile with another pile. During each merge, you put the contents in sorted order. This is fairly easy because each individual pile is already sorted.
+- Put the numbers in an unsorted pile.
+- Split the pile into two. Now, you have **two unsorted piles** of numbers.
+- Keep splitting the resulting piles until you cannot split anymore. In the end, you will have *n* piles with one number in each pile.
+- Begin to **merge** the piles together by pairing them sequentially. During each merge, put the contents in sorted order. This is fairly easy because each individual pile is already sorted.
 
 ## An example
 
 ### Splitting
 
-Let's say the numbers to sort are `[2, 1, 5, 4, 9]`. This is your unsorted pile. The goal is to keep splitting the pile until you can't split anymore. 
+Assume you are given an array of *n* numbers as`[2, 1, 5, 4, 9]`. This is an unsorted pile. The goal is to keep splitting the pile until you cannot split anymore. 
 
-First, split the array into two halves: `[2, 1]` and `[5, 4, 9]`. Can you keep splitting them? Yes you can!
+First, split the array into two halves: `[2, 1]` and `[5, 4, 9]`. Can you keep splitting them? Yes, you can!
 
-Focus on the left pile. `[2, 1]` will split into `[2]` and `[1]`. Can you keep splitting them? No. Time to check the other pile.
+Focus on the left pile. Split`[2, 1]` into `[2]` and `[1]`. Can you keep splitting them? No. Time to check the other pile.
 
-`[5, 4, 9]` splits to `[5]` and `[4, 9]`. Unsurprisingly, `[5]` can't be split anymore, but `[4, 9]` splits into `[4]` and `[9]`. 
+Split `[5, 4, 9]` into `[5]` and `[4, 9]`. Unsurprisingly, `[5]` cannot be split anymore, but `[4, 9]` can be split into `[4]` and `[9]`. 
 
 The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9]`. Notice that each pile consists of just one element.
 
 ### Merging
 
-Now that you've split the array, you'll **merge** the piles together **while sorting them**. Remember, the idea is to solve many small problems rather than a big one. For each merge iteration you'll only be concerned at merging one pile with another.
+Now that you have split the array, you should **merge** the piles together **while sorting them**. Remember, the idea is to solve many small problems rather than a big one. For each merge iteration, you must be concerned at merging one pile with another.
 
-Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1, 2]` and `[4, 5]` and `[9]`. Since `[9]` is the odd one out, you can't merge it with anything during this pass. 
+Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1, 2]` and `[4, 5]` and `[9]`. Since `[9]` is the odd one out, you cannot merge it with anything during this pass. 
 
-The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again since it's the odd one out. 
+The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again because it is the odd one out. 
 
-You're left with only two piles and `[9]` finally gets its chance to merge, resulting in the sorted array `[1, 2, 4, 5, 9]`. 
+You are left with only two piles and `[9]`, finally gets its chance to merge, resulting in the sorted array as `[1, 2, 4, 5, 9]`. 
 
 ## Top-down implementation
 
@@ -57,15 +57,15 @@ func mergeSort(_ array: [Int]) -> [Int] {
 
 A step-by-step explanation of how the code works:
 
-1. If the array is empty or only contains a single element, there's no way to split it into smaller pieces. You'll just return the array.
+1. If the array is empty or contains a single element, there is no way to split it into smaller pieces. You must just return the array.
 
 2. Find the middle index. 
 
 3. Using the middle index from the previous step, recursively split the left side of the array.
 
-4. Also recursively split the right side of the array.
+4. Also, recursively split the right side of the array.
 
-5. Finally, merge all the values together, making sure that it's always sorted.
+5. Finally, merge all the values together, making sure that it is always sorted.
 
 Here's the merging algorithm:
 
@@ -109,15 +109,15 @@ func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
 }
 ```
 
-This method may look scary but it is quite straightforward:
+This method may look scary, but it is quite straightforward:
 
 1. You need two indexes to keep track of your progress for the two arrays while merging.
 
-2. This is the merged array. It's empty right now, but you'll build it up in subsequent steps by appending elements from the other arrays.
+2. This is the merged array. It is empty right now, but you will build it up in subsequent steps by appending elements from the other arrays.
 
-3. This while loop will compare the elements from the left and right sides, and append them to the `orderedPile` while making sure that the result stays in order.
+3. This while-loop will compare the elements from the left and right sides and append them into the `orderedPile` while making sure that the result stays in order.
 
-4. If control exits from the previous while loop, it means that either `leftPile` or `rightPile` has its contents completely merged into the `orderedPile`. At this point, you no longer need to do comparisons. Just append the rest of the contents of the other array until there's no more to append.
+4. If control exits from the previous while-loop, it means that either the `leftPile` or the `rightPile` has its contents completely merged into the `orderedPile`. At this point, you no longer need to do comparisons. Just append the rest of the contents of the other array until there is no more to append.
 
 As an example of how `merge()` works, suppose that we have the following piles: `leftPile = [1, 7, 8]` and `rightPile = [3, 6, 9]`. Note that each of these piles is individually sorted already -- that is always true with merge sort. These are merged into one larger sorted pile in the following steps:
 
@@ -131,13 +131,13 @@ The left index, here represented as `l`, points at the first item from the left
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1 ]
       -->l           r
 
-Now `l` points at `7` but `r` is still at `3`. We add the smallest item to the ordered pile, so that's `3`. The situation is now:
+Now `l` points at `7` but `r` is still at `3`. We add the smallest item to the ordered pile, so that is `3`. The situation is now:
 
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3 ]
          l           -->r
 
-This process repeats. At each step we pick the smallest item from either `leftPile` or `rightPile` and add it to `orderedPile`:
+This process repeats. At each step, we pick the smallest item from either the `leftPile` or the `rightPile` and add the item into the `orderedPile`:
 
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6 ]
@@ -151,13 +151,13 @@ This process repeats. At each step we pick the smallest item from either `leftPi
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6, 7, 8 ]
             -->l           r
 
-Now there are no more items in the left pile. We simply add the remaining items from the right pile, and we're done. The merged pile is `[ 1, 3, 6, 7, 8, 9 ]`. 
+Now, there are no more items in the left pile. We simply add the remaining items from the right pile, and we are done. The merged pile is `[ 1, 3, 6, 7, 8, 9 ]`. 
 
-Notice that this algorithm is very simple: it moves from left-to-right through the two piles and at every step picks the smallest item. This works because we guarantee that each of the piles is already sorted.
+Notice that, this algorithm is very simple: it moves from left-to-right through the two piles and at every step picks the smallest item. This works because we guarantee that each of the piles is already sorted.
 
 ## Bottom-up implementation
 
-The implementation of merge sort you've seen so far is called "top-down" because it first splits the array into smaller piles and then merges them. When sorting an array (as opposed to, say, a linked list) you can actually skip the splitting step and immediately start merging the individual array elements. This is called the "bottom-up" approach.
+The implementation of the merge-sort algorithm you have seen so far is called the "top-down" approach because it first splits the array into smaller piles and then merges them. When sorting an array (as opposed to, say, a linked list) you can actually skip the splitting step and immediately start merging the individual array elements. This is called the "bottom-up" approach.
 
 Time to step up the game a little. :-) Here is a complete bottom-up implementation in Swift:
 
@@ -212,19 +212,19 @@ func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 }
 ```
 
-It looks a lot more intimidating than the top-down version but notice that the main body includes the same three `while` loops from `merge()`.
+It looks a lot more intimidating than the top-down version, but notice that the main body includes the same three `while` loops from `merge()`.
 
 Notable points:
 
-1. Merge sort needs a temporary working array because you can't merge the left and right piles and at the same time overwrite their contents. But allocating a new array for each merge is wasteful. Therefore, we're using two working arrays and we'll switch between them using the value of `d`, which is either 0 or 1. The array `z[d]` is used for reading, `z[1 - d]` is used for writing. This is called *double-buffering*.
+1. The Merge-sort algorithm needs a temporary working array because you cannot merge the left and right piles and at the same time overwrite their contents. Because allocating a new array for each merge is wasteful, we are using two working arrays, and we will switch between them using the value of `d`, which is either 0 or 1. The array `z[d]` is used for reading, and `z[1 - d]` is used for writing. This is called *double-buffering*.
 
-2. Conceptually, the bottom-up version works the same way as the top-down version. First, it merges small piles of 1 element each, then it merges piles of 2 elements each, then piles of 4 elements each, and so on. The size of the pile is given by `width`. Initially, `width` is `1` but at the end of each loop iteration we multiply it by 2. So this outer loop determines the size of the piles being merged. And in each step, the subarrays to merge become larger.
+2. Conceptually, the bottom-up version works the same way as the top-down version. First, it merges small piles of one element each, then it merges piles of two elements each, then piles of four elements each, and so on. The size of the pile is given by `width`. Initially, `width` is `1` but at the end of each loop iteration, we multiply it by two, so this outer loop determines the size of the piles being merged, and the subarrays to merge become larger in each step.
 
 3. The inner loop steps through the piles and merges each pair of piles into a larger one. The result is written in the array given by `z[1 - d]`.
 
-4. This is the same logic as in the top-down version. The main difference is that we're using double-buffering, so values are read from `z[d]` and written into `z[1 - d]`. It also uses an `isOrderedBefore` function to compare the elements rather than just `<`, so this merge sort is generic and you can use it to sort any kind of object you want.
+4. This is the same logic as in the top-down version. The main difference is that we're using double-buffering, so values are read from `z[d]` and written into `z[1 - d]`. It also uses an `isOrderedBefore` function to compare the elements rather than just `<`, so this merge-sort algorithm is generic, and you can use it to sort any kind of object you want.
 
-5. At this point, the piles of size `width` from array `z[d]` have been merged into larger piles of size `width * 2` in array `z[1 - d]`. Here we swap the active array, so that in the next step we'll read from the new piles we've just created.
+5. At this point, the piles of size `width` from array `z[d]` have been merged into larger piles of size `width * 2` in array `z[1 - d]`. Here, we swap the active array, so that in the next step we'll read from the new piles we have just created.
 
 This function is generic, so you can use it to sort any type you desire, as long as you provide a proper `isOrderedBefore` closure to compare the elements.
 
@@ -237,15 +237,15 @@ mergeSortBottomUp(array, <)   // [1, 2, 4, 5, 9]
 
 ## Performance
 
-The speed of merge sort is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do. 
+The speed of the merge-sort algorithm is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do. 
 
-Whether or not the initial array is sorted already doesn't affect the speed of merge sort since you'll be doing the same amount splits and comparisons regardless of the initial order of the elements.
+Whether or not the initial array is sorted already doesnot affect the speed of the merge-sort algorithm since you will be doing the same amount splits and comparisons regardless of the initial order of the elements.
 
 Therefore, the time complexity for the best, worst, and average case will always be **O(n log n)**. 
 
-A disadvantage of merge sort is that it needs a temporary "working" array equal in size to the array being sorted. It is not an **in-place** sort, unlike for example [quicksort](../Quicksort/).
+A disadvantage of the merge-sort algorithm is that it needs a temporary "working" array equal in size to the array being sorted. It is not an **in-place** sort, unlike for example [quicksort](../Quicksort/).
 
-Most implementations of merge sort produce a **stable** sort. This means that array elements that have identical sort keys will stay in the same order relative to each other after sorting. This is not important for simple values such as numbers or strings, but it can be an issue when sorting more complex objects.
+Most implementations of the merge-sort algorithm produce a **stable** sort. This means that array elements that have identical sort keys will stay in the same order relative to each other after sorting. This is not important for simple values such as numbers or strings, but it can be an issue when sorting more complex objects.
 
 ## See also
 

From b99c037c861f295f63470d394a66b2dcaed40303 Mon Sep 17 00:00:00 2001
From: Keizar <keizar95@hotmail.com>
Date: Fri, 3 Feb 2017 13:20:07 -0800
Subject: [PATCH 0802/1679] update README.markdown

---
 Bubble Sort/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index ceb2a98cb..93d370827 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,14 +1,14 @@
 # Bubble Sort
 
-Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
+Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
 
 ##### Runtime:
-- Average: O(N^2) 
+- Average: O(N^2)
 - Worst: O(N^2)
 
-##### Memory: 
+##### Memory:
 - O(1)
 
 ### Implementation:
 
-The implementation will not be shown because as you can see from the average and worst runtimes this is a very inefficient algorithm but having a grasp of the concept will help in getting to know the basics of simple sorting algorithms.
+The implementation will not be shown as the average and worst runtimes show that this is a very inefficient algorithm. However, having a grasp of the concept will help you understand the basics of simple sorting algorithms.

From c22799378133820468783a1699be31d13c0f9d29 Mon Sep 17 00:00:00 2001
From: Weihang Lo <weihanglotw@gmail.com>
Date: Sat, 4 Feb 2017 18:22:06 +0800
Subject: [PATCH 0803/1679] left/right tree should reconnect to new node

---
 .../Sources/BinarySearchTree.swift            |  8 +-
 .../Tests/BinarySearchTreeTests.swift         | 87 ++++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  5 +-
 .../xcshareddata/WorkspaceSettings.xcsettings |  8 ++
 4 files changed, 61 insertions(+), 47 deletions(-)
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 31ae99a2f..74399efef 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -109,10 +109,10 @@ extension BinarySearchTree {
     
     // Replacement for current node can be either biggest one on the left or
     // smallest one on the right, whichever is not nil
-    if let left = left {
-      replacement = left.maximum()
-    } else if let right = right {
+    if let right = right {
       replacement = right.minimum()
+    } else if let left = left {
+      replacement = left.maximum()
     } else {
       replacement = nil;
     }
@@ -122,6 +122,8 @@ extension BinarySearchTree {
     // Place the replacement on current node's position
     replacement?.right = right;
     replacement?.left = left;
+    right?.parent = replacement
+    left?.parent = replacement
     reconnectParentTo(node:replacement);
     
     // The current node is no longer part of the tree, so clean it up.
diff --git a/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift
index 7c7fd069b..30749d8e4 100755
--- a/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
+++ b/Binary Search Tree/Solution 1/Tests/BinarySearchTreeTests.swift	
@@ -17,8 +17,8 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertEqual(tree.count, 8)
     XCTAssertEqual(tree.toArray(), [3, 5, 6, 8, 9, 10, 12, 16])
 
-    XCTAssertEqual(tree.search(9)!.value, 9)
-    XCTAssertNil(tree.search(99))
+    XCTAssertEqual(tree.search(value: 9)!.value, 9)
+    XCTAssertNil(tree.search(value: 99))
 
     XCTAssertEqual(tree.minimum().value, 3)
     XCTAssertEqual(tree.maximum().value, 16)
@@ -26,17 +26,17 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertEqual(tree.height(), 3)
     XCTAssertEqual(tree.depth(), 0)
 
-    let node1 = tree.search(16)
+    let node1 = tree.search(value: 16)
     XCTAssertNotNil(node1)
     XCTAssertEqual(node1!.height(), 0)
     XCTAssertEqual(node1!.depth(), 3)
 
-    let node2 = tree.search(12)
+    let node2 = tree.search(value: 12)
     XCTAssertNotNil(node2)
     XCTAssertEqual(node2!.height(), 1)
     XCTAssertEqual(node2!.depth(), 2)
 
-    let node3 = tree.search(10)
+    let node3 = tree.search(value: 10)
     XCTAssertNotNil(node3)
     XCTAssertEqual(node3!.height(), 2)
     XCTAssertEqual(node3!.depth(), 1)
@@ -45,32 +45,32 @@ class BinarySearchTreeTest: XCTestCase {
   func testInsert() {
     let tree = BinarySearchTree(value: 8)
 
-    tree.insert(5)
+    tree.insert(value: 5)
     XCTAssertEqual(tree.count, 2)
     XCTAssertEqual(tree.height(), 1)
     XCTAssertEqual(tree.depth(), 0)
 
-    let node1 = tree.search(5)
+    let node1 = tree.search(value: 5)
     XCTAssertNotNil(node1)
     XCTAssertEqual(node1!.height(), 0)
     XCTAssertEqual(node1!.depth(), 1)
 
-    tree.insert(10)
+    tree.insert(value: 10)
     XCTAssertEqual(tree.count, 3)
     XCTAssertEqual(tree.height(), 1)
     XCTAssertEqual(tree.depth(), 0)
 
-    let node2 = tree.search(10)
+    let node2 = tree.search(value: 10)
     XCTAssertNotNil(node2)
     XCTAssertEqual(node2!.height(), 0)
     XCTAssertEqual(node2!.depth(), 1)
 
-    tree.insert(3)
+    tree.insert(value: 3)
     XCTAssertEqual(tree.count, 4)
     XCTAssertEqual(tree.height(), 2)
     XCTAssertEqual(tree.depth(), 0)
 
-    let node3 = tree.search(3)
+    let node3 = tree.search(value: 3)
     XCTAssertNotNil(node3)
     XCTAssertEqual(node3!.height(), 0)
     XCTAssertEqual(node3!.depth(), 2)
@@ -84,9 +84,9 @@ class BinarySearchTreeTest: XCTestCase {
 
   func testInsertDuplicates() {
     let tree = BinarySearchTree(array: [8, 5, 10])
-    tree.insert(8)
-    tree.insert(5)
-    tree.insert(10)
+    tree.insert(value: 8)
+    tree.insert(value: 5)
+    tree.insert(value: 10)
     XCTAssertEqual(tree.count, 6)
     XCTAssertEqual(tree.toArray(), [5, 5, 8, 8, 10, 10])
   }
@@ -108,7 +108,7 @@ class BinarySearchTreeTest: XCTestCase {
   }
 
   func testInsertSorted() {
-    let tree = BinarySearchTree(array: [8, 5, 10, 3, 12, 9, 6, 16].sort(<))
+    let tree = BinarySearchTree(array: [8, 5, 10, 3, 12, 9, 6, 16].sorted(by: <))
     XCTAssertEqual(tree.count, 8)
     XCTAssertEqual(tree.toArray(), [3, 5, 6, 8, 9, 10, 12, 16])
 
@@ -118,7 +118,7 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertEqual(tree.height(), 7)
     XCTAssertEqual(tree.depth(), 0)
 
-    let node1 = tree.search(16)
+    let node1 = tree.search(value: 16)
     XCTAssertNotNil(node1)
     XCTAssertEqual(node1!.height(), 0)
     XCTAssertEqual(node1!.depth(), 7)
@@ -127,15 +127,15 @@ class BinarySearchTreeTest: XCTestCase {
   func testRemoveLeaf() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4])
 
-    let node10 = tree.search(10)!
+    let node10 = tree.search(value: 10)!
     XCTAssertNil(node10.left)
     XCTAssertNil(node10.right)
     XCTAssertTrue(tree.right === node10)
 
-    let node5 = tree.search(5)!
+    let node5 = tree.search(value: 5)!
     XCTAssertTrue(tree.left === node5)
 
-    let node4 = tree.search(4)!
+    let node4 = tree.search(value: 4)!
     XCTAssertTrue(node5.left === node4)
     XCTAssertNil(node5.right)
 
@@ -158,8 +158,8 @@ class BinarySearchTreeTest: XCTestCase {
   func testRemoveOneChildLeft() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4, 9])
 
-    let node4 = tree.search(4)!
-    let node5 = tree.search(5)!
+    let node4 = tree.search(value: 4)!
+    let node5 = tree.search(value: 5)!
     XCTAssertTrue(node5.left === node4)
     XCTAssertTrue(node5 === node4.parent)
 
@@ -171,8 +171,8 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertEqual(tree.count, 4)
     XCTAssertEqual(tree.toArray(), [4, 8, 9, 10])
 
-    let node9 = tree.search(9)!
-    let node10 = tree.search(10)!
+    let node9 = tree.search(value: 9)!
+    let node10 = tree.search(value: 10)!
     XCTAssertTrue(node10.left === node9)
     XCTAssertTrue(node10 === node9.parent)
 
@@ -188,8 +188,8 @@ class BinarySearchTreeTest: XCTestCase {
   func testRemoveOneChildRight() {
     let tree = BinarySearchTree(array: [8, 5, 10, 6, 11])
 
-    let node6 = tree.search(6)!
-    let node5 = tree.search(5)!
+    let node6 = tree.search(value: 6)!
+    let node5 = tree.search(value: 5)!
     XCTAssertTrue(node5.right === node6)
     XCTAssertTrue(node5 === node6.parent)
 
@@ -201,8 +201,8 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertEqual(tree.count, 4)
     XCTAssertEqual(tree.toArray(), [6, 8, 10, 11])
 
-    let node11 = tree.search(11)!
-    let node10 = tree.search(10)!
+    let node11 = tree.search(value: 11)!
+    let node10 = tree.search(value: 10)!
     XCTAssertTrue(node10.right === node11)
     XCTAssertTrue(node10 === node11.parent)
 
@@ -218,9 +218,9 @@ class BinarySearchTreeTest: XCTestCase {
   func testRemoveTwoChildrenSimple() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4, 6, 9, 11])
 
-    let node4 = tree.search(4)!
-    let node5 = tree.search(5)!
-    let node6 = tree.search(6)!
+    let node4 = tree.search(value: 4)!
+    let node5 = tree.search(value: 5)!
+    let node6 = tree.search(value: 6)!
     XCTAssertTrue(node5.left === node4)
     XCTAssertTrue(node5.right === node6)
     XCTAssertTrue(node5 === node4.parent)
@@ -241,9 +241,9 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertEqual(tree.count, 6)
     XCTAssertEqual(tree.toArray(), [4, 6, 8, 9, 10, 11])
 
-    let node9 = tree.search(9)!
-    let node10 = tree.search(10)!
-    let node11 = tree.search(11)!
+    let node9 = tree.search(value: 9)!
+    let node10 = tree.search(value: 10)!
+    let node11 = tree.search(value: 11)!
     XCTAssertTrue(node10.left === node9)
     XCTAssertTrue(node10.right === node11)
     XCTAssertTrue(node10 === node9.parent)
@@ -268,11 +268,12 @@ class BinarySearchTreeTest: XCTestCase {
   func testRemoveTwoChildrenComplex() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4, 9, 20, 11, 15, 13])
 
-    let node9 = tree.search(9)!
-    let node10 = tree.search(10)!
-    let node11 = tree.search(11)!
-    let node15 = tree.search(15)!
-    let node20 = tree.search(20)!
+    let node9 = tree.search(value: 9)!
+    let node10 = tree.search(value: 10)!
+    let node11 = tree.search(value: 11)!
+    let node13 = tree.search(value: 13)!
+    let node15 = tree.search(value: 15)!
+    let node20 = tree.search(value: 20)!
     XCTAssertTrue(node10.left === node9)
     XCTAssertTrue(node10 === node9.parent)
     XCTAssertTrue(node10.right === node20)
@@ -290,8 +291,8 @@ class BinarySearchTreeTest: XCTestCase {
     XCTAssertTrue(node11 === node9.parent)
     XCTAssertTrue(node11.right === node20)
     XCTAssertTrue(node11 === node20.parent)
-    XCTAssertTrue(node20.left === node15)
-    XCTAssertTrue(node20 === node15.parent)
+    XCTAssertTrue(node20.left === node13)
+    XCTAssertTrue(node20 === node13.parent)
     XCTAssertNil(node20.right)
     XCTAssertNil(node10.left)
     XCTAssertNil(node10.right)
@@ -303,7 +304,7 @@ class BinarySearchTreeTest: XCTestCase {
   func testRemoveRoot() {
     let tree = BinarySearchTree(array: [8, 5, 10, 4, 9, 20, 11, 15, 13])
 
-    let node9 = tree.search(9)!
+    let node9 = tree.search(value: 9)!
 
     let newRoot = tree.remove()
     XCTAssertTrue(newRoot === node9)
@@ -319,7 +320,7 @@ class BinarySearchTreeTest: XCTestCase {
 
   func testPredecessor() {
     let tree = BinarySearchTree(array: [3, 1, 2, 5, 4])
-    let node = tree.search(5)
+    let node = tree.search(value: 5)
 
     XCTAssertEqual(node!.value, 5)
     XCTAssertEqual(node!.predecessor()!.value, 4)
@@ -331,7 +332,7 @@ class BinarySearchTreeTest: XCTestCase {
 
   func testSuccessor() {
     let tree = BinarySearchTree(array: [3, 1, 2, 5, 4])
-    let node = tree.search(1)
+    let node = tree.search(value: 1)
 
     XCTAssertEqual(node!.value, 1)
     XCTAssertEqual(node!.successor()!.value, 2)
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index 7ecfe593f..f4c3f65c7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -15,7 +15,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3D91C77A323003CECC7 /* BinarySearchTreeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BinarySearchTreeTests.swift; sourceTree = SOURCE_ROOT; };
-		9E5A58B81E304C3100DAB3BB /* BinarySearchTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearchTree.swift; path = ../BinarySearchTree.playground/Sources/BinarySearchTree.swift; sourceTree = "<group>"; };
+		9E5A58B81E304C3100DAB3BB /* BinarySearchTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BinarySearchTree.swift; path = ../BinarySearchTree.playground/Sources/BinarySearchTree.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -88,6 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -220,6 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>

From eef96f6431477e31598e884a72d3178c9b06e8f6 Mon Sep 17 00:00:00 2001
From: Weihang Lo <weihanglotw@gmail.com>
Date: Sat, 4 Feb 2017 17:59:53 +0800
Subject: [PATCH 0804/1679] unmark .travis.yml test for BinarySearchTree

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 80ced8b6c..2b2bafd14 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -13,7 +13,7 @@ script:
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Boyer-Moore/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 # - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests

From 78da2c7b4719f55faaa69f2ae0c0324eb3423db0 Mon Sep 17 00:00:00 2001
From: Weihang Lo <weihanglotw@gmail.com>
Date: Sat, 4 Feb 2017 17:36:46 +0800
Subject: [PATCH 0805/1679] lint files

---
 .../Sources/BinarySearchTree.swift            | 24 +++++++++----------
 .../Contents.swift                            |  2 --
 2 files changed, 12 insertions(+), 14 deletions(-)

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 74399efef..8a126e950 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -22,7 +22,7 @@ public class BinarySearchTree<T: Comparable> {
   public convenience init(array: [T]) {
     precondition(array.count > 0)
     self.init(value: array.first!)
-    for v in array.dropFirst() { 
+    for v in array.dropFirst() {
       insert(value: v)
     }
   }
@@ -106,7 +106,7 @@ extension BinarySearchTree {
   */
   @discardableResult public func remove() -> BinarySearchTree? {
     let replacement: BinarySearchTree?
-    
+
     // Replacement for current node can be either biggest one on the left or
     // smallest one on the right, whichever is not nil
     if let right = right {
@@ -114,24 +114,24 @@ extension BinarySearchTree {
     } else if let left = left {
       replacement = left.maximum()
     } else {
-      replacement = nil;
+      replacement = nil
     }
-    
-    replacement?.remove();
+
+    replacement?.remove()
 
     // Place the replacement on current node's position
-    replacement?.right = right;
-    replacement?.left = left;
+    replacement?.right = right
+    replacement?.left = left
     right?.parent = replacement
     left?.parent = replacement
-    reconnectParentTo(node:replacement);
-    
+    reconnectParentTo(node:replacement)
+
     // The current node is no longer part of the tree, so clean it up.
     parent = nil
     left = nil
     right = nil
-    
-    return replacement;
+
+    return replacement
   }
 
   private func reconnectParentTo(node: BinarySearchTree?) {
@@ -324,7 +324,7 @@ extension BinarySearchTree: CustomStringConvertible {
     }
     return s
   }
-   
+
    public func toArray() -> [T] {
       return map { $0 }
    }
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 8df69fb6a..2b5dcc341 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -12,5 +12,3 @@ print(tree)
 tree.search(x: 10)
 tree.search(x: 1)
 tree.search(x: 11)
-
-

From f47a45e967ec651b6091f1d81a352f15420fd564 Mon Sep 17 00:00:00 2001
From: Weihang Lo <weihanglotw@gmail.com>
Date: Sat, 4 Feb 2017 17:56:24 +0800
Subject: [PATCH 0806/1679] Update README.markdown

---
 Binary Search Tree/README.markdown | 75 ++++++++++++++++--------------
 1 file changed, 39 insertions(+), 36 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index e8d2f58e2..bd2a00c9e 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -58,7 +58,7 @@ Sometimes you don't want to look at just a single node, but at all of them.
 There are three ways to traverse a binary tree:
 
 1. *In-order* (or *depth-first*): first look at the left child of a node, then at the node itself, and finally at its right child.
-2. *Pre-order*: first look at a node, then its left and right children. 
+2. *Pre-order*: first look at a node, then its left and right children.
 3. *Post-order*: first look at the left and right children and process the node itself last.
 
 Once again, this happens recursively.
@@ -133,7 +133,7 @@ public class BinarySearchTree<T: Comparable> {
 }
 ```
 
-This class describes just a single node, not the entire tree. It's a generic type, so the node can store any kind of data. It also has references to its `left` and `right` child nodes and a `parent` node. 
+This class describes just a single node, not the entire tree. It's a generic type, so the node can store any kind of data. It also has references to its `left` and `right` child nodes and a `parent` node.
 
 Here's how you'd use it:
 
@@ -258,7 +258,7 @@ Here is the implementation of `search()`:
 
 I hope the logic is clear: this starts at the current node (usually the root) and compares the values. If the search value is less than the node's value, we continue searching in the left branch; if the search value is greater, we dive into the right branch.
 
-Of course, if there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree. 
+Of course, if there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree.
 
 > **Note:** In Swift that's very conveniently done with optional chaining; when you write `left?.search(value)` it automatically returns nil if `left` is nil. There's no need to explicitly check for this with an `if` statement.
 
@@ -300,21 +300,21 @@ The first three lines all return the corresponding `BinaryTreeNode` object. The
 Remember there are 3 different ways to look at all nodes in the tree? Here they are:
 
 ```swift
-  public func traverseInOrder(@noescape process: T -> Void) {
-    left?.traverseInOrder(process)
+  public func traverseInOrder(process: (T) -> Void) {
+    left?.traverseInOrder(process: process)
     process(value)
-    right?.traverseInOrder(process)
+    right?.traverseInOrder(process: process)
   }
-  
-  public func traversePreOrder(@noescape process: T -> Void) {
+
+  public func traversePreOrder(process: (T) -> Void) {
     process(value)
-    left?.traversePreOrder(process)
-    right?.traversePreOrder(process)
+    left?.traversePreOrder(process: process)
+    right?.traversePreOrder(process: process)
   }
-  
-  public func traversePostOrder(@noescape process: T -> Void) {
-    left?.traversePostOrder(process)
-    right?.traversePostOrder(process)
+
+  public func traversePostOrder(process: (T) -> Void) {
+    left?.traversePostOrder(process: process)
+    right?.traversePostOrder(process: process)
     process(value)
   }
 ```
@@ -339,11 +339,12 @@ This prints the following:
 You can also add things like `map()` and `filter()` to the tree. For example, here's an implementation of map:
 
 ```swift
-  public func map(@noescape formula: T -> T) -> [T] {
+
+  public func map(formula: (T) -> T) -> [T] {
     var a = [T]()
-    if let left = left { a += left.map(formula) }
+    if let left = left { a += left.map(formula: formula) }
     a.append(formula(value))
-    if let right = right { a += right.map(formula) }
+    if let right = right { a += right.map(formula: formula) }
     return a
   }
 ```
@@ -365,7 +366,7 @@ tree.toArray()   // [1, 2, 5, 7, 9, 10]
 ```
 
 As an exercise for yourself, see if you can implement filter and reduce.
- 
+
 ### Deleting nodes
 
 We can make the code much more readable by defining some helper functions.
@@ -395,7 +396,7 @@ We also need a function that returns the minimum and maximum of a node:
     }
     return node
   }
-  
+
   public func maximum() -> BinarySearchTree {
     var node = self
     while case let next? = node.right {
@@ -411,30 +412,32 @@ The rest of the code is pretty self-explanatory:
 ```swift
   @discardableResult public func remove() -> BinarySearchTree? {
     let replacement: BinarySearchTree?
-    
+
     // Replacement for current node can be either biggest one on the left or
     // smallest one on the right, whichever is not nil
-    if let left = left {
-      replacement = left.maximum()
-    } else if let right = right {
+    if let right = right {
       replacement = right.minimum()
+    } else if let left = left {
+      replacement = left.maximum()
     } else {
-      replacement = nil;
+      replacement = nil
     }
-    
-    replacement?.remove();
+
+    replacement?.remove()
 
     // Place the replacement on current node's position
-    replacement?.right = right;
-    replacement?.left = left;
-    reconnectParentTo(node:replacement);
-    
+    replacement?.right = right
+    replacement?.left = left
+    right?.parent = replacement
+    left?.parent = replacement
+    reconnectParentTo(node:replacement)
+
     // The current node is no longer part of the tree, so clean it up.
     parent = nil
     left = nil
     right = nil
-    
-    return replacement;
+
+    return replacement
   }
 ```
 
@@ -574,7 +577,7 @@ if let node1 = tree.search(1) {
 
 ## The code (solution 2)
 
-We've implemented the binary tree node as a class but you can also use an enum. 
+We've implemented the binary tree node as a class but you can also use an enum.
 
 The difference is reference semantics versus value semantics. Making a change to the class-based tree will update that same instance in memory. But the enum-based tree is immutable -- any insertions or deletions will give you an entirely new copy of the tree. Which one is best totally depends on what you want to use it for.
 
@@ -588,7 +591,7 @@ public enum BinarySearchTree<T: Comparable> {
 }
 ```
 
-The enum has three cases: 
+The enum has three cases:
 
 - `Empty` to mark the end of a branch (the class-based version used `nil` references for this).
 - `Leaf` for a leaf node that has no children.
@@ -606,7 +609,7 @@ As usual, we'll implement most functionality recursively. We'll treat each case
     case let .Node(left, _, right): return left.count + 1 + right.count
     }
   }
-  
+
   public var height: Int {
     switch self {
     case .Empty: return 0
@@ -623,7 +626,7 @@ Inserting new nodes looks like this:
     switch self {
     case .Empty:
       return .Leaf(newValue)
-      
+
     case .Leaf(let value):
       if newValue < value {
         return .Node(.Leaf(newValue), value, .Empty)

From 257e973125884983b42193d7e67d1a6155081b4c Mon Sep 17 00:00:00 2001
From: Julio Guzman <julio.guzman@me.com>
Date: Mon, 6 Feb 2017 16:32:26 -0600
Subject: [PATCH 0807/1679] Change last upgrade version

---
 .../Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..dfcf6de42 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 0b7a1f219da2cb96203c22e7e979ea43439ffeed Mon Sep 17 00:00:00 2001
From: Julio Guzman <julio.guzman@me.com>
Date: Mon, 6 Feb 2017 16:32:42 -0600
Subject: [PATCH 0808/1679] Change last upgrade check

---
 Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 33be43391..a04c95170 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -89,7 +89,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {

From c8ce274329483d25f8e3ddfb3917419dad7eb9b0 Mon Sep 17 00:00:00 2001
From: Julio Guzman <julio.guzman@me.com>
Date: Mon, 6 Feb 2017 16:40:38 -0600
Subject: [PATCH 0809/1679] Add assignation to remove warning

---
 Breadth-First Search/Tests/Graph.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/Tests/Graph.swift b/Breadth-First Search/Tests/Graph.swift
index ed71cab7c..09684da5b 100644
--- a/Breadth-First Search/Tests/Graph.swift	
+++ b/Breadth-First Search/Tests/Graph.swift	
@@ -86,7 +86,7 @@ public class Graph: CustomStringConvertible, Equatable {
     let duplicated = Graph()
 
     for node in nodes {
-      duplicated.addNode(node.label)
+      let _ = duplicated.addNode(node.label)
     }
 
     for node in nodes {

From e0a3b634d087a3376ba2f2478effd872cbe800f1 Mon Sep 17 00:00:00 2001
From: Julio Guzman <julio.guzman@me.com>
Date: Mon, 6 Feb 2017 16:51:01 -0600
Subject: [PATCH 0810/1679] Migrates Breadth First Search tests project to
 Swift 3 syntax

---
 Breadth-First Search/Tests/Graph.swift                    | 8 ++++----
 Breadth-First Search/Tests/Queue.swift                    | 2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj                 | 3 +++
 3 files changed, 8 insertions(+), 5 deletions(-)

diff --git a/Breadth-First Search/Tests/Graph.swift b/Breadth-First Search/Tests/Graph.swift
index 09684da5b..5e0837160 100644
--- a/Breadth-First Search/Tests/Graph.swift	
+++ b/Breadth-First Search/Tests/Graph.swift	
@@ -39,7 +39,7 @@ public class Node: CustomStringConvertible, Equatable {
   }
 
   public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
@@ -56,13 +56,13 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(label: String) -> Node {
+  public func addNode(_ label: String) -> Node {
     let node = Node(label: label)
     nodes.append(node)
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
+  public func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
     source.neighbors.append(edge)
   }
@@ -78,7 +78,7 @@ public class Graph: CustomStringConvertible, Equatable {
     return description
   }
 
-  public func findNodeWithLabel(label: String) -> Node {
+  public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
 
diff --git a/Breadth-First Search/Tests/Queue.swift b/Breadth-First Search/Tests/Queue.swift
index bf462bbdd..3d98f801c 100644
--- a/Breadth-First Search/Tests/Queue.swift	
+++ b/Breadth-First Search/Tests/Queue.swift	
@@ -13,7 +13,7 @@ public struct Queue<T> {
     return array.count
   }
 
-  public mutating func enqueue(element: T) {
+  public mutating func enqueue(_ element: T) {
     array.append(element)
   }
 
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index a04c95170..f86abf86e 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -94,6 +94,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -230,6 +231,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -242,6 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};

From ca8e7ff4be86d94c8f5fea31d50a74896362b0dc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-MacBook-Pro.local>
Date: Mon, 6 Feb 2017 17:26:07 -0800
Subject: [PATCH 0811/1679] Fixed spacing.

---
 .../ShuntingYard.playground/Contents.swift    | 174 ++++-----
 Shunting Yard/ShuntingYard.swift              | 366 +++++++++---------
 2 files changed, 270 insertions(+), 270 deletions(-)

diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index b341c673b..fa9f5745b 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -12,21 +12,21 @@ public enum OperatorType: CustomStringConvertible {
   case multiply
   case percent
   case exponent
-
+  
   public var description: String {
     switch self {
-      case .add:
-        return "+"
-      case .subtract:
-        return "-"
-      case .divide:
-        return "/"
-      case .multiply:
-        return "*"
-      case .percent:
-        return "%"
-      case .exponent:
-        return "^"
+    case .add:
+      return "+"
+    case .subtract:
+      return "-"
+    case .divide:
+      return "/"
+    case .multiply:
+      return "*"
+    case .percent:
+      return "%"
+    case .exponent:
+      return "^"
     }
   }
 }
@@ -36,48 +36,48 @@ public enum TokenType: CustomStringConvertible {
   case closeBracket
   case Operator(OperatorToken)
   case operand(Double)
-
+  
   public var description: String {
     switch self {
-      case .openBracket:
-        return "("
-      case .closeBracket:
-        return ")"
-      case .Operator(let operatorToken):
-        return operatorToken.description
-      case .operand(let value):
-        return "\(value)"
+    case .openBracket:
+      return "("
+    case .closeBracket:
+      return ")"
+    case .Operator(let operatorToken):
+      return operatorToken.description
+    case .operand(let value):
+      return "\(value)"
     }
   }
 }
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-
+  
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-
+  
   var precedence: Int {
     switch operatorType {
-      case .add, .subtract:
-        return 0
-      case .divide, .multiply, .percent:
-        return 5
-      case .exponent:
-        return 10
+    case .add, .subtract:
+      return 0
+    case .divide, .multiply, .percent:
+      return 5
+    case .exponent:
+      return 10
     }
   }
-
+  
   var associativity: OperatorAssociativity {
     switch operatorType {
-      case .add, .subtract, .divide, .multiply, .percent:
-        return .leftAssociative
-      case .exponent:
-        return .rightAssociative
+    case .add, .subtract, .divide, .multiply, .percent:
+      return .leftAssociative
+    case .exponent:
+      return .rightAssociative
     }
   }
-
+  
   public var description: String {
     return operatorType.description
   }
@@ -93,46 +93,46 @@ func < (left: OperatorToken, right: OperatorToken) -> Bool {
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-
+  
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-
+  
   init(operand: Double) {
     tokenType = .operand(operand)
   }
-
+  
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-
+  
   var isOpenBracket: Bool {
     switch tokenType {
-      case .openBracket:
-        return true
-      default:
-        return false
+    case .openBracket:
+      return true
+    default:
+      return false
     }
   }
-
+  
   var isOperator: Bool {
     switch tokenType {
-      case .Operator(_):
-        return true
-      default:
-        return false
+    case .Operator(_):
+      return true
+    default:
+      return false
     }
   }
-
+  
   var operatorToken: OperatorToken? {
     switch tokenType {
-      case .Operator(let operatorToken):
-        return operatorToken
-      default:
-        return nil
+    case .Operator(let operatorToken):
+      return operatorToken
+    default:
+      return nil
     }
   }
-
+  
   public var description: String {
     return tokenType.description
   }
@@ -140,27 +140,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-
+  
   public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-
+  
   public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-
+  
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .openBracket))
     return self
   }
-
+  
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .closeBracket))
     return self
   }
-
+  
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -169,46 +169,46 @@ public class InfixExpressionBuilder {
 
 // This returns the result of the shunting yard algorithm
 public func reversePolishNotation(_ expression: [Token]) -> String {
-
+  
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-
+  
   for token in expression {
     switch token.tokenType {
-      case .operand(_):
-        reversePolishNotation.append(token)
-
-      case .openBracket:
-        tokenStack.push(token)
-
-      case .closeBracket:
-        while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
-          reversePolishNotation.append(tempToken)
+    case .operand(_):
+      reversePolishNotation.append(token)
+      
+    case .openBracket:
+      tokenStack.push(token)
+      
+    case .closeBracket:
+      while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
+        reversePolishNotation.append(tempToken)
+      }
+      
+    case .Operator(let operatorToken):
+      for tempToken in tokenStack.makeIterator() {
+        if !tempToken.isOperator {
+          break
         }
-
-      case .Operator(let operatorToken):
-        for tempToken in tokenStack.makeIterator() {
-          if !tempToken.isOperator {
+        
+        if let tempOperatorToken = tempToken.operatorToken {
+          if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
+            || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
+            reversePolishNotation.append(tokenStack.pop()!)
+          } else {
             break
           }
-
-          if let tempOperatorToken = tempToken.operatorToken {
-            if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
-                || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
-              reversePolishNotation.append(tokenStack.pop()!)
-            } else {
-              break
-            }
-          }
         }
-        tokenStack.push(token)
+      }
+      tokenStack.push(token)
     }
   }
-
+  
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-
+  
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
 
diff --git a/Shunting Yard/ShuntingYard.swift b/Shunting Yard/ShuntingYard.swift
index b8f5f8e6b..97a72249d 100644
--- a/Shunting Yard/ShuntingYard.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -7,213 +7,213 @@
 //
 
 internal enum OperatorAssociativity {
-    case leftAssociative
-    case rightAssociative
+  case leftAssociative
+  case rightAssociative
 }
 
 public enum OperatorType: CustomStringConvertible {
-    case add
-    case subtract
-    case divide
-    case multiply
-    case percent
-    case exponent
-    
-    public var description: String {
-        switch self {
-        case .add:
-            return "+"
-        case .subtract:
-            return "-"
-        case .divide:
-            return "/"
-        case .multiply:
-            return "*"
-        case .percent:
-            return "%"
-        case .exponent:
-            return "^"
-        }
-    }
+  case add
+  case subtract
+  case divide
+  case multiply
+  case percent
+  case exponent
+  
+  public var description: String {
+    switch self {
+    case .add:
+      return "+"
+    case .subtract:
+      return "-"
+    case .divide:
+      return "/"
+    case .multiply:
+      return "*"
+    case .percent:
+      return "%"
+    case .exponent:
+      return "^"
+    }
+  }
 }
 
 public enum TokenType: CustomStringConvertible {
-    case openBracket
-    case closeBracket
-    case Operator(OperatorToken)
-    case operand(Double)
-    
-    public var description: String {
-        switch self {
-        case .openBracket:
-            return "("
-        case .closeBracket:
-            return ")"
-        case .Operator(let operatorToken):
-            return operatorToken.description
-        case .operand(let value):
-            return "\(value)"
-        }
-    }
+  case openBracket
+  case closeBracket
+  case Operator(OperatorToken)
+  case operand(Double)
+  
+  public var description: String {
+    switch self {
+    case .openBracket:
+      return "("
+    case .closeBracket:
+      return ")"
+    case .Operator(let operatorToken):
+      return operatorToken.description
+    case .operand(let value):
+      return "\(value)"
+    }
+  }
 }
 
 public struct OperatorToken: CustomStringConvertible {
-    let operatorType: OperatorType
-    
-    init(operatorType: OperatorType) {
-        self.operatorType = operatorType
-    }
-    
-    var precedence: Int {
-        switch operatorType {
-        case .add, .subtract:
-            return 0
-        case .divide, .multiply, .percent:
-            return 5
-        case .exponent:
-            return 10
-        }
-    }
-    
-    var associativity: OperatorAssociativity {
-        switch operatorType {
-        case .add, .subtract, .divide, .multiply, .percent:
-            return .leftAssociative
-        case .exponent:
-            return .rightAssociative
-        }
-    }
-    
-    public var description: String {
-        return operatorType.description
-    }
+  let operatorType: OperatorType
+  
+  init(operatorType: OperatorType) {
+    self.operatorType = operatorType
+  }
+  
+  var precedence: Int {
+    switch operatorType {
+    case .add, .subtract:
+      return 0
+    case .divide, .multiply, .percent:
+      return 5
+    case .exponent:
+      return 10
+    }
+  }
+  
+  var associativity: OperatorAssociativity {
+    switch operatorType {
+    case .add, .subtract, .divide, .multiply, .percent:
+      return .leftAssociative
+    case .exponent:
+      return .rightAssociative
+    }
+  }
+  
+  public var description: String {
+    return operatorType.description
+  }
 }
 
 func <= (left: OperatorToken, right: OperatorToken) -> Bool {
-    return left.precedence <= right.precedence
+  return left.precedence <= right.precedence
 }
 
 func < (left: OperatorToken, right: OperatorToken) -> Bool {
-    return left.precedence < right.precedence
+  return left.precedence < right.precedence
 }
 
 public struct Token: CustomStringConvertible {
-    let tokenType: TokenType
-    
-    init(tokenType: TokenType) {
-        self.tokenType = tokenType
-    }
-    
-    init(operand: Double) {
-        tokenType = .operand(operand)
-    }
-    
-    init(operatorType: OperatorType) {
-        tokenType = .Operator(OperatorToken(operatorType: operatorType))
-    }
-    
-    var isOpenBracket: Bool {
-        switch tokenType {
-        case .openBracket:
-            return true
-        default:
-            return false
-        }
-    }
-    
-    var isOperator: Bool {
-        switch tokenType {
-        case .Operator(_):
-            return true
-        default:
-            return false
-        }
-    }
-    
-    var operatorToken: OperatorToken? {
-        switch tokenType {
-        case .Operator(let operatorToken):
-            return operatorToken
-        default:
-            return nil
-        }
-    }
-    
-    public var description: String {
-        return tokenType.description
-    }
+  let tokenType: TokenType
+  
+  init(tokenType: TokenType) {
+    self.tokenType = tokenType
+  }
+  
+  init(operand: Double) {
+    tokenType = .operand(operand)
+  }
+  
+  init(operatorType: OperatorType) {
+    tokenType = .Operator(OperatorToken(operatorType: operatorType))
+  }
+  
+  var isOpenBracket: Bool {
+    switch tokenType {
+    case .openBracket:
+      return true
+    default:
+      return false
+    }
+  }
+  
+  var isOperator: Bool {
+    switch tokenType {
+    case .Operator(_):
+      return true
+    default:
+      return false
+    }
+  }
+  
+  var operatorToken: OperatorToken? {
+    switch tokenType {
+    case .Operator(let operatorToken):
+      return operatorToken
+    default:
+      return nil
+    }
+  }
+  
+  public var description: String {
+    return tokenType.description
+  }
 }
 
 public class InfixExpressionBuilder {
-    private var expression = [Token]()
-    
-    public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
-        expression.append(Token(operatorType: operatorType))
-        return self
-    }
-    
-    public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
-        expression.append(Token(operand: operand))
-        return self
-    }
-    
-    public func addOpenBracket() -> InfixExpressionBuilder {
-        expression.append(Token(tokenType: .openBracket))
-        return self
-    }
-    
-    public func addCloseBracket() -> InfixExpressionBuilder {
-        expression.append(Token(tokenType: .closeBracket))
-        return self
-    }
-    
-    public func build() -> [Token] {
-        // Maybe do some validation here
-        return expression
-    }
+  private var expression = [Token]()
+  
+  public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
+    expression.append(Token(operatorType: operatorType))
+    return self
+  }
+  
+  public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
+    expression.append(Token(operand: operand))
+    return self
+  }
+  
+  public func addOpenBracket() -> InfixExpressionBuilder {
+    expression.append(Token(tokenType: .openBracket))
+    return self
+  }
+  
+  public func addCloseBracket() -> InfixExpressionBuilder {
+    expression.append(Token(tokenType: .closeBracket))
+    return self
+  }
+  
+  public func build() -> [Token] {
+    // Maybe do some validation here
+    return expression
+  }
 }
 
 // This returns the result of the shunting yard algorithm
 public func reversePolishNotation(_ expression: [Token]) -> String {
-    
-    var tokenStack = Stack<Token>()
-    var reversePolishNotation = [Token]()
-    
-    for token in expression {
-        switch token.tokenType {
-        case .operand(_):
-            reversePolishNotation.append(token)
-            
-        case .openBracket:
-            tokenStack.push(token)
-            
-        case .closeBracket:
-            while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
-                reversePolishNotation.append(tempToken)
-            }
-            
-        case .Operator(let operatorToken):
-            for tempToken in tokenStack.makeIterator() {
-                if !tempToken.isOperator {
-                    break
-                }
-                
-                if let tempOperatorToken = tempToken.operatorToken {
-                    if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
-                        || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
-                        reversePolishNotation.append(tokenStack.pop()!)
-                    } else {
-                        break
-                    }
-                }
-            }
-            tokenStack.push(token)
+  
+  var tokenStack = Stack<Token>()
+  var reversePolishNotation = [Token]()
+  
+  for token in expression {
+    switch token.tokenType {
+    case .operand(_):
+      reversePolishNotation.append(token)
+      
+    case .openBracket:
+      tokenStack.push(token)
+      
+    case .closeBracket:
+      while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
+        reversePolishNotation.append(tempToken)
+      }
+      
+    case .Operator(let operatorToken):
+      for tempToken in tokenStack.makeIterator() {
+        if !tempToken.isOperator {
+          break
         }
-    }
-    
-    while tokenStack.count > 0 {
-        reversePolishNotation.append(tokenStack.pop()!)
-    }
-    
-    return reversePolishNotation.map({token in token.description}).joined(separator: " ")
+        
+        if let tempOperatorToken = tempToken.operatorToken {
+          if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
+            || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
+            reversePolishNotation.append(tokenStack.pop()!)
+          } else {
+            break
+          }
+        }
+      }
+      tokenStack.push(token)
+    }
+  }
+  
+  while tokenStack.count > 0 {
+    reversePolishNotation.append(tokenStack.pop()!)
+  }
+  
+  return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }

From 6eb7d9a172e3cded2c5be3e52c7193c9168def81 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 7 Feb 2017 18:43:38 +0100
Subject: [PATCH 0812/1679] old version with error

---
 Threaded Binary Tree/README.markdown          |  49 +-
 .../Contents.swift}                           |  52 +-
 .../Sources/ThreadedBinaryTree.swift          | 459 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Threaded Binary Tree/ThreadedBinaryTree.swift | 459 ------------------
 6 files changed, 519 insertions(+), 511 deletions(-)
 rename Threaded Binary Tree/{ThreadedBinaryTreeTests.swift => ThreadedBinaryTree.playground/Contents.swift} (53%)
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTree.playground/contents.xcplayground
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata
 delete mode 100644 Threaded Binary Tree/ThreadedBinaryTree.swift

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 0c533ad63..fd05113d8 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -158,31 +158,31 @@ outlined above.  We use these predecessor/successor attributes to great effect
 in this new algorithm for both forward and backward traversals:
 
 ```swift
-func traverseInOrderForward(visit: T -> Void) {
-  var n: ThreadedBinaryTree
-  n = minimum()
-  while true {
-    visit(n.value)
-    if let successor = n.successor() {
-      n = successor
-    } else {
-      break
+    public func traverseInOrderForward(_ visit: (T) -> Void) {
+        var n: ThreadedBinaryTree
+        n = minimum()
+        while true {
+            visit(n.value)
+            if let successor = n.successor() {
+                n = successor
+            } else {
+                break
+            }
+        }
     }
-  }
-}
 
-func traverseInOrderBackward(visit: T -> Void) {
-  var n: ThreadedBinaryTree
-  n = maximum()
-  while true {
-    visit(n.value)
-    if let predecessor = n.predecessor() {
-      n = predecessor
-    } else {
-      break
+    public func traverseInOrderBackward(_ visit: (T) -> Void) {
+        var n: ThreadedBinaryTree
+        n = maximum()
+        while true {
+            visit(n.value)
+            if let predecessor = n.predecessor() {
+                n = predecessor
+            } else {
+                break
+            }
+        }
     }
-  }
-}
 ```
 Again, this a method of `ThreadedBinaryTree`, so we'd call it via
 `node.traverseInorderForward(visitFunction)`.  Note that we are able to specify
@@ -221,7 +221,7 @@ continuously manage the `leftThread` and `rightThread` variables.  Rather than
 walking through some boring code, it is best to explain this with an example
 (although you can read through [the implementation](ThreadedBinaryTree.swift)
 if you want to know the finer details).  Please note that this requires
-knowledge of binary search trees, so make sure you have 
+knowledge of binary search trees, so make sure you have
 [read this first](../Binary Search Tree/).
 
 > Note: we do allow duplicate nodes in this implementation of a threaded binary
@@ -342,11 +342,12 @@ Many of these methods are inherent to binary search trees as well, so you can
 find [further documentation here](../Binary Search Tree/).
 
 
-## See also 
+## See also
 
 [Threaded Binary Tree on Wikipedia](https://en.wikipedia.org/wiki/Threaded_binary_tree)
 
 *Written for the Swift Algorithm Club by
 [Jayson Tung](https://github.com/JFTung)*
+*Migrated to Swift 3 by Jaap Wijnen*
 
 *Images made using www.draw.io*
diff --git a/Threaded Binary Tree/ThreadedBinaryTreeTests.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
similarity index 53%
rename from Threaded Binary Tree/ThreadedBinaryTreeTests.swift
rename to Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index 514c0db63..ff59f81d1 100644
--- a/Threaded Binary Tree/ThreadedBinaryTreeTests.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,35 +1,31 @@
-/*
-  TESTS
-  I don't have access to an Apple computer, so I can't make a Playground or any
-  of that fancy stuff.  Here's a simple demonstration of the ThreadedBinaryTree
-  class.  It follows the examples in the README.
-*/
+//: Playground - noun: a place where people can play
+
 
 // Simple little debug function to make testing output pretty
-func check(tree: ThreadedBinaryTree<Int>?) {
-  if let tree = tree {
-    print("\(tree.count) Total Nodes:")
-    print(tree)
-    print("Debug Info:")
-    print(tree.debugDescription)
-    print("In-Order Traversal:")
-    let myArray = tree.toArray()
-    for node in myArray {
-      print(node)
-    }
-    if tree.isBST(minValue: Int.min, maxValue: Int.max) {
-      print("This is a VALID binary search tree.")
-    } else {
-      print("This is an INVALID binary search tree.")
-    }
-    if tree.isThreaded() {
-      print("This is a VALID threaded binary tree.")
+func check(_ tree: ThreadedBinaryTree<Int>?) {
+    if let tree = tree {
+        print("\(tree.count) Total Nodes:")
+        print(tree)
+        print("Debug Info:")
+        print(tree.debugDescription)
+        print("In-Order Traversal:")
+        let myArray = tree.toArray()
+        for node in myArray {
+            print(node)
+        }
+        if tree.isBST(minValue: Int.min, maxValue: Int.max) {
+            print("This is a VALID binary search tree.")
+        } else {
+            print("This is an INVALID binary search tree.")
+        }
+        if tree.isThreaded() {
+            print("This is a VALID threaded binary tree.")
+        } else {
+            print("This is an INVALID threaded binary tree.")
+        }
     } else {
-      print("This is an INVALID threaded binary tree.")
+        print("This tree is nil.")
     }
-  } else {
-    print("This tree is nil.")
-  }
 }
 
 
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
new file mode 100644
index 000000000..4ae03238d
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -0,0 +1,459 @@
+/*
+ A Threaded Binary Tree.
+ Based on this club's Binary Search Tree implementation.
+ 
+ Each node stores a value and two children. The left child contains a smaller
+ value; the right a larger (or equal) value.
+ 
+ Any nodes that lack either a left or right child instead keep track of their
+ in-order predecessor and/or successor.
+ 
+ This tree allows duplicate elements (we break ties by defaulting right).
+ 
+ This tree does not automatically balance itself. To make sure it is balanced,
+ you should insert new values in randomized order, not in sorted order.
+ */
+public class ThreadedBinaryTree<T: Comparable> {
+    fileprivate(set) public var value: T
+    fileprivate(set) public var parent: ThreadedBinaryTree?
+    fileprivate(set) public var left: ThreadedBinaryTree?
+    fileprivate(set) public var right: ThreadedBinaryTree?
+    fileprivate(set) public var leftThread: ThreadedBinaryTree?
+    fileprivate(set) public var rightThread: ThreadedBinaryTree?
+    
+    public init(value: T) {
+        self.value = value
+    }
+    
+    public convenience init(array: [T]) {
+        precondition(array.count > 0)
+        self.init(value: array.first!)
+        for v in array.dropFirst() {
+            insert(v, parent: self)
+        }
+    }
+    
+    public var isRoot: Bool {
+        return parent == nil
+    }
+    
+    public var isLeaf: Bool {
+        return left == nil && right == nil
+    }
+    
+    public var isLeftChild: Bool {
+        return parent?.left === self
+    }
+    
+    public var isRightChild: Bool {
+        return parent?.right === self
+    }
+    
+    public var hasLeftChild: Bool {
+        return left != nil
+    }
+    
+    public var hasRightChild: Bool {
+        return right != nil
+    }
+    
+    public var hasAnyChild: Bool {
+        return hasLeftChild || hasRightChild
+    }
+    
+    public var hasBothChildren: Bool {
+        return hasLeftChild && hasRightChild
+    }
+    
+    /* How many nodes are in this subtree. Performance: O(n). */
+    public var count: Int {
+        return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+    }
+}
+
+// MARK: - Adding items
+
+extension ThreadedBinaryTree {
+    /*
+     Inserts a new element into the tree. You should only insert elements
+     at the root, to make to sure this remains a valid binary tree!
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func insert(_ value: T) {
+        insert(value, parent: self)
+    }
+    
+    fileprivate func insert(_ value: T, parent: ThreadedBinaryTree) {
+        if value < self.value {
+            if let left = left {
+                left.insert(value, parent: left)
+            } else {
+                left = ThreadedBinaryTree(value: value)
+                left?.parent = parent
+                left?.rightThread = parent
+                left?.leftThread = leftThread
+                leftThread = nil
+            }
+        } else {
+            if let right = right {
+                right.insert(value, parent: right)
+            } else {
+                right = ThreadedBinaryTree(value: value)
+                right?.parent = parent
+                right?.leftThread = parent
+                right?.rightThread = rightThread
+                rightThread = nil
+            }
+        }
+    }
+}
+
+// MARK: - Deleting items
+
+extension ThreadedBinaryTree {
+    /*
+     Deletes the "highest" node with the specified value.
+     
+     Returns the node that has replaced this removed one (or nil if this was a
+     leaf node). That is primarily useful for when you delete the root node, in
+     which case the tree gets a new root.
+     
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func remove(_ value: T) -> ThreadedBinaryTree? {
+        return search(value)?.remove()
+    }
+    
+    /*
+     Deletes "this" node from the tree.
+     */
+    public func remove() -> ThreadedBinaryTree? {
+        let replacement: ThreadedBinaryTree?
+        
+        if let left = left {
+            if let right = right {
+                replacement = removeNodeWithTwoChildren(left, right)
+                replacement?.leftThread = leftThread
+                replacement?.rightThread = rightThread
+                left.maximum().rightThread = replacement
+                right.minimum().leftThread = replacement
+            } else {
+                // This node only has a left child. The left child replaces the node.
+                replacement = left
+                left.maximum().rightThread = rightThread
+            }
+        } else if let right = right {
+            // This node only has a right child. The right child replaces the node.
+            replacement = right
+            right.minimum().leftThread = leftThread
+        } else {
+            // This node has no children. We just disconnect it from its parent.
+            replacement = nil
+            if isLeftChild {
+                parent?.leftThread = leftThread
+            } else {
+                parent?.rightThread = rightThread
+            }
+        }
+        
+        reconnectParentToNode(replacement)
+        
+        // The current node is no longer part of the tree, so clean it up.
+        parent = nil
+        left = nil
+        right = nil
+        leftThread = nil
+        rightThread = nil
+        
+        return replacement
+    }
+    
+    private func removeNodeWithTwoChildren(_ left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
+        // This node has two children. It must be replaced by the smallest
+        // child that is larger than this node's value, which is the leftmost
+        // descendent of the right child.
+        let successor = right.minimum()
+        
+        // If this in-order successor has a right child of its own (it cannot
+        // have a left child by definition), then that must take its place.
+        successor.remove()
+        
+        // Connect our left child with the new node.
+        successor.left = left
+        left.parent = successor
+        
+        // Connect our right child with the new node. If the right child does
+        // not have any left children of its own, then the in-order successor
+        // *is* the right child.
+        if right !== successor {
+            successor.right = right
+            right.parent = successor
+        } else {
+            successor.right = nil
+        }
+        
+        // And finally, connect the successor node to our parent.
+        return successor
+    }
+    
+    private func reconnectParentToNode(_ node: ThreadedBinaryTree?) {
+        if let parent = parent {
+            if isLeftChild {
+                parent.left = node
+            } else {
+                parent.right = node
+            }
+        }
+        node?.parent = parent
+    }
+}
+
+// MARK: - Searching
+
+extension ThreadedBinaryTree {
+    /*
+     Finds the "highest" node with the specified value.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func search(_ value: T) -> ThreadedBinaryTree? {
+        var node: ThreadedBinaryTree? = self
+        while case let n? = node {
+            if value < n.value {
+                node = n.left
+            } else if value > n.value {
+                node = n.right
+            } else {
+                return node
+            }
+        }
+        return nil
+    }
+    
+    /*
+     // Recursive version of search
+     // Educational but undesirable due to the overhead cost of recursion
+     public func search(value: T) -> ThreadedBinaryTree? {
+     if value < self.value {
+     return left?.search(value)
+     } else if value > self.value {
+     return right?.search(value)
+     } else {
+     return self
+     }
+     }
+     */
+    
+    public func contains(value: T) -> Bool {
+        return search(value) != nil
+    }
+    
+    /*
+     Returns the leftmost descendent. O(h) time.
+     */
+    public func minimum() -> ThreadedBinaryTree {
+        var node = self
+        while case let next? = node.left {
+            node = next
+        }
+        return node
+    }
+    
+    /*
+     Returns the rightmost descendent. O(h) time.
+     */
+    public func maximum() -> ThreadedBinaryTree {
+        var node = self
+        while case let next? = node.right {
+            node = next
+        }
+        return node
+    }
+    
+    /*
+     Calculates the depth of this node, i.e. the distance to the root.
+     Takes O(h) time.
+     */
+    public func depth() -> Int {
+        var node = self
+        var edges = 0
+        while case let parent? = node.parent {
+            node = parent
+            edges += 1
+        }
+        return edges
+    }
+    
+    /*
+     Calculates the height of this node, i.e. the distance to the lowest leaf.
+     Since this looks at all children of this node, performance is O(n).
+     */
+    public func height() -> Int {
+        if isLeaf {
+            return 0
+        } else {
+            return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+        }
+    }
+    
+    /*
+     Finds the node whose value precedes our value in sorted order.
+     */
+    public func predecessor() -> ThreadedBinaryTree<T>? {
+        if let left = left {
+            return left.maximum()
+        } else {
+            return leftThread
+        }
+    }
+    
+    /*
+     Finds the node whose value succeeds our value in sorted order.
+     */
+    public func successor() -> ThreadedBinaryTree<T>? {
+        if let right = right {
+            return right.minimum()
+        } else {
+            return rightThread
+        }
+    }
+}
+
+// MARK: - Traversal
+
+extension ThreadedBinaryTree {
+    public func traverseInOrderForward(_ visit: (T) -> Void) {
+        var n: ThreadedBinaryTree
+        n = minimum()
+        while true {
+            visit(n.value)
+            if let successor = n.successor() {
+                n = successor
+            } else {
+                break
+            }
+        }
+    }
+    
+    public func traverseInOrderBackward(_ visit: (T) -> Void) {
+        var n: ThreadedBinaryTree
+        n = maximum()
+        while true {
+            visit(n.value)
+            if let predecessor = n.predecessor() {
+                n = predecessor
+            } else {
+                break
+            }
+        }
+    }
+    
+    public func traversePreOrder(_ visit: (T) -> Void) {
+        visit(value)
+        left?.traversePreOrder(visit)
+        right?.traversePreOrder(visit)
+    }
+    
+    public func traversePostOrder(_ visit: (T) -> Void) {
+        left?.traversePostOrder(visit)
+        right?.traversePostOrder(visit)
+        visit(value)
+    }
+    
+    /*
+     Performs an in-order traversal and collects the results in an array.
+     */
+    public func map(formula: (T) -> T) -> [T] {
+        var a = [T]()
+        var n: ThreadedBinaryTree
+        n = minimum()
+        while true {
+            a.append(formula(n.value))
+            if let successor = n.successor() {
+                n = successor
+            } else {
+                break
+            }
+        }
+        return a
+    }
+}
+
+// MARK: - Verification
+
+extension ThreadedBinaryTree {
+    /*
+     Is this threaded binary tree a valid binary search tree?
+     */
+    public func isBST(minValue: T, maxValue: T) -> Bool {
+        if value < minValue || value > maxValue { return false }
+        let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+        let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+        return leftBST && rightBST
+    }
+    
+    /*
+     Is this binary tree properly threaded?
+     Either left or leftThread (but not both) must be nil (likewise for right).
+     The first and last nodes in the in-order traversal are exempt from this,
+     as the first has leftThread = nil, and the last has rightThread = nil.
+     */
+    public func isThreaded() -> Bool {
+        if left == nil && leftThread == nil {
+            if self !== minimum() { return false }
+        }
+        if left != nil && leftThread != nil {
+            return false
+        }
+        if right == nil && rightThread == nil {
+            if self !== maximum() { return false }
+        }
+        if right != nil && rightThread != nil {
+            return false
+        }
+        let leftThreaded = left?.isThreaded() ?? true
+        let rightThreaded = right?.isThreaded() ?? true
+        return leftThreaded && rightThreaded
+    }
+}
+
+// MARK: - Debugging
+
+extension ThreadedBinaryTree: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if let left = left {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(value)"
+        if let right = right {
+            s += " -> (\(right.description))"
+        }
+        return s
+    }
+}
+
+extension ThreadedBinaryTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = "value: \(value)"
+        if let parent = parent {
+            s += ", parent: \(parent.value)"
+        }
+        if let leftThread = leftThread {
+            s += ", leftThread: \(leftThread.value)"
+        }
+        if let rightThread = rightThread {
+            s += ", rightThread: \(rightThread.value)"
+        }
+        if let left = left {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = right {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
+    }
+    
+    public func toArray() -> [T] {
+        return map { $0 }
+    }
+}
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/contents.xcplayground b/Threaded Binary Tree/ThreadedBinaryTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.swift
deleted file mode 100644
index 98a23d013..000000000
--- a/Threaded Binary Tree/ThreadedBinaryTree.swift	
+++ /dev/null
@@ -1,459 +0,0 @@
-/*
-  A Threaded Binary Tree.
-  Based on this club's Binary Search Tree implementation.
-
-  Each node stores a value and two children. The left child contains a smaller
-  value; the right a larger (or equal) value.
-
-  Any nodes that lack either a left or right child instead keep track of their
-  in-order predecessor and/or successor.
-
-  This tree allows duplicate elements (we break ties by defaulting right).
-
-  This tree does not automatically balance itself. To make sure it is balanced,
-  you should insert new values in randomized order, not in sorted order.
-*/
-public class ThreadedBinaryTree<T: Comparable> {
-  private(set) public var value: T
-  private(set) public var parent: ThreadedBinaryTree?
-  private(set) public var left: ThreadedBinaryTree?
-  private(set) public var right: ThreadedBinaryTree?
-  private(set) public var leftThread: ThreadedBinaryTree?
-  private(set) public var rightThread: ThreadedBinaryTree?
-
-  public init(value: T) {
-    self.value = value
-  }
-
-  public convenience init(array: [T]) {
-    precondition(array.count > 0)
-    self.init(value: array.first!)
-    for v in array.dropFirst() {
-      insert(v, parent: self)
-    }
-  }
-
-  public var isRoot: Bool {
-    return parent == nil
-  }
-
-  public var isLeaf: Bool {
-    return left == nil && right == nil
-  }
-
-  public var isLeftChild: Bool {
-    return parent?.left === self
-  }
-
-  public var isRightChild: Bool {
-    return parent?.right === self
-  }
-
-  public var hasLeftChild: Bool {
-    return left != nil
-  }
-
-  public var hasRightChild: Bool {
-    return right != nil
-  }
-
-  public var hasAnyChild: Bool {
-    return hasLeftChild || hasRightChild
-  }
-
-  public var hasBothChildren: Bool {
-    return hasLeftChild && hasRightChild
-  }
-
-  /* How many nodes are in this subtree. Performance: O(n). */
-  public var count: Int {
-    return (left?.count ?? 0) + 1 + (right?.count ?? 0)
-  }
-}
-
-// MARK: - Adding items
-
-extension ThreadedBinaryTree {
-  /*
-    Inserts a new element into the tree. You should only insert elements
-    at the root, to make to sure this remains a valid binary tree!
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func insert(value: T) {
-    insert(value, parent: self)
-  }
-
-  private func insert(value: T, parent: ThreadedBinaryTree) {
-    if value < self.value {
-      if let left = left {
-        left.insert(value, parent: left)
-      } else {
-        left = ThreadedBinaryTree(value: value)
-        left?.parent = parent
-        left?.rightThread = parent
-        left?.leftThread = leftThread
-        leftThread = nil
-      }
-    } else {
-      if let right = right {
-        right.insert(value, parent: right)
-      } else {
-        right = ThreadedBinaryTree(value: value)
-        right?.parent = parent
-        right?.leftThread = parent
-        right?.rightThread = rightThread
-        rightThread = nil
-      }
-    }
-  }
-}
-
-// MARK: - Deleting items
-
-extension ThreadedBinaryTree {
-  /*
-    Deletes the "highest" node with the specified value.
-
-    Returns the node that has replaced this removed one (or nil if this was a
-    leaf node). That is primarily useful for when you delete the root node, in
-    which case the tree gets a new root.
-
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func remove(value: T) -> ThreadedBinaryTree? {
-    return search(value)?.remove()
-  }
-
-  /*
-    Deletes "this" node from the tree.
-  */
-  public func remove() -> ThreadedBinaryTree? {
-    let replacement: ThreadedBinaryTree?
-
-    if let left = left {
-      if let right = right {
-        replacement = removeNodeWithTwoChildren(left, right)
-        replacement?.leftThread = leftThread
-        replacement?.rightThread = rightThread
-        left.maximum().rightThread = replacement
-        right.minimum().leftThread = replacement
-      } else {
-        // This node only has a left child. The left child replaces the node.
-        replacement = left
-        left.maximum().rightThread = rightThread
-      }
-    } else if let right = right {
-      // This node only has a right child. The right child replaces the node.
-      replacement = right
-      right.minimum().leftThread = leftThread
-    } else {
-      // This node has no children. We just disconnect it from its parent.
-      replacement = nil
-      if isLeftChild {
-        parent?.leftThread = leftThread
-      } else {
-        parent?.rightThread = rightThread
-      }
-    }
-
-    reconnectParentToNode(replacement)
-
-    // The current node is no longer part of the tree, so clean it up.
-    parent = nil
-    left = nil
-    right = nil
-    leftThread = nil
-    rightThread = nil
-
-    return replacement
-  }
-
-  private func removeNodeWithTwoChildren(left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
-    // This node has two children. It must be replaced by the smallest
-    // child that is larger than this node's value, which is the leftmost
-    // descendent of the right child.
-    let successor = right.minimum()
-
-    // If this in-order successor has a right child of its own (it cannot
-    // have a left child by definition), then that must take its place.
-    successor.remove()
-
-    // Connect our left child with the new node.
-    successor.left = left
-    left.parent = successor
-
-    // Connect our right child with the new node. If the right child does
-    // not have any left children of its own, then the in-order successor
-    // *is* the right child.
-    if right !== successor {
-      successor.right = right
-      right.parent = successor
-    } else {
-      successor.right = nil
-    }
-
-    // And finally, connect the successor node to our parent.
-    return successor
-  }
-
-  private func reconnectParentToNode(node: ThreadedBinaryTree?) {
-    if let parent = parent {
-      if isLeftChild {
-        parent.left = node
-      } else {
-        parent.right = node
-      }
-    }
-    node?.parent = parent
-  }
-}
-
-// MARK: - Searching
-
-extension ThreadedBinaryTree {
-  /*
-    Finds the "highest" node with the specified value.
-    Performance: runs in O(h) time, where h is the height of the tree.
-  */
-  public func search(value: T) -> ThreadedBinaryTree? {
-    var node: ThreadedBinaryTree? = self
-    while case let n? = node {
-      if value < n.value {
-        node = n.left
-      } else if value > n.value {
-        node = n.right
-      } else {
-        return node
-      }
-    }
-    return nil
-  }
-
-  /*
-  // Recursive version of search
-  // Educational but undesirable due to the overhead cost of recursion
-  public func search(value: T) -> ThreadedBinaryTree? {
-    if value < self.value {
-      return left?.search(value)
-    } else if value > self.value {
-      return right?.search(value)
-    } else {
-      return self
-    }
-  }
-  */
-
-  public func contains(value: T) -> Bool {
-    return search(value) != nil
-  }
-
-  /*
-    Returns the leftmost descendent. O(h) time.
-  */
-  public func minimum() -> ThreadedBinaryTree {
-    var node = self
-    while case let next? = node.left {
-      node = next
-    }
-    return node
-  }
-
-  /*
-    Returns the rightmost descendent. O(h) time.
-  */
-  public func maximum() -> ThreadedBinaryTree {
-    var node = self
-    while case let next? = node.right {
-      node = next
-    }
-    return node
-  }
-
-  /*
-    Calculates the depth of this node, i.e. the distance to the root.
-    Takes O(h) time.
-  */
-  public func depth() -> Int {
-    var node = self
-    var edges = 0
-    while case let parent? = node.parent {
-      node = parent
-      edges += 1
-    }
-    return edges
-  }
-
-  /*
-    Calculates the height of this node, i.e. the distance to the lowest leaf.
-    Since this looks at all children of this node, performance is O(n).
-  */
-  public func height() -> Int {
-    if isLeaf {
-      return 0
-    } else {
-      return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
-    }
-  }
-
-  /*
-    Finds the node whose value precedes our value in sorted order.
-  */
-  public func predecessor() -> ThreadedBinaryTree<T>? {
-    if let left = left {
-      return left.maximum()
-    } else {
-      return leftThread
-    }
-  }
-
-  /*
-    Finds the node whose value succeeds our value in sorted order.
-  */
-  public func successor() -> ThreadedBinaryTree<T>? {
-    if let right = right {
-      return right.minimum()
-    } else {
-      return rightThread
-    }
-  }
-}
-
-// MARK: - Traversal
-
-extension ThreadedBinaryTree {
-  public func traverseInOrderForward(@noescape visit: T -> Void) {
-    var n: ThreadedBinaryTree
-    n = minimum()
-    while true {
-      visit(n.value)
-      if let successor = n.successor() {
-        n = successor
-      } else {
-        break
-      }
-    }
-  }
-
-  public func traverseInOrderBackward(@noescape visit: T -> Void) {
-    var n: ThreadedBinaryTree
-    n = maximum()
-    while true {
-      visit(n.value)
-      if let predecessor = n.predecessor() {
-        n = predecessor
-      } else {
-        break
-      }
-    }
-  }
-
-  public func traversePreOrder(@noescape visit: T -> Void) {
-    visit(value)
-    left?.traversePreOrder(visit)
-    right?.traversePreOrder(visit)
-  }
-
-  public func traversePostOrder(@noescape visit: T -> Void) {
-    left?.traversePostOrder(visit)
-    right?.traversePostOrder(visit)
-    visit(value)
-  }
-
-  /*
-    Performs an in-order traversal and collects the results in an array.
-  */
-  public func map(@noescape formula: T -> T) -> [T] {
-    var a = [T]()
-    var n: ThreadedBinaryTree
-    n = minimum()
-    while true {
-      a.append(formula(n.value))
-      if let successor = n.successor() {
-        n = successor
-      } else {
-        break
-      }
-    }
-    return a
-  }
-}
-
-// MARK: - Verification
-
-extension ThreadedBinaryTree {
-  /*
-    Is this threaded binary tree a valid binary search tree?
-  */
-  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
-    if value < minValue || value > maxValue { return false }
-    let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
-    let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
-    return leftBST && rightBST
-  }
-
-  /*
-    Is this binary tree properly threaded?
-    Either left or leftThread (but not both) must be nil (likewise for right).
-    The first and last nodes in the in-order traversal are exempt from this,
-    as the first has leftThread = nil, and the last has rightThread = nil.
-  */
-  public func isThreaded() -> Bool {
-    if left == nil && leftThread == nil {
-      if self !== minimum() { return false }
-    }
-    if left != nil && leftThread != nil {
-      return false
-    }
-    if right == nil && rightThread == nil {
-      if self !== maximum() { return false }
-    }
-    if right != nil && rightThread != nil {
-      return false
-    }
-    let leftThreaded = left?.isThreaded() ?? true
-    let rightThreaded = right?.isThreaded() ?? true
-    return leftThreaded && rightThreaded
-  }
-}
-
-// MARK: - Debugging
-
-extension ThreadedBinaryTree: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if let left = left {
-      s += "(\(left.description)) <- "
-    }
-    s += "\(value)"
-    if let right = right {
-      s += " -> (\(right.description))"
-    }
-    return s
-  }
-}
-
-extension ThreadedBinaryTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = "value: \(value)"
-    if let parent = parent {
-      s += ", parent: \(parent.value)"
-    }
-    if let leftThread = leftThread {
-      s += ", leftThread: \(leftThread.value)"
-    }
-    if let rightThread = rightThread {
-      s += ", rightThread: \(rightThread.value)"
-    }
-    if let left = left {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = right {
-      s += ", right = [" + right.debugDescription + "]"
-    }
-    return s
-  }
-
-  public func toArray() -> [T] {
-    return map { $0 }
-  }
-}

From 3fc54e61b6c727323e97cc026021141966aec193 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 7 Feb 2017 18:46:27 +0100
Subject: [PATCH 0813/1679] fix

---
 .../Sources/ThreadedBinaryTree.swift                            | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index 4ae03238d..e703d793a 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -120,7 +120,7 @@ extension ThreadedBinaryTree {
      
      Performance: runs in O(h) time, where h is the height of the tree.
      */
-    public func remove(_ value: T) -> ThreadedBinaryTree? {
+    @discardableResult public func remove(_ value: T) -> ThreadedBinaryTree? {
         return search(value)?.remove()
     }
     

From 92363b88477de2595c69924fb51c65679f9d0d85 Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Tue, 7 Feb 2017 19:01:31 +0100
Subject: [PATCH 0814/1679] fix spaces

---
 .../Contents.swift                            |  42 +-
 .../Sources/ThreadedBinaryTree.swift          | 752 +++++++++---------
 2 files changed, 397 insertions(+), 397 deletions(-)

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index ff59f81d1..e4b527664 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -3,28 +3,28 @@
 
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
-    if let tree = tree {
-        print("\(tree.count) Total Nodes:")
-        print(tree)
-        print("Debug Info:")
-        print(tree.debugDescription)
-        print("In-Order Traversal:")
-        let myArray = tree.toArray()
-        for node in myArray {
-            print(node)
-        }
-        if tree.isBST(minValue: Int.min, maxValue: Int.max) {
-            print("This is a VALID binary search tree.")
-        } else {
-            print("This is an INVALID binary search tree.")
-        }
-        if tree.isThreaded() {
-            print("This is a VALID threaded binary tree.")
-        } else {
-            print("This is an INVALID threaded binary tree.")
-        }
+  if let tree = tree {
+    print("\(tree.count) Total Nodes:")
+    print(tree)
+    print("Debug Info:")
+    print(tree.debugDescription)
+    print("In-Order Traversal:")
+    let myArray = tree.toArray()
+    for node in myArray {
+      print(node)
+    }
+    if tree.isBST(minValue: Int.min, maxValue: Int.max) {
+      print("This is a VALID binary search tree.")
+    } else {
+      print("This is an INVALID binary search tree.")
+    }
+    if tree.isThreaded() {
+      print("This is a VALID threaded binary tree.")
+    } else {
+      print("This is an INVALID threaded binary tree.")
+    }
     } else {
-        print("This tree is nil.")
+      print("This tree is nil.")
     }
 }
 
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index e703d793a..a4d308e77 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -14,446 +14,446 @@
  you should insert new values in randomized order, not in sorted order.
  */
 public class ThreadedBinaryTree<T: Comparable> {
-    fileprivate(set) public var value: T
-    fileprivate(set) public var parent: ThreadedBinaryTree?
-    fileprivate(set) public var left: ThreadedBinaryTree?
-    fileprivate(set) public var right: ThreadedBinaryTree?
-    fileprivate(set) public var leftThread: ThreadedBinaryTree?
-    fileprivate(set) public var rightThread: ThreadedBinaryTree?
-    
-    public init(value: T) {
-        self.value = value
-    }
-    
-    public convenience init(array: [T]) {
-        precondition(array.count > 0)
-        self.init(value: array.first!)
-        for v in array.dropFirst() {
-            insert(v, parent: self)
-        }
-    }
-    
-    public var isRoot: Bool {
-        return parent == nil
-    }
-    
-    public var isLeaf: Bool {
-        return left == nil && right == nil
-    }
-    
-    public var isLeftChild: Bool {
-        return parent?.left === self
-    }
-    
-    public var isRightChild: Bool {
-        return parent?.right === self
-    }
-    
-    public var hasLeftChild: Bool {
-        return left != nil
-    }
-    
-    public var hasRightChild: Bool {
-        return right != nil
-    }
-    
-    public var hasAnyChild: Bool {
-        return hasLeftChild || hasRightChild
-    }
-    
-    public var hasBothChildren: Bool {
-        return hasLeftChild && hasRightChild
-    }
-    
-    /* How many nodes are in this subtree. Performance: O(n). */
-    public var count: Int {
-        return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+  fileprivate(set) public var value: T
+  fileprivate(set) public var parent: ThreadedBinaryTree?
+  fileprivate(set) public var left: ThreadedBinaryTree?
+  fileprivate(set) public var right: ThreadedBinaryTree?
+  fileprivate(set) public var leftThread: ThreadedBinaryTree?
+  fileprivate(set) public var rightThread: ThreadedBinaryTree?
+
+  public init(value: T) {
+    self.value = value
+  }
+
+  public convenience init(array: [T]) {
+    precondition(array.count > 0)
+    self.init(value: array.first!)
+    for v in array.dropFirst() {
+      insert(v, parent: self)
     }
+  }
+
+  public var isRoot: Bool {
+    return parent == nil
+  }
+
+  public var isLeaf: Bool {
+    return left == nil && right == nil
+  }
+
+  public var isLeftChild: Bool {
+    return parent?.left === self
+  }
+
+  public var isRightChild: Bool {
+    return parent?.right === self
+  }
+
+  public var hasLeftChild: Bool {
+    return left != nil
+  }
+
+  public var hasRightChild: Bool {
+    return right != nil
+  }
+
+  public var hasAnyChild: Bool {
+    return hasLeftChild || hasRightChild
+  }
+
+  public var hasBothChildren: Bool {
+    return hasLeftChild && hasRightChild
+  }
+
+  /* How many nodes are in this subtree. Performance: O(n). */
+  public var count: Int {
+    return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+  }
 }
 
 // MARK: - Adding items
 
 extension ThreadedBinaryTree {
-    /*
-     Inserts a new element into the tree. You should only insert elements
-     at the root, to make to sure this remains a valid binary tree!
-     Performance: runs in O(h) time, where h is the height of the tree.
-     */
-    public func insert(_ value: T) {
-        insert(value, parent: self)
-    }
+  /*
+  Inserts a new element into the tree. You should only insert elements
+  at the root, to make to sure this remains a valid binary tree!
+  Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func insert(_ value: T) {
+    insert(value, parent: self)
+  }
     
-    fileprivate func insert(_ value: T, parent: ThreadedBinaryTree) {
-        if value < self.value {
-            if let left = left {
-                left.insert(value, parent: left)
-            } else {
-                left = ThreadedBinaryTree(value: value)
-                left?.parent = parent
-                left?.rightThread = parent
-                left?.leftThread = leftThread
-                leftThread = nil
-            }
-        } else {
-            if let right = right {
-                right.insert(value, parent: right)
-            } else {
-                right = ThreadedBinaryTree(value: value)
-                right?.parent = parent
-                right?.leftThread = parent
-                right?.rightThread = rightThread
-                rightThread = nil
-            }
-        }
+  fileprivate func insert(_ value: T, parent: ThreadedBinaryTree) {
+    if value < self.value {
+      if let left = left {
+        left.insert(value, parent: left)
+      } else {
+        left = ThreadedBinaryTree(value: value)
+        left?.parent = parent
+        left?.rightThread = parent
+        left?.leftThread = leftThread
+        leftThread = nil
+      }
+    } else {
+      if let right = right {
+        right.insert(value, parent: right)
+      } else {
+        right = ThreadedBinaryTree(value: value)
+        right?.parent = parent
+        right?.leftThread = parent
+        right?.rightThread = rightThread
+        rightThread = nil
+      }
     }
+  }
 }
 
 // MARK: - Deleting items
 
 extension ThreadedBinaryTree {
-    /*
-     Deletes the "highest" node with the specified value.
+  /*
+  Deletes the "highest" node with the specified value.
      
-     Returns the node that has replaced this removed one (or nil if this was a
-     leaf node). That is primarily useful for when you delete the root node, in
-     which case the tree gets a new root.
+  Returns the node that has replaced this removed one (or nil if this was a
+  leaf node). That is primarily useful for when you delete the root node, in
+  which case the tree gets a new root.
      
-     Performance: runs in O(h) time, where h is the height of the tree.
-     */
-    @discardableResult public func remove(_ value: T) -> ThreadedBinaryTree? {
-        return search(value)?.remove()
-    }
+  Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  @discardableResult public func remove(_ value: T) -> ThreadedBinaryTree? {
+    return search(value)?.remove()
+  }
     
-    /*
-     Deletes "this" node from the tree.
-     */
-    public func remove() -> ThreadedBinaryTree? {
-        let replacement: ThreadedBinaryTree?
+  /*
+  Deletes "this" node from the tree.
+  */
+  public func remove() -> ThreadedBinaryTree? {
+    let replacement: ThreadedBinaryTree?
         
-        if let left = left {
-            if let right = right {
-                replacement = removeNodeWithTwoChildren(left, right)
-                replacement?.leftThread = leftThread
-                replacement?.rightThread = rightThread
-                left.maximum().rightThread = replacement
-                right.minimum().leftThread = replacement
-            } else {
-                // This node only has a left child. The left child replaces the node.
-                replacement = left
-                left.maximum().rightThread = rightThread
-            }
-        } else if let right = right {
-            // This node only has a right child. The right child replaces the node.
-            replacement = right
-            right.minimum().leftThread = leftThread
-        } else {
-            // This node has no children. We just disconnect it from its parent.
-            replacement = nil
-            if isLeftChild {
-                parent?.leftThread = leftThread
-            } else {
-                parent?.rightThread = rightThread
-            }
-        }
+    if let left = left {
+      if let right = right {
+        replacement = removeNodeWithTwoChildren(left, right)
+        replacement?.leftThread = leftThread
+        replacement?.rightThread = rightThread
+        left.maximum().rightThread = replacement
+        right.minimum().leftThread = replacement
+      } else {
+        // This node only has a left child. The left child replaces the node.
+        replacement = left
+        left.maximum().rightThread = rightThread
+      }
+    } else if let right = right {
+      // This node only has a right child. The right child replaces the node.
+      replacement = right
+      right.minimum().leftThread = leftThread
+    } else {
+      // This node has no children. We just disconnect it from its parent.
+      replacement = nil
+      if isLeftChild {
+        parent?.leftThread = leftThread
+      } else {
+        parent?.rightThread = rightThread
+      }
+    }
         
-        reconnectParentToNode(replacement)
+    reconnectParentToNode(replacement)
         
-        // The current node is no longer part of the tree, so clean it up.
-        parent = nil
-        left = nil
-        right = nil
-        leftThread = nil
-        rightThread = nil
+    // The current node is no longer part of the tree, so clean it up.
+    parent = nil
+    left = nil
+    right = nil
+    leftThread = nil
+    rightThread = nil
         
-        return replacement
-    }
+    return replacement
+  }
     
-    private func removeNodeWithTwoChildren(_ left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
+  private func removeNodeWithTwoChildren(_ left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
+    // This node has two children. It must be replaced by the smallest
+    // child that is larger than this node's value, which is the leftmost
+    // descendent of the right child.
+    let successor = right.minimum()
         
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
+    // If this in-order successor has a right child of its own (it cannot
+    // have a left child by definition), then that must take its place.
+    successor.remove()
         
-        // Connect our left child with the new node.
-        successor.left = left
-        left.parent = successor
+    // Connect our left child with the new node.
+    successor.left = left
+    left.parent = successor
         
-        // Connect our right child with the new node. If the right child does
-        // not have any left children of its own, then the in-order successor
-        // *is* the right child.
-        if right !== successor {
-            successor.right = right
-            right.parent = successor
-        } else {
-            successor.right = nil
-        }
-        
-        // And finally, connect the successor node to our parent.
-        return successor
+    // Connect our right child with the new node. If the right child does
+    // not have any left children of its own, then the in-order successor
+    // *is* the right child.
+    if right !== successor {
+      successor.right = right
+      right.parent = successor
+    } else {
+      successor.right = nil
     }
+        
+    // And finally, connect the successor node to our parent.
+    return successor
+  }
     
-    private func reconnectParentToNode(_ node: ThreadedBinaryTree?) {
-        if let parent = parent {
-            if isLeftChild {
-                parent.left = node
-            } else {
-                parent.right = node
-            }
-        }
-        node?.parent = parent
-    }
+  private func reconnectParentToNode(_ node: ThreadedBinaryTree?) {
+    if let parent = parent {
+      if isLeftChild {
+        parent.left = node
+      } else {
+        parent.right = node
+      }
+    }
+    node?.parent = parent
+  }
 }
 
 // MARK: - Searching
 
 extension ThreadedBinaryTree {
-    /*
-     Finds the "highest" node with the specified value.
-     Performance: runs in O(h) time, where h is the height of the tree.
-     */
-    public func search(_ value: T) -> ThreadedBinaryTree? {
-        var node: ThreadedBinaryTree? = self
-        while case let n? = node {
-            if value < n.value {
-                node = n.left
-            } else if value > n.value {
-                node = n.right
-            } else {
-                return node
-            }
-        }
-        return nil
+  /*
+  Finds the "highest" node with the specified value.
+  Performance: runs in O(h) time, where h is the height of the tree.
+  */
+  public func search(_ value: T) -> ThreadedBinaryTree? {
+    var node: ThreadedBinaryTree? = self
+    while case let n? = node {
+      if value < n.value {
+        node = n.left
+      } else if value > n.value {
+        node = n.right
+      } else {
+        return node
+      }
     }
+    return nil
+  }
     
-    /*
-     // Recursive version of search
-     // Educational but undesirable due to the overhead cost of recursion
-     public func search(value: T) -> ThreadedBinaryTree? {
-     if value < self.value {
-     return left?.search(value)
-     } else if value > self.value {
-     return right?.search(value)
-     } else {
-     return self
-     }
-     }
-     */
+  /*
+  // Recursive version of search
+  // Educational but undesirable due to the overhead cost of recursion
+  public func search(value: T) -> ThreadedBinaryTree? {
+    if value < self.value {
+      return left?.search(value)
+    } else if value > self.value {
+      return right?.search(value)
+    } else {
+      return self
+    }
+  }
+  */
     
-    public func contains(value: T) -> Bool {
-        return search(value) != nil
-    }
+  public func contains(value: T) -> Bool {
+    return search(value) != nil
+  }
     
-    /*
-     Returns the leftmost descendent. O(h) time.
-     */
-    public func minimum() -> ThreadedBinaryTree {
-        var node = self
-        while case let next? = node.left {
-            node = next
-        }
-        return node
-    }
+  /*
+  Returns the leftmost descendent. O(h) time.
+  */
+  public func minimum() -> ThreadedBinaryTree {
+    var node = self
+    while case let next? = node.left {
+      node = next
+    }
+    return node
+  }
     
-    /*
-     Returns the rightmost descendent. O(h) time.
-     */
-    public func maximum() -> ThreadedBinaryTree {
-        var node = self
-        while case let next? = node.right {
-            node = next
-        }
-        return node
-    }
+  /*
+  Returns the rightmost descendent. O(h) time.
+  */
+  public func maximum() -> ThreadedBinaryTree {
+    var node = self
+    while case let next? = node.right {
+      node = next
+    }
+    return node
+  }
     
-    /*
-     Calculates the depth of this node, i.e. the distance to the root.
-     Takes O(h) time.
-     */
-    public func depth() -> Int {
-        var node = self
-        var edges = 0
-        while case let parent? = node.parent {
-            node = parent
-            edges += 1
-        }
-        return edges
-    }
+  /*
+  Calculates the depth of this node, i.e. the distance to the root.
+  Takes O(h) time.
+  */
+  public func depth() -> Int {
+    var node = self
+    var edges = 0
+    while case let parent? = node.parent {
+      node = parent
+      edges += 1
+    }
+    return edges
+  }
     
-    /*
-     Calculates the height of this node, i.e. the distance to the lowest leaf.
-     Since this looks at all children of this node, performance is O(n).
-     */
-    public func height() -> Int {
-        if isLeaf {
-            return 0
-        } else {
-            return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
-        }
-    }
+  /*
+  Calculates the height of this node, i.e. the distance to the lowest leaf.
+  Since this looks at all children of this node, performance is O(n).
+  */
+  public func height() -> Int {
+    if isLeaf {
+      return 0
+    } else {
+      return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+    }
+  }
     
-    /*
-     Finds the node whose value precedes our value in sorted order.
-     */
-    public func predecessor() -> ThreadedBinaryTree<T>? {
-        if let left = left {
-            return left.maximum()
-        } else {
-            return leftThread
-        }
-    }
+  /*
+  Finds the node whose value precedes our value in sorted order.
+  */
+  public func predecessor() -> ThreadedBinaryTree<T>? {
+    if let left = left {
+      return left.maximum()
+    } else {
+      return leftThread
+    }
+  }
     
-    /*
-     Finds the node whose value succeeds our value in sorted order.
-     */
-    public func successor() -> ThreadedBinaryTree<T>? {
-        if let right = right {
-            return right.minimum()
-        } else {
-            return rightThread
-        }
-    }
+  /*
+  Finds the node whose value succeeds our value in sorted order.
+  */
+  public func successor() -> ThreadedBinaryTree<T>? {
+    if let right = right {
+      return right.minimum()
+    } else {
+      return rightThread
+    }
+  }
 }
 
 // MARK: - Traversal
 
 extension ThreadedBinaryTree {
-    public func traverseInOrderForward(_ visit: (T) -> Void) {
-        var n: ThreadedBinaryTree
-        n = minimum()
-        while true {
-            visit(n.value)
-            if let successor = n.successor() {
-                n = successor
-            } else {
-                break
-            }
-        }
-    }
+  public func traverseInOrderForward(_ visit: (T) -> Void) {
+    var n: ThreadedBinaryTree
+    n = minimum()
+    while true {
+      visit(n.value)
+      if let successor = n.successor() {
+        n = successor
+      } else {
+        break
+      }
+    }
+  }
     
-    public func traverseInOrderBackward(_ visit: (T) -> Void) {
-        var n: ThreadedBinaryTree
-        n = maximum()
-        while true {
-            visit(n.value)
-            if let predecessor = n.predecessor() {
-                n = predecessor
-            } else {
-                break
-            }
-        }
-    }
+  public func traverseInOrderBackward(_ visit: (T) -> Void) {
+    var n: ThreadedBinaryTree
+    n = maximum()
+    while true {
+      visit(n.value)
+      if let predecessor = n.predecessor() {
+        n = predecessor
+      } else {
+        break
+      }
+    }
+  }
     
-    public func traversePreOrder(_ visit: (T) -> Void) {
-        visit(value)
-        left?.traversePreOrder(visit)
-        right?.traversePreOrder(visit)
-    }
+  public func traversePreOrder(_ visit: (T) -> Void) {
+    visit(value)
+    left?.traversePreOrder(visit)
+    right?.traversePreOrder(visit)
+  }
     
-    public func traversePostOrder(_ visit: (T) -> Void) {
-        left?.traversePostOrder(visit)
-        right?.traversePostOrder(visit)
-        visit(value)
-    }
+  public func traversePostOrder(_ visit: (T) -> Void) {
+    left?.traversePostOrder(visit)
+    right?.traversePostOrder(visit)
+    visit(value)
+  }
     
-    /*
-     Performs an in-order traversal and collects the results in an array.
-     */
-    public func map(formula: (T) -> T) -> [T] {
-        var a = [T]()
-        var n: ThreadedBinaryTree
-        n = minimum()
-        while true {
-            a.append(formula(n.value))
-            if let successor = n.successor() {
-                n = successor
-            } else {
-                break
-            }
-        }
-        return a
-    }
+  /*
+  Performs an in-order traversal and collects the results in an array.
+  */
+  public func map(formula: (T) -> T) -> [T] {
+    var a = [T]()
+    var n: ThreadedBinaryTree
+    n = minimum()
+    while true {
+      a.append(formula(n.value))
+      if let successor = n.successor() {
+        n = successor
+      } else {
+        break
+      }
+    }
+    return a
+  }
 }
 
 // MARK: - Verification
 
 extension ThreadedBinaryTree {
-    /*
-     Is this threaded binary tree a valid binary search tree?
-     */
-    public func isBST(minValue: T, maxValue: T) -> Bool {
-        if value < minValue || value > maxValue { return false }
-        let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
-        let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
-        return leftBST && rightBST
-    }
+  /*
+  Is this threaded binary tree a valid binary search tree?
+  */
+  public func isBST(minValue: T, maxValue: T) -> Bool {
+    if value < minValue || value > maxValue { return false }
+    let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+    let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+    return leftBST && rightBST
+  }
     
-    /*
-     Is this binary tree properly threaded?
-     Either left or leftThread (but not both) must be nil (likewise for right).
-     The first and last nodes in the in-order traversal are exempt from this,
-     as the first has leftThread = nil, and the last has rightThread = nil.
-     */
-    public func isThreaded() -> Bool {
-        if left == nil && leftThread == nil {
-            if self !== minimum() { return false }
-        }
-        if left != nil && leftThread != nil {
-            return false
-        }
-        if right == nil && rightThread == nil {
-            if self !== maximum() { return false }
-        }
-        if right != nil && rightThread != nil {
-            return false
-        }
-        let leftThreaded = left?.isThreaded() ?? true
-        let rightThreaded = right?.isThreaded() ?? true
-        return leftThreaded && rightThreaded
-    }
+  /*
+  Is this binary tree properly threaded?
+  Either left or leftThread (but not both) must be nil (likewise for right).
+  The first and last nodes in the in-order traversal are exempt from this,
+  as the first has leftThread = nil, and the last has rightThread = nil.
+  */
+  public func isThreaded() -> Bool {
+    if left == nil && leftThread == nil {
+      if self !== minimum() { return false }
+    }
+    if left != nil && leftThread != nil {
+      return false
+    }
+    if right == nil && rightThread == nil {
+      if self !== maximum() { return false }
+    }
+    if right != nil && rightThread != nil {
+      return false
+    }
+    let leftThreaded = left?.isThreaded() ?? true
+    let rightThreaded = right?.isThreaded() ?? true
+    return leftThreaded && rightThreaded
+  }
 }
 
 // MARK: - Debugging
 
 extension ThreadedBinaryTree: CustomStringConvertible {
-    public var description: String {
-        var s = ""
-        if let left = left {
-            s += "(\(left.description)) <- "
-        }
-        s += "\(value)"
-        if let right = right {
-            s += " -> (\(right.description))"
-        }
-        return s
+  public var description: String {
+    var s = ""
+    if let left = left {
+      s += "(\(left.description)) <- "
     }
+    s += "\(value)"
+    if let right = right {
+      s += " -> (\(right.description))"
+    }
+    return s
+  }
 }
 
 extension ThreadedBinaryTree: CustomDebugStringConvertible {
-    public var debugDescription: String {
-        var s = "value: \(value)"
-        if let parent = parent {
-            s += ", parent: \(parent.value)"
-        }
-        if let leftThread = leftThread {
-            s += ", leftThread: \(leftThread.value)"
-        }
-        if let rightThread = rightThread {
-            s += ", rightThread: \(rightThread.value)"
-        }
-        if let left = left {
-            s += ", left = [" + left.debugDescription + "]"
-        }
-        if let right = right {
-            s += ", right = [" + right.debugDescription + "]"
-        }
-        return s
+  public var debugDescription: String {
+    var s = "value: \(value)"
+    if let parent = parent {
+      s += ", parent: \(parent.value)"
     }
-    
-    public func toArray() -> [T] {
-        return map { $0 }
+    if let leftThread = leftThread {
+      s += ", leftThread: \(leftThread.value)"
     }
+    if let rightThread = rightThread {
+      s += ", rightThread: \(rightThread.value)"
+    }
+    if let left = left {
+      s += ", left = [" + left.debugDescription + "]"
+    }
+    if let right = right {
+      s += ", right = [" + right.debugDescription + "]"
+    }
+    return s
+  }
+    
+  public func toArray() -> [T] {
+    return map { $0 }
+  }
 }

From c1c1a55904bf2f02c426ddcda33633443fe82656 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Wed, 8 Feb 2017 00:29:35 -0500
Subject: [PATCH 0815/1679] fix warning

---
 .../Sources/ThreadedBinaryTree.swift                            | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index a4d308e77..6f438c0cf 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -176,7 +176,7 @@ extension ThreadedBinaryTree {
         
     // If this in-order successor has a right child of its own (it cannot
     // have a left child by definition), then that must take its place.
-    successor.remove()
+    _ = successor.remove()
         
     // Connect our left child with the new node.
     successor.left = left

From e149dac200ddd46d110fa94a39c539fde919adf4 Mon Sep 17 00:00:00 2001
From: Yurii Samsoniuk <mr.sigito@gmail.com>
Date: Sat, 11 Feb 2017 16:31:04 +0100
Subject: [PATCH 0816/1679] Create big enough array for merge results

---
 Merge Sort/MergeSort.swift | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index f77d1cd84..990c432fa 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -18,6 +18,9 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var leftIndex = 0
   var rightIndex = 0
   var orderedPile = [T]()
+  if orderedPile.capacity < leftPile.count + rightPile.count {
+    orderedPile.reserveCapacity(leftPile.count + rightPile.count)
+  }
 
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
     if leftPile[leftIndex] < rightPile[rightIndex] {

From bfef1ee575456b66f1cb483750f2f6164dcea7a5 Mon Sep 17 00:00:00 2001
From: Yurii Samsoniuk <mr.sigito@gmail.com>
Date: Sat, 11 Feb 2017 16:32:34 +0100
Subject: [PATCH 0817/1679] Also update workspace content

---
 Merge Sort/MergeSort.playground/Contents.swift | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index 2952fc299..137dd19e2 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -12,6 +12,9 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var leftIndex = 0
   var rightIndex = 0
   var orderedPile = [T]()
+  if orderedPile.capacity < leftPile.count + rightPile.count {
+    orderedPile.reserveCapacity(leftPile.count + rightPile.count)
+  }
 
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
     if leftPile[leftIndex] < rightPile[rightIndex] {

From 8f57fbb8635df485a125cad192c9685999b71b22 Mon Sep 17 00:00:00 2001
From: Yurii Samsoniuk <mr.sigito@gmail.com>
Date: Mon, 13 Feb 2017 09:49:30 +0100
Subject: [PATCH 0818/1679] Use string interpolation for the whole description
 string

---
 Binary Tree/BinaryTree.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index ad5fcfd13..61ae696c7 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -21,7 +21,7 @@ extension BinaryTree: CustomStringConvertible {
   public var description: String {
     switch self {
     case let .node(left, value, right):
-      return "value: \(value), left = [" + left.description + "], right = [" + right.description + "]"
+      return "value: \(value), left = [\(left.description)], right = [\(right.description)]"
     case .empty:
       return ""
     }

From b68b3b9309ecea1d56e8c5bf40779156abfafbe1 Mon Sep 17 00:00:00 2001
From: Yurii Samsoniuk <mr.sigito@gmail.com>
Date: Mon, 13 Feb 2017 09:50:24 +0100
Subject: [PATCH 0819/1679] Updated playground content

---
 Binary Tree/BinaryTree.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index b4d65ec1f..aa084e44d 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -18,7 +18,7 @@ extension BinaryTree: CustomStringConvertible {
   public var description: String {
     switch self {
     case let .node(left, value, right):
-      return "value: \(value), left = [" + left.description + "], right = [" + right.description + "]"
+      return "value: \(value), left = [\(left.description)], right = [\(right.description)]"
     case .empty:
       return ""
     }

From 0155784b6cb0860d66f877439ebfe0acfa8ff29f Mon Sep 17 00:00:00 2001
From: Yurii Samsoniuk <mr.sigito@gmail.com>
Date: Mon, 13 Feb 2017 09:51:23 +0100
Subject: [PATCH 0820/1679] Updated README content

---
 Binary Tree/README.markdown | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 52089b8e7..896116dda 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -58,8 +58,7 @@ extension BinaryTree: CustomStringConvertible {
   public var description: String {
     switch self {
     case let .node(left, value, right):
-      return "value: \(value), left = [" + left.description + "], right = [" 
-                                         + right.description + "]"
+      return "value: \(value), left = [\(left.description)], right = [\(right.description)]"
     case .empty:
       return ""
     }

From cb64ed6034f91f5a300d0f728f08a4c09cd3e8f0 Mon Sep 17 00:00:00 2001
From: abhisood <abhisood@gmail.com>
Date: Mon, 13 Feb 2017 03:13:53 -0800
Subject: [PATCH 0821/1679] Trie - Support prefix matching

Solves issue #378
---
 Trie/Trie/Trie/Trie.swift           | 54 ++++++++++++++++++++++++-----
 Trie/Trie/TrieTests/TrieTests.swift | 16 +++++++++
 2 files changed, 61 insertions(+), 9 deletions(-)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 0e11a9c61..cc310b9ee 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -135,7 +135,26 @@ extension Trie {
     }
     return currentNode.isTerminating
   }
-  
+
+
+  /// Attempts to walk to the last node of a word.  The
+  /// search will fail if the word is not present. Doesn't
+  /// check if the node is terminating
+  ///
+  /// - Parameter word: the word in question
+  /// - Returns: the node where the search ended, nil if the
+  /// search failed.
+  private func findLastNodeOf(word: String) -> Node? {
+      var currentNode = root
+      for character in word.lowercased().characters {
+          guard let childNode = currentNode.children[character] else {
+              return nil
+          }
+          currentNode = childNode
+      }
+      return currentNode
+  }
+
   /// Attempts to walk to the terminating node of a word.  The
   /// search will fail if the word is not present.
   ///
@@ -143,14 +162,11 @@ extension Trie {
   /// - Returns: the node where the search ended, nil if the
   /// search failed.
   private func findTerminalNodeOf(word: String) -> Node? {
-    var currentNode = root
-    for character in word.lowercased().characters {
-      guard let childNode = currentNode.children[character] else {
-        return nil
-      }
-      currentNode = childNode
+    if let lastNode = findLastNodeOf(word: word) {
+        return lastNode.isTerminating ? lastNode : nil
     }
-    return currentNode.isTerminating ? currentNode : nil
+    return nil
+
   }
   
   /// Deletes a word from the trie by starting with the last letter
@@ -201,7 +217,7 @@ extension Trie {
   ///   - rootNode: the root node of the subtrie
   ///   - partialWord: the letters collected by traversing to this node
   /// - Returns: the words in the subtrie
-  func wordsInSubtrie(rootNode: Node, partialWord: String) -> [String] {
+  fileprivate func wordsInSubtrie(rootNode: Node, partialWord: String) -> [String] {
     var subtrieWords = [String]()
     var previousLetters = partialWord
     if let value = rootNode.value {
@@ -216,4 +232,24 @@ extension Trie {
     }
     return subtrieWords
   }
+
+  /// Returns an array of words in a subtrie of the trie that start
+  /// with given prefix
+  ///
+  /// - Parameters:
+  ///   - prefix: the letters for word prefix
+  /// - Returns: the words in the subtrie that start with prefix
+  func findWordsWithPrefix(prefix: String) -> [String] {
+      var words = [String]()
+      if let lastNode = findLastNodeOf(word: prefix) {
+          if lastNode.isTerminating {
+              words.append(prefix)
+          }
+          for childNode in lastNode.children.values {
+              let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefix)
+              words += childWords
+          }
+      }
+      return words
+  }
 }
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index f8e934f0d..de41663a9 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -168,4 +168,20 @@ class TrieTests: XCTestCase {
         XCTAssertEqual(trieCopy.count, trie.count)
 
     }
+
+    func testFindWordsWithPrefix() {
+        let trie = Trie()
+        trie.insert(word: "test")
+        trie.insert(word: "another")
+        trie.insert(word: "exam")
+        let wordsAll = trie.findWordsWithPrefix(prefix: "")
+        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"]);
+        let words = trie.findWordsWithPrefix(prefix: "ex")
+        XCTAssertEqual(words, ["exam"]);
+        trie.insert(word: "examination")
+        let words2 = trie.findWordsWithPrefix(prefix: "exam")
+        XCTAssertEqual(words2, ["exam", "examination"]);
+        let noWords = trie.findWordsWithPrefix(prefix: "tee")
+        XCTAssertEqual(noWords, []);
+    }
 }

From 9c5a98dc5f64b941f38596088fd867f601a97af7 Mon Sep 17 00:00:00 2001
From: abhisood <abhisood@gmail.com>
Date: Mon, 13 Feb 2017 03:58:25 -0800
Subject: [PATCH 0822/1679] Handle uppercase prefix

---
 Trie/Trie/Trie/Trie.swift           | 7 ++++---
 Trie/Trie/TrieTests/TrieTests.swift | 8 ++++++++
 2 files changed, 12 insertions(+), 3 deletions(-)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index cc310b9ee..4321479c3 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -241,12 +241,13 @@ extension Trie {
   /// - Returns: the words in the subtrie that start with prefix
   func findWordsWithPrefix(prefix: String) -> [String] {
       var words = [String]()
-      if let lastNode = findLastNodeOf(word: prefix) {
+      let prefixLowerCased = prefix.lowercased()
+      if let lastNode = findLastNodeOf(word: prefixLowerCased) {
           if lastNode.isTerminating {
-              words.append(prefix)
+              words.append(prefixLowerCased)
           }
           for childNode in lastNode.children.values {
-              let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefix)
+              let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefixLowerCased)
               words += childWords
           }
       }
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index de41663a9..a75c35c62 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -183,5 +183,13 @@ class TrieTests: XCTestCase {
         XCTAssertEqual(words2, ["exam", "examination"]);
         let noWords = trie.findWordsWithPrefix(prefix: "tee")
         XCTAssertEqual(noWords, []);
+        let unicodeWord = "😬😎"
+        trie.insert(word: unicodeWord)
+        let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
+        XCTAssertEqual(wordsUnicode, [unicodeWord]);
+        trie.insert(word: "Team")
+        let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
+        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"]);
+
     }
 }

From ba3975281965852471a40f7a58514fa1d98d1578 Mon Sep 17 00:00:00 2001
From: Adrian <adrian.bolinger@me.com>
Date: Wed, 15 Feb 2017 18:11:12 -0500
Subject: [PATCH 0823/1679] Update CountingSort.swift to Swift 3.0 syntax

Updated to Swift 3.0 syntax
---
 Counting Sort/CountingSort.swift | 66 ++++++++++++++++----------------
 1 file changed, 34 insertions(+), 32 deletions(-)

diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index d37bb2eff..9a1ffb373 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -6,39 +6,41 @@
 //  Copyright © 2016 Ali Hafizji. All rights reserved.
 //
 
-enum CountingSortError: ErrorType {
-  case arrayEmpty
+import Foundation
+
+enum CountingSortError: Error {
+    case arrayEmpty
 }
 
 func countingSort(array: [Int]) throws -> [Int] {
-  guard array.count > 0 else {
-    throw CountingSortError.arrayEmpty
-  }
-
-  // Step 1
-  // Create an array to store the count of each element
-  let maxElement = array.maxElement() ?? 0
-
-  var countArray = [Int](count: Int(maxElement + 1), repeatedValue: 0)
-  for element in array {
-    countArray[element] += 1
-  }
-
-  // Step 2
-  // Set each value to be the sum of the previous two values
-  for index in 1 ..< countArray.count {
-    let sum = countArray[index] + countArray[index - 1]
-    countArray[index] = sum
-  }
-
-  print(countArray)
-
-  // Step 3
-  // Place the element in the final array as per the number of elements before it
-  var sortedArray = [Int](count: array.count, repeatedValue: 0)
-  for element in array {
-    countArray[element] -= 1
-    sortedArray[countArray[element]] = element
-  }
-  return sortedArray
+    guard array.count > 0 else {
+        throw CountingSortError.arrayEmpty
+    }
+    
+    // Step 1
+    // Create an array to store the count of each element
+    let maxElement = array.max() ?? 0
+    
+    var countArray = [Int](repeating: 0, count: Int(maxElement + 1))
+    for element in array {
+        countArray[element] += 1
+    }
+    
+    // Step 2
+    // Set each value to be the sum of the previous two values
+    for index in 1 ..< countArray.count {
+        let sum = countArray[index] + countArray[index - 1]
+        countArray[index] = sum
+    }
+    
+    print(countArray)
+    
+    // Step 3
+    // Place the element in the final array as per the number of elements before it
+    var sortedArray = [Int](repeating: 0, count: array.count)
+    for element in array {
+        countArray[element] -= 1
+        sortedArray[countArray[element]] = element
+    }
+    return sortedArray
 }

From 0b93a48f4dd66111fb9033e187cb4176d51d6dc0 Mon Sep 17 00:00:00 2001
From: Timur Galimov <timakgalimov@gmail.com>
Date: Sat, 18 Feb 2017 02:20:13 +0300
Subject: [PATCH 0824/1679] Quadtree

---
 QuadTree/QuadTree.playground/Contents.swift   |  14 +
 .../Sources/QuadTree.swift                    | 290 ++++++++++++++++++
 .../QuadTree.playground/contents.xcplayground |   4 +
 .../contents.xcworkspacedata                  |   7 +
 QuadTree/README.md                            | 158 ++++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 274 +++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 QuadTree/Tests/Tests/Info.plist               |  22 ++
 QuadTree/Tests/Tests/Tests.swift              |  85 +++++
 9 files changed, 861 insertions(+)
 create mode 100644 QuadTree/QuadTree.playground/Contents.swift
 create mode 100644 QuadTree/QuadTree.playground/Sources/QuadTree.swift
 create mode 100644 QuadTree/QuadTree.playground/contents.xcplayground
 create mode 100644 QuadTree/QuadTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 QuadTree/README.md
 create mode 100644 QuadTree/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 QuadTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 QuadTree/Tests/Tests/Info.plist
 create mode 100644 QuadTree/Tests/Tests/Tests.swift

diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
new file mode 100644
index 000000000..41e73147f
--- /dev/null
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -0,0 +1,14 @@
+
+import Foundation
+
+let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))
+
+for _ in 0..<40 {
+  let randomX = Double(arc4random_uniform(100)) / 10
+  let randomY = Double(arc4random_uniform(100)) / 10
+  let point = Point(randomX, randomY)
+  tree.add(point: point)
+}
+
+print(tree)
+print(tree.points(inRect: Rect(origin: Point(1, 1), size: Size(xLength: 5, yLength: 5))))
diff --git a/QuadTree/QuadTree.playground/Sources/QuadTree.swift b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
new file mode 100644
index 000000000..beec4a7b7
--- /dev/null
+++ b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
@@ -0,0 +1,290 @@
+
+public struct Point {
+  let x: Double
+  let y: Double
+  
+  public init(_ x: Double, _ y: Double) {
+    self.x = x
+    self.y = y
+  }
+}
+
+extension Point: CustomStringConvertible {
+  public var description: String {
+    return "Point(\(x), \(y))"
+  }
+}
+
+public struct Size: CustomStringConvertible {
+  var xLength: Double
+  var yLength: Double
+  
+  public init(xLength: Double, yLength: Double) {
+    precondition(xLength >= 0, "xLength can not be negative")
+    precondition(yLength >= 0, "yLength can not be negative")
+    self.xLength = xLength
+    self.yLength = yLength
+  }
+  
+  var half: Size {
+    return Size(xLength: xLength / 2, yLength: yLength / 2)
+  }
+  
+  public var description: String {
+    return "Size(\(xLength), \(yLength))"
+  }
+}
+
+public struct Rect {
+  // left top vertice
+  var origin: Point
+  var size: Size
+  
+  public init(origin: Point, size: Size) {
+    self.origin = origin
+    self.size = size
+  }
+  
+  var minX: Double {
+    return origin.x
+  }
+  
+  var minY: Double {
+    return origin.y
+  }
+  
+  var maxX: Double {
+    return origin.x + size.xLength
+  }
+  
+  var maxY: Double {
+    return origin.y + size.yLength
+  }
+  
+  func containts(point: Point) -> Bool {
+    return (minX <= point.x && point.x <= maxX) &&
+      (minY <= point.y && point.y <= maxY)
+  }
+  
+  var leftTopRect: Rect {
+    return Rect(origin: origin, size: size.half)
+  }
+  
+  var leftBottomRect: Rect {
+    return Rect(origin: Point(origin.x, origin.y + size.half.yLength), size: size.half)
+  }
+  
+  var rightTopRect: Rect {
+    return Rect(origin: Point(origin.x + size.half.xLength, origin.y), size: size.half)
+  }
+  
+  var rightBottomRect: Rect {
+    return Rect(origin: Point(origin.x + size.half.xLength, origin.y + size.half.yLength), size: size.half)
+  }
+  
+  func intersects(rect: Rect) -> Bool {
+
+    func lineSegmentsIntersect(lStart: Double, lEnd: Double, rStart: Double, rEnd: Double) -> Bool {
+      return max(lStart, rStart) <= min(lEnd, rEnd)
+    }
+    // to intersect, both horizontal and vertical projections need to intersect
+    // horizontal
+    if !lineSegmentsIntersect(lStart: minX, lEnd: maxX, rStart: rect.minX, rEnd: rect.maxX) {
+      return false
+    }
+    
+    // vertical
+    return lineSegmentsIntersect(lStart: minY, lEnd: maxY, rStart: rect.minY, rEnd: rect.maxY)
+  }
+}
+
+extension Rect: CustomStringConvertible {
+  public var description: String {
+    return "Rect(\(origin), \(size))"
+  }
+}
+
+protocol PointsContainter {
+  func add(point: Point) -> Bool
+  func points(inRect rect: Rect) -> [Point]
+}
+
+class QuadTreeNode {
+  
+  enum NodeType {
+    case leaf
+    case `internal`(children: Children)
+  }
+  
+  struct Children: Sequence {
+    let leftTop: QuadTreeNode
+    let leftBottom: QuadTreeNode
+    let rightTop: QuadTreeNode
+    let rightBottom: QuadTreeNode
+    
+    init(parentNode: QuadTreeNode) {
+      leftTop = QuadTreeNode(rect: parentNode.rect.leftTopRect)
+      leftBottom = QuadTreeNode(rect: parentNode.rect.leftBottomRect)
+      rightTop = QuadTreeNode(rect: parentNode.rect.rightTopRect)
+      rightBottom = QuadTreeNode(rect: parentNode.rect.rightBottomRect)
+    }
+    
+    struct ChildrenIterator: IteratorProtocol {
+      private var index = 0
+      private let children: Children
+      
+      init(children: Children) {
+        self.children = children
+      }
+      
+      mutating func next() -> QuadTreeNode? {
+        
+        defer { index += 1 }
+        
+        switch index {
+        case 0: return children.leftTop
+        case 1: return children.leftBottom
+        case 2: return children.rightTop
+        case 3: return children.rightBottom
+        default: return nil
+        }
+      }
+    }
+    
+    public func makeIterator() -> ChildrenIterator {
+      return ChildrenIterator(children: self)
+    }
+  }
+  
+  var points: [Point] = []
+  let rect: Rect
+  var type: NodeType = .leaf
+  
+  static let maxPointCapacity = 3
+  
+  init(rect: Rect) {
+    self.rect = rect
+  }
+  
+  var recursiveDescription: String {
+    return recursiveDescription(withTabCount: 0)
+  }
+  
+  private func recursiveDescription(withTabCount count: Int) -> String {
+    let indent = String(repeating: "\t", count: count)
+    var result = "\(indent)" + description + "\n"
+    switch type {
+    case .internal(let children):
+      for child in children {
+        result += child.recursiveDescription(withTabCount: count + 1)
+      }
+    default:
+      break
+    }
+    return result
+  }
+}
+
+extension QuadTreeNode: PointsContainter {
+  
+  @discardableResult
+  func add(point: Point) -> Bool {
+    if !rect.containts(point: point) {
+      return false
+    }
+    
+    switch type {
+    case .internal(let children):
+      // pass the point to one of the children
+      for child in children {
+        if child.add(point: point) {
+          return true
+        }
+      }
+      
+      fatalError("rect.containts evaluted to true, but none of the children added the point")
+    case .leaf:
+      points.append(point)
+      // if the max capacity was reached, become an internal node
+      if points.count == QuadTreeNode.maxPointCapacity {
+        subdivide()
+      }
+    }
+    return true
+  }
+  
+  private func subdivide() {
+    switch type {
+    case .leaf:
+      type = .internal(children: Children(parentNode: self))
+    case .internal:
+      preconditionFailure("Calling subdivide on an internal node")
+    }
+  }
+  
+  func points(inRect rect: Rect) -> [Point] {
+    
+    // if the node's rect and the given rect don't intersect, return an empty array,
+    // because there can't be any points that lie the node's (or its children's) rect and
+    // in the given rect
+    if !self.rect.intersects(rect: rect) {
+      return []
+    }
+    
+    var result: [Point] = []
+    
+    // collect the node's points that lie in the rect
+    for point in points {
+      if rect.containts(point: point) {
+        result.append(point)
+      }
+    }
+    
+    switch type {
+    case .leaf:
+      break
+    case .internal(let children):
+      // recursively add children's points that lie in the rect
+      for childNode in children {
+        result.append(contentsOf: childNode.points(inRect: rect))
+      }
+    }
+    
+    return result
+  }
+}
+
+extension QuadTreeNode: CustomStringConvertible {
+  var description: String {
+    switch type {
+    case .leaf:
+      return "leaf \(rect) Points: \(points)"
+    case .internal:
+      return "parent \(rect) Points: \(points)"
+    }
+  }
+}
+
+public class QuadTree: PointsContainter {
+  
+  let root: QuadTreeNode
+  
+  public init(rect: Rect) {
+    self.root = QuadTreeNode(rect: rect)
+  }
+  
+  @discardableResult
+  public func add(point: Point) -> Bool {
+    return root.add(point: point)
+  }
+  
+  public func points(inRect rect: Rect) -> [Point] {
+    return root.points(inRect: rect)
+  }
+}
+
+extension QuadTree: CustomStringConvertible {
+  public var description: String {
+    return "Quad tree\n" + root.recursiveDescription
+  }
+}
diff --git a/QuadTree/QuadTree.playground/contents.xcplayground b/QuadTree/QuadTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/QuadTree/QuadTree.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/QuadTree/QuadTree.playground/playground.xcworkspace/contents.xcworkspacedata b/QuadTree/QuadTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/QuadTree/QuadTree.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/QuadTree/README.md b/QuadTree/README.md
new file mode 100644
index 000000000..77ac8b8fa
--- /dev/null
+++ b/QuadTree/README.md
@@ -0,0 +1,158 @@
+# QuadTree
+
+A quadtree is a [tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Tree) in which each internal (not leaf) node has four children.
+
+### Problem
+
+Consider the following problem: your need to store a number of points (each point is a pair of `X` and `Y` coordinates) and then you need to answer which points lie in a certain rectangular region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though. 
+
+### A Better Approach
+
+Quadrees are most commonly used to partition a two-dimensional space by recursively subdividing it into four regions(quadrants). Let's see how we can use a Quadtree to store the points.
+
+Each node in the tree represents a rectangular region and stores a limited number(`maxPointCapacity`) of points that all lie in its region.
+
+```swift
+class QuadTreeNode {
+
+  enum NodeType {
+    case leaf
+    case `internal`(children: Children)
+  }
+
+  struct Children {
+    let leftTop: QuadTreeNode
+    let leftBottom: QuadTreeNode
+    let rightTop: QuadTreeNode
+    let rightBottom: QuadTreeNode
+
+    ...
+  }
+
+  var points: [Point] = []
+  let rect: Rect
+  var type: NodeType = .leaf
+
+  static let maxPointCapacity = 3
+
+  init(rect: Rect) {
+    self.rect = rect
+  }
+  
+  ...
+}
+
+```
+Once the limit in a leaf node is reached, four child nodes are added to the node and they represent `topLeft`, `topRight`, `bottomLeft`, `bottomRight` quadrants of the node's rect; each of the consequent points in the rect will be passed to one of the children. Thus, new points are always added to leaf nodes.
+
+```swift
+extension QuadTreeNode {
+
+  @discardableResult
+  func add(point: Point) -> Bool {
+    
+    if !rect.containts(point: point) {
+      return false
+    }
+    
+    switch type {
+    case .internal(let children):
+      // pass the point to one of the children
+      for child in children {
+        if child.add(point: point) {
+          return true
+        }
+      }
+      return false // should never happen
+    case .leaf:
+      points.append(point)
+      // if the max capacity was reached, become an internal node
+      if points.count == QuadTreeNode.maxPointCapacity {
+        subdivide()
+      }
+    }
+    return true
+  }
+  
+  private func subdivide() {
+    switch type {
+    case .leaf:
+      type = .internal(children: Children(parentNode: self))
+    case .internal:
+      preconditionFailure("Calling subdivide on an internal node")
+    }
+  }
+}
+
+extension Children {
+
+  init(parentNode: QuadTreeNode) {
+    leftTop = QuadTreeNode(rect: parentNode.rect.leftTopRect)
+    leftBottom = QuadTreeNode(rect: parentNode.rect.leftBottomRect)
+    rightTop = QuadTreeNode(rect: parentNode.rect.rightTopRect)
+    rightBottom = QuadTreeNode(rect: parentNode.rect.rightBottomRect)
+  }
+}
+
+```
+
+To find the points that lie in a given region we can now traverse the tree from top to bottom and collect the suitable points from nodes.
+
+```swift
+
+class QuadTree {
+
+  ...
+  
+  let root: QuadTreeNode
+  
+   public func points(inRect rect: Rect) -> [Point] {
+    return root.points(inRect: rect)
+  }
+}
+
+extension QuadTreeNode {
+  func points(inRect rect: Rect) -> [Point] {
+    
+    // if the node's rect and the given rect don't intersect, return an empty array,
+    // because there can't be any points that lie the node's (or its children's) rect and
+    // in the given rect
+    if !self.rect.intersects(rect: rect) {
+      return []
+    }
+    
+    var result: [Point] = []
+    
+    // collect the node's points that lie in the rect
+    for point in points {
+      if rect.containts(point: point) {
+        result.append(point)
+      }
+    }
+    
+    switch type {
+    case .leaf:
+      break
+    case .internal(children: let children):
+      // recursively add children's points that lie in the rect
+      for childNode in children {
+        result.append(contentsOf: childNode.points(inRect: rect))
+      }
+    }
+    
+    return result
+  }
+}
+
+```
+
+Both adding a point and searching can still take up to O(n) in the worst case, since the tree isn't balanced in any way. However, on average it runs significantly faster (something comparable to O(log n)).
+
+### See also
+
+Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Atricle](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
+
+More info on [Wiki](https://en.wikipedia.org/wiki/Quadtree)
+
+*Written for Swift Algorithm Club by Timur Galimov*
+
diff --git a/QuadTree/Tests/Tests.xcodeproj/project.pbxproj b/QuadTree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..a972bf534
--- /dev/null
+++ b/QuadTree/Tests/Tests.xcodeproj/project.pbxproj
@@ -0,0 +1,274 @@
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+{
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+	objects = {
+
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+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				DEVELOPMENT_TEAM = 34BUG46ZSN;
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = com.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		82EF3AA31E50E74900013ECB /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				82EF3AA41E50E74900013ECB /* Debug */,
+				82EF3AA51E50E74900013ECB /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		82EF3AB01E50E77800013ECB /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				82EF3AB11E50E77800013ECB /* Debug */,
+				82EF3AB21E50E77800013ECB /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 82EF3AA01E50E74900013ECB /* Project object */;
+}
diff --git a/QuadTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/QuadTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/QuadTree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/QuadTree/Tests/Tests/Info.plist b/QuadTree/Tests/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/QuadTree/Tests/Tests/Info.plist
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/QuadTree/Tests/Tests/Tests.swift b/QuadTree/Tests/Tests/Tests.swift
new file mode 100644
index 000000000..b7bcda4e6
--- /dev/null
+++ b/QuadTree/Tests/Tests/Tests.swift
@@ -0,0 +1,85 @@
+//
+//  Tests.swift
+//  Tests
+//
+//  Created by Timur Galimov on 12/02/2017.
+//
+//
+
+import XCTest
+
+extension Point: Equatable {
+
+}
+
+public func ==(lhs: Point, rhs: Point) -> Bool {
+  return lhs.x == rhs.x && lhs.y == rhs.y
+}
+
+class Tests: XCTestCase {
+  
+  func testRectContains() {
+    let rect = Rect(origin: Point(0, 0), size: Size(xLength: 3, yLength: 3))
+    
+    XCTAssertTrue(rect.containts(point: Point(1, 1)))
+    XCTAssertTrue(rect.containts(point: Point(0, 0)))
+    XCTAssertTrue(rect.containts(point: Point(0, 3)))
+    XCTAssertTrue(rect.containts(point: Point(3, 3)))
+    
+    XCTAssertFalse(rect.containts(point: Point(-1, 1)))
+    XCTAssertFalse(rect.containts(point: Point(-0.1, 0.1)))
+    XCTAssertFalse(rect.containts(point: Point(0, 3.1)))
+    XCTAssertFalse(rect.containts(point: Point(-4, 1)))
+  }
+  
+  func testIntersects() {
+    let rect = Rect(origin: Point(0, 0), size: Size(xLength: 5, yLength: 5))
+    let rect2 = Rect(origin: Point(1, 1), size: Size(xLength: 1, yLength: 1))
+    XCTAssertTrue(rect.intersects(rect: rect2))
+    
+    let rect3 = Rect(origin: Point(1, 0), size: Size(xLength: 1, yLength: 10))
+    let rect4 = Rect(origin: Point(0, 1), size: Size(xLength: 10, yLength: 1))
+    XCTAssertTrue(rect3.intersects(rect: rect4))
+    
+    let rect5 = Rect(origin: Point(0, 0), size: Size(xLength: 4, yLength: 4))
+    let rect6 = Rect(origin: Point(2, 2), size: Size(xLength: 4, yLength: 4))
+    XCTAssertTrue(rect5.intersects(rect: rect6))
+    
+    let rect7 = Rect(origin: Point(0, 0), size: Size(xLength: 4, yLength: 4))
+    let rect8 = Rect(origin: Point(4, 4), size: Size(xLength: 1, yLength: 1))
+    XCTAssertTrue(rect7.intersects(rect: rect8))
+    
+    let rect9 = Rect(origin: Point(-1, -1), size: Size(xLength: 0.5, yLength: 0.5))
+    let rect10 = Rect(origin: Point(0, 0), size: Size(xLength: 1, yLength: 1))
+    XCTAssertFalse(rect9.intersects(rect: rect10))
+    
+    let rect11 = Rect(origin: Point(0, 0), size: Size(xLength: 2, yLength: 1))
+    let rect12 = Rect(origin: Point(3, 0), size: Size(xLength: 1, yLength: 1))
+    XCTAssertFalse(rect11.intersects(rect: rect12))
+  }
+  
+  func testQuadTree() {
+    let rect = Rect(origin: Point(0, 0), size: Size(xLength: 5, yLength: 5))
+    let qt = QuadTree(rect: rect)
+    
+    XCTAssertTrue(qt.points(inRect: rect) == [Point]())
+    
+    XCTAssertFalse(qt.add(point: Point(-0.1, 0.1)))
+    
+    XCTAssertTrue(qt.points(inRect: rect) == [Point]())
+    
+    XCTAssertTrue(qt.add(point: Point(1, 1)))
+    XCTAssertTrue(qt.add(point: Point(3, 3)))
+    XCTAssertTrue(qt.add(point: Point(4, 4)))
+    XCTAssertTrue(qt.add(point: Point(0.5, 0.5)))
+    
+    XCTAssertFalse(qt.add(point: Point(5.5, 0)))
+    XCTAssertFalse(qt.add(point: Point(5.5, 1)))
+    XCTAssertFalse(qt.add(point: Point(5.5, 2)))
+    
+    XCTAssertTrue(qt.add(point: Point(1.5, 1.5)))
+    
+    let rect2 = Rect(origin: Point(0, 0), size: Size(xLength: 2, yLength: 2))
+    XCTAssertTrue(qt.points(inRect: rect2) == [Point(1, 1), Point(0.5, 0.5), Point(1.5, 1.5)])
+  }
+}

From c1952ec2f66b4ce98d82d3e948e43af4be77809d Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <JaapWijnen@users.noreply.github.com>
Date: Sat, 18 Feb 2017 02:18:53 +0100
Subject: [PATCH 0825/1679] finalize migration tests (#381)

* finalize migration tests

* fix

* fixes

* test fixes

* fix bounded priority queue
---
 .travis.yml                                   | 23 ++++---
 .../Sources/BoundedPriorityQueue.swift        |  2 +-
 .../BoundedPriorityQueue.swift                | 30 ++++-----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 42 +++++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 Counting Sort/CountingSort.swift              | 66 +++++++++----------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 Depth-First Search/Tests/Graph.swift          | 38 +++++------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 Graph/Graph.xcodeproj/project.pbxproj         |  5 +-
 Graph/GraphTests/GraphTests.swift             | 24 +++----
 Heap/Tests/HeapTests.swift                    | 12 ++--
 Heap/Tests/Tests.xcodeproj/project.pbxproj    |  2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     |  2 +-
 Quicksort/Quicksort.swift                     | 20 +++---
 Quicksort/Tests/QuicksortTests.swift          |  6 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Tests/MaximumTests.swift                  |  2 +-
 .../Tests/MinimumMaximumPairsTests.swift      |  4 +-
 .../Tests/MinimumTests.swift                  |  2 +-
 Select Minimum Maximum/Tests/TestHelper.swift |  2 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     | 10 ++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 26 files changed, 202 insertions(+), 130 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 2b2bafd14..b6ff6190c 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -15,30 +15,29 @@ script:
 - xcodebuild test -project ./Boyer-Moore/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
-# - xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
+- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
-# - xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
 - xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift
index fc399811d..b94863afc 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Sources/BoundedPriorityQueue.swift	
@@ -9,7 +9,7 @@ public class LinkedListNode<T: Comparable> {
 }
 
 public class BoundedPriorityQueue<T: Comparable> {
-  private typealias Node = LinkedListNode<T>
+  fileprivate typealias Node = LinkedListNode<T>
 
   private(set) public var count = 0
   fileprivate var head: Node?
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.swift b/Bounded Priority Queue/BoundedPriorityQueue.swift
index fbd8d5450..d882a7698 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.swift	
@@ -1,4 +1,4 @@
-public class LinkedListNode<T: Comparable> {
+open class LinkedListNode<T: Comparable> {
   var value: T
   var next: LinkedListNode?
   var previous: LinkedListNode?
@@ -8,27 +8,27 @@ public class LinkedListNode<T: Comparable> {
   }
 }
 
-public class BoundedPriorityQueue<T: Comparable> {
-  private typealias Node = LinkedListNode<T>
+open class BoundedPriorityQueue<T: Comparable> {
+  fileprivate typealias Node = LinkedListNode<T>
 
-  private(set) public var count = 0
-  private var head: Node?
-  private var tail: Node?
-  private var maxElements: Int
+  fileprivate(set) open var count = 0
+  fileprivate var head: Node?
+  fileprivate var tail: Node?
+  fileprivate var maxElements: Int
 
   public init(maxElements: Int) {
     self.maxElements = maxElements
   }
 
-  public var isEmpty: Bool {
+  open var isEmpty: Bool {
     return count == 0
   }
 
-  public func peek() -> T? {
+  open func peek() -> T? {
     return head?.value
   }
 
-  public func enqueue(value: T) {
+  open func enqueue(_ value: T) {
     if let node = insert(value, after: findInsertionPoint(value)) {
       // If the newly inserted node is the last one in the list, then update
       // the tail pointer.
@@ -44,7 +44,7 @@ public class BoundedPriorityQueue<T: Comparable> {
     }
   }
 
-  private func insert(value: T, after: Node?) -> Node? {
+  fileprivate func insert(_ value: T, after: Node?) -> Node? {
     if let previous = after {
 
       // If the queue is full and we have to insert at the end of the list,
@@ -78,18 +78,18 @@ public class BoundedPriorityQueue<T: Comparable> {
 
   /* Find the node after which to insert the new value. If this returns nil,
    the new value should be inserted at the head of the list. */
-  private func findInsertionPoint(value: T) -> Node? {
+  fileprivate func findInsertionPoint(_ value: T) -> Node? {
     var node = head
     var prev: Node? = nil
 
-    while let current = node where value < current.value {
+    while let current = node, value < current.value {
       prev = node
       node = current.next
     }
     return prev
   }
 
-  private func removeLeastImportantElement() {
+  fileprivate func removeLeastImportantElement() {
     if let last = tail {
       tail = last.previous
       tail?.next = nil
@@ -101,7 +101,7 @@ public class BoundedPriorityQueue<T: Comparable> {
     // this is much slower on large lists.
   }
 
-  public func dequeue() -> T? {
+  open func dequeue() -> T? {
     if let first = head {
       count -= 1
       if count == 0 {
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 6fd5c0b46..842c51695 100644
--- a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -82,10 +82,11 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				TargetAttributes = {
 					B80004B21C83E342001FE2D7 = {
 						CreatedOnToolsVersion = 7.2.1;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -132,12 +133,49 @@
 		B80004AD1C83E324001FE2D7 /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				ONLY_ACTIVE_ARCH = YES;
 			};
 			name = Debug;
 		};
 		B80004AE1C83E324001FE2D7 /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -188,6 +226,7 @@
 				SDKROOT = macosx;
 				SWIFT_OBJC_BRIDGING_HEADER = "";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -230,6 +269,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OBJC_BRIDGING_HEADER = "";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 0416248f1..8bb763edd 100644
--- a/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index 9a1ffb373..abece0213 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -6,41 +6,39 @@
 //  Copyright © 2016 Ali Hafizji. All rights reserved.
 //
 
-import Foundation
-
 enum CountingSortError: Error {
-    case arrayEmpty
+  case arrayEmpty
 }
 
-func countingSort(array: [Int]) throws -> [Int] {
-    guard array.count > 0 else {
-        throw CountingSortError.arrayEmpty
-    }
-    
-    // Step 1
-    // Create an array to store the count of each element
-    let maxElement = array.max() ?? 0
-    
-    var countArray = [Int](repeating: 0, count: Int(maxElement + 1))
-    for element in array {
-        countArray[element] += 1
-    }
-    
-    // Step 2
-    // Set each value to be the sum of the previous two values
-    for index in 1 ..< countArray.count {
-        let sum = countArray[index] + countArray[index - 1]
-        countArray[index] = sum
-    }
-    
-    print(countArray)
-    
-    // Step 3
-    // Place the element in the final array as per the number of elements before it
-    var sortedArray = [Int](repeating: 0, count: array.count)
-    for element in array {
-        countArray[element] -= 1
-        sortedArray[countArray[element]] = element
-    }
-    return sortedArray
+func countingSort(_ array: [Int]) throws -> [Int] {
+  guard array.count > 0 else {
+    throw CountingSortError.arrayEmpty
+  }
+
+  // Step 1
+  // Create an array to store the count of each element
+  let maxElement = array.max() ?? 0
+
+  var countArray = [Int](repeating: 0, count: Int(maxElement + 1))
+  for element in array {
+    countArray[element] += 1
+  }
+
+  // Step 2
+  // Set each value to be the sum of the previous two values
+  for index in 1 ..< countArray.count {
+    let sum = countArray[index] + countArray[index - 1]
+    countArray[index] = sum
+  }
+
+  print(countArray)
+
+  // Step 3
+  // Place the element in the final array as per the number of elements before it
+  var sortedArray = [Int](repeating: 0, count: array.count)
+  for element in array {
+    countArray[element] -= 1
+    sortedArray[countArray[element]] = element
+  }
+  return sortedArray
 }
diff --git a/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj
index 6801bb587..5cbb0d4aa 100644
--- a/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,11 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -145,8 +146,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -189,8 +192,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +214,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -220,6 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -231,6 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..dfcf6de42 100644
--- a/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Counting Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Depth-First Search/Tests/Graph.swift b/Depth-First Search/Tests/Graph.swift
index ed71cab7c..a52b3c419 100644
--- a/Depth-First Search/Tests/Graph.swift	
+++ b/Depth-First Search/Tests/Graph.swift	
@@ -1,7 +1,7 @@
 // MARK: - Edge
 
-public class Edge: Equatable {
-  public var neighbor: Node
+open class Edge: Equatable {
+  open var neighbor: Node
 
   public init(neighbor: Node) {
     self.neighbor = neighbor
@@ -14,12 +14,12 @@ public func == (lhs: Edge, rhs: Edge) -> Bool {
 
 // MARK: - Node
 
-public class Node: CustomStringConvertible, Equatable {
-  public var neighbors: [Edge]
+open class Node: CustomStringConvertible, Equatable {
+  open var neighbors: [Edge]
 
-  public private(set) var label: String
-  public var distance: Int?
-  public var visited: Bool
+  open fileprivate(set) var label: String
+  open var distance: Int?
+  open var visited: Bool
 
   public init(label: String) {
     self.label = label
@@ -27,19 +27,19 @@ public class Node: CustomStringConvertible, Equatable {
     visited = false
   }
 
-  public var description: String {
+  open var description: String {
     if let distance = distance {
       return "Node(label: \(label), distance: \(distance))"
     }
     return "Node(label: \(label), distance: infinity)"
   }
 
-  public var hasDistance: Bool {
+  open var hasDistance: Bool {
     return distance != nil
   }
 
-  public func remove(edge: Edge) {
-    neighbors.removeAtIndex(neighbors.indexOf { $0 === edge }!)
+  open func remove(_ edge: Edge) {
+    neighbors.remove(at: neighbors.index { $0 === edge }!)
   }
 }
 
@@ -49,25 +49,25 @@ public func == (lhs: Node, rhs: Node) -> Bool {
 
 // MARK: - Graph
 
-public class Graph: CustomStringConvertible, Equatable {
-  public private(set) var nodes: [Node]
+open class Graph: CustomStringConvertible, Equatable {
+  open fileprivate(set) var nodes: [Node]
 
   public init() {
     self.nodes = []
   }
 
-  public func addNode(label: String) -> Node {
+  open func addNode(_ label: String) -> Node {
     let node = Node(label: label)
     nodes.append(node)
     return node
   }
 
-  public func addEdge(source: Node, neighbor: Node) {
+  open func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor: neighbor)
     source.neighbors.append(edge)
   }
 
-  public var description: String {
+  open var description: String {
     var description = ""
 
     for node in nodes {
@@ -78,15 +78,15 @@ public class Graph: CustomStringConvertible, Equatable {
     return description
   }
 
-  public func findNodeWithLabel(label: String) -> Node {
+  open func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
 
-  public func duplicate() -> Graph {
+  open func duplicate() -> Graph {
     let duplicated = Graph()
 
     for node in nodes {
-      duplicated.addNode(node.label)
+      _ = duplicated.addNode(node.label)
     }
 
     for node in nodes {
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 9e2872f88..dbc44ecd4 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,11 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -149,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -226,6 +232,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -238,6 +245,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index e5bd10d97..4462aede0 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0730"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index 82a5f2377..ba07c3c26 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -163,10 +163,11 @@
 				TargetAttributes = {
 					49BFA2FC1CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 0820;
 					};
 					49BFA3061CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -381,6 +382,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.GraphTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -392,6 +394,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.GraphTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 766ce91cf..289d9aa64 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -54,7 +54,7 @@ class GraphTests: XCTestCase {
     }
   }
 
-  func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(graphType: AbstractGraph<Int>.Type) {
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(_ graphType: AbstractGraph<Int>.Type) {
     let graph = graphType.init()
 
     let a = graph.createVertex(1)
@@ -71,7 +71,7 @@ class GraphTests: XCTestCase {
     XCTAssertEqual(edgesFromA.first?.to, b)
   }
 
-  func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(graphType: AbstractGraph<Int>.Type) {
+  func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(_ graphType: AbstractGraph<Int>.Type) {
     let graph = graphType.init()
 
     let a = graph.createVertex(1)
@@ -89,7 +89,7 @@ class GraphTests: XCTestCase {
     XCTAssertEqual(edgesFromB.first?.to, a)
   }
 
-  func testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(graphType: AbstractGraph<Int>.Type) {
+  func testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(_ graphType: AbstractGraph<Int>.Type) {
     let graph = graphType.init()
 
     let a = graph.createVertex(1)
@@ -99,7 +99,7 @@ class GraphTests: XCTestCase {
     XCTAssertEqual(graph.edgesFrom(b).count, 0)
   }
 
-  func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(graphType: AbstractGraph<Int>.Type) {
+  func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(_ graphType: AbstractGraph<Int>.Type) {
     let graph = graphType.init()
     let verticesCount = 100
     var vertices: [Vertex<Int>] = []
@@ -125,34 +125,34 @@ class GraphTests: XCTestCase {
   }
 
   func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedMatrixGraph() {
-    testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(AdjacencyMatrixGraph<Int>)
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(AdjacencyMatrixGraph<Int>.self)
   }
 
   func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedMatrixGraph() {
-    testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(AdjacencyMatrixGraph<Int>)
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(AdjacencyMatrixGraph<Int>.self)
   }
 
   func testEdgesFromReturnsNoInNoEdgeMatrixGraph() {
-    testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(AdjacencyMatrixGraph<Int>)
+    testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(AdjacencyMatrixGraph<Int>.self)
   }
 
   func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedMatrixGraph() {
-    testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(AdjacencyMatrixGraph<Int>)
+    testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(AdjacencyMatrixGraph<Int>.self)
   }
 
   func testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedListGraph() {
-    testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(AdjacencyListGraph<Int>)
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeDirecedGraphWithType(AdjacencyListGraph<Int>.self)
   }
 
   func testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedListGraph() {
-    testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(AdjacencyListGraph<Int>)
+    testEdgesFromReturnsCorrectEdgeInSingleEdgeUndirectedGraphWithType(AdjacencyListGraph<Int>.self)
   }
 
   func testEdgesFromReturnsNoInNoEdgeListGraph() {
-    testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(AdjacencyListGraph<Int>)
+    testEdgesFromReturnsNoEdgesInNoEdgeGraphWithType(AdjacencyListGraph<Int>.self)
   }
 
   func testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedListGraph() {
-    testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(AdjacencyListGraph<Int>)
+    testEdgesFromReturnsCorrectEdgesInBiggerGraphInDirectedGraphWithType(AdjacencyListGraph<Int>.self)
   }
 }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index c5b479f14..0e6c504f3 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -197,27 +197,27 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
 
     //test index out of bounds
-    let v = h.removeAt(index: 10)
+    let v = h.removeAt(10)
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
     
-    let v1 = h.removeAt(index: 5)
+    let v1 = h.removeAt(5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
 
-    let v2 = h.removeAt(index: 4)
+    let v2 = h.removeAt(4)
     XCTAssertEqual(v2, 20)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
 
-    let v3 = h.removeAt(index: 4)
+    let v3 = h.removeAt(4)
     XCTAssertEqual(v3, 50)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 65, 70, 10])
 
-    let v4 = h.removeAt(index: 0)
+    let v4 = h.removeAt(0)
     XCTAssertEqual(v4, 100)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [70, 65, 10])
@@ -270,7 +270,7 @@ class HeapTests: XCTestCase {
       let m = (n + 1)/2
       for k in 1...m {
         let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        let v = h.removeAt(index: i)!
+        let v = h.removeAt(i)!
         let j = a.index(of: v)!
         a.remove(at: j)
 
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
index 9319e2089..22112fa60 100644
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -88,7 +88,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
diff --git a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 77423c57a..0f7d84be9 100644
--- a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -91,7 +91,7 @@
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
diff --git a/Quicksort/Quicksort.swift b/Quicksort/Quicksort.swift
index 6448dd815..39fa27b66 100644
--- a/Quicksort/Quicksort.swift
+++ b/Quicksort/Quicksort.swift
@@ -3,7 +3,7 @@ import Foundation
 /*
   Easy to understand but not very efficient.
 */
-func quicksort<T: Comparable>(a: [T]) -> [T] {
+func quicksort<T: Comparable>(_ a: [T]) -> [T] {
   guard a.count > 1 else { return a }
 
   let pivot = a[a.count/2]
@@ -29,7 +29,7 @@ func quicksort<T: Comparable>(a: [T]) -> [T] {
   if the pivot value occurs more than once, its duplicates will be found in the
   left partition.
 */
-func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   // We always use the highest item as the pivot.
   let pivot = a[high]
 
@@ -56,7 +56,7 @@ func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
 /*
   Recursive, in-place version that uses Lomuto's partioning scheme.
 */
-func quicksortLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let p = partitionLomuto(&a, low: low, high: high)
     quicksortLomuto(&a, low: low, high: p - 1)
@@ -80,7 +80,7 @@ func quicksortLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) {
   Hoare scheme is more efficient than Lomuto's partition scheme; it performs
   fewer swaps.
 */
-func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[low]
   var i = low - 1
   var j = high + 1
@@ -101,7 +101,7 @@ func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
   Recursive, in-place version that uses Hoare's partioning scheme. Because of
   the choice of pivot, this performs badly if the array is already sorted.
 */
-func quicksortHoare<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let p = partitionHoare(&a, low: low, high: high)
     quicksortHoare(&a, low: low, high: p)
@@ -112,7 +112,7 @@ func quicksortHoare<T: Comparable>(inout a: [T], low: Int, high: Int) {
 // MARK: - Randomized sort
 
 /* Returns a random integer in the range min...max, inclusive. */
-public func random(min min: Int, max: Int) -> Int {
+public func random(min: Int, max: Int) -> Int {
   assert(min < max)
   return min + Int(arc4random_uniform(UInt32(max - min + 1)))
 }
@@ -121,7 +121,7 @@ public func random(min min: Int, max: Int) -> Int {
   Uses a random pivot index. On average, this results in a well-balanced split
   of the input array.
 */
-func quicksortRandom<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortRandom<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     // Create a random pivot index in the range [low...high].
     let pivotIndex = random(min: low, max: high)
@@ -142,7 +142,7 @@ func quicksortRandom<T: Comparable>(inout a: [T], low: Int, high: Int) {
   Swift's swap() doesn't like it if the items you're trying to swap refer to
   the same memory location. This little wrapper simply ignores such swaps.
 */
-public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
+public func swap<T>(_ a: inout [T], _ i: Int, _ j: Int) {
   if i != j {
     swap(&a[i], &a[j])
   }
@@ -165,7 +165,7 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
 
   Time complexity is O(n), space complexity is O(1).
 */
-func partitionDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
+func partitionDutchFlag<T: Comparable>(_ a: inout [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
   let pivot = a[pivotIndex]
 
   var smaller = low
@@ -195,7 +195,7 @@ func partitionDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int, pivotI
 /*
   Uses Dutch national flag partitioning and a random pivot index.
 */
-func quicksortDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int) {
+func quicksortDutchFlag<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
   if low < high {
     let pivotIndex = random(min: low, max: high)
     let (p, q) = partitionDutchFlag(&a, low: low, high: high, pivotIndex: pivotIndex)
diff --git a/Quicksort/Tests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
index 00135b31f..c8d9a62e6 100644
--- a/Quicksort/Tests/QuicksortTests.swift
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -5,12 +5,12 @@ class QuicksortTests: XCTestCase {
     checkSortAlgorithm(quicksort)
   }
 
-  private typealias QuicksortFunction = (inout [Int], low: Int, high: Int) -> Void
+  fileprivate typealias QuicksortFunction = (inout [Int], _ low: Int, _ high: Int) -> Void
 
-  private func checkQuicksort(function: QuicksortFunction) {
+  fileprivate func checkQuicksort(_ function: QuicksortFunction) {
     checkSortAlgorithm { (a: [Int]) -> [Int] in
       var b = a
-      function(&b, low: 0, high: b.count - 1)
+      function(&b, 0, b.count - 1)
       return b
     }
   }
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj b/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
index 8aecb59f8..2d8ee18ff 100644
--- a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
@@ -86,11 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -149,8 +150,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,8 +196,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -213,6 +218,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -224,6 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -235,6 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..dfcf6de42 100644
--- a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Select Minimum Maximum/Tests/MaximumTests.swift b/Select Minimum Maximum/Tests/MaximumTests.swift
index cd63ac0a3..4a956dbfb 100644
--- a/Select Minimum Maximum/Tests/MaximumTests.swift	
+++ b/Select Minimum Maximum/Tests/MaximumTests.swift	
@@ -49,7 +49,7 @@ class MaximumTests: XCTestCase {
 
         let result = maximum(array)
 
-        XCTAssertEqual(result, array.maxElement())
+        XCTAssertEqual(result, array.max())
       }
     }
   }
diff --git a/Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift b/Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift
index 6cde21021..4d2162617 100644
--- a/Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift	
+++ b/Select Minimum Maximum/Tests/MinimumMaximumPairsTests.swift	
@@ -71,8 +71,8 @@ class MinimumMaximumPairsTests: XCTestCase {
 
         let result = minimumMaximum(array)!
 
-        XCTAssertEqual(result.minimum, array.minElement())
-        XCTAssertEqual(result.maximum, array.maxElement())
+        XCTAssertEqual(result.minimum, array.min())
+        XCTAssertEqual(result.maximum, array.max())
       }
     }
   }
diff --git a/Select Minimum Maximum/Tests/MinimumTests.swift b/Select Minimum Maximum/Tests/MinimumTests.swift
index ed4fbe1f0..c01d25fac 100644
--- a/Select Minimum Maximum/Tests/MinimumTests.swift	
+++ b/Select Minimum Maximum/Tests/MinimumTests.swift	
@@ -49,7 +49,7 @@ class MinimumTests: XCTestCase {
 
         let result = minimum(array)
 
-        XCTAssertEqual(result, array.minElement())
+        XCTAssertEqual(result, array.min())
       }
     }
   }
diff --git a/Select Minimum Maximum/Tests/TestHelper.swift b/Select Minimum Maximum/Tests/TestHelper.swift
index cd782d305..062025a2b 100644
--- a/Select Minimum Maximum/Tests/TestHelper.swift	
+++ b/Select Minimum Maximum/Tests/TestHelper.swift	
@@ -1,5 +1,5 @@
 import Foundation
 
-func createRandomList(numberOfElements: Int) -> [UInt32] {
+func createRandomList(_ numberOfElements: Int) -> [UInt32] {
   return (1...numberOfElements).map {_ in arc4random()}
 }
diff --git a/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj b/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj
index e2857d2b7..fb70d6970 100644
--- a/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Select Minimum Maximum/Tests/Tests.xcodeproj/project.pbxproj	
@@ -98,11 +98,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
@@ -165,8 +166,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,8 +212,10 @@
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -229,6 +234,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -240,6 +246,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -251,6 +258,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..dfcf6de42 100644
--- a/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Select Minimum Maximum/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0820"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 89d84fcd5be39d7a88357b5d6da5de7cec88c8fb Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Sun, 19 Feb 2017 14:58:50 +0100
Subject: [PATCH 0826/1679] Convex Hull algorithm

---
 .../Convex Hull.xcodeproj/project.pbxproj     | 297 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 Convex Hull/Convex Hull/AppDelegate.swift     |  57 ++++
 .../AppIcon.appiconset/Contents.json          |  93 ++++++
 .../Base.lproj/LaunchScreen.storyboard        |  27 ++
 Convex Hull/Convex Hull/Info.plist            |  47 +++
 Convex Hull/Convex Hull/View.swift            | 177 +++++++++++
 Convex Hull/README.md                         |  41 +++
 8 files changed, 746 insertions(+)
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/project.pbxproj
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Convex Hull/Convex Hull/AppDelegate.swift
 create mode 100644 Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard
 create mode 100644 Convex Hull/Convex Hull/Info.plist
 create mode 100644 Convex Hull/Convex Hull/View.swift
 create mode 100644 Convex Hull/README.md

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..2f236b013
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -0,0 +1,297 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68B91E59989400161780 /* AppDelegate.swift */; };
+		8E6D68C11E59989400161780 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C01E59989400161780 /* Assets.xcassets */; };
+		8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C21E59989400161780 /* LaunchScreen.storyboard */; };
+		8E6D68CC1E599CF100161780 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		8E6D68B61E59989400161780 /* Convex Hull.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = "Convex Hull.app"; sourceTree = BUILT_PRODUCTS_DIR; };
+		8E6D68B91E59989400161780 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
+		8E6D68C01E59989400161780 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
+		8E6D68C31E59989400161780 /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.storyboard; name = Base; path = Base.lproj/LaunchScreen.storyboard; sourceTree = "<group>"; };
+		8E6D68C51E59989400161780 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		8E6D68CB1E599CF100161780 /* View.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = View.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		8E6D68B31E59989400161780 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		8E6D68AD1E59989400161780 = {
+			isa = PBXGroup;
+			children = (
+				8E6D68B81E59989400161780 /* Convex Hull */,
+				8E6D68B71E59989400161780 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		8E6D68B71E59989400161780 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				8E6D68B61E59989400161780 /* Convex Hull.app */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		8E6D68B81E59989400161780 /* Convex Hull */ = {
+			isa = PBXGroup;
+			children = (
+				8E6D68B91E59989400161780 /* AppDelegate.swift */,
+				8E6D68CB1E599CF100161780 /* View.swift */,
+				8E6D68C01E59989400161780 /* Assets.xcassets */,
+				8E6D68C21E59989400161780 /* LaunchScreen.storyboard */,
+				8E6D68C51E59989400161780 /* Info.plist */,
+			);
+			path = "Convex Hull";
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		8E6D68B51E59989400161780 /* Convex Hull */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 8E6D68C81E59989400161780 /* Build configuration list for PBXNativeTarget "Convex Hull" */;
+			buildPhases = (
+				8E6D68B21E59989400161780 /* Sources */,
+				8E6D68B31E59989400161780 /* Frameworks */,
+				8E6D68B41E59989400161780 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = "Convex Hull";
+			productName = "Convex Hull";
+			productReference = 8E6D68B61E59989400161780 /* Convex Hull.app */;
+			productType = "com.apple.product-type.application";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		8E6D68AE1E59989400161780 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0820;
+				LastUpgradeCheck = 0820;
+				ORGANIZATIONNAME = Workmoose;
+				TargetAttributes = {
+					8E6D68B51E59989400161780 = {
+						CreatedOnToolsVersion = 8.2.1;
+						DevelopmentTeam = 7C4LVS3ZVC;
+						ProvisioningStyle = Automatic;
+					};
+				};
+			};
+			buildConfigurationList = 8E6D68B11E59989400161780 /* Build configuration list for PBXProject "Convex Hull" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 8E6D68AD1E59989400161780;
+			productRefGroup = 8E6D68B71E59989400161780 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				8E6D68B51E59989400161780 /* Convex Hull */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		8E6D68B41E59989400161780 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */,
+				8E6D68C11E59989400161780 /* Assets.xcassets in Resources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		8E6D68B21E59989400161780 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */,
+				8E6D68CC1E599CF100161780 /* View.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin PBXVariantGroup section */
+		8E6D68C21E59989400161780 /* LaunchScreen.storyboard */ = {
+			isa = PBXVariantGroup;
+			children = (
+				8E6D68C31E59989400161780 /* Base */,
+			);
+			name = LaunchScreen.storyboard;
+			sourceTree = "<group>";
+		};
+/* End PBXVariantGroup section */
+
+/* Begin XCBuildConfiguration section */
+		8E6D68C61E59989400161780 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				IPHONEOS_DEPLOYMENT_TARGET = 10.2;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = iphoneos;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				TARGETED_DEVICE_FAMILY = "1,2";
+			};
+			name = Debug;
+		};
+		8E6D68C71E59989400161780 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				IPHONEOS_DEPLOYMENT_TARGET = 10.2;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = iphoneos;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				TARGETED_DEVICE_FAMILY = "1,2";
+				VALIDATE_PRODUCT = YES;
+			};
+			name = Release;
+		};
+		8E6D68C91E59989400161780 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				INFOPLIST_FILE = "Convex Hull/Info.plist";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		8E6D68CA1E59989400161780 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				INFOPLIST_FILE = "Convex Hull/Info.plist";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		8E6D68B11E59989400161780 /* Build configuration list for PBXProject "Convex Hull" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8E6D68C61E59989400161780 /* Debug */,
+				8E6D68C71E59989400161780 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		8E6D68C81E59989400161780 /* Build configuration list for PBXNativeTarget "Convex Hull" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8E6D68C91E59989400161780 /* Debug */,
+				8E6D68CA1E59989400161780 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 8E6D68AE1E59989400161780 /* Project object */;
+}
diff --git a/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..dfcd4bc52
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Convex Hull.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
new file mode 100644
index 000000000..1901083a8
--- /dev/null
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -0,0 +1,57 @@
+//
+//  AppDelegate.swift
+//  Convex Hull
+//
+//  Created by Jaap Wijnen on 19/02/2017.
+//  Copyright © 2017 Workmoose. All rights reserved.
+//
+
+import UIKit
+
+@UIApplicationMain
+class AppDelegate: UIResponder, UIApplicationDelegate {
+
+    var window: UIWindow?
+
+
+    func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
+
+        let screenBounds = UIScreen.main.bounds
+        
+        window = UIWindow(frame: screenBounds)
+        
+        let viewController = UIViewController()
+        viewController.view = View(frame: (window?.frame)!)
+        viewController.view.backgroundColor = .white
+        
+        window?.rootViewController = viewController
+        window?.makeKeyAndVisible()
+        
+        return true
+    }
+
+    func applicationWillResignActive(_ application: UIApplication) {
+        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
+        // Use this method to pause ongoing tasks, disable timers, and invalidate graphics rendering callbacks. Games should use this method to pause the game.
+    }
+
+    func applicationDidEnterBackground(_ application: UIApplication) {
+        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
+        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
+    }
+
+    func applicationWillEnterForeground(_ application: UIApplication) {
+        // Called as part of the transition from the background to the active state; here you can undo many of the changes made on entering the background.
+    }
+
+    func applicationDidBecomeActive(_ application: UIApplication) {
+        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
+    }
+
+    func applicationWillTerminate(_ application: UIApplication) {
+        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
+    }
+
+
+}
+
diff --git a/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..1d060ed28
--- /dev/null
+++ b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json	
@@ -0,0 +1,93 @@
+{
+  "images" : [
+    {
+      "idiom" : "iphone",
+      "size" : "20x20",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "20x20",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "20x20",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "20x20",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "83.5x83.5",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard b/Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard
new file mode 100644
index 000000000..fdf3f97d1
--- /dev/null
+++ b/Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard	
@@ -0,0 +1,27 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="11134" systemVersion="15F34" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" colorMatched="YES" initialViewController="01J-lp-oVM">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="11106"/>
+        <capability name="documents saved in the Xcode 8 format" minToolsVersion="8.0"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="EHf-IW-A2E">
+            <objects>
+                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
+                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
+                        <rect key="frame" x="0.0" y="0.0" width="375" height="667"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <color key="backgroundColor" red="1" green="1" blue="1" alpha="1" colorSpace="custom" customColorSpace="sRGB"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="53" y="375"/>
+        </scene>
+    </scenes>
+</document>
diff --git a/Convex Hull/Convex Hull/Info.plist b/Convex Hull/Convex Hull/Info.plist
new file mode 100644
index 000000000..390c5347e
--- /dev/null
+++ b/Convex Hull/Convex Hull/Info.plist	
@@ -0,0 +1,47 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSRequiresIPhoneOS</key>
+	<true/>
+	<key>UILaunchStoryboardName</key>
+	<string>LaunchScreen</string>
+	<key>UIRequiredDeviceCapabilities</key>
+	<array>
+		<string>armv7</string>
+	</array>
+	<key>UIRequiresFullScreen</key>
+	<true/>
+	<key>UIStatusBarHidden</key>
+	<true/>
+	<key>UISupportedInterfaceOrientations</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>UISupportedInterfaceOrientations~ipad</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationPortraitUpsideDown</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+</dict>
+</plist>
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
new file mode 100644
index 000000000..2d7157e6f
--- /dev/null
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -0,0 +1,177 @@
+//
+//  View.swift
+//  Convex Hull
+//
+//  Created by Jaap Wijnen on 19/02/2017.
+//  Copyright © 2017 Workmoose. All rights reserved.
+//
+
+import UIKit
+
+class View: UIView {
+    
+    let MAX_POINTS = 100
+    
+    var points = [CGPoint]()
+    
+    var convexHull = [CGPoint]()
+    
+    override init(frame: CGRect) {
+        super.init(frame: frame)
+        
+        generatePoints()
+        quickHull(points: points)
+    }
+    
+    required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+    
+    func generatePoints() {
+        for _ in 0..<MAX_POINTS {
+            let offset: CGFloat = 50
+            let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
+            let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
+            let point = CGPoint(x: xrand, y: yrand)
+            points.append(point)
+        }
+        
+        points.sort { (a: CGPoint, b: CGPoint) -> Bool in
+            return a.x < b.x
+        }
+    }
+    
+    func quickHull(points: [CGPoint]) {
+        var pts = points
+                
+        // Assume points has at least 2 points
+        // Assume list is ordered on x
+        
+        // left most point
+        let p1 = pts.removeFirst()
+        // right most point
+        let p2 = pts.removeLast()
+        
+        // p1 and p2 are outer most points and thus are part of the hull
+        convexHull.append(p1)
+        convexHull.append(p2)
+        
+        // points to the right of oriented line from p1 to p2
+        var s1 = [CGPoint]()
+        
+        // points to the right of oriented line from p2 to p1
+        var s2 = [CGPoint]()
+        
+        // p1 to p2 line
+        let lineVec1 = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
+        
+        for p in pts { // per point check if point is to right or left of p1 to p2 line
+            let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y)
+            let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // cross product to check on which side of the line point p is.
+            
+            if sign1 > 0 { // right of p1 p2 line (in a normal xy coordinate system this would be < 0 but due to the weird iPhone screen coordinates this is > 0
+                s1.append(p)
+            } else { // right of p2 p1 line
+                s2.append(p)
+            }
+        }
+        
+        // find new hull points
+        findHull(s1, p1, p2)
+        findHull(s2, p2, p1)
+    }
+    
+    func findHull(_ points: [CGPoint], _ p1: CGPoint, _ p2: CGPoint) {
+        // if set of points is empty there are no points to the right of this line so this line is part of the hull.
+        if points.isEmpty {
+            return
+        }
+        
+        var pts = points
+        
+        // calculate parameters of general line equation y = a * x + b
+        let a = (p1.y - p2.y) / (p1.x - p2.x)
+        let b = p1.y - a * p1.x
+        
+        // calculate normal line's growth factor
+        let a1 = -1 / a
+        
+        var maxDist: CGFloat = -1
+        var maxPoint: CGPoint = pts.first!
+        
+        for p in pts { // for every point check the distance from our line
+            let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
+            let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
+            let y = a * x + b // calculate y value of this intersect point
+            
+            let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
+            if dist > maxDist { // if distance is larger than current maxDist remember new point p
+                maxDist = dist
+                maxPoint = p
+            }
+        }
+        
+        convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
+        
+        pts.remove(at: pts.index(of: maxPoint)!) // remove maxPoint from points array as we are going to split this array in points left and right of the line
+        
+        // points to the right of oriented line from p1 to maxPoint
+        var s1 = [CGPoint]()
+        
+        // points to the right of oriented line from maxPoint to p2
+        var s2 = [CGPoint]()
+        
+        // p1 to maxPoint line
+        let lineVec1 = CGPoint(x: maxPoint.x - p1.x, y: maxPoint.y - p1.y)
+        // maxPoint to p2 line
+        let lineVec2 = CGPoint(x: p2.x - maxPoint.x, y: p2.y - maxPoint.y)
+        
+        for p in pts {
+            let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y) // vector from p1 to p
+            let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // sign to check is p is to the right or left of lineVec1
+            
+            let pVec2 = CGPoint(x: p.x - maxPoint.x, y: p.y - maxPoint.y) // vector from p2 to p
+            let sign2 = lineVec2.x * pVec2.y - pVec2.x * lineVec2.y // sign to check is p is to the right or left of lineVec2
+
+            if sign1 > 0 { // right of p1 maxPoint line
+                s1.append(p)
+            } else if sign2 > 0 { // right of maxPoint p2 line
+                s2.append(p)
+            }
+        }
+        
+        // find new hull points
+        findHull(s1, p1, maxPoint)
+        findHull(s2, maxPoint, p2)
+    }
+
+    override func draw(_ rect: CGRect) {
+        
+        let context = UIGraphicsGetCurrentContext()
+        
+        // Draw hull
+        let lineWidth:CGFloat = 2.0
+        
+        context!.setFillColor(UIColor.black.cgColor)
+        context!.setLineWidth(lineWidth)
+        context!.setStrokeColor(UIColor.red.cgColor)
+        context!.setFillColor(UIColor.black.cgColor)
+        
+        let firstPoint = convexHull.first!
+        context!.move(to: firstPoint)
+        
+        for p in convexHull.dropFirst() {
+            context!.addLine(to: p)
+        }
+        context!.addLine(to: firstPoint)
+        
+        context!.strokePath()
+        
+        // Draw points
+        for p in points {
+            let radius: CGFloat = 5
+            let circleRect = CGRect(x: p.x - radius, y: p.y - radius, width: 2 * radius, height: 2 * radius)
+            context!.fillEllipse(in: circleRect)
+        }
+    }
+}
diff --git a/Convex Hull/README.md b/Convex Hull/README.md
new file mode 100644
index 000000000..b73f66176
--- /dev/null
+++ b/Convex Hull/README.md	
@@ -0,0 +1,41 @@
+# Convex Hull
+
+There are multiple Convex Hull algorithms. This particular implementation uses the Quickhull algorithm.
+
+Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimention. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
+
+## Quickhull
+
+The quickhull algorithm works as follows.
+The algorithm takes an input of a collection of points. These points should be ordered on their x coordinate value. We pick the two points A and B with the smallest(A) and the largest(B) x coordinate. These of course have to be part of the hull. Imagine a line from point A to point B. All points to the right of this line are grouped in an array S1. Imagine now a line from point B to point A. (this is of course the same line as before just with opposite direction) Again all points to the right of this line are grouped in an array, S2 this time.
+We now define the following recursive function:
+
+`findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`
+
+```
+findHull(S1, A, B)
+findHull(S2, B, A)
+```
+
+What this function does is the following:
+1. If `points` is empty we return as there are no points to the right of our line to add to our hull.
+2. Draw a line from `p1` to `p2`.
+3. Find the point in `points` that is furthest away from this line. (`maxPoint`)
+4. Add `maxPoint` to the hull right after `p1`.
+5. Draw a line (`line1`) from `p1` to `maxPoint`.
+6. Draw a line (`line2`) from `maxPoint` to `p2`. (These lines now form a triangle)
+7. All points within this triangle are of course not part of the hull and thus can be ignored. We check which points in `points` are to the right of `line1` these are grouped in an array `s1`.
+8. All points that are to the right of `line2` are grouped in an array `s2`. Note that there are no points that are both to the right of `line1` and `line2` as then `maxPoint` wouldn't be the point furthest away from our initial line between `p1` and `p2`.
+9. We call `findHull(_, _, _)` again on our new groups of points to find more hull points.
+```
+findHull(s1, p1, maxPoint)
+findHull(s2, maxPoint, p2)
+```
+
+This eventually leaves us with an array of points describing the convex hull.
+
+## See also
+
+[Convex Hull on Wikipedia](https://en.wikipedia.org/wiki/Convex_hull_algorithms)
+
+*Written for the Swift Algorithm Club by Jaap Wijnen.*

From 94c9b5f2b0306e9924c01486889b69934f34575a Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 19 Feb 2017 16:46:31 +0100
Subject: [PATCH 0827/1679] initial implementation fro Splay Trees

Test in progress
Debug in progress
Playground in progress
Documentation not started
---
 .../SplayTree.playground/Contents.swift       |   7 +
 .../Sources/SplayTree.swift                   | 509 ++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Splay Tree/SplayTree.swift                    | 552 ++++++++++++++++++
 Splay Tree/Tests/Info.plist                   |  22 +
 Splay Tree/Tests/SplayTreeTests.swift         |  19 +
 Splay Tree/Tests/Tests-Bridging-Header.h      |   4 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 279 +++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     | 101 ++++
 11 files changed, 1511 insertions(+)
 create mode 100644 Splay Tree/SplayTree.playground/Contents.swift
 create mode 100644 Splay Tree/SplayTree.playground/Sources/SplayTree.swift
 create mode 100644 Splay Tree/SplayTree.playground/contents.xcplayground
 create mode 100644 Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Splay Tree/SplayTree.swift
 create mode 100644 Splay Tree/Tests/Info.plist
 create mode 100644 Splay Tree/Tests/SplayTreeTests.swift
 create mode 100644 Splay Tree/Tests/Tests-Bridging-Header.h
 create mode 100644 Splay Tree/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
new file mode 100644
index 000000000..951ad4c5c
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -0,0 +1,7 @@
+//: Playground - Splay Tree Implementation
+
+
+let splayTree = SplayTree(array: [1])
+splayTree.insert(value: 2)
+splayTree.insert(value: 10)
+splayTree.insert(value: 6)
diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
new file mode 100644
index 000000000..f0c45e831
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -0,0 +1,509 @@
+/*
+ *  Splay Tree 
+ *
+ * Based on Binary Search Tree Implementation written by Nicolas Ameghino and Matthijs Hollemans for Swift Algorithms Club
+ * https://github.com/raywenderlich/swift-algorithm-club/blob/master/Binary%20Search%20Tree
+ * And extended for the specifics of a Splay Tree by Barbara Martina Rodeker
+ *
+ */
+
+/**
+    Represent the 3 possible operations (combinations of rotations) that
+    could be performed during the Splay phase in Splay Trees
+ 
+    - zigZag       Left child of a right child OR right child of a left child
+    - zigZig       Left child of a left child OR right child of a right child
+    - zig          Only 1 parent and that parent is the root
+ 
+ */
+public enum SplayOperation {
+    case zigZag
+    case zigZig
+    case zig
+    
+    
+    /**
+        Splay the given node up to the root of the tree
+     
+        - Parameters:
+            - node      SplayTree node to move up to the root
+     */
+    public static func splay<T: Comparable>(node: SplayTree<T>) {
+        
+        while (node.parent != nil) {
+            operation(forNode: node).apply(onNode: node)
+        }
+    }
+    
+    /**
+        Compares the node and its parent and determine
+        if the rotations should be performed in a zigZag, zigZig or zig case.
+     
+        - Parmeters:
+            - forNode       SplayTree node to be checked
+        - Returns
+            - Operation     Case zigZag - zigZig - zig
+     */
+    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+        
+        if let parent = node.parent, let grandParent = parent.parent {
+            if (node.isLeftChild && grandParent.isRightChild) || (node.isRightChild && grandParent.isLeftChild) {
+                return .zigZag
+            }
+            return .zigZig
+        }
+        return .zig
+    }
+    
+    /**
+        Applies the rotation associated to the case 
+        Modifying the splay tree and briging the received node further to the top of the tree
+     
+        - Parameters:
+            - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
+     */
+    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+        switch self {
+        case .zigZag:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node, parent: node.parent!)
+            rotate(child: node, parent: node.parent!)
+
+        case .zigZig:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node.parent!, parent: node.parent!.parent!)
+            rotate(child: node, parent: node.parent!)
+        
+        case .zig:
+            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+            rotate(child: node, parent: node.parent!)
+        }
+    }
+    
+    /**
+        Performs a single rotation from a node to its parent
+        re-arranging the children properly
+     */
+    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+        
+        assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
+        
+        var grandchildToMode: SplayTree<T>?
+        if child.isLeftChild {
+            
+            grandchildToMode = child.right
+            child.right = parent
+            parent.left = grandchildToMode
+            
+        } else {
+            
+            grandchildToMode = child.left
+            child.left = parent
+            parent.right = grandchildToMode
+        }
+
+        let grandParent = parent.parent
+        parent.parent = child
+        child.parent = grandParent
+    }
+}
+
+public class SplayTree<T: Comparable> {
+    
+    fileprivate(set) public var value: T
+    fileprivate(set) public var parent: SplayTree?
+    fileprivate(set) public var left: SplayTree?
+    fileprivate(set) public var right: SplayTree?
+    
+    public init(value: T) {
+        self.value = value
+    }
+    
+    public convenience init(array: [T]) {
+        precondition(array.count > 0)
+        self.init(value: array.first!)
+        for v in array.dropFirst() {
+            insert(value: v)
+        }
+    }
+    
+    public var isRoot: Bool {
+        return parent == nil
+    }
+    
+    public var isLeaf: Bool {
+        return left == nil && right == nil
+    }
+    
+    public var isLeftChild: Bool {
+        return parent?.left === self
+    }
+    
+    public var isRightChild: Bool {
+        return parent?.right === self
+    }
+    
+    public var hasLeftChild: Bool {
+        return left != nil
+    }
+    
+    public var hasRightChild: Bool {
+        return right != nil
+    }
+    
+    public var hasAnyChild: Bool {
+        return hasLeftChild || hasRightChild
+    }
+    
+    public var hasBothChildren: Bool {
+        return hasLeftChild && hasRightChild
+    }
+    
+    /* How many nodes are in this subtree. Performance: O(n). */
+    public var count: Int {
+        return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+    }
+}
+
+// MARK: - Adding items
+
+extension SplayTree {
+    
+    /*
+     Inserts a new element into the tree. You should only insert elements
+     at the root, to make to sure this remains a valid binary tree!
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func insert(value: T) {
+        if value < self.value {
+            if let left = left {
+                left.insert(value: value)
+            } else {
+                
+                left = SplayTree(value: value)
+                left?.parent = self
+                
+                if let left = left {
+                    SplayOperation.splay(node: left)
+                    self.parent = nil
+                    self.value = left.value
+                    self.left = left.left
+                    self.right = left.right
+                }
+            }
+        } else {
+            
+            if let right = right {
+                right.insert(value: value)
+            } else {
+                
+                right = SplayTree(value: value)
+                right?.parent = self
+                
+                if let right = right {
+                    SplayOperation.splay(node: right)
+                    self.parent = nil
+                    self.value = right.value
+                    self.left = right.left
+                    self.right = right.right
+                }
+            }
+        }
+    }
+}
+
+// MARK: - Deleting items
+
+extension SplayTree {
+    /*
+     Deletes a node from the tree.
+     Returns the node that has replaced this removed one (or nil if this was a
+     leaf node). That is primarily useful for when you delete the root node, in
+     which case the tree gets a new root.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    @discardableResult public func remove() -> SplayTree? {
+        let replacement: SplayTree?
+        
+        if let left = left {
+            if let right = right {
+                replacement = removeNodeWithTwoChildren(left, right)
+            } else {
+                // This node only has a left child. The left child replaces the node.
+                replacement = left
+            }
+        } else if let right = right {
+            // This node only has a right child. The right child replaces the node.
+            replacement = right
+        } else {
+            // This node has no children. We just disconnect it from its parent.
+            replacement = nil
+        }
+
+        // Save the parent to splay before reconnecting
+        var parentToSplay: SplayTree?
+        if let replacement = replacement {
+            parentToSplay = replacement.parent
+        } else {
+            parentToSplay = self.parent
+        }
+        
+        reconnectParentTo(node: replacement)
+        
+        // performs the splay operation
+        if let parentToSplay = parentToSplay {
+            SplayOperation.splay(node: parentToSplay)
+        }
+        
+        // The current node is no longer part of the tree, so clean it up.
+        parent = nil
+        left = nil
+        right = nil
+        
+        return replacement
+    }
+    
+    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+        // This node has two children. It must be replaced by the smallest
+        // child that is larger than this node's value, which is the leftmost
+        // descendent of the right child.
+        let successor = right.minimum()
+        
+        // If this in-order successor has a right child of its own (it cannot
+        // have a left child by definition), then that must take its place.
+        successor.remove()
+        
+        // Connect our left child with the new node.
+        successor.left = left
+        left.parent = successor
+        
+        // Connect our right child with the new node. If the right child does
+        // not have any left children of its own, then the in-order successor
+        // *is* the right child.
+        if right !== successor {
+            successor.right = right
+            right.parent = successor
+        } else {
+            successor.right = nil
+        }
+        
+        // And finally, connect the successor node to our parent.
+        return successor
+    }
+    
+    private func reconnectParentTo(node: SplayTree?) {
+        if let parent = parent {
+            if isLeftChild {
+                parent.left = node
+            } else {
+                parent.right = node
+            }
+        }
+        node?.parent = parent
+    }
+}
+
+// MARK: - Searching
+
+extension SplayTree {
+    
+    /*
+     Finds the "highest" node with the specified value.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func search(value: T) -> SplayTree? {
+        var node: SplayTree? = self
+        while case let n? = node {
+            if value < n.value {
+                node = n.left
+            } else if value > n.value {
+                node = n.right
+            } else {
+                
+                if let node = node {
+                    SplayOperation.splay(node: node)
+                }
+                
+                return node
+            }
+        }
+        
+        if let node = node {
+            SplayOperation.splay(node: node)
+        }
+        
+        return nil
+    }
+    
+    public func contains(value: T) -> Bool {
+        return search(value: value) != nil
+    }
+    
+    /*
+     Returns the leftmost descendent. O(h) time.
+     */
+    public func minimum() -> SplayTree {
+        var node = self
+        while case let next? = node.left {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+
+        return node
+    }
+    
+    /*
+     Returns the rightmost descendent. O(h) time.
+     */
+    public func maximum() -> SplayTree {
+        var node = self
+        while case let next? = node.right {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+        
+        return node
+    }
+    
+    /*
+     Calculates the depth of this node, i.e. the distance to the root.
+     Takes O(h) time.
+     */
+    public func depth() -> Int {
+        var node = self
+        var edges = 0
+        while case let parent? = node.parent {
+            node = parent
+            edges += 1
+        }
+        return edges
+    }
+    
+    /*
+     Calculates the height of this node, i.e. the distance to the lowest leaf.
+     Since this looks at all children of this node, performance is O(n).
+     */
+    public func height() -> Int {
+        if isLeaf {
+            return 0
+        } else {
+            return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+        }
+    }
+    
+    /*
+     Finds the node whose value precedes our value in sorted order.
+     */
+    public func predecessor() -> SplayTree<T>? {
+        if let left = left {
+            return left.maximum()
+        } else {
+            var node = self
+            while case let parent? = node.parent {
+                if parent.value < value { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+    
+    /*
+     Finds the node whose value succeeds our value in sorted order.
+     */
+    public func successor() -> SplayTree<T>? {
+        if let right = right {
+            return right.minimum()
+        } else {
+            var node = self
+            while case let parent? = node.parent {
+                if parent.value > value { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+}
+
+// MARK: - Traversal
+extension SplayTree {
+    
+    public func traverseInOrder(process: (T) -> Void) {
+        left?.traverseInOrder(process: process)
+        process(value)
+        right?.traverseInOrder(process: process)
+    }
+    
+    public func traversePreOrder(process: (T) -> Void) {
+        process(value)
+        left?.traversePreOrder(process: process)
+        right?.traversePreOrder(process: process)
+    }
+    
+    public func traversePostOrder(process: (T) -> Void) {
+        left?.traversePostOrder(process: process)
+        right?.traversePostOrder(process: process)
+        process(value)
+    }
+    
+    /*
+     Performs an in-order traversal and collects the results in an array.
+     */
+    public func map(formula: (T) -> T) -> [T] {
+        var a = [T]()
+        if let left = left { a += left.map(formula: formula) }
+        a.append(formula(value))
+        if let right = right { a += right.map(formula: formula) }
+        return a
+    }
+}
+
+/*
+ Is this binary tree a valid binary search tree?
+ */
+extension SplayTree {
+    
+    public func isBST(minValue: T, maxValue: T) -> Bool {
+        if value < minValue || value > maxValue { return false }
+        let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+        let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+        return leftBST && rightBST
+    }
+}
+
+// MARK: - Debugging
+
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if let left = left {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(value)"
+        if let right = right {
+            s += " -> (\(right.description))"
+        }
+        return s
+    }
+}
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = "value: \(value)"
+        if let parent = parent {
+            s += ", parent: \(parent.value)"
+        }
+        if let left = left {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = right {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
+    }
+    
+    public func toArray() -> [T] {
+        return map { $0 }
+    }
+}
diff --git a/Splay Tree/SplayTree.playground/contents.xcplayground b/Splay Tree/SplayTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
new file mode 100644
index 000000000..727ff8f50
--- /dev/null
+++ b/Splay Tree/SplayTree.swift	
@@ -0,0 +1,552 @@
+/*
+ *  Splay Tree 
+ *
+ * Based on Binary Search Tree Implementation written by Nicolas Ameghino and Matthijs Hollemans for Swift Algorithms Club
+ * https://github.com/raywenderlich/swift-algorithm-club/blob/master/Binary%20Search%20Tree
+ * And extended for the specifics of a Splay Tree by Barbara Martina Rodeker
+ *
+ */
+
+/**
+    Represent the 3 possible operations (combinations of rotations) that
+    could be performed during the Splay phase in Splay Trees
+ 
+    - zigZag       Left child of a right child OR right child of a left child
+    - zigZig       Left child of a left child OR right child of a right child
+    - zig          Only 1 parent and that parent is the root
+ 
+ */
+public enum SplayOperation {
+    case zigZag
+    case zigZig
+    case zig
+    
+    
+    /**
+        Splay the given node up to the root of the tree
+     
+        - Parameters:
+            - node      SplayTree node to move up to the root
+     */
+    public static func splay<T: Comparable>(node: SplayTree<T>) {
+        
+        while (node.parent != nil) {
+            operation(forNode: node).apply(onNode: node)
+        }
+    }
+    
+    /**
+        Compares the node and its parent and determine
+        if the rotations should be performed in a zigZag, zigZig or zig case.
+     
+        - Parmeters:
+            - forNode       SplayTree node to be checked
+        - Returns
+            - Operation     Case zigZag - zigZig - zig
+     */
+    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+        
+        if let parent = node.parent, let _ = parent.parent {
+            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
+                return .zigZag
+            }
+            return .zigZig
+        }
+        return .zig
+    }
+    
+    /**
+        Applies the rotation associated to the case 
+        Modifying the splay tree and briging the received node further to the top of the tree
+     
+        - Parameters:
+            - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
+     */
+    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+        switch self {
+        case .zigZag:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node, parent: node.parent!)
+            rotate(child: node, parent: node.parent!)
+
+        case .zigZig:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node.parent!, parent: node.parent!.parent!)
+            rotate(child: node, parent: node.parent!)
+        
+        case .zig:
+            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+            rotate(child: node, parent: node.parent!)
+        }
+    }
+    
+    /**
+        Performs a single rotation from a node to its parent
+        re-arranging the children properly
+     */
+    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+        
+        assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
+        
+        var grandchildToMode: SplayTree<T>?
+        if child.isLeftChild {
+            
+            grandchildToMode = child.right
+            child.right = parent
+            parent.left = grandchildToMode
+            
+        } else {
+            
+            grandchildToMode = child.left
+            child.left = parent
+            parent.right = grandchildToMode
+        }
+
+        let grandParent = parent.parent
+        parent.parent = child
+        child.parent = grandParent
+    }
+}
+
+public class Node<T: Comparable> {
+    
+    fileprivate(set) public var value: T
+    fileprivate(set) public var parent: SplayTree<T>?
+    fileprivate(set) public var left: SplayTree<T>?
+    fileprivate(set) public var right: SplayTree<T>?
+    
+    init(value: T){
+        self.value = value
+    }
+}
+
+public class SplayTree<T: Comparable> {
+
+
+    fileprivate(set) public var root: Node<T>?
+    public var value: T? {
+        get {
+            return root?.value
+        }
+        set {
+            if let value = newValue {
+                root?.value = value
+            }
+        }
+    }
+
+    fileprivate(set) public var parent: SplayTree? {
+        get {
+            return root?.parent
+        }
+        set {
+            root?.parent = newValue
+        }
+    }
+    
+    fileprivate(set) public var left: SplayTree? {
+        get {
+            return root?.left
+        }
+        set {
+            root?.left = newValue
+        }
+    }
+    fileprivate(set) public var right: SplayTree? {
+        get {
+            return root?.right
+        }
+        set {
+            root?.right = newValue
+        }
+    }
+
+    //MARK: - Initializer
+    
+    public init(value: T) {
+        self.root = Node(value:value)
+    }
+    
+    public var isRoot: Bool {
+        return parent == nil
+    }
+    
+    public var isLeaf: Bool {
+        return left == nil && right == nil
+    }
+    
+    public var isLeftChild: Bool {
+        return parent?.left === self
+    }
+    
+    public var isRightChild: Bool {
+        return parent?.right === self
+    }
+    
+    public var hasLeftChild: Bool {
+        return left != nil
+    }
+    
+    public var hasRightChild: Bool {
+        return right != nil
+    }
+    
+    public var hasAnyChild: Bool {
+        return hasLeftChild || hasRightChild
+    }
+    
+    public var hasBothChildren: Bool {
+        return hasLeftChild && hasRightChild
+    }
+    
+    /* How many nodes are in this subtree. Performance: O(n). */
+    public var count: Int {
+        return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+    }
+}
+
+// MARK: - Adding items
+
+extension SplayTree {
+    
+    /*
+     Inserts a new element into the tree. You should only insert elements
+     at the root, to make to sure this remains a valid binary tree!
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func insert(value: T) -> SplayTree? {
+        if let selfValue = self.value {
+            if value < selfValue {
+                if let left = left {
+                    return left.insert(value: value)
+                } else {
+                    
+                    left = SplayTree(value: value)
+                    left?.parent = self
+                    
+                    if let left = left {
+                        SplayOperation.splay(node: left)
+                        return left
+                    }
+                }
+            } else {
+                
+                if let right = right {
+                    return right.insert(value: value)
+                } else {
+                    
+                    right = SplayTree(value: value)
+                    right?.parent = self
+                    
+                    if let right = right {
+                        SplayOperation.splay(node: right)
+                        return right
+                    }
+                }
+            }
+        } else {
+            self.root = Node(value: value)
+            return self
+        }
+        return nil
+    }
+}
+
+// MARK: - Deleting items
+
+extension SplayTree {
+    /*
+     Deletes a node from the tree.
+     Returns the node that has replaced this removed one (or nil if this was a
+     leaf node). That is primarily useful for when you delete the root node, in
+     which case the tree gets a new root.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    @discardableResult public func remove() -> SplayTree? {
+        let replacement: SplayTree?
+        
+        if let left = left {
+            if let right = right {
+                replacement = removeNodeWithTwoChildren(left, right)
+            } else {
+                // This node only has a left child. The left child replaces the node.
+                replacement = left
+            }
+        } else if let right = right {
+            // This node only has a right child. The right child replaces the node.
+            replacement = right
+        } else {
+            // This node has no children. We just disconnect it from its parent.
+            replacement = nil
+        }
+
+        // Save the parent to splay before reconnecting
+        var parentToSplay: SplayTree?
+        if let replacement = replacement {
+            parentToSplay = replacement.parent
+        } else {
+            parentToSplay = self.parent
+        }
+        
+        reconnectParentTo(node: replacement)
+        
+        // performs the splay operation
+        if let parentToSplay = parentToSplay {
+            SplayOperation.splay(node: parentToSplay)
+        }
+        
+        // The current node is no longer part of the tree, so clean it up.
+        parent = nil
+        left = nil
+        right = nil
+        
+        return replacement
+    }
+    
+    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+        // This node has two children. It must be replaced by the smallest
+        // child that is larger than this node's value, which is the leftmost
+        // descendent of the right child.
+        let successor = right.minimum()
+        
+        // If this in-order successor has a right child of its own (it cannot
+        // have a left child by definition), then that must take its place.
+        successor.remove()
+        
+        // Connect our left child with the new node.
+        successor.left = left
+        left.parent = successor
+        
+        // Connect our right child with the new node. If the right child does
+        // not have any left children of its own, then the in-order successor
+        // *is* the right child.
+        if right !== successor {
+            successor.right = right
+            right.parent = successor
+        } else {
+            successor.right = nil
+        }
+        
+        // And finally, connect the successor node to our parent.
+        return successor
+    }
+    
+    private func reconnectParentTo(node: SplayTree?) {
+        if let parent = parent {
+            if isLeftChild {
+                parent.left = node
+            } else {
+                parent.right = node
+            }
+        }
+        node?.parent = parent
+    }
+}
+
+// MARK: - Searching
+
+extension SplayTree {
+    
+    /*
+     Finds the "highest" node with the specified value.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func search(value: T) -> SplayTree? {
+        var node: SplayTree? = self
+        while case let n? = node, n.value != nil {
+            if value < n.value! {
+                node = n.left
+            } else if value > n.value! {
+                node = n.right
+            } else {
+                
+                if let node = node {
+                    SplayOperation.splay(node: node)
+                }
+                
+                return node
+            }
+        }
+        
+        if let node = node {
+            SplayOperation.splay(node: node)
+        }
+        
+        return nil
+    }
+    
+    public func contains(value: T) -> Bool {
+        return search(value: value) != nil
+    }
+    
+    /*
+     Returns the leftmost descendent. O(h) time.
+     */
+    public func minimum() -> SplayTree {
+        var node = self
+        while case let next? = node.left {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+
+        return node
+    }
+    
+    /*
+     Returns the rightmost descendent. O(h) time.
+     */
+    public func maximum() -> SplayTree {
+        var node = self
+        while case let next? = node.right {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+        
+        return node
+    }
+    
+    /*
+     Calculates the depth of this node, i.e. the distance to the root.
+     Takes O(h) time.
+     */
+    public func depth() -> Int {
+        var node = self
+        var edges = 0
+        while case let parent? = node.parent {
+            node = parent
+            edges += 1
+        }
+        return edges
+    }
+    
+    /*
+     Calculates the height of this node, i.e. the distance to the lowest leaf.
+     Since this looks at all children of this node, performance is O(n).
+     */
+    public func height() -> Int {
+        if isLeaf {
+            return 0
+        } else {
+            return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+        }
+    }
+    
+    /*
+     Finds the node whose value precedes our value in sorted order.
+     */
+    public func predecessor() -> SplayTree<T>? {
+        if let left = left {
+            return left.maximum()
+        } else {
+            var node = self
+            while case let parent? = node.parent, parent.value != nil, value != nil {
+                if parent.value! < value! { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+    
+    /*
+     Finds the node whose value succeeds our value in sorted order.
+     */
+    public func successor() -> SplayTree<T>? {
+        if let right = right {
+            return right.minimum()
+        } else {
+            var node = self
+            while case let parent? = node.parent, parent.value != nil , value != nil {
+                if parent.value! > value! { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+}
+
+// MARK: - Traversal
+extension SplayTree {
+    
+    public func traverseInOrder(process: (T) -> Void) {
+        left?.traverseInOrder(process: process)
+        process(value!)
+        right?.traverseInOrder(process: process)
+    }
+    
+    public func traversePreOrder(process: (T) -> Void) {
+        process(value!)
+        left?.traversePreOrder(process: process)
+        right?.traversePreOrder(process: process)
+    }
+    
+    public func traversePostOrder(process: (T) -> Void) {
+        left?.traversePostOrder(process: process)
+        right?.traversePostOrder(process: process)
+        process(value!)
+    }
+    
+    /*
+     Performs an in-order traversal and collects the results in an array.
+     */
+    public func map(formula: (T) -> T) -> [T] {
+        var a = [T]()
+        if let left = left { a += left.map(formula: formula) }
+        a.append(formula(value!))
+        if let right = right { a += right.map(formula: formula) }
+        return a
+    }
+}
+
+/*
+ Is this binary tree a valid binary search tree?
+ */
+extension SplayTree {
+    
+    public func isBST(minValue: T, maxValue: T) -> Bool {
+        if let value = value {
+            if value < minValue || value > maxValue { return false }
+            let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+            let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+            return leftBST && rightBST
+        }
+        return false
+    }
+}
+
+// MARK: - Debugging
+
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if let left = left {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(value)"
+        if let right = right {
+            s += " -> (\(right.description))"
+        }
+        return s
+    }
+}
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = "value: \(value)"
+        if let parent = parent {
+            s += ", parent: \(parent.value)"
+        }
+        if let left = left {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = right {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
+    }
+    
+    public func toArray() -> [T] {
+        return map { $0 }
+    }
+}
diff --git a/Splay Tree/Tests/Info.plist b/Splay Tree/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Splay Tree/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
new file mode 100644
index 000000000..35bdedb71
--- /dev/null
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -0,0 +1,19 @@
+import XCTest
+
+class SplayTreeTests: XCTestCase {
+  var tree: SplayTree<Int>!
+  
+  override func setUp() {
+    super.setUp()
+    tree = SplayTree<Int>(value: 1)
+  }
+  
+  func testElements() {
+    print(tree)
+    let tree1 = tree.insert(value: 10)
+    print(tree1!)
+    let tree2 = tree1!.insert(value: 2)
+    print(tree2!)
+  }
+
+}
diff --git a/Splay Tree/Tests/Tests-Bridging-Header.h b/Splay Tree/Tests/Tests-Bridging-Header.h
new file mode 100644
index 000000000..1b2cb5d6d
--- /dev/null
+++ b/Splay Tree/Tests/Tests-Bridging-Header.h	
@@ -0,0 +1,4 @@
+//
+//  Use this file to import your target's public headers that you would like to expose to Swift.
+//
+
diff --git a/Splay Tree/Tests/Tests.xcodeproj/project.pbxproj b/Splay Tree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..8a900fcd3
--- /dev/null
+++ b/Splay Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,279 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
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+/* End PBXFrameworksBuildPhase section */
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+	rootObject = 056E92861E25D03300B30F52 /* Project object */;
+}
diff --git a/Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..b3f6d696a
--- /dev/null
+++ b/Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,101 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0820"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 217cad58d2501c10d040fd72cbcaea96d366fc72 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Mon, 20 Feb 2017 10:25:31 +0800
Subject: [PATCH 0828/1679] Update README.markdown

add swift version
---
 Shell Sort/README.markdown | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index 6cb682035..a2ac843c7 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -111,6 +111,28 @@ This is an old Commodore 64 BASIC version of shell sort that Matthijs used a lon
 	61300 GOTO 61220
 	61310 RETURN
 
+## The Code:
+Here is an implementation of Shell Sort in Swift:
+```
+var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
+
+var n = arr.count / 2
+
+repeat
+{
+    for index in 0..<arr.count{
+        
+        if (index + n) < arr.count && arr[index] > arr[index + n]{
+        
+            swap(&arr[index], &arr[index + n])
+        }
+    }
+    
+    n = n / 2
+    
+}while n > 0
+```
+
 ## See also
 
 [Shellsort on Wikipedia](https://en.wikipedia.org/wiki/Shellsort)

From 31b89968878506cadb76ae2a650edbe651d5f58c Mon Sep 17 00:00:00 2001
From: Timur Galimov <timakgalimov@gmail.com>
Date: Tue, 21 Feb 2017 22:04:11 +0300
Subject: [PATCH 0829/1679] fix typo in PointsContainer protocol

---
 QuadTree/QuadTree.playground/Sources/QuadTree.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/QuadTree/QuadTree.playground/Sources/QuadTree.swift b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
index beec4a7b7..65c55d49e 100644
--- a/QuadTree/QuadTree.playground/Sources/QuadTree.swift
+++ b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
@@ -104,7 +104,7 @@ extension Rect: CustomStringConvertible {
   }
 }
 
-protocol PointsContainter {
+protocol PointsContainer {
   func add(point: Point) -> Bool
   func points(inRect rect: Rect) -> [Point]
 }
@@ -185,7 +185,7 @@ class QuadTreeNode {
   }
 }
 
-extension QuadTreeNode: PointsContainter {
+extension QuadTreeNode: PointsContainer {
   
   @discardableResult
   func add(point: Point) -> Bool {
@@ -265,7 +265,7 @@ extension QuadTreeNode: CustomStringConvertible {
   }
 }
 
-public class QuadTree: PointsContainter {
+public class QuadTree: PointsContainer {
   
   let root: QuadTreeNode
   

From 2e5a5748fdbf92bb1f7c191af7a1c7a0e8b64de6 Mon Sep 17 00:00:00 2001
From: Timur Galimov <timakgalimov@gmail.com>
Date: Tue, 21 Feb 2017 22:28:50 +0300
Subject: [PATCH 0830/1679] Add quadtree diagram

---
 QuadTree/Images/quadtree.png | Bin 0 -> 110070 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 QuadTree/Images/quadtree.png

diff --git a/QuadTree/Images/quadtree.png b/QuadTree/Images/quadtree.png
new file mode 100644
index 0000000000000000000000000000000000000000..53af6fb082a3e6172090bd167e4178a4b8e99e36
GIT binary patch
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HcmV?d00001


From 42032b4bec864013c7e51fff3443ec602b295741 Mon Sep 17 00:00:00 2001
From: Timur Galimov <timakgalimov@gmail.com>
Date: Wed, 22 Feb 2017 01:04:55 +0300
Subject: [PATCH 0831/1679] Update README.md

---
 QuadTree/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/QuadTree/README.md b/QuadTree/README.md
index 77ac8b8fa..3fc682547 100644
--- a/QuadTree/README.md
+++ b/QuadTree/README.md
@@ -2,6 +2,8 @@
 
 A quadtree is a [tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Tree) in which each internal (not leaf) node has four children.
 
+<img src="https://github.com/timaktimak/swift-algorithm-club/blob/master/QuadTree/Images/quadtree.png" width="500">
+
 ### Problem
 
 Consider the following problem: your need to store a number of points (each point is a pair of `X` and `Y` coordinates) and then you need to answer which points lie in a certain rectangular region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though. 

From 71bfd719ce6024944e7c17847952d77094be6cc8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Sun, 26 Feb 2017 12:41:50 +0800
Subject: [PATCH 0832/1679] add file ShellSortExample.swift

update code
---
 Shell Sort/ShellSortExample.swift | 33 +++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 Shell Sort/ShellSortExample.swift

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
new file mode 100644
index 000000000..eea80e539
--- /dev/null
+++ b/Shell Sort/ShellSortExample.swift	
@@ -0,0 +1,33 @@
+//
+//  ShellSortExample.swift
+//  
+//
+//  Created by Cheer on 2017/2/26.
+//
+//
+
+import Foundation
+
+public func shellSort(_ list : inout [Int])
+{
+    var sublistCount = list.count / 2
+    
+    while sublistCount > 0
+    {
+        for index in 0..<arr.count{
+            
+            guard index + sublistCount < arr.count else { break }
+            
+            if arr[index] > arr[index + sublistCount]{
+                swap(&arr[index], &arr[index + sublistCount])
+            }
+            
+            guard sublistCount == 1 && index > 0 else { continue }
+            
+            if arr[index - 1] > arr[index]{
+                swap(&arr[index - 1], &arr[index])
+            }
+        }
+        sublistCount = sublistCount / 2
+    }
+}

From 8202cf1668a535b61fbac12962ebc5a639631ee1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Mon, 27 Feb 2017 10:52:37 +0800
Subject: [PATCH 0833/1679] Update ShellSortExample.swift

Fix my code mistakes
---
 Shell Sort/ShellSortExample.swift | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index eea80e539..68cd9ead1 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -14,18 +14,18 @@ public func shellSort(_ list : inout [Int])
     
     while sublistCount > 0
     {
-        for index in 0..<arr.count{
+        for index in 0..<list.count{
             
-            guard index + sublistCount < arr.count else { break }
+            guard index + sublistCount < list.count else { break }
             
-            if arr[index] > arr[index + sublistCount]{
-                swap(&arr[index], &arr[index + sublistCount])
+            if list[index] > list[index + sublistCount]{
+                swap(&list[index], &list[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
             
-            if arr[index - 1] > arr[index]{
-                swap(&arr[index - 1], &arr[index])
+            if list[index - 1] > list[index]{
+                swap(&list[index - 1], &list[index])
             }
         }
         sublistCount = sublistCount / 2

From 69cb42eef48c610f2f42e6c5d51781fdb3482e6a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Wed, 1 Mar 2017 12:13:54 +0800
Subject: [PATCH 0834/1679] Update ShellSortExample.swift

let code to suit style guide
---
 Shell Sort/ShellSortExample.swift | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 68cd9ead1..efa035da3 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -8,23 +8,23 @@
 
 import Foundation
 
-public func shellSort(_ list : inout [Int])
-{
-    var sublistCount = list.count / 2
+public func shellSort(_ list: inout [Int]) {
     
-    while sublistCount > 0
-    {
-        for index in 0..<list.count{
-            
+    var sublistCount = list.count / 2
+   
+    while sublistCount > 0 {
+        
+        for index in 0..<list.count {
+           
             guard index + sublistCount < list.count else { break }
             
-            if list[index] > list[index + sublistCount]{
+            if list[index] > list[index + sublistCount] {
                 swap(&list[index], &list[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
             
-            if list[index - 1] > list[index]{
+            if list[index - 1] > list[index] {
                 swap(&list[index - 1], &list[index])
             }
         }

From a69e3d84fcdc3bb8ab1d9e788f8826e5e9ab4254 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Thu, 2 Mar 2017 10:47:14 +0800
Subject: [PATCH 0835/1679] Update README.markdown

update sample code
---
 Shell Sort/README.markdown | 34 ++++++++++++++++++++++------------
 1 file changed, 22 insertions(+), 12 deletions(-)

diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index a2ac843c7..9c4bdf076 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -116,21 +116,31 @@ Here is an implementation of Shell Sort in Swift:
 ```
 var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
 
-var n = arr.count / 2
-
-repeat
-{
-    for index in 0..<arr.count{
-        
-        if (index + n) < arr.count && arr[index] > arr[index + n]{
+public func shellSort(_ list: inout [Int]) {
+    
+    var sublistCount = list.count / 2
+   
+    while sublistCount > 0 {
         
-            swap(&arr[index], &arr[index + n])
+        for index in 0..<list.count {
+           
+            guard index + sublistCount < list.count else { break }
+            
+            if list[index] > list[index + sublistCount] {
+                swap(&list[index], &list[index + sublistCount])
+            }
+            
+            guard sublistCount == 1 && index > 0 else { continue }
+            
+            if list[index - 1] > list[index] {
+                swap(&list[index - 1], &list[index])
+            }
         }
+        sublistCount = sublistCount / 2
     }
-    
-    n = n / 2
-    
-}while n > 0
+}
+
+shellSort(&arr)
 ```
 
 ## See also

From b4e4ef1c8095405c21e69284807095f548fea537 Mon Sep 17 00:00:00 2001
From: John Pham <hprobotic@gmail.com>
Date: Thu, 2 Mar 2017 17:10:59 +0700
Subject: [PATCH 0836/1679] Update dim func follow syntax change of swift 3

---
 Array2D/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 51e77435e..b98a09593 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -36,7 +36,7 @@ var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 but that's just ugly. To be fair, you can hide the ugliness in a helper function:
 
 ```swift
-func dim<T>(count: Int, _ value: T) -> [T] {
+func dim<T>(_ count: Int, _ value: T) -> [T] {
   return [T](repeating: value, count: count)
 }
 ```

From 0837113e9e8a0fa69d2e8deb8302bb0a72c5d5b5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Thu, 2 Mar 2017 19:19:18 +0800
Subject: [PATCH 0837/1679] Add files via upload

upload a radix sort implement,faster than original code
---
 Radix Sort/RadixSortExample.swift | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 Radix Sort/RadixSortExample.swift

diff --git a/Radix Sort/RadixSortExample.swift b/Radix Sort/RadixSortExample.swift
new file mode 100644
index 000000000..7d9461c5c
--- /dev/null
+++ b/Radix Sort/RadixSortExample.swift	
@@ -0,0 +1,29 @@
+//
+//  RadixSortExample.swift
+//  
+//
+//  Created by Cheer on 2017/3/2.
+//
+//
+
+import Foundation
+
+func radixSort1(_ arr: inout [Int]) {
+   
+    var temp = [[Int]](repeating: [], count: 10)
+    
+    for num in arr { temp[num % 10].append(num) }
+    
+    for i in 1...Int(arr.max()!.description.characters.count) {
+        
+        for index in 0..<temp.count {
+           
+            for num in temp[index] {
+                temp[index].remove(at: temp[index].index(of: num)!)
+                temp[(num / Int(pow(10, Double(i)))) % 10].append(num)
+            }
+        }
+    }
+    
+    arr = temp[0]
+}

From 10615dfff7a40ca130d6b2c02a9bedc0c161faac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Fri, 3 Mar 2017 11:13:22 +0800
Subject: [PATCH 0838/1679] Update LinearSearch.swift

more swift
---
 Linear Search/LinearSearch.swift | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Linear Search/LinearSearch.swift b/Linear Search/LinearSearch.swift
index 882795180..c5374d0a4 100644
--- a/Linear Search/LinearSearch.swift	
+++ b/Linear Search/LinearSearch.swift	
@@ -4,3 +4,7 @@ func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
   }
   return nil
 }
+
+func linearSearch1<T: Equatable>(_ array: [T], _ object: T) -> Array<T>.Index? {
+    return array.index { $0 == object }
+}

From 12b0bdbb8488f7746edac33623b2f86c57564a31 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Fri, 3 Mar 2017 11:34:04 +0800
Subject: [PATCH 0839/1679] Update README.markdown

update some details
---
 Select Minimum Maximum/README.markdown | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index 09ca97039..fa0f8fed8 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -68,6 +68,13 @@ array.minElement()   // This will return 3
 array.maxElement()   // This will return 9
 ```
 
+```
+let array = [ 8, 3, 9, 4, 6 ]
+//swift3
+array.min()   // This will return 3
+array.max()   // This will return 9
+```
+
 ## Maximum and minimum
 
 To find both the maximum and minimum values contained in array while minimizing the number of comparisons we can compare the items in pairs. 

From cc973dcb62d310f1af0d08d408c782a57e3523cb Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Fri, 3 Mar 2017 21:01:11 +0100
Subject: [PATCH 0840/1679] Fixes for connecting nodes during rotations

---
 Splay Tree/SplayTree.swift            | 53 ++++++++++++++++++---------
 Splay Tree/Tests/SplayTreeTests.swift | 41 +++++++++++++--------
 2 files changed, 61 insertions(+), 33 deletions(-)

diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index 727ff8f50..2e008ba50 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -44,7 +44,7 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+    public static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -62,7 +62,7 @@ public enum SplayOperation {
         - Parameters:
             - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+    public func apply<T: Comparable>(onNode node: SplayTree<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,7 +84,7 @@ public enum SplayOperation {
         Performs a single rotation from a node to its parent
         re-arranging the children properly
      */
-    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+    public func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
@@ -95,16 +95,22 @@ public enum SplayOperation {
             child.right = parent
             parent.left = grandchildToMode
             
+    
+
         } else {
             
             grandchildToMode = child.left
             child.left = parent
             parent.right = grandchildToMode
-        }
 
+        }
+        
         let grandParent = parent.parent
         parent.parent = child
         child.parent = grandParent
+        
+        grandParent?.left = child
+
     }
 }
 
@@ -210,9 +216,15 @@ public class SplayTree<T: Comparable> {
 extension SplayTree {
     
     /*
-     Inserts a new element into the tree. You should only insert elements
-     at the root, to make to sure this remains a valid binary tree!
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Inserts a new element into the tree. 
+     Returns the new Tree generated by the insertion.
+     
+     - Parameters:
+            - value T value to be inserted. Will be splayed to the root position
+     
+     - Returns
+            - SplayTree Containing the inserted value in the root node
+     
      */
     public func insert(value: T) -> SplayTree? {
         if let selfValue = self.value {
@@ -255,14 +267,17 @@ extension SplayTree {
 // MARK: - Deleting items
 
 extension SplayTree {
+    
     /*
-     Deletes a node from the tree.
-     Returns the node that has replaced this removed one (or nil if this was a
-     leaf node). That is primarily useful for when you delete the root node, in
-     which case the tree gets a new root.
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Deletes the given node from the tree.
+     Return the new tree generated by the removal. 
+     The removed node (not necessarily the one containing the value), will be splayed to the root.
+     
+     - Returns:
+            - SplayTree     Resulting from the deletion and the splaying of the removed node
+     
      */
-    @discardableResult public func remove() -> SplayTree? {
+    public func remove() -> SplayTree? {
         let replacement: SplayTree?
         
         if let left = left {
@@ -521,11 +536,13 @@ extension SplayTree: CustomStringConvertible {
     public var description: String {
         var s = ""
         if let left = left {
-            s += "(\(left.description)) <- "
+            s += "left: (\(left.description)) <- "
+        }
+        if let v = value {
+            s += "\(v)"
         }
-        s += "\(value)"
         if let right = right {
-            s += " -> (\(right.description))"
+            s += " -> (right: \(right.description))"
         }
         return s
     }
@@ -534,8 +551,8 @@ extension SplayTree: CustomStringConvertible {
 extension SplayTree: CustomDebugStringConvertible {
     public var debugDescription: String {
         var s = "value: \(value)"
-        if let parent = parent {
-            s += ", parent: \(parent.value)"
+        if let parent = parent, let v = parent.value {
+            s += ", parent: \(v)"
         }
         if let left = left {
             s += ", left = [" + left.debugDescription + "]"
diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 35bdedb71..998c6d3c4 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -1,19 +1,30 @@
 import XCTest
 
 class SplayTreeTests: XCTestCase {
-  var tree: SplayTree<Int>!
-  
-  override func setUp() {
-    super.setUp()
-    tree = SplayTree<Int>(value: 1)
-  }
-  
-  func testElements() {
-    print(tree)
-    let tree1 = tree.insert(value: 10)
-    print(tree1!)
-    let tree2 = tree1!.insert(value: 2)
-    print(tree2!)
-  }
-
+   
+    var tree: SplayTree<Int>!
+    var tree1: SplayTree<Int>!
+    
+    override func setUp() {
+        super.setUp()
+        tree = SplayTree<Int>(value: 1)
+        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)//?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
+    }
+    
+    func testInsertion() {
+        let tree1 = tree.insert(value: 10)
+        assert(tree1?.root?.value == 10)
+        
+        let tree2 = tree1!.insert(value: 2)
+        assert(tree2?.root?.value == 2)
+    }
+    
+    
+    func testDeleteExisting() {
+        print(tree1)
+        let tree2 = tree1.search(value: 6)?.remove()
+        
+    }
+    
+    
 }

From 72740a17e7bd9b74716e32f1ef9ef4a92534b302 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sat, 4 Mar 2017 09:20:25 +0100
Subject: [PATCH 0841/1679] Test for search function + fixes for rotations

---
 Splay Tree/SplayTree.swift            | 17 +++++++++--------
 Splay Tree/Tests/SplayTreeTests.swift |  7 ++++---
 2 files changed, 13 insertions(+), 11 deletions(-)

diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index 2e008ba50..bbe8491e2 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -94,7 +94,7 @@ public enum SplayOperation {
             grandchildToMode = child.right
             child.right = parent
             parent.left = grandchildToMode
-            
+            grandchildToMode?.parent = parent
     
 
         } else {
@@ -102,6 +102,7 @@ public enum SplayOperation {
             grandchildToMode = child.left
             child.left = parent
             parent.right = grandchildToMode
+            grandchildToMode?.parent = parent
 
         }
         
@@ -368,23 +369,23 @@ extension SplayTree {
      */
     public func search(value: T) -> SplayTree? {
         var node: SplayTree? = self
+        var nodeParent: SplayTree? = self
         while case let n? = node, n.value != nil {
             if value < n.value! {
+                if n.left != nil { nodeParent = n.left }
                 node = n.left
             } else if value > n.value! {
                 node = n.right
-            } else {
-                
-                if let node = node {
-                    SplayOperation.splay(node: node)
-                }
-                
-                return node
+                if n.right != nil { nodeParent = n.right }
             }
         }
         
         if let node = node {
             SplayOperation.splay(node: node)
+            return node
+        } else if let nodeParent = nodeParent {
+            SplayOperation.splay(node: nodeParent)
+            return nodeParent
         }
         
         return nil
diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 998c6d3c4..042344193 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -8,7 +8,7 @@ class SplayTreeTests: XCTestCase {
     override func setUp() {
         super.setUp()
         tree = SplayTree<Int>(value: 1)
-        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)//?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
+        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
     }
     
     func testInsertion() {
@@ -20,9 +20,10 @@ class SplayTreeTests: XCTestCase {
     }
     
     
-    func testDeleteExisting() {
+    func testSearchNonExisting() {
         print(tree1)
-        let tree2 = tree1.search(value: 6)?.remove()
+        let tree2 = tree1.search(value: 5)
+        assert(tree2?.root?.value == 10)
         
     }
     

From 84e75b73e246e76fe8a22c97ef49c9d5277ea35b Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:23:31 +0100
Subject: [PATCH 0842/1679] Completing implementation + debug fixes of Splay
 Tree

---
 Splay Tree/SplayTree.swift | 321 +++++++++++++++++++++----------------
 1 file changed, 186 insertions(+), 135 deletions(-)

diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index bbe8491e2..f50af7349 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -28,7 +28,7 @@ public enum SplayOperation {
         - Parameters:
             - node      SplayTree node to move up to the root
      */
-    public static func splay<T: Comparable>(node: SplayTree<T>) {
+    public static func splay<T: Comparable>(node: Node<T>) {
         
         while (node.parent != nil) {
             operation(forNode: node).apply(onNode: node)
@@ -44,7 +44,7 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    public static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -62,7 +62,7 @@ public enum SplayOperation {
         - Parameters:
             - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    public func apply<T: Comparable>(onNode node: SplayTree<T>) {
+    public func apply<T: Comparable>(onNode node: Node<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,95 +84,65 @@ public enum SplayOperation {
         Performs a single rotation from a node to its parent
         re-arranging the children properly
      */
-    public func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+    public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
-        var grandchildToMode: SplayTree<T>?
+        var grandchildToMode: Node<T>?
+        
         if child.isLeftChild {
             
             grandchildToMode = child.right
-            child.right = parent
             parent.left = grandchildToMode
             grandchildToMode?.parent = parent
+
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.right = parent
+            parent.parent = child
     
 
         } else {
             
             grandchildToMode = child.left
-            child.left = parent
             parent.right = grandchildToMode
             grandchildToMode?.parent = parent
 
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.left = parent
+            parent.parent = child
+
         }
         
-        let grandParent = parent.parent
-        parent.parent = child
-        child.parent = grandParent
-        
-        grandParent?.left = child
 
     }
 }
 
 public class Node<T: Comparable> {
     
-    fileprivate(set) public var value: T
-    fileprivate(set) public var parent: SplayTree<T>?
-    fileprivate(set) public var left: SplayTree<T>?
-    fileprivate(set) public var right: SplayTree<T>?
+    fileprivate(set) public var value: T?
+    fileprivate(set) public var parent: Node<T>?
+    fileprivate(set) public var left: Node<T>?
+    fileprivate(set) public var right: Node<T>?
     
-    init(value: T){
+    init(value: T) {
         self.value = value
     }
-}
-
-public class SplayTree<T: Comparable> {
-
-
-    fileprivate(set) public var root: Node<T>?
-    public var value: T? {
-        get {
-            return root?.value
-        }
-        set {
-            if let value = newValue {
-                root?.value = value
-            }
-        }
-    }
-
-    fileprivate(set) public var parent: SplayTree? {
-        get {
-            return root?.parent
-        }
-        set {
-            root?.parent = newValue
-        }
-    }
-    
-    fileprivate(set) public var left: SplayTree? {
-        get {
-            return root?.left
-        }
-        set {
-            root?.left = newValue
-        }
-    }
-    fileprivate(set) public var right: SplayTree? {
-        get {
-            return root?.right
-        }
-        set {
-            root?.right = newValue
-        }
-    }
-
-    //MARK: - Initializer
-    
-    public init(value: T) {
-        self.root = Node(value:value)
-    }
     
     public var isRoot: Bool {
         return parent == nil
@@ -212,29 +182,66 @@ public class SplayTree<T: Comparable> {
     }
 }
 
+public class SplayTree<T: Comparable> {
+
+    internal var root: Node<T>?
+    
+    var value: T? {
+        return root?.value
+    }
+
+    //MARK: - Initializer
+    
+    public init(value: T) {
+        self.root = Node(value:value)
+    }
+    
+    public func insert(value: T) {
+        root = root?.insert(value: value)
+    }
+    
+    public func remove(value: T) {
+        root = root?.remove(value: value)
+    }
+
+    public func search(value: T) -> Node<T>? {
+        root = root?.search(value: value)
+        return root
+    }
+    
+    public func minimum() -> Node<T>? {
+        root = root?.minimum(splayed: true)
+        return root
+    }
+    
+    public func maximum() -> Node<T>? {
+        root = root?.maximum(splayed: true)
+        return root
+    }
+    
+}
+
 // MARK: - Adding items
 
-extension SplayTree {
+extension Node {
     
     /*
-     Inserts a new element into the tree. 
-     Returns the new Tree generated by the insertion.
+     Inserts a new element into the node tree.
      
      - Parameters:
             - value T value to be inserted. Will be splayed to the root position
      
-     - Returns
-            - SplayTree Containing the inserted value in the root node
-     
+     - Returns:
+            - Node inserted
      */
-    public func insert(value: T) -> SplayTree? {
+    public func insert(value: T) -> Node {
         if let selfValue = self.value {
             if value < selfValue {
                 if let left = left {
                     return left.insert(value: value)
                 } else {
                     
-                    left = SplayTree(value: value)
+                    left = Node(value: value)
                     left?.parent = self
                     
                     if let left = left {
@@ -248,7 +255,7 @@ extension SplayTree {
                     return right.insert(value: value)
                 } else {
                     
-                    right = SplayTree(value: value)
+                    right = Node(value: value)
                     right?.parent = self
                     
                     if let right = right {
@@ -257,78 +264,104 @@ extension SplayTree {
                     }
                 }
             }
-        } else {
-            self.root = Node(value: value)
-            return self
         }
-        return nil
+        return self
     }
 }
 
 // MARK: - Deleting items
 
-extension SplayTree {
+extension Node {
     
     /*
-     Deletes the given node from the tree.
+     Deletes the given node from the nodes tree.
      Return the new tree generated by the removal. 
      The removed node (not necessarily the one containing the value), will be splayed to the root.
      
+     - Parameters:
+            - value         To be removed
+     
      - Returns:
-            - SplayTree     Resulting from the deletion and the splaying of the removed node
+            - Node     Resulting from the deletion and the splaying of the removed node
      
      */
-    public func remove() -> SplayTree? {
-        let replacement: SplayTree?
+    public func remove(value: T) -> Node<T>? {
+        let replacement: Node<T>?
         
-        if let left = left {
-            if let right = right {
-                replacement = removeNodeWithTwoChildren(left, right)
+        if let v = self.value, v == value {
+            
+            var parentToSplay: Node<T>?
+            if let left = left {
+                if let right = right {
+                    
+                    replacement = removeNodeWithTwoChildren(left, right)
+                    
+                    if let replacement = replacement,
+                        let replacementParent = replacement.parent,
+                        replacementParent.value != self.value {
+                        
+                        parentToSplay = replacement.parent
+                        
+                    } else {
+                        parentToSplay = self.parent
+                    }
+                    
+                } else {
+                    // This node only has a left child. The left child replaces the node.
+                    replacement = left
+                    parentToSplay = parent
+                }
+            } else if let right = right {
+                // This node only has a right child. The right child replaces the node.
+                replacement = right
+                parentToSplay = parent
             } else {
-                // This node only has a left child. The left child replaces the node.
-                replacement = left
+                // This node has no children. We just disconnect it from its parent.
+                replacement = nil
+                parentToSplay = parent
             }
-        } else if let right = right {
-            // This node only has a right child. The right child replaces the node.
-            replacement = right
-        } else {
-            // This node has no children. We just disconnect it from its parent.
-            replacement = nil
-        }
+            
+            reconnectParentTo(node: replacement)
+            
+            // performs the splay operation
+            if let parentToSplay = parentToSplay {
+                SplayOperation.splay(node: parentToSplay)
+            }
+            
+            // The current node is no longer part of the tree, so clean it up.
+            parent = nil
+            left = nil
+            right = nil
 
-        // Save the parent to splay before reconnecting
-        var parentToSplay: SplayTree?
-        if let replacement = replacement {
-            parentToSplay = replacement.parent
+            return parentToSplay
+            
+        } else if let v = self.value, value < v {
+            if left != nil {
+                return left!.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         } else {
-            parentToSplay = self.parent
-        }
-        
-        reconnectParentTo(node: replacement)
-        
-        // performs the splay operation
-        if let parentToSplay = parentToSplay {
-            SplayOperation.splay(node: parentToSplay)
+            if right != nil {
+                return right?.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         }
-        
-        // The current node is no longer part of the tree, so clean it up.
-        parent = nil
-        left = nil
-        right = nil
-        
-        return replacement
     }
     
-    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
         // This node has two children. It must be replaced by the smallest
         // child that is larger than this node's value, which is the leftmost
         // descendent of the right child.
         let successor = right.minimum()
         
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
-        
         // Connect our left child with the new node.
         successor.left = left
         left.parent = successor
@@ -347,7 +380,7 @@ extension SplayTree {
         return successor
     }
     
-    private func reconnectParentTo(node: SplayTree?) {
+    private func reconnectParentTo(node: Node?) {
         if let parent = parent {
             if isLeftChild {
                 parent.left = node
@@ -361,15 +394,15 @@ extension SplayTree {
 
 // MARK: - Searching
 
-extension SplayTree {
+extension Node {
     
     /*
      Finds the "highest" node with the specified value.
      Performance: runs in O(h) time, where h is the height of the tree.
      */
-    public func search(value: T) -> SplayTree? {
-        var node: SplayTree? = self
-        var nodeParent: SplayTree? = self
+    public func search(value: T) -> Node<T>? {
+        var node: Node? = self
+        var nodeParent: Node? = self
         while case let n? = node, n.value != nil {
             if value < n.value! {
                 if n.left != nil { nodeParent = n.left }
@@ -377,6 +410,8 @@ extension SplayTree {
             } else if value > n.value! {
                 node = n.right
                 if n.right != nil { nodeParent = n.right }
+            } else {
+                break
             }
         }
         
@@ -398,27 +433,31 @@ extension SplayTree {
     /*
      Returns the leftmost descendent. O(h) time.
      */
-    public func minimum() -> SplayTree {
+    public func minimum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.left {
             node = next
         }
         
-        SplayOperation.splay(node: node)
-
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
+        
         return node
     }
     
     /*
      Returns the rightmost descendent. O(h) time.
      */
-    public func maximum() -> SplayTree {
+    public func maximum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.right {
             node = next
         }
         
-        SplayOperation.splay(node: node)
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
         
         return node
     }
@@ -452,7 +491,7 @@ extension SplayTree {
     /*
      Finds the node whose value precedes our value in sorted order.
      */
-    public func predecessor() -> SplayTree<T>? {
+    public func predecessor() -> Node<T>? {
         if let left = left {
             return left.maximum()
         } else {
@@ -468,7 +507,7 @@ extension SplayTree {
     /*
      Finds the node whose value succeeds our value in sorted order.
      */
-    public func successor() -> SplayTree<T>? {
+    public func successor() -> Node<T>? {
         if let right = right {
             return right.minimum()
         } else {
@@ -483,7 +522,7 @@ extension SplayTree {
 }
 
 // MARK: - Traversal
-extension SplayTree {
+extension Node {
     
     public func traverseInOrder(process: (T) -> Void) {
         left?.traverseInOrder(process: process)
@@ -518,7 +557,7 @@ extension SplayTree {
 /*
  Is this binary tree a valid binary search tree?
  */
-extension SplayTree {
+extension Node {
     
     public func isBST(minValue: T, maxValue: T) -> Bool {
         if let value = value {
@@ -533,7 +572,7 @@ extension SplayTree {
 
 // MARK: - Debugging
 
-extension SplayTree: CustomStringConvertible {
+extension Node: CustomStringConvertible {
     public var description: String {
         var s = ""
         if let left = left {
@@ -549,7 +588,13 @@ extension SplayTree: CustomStringConvertible {
     }
 }
 
-extension SplayTree: CustomDebugStringConvertible {
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        return root?.description ?? "Empty tree"
+    }
+}
+
+extension Node: CustomDebugStringConvertible {
     public var debugDescription: String {
         var s = "value: \(value)"
         if let parent = parent, let v = parent.value {
@@ -568,3 +613,9 @@ extension SplayTree: CustomDebugStringConvertible {
         return map { $0 }
     }
 }
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        return root?.debugDescription ?? "Empty tree"
+    }
+}

From efa2f4856c6e80ccd36e8de11f3fb279974d9e3e Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:23:43 +0100
Subject: [PATCH 0843/1679] Tests for max, min, search, insert and remove

---
 Splay Tree/Tests/SplayTreeTests.swift | 52 ++++++++++++++++++++-------
 1 file changed, 40 insertions(+), 12 deletions(-)

diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 042344193..0209f8afe 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -2,30 +2,58 @@ import XCTest
 
 class SplayTreeTests: XCTestCase {
    
-    var tree: SplayTree<Int>!
     var tree1: SplayTree<Int>!
+    var tree2: SplayTree<Int>!
     
     override func setUp() {
         super.setUp()
-        tree = SplayTree<Int>(value: 1)
-        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
+        tree1 = SplayTree<Int>(value: 1)
+        
+        tree2 = SplayTree<Int>(value: 1)
+        tree2.insert(value: 10)
+        tree2.insert(value: 20)
+        tree2.insert(value: 3)
+        tree2.insert(value: 6)
+        tree2.insert(value: 100)
+        tree2.insert(value: 44)
     }
     
     func testInsertion() {
-        let tree1 = tree.insert(value: 10)
-        assert(tree1?.root?.value == 10)
+        tree1.insert(value: 10)
+        assert(tree1.value == 10)
         
-        let tree2 = tree1!.insert(value: 2)
-        assert(tree2?.root?.value == 2)
+        tree2.insert(value: 2)
+        assert(tree2.root?.value == 2)
     }
     
-    
     func testSearchNonExisting() {
-        print(tree1)
-        let tree2 = tree1.search(value: 5)
-        assert(tree2?.root?.value == 10)
-        
+        let t = tree2.search(value: 5)
+        assert(t?.value == 10)
+    }
+
+    func testSearchExisting() {
+        let t = tree2.search(value: 6)
+        assert(t?.value == 6)
+    }
+    
+    func testDeleteExistingOnlyLeftChild() {
+        tree2.remove(value: 3)
+        assert(tree2.value == 6)
+    }
+
+    func testDeleteExistingOnly2Children() {
+        tree2.remove(value: 6)
+        assert(tree2.value == 20)
     }
     
+    func testMinimum() {
+        let v = tree2.minimum()
+        assert(v?.value == 1)
+    }
+
+    func testMaximum() {
+        let v = tree2.maximum()
+        assert(v?.value == 100)
+    }
     
 }

From c27fdde75dc064f55ea7dfdcd5c7d0d4a44aaea6 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:24:22 +0100
Subject: [PATCH 0844/1679] Replacing SplayTree implementation inside
 Playground

---
 .../Sources/SplayTree.swift                   | 398 +++++++++++-------
 1 file changed, 255 insertions(+), 143 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index f0c45e831..f50af7349 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -28,7 +28,7 @@ public enum SplayOperation {
         - Parameters:
             - node      SplayTree node to move up to the root
      */
-    public static func splay<T: Comparable>(node: SplayTree<T>) {
+    public static func splay<T: Comparable>(node: Node<T>) {
         
         while (node.parent != nil) {
             operation(forNode: node).apply(onNode: node)
@@ -44,10 +44,10 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
         
-        if let parent = node.parent, let grandParent = parent.parent {
-            if (node.isLeftChild && grandParent.isRightChild) || (node.isRightChild && grandParent.isLeftChild) {
+        if let parent = node.parent, let _ = parent.parent {
+            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
                 return .zigZag
             }
             return .zigZig
@@ -62,7 +62,7 @@ public enum SplayOperation {
         - Parameters:
             - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+    public func apply<T: Comparable>(onNode node: Node<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,49 +84,66 @@ public enum SplayOperation {
         Performs a single rotation from a node to its parent
         re-arranging the children properly
      */
-    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+    public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
-        var grandchildToMode: SplayTree<T>?
+        var grandchildToMode: Node<T>?
+        
         if child.isLeftChild {
             
             grandchildToMode = child.right
-            child.right = parent
             parent.left = grandchildToMode
-            
+            grandchildToMode?.parent = parent
+
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.right = parent
+            parent.parent = child
+    
+
         } else {
             
             grandchildToMode = child.left
-            child.left = parent
             parent.right = grandchildToMode
+            grandchildToMode?.parent = parent
+
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.left = parent
+            parent.parent = child
+
         }
+        
 
-        let grandParent = parent.parent
-        parent.parent = child
-        child.parent = grandParent
     }
 }
 
-public class SplayTree<T: Comparable> {
+public class Node<T: Comparable> {
     
-    fileprivate(set) public var value: T
-    fileprivate(set) public var parent: SplayTree?
-    fileprivate(set) public var left: SplayTree?
-    fileprivate(set) public var right: SplayTree?
+    fileprivate(set) public var value: T?
+    fileprivate(set) public var parent: Node<T>?
+    fileprivate(set) public var left: Node<T>?
+    fileprivate(set) public var right: Node<T>?
     
-    public init(value: T) {
+    init(value: T) {
         self.value = value
     }
     
-    public convenience init(array: [T]) {
-        precondition(array.count > 0)
-        self.init(value: array.first!)
-        for v in array.dropFirst() {
-            insert(value: v)
-        }
-    }
-    
     public var isRoot: Bool {
         return parent == nil
     }
@@ -165,114 +182,186 @@ public class SplayTree<T: Comparable> {
     }
 }
 
+public class SplayTree<T: Comparable> {
+
+    internal var root: Node<T>?
+    
+    var value: T? {
+        return root?.value
+    }
+
+    //MARK: - Initializer
+    
+    public init(value: T) {
+        self.root = Node(value:value)
+    }
+    
+    public func insert(value: T) {
+        root = root?.insert(value: value)
+    }
+    
+    public func remove(value: T) {
+        root = root?.remove(value: value)
+    }
+
+    public func search(value: T) -> Node<T>? {
+        root = root?.search(value: value)
+        return root
+    }
+    
+    public func minimum() -> Node<T>? {
+        root = root?.minimum(splayed: true)
+        return root
+    }
+    
+    public func maximum() -> Node<T>? {
+        root = root?.maximum(splayed: true)
+        return root
+    }
+    
+}
+
 // MARK: - Adding items
 
-extension SplayTree {
+extension Node {
     
     /*
-     Inserts a new element into the tree. You should only insert elements
-     at the root, to make to sure this remains a valid binary tree!
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Inserts a new element into the node tree.
+     
+     - Parameters:
+            - value T value to be inserted. Will be splayed to the root position
+     
+     - Returns:
+            - Node inserted
      */
-    public func insert(value: T) {
-        if value < self.value {
-            if let left = left {
-                left.insert(value: value)
-            } else {
-                
-                left = SplayTree(value: value)
-                left?.parent = self
-                
+    public func insert(value: T) -> Node {
+        if let selfValue = self.value {
+            if value < selfValue {
                 if let left = left {
-                    SplayOperation.splay(node: left)
-                    self.parent = nil
-                    self.value = left.value
-                    self.left = left.left
-                    self.right = left.right
+                    return left.insert(value: value)
+                } else {
+                    
+                    left = Node(value: value)
+                    left?.parent = self
+                    
+                    if let left = left {
+                        SplayOperation.splay(node: left)
+                        return left
+                    }
                 }
-            }
-        } else {
-            
-            if let right = right {
-                right.insert(value: value)
             } else {
                 
-                right = SplayTree(value: value)
-                right?.parent = self
-                
                 if let right = right {
-                    SplayOperation.splay(node: right)
-                    self.parent = nil
-                    self.value = right.value
-                    self.left = right.left
-                    self.right = right.right
+                    return right.insert(value: value)
+                } else {
+                    
+                    right = Node(value: value)
+                    right?.parent = self
+                    
+                    if let right = right {
+                        SplayOperation.splay(node: right)
+                        return right
+                    }
                 }
             }
         }
+        return self
     }
 }
 
 // MARK: - Deleting items
 
-extension SplayTree {
+extension Node {
+    
     /*
-     Deletes a node from the tree.
-     Returns the node that has replaced this removed one (or nil if this was a
-     leaf node). That is primarily useful for when you delete the root node, in
-     which case the tree gets a new root.
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Deletes the given node from the nodes tree.
+     Return the new tree generated by the removal. 
+     The removed node (not necessarily the one containing the value), will be splayed to the root.
+     
+     - Parameters:
+            - value         To be removed
+     
+     - Returns:
+            - Node     Resulting from the deletion and the splaying of the removed node
+     
      */
-    @discardableResult public func remove() -> SplayTree? {
-        let replacement: SplayTree?
+    public func remove(value: T) -> Node<T>? {
+        let replacement: Node<T>?
         
-        if let left = left {
-            if let right = right {
-                replacement = removeNodeWithTwoChildren(left, right)
+        if let v = self.value, v == value {
+            
+            var parentToSplay: Node<T>?
+            if let left = left {
+                if let right = right {
+                    
+                    replacement = removeNodeWithTwoChildren(left, right)
+                    
+                    if let replacement = replacement,
+                        let replacementParent = replacement.parent,
+                        replacementParent.value != self.value {
+                        
+                        parentToSplay = replacement.parent
+                        
+                    } else {
+                        parentToSplay = self.parent
+                    }
+                    
+                } else {
+                    // This node only has a left child. The left child replaces the node.
+                    replacement = left
+                    parentToSplay = parent
+                }
+            } else if let right = right {
+                // This node only has a right child. The right child replaces the node.
+                replacement = right
+                parentToSplay = parent
             } else {
-                // This node only has a left child. The left child replaces the node.
-                replacement = left
+                // This node has no children. We just disconnect it from its parent.
+                replacement = nil
+                parentToSplay = parent
             }
-        } else if let right = right {
-            // This node only has a right child. The right child replaces the node.
-            replacement = right
-        } else {
-            // This node has no children. We just disconnect it from its parent.
-            replacement = nil
-        }
+            
+            reconnectParentTo(node: replacement)
+            
+            // performs the splay operation
+            if let parentToSplay = parentToSplay {
+                SplayOperation.splay(node: parentToSplay)
+            }
+            
+            // The current node is no longer part of the tree, so clean it up.
+            parent = nil
+            left = nil
+            right = nil
 
-        // Save the parent to splay before reconnecting
-        var parentToSplay: SplayTree?
-        if let replacement = replacement {
-            parentToSplay = replacement.parent
+            return parentToSplay
+            
+        } else if let v = self.value, value < v {
+            if left != nil {
+                return left!.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         } else {
-            parentToSplay = self.parent
-        }
-        
-        reconnectParentTo(node: replacement)
-        
-        // performs the splay operation
-        if let parentToSplay = parentToSplay {
-            SplayOperation.splay(node: parentToSplay)
+            if right != nil {
+                return right?.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         }
-        
-        // The current node is no longer part of the tree, so clean it up.
-        parent = nil
-        left = nil
-        right = nil
-        
-        return replacement
     }
     
-    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
         // This node has two children. It must be replaced by the smallest
         // child that is larger than this node's value, which is the leftmost
         // descendent of the right child.
         let successor = right.minimum()
         
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
-        
         // Connect our left child with the new node.
         successor.left = left
         left.parent = successor
@@ -291,7 +380,7 @@ extension SplayTree {
         return successor
     }
     
-    private func reconnectParentTo(node: SplayTree?) {
+    private func reconnectParentTo(node: Node?) {
         if let parent = parent {
             if isLeftChild {
                 parent.left = node
@@ -305,31 +394,33 @@ extension SplayTree {
 
 // MARK: - Searching
 
-extension SplayTree {
+extension Node {
     
     /*
      Finds the "highest" node with the specified value.
      Performance: runs in O(h) time, where h is the height of the tree.
      */
-    public func search(value: T) -> SplayTree? {
-        var node: SplayTree? = self
-        while case let n? = node {
-            if value < n.value {
+    public func search(value: T) -> Node<T>? {
+        var node: Node? = self
+        var nodeParent: Node? = self
+        while case let n? = node, n.value != nil {
+            if value < n.value! {
+                if n.left != nil { nodeParent = n.left }
                 node = n.left
-            } else if value > n.value {
+            } else if value > n.value! {
                 node = n.right
+                if n.right != nil { nodeParent = n.right }
             } else {
-                
-                if let node = node {
-                    SplayOperation.splay(node: node)
-                }
-                
-                return node
+                break
             }
         }
         
         if let node = node {
             SplayOperation.splay(node: node)
+            return node
+        } else if let nodeParent = nodeParent {
+            SplayOperation.splay(node: nodeParent)
+            return nodeParent
         }
         
         return nil
@@ -342,27 +433,31 @@ extension SplayTree {
     /*
      Returns the leftmost descendent. O(h) time.
      */
-    public func minimum() -> SplayTree {
+    public func minimum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.left {
             node = next
         }
         
-        SplayOperation.splay(node: node)
-
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
+        
         return node
     }
     
     /*
      Returns the rightmost descendent. O(h) time.
      */
-    public func maximum() -> SplayTree {
+    public func maximum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.right {
             node = next
         }
         
-        SplayOperation.splay(node: node)
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
         
         return node
     }
@@ -396,13 +491,13 @@ extension SplayTree {
     /*
      Finds the node whose value precedes our value in sorted order.
      */
-    public func predecessor() -> SplayTree<T>? {
+    public func predecessor() -> Node<T>? {
         if let left = left {
             return left.maximum()
         } else {
             var node = self
-            while case let parent? = node.parent {
-                if parent.value < value { return parent }
+            while case let parent? = node.parent, parent.value != nil, value != nil {
+                if parent.value! < value! { return parent }
                 node = parent
             }
             return nil
@@ -412,13 +507,13 @@ extension SplayTree {
     /*
      Finds the node whose value succeeds our value in sorted order.
      */
-    public func successor() -> SplayTree<T>? {
+    public func successor() -> Node<T>? {
         if let right = right {
             return right.minimum()
         } else {
             var node = self
-            while case let parent? = node.parent {
-                if parent.value > value { return parent }
+            while case let parent? = node.parent, parent.value != nil , value != nil {
+                if parent.value! > value! { return parent }
                 node = parent
             }
             return nil
@@ -427,16 +522,16 @@ extension SplayTree {
 }
 
 // MARK: - Traversal
-extension SplayTree {
+extension Node {
     
     public func traverseInOrder(process: (T) -> Void) {
         left?.traverseInOrder(process: process)
-        process(value)
+        process(value!)
         right?.traverseInOrder(process: process)
     }
     
     public func traversePreOrder(process: (T) -> Void) {
-        process(value)
+        process(value!)
         left?.traversePreOrder(process: process)
         right?.traversePreOrder(process: process)
     }
@@ -444,7 +539,7 @@ extension SplayTree {
     public func traversePostOrder(process: (T) -> Void) {
         left?.traversePostOrder(process: process)
         right?.traversePostOrder(process: process)
-        process(value)
+        process(value!)
     }
     
     /*
@@ -453,7 +548,7 @@ extension SplayTree {
     public func map(formula: (T) -> T) -> [T] {
         var a = [T]()
         if let left = left { a += left.map(formula: formula) }
-        a.append(formula(value))
+        a.append(formula(value!))
         if let right = right { a += right.map(formula: formula) }
         return a
     }
@@ -462,37 +557,48 @@ extension SplayTree {
 /*
  Is this binary tree a valid binary search tree?
  */
-extension SplayTree {
+extension Node {
     
     public func isBST(minValue: T, maxValue: T) -> Bool {
-        if value < minValue || value > maxValue { return false }
-        let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
-        let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
-        return leftBST && rightBST
+        if let value = value {
+            if value < minValue || value > maxValue { return false }
+            let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+            let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+            return leftBST && rightBST
+        }
+        return false
     }
 }
 
 // MARK: - Debugging
 
-extension SplayTree: CustomStringConvertible {
+extension Node: CustomStringConvertible {
     public var description: String {
         var s = ""
         if let left = left {
-            s += "(\(left.description)) <- "
+            s += "left: (\(left.description)) <- "
+        }
+        if let v = value {
+            s += "\(v)"
         }
-        s += "\(value)"
         if let right = right {
-            s += " -> (\(right.description))"
+            s += " -> (right: \(right.description))"
         }
         return s
     }
 }
 
-extension SplayTree: CustomDebugStringConvertible {
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        return root?.description ?? "Empty tree"
+    }
+}
+
+extension Node: CustomDebugStringConvertible {
     public var debugDescription: String {
         var s = "value: \(value)"
-        if let parent = parent {
-            s += ", parent: \(parent.value)"
+        if let parent = parent, let v = parent.value {
+            s += ", parent: \(v)"
         }
         if let left = left {
             s += ", left = [" + left.debugDescription + "]"
@@ -507,3 +613,9 @@ extension SplayTree: CustomDebugStringConvertible {
         return map { $0 }
     }
 }
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        return root?.debugDescription ?? "Empty tree"
+    }
+}

From 4aaec9d94b5b6a5c75b07c35fd0e4def6830ac44 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:38:15 +0100
Subject: [PATCH 0845/1679] Test for root removal and multiple operations
 executed

---
 Splay Tree/Tests/SplayTreeTests.swift | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 0209f8afe..01201a108 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -46,6 +46,11 @@ class SplayTreeTests: XCTestCase {
         assert(tree2.value == 20)
     }
     
+    func testDeleteRoot() {
+        tree2.remove(value: 44)
+        assert(tree2.value == 100)
+    }
+    
     func testMinimum() {
         let v = tree2.minimum()
         assert(v?.value == 1)
@@ -56,4 +61,16 @@ class SplayTreeTests: XCTestCase {
         assert(v?.value == 100)
     }
     
+    func testInsertionRemovals() {
+        let splayTree = SplayTree(value: 1)
+        splayTree.insert(value: 2)
+        splayTree.insert(value: 10)
+        splayTree.insert(value: 6)
+        
+        splayTree.remove(value: 10)
+        splayTree.remove(value: 6)
+        
+        assert(splayTree.value == 2)
+    }
+    
 }

From 9da711ddf62bdc9b77d73ad64da8285a94f2b4cc Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:38:47 +0100
Subject: [PATCH 0846/1679] Fixes for root removal & insertions with nil root

---
 .../Sources/SplayTree.swift                   | 106 ++++++++++--------
 Splay Tree/SplayTree.swift                    |  22 +++-
 2 files changed, 78 insertions(+), 50 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index f50af7349..a4feda7ef 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -1,5 +1,5 @@
 /*
- *  Splay Tree 
+ *  Splay Tree
  *
  * Based on Binary Search Tree Implementation written by Nicolas Ameghino and Matthijs Hollemans for Swift Algorithms Club
  * https://github.com/raywenderlich/swift-algorithm-club/blob/master/Binary%20Search%20Tree
@@ -8,12 +8,12 @@
  */
 
 /**
-    Represent the 3 possible operations (combinations of rotations) that
-    could be performed during the Splay phase in Splay Trees
+ Represent the 3 possible operations (combinations of rotations) that
+ could be performed during the Splay phase in Splay Trees
  
-    - zigZag       Left child of a right child OR right child of a left child
-    - zigZig       Left child of a left child OR right child of a right child
-    - zig          Only 1 parent and that parent is the root
+ - zigZag       Left child of a right child OR right child of a left child
+ - zigZig       Left child of a left child OR right child of a right child
+ - zig          Only 1 parent and that parent is the root
  
  */
 public enum SplayOperation {
@@ -23,10 +23,10 @@ public enum SplayOperation {
     
     
     /**
-        Splay the given node up to the root of the tree
+     Splay the given node up to the root of the tree
      
-        - Parameters:
-            - node      SplayTree node to move up to the root
+     - Parameters:
+     - node      SplayTree node to move up to the root
      */
     public static func splay<T: Comparable>(node: Node<T>) {
         
@@ -36,13 +36,13 @@ public enum SplayOperation {
     }
     
     /**
-        Compares the node and its parent and determine
-        if the rotations should be performed in a zigZag, zigZig or zig case.
+     Compares the node and its parent and determine
+     if the rotations should be performed in a zigZag, zigZig or zig case.
      
-        - Parmeters:
-            - forNode       SplayTree node to be checked
-        - Returns
-            - Operation     Case zigZag - zigZig - zig
+     - Parmeters:
+     - forNode       SplayTree node to be checked
+     - Returns
+     - Operation     Case zigZag - zigZig - zig
      */
     public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
         
@@ -56,11 +56,11 @@ public enum SplayOperation {
     }
     
     /**
-        Applies the rotation associated to the case 
-        Modifying the splay tree and briging the received node further to the top of the tree
+     Applies the rotation associated to the case
+     Modifying the splay tree and briging the received node further to the top of the tree
      
-        - Parameters:
-            - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
+     - Parameters:
+     - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
     public func apply<T: Comparable>(onNode node: Node<T>) {
         switch self {
@@ -68,12 +68,12 @@ public enum SplayOperation {
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
             rotate(child: node, parent: node.parent!)
             rotate(child: node, parent: node.parent!)
-
+            
         case .zigZig:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
             rotate(child: node.parent!, parent: node.parent!.parent!)
             rotate(child: node, parent: node.parent!)
-        
+            
         case .zig:
             assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
             rotate(child: node, parent: node.parent!)
@@ -81,8 +81,8 @@ public enum SplayOperation {
     }
     
     /**
-        Performs a single rotation from a node to its parent
-        re-arranging the children properly
+     Performs a single rotation from a node to its parent
+     re-arranging the children properly
      */
     public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
         
@@ -95,41 +95,41 @@ public enum SplayOperation {
             grandchildToMode = child.right
             parent.left = grandchildToMode
             grandchildToMode?.parent = parent
-
+            
             let grandParent = parent.parent
             child.parent = grandParent
-
+            
             if parent.isLeftChild {
                 grandParent?.left = child
             } else {
                 grandParent?.right = child
             }
-
+            
             child.right = parent
             parent.parent = child
-    
-
+            
+            
         } else {
             
             grandchildToMode = child.left
             parent.right = grandchildToMode
             grandchildToMode?.parent = parent
-
+            
             let grandParent = parent.parent
             child.parent = grandParent
-
+            
             if parent.isLeftChild {
                 grandParent?.left = child
             } else {
                 grandParent?.right = child
             }
-
+            
             child.left = parent
             parent.parent = child
-
+            
         }
         
-
+        
     }
 }
 
@@ -183,13 +183,13 @@ public class Node<T: Comparable> {
 }
 
 public class SplayTree<T: Comparable> {
-
+    
     internal var root: Node<T>?
     
     var value: T? {
         return root?.value
     }
-
+    
     //MARK: - Initializer
     
     public init(value: T) {
@@ -197,13 +197,17 @@ public class SplayTree<T: Comparable> {
     }
     
     public func insert(value: T) {
-        root = root?.insert(value: value)
+        if let root = root {
+            self.root = root.insert(value: value)
+        } else {
+            root = Node(value: value)
+        }
     }
     
     public func remove(value: T) {
         root = root?.remove(value: value)
     }
-
+    
     public func search(value: T) -> Node<T>? {
         root = root?.search(value: value)
         return root
@@ -229,10 +233,10 @@ extension Node {
      Inserts a new element into the node tree.
      
      - Parameters:
-            - value T value to be inserted. Will be splayed to the root position
+     - value T value to be inserted. Will be splayed to the root position
      
      - Returns:
-            - Node inserted
+     - Node inserted
      */
     public func insert(value: T) -> Node {
         if let selfValue = self.value {
@@ -275,14 +279,14 @@ extension Node {
     
     /*
      Deletes the given node from the nodes tree.
-     Return the new tree generated by the removal. 
+     Return the new tree generated by the removal.
      The removed node (not necessarily the one containing the value), will be splayed to the root.
      
      - Parameters:
-            - value         To be removed
+     - value         To be removed
      
      - Returns:
-            - Node     Resulting from the deletion and the splaying of the removed node
+     - Node     Resulting from the deletion and the splaying of the removed node
      
      */
     public func remove(value: T) -> Node<T>? {
@@ -302,19 +306,29 @@ extension Node {
                         
                         parentToSplay = replacement.parent
                         
-                    } else {
+                    } else if self.parent != nil {
                         parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
                     }
                     
                 } else {
                     // This node only has a left child. The left child replaces the node.
                     replacement = left
-                    parentToSplay = parent
+                    if self.parent != nil {
+                        parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
+                    }
                 }
             } else if let right = right {
                 // This node only has a right child. The right child replaces the node.
                 replacement = right
-                parentToSplay = parent
+                if self.parent != nil {
+                    parentToSplay = self.parent
+                } else {
+                    parentToSplay = replacement
+                }
             } else {
                 // This node has no children. We just disconnect it from its parent.
                 replacement = nil
@@ -332,7 +346,7 @@ extension Node {
             parent = nil
             left = nil
             right = nil
-
+            
             return parentToSplay
             
         } else if let v = self.value, value < v {
diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index f50af7349..a7b20743d 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -197,7 +197,11 @@ public class SplayTree<T: Comparable> {
     }
     
     public func insert(value: T) {
-        root = root?.insert(value: value)
+        if let root = root {
+            self.root = root.insert(value: value)
+        } else {
+            root = Node(value: value)
+        }
     }
     
     public func remove(value: T) {
@@ -302,19 +306,29 @@ extension Node {
                         
                         parentToSplay = replacement.parent
                         
-                    } else {
+                    } else if self.parent != nil {
                         parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
                     }
                     
                 } else {
                     // This node only has a left child. The left child replaces the node.
                     replacement = left
-                    parentToSplay = parent
+                    if self.parent != nil {
+                        parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
+                    }
                 }
             } else if let right = right {
                 // This node only has a right child. The right child replaces the node.
                 replacement = right
-                parentToSplay = parent
+                if self.parent != nil {
+                    parentToSplay = self.parent
+                } else {
+                    parentToSplay = replacement
+                }
             } else {
                 // This node has no children. We just disconnect it from its parent.
                 replacement = nil

From ecba738935641768526277d908153adc3f9d8ca6 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:38:55 +0100
Subject: [PATCH 0847/1679] Playground Splay Tree

---
 .../SplayTree.playground/Contents.swift       | 24 ++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
index 951ad4c5c..4406a759d 100644
--- a/Splay Tree/SplayTree.playground/Contents.swift	
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -1,7 +1,29 @@
 //: Playground - Splay Tree Implementation
 
 
-let splayTree = SplayTree(array: [1])
+let splayTree = SplayTree(value: 1)
 splayTree.insert(value: 2)
 splayTree.insert(value: 10)
 splayTree.insert(value: 6)
+
+splayTree.remove(value: 10)
+splayTree.remove(value: 6)
+
+splayTree.insert(value: 55)
+splayTree.insert(value: 559)
+splayTree.remove(value: 2)
+splayTree.remove(value: 1)
+splayTree.remove(value: 55)
+splayTree.remove(value: 559)
+
+splayTree.insert(value: 1843000)
+splayTree.insert(value: 1238)
+splayTree.insert(value: -1)
+splayTree.insert(value: 87)
+
+splayTree.minimum()
+splayTree.maximum()
+
+
+
+

From cae6d08a8c1ea02fdf37c6481e965b74457b0eaa Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Mon, 6 Mar 2017 15:15:06 -0500
Subject: [PATCH 0848/1679] Update link for radix sort

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index e2d99e2bc..dfe451478 100644
--- a/README.markdown
+++ b/README.markdown
@@ -80,7 +80,7 @@ Fast sorts:
 Special-purpose sorts:
 
 - [Counting Sort](Counting Sort/)
-- Radix Sort
+- [Radix Sort](Radix Sort/)
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):

From ce1ec8842561fb69c02f835278539f4bab287a8e Mon Sep 17 00:00:00 2001
From: "JUNYEONG.YOO" <woody.chiz@gmail.com>
Date: Tue, 7 Mar 2017 19:31:50 +0900
Subject: [PATCH 0849/1679] Modified typo in README.md of QuickSort

---
 Quicksort/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index e3d284333..d359ecb5c 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -30,7 +30,7 @@ Here's how it works. When given an array, `quicksort()` splits it up into three
 
 All the elements less than the pivot go into a new array called `less`. All the elements equal to the pivot go into the `equal` array. And you guessed it, all elements greater than the pivot go into the third array, `greater`. This is why the generic type `T` must be `Comparable`, so we can compare the elements with `<`, `==`, and `>`.
 
-Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `right` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
+Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `greater` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
 
 ## An example
 
@@ -44,7 +44,7 @@ First, we pick the pivot element. That is `8` because it's in the middle of the
 	equal:   [ 8, 8 ]
 	greater: [ 10, 9, 14, 27, 26 ]
 
-This is a good split because `less` and `equal` roughly contain the same number of elements. So we've picked a good pivot that chopped the array right down the middle.
+This is a good split because `less` and `greater` roughly contain the same number of elements. So we've picked a good pivot that chopped the array right down the middle.
 
 Note that the `less` and `greater` arrays aren't sorted yet, so we call `quicksort()` again to sort those two subarrays. That does the exact same thing: pick a pivot and split the subarray into three even smaller parts.
 

From 7a5700dbae300b075195842482cb74981ae5fc9e Mon Sep 17 00:00:00 2001
From: Daniel Santos <dsantosp12@gmail.com>
Date: Wed, 8 Mar 2017 19:44:06 -0500
Subject: [PATCH 0850/1679] added ExpressibleByArrayLiteral to the Linked List
 and wrote test for the new initializer.

---
 .../LinkedList.playground/Contents.swift      | 22 +++++++++++++++++--
 Linked List/LinkedList.swift                  | 10 ++++++++-
 Linked List/Tests/LinkedListTests.swift       | 22 +++++++++++++++++++
 3 files changed, 51 insertions(+), 3 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index a90b7180c..1f7aa7dae 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -10,7 +10,7 @@ public class LinkedListNode<T> {
   }
 }
 
-public class LinkedList<T> {
+public final class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
   fileprivate var head: Node?
@@ -187,7 +187,7 @@ extension LinkedList {
   }
 }
 
-extension LinkedList {
+extension LinkedList: ExpressibleByArrayLiteral {
   convenience init(array: Array<T>) {
     self.init()
         
@@ -195,6 +195,14 @@ extension LinkedList {
       self.append(element)
     }
   }
+    
+  public convenience init(arrayLiteral elements: T...) {
+      self.init()
+    
+      for element in elements {
+          self.append(element)
+      }
+  }
 }
 
 let list = LinkedList<String>()
@@ -255,3 +263,13 @@ list[0]                        // "Swift"
 
 list.remove(atIndex: 0)        // "Swift"
 list.count                     // 0
+
+let linkedList: LinkedList<Int> = [1, 2, 3, 4] // [1, 2, 3, 4]
+linkedList.count               // 4
+linkedList[0]                  // 1
+
+// Infer the type from the array
+let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
+listArrayLiteral2.count        // 3
+listArrayLiteral2[0]           // "Swift"
+listArrayLiteral2.removeLast() // "Club"
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 83f898f6c..792215a72 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -8,7 +8,7 @@ public class LinkedListNode<T> {
     }
 }
 
-public class LinkedList<T> {
+public final class LinkedList<T>: ExpressibleByArrayLiteral {
     public typealias Node = LinkedListNode<T>
     
     fileprivate var head: Node?
@@ -203,4 +203,12 @@ extension LinkedList {
             self.append(element)
         }
     }
+  
+    public convenience init(arrayLiteral elements: T...) {
+      self.init()
+    
+      for element in elements {
+        self.append(element)
+      }
+    }
 }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 367ec8c6b..6f58d9775 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -248,4 +248,26 @@ class LinkedListTest: XCTestCase {
     XCTAssertTrue(last === list.first)
     XCTAssertEqual(nodeCount, list.count)
   }
+  
+  func testArrayLiteralInitTypeInfer() {
+    let arrayLiteralInitInfer: LinkedList = [1.0, 2.0, 3.0]
+    
+    XCTAssertEqual(arrayLiteralInitInfer.count, 3)
+    XCTAssertEqual(arrayLiteralInitInfer.first?.value, 1.0)
+    XCTAssertEqual(arrayLiteralInitInfer.last?.value, 3.0)
+    XCTAssertEqual(arrayLiteralInitInfer[1], 2.0)
+    XCTAssertEqual(arrayLiteralInitInfer.removeLast(), 3.0)
+    XCTAssertEqual(arrayLiteralInitInfer.count, 2)
+  }
+  
+  func testArrayLiteralInitExplicit() {
+    let arrayLiteralInitExplicit: LinkedList<Int> = [1, 2, 3]
+    
+    XCTAssertEqual(arrayLiteralInitExplicit.count, 3)
+    XCTAssertEqual(arrayLiteralInitExplicit.first?.value, 1)
+    XCTAssertEqual(arrayLiteralInitExplicit.last?.value, 3)
+    XCTAssertEqual(arrayLiteralInitExplicit[1], 2)
+    XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
+    XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
+  }
 }

From 6863590f96aa24a004af813f6c82272267c5b742 Mon Sep 17 00:00:00 2001
From: Daniel Santos <dsantosp12@gmail.com>
Date: Wed, 8 Mar 2017 19:53:20 -0500
Subject: [PATCH 0851/1679] implemented the ExpressibleByArrayLiteral for the
 Linked List in a new extension instead of the class declaration for
 readability

---
 .../LinkedList.playground/Contents.swift      | 80 +++++++++++--------
 Linked List/LinkedList.swift                  | 16 ++--
 2 files changed, 55 insertions(+), 41 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 1f7aa7dae..ed46331d8 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -4,7 +4,7 @@ public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
   weak var previous: LinkedListNode?
-
+  
   public init(value: T) {
     self.value = value
   }
@@ -12,17 +12,19 @@ public class LinkedListNode<T> {
 
 public final class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
-
+  
   fileprivate var head: Node?
-
+  
+  public init() {}
+  
   public var isEmpty: Bool {
     return head == nil
   }
-
+  
   public var first: Node? {
     return head
   }
-
+  
   public var last: Node? {
     if var node = head {
       while case let next? = node.next {
@@ -33,7 +35,7 @@ public final class LinkedList<T> {
       return nil
     }
   }
-
+  
   public var count: Int {
     if var node = head {
       var c = 1
@@ -46,7 +48,7 @@ public final class LinkedList<T> {
       return 0
     }
   }
-
+  
   public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -59,15 +61,19 @@ public final class LinkedList<T> {
     }
     return nil
   }
-
+  
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
-
+  
   public func append(_ value: T) {
     let newNode = Node(value: value)
+    self.append(newNode)
+  }
+  
+  public func append(_ newNode: Node) {
     if let lastNode = last {
       newNode.previous = lastNode
       lastNode.next = newNode
@@ -75,64 +81,68 @@ public final class LinkedList<T> {
       head = newNode
     }
   }
-
+  
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-
+    
     var i = index
     var next = head
     var prev: Node?
-
+    
     while next != nil && i > 0 {
       i -= 1
       prev = next
       next = next!.next
     }
     assert(i == 0)  // if > 0, then specified index was too large
-
+    
     return (prev, next)
   }
-
+  
   public func insert(_ value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index: index)
-
     let newNode = Node(value: value)
+    self.insert(newNode, atIndex: index)
+  }
+  
+  public func insert(_ newNode: Node, atIndex index: Int) {
+    let (prev, next) = nodesBeforeAndAfter(index: index)
+    
     newNode.previous = prev
     newNode.next = next
     prev?.next = newNode
     next?.previous = newNode
-
+    
     if prev == nil {
       head = newNode
     }
   }
-
+  
   public func removeAll() {
     head = nil
   }
-
-  public func remove(node: Node) -> T {
+  
+  @discardableResult public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
-
+    
     if let prev = prev {
       prev.next = next
     } else {
       head = next
     }
     next?.previous = prev
-
+    
     node.previous = nil
     node.next = nil
     return node.value
   }
-
-  public func removeLast() -> T {
+  
+  @discardableResult public func removeLast() -> T {
     assert(!isEmpty)
     return remove(node: last!)
   }
-
-  public func remove(atIndex index: Int) -> T {
+  
+  @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return remove(node: node!)
@@ -173,7 +183,7 @@ extension LinkedList {
     }
     return result
   }
-
+  
   public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
@@ -187,21 +197,23 @@ extension LinkedList {
   }
 }
 
-extension LinkedList: ExpressibleByArrayLiteral {
+extension LinkedList {
   convenience init(array: Array<T>) {
     self.init()
-        
+    
     for element in array {
       self.append(element)
     }
   }
-    
+}
+
+extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
-      self.init()
+    self.init()
     
-      for element in elements {
-          self.append(element)
-      }
+    for element in elements {
+      self.append(element)
+    }
   }
 }
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 792215a72..53dc77a06 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -8,7 +8,7 @@ public class LinkedListNode<T> {
     }
 }
 
-public final class LinkedList<T>: ExpressibleByArrayLiteral {
+public final class LinkedList<T> {
     public typealias Node = LinkedListNode<T>
     
     fileprivate var head: Node?
@@ -203,12 +203,14 @@ extension LinkedList {
             self.append(element)
         }
     }
-  
-    public convenience init(arrayLiteral elements: T...) {
-      self.init()
+}
+
+extension LinkedList: ExpressibleByArrayLiteral {
+  public convenience init(arrayLiteral elements: T...) {
+    self.init()
     
-      for element in elements {
-        self.append(element)
-      }
+    for element in elements {
+      self.append(element)
     }
+  }
 }

From 345f8441b64003258779cd3fed692c5549a4cbd3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Thu, 9 Mar 2017 18:35:26 +0800
Subject: [PATCH 0852/1679] add SelectionSamplingExample.swift

---
 .../SelectionSamplingExample.swift            | 32 +++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 Selection Sampling/SelectionSamplingExample.swift

diff --git a/Selection Sampling/SelectionSamplingExample.swift b/Selection Sampling/SelectionSamplingExample.swift
new file mode 100644
index 000000000..66648a934
--- /dev/null
+++ b/Selection Sampling/SelectionSamplingExample.swift	
@@ -0,0 +1,32 @@
+//
+//  Select.swift
+//  
+//
+//  Created by Cheer on 2017/3/9.
+//
+//
+
+import Foundation
+
+func select<T>(from a: [T], count requested: Int) -> [T] {
+    
+    // if requested > a.count, will throw ==> fatal error: Index out of range
+    
+    if requested < a.count {
+        var arr = a
+        for i in 0..<requested {
+            
+            //arc4random_uniform(n) ==> the range is [0...n-1]
+            //So: arc4random_uniform(UInt32(arr.count - i - 2)) + (i + 1) ==> [0...arr.count - (i + 1) - 1] + (i + 1) ==> the range is [(i + 1)...arr.count - 1]
+            //Why start index is "(i + 1)"?  Because in "swap(&A,&B)", if A's index == B's index, will throw a error: "swapping a location with itself is not supported"
+            
+            let nextIndex = Int(arc4random_uniform(UInt32(arr.count - i - 2))) + (i + 1)
+            swap(&arr[nextIndex], &arr[i])
+        }
+        return Array(arr[0..<requested])
+    }
+    
+    if requested == a.count { return a }
+    
+    return [T]()
+}

From 1c43c804633f9fd36e67f9988d17e8402ac258d8 Mon Sep 17 00:00:00 2001
From: Arkalyk Akash <arkalyk@arkalyks-macbook-pro.local>
Date: Mon, 13 Mar 2017 17:00:42 +0600
Subject: [PATCH 0853/1679] Egg Drop Dynamic Problem Added

---
 Egg Drop Problem/EggDrop.swift                | 31 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  7 +++++
 2 files changed, 38 insertions(+)
 create mode 100644 Egg Drop Problem/EggDrop.swift

diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
new file mode 100644
index 000000000..6d0aab2a1
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -0,0 +1,31 @@
+func eggDrop(_ numberOfEggs: Int, numberOfFloors: Int) -> Int {
+    var eggFloor: [[Int]] = [] //egg(rows) floor(cols) array to store the solutions
+    var attempts: Int = 0
+    
+    for var i in (0..<numberOfFloors){
+        eggFloor[1][i] = i
+    }
+    eggFloor[2][1] = 1
+    
+    for var i in (2..<=numberOfEggs){
+        for var j in (2..numberOfFloors){
+            eggFloor[i][j] = 1000000
+            for var k in (1..<=j){
+                //there are two cases
+                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> k-1
+                //case 2: egg doesn't break. meaning we'll still have 'i' number of eggs, and we'll go upstairs -> j-k
+                attempts = 1 + max(eggFloor[i-1][k-1], eggFloor[i][j-k])//we add one taking into account the attempt we're taking at the moment
+                
+                if attempts < eggFloor[i][j]{ //finding the min
+                    eggFloor[i][j] = attempts;
+                }
+            }
+        }
+    }
+    
+    return eggFloor[numberOfEggs][numberOfFloors]
+}
+
+func max(_ x1: Int, _ x2: Int){
+    return x1 > x2 ? x1 : x2
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index b2ffce836..5ac8577f5 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1,6 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Workspace
    version = "1.0">
+   <Group
+      location = "group:Egg Drop Problem"
+      name = "Egg Drop Problem">
+      <FileRef
+         location = "group:/Users/arkalyk/Desktop/SwiftAlgorithmClub/swift-algorithm-club/Egg Drop Problem/EggDrop.swift">
+      </FileRef>
+   </Group>
    <FileRef
       location = "group:README.markdown">
    </FileRef>

From 5205fc8cf7ac1091448aecd9e7680b25779c9a88 Mon Sep 17 00:00:00 2001
From: Deep Parekh <dparekh@tripadvisor.com>
Date: Thu, 23 Feb 2017 00:08:21 -0500
Subject: [PATCH 0854/1679] Added checks for subscript and fixed initializer
 compile error

---
 Array2D/Array2D.playground/Contents.swift | 69 +++++++++++++----------
 1 file changed, 40 insertions(+), 29 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 7064de59c..38d4eff23 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,31 +1,42 @@
 /*
-  Two-dimensional array with a fixed number of rows and columns.
-  This is mostly handy for games that are played on a grid, such as chess.
-  Performance is always O(1).
-*/
+ Two-dimensional array with a fixed number of rows and columns.
+ This is mostly handy for games that are played on a grid, such as chess.
+ Performance is always O(1).
+ */
 public struct Array2D<T> {
-  public let columns: Int
-  public let rows: Int
-  fileprivate var array: [T]
-
-  public init(columns: Int, rows: Int, initialValue: T) {
-    self.columns = columns
-    self.rows = rows
-    array = .init(repeatElement(initialValue, count: rows*columns))
-  }
-
-  public subscript(column: Int, row: Int) -> T {
-    get {
-      return array[row*columns + column]
+    public let columns: Int
+    public let rows: Int
+    public var array: [T]
+    
+    public init(columns: Int, rows: Int, initialValue: T) {
+        self.columns = columns
+        self.rows = rows
+        array = [T](repeating: initialValue, count: rows*columns)
     }
-    set {
-      array[row*columns + column] = newValue
+    
+    public subscript(column: Int, row: Int) -> T {
+        get {
+            if isValidSubscript(column: column, row: row) {
+                return array[row*columns + column]
+            } else {
+                fatalError("Not a valid subscript")
+            }
+        }
+        set {
+            if isValidSubscript(column: column, row: row) {
+                array[row*columns + column] = newValue
+            } else {
+                fatalError("Not a valid subscript")
+            }
+        }
+    }
+    
+    private func isValidSubscript(column: Int, row: Int) -> Bool {
+        return column < columns && row < rows
     }
-  }
 }
 
 
-
 // initialization
 var matrix = Array2D(columns: 3, rows: 5, initialValue: 0)
 
@@ -51,13 +62,13 @@ print(matrix.array)
 
 // print out the 2D array with a reference around the grid
 for i in 0..<matrix.rows {
-  print("[", terminator: "")
-  for j in 0..<matrix.columns {
-    if j == matrix.columns - 1 {
-      print("\(matrix[j, i])", terminator: "")
-    } else {
-      print("\(matrix[j, i]) ", terminator: "")
+    print("[", terminator: "")
+    for j in 0..<matrix.columns {
+        if j == matrix.columns - 1 {
+            print("\(matrix[j, i])", terminator: "")
+        } else {
+            print("\(matrix[j, i]) ", terminator: "")
+        }
     }
-  }
-  print("]")
+    print("]")
 }

From 40be0d2bbb539fa6d89c2149198a5faa92d66d32 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Wed, 15 Mar 2017 19:48:51 -0700
Subject: [PATCH 0855/1679] availability check, native array loop for signal

---
 DiningPhilosophers/Sources/main.swift | 46 +++++++++++++--------------
 1 file changed, 22 insertions(+), 24 deletions(-)

diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index deff344b9..285402d53 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -7,17 +7,16 @@
 //
 
 
-import Foundation
 import Dispatch
 
 let numberOfPhilosophers = 4
 
 struct ForkPair {
-    static let forksSemaphore:[DispatchSemaphore] = Array(repeating: DispatchSemaphore(value: 1), count: numberOfPhilosophers)
-    
+    static let forksSemaphore: [DispatchSemaphore] = Array(repeating: DispatchSemaphore(value: 1), count: numberOfPhilosophers)
+
     let leftFork: DispatchSemaphore
     let rightFork: DispatchSemaphore
-    
+
     init(leftIndex: Int, rightIndex: Int) {
         //Order forks by index to prevent deadlock
         if leftIndex > rightIndex {
@@ -35,7 +34,7 @@ struct ForkPair {
         leftFork.wait()
         rightFork.wait()
     }
-    
+
     func putDown() {
         //The order does not matter here
         leftFork.signal()
@@ -47,61 +46,60 @@ struct ForkPair {
 struct Philosophers {
     let forkPair: ForkPair
     let philosopherIndex: Int
-    
+
     var leftIndex = -1
     var rightIndex = -1
-    
+
     init(philosopherIndex: Int) {
         leftIndex = philosopherIndex
         rightIndex = philosopherIndex - 1
-        
+
         if rightIndex < 0 {
             rightIndex += numberOfPhilosophers
         }
 
         self.forkPair = ForkPair(leftIndex: leftIndex, rightIndex: rightIndex)
         self.philosopherIndex = philosopherIndex
-        
+
         print("Philosopher: \(philosopherIndex)  left: \(leftIndex)  right: \(rightIndex)")
     }
-    
+
     func run() {
         while true {
-            print("Acquiring lock for Philosofer: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
+            print("Acquiring lock for Philosopher: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
             forkPair.pickUp()
             print("Start Eating Philosopher: \(philosopherIndex)")
             //sleep(1000)
-            print("Releasing lock for Philosofer: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
+            print("Releasing lock for Philosopher: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
             forkPair.putDown()
         }
     }
 }
 
 
-// Layout of the table (P = philosopher, f = fork) for 4 Philosopher
+// Layout of the table (P = philosopher, f = fork) for 4 Philosophers
 //          P0
 //       f3    f0
 //     P3        P1
 //       f2    f1
 //          P2
-
 let globalSem = DispatchSemaphore(value: 0)
 
 for i in 0..<numberOfPhilosophers {
-    DispatchQueue.global(qos: .background).async {
-        let p = Philosophers(philosopherIndex: i)
-        
-        p.run()
+    if #available(macOS 10.10, *) {
+        DispatchQueue.global(qos: .background).async {
+            let p = Philosophers(philosopherIndex: i)
+
+            p.run()
+        }
     }
 }
 
-//start the thread signaling the semaphore
-for i in 0..<numberOfPhilosophers {
-    ForkPair.forksSemaphore[i].signal()
+//Start the thread signaling the semaphore
+for semaphore in ForkPair.forksSemaphore {
+    semaphore.signal()
 }
 
 
-//wait forever
+//Wait forever
 globalSem.wait()
-
-

From 8d30d35c4aaaac8ee852437a296859b84eeb2912 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Wed, 15 Mar 2017 19:53:29 -0700
Subject: [PATCH 0856/1679] links

---
 DiningPhilosophers/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 29b5916e9..ec1611c65 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -1,5 +1,5 @@
 # Dining Philosophers
-Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using GCD and Semaphore in Swift)
+Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using [GCD](https://apple.github.io/swift-corelibs-libdispatch/) and [Semaphore](https://developer.apple.com/reference/dispatch/dispatchsemaphore) in Swift)
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi
 

From a9655534e55620364e975cabb78242dca9db0c11 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Fri, 17 Mar 2017 11:06:13 +0800
Subject: [PATCH 0857/1679] Update ShellSortExample.swift

Fix bug. Origin code probally get wrong answer.My fault.
---
 Shell Sort/ShellSortExample.swift | 27 ++++++++++++++-------------
 1 file changed, 14 insertions(+), 13 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index efa035da3..c41eb8889 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -8,24 +8,25 @@
 
 import Foundation
 
-public func shellSort(_ list: inout [Int]) {
-    
+public func shellSort(_ list : inout [Int])
+{
     var sublistCount = list.count / 2
-   
-    while sublistCount > 0 {
-        
-        for index in 0..<list.count {
-           
-            guard index + sublistCount < list.count else { break }
+    
+    while sublistCount > 0
+    {
+        for var index in 0..<arr.count{
+            
+            guard index + sublistCount < arr.count else { break }
             
-            if list[index] > list[index + sublistCount] {
-                swap(&list[index], &list[index + sublistCount])
+            if arr[index] > arr[index + sublistCount]{
+                swap(&arr[index], &arr[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
-            
-            if list[index - 1] > list[index] {
-                swap(&list[index - 1], &list[index])
+
+            while arr[index - 1] > arr[index] && index - 1 > 0  {
+                swap(&arr[index - 1], &arr[index])
+                index -= 1
             }
         }
         sublistCount = sublistCount / 2

From beddc9a7f4dd96b9122e849ace3c7dba57caaea7 Mon Sep 17 00:00:00 2001
From: Brandon05 <brandonsanchez05@gmail.com>
Date: Fri, 17 Mar 2017 13:41:49 -0400
Subject: [PATCH 0858/1679] Updated syntax for Swift 3

Hello, I was recreating this file in playground and I noticed you still had the explicit @noescape . Thought I can lend a hand by removing it. Thanks for this awesome repository!
---
 Binary Tree/BinaryTree.swift | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index 61ae696c7..102f23e06 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -29,26 +29,26 @@ extension BinaryTree: CustomStringConvertible {
 }
 
 extension BinaryTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
+  public func traverseInOrder(process: T -> Void) {
     if case let .node(left, value, right) = self {
-      left.traverseInOrder(process)
+      left.traverseInOrder(process: process)
       process(value)
-      right.traverseInOrder(process)
+      right.traverseInOrder(process: process)
     }
   }
 
-  public func traversePreOrder(@noescape process: T -> Void) {
+  public func traversePreOrder(process: T -> Void) {
     if case let .node(left, value, right) = self {
       process(value)
-      left.traversePreOrder(process)
-      right.traversePreOrder(process)
+      left.traversePreOrder(process: process)
+      right.traversePreOrder(process: process)
     }
   }
 
-  public func traversePostOrder(@noescape process: T -> Void) {
+  public func traversePostOrder(process: T -> Void) {
     if case let .node(left, value, right) = self {
-      left.traversePostOrder(process)
-      right.traversePostOrder(process)
+      left.traversePostOrder(process: process)
+      right.traversePostOrder(process: process)
       process(value)
     }
   }

From 9677b8c0e6bbd32831b6eca6c69c6f09d64f9f37 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Fri, 17 Mar 2017 20:10:53 -0700
Subject: [PATCH 0859/1679] Fixed indenting, and changed a scope modifier on
 the array property from public to fileprivate.

---
 Array2D/Array2D.playground/Contents.swift | 72 +++++++++++------------
 Array2D/README.markdown                   | 24 ++++++--
 2 files changed, 54 insertions(+), 42 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 38d4eff23..8b18a333f 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -4,36 +4,36 @@
  Performance is always O(1).
  */
 public struct Array2D<T> {
-    public let columns: Int
-    public let rows: Int
-    public var array: [T]
-    
-    public init(columns: Int, rows: Int, initialValue: T) {
-        self.columns = columns
-        self.rows = rows
-        array = [T](repeating: initialValue, count: rows*columns)
+  public let columns: Int
+  public let rows: Int
+  fileprivate var array: [T]
+  
+  public init(columns: Int, rows: Int, initialValue: T) {
+    self.columns = columns
+    self.rows = rows
+    array = [T](repeating: initialValue, count: rows*columns)
+  }
+  
+  public subscript(column: Int, row: Int) -> T {
+    get {
+      if isValidSubscript(column: column, row: row) {
+        return array[row*columns + column]
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
-    
-    public subscript(column: Int, row: Int) -> T {
-        get {
-            if isValidSubscript(column: column, row: row) {
-                return array[row*columns + column]
-            } else {
-                fatalError("Not a valid subscript")
-            }
-        }
-        set {
-            if isValidSubscript(column: column, row: row) {
-                array[row*columns + column] = newValue
-            } else {
-                fatalError("Not a valid subscript")
-            }
-        }
-    }
-    
-    private func isValidSubscript(column: Int, row: Int) -> Bool {
-        return column < columns && row < rows
+    set {
+      if isValidSubscript(column: column, row: row) {
+        array[row*columns + column] = newValue
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
+  }
+  
+  private func isValidSubscript(column: Int, row: Int) -> Bool {
+    return column < columns && row < rows
+  }
 }
 
 
@@ -62,13 +62,13 @@ print(matrix.array)
 
 // print out the 2D array with a reference around the grid
 for i in 0..<matrix.rows {
-    print("[", terminator: "")
-    for j in 0..<matrix.columns {
-        if j == matrix.columns - 1 {
-            print("\(matrix[j, i])", terminator: "")
-        } else {
-            print("\(matrix[j, i]) ", terminator: "")
-        }
+  print("[", terminator: "")
+  for j in 0..<matrix.columns {
+    if j == matrix.columns - 1 {
+      print("\(matrix[j, i])", terminator: "")
+    } else {
+      print("\(matrix[j, i]) ", terminator: "")
     }
-    print("]")
+  }
+  print("]")
 }
diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 51e77435e..6550dc943 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -67,22 +67,34 @@ So instead let's create our own type that acts like a 2-D array and that is more
 public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
-  private var array: [T]
-
+  fileprivate var array: [T]
+  
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = .init(repeating: initialValue, count: rows*columns)
+    array = [T](repeating: initialValue, count: rows*columns)
   }
-
+  
   public subscript(column: Int, row: Int) -> T {
     get {
-      return array[row*columns + column]
+      if isValidSubscript(column: column, row: row) {
+        return array[row*columns + column]
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
     set {
-      array[row*columns + column] = newValue
+      if isValidSubscript(column: column, row: row) {
+        array[row*columns + column] = newValue
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
   }
+  
+  private func isValidSubscript(column: Int, row: Int) -> Bool {
+    return column < columns && row < rows
+  }
 }
 ```
 

From c4d39ec0dc41060f2ff5b5532e9fa69489c9bbef Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Fri, 17 Mar 2017 20:16:01 -0700
Subject: [PATCH 0860/1679] Updated the subscript check to use preconditions
 instead of a custom function.

---
 Array2D/Array2D.playground/Contents.swift | 22 +++++++---------------
 Array2D/Array2D.swift                     |  9 +++++----
 Array2D/README.markdown                   | 22 +++++++---------------
 3 files changed, 19 insertions(+), 34 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 8b18a333f..d088c99af 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -11,29 +11,21 @@ public struct Array2D<T> {
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = [T](repeating: initialValue, count: rows*columns)
+    array = .init(repeating: initialValue, count: rows*columns)
   }
   
   public subscript(column: Int, row: Int) -> T {
     get {
-      if isValidSubscript(column: column, row: row) {
-        return array[row*columns + column]
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      return array[row*columns + column]
     }
     set {
-      if isValidSubscript(column: column, row: row) {
-        array[row*columns + column] = newValue
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      array[row*columns + column] = newValue
     }
   }
-  
-  private func isValidSubscript(column: Int, row: Int) -> Bool {
-    return column < columns && row < rows
-  }
 }
 
 
diff --git a/Array2D/Array2D.swift b/Array2D/Array2D.swift
index 6d6c01902..df4822916 100644
--- a/Array2D/Array2D.swift
+++ b/Array2D/Array2D.swift
@@ -7,21 +7,22 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   fileprivate var array: [T]
-
+  
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(repeating: initialValue, count: rows*columns)
   }
-
+  
   public subscript(column: Int, row: Int) -> T {
     get {
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
       return array[row*columns + column]
     }
     set {
-      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
       precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
-        
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
       array[row*columns + column] = newValue
     }
   }
diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 6550dc943..04afb9510 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -72,29 +72,21 @@ public struct Array2D<T> {
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = [T](repeating: initialValue, count: rows*columns)
+    array = .init(repeating: initialValue, count: rows*columns)
   }
   
   public subscript(column: Int, row: Int) -> T {
     get {
-      if isValidSubscript(column: column, row: row) {
-        return array[row*columns + column]
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      return array[row*columns + column]
     }
     set {
-      if isValidSubscript(column: column, row: row) {
-        array[row*columns + column] = newValue
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      array[row*columns + column] = newValue
     }
   }
-  
-  private func isValidSubscript(column: Int, row: Int) -> Bool {
-    return column < columns && row < rows
-  }
 }
 ```
 

From 162c3453bab7fa216cd3f11a9a45488ce9515c5c Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:21:59 +0100
Subject: [PATCH 0861/1679] Exchanged old red-black tree implementation with
 new one, also updated redmea

---
 Red-Black Tree/README.markdown                | 259 +++---
 .../RedBlackTree.playground/Contents.swift    |  22 +
 .../Sources/RedBlackTree.swift                | 740 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 4 files changed, 930 insertions(+), 95 deletions(-)
 create mode 100644 Red-Black Tree/RedBlackTree.playground/Contents.swift
 create mode 100644 Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
 create mode 100644 Red-Black Tree/RedBlackTree.playground/contents.xcplayground

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 05993f016..74fffa415 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -1,120 +1,189 @@
 # Red-Black Tree
 
-A Red-Black tree is a special version of a [Binary Search  Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Search%20Tree). Binary search trees(BSTs) can become unbalanced after a lot of insertions/deletions. The only difference between a node from a BST and a Red-Black Tree(RBT) is that RBT nodes have a color property added to them which can either be red or black. A RBT rebalances itself by making sure the following properties hold:
+A red-black tree (RBT) is a balanced version of a [Binary Search Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Search%20Tree) guaranteeing that the basic operations (search, predecessor, successor, minimum, maximum, insert and delete) have a logarithmic worst case performance.
 
-## Properties
-1. A node is either red or black
-2. The root is always black
-3. All leaves are black
-4. If a node is red, both of its children are black
-5. Every path to a leaf contains the same number of black nodes (The amount of black nodes met when going down a RBT is called the black-depth of the tree.)
-
-## Methods
-* `insert(_ value: T)` inserts the value into the tree
-* `insert(_ values: [T])` inserts an array of values into the tree
-* `delete(_ value: T)` deletes the value from the tree
-* `find(_ value: T) -> RBTNode<T>` looks for a node in the tree with given value and returns it
-* `minimum(n: RBTNode<T>) -> RBTNode<T>` looks for the maximum value of a subtree starting at the given node
-* `maximum(n: RBTNode<T>) -> RBTNode<T>` looks for the minimum value of a subtree starting at the given node
-* `func verify()` verifies if the tree is still valid. Prints warning messages if this is not the case
-
-## Rotation
+Binary search trees (BSTs) have the disadvantage that they can become unbalanced after some insert or delete operations. In the worst case, this could lead to a tree where the nodes build a linked list as shown in the following example:
 
-In order to rebalance their nodes RBTs use an operation known as rotation. You can either left or right rotate a node and its child. Rotating a node and its child swaps the nodes and interchanges their subtrees. Left rotation swaps the parent node with its right child. while right rotation swaps the parent node with its left child.
-
-Left rotation:
-```
-before left rotating p       after left rotating p  
-     p                         b
-   /   \                     /   \
-  a     b          ->       p     n
- / \   / \                 / \   
-n   n  n  n               a   n
-                         / \
-                        n   n
-```
-Right rotation:
 ```
-before right rotating p       after right rotating p  
-     p                         a
-   /   \                     /   \
-  a     b          ->       n     p
- / \   / \                       / \   
-n   n  n  n                     n   b
-                                   / \
-                                  n   n
+a
+  \
+   b
+    \
+     c
+      \
+       d
 ```
+To prevent this issue, RBTs perform rebalancing operations after an insert or delete and store an additional color property at each node which can either be red or black. After each operation a RBT satisfies the following properties:
 
-## Insertion
-
-We create a new node with the value to be inserted into the tree. The color of this new node is always red.
-We perform a standard BST insert with this node. Now the three might not be a valid RBT anymore.
-We now go through several insertion steps in order to make the tree valid again. We call the just inserted node n.  
-
-**Step 1**: We check if n is the rootNode, if so we paint it black and we are done. If not we go to Step 2.
-
-We now know that n at least has a parent as it is not the rootNode.
-
-**Step 2**: We check if the parent of n is black if so we are done. If not we go to Step 3.
-
-We now know the parent is also not the root node as the parent is red. Thus n also has a grandparent and thus also an uncle as every node has two children. This uncle may however be a nullLeaf
-
-**Step 3**: We check if n's uncle is red. If not we go to Step 4. If n's uncle is indeed red we recolor uncle and parent to black and n's grandparent to red. We now go back to step 1 performing the same logic on n's grandparent.
-
-From here there are four cases:
-- **The left left case.** n's parent is the left child of its parent and n is the left child of its parent.
-- **The left right case** n's parent is the left child of its parent and n is the right child of its parent.
-- **The right right case** n's parent is the right child of its parent and n is the right child of its parent.
-- **The right left case** n's parent is the right child of its parent and n is the left child of its parent.
-
-**Step 4**: checks if either the **left right** case or the **right left** case applies to the current situation.
-  - If we find the **left right case**, we left rotate n's parent and go to Step 5 while setting n to n's parent. (This transforms the **left right** case into the **left left** case)
-  - If we find the **right left case**, we right rotate n's parent and go to Step 5 while setting n to n's parent. (This transforms the **right left** case into the **right right** case)
-  - If we find neither of these two we proceed to Step 5.
+## Properties
 
-n's parent is now red, while n's grandparent is black.
+1. Every node is either red or black
+2. The root is black
+3. Every leaf (nullLeaf) is black
+4. If a node is red, then both its children are black
+5. For each node, all paths from the node to descendant leaves contain the same number of black nodes
 
-**Step 5**: We swap the colors of n's parent and grandparent.
-  - We either right rotate n's grandparent in case of the **left left** case
-  - Or we left rotate n's grandparent in case of the **right right** case
+Property 5 includes the definition of the black-height of a node x, bh(x), which is the number of black nodes on a path from this node down to a leaf not counting the node itself.
+From [CLRS]
 
-Reaching the end we have successfully made the tree valid again.
+## Methods
 
-# Deletion
+Nodes:
+* `nodeX.getSuccessor()` Returns the inorder successor of nodeX
+* `nodeX.minimum()` Returns the node with the minimum key of the subtree of nodeX
+* `nodeX.maximum()` Returns the node with the maximum key of the subtree of nodeX
+Tree:
+* `search(input:)` Returns the node with the given key value
+* `minValue()` Returns the minimum key value of the whole tree
+* `maxValue()` Returns the maximum key value of the whole tree
+* `insert(key:)` Inserts the key value into the tree
+* `delete(key:)` Delete the node with the respective key value from the tree
+* `verify()` Verifies that the given tree fulfills the red-black tree properties
 
-Deletion is a little more complicated than insertion. In the following we call del the node to be deleted.
-First we try and find the node to be deleted using find()
-we send the result of find to del.
-We now go through the following steps in order to delete the node del.
+The rotation, insertion and deletion algorithms are implemented based on the pseudo-code provided in [CLRS]
 
-First we do a few checks:
-- Is del the rootNode if so set the root to a nullLeaf and we are done.
-- If del has 2 nullLeaf children and is red. We check if del is either a left or a right child and set del's parent left or right to a nullLeaf.
-- If del has two non nullLeaf children we look for the maximum value in del's left subtree. We set del's value to this maximum value and continue to instead delete this maximum node. Which we will now call del.
+## Implementation Details
 
-Because of these checks we now know that del has at most 1 non nullLeaf child. It has either two nullLeaf children or one nullLeaf and one regular red child. (The child is red otherwise the black-depth wouldn't be the same for every leaf)
+For convenience, all nil-pointers to children or the parent (except the parent of the root) of a node are exchanged with a nullLeaf. This is an ordinary node object, like all other nodes in the tree, but with a black color, and in this case a nil value for its children, parent and key. Therefore, an empty tree consists of exactly one nullLeaf at the root.
 
-We now call the non nullLeaf child of del, child. If del has two nullLeaf children child will be a nullLeaf. This means child can either be a nullLeaf or a red node.
+## Rotation
 
-We now have three options
+Left rotation (around x):
+Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y, makes y the new root of the subtree with x as y's left child and y's left child as x's right child, where n = a node, [n] = a subtree
+```
+      |                |
+      x                y
+    /   \     ~>     /   \
+  [A]    y          x    [C]
+        / \        / \
+      [B] [C]    [A] [B]
+```
+Right rotation (around y):
+Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x, makes x the new root of the subtree with y as x's right child and x's right child as y's left child, where n = a node, [n] = a subtree
+```
+      |                |
+      x                y
+    /   \     <~     /   \
+  [A]    y          x    [C]
+        / \        / \
+      [B] [C]    [A] [B]
+```
+As rotation is a local operation only exchanging pointers it's runtime is O(1).
 
-- If del is red its child is a nullLeaf and we can just delete it as it doesn't change the black-depth of the tree. We are done
+## Insertion
 
-- If child is red we recolor it black and child's parent to del's parent. del is now deleted and we are done.
+We create a node with the given key and set its color to red. Then we insert it into the the tree by performing a standard insert into a BST. After this, the tree might not be a valid RBT anymore, so we fix the red-black properties by calling the insertFixup algorithm.
+The only violation of the red-black properties occurs at the inserted node z and its parent. Either both are red, or the parent does not exist (so there is a violation since the root must be black).
+We have three distinct cases:
+**Case 1:** The uncle of z is red. If z.parent is left child, z's uncle is z.grandparent's right child. If this is the case, we recolor and move z to z.grandparent, then we check again for this new z. In the following cases, we denote a red node with (x) and a black node with {x}, p = parent, gp = grandparent and u = uncle
+```
+         |                   |
+        {gp}               (newZ)
+       /    \     ~>       /    \
+    (p)     (u)         {p}     {u}
+    / \     / \         / \     / \
+  (z)  [C] [D] [E]    (z) [C] [D] [E]
+  / \                 / \
+[A] [B]             [A] [B]
 
-- Both del and child are black we go through
+```
+**Case 2a:** The uncle of z is black and z is right child. Here, we move z upwards, so z's parent is the newZ and then we rotate around this newZ. After this, we have Case 2b.
+```
+         |                   |
+        {gp}                {gp}
+       /    \     ~>       /    \
+    (p)      {u}         (z)     {u}
+    / \      / \         / \     / \
+  [A]  (z)  [D] [E]  (newZ) [C] [D] [E]
+       / \            / \
+     [B] [C]        [A] [B]
 
-If both del and child are black we introduce a new variable sibling. Which is del's sibling. We also replace del with child and recolor it doubleBlack. del is now deleted and child and sibling are siblings.
+```
+**Case 2b:** The uncle of z is black and z is left child. In this case, we recolor z.parent to black and z.grandparent to red. Then we rotate around z's grandparent. Afterwards we have valid red-black tree.
+```
+         |                   |
+        {gp}                {p}
+       /    \     ~>       /    \
+    (p)      {u}         (z)    (gp)
+    / \      / \         / \     / \
+  (z)  [C] [D] [E]    [A] [B]  [C]  {u}
+  / \                               / \
+[A] [B]                           [D] [E]
 
-We now have to go through a lot of steps in order to remove this doubleBlack color. Which are hard to explain in text without just writing the full code in text. This is due the many possible combination of nodes and colors. The code is commented, but if you don't quite understand please leave me a message. Also part of the deletion is described by the final link in the Also See section.
+```
+Running time of this algorithm: 
+* Only case 1 may repeat, but this only h/2 steps, where h is the height of the tree
+* Case 2a -> Case 2b -> red-black tree
+* Case 2b -> red-black tree
+As we perform case 1 at most O(log n) times and all other cases at most once, we have O(log n) recolorings and at most 2 rotations. 
+The overall runtime of insert is O(log n).
+
+## Deletion
+
+We search for the node with the given key, and if it exists we delete it by performing a standard delete from a BST. If the deleted nodes' color was red everything is fine, otherwise red-black properties may be violated so we call the fixup procedure deleteFixup.
+Violations can be that the parent and child of the deleted node x where red, so we now have two adjacent red nodes, or if we deleted the root, the root could now be red, or the black height property is violated.
+We have 4 cases: We call deleteFixup on node x
+**Case 1:** The sibling of x is red. The sibling is the other child of x's parent, which is not x itself. In this case, we recolor the parent of x and x.sibling then we left rotate around x's parent. In the following cases s = sibling of x, (x) = red, {x} = black, |x| = red/black.
+```
+        |                   |
+       {p}                 {s}
+      /    \     ~>       /    \
+    {x}    (s)         (p)     [D]
+    / \    / \         / \     
+  [A] [B] [C] [D]    {x} [C]
+                     / \  
+                   [A] [B]
 
-## Also see
+```
+**Case 2:** The sibling of x is black and has two black children. Here, we recolor x.sibling to red, move x upwards to x.parent and check again for this newX.
+```
+        |                    |
+       |p|                 |newX|
+      /    \     ~>       /     \
+    {x}     {s}          {x}     (s)
+    / \    /   \          / \   /   \
+  [A] [B] {l}  {r}     [A] [B] {l}  {r}
+          / \  / \             / \  / \
+        [C][D][E][F]         [C][D][E][F]
 
-* [Wikipedia](https://en.wikipedia.org/wiki/Red–black_tree)
-* [GeeksforGeeks - introduction](http://www.geeksforgeeks.org/red-black-tree-set-1-introduction-2/)
-* [GeeksforGeeks - insertion](http://www.geeksforgeeks.org/red-black-tree-set-2-insert/)
-* [GeeksforGeeks - deletion](http://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/)
+```
+**Case 3:** The sibling of x is black with one black child to the right. In this case, we recolor the sibling to red and sibling.leftChild to black, then we right rotate around the sibling. After this we have case 4.
+```
+        |                    |
+       |p|                  |p|
+      /    \     ~>       /     \
+    {x}     {s}          {x}     {l}
+    / \    /   \         / \    /   \
+  [A] [B] (l)  {r}     [A] [B] [C]  (s)
+          / \  / \                  / \
+        [C][D][E][F]               [D]{e}
+                                      / \
+                                    [E] [F]
 
-Important to note is that GeeksforGeeks doesn't mention a few deletion cases that do occur. The code however does implement these.
+```
+**Case 4:** The sibling of x is black with one red child to the right. Here, we recolor the sibling to the color of x.parent and x.parent and sibling.rightChild to black. Then we left rotate around x.parent. After this operation we have a valid red-black tree. Here, ||x|| denotes that x can have either color red or black, but that this can be different to |x| color. This is important, as s gets the same color as p.
+```
+        |                        |
+       ||p||                   ||s||
+      /    \     ~>           /     \
+    {x}     {s}              {p}     {r}
+    / \    /   \            /  \     /  \
+  [A] [B] |l|  (r)        {x}  |l|  [E] [F]
+          / \  / \        / \  / \
+        [C][D][E][F]    [A][B][C][D]
 
-*Written for Swift Algorithm Club by Jaap Wijnen. Updated from Ashwin Raghuraman's contribution.*
+```
+Running time of this algorithm:
+* Only case 2 can repeat, but this only h many times, where h is the height of the tree
+* Case 1 -> case 2 -> red-black tree
+  Case 1 -> case 3 -> case 4 -> red-black tree
+  Case 1 -> case 4 -> red-black tree
+* Case 3 -> case 4 -> red-black tree
+* Case 4 -> red-black tree
+As we perform case 2 at most O(log n) times and all other steps at most once, we have O(log n) recolorings and at most 3 rotations.
+The overall runtime of delete is O(log n).
+
+## Resources:
+[CLRS]  T. Cormen, C. Leiserson, R. Rivest, and C. Stein. "Introduction to Algorithms", Third Edition. 2009
+
+*Written for Swift Algorithm Club by Ute Schiehlen. Updated from Jaap Wijnen and Ashwin Raghuraman's contributions.*
diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
new file mode 100644
index 000000000..5b19f9bd1
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -0,0 +1,22 @@
+//: Playground - noun: a place where people can play
+// Test for  the RedBlackTree implementation provided in the Source folder of this Playground
+import Foundation
+
+let redBlackTree = RedBlackTree<Double>()
+
+let randomMax = Double(0x10000000)
+var values = [Double]()
+for _ in 0..<1000 {
+  let value = Double(arc4random()) / randomMax
+  values.append(value)
+  redBlackTree.insert(key: value)
+}
+redBlackTree.verify()
+
+for _ in 0..<1000 {
+  let rand = arc4random_uniform(UInt32(values.count))
+  let index = Int(rand)
+  let value = values.remove(at: index)
+  redBlackTree.delete(key: value)
+}
+redBlackTree.verify()
diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
new file mode 100644
index 000000000..057909b07
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -0,0 +1,740 @@
+//
+//  RedBlackTree.swift
+//
+//  Created by Ute Schiehlen on 14.03.17.
+//  Copyright © 2017 Ute Schiehlen. All rights reserved.
+//
+
+import Foundation
+
+private enum RBTreeColor {
+  case red
+  case black
+}
+
+private enum rotationDirection {
+  case left
+  case right
+}
+
+// MARK: - RBNode
+
+public class RBTreeNode<Key: Comparable>: Equatable {
+  public typealias RBNode = RBTreeNode<Key>
+  
+  fileprivate var color: RBTreeColor = .black
+  fileprivate var key: Key?
+  fileprivate var isNullLeaf = true
+  var leftChild: RBNode?
+  var rightChild: RBNode?
+  fileprivate weak var parent: RBNode?
+  
+  public init(key: Key?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+    self.key = key
+    self.leftChild = leftChild
+    self.rightChild = rightChild
+    self.parent = parent
+    
+    self.leftChild?.parent = self
+    self.rightChild?.parent = self
+  }
+  
+  public convenience init(key: Key?) {
+    self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
+    self.isNullLeaf = false
+  }
+  
+  // For initialising the nullLeaf
+  public convenience init() {
+    self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
+    self.color = .black
+    self.isNullLeaf = true
+  }
+  
+  var isRoot: Bool {
+    return parent == nil
+  }
+  
+  var isLeaf: Bool {
+    return rightChild == nil && leftChild == nil
+  }
+  
+  var isLeftCild: Bool {
+    return parent?.leftChild === self
+  }
+  
+  var isRightChild: Bool {
+    return parent?.rightChild === self
+  }
+  
+  var grandparent: RBNode? {
+    return parent?.parent
+  }
+  
+  var sibling: RBNode? {
+    if isLeftCild {
+      return parent?.rightChild
+    } else {
+      return parent?.leftChild
+    }
+  }
+  
+  var uncle: RBNode? {
+    return parent?.sibling
+  }
+}
+
+// MARK: - RedBlackTree
+
+public class RedBlackTree<Key: Comparable> {
+  public typealias RBNode = RBTreeNode<Key>
+  
+  fileprivate(set) var root: RBNode
+  fileprivate(set) var size = 0
+  fileprivate let nullLeaf = RBNode()
+  
+  public init() {
+    root = nullLeaf
+  }
+}
+
+// MARK: - Equatable protocol
+
+extension RBTreeNode {
+  static public func ==<T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+    return lhs.key == rhs.key
+  }
+}
+
+// MARK: - Finding a nodes successor
+
+extension RBTreeNode {
+  /*
+   * Returns the inorder successor node of a node
+   * The successor is a node with the next larger key value of the current node
+   */
+  public func getSuccessor() -> RBNode? {
+    // If node has right child: successor min of this right tree
+    if let rightChild = self.rightChild {
+      if !rightChild.isNullLeaf {
+        return rightChild.minimum()
+      }
+    }
+    // Else go upward until node left child
+    var currentNode = self
+    var parent = currentNode.parent
+    while currentNode.isRightChild {
+      if let parent = parent {
+        currentNode = parent
+      }
+      parent = currentNode.parent
+    }
+    return parent
+  }
+}
+
+// MARK: - Searching
+
+extension RBTreeNode {
+  /*
+   * Returns the node with the minimum key of the current subtree
+   */
+  public func minimum() -> RBNode? {
+    if let leftChild = leftChild {
+      if !leftChild.isNullLeaf {
+        return leftChild.minimum()
+      }
+      return self
+    }
+    return self
+  }
+  
+  /*
+   * Returns the node with the maximum key of the current subtree
+   */
+  public func maximum() -> RBNode? {
+    if let rightChild = rightChild {
+      if !rightChild.isNullLeaf {
+        return rightChild.maximum()
+      }
+      return self
+    }
+    return self
+  }
+}
+
+extension RedBlackTree {
+  /*
+   * Returns the node with the given key |input| if existing
+   */
+  public func search(input: Key) -> RBNode? {
+    return search(key: input, node: root)
+  }
+  
+  /*
+   * Returns the node with given |key| in subtree of |node|
+   */
+  fileprivate func search(key: Key, node: RBNode?) -> RBNode? {
+    // If node nil -> key not found
+    guard let node = node else {
+      return nil
+    }
+    // If node is nullLeaf == semantically same as if nil
+    if !node.isNullLeaf {
+      if let nodeKey = node.key {
+        // Node found
+        if key == nodeKey {
+          return node
+        } else if key < nodeKey {
+          return search(key: key, node: node.leftChild)
+        } else {
+          return search(key: key, node: node.rightChild)
+        }
+      }
+    }
+    return nil
+  }
+}
+
+// MARK: - Finding maximum and minimum value
+
+extension RedBlackTree {
+  /*
+   * Returns the minimum key value of the whole tree
+   */
+  public func minValue() -> Key? {
+    if let minNode = root.minimum() {
+       return minNode.key
+    } else {
+      return nil
+    }
+  }
+  
+  /*
+   * Returns the maximum key value of the whole tree
+   */
+  public func maxValue() -> Key? {
+      if let maxNode = root.maximum() {
+        return maxNode.key
+      } else {
+        return nil
+    }
+  }
+}
+
+// MARK: - Inserting new nodes
+
+extension RedBlackTree {
+  /*
+   * Insert a node with key |key| into the tree
+   * 1. Perform normal insert operation as in a binary search tree
+   * 2. Fix red-black properties
+   * Runntime: O(log n)
+   */
+  public func insert(key: Key) {
+    if root.isNullLeaf {
+      root = RBNode(key: key)
+    } else {
+      insert(input: RBNode(key: key), node: root)
+    }
+    
+    size += 1
+  }
+  
+  /*
+   * Nearly identical insert operation as in a binary search tree
+   * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
+   * after inserting we call insertFixup to maintain the red-black properties
+   */
+  private func insert(input: RBNode, node: RBNode) {
+    guard let inputKey = input.key, let nodeKey = node.key else {
+        return
+    }
+    if inputKey < nodeKey {
+      guard let child = node.leftChild else {
+        addAsLeftChild(child: input, parent: node)
+        return
+      }
+      if child.isNullLeaf {
+        addAsLeftChild(child: input, parent: node)
+      } else {
+        insert(input: input, node: child)
+      }
+    } else {
+      guard let child = node.rightChild else {
+        addAsRightChild(child: input, parent: node)
+        return
+      }
+      if child.isNullLeaf {
+        addAsRightChild(child: input, parent: node)
+      } else {
+        insert(input: input, node: child)
+      }
+    }
+  }
+  
+  private func addAsLeftChild(child: RBNode, parent: RBNode) {
+    parent.leftChild = child
+    child.parent = parent
+    child.color = .red
+    insertFixup(node: child)
+  }
+  
+  private func addAsRightChild(child: RBNode, parent: RBNode) {
+    parent.rightChild = child
+    child.parent = parent
+    child.color = .red
+    insertFixup(node: child)
+  }
+  
+  /*
+   * Fixes possible violations of the red-black property after insertion
+   * Only violation of red-black properties occurs at inserted node |z| and z.parent
+   * We have 3 distinct cases: case 1, 2a and 2b
+   * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
+   * - case 2a -> case 2b -> red-black tree
+   * - case 2b -> red-black tree
+   */
+  private func insertFixup(node z: RBNode) {
+    if(!z.isNullLeaf) {
+      guard let parentZ = z.parent else{
+        return
+      }
+      // If both |z| and his parent are red -> violation of red-black property -> need to fix it
+      if parentZ.color == .red {
+        guard let uncle = z.uncle else {
+          return
+        }
+        // Case 1: Uncle red -> recolor + move z
+        if uncle.color == .red {
+          parentZ.color = .black
+          uncle.color = .black
+          if let grandparentZ = parentZ.parent {
+            grandparentZ.color = .red
+            // Move z to grandparent and check again
+            insertFixup(node: grandparentZ)
+          }
+        }
+        // Case 2: Uncle black
+        else {
+          var zNew = z
+          // Case 2.a: z right child -> rotate
+          if parentZ.isLeftCild && z.isRightChild {
+            zNew = parentZ
+            leftRotate(node: zNew)
+          } else if parentZ.isRightChild && z.isLeftCild {
+            zNew = parentZ
+            rightRotate(node: zNew)
+          }
+          // Case 2.b: z left child -> recolor + rotate
+          zNew.parent?.color = .black
+          if let grandparentZnew = zNew.grandparent {
+            grandparentZnew.color = .red
+            if z.isLeftCild {
+              rightRotate(node: grandparentZnew)
+            } else {
+              leftRotate(node: grandparentZnew)
+            }
+            // We have a valid red-black-tree
+          }
+        }
+      }
+    }
+    root.color = .black
+  }
+}
+
+// MARK: - Deleting a node
+extension RedBlackTree {
+  /*
+   * Delete a node with key |key| from the tree
+   * 1. Perform standard delete operation as in a binary search tree
+   * 2. Fix red-black properties
+   * Runntime: O(log n)
+   */
+  public func delete(key: Key) {
+    if size == 1 {
+      root = nullLeaf
+      size -= 1
+    } else if let node = search(key: key, node: root) {
+      if !node.isNullLeaf {
+        delete(node: node)
+        size -= 1
+      }
+    }
+  }
+  
+  /*
+   * Nearly identical delete operation as in a binary search tree
+   * Differences: All nil pointers are replaced by the nullLeaf,
+   * after deleting we call insertFixup to maintain the red-black properties if the delted node was
+   * black (as if it was red -> no violation of red-black properties)
+   */
+  private func delete(node z: RBNode) {
+    var nodeY = RBNode()
+    var nodeX = RBNode()
+    if let leftChild = z.leftChild, let rightChild = z.rightChild {
+      if leftChild.isNullLeaf || rightChild.isNullLeaf {
+        nodeY = z
+      } else {
+        if let successor = z.getSuccessor() {
+          nodeY = successor
+        }
+      }
+    }
+    if let leftChild = nodeY.leftChild {
+      if !leftChild.isNullLeaf {
+        nodeX = leftChild
+      } else if let rightChild = nodeY.rightChild {
+        nodeX = rightChild
+      }
+    }
+    nodeX.parent = nodeY.parent
+    if let parentY = nodeY.parent {
+      // Should never be the case, as parent of root = nil
+      if parentY.isNullLeaf {
+        root = nodeX
+      } else {
+        if nodeY.isLeftCild {
+          parentY.leftChild = nodeX
+        } else {
+          parentY.rightChild = nodeX
+        }
+      }
+    } else {
+      root = nodeX
+    }
+    if nodeY != z {
+      z.key = nodeY.key
+    }
+    // If sliced out node was red -> nothing to do as red-black-property holds
+    // If it was black -> fix red-black-property
+    if nodeY.color == .black {
+      deleteFixup(node: nodeX)
+    }
+  }
+  
+  /*
+   * Fixes possible violations of the red-black property after deletion
+   * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height 
+   * of the tree
+   * - case 1 -> case 2 -> red-black tree
+   *   case 1 -> case 3 -> case 4 -> red-black tree
+   *   case 1 -> case 4 -> red-black tree
+   * - case 3 -> case 4 -> red-black tree
+   * - case 4 -> red-black tree
+   */
+  private func deleteFixup(node x: RBNode) {
+    var xTmp = x
+    if !x.isRoot && x.color == .black {
+      guard var sibling = x.sibling else {
+        return
+      }
+      // Case 1: Sibling of x is red
+      if sibling.color == .red {
+        // Recolor
+        sibling.color = .black
+        if let parentX = x.parent {
+          parentX.color = .red
+          // Rotation
+          if x.isLeftCild {
+            leftRotate(node: parentX)
+          } else {
+            rightRotate(node: parentX)
+          }
+          // Update sibling
+          if let sibl = x.sibling {
+            sibling = sibl
+          }
+        }
+      }
+      // Case 2: Sibling is black with two black children
+      if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
+        // Recolor
+        sibling.color = .red
+        // Move fake black unit upwards
+        if let parentX = x.parent {
+          deleteFixup(node: parentX)
+        }
+        // We have a valid red-black-tree
+      } else {
+        // Case 3: a. Sibling black with one black child to the right
+        if x.isLeftCild && sibling.rightChild?.color == .black {
+          // Recolor
+          sibling.leftChild?.color = .black
+          sibling.color = .red
+          // Rotate
+          rightRotate(node: sibling)
+          // Update sibling of x
+          if let sibl = x.sibling {
+            sibling = sibl
+          }
+        }
+        // Still case 3: b. One black child to the left
+        else if x.isRightChild && sibling.leftChild?.color == .black {
+          // Recolor
+          sibling.rightChild?.color = .black
+          sibling.color = .red
+          // Rotate
+          leftRotate(node: sibling)
+          // Update sibling of x
+          if let sibl = x.sibling {
+            sibling = sibl
+          }
+        }
+        // Case 4: Sibling is black with red right child
+        // Recolor
+        if let parentX = x.parent {
+          sibling.color = parentX.color
+          parentX.color = .black
+          // a. x left and sibling with red right child
+          if x.isLeftCild {
+            sibling.rightChild?.color = .black
+            // Rotate
+            leftRotate(node: parentX)
+          }
+          // b. x right and sibling with red left child
+          else {
+            sibling.leftChild?.color = .black
+            //Rotate
+            rightRotate(node: parentX)
+          }
+          // We have a valid red-black-tree
+          xTmp = root
+        }
+      }
+    }
+    xTmp.color = .black
+  }
+}
+
+// MARK: - Rotation
+extension RedBlackTree {
+  /*
+   * Left rotation around node x
+   * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
+   * makes y the new root of the subtree with x as y's left child and y's left child as x's right 
+   * child, where n = a node, [n] = a subtree
+   *     |                |
+   *     x                y
+   *   /   \     ~>     /   \
+   * [A]    y          x    [C]
+   *       / \        / \
+   *     [B] [C]    [A] [B]
+   */
+  fileprivate func leftRotate(node x: RBNode) {
+    rotate(node: x, direction: .left)
+  }
+  
+  
+  /*
+   * Right rotation around node y
+   * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
+   * makes x the new root of the subtree with y as x's right child and x's right child as y's left
+   * child, where n = a node, [n] = a subtree
+   *     |                |
+   *     x                y
+   *   /   \     <~     /   \
+   * [A]    y          x    [C]
+   *       / \        / \
+   *     [B] [C]    [A] [B]
+   */
+  fileprivate func rightRotate(node x: RBNode) {
+    rotate(node: x, direction: .right)
+  }
+  
+  /*
+   * Rotation around a node x
+   * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
+   * Runntime: O(1)
+   */
+  private func rotate(node x: RBNode, direction: rotationDirection) {
+    var nodeY: RBNode? = RBNode()
+    
+    // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
+    switch direction {
+    case .left:
+      nodeY = x.rightChild
+      x.rightChild = nodeY?.leftChild
+      x.rightChild?.parent = x
+    case .right:
+      nodeY = x.leftChild
+      x.leftChild = nodeY?.rightChild
+      x.leftChild?.parent = x
+    }
+    
+    // Link |x|'s parent to nodeY
+    nodeY?.parent = x.parent
+    if x.isRoot {
+      if let node = nodeY {
+        root = node
+      }
+    } else if x.isLeftCild {
+      x.parent?.leftChild = nodeY
+    } else if x.isRightChild {
+      x.parent?.rightChild = nodeY
+    }
+    
+    // Put |x| on |nodeY|'s left
+    switch direction {
+    case .left:
+      nodeY?.leftChild = x
+    case .right:
+      nodeY?.rightChild = x
+    }
+    x.parent = nodeY
+  }
+}
+
+// MARK: - Verify
+extension RedBlackTree {
+  /*
+   * Verifies that the existing tree fulfills all red-black properties
+   * Returns true if the tree is a valid red-black tree, false otherwise
+   */
+  public func verify() -> Bool {
+    if root.isNullLeaf {
+      print("The tree is empty")
+      return true
+    }
+    return property2() && property4() && property5()
+  }
+  
+  // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
+  // RBTreeColor
+  
+  
+  // Property 2: The root is black
+  private func property2() -> Bool {
+    if root.color == .red {
+      print("Property-Error: Root is red")
+      return false
+    }
+    return true
+  }
+  
+  // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
+  
+  // Property 4: If a node is red, then both its children are black
+  private func property4() -> Bool {
+    return property4(node: root)
+  }
+  
+  private func property4(node: RBNode) -> Bool {
+    if node.isNullLeaf {
+      return true
+    }
+    if let leftChild = node.leftChild, let rightChild = node.rightChild {
+      if node.color == .red {
+        if !leftChild.isNullLeaf && leftChild.color == .red {
+          print("Property-Error: Red node with key \(node.key ?? nil) has red left child")
+          return false
+        }
+        if !rightChild.isNullLeaf && rightChild.color == .red {
+          print("Property-Error: Red node with key \(node.key ?? nil) has red right child")
+          return false
+        }
+      }
+      return property4(node: leftChild) && property4(node: rightChild)
+    }
+    return false
+  }
+  
+  // Property 5: For each node, all paths from the node to descendant leaves contain the same number
+  // of black nodes (same blackheight)
+  private func property5() -> Bool {
+    if property5(node: root) == -1 {
+      return false
+    } else {
+      return true
+    }
+  }
+  
+  private func property5(node: RBNode) -> Int {
+    if node.isNullLeaf {
+      return 0
+    }
+    guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
+      return -1
+    }
+    let left = property5(node: leftChild)
+    let right = property5(node: rightChild)
+    
+    if left == -1 || right == -1 {
+      return -1
+    } else if left == right {
+      let addedHeight = node.color == .black ? 1 : 0
+      return left + addedHeight
+    } else {
+      print("Property-Error: Black height violated at node with key \(node.key ?? nil)")
+      return -1
+    }
+  }
+}
+
+// MARK: - Debugging
+
+extension RBTreeNode: CustomDebugStringConvertible {
+  public var debugDescription: String {
+    var s = ""
+    if isNullLeaf {
+      s = "nullLeaf"
+    } else {
+      if let key = key {
+        s = "key: \(key)"
+      } else {
+        s = "key: nil"
+      }
+      if let parent = parent {
+        s += ", parent: \(parent.key)"
+      }
+      if let left = leftChild {
+        s += ", left = [" + left.debugDescription + "]"
+      }
+      if let right = rightChild {
+        s += ", right = [" + right.debugDescription + "]"
+      }
+      s += ", color = \(color)"
+    }
+    return s
+  }
+}
+
+extension RedBlackTree: CustomDebugStringConvertible {
+  public var debugDescription: String {
+    return root.debugDescription
+  }
+}
+
+extension RBTreeNode: CustomStringConvertible {
+  public var description: String {
+    var s = ""
+    if isNullLeaf {
+      s += "nullLeaf"
+    } else {
+      if let left = leftChild {
+        s += "(\(left.description)) <- "
+      }
+      if let key = key {
+        s += "\(key)"
+      } else {
+        s += "nil"
+      }
+      s += ", \(color)"
+      if let right = rightChild {
+        s += " -> (\(right.description))"
+      }
+    }
+    return s
+  }
+}
+
+extension RedBlackTree: CustomStringConvertible {
+  public var description: String {
+    if root.isNullLeaf {
+      return "[]"
+    } else{
+      return root.description
+    }
+  }
+}
diff --git a/Red-Black Tree/RedBlackTree.playground/contents.xcplayground b/Red-Black Tree/RedBlackTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From cf91833f5688398045bb7b76150bc988df747580 Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:23:37 +0100
Subject: [PATCH 0862/1679] Deleted old version

---
 .../Contents.swift                            |  20 -
 .../Sources/RBTree.swift                      | 521 ------------------
 .../contents.xcplayground                     |   4 -
 .../contents.xcworkspacedata                  |   0
 4 files changed, 545 deletions(-)
 delete mode 100644 Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
 delete mode 100644 Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
 delete mode 100644 Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground
 rename Red-Black Tree/{Red-Black Tree 2.playground => RedBlackTree.playground}/playground.xcworkspace/contents.xcworkspacedata (100%)

diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
deleted file mode 100644
index d55c153d5..000000000
--- a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift	
+++ /dev/null
@@ -1,20 +0,0 @@
-//: Playground - noun: a place where people can play
-import Foundation
-
-let tree = RBTree<Double>()
-let randomMax = Double(0x100000000)
-var values = [Double]()
-for _ in 0..<1000 {
-    let value = Double(arc4random()) / randomMax
-    values.append(value)
-    tree.insert(value)
-}
-tree.verify()
- 
-for _ in 0..<1000 {
-    let rand = arc4random_uniform(UInt32(values.count))
-    let index = Int(rand)
-    let value = values.remove(at: index)
-    tree.delete(value)
-}
-tree.verify()
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
deleted file mode 100644
index 1735798d5..000000000
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ /dev/null
@@ -1,521 +0,0 @@
-
-private enum RBTColor {
-    case red
-    case black
-    case doubleBlack
-}
-
-public class RBTNode<T: Comparable>: CustomStringConvertible {
-    fileprivate var color: RBTColor = .red
-    public var value: T! = nil
-    public var right:  RBTNode<T>!
-    public var left:  RBTNode<T>!
-    public var parent:  RBTNode<T>!
-    
-    public var description: String {
-        if self.value == nil {
-            return "null"
-        } else {
-            var nodeValue: String
-            
-            // If the value is encapsulated by parentheses it is red
-            // If the value is encapsulated by pipes it is black
-            // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
-            if self.isRed {
-                nodeValue = "(\(self.value!))"
-            } else if self.isBlack{
-                nodeValue = "|\(self.value!)|"
-            } else {
-                nodeValue = "||\(self.value!)||"
-            }
-            
-            return "(\(self.left.description)<-\(nodeValue)->\(self.right.description))"
-        }
-    }
-    
-    init(tree: RBTree<T>) {
-        right = tree.nullLeaf
-        left = tree.nullLeaf
-        parent = tree.nullLeaf
-    }
-    
-    init() {
-        //This method is here to support the creation of a nullLeaf
-    }
-    
-    public var isLeftChild: Bool {
-        return self.parent.left === self
-    }
-    
-    public var isRightChild: Bool {
-        return self.parent.right === self
-    }
-    
-    public var grandparent: RBTNode<T> {
-        return parent.parent
-    }
-    
-    public var sibling: RBTNode<T> {
-        if isLeftChild {
-            return self.parent.right
-        } else {
-            return self.parent.left
-        }
-    }
-    
-    public var uncle: RBTNode<T> {
-        return parent.sibling
-    }
-    
-    fileprivate var isRed: Bool {
-        return color == .red
-    }
-    
-    fileprivate var isBlack: Bool {
-        return color == .black
-    }
-    
-    fileprivate var isDoubleBlack: Bool {
-        return color == .doubleBlack
-    }
-}
-
-public class RBTree<T: Comparable>: CustomStringConvertible {
-    public var root: RBTNode<T>
-    fileprivate let nullLeaf: RBTNode<T>
-    
-    public var description: String {
-        return root.description
-    }
-    
-    public init() {
-        nullLeaf = RBTNode<T>()
-        nullLeaf.color = .black
-        root = nullLeaf
-    }
-    
-    public convenience init(withValue value: T) {
-        self.init()
-        insert(value)
-    }
-    
-    public convenience init(withArray array: [T]) {
-        self.init()
-        insert(array)
-    }
-    
-    public func insert(_ value: T) {
-        let newNode = RBTNode<T>(tree: self)
-        newNode.value = value
-        insertNode(n: newNode)
-    }
-    
-    public func insert(_ values: [T]) {
-        for value in values {
-            print(value)
-            insert(value)
-        }
-    }
-    
-    public func delete(_ value: T) {
-        let nodeToDelete = find(value)
-        if nodeToDelete !== nullLeaf {
-            deleteNode(n: nodeToDelete)
-        }
-    }
-    
-    public func find(_ value: T) -> RBTNode<T> {
-        let foundNode = findNode(rootNode: root, value: value)
-        return foundNode
-    }
-    
-    public func minimum(n: RBTNode<T>) -> RBTNode<T> {
-        var min = n
-        if n.left !== nullLeaf {
-            min = minimum(n: n.left)
-        }
-        
-        return min
-    }
-    
-    public func maximum(n: RBTNode<T>) -> RBTNode<T> {
-        var max = n
-        if n.right !== nullLeaf {
-            max = maximum(n: n.right)
-        }
-        
-        return max
-    }
-    
-    public func verify() {
-        if self.root === nullLeaf {
-            print("The tree is empty")
-            return
-        }
-        property1()
-        property2(n: self.root)
-        property3()
-    }
-    
-    private func findNode(rootNode: RBTNode<T>, value: T) -> RBTNode<T> {
-        var nextNode = rootNode
-        if rootNode !== nullLeaf && value != rootNode.value {
-            if value < rootNode.value {
-                nextNode = findNode(rootNode: rootNode.left, value: value)
-            } else {
-                nextNode = findNode(rootNode: rootNode.right, value: value)
-            }
-        }
-        
-        return nextNode
-    }
-    
-    private func insertNode(n: RBTNode<T>) {
-        BSTInsertNode(n: n, parent: root)
-        insertCase1(n: n)
-    }
-    
-    private func BSTInsertNode(n: RBTNode<T>, parent: RBTNode<T>) {
-        if parent === nullLeaf {
-            self.root = n
-        } else if n.value < parent.value {
-            if parent.left !== nullLeaf {
-                BSTInsertNode(n: n, parent: parent.left)
-            } else {
-                parent.left = n
-                parent.left.parent = parent
-            }
-        } else {
-            if parent.right !== nullLeaf {
-                BSTInsertNode(n: n, parent: parent.right)
-            } else {
-                parent.right = n
-                parent.right.parent = parent
-            }
-        }
-    }
-    
-    // if node is root change color to black, else move on
-    private func insertCase1(n: RBTNode<T>) {
-        if n === root {
-            n.color = .black
-        } else {
-            insertCase2(n: n)
-        }
-    }
-    
-    // if parent of node is not black, and node is not root move on
-    private func insertCase2(n: RBTNode<T>) {
-        if !n.parent.isBlack {
-            insertCase3(n: n)
-        }
-    }
-    
-    // if uncle is red do stuff otherwise move to 4
-    private func insertCase3(n: RBTNode<T>) {
-        if n.uncle.isRed { // node must have grandparent as children of root have a black parent
-            // both parent and uncle are red, so grandparent must be black.
-            n.parent.color = .black
-            n.uncle.color = .black
-            n.grandparent.color = .red
-            // now both parent and uncle are black and grandparent is red.
-            // we repeat for the grandparent
-            insertCase1(n: n.grandparent)
-        } else {
-            insertCase4(n: n)
-        }
-    }
-    
-    // parent is red, grandparent is black, uncle is black
-    // There are 4 cases left:
-    // - left left
-    // - left right
-    // - right right
-    // - right left
-    
-    // the cases "left right" and "right left" can be rotated into the other two
-    // so if either of the two is detected we apply a rotation and then move on to
-    // deal with the final two cases, if neither is detected we move on to those cases anyway
-    private func insertCase4(n: RBTNode<T>) {
-        if n.parent.isLeftChild && n.isRightChild { // left right case
-            leftRotate(n: n.parent)
-            insertCase5(n: n.left)
-        } else if n.parent.isRightChild && n.isLeftChild { // right left case
-            rightRotate(n: n.parent)
-            insertCase5(n: n.right)
-        } else {
-            insertCase5(n: n)
-        }
-    }
-    
-    private func insertCase5(n: RBTNode<T>) {
-        // swap color of parent and grandparent
-        // parent is red grandparent is black
-        n.parent.color = .black
-        n.grandparent.color = .red
-        
-        if n.isLeftChild { // left left case
-            rightRotate(n: n.grandparent)
-        } else { // right right case
-            leftRotate(n: n.grandparent)
-        }
-    }
-    
-    private func deleteNode(n: RBTNode<T>) {
-        var toDel = n
-        
-        if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.parent === nullLeaf {
-            self.root = nullLeaf
-            return
-        }
-        
-        if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.isRed {
-            if toDel.isLeftChild {
-                toDel.parent.left = nullLeaf
-            } else {
-                toDel.parent.right = nullLeaf
-            }
-            return
-        }
-        
-        if toDel.left !== nullLeaf && toDel.right !== nullLeaf {
-            let pred = maximum(n: toDel.left)
-            toDel.value = pred.value
-            toDel = pred
-        }
-        
-        // from here toDel has at most 1 non nullLeaf child
-        
-        var child: RBTNode<T>
-        if toDel.left !== nullLeaf {
-            child = toDel.left
-        } else {
-            child = toDel.right
-        }
-        
-        if toDel.isRed || child.isRed {
-            child.color = .black
-            
-            if toDel.isLeftChild {
-                toDel.parent.left = child
-            } else {
-                toDel.parent.right = child
-            }
-            
-            if child !== nullLeaf {
-                child.parent = toDel.parent
-            }
-        } else { // both toDel and child are black
-            
-            var sibling = toDel.sibling
-            
-            if toDel.isLeftChild {
-                toDel.parent.left = child
-            } else {
-                toDel.parent.right = child
-            }
-            if child !== nullLeaf {
-                child.parent = toDel.parent
-            }
-            child.color = .doubleBlack
-            
-            while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
-                if sibling.isBlack {
-                    
-                    var leftRedChild: RBTNode<T>! = nil
-                    if sibling.left.isRed {
-                        leftRedChild = sibling.left
-                    }
-                    var rightRedChild: RBTNode<T>! = nil
-                    if sibling.right.isRed {
-                        rightRedChild = sibling.right
-                    }
-                    
-                    if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
-                        child.color = .black
-                        if sibling.isLeftChild {
-                            if leftRedChild != nil { // left left case
-                                sibling.left.color = .black
-                                let tempColor = sibling.parent.color
-                                sibling.parent.color = sibling.color
-                                sibling.color = tempColor
-                                rightRotate(n: sibling.parent)
-                            } else { // left right case
-                                if sibling.parent.isRed {
-                                    sibling.parent.color = .black
-                                } else {
-                                    sibling.right.color = .black
-                                }
-                                leftRotate(n: sibling)
-                                rightRotate(n: sibling.grandparent)
-                            }
-                        } else {
-                            if rightRedChild != nil { // right right case
-                                sibling.right.color = .black
-                                let tempColor = sibling.parent.color
-                                sibling.parent.color = sibling.color
-                                sibling.color = tempColor
-                                leftRotate(n: sibling.parent)
-                            } else { // right left case
-                                if sibling.parent.isRed {
-                                    sibling.parent.color = .black
-                                } else {
-                                    sibling.left.color = .black
-                                }
-                                rightRotate(n: sibling)
-                                leftRotate(n: sibling.grandparent)
-                            }
-                        }
-                        break
-                    } else { // both sibling's children are black
-                        child.color = .black
-                        sibling.color = .red
-                        if sibling.parent.isRed {
-                            sibling.parent.color = .black
-                            break
-                        }
-                        /*
-                        sibling.parent.color = .doubleBlack
-                        child = sibling.parent
-                        sibling = child.sibling
-                        */
-                        if sibling.parent.parent === nullLeaf { // parent of child is root
-                            break
-                        } else {
-                            sibling.parent.color = .doubleBlack
-                            child = sibling.parent
-                            sibling = child.sibling // can become nill if child is root as parent is nullLeaf
-                        }
-                        //---------------
-                    }
-                } else { // sibling is red
-                    sibling.color = .black
-                    
-                    if sibling.isLeftChild { // left case
-                        rightRotate(n: sibling.parent)
-                        sibling = sibling.right.left
-                        sibling.parent.color = .red
-                    } else { // right case
-                        leftRotate(n: sibling.parent)
-                        sibling = sibling.left.right
-                        sibling.parent.color = .red
-                    }
-                }
-                
-                // sibling check is here for when child is a nullLeaf and thus does not have a parent.
-                // child is here as sibling can become nil when child is the root
-                if (sibling.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
-                    child.color = .black
-                }
-            }
-        }
-    }
-    
-    private func property1() {
-        
-        if self.root.isRed {
-            print("Root is not black")
-        }
-    }
-    
-    private func property2(n: RBTNode<T>) {
-        if n === nullLeaf {
-            return
-        }
-        if n.isRed {
-            if n.left !== nullLeaf && n.left.isRed {
-                print("Red node: \(n.value), has red left child")
-            } else if n.right !== nullLeaf && n.right.isRed {
-                print("Red node: \(n.value), has red right child")
-            }
-        }
-        property2(n: n.left)
-        property2(n: n.right)
-    }
-    
-    private func property3() {
-        let bDepth = blackDepth(root: self.root)
-        
-        let leaves:[RBTNode<T>] = getLeaves(n: self.root)
-        
-        for leaflet in leaves {
-            var leaf = leaflet
-            var i = 0
-            
-            while leaf !== nullLeaf {
-                if leaf.isBlack {
-                    i = i + 1
-                }
-                leaf = leaf.parent
-            }
-            
-            if i != bDepth {
-                print("black depth: \(bDepth), is not equal (depth: \(i)) for leaf with value: \(leaflet.value)")
-            }
-        }
-        
-    }
-    
-    private func getLeaves(n: RBTNode<T>) -> [RBTNode<T>] {
-        var leaves = [RBTNode<T>]()
-        
-        if n !== nullLeaf {
-            if n.left === nullLeaf && n.right === nullLeaf {
-                leaves.append(n)
-            } else {
-                let leftLeaves = getLeaves(n: n.left)
-                let rightLeaves = getLeaves(n: n.right)
-                
-                leaves.append(contentsOf: leftLeaves)
-                leaves.append(contentsOf: rightLeaves)
-            }
-        }
-        
-        return leaves
-    }
-    
-    private func blackDepth(root: RBTNode<T>) -> Int {
-        if root === nullLeaf {
-            return 0
-        } else {
-            let returnValue = root.isBlack ? 1 : 0
-            return returnValue + (max(blackDepth(root: root.left), blackDepth(root: root.right)))
-        }
-    }
-    
-    private func leftRotate(n: RBTNode<T>) {
-        let newRoot = n.right!
-        n.right = newRoot.left!
-        if newRoot.left !== nullLeaf {
-            newRoot.left.parent = n
-        }
-        newRoot.parent = n.parent
-        if n.parent === nullLeaf {
-            self.root = newRoot
-        } else if n.isLeftChild {
-            n.parent.left = newRoot
-        } else {
-            n.parent.right = newRoot
-        }
-        newRoot.left = n
-        n.parent = newRoot
-    }
-    
-    private func rightRotate(n: RBTNode<T>) {
-        let newRoot = n.left!
-        n.left = newRoot.right!
-        if newRoot.right !== nullLeaf {
-            newRoot.right.parent = n
-        }
-        newRoot.parent = n.parent
-        if n.parent === nullLeaf {
-            self.root = newRoot
-        } else if n.isRightChild {
-            n.parent.right = newRoot
-        } else {
-            n.parent.left = newRoot
-        }
-        newRoot.right = n
-        n.parent = newRoot
-    }
-}
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground b/Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata b/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Red-Black Tree/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/contents.xcworkspacedata

From dc460542ffe226bbb0175fec35a9195eac87d9a3 Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:30:51 +0100
Subject: [PATCH 0863/1679] Added licence to file

---
 .../Sources/RedBlackTree.swift                | 19 ++++++++++++++++---
 1 file changed, 16 insertions(+), 3 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 057909b07..a588ea6bc 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -1,9 +1,22 @@
+//Copyright (c) 2016 Matthijs Hollemans and contributors
 //
-//  RedBlackTree.swift
+//Permission is hereby granted, free of charge, to any person obtaining a copy
+//of this software and associated documentation files (the "Software"), to deal
+//in the Software without restriction, including without limitation the rights
+//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//copies of the Software, and to permit persons to whom the Software is
+//furnished to do so, subject to the following conditions:
 //
-//  Created by Ute Schiehlen on 14.03.17.
-//  Copyright © 2017 Ute Schiehlen. All rights reserved.
+//The above copyright notice and this permission notice shall be included in
+//all copies or substantial portions of the Software.
 //
+//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+//THE SOFTWARE.
 
 import Foundation
 

From 37d7300627bda5538381127db68571bf7b38f57e Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:51:08 +0100
Subject: [PATCH 0864/1679] Incorporated major swiftlint warnings

---
 .../Sources/RedBlackTree.swift                     | 14 ++++++--------
 1 file changed, 6 insertions(+), 8 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index a588ea6bc..6f3b16b86 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -25,7 +25,7 @@ private enum RBTreeColor {
   case black
 }
 
-private enum rotationDirection {
+private enum RotationDirection {
   case left
   case right
 }
@@ -114,7 +114,7 @@ public class RedBlackTree<Key: Comparable> {
 // MARK: - Equatable protocol
 
 extension RBTreeNode {
-  static public func ==<T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+  static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
     return lhs.key == rhs.key
   }
 }
@@ -309,8 +309,8 @@ extension RedBlackTree {
    * - case 2b -> red-black tree
    */
   private func insertFixup(node z: RBNode) {
-    if(!z.isNullLeaf) {
-      guard let parentZ = z.parent else{
+    if !z.isNullLeaf {
+      guard let parentZ = z.parent else {
         return
       }
       // If both |z| and his parent are red -> violation of red-black property -> need to fix it
@@ -539,7 +539,6 @@ extension RedBlackTree {
     rotate(node: x, direction: .left)
   }
   
-  
   /*
    * Right rotation around node y
    * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
@@ -561,7 +560,7 @@ extension RedBlackTree {
    * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
    * Runntime: O(1)
    */
-  private func rotate(node x: RBNode, direction: rotationDirection) {
+  private func rotate(node x: RBNode, direction: RotationDirection) {
     var nodeY: RBNode? = RBNode()
     
     // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
@@ -616,7 +615,6 @@ extension RedBlackTree {
   // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
   // RBTreeColor
   
-  
   // Property 2: The root is black
   private func property2() -> Bool {
     if root.color == .red {
@@ -746,7 +744,7 @@ extension RedBlackTree: CustomStringConvertible {
   public var description: String {
     if root.isNullLeaf {
       return "[]"
-    } else{
+    } else {
       return root.description
     }
   }

From 306ef65bd3ef8b652b1120bc8a5b6770583c3e35 Mon Sep 17 00:00:00 2001
From: kyungkoo <mc2e.dev@gmail.com>
Date: Fri, 24 Mar 2017 17:29:41 +0900
Subject: [PATCH 0865/1679] fixed broken link

---
 README.markdown | 100 ++++++++++++++++++++++++------------------------
 1 file changed, 50 insertions(+), 50 deletions(-)

diff --git a/README.markdown b/README.markdown
index dfe451478..fc034f71b 100644
--- a/README.markdown
+++ b/README.markdown
@@ -34,31 +34,31 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 
 - [Stack](Stack/)
 - [Queue](Queue/)
-- [Insertion Sort](Insertion Sort/)
-- [Binary Search](Binary Search/) and [Binary Search Tree](Binary Search Tree/)
-- [Merge Sort](Merge Sort/)
+- [Insertion Sort](Insertion%20Sort/)
+- [Binary Search](Binary%20Search/) and [Binary Search Tree](Binary%20Search%20Tree/)
+- [Merge Sort](Merge%20Sort/)
 - [Boyer-Moore string search](Boyer-Moore/)
 
 ## The algorithms
 
 ### Searching
 
-- [Linear Search](Linear Search/). Find an element in an array.
-- [Binary Search](Binary Search/). Quickly find elements in a sorted array.
-- [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
-- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
-- [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
-- [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
+- [Linear Search](Linear%20Search/). Find an element in an array.
+- [Binary Search](Binary%20Search/). Quickly find elements in a sorted array.
+- [Count Occurrences](Count%20Occurrences/). Count how often a value appears in an array.
+- [Select Minimum / Maximum](Select%20Minimum%20Maximum). Find the minimum/maximum value in an array.
+- [k-th Largest Element](Kth%20Largest%20Element/). Find the *k*-th largest element in an array, such as the median.
+- [Selection Sampling](Selection%20Sampling/). Randomly choose a bunch of items from a collection.
 - [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
 
 
 ### String Search
 
-- [Brute-Force String Search](Brute-Force String Search/). A naive method.
+- [Brute-Force String Search](Brute-Force%20String%20Search/). A naive method.
 - [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
 - Knuth-Morris-Pratt
 - [Rabin-Karp](Rabin-Karp/)  Faster search by using hashing.
-- [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
+- [Longest Common Subsequence](Longest%20Common%20Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
 - [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
 
 ### Sorting
@@ -67,51 +67,51 @@ It's fun to see how sorting algorithms work, but in practice you'll almost never
 
 Basic sorts:
 
-- [Insertion Sort](Insertion Sort/)
-- [Selection Sort](Selection Sort/)
-- [Shell Sort](Shell Sort/)
+- [Insertion Sort](Insertion%20Sort/)
+- [Selection Sort](Selection%20Sort/)
+- [Shell Sort](Shell%20Sort/)
 
 Fast sorts:
 
 - [Quicksort](Quicksort/)
-- [Merge Sort](Merge Sort/)
-- [Heap Sort](Heap Sort/)
+- [Merge Sort](Merge%20Sort/)
+- [Heap Sort](Heap%20Sort/)
 
 Special-purpose sorts:
 
-- [Counting Sort](Counting Sort/)
-- [Radix Sort](Radix Sort/)
-- [Topological Sort](Topological Sort/)
+- [Counting Sort](Counting%20Sort/)
+- [Radix Sort](Radix%20Sort/)
+- [Topological Sort](Topological%20Sort/)
 
 Bad sorting algorithms (don't use these!):
 
-- [Bubble Sort](Bubble Sort/)
-- [Slow Sort](Slow Sort/)
+- [Bubble Sort](Bubble%20Sort/)
+- [Slow Sort](Slow%20Sort/)
 
 ### Compression
 
-- [Run-Length Encoding (RLE)](Run-Length Encoding/). Store repeated values as a single byte and a count.
-- [Huffman Coding](Huffman Coding/). Store more common elements using a smaller number of bits.
+- [Run-Length Encoding (RLE)](Run-Length%20Encoding/). Store repeated values as a single byte and a count.
+- [Huffman Coding](Huffman%20Coding/). Store more common elements using a smaller number of bits.
 
 ### Miscellaneous
 
 - [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
-- [Comb Sort](Comb Sort/). An improve upon the Bubble Sort algorithm.
+- [Comb Sort](Comb%20Sort/). An improve upon the Bubble Sort algorithm.
 
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
 - [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
-- [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
+- [Shunting Yard Algorithm](Shunting%20Yard/). Convert infix expressions to postfix.
 - Statistics
-- [Karatsuba Multiplication](Karatsuba Multiplication/). Another take on elementary multiplication.
+- [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
 
 ### Machine learning
 
 - [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
-- [Linear Regression](Linear Regression/)
+- [Linear Regression](Linear%20Regression/)
 - Logistic Regression
 - Neural Networks
 - PageRank
@@ -129,33 +129,33 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 ### Variations on arrays
 
 - [Array2D](Array2D/). A two-dimensional array with fixed dimensions. Useful for board games.
-- [Bit Set](Bit Set/). A fixed-size sequence of *n* bits.
-- [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
-- [Ordered Array](Ordered Array/). An array that is always sorted.
-- [Rootish Array Stack](Rootish Array Stack/). A space and time efficient variation on Swift arrays.
+- [Bit Set](Bit%20Set/). A fixed-size sequence of *n* bits.
+- [Fixed Size Array](Fixed%20Size%20Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
+- [Ordered Array](Ordered%20Array/). An array that is always sorted.
+- [Rootish Array Stack](Rootish%20Array%20Stack/). A space and time efficient variation on Swift arrays.
 
 ### Queues
 
 - [Stack](Stack/). Last-in, first-out!
 - [Queue](Queue/). First-in, first-out!
 - [Deque](Deque/). A double-ended queue.
-- [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
-- [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
+- [Priority Queue](Priority%20Queue). A queue where the most important element is always at the front.
+- [Ring Buffer](Ring%20Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
 
 ### Lists
 
-- [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
+- [Linked List](Linked%20List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
 - [Skip-List](Skip-List/). Skip List is a probablistic data-structure with same logarithmic time bound and efficiency as AVL/ or Red-Black tree and provides a clever compromise to efficiently support search and update operations.
 
 ### Trees
 
 - [Tree](Tree/). A general-purpose tree structure.
-- [Binary Tree](Binary Tree/). A tree where each node has at most two children.
-- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
+- [Binary Tree](Binary%20Tree/). A tree where each node has at most two children.
+- [Binary Search Tree (BST)](Binary%20Search%20Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - Red-Black Tree
 - Splay Tree
 - Threaded Binary Tree
-- [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
+- [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
@@ -164,33 +164,33 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 ### Hashing
 
-- [Hash Table](Hash Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
+- [Hash Table](Hash%20Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
 - Hash Functions
 
 ### Sets
 
-- [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
-- [Hash Set](Hash Set/). A set implemented using a hash table.
+- [Bloom Filter](Bloom%20Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
+- [Hash Set](Hash%20Set/). A set implemented using a hash table.
 - Multiset
-- [Ordered Set](Ordered Set/). A set where the order of items matters.
+- [Ordered Set](Ordered%20Set/). A set where the order of items matters.
 
 ### Graphs
 
 - [Graph](Graph/)
-- [Breadth-First Search (BFS)](Breadth-First Search/)
-- [Depth-First Search (DFS)](Depth-First Search/)
-- [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
-- [Single-Source Shortest Paths](Single-Source Shortest Paths (Weighted)/)
-- [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
-- [All-Pairs Shortest Paths](All-Pairs Shortest Paths/)
+- [Breadth-First Search (BFS)](Breadth-First%20Search/)
+- [Depth-First Search (DFS)](Depth-First%20Search/)
+- [Shortest Path](Shortest%20Path%20%28Unweighted%29/) on an unweighted tree
+- [Single-Source Shortest Paths](Single-Source%20Shortest%20Paths%20(Weighted)/)
+- [Minimum Spanning Tree](Minimum%20Spanning%20Tree%20%28Unweighted%29/) on an unweighted tree
+- [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 
 ## Puzzles
 
 A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see [here](http://elementsofprogramminginterviews.com/) and [here](http://www.crackingthecodinginterview.com).
 
-- [Two-Sum Problem](Two-Sum Problem/)
-- [Fizz Buzz](Fizz Buzz/)
-- [Monty Hall Problem](Monty Hall Problem/)
+- [Two-Sum Problem](Two-Sum%20Problem/)
+- [Fizz Buzz](Fizz%20Buzz/)
+- [Monty Hall Problem](Monty%20Hall%20Problem/)
 - [Finding Palindromes](Palindromes/)
 - [Dining Philosophers](DiningPhilosophers/)
 

From 943ad7e48fe966f7679c4addfafa7baa5fb81fb2 Mon Sep 17 00:00:00 2001
From: kyungkoo <mc2e.dev@gmail.com>
Date: Fri, 24 Mar 2017 18:25:24 +0900
Subject: [PATCH 0866/1679] fixed important links section link

---
 README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/README.markdown b/README.markdown
index fc034f71b..023f151fb 100644
--- a/README.markdown
+++ b/README.markdown
@@ -16,17 +16,17 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 ## Important links
 
-[What are algorithms and data structures?](What are Algorithms.markdown) Pancakes!
+[What are algorithms and data structures?](What%20are%20Algorithms.markdown) Pancakes!
 
-[Why learn algorithms?](Why Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
+[Why learn algorithms?](Why%20Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
 
-[Big-O notation](Big-O Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
+[Big-O notation](Big-O%20Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
 
-[Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
+[Algorithm design techniques](Algorithm%20Design.markdown). How do you create your own algorithms?
 
-[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
+[How to contribute](How%20to%20Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
 
-[Under construction](Under Construction.markdown). Algorithms that are under construction.
+[Under construction](Under%20Construction.markdown). Algorithms that are under construction.
 
 ## Where to start?
 

From a54e722b035ffc5eeba63fcd5b1648e56f732ec0 Mon Sep 17 00:00:00 2001
From: Jake Romer <jkrmr.io@gmail.com>
Date: Fri, 24 Mar 2017 07:58:19 -0700
Subject: [PATCH 0867/1679] Fix links to related articles

Fixes links to Linked List, Ring Buffer, and Priority Queue directories.
---
 Queue/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Queue/README.markdown b/Queue/README.markdown
index f8259c31c..9efce66b9 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -255,8 +255,8 @@ The `nil` objects at the front have been removed and the array is no longer wast
 
 ## See also
 
-There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or a [heap](../Heap/). 
+There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or a [heap](../Heap/). 
 
-Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority Queue/), a sorted queue where the "most important" item is always at the front.
+Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority%20Queue/), a sorted queue where the "most important" item is always at the front.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 3d033740b0d3b727d488a14121da68f822b578a2 Mon Sep 17 00:00:00 2001
From: Jake Romer <jkrmr.io@gmail.com>
Date: Sat, 25 Mar 2017 07:47:49 -0700
Subject: [PATCH 0868/1679] URL encode links in Markdown files

There are a ton of broken markdown links in the READMEs throughout this
repo because the files and directories they refer to have spaces in
their names but these aren't HTML encoded in their links. This commit
just replaces spaces with %20 to fix these.
---
 AVL Tree/README.markdown                   |  8 ++++----
 Big-O Notation.markdown                    |  2 +-
 Binary Search Tree/README.markdown         | 10 +++++-----
 Binary Search/README.markdown              |  2 +-
 Binary Tree/README.markdown                |  2 +-
 Bloom Filter/README.markdown               |  2 +-
 Bounded Priority Queue/README.markdown     |  2 +-
 Boyer-Moore/README.markdown                |  2 +-
 Breadth-First Search/README.markdown       |  4 ++--
 Count Occurrences/README.markdown          |  4 ++--
 Hash Set/README.markdown                   |  2 +-
 How to Contribute.markdown                 |  2 +-
 Ordered Array/README.markdown              |  2 +-
 Ordered Set/README.markdown                |  2 +-
 Selection Sort/README.markdown             |  6 +++---
 Shell Sort/README.markdown                 |  2 +-
 Shortest Path (Unweighted)/README.markdown |  8 ++++----
 Threaded Binary Tree/README.markdown       | 10 +++++-----
 Topological Sort/README.markdown           |  2 +-
 Tree/README.markdown                       |  4 ++--
 Under Construction.markdown                | 20 ++++++++++----------
 21 files changed, 49 insertions(+), 49 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 355204587..a9218203a 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -1,6 +1,6 @@
 # AVL Tree
 
-An AVL tree is a self-balancing form of a [binary search tree](../Binary Search Tree/), in which the height of subtrees differ at most by only 1.
+An AVL tree is a self-balancing form of a [binary search tree](../Binary%20Search%20Tree/), in which the height of subtrees differ at most by only 1.
 
 A binary tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. That is what makes searching the tree really fast. But if a binary search tree is unbalanced, searching can become really slow.
 
@@ -8,7 +8,7 @@ This is an example of an unbalanced tree:
 
 ![Unbalanced tree](Images/Unbalanced.png)
 
-All the children are in the left branch and none are in the right. This is essentially the same as a [linked list](../Linked List/). As a result, searching takes **O(n)** time instead of the much faster **O(log n)** that you'd expect from a binary search tree.
+All the children are in the left branch and none are in the right. This is essentially the same as a [linked list](../Linked%20List/). As a result, searching takes **O(n)** time instead of the much faster **O(log n)** that you'd expect from a binary search tree.
 
 A balanced version of that tree would look like this:
 
@@ -78,7 +78,7 @@ Insertion never needs more than 2 rotations. Removal might require up to __log(n
 
 Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
 
-> **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary Search Tree/). It will make the rest of the AVL tree easier to understand.
+> **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary%20Search%20Tree/). It will make the rest of the AVL tree easier to understand.
 
 The interesting bits are in the `balance()` method which is called after inserting or deleting a node.
 
@@ -86,6 +86,6 @@ The interesting bits are in the `balance()` method which is called after inserti
 
 [AVL tree on Wikipedia](https://en.wikipedia.org/wiki/AVL_tree)
 
-AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black Tree/) seems to be more popular.
+AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black%20Tree/) seems to be more popular.
 
 *Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*
diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 8cb988168..09fbb04aa 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -19,6 +19,6 @@ Big-O | Name | Description
 
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
 
-Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!
+Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!
 
 If you find this confusing, don't let this Big-O stuff bother you too much. It's mostly useful when comparing two algorithms to figure out which one is better. But in the end you still want to test in practice which one really is the best. And if the amount of data is relatively small, then even a slow algorithm will be fast enough for practical use.
diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index bd2a00c9e..a3a84c03d 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -1,6 +1,6 @@
 # Binary Search Tree (BST)
 
-A binary search tree is a special kind of [binary tree](../Binary Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
+A binary search tree is a special kind of [binary tree](../Binary%20Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
 
 If you don't know what a tree is or what it is for, then [read this first](../Tree/).
 
@@ -49,7 +49,7 @@ If we were looking for the value `5` in the example, it would go as follows:
 
 ![Searching the tree](Images/Searching.png)
 
-Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary Search) in an array.)
+Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary%20Search) in an array.)
 
 ## Traversing the tree
 
@@ -535,7 +535,7 @@ The code for `successor()` works the exact same way but mirrored:
 
 Both these methods run in **O(h)** time.
 
-> **Note:** There is a cool variation called a ["threaded" binary tree](../Threaded Binary Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
+> **Note:** There is a cool variation called a ["threaded" binary tree](../Threaded%20Binary%20Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
 
 ### Is the search tree valid?
 
@@ -713,11 +713,11 @@ The root node is in the middle; a dot means there is no child at that position.
 
 A binary search tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That's the ideal situation.
 
-However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
+However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked%20List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
 
 One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree quite nicely. But it doesn't guarantee success, nor is it always practical.
 
-The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. See [AVL tree](../AVL Tree) and [red-black tree](../Red-Black Tree) for examples.
+The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. See [AVL tree](../AVL%20Tree) and [red-black tree](../Red-Black%20Tree) for examples.
 
 ## See also
 
diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index c65d0b5fd..09b141e04 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -12,7 +12,7 @@ let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 4
 numbers.indexOf(43)  // returns 15
 ```
 
-The built-in `indexOf()` function performs a [linear search](../Linear Search/). In code that looks something like this:
+The built-in `indexOf()` function performs a [linear search](../Linear%20Search/). In code that looks something like this:
 
 ```swift
 func linearSearch<T: Equatable>(_ a: [T], _ key: T) -> Int? {
diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 896116dda..8ce398804 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -8,7 +8,7 @@ The child nodes are usually called the *left* child and the *right* child. If a
 
 Often nodes will have a link back to their parent but this is not strictly necessary.
 
-Binary trees are often used as [binary search trees](../Binary Search Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
+Binary trees are often used as [binary search trees](../Binary%20Search%20Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
 
 For example, here is a binary tree that represents a sequence of arithmetical operations, `(5 * (a - 10)) + (-4 * (3 / b))`:
 
diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index a85d71be4..3fff0a379 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -18,7 +18,7 @@ An advantage of the Bloom Filter over a hash table is that the former maintains
 
 ## Inserting objects into the set
 
-A Bloom Filter is essentially a fixed-length [bit vector](../Bit Set/), an array of bits. When we insert objects, we set some of these bits to `1`, and when we query for objects we check if certain bits are `0` or `1`. Both operations use hash functions.
+A Bloom Filter is essentially a fixed-length [bit vector](../Bit%20Set/), an array of bits. When we insert objects, we set some of these bits to `1`, and when we query for objects we check if certain bits are `0` or `1`. Both operations use hash functions.
 
 To insert an element in the filter, the element is hashed with several different hash functions. Each hash function returns a value that we map to an index in the array. We then set the bits at these indices to `1` or true.
 
diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
index 8d47adefb..4e4c89272 100644
--- a/Bounded Priority Queue/README.markdown	
+++ b/Bounded Priority Queue/README.markdown	
@@ -1,6 +1,6 @@
 # Bounded Priority queue
 
-A bounded priority queue is similar to a regular [priority queue](../Priority Queue/), except that there is a fixed upper bound on the number of elements that can be stored. When a new element is added to the queue while the queue is at capacity, the element with the highest priority value is ejected from the queue.
+A bounded priority queue is similar to a regular [priority queue](../Priority%20Queue/), except that there is a fixed upper bound on the number of elements that can be stored. When a new element is added to the queue while the queue is at capacity, the element with the highest priority value is ejected from the queue.
 
 ## Example
 
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index e821b812e..5b3841eca 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -24,7 +24,7 @@ animals.indexOf(pattern: "🐮")
 
 > **Note:** The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
 
-The [brute-force approach](../Brute-Force String Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at _every_ character from the source string -- you can often skip ahead multiple characters.
+The [brute-force approach](../Brute-Force%20String%20Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at _every_ character from the source string -- you can often skip ahead multiple characters.
 
 The skip-ahead algorithm is called [Boyer-Moore](https://en.wikipedia.org/wiki/Boyer–Moore_string_search_algorithm) and it has been around for a long time. It is considered the benchmark for all string search algorithms.
 
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 084f4611a..2ef92fd73 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -148,7 +148,7 @@ This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
 
 Breadth-first search can be used to solve many problems. A small selection:
 
-* Computing the [shortest path](../Shortest Path/) between a source node and each of the other nodes (only for unweighted graphs).
-* Calculating the [minimum spanning tree](../Minimum Spanning Tree (Unweighted)/) on an unweighted graph.
+* Computing the [shortest path](../Shortest%20Path/) between a source node and each of the other nodes (only for unweighted graphs).
+* Calculating the [minimum spanning tree](../Minimum%20Spanning%20Tree%20(Unweighted)/) on an unweighted graph.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 90a9ec2f3..4c65c4219 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -2,9 +2,9 @@
 
 Goal: Count how often a certain value appears in an array.
 
-The obvious way to do this is with a [linear search](../Linear Search/) from the beginning of the array until the end, keeping count of how often you come across the value. That is an **O(n)** algorithm.
+The obvious way to do this is with a [linear search](../Linear%20Search/) from the beginning of the array until the end, keeping count of how often you come across the value. That is an **O(n)** algorithm.
 
-However, if the array is sorted you can do it much faster, in **O(log n)** time, by using a modification of [binary search](../Binary Search/).
+However, if the array is sorted you can do it much faster, in **O(log n)** time, by using a modification of [binary search](../Binary%20Search/).
 
 Let's say we have the following array:
 
diff --git a/Hash Set/README.markdown b/Hash Set/README.markdown
index 368920a1c..fb829c313 100644
--- a/Hash Set/README.markdown	
+++ b/Hash Set/README.markdown	
@@ -196,7 +196,7 @@ difference2.allElements()                // [5, 6]
 
 If you look at the [documentation](http://swiftdoc.org/v2.1/type/Set/) for Swift's own `Set`, you'll notice it has tons more functionality. An obvious extension would be to make `HashSet` conform to `SequenceType` so that you can iterate it with a `for`...`in` loop.
 
-Another thing you could do is replace the `Dictionary` with an actual [hash table](../Hash Table), but one that just stores the keys and doesn't associate them with anything. So you wouldn't need the `Bool` values anymore.
+Another thing you could do is replace the `Dictionary` with an actual [hash table](../Hash%20Table), but one that just stores the keys and doesn't associate them with anything. So you wouldn't need the `Bool` values anymore.
 
 If you often need to look up whether an element belongs to a set and perform unions, then the [union-find](../Union-Find/) data structure may be more suitable. It uses a tree structure instead of a dictionary to make the find and union operations very efficient.
 
diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 258357e8b..1235f07ff 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -6,7 +6,7 @@ Want to help out with the Swift Algorithm Club? Great!
 
 Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
 
-Algorithms in the [Under construction](Under Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
+Algorithms in the [Under construction](Under%20Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
 
 New algorithms and data structures are always welcome (even if they aren't on the list).
 
diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index ca088c325..974a42cae 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -83,7 +83,7 @@ a              // [-2, -1, 1, 3, 4, 5, 7, 9, 10]
 
 The array's contents will always be sorted from low to high, now matter what.
 
-Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array. We can speed this up by using a [binary search](../Binary Search) to find the insertion point.
+Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array. We can speed this up by using a [binary search](../Binary%20Search) to find the insertion point.
 
 Here is the new version:
 
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 0525a31ed..1c0d5a8ac 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -115,7 +115,7 @@ The next function is `indexOf()`, which takes in an object of type `T` and retur
   }
 ```
 
-> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary Search).
+> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary%20Search).
 
 However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item.
 
diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index c583b47ea..e95749d14 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -6,7 +6,7 @@ You are given an array of numbers and need to put them in the right order. The s
 
 	[ ...sorted numbers... | ...unsorted numbers... ]
 
-This is similar to [insertion sort](../Insertion Sort/), but the difference is in how new numbers are added to the sorted portion.
+This is similar to [insertion sort](../Insertion%20Sort/), but the difference is in how new numbers are added to the sorted portion.
 
 It works as follows:
 
@@ -108,9 +108,9 @@ The source file [SelectionSort.swift](SelectionSort.swift) has a version of this
 
 ## Performance
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
 
-[Heap sort](../Heap Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
+[Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
 
 ## See also
 
diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index 9c4bdf076..c21c29685 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -39,7 +39,7 @@ As you can see, each sublist contains only every 4th item from the original arra
 
 We now call `insertionSort()` once on each sublist.
 
-This particular version of [insertion sort](../Insertion Sort/) sorts from the back to the front. Each item in the sublist is compared against the others. If they're in the wrong order, the value is swapped and travels all the way down until we reach the start of the sublist.
+This particular version of [insertion sort](../Insertion%20Sort/) sorts from the back to the front. Each item in the sublist is compared against the others. If they're in the wrong order, the value is swapped and travels all the way down until we reach the start of the sublist.
 
 So for sublist 0, we swap `4` with `72`, then swap `4` with `64`. After sorting, this sublist looks like:
 
diff --git a/Shortest Path (Unweighted)/README.markdown b/Shortest Path (Unweighted)/README.markdown
index a16519260..4c3c34d9c 100644
--- a/Shortest Path (Unweighted)/README.markdown	
+++ b/Shortest Path (Unweighted)/README.markdown	
@@ -12,11 +12,11 @@ If the [graph is unweighed](../Graph/), then finding the shortest path is easy:
 
 ## Unweighted graph: breadth-first search
 
-[Breadth-first search](../Breadth-First Search/) is a method for traversing a tree or graph data structure. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors. As a convenient side effect, it automatically computes the shortest path between a source node and each of the other nodes in the tree or graph.
+[Breadth-first search](../Breadth-First%20Search/) is a method for traversing a tree or graph data structure. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors. As a convenient side effect, it automatically computes the shortest path between a source node and each of the other nodes in the tree or graph.
 
 The result of the breadth-first search can be represented with a tree:
 
-![The BFS tree](../Breadth-First Search/Images/TraversalTree.png)
+![The BFS tree](../Breadth-First%20Search/Images/TraversalTree.png)
 
 The root of the tree is the node you started the breadth-first search from. To find the distance from node `A` to any other node, we simply count the number of edges in the tree. And so we find that the shortest path between `A` and `F` is 2. The tree not only tells you how long that path is, but also how to actually get from `A` to `F` (or any of the other nodes).
 
@@ -57,7 +57,7 @@ queue.enqueue(element: G)
 G.distance = C.distance + 1   // result: 2
 ```
 
-This continues until the queue is empty and we've visited all the nodes. Each time we discover a new node, it gets the `distance` of its parent plus 1. As you can see, this is exactly what the [breadth-first search](../Breadth-First Search/) algorithm does, except that we now also keep track of the distance travelled.
+This continues until the queue is empty and we've visited all the nodes. Each time we discover a new node, it gets the `distance` of its parent plus 1. As you can see, this is exactly what the [breadth-first search](../Breadth-First%20Search/) algorithm does, except that we now also keep track of the distance travelled.
 
 Here's the code:
 
@@ -97,6 +97,6 @@ This will output:
 	Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
 	Node(label: g, distance: 2), Node(label: h, distance: 3)
 
-> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum Spanning Tree (Unweighted)/) on how you can convert the graph into a tree by removing edges.
+> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum%20Spanning%20Tree%20(Unweighted)/) on how you can convert the graph into a tree by removing edges.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index fd05113d8..8a1c518f1 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -1,6 +1,6 @@
 # Threaded Binary Tree
 
-A threaded binary tree is a special kind of [binary tree](../Binary Tree/) (a
+A threaded binary tree is a special kind of [binary tree](../Binary%20Tree/) (a
 tree in which each node has at most two children) that maintains a few extra
 variables to allow cheap and fast **in-order traversal** of the tree.  We will
 explore the general structure of threaded binary trees, as well as
@@ -17,7 +17,7 @@ The main motivation behind using a threaded binary tree over a simpler and
 smaller standard binary tree is to increase the speed of an in-order traversal
 of the tree.  An in-order traversal of a binary tree visits the nodes in the
 order in which they are stored, which matches the underlying ordering of a
-[binary search tree](../Binary Search Tree/).  This means most threaded binary
+[binary search tree](../Binary%20Search%20Tree/).  This means most threaded binary
 trees are also binary search trees.  The idea is to visit all the left children
 of a node first, then visit the node itself, and then visit the right children
 last.
@@ -47,7 +47,7 @@ tree, to **O(n)** to a very unbalanced tree.
 
 A threaded binary tree fixes this problem.
 
-> For more information about in-order traversals [see here](../Binary Tree/).
+> For more information about in-order traversals [see here](../Binary%20Tree/).
 
 
 ## Predecessors and successors
@@ -222,7 +222,7 @@ walking through some boring code, it is best to explain this with an example
 (although you can read through [the implementation](ThreadedBinaryTree.swift)
 if you want to know the finer details).  Please note that this requires
 knowledge of binary search trees, so make sure you have
-[read this first](../Binary Search Tree/).
+[read this first](../Binary%20Search%20Tree/).
 
 > Note: we do allow duplicate nodes in this implementation of a threaded binary
 > tree.  We break ties by defaulting insertion to the right.
@@ -339,7 +339,7 @@ such as `searching()` for a node in the tree, finding the `depth()` or
 `height()` of a node, etc.  You can check
 [the implementation](ThreadedBinaryTree.swift) for the full technical details.
 Many of these methods are inherent to binary search trees as well, so you can
-find [further documentation here](../Binary Search Tree/).
+find [further documentation here](../Binary%20Search%20Tree/).
 
 
 ## See also
diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index 4429a0754..5659dc3fd 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -22,7 +22,7 @@ The following is not a valid topological sort for this graph, since **X** and **
 
 Let's consider that you want to learn all the algorithms and data structures from the Swift Algorithm Club. This might seem daunting at first but we can use topological sort to get things organized.
 
-Since you're learning about topological sort, let's take this topic as an example. What else do you need to learn first before you can fully understand topological sort? Well, topological sort uses [depth-first search](../Depth-First Search/) as well as a [stack](../Stack/). But before you can learn about the depth-first search algorithm, you need to know what a [graph](../Graph/) is, and it helps to know what a [tree](../Tree/) is. In turn, graphs and trees use the idea of linking objects together, so you may need to read up on that first. And so on...
+Since you're learning about topological sort, let's take this topic as an example. What else do you need to learn first before you can fully understand topological sort? Well, topological sort uses [depth-first search](../Depth-First%20Search/) as well as a [stack](../Stack/). But before you can learn about the depth-first search algorithm, you need to know what a [graph](../Graph/) is, and it helps to know what a [tree](../Tree/) is. In turn, graphs and trees use the idea of linking objects together, so you may need to read up on that first. And so on...
 
 If we were to represent these objectives in the form of a graph it would look as follows:
 
diff --git a/Tree/README.markdown b/Tree/README.markdown
index 529a68cf1..440d9c9a4 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -16,7 +16,7 @@ The pointers in a tree do not form cycles. This is not a tree:
 
 ![Not a tree](Images/Cycles.png)
 
-Such a structure is called a [graph](../Graph/). A tree is really a very simple form of a graph. (In a similar vein, a [linked list](../Linked List/) is a simple version of a tree. Think about it!)
+Such a structure is called a [graph](../Graph/). A tree is really a very simple form of a graph. (In a similar vein, a [linked list](../Linked%20List/) is a simple version of a tree. Think about it!)
 
 This article talks about a general-purpose tree. That's a tree without any kind of restrictions on how many children each node may have, or on the order of the nodes in the tree.
 
@@ -119,7 +119,7 @@ We often use the following definitions when talking about trees:
 
 - **Depth of a node.** The number of links between this node and the root node. For example, the depth of `tea` is 2 because it takes two jumps to reach the root. (The root itself has depth 0.)
 
-There are many different ways to construct trees. For example, sometimes you don't need to have a `parent` property at all. Or maybe you only need to give each node a maximum of two children -- such a tree is called a [binary tree](../Binary Tree/). A very common type of tree is the [binary search tree](../Binary Search Tree/) (or BST), a stricter version of a binary tree where the nodes are ordered in a particular way to speed up searches.
+There are many different ways to construct trees. For example, sometimes you don't need to have a `parent` property at all. Or maybe you only need to give each node a maximum of two children -- such a tree is called a [binary tree](../Binary%20Tree/). A very common type of tree is the [binary search tree](../Binary%20Search%20Tree/) (or BST), a stricter version of a binary tree where the nodes are ordered in a particular way to speed up searches.
 
 The general purpose tree I've shown here is great for describing hierarchical data, but it really depends on your application what kind of extra functionality it needs to have.
 
diff --git a/Under Construction.markdown b/Under Construction.markdown
index 0c59d90c1..be53e01b0 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -5,27 +5,27 @@ Here you'll find algorithms that are currently under construction. Suggestions a
 ### Sorting
 
 Special-purpose sorts:
- - [Radix Sort](Radix Sort/)
+ - [Radix Sort](Radix%20Sort/)
 
 ### Special-purpose sorts:
 
-- [Bucket Sort](Bucket Sort/)
+- [Bucket Sort](Bucket%20Sort/)
 
 ### Queues
 
-- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements.
+- [Bounded Priority Queue](Bounded%20Priority%20Queue). A queue that is bounded to have a limited number of elements.
 
 ### Trees
 
-- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
-- [Red-Black Tree](Red-Black Tree/)
-- [Threaded Binary Tree](Threaded Binary Tree/)
-- [Ternary Search Tree](Ternary Search Tree/)
+- [AVL Tree](AVL%20Tree/). A binary search tree that balances itself using rotations.
+- [Red-Black Tree](Red-Black%20Tree/)
+- [Threaded Binary Tree](Threaded%20Binary%20Tree/)
+- [Ternary Search Tree](Ternary%20Search%20Tree/)
 - [Trie](Trie/)
-- [Radix Tree](Radix Tree/)
+- [Radix Tree](Radix%20Tree/)
 
 ### Miscellaneous
 
-- [Minimum Edit Distance](Minimum Edit Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
+- [Minimum Edit Distance](Minimum%20Edit%20Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
 - [Treap](Treap/)
-- [Set Cover (Unweighted)](Set Cover (Unweighted)/)
+- [Set Cover (Unweighted)](Set%20Cover%20(Unweighted)/)

From bd35ff8f1bb984bf5cf5eeb8375539dfcdd248ad Mon Sep 17 00:00:00 2001
From: Hunter Maximillion Monk <hunter.monk@gmail.com>
Date: Sat, 25 Mar 2017 21:57:12 -0500
Subject: [PATCH 0869/1679] Fix binary search tree link

Just need to convert spaces into %20 for relative URLs
with spaces to work.
---
 Binary Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 896116dda..8ce398804 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -8,7 +8,7 @@ The child nodes are usually called the *left* child and the *right* child. If a
 
 Often nodes will have a link back to their parent but this is not strictly necessary.
 
-Binary trees are often used as [binary search trees](../Binary Search Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
+Binary trees are often used as [binary search trees](../Binary%20Search%20Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
 
 For example, here is a binary tree that represents a sequence of arithmetical operations, `(5 * (a - 10)) + (-4 * (3 / b))`:
 

From eb68b1d69836d3d2d1bb1cba269466a94f837aea Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 15:38:26 -0700
Subject: [PATCH 0870/1679] updated readme

---
 .../README.markdown                           | 459 +++++++++++++++++-
 .../Contents.swift                            |   2 +
 .../Sources/Matrix.swift                      | 180 ++++---
 .../Sources/MatrixSize.swift                  |  19 +-
 .../Sources/Number.swift                      |  12 +-
 5 files changed, 571 insertions(+), 101 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index d07004bad..e4222b4f4 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -1 +1,458 @@
-## TODO: Examples & Explanation
+# Strassen Matrix Multiplication
+
+## Goal
++ To quickly perform a matrix multiplication operation on two matricies
+
+## What is Matrix Multiplication??
+
+> Note: If you are already familiar with Linear Algebra/Matrix Multiplication, feel free to skip this section
+
+Before we begin, you may ask what is matrix multiplication? Great question! It is **NOT** multiplying two matricies term-by-term. Matrix multiplication is a mathematical operation that combines two matricies into a single one. Sounds like multiplying term-by-term huh? It's not... our lives would be much easier if it were. To see how matrix multiplcation works, let's look at an example.
+
+### Example: Matrix Multiplication
+
+	matrix A = |1 2|
+	           |3 4|
+				 
+	matrix B = |5 6|
+	           |7 8|
+	
+	A * B = C
+	
+	|1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
+	|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+	
+What's going on here? To start, we're multiplying matricies A & B. Our new matrix, C's, elements `[i, j]` are determined by the dot product of the first matrix's ith row and the second matrix's jth column. See [here](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length) for a refresher on the dot product.
+
+So the upper left element `[i=1, j=1]` of our new matrix is a combination of A's 1st row and B's 1st column.
+
+	A's first row = [1, 2]
+	B's first column = [5, 7]
+
+	[1, 2] dot [5, 7] = [1*5 + 2*7] = [19] = C[1, 1]
+
+Now let's try this for `[i=1, j=2]`. Because `i=1` and `j=2`, this will represent the upper right element in our new matrix, C.
+
+	A's first row = [1, 2]
+	B's second column = [6, 8]
+	
+	[1, 2] dot [6, 8] = [1*6 + 2*8] = [22] = C[1, 2]
+
+If we do this for each row & column of A & B we'll get our result matrix C!
+
+Here's a great graphic that visually shows you what's going on.
+
+![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Matrix_multiplication_principle.svg/1024px-Matrix_multiplication_principle.svg.png)
+
+[Source](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Matrix_multiplication_principle.svg/1024px-Matrix_multiplication_principle.svg.png)
+
+
+## Matix Multiplication Algorithm
+
+So how do we implement matrix multiplication in an algoirthm? We'll start with the basic version and from there move on to Strassen's Algorithm.
+
++ [Basic Version](#basic-version)
++ [Strassen's Algorithm](#strassens-algorithm)
+
+### Basic Version
+
+Remember the method we used to solve matrix multiplication [above](#what-is-matrix-multiplication??)? Let's try to implement that first! We first assert that the two matricies are the right size. 
+
+`assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")`
+
+> **NOTE:** A's # of columns HAS to equal B's # of rows for matrix multiplication to work
+
+Next, we loop over A's columns and B's rows. Because we know both A's columns & B's rows are the same length, we set that length equal to `n`.
+
+```swift
+for i in 0..<n {
+	for j in 0..<n {
+```
+
+Then, for each row in A and column in B, we take the dot product of the ith row in A with the jth column in B and set that result equal to the `[i, j]` element in C. Or `C[i, j]`.
+
+```swift
+for k in 0..<n {
+	C[i, j] = A[i, k] * B[k, j]
+}
+```
+
+Finally, we return our new matrix C!
+
+Here's the full implementation:
+
+```swift
+public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+	let A = self
+	assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+	let n = A.columns
+	var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+	for i in 0..<n {
+		for j in 0..<n {
+			for k in 0..<n {
+				C[i, j] = A[i, k] * B[k, j]
+			}
+		}
+	}
+    
+	return C
+}
+```
+
+This algorithm has a runtime of **O(n^3)**. The **O(n^3)** comes from the three `for` loops. Two from the loop over the rows & columns and one from the dot product!
+
+Now, **O(n^3)** is not very fast and a great question we should ask is can we do better? Indeed we can!
+
+### Strassens Algorithm
+
+Volker Strassen first published his algorithm in 1969. It was the first algorithm to prove that the basic **O(n^3)** runtime was not optiomal. 
+
+The basic idea behind Strassen's algorithm is to split A & B into 8 submatricies and then recursively compute the submatricies of C. This strategy is called *Divide and Conquer*.
+
+	matrix A = |a b|
+	  		   |c d|
+	matrix B = |e f|
+			   |g h|
+
+*There will be 8 recursive calls:*
+
+1. a * e
+2. b * g
+3. a * f 
+4. b * h
+5. c * e
+6. d * g 
+7. c * f 
+8. d * h
+
+We then use these results to compute C's submatricies.
+
+	matrix C = |ae+bg af+bh|
+			   |ce+dg cf+dh| 
+
+![http://d1hyf4ir1gqw6c.cloudfront.net//wp-content/uploads/strassen_new.png](http://d1hyf4ir1gqw6c.cloudfront.net//wp-content/uploads/strassen_new.png)
+
+This step alone, however, doesn't help our runtime at all. Using the [Master Theorem](https://en.wikipedia.org/wiki/Master_theorem) with `T(n) = 8T(n/2) + O(n^2)` we still get a runtime of `O(n^3)`.
+
+Strassen's insight was that we don't actually need **8** recursive calls to complete this process. We can finish the call with **7** recursive calls and a little bit of addition and subtraction.
+
+Strassen's **7** calls are as follows:
+
+1. a * (f - h)
+2. (a + b) * h
+3. (c + d) * e
+4. d * (g - e)
+5. (a + d) * (e + h)
+6. (b - d) * (g + h)
+7. (a - c) * (e + f)
+
+Now we can compute our new matrix C's new quardents!
+
+	matrix C = |p5+p4-p2+p6    p1+p2   |
+			   |   p3+p4    p1+p5-p3-p7|    
+
+
+A great reaction right now would be !!??!?!?!!?! How does this even work??
+
+Let's prove it!
+
+**First** Submatrix:
+
+	p5+p4-p2+p6 = (a+d)*(e+h) + d*(g-e) - (a+b)*h + (b-d)*(g+h)
+				= (ae+de+ah+dh) + (dg-de) - (ah+bh) + (bg-dg+bh-dh)
+				= ae+bg ✅
+				
+Exactly what we got the first time!
+
+Now let's prove the others.
+
+**Second** submatrix:
+
+	p1+p2 = a*(f-h) + (a+b)*h
+		  = (af-ah) + (ah+bh)
+		  = af+bh ✅
+		  
+**Third** submatrix:
+
+	p3+p4 = (c+d)*e + d*(g-e)
+		  = (ce+de) + (dg-de)
+		  = ce+dg ✅
+
+**Fourth** submatrix: 
+
+	p1+p5-p3-p7 = a*(f-h) + (a+d)*(e+h) - (c+d)*e - (a-c)*(e+f)
+				= (af-ah) + (ae+de+ah+dh) -(ce+de) - (ae-ce+af-cf)
+				= cf+dh ✅
+
+Great! The math checks out!
+
+Here's the process in action.
+
+![](http://d1hyf4ir1gqw6c.cloudfront.net//wp-content/uploads/stressen_formula_new_new.png)
+
+[Source](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
+
+#### Implementation
+
+Ok so now to the implementation. We'll start with the same first step from the basic implementation. We need to assert that A's # of columns are equal to B's number of rows.
+
+	assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+	
+Now time for some prep work! We make each matrix a square and increase it's size to the next power of two. This ensures makes Strassen's Algorithm much easier to manage. We now only need to deal with square matricies that can be broken up an even number of times!
+
+```swift
+let n = max(A.rows, A.columns, B.rows, B.columns)
+let m = nextPowerOfTwo(after: n)
+    
+var APrep = Matrix(size: m)
+var BPrep = Matrix(size: m)
+   
+for i in A.rows {
+	for j in A.columns {
+		APrep[i, j] = A[i,j]
+	}
+}
+
+for i in B.rows {
+	for j in B.columns {
+		BPrep[i, j] = B[i, j]
+	}
+}
+```
+
+Finally, we recusrisvely compute the matrix using Strassen's algorithm and the transform our new matrix `C` back to the correct dimensions!
+
+```swift
+let CPrep = APrep.strassenR(by: BPrep)
+var C = Matrix(rows: A.rows, columns: B.columns)
+    
+for i in 0..<A.rows {
+	for j in 0..<B.columns {
+		C[i,j] = CPrep[i,j]
+	}
+}
+```
+
+#### Recursively Computing the Matrix Multiplication
+
+Next let's explore this recursive function `strassenR`.
+
+We start by initializing 8 submatricies.
+
+```swift
+var a = Matrix(size: nBy2)
+var b = Matrix(size: nBy2)
+var c = Matrix(size: nBy2)
+var d = Matrix(size: nBy2)
+var e = Matrix(size: nBy2)
+var f = Matrix(size: nBy2)
+var g = Matrix(size: nBy2)
+var h = Matrix(size: nBy2)
+    
+for i in 0..<nBy2 {
+	for j in 0..<nBy2 {
+		a[i,j] = A[i,j]
+       b[i,j] = A[i, j+nBy2]
+       c[i,j] = A[i+nBy2, j]
+       d[i,j] = A[i+nBy2, j+nBy2]
+       e[i,j] = B[i,j]
+       f[i,j] = B[i, j+nBy2]
+       g[i,j] = B[i+nBy2, j]
+       h[i,j] = B[i+nBy2, j+nBy2]
+	}
+}
+```
+
+We next recursively compute the 7 matrix multiplications.
+
+```swift
+let p1 = a.strassenR(by: f-h)       // a * (f - h)
+let p2 = (a+b).strassenR(by: h)     // (a + b) * h
+let p3 = (c+d).strassenR(by: e)     // (c + d) * e
+let p4 = d.strassenR(by: g-e)       // d * (g - e)
+let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
+let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
+let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
+```
+
+Next, we compute the submatricies of C.
+
+```swift
+let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
+let c12 = p1 + p2                   // p1 + p2
+let c21 = p3 + p4                   // p3 + p4
+let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
+```
+
+And finally, we combine these submatricies into our new matrix C!
+
+```swift
+var C = Matrix(size: n)    
+for i in 0..<nBy2 {
+	for j in 0..<nBy2 {
+		C[i, j]           = c11[i,j]
+		C[i, j+nBy2]      = c12[i,j]
+		C[i+nBy2, j]      = c21[i,j]
+		C[i+nBy2, j+nBy2] = c22[i,j]
+	}
+}
+```
+
+As before, we can analyze the time completxity using the [Master Theorem](https://en.wikipedia.org/wiki/Master_theorem). `T(n) = 7T(n/2) +  O(n^2)` which leads to `O(n^log(7))` runtime. This comes out to approxiamtely `O(n^2.8074)` which is better than `O(n^3)`!
+
+And that's Strassen's algorithm! Here's the full implementation:
+
+```swift
+// MARK: - Strassen Multiplication
+
+extension Matrix {
+  public func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(after: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
+    guard A.rows > 1 && B.rows > 1 else { return A * B }
+    
+    let n    = A.rows
+    let nBy2 = n / 2
+    
+    /*
+    Assume submatricies are allocated as follows
+    
+     matrix A = |a b|,    matrix B = |e f|
+                |c d|                |g h|
+    */
+    
+    var a = Matrix(size: nBy2)
+    var b = Matrix(size: nBy2)
+    var c = Matrix(size: nBy2)
+    var d = Matrix(size: nBy2)
+    var e = Matrix(size: nBy2)
+    var f = Matrix(size: nBy2)
+    var g = Matrix(size: nBy2)
+    var h = Matrix(size: nBy2)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        a[i,j] = A[i,j]
+        b[i,j] = A[i, j+nBy2]
+        c[i,j] = A[i+nBy2, j]
+        d[i,j] = A[i+nBy2, j+nBy2]
+        e[i,j] = B[i,j]
+        f[i,j] = B[i, j+nBy2]
+        g[i,j] = B[i+nBy2, j]
+        h[i,j] = B[i+nBy2, j+nBy2]
+      }
+    }
+    
+    let p1 = a.strassenR(by: f-h)       // a * (f - h)
+    let p2 = (a+b).strassenR(by: h)     // (a + b) * h
+    let p3 = (c+d).strassenR(by: e)     // (c + d) * e
+    let p4 = d.strassenR(by: g-e)       // d * (g - e)
+    let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
+    let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
+    let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
+    
+    let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
+    let c12 = p1 + p2                   // p1 + p2
+    let c21 = p3 + p4                   // p3 + p4
+    let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
+    
+    var C = Matrix(size: n)
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        C[i, j]           = c11[i,j]
+        C[i, j+nBy2]      = c12[i,j]
+        C[i+nBy2, j]      = c21[i,j]
+        C[i+nBy2, j+nBy2] = c22[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func nextPowerOfTwo(after n: Int) -> Int {
+    return Int(pow(2, ceil(log2(Double(n)))))
+  }
+}
+```
+
+
+## Appendix
+
+### Number Protocol
+
+I use a number protocol to enable by Matrix to be generic. 
+
+The Number protocol ensures three things:
+
+1. Everything that is a number can be multiplied
+2. Everything that is a number can be added/subtracted
+3. Everything that is a number has a zero value
+
+Extending `Int`, `Float`, and `Double` to conform to this protocol is now very straightforward. All you need to do is implement the `static var zero`! 
+
+```swift
+public protocol Number: Multipliable, Addable {
+  static var zero: Self { get }
+}
+
+public protocol Addable {
+  static func +(lhs: Self, rhs: Self) -> Self
+  static func -(lhs: Self, rhs: Self) -> Self
+}
+
+public protocol Multipliable {
+  static func *(lhs: Self, rhs: Self) -> Self
+}
+```
+
+### Dot Product
+
+I extend `Array` to include a dot product function for when the Array's element conform to the `Number` protocol.
+
+```swift
+extension Array where Element: Number {
+  public func dot(_ b: Array<Element>) -> Element {
+    let a = self
+    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
+    let c = a.indices.map{ a[$0] * b[$0] }
+    return c.reduce(Element.zero, { $0 + $1 })
+  }
+}
+```
+
+##Resources
++ [Intro to Matrix Multiplication | Khan Academy](https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro)
++ [Matrix Multiplication | Wikipedia](https://en.wikipedia.org/wiki/Matrix_multiplication)
++ [Strassen Algorithm | Wikipedia](https://en.wikipedia.org/wiki/Strassen_algorithm)
++ [Strassen Algorithm | Wolfram MathWorld](http://mathworld.wolfram.com/StrassenFormulas.html)
++ [Strassens Algorithm | Geeks for Geeks](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
\ No newline at end of file
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 50af60a6f..5d82244a3 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -8,9 +8,11 @@ A[.row, 0] = [2, 3, -1, 0]
 A[.row, 1] = [-7, 2, 1, 10]
 
 var B = Matrix(rows: 4, columns: 2, initialValue: 0)
+print(B)
 B[.column, 0] = [3, 2, -1, 2]
 B[.column, 1] = [4, 1, 2, 7]
 
+
 let C = A.matrixMultiply(by: B)
 let D = A.strassenMatrixMultiply(by: B)
 let E = B.matrixMultiply(by: A)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index eba49ce9a..77ced4632 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -40,23 +40,26 @@ public struct Matrix<T: Number> {
     self.columns = size
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
-}
-
-// MARK: - Public Functions
-
-public extension Matrix {
-  subscript(row: Int, column: Int) -> T {
+  
+  // MARK: - Private Functions
+  
+  fileprivate func indexIsValid(row: Int, column: Int) -> Bool {
+    return row >= 0 && row < rows && column >= 0 && column < columns
+  }
+  
+  // MARK: - Subscript
+  
+  public subscript(row: Int, column: Int) -> T {
     get {
       assert(indexIsValid(row: row, column: column), "Index out of range")
       return grid[(row * columns) + column]
-    }
-    set {
+    } set {
       assert(indexIsValid(row: row, column: column), "Index out of range")
       grid[(row * columns) + column] = newValue
     }
   }
   
-  subscript(type: RowOrColumn, value: Int) -> [T] {
+  public subscript(type: RowOrColumn, value: Int) -> [T] {
     get {
       switch type {
       case .row:
@@ -64,15 +67,11 @@ public extension Matrix {
         return Array(grid[(value * columns)..<(value * columns) + columns])
       case .column:
         assert(indexIsValid(row: 0, column: value), "Index out of range")
-        var columns: [T] = []
-        for row in 0..<rows {
-          for column in 0..<self.columns {
-            if column == value {
-              columns.append(grid[(row * self.columns) + value])
-            }
-          }
+        let column = (0..<rows).map { (currentRow) -> T in
+          let currentColumnIndex = currentRow * columns + value
+          return grid[currentColumnIndex]
         }
-        return columns
+        return column
       }
     } set {
       switch type {
@@ -90,59 +89,84 @@ public extension Matrix {
     }
   }
   
-  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+  // MARK: - Public Functions
+  
+  public func row(for columnIndex: Int) -> [T] {
+    assert(indexIsValid(row: columnIndex, column: 0), "Index out of range")
+    return Array(grid[(columnIndex * columns)..<(columnIndex * columns) + columns])
+  }
+  
+  public func column(for rowIndex: Int) -> [T] {
+    assert(indexIsValid(row: 0, column: rowIndex), "Index out of range")
+    
+    let column = (0..<rows).map { (currentRow) -> T in
+      let currentColumnIndex = currentRow * columns + rowIndex
+      return grid[currentColumnIndex]
+    }
+    return column
+  }
+  
+  public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try body(row, column)
+      }
+    }
+  }
+}
+
+// MARK: - Matrix Multiplication Function
+
+extension Matrix {
+  public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+// MARK: - Strassen Multiplication
+
+extension Matrix {
+  public func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
     
     let n = max(A.rows, A.columns, B.rows, B.columns)
-    let m = nextPowerOfTwo(of: n)
+    let m = nextPowerOfTwo(after: n)
     
     var APrep = Matrix(size: m)
     var BPrep = Matrix(size: m)
     
-    A.size.forEach { (i, j) in
+    A.forEach { (i, j) in
       APrep[i,j] = A[i,j]
     }
     
-    B.size.forEach { (i, j) in
+    B.forEach { (i, j) in
       BPrep[i,j] = B[i,j]
     }
     
     let CPrep = APrep.strassenR(by: BPrep)
     var C = Matrix(rows: A.rows, columns: B.columns)
-    
     for i in 0..<A.rows {
       for j in 0..<B.columns {
         C[i,j] = CPrep[i,j]
       }
     }
-    return C
-  }
-  
-  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i, j] = A[.row, i].dot(B[.column, j])
-      }
-    }
     
     return C
   }
-}
-
-// MARK: - Private Functions
-
-fileprivate extension Matrix {
-  func indexIsValid(row: Int, column: Int) -> Bool {
-    return row >= 0 && row < rows && column >= 0 && column < columns
-  }
   
-  func strassenR(by B: Matrix<T>) -> Matrix<T> {
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.isSquare && B.isSquare, "This function requires square matricies!")
     guard A.rows > 1 && B.rows > 1 else { return A * B }
@@ -150,42 +174,49 @@ fileprivate extension Matrix {
     let n    = A.rows
     let nBy2 = n / 2
     
-    var a11 = Matrix(size: nBy2)
-    var a12 = Matrix(size: nBy2)
-    var a21 = Matrix(size: nBy2)
-    var a22 = Matrix(size: nBy2)
-    var b11 = Matrix(size: nBy2)
-    var b12 = Matrix(size: nBy2)
-    var b21 = Matrix(size: nBy2)
-    var b22 = Matrix(size: nBy2)
+    /*
+    Assume submatricies are allocated as follows
+    
+     matrix A = |a b|,    matrix B = |e f|
+                |c d|                |g h|
+    */
+    
+    var a = Matrix(size: nBy2)
+    var b = Matrix(size: nBy2)
+    var c = Matrix(size: nBy2)
+    var d = Matrix(size: nBy2)
+    var e = Matrix(size: nBy2)
+    var f = Matrix(size: nBy2)
+    var g = Matrix(size: nBy2)
+    var h = Matrix(size: nBy2)
     
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
-        a11[i,j] = A[i,j]
-        a12[i,j] = A[i, j+nBy2]
-        a21[i,j] = A[i+nBy2, j]
-        a22[i,j] = A[i+nBy2, j+nBy2]
-        b11[i,j] = B[i,j]
-        b12[i,j] = B[i, j+nBy2]
-        b21[i,j] = B[i+nBy2, j]
-        b22[i,j] = B[i+nBy2, j+nBy2]
+        a[i,j] = A[i,j]
+        b[i,j] = A[i, j+nBy2]
+        c[i,j] = A[i+nBy2, j]
+        d[i,j] = A[i+nBy2, j+nBy2]
+        e[i,j] = B[i,j]
+        f[i,j] = B[i, j+nBy2]
+        g[i,j] = B[i+nBy2, j]
+        h[i,j] = B[i+nBy2, j+nBy2]
       }
     }
     
-    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
-    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
-    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
-    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
-    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
-    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
-    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
+    let p1 = a.strassenR(by: f-h)       // a * (f - h)
+    let p2 = (a+b).strassenR(by: h)     // (a + b) * h
+    let p3 = (c+d).strassenR(by: e)     // (c + d) * e
+    let p4 = d.strassenR(by: g-e)       // d * (g - e)
+    let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
+    let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
+    let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
     
-    let c11 = q1 + q4 - q5 + q7
-    let c12 = q3 + q5
-    let c21 = q2 + q4
-    let c22 = q1 + q3 - q2 + q6
-    var C   = Matrix(size: n)
+    let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
+    let c12 = p1 + p2                   // p1 + p2
+    let c21 = p3 + p4                   // p3 + p4
+    let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
     
+    var C = Matrix(size: n)
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
         C[i, j]           = c11[i,j]
@@ -198,12 +229,11 @@ fileprivate extension Matrix {
     return C
   }
   
-  func nextPowerOfTwo(of n: Int) -> Int {
+  private func nextPowerOfTwo(after n: Int) -> Int {
     return Int(pow(2, ceil(log2(Double(n)))))
   }
 }
 
-
 // Term-by-term Matrix Math
 
 extension Matrix: Addable {
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
index f4a604ade..e0d957607 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
@@ -8,26 +8,13 @@
 
 import Foundation
 
-public struct MatrixSize: Equatable {
+public struct MatrixSize {
   let rows: Int
   let columns: Int
-  
-  public init(rows: Int, columns: Int) {
-    self.rows = rows
-    self.columns = columns
-  }
-  
-  public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
-    for row in 0..<rows {
-      for column in 0..<columns {
-        try? body(row, column)
-      }
-    }
-  }
 }
 
-public extension MatrixSize {
-  static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+extension MatrixSize: Equatable {
+  public static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
     return lhs.columns == rhs.columns && lhs.rows == rhs.rows
   }
 }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 9f4c7f4ab..7da1eee60 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -22,21 +22,15 @@ public protocol Multipliable {
 }
 
 extension Int: Number {
-  public static var zero: Int {
-    return 0
-  }
+  public static var zero: Int { return 0 }
 }
 
 extension Double: Number {
-  public static var zero: Double {
-    return 0.0
-  }
+  public static var zero: Double { return 0.0 }
 }
 
 extension Float: Number {
-  public static var zero: Float {
-    return 0.0
-  }
+  public static var zero: Float { return 0.0 }
 }
 
 extension Array where Element: Number {

From c94fbab56dcd0b3f483ec8a1fec718de7ef97ba2 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 15:53:58 -0700
Subject: [PATCH 0871/1679] added authorship to readme

---
 Strassen Matrix Multiplication/README.markdown | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index e4222b4f4..6949f906c 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -405,7 +405,6 @@ extension Matrix {
 }
 ```
 
-
 ## Appendix
 
 ### Number Protocol
@@ -455,4 +454,6 @@ extension Array where Element: Number {
 + [Matrix Multiplication | Wikipedia](https://en.wikipedia.org/wiki/Matrix_multiplication)
 + [Strassen Algorithm | Wikipedia](https://en.wikipedia.org/wiki/Strassen_algorithm)
 + [Strassen Algorithm | Wolfram MathWorld](http://mathworld.wolfram.com/StrassenFormulas.html)
-+ [Strassens Algorithm | Geeks for Geeks](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
\ No newline at end of file
++ [Strassens Algorithm | Geeks for Geeks](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
+
+*Written for Swift Algorithm Club by Richard Ash*
\ No newline at end of file

From 09848a79e92c266b3e33006781732c1e288d7f6f Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 15:55:13 -0700
Subject: [PATCH 0872/1679] fixed the display of the resources header

---
 Strassen Matrix Multiplication/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index 6949f906c..713ab1801 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -449,7 +449,8 @@ extension Array where Element: Number {
 }
 ```
 
-##Resources
+## Resources
+
 + [Intro to Matrix Multiplication | Khan Academy](https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro)
 + [Matrix Multiplication | Wikipedia](https://en.wikipedia.org/wiki/Matrix_multiplication)
 + [Strassen Algorithm | Wikipedia](https://en.wikipedia.org/wiki/Strassen_algorithm)

From ab37359616c210f84363b885ef0308b17cadc202 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 16:05:27 -0700
Subject: [PATCH 0873/1679] fixed layout of code in readme

---
 .../README.markdown                           | 142 +++++++++---------
 1 file changed, 75 insertions(+), 67 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index 713ab1801..fa822d310 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -11,17 +11,16 @@ Before we begin, you may ask what is matrix multiplication? Great question! It i
 
 ### Example: Matrix Multiplication
 
-	matrix A = |1 2|
-	           |3 4|
-				 
-	matrix B = |5 6|
-	           |7 8|
-	
-	A * B = C
+```
+matrix A = |1 2|, matrix B = |5 6|
+           |3 4|             |7 8|
 	
-	|1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
-	|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+A * B = C
 	
+|1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
+|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+```
+
 What's going on here? To start, we're multiplying matricies A & B. Our new matrix, C's, elements `[i, j]` are determined by the dot product of the first matrix's ith row and the second matrix's jth column. See [here](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length) for a refresher on the dot product.
 
 So the upper left element `[i=1, j=1]` of our new matrix is a combination of A's 1st row and B's 1st column.
@@ -66,14 +65,14 @@ Next, we loop over A's columns and B's rows. Because we know both A's columns &
 
 ```swift
 for i in 0..<n {
-	for j in 0..<n {
+  for j in 0..<n {
 ```
 
 Then, for each row in A and column in B, we take the dot product of the ith row in A with the jth column in B and set that result equal to the `[i, j]` element in C. Or `C[i, j]`.
 
 ```swift
 for k in 0..<n {
-	C[i, j] = A[i, k] * B[k, j]
+  C[i, j] = A[i, k] * B[k, j]
 }
 ```
 
@@ -83,20 +82,20 @@ Here's the full implementation:
 
 ```swift
 public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-	let A = self
-	assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-	let n = A.columns
-	var C = Matrix<T>(rows: A.rows, columns: B.columns)
+  let A = self
+  assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+  let n = A.columns
+  var C = Matrix<T>(rows: A.rows, columns: B.columns)
     
-	for i in 0..<n {
-		for j in 0..<n {
-			for k in 0..<n {
-				C[i, j] = A[i, k] * B[k, j]
-			}
-		}
-	}
+  for i in 0..<n {
+    for j in 0..<n {
+      for k in 0..<n {
+        C[i, j] = A[i, k] * B[k, j]
+      }
+    }
+  }
     
-	return C
+  return C
 }
 ```
 
@@ -110,10 +109,10 @@ Volker Strassen first published his algorithm in 1969. It was the first algorith
 
 The basic idea behind Strassen's algorithm is to split A & B into 8 submatricies and then recursively compute the submatricies of C. This strategy is called *Divide and Conquer*.
 
-	matrix A = |a b|
-	  		   |c d|
-	matrix B = |e f|
-			   |g h|
+```
+matrix A = |a b|, matrix B = |e f|
+           |c d|             |g h|
+```
 
 *There will be 8 recursive calls:*
 
@@ -149,9 +148,10 @@ Strassen's **7** calls are as follows:
 
 Now we can compute our new matrix C's new quardents!
 
-	matrix C = |p5+p4-p2+p6    p1+p2   |
-			   |   p3+p4    p1+p5-p3-p7|    
-
+```
+matrix C = |p5+p4-p2+p6    p1+p2   |
+           |   p3+p4    p1+p5-p3-p7|    
+```
 
 A great reaction right now would be !!??!?!?!!?! How does this even work??
 
@@ -159,9 +159,11 @@ Let's prove it!
 
 **First** Submatrix:
 
-	p5+p4-p2+p6 = (a+d)*(e+h) + d*(g-e) - (a+b)*h + (b-d)*(g+h)
-				= (ae+de+ah+dh) + (dg-de) - (ah+bh) + (bg-dg+bh-dh)
-				= ae+bg ✅
+```
+p5+p4-p2+p6 = (a+d)*(e+h) + d*(g-e) - (a+b)*h + (b-d)*(g+h)
+            = (ae+de+ah+dh) + (dg-de) - (ah+bh) + (bg-dg+bh-dh)
+            = ae+bg ✅
+```
 				
 Exactly what we got the first time!
 
@@ -169,21 +171,27 @@ Now let's prove the others.
 
 **Second** submatrix:
 
-	p1+p2 = a*(f-h) + (a+b)*h
-		  = (af-ah) + (ah+bh)
-		  = af+bh ✅
+```
+p1+p2 = a*(f-h) + (a+b)*h
+      = (af-ah) + (ah+bh)
+      = af+bh ✅
+```
 		  
 **Third** submatrix:
 
-	p3+p4 = (c+d)*e + d*(g-e)
-		  = (ce+de) + (dg-de)
-		  = ce+dg ✅
+```
+p3+p4 = (c+d)*e + d*(g-e)
+      = (ce+de) + (dg-de)
+      = ce+dg ✅
+```
 
 **Fourth** submatrix: 
 
-	p1+p5-p3-p7 = a*(f-h) + (a+d)*(e+h) - (c+d)*e - (a-c)*(e+f)
-				= (af-ah) + (ae+de+ah+dh) -(ce+de) - (ae-ce+af-cf)
-				= cf+dh ✅
+```
+p1+p5-p3-p7 = a*(f-h) + (a+d)*(e+h) - (c+d)*e - (a-c)*(e+f)
+            = (af-ah) + (ae+de+ah+dh) -(ce+de) - (ae-ce+af-cf)
+            = cf+dh ✅
+```
 
 Great! The math checks out!
 
@@ -209,15 +217,15 @@ var APrep = Matrix(size: m)
 var BPrep = Matrix(size: m)
    
 for i in A.rows {
-	for j in A.columns {
-		APrep[i, j] = A[i,j]
-	}
+  for j in A.columns {
+    APrep[i, j] = A[i,j]
+  }
 }
 
 for i in B.rows {
-	for j in B.columns {
-		BPrep[i, j] = B[i, j]
-	}
+  for j in B.columns {
+    BPrep[i, j] = B[i, j]
+  }
 }
 ```
 
@@ -228,9 +236,9 @@ let CPrep = APrep.strassenR(by: BPrep)
 var C = Matrix(rows: A.rows, columns: B.columns)
     
 for i in 0..<A.rows {
-	for j in 0..<B.columns {
-		C[i,j] = CPrep[i,j]
-	}
+  for j in 0..<B.columns {
+    C[i,j] = CPrep[i,j]
+  }
 }
 ```
 
@@ -251,16 +259,16 @@ var g = Matrix(size: nBy2)
 var h = Matrix(size: nBy2)
     
 for i in 0..<nBy2 {
-	for j in 0..<nBy2 {
-		a[i,j] = A[i,j]
-       b[i,j] = A[i, j+nBy2]
-       c[i,j] = A[i+nBy2, j]
-       d[i,j] = A[i+nBy2, j+nBy2]
-       e[i,j] = B[i,j]
-       f[i,j] = B[i, j+nBy2]
-       g[i,j] = B[i+nBy2, j]
-       h[i,j] = B[i+nBy2, j+nBy2]
-	}
+  for j in 0..<nBy2 {
+    a[i,j] = A[i,j]
+    b[i,j] = A[i, j+nBy2]
+    c[i,j] = A[i+nBy2, j]
+    d[i,j] = A[i+nBy2, j+nBy2]
+    e[i,j] = B[i,j]
+    f[i,j] = B[i, j+nBy2]
+    g[i,j] = B[i+nBy2, j]
+    h[i,j] = B[i+nBy2, j+nBy2]
+  }
 }
 ```
 
@@ -290,12 +298,12 @@ And finally, we combine these submatricies into our new matrix C!
 ```swift
 var C = Matrix(size: n)    
 for i in 0..<nBy2 {
-	for j in 0..<nBy2 {
-		C[i, j]           = c11[i,j]
-		C[i, j+nBy2]      = c12[i,j]
-		C[i+nBy2, j]      = c21[i,j]
-		C[i+nBy2, j+nBy2] = c22[i,j]
-	}
+  for j in 0..<nBy2 {
+    C[i, j]           = c11[i,j]
+    C[i, j+nBy2]      = c12[i,j]
+    C[i+nBy2, j]      = c21[i,j]
+    C[i+nBy2, j+nBy2] = c22[i,j]
+  }
 }
 ```
 

From ae1da6fc3c88d84ae4620f3c58500816fac10499 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Mon, 27 Mar 2017 16:33:26 +0800
Subject: [PATCH 0874/1679] Delete SelectionSamplingExample.swift

---
 .../SelectionSamplingExample.swift            | 32 -------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 Selection Sampling/SelectionSamplingExample.swift

diff --git a/Selection Sampling/SelectionSamplingExample.swift b/Selection Sampling/SelectionSamplingExample.swift
deleted file mode 100644
index 66648a934..000000000
--- a/Selection Sampling/SelectionSamplingExample.swift	
+++ /dev/null
@@ -1,32 +0,0 @@
-//
-//  Select.swift
-//  
-//
-//  Created by Cheer on 2017/3/9.
-//
-//
-
-import Foundation
-
-func select<T>(from a: [T], count requested: Int) -> [T] {
-    
-    // if requested > a.count, will throw ==> fatal error: Index out of range
-    
-    if requested < a.count {
-        var arr = a
-        for i in 0..<requested {
-            
-            //arc4random_uniform(n) ==> the range is [0...n-1]
-            //So: arc4random_uniform(UInt32(arr.count - i - 2)) + (i + 1) ==> [0...arr.count - (i + 1) - 1] + (i + 1) ==> the range is [(i + 1)...arr.count - 1]
-            //Why start index is "(i + 1)"?  Because in "swap(&A,&B)", if A's index == B's index, will throw a error: "swapping a location with itself is not supported"
-            
-            let nextIndex = Int(arc4random_uniform(UInt32(arr.count - i - 2))) + (i + 1)
-            swap(&arr[nextIndex], &arr[i])
-        }
-        return Array(arr[0..<requested])
-    }
-    
-    if requested == a.count { return a }
-    
-    return [T]()
-}

From 7dd9de00802ea1ff0d03e3fb09d547c867f83a81 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Tue, 28 Mar 2017 15:54:51 +0800
Subject: [PATCH 0875/1679] Update ShellSortExample.swift

fix code. And apologize for my carelessness.
---
 Shell Sort/ShellSortExample.swift | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index c41eb8889..0beac00a3 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -14,18 +14,18 @@ public func shellSort(_ list : inout [Int])
     
     while sublistCount > 0
     {
-        for var index in 0..<arr.count{
+        for var index in 0..<list.count{
             
-            guard index + sublistCount < arr.count else { break }
+            guard index + sublistCount < list.count else { break }
             
-            if arr[index] > arr[index + sublistCount]{
-                swap(&arr[index], &arr[index + sublistCount])
+            if list[index] > list[index + sublistCount]{
+                swap(&list[index], &list[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
-
-            while arr[index - 1] > arr[index] && index - 1 > 0  {
-                swap(&arr[index - 1], &arr[index])
+            
+            while list[index - 1] > list[index] && index - 1 > 0  {
+                swap(&list[index - 1], &list[index])
                 index -= 1
             }
         }

From 14fe78745ccceb2de88ed2a3dc05835d99317e90 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Tue, 28 Mar 2017 15:55:45 +0800
Subject: [PATCH 0876/1679] Update ShellSortExample.swift

---
 Shell Sort/ShellSortExample.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 0beac00a3..05ab2518b 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -14,11 +14,11 @@ public func shellSort(_ list : inout [Int])
     
     while sublistCount > 0
     {
-        for var index in 0..<list.count{
+        for var index in 0..<list.count {
             
             guard index + sublistCount < list.count else { break }
             
-            if list[index] > list[index + sublistCount]{
+            if list[index] > list[index + sublistCount] {
                 swap(&list[index], &list[index + sublistCount])
             }
             

From cf1561f885c414d8c4bb260cd21720c109468b9e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Tue, 28 Mar 2017 15:56:26 +0800
Subject: [PATCH 0877/1679] Update ShellSortExample.swift

---
 Shell Sort/ShellSortExample.swift | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 05ab2518b..9174b935b 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -8,12 +8,10 @@
 
 import Foundation
 
-public func shellSort(_ list : inout [Int])
-{
+public func shellSort(_ list : inout [Int]) {
     var sublistCount = list.count / 2
     
-    while sublistCount > 0
-    {
+    while sublistCount > 0 {
         for var index in 0..<list.count {
             
             guard index + sublistCount < list.count else { break }

From 3be78947ea3dba5905e6526776ab6cee13861159 Mon Sep 17 00:00:00 2001
From: Kevin VanderLugt <kevin.vanderlugt@gmail.com>
Date: Tue, 28 Mar 2017 20:01:36 -0700
Subject: [PATCH 0878/1679] Update How to Contribute link

Super simple but just something I noticed while getting started.
Cheers!
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 023f151fb..5e6cfbfe4 100644
--- a/README.markdown
+++ b/README.markdown
@@ -227,7 +227,7 @@ The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://
 
 It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka) and [Kelvin Lau](https://github.com/kelvinlauKL).
 
-The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How to Contribute.markdown)? :]
+The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How%20to%20Contribute.markdown)? :]
 
 ## License
 

From edee6981d7e77ff88186439b2536b8cc212354c5 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Tue, 28 Mar 2017 21:31:33 -0700
Subject: [PATCH 0879/1679] =?UTF-8?q?updated=20syntax=20for=20Swift=203.1!?=
 =?UTF-8?q?=20=F0=9F=98=81=F0=9F=94=A5?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../Contents.swift                            |  1 -
 .../Sources/Matrix.swift                      | 31 ++++++++++++-------
 .../Sources/MatrixSize.swift                  | 20 ------------
 3 files changed, 19 insertions(+), 33 deletions(-)
 delete mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 5d82244a3..9e11cb6a1 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,5 +1,4 @@
 //: Playground - noun: a place where people can play
-// Reference - http://mathworld.wolfram.com/StrassenFormulas.html
 
 import Foundation
 
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index 77ced4632..c13b3eeee 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -8,37 +8,44 @@
 
 import Foundation
 
-public enum RowOrColumn {
-  case row, column
-}
-
 public struct Matrix<T: Number> {
   
+  // MARK: - Martix Objects
+  
+  public enum Index {
+    case row, column
+  }
+  
+  public struct Size: Equatable {
+    let rows: Int, columns: Int
+    
+    public static func ==(lhs: Size, rhs: Size) -> Bool {
+      return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+    }
+  }
+  
   // MARK: - Variables
   
   let rows: Int, columns: Int
+  let size: Size
+  
   var grid: [T]
   
   var isSquare: Bool {
     return rows == columns
   }
   
-  var size: MatrixSize {
-    return MatrixSize(rows: rows, columns: columns)
-  }
-  
   // MARK: - Init
   
   public init(rows: Int, columns: Int, initialValue: T = T.zero) {
     self.rows = rows
     self.columns = columns
+    self.size = Size(rows: rows, columns: columns)
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
   
   public init(size: Int, initialValue: T = T.zero) {
-    self.rows = size
-    self.columns = size
-    self.grid = Array(repeating: initialValue, count: rows * columns)
+    self.init(rows: size, columns: size, initialValue: initialValue)
   }
   
   // MARK: - Private Functions
@@ -59,7 +66,7 @@ public struct Matrix<T: Number> {
     }
   }
   
-  public subscript(type: RowOrColumn, value: Int) -> [T] {
+  public subscript(type: Matrix.Index, value: Int) -> [T] {
     get {
       switch type {
       case .row:
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
deleted file mode 100644
index e0d957607..000000000
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
+++ /dev/null
@@ -1,20 +0,0 @@
-//
-//  MatrixSize.swift
-//  
-//
-//  Created by Richard Ash on 10/28/16.
-//
-//
-
-import Foundation
-
-public struct MatrixSize {
-  let rows: Int
-  let columns: Int
-}
-
-extension MatrixSize: Equatable {
-  public static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
-    return lhs.columns == rhs.columns && lhs.rows == rhs.rows
-  }
-}

From 4d1b9ff02cb46640b55f8b462be8d4536ca182bf Mon Sep 17 00:00:00 2001
From: Jim Rhoades <jim@crushapps.com>
Date: Wed, 29 Mar 2017 18:02:32 -0400
Subject: [PATCH 0880/1679] Update Big-O Notation.markdown

Fixed the link to "merge sort".
---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 09fbb04aa..746cba8a3 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -19,6 +19,6 @@ Big-O | Name | Description
 
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
 
-Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!
+Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge%20Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!
 
 If you find this confusing, don't let this Big-O stuff bother you too much. It's mostly useful when comparing two algorithms to figure out which one is better. But in the end you still want to test in practice which one really is the best. And if the amount of data is relatively small, then even a slow algorithm will be fast enough for practical use.

From 6d4a1eec73c92713e2e4e880b486694da545dbf9 Mon Sep 17 00:00:00 2001
From: darrellhz <zh0521@gmail.com>
Date: Thu, 30 Mar 2017 14:30:01 +0900
Subject: [PATCH 0881/1679] Update README.markdown

updated to swift 3 syntax
---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index a3a84c03d..b3b955c61 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -195,7 +195,7 @@ For convenience, let's add an init method that calls `insert()` for all the elem
     precondition(array.count > 0)
     self.init(value: array.first!)
     for v in array.dropFirst() {
-      insert(v, parent: self)
+      insert(value: v)
     }
   }
 ```

From da0be01444b4dfc2cdbd2259a3e5c524e9d37434 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Sat, 1 Apr 2017 14:29:56 -0700
Subject: [PATCH 0882/1679] Update README.markdown

Hello,
I have revised one of your documents for my assignment. I still need to revise more documents (10 in total). I hope it will be fine if I choose some documents from your account.
Thanks,
Parvaneh
---
 Heap/README.markdown | 116 +++++++++++++++++++++----------------------
 1 file changed, 58 insertions(+), 58 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 88ea25eeb..3935950a6 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,19 +1,19 @@
 # Heap
 
-A heap is a [binary tree](../Binary Tree/) that lives inside an array, so it doesn't use parent/child pointers. The tree is partially sorted according to something called the "heap property" that determines the order of the nodes in the tree.
+A heap is a [binary tree](../Binary Tree/) inside an array, so it doesn't use parent/child pointers. A heap is sorted based on the "heap property" that determines the order of the nodes in the tree.
 
 Common uses for heap:
 
-- For building [priority queues](../Priority Queue/).
-- The heap is the data structure supporting [heap sort](../Heap Sort/).
-- Heaps are fast for when you often need to compute the minimum (or maximum) element of a collection.
-- Impressing your non-programmer friends.
+- To build [priority queues](../Priority Queue/).
+- To support [heap sorts](../Heap Sort/).
+- To compute the minimum (or maximum) element of a collection quickly.
+- To impress your non-programmer friends.
 
 ## The heap property
 
-There are two kinds of heaps: a *max-heap* and a *min-heap*. They are identical, except that the order in which they store the tree nodes is opposite.
+There are two kinds of heaps: a *max-heap* and a *min-heap* which are different by the order in which they store the tree nodes.
 
-In a max-heap, parent nodes must always have a greater value than each of their children. For a min-heap it's the other way around: every parent node has a smaller value than its child nodes. This is called the "heap property" and it is true for every single node in the tree.
+In a max-heap, parent nodes have a greater value than each of their children. In a min-heap, every parent node has a smaller value than its child nodes. This is called the "heap property", and it is true for every single node in the tree.
 
 An example:
 
@@ -21,33 +21,33 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority Queue/) where you want to quickly access the "most important" element.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority Queue/)to access the "most important" element quickly.
 
-> **Note:** You can't really say anything else about the sort order of the heap. For example, in a max-heap the maximum element is always at index 0 but the minimum element isn’t necessarily the last one -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
+> **Note:** The root of the heap has the maximum or minimum element, but the sort order of other elements are not predictable. For example, the maximum element is always at index 0 in a max-heap, but the minimum element isn’t necessarily the last one. -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
-## How does heap compare to regular trees?
+## How does a heap can be compared to regular trees?
 
-A heap isn't intended to be a replacement for a binary search tree. But there are many similarities between the two and also some differences. Here are some of the bigger differences:
+A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
 
-**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
+**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must be smaller than its parent and the right child must be greater. This is not true for a heap. In a max-heap both children must be smaller than the parent; in a min-heap they both must be greater.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL Tree/) or [red-black tree](../Red-Black Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
+**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL Tree/) or [red-black tree](../Red-Black Tree/), but with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
-**Searching.** Searching a binary tree is really fast -- that's its whole purpose. In a heap, searching is slow. The purpose of a heap is to always put the largest (or smallest) node at the front, and to allow relatively fast inserts and deletes. Searching isn't a top priority.
+**Searching.** Whereas searching is fast in a binary tree, it is slow in a heap. Searching isn't a top priority in a heap since the purpose of a heap is to put the largest (or smallest) node at the front and to allow relatively fast inserts and deletes. 
 
-## The tree that lived in an array
+## The tree inside an array
 
-An array may seem like an odd way to implement a tree-like structure but it is very efficient in both time and space.
+An array may seem like an odd way to implement a tree-like structure, but it is efficient in both time and space.
 
-This is how we're going to store the tree from the above example:
+This is how we are going to store the tree from the above example:
 
 	[ 10, 7, 2, 5, 1 ]
 
 That's all there is to it! We don't need any more storage than just this simple array.
 
-So how do we know which nodes are the parents and which are the children if we're not allowed to use any pointers? Good question! There is a well-defined relationship between the array index of a tree node and the array indices of its parent and children.
+So how do we know which nodes are the parents and which are the children if we are not allowed to use any pointers? Good question! There is a well-defined relationship between the array index of a tree node and the array indices of its parent and children.
 
 If `i` is the index of a node, then the following formulas give the array indices of its parent and child nodes:
 
@@ -69,7 +69,7 @@ Let's use these formulas on the example. Fill in the array index and we should g
 
 Verify for yourself that these array indices indeed correspond to the picture of the tree.
 
-> **Note:** The root node `(10)` doesn't have a parent because `-1` is not a valid array index. Likewise, nodes `(2)`, `(5)`, and `(1)` don't have children because those indices are greater than the array size. So we always have to make sure the indices we calculate are actually valid before we use them.
+> **Note:** The root node `(10)` does not have a parent because `-1` is not a valid array index. Likewise, nodes `(2)`, `(5)`, and `(1)` do not have children because those indices are greater than the array size, so we always have to make sure the indices we calculate are actually valid before we use them.
 
 Recall that in a max-heap, the parent's value is always greater than (or equal to) the values of its children. This means the following must be true for all array indices `i`:
 
@@ -79,27 +79,27 @@ array[parent(i)] >= array[i]
 	
 Verify that this heap property holds for the array from the example heap.
 
-As you can see, these equations let us find the parent or child index for any node without the need for pointers. True, it's slightly more complicated than just dereferencing a pointer but that's the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
+As you can see, these equations allow us to find the parent or child index for any node without the need for pointers. It is complicated than just dereferencing a pointer, but that is the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
 
-It's important to understand this relationship between array index and position in the tree. Here's a slightly larger heap, this tree has 15 nodes divided over four levels:
+It is important to understand this relationship between array index and position in the tree. Here is a larger heap which has 15 nodes divided over four levels:
 
 ![Large heap](Images/LargeHeap.png)
 
-The numbers in this picture aren't the values of the nodes but the array indices that store the nodes! Those array indices correspond to the different levels of the tree like this:
+The numbers in this picture are not the values of the nodes but the array indices that store the nodes! Here is the array indices correspond to the different levels of the tree:
 
 ![The heap array](Images/Array.png)
 
-For the formulas to work, parent nodes must always appear before child nodes in the array. You can see that in the above picture.
+For the formulas to work, parent nodes must appear before child nodes in the array. You can see that in the above picture.
 
 Note that this scheme has limitations. You can do the following with a regular binary tree but not with a heap:
 
 ![Impossible with a heap](Images/RegularTree.png)
 
-You can’t start a new level unless the current lowest level is completely full. So heaps always have this kind of shape:
+You can not start a new level unless the current lowest level is completely full, so heaps always have this kind of shape:
 
 ![The shape of a heap](Images/HeapShape.png)
 
-> **Note:** Technically speaking you *could* emulate a regular binary tree with a heap, but it would waste a lot of space and you’d need some way to mark array indices as being empty.
+> **Note:** You *could* emulate a regular binary tree with a heap, but it would be a waste of space, and you would need to mark array indices as being empty.
 
 Pop quiz! Let's say we have the array:
 
@@ -111,15 +111,15 @@ Is this a valid heap? The answer is yes! A sorted array from low-to-high is a va
 
 The heap property holds for each node because a parent is always smaller than its children. (Verify for yourself that an array sorted from high-to-low is always a valid max-heap.)
 
-> **Note:** But not every min-heap is necessarily a sorted array! It only works one way... To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
+> **Note:** But not every min-heap is necessarily a sorted array! It only works one way. To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
 
 ## More math!
 
-In case you are curious, here are a few more formulas that describe certain properties of a heap. You don't need to know these by heart but they come in handy sometimes. Feel free to skip this section!
+In case you are curious, here are a few more formulas that describe certain properties of a heap. You do not need to know these by heart, but they come in handy sometimes. Feel free to skip this section!
 
-The *height* of a tree is defined as the number of steps it takes to go from the root node to the lowest leaf node. Or more formally: the height is the maximum number of edges between the nodes. A heap of height *h* has *h + 1* levels.
+The *height* of a tree is defined as the number of steps it takes to go from the root node to the lowest leaf node, or more formally: the height is the maximum number of edges between the nodes. A heap of height *h* has *h + 1* levels.
 
-This heap has height 3 and therefore has 4 levels:
+This heap has height 3, so it has 4 levels:
 
 ![Large heap](Images/LargeHeap.png)
 
@@ -145,31 +145,31 @@ There are two primitive operations necessary to make sure the heap is a valid ma
 
 Shifting up or down is a recursive procedure that takes **O(log n)** time.
 
-The other operations are built on these primitives. They are:
+Here are other operations that are built on primitive operations: 
 
 - `insert(value)`: Adds the new element to the end of the heap and then uses `shiftUp()` to fix the heap.
 
-- `remove()`: Removes and returns the maximum value (max-heap) or the minimum value (min-heap). To fill up the hole that's left by removing the element, the very last element is moved to the root position and then `shiftDown()` fixes up the heap. (This is sometimes called "extract min" or "extract max".)
+- `remove()`: Removes and returns the maximum value (max-heap) or the minimum value (min-heap). To fill up the hole left by removing the element, the very last element is moved to the root position and then `shiftDown()` fixes up the heap. (This is sometimes called "extract min" or "extract max".)
 
-- `removeAtIndex(index)`: Just like `remove()` except it lets you remove any item from the heap, not just the root. This calls both `shiftDown()`, in case the new element is out-of-order with its children, and `shiftUp()`, in case the element is out-of-order with its parents.
+- `removeAtIndex(index)`: Just like `remove()` with the exception that it allows you to remove any item from the heap, not just the root. This calls both `shiftDown()`, in case the new element is out-of-order with its children, and `shiftUp()`, in case the element is out-of-order with its parents.
 
-- `replace(index, value)`: Assigns a smaller (min-heap) or larger (max-heap)  value to a node. Because this invalidates the heap property, it uses `shiftUp()` to patch things up. (Also called "decrease key" and "increase key".)
+- `replace(index, value)`: Assigns a smaller (min-heap) or larger (max-heap) value to a node. Because this invalidates the heap property, it uses `shiftUp()` to patch things up. (Also called "decrease key" and "increase key".)
 
-All of the above take time **O(log n)** because shifting up or down is the most expensive thing they do. There are also a few operations that take more time:
+All of the above take time **O(log n)** because shifting up or down is expensive. There are also a few operations that take more time:
 
-- `search(value)`. Heaps aren't built for efficient searches but the `replace()` and `removeAtIndex()` operations require the array index of the node, so you need to find that index somehow. Time: **O(n)**.
+- `search(value)`. Heaps are not built for efficient searches, but the `replace()` and `removeAtIndex()` operations require the array index of the node, so you need to find that index. Time: **O(n)**.
 
-- `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you’re smart about this, it can be done in **O(n)** time.
+- `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you are smart about this, it can be done in **O(n)** time.
 
-- [Heap sort](../Heap Sort/). Since the heap is really an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
+- [Heap sort](../Heap Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
 
 The heap also has a `peek()` function that returns the maximum (max-heap) or minimum (min-heap) element, without removing it from the heap. Time: **O(1)**.
 
-> **Note:** By far the most common things you'll do with a heap are inserting new values with `insert()` and removing the maximum or minimum value with `remove()`. Both take **O(log n)** time. The other operations exist to support more advanced usage, such as building a priority queue where the "importance" of items can change after they've been added to the queue.
+> **Note:** By far the most common things you will do with a heap are inserting new values with `insert()` and removing the maximum or minimum value with `remove()`. Both take **O(log n)** time. The other operations exist to support more advanced usage, such as building a priority queue where the "importance" of items can change after they have been added to the queue.
 
 ## Inserting into the heap
 
-Let's go through an example insertion to see in more detail how this works. We'll insert the value `16` into this heap:
+Let's go through an example of insertion to see in details how this works. We will insert the value `16` into this heap:
 
 ![The heap before insertion](Images/Heap1.png)
 
@@ -185,13 +185,13 @@ This corresponds to the following tree:
 
 The `(16)` was added to the first available space on the last row.
 
-Unfortunately, the heap property is no longer satisfied because `(2)` is above `(16)` and we want higher numbers above lower numbers. (This is a max-heap.)
+Unfortunately, the heap property is no longer satisfied because `(2)` is above `(16)`, and we want higher numbers above lower numbers. (This is a max-heap.)
 
-To restore the heap property, we're going to swap `(16)` and `(2)`. 
+To restore the heap property, we are going to swap `(16)` and `(2)`. 
 
 ![The heap before insertion](Images/Insert2.png)
 
-We're not done yet because `(10)` is also smaller than `(16)`. We keep swapping our inserted value with its parent, until the parent is larger or we reach the top of the tree. This is called **shift-up** or **sifting** and is done after every insertion. It makes a number that is too large or too small "float up" the tree.
+We are not done yet because `(10)` is also smaller than `(16)`. We keep swapping our inserted value with its parent, until the parent is larger or we reach the top of the tree. This is called **shift-up** or **sifting** and is done after every insertion. It makes a number that is too large or too small "float up" the tree.
 
 Finally, we get:
 
@@ -199,7 +199,7 @@ Finally, we get:
 
 And now every parent is greater than its children again.
 
-The time required for shifting up is proportional to the height of the tree so it takes **O(log n)** time. (The time it takes to append the node to the end of the array is only **O(1)**, so that doesn't slow it down.)
+The time required for shifting up is proportional to the height of the tree, so it takes **O(log n)** time. (The time it takes to append the node to the end of the array is only **O(1)**, so that does not slow it down.)
 
 ## Removing the root
 
@@ -211,7 +211,7 @@ What happens to the empty spot at the top?
 
 ![The root is gone](Images/Remove1.png)
 
-When inserting, we put the new value at the end of the array. Here, we'll do the opposite: we're going to take the last object we have, stick it up on top of the tree, and restore the heap property. 
+When inserting, we put the new value at the end of the array. Here, we will do the opposite: we are going to take the last object we have, stick it up on top of the tree, and restore the heap property. 
 
 ![The last node goes to the root](Images/Remove2.png)
 
@@ -219,19 +219,19 @@ Let's look at how to **shift-down** `(1)`. To maintain the heap property for thi
 
 ![The last node goes to the root](Images/Remove3.png)
 
-Keep shifting down until the node doesn't have any children or it is larger than both its children. For our heap we only need one more swap to restore the heap property:
+Keep shifting down until the node does not have any children or it is larger than both its children. For our heap, we only need one more swap to restore the heap property:
 
 ![The last node goes to the root](Images/Remove4.png)
 
-The time required for shifting all the way down is proportional to the height of the tree so it takes **O(log n)** time. 
+The time required for shifting all the way down is proportional to the height of the tree, so it takes **O(log n)** time. 
 
 > **Note:** `shiftUp()` and `shiftDown()` can only fix one out-of-place element at a time. If there are multiple elements in the wrong place, you need to call these functions once for each of those elements.
 
 ## Removing any node
 
-The vast majority of the time you'll be removing the object at the root of the heap because that's what heaps are designed for.
+The vast majority of the time you will be removing the object at the root of the heap because that is what heaps are designed for.
 
-However, it can be useful to remove an arbitrary element. This is a more general version of `remove()` and may involve either `shiftDown()` or `shiftUp()`.
+However, it can be useful to remove an arbitrary element. This is a general version of `remove()` and may involve either `shiftDown()` or `shiftUp()`.
 
 Let's take the example tree again and remove `(7)`:
 
@@ -241,13 +241,13 @@ As a reminder, the array is:
 
 	[ 10, 7, 2, 5, 1 ]
 
-As you know, removing an element could potentially invalidate the max-heap or min-heap property. To fix this, we swap the node that we're removing with the last element:
+As you know, removing an element could potentially invalidate the max-heap or min-heap property. To fix this, we swap the node that we are removing with the last element:
 
 	[ 10, 1, 2, 5, 7 ]
 
-The last element is the one that we'll return; we'll call `removeLast()` to remove it from the heap. The `(1)` is now out-of-order because it's smaller than its child, `(5)`, but sits higher in the tree. We call `shiftDown()` to repair this.
+The last element is the one that we will return; we will call `removeLast()` to remove it from the heap. The `(1)` is now out-of-order because it is smaller than its child, `(5)` but sits higher in the tree. We call `shiftDown()` to repair this.
 
-However, shifting down is not the only situation we need to handle -- it may also happen that the new element must be shifted up. Consider what happens if you remove `(5)` from the following heap:
+However, shifting down is not the only situation we need to handle. It may also happen that the new element must be shifted up. Consider what happens if you remove `(5)` from the following heap:
 
 ![We need to shift up](Images/Remove5.png)
 
@@ -267,7 +267,7 @@ In code it would look like this:
   }
 ```
 
-We simply call `insert()` for each of the values in the array. Simple enough, but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
+We simply call `insert()` for each of the values in the array. Simple enough but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
 
 If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order. 
 
@@ -286,9 +286,9 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 ## Searching the heap
 
-Heaps aren't made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element somehow. Searching is one way to do this but it's kind of slow.
+Heaps are not made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element. Searching is one way to do this, but it is slow.
 
-In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
+In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently, so a binary search will not work. You need to look at every node in the tree.
 
 Let's take our example heap again:
 
@@ -296,9 +296,9 @@ Let's take our example heap again:
 
 If we want to search for the index of node `(1)`, we could just step through the array `[ 10, 7, 2, 5, 1 ]` with a linear search.
 
-But even though the heap property wasn't conceived with searching in mind, we can still take advantage of it. We know that in a max-heap a parent node is always larger than its children, so we can ignore those children (and their children, and so on...) if the parent is already smaller than the value we're looking for.
+Even though the heap property was not conceived with searching in mind, we can still take advantage of it. We know that in a max-heap a parent node is always larger than its children, so we can ignore those children (and their children, and so on...) if the parent is already smaller than the value we are looking for.
 
-Let's say we want to see if the heap contains the value `8` (it doesn't). We start at the root `(10)`. This is obviously not what we're looking for, so we recursively look at its left and right child. The left child is `(7)`. That is also not what we want, but since this is a max-heap, we know there's no point in looking at the children of `(7)`. They will always be smaller than `7` and are therefore never equal to `8`. Likewise for the right child, `(2)`.
+Let's say we want to see if the heap contains the value `8` (it doesn't). We start at the root `(10)`. This is not what we are looking for, so we recursively look at its left and right child. The left child is `(7)`. That is also not what we want, but since this is a max-heap, we know there is no point in looking at the children of `(7)`. They will always be smaller than `7` and are therefore never equal to `8`; likewise, for the right child, `(2)`.
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
@@ -308,9 +308,9 @@ Despite this small optimization, searching is still an **O(n)** operation.
 
 See [Heap.swift](Heap.swift) for the implementation of these concepts in Swift. Most of the code is quite straightforward. The only tricky bits are in `shiftUp()` and `shiftDown()`.
 
-You've seen that there are two types of heaps: a max-heap and a min-heap. The only difference between them is in how they order their nodes: largest value first or smallest value first.
+You have seen that there are two types of heaps: a max-heap and a min-heap. The only difference between them is in how they order their nodes: largest value first or smallest value first.
 
-Rather than create two different versions, `MaxHeap` and `MinHeap`, there is just one `Heap` object and it takes an `isOrderedBefore` closure. This closure contains the logic that determines the order of two values. You've probably seen this before because it's also how Swift's `sort()` works.
+Rather than create two different versions, `MaxHeap` and `MinHeap`, there is just one `Heap` object and it takes an `isOrderedBefore` closure. This closure contains the logic that determines the order of two values. You have probably seen this before because it is also how Swift's `sort()` works.
 
 To make a max-heap of integers, you write:
 

From 52855ccbd3fb95704cd6375d44f1fa22512d04e1 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Sat, 1 Apr 2017 19:38:22 -0700
Subject: [PATCH 0883/1679] Update README.markdown

For an assignment in technical writings, I have revised this document.

Thanks,
Parvaneh
---
 Hash Table/README.markdown | 69 +++++++++++++++++++-------------------
 1 file changed, 34 insertions(+), 35 deletions(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 4399b0f86..958c3595a 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -2,13 +2,13 @@
 
 A hash table allows you to store and retrieve objects by a "key".
 
-Also called dictionary, map, associative array. There are other ways to implement these, such as with a tree or even a plain array, but hash table is the most common.
+A hash table is used to implement structures, such as a dictionary, a map, and an associative array. These structures can be implemented by a tree or a plain array, but it is efficient to use a hash table.
 
-This should explain why Swift's built-in `Dictionary` type requires that keys conform to the `Hashable` protocol: internally it uses a hash table, just like the one you'll learn about here.
+This should explain why Swift's built-in `Dictionary` type requires that keys conform to the `Hashable` protocol: internally it uses a hash table, like the one you will learn about here.
 
 ## How it works
 
-At its most basic, a hash table is nothing more than an array. Initially, this array is empty. When you put a value into the hash table under a certain key, it uses that key to calculate an index in the array, like so:
+A hash table is nothing more than an array. Initially, this array is empty. When you put a value into the hash table under a certain key, it uses that key to calculate an index in the array. Here is an example:
 
 ```swift
 hashTable["firstName"] = "Steve"
@@ -48,33 +48,33 @@ hashTable["hobbies"] = "Programming Swift"
 	+--------------+
 ```
 
-The trick is in how the hash table calculates those array indices. That's where the hashing comes in. When you write,
+The trick is how the hash table calculates those array indices. That is where the hashing comes in. When you write the following statement,
 
 ```swift
 hashTable["firstName"] = "Steve"
 ```
 
-the hash table takes the key `"firstName"` and asks it for its `hashValue` property. That's why keys must be `Hashable`. 
+the hash table takes the key `"firstName"` and asks it for its `hashValue` property. Hence, keys must be `Hashable`.
 
-When you do `"firstName".hashValue`, it returns a big integer: -4799450059917011053. Likewise, `"hobbies".hashValue` has the hash value 4799450060928805186. (The values you see may vary.)
+When you write `"firstName".hashValue`, it returns a big integer: -4799450059917011053. Likewise, `"hobbies".hashValue` has the hash value 4799450060928805186. (The values you see may vary.)
 
-Of course, these numbers are way too big to be used as indices into our array. One of them is even negative! A common way to make these big numbers more suitable is to first make the hash positive and then take the modulo with the array size.
+These numbers are big to be used as indices into our array, and one of them is even negative! A common way to make these big numbers  suitable is to first make the hash positive and then take the modulo with the array size.
 
-Our array has size 5, so the index for the `"firstName"` key becomes `abs(-4799450059917011053) % 5 = 3`. You can calculate for yourself that the array index for `"hobbies"` is 1.
+Our array has size 5, so the index for the `"firstName"` key becomes `abs(-4799450059917011053) % 5 = 3`. You can calculate that the array index for `"hobbies"` is 1.
 
-Using hashes in this manner is what makes the dictionary so efficient: to find an element in the hash table you only have to hash the key to get an array index and then look up the element in the underlying array. All these operations take a constant amount of time, so inserting, retrieving, and removing are all **O(1)**.
+Using hashes in this manner is what makes the dictionary efficient: to find an element in the hash table, you must hash the key to get an array index and then look up the element in the underlying array. All these operations take a constant amount of time, so inserting, retrieving, and removing are all **O(1)**.
 
-> **Note:** As you can see, it's hard to predict where in the array your objects end up. That's why dictionaries do not guarantee any particular order of the elements in the hash table.
+> **Note:** It is difficult to predict where in the array your objects end up. Hence, dictionaries do not guarantee any particular order of the elements in the hash table.
 
 ## Avoiding collisions
 
 There is one problem: because we take the modulo of the hash value with the size of the array, it can happen that two or more keys get assigned the same array index. This is called a collision.
 
-One way to avoid collisions is to have a very large array. That reduces the likelihood of two keys mapping to the same index. Another trick is to use a prime number for the array size. However, collisions are bound to occur so you need some way to handle them.
+One way to avoid collisions is to have a large array which reduces the likelihood of two keys mapping to the same index. Another trick is to use a prime number for the array size. However, collisions are bound to occur, so you need to find a way to handle them.
 
-Because our table is so small it's easy to show a collision. For example, the array index for the key `"lastName"` is also 3. That's a problem, as we don't want to overwrite the value that's already at this array index.
+Because our table is small, it is easy to show a collision. For example, the array index for the key `"lastName"` is also 3, but we do not want to overwrite the value that is already at this array index.
 
-There are a few ways to handle collisions. A common one is to use chaining. The array now looks as follows:
+A common way to handle collisions is to use chaining. The array looks as follows:
 
 ```swift
 	buckets:
@@ -91,25 +91,25 @@ There are a few ways to handle collisions. A common one is to use chaining. The
 	+-----+
 ```
 
-With chaining, keys and their values are not stored directly in the array. Instead, each array element is really a list of zero or more key/value pairs. The array elements are usually called the *buckets* and the lists are called the *chains*. So here we have 5 buckets and two of these buckets have chains. The other three buckets are empty.
+With chaining, keys and their values are not stored directly in the array. Instead, each array element is a list of zero or more key/value pairs. The array elements are usually called the *buckets* and the lists are called the *chains*. Here we have 5 buckets, and two of these buckets have chains. The other three buckets are empty.
 
-If we now write the following to retrieve an item from the hash table,
+If we write the following statement to retrieve an item from the hash table,
 
 ```swift
 let x = hashTable["lastName"]
 ```
 
-then this first hashes the key `"lastName"` to calculate the array index, which is 3. Bucket 3 has a chain, so we step through that list to find the value with the key `"lastName"`. That is done by comparing the keys, so here that involves a string comparison. The hash table sees that this key belongs to the last item in the chain and returns the corresponding value, `"Jobs"`.
+it first hashes the key `"lastName"` to calculate the array index, which is 3. Since bucket 3 has a chain, we step through the list to find the value with the key `"lastName"`. This is done by comparing the keys using a string comparison. The hash table checks that the key belongs to the last item in the chain and returns the corresponding value, `"Jobs"`.
 
-Common ways to implement this chaining mechanism are to use a linked list or another array. Technically speaking the order of the items in the chain doesn't matter, so you also can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
+Common ways to implement this chaining mechanism are to use a linked list or another array. Since the order of the items in the chain does not matter, you can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-It's important that chains do not become too long or looking up items in the hash table becomes really slow. Ideally, we would have no chains at all but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets and by using high-quality hash functions.
+Chains should not become long becasuse the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
 
-> **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. Of course, this approach has its own upsides and downsides.
+> **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. This approach has its own upsides and downsides.
 
 ## The code
 
-Let's look at a basic implementation of a hash table in Swift. We'll build it up step-by-step.
+Let's look at a basic implementation of a hash table in Swift. We will build it up step-by-step.
 
 ```swift
 public struct HashTable<Key: Hashable, Value> {
@@ -127,9 +127,9 @@ public struct HashTable<Key: Hashable, Value> {
   }
 ```
 
-The `HashTable` is a generic container and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for use in a chain and `Bucket` is an array of such `Elements`.
+The `HashTable` is a generic container, and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for useing in a chain, and `Bucket` is an array of such `Elements`.
 
-The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We're also keeping track of how many items have been added to the hash table using the `count` variable.
+The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We are also keeping track of how many items have been added to the hash table using the `count` variable.
 
 An example of how to create a new hash table object:
 
@@ -137,7 +137,7 @@ An example of how to create a new hash table object:
 var hashTable = HashTable<String, String>(capacity: 5)
 ```
 
-Currently the hash table doesn't do anything yet, so let's add the remaining functionality. First, add a helper method that calculates the array index for a given key:
+The hash table does not do anything yet, so let's add the remaining functionality. First, add a helper method that calculates the array index for a given key:
 
 ```swift
   private func index(forKey key: Key) -> Int {
@@ -145,9 +145,9 @@ Currently the hash table doesn't do anything yet, so let's add the remaining fun
   }
 ```
 
-This performs the calculation you saw earlier: it takes the absolute value of the key's `hashValue` modulo the size of the buckets array. We've put this in a function of its own because it gets used in a few different places.
+This performs the calculation you saw earlier: it takes the absolute value of the key's `hashValue` modulo the size of the buckets array. We have put this in a function of its own because it gets used in a few different places.
 
-There are four common things you'll do with a hash table or dictionary: 
+There are four common things you will do with a hash table or dictionary: 
 
 - insert a new element
 - look up an element
@@ -180,7 +180,7 @@ We can do all these things with a `subscript` function:
   }
 ```
 
-This calls three helper functions to do the actual work. Let's take a look at `value(forKey:)` first, which retrieves an object from the hash table.
+This calls three helper functions to do the actual work. Let's take a look at `value(forKey:)`which retrieves an object from the hash table.
 
 ```swift
   public func value(forKey key: Key) -> Value? {
@@ -193,10 +193,9 @@ This calls three helper functions to do the actual work. Let's take a look at `v
     return nil  // key not in hash table
   }
 ```
+First it calls `index(forKey:)` to convert the key into an array index. That gives us the bucket number, but this bucket may be used by more than one key if there were collisions. The `value(forKey:)` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
 
-First it calls `index(forKey:)` to convert the key into an array index. That gives us the bucket number, but if there were collisions this bucket may be used by more than one key. So `value(forKey:)` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
-
-The code to insert a new element or update an existing element lives in `updateValue(_:forKey:)`. It's a little bit more complicated:
+The code to insert a new element or update an existing element lives in `updateValue(_:forKey:)`. This is more complicated:
 
 ```swift
   public mutating func updateValue(_ value: Value, forKey key: Key) -> Value? {
@@ -218,9 +217,9 @@ The code to insert a new element or update an existing element lives in `updateV
   }
 ```
 
-Again, the first thing we do is convert the key into an array index to find the bucket. Then we loop through the chain for that bucket. If we find the key in the chain, it means we must update it with the new value. If the key is not in the chain, we insert the new key/value pair to the end of the chain.
+Again, the first step is to convert the key into an array index to find the bucket. Then we loop through the chain for that bucket. If we find the key in the chain, we must update it with the new value. If the key is not in the chain, we insert the new key/value pair to the end of the chain.
 
-As you can see, it's important that chains are kept short (by making the hash table large enough). Otherwise, you spend a lot of time in these `for`...`in` loops and the performance of the hash table will no longer be **O(1)** but more like **O(n)**.
+As you can see, it is important to keep the chains short (by making the hash table large enough). Otherwise, you spend excessive time in these `for`...`in` loops and the performance of the hash table will no longer be **O(1)** but more like **O(n)**.
 
 Removing is similar in that again it loops through the chain:
 
@@ -246,16 +245,16 @@ Try this stuff out in a playground. It should work just like a standard Swift `D
 
 ## Resizing the hash table
 
-This version of `HashTable` always uses an array of a fixed size or capacity. That's fine if you've got a good idea of many items you'll be storing in the hash table. For the capacity, choose a prime number that is greater than the maximum number of items you expect to store and you're good to go.
+This version of `HashTable` always uses an array of a fixed size or capacity. If you have many items to store in the hash table, for the capacity, choose a prime number greater than the maximum number of items.
 
 The *load factor* of a hash table is the percentage of the capacity that is currently used. If there are 3 items in a hash table with 5 buckets, then the load factor is `3/5 = 60%`.
 
-If the hash table is too small and the chains are long, the load factor can become greater than 1. That's not a good idea.
+If the hash table is small, and the chains are long, the load factor can become greater than 1, that is not a good idea.
 
-If the load factor becomes too high, say > 75%, you can resize the hash table. Adding the code for this is left as an exercise for the reader. Keep in mind that making the buckets array larger will change the array indices that the keys map to! To account for this, you'll have to insert all the elements again after resizing the array.
+If the load factor becomes high, greater than 75%, you can resize the hash table. Adding the code for this condition is left as an exercise for the reader. Keep in mind that making the buckets array larger will change the array indices that the keys map to! This requires you to insert all the elements again after resizing the array.
 
 ## Where to go from here?
 
-`HashTable` is quite basic. It might be fun to integrate it better with the Swift standard library by making it a `SequenceType`, for example.
+`HashTable` is quite basic. It might be efficient to integrate it with the Swift standard library by making it a `SequenceType`.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 7010d4ff4e28871cd06067aad15dcde031e745c8 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Sun, 2 Apr 2017 18:28:48 -0400
Subject: [PATCH 0884/1679] Fixed an issue with links that has spaces in the
 address

---
 Graph/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index 1ff1a82ac..a2531e808 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -28,7 +28,7 @@ The following are also graphs:
 
 ![Tree and linked list](Images/TreeAndList.png)
 
-On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
+On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked%20List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
 
 The very first graph I showed you contained *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
 
@@ -42,7 +42,7 @@ Like a tree this does not have any cycles in it (no matter where you start, ther
 
 Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that graphs are an extremely useful data structure.
 
-If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First Search/) or [depth-first search](../Depth-First Search) to find a solution.
+If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First%20Search/) or [depth-first search](../Depth-First%20Search) to find a solution.
 
 For example, let's say you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
 
@@ -50,7 +50,7 @@ For example, let's say you have a list of tasks where some tasks have to wait on
 
 Each vertex represents a task. Here, an edge between two vertices means that the source task must be completed before the destination task can start. So task C cannot start before B and D are finished, and B nor D can start before A is finished.
 
-Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
+Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological%20Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
 
 Whenever you're faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationship".
 

From 79255d2bb83cfbbcab0fb3f983bdc96e25c0bd4b Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Sun, 2 Apr 2017 19:43:48 -0400
Subject: [PATCH 0885/1679] Fixed white-space encoding in markdown links

---
 Heap/README.markdown | 40 ++++++++++++++++++++--------------------
 1 file changed, 20 insertions(+), 20 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 88ea25eeb..1bcb05e1b 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,11 +1,11 @@
 # Heap
 
-A heap is a [binary tree](../Binary Tree/) that lives inside an array, so it doesn't use parent/child pointers. The tree is partially sorted according to something called the "heap property" that determines the order of the nodes in the tree.
+A heap is a [binary tree](../Binary%20Tree/) that lives inside an array, so it doesn't use parent/child pointers. The tree is partially sorted according to something called the "heap property" that determines the order of the nodes in the tree.
 
 Common uses for heap:
 
-- For building [priority queues](../Priority Queue/).
-- The heap is the data structure supporting [heap sort](../Heap Sort/).
+- For building [priority queues](../Priority%20Queue/).
+- The heap is the data structure supporting [heap sort](../Heap%20Sort/).
 - Heaps are fast for when you often need to compute the minimum (or maximum) element of a collection.
 - Impressing your non-programmer friends.
 
@@ -21,7 +21,7 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority Queue/) where you want to quickly access the "most important" element.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority%20Queue/) where you want to quickly access the "most important" element.
 
 > **Note:** You can't really say anything else about the sort order of the heap. For example, in a max-heap the maximum element is always at index 0 but the minimum element isn’t necessarily the last one -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
@@ -29,11 +29,11 @@ As a result of this heap property, a max-heap always stores its largest item at
 
 A heap isn't intended to be a replacement for a binary search tree. But there are many similarities between the two and also some differences. Here are some of the bigger differences:
 
-**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
+**Order of the nodes.** In a [binary search tree (BST)](../Binary%20Search%20Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL Tree/) or [red-black tree](../Red-Black Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
+**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL%20Tree/) or [red-black tree](../Red-Black%20Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
 **Searching.** Searching a binary tree is really fast -- that's its whole purpose. In a heap, searching is slow. The purpose of a heap is to always put the largest (or smallest) node at the front, and to allow relatively fast inserts and deletes. Searching isn't a top priority.
 
@@ -54,7 +54,7 @@ If `i` is the index of a node, then the following formulas give the array indice
     parent(i) = floor((i - 1)/2)
     left(i)   = 2i + 1
     right(i)  = 2i + 2
-    
+
 Note that `right(i)` is simply `left(i) + 1`. The left and right nodes are always stored right next to each other.
 
 Let's use these formulas on the example. Fill in the array index and we should get the positions of the parent and child nodes in the array:
@@ -63,7 +63,7 @@ Let's use these formulas on the example. Fill in the array index and we should g
 |------|-------------|--------------|------------|-------------|
 | 10 | 0 | -1 | 1 | 2 |
 | 7 | 1 | 0 | 3 | 4 |
-| 2 | 2 | 0 | 5 | 6 | 
+| 2 | 2 | 0 | 5 | 6 |
 | 5 | 3 | 1 | 7 | 8 |
 | 1 | 4 | 1 | 9 | 10 |
 
@@ -76,7 +76,7 @@ Recall that in a max-heap, the parent's value is always greater than (or equal t
 ```swift
 array[parent(i)] >= array[i]
 ```
-	
+
 Verify that this heap property holds for the array from the example heap.
 
 As you can see, these equations let us find the parent or child index for any node without the need for pointers. True, it's slightly more complicated than just dereferencing a pointer but that's the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
@@ -104,14 +104,14 @@ You can’t start a new level unless the current lowest level is completely full
 Pop quiz! Let's say we have the array:
 
 	[ 10, 14, 25, 33, 81, 82, 99 ]
-	
+
 Is this a valid heap? The answer is yes! A sorted array from low-to-high is a valid min-heap. We can draw this heap as follows:
 
 ![A sorted array is a valid heap](Images/SortedArray.png)
 
 The heap property holds for each node because a parent is always smaller than its children. (Verify for yourself that an array sorted from high-to-low is always a valid max-heap.)
 
-> **Note:** But not every min-heap is necessarily a sorted array! It only works one way... To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
+> **Note:** But not every min-heap is necessarily a sorted array! It only works one way... To turn a heap back into a sorted array, you need to use [heap sort](../Heap%20Sort/).
 
 ## More math!
 
@@ -129,7 +129,7 @@ If the lowest level is completely full, then that level contains *2^h* nodes. Th
 
 The total number of nodes *n* in the entire heap is therefore *2^(h+1) - 1*. In the example, `2^4 - 1 = 16 - 1 = 15`.
 
-There are at most *ceil(n/2^(h+1))* nodes of height *h* in an *n*-element heap. 
+There are at most *ceil(n/2^(h+1))* nodes of height *h* in an *n*-element heap.
 
 The leaf nodes are always located at array indices *floor(n/2)* to *n-1*. We will make use of this fact to quickly build up the heap from an array. Verify this for the example if you don't believe it. ;-)
 
@@ -141,7 +141,7 @@ There are two primitive operations necessary to make sure the heap is a valid ma
 
 - `shiftUp()`: If the element is greater (max-heap) or smaller (min-heap) than its parent, it needs to be swapped with the parent. This makes it move up the tree.
 
-- `shiftDown()`. If the element is smaller (max-heap) or greater (min-heap) than its children, it needs to move down the tree. This operation is also called "heapify". 
+- `shiftDown()`. If the element is smaller (max-heap) or greater (min-heap) than its children, it needs to move down the tree. This operation is also called "heapify".
 
 Shifting up or down is a recursive procedure that takes **O(log n)** time.
 
@@ -161,7 +161,7 @@ All of the above take time **O(log n)** because shifting up or down is the most
 
 - `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you’re smart about this, it can be done in **O(n)** time.
 
-- [Heap sort](../Heap Sort/). Since the heap is really an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
+- [Heap sort](../Heap%20Sort/). Since the heap is really an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
 
 The heap also has a `peek()` function that returns the maximum (max-heap) or minimum (min-heap) element, without removing it from the heap. Time: **O(1)**.
 
@@ -187,7 +187,7 @@ The `(16)` was added to the first available space on the last row.
 
 Unfortunately, the heap property is no longer satisfied because `(2)` is above `(16)` and we want higher numbers above lower numbers. (This is a max-heap.)
 
-To restore the heap property, we're going to swap `(16)` and `(2)`. 
+To restore the heap property, we're going to swap `(16)` and `(2)`.
 
 ![The heap before insertion](Images/Insert2.png)
 
@@ -211,7 +211,7 @@ What happens to the empty spot at the top?
 
 ![The root is gone](Images/Remove1.png)
 
-When inserting, we put the new value at the end of the array. Here, we'll do the opposite: we're going to take the last object we have, stick it up on top of the tree, and restore the heap property. 
+When inserting, we put the new value at the end of the array. Here, we'll do the opposite: we're going to take the last object we have, stick it up on top of the tree, and restore the heap property.
 
 ![The last node goes to the root](Images/Remove2.png)
 
@@ -223,7 +223,7 @@ Keep shifting down until the node doesn't have any children or it is larger than
 
 ![The last node goes to the root](Images/Remove4.png)
 
-The time required for shifting all the way down is proportional to the height of the tree so it takes **O(log n)** time. 
+The time required for shifting all the way down is proportional to the height of the tree so it takes **O(log n)** time.
 
 > **Note:** `shiftUp()` and `shiftDown()` can only fix one out-of-place element at a time. If there are multiple elements in the wrong place, you need to call these functions once for each of those elements.
 
@@ -269,7 +269,7 @@ In code it would look like this:
 
 We simply call `insert()` for each of the values in the array. Simple enough, but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
 
-If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order. 
+If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order.
 
 In code:
 
@@ -288,7 +288,7 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 Heaps aren't made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element somehow. Searching is one way to do this but it's kind of slow.
 
-In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
+In a [binary search tree](../Binary%20Search%20Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
 
 Let's take our example heap again:
 
@@ -302,7 +302,7 @@ Let's say we want to see if the heap contains the value `8` (it doesn't). We sta
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
-> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority Queue/) that's built on a heap.
+> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority%20Queue/) that's built on a heap.
 
 ## The code
 

From bdb1b157cc2698b3e211069475399ef19958261e Mon Sep 17 00:00:00 2001
From: Jacopo <jmangia@kywix.com>
Date: Mon, 3 Apr 2017 21:26:14 +0100
Subject: [PATCH 0886/1679] Minimum Coin Change Problem - Dynamic Programming
 in Swift

---
 MinimumCoinChange/LICENSE                     | 201 ++++++++++++++++++
 MinimumCoinChange/Package.swift               |   7 +
 MinimumCoinChange/README.md                   |  41 ++++
 .../Sources/MinimumCoinChange.swift           |  76 +++++++
 MinimumCoinChange/Tests/LinuxMain.swift       |   6 +
 .../MinimumCoinChangeTests.swift              |  21 ++
 MinimumCoinChange/eurocoins.gif               | Bin 0 -> 90051 bytes
 7 files changed, 352 insertions(+)
 create mode 100755 MinimumCoinChange/LICENSE
 create mode 100644 MinimumCoinChange/Package.swift
 create mode 100755 MinimumCoinChange/README.md
 create mode 100644 MinimumCoinChange/Sources/MinimumCoinChange.swift
 create mode 100644 MinimumCoinChange/Tests/LinuxMain.swift
 create mode 100644 MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
 create mode 100644 MinimumCoinChange/eurocoins.gif

diff --git a/MinimumCoinChange/LICENSE b/MinimumCoinChange/LICENSE
new file mode 100755
index 000000000..8dada3eda
--- /dev/null
+++ b/MinimumCoinChange/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
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diff --git a/MinimumCoinChange/Package.swift b/MinimumCoinChange/Package.swift
new file mode 100644
index 000000000..749073782
--- /dev/null
+++ b/MinimumCoinChange/Package.swift
@@ -0,0 +1,7 @@
+// swift-tools-version:3.1
+
+import PackageDescription
+
+let package = Package(
+    name: "MinimumCoinChange"
+)
diff --git a/MinimumCoinChange/README.md b/MinimumCoinChange/README.md
new file mode 100755
index 000000000..c9cd71cd1
--- /dev/null
+++ b/MinimumCoinChange/README.md
@@ -0,0 +1,41 @@
+# Minimum Coin Change
+Minimum Coin Change problem algorithm implemented in Swift comparing dynamic programming algorithm design to traditional greedy approach.
+
+Written for Swift Algorithm Club by Jacopo Mangiavacchi
+
+![Coins](eurocoins.gif)
+
+# Introduction
+
+In the traditional coin change problem you have to find all the different ways to change some given money in a particular amount of coins using a given amount of set of coins (i.e. 1 cent, 2 cents, 5 cents, 10 cents etc.).
+
+For example using Euro cents the total of 4 cents value of money can be changed in these possible ways:
+
+- Four 1 cent coins
+- Two 2 cent coins
+- One 2 cent coin and two 1 cent coins
+
+The minimum coin change problem is a variation of the generic coin change problem where you need to find the best option for changing the money returning the less number of coins.
+
+For example using Euro cents the best possible change for 4 cents are two 2 cent coins with a total of two coins.
+
+
+# Greedy Solution
+
+A simple approach for implementing the Minimum Coin Change algorithm in a very efficient way is to start subtracting from the input value the greater possible coin value from the given amount of set of coins available and iterate subtracting the next greater possible coin value on the resulting difference.
+
+For example from the total of 4 Euro cents of the example above you can subtract initially 2 cents as  the other biggest coins value (from 5 cents to above) are to bigger for the current 4 Euro cent value. Once used the first 2 cents coin you iterate again with the same logic for the rest of 2 cents and select another 2 cents coin and finally return the two 2 cents coins as the best change.
+
+Most of the time the result for this greedy approach is optimal but for some set of coins the result will not be the optimal.
+
+Indeed, if we use the a set of these three different coins set with values 1, 3 and 4 and execute this  greedy algorithm for asking the best change for the value 6 we will get one coin of 4 and two coins of 1 instead of two coins of 3.
+
+
+# Dynamic Programming Solution
+
+A classic dynamic programming strategy will iterate selecting in order a possible coin from the given amount of set of coins and finding using recursive calls the minimum coin change on the difference from the passed value and the selected coin. For any interaction the algorithm select from all possible combinations the one with the less number of coins used.
+
+The dynamic programming approach will always select the optimal change but it will require a number of steps that is at least quadratic in the goal amount to change.
+
+In this Swift implementation in order to optimize the overall performance we use an internal data structure for caching the result for best minimum coin change for previous values.
+
diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
new file mode 100644
index 000000000..db7edecbe
--- /dev/null
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -0,0 +1,76 @@
+//
+//  Minimum Coin Change Problem 
+//  Compare Greedy Algorithm and Dynamic Programming Algorithm in Swift
+//
+//  Created by Jacopo Mangiavacchi on 04/03/17.
+//
+
+import Foundation
+
+public struct MinimumCoinChange {
+    private let sortedCoinSet: [Int]
+    private var cache: [Int : [Int]]
+    
+    public init(coinSet: [Int]) {
+        self.sortedCoinSet = coinSet.sorted(by: { $0 > $1} )
+        self.cache = [:]
+    }
+
+    //Greedy Algorithm
+    public func changeGreedy(_ value: Int) -> [Int] {
+        var change:  [Int] = []
+        var newValue = value
+        
+        for coin in sortedCoinSet {
+            while newValue - coin >= 0 {
+                change.append(coin)
+                newValue -= coin
+            }
+
+            if newValue  == 0 {
+                break
+            }
+        }
+        
+        return change
+    }
+
+    //Dynamic Programming Algorithm
+    public mutating func changeDynamic(_ value: Int) -> [Int] {
+        if value <= 0 {
+            return []
+        }
+        
+        if let cached = cache[value] {
+            return cached
+        }
+        
+        var change:  [Int] = []
+        
+        var potentialChangeArray: [[Int]] = []
+        
+        for coin in sortedCoinSet {
+            if value - coin >= 0 {
+                var potentialChange: [Int] = []
+                 potentialChange.append(coin)
+                let newPotentialValue = value - coin
+
+                if value  > 0 {
+                    potentialChange.append(contentsOf: changeDynamic(newPotentialValue))
+                }
+
+                //print("value: \(value) coin: \(coin) potentialChange: \(potentialChange)")
+                potentialChangeArray.append(potentialChange)
+            }
+        }
+        
+        if potentialChangeArray.count > 0 {
+            let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
+            change = sortedPotentialChangeArray[0]
+        }
+        
+        cache[value] = change
+        return change
+    }
+}
+
diff --git a/MinimumCoinChange/Tests/LinuxMain.swift b/MinimumCoinChange/Tests/LinuxMain.swift
new file mode 100644
index 000000000..db61c6011
--- /dev/null
+++ b/MinimumCoinChange/Tests/LinuxMain.swift
@@ -0,0 +1,6 @@
+import XCTest
+@testable import MinimumCoinChangeTests
+
+XCTMain([
+    testCase(MinimumCoinChangeTests.allTests),
+])
diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
new file mode 100644
index 000000000..86c9007ba
--- /dev/null
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -0,0 +1,21 @@
+import XCTest
+@testable import MinimumCoinChange
+
+class MinimumCoinChangeTests: XCTestCase {
+    func testExample() {
+        var mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+
+        for i in 0..<100 {
+            let greedy = mcc.changeGreedy(i)
+            let dynamic = mcc.changeDynamic(i)
+
+            if greedy.count != dynamic.count {
+                print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
+            }
+        }
+    }
+
+    static var allTests = [
+        ("testExample", testExample),
+    ]
+}
diff --git a/MinimumCoinChange/eurocoins.gif b/MinimumCoinChange/eurocoins.gif
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From 3f7aaa2799db7c94076bb3155a83811a7c596708 Mon Sep 17 00:00:00 2001
From: Weihang Lo <weihanglotw@gmail.com>
Date: Tue, 4 Apr 2017 09:19:14 +0800
Subject: [PATCH 0887/1679] fix: broken links

---
 AVL Tree/README.markdown                      |  4 +-
 Bounded Priority Queue/README.markdown        |  2 +-
 Count Occurrences/README.markdown             |  6 +--
 Depth-First Search/README.markdown            |  6 +--
 Deque/README.markdown                         | 42 +++++++++----------
 Heap Sort/README.markdown                     |  2 +-
 Huffman Coding/README.markdown                | 28 ++++++-------
 Knuth-Morris-Pratt/README.markdown            | 32 +++++++-------
 Kth Largest Element/README.markdown           |  6 +--
 .../README.markdown                           |  4 +-
 Priority Queue/README.markdown                |  6 +--
 Quicksort/README.markdown                     | 24 +++++------
 Segment Tree/README.markdown                  | 12 +++---
 Selection Sort/README.markdown                | 10 ++---
 14 files changed, 92 insertions(+), 92 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index a9218203a..c8d8d4628 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -53,7 +53,7 @@ For the rotation we're using the terminology:
 * *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
 * *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation
 
-Let take an example of balancing the unbalanced tree using *Right* (clockwise direction) rotation: 
+Let take an example of balancing the unbalanced tree using *Right* (clockwise direction) rotation:
 
 ![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)
 
@@ -76,7 +76,7 @@ Insertion never needs more than 2 rotations. Removal might require up to __log(n
 
 ## The code
 
-Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
+Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary%20Search%20Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
 
 > **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary%20Search%20Tree/). It will make the rest of the AVL tree easier to understand.
 
diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
index 4e4c89272..8cbaa85b2 100644
--- a/Bounded Priority Queue/README.markdown	
+++ b/Bounded Priority Queue/README.markdown	
@@ -26,7 +26,7 @@ Suppose that we wish to insert the element `G` with priority 0.1 into this BPQ.
 
 ## Implementation
 
-While a [heap](../Heap/) may be a really simple implementation for a priority queue, a sorted [linked list](../Linked List/) allows for **O(k)** insertion and **O(1)** deletion, where **k** is the bounding number of elements.
+While a [heap](../Heap/) may be a really simple implementation for a priority queue, a sorted [linked list](../Linked%20List/) allows for **O(k)** insertion and **O(1)** deletion, where **k** is the bounding number of elements.
 
 Here's how you could implement it in Swift:
 
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 4c65c4219..85b77d2d0 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -36,7 +36,7 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     }
     return low
   }
-  
+
   func rightBoundary() -> Int {
     var low = 0
     var high = a.count
@@ -50,12 +50,12 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     }
     return low
   }
-  
+
   return rightBoundary() - leftBoundary()
 }
 ```
 
-Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the [binary search](../Binary Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.
+Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.
 
 To test this algorithm, copy the code to a playground and then do:
 
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index 9e1a5112d..98a19e0cb 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -40,7 +40,7 @@ func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
 }
 ```
 
-Where a [breadth-first search](../Breadth-First Search/) visits all immediate neighbors first, a depth-first search tries to go as deep down the tree or graph as it can.
+Where a [breadth-first search](../Breadth-First%20Search/) visits all immediate neighbors first, a depth-first search tries to go as deep down the tree or graph as it can.
 
 Put this code in a playground and test it like so:
 
@@ -71,13 +71,13 @@ print(nodesExplored)
 ```
 
 This will output: `["a", "b", "d", "e", "h", "f", "g", "c"]`
-   
+
 ## What is DFS good for?
 
 Depth-first search can be used to solve many problems, for example:
 
 * Finding connected components of a sparse graph
-* [Topological sorting](../Topological Sort/) of nodes in a graph
+* [Topological sorting](../Topological%20Sort/) of nodes in a graph
 * Finding bridges of a graph (see: [Bridges](https://en.wikipedia.org/wiki/Bridge_(graph_theory)#Bridge-finding_algorithm))
 * And lots of others!
 
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 67a734576..fda1de5f8 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -9,23 +9,23 @@ Here is a very basic implementation of a deque in Swift:
 ```swift
 public struct Deque<T> {
   private var array = [T]()
-  
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public mutating func enqueue(_ element: T) {
     array.append(element)
   }
-  
+
   public mutating func enqueueFront(_ element: T) {
     array.insert(element, atIndex: 0)
   }
-  
+
   public mutating func dequeue() -> T? {
     if isEmpty {
       return nil
@@ -33,7 +33,7 @@ public struct Deque<T> {
       return array.removeFirst()
     }
   }
-  
+
   public mutating func dequeueBack() -> T? {
     if isEmpty {
       return nil
@@ -41,11 +41,11 @@ public struct Deque<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peekFront() -> T? {
     return array.first
   }
-  
+
   public func peekBack() -> T? {
     return array.last
   }
@@ -73,7 +73,7 @@ deque.dequeue()       // 5
 This particular implementation of `Deque` is simple but not very efficient. Several operations are **O(n)**, notably `enqueueFront()` and `dequeue()`. I've included it only to show the principle of what a deque does.
 
 ## A more efficient version
-  
+
 The reason that `dequeue()` and `enqueueFront()` are **O(n)** is that they work on the front of the array. If you remove an element at the front of an array, what happens is that all the remaining elements need to be shifted in memory.
 
 Let's say the deque's array contains the following items:
@@ -92,7 +92,7 @@ Likewise, inserting an element at the front of the array is expensive because it
 
 First, the elements `2`, `3`, and `4` are moved up by one position in the computer's memory, and then the new element `5` is inserted at the position where `2` used to be.
 
-Why is this not an issue at for `enqueue()` and `dequeueBack()`? Well, these operations are performed at the end of the array. The way resizable arrays are implemented in Swift is by reserving a certain amount of free space at the back. 
+Why is this not an issue at for `enqueue()` and `dequeueBack()`? Well, these operations are performed at the end of the array. The way resizable arrays are implemented in Swift is by reserving a certain amount of free space at the back.
 
 Our initial array `[ 1, 2, 3, 4]` actually looks like this in memory:
 
@@ -120,26 +120,26 @@ public struct Deque<T> {
   private var head: Int
   private var capacity: Int
   private let originalCapacity:Int
-  
+
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
     originalCapacity = self.capacity
     array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
-  
+
   public var count: Int {
     return array.count - head
   }
-  
+
   public mutating func enqueue(_ element: T) {
     array.append(element)
   }
-  
+
   public mutating func enqueueFront(_ element: T) {
     // this is explained below
   }
@@ -155,7 +155,7 @@ public struct Deque<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peekFront() -> T? {
     if isEmpty {
       return nil
@@ -163,7 +163,7 @@ public struct Deque<T> {
       return array[head]
     }
   }
-  
+
   public func peekBack() -> T? {
     if isEmpty {
       return nil
@@ -176,7 +176,7 @@ public struct Deque<T> {
 
 It still largely looks the same -- `enqueue()` and `dequeueBack()` haven't changed -- but there are also a few important differences. The array now stores objects of type `T?` instead of just `T` because we need some way to mark array elements as being empty.
 
-The `init` method allocates a new array that contains a certain number of `nil` values. This is the free room we have to work with at the beginning of the array. By default this creates 10 empty spots. 
+The `init` method allocates a new array that contains a certain number of `nil` values. This is the free room we have to work with at the beginning of the array. By default this creates 10 empty spots.
 
 The `head` variable is the index in the array of the front-most object. Since the queue is currently empty, `head` points at an index beyond the end of the array.
 
@@ -219,7 +219,7 @@ Notice how the array has resized itself. There was no room to add the `1`, so Sw
 	                          |
 	                          head
 
-> **Note:** You won't see those empty spots at the back of the array when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up. 
+> **Note:** You won't see those empty spots at the back of the array when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up.
 
 The `dequeue()` method does the opposite of `enqueueFront()`, it reads the value at `head`, sets the array element back to `nil`, and then moves `head` one position to the right:
 
@@ -250,7 +250,7 @@ There is one tiny problem... If you enqueue a lot of objects at the front, you'r
   }
 ```
 
-If `head` equals 0, there is no room left at the front. When that happens, we add a whole bunch of new `nil` elements to the array. This is an **O(n)** operation but since this cost gets divided over all the `enqueueFront()`s, each individual call to `enqueueFront()` is still **O(1)** on average. 
+If `head` equals 0, there is no room left at the front. When that happens, we add a whole bunch of new `nil` elements to the array. This is an **O(n)** operation but since this cost gets divided over all the `enqueueFront()`s, each individual call to `enqueueFront()` is still **O(1)** on average.
 
 > **Note:** We also multiply the capacity by 2 each time this happens, so if your queue grows bigger and bigger, the resizing happens less often. This is also what Swift arrays automatically do at the back.
 
@@ -302,7 +302,7 @@ This way we can strike a balance between fast enqueuing and dequeuing at the fro
 
 ## See also
 
-Other ways to implement deque are by using a [doubly linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or two [stacks](../Stack/) facing opposite directions.
+Other ways to implement deque are by using a [doubly linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or two [stacks](../Stack/) facing opposite directions.
 
 [A fully-featured deque implementation in Swift](https://github.com/lorentey/Deque)
 
diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index 5f047f82b..7fdd8d2ca 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -40,7 +40,7 @@ And fix up the heap to make it valid max-heap again:
 
 As you can see, the largest items are making their way to the back. We repeat this process until we arrive at the root node and then the whole array is sorted.
 
-> **Note:** This process is very similar to [selection sort](../Selection Sort/), which repeatedly looks for the minimum item in the remainder of the array. Extracting the minimum or maximum value is what heaps are good at.
+> **Note:** This process is very similar to [selection sort](../Selection%20Sort/), which repeatedly looks for the minimum item in the remainder of the array. Extracting the minimum or maximum value is what heaps are good at.
 
 Performance of heap sort is **O(n lg n)** in best, worst, and average case. Because we modify the array directly, heap sort can be performed in-place. But it is not a stable sort: the relative order of identical elements is not preserved.
 
diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 6b2c0d245..4e6f75514 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -16,7 +16,7 @@ If you count how often each byte appears, you can clearly see that some bytes oc
 	    c: 2	              p: 1
 	    r: 2	              e: 1
 	    n: 2	              i: 1
-	
+
 We can assign bit strings to each of these bytes. The more common a byte is, the fewer bits we assign to it. We might get something like this:
 
 	space: 5    010           u: 1    11001
@@ -30,12 +30,12 @@ We can assign bit strings to each of these bytes. The more common a byte is, the
 
 Now if we replace the original bytes with these bit strings, the compressed output becomes:
 
-	101 000 010 111 11001 0011 10001 010 0010 000 1001 11010 101 
+	101 000 010 111 11001 0011 10001 010 0010 000 1001 11010 101
 	s   o   _   m   u     c    h     _   w    o   r    d     s
-	
+
 	010 0010 000 0010 010 111 11011 0110 01111 010 0011 000 111
 	_   w    o   w    _   m   a     n    y     _   c    o   m
-	
+
 	11000 1001 01110 101 101 10000 000 0110 0
 	p     r    e     s   s   i     o   n
 
@@ -57,7 +57,7 @@ The edges between the nodes either say "1" or "0". These correspond to the bit-e
 
 Compression is then a matter of looping through the input bytes, and for each byte traverse the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
 
-For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`. 
+For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`.
 
 Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until we get to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
 
@@ -137,7 +137,7 @@ Here are the definitions we need:
 ```swift
 class Huffman {
   typealias NodeIndex = Int
- 
+
   struct Node {
     var count = 0
     var index: NodeIndex = -1
@@ -152,7 +152,7 @@ class Huffman {
 }
 ```
 
-The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
+The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary%20Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
 
 Note that `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we'll add more nodes as we build up the actual tree. For the moment there isn't a tree yet, just 256 separate leaf nodes with no connections between them. All the node counts are 0.
 
@@ -183,7 +183,7 @@ Instead, we'll add a method to export the frequency table without all the pieces
     var byte: UInt8 = 0
     var count = 0
   }
-  
+
   func frequencyTable() -> [Freq] {
     var a = [Freq]()
     for i in 0..<256 where tree[i].count > 0 {
@@ -209,7 +209,7 @@ To build the tree, we do the following:
 2. Create a new parent node that links these two nodes together.
 3. This repeats over and over until only one node with no parent remains. This becomes the root node of the tree.
 
-This is an ideal place to use a [priority queue](../Priority Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
+This is an ideal place to use a [priority queue](../Priority%20Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
 
 The function `buildTree()` then becomes:
 
@@ -233,7 +233,7 @@ The function `buildTree()` then becomes:
 
       tree[node1.index].parent = parentNode.index    // 4
       tree[node2.index].parent = parentNode.index
-      
+
       queue.enqueue(parentNode)                      // 5
     }
 
@@ -286,7 +286,7 @@ Now that we know how to build the compression tree from the frequency table, we
   }
 ```
 
-This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits. 
+This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits.
 
 Then it loops through the entire input and for each byte calls `traverseTree()`. That method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
 
@@ -309,7 +309,7 @@ The interesting stuff happens in `traverseTree()`. This is a recursive method:
   }
 ```
 
-When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again. 
+When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again.
 
 As we're going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it's the right node, we emit a 0.
 
@@ -395,10 +395,10 @@ Here's how you would use the decompression method:
 
 ```swift
   let frequencyTable = huffman1.frequencyTable()
-  
+
   let huffman2 = Huffman()
   let decompressedData = huffman2.decompressData(compressedData, frequencyTable: frequencyTable)
-  
+
   let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
 ```
 
diff --git a/Knuth-Morris-Pratt/README.markdown b/Knuth-Morris-Pratt/README.markdown
index f01b87b3d..95fdea9e9 100644
--- a/Knuth-Morris-Pratt/README.markdown
+++ b/Knuth-Morris-Pratt/README.markdown
@@ -1,9 +1,9 @@
 # Knuth-Morris-Pratt String Search
 
-Goal: Write a linear-time string matching algorithm in Swift that returns the indexes of all the occurrencies of a given pattern. 
- 
+Goal: Write a linear-time string matching algorithm in Swift that returns the indexes of all the occurrencies of a given pattern.
+
 In other words, we want to implement an `indexesOf(pattern: String)` extension on `String` that returns an array `[Int]` of integers, representing all occurrences' indexes of the search pattern, or `nil` if the pattern could not be found inside the string.
- 
+
 For example:
 
 ```swift
@@ -16,7 +16,7 @@ concert.indexesOf(ptnr: "🎻🎷")   // Output: [6]
 
 The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm) is considered one of the best algorithms for solving the pattern matching problem. Although in practice [Boyer-Moore](../Boyer-Moore/) is usually preferred, the algorithm that we will introduce is simpler, and has the same (linear) running time.
 
-The idea behind the algorithm is not too different from the [naive string search](../Brute-Force String Search/) procedure. As it, Knuth-Morris-Pratt aligns the text with the pattern and goes with character comparisons from left to right. But, instead of making a shift of one character when a mismatch occurs, it uses a more intelligent way to move the pattern along the text. In fact, the algorithm features a pattern pre-processing stage where it acquires all the informations that will make the algorithm skip redundant comparisons, resulting in larger shifts.
+The idea behind the algorithm is not too different from the [naive string search](../Brute-Force%20String%20Search/) procedure. As it, Knuth-Morris-Pratt aligns the text with the pattern and goes with character comparisons from left to right. But, instead of making a shift of one character when a mismatch occurs, it uses a more intelligent way to move the pattern along the text. In fact, the algorithm features a pattern pre-processing stage where it acquires all the informations that will make the algorithm skip redundant comparisons, resulting in larger shifts.
 
 The pre-processing stage produces an array (called `suffixPrefix` in the code) of integers in which every element `suffixPrefix[i]` records the length of the longest proper suffix of `P[0...i]` (where `P` is the pattern) that matches a prefix of `P`. In other words, `suffixPrefix[i]` is the longest proper substring of `P` that ends at position `i` and that is a prefix of `P`. Just a quick example. Consider `P = "abadfryaabsabadffg"`, then `suffixPrefix[4] = 0`, `suffixPrefix[9] = 2`, `suffixPrefix[14] = 4`.
 There are different ways to obtain the values of `SuffixPrefix` array. We will use the method based on the [Z-Algorithm](../Z-Algorithm/). This function takes in input the pattern and produces an array of integers. Each element represents the length of the longest substring starting at position `i` of `P` and that matches a prefix of `P`. You can notice that the two arrays are similar, they record the same informations but on the different places. We only have to find a method to map `Z[i]` to `suffixPrefix[j]`. It is not that difficult and this is the code that will do for us:
@@ -93,10 +93,10 @@ extension String {
 ```
 
 Let's make an example reasoning with the code above. Let's consider the string `P = ACTGACTA"`, the consequentially obtained `suffixPrefix` array equal to `[0, 0, 0, 0, 0, 0, 3, 1]`, and the text `T = "GCACTGACTGACTGACTAG"`. The algorithm begins with the text and the pattern aligned like below. We have to compare `T[0]` with `P[0]`.  
-  
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:      ^
     pattern:        ACTGACTA
     patternIndex:   ^
@@ -104,54 +104,54 @@ Let's make an example reasoning with the code above. Let's consider the string `
     suffixPrefix:   00000031
 
 We have a mismatch and we move on comparing `T[1]` and `P[0]`. We have to check if a pattern occurrence is present but there is not. So, we have to shift the pattern right and by doing so we have to check `suffixPrefix[1 - 1]`. Its value is `0` and we restart by comparing `T[1]` with `P[0]`. Again a mismath occurs, so we go on with `T[2]` and `P[0]`.
-  
+
                               1      
                     0123456789012345678
     text:           GCACTGACTGACTGACTAG
-    textIndex:        ^ 
+    textIndex:        ^
     pattern:          ACTGACTA
     patternIndex:     ^
     suffixPrefix:     00000031
 
 This time we have a match. And it continues until position `8`. Unfortunately the length of the match is not equal to the pattern length, we cannot report an occurrence. But we are still lucky because we can use the values computed in the `suffixPrefix` array now. In fact, the length of the match is `7`, and if we look at the element `suffixPrefix[7 - 1]` we discover that is `3`. This information tell us that that the prefix of `P` matches the suffix of the susbtring `T[0...8]`. So the `suffixPrefix` array guarantees us that the two substring match and that we do not have to compare their characters, so we can shift right the pattern for more than one character!
 The comparisons restart from `T[9]` and `P[3]`.  
-      
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:               ^
     pattern:              ACTGACTA
     patternIndex:            ^
     suffixPrefix:         00000031
 
 They match so we continue the compares until position `13` where a misatch occurs beetwen charcter `G` and `A`. Just like before, we are lucky and we can use the `suffixPrefix` array to shift right the pattern.
-      
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:                   ^
     pattern:                  ACTGACTA
     patternIndex:                ^
     suffixPrefix:             00000031
 
 Again, we have to compare. But this time the comparisons finally take us to an occurrence, at position `17 - 7 = 10`.
-      
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:                       ^
     pattern:                  ACTGACTA
     patternIndex:                    ^
     suffixPrefix:             00000031
 
 The algorithm than tries to compare `T[18]` with `P[1]` (because we used the element `suffixPrefix[8 - 1] = 1`) but it fails and at the next iteration it ends its work.
- 
+
 
 The pre-processing stage involves only the pattern. The running time of the Z-Algorithm is linear and takes `O(n)`, where `n` is the length of the pattern `P`. After that, the search stage does not "overshoot" the length of the text `T` (call it `m`). It can be be proved that number of comparisons of the search stage is bounded by `2 * m`. The final running time of the Knuth-Morris-Pratt algorithm is `O(n + m)`.
 
 
 > **Note:** To execute the code in the [KnuthMorrisPratt.swift](./KnuthMorrisPratt.swift) you have to copy the [ZAlgorithm.swift](../Z-Algorithm/ZAlgorithm.swift) file contained in the [Z-Algorithm](../Z-Algorithm/) folder. The [KnuthMorrisPratt.playground](./KnuthMorrisPratt.playground) already includes the definition of the `Zeta` function.
 
-Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"](https://books.google.it/books/about/Algorithms_on_Strings_Trees_and_Sequence.html?id=Ofw5w1yuD8kC&redir_esc=y) by Dan Gusfield, Cambridge University Press, 1997. 
+Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"](https://books.google.it/books/about/Algorithms_on_Strings_Trees_and_Sequence.html?id=Ofw5w1yuD8kC&redir_esc=y) by Dan Gusfield, Cambridge University Press, 1997.
 
 *Written for Swift Algorithm Club by Matteo Dunnhofer*
diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index d50d691a1..53bec1c1c 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -44,7 +44,7 @@ Of course, if you were looking for the k-th *smallest* element, you'd use `a[k]`
 
 ## A faster solution
 
-There is a clever algorithm that combines the ideas of [binary search](../Binary Search/) and [quicksort](../Quicksort/) to arrive at an **O(n)** solution.
+There is a clever algorithm that combines the ideas of [binary search](../Binary%20Search/) and [quicksort](../Quicksort/) to arrive at an **O(n)** solution.
 
 Recall that binary search splits the array in half over and over again, to quickly narrow in on the value you're searching for. That's what we'll do here too.
 
@@ -86,7 +86,7 @@ The following function implements these ideas:
 ```swift
 public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
   var a = array
-  
+
   func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
     swap(&a, pivotIndex, high)
@@ -120,7 +120,7 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
       return a[low]
     }
   }
-  
+
   precondition(a.count > 0)
   return randomizedSelect(&a, 0, a.count - 1, k)
 }
diff --git a/Minimum Spanning Tree (Unweighted)/README.markdown b/Minimum Spanning Tree (Unweighted)/README.markdown
index cfd29c987..23f18c335 100644
--- a/Minimum Spanning Tree (Unweighted)/README.markdown	
+++ b/Minimum Spanning Tree (Unweighted)/README.markdown	
@@ -16,7 +16,7 @@ Drawn as a more conventional tree it looks like this:
 
 ![An actual tree](Images/Tree.png)
 
-To calculate the minimum spanning tree on an unweighted graph, we can use the [breadth-first search](../Breadth-First Search/) algorithm. Breadth-first search starts at a source node and traverses the graph by exploring the immediate neighbor nodes first, before moving to the next level neighbors. If we tweak this algorithm by selectively removing edges, then it can convert the graph into the minimum spanning tree.
+To calculate the minimum spanning tree on an unweighted graph, we can use the [breadth-first search](../Breadth-First%20Search/) algorithm. Breadth-first search starts at a source node and traverses the graph by exploring the immediate neighbor nodes first, before moving to the next level neighbors. If we tweak this algorithm by selectively removing edges, then it can convert the graph into the minimum spanning tree.
 
 Let's step through the example. We start with the source node `a`, add it to a queue and mark it as visited.
 
@@ -185,6 +185,6 @@ print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
                            // [node: h edges: ["g", "i"]]
 ```
 
-> **Note:** On an unweighed graph, any spanning tree is always a minimal spanning tree. This means you can also use a [depth-first search](../Depth-First Search) to find the minimum spanning tree.
+> **Note:** On an unweighed graph, any spanning tree is always a minimal spanning tree. This means you can also use a [depth-first search](../Depth-First%20Search) to find the minimum spanning tree.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Priority Queue/README.markdown b/Priority Queue/README.markdown
index 8308ec16f..fbbcaa0f3 100644
--- a/Priority Queue/README.markdown	
+++ b/Priority Queue/README.markdown	
@@ -12,7 +12,7 @@ Examples of algorithms that can benefit from a priority queue:
 
 - Event-driven simulations. Each event is given a timestamp and you want events to be performed in order of their timestamps. The priority queue makes it easy to find the next event that needs to be simulated.
 - Dijkstra's algorithm for graph searching uses a priority queue to calculate the minimum cost.
-- [Huffman coding](../Huffman Coding/) for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.
+- [Huffman coding](../Huffman%20Coding/) for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.
 - A* pathfinding for artificial intelligence.
 - Lots of other places!
 
@@ -31,8 +31,8 @@ Common operations on a priority queue:
 
 There are different ways to implement priority queues:
 
-- As a [sorted array](../Ordered Array/). The most important item is at the end of the array. Downside: inserting new items is slow because they must be inserted in sorted order.
-- As a balanced [binary search tree](../Binary Search Tree/). This is great for making a double-ended priority queue because it implements both "find minimum" and "find maximum" efficiently.
+- As a [sorted array](../Ordered%20Array/). The most important item is at the end of the array. Downside: inserting new items is slow because they must be inserted in sorted order.
+- As a balanced [binary search tree](../Binary%20Search%20Tree/). This is great for making a double-ended priority queue because it implements both "find minimum" and "find maximum" efficiently.
 - As a [heap](../Heap/). The heap is a natural data structure for a priority queue. In fact, the two terms are often used as synonyms. A heap is more efficient than a sorted array because a heap only has to be partially sorted. All heap operations are **O(log n)**.
 
 Here's a Swift priority queue based on a heap:
diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index d359ecb5c..e0bd8e604 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -14,7 +14,7 @@ func quicksort<T: Comparable>(_ a: [T]) -> [T] {
   let less = a.filter { $0 < pivot }
   let equal = a.filter { $0 == pivot }
   let greater = a.filter { $0 > pivot }
-  
+
   return quicksort(less) + equal + quicksort(greater)
 }
 ```
@@ -30,7 +30,7 @@ Here's how it works. When given an array, `quicksort()` splits it up into three
 
 All the elements less than the pivot go into a new array called `less`. All the elements equal to the pivot go into the `equal` array. And you guessed it, all elements greater than the pivot go into the third array, `greater`. This is why the generic type `T` must be `Comparable`, so we can compare the elements with `<`, `==`, and `>`.
 
-Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `greater` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
+Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `greater` array, then glues those sorted subarrays back together with the `equal` array to get the final result.
 
 ## An example
 
@@ -73,7 +73,7 @@ The `less` array is empty because there was no value smaller than `-1`; the othe
 That `greater` array was:
 
 	[ 3, 2, 5 ]
-	
+
 This works just the same way as before: we pick the middle element `2` as the pivot and fill up the subarrays:
 
 	less:    [ ]
@@ -122,7 +122,7 @@ There is no guarantee that partitioning keeps the elements in the same relative
 
 	[ 3, 0, 5, 2, -1, 1, 8, 8, 14, 26, 10, 27, 9 ]
 
-The only guarantee is that to the left of the pivot are all the smaller elements and to the right are all the larger elements. Because partitioning can change the original order of equal elements, quicksort does not produce a "stable" sort (unlike [merge sort](../Merge Sort/), for example). Most of the time that's not a big deal.
+The only guarantee is that to the left of the pivot are all the smaller elements and to the right are all the larger elements. Because partitioning can change the original order of equal elements, quicksort does not produce a "stable" sort (unlike [merge sort](../Merge%20Sort/), for example). Most of the time that's not a big deal.
 
 ## Lomuto's partitioning scheme
 
@@ -133,7 +133,7 @@ Here's an implementation of Lomuto's partitioning scheme in Swift:
 ```swift
 func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[high]
-  
+
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
@@ -141,7 +141,7 @@ func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int
       i += 1
     }
   }
-  
+
   (a[i], a[high]) = (a[high], a[i])
   return i
 }
@@ -168,7 +168,7 @@ After partitioning, the array looks like this:
 
 The variable `p` contains the return value of the call to `partitionLomuto()` and is 7. This is the index of the pivot element in the new array (marked with a star).
 
-The left partition goes from 0 to `p-1` and is `[ 0, 3, 2, 1, 5, 8, -1 ]`. The right partition goes from `p+1` to the end, and is `[ 9, 10, 14, 26, 27 ]` (the fact that the right partition is already sorted is a coincidence). 
+The left partition goes from 0 to `p-1` and is `[ 0, 3, 2, 1, 5, 8, -1 ]`. The right partition goes from `p+1` to the end, and is `[ 9, 10, 14, 26, 27 ]` (the fact that the right partition is already sorted is a coincidence).
 
 You may notice something interesting... The value `8` occurs more than once in the array. One of those `8`s did not end up neatly in the middle but somewhere in the left partition. That's a small downside of the Lomuto algorithm as it makes quicksort slower if there are a lot of duplicate elements.
 
@@ -281,11 +281,11 @@ func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[low]
   var i = low - 1
   var j = high + 1
-  
+
   while true {
     repeat { j -= 1 } while a[j] > pivot
     repeat { i += 1 } while a[i] < pivot
-    
+
     if i < j {
       swap(&a[i], &a[j])
     } else {
@@ -309,9 +309,9 @@ The result is:
 
 	[ -1, 0, 3, 8, 2, 5, 1, 27, 10, 14, 9, 8, 26 ]
 
-Note that this time the pivot isn't in the middle at all. Unlike with Lomuto's scheme, the return value is not necessarily the index of the pivot element in the new array. 
+Note that this time the pivot isn't in the middle at all. Unlike with Lomuto's scheme, the return value is not necessarily the index of the pivot element in the new array.
 
-Instead, the array is partitioned into the regions `[low...p]` and `[p+1...high]`. Here, the return value `p` is 6, so the two partitions are `[ -1, 0, 3, 8, 2, 5, 1 ]` and `[ 27, 10, 14, 9, 8, 26 ]`. 
+Instead, the array is partitioned into the regions `[low...p]` and `[p+1...high]`. Here, the return value `p` is 6, so the two partitions are `[ -1, 0, 3, 8, 2, 5, 1 ]` and `[ 27, 10, 14, 9, 8, 26 ]`.
 
 The pivot is placed somewhere inside one of the two partitions, but the algorithm doesn't tell you which one or where. If the pivot value occurs more than once, then some instances may appear in the left partition and others may appear in the right partition.
 
@@ -357,7 +357,7 @@ And again:
 
 And so on...
 
-That's no good, because this pretty much reduces quicksort to the much slower insertion sort. For quicksort to be efficient, it needs to split the array into roughly two halves. 
+That's no good, because this pretty much reduces quicksort to the much slower insertion sort. For quicksort to be efficient, it needs to split the array into roughly two halves.
 
 The optimal pivot for this example would have been `4`, so we'd get:
 
diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 15b1a3227..9897c9c3b 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -18,7 +18,7 @@ var a = [ 20, 3, -1, 101, 14, 29, 5, 61, 99 ]
 We want to query this array on the interval from 3 to 7 for the function "sum". That means we do the following:
 
 	101 + 14 + 29 + 5 + 61 = 210
-	
+
 because `101` is at index 3 in the array and `61` is at index 7. So we pass all the numbers between `101` and `61` to the sum function, which adds them all up. If we had used the "min" function, the result would have been `5` because that's the smallest number in the interval from 3 to 7.
 
 Here's naive approach if our array's type is `Int` and **f** is just the sum of two integers:
@@ -43,7 +43,7 @@ The main idea of segment trees is simple: we precalculate some segments in our a
 
 ## Structure of segment tree
 
-A segment tree is just a [binary tree](../Binary Tree/) where each node is an instance of the `SegmentTree` class:
+A segment tree is just a [binary tree](../Binary%20Tree/) where each node is an instance of the `SegmentTree` class:
 
 ```swift
 public class SegmentTree<T> {
@@ -116,18 +116,18 @@ Here's the code:
     if self.leftBound == leftBound && self.rightBound == rightBound {
       return self.value
     }
-    
+
     guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-    
+
     // 2
     if leftChild.rightBound < leftBound {
       return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
-      
+
     // 3
     } else if rightChild.leftBound > rightBound {
       return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
-      
+
     // 4
     } else {
       let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index e95749d14..cb8ed59c2 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -2,7 +2,7 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted. 
+You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted.
 
 	[ ...sorted numbers... | ...unsorted numbers... ]
 
@@ -23,7 +23,7 @@ It's called a "selection" sort, because at every step you search through the res
 
 ## An example
 
-Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol. 
+Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol.
 
 Initially, the sorted portion is empty:
 
@@ -65,14 +65,14 @@ func selectionSort(_ array: [Int]) -> [Int] {
   var a = array                    // 2
 
   for x in 0 ..< a.count - 1 {     // 3
-    
+
     var lowest = x
     for y in x + 1 ..< a.count {   // 4
       if a[y] < a[lowest] {
         lowest = y
       }
     }
-    
+
     if x != lowest {               // 5
       swap(&a[x], &a[lowest])
     }
@@ -108,7 +108,7 @@ The source file [SelectionSort.swift](SelectionSort.swift) has a version of this
 
 ## Performance
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
 
 [Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
 

From 93cbde7ae9f22d800bb30050b504e13a652ce5a2 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Tue, 4 Apr 2017 02:46:04 -0400
Subject: [PATCH 0888/1679] Fixed a bug when appending or inserting a node

---
 .../LinkedList.playground/Contents.swift      | 27 ++++++++++---------
 1 file changed, 14 insertions(+), 13 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index ed46331d8..6e743ba89 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -73,7 +73,8 @@ public final class LinkedList<T> {
     self.append(newNode)
   }
   
-  public func append(_ newNode: Node) {
+  public func append(_ node: Node) {
+    let newNode = LinkedListNode(value: node.value)
     if let lastNode = last {
       newNode.previous = lastNode
       lastNode.next = newNode
@@ -104,9 +105,9 @@ public final class LinkedList<T> {
     self.insert(newNode, atIndex: index)
   }
   
-  public func insert(_ newNode: Node, atIndex index: Int) {
+  public func insert(_ node: Node, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index: index)
-    
+    let newNode = LinkedListNode(value: node.value)
     newNode.previous = prev
     newNode.next = next
     prev?.next = newNode
@@ -264,16 +265,16 @@ f    // [Universe, Swifty]
 //list.removeAll()
 //list.isEmpty
 
-list.remove(node: list.first!) // "Hello"
+list.remove(node: list.first!) // "Universe"
 list.count                     // 2
-list[0]                        // "Swift"
-list[1]                        // "World"
+list[0]                        // "Swifty"
+list[1]                        // "Hello"
 
-list.removeLast()              // "World"
+list.removeLast()              // "Hello"
 list.count                     // 1
-list[0]                        // "Swift"
+list[0]                        // "Swifty"
 
-list.remove(atIndex: 0)        // "Swift"
+list.remove(atIndex: 0)        // "Swifty"
 list.count                     // 0
 
 let linkedList: LinkedList<Int> = [1, 2, 3, 4] // [1, 2, 3, 4]
@@ -281,7 +282,7 @@ linkedList.count               // 4
 linkedList[0]                  // 1
 
 // Infer the type from the array
-let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
-listArrayLiteral2.count        // 3
-listArrayLiteral2[0]           // "Swift"
-listArrayLiteral2.removeLast() // "Club"
+let listArrayLiteral2: LinkedList? = ["Swift", "Algorithm", "Club"]
+listArrayLiteral2?.count        // 3
+listArrayLiteral2?[0]           // "Swift"
+listArrayLiteral2?.removeLast()  // "Club"

From 3028c6500f4b2bf8ac4fe899f238b32f946fa879 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Tue, 4 Apr 2017 03:07:05 -0400
Subject: [PATCH 0889/1679] Corrected comments in playground. Fixed a logic bug
 when inserting/appending a node

---
 Linked List/LinkedList.playground/Contents.swift | 8 ++++----
 Linked List/LinkedList.swift                     | 7 ++++---
 2 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 6e743ba89..abbb90467 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -282,7 +282,7 @@ linkedList.count               // 4
 linkedList[0]                  // 1
 
 // Infer the type from the array
-let listArrayLiteral2: LinkedList? = ["Swift", "Algorithm", "Club"]
-listArrayLiteral2?.count        // 3
-listArrayLiteral2?[0]           // "Swift"
-listArrayLiteral2?.removeLast()  // "Club"
+let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
+listArrayLiteral2.count        // 3
+listArrayLiteral2[0]           // "Swift"
+listArrayLiteral2.removeLast()  // "Club"
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 53dc77a06..55593cdc9 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -71,7 +71,8 @@ public final class LinkedList<T> {
         self.append(newNode)
     }
     
-    public func append(_ newNode: Node) {
+    public func append(_ node: Node) {
+        let newNode = Node(value: node.value)
         if let lastNode = last {
             newNode.previous = lastNode
             lastNode.next = newNode
@@ -102,9 +103,9 @@ public final class LinkedList<T> {
         self.insert(newNode, atIndex: index)
     }
     
-    public func insert(_ newNode: Node, atIndex index: Int) {
+    public func insert(_ node: Node, atIndex index: Int) {
         let (prev, next) = nodesBeforeAndAfter(index: index)
-        
+        let newNode = Node(value: node.value)
         newNode.previous = prev
         newNode.next = next
         prev?.next = newNode

From b0204d3e0a9a84c8ddb4fdce3fa9dc8276e755ed Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 4 Apr 2017 10:08:48 +0300
Subject: [PATCH 0890/1679] Dijkstra's algorithm

---
 .../Dijkstra.playground/Contents.swift        | 122 +++++++
 .../Dijkstra.playground/contents.xcplayground |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Dijkstra Algorithm/README.md                  |  23 ++
 .../Screenshots/screenshot1.jpg               | Bin 0 -> 214771 bytes
 .../Screenshots/screenshot2.jpg               | Bin 0 -> 225916 bytes
 .../Screenshots/screenshot3.jpg               | Bin 0 -> 224243 bytes
 .../Contents.swift                            |  57 ++++
 .../Resources/Pause.png                       | Bin 0 -> 712 bytes
 .../Resources/Start.png                       | Bin 0 -> 1044 bytes
 .../Resources/Stop.png                        | Bin 0 -> 498 bytes
 .../Sources/CustomUI/EdgeRepresentation.swift | 109 ++++++
 .../Sources/CustomUI/ErrorView.swift          |  30 ++
 .../Sources/CustomUI/MyShapeLayer.swift       |   7 +
 .../Sources/CustomUI/RoundedButton.swift      |  20 ++
 .../Sources/CustomUI/VertexView.swift         |  63 ++++
 .../Sources/Graph.swift                       | 308 +++++++++++++++++
 .../Sources/GraphColors.swift                 |  15 +
 .../Sources/GraphView.swift                   | 246 ++++++++++++++
 .../Sources/SimpleObjects/Edge.swift          |  12 +
 .../Sources/SimpleObjects/Vertex.swift        |  62 ++++
 .../Sources/Window.swift                      | 319 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../timeline.xctimeline                       |   6 +
 README.markdown                               |   1 +
 26 files changed, 1422 insertions(+)
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/Contents.swift
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Dijkstra Algorithm/README.md
 create mode 100644 Dijkstra Algorithm/Screenshots/screenshot1.jpg
 create mode 100644 Dijkstra Algorithm/Screenshots/screenshot2.jpg
 create mode 100644 Dijkstra Algorithm/Screenshots/screenshot3.jpg
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Pause.png
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Start.png
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Stop.png
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
new file mode 100644
index 000000000..8d600d577
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -0,0 +1,122 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+import UIKit
+
+open class ProductVertex: Vertex {}
+
+open class Vertex: Hashable, Equatable {
+
+    open var identifier: String!
+    open var neighbors: [(Vertex, Double)] = []
+    open var pathLengthFromStart: Double = Double.infinity
+    open var pathVerticesFromStart: [Vertex] = []
+//    open var point: CGPoint!
+
+    public init(identifier: String/*, point: CGPoint*/) {
+        self.identifier = identifier
+//        self.point = point
+    }
+
+    open var hashValue: Int {
+        return self.identifier.hashValue
+    }
+
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        if lhs.hashValue == rhs.hashValue {
+            return true
+        }
+        return false
+    }
+
+    open func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+    }
+}
+
+public class Dijkstra {
+    private var totalVertices: Set<Vertex>
+
+    public init(vertices: Set<Vertex>) {
+        self.totalVertices = vertices
+    }
+
+    private func clearCache() {
+        self.totalVertices.forEach { $0.clearCache() }
+    }
+
+    public func findShortestPaths(from startVertex: Vertex) {
+        self.clearCache()
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
+        var currentVertex: Vertex! = startVertex
+        while currentVertex != nil {
+            totalVertices.remove(currentVertex)
+            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
+            for neighbor in filteredNeighbors {
+                let neighborVertex = neighbor.0
+                let weight = neighbor.1
+
+                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+                }
+            }
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+    }
+}
+
+var _vertices: Set<Vertex> = Set()
+
+func createNotConnectedVertices() {
+    for i in 0..<15 {
+        let vertex = Vertex(identifier: "\(i)")
+        _vertices.insert(vertex)
+    }
+}
+
+func setupConnections() {
+    for vertex in _vertices {
+        let randomEdgesCount = arc4random_uniform(4) + 1
+        for _ in 0..<randomEdgesCount {
+            let randomWeight = Double(arc4random_uniform(10))
+            let neighborVertex = randomVertex(except: vertex)
+            if vertex.neighbors.contains(where: { $0.0 == neighborVertex }) {
+                continue
+            }
+            let neighbor1 = (neighborVertex, randomWeight)
+            let neighbor2 = (vertex, randomWeight)
+            vertex.neighbors.append(neighbor1)
+            neighborVertex.neighbors.append(neighbor2)
+        }
+    }
+}
+
+func randomVertex(except vertex: Vertex) -> Vertex {
+    var newSet = _vertices
+    newSet.remove(vertex)
+    let offset = Int(arc4random_uniform(UInt32(newSet.count)))
+    let index = newSet.index(newSet.startIndex, offsetBy: offset)
+    return newSet[index]
+}
+
+createNotConnectedVertices()
+setupConnections()
+let dijkstra = Dijkstra(vertices: _vertices)
+let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
+let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
+let startVertex = _vertices[index]
+dijkstra.findShortestPaths(from: startVertex)
+let destinationVertex = randomVertex(except: startVertex)
+destinationVertex.pathLengthFromStart
+destinationVertex.pathVerticesFromStart
+
+
diff --git a/Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground b/Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
new file mode 100644
index 000000000..872e9f851
--- /dev/null
+++ b/Dijkstra Algorithm/README.md	
@@ -0,0 +1,23 @@
+# Dijkstra-algorithm
+WWDC 2017 Scholarship Project
+Created by [Taras Nikulin](https://github.com/crabman448)
+
+## About
+Dijkstra's algorithm is used for finding shortest paths from start vertex in graph(with weighted vertices) to all other vertices. 
+More algorithm's description can be found in playground or on wikipedia:
+[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+
+To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
+
+If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
+
+## Demo video
+Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
+
+## Screenshots
+
+<img src="Screenshots/screenshot1.jpg" height="400" />
+
+<img src="Screenshots/screenshot2.jpg" height="400" />
+
+<img src="Screenshots/screenshot3.jpg" height="400" />
diff --git a/Dijkstra Algorithm/Screenshots/screenshot1.jpg b/Dijkstra Algorithm/Screenshots/screenshot1.jpg
new file mode 100644
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diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
new file mode 100644
index 000000000..e4b3e6732
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
@@ -0,0 +1,57 @@
+/*:
+ ## Dijkstra's algorithm visualization
+ This playground is about the [Dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm).
+ Plyground works in 2 modes:
+ * Auto visualization
+ * Interactive visualization
+
+ */
+import UIKit
+import PlaygroundSupport
+/*:
+ First of all, let's set up colors for our window and graph. The visited color will be applied to visited vertices. The checking color will be applied to an edge and an edge neighbor every time the algorithm is checking some vertex neighbors. And default colors are just initial colors for elements.
+ */
+GraphColors.sharedInstance.visitedColor = #colorLiteral(red: 0, green: 0.5898008943, blue: 1, alpha: 1)
+GraphColors.sharedInstance.checkingColor = #colorLiteral(red: 0.9411764741, green: 0.4980392158, blue: 0.3529411852, alpha: 1)
+GraphColors.sharedInstance.defaultEdgeColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+GraphColors.sharedInstance.defaultVertexColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+
+GraphColors.sharedInstance.mainWindowBackgroundColor = #colorLiteral(red: 0.921431005, green: 0.9214526415, blue: 0.9214410186, alpha: 1)
+GraphColors.sharedInstance.topViewBackgroundColor = #colorLiteral(red: 1, green: 0.4932718873, blue: 0.4739984274, alpha: 1)
+GraphColors.sharedInstance.buttonsBackgroundColor = #colorLiteral(red: 0, green: 0.3285208941, blue: 0.5748849511, alpha: 1)
+GraphColors.sharedInstance.graphBackgroundColor = #colorLiteral(red: 1, green: 1, blue: 1, alpha: 1)
+/*:
+ Now, we need to create some graph. You can create graph with any vertices amount but I aware you from setting up too many, otherwise it will be hard to place all of them nicely on the screen. Also, you can change the animations' duration: slow down or speed up.
+ */
+let graph = Graph(verticesCount: 6)
+graph.interactiveNeighborCheckAnimationDuration = 1.2
+graph.visualizationNeighborCheckAnimationDuration = 1.2
+/*:
+ Now, let's configure the graph's visual representation by passing the virtual graph to our window. For better perception open live view in full screen.
+ */
+let screenBounds = UIScreen.main.bounds
+let frame = CGRect(x: 0, y: 0, width: screenBounds.width * 0.8, height: screenBounds.height * 0.8)
+let window = Window(frame: frame)
+window.configure(graph: graph)
+PlaygroundPage.current.liveView = window
+/*:
+ **Great!**
+
+ Now we have graph on the screen. It is beautiful, isn't it? ;) Before the visualization starts, I recommend you to move vertices around the screen using you finger to be sure that all vertices and edges are properly visible.
+ 
+ And a final step! Before you will see the visualization **(by pressing "Visualization" button),** please, read explanation of how the Dijkstra's algorithm works.
+
+ Algorithm's flow:
+ First of all, this program randomly decides which vertex will be the start one, then the program assigns a zero value to the start vertex path length from the start.
+
+ Then the algorithm repeats following cycle until all vertices are marked as visited.
+ Cycle:
+ 1) From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+ 2) The algorithm marks picked vertex as visited.
+ 3) The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+ When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+ 
+ Now, try yourself at the Dijkstra's algorithm. Press **"Interactive" button.** The program will mark the start vertex as visited and calculate new paths for its neighbors. You have to pick next vertex for the algorithm to check. If you are wrong, you will see a message on the screen.
+ 
+ Good luck and have fun! ;)
+ */
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Pause.png b/Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Pause.png
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diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift
new file mode 100644
index 000000000..5ff656dab
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift	
@@ -0,0 +1,109 @@
+import UIKit
+
+public class EdgeRepresentation: Equatable {
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public private(set)var label: UILabel!
+    public private(set)var layer: MyShapeLayer!
+
+    public init(from vertex1: Vertex, to vertex2: Vertex, weight: Double) {
+        guard let vertex1View = vertex1.view, let vertex2View = vertex2.view else {
+            assertionFailure("passed vertices without configured views")
+            return
+        }
+        let x1 = vertex1View.frame.origin.x
+        let y1 = vertex1View.frame.origin.y
+        let width1 = vertex1View.frame.width
+        let height1 = vertex1View.frame.height
+
+        let x2 = vertex2View.frame.origin.x
+        let y2 = vertex2View.frame.origin.y
+        let width2 = vertex2View.frame.width
+        let height2 = vertex2View.frame.height
+
+        var startPoint: CGPoint
+        var endPoint: CGPoint
+
+        if y1 == y2 {
+            if x1 < x2 {
+                startPoint = CGPoint(x: x1 + width1, y: y1 + height1 / 2)
+                endPoint = CGPoint(x: x2, y: y2 + height2 / 2)
+            } else {
+                startPoint = CGPoint(x: x1, y: y1 + height1 / 2)
+                endPoint = CGPoint(x: x2 + width2, y: y2 + height2 / 2)
+            }
+        } else {
+            startPoint = CGPoint(x: x1 + width1 / 2, y: y1 + height1)
+            endPoint = CGPoint(x: x2 + width2 / 2, y: y2)
+        }
+
+        let arcDiameter: CGFloat = 20
+        var circleOrigin: CGPoint!
+
+        if endPoint.x == startPoint.x {
+            startPoint.y -= 1
+            endPoint.y += 1
+            let x = startPoint.x - arcDiameter / 2
+            let y = startPoint.y + ((endPoint.y - startPoint.y) / 2 * 1.25 - arcDiameter / 2)
+            circleOrigin = CGPoint(x: x, y: y)
+        } else if endPoint.y == startPoint.y {
+            let x = startPoint.x + ((endPoint.x - startPoint.x) / 2 * 1.25 - arcDiameter / 2)
+            let y = startPoint.y + ((endPoint.y - startPoint.y) / 2 * 1.25 - arcDiameter / 2)
+            circleOrigin = CGPoint(x: x, y: y)
+        } else {
+            startPoint.x -= 1
+            endPoint.x += 1
+            startPoint.y -= 1
+            endPoint.y += 1
+            let x = startPoint.x + ((endPoint.x - startPoint.x) / 2 * 1.25 - arcDiameter / 2)
+            let y = startPoint.y + ((endPoint.y - startPoint.y) / 2 * 1.25 - arcDiameter / 2)
+            circleOrigin = CGPoint(x: x, y: y)
+        }
+
+
+        let path = UIBezierPath()
+        path.move(to: startPoint)
+        path.addLine(to: endPoint)
+
+        let label = UILabel(frame: CGRect(origin: circleOrigin, size: CGSize(width: arcDiameter, height: arcDiameter)))
+        label.textAlignment = .center
+        label.backgroundColor = self.graphColors.defaultEdgeColor
+        label.clipsToBounds = true
+        label.adjustsFontSizeToFitWidth = true
+        label.layer.cornerRadius = arcDiameter / 2
+        label.text = ""
+
+        let shapeLayer = MyShapeLayer()
+        shapeLayer.path = path.cgPath
+        shapeLayer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
+        shapeLayer.fillColor = UIColor.clear.cgColor
+        shapeLayer.lineWidth = 2.0
+        shapeLayer.startPoint = startPoint
+        shapeLayer.endPoint = endPoint
+        shapeLayer.actions = ["position" : NSNull(), "bounds" : NSNull(), "path" : NSNull()]
+        self.layer = shapeLayer
+        self.label = label
+        self.label.text = "\(weight)"
+    }
+
+    public func setCheckingColor() {
+        self.layer.strokeColor = self.graphColors.checkingColor.cgColor
+        self.label.backgroundColor = self.graphColors.checkingColor
+    }
+
+    public func setDefaultColor() {
+        self.layer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
+        self.label.backgroundColor = self.graphColors.defaultEdgeColor
+    }
+
+    public func setText(text: String) {
+        self.label.text = text
+    }
+
+    public static func ==(lhs: EdgeRepresentation, rhs: EdgeRepresentation) -> Bool {
+        if lhs.label.hashValue == rhs.label.hashValue && lhs.layer.hashValue == rhs.layer.hashValue {
+            return true
+        }
+        return false
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift
new file mode 100644
index 000000000..69874e5d7
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift	
@@ -0,0 +1,30 @@
+import UIKit
+
+public class ErrorView: UIView {
+    private var label: UILabel!
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.commonInit()
+    }
+
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    private func commonInit() {
+        self.backgroundColor = UIColor(red: 242/255, green: 156/255, blue: 84/255, alpha: 1)
+        self.layer.cornerRadius = 10
+
+        let labelFrame = CGRect(x: 10, y: 10, width: self.frame.width - 20, height: self.frame.height - 20)
+        self.label = UILabel(frame: labelFrame)
+        self.label.numberOfLines = 0
+        self.label.adjustsFontSizeToFitWidth = true
+        self.label.textAlignment = .center
+        self.label.textColor = UIColor.white
+        self.addSubview(self.label)
+    }
+
+    public func setText(text: String) {
+        self.label.text = text
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift
new file mode 100644
index 000000000..54147f5e1
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift	
@@ -0,0 +1,7 @@
+import Foundation
+import UIKit
+
+public class MyShapeLayer: CAShapeLayer {
+    public var startPoint: CGPoint?
+    public var endPoint: CGPoint?
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift
new file mode 100644
index 000000000..2647c4525
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift	
@@ -0,0 +1,20 @@
+import UIKit
+
+public class RoundedButton: UIButton {
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+    
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.commonInit()
+    }
+    
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    private func commonInit() {
+        self.backgroundColor = self.graphColors.buttonsBackgroundColor
+        self.titleLabel?.adjustsFontSizeToFitWidth = true
+        self.layer.cornerRadius = 7
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift
new file mode 100644
index 000000000..29c971411
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift	
@@ -0,0 +1,63 @@
+import UIKit
+
+public class VertexView: UIButton {
+
+    public var vertex: Vertex?
+    private var idLabel: UILabel!
+    private var pathLengthLabel: UILabel!
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    public override init(frame: CGRect) {
+        precondition(frame.height == frame.width)
+        precondition(frame.height >= 30)
+        super.init(frame: frame)
+        self.backgroundColor = self.graphColors.defaultVertexColor
+        self.layer.cornerRadius = frame.width / 2
+        self.clipsToBounds = true
+        self.setupIdLabel()
+        self.setupPathLengthFromStartLabel()
+    }
+
+    private func setupIdLabel() {
+        let x: CGFloat = self.frame.width * 0.2
+        let y: CGFloat = 0
+        let width: CGFloat = self.frame.width * 0.6
+        let height: CGFloat = self.frame.height / 2
+        let idLabelFrame = CGRect(x: x, y: y, width: width, height: height)
+
+        self.idLabel = UILabel(frame: idLabelFrame)
+        self.idLabel.textAlignment = .center
+        self.idLabel.adjustsFontSizeToFitWidth = true
+        self.addSubview(self.idLabel)
+    }
+
+    private func setupPathLengthFromStartLabel() {
+        let x: CGFloat = self.frame.width * 0.2
+        let y: CGFloat = self.frame.height / 2
+        let width: CGFloat = self.frame.width * 0.6
+        let height: CGFloat = self.frame.height / 2
+        let pathLengthLabelFrame = CGRect(x: x, y: y, width: width, height: height)
+
+        self.pathLengthLabel = UILabel(frame: pathLengthLabelFrame)
+        self.pathLengthLabel.textAlignment = .center
+        self.pathLengthLabel.adjustsFontSizeToFitWidth = true
+        self.addSubview(self.pathLengthLabel)
+    }
+
+    public func setIdLabel(text: String) {
+        self.idLabel.text = text
+    }
+
+    public func setPathLengthLabel(text: String) {
+        self.pathLengthLabel.text = text
+    }
+
+    public func setLabelsTextColor(color: UIColor) {
+        self.idLabel.textColor = color
+        self.pathLengthLabel.textColor = color
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
new file mode 100644
index 000000000..0b0b97b92
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -0,0 +1,308 @@
+import Foundation
+import UIKit
+
+public enum GraphState {
+    case initial
+    case autoVisualization
+    case interactiveVisualization
+    case parsing
+    case completed
+}
+
+public class Graph {
+    private init() { }
+
+    private var verticesCount: UInt!
+    private var _vertices: Set<Vertex> = Set()
+    public weak var delegate: GraphDelegate?
+    public var nextVertices: [Vertex] = []
+    public var state: GraphState = .initial
+    public var pauseVisualization: Bool = false
+    public var stopVisualization: Bool = false
+    public var startVertex: Vertex!
+    public var interactiveNeighborCheckAnimationDuration: Double = 1.8 {
+        didSet {
+            self._interactiveOneSleepDuration = UInt32(self.interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+        }
+    }
+    private var _interactiveOneSleepDuration: UInt32 = 600000
+
+    public var visualizationNeighborCheckAnimationDuration: Double = 2.25 {
+        didSet {
+            self._visualizationOneSleepDuration = UInt32(self.visualizationNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+        }
+    }
+    private var _visualizationOneSleepDuration: UInt32 = 750000
+
+    public var vertices: Set<Vertex> {
+        return self._vertices
+    }
+
+    public init(verticesCount: UInt) {
+        self.verticesCount = verticesCount
+    }
+
+    public func removeGraph() {
+        self._vertices.removeAll()
+        self.startVertex = nil
+    }
+
+    public func createNewGraph() {
+        guard self._vertices.isEmpty, self.startVertex == nil else {
+            assertionFailure("Clear graph before creating new one")
+            return
+        }
+        self.createNotConnectedVertices()
+        self.setupConnections()
+        let offset = Int(arc4random_uniform(UInt32(self._vertices.count)))
+        let index = self._vertices.index(self._vertices.startIndex, offsetBy: offset)
+        self.startVertex =  self._vertices[index]
+        self.setVertexLevels()
+    }
+    
+    private func clearCache() {
+        self._vertices.forEach { $0.clearCache() }
+    }
+
+    public func reset() {
+        for vertex in self._vertices {
+            vertex.clearCache()
+        }
+    }
+
+    private func createNotConnectedVertices() {
+        for i in 0..<self.verticesCount {
+            let vertex = Vertex(identifier: "\(i)")
+            self._vertices.insert(vertex)
+        }
+    }
+
+    private func setupConnections() {
+        for vertex in self._vertices {
+            let randomEdgesCount = arc4random_uniform(4) + 1
+            for _ in 0..<randomEdgesCount {
+                let randomWeight = Double(arc4random_uniform(10))
+                let neighbor = self.randomVertex(except: vertex)
+                let edge1 = Edge(vertex: neighbor, weight: randomWeight)
+                if vertex.edges.contains(where: { $0.neighbor == neighbor }) {
+                    continue
+                }
+                let edge2 = Edge(vertex: vertex, weight: randomWeight)
+                vertex.edges.append(edge1)
+                neighbor.edges.append(edge2)
+            }
+        }
+    }
+
+    private func randomVertex(except vertex: Vertex) -> Vertex {
+        var newSet = self._vertices
+        newSet.remove(vertex)
+        let offset = Int(arc4random_uniform(UInt32(newSet.count)))
+        let index = newSet.index(newSet.startIndex, offsetBy: offset)
+        return newSet[index]
+    }
+
+    private func setVertexLevels() {
+        self._vertices.forEach { $0.clearLevelInfo() }
+        guard let startVertex = self.startVertex else {
+            assertionFailure()
+            return
+        }
+        var queue: [Vertex] = [startVertex]
+        startVertex.levelChecked = true
+
+        //BFS
+        while !queue.isEmpty {
+            let currentVertex = queue.first!
+            for edge in currentVertex.edges {
+                let neighbor = edge.neighbor
+                if !neighbor.levelChecked {
+                    neighbor.levelChecked = true
+                    neighbor.level = currentVertex.level + 1
+                    queue.append(neighbor)
+                }
+            }
+            queue.removeFirst()
+        }
+    }
+
+    public func findShortestPathsWithVisualization(completion: () -> Void) {
+        self.clearCache()
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(self.startVertex)
+        var currentVertex: Vertex! = self.startVertex
+
+        var totalVertices = self._vertices
+
+        breakableLoop: while currentVertex != nil {
+            totalVertices.remove(currentVertex)
+            while self.pauseVisualization == true {
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+            }
+            if self.stopVisualization == true {
+                break breakableLoop
+            }
+            DispatchQueue.main.async {
+                currentVertex.setVisitedColor()
+            }
+            usleep(750000)
+            currentVertex.visited = true
+            let filteredEdges = currentVertex.edges.filter { !$0.neighbor.visited }
+            for edge in filteredEdges {
+                let neighbor = edge.neighbor
+                let weight = edge.weight
+                let edgeRepresentation = edge.edgeRepresentation
+
+                while self.pauseVisualization == true {
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                }
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+                DispatchQueue.main.async {
+                    edgeRepresentation?.setCheckingColor()
+                    neighbor.setCheckingPathColor()
+                    self.delegate?.willCompareVertices(startVertexPathLength: currentVertex.pathLengthFromStart,
+                                                       edgePathLength: weight,
+                                                       endVertexPathLength: neighbor.pathLengthFromStart)
+                }
+                usleep(self._visualizationOneSleepDuration)
+
+
+                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+
+                if theoreticNewWeight < neighbor.pathLengthFromStart {
+                    while self.pauseVisualization == true {
+                        if self.stopVisualization == true {
+                            break breakableLoop
+                        }
+                    }
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                    neighbor.pathLengthFromStart = theoreticNewWeight
+                    neighbor.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighbor.pathVerticesFromStart.append(neighbor)
+                }
+                usleep(self._visualizationOneSleepDuration)
+
+                DispatchQueue.main.async {
+                    self.delegate?.didFinishCompare()
+                    edge.edgeRepresentation?.setDefaultColor()
+                    edge.neighbor.setDefaultColor()
+                }
+                usleep(self._visualizationOneSleepDuration)
+            }
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+        if self.stopVisualization == true {
+            DispatchQueue.main.async {
+                self.delegate?.didStop()
+            }
+        } else {
+            completion()
+        }
+    }
+
+    public func parseNeighborsFor(vertex: Vertex, completion: @escaping () -> ()) {
+        DispatchQueue.main.async {
+            vertex.setVisitedColor()
+        }
+        DispatchQueue.global(qos: .background).async {
+            vertex.visited = true
+
+            let nonVisitedVertices = self._vertices.filter { $0.visited == false }
+            if nonVisitedVertices.isEmpty {
+                self.state = .completed
+                DispatchQueue.main.async {
+                    self.delegate?.didCompleteGraphParsing()
+                }
+                return
+            }
+
+            let filteredEdges = vertex.edges.filter { !$0.neighbor.visited }
+            breakableLoop: for edge in filteredEdges {
+                while self.pauseVisualization == true {
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                }
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+                let weight = edge.weight
+                let neighbor = edge.neighbor
+
+                DispatchQueue.main.async {
+                    edge.neighbor.setCheckingPathColor()
+                    edge.edgeRepresentation?.setCheckingColor()
+                    self.delegate?.willCompareVertices(startVertexPathLength: vertex.pathLengthFromStart,
+                                                       edgePathLength: weight,
+                                                       endVertexPathLength: neighbor.pathLengthFromStart)
+                }
+                usleep(self._interactiveOneSleepDuration)
+                
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
+                if theoreticNewWeight < neighbor.pathLengthFromStart {
+                    while self.pauseVisualization == true {
+                        if self.stopVisualization == true {
+                            break breakableLoop
+                        }
+                    }
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                    neighbor.pathLengthFromStart = theoreticNewWeight
+                    neighbor.pathVerticesFromStart = vertex.pathVerticesFromStart
+                    neighbor.pathVerticesFromStart.append(neighbor)
+                }
+
+                usleep(self._interactiveOneSleepDuration)
+                while self.pauseVisualization == true {
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                }
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+                DispatchQueue.main.async {
+                    self.delegate?.didFinishCompare()
+                    edge.neighbor.setDefaultColor()
+                    edge.edgeRepresentation?.setDefaultColor()
+                }
+                usleep(self._interactiveOneSleepDuration)
+            }
+            if self.stopVisualization == true {
+                DispatchQueue.main.async {
+                    self.delegate?.didStop()
+                }
+            } else {
+                let nextVertexPathLength = nonVisitedVertices.sorted { $0.pathLengthFromStart < $1.pathLengthFromStart }.first!.pathLengthFromStart
+                self.nextVertices = nonVisitedVertices.filter { $0.pathLengthFromStart == nextVertexPathLength }
+                completion()
+            }
+        }
+    }
+
+    public func didTapVertex(vertex: Vertex) {
+        if self.nextVertices.contains(vertex) {
+            self.delegate?.willStartVertexNeighborsChecking()
+            self.state = .parsing
+            self.parseNeighborsFor(vertex: vertex) {
+                self.state = .interactiveVisualization
+                self.delegate?.didFinishVertexNeighborsChecking()
+            }
+        } else {
+            self.delegate?.didTapWrongVertex()
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift
new file mode 100644
index 000000000..95e9b8d74
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift	
@@ -0,0 +1,15 @@
+import UIKit
+
+public class GraphColors {
+    public static let sharedInstance: GraphColors = GraphColors()
+    private init() { }
+
+    public var mainWindowBackgroundColor: UIColor = #colorLiteral(red: 0.921431005, green: 0.9214526415, blue: 0.9214410186, alpha: 1)
+    public var topViewBackgroundColor: UIColor = #colorLiteral(red: 1, green: 0.4932718873, blue: 0.4739984274, alpha: 1)
+    public var graphBackgroundColor: UIColor = #colorLiteral(red: 1, green: 1, blue: 1, alpha: 1)
+    public var defaultVertexColor: UIColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+    public var defaultEdgeColor: UIColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+    public var checkingColor: UIColor = #colorLiteral(red: 0.9411764741, green: 0.4980392158, blue: 0.3529411852, alpha: 1)
+    public var visitedColor: UIColor = #colorLiteral(red: 0, green: 0.5898008943, blue: 1, alpha: 1)
+    public var buttonsBackgroundColor: UIColor = #colorLiteral(red: 0, green: 0.3285208941, blue: 0.5748849511, alpha: 1)
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
new file mode 100644
index 000000000..49bc6853f
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
@@ -0,0 +1,246 @@
+import UIKit
+
+public class GraphView: UIView {
+    private var graph: Graph!
+    private var panningView: VertexView? = nil
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.backgroundColor = self.graphColors.graphBackgroundColor
+    }
+    
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    
+    }
+
+    public func configure(graph: Graph) {
+        self.graph = graph
+    }
+
+    public func removeGraph() {
+        for vertex in self.graph.vertices {
+            if let view = vertex.view {
+                view.removeFromSuperview()
+                vertex.view = nil
+            }
+        }
+        for vertex in self.graph.vertices {
+            for edge in vertex.edges {
+                if let edgeRepresentation = edge.edgeRepresentation {
+                    edgeRepresentation.layer.removeFromSuperlayer()
+                    edgeRepresentation.label.removeFromSuperview()
+                    edge.edgeRepresentation = nil
+                }
+            }
+        }
+    }
+
+    public func createNewGraph() {
+        self.setupVertexViews()
+        self.setupEdgeRepresentations()
+        self.addGraph()
+    }
+
+    public func reset() {
+        for vertex in self.graph.vertices {
+            vertex.edges.forEach { $0.edgeRepresentation?.setDefaultColor() }
+            vertex.setDefaultColor()
+        }
+    }
+
+    private func addGraph() {
+        for vertex in self.graph.vertices {
+            for edge in vertex.edges {
+                if let edgeRepresentation = edge.edgeRepresentation {
+                    self.layer.addSublayer(edgeRepresentation.layer)
+                    self.addSubview(edgeRepresentation.label)
+                }
+            }
+        }
+        for vertex in self.graph.vertices {
+            if let view = vertex.view {
+                self.addSubview(view)
+            }
+        }
+    }
+
+    private func setupVertexViews() {
+        var level = 0
+        var buildViewQueue = [self.graph.startVertex!]
+        let itemWidth: CGFloat = 40
+        while !buildViewQueue.isEmpty {
+            let levelItemsCount = CGFloat(buildViewQueue.count)
+            let xStep = (self.frame.width - levelItemsCount * itemWidth) / (levelItemsCount + 1)
+            var previousVertexMaxX: CGFloat = 0.0
+            for vertex in buildViewQueue {
+                let x: CGFloat = previousVertexMaxX + xStep
+                let y: CGFloat = CGFloat(level * 100)
+                previousVertexMaxX = x + itemWidth
+                let frame = CGRect(x: x, y: y, width: itemWidth, height: itemWidth)
+                let vertexView = VertexView(frame: frame)
+                vertex.view = vertexView
+                vertexView.vertex = vertex
+                vertex.view?.setIdLabel(text: vertex.identifier)
+                vertex.view?.setPathLengthLabel(text: "\(vertex.pathLengthFromStart)")
+                vertex.view?.addTarget(self, action: #selector(self.didTapVertex(sender:)), for: .touchUpInside)
+                let panGesture = UIPanGestureRecognizer(target: self, action: #selector(self.handlePan(recognizer:)))
+                vertex.view?.addGestureRecognizer(panGesture)
+            }
+            level += 1
+            buildViewQueue = self.graph.vertices.filter { $0.level == level }
+        }
+    }
+
+    private var movingVertexInputEdges: [EdgeRepresentation] = []
+    private var movingVertexOutputEdges: [EdgeRepresentation] = []
+
+    @objc private func handlePan(recognizer: UIPanGestureRecognizer) {
+        guard let vertexView = recognizer.view as? VertexView, let vertex = vertexView.vertex else {
+            return
+        }
+        if self.panningView != nil {
+            if self.panningView != vertexView {
+                return
+            }
+        }
+
+        switch recognizer.state {
+        case .began:
+            let movingVertexViewFrame = vertexView.frame
+            let sizedVertexView = CGRect(x: movingVertexViewFrame.origin.x - 10,
+                                         y: movingVertexViewFrame.origin.y - 10,
+                                         width: movingVertexViewFrame.width + 20,
+                                         height: movingVertexViewFrame.height + 20)
+            vertex.edges.forEach { edge in
+                if let edgeRepresentation = edge.edgeRepresentation{
+                    if sizedVertexView.contains(edgeRepresentation.layer.startPoint!) {
+                        movingVertexOutputEdges.append(edgeRepresentation)
+                    } else {
+                        movingVertexInputEdges.append(edgeRepresentation)
+                    }
+                }
+            }
+            self.panningView = vertexView
+        case .changed:
+            if self.movingVertexOutputEdges.isEmpty && self.movingVertexInputEdges.isEmpty {
+                return
+            }
+            let translation = recognizer.translation(in: self)
+            if vertexView.frame.origin.x + translation.x <= 0
+                || vertexView.frame.origin.y + translation.y <= 0
+                || (vertexView.frame.origin.x + vertexView.frame.width + translation.x) >= self.frame.width
+                || (vertexView.frame.origin.y + vertexView.frame.height + translation.y) >= self.frame.height {
+                break
+            }
+            self.movingVertexInputEdges.forEach { edgeRepresentation in
+                let originalLabelCenter = edgeRepresentation.label.center
+                edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.625,
+                                                          y: originalLabelCenter.y + translation.y * 0.625)
+
+                CATransaction.begin()
+                CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
+                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: false)
+                edgeRepresentation.layer.path = newPath
+                CATransaction.commit()
+
+            }
+
+            self.movingVertexOutputEdges.forEach { edgeRepresentation in
+                let originalLabelCenter = edgeRepresentation.label.center
+                edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.375,
+                                                          y: originalLabelCenter.y + translation.y * 0.375)
+
+                CATransaction.begin()
+                CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
+                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: true)
+                edgeRepresentation.layer.path = newPath
+                CATransaction.commit()
+            }
+
+            vertexView.center = CGPoint(x: vertexView.center.x + translation.x,
+                                        y: vertexView.center.y + translation.y)
+            recognizer.setTranslation(CGPoint.zero, in: self)
+        case .ended:
+            self.movingVertexInputEdges = []
+            self.movingVertexOutputEdges = []
+            self.panningView = nil
+        default:
+            break
+        }
+    }
+
+    private func path(fromEdgeRepresentation edgeRepresentation: EdgeRepresentation, movingVertex: Vertex, translation: CGPoint, outPath: Bool) -> CGPath {
+        let bezier = UIBezierPath()
+
+        if outPath == true {
+            bezier.move(to: edgeRepresentation.layer.endPoint!)
+            let startPoint = CGPoint(x: edgeRepresentation.layer.startPoint!.x + translation.x,
+                                     y: edgeRepresentation.layer.startPoint!.y + translation.y)
+            edgeRepresentation.layer.startPoint = startPoint
+            bezier.addLine(to: startPoint)
+        } else {
+            bezier.move(to: edgeRepresentation.layer.startPoint!)
+            let endPoint = CGPoint(x: edgeRepresentation.layer.endPoint!.x + translation.x,
+                                   y: edgeRepresentation.layer.endPoint!.y + translation.y)
+            edgeRepresentation.layer.endPoint = endPoint
+            bezier.addLine(to: endPoint)
+        }
+        return bezier.cgPath
+    }
+
+    @objc private func didTapVertex(sender: AnyObject) {
+        DispatchQueue.main.async {
+            if self.graph.state == .completed {
+                for vertex in self.graph.vertices {
+                    vertex.edges.forEach { $0.edgeRepresentation?.setDefaultColor() }
+                    vertex.setVisitedColor()
+                }
+                if let vertexView = sender as? VertexView, let vertex = vertexView.vertex {
+                    for (index, pathVertex) in vertex.pathVerticesFromStart.enumerated() {
+                        pathVertex.setCheckingPathColor()
+                        if vertex.pathVerticesFromStart.count > index + 1 {
+                            let nextVertex = vertex.pathVerticesFromStart[index + 1]
+
+                            if let edge = pathVertex.edges.filter({ $0.neighbor == nextVertex }).first {
+                                edge.edgeRepresentation?.setCheckingColor()
+                            }
+                        }
+
+                    }
+                }
+            } else if self.graph.state == .interactiveVisualization {
+                if let vertexView = sender as? VertexView, let vertex = vertexView.vertex {
+                    if vertex.visited {
+                        return
+                    } else {
+                        self.graph.didTapVertex(vertex: vertex)
+                    }
+                }
+            }
+        }
+    }
+
+    private func setupEdgeRepresentations() {
+        var edgeQueue: [Vertex] = [self.graph.startVertex!]
+
+        //BFS
+        while !edgeQueue.isEmpty {
+            let currentVertex = edgeQueue.first!
+            currentVertex.haveAllEdges = true
+            for edge in currentVertex.edges {
+                let neighbor = edge.neighbor
+                let weight = edge.weight
+                if !neighbor.haveAllEdges {
+                    let edgeRepresentation = EdgeRepresentation(from: currentVertex, to: neighbor, weight: weight)
+                    edge.edgeRepresentation = edgeRepresentation
+                    let index = neighbor.edges.index(where: { $0.neighbor == currentVertex })!
+                    neighbor.edges[index].edgeRepresentation = edgeRepresentation
+                    edgeQueue.append(neighbor)
+                }
+            }
+            edgeQueue.removeFirst()
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift
new file mode 100644
index 000000000..6f4493bbe
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift	
@@ -0,0 +1,12 @@
+import Foundation
+
+public class Edge {
+    public var neighbor: Vertex
+    public var weight: Double
+    public var edgeRepresentation: EdgeRepresentation?
+
+    public init(vertex: Vertex, weight: Double) {
+        self.neighbor = vertex
+        self.weight = weight
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift
new file mode 100644
index 000000000..c9270b0df
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift	
@@ -0,0 +1,62 @@
+import UIKit
+
+public class Vertex: Hashable, Equatable {
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public var identifier: String
+    public var edges: [Edge] = []
+    public var pathLengthFromStart: Double = Double.infinity {
+        didSet {
+            DispatchQueue.main.async {
+                self.view?.setPathLengthLabel(text: "\(self.pathLengthFromStart)")
+            }
+        }
+    }
+    public var pathVerticesFromStart: [Vertex] = []
+    public var level: Int = 0
+    public var levelChecked: Bool = false
+    public var haveAllEdges: Bool = false
+    public var visited: Bool = false
+
+    public var view: VertexView?
+
+    public init(identifier: String) {
+        self.identifier = identifier
+    }
+
+    public var hashValue: Int {
+        return self.identifier.hashValue
+    }
+
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        if lhs.hashValue == rhs.hashValue {
+            return true
+        }
+        return false
+    }
+
+    public func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+        self.visited = false
+    }
+
+    public func clearLevelInfo() {
+        self.level = 0
+        self.levelChecked = false
+    }
+
+    public func setVisitedColor() {
+        self.view?.backgroundColor = self.graphColors.visitedColor
+        self.view?.setLabelsTextColor(color: UIColor.white)
+    }
+
+    public func setCheckingPathColor() {
+        self.view?.backgroundColor = self.graphColors.checkingColor
+    }
+
+    public func setDefaultColor() {
+        self.view?.backgroundColor = self.graphColors.defaultVertexColor
+        self.view?.setLabelsTextColor(color: UIColor.black)
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
new file mode 100644
index 000000000..e8aabad27
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -0,0 +1,319 @@
+import Foundation
+import UIKit
+
+public protocol GraphDelegate: class {
+    func willCompareVertices(startVertexPathLength: Double, edgePathLength: Double, endVertexPathLength: Double)
+    func didFinishCompare()
+    func didCompleteGraphParsing()
+    func didTapWrongVertex()
+    func didStop()
+    func willStartVertexNeighborsChecking()
+    func didFinishVertexNeighborsChecking()
+}
+
+public class Window: UIView, GraphDelegate {
+    public var graphView: GraphView!
+
+    private var topView: UIView!
+    private var createGraphButton: RoundedButton!
+    private var startVisualizationButton: RoundedButton!
+    private var startInteractiveVisualizationButton: RoundedButton!
+    private var startButton: UIButton!
+    private var pauseButton: UIButton!
+    private var stopButton: UIButton!
+    private var comparisonLabel: UILabel!
+    private var activityIndicator: UIActivityIndicatorView!
+    private var graph: Graph!
+    private var numberOfVertices: UInt!
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.frame = frame
+        self.backgroundColor = self.graphColors.mainWindowBackgroundColor
+    }
+    
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    public func configure(graph: Graph) {
+        self.graph = graph
+        self.graph.createNewGraph()
+        self.graph.delegate = self
+        let frame = CGRect(x: 10, y: 170, width: self.frame.width - 20, height: self.frame.height - 180)
+        self.graphView = GraphView(frame: frame)
+        self.graphView.layer.cornerRadius = 15
+
+        self.graphView.configure(graph: self.graph)
+        self.graphView.createNewGraph()
+        self.addSubview(self.graphView)
+
+        self.configureCreateGraphButton()
+        self.configureStartVisualizationButton()
+        self.configureStartInteractiveVisualizationButton()
+        self.configureStartButton()
+        self.configurePauseButton()
+        self.configureStopButton()
+        self.configureComparisonLabel()
+        self.configureActivityIndicator()
+
+        self.topView = UIView(frame: CGRect(x: 10, y: 10, width: self.frame.width - 20, height: 150))
+        self.topView.backgroundColor = self.graphColors.topViewBackgroundColor
+        self.topView.layer.cornerRadius = 15
+        self.addSubview(self.topView)
+
+        self.topView.addSubview(self.createGraphButton)
+        self.topView.addSubview(self.startVisualizationButton)
+        self.topView.addSubview(self.startInteractiveVisualizationButton)
+        self.topView.addSubview(self.startButton)
+        self.topView.addSubview(self.pauseButton)
+        self.topView.addSubview(self.stopButton)
+        self.topView.addSubview(self.comparisonLabel)
+        self.topView.addSubview(self.activityIndicator)
+    }
+
+    private func configureCreateGraphButton() {
+        let frame = CGRect(x: self.center.x - 200, y: 12, width: 100, height: 34)
+        self.createGraphButton = RoundedButton(frame: frame)
+        self.createGraphButton.setTitle("New graph", for: .normal)
+        self.createGraphButton.addTarget(self, action: #selector(self.createGraphButtonTap), for: .touchUpInside)
+    }
+
+    private func configureStartVisualizationButton() {
+        let frame = CGRect(x: self.center.x - 50, y: 12, width: 100, height: 34)
+        self.startVisualizationButton = RoundedButton(frame: frame)
+        self.startVisualizationButton.setTitle("Auto", for: .normal)
+        self.startVisualizationButton.addTarget(self, action: #selector(self.startVisualizationButtonDidTap), for: .touchUpInside)
+    }
+
+    private func configureStartInteractiveVisualizationButton() {
+        let frame = CGRect(x: self.center.x + 100, y: 12, width: 100, height: 34)
+        self.startInteractiveVisualizationButton = RoundedButton(frame: frame)
+        self.startInteractiveVisualizationButton.setTitle("Interactive", for: .normal)
+        self.startInteractiveVisualizationButton.addTarget(self, action: #selector(self.startInteractiveVisualizationButtonDidTap), for: .touchUpInside)
+    }
+
+    private func configureStartButton() {
+        let frame = CGRect(x: self.center.x - 65, y: 56, width: 30, height: 30)
+        self.startButton = UIButton(frame: frame)
+        let playImage = UIImage(named: "Start.png")
+        self.startButton.setImage(playImage, for: .normal)
+        self.startButton.isEnabled = false
+        self.startButton.addTarget(self, action: #selector(self.didTapStartButton), for: .touchUpInside)
+    }
+
+    private func configurePauseButton() {
+        let frame = CGRect(x: self.center.x - 15, y: 56, width: 30, height: 30)
+        self.pauseButton = UIButton(frame: frame)
+        let pauseImage = UIImage(named: "Pause.png")
+        self.pauseButton.setImage(pauseImage, for: .normal)
+        self.pauseButton.isEnabled = false
+        self.pauseButton.addTarget(self, action: #selector(self.didTapPauseButton), for: .touchUpInside)
+    }
+
+    private func configureStopButton() {
+        let frame = CGRect(x: self.center.x + 35, y: 56, width: 30, height: 30)
+        self.stopButton = UIButton(frame: frame)
+        let stopImage = UIImage(named: "Stop.png")
+        self.stopButton.setImage(stopImage, for: .normal)
+        self.stopButton.isEnabled = false
+        self.stopButton.addTarget(self, action: #selector(self.didTapStopButton), for: .touchUpInside)
+    }
+
+    private func configureComparisonLabel() {
+        let size = CGSize(width: 250, height: 42)
+        let origin = CGPoint(x: self.center.x - 125, y: 96)
+        let frame = CGRect(origin: origin, size: size)
+        self.comparisonLabel = UILabel(frame: frame)
+        self.comparisonLabel.textAlignment = .center
+        self.comparisonLabel.text = "Have fun!"
+    }
+
+    private func configureActivityIndicator() {
+        let size = CGSize(width: 50, height: 42)
+        let origin = CGPoint(x: self.center.x - 25, y: 100)
+        let activityIndicatorFrame = CGRect(origin: origin, size: size)
+        self.activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
+        self.activityIndicator.activityIndicatorViewStyle = .whiteLarge
+    }
+
+    @objc private func createGraphButtonTap() {
+        self.comparisonLabel.text = ""
+        self.graphView.removeGraph()
+        self.graph.removeGraph()
+        self.graph.createNewGraph()
+        self.graphView.createNewGraph()
+        self.graph.state = .initial
+    }
+
+    @objc private func startVisualizationButtonDidTap() {
+        self.comparisonLabel.text = ""
+        self.pauseButton.isEnabled = true
+        self.stopButton.isEnabled = true
+        self.createGraphButton.isEnabled = false
+        self.startVisualizationButton.isEnabled = false
+        self.startInteractiveVisualizationButton.isEnabled = false
+        self.createGraphButton.alpha = 0.5
+        self.startVisualizationButton.alpha = 0.5
+        self.startInteractiveVisualizationButton.alpha = 0.5
+
+        if self.graph.state == .completed {
+            self.graphView.reset()
+            self.graph.reset()
+        }
+        self.graph.state = .autoVisualization
+        DispatchQueue.global(qos: .background).async {
+            self.graph.findShortestPathsWithVisualization {
+                self.graph.state = .completed
+
+                DispatchQueue.main.async {
+                    self.startButton.isEnabled = false
+                    self.pauseButton.isEnabled = false
+                    self.stopButton.isEnabled = false
+                    self.createGraphButton.isEnabled = true
+                    self.startVisualizationButton.isEnabled = true
+                    self.startInteractiveVisualizationButton.isEnabled = true
+                    self.createGraphButton.alpha = 1
+                    self.startVisualizationButton.alpha = 1
+                    self.startInteractiveVisualizationButton.alpha = 1
+                    self.comparisonLabel.text = "Completed!"
+                }
+            }
+        }
+    }
+
+    @objc private func startInteractiveVisualizationButtonDidTap() {
+        self.comparisonLabel.text = ""
+        self.pauseButton.isEnabled = true
+        self.stopButton.isEnabled = true
+        self.createGraphButton.isEnabled = false
+        self.startVisualizationButton.isEnabled = false
+        self.startInteractiveVisualizationButton.isEnabled = false
+        self.createGraphButton.alpha = 0.5
+        self.startVisualizationButton.alpha = 0.5
+        self.startInteractiveVisualizationButton.alpha = 0.5
+
+        if self.graph.state == .completed {
+            self.graphView.reset()
+            self.graph.reset()
+        }
+        
+        self.graph.startVertex.pathLengthFromStart = 0
+        self.graph.startVertex.pathVerticesFromStart.append(self.graph.startVertex)
+        self.graph.state = .parsing
+        self.graph.parseNeighborsFor(vertex: self.graph.startVertex) {
+            self.graph.state = .interactiveVisualization
+            DispatchQueue.main.async {
+                self.comparisonLabel.text = "Pick next vertex"
+            }
+        }
+    }
+
+    @objc private func didTapStartButton() {
+        self.startButton.isEnabled = false
+        self.pauseButton.isEnabled = true
+        DispatchQueue.global(qos: .utility).async {
+            self.graph.pauseVisualization = false
+        }
+    }
+
+    @objc private func didTapPauseButton() {
+        self.startButton.isEnabled = true
+        self.pauseButton.isEnabled = false
+        DispatchQueue.global(qos: .utility).async {
+            self.graph.pauseVisualization = true
+        }
+    }
+
+    @objc private func didTapStopButton() {
+        self.startButton.isEnabled = false
+        self.pauseButton.isEnabled = false
+        self.comparisonLabel.text = ""
+        self.activityIndicator.startAnimating()
+        if self.graph.state == .parsing || self.graph.state == .autoVisualization {
+            self.graph.stopVisualization = true
+        } else if self.graph.state == .interactiveVisualization {
+            self.didStop()
+        }
+    }
+
+    private func setButtonsToInitialState() {
+        self.createGraphButton.isEnabled = true
+        self.startVisualizationButton.isEnabled = true
+        self.startInteractiveVisualizationButton.isEnabled = true
+        self.startButton.isEnabled = false
+        self.pauseButton.isEnabled = false
+        self.stopButton.isEnabled = false
+        self.createGraphButton.alpha = 1
+        self.startVisualizationButton.alpha = 1
+        self.startInteractiveVisualizationButton.alpha = 1
+    }
+
+    private func showError(error: String) {
+        DispatchQueue.main.async {
+            let size = CGSize(width: 250, height: 42)
+            let origin = CGPoint(x: self.topView.center.x - 125, y: 96)
+            let frame = CGRect(origin: origin, size: size)
+            let errorView = ErrorView(frame: frame)
+            errorView.setText(text: error)
+            self.topView.addSubview(errorView)
+            UIView.animate(withDuration: 2, animations: {
+                errorView.alpha = 0
+            }, completion: { _ in
+                errorView.removeFromSuperview()
+            })
+        }
+    }
+
+    // MARK: GraphDelegate
+    public func didCompleteGraphParsing() {
+        self.graph.state = .completed
+        self.setButtonsToInitialState()
+        self.comparisonLabel.text = "Completed!"
+    }
+
+    public func didTapWrongVertex() {
+        if !self.subviews.contains { $0 is ErrorView } {
+            self.showError(error: "You have picked wrong next vertex")
+        }
+    }
+
+    public func willCompareVertices(startVertexPathLength: Double, edgePathLength: Double, endVertexPathLength: Double) {
+        DispatchQueue.main.async {
+            if startVertexPathLength + edgePathLength < endVertexPathLength {
+                self.comparisonLabel.text = "\(startVertexPathLength) + \(edgePathLength) < \(endVertexPathLength) 👍"
+            } else {
+                self.comparisonLabel.text = "\(startVertexPathLength) + \(edgePathLength) >= \(endVertexPathLength) 👎"
+            }
+        }
+    }
+
+    public func didFinishCompare() {
+        DispatchQueue.main.async {
+            self.comparisonLabel.text = ""
+        }
+    }
+
+    public func didStop() {
+        self.graph.state = .initial
+        self.graph.stopVisualization = false
+        self.graph.pauseVisualization = false
+        self.graphView.reset()
+        self.graph.reset()
+        self.setButtonsToInitialState()
+        self.activityIndicator.stopAnimating()
+    }
+
+    public func willStartVertexNeighborsChecking() {
+        DispatchQueue.main.async {
+            self.comparisonLabel.text = ""
+        }
+    }
+
+    public func didFinishVertexNeighborsChecking() {
+        DispatchQueue.main.async {
+            self.comparisonLabel.text = "Pick next vertex"
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground b/Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground
new file mode 100644
index 000000000..35968656f
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' display-mode='raw'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline b/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/README.markdown b/README.markdown
index 5e6cfbfe4..eee5cbb46 100644
--- a/README.markdown
+++ b/README.markdown
@@ -183,6 +183,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Single-Source Shortest Paths](Single-Source%20Shortest%20Paths%20(Weighted)/)
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree%20%28Unweighted%29/) on an unweighted tree
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
+- [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
 
 ## Puzzles
 

From 8efb7354645763fce0823ec74c2fe3ffb904f4df Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Tue, 4 Apr 2017 10:25:36 +0100
Subject: [PATCH 0891/1679] MIT License

---
 MinimumCoinChange/LICENSE | 222 ++++----------------------------------
 1 file changed, 21 insertions(+), 201 deletions(-)

diff --git a/MinimumCoinChange/LICENSE b/MinimumCoinChange/LICENSE
index 8dada3eda..fda6e6146 100755
--- a/MinimumCoinChange/LICENSE
+++ b/MinimumCoinChange/LICENSE
@@ -1,201 +1,21 @@
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-                        http://www.apache.org/licenses/
-
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+MIT License
+
+Copyright (c) 2017 Jacopo Mangiavacchi
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
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+
+The above copyright notice and this permission notice shall be included in all
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+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

From 63257f629f99ba76a7997a1e0b18b8236cefa57b Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Tue, 4 Apr 2017 13:37:53 -0700
Subject: [PATCH 0892/1679] fixed typos in readme

---
 Strassen Matrix Multiplication/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index fa822d310..07ce534b2 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -18,7 +18,7 @@ matrix A = |1 2|, matrix B = |5 6|
 A * B = C
 	
 |1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
-|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 50|
 ```
 
 What's going on here? To start, we're multiplying matricies A & B. Our new matrix, C's, elements `[i, j]` are determined by the dot product of the first matrix's ith row and the second matrix's jth column. See [here](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length) for a refresher on the dot product.
@@ -72,7 +72,7 @@ Then, for each row in A and column in B, we take the dot product of the ith row
 
 ```swift
 for k in 0..<n {
-  C[i, j] = A[i, k] * B[k, j]
+  C[i, j] += A[i, k] * B[k, j]
 }
 ```
 
@@ -90,7 +90,7 @@ public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
   for i in 0..<n {
     for j in 0..<n {
       for k in 0..<n {
-        C[i, j] = A[i, k] * B[k, j]
+        C[i, j] += A[i, k] * B[k, j]
       }
     }
   }
@@ -229,7 +229,7 @@ for i in B.rows {
 }
 ```
 
-Finally, we recusrisvely compute the matrix using Strassen's algorithm and the transform our new matrix `C` back to the correct dimensions!
+Finally, we recursively compute the matrix using Strassen's algorithm and the transform our new matrix `C` back to the correct dimensions!
 
 ```swift
 let CPrep = APrep.strassenR(by: BPrep)

From e8c256eae82b8c30ca32ba28acce5c792edfe79c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 4 Apr 2017 14:07:19 -0700
Subject: [PATCH 0893/1679] Update README.markdown

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 5e6cfbfe4..067de2418 100644
--- a/README.markdown
+++ b/README.markdown
@@ -106,6 +106,7 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 - [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
+- [Strassen's Multiplication Matrix](Strassen%20Multiplication%20Matrix). Efficient way to handle matrix multiplication.
 
 ### Machine learning
 

From bbba068205500a62943a601540d4dfba205586f2 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 4 Apr 2017 14:09:02 -0700
Subject: [PATCH 0894/1679] Updated a link to Strassen Multiplication Matrix.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 067de2418..29fc9d748 100644
--- a/README.markdown
+++ b/README.markdown
@@ -106,7 +106,7 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 - [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
-- [Strassen's Multiplication Matrix](Strassen%20Multiplication%20Matrix). Efficient way to handle matrix multiplication.
+- [Strassen's Multiplication Matrix](Strassen%20Matrix%20Multiplication/). Efficient way to handle matrix multiplication.
 
 ### Machine learning
 

From 20d7c1fd66b93c2a3933abe5d048169cea888ced Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Tue, 4 Apr 2017 17:46:46 -0700
Subject: [PATCH 0895/1679] Revisions in README.md

# Coherence & Sentence structures
# Grammar and spelling
---
 DiningPhilosophers/README.md | 29 +++++++++++++----------------
 1 file changed, 13 insertions(+), 16 deletions(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index ec1611c65..0bf4f28ce 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -1,22 +1,22 @@
 # Dining Philosophers
-Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using [GCD](https://apple.github.io/swift-corelibs-libdispatch/) and [Semaphore](https://developer.apple.com/reference/dispatch/dispatchsemaphore) in Swift)
+The dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using [GCD](https://apple.github.io/swift-corelibs-libdispatch/) and [Semaphore](https://developer.apple.com/reference/dispatch/dispatchsemaphore) in Swift)
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi
 
 
 # Introduction
 
-In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
+In computer science, the dining philosophers problem is often used in the concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
 
 It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.
 
-This Swift implementation is based on the Chandy/Misra solution and it use GCD Dispatch and Semaphone on Swift cross platform
+This Swift implementation is based on the Chandy/Misra solution, and it uses the GCD Dispatch and Semaphone on the Swift cross platform.
 
 # Problem statement
 
 Five silent philosophers sit at a round table with bowls of spaghetti. Forks are placed between each pair of adjacent philosophers.
 
-Each philosopher must alternately think and eat. However, a philosopher can only eat spaghetti when they have both left and right forks. Each fork can be held by only one philosopher and so a philosopher can use the fork only if it is not being used by another philosopher. After an individual philosopher finishes eating, they need to put down both forks so that the forks become available to others. A philosopher can take the fork on their right or the one on their left as they become available, but cannot start eating before getting both forks.
+Each philosopher must alternately think and eat. A philosopher can only eat spaghetti when they have both left and right forks. Since each fork can be held by only one philosopher, a philosopher can use the fork only if it is not being used by another philosopher. When a philosopher finishes eating, they need to put down both forks so that the forks become available to others. A philosopher can take the fork on their right or the one on their left as they become available, but they cannot start eating before getting both forks.
 
 Eating is not limited by the remaining amounts of spaghetti or stomach space; an infinite supply and an infinite demand are assumed.
 
@@ -26,35 +26,32 @@ This is an illustration of an dinining table:
 
 ![Dining Philosophers table](https://upload.wikimedia.org/wikipedia/commons/7/7b/An_illustration_of_the_dining_philosophers_problem.png)
 
-
 # Solution
-There are different solutions for this classic algorithm and this Swift implementation is based on the on the Chandy/Misra solution that more generally allows for arbitrary agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
-
-However, it is very important to note here that this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
+There are different solutions for this classic algorithm, and this Swift implementation is based on the Chandy/Misra solution. This implementation allows agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
 
+However, this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
 
 # Description
 For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with the lower ID (n for agent Pn). Each fork can either be dirty or clean. Initially, all forks are dirty.
-When a philosopher wants to use a set of resources (i.e. eat), said philosopher must obtain the forks from their contending neighbors. For all such forks the philosopher does not have, they send a request message.
-When a philosopher with a fork receives a request message, they keep the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, they clean the fork before doing so.
+When a philosopher wants to use a set of resources (i.e. eat), said philosopher must obtain the forks from their contending neighbors. The philospher send a message for all such forks needed. When a philosopher with a fork receives a request message, they keep the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, they clean the fork before doing so.
 After a philosopher is done eating, all their forks become dirty. If another philosopher had previously requested one of the forks, the philosopher that has just finished eating cleans the fork and sends it.
-This solution also allows for a large degree of concurrency, and will solve an arbitrarily large problem.
+This solution also allows for a large degree of concurrency, and it will solve an arbitrarily large problem.
 
-It also solves the starvation problem. The clean / dirty labels act as a way of giving preference to the most "starved" processes, and a disadvantage to processes that have just "eaten". One could compare their solution to one where philosophers are not allowed to eat twice in a row without letting others use the forks in between. Chandy and Misra's solution is more flexible than that, but has an element tending in that direction.
+In addition, it solves the starvation problem. The clean / dirty labels give a preference to the most "starved" processes and a disadvantage to processes that have just "eaten". One could compare their solution to one where philosophers are not allowed to eat twice in a row without letting others use the forks in between. The Chandy and Misra's solution is more flexible but has an element tending in that direction.
 
-In their analysis they derive a system of preference levels from the distribution of the forks and their clean/dirty states. They show that this system may describe an acyclic graph, and if so, the operations in their protocol cannot turn that graph into a cyclic one. This guarantees that deadlock cannot occur. However, if the system is initialized to a perfectly symmetric state, like all philosophers holding their left side forks, then the graph is cyclic at the outset, and their solution cannot prevent a deadlock. Initializing the system so that philosophers with lower IDs have dirty forks ensures the graph is initially acyclic.
+Based on the Chandy and Misra's analysis, a system of preference levels is derived from the distribution of the forks and their clean/dirty states. This system may describe an acyclic graph, and if so, the solution's protocol cannot turn that graph into a cyclic one. This guarantees that deadlock cannot occur. However, if the system is initialized to a perfectly symmetric state, such as all philosophers holding their left side forks, then the graph is cyclic at the outset, and the solution cannot prevent a deadlock. Initializing the system so that philosophers with lower IDs have dirty forks ensures the graph is initially acyclic.
 
 
 # Swift implementation
 
-This Swift 3.0 implementation of the Chandy/Misra solution is based on GCD and Semaphore tecnique and it could be built on both macOS and Linux.
+This Swift 3.0 implementation of the Chandy/Misra solution is based on the GCD and Semaphore tecnique that can be built on both macOS and Linux.
 
 The code is based on a ForkPair struct used for holding an array of DispatchSemaphore and a Philosopher struct for associate a couple of forks to each Philosopher.
 
 The ForkPair DispatchSemaphore static array is used for waking the neighbour Philosophers any time a fork pair is put down on the table.
 
-A background DispatchQueue is then used to let any Philosopher run asyncrounosly on the background and a global DispatchSemaphore is simply used in order to keep the main thread on wait forever and let the Philosophers contienue forever in their alternate think and eat cycle.
-
+A background DispatchQueue is then used to let any Philosopher run asyncrounosly on the background, and a global DispatchSemaphore is used to keep the main thread on wait forever and let the Philosophers continue forever in their alternate think and eat cycle.
+  
 # See also
 
 Dining Philosophers on Wikipedia https://en.wikipedia.org/wiki/Dining_philosophers_problem

From 56c5ecf2c5c6baf4b7442dbf46db5c9d13fda523 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Tue, 4 Apr 2017 19:31:26 -0700
Subject: [PATCH 0896/1679] Revisions in README.markdown

1- Coherence, Sentence structure, & Consistency
2- Grammar, Word choice, & Spelling
---
 Huffman Coding/README.markdown | 82 +++++++++++++++++-----------------
 1 file changed, 41 insertions(+), 41 deletions(-)

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 4e6f75514..69e105c87 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -1,12 +1,12 @@
 # Huffman Coding
 
-The idea: Encode objects that occur often with a smaller number of bits than objects that occur less frequently.
+The idea: To encode objects that occur with a smaller number of bits than objects that occur less frequently.
 
-Although you can encode any type of objects with this scheme, it's most common to compress a stream of bytes. Let's say you have the following text, where each character is one byte:
+Although any type of objects can be encoded with this scheme, it is common to compress a stream of bytes. Suppose you have the following text, where each character is one byte:
 
 	so much words wow many compression
 
-If you count how often each byte appears, you can clearly see that some bytes occur more than others:
+If you count how often each byte appears, you can see some bytes occur more than others:
 
 	space: 5                  u: 1
 	    o: 5	              h: 1
@@ -41,11 +41,11 @@ Now if we replace the original bytes with these bit strings, the compressed outp
 
 The extra 0-bit at the end is there to make a full number of bytes. We were able to compress the original 34 bytes into merely 16 bytes, a space savings of over 50%!
 
-But hold on... to be able to decode these bits we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data, otherwise the decoder doesn't know how to interpret the bits. Because of the overhead of this frequency table (about 1 kilobyte), it doesn't really pay to use Huffman encoding on very small inputs.
+To be able to decode these bits, we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data. Otherwise, the decoder does not know how to interpret the bits. Because of the overhead of this frequency table (about 1 kilobyte), it is not beneficial to use Huffman encoding on small inputs.
 
 ## How it works
 
-When compressing a stream of bytes, the algorithm first creates a frequency table that counts how often each byte occurs. Based on this table it creates a binary tree that describes the bit strings for each of the input bytes.
+When compressing a stream of bytes, the algorithm first creates a frequency table that counts how often each byte occurs. Based on this table, the algorithm creates a binary tree that describes the bit strings for each of the input bytes.
 
 For our example, the tree looks like this:
 
@@ -53,17 +53,17 @@ For our example, the tree looks like this:
 
 Note that the tree has 16 leaf nodes (the grey ones), one for each byte value from the input. Each leaf node also shows the count of how often it occurs. The other nodes are "intermediate" nodes. The number shown in these nodes is the sum of the counts of their child nodes. The count of the root node is therefore the total number of bytes in the input.
 
-The edges between the nodes either say "1" or "0". These correspond to the bit-encodings of the leaf nodes. Notice how each left branch is always 1 and each right branch is always 0.
+The edges between the nodes are either "1" or "0". These correspond to the bit-encodings of the leaf nodes. Notice how each left branch is always 1 and each right branch is always 0.
 
-Compression is then a matter of looping through the input bytes, and for each byte traverse the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
+Compression is then a matter of looping through the input bytes and for each byte traversing the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
 
-For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`.
+For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). This gives the Huffman code as `0011` for `c`.
 
-Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until we get to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
+Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until it reaches to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
 
 ## The code
 
-Before we get to the actual Huffman coding scheme, it's useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte, but we're dealing in bits, so we need to translate between the two.
+Before we get to the actual Huffman coding scheme, it is useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte, but we are dealing in bits, so we need to translate between the two.
 
 ```swift
 public class BitWriter {
@@ -92,11 +92,11 @@ public class BitWriter {
 }
 ```
 
-To add a bit to the `NSData` you call `writeBit()`. This stuffs each new bit into the `outByte` variable. Once you've written 8 bits, `outByte` gets added to the `NSData` object for real.
+To add a bit to the `NSData`, you can call `writeBit()`. This helper object stuffs each new bit into the `outByte` variable. Once you have written 8 bits, `outByte` gets added to the `NSData` object for real.
 
 The `flush()` method is used for outputting the very last byte. There is no guarantee that the number of compressed bits is a nice round multiple of 8, in which case there may be some spare bits at the end. If so, `flush()` adds a few 0-bits to make sure that we write a full byte.
 
-We'll use a similar helper object for reading individual bits from `NSData`:
+Here is a similar helper object for reading individual bits from `NSData`:
 
 ```swift
 public class BitReader {
@@ -122,15 +122,15 @@ public class BitReader {
 }
 ```
 
-This works in a similar fashion. We read one whole byte from the `NSData` object and put it in `inByte`. Then `readBit()` returns the individual bits from that byte. Once `readBit()` has been called 8 times, we read the next byte from the `NSData`.
+By using this helper object, we can read one whole byte from the `NSData` object and put it in `inByte`. Then, `readBit()` returns the individual bits from that byte. Once `readBit()` has been called 8 times, we read the next byte from the `NSData`.
 
-> **Note:** It's no big deal if you're unfamiliar with this sort of bit manipulation. Just know that these two helper objects make it simple for us to write and read bits and not worry about all the messy stuff of making sure they end up in the right place.
+> **Note:** If you are unfamiliar with this type of bit manipulation, just know that these two helper objects make it simple for us to write and read bits.
 
 ## The frequency table
 
-The first step in Huffman compression is to read the entire input stream and build a frequency table. This table contains a list of all 256 possible byte values and how often each of these bytes occurs in the input data.
+The first step in the Huffman compression is to read the entire input stream and build a frequency table. This table contains a list of all 256 possible byte values and shows how often each of these bytes occurs in the input data.
 
-We could store this frequency information in a dictionary or an array, but since we're going to need to build a tree anyway, we might as well store the frequency table as the leaves of the tree.
+We could store this frequency information in a dictionary or an array, but since we need to build a tree, we might store the frequency table as the leaves of the tree.
 
 Here are the definitions we need:
 
@@ -152,9 +152,9 @@ class Huffman {
 }
 ```
 
-The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary%20Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
+The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary%20Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, these nodes do not use pointers to refer to each other but use simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
 
-Note that `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we'll add more nodes as we build up the actual tree. For the moment there isn't a tree yet, just 256 separate leaf nodes with no connections between them. All the node counts are 0.
+Note that the `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we will add more nodes as we build up the actual tree. For the moment, there is not a tree yet. It includes 256 separate leaf nodes with no connections between them. All the node counts are 0.
 
 We use the following method to count how often each byte occurs in the input data:
 
@@ -170,13 +170,13 @@ We use the following method to count how often each byte occurs in the input dat
   }
 ```
 
-This steps through the `NSData` object from beginning to end and for each byte increments the `count` of the corresponding leaf node. That's all there is to it. After `countByteFrequency()` completes, the first 256 `Node` objects in the `tree` array represent the frequency table.
+This steps through the `NSData` object from beginning to end and for each byte increments the `count` of the corresponding leaf node. After `countByteFrequency()` completes, the first 256 `Node` objects in the `tree` array represent the frequency table.
 
-Now, I mentioned that in order to decompress a Huffman-encoded block of data, you also need to have the original frequency table. If you were writing the compressed data to a file, then somewhere in the file you'd include the frequency table.
+To decompress a Huffman-encoded block of data, we need to have the original frequency table. If we were writing the compressed data to a file, then somewhere in the file we should include the frequency table.
 
-You could simply dump the first 256 elements from the `tree` array but that's not very efficient. It's likely that not all of these 256 elements will be used, plus you don't need to serialize the `parent`, `right`, and `left` pointers. All we need is the frequency information, not the entire tree.
+We could dump the first 256 elements from the `tree` array, but that is not efficient. Not all of these 256 elements will be used, and we do not need to serialize the `parent`, `right`, and `left` pointers. All we need is the frequency information and not the entire tree.
 
-Instead, we'll add a method to export the frequency table without all the pieces we don't need:
+Instead, we will add a method to export the frequency table without all the pieces we do not need:
 
 ```swift
   struct Freq {
@@ -193,7 +193,7 @@ Instead, we'll add a method to export the frequency table without all the pieces
   }
 ```
 
-The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are actually used, without the `parent`, `left`, and `right` pointers. It returns an array of `Freq` objects. You have to serialize this array along with the compressed data so that it can be properly decompressed later.
+The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are used, without the `parent`, `left`, and `right` pointers. It returns an array of `Freq` objects. You have to serialize this array along with the compressed data, so that it can be properly decompressed later.
 
 ## The tree
 
@@ -201,7 +201,7 @@ As a reminder, there is the compression tree for the example:
 
 ![The compression tree](Images/Tree.png)
 
-The leaf nodes represent the actual bytes that are present in the input data. The intermediary nodes connect the leaves in such a way that the path from the root to a frequently-used byte value is shorter than the path to a less common byte value. As you can see, `m`, `s`, space, and `o` are the most common letters in our input data and therefore they are highest up in the tree.
+The leaf nodes represent the actual bytes that are present in the input data. The intermediary nodes connect the leaves in such a way that the path from the root to a frequently-used byte value is shorter than the path to a less common byte value. As you can see, `m`, `s`, space, and `o` are the most common letters in our input data and the highest up in the tree.
 
 To build the tree, we do the following:
 
@@ -209,7 +209,7 @@ To build the tree, we do the following:
 2. Create a new parent node that links these two nodes together.
 3. This repeats over and over until only one node with no parent remains. This becomes the root node of the tree.
 
-This is an ideal place to use a [priority queue](../Priority%20Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
+This is an ideal place to use a [priority queue](../Priority%20Queue/). A priority queue is a data structure that is optimized, so that finding the minimum value is always fast. Here, we repeatedly need to find the node with the smallest count.
 
 The function `buildTree()` then becomes:
 
@@ -252,15 +252,15 @@ Here is how it works step-by-step:
 
 4. Link the two nodes into their new parent node. Now this new intermediate node has become part of the tree.
 
-5. Put the new intermediate node back into the queue. At this point we're done with `node1` and `node2`, but the `parentNode` still need to be connected to other nodes in the tree.
+5. Put the new intermediate node back into the queue. At this point we are done with `node1` and `node2`, but the `parentNode` still needs to be connected to other nodes in the tree.
 
-6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we're done.
+6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we are done.
 
 The animation shows what the process looks like:
 
 ![Building the tree](Images/BuildTree.gif)
 
-> **Note:** Instead of using a priority queue, you can repeatedly iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor quite slow, **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
+> **Note:** Instead of using a priority queue, you can repeatedly iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor slow as **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
 
 > **Fun fact:** Due to the nature of binary trees, if we have *x* leaf nodes we can at most add *x - 1* additional nodes to the tree. Given that at most there will be 256 leaf nodes, the tree will never contain more than 511 nodes total.
 
@@ -286,11 +286,11 @@ Now that we know how to build the compression tree from the frequency table, we
   }
 ```
 
-This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits.
+This first calls `countByteFrequency()` to build the frequency table and then calls `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits.
 
-Then it loops through the entire input and for each byte calls `traverseTree()`. That method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
+Then, it loops through the entire input and calls `traverseTree()`for each byte. This method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
 
-> **Note:** Compression always requires two passes through the entire input data: first to build the frequency table, second to convert the bytes to their compressed bit sequences.
+> **Note:** Compression always requires two passes through the entire input data: first to build the frequency table, and second to convert the bytes to their compressed bit sequences.
 
 The interesting stuff happens in `traverseTree()`. This is a recursive method:
 
@@ -309,15 +309,15 @@ The interesting stuff happens in `traverseTree()`. This is a recursive method:
   }
 ```
 
-When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again.
+When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we need to encode. This method recursively walks the tree from a leaf node up to the root and then back again.
 
-As we're going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it's the right node, we emit a 0.
+As we are going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it is the right node, we emit a 0.
 
 In a picture:
 
 ![How compression works](Images/Compression.png)
 
-Even though the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 aren't actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we're going in is enough to determine what bit value to write.
+Even though the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 are not actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we are going in is enough to determine what bit value to write.
 
 You use the `compressData()` method as follows:
 
@@ -332,9 +332,9 @@ if let originalData = s1.dataUsingEncoding(NSUTF8StringEncoding) {
 
 ## Decompression
 
-Decompression is pretty much compression in reverse. However, the compressed bits are useless to us without the frequency table. Earlier you saw the `frequencyTable()` method that returns an array of `Freq` objects. The idea is that if you were saving the compressed data into a file or sending it across the network, you'd also save that `[Freq]` array along with it.
+Decompression is the compression in reverse. However, the compressed bits are useless without the frequency table. As mentioned, the `frequencyTable()` method returns an array of `Freq` objects. If we were saving the compressed data into a file or sending it across the network, we'd also save that `[Freq]` array along with it.
 
-We first need some way to turn the `[Freq]` array back into a compression tree. Fortunately, this is pretty easy:
+We first need some way to turn the `[Freq]` array back into a compression tree:
 
 ```swift
   fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
@@ -349,7 +349,7 @@ We first need some way to turn the `[Freq]` array back into a compression tree.
 
 We convert the `Freq` objects into leaf nodes and then call `buildTree()` to do the rest.
 
-Here is the code for `decompressData()`, which takes an `NSData` object with Huffman-encoded bits and a frequency table, and returns the original data:
+Here is the code for `decompressData()`, which takes an `NSData` object with Huffman-encoded bits and a frequency table, and it returns the original data:
 
 ```swift
   func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
@@ -385,13 +385,13 @@ This also uses a helper method to traverse the tree:
   }
 ```
 
-`findLeafNode()` walks the tree from the root down to the leaf node given by `nodeIndex`. At each intermediate node we read a new bit and then step to the left (bit is 1) or the right (bit is 0). When we get to the leaf node, we simply return its index, which is equal to the original byte value.
+`findLeafNode()` walks the tree from the root down to the leaf node given by `nodeIndex`. At each intermediate node, we read a new bit and then step to the left (bit is 1) or the right (bit is 0). When we get to the leaf node, we simply return its index, which is equal to the original byte value.
 
 In a picture:
 
 ![How decompression works](Images/Decompression.png)
 
-Here's how you would use the decompression method:
+Here is how we use the decompression method:
 
 ```swift
   let frequencyTable = huffman1.frequencyTable()
@@ -402,9 +402,9 @@ Here's how you would use the decompression method:
   let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
 ```
 
-First you get the frequency table from somewhere (in this case the `Huffman` object we used to encode the data) and then call `decompressData()`. The string that results should be equal to the one you compressed in the first place.
+First we get the frequency table from somewhere (in this case the `Huffman` object we used to encode the data) and then call `decompressData()`. The string that results should be equal to the one we compressed in the first place.
 
-You can see how this works in more detail in the Playground.
+we can see how this works in more detail in the Playground.
 
 ## See also
 

From d70f40ed8668e60584dc1bd9d5b859b7ad2e91de Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Wed, 5 Apr 2017 10:34:21 -0700
Subject: [PATCH 0897/1679] Revisions in README.markdown

I have revised your document to be simplified and concise.
---
 Array2D/README.markdown | 30 ++++++++++++++----------------
 1 file changed, 14 insertions(+), 16 deletions(-)

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index d67079691..88f25c99a 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -1,14 +1,14 @@
 # Array2D
 
-In C and Objective-C you can write the following line,
+In C and Objective-C, you can write the following line,
 
 	int cookies[9][7];
 	
-to make a 9x7 grid of cookies. This would create a two-dimensional array of 63 elements. To find the cookie at column 3, row 6, you'd write:
+to make a 9x7 grid of cookies. This creates a two-dimensional array of 63 elements. To find the cookie at column 3 and row 6, you can write:
 
 	myCookie = cookies[3][6];
 	
-Unfortunately, you can't write the above in Swift. To create a multi-dimensional array in Swift you'd have to do something like this:
+This statement is not acceptable in Swift. To create a multi-dimensional array in Swift, you can write:
 
 ```swift
 var cookies = [[Int]]()
@@ -21,19 +21,19 @@ for _ in 1...9 {
 }
 ```
 
-And then to find a cookie:
+Then, to find a cookie, you can write:
 
 ```swift
 let myCookie = cookies[3][6]
 ```
 
-Actually, you could create the array in a single line of code, like so:
+You can also create the array in a single line of code:
 
 ```swift
 var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 ```
 
-but that's just ugly. To be fair, you can hide the ugliness in a helper function:
+This looks complicated, but can simplfy it in a helper function:
 
 ```swift
 func dim<T>(_ count: Int, _ value: T) -> [T] {
@@ -41,13 +41,13 @@ func dim<T>(_ count: Int, _ value: T) -> [T] {
 }
 ```
 
-And then creating the array looks like this:
+Then, you can create the array:
 
 ```swift
 var cookies = dim(9, dim(7, 0))
 ```
 
-Swift infers that the datatype of the array should be `Int` because you specified `0` as the default value of the array elements. To use a string instead, you'd write:
+Swift infers that the datatype of the array must be `Int` because you specified `0` as the default value of the array elements. To use a string instead, you can write:
 
 ```swift
 var cookies = dim(9, dim(7, "yum"))
@@ -59,9 +59,9 @@ The `dim()` function makes it easy to go into even more dimensions:
 var threeDimensions = dim(2, dim(3, dim(4, 0)))
 ```
 
-The downside of using multi-dimensional arrays in this fashion -- actually, multiple nested arrays -- is that it's easy to lose track of what dimension represents what.
+The downside of using multi-dimensional arrays or multiple nested arrays in this way is to lose track of what dimension represents what.
 
-So instead let's create our own type that acts like a 2-D array and that is more convenient to use. Here it is, short and sweet:
+Instead, you can create your own type that acts like a 2-D array which is more convenient to use:
 
 ```swift
 public struct Array2D<T> {
@@ -92,26 +92,24 @@ public struct Array2D<T> {
 
 `Array2D` is a generic type, so it can hold any kind of object, not just numbers.
 
-To create an instance of `Array2D` you'd write:
+To create an instance of `Array2D`, you can write:
 
 ```swift
 var cookies = Array2D(columns: 9, rows: 7, initialValue: 0)
 ```
 
-Thanks to the `subscript` function, you can do the following to retrieve an object from the array:
+By using the `subscript` function, you can retrieve an object from the array:
 
 ```swift
 let myCookie = cookies[column, row]
 ```
 
-Or change it:
+Or, you can change it:
 
 ```swift
 cookies[column, row] = newCookie
 ```
 
-Internally, `Array2D` uses a single one-dimensional array to store the data. The index of an object in that array is given by `(row x numberOfColumns) + column`. But as a user of `Array2D` you don't have to worry about that; you only have to think in terms of "column" and "row", and let `Array2D` figure out the details for you. That's the advantage of wrapping primitive types into a wrapper class or struct.
-
-And that's all there is to it.
+Internally, `Array2D` uses a single one-dimensional array to store the data. The index of an object in that array is given by `(row x numberOfColumns) + column`, but as a user of `Array2D`, you only need to think in terms of "column" and "row", and the details will be done by `Array2D`. This is the advantage of wrapping primitive types into a wrapper class or struct.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 777bf7b948e75d77bbac8cbba5dc40716c6b5d61 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 6 Apr 2017 16:34:58 +0300
Subject: [PATCH 0898/1679] Deleted unnecessary code and added comments

---
 .../Dijkstra.playground/Contents.swift        | 37 +++++++++++++------
 1 file changed, 26 insertions(+), 11 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 8d600d577..13087a8f9 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -3,19 +3,15 @@
 import Foundation
 import UIKit
 
-open class ProductVertex: Vertex {}
-
 open class Vertex: Hashable, Equatable {
 
     open var identifier: String!
     open var neighbors: [(Vertex, Double)] = []
     open var pathLengthFromStart: Double = Double.infinity
     open var pathVerticesFromStart: [Vertex] = []
-//    open var point: CGPoint!
 
-    public init(identifier: String/*, point: CGPoint*/) {
+    public init(identifier: String) {
         self.identifier = identifier
-//        self.point = point
     }
 
     open var hashValue: Int {
@@ -77,7 +73,9 @@ public class Dijkstra {
 var _vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
-    for i in 0..<15 {
+    //change this value to increase or decrease amount of vertices in the graph
+    let numberOfVerticesInGraph = 15
+    for i in 0..<numberOfVerticesInGraph {
         let vertex = Vertex(identifier: "\(i)")
         _vertices.insert(vertex)
     }
@@ -108,15 +106,32 @@ func randomVertex(except vertex: Vertex) -> Vertex {
     return newSet[index]
 }
 
+func randomVertex() -> Vertex {
+    let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
+    let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
+    return _vertices[index]
+}
+
+//initialize random graph
 createNotConnectedVertices()
 setupConnections()
+
+//initialize Dijkstra algorithm with graph vertices
 let dijkstra = Dijkstra(vertices: _vertices)
-let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
-let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
-let startVertex = _vertices[index]
+
+//decide which vertex will be the starting one
+let startVertex = randomVertex()
+
+//ask algorithm to find shortest paths from start vertex to all others
 dijkstra.findShortestPaths(from: startVertex)
+
+//printing results
 let destinationVertex = randomVertex(except: startVertex)
-destinationVertex.pathLengthFromStart
-destinationVertex.pathVerticesFromStart
+print(destinationVertex.pathLengthFromStart)
+var pathVerticesFromStartString: [String] = []
+for vertex in destinationVertex.pathVerticesFromStart {
+    pathVerticesFromStartString.append(vertex.identifier)
+}
+print(pathVerticesFromStartString.joined(separator: "->"))
 
 

From 11fdc6ca756b4d402e807a0f9b6063fd6f38dab1 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 11:57:03 -0700
Subject: [PATCH 0899/1679] Revisions in README.markdown

I have revised your document to be more concise.
---
 Graph/README.markdown | 62 +++++++++++++++++++++----------------------
 1 file changed, 31 insertions(+), 31 deletions(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index a2531e808..bc33b044a 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,26 +1,26 @@
 # Graph
 
-A graph is something that looks like this:
+A graph looks like the following picture:
 
 ![A graph](Images/Graph.png)
 
-In computer-science lingo, a graph is a set of *vertices* paired with a set of *edges*. The vertices are the round things and the edges are the lines between them. Edges connect a vertex to other vertices.
+In computer science, a graph is defined as a set of *vertices* paired with a set of *edges*. The vertices are represented by circles, and the edges are the lines between them. Edges connect a vertex to other vertices.
 
-> **Note:** Vertices are sometimes also called "nodes" and edges are also called "links".
+> **Note:** Vertices are sometimes called "nodes", and edges are called "links".
 
-For example, a graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges. A somewhat historically inaccurate example:
+A graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges. Here is a somewhat historically inaccurate example:
 
 ![Social network](Images/SocialNetwork.png)
 
-Graphs come in all kinds of shapes and sizes. The edges can have a *weight*, where a positive or negative numeric value is assigned to each edge. Consider an example of a graph representing airplane flights. Cities can be vertices, and flights can be edges. Then an edge weight could describe flight time or the price of a ticket.
+Graphs have various shapes and sizes. The edges can have a *weight*, where a positive or negative numeric value is assigned to each edge. Consider an example of a graph representing airplane flights. Cities can be vertices, and flights can be edges. Then, an edge weight could describe flight time or the price of a ticket.
 
 ![Airplane flights](Images/Flights.png)
 
 With this hypothetical airline, flying from San Francisco to Moscow is cheapest by going through New York.
 
-Edges can also be *directed*. So far the edges you've seen have been undirected, so if Ada knows Charles, then Charles also knows Ada. A directed edge, on the other hand, implies a one-way relationship. A directed edge from vertex X to vertex Y connects X to Y, but *not* Y to X.
+Edges can also be *directed*. In examples mentioned above, the edges are undirected. For instance, if Ada knows Charles, then Charles also knows Ada. A directed edge, on the other hand, implies a one-way relationship. A directed edge from vertex X to vertex Y connects X to Y, but *not* Y to X.
 
-Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back).
+Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska indicates that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back).
 
 ![One-way flights](Images/FlightsDirected.png)
 
@@ -28,51 +28,51 @@ The following are also graphs:
 
 ![Tree and linked list](Images/TreeAndList.png)
 
-On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked%20List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
+On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked%20List/). They can be considered graphs but in a simpler form. They both have vertices (nodes) and edges (links).
 
-The very first graph I showed you contained *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
+The first graph includes *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
 
-Another very common type of graph is the *directed acyclic graph* or DAG:
+Another common type of graph is the *directed acyclic graph* or DAG:
 
 ![DAG](Images/DAG.png)
 
-Like a tree this does not have any cycles in it (no matter where you start, there is no path back to the starting vertex), but unlike a tree the edges are directional and the shape doesn't necessarily form a hierarchy.
+Like a tree, this graph does not have any cycles (no matter where you start, there is no path back to the starting vertex), but this graph has directional edges with the shape that does not necessarily form a hierarchy.
 
 ## Why use graphs?
 
-Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that graphs are an extremely useful data structure.
+Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that a graph is a useful data structure.
 
-If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First%20Search/) or [depth-first search](../Depth-First%20Search) to find a solution.
+If you have a programming problem where you can represent your data as vertices and edges, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First%20Search/) or [depth-first search](../Depth-First%20Search) to find a solution.
 
-For example, let's say you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
+For example, suppose you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
 
 ![Tasks as a graph](Images/Tasks.png)
 
-Each vertex represents a task. Here, an edge between two vertices means that the source task must be completed before the destination task can start. So task C cannot start before B and D are finished, and B nor D can start before A is finished.
+Each vertex represents a task. An edge between two vertices means the source task must be completed before the destination task can start. As an example, task C cannot start before B and D are finished, and B nor D can start before A is finished.
 
 Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological%20Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
 
-Whenever you're faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationship".
+Whenever you are faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationships".
 
-If you're a musician you might appreciate this graph:
+If you are a musician you might appreciate this graph:
 
 ![Chord map](Images/ChordMap.png)
 
-The vertices are chords from the C major scale. The edges -- the relationships between the chords -- represent how [likely one chord is to follow another](http://mugglinworks.com/chordmaps/genmap.htm). This is a directed graph, so the direction of the arrows shows how you can go from one chord to the next. It's also a weighted graph, where the weight of the edges -- portrayed here by line thickness -- shows a strong relationship between two chords. As you can see, a G7-chord is very likely to be followed by a C chord, and much less likely by a Am chord.
+The vertices are chords from the C major scale. The edges -- the relationships between the chords -- represent how [likely one chord is to follow another](http://mugglinworks.com/chordmaps/genmap.htm). This is a directed graph, so the direction of the arrows shows how you can go from one chord to the next. It is also a weighted graph, where the weight of the edges -- portrayed here by line thickness -- shows a strong relationship between two chords. As you can see, a G7-chord is very likely to be followed by a C chord, and much less likely by a Am chord.
 
-You're probably already using graphs without even knowing it. Your data model is also a graph (from Apple's Core Data documentation):
+You are probably already using graphs without even knowing it. Your data model is also a graph (from Apple's Core Data documentation):
 
 ![Core Data model](https://developer.apple.com/library/ios/documentation/Cocoa/Conceptual/CoreDataVersioning/Art/recipe_version2.0.jpg)
 
-Another common graph that's used by programmers is the state machine, where edges depict the conditions for transitioning between states. Here is a state machine that models my cat:
+Another common graph used by programmers is the state machine, where edges depict the conditions for transitioning between states. Here is a state machine that models my cat:
 
 ![State machine](Images/StateMachine.png)
 
-Graphs are awesome. Facebook made a fortune from their social graph. If you're going to learn any data structure, it should be the graph and the vast collection of standard graph algorithms.
+Graphs are awesome. Facebook made a fortune from their social graph. If you are going to learn any data structure, you must choose the graph and the vast collection of standard graph algorithms.
 
 ## Vertices and edges, oh my!
 
-In theory, a graph is just a bunch of vertex objects and a bunch of edge objects. But how do you describe these in code?
+In theory, a graph is just a bunch of vertex and edge objects, but how do you describe this in code?
 
 There are two main strategies: adjacency list and adjacency matrix.
 
@@ -80,9 +80,9 @@ There are two main strategies: adjacency list and adjacency matrix.
 
 ![Adjacency list](Images/AdjacencyList.png)
 
-The adjacency list describes outgoing edges. A has an edge to B but B does not have an edge back to A, so A does not appear in B's adjacency list. Finding an edge or weight between two vertices can be expensive because there is no random access to edges–you must traverse the adjacency lists until it is found.
+The adjacency list describes outgoing edges. A has an edge to B, but B does not have an edge back to A, so A does not appear in B's adjacency list. Finding an edge or weight between two vertices can be expensive because there is no random access to edges. You must traverse the adjacency lists until it is found.
 
-**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for vertex A, column for vertex B would have value 5.6:
+**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for vertex A and column for vertex B would have the value 5.6:
 
 ![Adjacency matrix](Images/AdjacencyMatrix.png)
 
@@ -103,7 +103,7 @@ Let *V* be the number of vertices in the graph, and *E* the number of edges.  Th
 
 In the case of a *sparse* graph, where each vertex is connected to only a handful of other vertices, an adjacency list is the best way to store the edges. If the graph is *dense*, where each vertex is connected to most of the other vertices, then a matrix is preferred.
 
-We'll show you sample implementations of both adjacency list and adjacency matrix.
+Here are sample implementations of both adjacency list and adjacency matrix:
 
 ## The code: edges and vertices
 
@@ -137,9 +137,9 @@ It stores arbitrary data with a generic type `T`, which is `Hashable` to enforce
 
 ## The code: graphs
 
-> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
+> **Note:** There are many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you are trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
 
-Here's an example of a very simple graph:
+Here is an example of a simple graph:
 
 ![Demo](Images/Demo1.png)
 
@@ -165,7 +165,7 @@ for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 }
 ```
 
-As mentioned earlier, to create an undirected edge you need to make two directed edges. If we wanted undirected graphs, we'd call this method instead, which takes care of that work for us:
+As mentioned earlier, to create an undirected edge you need to make two directed edges. For undirected graphs, we call the following method instead:
 
 ```swift
   graph.addUndirectedEdge(v1, to: v2, withWeight: 1.0)
@@ -198,7 +198,7 @@ private class EdgeList<T> where T: Equatable, T: Hashable {
 }
 ```
 
-They are implemented as a class as opposed to structs so we can modify them by reference, in place, like when adding an edge to a new vertex, where the source vertex already has an edge list:
+They are implemented as a class as opposed to structs, so we can modify them by reference, in place, like when adding an edge to a new vertex, where the source vertex already has an edge list:
 
 ```swift
 open override func createVertex(_ data: T) -> Vertex<T> {
@@ -231,7 +231,7 @@ where the general form `a -> [(b: w), ...]` means an edge exists from `a` to `b`
 
 ## The code: adjacency matrix
 
-We'll keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight. If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
+We will keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight. If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
 
 To index into the matrix using vertices, we use the `index` property in `Vertex`, which is assigned when creating the vertex through the graph object. When creating a new vertex, the graph must resize the matrix:
 
@@ -277,6 +277,6 @@ Then the adjacency matrix looks like this:
 
 ## See also
 
-This article described what a graph is and how you can implement the basic data structure. But we have many more articles on practical uses for graphs, so check those out too!
+This article described what a graph is, and how you can implement the basic data structure. We have other articles on practical uses of graphs, so check those out too!
 
 *Written by Donald Pinckney and Matthijs Hollemans*

From 0a77b0685a7c26512377ba57ed02d2ee4644a880 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 13:57:39 -0700
Subject: [PATCH 0900/1679] Revisions in README.markdown

I have revised your document to be more concise.
---
 Binary Search Tree/README.markdown | 138 ++++++++++++++---------------
 1 file changed, 69 insertions(+), 69 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index b3b955c61..14ef931b9 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -2,7 +2,7 @@
 
 A binary search tree is a special kind of [binary tree](../Binary%20Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
 
-If you don't know what a tree is or what it is for, then [read this first](../Tree/).
+For more iformation about a tree, [read this first](../Tree/).
 
 ## "Always sorted" property
 
@@ -12,56 +12,56 @@ Here is an example of a valid binary search tree:
 
 Notice how each left child is smaller than its parent node, and each right child is greater than its parent node. This is the key feature of a binary search tree.
 
-For example, `2` is smaller than `7` so it goes on the left; `5` is greater than `2` so it goes on the right.
+For example, `2` is smaller than `7`, so it goes on the left; `5` is greater than `2`, so it goes on the right.
 
 ## Inserting new nodes
 
 When performing an insertion, we first compare the new value to the root node. If the new value is smaller, we take the *left* branch; if greater, we take the *right* branch. We work our way down the tree this way until we find an empty spot where we can insert the new value.
 
-Say we want to insert the new value `9`:
+Suppose we want to insert the new value `9`:
 
 - We start at the root of the tree (the node with the value `7`) and compare it to the new value `9`.
 - `9 > 7`, so we go down the right branch and repeat the same procedure but this time on node `10`.
 - Because `9 < 10`, we go down the left branch.
-- We've now arrived at a point where there are no more values to compare with. A new node for `9` is inserted at that location.
+- We now arrived at a point where there are no more values to compare with. A new node for `9` is inserted at that location.
 
-The tree now looks like this:
+Here is the tree after inserting the new value `9`:
 
 ![After adding 9](Images/Tree2.png)
 
-There is always only one possible place where the new element can be inserted in the tree. Finding this place is usually pretty quick. It takes **O(h)** time, where **h** is the height of the tree.
+There is only one possible place where the new element can be inserted in the tree. Finding this place is usually quick. It takes **O(h)** time, where **h** is the height of the tree.
 
 > **Note:** The *height* of a node is the number of steps it takes to go from that node to its lowest leaf. The height of the entire tree is the distance from the root to the lowest leaf. Many of the operations on a binary search tree are expressed in terms of the tree's height.
 
-By following this simple rule -- smaller values on the left, larger values on the right -- we keep the tree sorted in a way such that whenever we query it, we can quickly check if a value is in the tree.
+By following this simple rule -- smaller values on the left, larger values on the right -- we keep the tree sorted, so whenever we query it, we can check if a value is in the tree.
 
 ## Searching the tree
 
-To find a value in the tree, we essentially perform the same steps as with insertion:
+To find a value in the tree, we perform the same steps as with insertion:
 
 - If the value is less than the current node, then take the left branch.
 - If the value is greater than the current node, take the right branch.
-- And if the value is equal to the current node, we've found it!
+- If the value is equal to the current node, we've found it!
 
-Like most tree operations, this is performed recursively until either we find what we're looking for, or run out of nodes to look at.
+Like most tree operations, this is performed recursively until either we find what we are looking for or run out of nodes to look at.
 
-If we were looking for the value `5` in the example, it would go as follows:
+Here is an example for searching the value `5`:
 
 ![Searching the tree](Images/Searching.png)
 
-Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary%20Search) in an array.)
+Searching is fast using the structure of the tree. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary%20Search) in an array.)
 
 ## Traversing the tree
 
-Sometimes you don't want to look at just a single node, but at all of them.
+Sometimes you need to look at all nodes rather than only one.
 
 There are three ways to traverse a binary tree:
 
-1. *In-order* (or *depth-first*): first look at the left child of a node, then at the node itself, and finally at its right child.
-2. *Pre-order*: first look at a node, then its left and right children.
+1. *In-order* (or *depth-first*): first look at the left child of a node then at the node itself and finally at its right child.
+2. *Pre-order*: first look at a node then its left and right children.
 3. *Post-order*: first look at the left and right children and process the node itself last.
 
-Once again, this happens recursively.
+Traversing the tree also happens recursively.
 
 If you traverse a binary search tree in-order, it looks at all the nodes as if they were sorted from low to high. For the example tree, it would print `1, 2, 5, 7, 9, 10`:
 
@@ -69,7 +69,7 @@ If you traverse a binary search tree in-order, it looks at all the nodes as if t
 
 ## Deleting nodes
 
-Removing nodes is also easy. After removing a node, we replace the node with either its biggest child on the left or its smallest child on the right. That way the tree is still sorted after the removal. In following example, 10 is removed and replaced with either 9 (Figure 2), or 11 (Figure 3).
+Removing nodes is easy. After removing a node, we replace the node with either its biggest child on the left or its smallest child on the right. That way the tree is still sorted after the removal. In the following example, 10 is removed and replaced with either 9 (Figure 2) or 11 (Figure 3).
 
 ![Deleting a node with two children](Images/DeleteTwoChildren.png)
 
@@ -80,9 +80,9 @@ Note the replacement needs to happen when the node has at least one child. If it
 
 ## The code (solution 1)
 
-So much for the theory. Let's see how we can implement a binary search tree in Swift. There are different approaches you can take. First, I'll show you how to make a class-based version but we'll also look at how to make one using enums.
+So much for the theory. Let's see how we can implement a binary search tree in Swift. There are different approaches you can take. First, I will show you how to make a class-based version, but we will also look at how to make one using enums.
 
-Here's a first stab at a `BinarySearchTree` class:
+Here is an example for a `BinarySearchTree` class:
 
 ```swift
 public class BinarySearchTree<T: Comparable> {
@@ -133,21 +133,21 @@ public class BinarySearchTree<T: Comparable> {
 }
 ```
 
-This class describes just a single node, not the entire tree. It's a generic type, so the node can store any kind of data. It also has references to its `left` and `right` child nodes and a `parent` node.
+This class describes just a single node not the entire tree. It is a generic type, so the node can store any kind of data. It also has references to its `left` and `right` child nodes and a `parent` node.
 
-Here's how you'd use it:
+Here is how you can use it:
 
 ```swift
 let tree = BinarySearchTree<Int>(value: 7)
 ```
 
-The `count` property determines how many nodes are in the subtree described by this node. This doesn't just count the node's immediate children but also their children and their children's children, and so on. If this particular object is the root node, then it counts how many nodes are in the entire tree. Initially, `count = 0`.
+The `count` property determines how many nodes are in the subtree described by this node. This does not just count the node's immediate children but also their children and their children's children, and so on. If this particular object is the root node, then it counts how many nodes are in the entire tree. Initially, `count = 0`.
 
-> **Note:** Because `left`, `right`, and `parent` are optionals, we can make good use of Swift's optional chaining (`?`) and nil-coalescing operators (`??`). You could also write this sort of thing with `if let` but that is less concise.
+> **Note:** Because `left`, `right`, and `parent` are optional, we can make good use of Swift's optional chaining (`?`) and nil-coalescing operators (`??`). You could also write this sort of thing with `if let`, but that is less concise.
 
 ### Inserting nodes
 
-A tree node by itself is pretty useless, so here is how you would add new nodes to the tree:
+A tree node by itself is useless, so here is how you would add new nodes to the tree:
 
 ```swift
   public func insert(value: T) {
@@ -173,9 +173,9 @@ Like so many other tree operations, insertion is easiest to implement with recur
 
 If there is no more left or right child to look at, we create a `BinarySearchTree` object for the new node and connect it to the tree by setting its `parent` property.
 
-> **Note:** Because the whole point of a binary search tree is to have smaller nodes on the left and larger ones on the right, you should always insert elements at the root, to make to sure this remains a valid binary tree!
+> **Note:** Because the whole point of a binary search tree is to have smaller nodes on the left and larger ones on the right, you should always insert elements at the root to make sure this remains a valid binary tree!
 
-To build the complete tree from the example you'd do:
+To build the complete tree from the example you can do:
 
 ```swift
 let tree = BinarySearchTree<Int>(value: 7)
@@ -186,7 +186,7 @@ tree.insert(9)
 tree.insert(1)
 ```
 
-> **Note:** For reasons that will become clear later, you should insert the numbers in a somewhat random order. If you insert them in sorted order, the tree won't have the right shape.
+> **Note:** For reasons that will become clear later, you should insert the numbers in a random order. If you insert them in a sorted order, the tree will not have the right shape.
 
 For convenience, let's add an init method that calls `insert()` for all the elements in an array:
 
@@ -210,7 +210,7 @@ The first value in the array becomes the root of the tree.
 
 ### Debug output
 
-When working with somewhat complicated data structures such as this, it's useful to have human-readable debug output.
+When working with complicated data structures, it is useful to have human-readable debug output.
 
 ```swift
 extension BinarySearchTree: CustomStringConvertible {
@@ -236,11 +236,11 @@ The root node is in the middle. With some imagination, you should see that this
 
 ![The tree](Images/Tree2.png)
 
-By the way, you may be wondering what happens when you insert duplicate items? We always insert those in the right branch. Try it out!
+You may be wondering what happens when you insert duplicate items? We always insert those in the right branch. Try it out!
 
 ### Searching
 
-What do we do now that we have some values in our tree? Search for them, of course! Being able to find items quickly is the entire purpose of a binary search tree. :-)
+What do we do now that we have some values in our tree? Search for them, of course! To find items quickly is the main purpose of a binary search tree. :-)
 
 Here is the implementation of `search()`:
 
@@ -258,11 +258,11 @@ Here is the implementation of `search()`:
 
 I hope the logic is clear: this starts at the current node (usually the root) and compares the values. If the search value is less than the node's value, we continue searching in the left branch; if the search value is greater, we dive into the right branch.
 
-Of course, if there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree.
+If there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree.
 
-> **Note:** In Swift that's very conveniently done with optional chaining; when you write `left?.search(value)` it automatically returns nil if `left` is nil. There's no need to explicitly check for this with an `if` statement.
+> **Note:** In Swift, that is conveniently done with optional chaining; when you write `left?.search(value)` it automatically returns nil if `left` is nil. There is no need to explicitly check for this with an `if` statement.
 
-Searching is a recursive process but you can also implement it with a simple loop instead:
+Searching is a recursive process, but you can also implement it with a simple loop instead:
 
 ```swift
   public func search(value: T) -> BinarySearchTree? {
@@ -280,9 +280,9 @@ Searching is a recursive process but you can also implement it with a simple loo
   }
 ```
 
-Verify for yourself that you understand that these two implementations are equivalent. Personally, I prefer to use iterative code over recursive code but your opinion may differ. ;-)
+Verify that you understand these two implementations are equivalent. Personally, I prefer to use iterative code over recursive code, but your opinion may differ. ;-)
 
-Here's how to test searching:
+Here is how to test searching:
 
 ```swift
 tree.search(5)
@@ -291,9 +291,9 @@ tree.search(7)
 tree.search(6)   // nil
 ```
 
-The first three lines all return the corresponding `BinaryTreeNode` object. The last line returns `nil` because there is no node with value `6`.
+The first three lines return the corresponding `BinaryTreeNode` object. The last line returns `nil` because there is no node with value `6`.
 
-> **Note:** If there are duplicate items in the tree, `search()` always returns the "highest" node. That makes sense, because we start searching from the root downwards.
+> **Note:** If there are duplicate items in the tree, `search()` returns the "highest" node. That makes sense, because we start searching from the root downwards.
 
 ### Traversal
 
@@ -319,9 +319,9 @@ Remember there are 3 different ways to look at all nodes in the tree? Here they
   }
 ```
 
-They all do pretty much the same thing but in different orders. Notice once again that all the work is done recursively. Thanks to Swift's optional chaining, the calls to `traverseInOrder()` etc are ignored when there is no left or right child.
+They all work the same but in different orders. Notice that all the work is done recursively. The Swift's optional chaining makes it clear that the calls to `traverseInOrder()` etc are ignored when there is no left or right child.
 
-To print out all the values from the tree sorted from low to high you can write:
+To print out all the values of the tree sorted from low to high you can write:
 
 ```swift
 tree.traverseInOrder { value in print(value) }
@@ -336,7 +336,7 @@ This prints the following:
 	9
 	10
 
-You can also add things like `map()` and `filter()` to the tree. For example, here's an implementation of map:
+You can also add things like `map()` and `filter()` to the tree. For example, here is an implementation of map:
 
 ```swift
 
@@ -365,11 +365,11 @@ This turns the contents of the tree back into a sorted array. Try it out in the
 tree.toArray()   // [1, 2, 5, 7, 9, 10]
 ```
 
-As an exercise for yourself, see if you can implement filter and reduce.
+As an exercise, see if you can implement filter and reduce.
 
 ### Deleting nodes
 
-We can make the code much more readable by defining some helper functions.
+We can make the code more readable by defining some helper functions.
 
 ```swift
   private func reconnectParentToNode(node: BinarySearchTree?) {
@@ -384,7 +384,7 @@ We can make the code much more readable by defining some helper functions.
   }
 ```
 
-Making changes to the tree involves changing a bunch of `parent` and `left` and `right` pointers. This function helps with that. It takes the parent of the current node -- that is `self` -- and connects it to another node. Usually that other node will be one of the children of `self`.
+Making changes to the tree involves changing a bunch of `parent` and `left` and `right` pointers. This function helps with this implementation. It takes the parent of the current node -- that is `self` -- and connects it to another node which will be one of the children of `self`.
 
 We also need a function that returns the minimum and maximum of a node:
 
@@ -407,7 +407,7 @@ We also need a function that returns the minimum and maximum of a node:
 
 ```
 
-The rest of the code is pretty self-explanatory:
+The rest of the code is self-explanatory:
 
 ```swift
   @discardableResult public func remove() -> BinarySearchTree? {
@@ -457,7 +457,7 @@ Recall that the height of a node is the distance to its lowest leaf. We can calc
 
 We look at the heights of the left and right branches and take the highest one. Again, this is a recursive procedure. Since this looks at all children of this node, performance is **O(n)**.
 
-> **Note:** Swift's null-coalescing operator is used as shorthand to deal with `left` or `right` pointers that are nil. You could write this with `if let` but this is a lot more concise.
+> **Note:** Swift's null-coalescing operator is used as shorthand to deal with `left` or `right` pointers that are nil. You could write this with `if let`, but this is more concise.
 
 Try it out:
 
@@ -479,7 +479,7 @@ You can also calculate the *depth* of a node, which is the distance to the root.
   }
 ```
 
-It steps upwards through the tree, following the `parent` pointers until we reach the root node (whose `parent` is nil). This takes **O(h)** time. Example:
+It steps upwards through the tree, following the `parent` pointers until we reach the root node (whose `parent` is nil). This takes **O(h)** time. Here is an example:
 
 ```swift
 if let node9 = tree.search(9) {
@@ -489,11 +489,11 @@ if let node9 = tree.search(9) {
 
 ### Predecessor and successor
 
-The binary search tree is always "sorted" but that doesn't mean that consecutive numbers are actually next to each other in the tree.
+The binary search tree is always "sorted" but that does not mean that consecutive numbers are actually next to each other in the tree.
 
 ![Example](Images/Tree2.png)
 
-Note that you can't find the number that comes before `7` by just looking at its left child node. The left child is `2`, not `5`. Likewise for the number that comes after `7`.
+Note that you cannot find the number that comes before `7` by just looking at its left child node. The left child is `2`, not `5`. Likewise for the number that comes after `7`.
 
 The `predecessor()` function returns the node whose value precedes the current value in sorted order:
 
@@ -512,11 +512,11 @@ The `predecessor()` function returns the node whose value precedes the current v
   }
 ```
 
-It's easy if we have a left subtree. In that case, the immediate predecessor is the maximum value in that subtree. You can verify in the above picture that `5` is indeed the maximum value in `7`'s left branch.
+It is easy if we have a left subtree. In that case, the immediate predecessor is the maximum value in that subtree. You can verify in the above picture that `5` is indeed the maximum value in `7`'s left branch.
 
-However, if there is no left subtree then we have to look at our parent nodes until we find a smaller value. So if we want to know what the predecessor is of node `9`, we keep going up until we find the first parent with a smaller value, which is `7`.
+If there is no left subtree, then we have to look at our parent nodes until we find a smaller value. If we want to know what the predecessor is of node `9`, we keep going up until we find the first parent with a smaller value, which is `7`.
 
-The code for `successor()` works the exact same way but mirrored:
+The code for `successor()` works the same way but mirrored:
 
 ```swift
   public func successor() -> BinarySearchTree<T>? {
@@ -535,11 +535,11 @@ The code for `successor()` works the exact same way but mirrored:
 
 Both these methods run in **O(h)** time.
 
-> **Note:** There is a cool variation called a ["threaded" binary tree](../Threaded%20Binary%20Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
+> **Note:** There is a variation called a ["threaded" binary tree](../Threaded%20Binary%20Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
 
 ### Is the search tree valid?
 
-If you were intent on sabotage you could turn the binary search tree into an invalid tree by calling `insert()` on a node that is not the root, like so:
+If you were intent on sabotage you could turn the binary search tree into an invalid tree by calling `insert()` on a node that is not the root. Here is an example:
 
 ```swift
 if let node1 = tree.search(1) {
@@ -547,7 +547,7 @@ if let node1 = tree.search(1) {
 }
 ```
 
-The value of the root node is `7`, so a node with value `100` is supposed to be in the tree's right branch. However, you're not inserting at the root but at a leaf node in the tree's left branch. So the new `100` node is in the wrong place in the tree!
+The value of the root node is `7`, so a node with value `100`must be in the tree's right branch. However, you are not inserting at the root but at a leaf node in the tree's left branch. So the new `100` node is in the wrong place in the tree!
 
 As a result, doing `tree.search(100)` gives nil.
 
@@ -562,7 +562,7 @@ You can check whether a tree is a valid binary search tree with the following me
   }
 ```
 
-This verifies that the left branch does indeed contain values that are less than the current node's value, and that the right branch only contains values that are larger.
+This verifies the left branch contains values that are less than the current node's value, and that the right branch only contains values that are larger.
 
 Call it as follows:
 
@@ -577,11 +577,11 @@ if let node1 = tree.search(1) {
 
 ## The code (solution 2)
 
-We've implemented the binary tree node as a class but you can also use an enum.
+We have implemented the binary tree node as a class, but you can also use an enum.
 
-The difference is reference semantics versus value semantics. Making a change to the class-based tree will update that same instance in memory. But the enum-based tree is immutable -- any insertions or deletions will give you an entirely new copy of the tree. Which one is best totally depends on what you want to use it for.
+The difference is reference semantics versus value semantics. Making a change to the class-based tree will update that same instance in memory, but the enum-based tree is immutable -- any insertions or deletions will give you an entirely new copy of the tree. Which one is best, totally depends on what you want to use it for.
 
-Here's how you'd make a binary search tree using an enum:
+Here is how you can make a binary search tree using an enum:
 
 ```swift
 public enum BinarySearchTree<T: Comparable> {
@@ -597,9 +597,9 @@ The enum has three cases:
 - `Leaf` for a leaf node that has no children.
 - `Node` for a node that has one or two children. This is marked `indirect` so that it can hold `BinarySearchTree` values. Without `indirect` you can't make recursive enums.
 
-> **Note:** The nodes in this binary tree don't have a reference to their parent node. It's not a major impediment but it will make certain operations slightly more cumbersome to implement.
+> **Note:** The nodes in this binary tree do not have a reference to their parent node. It is not a major impediment, but it will make certain operations more cumbersome to implement.
 
-As usual, we'll implement most functionality recursively. We'll treat each case of the enum slightly differently. For example, this is how you could calculate the number of nodes in the tree and the height of the tree:
+This implementation is recursive, and each case of the enum will be treated differently. For example, this is how you can calculate the number of nodes in the tree and the height of the tree:
 
 ```swift
   public var count: Int {
@@ -655,7 +655,7 @@ tree = tree.insert(9)
 tree = tree.insert(1)
 ```
 
-Notice that each time you insert something, you get back a completely new tree object. That's why you need to assign the result back to the `tree` variable.
+Notice that for each insertion, you get back a new tree object, so you need to assign the result back to the `tree` variable.
 
 Here is the all-important search function:
 
@@ -678,7 +678,7 @@ Here is the all-important search function:
   }
 ```
 
-As you can see, most of these functions have the same structure.
+Most of these functions have the same structure.
 
 Try it out in a playground:
 
@@ -688,7 +688,7 @@ tree.search(1)
 tree.search(11)   // nil
 ```
 
-To print the tree for debug purposes you can use this method:
+To print the tree for debug purposes, you can use this method:
 
 ```swift
 extension BinarySearchTree: CustomDebugStringConvertible {
@@ -703,21 +703,21 @@ extension BinarySearchTree: CustomDebugStringConvertible {
 }
 ```
 
-When you do `print(tree)` it will look something like this:
+When you do `print(tree)`, it will look like this:
 
 	((1 <- 2 -> 5) <- 7 -> (9 <- 10 -> .))
 
-The root node is in the middle; a dot means there is no child at that position.
+The root node is in the middle, and a dot means there is no child at that position.
 
 ## When the tree becomes unbalanced...
 
-A binary search tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That's the ideal situation.
+A binary search tree is *balanced* when its left and right subtrees contain the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That is the ideal situation.
 
-However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked%20List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
+If one branch is significantly longer than the other, searching becomes very slow. We end up checking more values than we need. In the worst case, the height of the tree can become *n*. Such a tree acts like a [linked list](../Linked%20List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
 
-One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree quite nicely. But it doesn't guarantee success, nor is it always practical.
+One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree well, but it not guaranteed, nor is it always practical.
 
-The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. See [AVL tree](../AVL%20Tree) and [red-black tree](../Red-Black%20Tree) for examples.
+The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. To see examples, check [AVL tree](../AVL%20Tree) and [red-black tree](../Red-Black%20Tree).
 
 ## See also
 

From 499bd86cd7ffab858dac481735b532f1789c0ab9 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 17:07:38 -0700
Subject: [PATCH 0901/1679] Revisions in README.markdown

I have revised your document to be more concise. Some words and phrases are removed or replaced due to redundancy.
---
 Queue/README.markdown | 52 +++++++++++++++++++++----------------------
 1 file changed, 26 insertions(+), 26 deletions(-)

diff --git a/Queue/README.markdown b/Queue/README.markdown
index 9efce66b9..8938e0cf1 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -2,11 +2,11 @@
 
 A queue is a list where you can only insert new items at the back and remove items from the front. This ensures that the first item you enqueue is also the first item you dequeue. First come, first serve!
 
-Why would you need this? Well, in many algorithms you want to add objects to a temporary list at some point and then pull them off this list again at a later time. Often the order in which you add and remove these objects matters.
+Why would you need this? Well, in many algorithms you want to add objects to a temporary list and pull them off this list later. Often the order in which you add and remove these objects matters.
 
-A queue gives you a FIFO or first-in, first-out order. The element you inserted first is also the first one to come out again. It's only fair! (A very similar data structure, the [stack](../Stack/), is LIFO or last-in first-out.)
+A queue gives you a FIFO or first-in, first-out order. The element you inserted first is the first one to come out. It is only fair! (A similar data structure, the [stack](../Stack/), is LIFO or last-in first-out.)
 
-For example, let's enqueue a number:
+Here is an example to enqueue a number:
 
 ```swift
 queue.enqueue(10)
@@ -38,11 +38,11 @@ queue.dequeue()
 
 This returns `3`, the next dequeue returns `57`, and so on. If the queue is empty, dequeuing returns `nil` or in some implementations it gives an error message.
 
-> **Note:** A queue is not always the best choice. If the order in which the items are added and removed from the list isn't important, you might as well use a [stack](../Stack/) instead of a queue. Stacks are simpler and faster.
+> **Note:** A queue is not always the best choice. If the order in which the items are added and removed from the list is not important, you can use a [stack](../Stack/) instead of a queue. Stacks are simpler and faster.
 
 ## The code
 
-Here is a very simplistic implementation of a queue in Swift. It's just a wrapper around an array that lets you enqueue, dequeue, and peek at the front-most item:
+Here is a simplistic implementation of a queue in Swift. It is a wrapper around an array to enqueue, dequeue, and peek at the front-most item:
 
 ```swift
 public struct Queue<T> {
@@ -74,11 +74,11 @@ public struct Queue<T> {
 }
 ```
 
-This queue works just fine but it is not optimal.
+This queue works well, but it is not optimal.
 
-Enqueuing is an **O(1)** operation because adding to the end of an array always takes the same amount of time, regardless of the size of the array. So that's great.
+Enqueuing is an **O(1)** operation because adding to the end of an array always takes the same amount of time regardless of the size of the array.
 
-You might be wondering why appending items to an array is **O(1)**, or a constant-time operation. That is so because an array in Swift always has some empty space at the end. If we do the following:
+You might be wondering why appending items to an array is **O(1)** or a constant-time operation. That is because an array in Swift always has some empty space at the end. If we do the following:
 
 ```swift
 var queue = Queue<String>()
@@ -95,13 +95,13 @@ where `xxx` is memory that is reserved but not filled in yet. Adding a new eleme
 
 	[ "Ada", "Steve", "Tim", "Grace", xxx, xxx ]
 
-This is simply matter of copying memory from one place to another, a constant-time operation.
+This results by copying memory from one place to another which is a constant-time operation.
 
-Of course, there are only a limited number of such unused spots at the end of the array. When the last `xxx` gets used and you want to add another item, the array needs to resize to make more room.
+There are only a limited number of unused spots at the end of the array. When the last `xxx` gets used, and you want to add another item, the array needs to resize to make more room.
 
-Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process, so it's relatively slow. But since it happens only every so often, the time for appending a new element to the end of the array is still **O(1)** on average, or **O(1)** "amortized".
+Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process which is relatively slow. Since it happens occasionally, the time for appending a new element to the end of the array is still **O(1)** on average or **O(1)** "amortized".
 
-The story for dequeueing is slightly different. To dequeue we remove the element from the *beginning* of the array, not the end. This is always an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
+The story for dequeueing is different. To dequeue, we remove the element from the *beginning* of the array. This is always an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
 
 In our example, dequeuing the first element `"Ada"` copies `"Steve"` in the place of `"Ada"`, `"Tim"` in the place of `"Steve"`, and `"Grace"` in the place of `"Tim"`:
 
@@ -112,13 +112,13 @@ In our example, dequeuing the first element `"Ada"` copies `"Steve"` in the plac
 	                /       /      /
 	 after   [ "Steve", "Tim", "Grace", xxx, xxx, xxx ]
  
-Moving all these elements in memory is always an **O(n)** operation. So with our simple implementation of a queue, enqueuing is efficient but dequeueing leaves something to be desired...
+Moving all these elements in memory is always an **O(n)** operation. So with our simple implementation of a queue, enqueuing is efficient, but dequeueing leaves something to be desired...
 
 ## A more efficient queue
 
-To make dequeuing more efficient, we can use the same trick of reserving some extra free space, but this time do it at the front of the array. We're going to have to write this code ourselves as the built-in Swift array doesn't support this out of the box.
+To make dequeuing efficient, we can also reserve some extra free space but this time at the front of the array. We must write this code ourselves because the built-in Swift array does not support it.
 
-The idea is as follows: whenever we dequeue an item, we don't shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
+The main idea is whenever we dequeue an item, we do not shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
 
 	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
 
@@ -126,13 +126,13 @@ After dequeuing `"Steve"`, the array is:
 
 	[ xxx, xxx, "Tim", "Grace", xxx, xxx ]
 
-These empty spots at the front never get reused for anything, so they're wasting space. Every so often you can trim the array by moving the remaining elements to the front again:
+Because these empty spots at the front never get reused, you can periodically trim the array by moving the remaining elements to the front:
 
 	[ "Tim", "Grace", xxx, xxx, xxx, xxx ]
 
-This trimming procedure involves shifting memory so it's an **O(n)** operation. But because it only happens once in a while, dequeuing is now **O(1)** on average.
+This trimming procedure involves shifting memory which is an **O(n)** operation. Because this only happens once in a while, dequeuing is **O(1)** on average.
 
-Here is how you could implement this version of `Queue`:
+Here is how you can implement this version of `Queue`:
 
 ```swift
 public struct Queue<T> {
@@ -176,9 +176,9 @@ public struct Queue<T> {
 }
 ```
 
-The array now stores objects of type `T?` instead of just `T` because we need some way to mark array elements as being empty. The `head` variable is the index in the array of the front-most object.
+The array now stores objects of type `T?` instead of just `T` because we need to mark array elements as being empty. The `head` variable is the index in the array of the front-most object.
 
-Most of the new functionality sits in `dequeue()`. When we dequeue an item, we first set `array[head]` to `nil` to remove the object from the array. Then we increment `head` because now the next item has become the front one.
+Most of the new functionality sits in `dequeue()`. When we dequeue an item, we first set `array[head]` to `nil` to remove the object from the array. Then, we increment `head` because the next item has become the front one.
 
 We go from this:
 
@@ -190,9 +190,9 @@ to this:
 	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
 	        head
 
-It's like some weird supermarket where the people in the checkout lane don't shuffle forward towards the cash register, but the cash register moves up the queue.
+It is like if in a supermarket the people in the checkout lane do not shuffle forward towards the cash register, but the cash register moves up the queue.
 
-Of course, if we never remove those empty spots at the front then the array will keep growing as we enqueue and dequeue elements. To periodically trim down the array, we do the following:
+If we never remove those empty spots at the front then the array will keep growing as we enqueue and dequeue elements. To periodically trim down the array, we do the following:
 
 ```swift
     let percentage = Double(head)/Double(array.count)
@@ -202,11 +202,11 @@ Of course, if we never remove those empty spots at the front then the array will
     }
 ```
 
-This calculates the percentage of empty spots at the beginning as a ratio of the total array size. If more than 25% of the array is unused, we chop off that wasted space. However, if the array is small we don't want to resize it all the time, so there must be at least 50 elements in the array before we try to trim it. 
+This calculates the percentage of empty spots at the beginning as a ratio of the total array size. If more than 25% of the array is unused, we chop off that wasted space. However, if the array is small we do not resize it all the time, so there must be at least 50 elements in the array before we try to trim it. 
 
 > **Note:** I just pulled these numbers out of thin air -- you may need to tweak them based on the behavior of your app in a production environment.
 
-To test this in a playground, do:
+To test this in a playground, do the following:
 
 ```swift
 var q = Queue<String>()
@@ -251,11 +251,11 @@ q.array             // [{Some "Grace"}]
 q.count             // 1
 ```
 
-The `nil` objects at the front have been removed and the array is no longer wasting space. This new version of `Queue` isn't much more complicated than the first one but dequeuing is now also an **O(1)** operation, just because we were a bit smarter about how we used the array.
+The `nil` objects at the front have been removed, and the array is no longer wasting space. This new version of `Queue` is not more complicated than the first one but dequeuing is now also an **O(1)** operation, just because we were aware about how we used the array.
 
 ## See also
 
-There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or a [heap](../Heap/). 
+There are many ways to create a queue. Alternative implementations use a [linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or a [heap](../Heap/). 
 
 Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority%20Queue/), a sorted queue where the "most important" item is always at the front.
 

From 0f4baf57b3485af6391de0bc06f626e8efc88c82 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 17:38:53 -0700
Subject: [PATCH 0902/1679] Revisions in README.markdown

I have revised your document to be more concise.
---
 Selection Sort/README.markdown | 34 +++++++++++++++++-----------------
 1 file changed, 17 insertions(+), 17 deletions(-)

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index cb8ed59c2..daebc64f4 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Selection Sort
 
-Goal: Sort an array from low to high (or high to low).
+Goal: To sort an array from low to high (or high to low).
 
 You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted.
 
@@ -10,20 +10,20 @@ This is similar to [insertion sort](../Insertion%20Sort/), but the difference is
 
 It works as follows:
 
-- Find the lowest number in the array. You start at index 0, loop through all the numbers in the array, and keep track of what the lowest number is.
-- Swap the lowest number you've found with the number at index 0. Now the sorted portion consists of just the number at index 0.
+- Find the lowest number in the array. You must start at index 0, loop through all the numbers in the array, and keep track of what the lowest number is.
+- Swap the lowest number with the number at index 0. Now, the sorted portion consists of just the number at index 0.
 - Go to index 1.
 - Find the lowest number in the rest of the array. This time you start looking from index 1. Again you loop until the end of the array and keep track of the lowest number you come across.
-- Swap it with the number at index 1. Now the sorted portion contains two numbers and extends from index 0 to index 1.
+- Swap  the lowest number with the number at index 1. Now, the sorted portion contains two numbers and extends from index 0 to index 1.
 - Go to index 2.
-- Find the lowest number in the rest of the array, starting from index 2, and swap it with the one at index 2. Now the array is sorted from index 0 to 2; this range contains the three lowest numbers in the array.
-- And so on... until no numbers remain to be sorted.
+- Find the lowest number in the rest of the array, starting from index 2, and swap it with the one at index 2. Now, the array is sorted from index 0 to 2; this range contains the three lowest numbers in the array.
+- And continue until no numbers remain to be sorted.
 
-It's called a "selection" sort, because at every step you search through the rest of the array to select the next lowest number.
+It nis called a "selection" sort because at every step you search through the rest of the array to select the next lowest number.
 
 ## An example
 
-Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol.
+Suppose the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol.
 
 Initially, the sorted portion is empty:
 
@@ -43,7 +43,7 @@ Again, we look for the lowest number, starting from the `|` bar. We find `4` and
 	[ 3, 4 | 5, 8, 6 ]
 	     *      *
 
-With every step, the `|` bar moves one position to the right. We again look through the rest of the array and find `5` as the lowest number. There's no need to swap `5` with itself and we simply move forward:
+With every step, the `|` bar moves one position to the right. We again look through the rest of the array and find `5` as the lowest number. There is no need to swap `5` with itself, and we simply move forward:
 
 	[ 3, 4, 5 | 8, 6 ]
 	        *
@@ -52,7 +52,7 @@ This process repeats until the array is sorted. Note that everything to the left
 
 	[ 3, 4, 5, 6, 8 |]
 
-As you can see, selection sort is an *in-place* sort because everything happens in the same array; no additional memory is necessary. You can also implement this as a *stable* sort so that identical elements do not get swapped around relative to each other (note that the version given below isn't stable).
+The selection sort is an *in-place* sort because everything happens in the same array without using additional memory. You can also implement this as a *stable* sort so that identical elements do not get swapped around relative to each other (note that the version given below is not stable).
 
 ## The code
 
@@ -90,9 +90,9 @@ selectionSort(list)
 
 A step-by-step explanation of how the code works:
 
-1. If the array is empty or only contains a single element, then there's not much point to sorting it.
+1. If the array is empty or only contains a single element, then there is no need to sort.
 
-2. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly in Swift. Like Swift's own `sort()`, the `selectionSort()` function will return a sorted *copy* of the original array.
+2. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly in Swift. Like the Swift's `sort()` function, the `selectionSort()` function will return a sorted *copy* of the original array.
 
 3. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what moves the `|` bar forward.
 
@@ -100,17 +100,17 @@ A step-by-step explanation of how the code works:
 
 5. Swap the lowest number with the current array index. The `if` check is necessary because you can't `swap()` an element with itself in Swift.
 
-In summary: For each element of the array, selection sort swaps positions with the lowest value from the rest of the array. As a result, the array gets sorted from the left to the right. (You can also do it right-to-left, in which case you always look for the largest number in the array. Give that a try!)
+In summary: For each element of the array, the selection sort swaps positions with the lowest value from the rest of the array. As a result, the array gets sorted from the left to the right. (You can also do it right-to-left, in which case you always look for the largest number in the array. Give that a try!)
 
-> **Note:** The outer loop ends at index `a.count - 2`. The very last element will automatically always be in the correct position because at that point there are no other smaller elements left.
+> **Note:** The outer loop ends at index `a.count - 2`. The very last element will automatically be in the correct position because at that point there are no other smaller elements left.
 
-The source file [SelectionSort.swift](SelectionSort.swift) has a version of this function that uses generics, so you can also use it to sort strings and other types.
+The source file [SelectionSort.swift](SelectionSort.swift) has a version of this function that uses generics, so you can also use it to sort strings and other data types.
 
 ## Performance
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+The selection sort is easy to understand but it performs slow as **O(n^2)**. It is worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). Finding the lowest element in the rest of the array is slow, especially since the inner loop will be performed repeatedly .
 
-[Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
+The [Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a fast method for finding the minimum value in the rest of the array. The heap sort' performance is **O(n log n)**.
 
 ## See also
 

From 8d84f6fdb9996e0a8b84360fd54eeb9892965e04 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Thu, 6 Apr 2017 22:25:17 -0400
Subject: [PATCH 0903/1679] Spelling error

---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 14ef931b9..80c2df7df 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -2,7 +2,7 @@
 
 A binary search tree is a special kind of [binary tree](../Binary%20Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
 
-For more iformation about a tree, [read this first](../Tree/).
+For more information about a tree, [read this first](../Tree/).
 
 ## "Always sorted" property
 

From 8080f271109d494eed485137392363bed2d462f4 Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <Jacopo.Mangiavacchi@uk.ibm.com>
Date: Fri, 7 Apr 2017 19:18:26 +0200
Subject: [PATCH 0904/1679] Fix and optimizations

---
 .../Sources/MinimumCoinChange.swift           | 89 +++++++++++--------
 .../MinimumCoinChangeTests.swift              | 20 +++--
 2 files changed, 66 insertions(+), 43 deletions(-)

diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index db7edecbe..c995063ab 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -1,5 +1,5 @@
 //
-//  Minimum Coin Change Problem 
+//  Minimum Coin Change Problem Playground
 //  Compare Greedy Algorithm and Dynamic Programming Algorithm in Swift
 //
 //  Created by Jacopo Mangiavacchi on 04/03/17.
@@ -7,70 +7,85 @@
 
 import Foundation
 
+public enum MinimumCoinChangeError: Error {
+    case noRestPossibleForTheGivenValue
+}
+
 public struct MinimumCoinChange {
-    private let sortedCoinSet: [Int]
-    private var cache: [Int : [Int]]
+    internal let sortedCoinSet: [Int]
     
     public init(coinSet: [Int]) {
         self.sortedCoinSet = coinSet.sorted(by: { $0 > $1} )
-        self.cache = [:]
     }
 
     //Greedy Algorithm
-    public func changeGreedy(_ value: Int) -> [Int] {
+    public func changeGreedy(_ value: Int) throws -> [Int] {
+        guard value > 0 else { return [] }
+
         var change:  [Int] = []
         var newValue = value
-        
+
         for coin in sortedCoinSet {
             while newValue - coin >= 0 {
                 change.append(coin)
                 newValue -= coin
             }
 
-            if newValue  == 0 {
+            if newValue == 0 {
                 break
             }
         }
         
+        if newValue > 0 { 
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
+        } 
+
         return change
     }
 
     //Dynamic Programming Algorithm
-    public mutating func changeDynamic(_ value: Int) -> [Int] {
-        if value <= 0 {
-            return []
-        }
+    public func changeDynamic(_ value: Int) throws -> [Int] {
+        guard value > 0 else { return [] }
         
-        if let cached = cache[value] {
-            return cached
-        }
-        
-        var change:  [Int] = []
-        
-        var potentialChangeArray: [[Int]] = []
-        
-        for coin in sortedCoinSet {
-            if value - coin >= 0 {
-                var potentialChange: [Int] = []
-                 potentialChange.append(coin)
-                let newPotentialValue = value - coin
+        var cache: [Int : [Int]] = [:]
 
-                if value  > 0 {
-                    potentialChange.append(contentsOf: changeDynamic(newPotentialValue))
-                }
+        func _changeDynamic(_ value: Int) -> [Int] {
+            guard value > 0 else { return [] }
 
-                //print("value: \(value) coin: \(coin) potentialChange: \(potentialChange)")
-                potentialChangeArray.append(potentialChange)
+            if let cached = cache[value] {
+                return cached
             }
+            
+            var change: [Int] = []
+            
+            var potentialChangeArray: [[Int]] = []
+            
+            for coin in sortedCoinSet {
+                if value - coin >= 0 {
+                    var potentialChange: [Int] = [coin]
+                    potentialChange.append(contentsOf: _changeDynamic(value - coin))
+                    potentialChangeArray.append(potentialChange)
+                }
+            }
+            
+            if potentialChangeArray.count > 0 {
+                let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
+                change = sortedPotentialChangeArray[0]
+            }
+            
+            if change.reduce(0, +) == value { 
+                cache[value] = change
+            } 
+
+            return change
         }
-        
-        if potentialChangeArray.count > 0 {
-            let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
-            change = sortedPotentialChangeArray[0]
-        }
-        
-        cache[value] = change
+
+        let change: [Int] = _changeDynamic(value)
+
+        if change.reduce(0, +) != value { 
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
+        } 
+
         return change
     }
 }
-
diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
index 86c9007ba..705113e92 100644
--- a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -3,16 +3,24 @@ import XCTest
 
 class MinimumCoinChangeTests: XCTestCase {
     func testExample() {
-        var mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+        let mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+        print("Coin set: \(mcc.sortedCoinSet)")
 
-        for i in 0..<100 {
-            let greedy = mcc.changeGreedy(i)
-            let dynamic = mcc.changeDynamic(i)
+        do {
+            for i in 0..<100 {
+                let greedy = try mcc.changeGreedy(i)
+                let dynamic = try mcc.changeDynamic(i)
 
-            if greedy.count != dynamic.count {
-                print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
+                XCTAssertEqual(greedy.reduce(0, +), dynamic.reduce(0, +), "Greedy and Dynamic return two different changes")
+
+                if greedy.count != dynamic.count {
+                    print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
+                }
             }
         }
+        catch {
+            XCTFail("Test Failed: impossible to change with the given coin set")
+        }
     }
 
     static var allTests = [

From 7abd8765deff7437e591730ea5c4cbf263ec9fc6 Mon Sep 17 00:00:00 2001
From: Ievgen Pavliuk <ievgen.pavliuk@virtual-solution.com>
Date: Sat, 8 Apr 2017 14:30:42 +0200
Subject: [PATCH 0905/1679] Fixed typo in AVL

---
 AVL Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index c8d8d4628..e7515d99f 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -48,7 +48,7 @@ Each tree node keeps track of its current balance factor in a variable. After in
 ![Rotation0](Images/RotationStep0.jpg)
 
 For the rotation we're using the terminology:
-* *Root* - the parent not of the subtrees that will be rotated;
+* *Root* - the parent node of the subtrees that will be rotated;
 * *Pivot* - the node that will become parent (basically will be on the *Root*'s position) after rotation;
 * *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
 * *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation

From 3e62df6cff7e3408647b8da016ca4230fb2a191c Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Mon, 10 Apr 2017 11:18:34 +0200
Subject: [PATCH 0906/1679] Silenced warnings in print statements

---
 .../RedBlackTree.playground/Sources/RedBlackTree.swift    | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 6f3b16b86..351f89a9d 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -638,11 +638,11 @@ extension RedBlackTree {
     if let leftChild = node.leftChild, let rightChild = node.rightChild {
       if node.color == .red {
         if !leftChild.isNullLeaf && leftChild.color == .red {
-          print("Property-Error: Red node with key \(node.key ?? nil) has red left child")
+            print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
           return false
         }
         if !rightChild.isNullLeaf && rightChild.color == .red {
-          print("Property-Error: Red node with key \(node.key ?? nil) has red right child")
+          print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
           return false
         }
       }
@@ -677,7 +677,7 @@ extension RedBlackTree {
       let addedHeight = node.color == .black ? 1 : 0
       return left + addedHeight
     } else {
-      print("Property-Error: Black height violated at node with key \(node.key ?? nil)")
+      print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
       return -1
     }
   }
@@ -697,7 +697,7 @@ extension RBTreeNode: CustomDebugStringConvertible {
         s = "key: nil"
       }
       if let parent = parent {
-        s += ", parent: \(parent.key)"
+        s += ", parent: \(String(describing: parent.key))"
       }
       if let left = leftChild {
         s += ", left = [" + left.debugDescription + "]"

From 51d36815aaf49d23cc0630ed36459141acbdab9e Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 15:38:52 -0400
Subject: [PATCH 0907/1679] Updated a comment about nested class declarations
 for Swift 3. Formatted the signature at the bottom

---
 Linked List/README.markdown | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 1884aeb23..c5a752e13 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -79,18 +79,18 @@ public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
   private var head: Node?
-  
+
   public var isEmpty: Bool {
     return head == nil
   }
-  
+
   public var first: Node? {
     return head
   }
 }
 ```
 
-Ideally, I'd like to put the `LinkedListNode` class inside `LinkedList` but Swift currently doesn't allow generic types to have nested types. Instead we're using a typealias so inside `LinkedList` we can write the shorter `Node` instead of `LinkedListNode<T>`.
+Ideally, we would want a class name to be as descriptive as possible, yet, we don't want to type a long name every time we want to use the class, therefore, we're using a typealias so inside `LinkedList` we can write the shorter `Node` instead of `LinkedListNode<T>`.
 
 This linked list only has a `head` pointer, not a tail. Adding a tail pointer is left as an exercise for the reader. (I'll point out which functions would be different if we also had a tail pointer.)
 
@@ -267,7 +267,7 @@ Let's write a method that lets you insert a new node at any index in the list. F
 ```swift
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-    
+
     var i = index
     var next = head
     var prev: Node?
@@ -283,13 +283,13 @@ Let's write a method that lets you insert a new node at any index in the list. F
   }
 ```
 
-This returns a tuple containing the node currently at the specified index and the node that immediately precedes it, if any. The loop is very similar to `nodeAtIndex()`, except that here we also keep track of what the previous node is as we iterate through the list. 
+This returns a tuple containing the node currently at the specified index and the node that immediately precedes it, if any. The loop is very similar to `nodeAtIndex()`, except that here we also keep track of what the previous node is as we iterate through the list.
 
 Let's look at an example. Suppose we have the following list:
 
 	head --> A --> B --> C --> D --> E --> nil
 
-We want to find the nodes before and after index 3. As we start the loop, `i = 3`, `next` points at `"A"`, and `prev` is nil. 
+We want to find the nodes before and after index 3. As we start the loop, `i = 3`, `next` points at `"A"`, and `prev` is nil.
 
 	head --> A --> B --> C --> D --> E --> nil
 	        next
@@ -320,7 +320,7 @@ Now that we have this helper function, we can write the method for inserting nod
 ```swift
   public func insert(value: T, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index)     // 1
-    
+
     let newNode = Node(value: value)    // 2
     newNode.previous = prev
     newNode.next = next
@@ -364,20 +364,20 @@ What else do we need? Removing nodes, of course! First we'll do `removeAll()`, w
 
 If you had a tail pointer, you'd set it to `nil` here too.
 
-Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first. 
+Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first.
 
 ```swift
   public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
-    
+
     if let prev = prev {
       prev.next = next
     } else {
       head = next
     }
     next?.previous = prev
-    
+
     node.previous = nil
     node.next = nil
     return node.value
@@ -412,7 +412,7 @@ If you don't have a reference to the node, you can use `removeLast()` or `remove
   }
 ```
 
-All these removal functions also return the value from the removed element. 
+All these removal functions also return the value from the removed element.
 
 ```swift
 list.removeLast()              // "World"
@@ -543,4 +543,4 @@ When performing operations on a linked list, you always need to be careful to up
 
 When processing lists, you can often use recursion: process the first element and then recursively call the function again on the rest of the list. You’re done when there is no next element. This is why linked lists are the foundation of functional programming languages such as LISP.
 
-*Written for Swift Algorithm Club by Matthijs Hollemans*
+*Originally written by Matthijs Hollemans for Ray Wenderlich's Swift Algorithm Club*

From a613ca599c03a98e588e32982d57097d5b388909 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 16:39:50 -0400
Subject: [PATCH 0908/1679] Updated the Playground file with more comments and
 added an overloadded implementations of 'insert' & 'append' to accept a whole
 list as an argument

---
 .../LinkedList.playground/Contents.swift      | 96 +++++++++++++++----
 .../contents.xcplayground                     |  2 +-
 2 files changed, 81 insertions(+), 17 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index abbb90467..93ed4246d 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -1,30 +1,41 @@
-//: Playground - noun: a place where people can play
+//: # Linked Lists
 
-public class LinkedListNode<T> {
-  var value: T
-  var next: LinkedListNode?
-  weak var previous: LinkedListNode?
-  
-  public init(value: T) {
-    self.value = value
-  }
-}
+// For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
+//: Linked List Class Declaration:
 public final class LinkedList<T> {
+  
+  // Linked List's Node Class Declaration
+  public class LinkedListNode<T> {
+    var value: T
+    var next: LinkedListNode?
+    weak var previous: LinkedListNode?
+    
+    public init(value: T) {
+      self.value = value
+    }
+  }
+  
+  // Typealiasing the node class to increase readability of code
   public typealias Node = LinkedListNode<T>
   
+  // The head of the Linked List
   fileprivate var head: Node?
   
+  // Default initializer
   public init() {}
   
+  // Computed property to check if the linked list is empty
   public var isEmpty: Bool {
     return head == nil
   }
   
+  // Computed property to get the first node in the linked list (if any)
   public var first: Node? {
     return head
   }
   
+  // Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
     if var node = head {
       while case let next? = node.next {
@@ -36,6 +47,7 @@ public final class LinkedList<T> {
     }
   }
   
+  // Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
     if var node = head {
       var c = 1
@@ -49,6 +61,7 @@ public final class LinkedList<T> {
     }
   }
   
+  // Function to return the node at a specific index
   public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -62,17 +75,20 @@ public final class LinkedList<T> {
     return nil
   }
   
+  // Subscript function to return the node at a specific index
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
   
+  // Append a value
   public func append(_ value: T) {
     let newNode = Node(value: value)
     self.append(newNode)
   }
   
+  // Append a node without taking ownership (appends a copy)
   public func append(_ node: Node) {
     let newNode = LinkedListNode(value: node.value)
     if let lastNode = last {
@@ -83,6 +99,16 @@ public final class LinkedList<T> {
     }
   }
   
+  // Append a whole linked list without taking ownership (appends a copy)
+  public func append(_ list: LinkedList) {
+    var nodeToCopy = list.head
+    while let node = nodeToCopy {
+      self.append(node.value)
+      nodeToCopy = node.next
+    }
+  }
+  
+  // Private helper function to return the nodes (in a tuple) before and after a specific index
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
     
@@ -100,11 +126,13 @@ public final class LinkedList<T> {
     return (prev, next)
   }
   
+  // Insert a value at a specific index
   public func insert(_ value: T, atIndex index: Int) {
     let newNode = Node(value: value)
     self.insert(newNode, atIndex: index)
   }
   
+  // Insert a node at a specific index without taking ownership (inserts a copy)
   public func insert(_ node: Node, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index: index)
     let newNode = LinkedListNode(value: node.value)
@@ -118,10 +146,33 @@ public final class LinkedList<T> {
     }
   }
   
+  // Insert a whole linked list at a specific index without taking ownership (inserts a copy)
+  public func insert(_ list: LinkedList, atIndex index: Int) {
+    if list.isEmpty { return }
+    var (prev, next) = nodesBeforeAndAfter(index: index)
+    var nodeToCopy = list.head
+    var newNode:Node?
+    while let node = nodeToCopy {
+      newNode = Node(value: node.value)
+      newNode?.previous = prev
+      if let previous = prev {
+        previous.next = newNode
+      } else {
+        self.head = newNode
+      }
+      nodeToCopy = nodeToCopy?.next
+      prev = newNode
+    }
+    prev?.next = next
+    next?.previous = prev
+  }
+  
+  // Function to remove all nodes from the list
   public func removeAll() {
     head = nil
   }
   
+  // Function to remove a specific node from the list and return its value
   @discardableResult public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
@@ -138,11 +189,13 @@ public final class LinkedList<T> {
     return node.value
   }
   
+  // Function to remove the last node in the list
   @discardableResult public func removeLast() -> T {
     assert(!isEmpty)
     return remove(node: last!)
   }
   
+  // Function to remove the node at a specific index from the list
   @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
@@ -150,6 +203,7 @@ public final class LinkedList<T> {
   }
 }
 
+//: End of the base class declarations & beginning of extensions' declarations:
 extension LinkedList: CustomStringConvertible {
   public var description: String {
     var s = "["
@@ -218,6 +272,8 @@ extension LinkedList: ExpressibleByArrayLiteral {
   }
 }
 
+
+//: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
 list.first                    // nil
@@ -247,10 +303,20 @@ list[0]     // "Hello"
 list[1]     // "World"
 //list[2]   // crash!
 
+let list2 = LinkedList<String>()
+list2.append("Goodbye")
+list2.append("World")
+list.append(list2)            // [Hello, World, Goodbye, World]
+list2.removeAll()             // [ ]
+list2.isEmpty                 // true
+list.removeLast()             // "World"
+list.remove(atIndex: 2)       // "Goodbye"
+
+
 list.insert("Swift", atIndex: 1)
-list[0]
-list[1]
-list[2]
+list[0]     // "Hello"
+list[1]     // "Swift"
+list[2]     // "World"
 print(list)
 
 list.reverse()   // [World, Swift, Hello]
@@ -262,9 +328,6 @@ m    // [8, 6, 5]
 let f = list.filter { s in s.characters.count > 5 }
 f    // [Universe, Swifty]
 
-//list.removeAll()
-//list.isEmpty
-
 list.remove(node: list.first!) // "Universe"
 list.count                     // 2
 list[0]                        // "Swifty"
@@ -286,3 +349,4 @@ let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
 listArrayLiteral2.count        // 3
 listArrayLiteral2[0]           // "Swift"
 listArrayLiteral2.removeLast()  // "Club"
+
diff --git a/Linked List/LinkedList.playground/contents.xcplayground b/Linked List/LinkedList.playground/contents.xcplayground
index 06828af92..3de2b51ba 100644
--- a/Linked List/LinkedList.playground/contents.xcplayground	
+++ b/Linked List/LinkedList.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' display-mode='rendered'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 45ef5cc2e0fb0f340744812a43b0fa329b20f867 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 16:57:12 -0400
Subject: [PATCH 0909/1679] Added 2 overloaded 'insert' & 'append' funcs that
 take a List as an argument to LinkedList.swift. Added 5 tests to
 LinkedListTests.swift to check the added 2 functions

---
 Linked List/LinkedList.swift            | 51 ++++++++++++++++-----
 Linked List/Tests/LinkedListTests.swift | 60 +++++++++++++++++++++++++
 2 files changed, 100 insertions(+), 11 deletions(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 55593cdc9..a7ef9bf5e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,14 +1,15 @@
-public class LinkedListNode<T> {
-    var value: T
-    var next: LinkedListNode?
-    weak var previous: LinkedListNode?
+public final class LinkedList<T> {
     
-    public init(value: T) {
-        self.value = value
+    public class LinkedListNode<T> {
+        var value: T
+        var next: LinkedListNode?
+        weak var previous: LinkedListNode?
+        
+        public init(value: T) {
+            self.value = value
+        }
     }
-}
-
-public final class LinkedList<T> {
+  
     public typealias Node = LinkedListNode<T>
     
     fileprivate var head: Node?
@@ -72,7 +73,7 @@ public final class LinkedList<T> {
     }
     
     public func append(_ node: Node) {
-        let newNode = Node(value: node.value)
+        let newNode = LinkedListNode(value: node.value)
         if let lastNode = last {
             newNode.previous = lastNode
             lastNode.next = newNode
@@ -81,6 +82,14 @@ public final class LinkedList<T> {
         }
     }
     
+    public func append(_ list: LinkedList) {
+        var nodeToCopy = list.head
+        while let node = nodeToCopy {
+            self.append(node.value)
+            nodeToCopy = node.next
+        }
+    }
+    
     private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
         assert(index >= 0)
         
@@ -105,7 +114,7 @@ public final class LinkedList<T> {
     
     public func insert(_ node: Node, atIndex index: Int) {
         let (prev, next) = nodesBeforeAndAfter(index: index)
-        let newNode = Node(value: node.value)
+        let newNode = LinkedListNode(value: node.value)
         newNode.previous = prev
         newNode.next = next
         prev?.next = newNode
@@ -116,6 +125,26 @@ public final class LinkedList<T> {
         }
     }
     
+    public func insert(_ list: LinkedList, atIndex index: Int) {
+        if list.isEmpty { return }
+        var (prev, next) = nodesBeforeAndAfter(index: index)
+        var nodeToCopy = list.head
+        var newNode:Node?
+        while let node = nodeToCopy {
+            newNode = Node(value: node.value)
+            newNode?.previous = prev
+            if let previous = prev {
+                previous.next = newNode
+            } else {
+                self.head = newNode
+            }
+            nodeToCopy = nodeToCopy?.next
+            prev = newNode
+        }
+        prev?.next = next
+        next?.previous = prev
+    }
+    
     public func removeAll() {
         head = nil
     }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 6f58d9775..ea063cacb 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -165,7 +165,67 @@ class LinkedListTest: XCTestCase {
     XCTAssertTrue(prev!.next === node)
     XCTAssertTrue(next!.previous === node)
   }
+  
+  func testInsertListAtIndex() {
+    let list = buildList()
+    let list2 = LinkedList<Int>()
+    list2.append(99)
+    list2.append(102)
+    list.insert(list2, atIndex: 2)
+    XCTAssertTrue(list.count == 8)
+    XCTAssertEqual(list.node(atIndex: 1)?.value, 2)
+    XCTAssertEqual(list.node(atIndex: 2)?.value, 99)
+    XCTAssertEqual(list.node(atIndex: 3)?.value, 102)
+    XCTAssertEqual(list.node(atIndex: 4)?.value, 10)
+  }
 
+  func testInsertListAtFirstIndex() {
+    let list = buildList()
+    let list2 = LinkedList<Int>()
+    list2.append(99)
+    list2.append(102)
+    list.insert(list2, atIndex: 0)
+    XCTAssertTrue(list.count == 8)
+    XCTAssertEqual(list.node(atIndex: 0)?.value, 99)
+    XCTAssertEqual(list.node(atIndex: 1)?.value, 102)
+    XCTAssertEqual(list.node(atIndex: 2)?.value, 8)
+  }
+  
+  func testInsertListAtLastIndex() {
+    let list = buildList()
+    let list2 = LinkedList<Int>()
+    list2.append(99)
+    list2.append(102)
+    list.insert(list2, atIndex: list.count)
+    XCTAssertTrue(list.count == 8)
+    XCTAssertEqual(list.node(atIndex: 5)?.value, 5)
+    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
+    XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
+  }
+  
+  func testAppendList() {
+    let list = buildList()
+    let list2 = LinkedList<Int>()
+    list2.append(99)
+    list2.append(102)
+    list.append(list2)
+    XCTAssertTrue(list.count == 8)
+    XCTAssertEqual(list.node(atIndex: 5)?.value, 5)
+    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
+    XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
+  }
+  
+  func testAppendListToEmptyList() {
+    let list = LinkedList<Int>()
+    let list2 = LinkedList<Int>()
+    list2.append(5)
+    list2.append(10)
+    list.append(list2)
+    XCTAssertTrue(list.count == 2)
+    XCTAssertEqual(list.node(atIndex: 0)?.value, 5)
+    XCTAssertEqual(list.node(atIndex: 1)?.value, 10)
+  }
+  
   func testRemoveAtIndexOnListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)

From c74bec1667b6be79b6a8dd56dd09b9c0076c1ef7 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 19:24:50 -0400
Subject: [PATCH 0910/1679] Updated the xcode version in .travis.yml

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index b6ff6190c..d413140fc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 language: objective-c
-osx_image: xcode8
+osx_image: xcode8.3
 # sudo: false
 
 install:

From 84009ae732937157fd3f071b78430895968d500b Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Tue, 11 Apr 2017 19:33:40 -0400
Subject: [PATCH 0911/1679] Added proper annotation to the Linked List
 playground files

---
 .../LinkedList.playground/Contents.swift      | 82 ++++++++++++++-----
 1 file changed, 61 insertions(+), 21 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 93ed4246d..b86fbf0b4 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -5,7 +5,7 @@
 //: Linked List Class Declaration:
 public final class LinkedList<T> {
   
-  // Linked List's Node Class Declaration
+  /// Linked List's Node Class Declaration
   public class LinkedListNode<T> {
     var value: T
     var next: LinkedListNode?
@@ -16,26 +16,26 @@ public final class LinkedList<T> {
     }
   }
   
-  // Typealiasing the node class to increase readability of code
+  /// Typealiasing the node class to increase readability of code
   public typealias Node = LinkedListNode<T>
   
-  // The head of the Linked List
+  /// The head of the Linked List
   fileprivate var head: Node?
   
-  // Default initializer
+  /// Default initializer
   public init() {}
   
-  // Computed property to check if the linked list is empty
+  /// Computed property to check if the linked list is empty
   public var isEmpty: Bool {
     return head == nil
   }
   
-  // Computed property to get the first node in the linked list (if any)
+  /// Computed property to get the first node in the linked list (if any)
   public var first: Node? {
     return head
   }
   
-  // Computed property to iterate through the linked list and return the last node in the list (if any)
+  /// Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
     if var node = head {
       while case let next? = node.next {
@@ -47,7 +47,7 @@ public final class LinkedList<T> {
     }
   }
   
-  // Computed property to iterate through the linked list and return the total number of nodes
+  /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
     if var node = head {
       var c = 1
@@ -61,7 +61,10 @@ public final class LinkedList<T> {
     }
   }
   
-  // Function to return the node at a specific index
+  /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
+  ///
+  /// - Parameter index: Integer value of the node's index to be returned
+  /// - Returns: Optional LinkedListNode
   public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -75,20 +78,26 @@ public final class LinkedList<T> {
     return nil
   }
   
-  // Subscript function to return the node at a specific index
+  /// Subscript function to return the node at a specific index
+  ///
+  /// - Parameter index: Integer value of the requested value's index
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
   
-  // Append a value
+  /// Append a value to the end of the list
+  ///
+  /// - Parameter value: The data value to be appended
   public func append(_ value: T) {
     let newNode = Node(value: value)
     self.append(newNode)
   }
   
-  // Append a node without taking ownership (appends a copy)
+  /// Append a copy of a LinkedListNode to the end of the list.
+  ///
+  /// - Parameter node: The node containing the value to be appended
   public func append(_ node: Node) {
     let newNode = LinkedListNode(value: node.value)
     if let lastNode = last {
@@ -99,7 +108,9 @@ public final class LinkedList<T> {
     }
   }
   
-  // Append a whole linked list without taking ownership (appends a copy)
+  /// Append a copy of a LinkedList to the end of the list.
+  ///
+  /// - Parameter list: The list to be copied and appended.
   public func append(_ list: LinkedList) {
     var nodeToCopy = list.head
     while let node = nodeToCopy {
@@ -108,7 +119,10 @@ public final class LinkedList<T> {
     }
   }
   
-  // Private helper function to return the nodes (in a tuple) before and after a specific index
+  /// A private helper funciton to find the nodes before and after a specified index. Crashes if index is out of bounds (0...self.count)
+  ///
+  /// - Parameter index: Integer value of the index between the nodes.
+  /// - Returns: A tuple of 2 nodes before & after the specified index respectively.
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
     
@@ -126,13 +140,21 @@ public final class LinkedList<T> {
     return (prev, next)
   }
   
-  // Insert a value at a specific index
+  /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
+  ///
+  /// - Parameters:
+  ///   - value: The data value to be inserted
+  ///   - index: Integer value of the index to be insterted at
   public func insert(_ value: T, atIndex index: Int) {
     let newNode = Node(value: value)
     self.insert(newNode, atIndex: index)
   }
   
-  // Insert a node at a specific index without taking ownership (inserts a copy)
+  /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
+  ///
+  /// - Parameters:
+  ///   - node: The node containing the value to be inserted
+  ///   - index: Integer value of the index to be inserted at
   public func insert(_ node: Node, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index: index)
     let newNode = LinkedListNode(value: node.value)
@@ -146,7 +168,11 @@ public final class LinkedList<T> {
     }
   }
   
-  // Insert a whole linked list at a specific index without taking ownership (inserts a copy)
+  /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
+  ///
+  /// - Parameters:
+  ///   - list: The LinkedList to be copied and inserted
+  ///   - index: Integer value of the index to be inserted at
   public func insert(_ list: LinkedList, atIndex index: Int) {
     if list.isEmpty { return }
     var (prev, next) = nodesBeforeAndAfter(index: index)
@@ -167,12 +193,15 @@ public final class LinkedList<T> {
     next?.previous = prev
   }
   
-  // Function to remove all nodes from the list
+  /// Function to remove all nodes/value from the list
   public func removeAll() {
     head = nil
   }
   
-  // Function to remove a specific node from the list and return its value
+  /// Function to remove a specific node.
+  ///
+  /// - Parameter node: The node to be deleted
+  /// - Returns: The data value contained in the deleted node.
   @discardableResult public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
@@ -189,13 +218,18 @@ public final class LinkedList<T> {
     return node.value
   }
   
-  // Function to remove the last node in the list
+  /// Function to remove the last node/value in the list. Crashes if the list is empty
+  ///
+  /// - Returns: The data value contained in the deleted node.
   @discardableResult public func removeLast() -> T {
     assert(!isEmpty)
     return remove(node: last!)
   }
   
-  // Function to remove the node at a specific index from the list
+  /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
+  ///
+  /// - Parameter index: Integer value of the index of the node to be removed
+  /// - Returns: The data value contained in the deleted node
   @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
@@ -204,6 +238,8 @@ public final class LinkedList<T> {
 }
 
 //: End of the base class declarations & beginning of extensions' declarations:
+
+// MARK: - Extension to enable the standard conversion of a list to String 
 extension LinkedList: CustomStringConvertible {
   public var description: String {
     var s = "["
@@ -217,6 +253,7 @@ extension LinkedList: CustomStringConvertible {
   }
 }
 
+// MARK: - Extension to add a 'reverse' function to the list
 extension LinkedList {
   public func reverse() {
     var node = head
@@ -228,6 +265,7 @@ extension LinkedList {
   }
 }
 
+// MARK: - An extension with an implementation of 'map' & 'filter' functions
 extension LinkedList {
   public func map<U>(transform: (T) -> U) -> LinkedList<U> {
     let result = LinkedList<U>()
@@ -252,6 +290,7 @@ extension LinkedList {
   }
 }
 
+// MARK: - Extension to enable initialization from an Array
 extension LinkedList {
   convenience init(array: Array<T>) {
     self.init()
@@ -262,6 +301,7 @@ extension LinkedList {
   }
 }
 
+// MARK: - Extension to enable initialization from an Array Literal
 extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
     self.init()

From 621a28da46cebf8bcd003ef6e80afb7e63b01136 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Thu, 13 Apr 2017 21:07:51 -0400
Subject: [PATCH 0912/1679] Update README.markdown

---
 Hash Table/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 958c3595a..bc9636195 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -103,7 +103,7 @@ it first hashes the key `"lastName"` to calculate the array index, which is 3. S
 
 Common ways to implement this chaining mechanism are to use a linked list or another array. Since the order of the items in the chain does not matter, you can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-Chains should not become long becasuse the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
+Chains should not become long because the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
 
 > **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. This approach has its own upsides and downsides.
 
@@ -127,7 +127,7 @@ public struct HashTable<Key: Hashable, Value> {
   }
 ```
 
-The `HashTable` is a generic container, and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for useing in a chain, and `Bucket` is an array of such `Elements`.
+The `HashTable` is a generic container, and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for using in a chain, and `Bucket` is an array of such `Elements`.
 
 The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We are also keeping track of how many items have been added to the hash table using the `count` variable.
 

From 55c11cadd38ee59e89a3128860b53f63e8b0457d Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Fri, 14 Apr 2017 21:37:24 +0200
Subject: [PATCH 0913/1679] Claim Naive Bayes Classifier

---
 Naive Bayes Classifier/README.md | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Naive Bayes Classifier/README.md

diff --git a/Naive Bayes Classifier/README.md b/Naive Bayes Classifier/README.md
new file mode 100644
index 000000000..e69de29bb

From 85f8085de5131657a9f8f5e7ab8f8d3e42f39edf Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Fri, 14 Apr 2017 21:38:44 +0200
Subject: [PATCH 0914/1679] Add initial version of NB

---
 Naive Bayes Classifier/NaiveBayes.swift | 141 ++++++++++++++++++++++++
 1 file changed, 141 insertions(+)
 create mode 100644 Naive Bayes Classifier/NaiveBayes.swift

diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
new file mode 100644
index 000000000..c988cacbe
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -0,0 +1,141 @@
+//
+//  main.swift
+//  NaiveBayes
+//
+//  Created by Philipp Gabriel on 14.04.17.
+//  Copyright © 2017 ph1ps. All rights reserved.
+//
+
+//TODO naming
+import Foundation
+
+extension Array where Element == Double {
+
+    func mean() -> Double {
+        return self.reduce(0, +) / Double(count)
+    }
+    
+    func standardDeviation() -> Double {
+        let calculatedMean = mean()
+        
+        let sum = self.reduce(0.0) { (previous, next) in
+            return previous + pow(next - calculatedMean, 2)
+        }
+        
+        return sqrt(sum / Double(count - 1))
+    }
+}
+
+extension Array where Element == Int {
+    
+    //Is this the best way?!
+    func uniques() -> [Int] {
+        return Array(Set(self))
+    }
+    
+}
+
+class NaiveBayes {
+
+    var data: [[Double]]
+    var classes: [Int]
+    var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
+    
+    init(data: [[Double]], classes: [Int]) {
+        self.data = data
+        self.classes = classes
+        self.variables = [Int: [(feature: Int, mean: Double, stDev: Double)]]()
+    }
+    
+    //TODO
+    //init(dataAndClasses: [[Double]], index ofClassRow: Int) {}
+
+    //TODO: Does it really need to be n^2 runtime?
+    func train() {
+
+        for `class` in 0..<classes.uniques().count {
+            variables[`class`] = [(feature: Int, mean: Double, stDev: Double)]()
+            
+            for feature in 0..<data[0].count {
+                
+                let values = data.map{ $0[feature] }.enumerated().filter { (offset, _) in
+                    return classes[offset] == `class`
+                }.map { $0.element }
+
+                variables[`class`]?.append((feature, values.mean(), values.standardDeviation()))
+            }
+        }
+
+        data.removeAll(keepingCapacity: false)
+    }
+    
+    func predictClass(input: [Double]) -> Int {
+        let likelihoods = predictLikelihood(input: input).max { (first, second) -> Bool in
+            return first.1 < second.1
+        }
+        
+        guard let `class` = likelihoods?.0 else {
+            return -1
+        }
+        
+        return `class`
+    }
+    
+    func predictLikelihood(input: [Double]) -> [(Int, Double)] {
+    
+        var probabilityOfClasses = [Int: Double]()
+        let amount = classes.uniques().count
+        
+        classes.forEach { `class` in
+            let individual = classes.filter { $0 == `class` }.count
+            probabilityOfClasses[`class`] = Double(amount) / Double(individual)
+        }
+        
+        let probaClass = variables.map { (key, value) -> (Int, [Double]) in
+            let probaFeature = value.map { (feature, mean, stDev) -> Double in
+                let featureValue = input[feature]
+                let eulerPart = pow(M_E, -1 * pow(featureValue - mean, 2) / (2 * pow(stDev, 2)))
+                let distribution = eulerPart / sqrt(2 * .pi) / stDev
+                return distribution
+            }
+            return (key, probaFeature)
+        }
+        
+        let likelihoods = probaClass.map { (key, probaFeature) in
+            return (key, probaFeature.reduce(1, *) * (probabilityOfClasses[key] ?? 1.0))
+        }
+
+        let sum = likelihoods.map { $0.1 }.reduce(0, +)
+        let normalized = likelihoods.map { (`class`, likelihood) in
+            return (`class`, likelihood / sum)
+        }
+        
+        return normalized
+    }
+}
+
+let data: [[Double]] = [
+    [6,180,12],
+    [5.92,190,11],
+    [5.58,170,12],
+    [5.92,165,10],
+    [5,100,6],
+    [5.5,150,8],
+    [5.42,130,7],
+    [5.75,150,9]
+]
+
+let classes = [0,0,0,0,1,1,1,1]
+
+let naive = NaiveBayes(data: data, classes: classes)
+naive.train()
+let result = naive.predictLikelihood(input: [6,130,8])
+print(result)
+
+
+
+
+
+
+
+

From be4ac46a126d4f1b744bb84216ab0ef68686e2e7 Mon Sep 17 00:00:00 2001
From: Philipp Gabriel <ph1ps@users.noreply.github.com>
Date: Fri, 14 Apr 2017 21:40:52 +0200
Subject: [PATCH 0915/1679] Add NB to README

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 29fc9d748..7df847960 100644
--- a/README.markdown
+++ b/README.markdown
@@ -116,6 +116,7 @@ Bad sorting algorithms (don't use these!):
 - Logistic Regression
 - Neural Networks
 - PageRank
+- [Naive Bayes Classifier](Naive%20Bayes%20Classifier/)
 
 ## Data structures
 

From f536ff10804f32066a5fdea1becfc6b80ebbf25f Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk@ARKALYKs-MacBook-Pro.local>
Date: Sat, 15 Apr 2017 02:06:55 +0600
Subject: [PATCH 0916/1679] Bugs fied. Readme added.

---
 .../EggDrop.playground/Contents.swift         |  5 +++
 .../EggDrop.playground/Sources/EggDrop.swift  | 41 +++++++++++++++++
 .../EggDrop.playground/contents.xcplayground  |  4 ++
 Egg Drop Problem/EggDrop.swift                | 36 +++++++++------
 Egg Drop Problem/README.markdown              | 44 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  6 +++
 6 files changed, 123 insertions(+), 13 deletions(-)
 create mode 100644 Egg Drop Problem/EggDrop.playground/Contents.swift
 create mode 100644 Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
 create mode 100644 Egg Drop Problem/EggDrop.playground/contents.xcplayground
 create mode 100644 Egg Drop Problem/README.markdown

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
new file mode 100644
index 000000000..4ddb936b3
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -0,0 +1,5 @@
+ //: Playground - noun: a place where people can play
+
+import Cocoa
+
+eggDrop(numberOfEggs: 2, numberOfFloors: 4)
diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
new file mode 100644
index 000000000..f69284491
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -0,0 +1,41 @@
+public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
+    if numberOfEggs == 0 || numberOfFloors == 0{
+        return 0
+    }
+    if numberOfEggs == 1 || numberOfFloors == 1{
+        return 1
+    }
+    
+    var eggFloor = [[Int]](repeating: [Int](repeating: 0, count: numberOfFloors+1), count: numberOfEggs+1) //egg(rows) floor(cols) array to store the solutions
+    var attempts: Int = 0
+    
+    for var floorNumber in (0..<(numberOfFloors+1)){
+        eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
+        for var eggNumber in (2..<(numberOfEggs+1)){
+            eggFloor[eggNumber][floorNumber] = 0
+        }
+    }
+    eggFloor[2][1] = 1 //base case: if there's are two eggs and one floor, it takes one attempt
+    
+    for var eggNumber in (2..<(numberOfEggs+1)){
+        for var floorNumber in (2..<(numberOfFloors+1)){
+            eggFloor[eggNumber][floorNumber] = 1000000
+            for var visitingFloor in (1..<(floorNumber+1)){
+                //there are two cases
+                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
+                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floorNumber-visitingFloor
+                attempts = 1 + max(eggFloor[eggNumber-1][visitingFloor-1], eggFloor[eggNumber][floorNumber-visitingFloor])//we add one taking into account the attempt we're taking at the moment
+                
+                if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
+                    eggFloor[eggNumber][floorNumber] = attempts;
+                }
+            }
+        }
+    }
+    
+    return eggFloor[numberOfEggs][numberOfFloors]
+}
+
+public func max(_ x1: Int, _ x2: Int) -> Int{
+    return x1 > x2 ? x1 : x2
+}
diff --git a/Egg Drop Problem/EggDrop.playground/contents.xcplayground b/Egg Drop Problem/EggDrop.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index 6d0aab2a1..a525793db 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -1,23 +1,33 @@
-func eggDrop(_ numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    var eggFloor: [[Int]] = [] //egg(rows) floor(cols) array to store the solutions
+public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
+    if numberOfEggs == 0 || numberOfFloors == 0{
+        return 0
+    }
+    if numberOfEggs == 1 || numberOfFloors == 1{
+        return 1
+    }
+    
+    var eggFloor = [[Int]](repeating: [Int](repeating: 0, count: numberOfFloors+1), count: numberOfEggs+1) //egg(rows) floor(cols) array to store the solutions
     var attempts: Int = 0
     
-    for var i in (0..<numberOfFloors){
-        eggFloor[1][i] = i
+    for var floorNumber in (0..<(numberOfFloors+1)){
+        eggFloor[1][floorNumber] = floorNumber
+        for var eggNumber in (2..<(numberOfEggs+1)){
+            eggFloor[eggNumber][floorNumber] = 0
+        }
     }
     eggFloor[2][1] = 1
     
-    for var i in (2..<=numberOfEggs){
-        for var j in (2..numberOfFloors){
-            eggFloor[i][j] = 1000000
-            for var k in (1..<=j){
+    for var eggNumber in (2..<(numberOfEggs+1)){
+        for var floorNumber in (2..<(numberOfFloors+1)){
+            eggFloor[eggNumber][floorNumber] = 1000000
+            for var floors in (1..<(floorNumber+1)){
                 //there are two cases
                 //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> k-1
-                //case 2: egg doesn't break. meaning we'll still have 'i' number of eggs, and we'll go upstairs -> j-k
-                attempts = 1 + max(eggFloor[i-1][k-1], eggFloor[i][j-k])//we add one taking into account the attempt we're taking at the moment
+                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floors-k
+                attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
                 
-                if attempts < eggFloor[i][j]{ //finding the min
-                    eggFloor[i][j] = attempts;
+                if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
+                    eggFloor[eggNumber][floorNumber] = attempts;
                 }
             }
         }
@@ -26,6 +36,6 @@ func eggDrop(_ numberOfEggs: Int, numberOfFloors: Int) -> Int {
     return eggFloor[numberOfEggs][numberOfFloors]
 }
 
-func max(_ x1: Int, _ x2: Int){
+public func max(_ x1: Int, _ x2: Int) -> Int{
     return x1 > x2 ? x1 : x2
 }
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
new file mode 100644
index 000000000..a58827ba3
--- /dev/null
+++ b/Egg Drop Problem/README.markdown	
@@ -0,0 +1,44 @@
+#Egg Drop Dynamic Problem
+
+#Problem Description 
+
+Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
+
+Suppose that we wish to know which stories in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing. We make a few assumptions:
+
+- An egg that survives a fall can be used again.
+- A broken egg must be discarded.
+- The effect of a fall is the same for all eggs.
+- If an egg breaks when dropped, then it would break if dropped from a higher floor.
+- If an egg survives a fall then it would survive a shorter fall.
+
+If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
+The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
+
+#Solution
+We store all the solutions in a 2D array. Where rows represents number of eggs and columns represent number of floors. 
+
+First, we set base cases:
+1) If there's only one egg, it takes as many attempts as number of floors
+2) If there's are two eggs and one floor, it takes one attempt
+
+eggNumber ==> Number of eggs at the moment
+floorNumber ==> Floor number at the moment
+visitingFloor ==> Floor being visited at the moment
+attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
+
+When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
+
+1) If the egg breaks after dropping from 'floorNumberth' floor, then we only need to check for floors lower than 'floorNumber' with remaining eggs; so the problem reduces to 'floorNumber'-1 floors and 'eggNumber'-1 eggs
+2) If the egg doesn’t break after dropping from the xth floor, then we only need to check for floors higher than 'floorNumber'; so the problem reduces to floors-'floorNumber' floors and 'eggNumber' eggs.
+
+Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
+
+```swift
+
+attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
+
+if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
+    eggFloor[eggNumber][floorNumber] = attempts;
+}
+```
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5ac8577f5..1c6b407c3 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -7,6 +7,12 @@
       <FileRef
          location = "group:/Users/arkalyk/Desktop/SwiftAlgorithmClub/swift-algorithm-club/Egg Drop Problem/EggDrop.swift">
       </FileRef>
+      <FileRef
+         location = "group:EggDrop.playground">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
    </Group>
    <FileRef
       location = "group:README.markdown">

From 75d3b5b59977a1cc54bcac2ce42e2c884eab5e69 Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 02:12:30 +0600
Subject: [PATCH 0917/1679] Bugs fixed

---
 Egg Drop Problem/README.markdown | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index a58827ba3..44af8174a 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -23,19 +23,21 @@ First, we set base cases:
 2) If there's are two eggs and one floor, it takes one attempt
 
 eggNumber ==> Number of eggs at the moment
+
 floorNumber ==> Floor number at the moment
+
 visitingFloor ==> Floor being visited at the moment
+
 attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
 
 When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
 
-1) If the egg breaks after dropping from 'floorNumberth' floor, then we only need to check for floors lower than 'floorNumber' with remaining eggs; so the problem reduces to 'floorNumber'-1 floors and 'eggNumber'-1 eggs
-2) If the egg doesn’t break after dropping from the xth floor, then we only need to check for floors higher than 'floorNumber'; so the problem reduces to floors-'floorNumber' floors and 'eggNumber' eggs.
+1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
+2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
 
 Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
 
 ```swift
-
 attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
 
 if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min

From 61949ab24314ee060f888642c59d6d20bcfa4841 Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:09:53 +0600
Subject: [PATCH 0918/1679] Minor changes in README

---
 .../EggDrop.playground/Sources/EggDrop.swift  |  9 +++------
 Egg Drop Problem/EggDrop.swift                | 16 ++++++++--------
 Egg Drop Problem/README.markdown              | 19 ++++++++++++-------
 3 files changed, 23 insertions(+), 21 deletions(-)

diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
index f69284491..897ba2dee 100644
--- a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -1,5 +1,5 @@
 public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    if numberOfEggs == 0 || numberOfFloors == 0{
+    if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
     if numberOfEggs == 1 || numberOfFloors == 1{
@@ -11,15 +11,12 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     
     for var floorNumber in (0..<(numberOfFloors+1)){
         eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
-        for var eggNumber in (2..<(numberOfEggs+1)){
-            eggFloor[eggNumber][floorNumber] = 0
-        }
     }
-    eggFloor[2][1] = 1 //base case: if there's are two eggs and one floor, it takes one attempt
+    eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
     
     for var eggNumber in (2..<(numberOfEggs+1)){
         for var floorNumber in (2..<(numberOfFloors+1)){
-            eggFloor[eggNumber][floorNumber] = 1000000
+            eggFloor[eggNumber][floorNumber] = Int.max   //setting the final result a high number to find out minimum
             for var visitingFloor in (1..<(floorNumber+1)){
                 //there are two cases
                 //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index a525793db..7be691f57 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -1,5 +1,5 @@
 public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    if numberOfEggs == 0 || numberOfFloors == 0{
+    if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
     if numberOfEggs == 1 || numberOfFloors == 1{
@@ -10,21 +10,21 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     var attempts: Int = 0
     
     for var floorNumber in (0..<(numberOfFloors+1)){
-        eggFloor[1][floorNumber] = floorNumber
+        eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
         for var eggNumber in (2..<(numberOfEggs+1)){
             eggFloor[eggNumber][floorNumber] = 0
         }
     }
-    eggFloor[2][1] = 1
+    eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
     
     for var eggNumber in (2..<(numberOfEggs+1)){
         for var floorNumber in (2..<(numberOfFloors+1)){
-            eggFloor[eggNumber][floorNumber] = 1000000
-            for var floors in (1..<(floorNumber+1)){
+            eggFloor[eggNumber][floorNumber] = Int.max   //setting the final result a high number to find out minimum
+            for var visitingFloor in (1..<(floorNumber+1)){
                 //there are two cases
-                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> k-1
-                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floors-k
-                attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
+                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
+                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floorNumber-visitingFloor
+                attempts = 1 + max(eggFloor[eggNumber-1][visitingFloor-1], eggFloor[eggNumber][floorNumber-visitingFloor])//we add one taking into account the attempt we're taking at the moment
                 
                 if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
                     eggFloor[eggNumber][floorNumber] = attempts;
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 44af8174a..2df3088b5 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -22,19 +22,24 @@ First, we set base cases:
 1) If there's only one egg, it takes as many attempts as number of floors
 2) If there's are two eggs and one floor, it takes one attempt
 
-eggNumber ==> Number of eggs at the moment
-
-floorNumber ==> Floor number at the moment
-
-visitingFloor ==> Floor being visited at the moment
-
-attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
+- eggNumber ==> Number of eggs at the moment
+- floorNumber ==> Floor number at the moment
+- visitingFloor ==> Floor being visited at the moment
+- attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
 
 When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
 
 1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
 2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
 
+```swift
+for var floorNumber in (0..<(numberOfFloors+1)){
+    eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
+}
+
+eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
+```
+
 Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
 
 ```swift

From 4ab987c592763cd13719411b829d8d513a64707b Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:14:18 +0600
Subject: [PATCH 0919/1679] Minor changes in README

---
 Egg Drop Problem/README.markdown | 25 +++++++++++++------------
 1 file changed, 13 insertions(+), 12 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 2df3088b5..eda28fa6f 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -16,32 +16,33 @@ If only one egg is available and we wish to be sure of obtaining the right resul
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
 #Solution
+- eggNumber -> Number of eggs at the moment
+- floorNumber -> Floor number at the moment
+- visitingFloor -> Floor being visited at the moment
+- attempts -> Minimum number of attempts it will take to find out from which floor egg will break
+
 We store all the solutions in a 2D array. Where rows represents number of eggs and columns represent number of floors. 
 
 First, we set base cases:
 1) If there's only one egg, it takes as many attempts as number of floors
 2) If there's are two eggs and one floor, it takes one attempt
 
-- eggNumber ==> Number of eggs at the moment
-- floorNumber ==> Floor number at the moment
-- visitingFloor ==> Floor being visited at the moment
-- attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
-
-When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
-
-1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
-2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
-
 ```swift
 for var floorNumber in (0..<(numberOfFloors+1)){
-    eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
+eggFloor[1][floorNumber] = floorNumber      //base case 1: if there's only one egg, it takes 'numberOfFloors' attempts
 }
 
-eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
+eggFloor[2][1] = 1 //base case 2: if there are two eggs and one floor, it takes one attempt
 ```
 
+When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
+
+1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
+2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
+
 Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
 
+We find the answer based on the base cases and previously found answers as follows. 
 ```swift
 attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
 

From 1fbb40efe14b80d6187a9ebd698960ba3520fe3b Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:35:40 +0600
Subject: [PATCH 0920/1679] Example added

---
 Egg Drop Problem/EggDrop.playground/Contents.swift |  6 +++++-
 Egg Drop Problem/EggDrop.swift                     |  3 ---
 Egg Drop Problem/README.markdown                   | 14 +++++++++++++-
 3 files changed, 18 insertions(+), 5 deletions(-)

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
index 4ddb936b3..d452e7f9f 100644
--- a/Egg Drop Problem/EggDrop.playground/Contents.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -2,4 +2,8 @@
 
 import Cocoa
 
-eggDrop(numberOfEggs: 2, numberOfFloors: 4)
+eggDrop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
+eggDrop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
+eggDrop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
+eggDrop(numberOfEggs: 5, numberOfFloors: 5) //expected answer: 2
+eggDrop(numberOfEggs: 5, numberOfFloors: 20) //expected answer: 4
\ No newline at end of file
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index 7be691f57..897ba2dee 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -11,9 +11,6 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     
     for var floorNumber in (0..<(numberOfFloors+1)){
         eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
-        for var eggNumber in (2..<(numberOfEggs+1)){
-            eggFloor[eggNumber][floorNumber] = 0
-        }
     }
     eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
     
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index eda28fa6f..1a436c374 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -25,7 +25,7 @@ We store all the solutions in a 2D array. Where rows represents number of eggs a
 
 First, we set base cases:
 1) If there's only one egg, it takes as many attempts as number of floors
-2) If there's are two eggs and one floor, it takes one attempt
+2) If there are two eggs and one floor, it takes one attempt
 
 ```swift
 for var floorNumber in (0..<(numberOfFloors+1)){
@@ -50,3 +50,15 @@ if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
     eggFloor[eggNumber][floorNumber] = attempts;
 }
 ```
+Example:
+Let's assume we have 2 eggs and 2 floors.
+1) We drop one egg from the first floor. If it breaks, then we get the answer. If it doesn't we'll have 2 eggs and 1 floors to work with.
+    attempts = 1 + maximum of 0(got the answer) and eggFloor[2][1] (base case 2 which gives us 1)
+    attempts = 1 + 1 = 2
+2) We drop one egg from the second floor. If it breaks, we'll have 1 egg and 1 floors to work with. If it doesn't, we'll get the answer.
+    attempts = 1 + maximum of eggFloor[1][1](base case 1 which gives us 1) and 0(got the answer)
+    attempts = 1 + 1 = 2
+3) Finding the minimum of 2 and 2 gives us 2, so the answer is 2. 
+   2 is the minimum number of attempts it will take to find out from which floor egg will break.
+
+

From 082385a5ac58967b8eaf565654f1620444383ebf Mon Sep 17 00:00:00 2001
From: Arkalyk Akash <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:37:09 +0600
Subject: [PATCH 0921/1679] Update README.markdown

---
 Egg Drop Problem/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 1a436c374..5ff6ebb1d 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -1,6 +1,6 @@
-#Egg Drop Dynamic Problem
+# Egg Drop Dynamic Problem
 
-#Problem Description 
+# Problem Description 
 
 Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
 
@@ -15,7 +15,7 @@ Suppose that we wish to know which stories in a 36-story building are safe to dr
 If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
-#Solution
+# Solution
 - eggNumber -> Number of eggs at the moment
 - floorNumber -> Floor number at the moment
 - visitingFloor -> Floor being visited at the moment

From ffea424eec7b80d010d731f6f1b44c442c26cab8 Mon Sep 17 00:00:00 2001
From: Arkalyk Akash <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:37:55 +0600
Subject: [PATCH 0922/1679] Update README.markdown

---
 Egg Drop Problem/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 5ff6ebb1d..82543502d 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -1,6 +1,6 @@
 # Egg Drop Dynamic Problem
 
-# Problem Description 
+## Problem Description 
 
 Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
 
@@ -15,7 +15,7 @@ Suppose that we wish to know which stories in a 36-story building are safe to dr
 If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
-# Solution
+## Solution
 - eggNumber -> Number of eggs at the moment
 - floorNumber -> Floor number at the moment
 - visitingFloor -> Floor being visited at the moment
@@ -50,7 +50,7 @@ if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
     eggFloor[eggNumber][floorNumber] = attempts;
 }
 ```
-Example:
+## Example
 Let's assume we have 2 eggs and 2 floors.
 1) We drop one egg from the first floor. If it breaks, then we get the answer. If it doesn't we'll have 2 eggs and 1 floors to work with.
     attempts = 1 + maximum of 0(got the answer) and eggFloor[2][1] (base case 2 which gives us 1)

From 260948a2b7af625ea0fe6590e3cf966975c420dd Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:41:32 +0600
Subject: [PATCH 0923/1679] Comments added

---
 Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift | 3 ++-
 Egg Drop Problem/EggDrop.swift                            | 3 ++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
index 897ba2dee..db1e48b95 100644
--- a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -2,7 +2,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
-    if numberOfEggs == 1 || numberOfFloors == 1{
+    if numberOfEggs == 1 || numberOfFloors == 1{ //edge case: When either number of eggs or number of floors is 1, answer is 1
         return 1
     }
     
@@ -33,6 +33,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     return eggFloor[numberOfEggs][numberOfFloors]
 }
 
+//Helper function to find max of two integers
 public func max(_ x1: Int, _ x2: Int) -> Int{
     return x1 > x2 ? x1 : x2
 }
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index 897ba2dee..db1e48b95 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -2,7 +2,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
-    if numberOfEggs == 1 || numberOfFloors == 1{
+    if numberOfEggs == 1 || numberOfFloors == 1{ //edge case: When either number of eggs or number of floors is 1, answer is 1
         return 1
     }
     
@@ -33,6 +33,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     return eggFloor[numberOfEggs][numberOfFloors]
 }
 
+//Helper function to find max of two integers
 public func max(_ x1: Int, _ x2: Int) -> Int{
     return x1 > x2 ? x1 : x2
 }

From 903ce26995d275e858dc535726df8a649260a4cd Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Sun, 16 Apr 2017 14:37:34 +0200
Subject: [PATCH 0924/1679] Add fully functional gaussian NB & examples

---
 Naive Bayes Classifier/NaiveBayes.swift | 122 ++++++++++++++----------
 1 file changed, 74 insertions(+), 48 deletions(-)

diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index c988cacbe..63edd9981 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -1,16 +1,15 @@
 //
-//  main.swift
+//  NaiveBayes.swift
 //  NaiveBayes
 //
 //  Created by Philipp Gabriel on 14.04.17.
 //  Copyright © 2017 ph1ps. All rights reserved.
 //
 
-//TODO naming
 import Foundation
 
 extension Array where Element == Double {
-
+    
     func mean() -> Double {
         return self.reduce(0, +) / Double(count)
     }
@@ -28,18 +27,17 @@ extension Array where Element == Double {
 
 extension Array where Element == Int {
     
-    //Is this the best way?!
-    func uniques() -> [Int] {
-        return Array(Set(self))
+    func uniques() -> Set<Element> {
+        return Set(self)
     }
     
 }
 
 class NaiveBayes {
-
-    var data: [[Double]]
-    var classes: [Int]
-    var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
+    
+    private var data: [[Double]]
+    private var classes: [Int]
+    private var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
     
     init(data: [[Double]], classes: [Int]) {
         self.data = data
@@ -47,30 +45,37 @@ class NaiveBayes {
         self.variables = [Int: [(feature: Int, mean: Double, stDev: Double)]]()
     }
     
-    //TODO
-    //init(dataAndClasses: [[Double]], index ofClassRow: Int) {}
-
-    //TODO: Does it really need to be n^2 runtime?
+    convenience init(dataAndClasses: [[Double]], rowOfClass: Int) {
+        let classes = dataAndClasses.map { Int($0[rowOfClass]) }
+        let data = dataAndClasses.map { row in
+            return row.enumerated().filter { $0.offset != rowOfClass }.map { $0.element }
+        }
+        
+        self.init(data: data, classes: classes)
+    }
+    
     func train() {
-
-        for `class` in 0..<classes.uniques().count {
+        
+        for `class` in classes.uniques() {
+            
             variables[`class`] = [(feature: Int, mean: Double, stDev: Double)]()
             
             for feature in 0..<data[0].count {
                 
-                let values = data.map{ $0[feature] }.enumerated().filter { (offset, _) in
+                let values = data.map { $0[feature] }.enumerated().filter { (offset, _) in
                     return classes[offset] == `class`
-                }.map { $0.element }
-
+                    }.map { $0.element }
+                
                 variables[`class`]?.append((feature, values.mean(), values.standardDeviation()))
             }
         }
-
+        
+        //This is just for the sake of clearing RAM
         data.removeAll(keepingCapacity: false)
     }
     
-    func predictClass(input: [Double]) -> Int {
-        let likelihoods = predictLikelihood(input: input).max { (first, second) -> Bool in
+    func classify(with input: [Double]) -> Int {
+        let likelihoods = calcLikelihoods(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
         
@@ -81,30 +86,30 @@ class NaiveBayes {
         return `class`
     }
     
-    func predictLikelihood(input: [Double]) -> [(Int, Double)] {
-    
-        var probabilityOfClasses = [Int: Double]()
-        let amount = classes.uniques().count
+    func calcLikelihoods(with input: [Double]) -> [(Int, Double)] {
+        
+        var probaClass = [Int: Double]()
+        let amount = classes.count
         
         classes.forEach { `class` in
             let individual = classes.filter { $0 == `class` }.count
-            probabilityOfClasses[`class`] = Double(amount) / Double(individual)
+            probaClass[`class`] = Double(individual) / Double(amount)
         }
         
-        let probaClass = variables.map { (key, value) -> (Int, [Double]) in
-            let probaFeature = value.map { (feature, mean, stDev) -> Double in
+        let classesAndFeatures = variables.map { (key, value) -> (Int, [Double]) in
+            let distributions = value.map { (feature, mean, stDev) -> Double in
                 let featureValue = input[feature]
                 let eulerPart = pow(M_E, -1 * pow(featureValue - mean, 2) / (2 * pow(stDev, 2)))
                 let distribution = eulerPart / sqrt(2 * .pi) / stDev
                 return distribution
             }
-            return (key, probaFeature)
+            return (key, distributions)
         }
         
-        let likelihoods = probaClass.map { (key, probaFeature) in
-            return (key, probaFeature.reduce(1, *) * (probabilityOfClasses[key] ?? 1.0))
+        let likelihoods = classesAndFeatures.map { (key, probaFeature) in
+            return (key, probaFeature.reduce(1, *) * (probaClass[key] ?? 1.0))
         }
-
+        
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
         let normalized = likelihoods.map { (`class`, likelihood) in
             return (`class`, likelihood / sum)
@@ -115,27 +120,48 @@ class NaiveBayes {
 }
 
 let data: [[Double]] = [
-    [6,180,12],
-    [5.92,190,11],
-    [5.58,170,12],
-    [5.92,165,10],
-    [5,100,6],
-    [5.5,150,8],
-    [5.42,130,7],
-    [5.75,150,9]
+    [6, 180, 12],
+    [5.92, 190, 11],
+    [5.58, 170, 12],
+    [5.92, 165, 10],
+    [5, 100, 6],
+    [5.5, 150, 8],
+    [5.42, 130, 7],
+    [5.75, 150, 9]
 ]
 
-let classes = [0,0,0,0,1,1,1,1]
+let classes = [0, 0, 0, 0, 1, 1, 1, 1]
 
 let naive = NaiveBayes(data: data, classes: classes)
 naive.train()
-let result = naive.predictLikelihood(input: [6,130,8])
-print(result)
-
-
-
-
+print(naive.classify(with: [6, 130, 8]))
+
+let otherData: [[Double]] = [
+    [6, 180, 12, 0],
+    [5.92, 190, 11, 0],
+    [5.58, 170, 12, 0],
+    [5.92, 165, 10, 0],
+    [5, 100, 6, 1],
+    [5.5, 150, 8, 1],
+    [5.42, 130, 7, 1],
+    [5.75, 150, 9, 1]
+]
 
+let otherNaive = NaiveBayes(dataAndClasses: otherData, rowOfClass: 3)
+otherNaive.train()
+print(otherNaive.calcLikelihoods(with: [6, 130, 8]))
 
+guard let csv = try? String(contentsOfFile: "/Users/ph1ps/Desktop/wine.csv") else {
+    print("file not found")
+    exit(0)
+}
 
+let rows = csv.characters.split(separator: "\r\n").map { String($0) }
+let wineData = rows.map { row -> [Double] in
+    let split = row.characters.split(separator: ";")
+    return split.map { Double(String($0))! }
+}
 
+let wineNaive = NaiveBayes(dataAndClasses: wineData, rowOfClass: 0)
+wineNaive.train()
+print(wineNaive.calcLikelihoods(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))

From b6d40144c5ac91bd3155036fbcefca231a6dba0d Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Sun, 16 Apr 2017 23:52:57 +0200
Subject: [PATCH 0925/1679] Split into seperate types of NB classifier,
 implement strategy pattern

---
 Naive Bayes Classifier/NaiveBayes.swift | 209 +++++++++++++++++-------
 1 file changed, 146 insertions(+), 63 deletions(-)

diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index 63edd9981..dbbf3cd9f 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -33,49 +33,143 @@ extension Array where Element == Int {
     
 }
 
+enum NBType {
+    
+    case gaussian(data: [[Double]], classes: [Int])
+    case multinomial(data: [[Int]], classes: [Int])
+    //case bernoulli(data: [[Bool]], classes: [Int]) --> TODO
+    
+    var classes: [Int] {
+        if case .gaussian(_, let classes) = self {
+            return classes
+        } else if case .multinomial(_, let classes) = self {
+            return classes
+        }
+        
+        return []
+    }
+    
+    var data: [[Any]] {
+        if case .gaussian(let data, _) = self {
+            return data
+        } else if case .multinomial(let data, _) = self {
+            return data
+        }
+        
+        return []
+    }
+    
+    func calcLikelihood(variables: [Any], input: Any) -> Double? {
+        
+        if case .gaussian = self {
+            
+            guard let input = input as? Double else {
+                return nil
+            }
+            
+            guard let mean = variables[0] as? Double else {
+                return nil
+            }
+            
+            guard let stDev = variables[1] as? Double else {
+                return nil
+            }
+            
+            let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
+            let distribution = eulerPart / sqrt(2 * .pi) / stDev
+            
+            return distribution
+            
+        } else if case .multinomial = self {
+            
+            guard let variables = variables as? [(category: Int, probability: Double)] else {
+                return nil
+            }
+            
+            guard let input = input as? Double else {
+                return nil
+            }
+            
+            return variables.first { variable in
+                return variable.category == Int(input)
+                }?.probability
+            
+        }
+        
+        return nil
+    }
+    
+    func train(values: [Any]) -> [Any]? {
+        
+        if case .gaussian = self {
+            
+            guard let values = values as? [Double] else {
+                return nil
+            }
+            
+            return [values.mean(), values.standardDeviation()]
+            
+        } else if case .multinomial = self {
+            
+            guard let values = values as? [Int] else {
+                return nil
+            }
+            
+            let count = values.count
+            let categoryProba = values.uniques().map { value -> (Int, Double) in
+                return (value, Double(values.filter { $0 == value }.count) / Double(count))
+            }
+            return categoryProba
+        }
+        
+        return nil
+    }
+}
+
 class NaiveBayes {
     
-    private var data: [[Double]]
-    private var classes: [Int]
-    private var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
+    private var variables: [Int: [(feature: Int, variables: [Any])]]
+    private var type: NBType
     
-    init(data: [[Double]], classes: [Int]) {
-        self.data = data
-        self.classes = classes
-        self.variables = [Int: [(feature: Int, mean: Double, stDev: Double)]]()
+    init(type: NBType) {
+        self.type = type
+        self.variables = [Int: [(Int, [Any])]]()
     }
     
-    convenience init(dataAndClasses: [[Double]], rowOfClass: Int) {
-        let classes = dataAndClasses.map { Int($0[rowOfClass]) }
+    static func convert<T: Any>(dataAndClasses: [[T]], rowOfClasses: Int) -> (data: [[T]], classes: [Int]) {
+        let classes = dataAndClasses.map { Int($0[rowOfClasses] as! Double) } //TODO
+        
         let data = dataAndClasses.map { row in
-            return row.enumerated().filter { $0.offset != rowOfClass }.map { $0.element }
+            return row.enumerated().filter { $0.offset != rowOfClasses }.map { $0.element }
         }
         
-        self.init(data: data, classes: classes)
+        return (data, classes)
     }
     
+    //TODO remake pliss, i dont like this at all
     func train() {
         
+        var classes = type.classes
+        
         for `class` in classes.uniques() {
             
-            variables[`class`] = [(feature: Int, mean: Double, stDev: Double)]()
+            variables[`class`] = [(Int, [Any])]()
             
-            for feature in 0..<data[0].count {
+            for feature in 0..<type.data[0].count {
                 
-                let values = data.map { $0[feature] }.enumerated().filter { (offset, _) in
+                let values = type.data.map { $0[feature] }.enumerated().filter { (offset, _) in
                     return classes[offset] == `class`
                     }.map { $0.element }
                 
-                variables[`class`]?.append((feature, values.mean(), values.standardDeviation()))
+                let trained = type.train(values: values) ?? [Any]()
+                
+                variables[`class`]?.append((feature, trained))
             }
         }
-        
-        //This is just for the sake of clearing RAM
-        data.removeAll(keepingCapacity: false)
     }
     
     func classify(with input: [Double]) -> Int {
-        let likelihoods = calcLikelihoods(with: input).max { (first, second) -> Bool in
+        let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
         
@@ -86,8 +180,10 @@ class NaiveBayes {
         return `class`
     }
     
-    func calcLikelihoods(with input: [Double]) -> [(Int, Double)] {
+    //TODO fix this doesnt have to be a double
+    func classifyProba(with input: [Double]) -> [(Int, Double)] {
         
+        let classes = type.classes
         var probaClass = [Int: Double]()
         let amount = classes.count
         
@@ -96,18 +192,15 @@ class NaiveBayes {
             probaClass[`class`] = Double(individual) / Double(amount)
         }
         
-        let classesAndFeatures = variables.map { (key, value) -> (Int, [Double]) in
-            let distributions = value.map { (feature, mean, stDev) -> Double in
-                let featureValue = input[feature]
-                let eulerPart = pow(M_E, -1 * pow(featureValue - mean, 2) / (2 * pow(stDev, 2)))
-                let distribution = eulerPart / sqrt(2 * .pi) / stDev
-                return distribution
+        let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
+            let distribution = value.map { (feature, variables) -> Double in
+                return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
             }
-            return (key, distributions)
+            return (`class`, distribution)
         }
         
-        let likelihoods = classesAndFeatures.map { (key, probaFeature) in
-            return (key, probaFeature.reduce(1, *) * (probaClass[key] ?? 1.0))
+        let likelihoods = classesAndFeatures.map { (`class`, distribution) in
+            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 1.0))
         }
         
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
@@ -119,38 +212,6 @@ class NaiveBayes {
     }
 }
 
-let data: [[Double]] = [
-    [6, 180, 12],
-    [5.92, 190, 11],
-    [5.58, 170, 12],
-    [5.92, 165, 10],
-    [5, 100, 6],
-    [5.5, 150, 8],
-    [5.42, 130, 7],
-    [5.75, 150, 9]
-]
-
-let classes = [0, 0, 0, 0, 1, 1, 1, 1]
-
-let naive = NaiveBayes(data: data, classes: classes)
-naive.train()
-print(naive.classify(with: [6, 130, 8]))
-
-let otherData: [[Double]] = [
-    [6, 180, 12, 0],
-    [5.92, 190, 11, 0],
-    [5.58, 170, 12, 0],
-    [5.92, 165, 10, 0],
-    [5, 100, 6, 1],
-    [5.5, 150, 8, 1],
-    [5.42, 130, 7, 1],
-    [5.75, 150, 9, 1]
-]
-
-let otherNaive = NaiveBayes(dataAndClasses: otherData, rowOfClass: 3)
-otherNaive.train()
-print(otherNaive.calcLikelihoods(with: [6, 130, 8]))
-
 guard let csv = try? String(contentsOfFile: "/Users/ph1ps/Desktop/wine.csv") else {
     print("file not found")
     exit(0)
@@ -162,6 +223,28 @@ let wineData = rows.map { row -> [Double] in
     return split.map { Double(String($0))! }
 }
 
-let wineNaive = NaiveBayes(dataAndClasses: wineData, rowOfClass: 0)
+let convertedWine = NaiveBayes.convert(dataAndClasses: wineData, rowOfClasses: 0)
+let wineNaive = NaiveBayes(type: .gaussian(data: convertedWine.data, classes: convertedWine.classes))
 wineNaive.train()
-print(wineNaive.calcLikelihoods(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))
+print(wineNaive.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))
+
+let golfData = [
+    [0, 0, 0, 0],
+    [0, 0, 0, 1],
+    [1, 0, 0, 0],
+    [2, 1, 0, 0],
+    [2, 2, 1, 0],
+    [2, 2, 1, 1],
+    [1, 2, 1, 1],
+    [0, 1, 0, 0],
+    [0, 2, 1, 0],
+    [2, 1, 1, 0],
+    [0, 1, 1, 1],
+    [1, 1, 0, 1],
+    [1, 0, 1, 0],
+    [2, 1, 0, 1]
+]
+let golfClasses =  [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]
+let golfNaive = NaiveBayes(type: .multinomial(data: golfData, classes: golfClasses))
+golfNaive.train()
+print(golfNaive.classifyProba(with: [0, 2, 0, 1]))

From 42db9a9d9a823a5bd0f2acf5f629881265ba7a83 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:12:10 +0300
Subject: [PATCH 0926/1679] Removed extra screenshots

---
 Dijkstra Algorithm/README.md                  |   4 ----
 .../Screenshots/screenshot1.jpg               | Bin 214771 -> 224243 bytes
 .../Screenshots/screenshot2.jpg               | Bin 225916 -> 0 bytes
 .../Screenshots/screenshot3.jpg               | Bin 224243 -> 0 bytes
 4 files changed, 4 deletions(-)
 delete mode 100644 Dijkstra Algorithm/Screenshots/screenshot2.jpg
 delete mode 100644 Dijkstra Algorithm/Screenshots/screenshot3.jpg

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 872e9f851..10166a63f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -17,7 +17,3 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Screenshots
 
 <img src="Screenshots/screenshot1.jpg" height="400" />
-
-<img src="Screenshots/screenshot2.jpg" height="400" />
-
-<img src="Screenshots/screenshot3.jpg" height="400" />
diff --git a/Dijkstra Algorithm/Screenshots/screenshot1.jpg b/Dijkstra Algorithm/Screenshots/screenshot1.jpg
index 390bc658224310c7720678cffd68bf1654b5c045..e9f7a1207f315e8f5aa20c72f3264c65edafd3a8 100644
GIT binary patch
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From a6020a54187ff8f473b1bccae3229846b7716258 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:13:19 +0300
Subject: [PATCH 0927/1679] Credits to the bottom

---
 Dijkstra Algorithm/README.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 10166a63f..bf158def9 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,6 +1,4 @@
 # Dijkstra-algorithm
-WWDC 2017 Scholarship Project
-Created by [Taras Nikulin](https://github.com/crabman448)
 
 ## About
 Dijkstra's algorithm is used for finding shortest paths from start vertex in graph(with weighted vertices) to all other vertices. 
@@ -17,3 +15,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Screenshots
 
 <img src="Screenshots/screenshot1.jpg" height="400" />
+
+## Credits
+WWDC 2017 Scholarship Project
+Created by [Taras Nikulin](https://github.com/crabman448)

From a76764eaa0907a8ec455f911af14a0ad27087a95 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:16:05 +0300
Subject: [PATCH 0928/1679] Moved Vertex and Dijkstra classes to sources

---
 .../Dijkstra.playground/Contents.swift        | 69 -------------------
 .../Sources/Dijkstra.swift                    | 40 +++++++++++
 .../Dijkstra.playground/Sources/Vertex.swift  | 29 ++++++++
 3 files changed, 69 insertions(+), 69 deletions(-)
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 13087a8f9..cd08e26fb 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,74 +1,5 @@
 //: Playground - noun: a place where people can play
-
 import Foundation
-import UIKit
-
-open class Vertex: Hashable, Equatable {
-
-    open var identifier: String!
-    open var neighbors: [(Vertex, Double)] = []
-    open var pathLengthFromStart: Double = Double.infinity
-    open var pathVerticesFromStart: [Vertex] = []
-
-    public init(identifier: String) {
-        self.identifier = identifier
-    }
-
-    open var hashValue: Int {
-        return self.identifier.hashValue
-    }
-
-    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
-        if lhs.hashValue == rhs.hashValue {
-            return true
-        }
-        return false
-    }
-
-    open func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
-    }
-}
-
-public class Dijkstra {
-    private var totalVertices: Set<Vertex>
-
-    public init(vertices: Set<Vertex>) {
-        self.totalVertices = vertices
-    }
-
-    private func clearCache() {
-        self.totalVertices.forEach { $0.clearCache() }
-    }
-
-    public func findShortestPaths(from startVertex: Vertex) {
-        self.clearCache()
-        startVertex.pathLengthFromStart = 0
-        startVertex.pathVerticesFromStart.append(startVertex)
-        var currentVertex: Vertex! = startVertex
-        while currentVertex != nil {
-            totalVertices.remove(currentVertex)
-            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
-            for neighbor in filteredNeighbors {
-                let neighborVertex = neighbor.0
-                let weight = neighbor.1
-
-                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
-                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
-                    neighborVertex.pathLengthFromStart = theoreticNewWeight
-                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
-                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
-                }
-            }
-            if totalVertices.isEmpty {
-                currentVertex = nil
-                break
-            }
-            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
-        }
-    }
-}
 
 var _vertices: Set<Vertex> = Set()
 
diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
new file mode 100644
index 000000000..0ae83589e
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -0,0 +1,40 @@
+import Foundation
+
+public class Dijkstra {
+    private var totalVertices: Set<Vertex>
+
+    public init(vertices: Set<Vertex>) {
+        self.totalVertices = vertices
+    }
+
+    private func clearCache() {
+        self.totalVertices.forEach { $0.clearCache() }
+    }
+
+    public func findShortestPaths(from startVertex: Vertex) {
+        self.clearCache()
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
+        var currentVertex: Vertex! = startVertex
+        while currentVertex != nil {
+            totalVertices.remove(currentVertex)
+            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
+            for neighbor in filteredNeighbors {
+                let neighborVertex = neighbor.0
+                let weight = neighbor.1
+
+                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+                }
+            }
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
new file mode 100644
index 000000000..035db2713
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -0,0 +1,29 @@
+import Foundation
+
+open class Vertex: Hashable, Equatable {
+
+    open var identifier: String!
+    open var neighbors: [(Vertex, Double)] = []
+    open var pathLengthFromStart: Double = Double.infinity
+    open var pathVerticesFromStart: [Vertex] = []
+
+    public init(identifier: String) {
+        self.identifier = identifier
+    }
+
+    open var hashValue: Int {
+        return self.identifier.hashValue
+    }
+
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        if lhs.hashValue == rhs.hashValue {
+            return true
+        }
+        return false
+    }
+
+    open func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+    }
+}

From 3bdb63de34cba4abcc581980c83da650bc8d3ba4 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:17:45 +0300
Subject: [PATCH 0929/1679] Hashable, Equatable to Extensions

---
 .../Dijkstra.playground/Sources/Vertex.swift     | 16 ++++++++++------
 1 file changed, 10 insertions(+), 6 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 035db2713..67ba3791e 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -1,6 +1,6 @@
 import Foundation
 
-open class Vertex: Hashable, Equatable {
+open class Vertex {
 
     open var identifier: String!
     open var neighbors: [(Vertex, Double)] = []
@@ -11,19 +11,23 @@ open class Vertex: Hashable, Equatable {
         self.identifier = identifier
     }
 
+    open func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+    }
+}
+
+extension Vertex: Hashable {
     open var hashValue: Int {
         return self.identifier.hashValue
     }
+}
 
+extension Vertex: Equatable {
     public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
         if lhs.hashValue == rhs.hashValue {
             return true
         }
         return false
     }
-
-    open func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
-    }
 }

From b2c5674b0c7d818cf061309e1cb7988e808d294b Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:18:44 +0300
Subject: [PATCH 0930/1679] Removed simplicity unwrapped for initialized
 variable

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 67ba3791e..22c04a0e1 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -2,7 +2,7 @@ import Foundation
 
 open class Vertex {
 
-    open var identifier: String!
+    open var identifier: String
     open var neighbors: [(Vertex, Double)] = []
     open var pathLengthFromStart: Double = Double.infinity
     open var pathVerticesFromStart: [Vertex] = []

From f0d057b89058c10cfe749990d5bdc3c669696610 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:19:34 +0300
Subject: [PATCH 0931/1679] Removed unnecessary explicit typing

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 22c04a0e1..dcdc64691 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -4,7 +4,7 @@ open class Vertex {
 
     open var identifier: String
     open var neighbors: [(Vertex, Double)] = []
-    open var pathLengthFromStart: Double = Double.infinity
+    open var pathLengthFromStart = Double.infinity
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {

From d0c68887780424e343f6663391eb5d70998fe166 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:20:05 +0300
Subject: [PATCH 0932/1679] Refactor Equatable extension

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index dcdc64691..89e66c68d 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -25,9 +25,6 @@ extension Vertex: Hashable {
 
 extension Vertex: Equatable {
     public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
-        if lhs.hashValue == rhs.hashValue {
-            return true
-        }
-        return false
+        return lhs.hashValue == rhs.hashValue
     }
 }

From 222e96d2f221c2f0549b5292be8b60adee93e1de Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:23:14 +0300
Subject: [PATCH 0933/1679] Made vertex optional

---
 .../Dijkstra.playground/Sources/Dijkstra.swift       | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index 0ae83589e..f0a9386b4 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -15,18 +15,18 @@ public class Dijkstra {
         self.clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
-        var currentVertex: Vertex! = startVertex
-        while currentVertex != nil {
-            totalVertices.remove(currentVertex)
-            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
+        var currentVertex: Vertex? = startVertex
+        while let vertex = currentVertex {
+            totalVertices.remove(vertex)
+            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
             for neighbor in filteredNeighbors {
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 
-                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
-                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }

From e2561032e31912df5dab472f7d63a3900d05ac70 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:26:57 +0300
Subject: [PATCH 0934/1679] Removed unnecessary self

---
 .../Dijkstra.playground/Sources/Dijkstra.swift              | 6 +++---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 6 +++---
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index f0a9386b4..f4cd8503a 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -4,15 +4,15 @@ public class Dijkstra {
     private var totalVertices: Set<Vertex>
 
     public init(vertices: Set<Vertex>) {
-        self.totalVertices = vertices
+        totalVertices = vertices
     }
 
     private func clearCache() {
-        self.totalVertices.forEach { $0.clearCache() }
+        totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-        self.clearCache()
+        clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
         var currentVertex: Vertex? = startVertex
diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 89e66c68d..a3587e04e 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -12,14 +12,14 @@ open class Vertex {
     }
 
     open func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
+        pathLengthFromStart = Double.infinity
+        pathVerticesFromStart = []
     }
 }
 
 extension Vertex: Hashable {
     open var hashValue: Int {
-        return self.identifier.hashValue
+        return identifier.hashValue
     }
 }
 

From 5060d788da63363809c93996aa9851751131e2d2 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:53:05 +0300
Subject: [PATCH 0935/1679] Removed self, unnecessary imports

---
 .../Sources/CustomUI/EdgeRepresentation.swift |  24 +-
 .../Sources/CustomUI/ErrorView.swift          |  23 +-
 .../Sources/CustomUI/MyShapeLayer.swift       |   1 -
 .../Sources/CustomUI/RoundedButton.swift      |   8 +-
 .../Sources/CustomUI/VertexView.swift         |  48 ++--
 .../Sources/Graph.swift                       |  84 +++---
 .../Sources/GraphView.swift                   |  62 ++--
 .../Sources/SimpleObjects/Vertex.swift        |  59 ++--
 .../Sources/Window.swift                      | 272 +++++++++---------
 9 files changed, 291 insertions(+), 290 deletions(-)

diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift
index 5ff656dab..d827d3924 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift	
@@ -1,6 +1,6 @@
 import UIKit
 
-public class EdgeRepresentation: Equatable {
+public class EdgeRepresentation {
     private var graphColors: GraphColors = GraphColors.sharedInstance
 
     public private(set)var label: UILabel!
@@ -67,7 +67,7 @@ public class EdgeRepresentation: Equatable {
 
         let label = UILabel(frame: CGRect(origin: circleOrigin, size: CGSize(width: arcDiameter, height: arcDiameter)))
         label.textAlignment = .center
-        label.backgroundColor = self.graphColors.defaultEdgeColor
+        label.backgroundColor = graphColors.defaultEdgeColor
         label.clipsToBounds = true
         label.adjustsFontSizeToFitWidth = true
         label.layer.cornerRadius = arcDiameter / 2
@@ -75,35 +75,35 @@ public class EdgeRepresentation: Equatable {
 
         let shapeLayer = MyShapeLayer()
         shapeLayer.path = path.cgPath
-        shapeLayer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
+        shapeLayer.strokeColor = graphColors.defaultEdgeColor.cgColor
         shapeLayer.fillColor = UIColor.clear.cgColor
         shapeLayer.lineWidth = 2.0
         shapeLayer.startPoint = startPoint
         shapeLayer.endPoint = endPoint
         shapeLayer.actions = ["position" : NSNull(), "bounds" : NSNull(), "path" : NSNull()]
+
         self.layer = shapeLayer
         self.label = label
         self.label.text = "\(weight)"
     }
 
     public func setCheckingColor() {
-        self.layer.strokeColor = self.graphColors.checkingColor.cgColor
-        self.label.backgroundColor = self.graphColors.checkingColor
+        layer.strokeColor = graphColors.checkingColor.cgColor
+        label.backgroundColor = graphColors.checkingColor
     }
 
     public func setDefaultColor() {
-        self.layer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
-        self.label.backgroundColor = self.graphColors.defaultEdgeColor
+        layer.strokeColor = graphColors.defaultEdgeColor.cgColor
+        label.backgroundColor = graphColors.defaultEdgeColor
     }
 
     public func setText(text: String) {
-        self.label.text = text
+        label.text = text
     }
+}
 
+extension EdgeRepresentation: Equatable {
     public static func ==(lhs: EdgeRepresentation, rhs: EdgeRepresentation) -> Bool {
-        if lhs.label.hashValue == rhs.label.hashValue && lhs.layer.hashValue == rhs.layer.hashValue {
-            return true
-        }
-        return false
+        return lhs.label.hashValue == rhs.label.hashValue && lhs.layer.hashValue == rhs.layer.hashValue
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift
index 69874e5d7..a63655dd9 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift	
@@ -2,9 +2,10 @@ import UIKit
 
 public class ErrorView: UIView {
     private var label: UILabel!
+
     public override init(frame: CGRect) {
         super.init(frame: frame)
-        self.commonInit()
+        commonInit()
     }
 
     public required init?(coder aDecoder: NSCoder) {
@@ -12,19 +13,19 @@ public class ErrorView: UIView {
     }
 
     private func commonInit() {
-        self.backgroundColor = UIColor(red: 242/255, green: 156/255, blue: 84/255, alpha: 1)
-        self.layer.cornerRadius = 10
+        backgroundColor = UIColor(red: 242/255, green: 156/255, blue: 84/255, alpha: 1)
+        layer.cornerRadius = 10
 
-        let labelFrame = CGRect(x: 10, y: 10, width: self.frame.width - 20, height: self.frame.height - 20)
-        self.label = UILabel(frame: labelFrame)
-        self.label.numberOfLines = 0
-        self.label.adjustsFontSizeToFitWidth = true
-        self.label.textAlignment = .center
-        self.label.textColor = UIColor.white
-        self.addSubview(self.label)
+        let labelFrame = CGRect(x: 10, y: 10, width: frame.width - 20, height: frame.height - 20)
+        label = UILabel(frame: labelFrame)
+        label.numberOfLines = 0
+        label.adjustsFontSizeToFitWidth = true
+        label.textAlignment = .center
+        label.textColor = UIColor.white
+        addSubview(label)
     }
 
     public func setText(text: String) {
-        self.label.text = text
+        label.text = text
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift
index 54147f5e1..33bf4a515 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift	
@@ -1,4 +1,3 @@
-import Foundation
 import UIKit
 
 public class MyShapeLayer: CAShapeLayer {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift
index 2647c4525..819fcfc5c 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift	
@@ -5,7 +5,7 @@ public class RoundedButton: UIButton {
     
     public override init(frame: CGRect) {
         super.init(frame: frame)
-        self.commonInit()
+        commonInit()
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -13,8 +13,8 @@ public class RoundedButton: UIButton {
     }
 
     private func commonInit() {
-        self.backgroundColor = self.graphColors.buttonsBackgroundColor
-        self.titleLabel?.adjustsFontSizeToFitWidth = true
-        self.layer.cornerRadius = 7
+        backgroundColor = graphColors.buttonsBackgroundColor
+        titleLabel?.adjustsFontSizeToFitWidth = true
+        layer.cornerRadius = 7
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift
index 29c971411..e785e120b 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift	
@@ -15,49 +15,49 @@ public class VertexView: UIButton {
         precondition(frame.height == frame.width)
         precondition(frame.height >= 30)
         super.init(frame: frame)
-        self.backgroundColor = self.graphColors.defaultVertexColor
-        self.layer.cornerRadius = frame.width / 2
-        self.clipsToBounds = true
-        self.setupIdLabel()
-        self.setupPathLengthFromStartLabel()
+        backgroundColor = graphColors.defaultVertexColor
+        layer.cornerRadius = frame.width / 2
+        clipsToBounds = true
+        setupIdLabel()
+        setupPathLengthFromStartLabel()
     }
 
     private func setupIdLabel() {
-        let x: CGFloat = self.frame.width * 0.2
+        let x: CGFloat = frame.width * 0.2
         let y: CGFloat = 0
-        let width: CGFloat = self.frame.width * 0.6
-        let height: CGFloat = self.frame.height / 2
+        let width: CGFloat = frame.width * 0.6
+        let height: CGFloat = frame.height / 2
         let idLabelFrame = CGRect(x: x, y: y, width: width, height: height)
 
-        self.idLabel = UILabel(frame: idLabelFrame)
-        self.idLabel.textAlignment = .center
-        self.idLabel.adjustsFontSizeToFitWidth = true
-        self.addSubview(self.idLabel)
+        idLabel = UILabel(frame: idLabelFrame)
+        idLabel.textAlignment = .center
+        idLabel.adjustsFontSizeToFitWidth = true
+        addSubview(idLabel)
     }
 
     private func setupPathLengthFromStartLabel() {
-        let x: CGFloat = self.frame.width * 0.2
-        let y: CGFloat = self.frame.height / 2
-        let width: CGFloat = self.frame.width * 0.6
-        let height: CGFloat = self.frame.height / 2
+        let x: CGFloat = frame.width * 0.2
+        let y: CGFloat = frame.height / 2
+        let width: CGFloat = frame.width * 0.6
+        let height: CGFloat = frame.height / 2
         let pathLengthLabelFrame = CGRect(x: x, y: y, width: width, height: height)
 
-        self.pathLengthLabel = UILabel(frame: pathLengthLabelFrame)
-        self.pathLengthLabel.textAlignment = .center
-        self.pathLengthLabel.adjustsFontSizeToFitWidth = true
-        self.addSubview(self.pathLengthLabel)
+        pathLengthLabel = UILabel(frame: pathLengthLabelFrame)
+        pathLengthLabel.textAlignment = .center
+        pathLengthLabel.adjustsFontSizeToFitWidth = true
+        addSubview(pathLengthLabel)
     }
 
     public func setIdLabel(text: String) {
-        self.idLabel.text = text
+        idLabel.text = text
     }
 
     public func setPathLengthLabel(text: String) {
-        self.pathLengthLabel.text = text
+        pathLengthLabel.text = text
     }
 
     public func setLabelsTextColor(color: UIColor) {
-        self.idLabel.textColor = color
-        self.pathLengthLabel.textColor = color
+        idLabel.textColor = color
+        pathLengthLabel.textColor = color
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
index 0b0b97b92..7c4a8e373 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -22,20 +22,20 @@ public class Graph {
     public var startVertex: Vertex!
     public var interactiveNeighborCheckAnimationDuration: Double = 1.8 {
         didSet {
-            self._interactiveOneSleepDuration = UInt32(self.interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+            _interactiveOneSleepDuration = UInt32(interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
         }
     }
     private var _interactiveOneSleepDuration: UInt32 = 600000
 
     public var visualizationNeighborCheckAnimationDuration: Double = 2.25 {
         didSet {
-            self._visualizationOneSleepDuration = UInt32(self.visualizationNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+            _visualizationOneSleepDuration = UInt32(visualizationNeighborCheckAnimationDuration * 1000000.0 / 3.0)
         }
     }
     private var _visualizationOneSleepDuration: UInt32 = 750000
 
     public var vertices: Set<Vertex> {
-        return self._vertices
+        return _vertices
     }
 
     public init(verticesCount: UInt) {
@@ -43,46 +43,46 @@ public class Graph {
     }
 
     public func removeGraph() {
-        self._vertices.removeAll()
-        self.startVertex = nil
+        _vertices.removeAll()
+        startVertex = nil
     }
 
     public func createNewGraph() {
-        guard self._vertices.isEmpty, self.startVertex == nil else {
+        guard _vertices.isEmpty, startVertex == nil else {
             assertionFailure("Clear graph before creating new one")
             return
         }
-        self.createNotConnectedVertices()
-        self.setupConnections()
-        let offset = Int(arc4random_uniform(UInt32(self._vertices.count)))
-        let index = self._vertices.index(self._vertices.startIndex, offsetBy: offset)
-        self.startVertex =  self._vertices[index]
-        self.setVertexLevels()
+        createNotConnectedVertices()
+        setupConnections()
+        let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
+        let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
+        startVertex =  _vertices[index]
+        setVertexLevels()
     }
     
     private func clearCache() {
-        self._vertices.forEach { $0.clearCache() }
+        _vertices.forEach { $0.clearCache() }
     }
 
     public func reset() {
-        for vertex in self._vertices {
+        for vertex in _vertices {
             vertex.clearCache()
         }
     }
 
     private func createNotConnectedVertices() {
-        for i in 0..<self.verticesCount {
+        for i in 0..<verticesCount {
             let vertex = Vertex(identifier: "\(i)")
-            self._vertices.insert(vertex)
+            _vertices.insert(vertex)
         }
     }
 
     private func setupConnections() {
-        for vertex in self._vertices {
+        for vertex in _vertices {
             let randomEdgesCount = arc4random_uniform(4) + 1
             for _ in 0..<randomEdgesCount {
                 let randomWeight = Double(arc4random_uniform(10))
-                let neighbor = self.randomVertex(except: vertex)
+                let neighbor = randomVertex(except: vertex)
                 let edge1 = Edge(vertex: neighbor, weight: randomWeight)
                 if vertex.edges.contains(where: { $0.neighbor == neighbor }) {
                     continue
@@ -95,7 +95,7 @@ public class Graph {
     }
 
     private func randomVertex(except vertex: Vertex) -> Vertex {
-        var newSet = self._vertices
+        var newSet = _vertices
         newSet.remove(vertex)
         let offset = Int(arc4random_uniform(UInt32(newSet.count)))
         let index = newSet.index(newSet.startIndex, offsetBy: offset)
@@ -103,8 +103,8 @@ public class Graph {
     }
 
     private func setVertexLevels() {
-        self._vertices.forEach { $0.clearLevelInfo() }
-        guard let startVertex = self.startVertex else {
+        _vertices.forEach { $0.clearLevelInfo() }
+        guard let startVertex = startVertex else {
             assertionFailure()
             return
         }
@@ -127,21 +127,21 @@ public class Graph {
     }
 
     public func findShortestPathsWithVisualization(completion: () -> Void) {
-        self.clearCache()
+        clearCache()
         startVertex.pathLengthFromStart = 0
-        startVertex.pathVerticesFromStart.append(self.startVertex)
-        var currentVertex: Vertex! = self.startVertex
+        startVertex.pathVerticesFromStart.append(startVertex)
+        var currentVertex: Vertex! = startVertex
 
-        var totalVertices = self._vertices
+        var totalVertices = _vertices
 
         breakableLoop: while currentVertex != nil {
             totalVertices.remove(currentVertex)
-            while self.pauseVisualization == true {
-                if self.stopVisualization == true {
+            while pauseVisualization == true {
+                if stopVisualization == true {
                     break breakableLoop
                 }
             }
-            if self.stopVisualization == true {
+            if stopVisualization == true {
                 break breakableLoop
             }
             DispatchQueue.main.async {
@@ -155,12 +155,12 @@ public class Graph {
                 let weight = edge.weight
                 let edgeRepresentation = edge.edgeRepresentation
 
-                while self.pauseVisualization == true {
-                    if self.stopVisualization == true {
+                while pauseVisualization == true {
+                    if stopVisualization == true {
                         break breakableLoop
                     }
                 }
-                if self.stopVisualization == true {
+                if stopVisualization == true {
                     break breakableLoop
                 }
                 DispatchQueue.main.async {
@@ -170,32 +170,32 @@ public class Graph {
                                                        edgePathLength: weight,
                                                        endVertexPathLength: neighbor.pathLengthFromStart)
                 }
-                usleep(self._visualizationOneSleepDuration)
+                usleep(_visualizationOneSleepDuration)
 
 
                 let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
 
                 if theoreticNewWeight < neighbor.pathLengthFromStart {
-                    while self.pauseVisualization == true {
-                        if self.stopVisualization == true {
+                    while pauseVisualization == true {
+                        if stopVisualization == true {
                             break breakableLoop
                         }
                     }
-                    if self.stopVisualization == true {
+                    if stopVisualization == true {
                         break breakableLoop
                     }
                     neighbor.pathLengthFromStart = theoreticNewWeight
                     neighbor.pathVerticesFromStart = currentVertex.pathVerticesFromStart
                     neighbor.pathVerticesFromStart.append(neighbor)
                 }
-                usleep(self._visualizationOneSleepDuration)
+                usleep(_visualizationOneSleepDuration)
 
                 DispatchQueue.main.async {
                     self.delegate?.didFinishCompare()
                     edge.edgeRepresentation?.setDefaultColor()
                     edge.neighbor.setDefaultColor()
                 }
-                usleep(self._visualizationOneSleepDuration)
+                usleep(_visualizationOneSleepDuration)
             }
             if totalVertices.isEmpty {
                 currentVertex = nil
@@ -203,7 +203,7 @@ public class Graph {
             }
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
-        if self.stopVisualization == true {
+        if stopVisualization == true {
             DispatchQueue.main.async {
                 self.delegate?.didStop()
             }
@@ -294,10 +294,10 @@ public class Graph {
     }
 
     public func didTapVertex(vertex: Vertex) {
-        if self.nextVertices.contains(vertex) {
-            self.delegate?.willStartVertexNeighborsChecking()
-            self.state = .parsing
-            self.parseNeighborsFor(vertex: vertex) {
+        if nextVertices.contains(vertex) {
+            delegate?.willStartVertexNeighborsChecking()
+            state = .parsing
+            parseNeighborsFor(vertex: vertex) {
                 self.state = .interactiveVisualization
                 self.delegate?.didFinishVertexNeighborsChecking()
             }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
index 49bc6853f..bdeab7669 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
@@ -7,7 +7,7 @@ public class GraphView: UIView {
 
     public override init(frame: CGRect) {
         super.init(frame: frame)
-        self.backgroundColor = self.graphColors.graphBackgroundColor
+        backgroundColor = graphColors.graphBackgroundColor
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -20,13 +20,13 @@ public class GraphView: UIView {
     }
 
     public func removeGraph() {
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             if let view = vertex.view {
                 view.removeFromSuperview()
                 vertex.view = nil
             }
         }
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             for edge in vertex.edges {
                 if let edgeRepresentation = edge.edgeRepresentation {
                     edgeRepresentation.layer.removeFromSuperlayer()
@@ -38,41 +38,41 @@ public class GraphView: UIView {
     }
 
     public func createNewGraph() {
-        self.setupVertexViews()
-        self.setupEdgeRepresentations()
-        self.addGraph()
+        setupVertexViews()
+        setupEdgeRepresentations()
+        addGraph()
     }
 
     public func reset() {
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             vertex.edges.forEach { $0.edgeRepresentation?.setDefaultColor() }
             vertex.setDefaultColor()
         }
     }
 
     private func addGraph() {
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             for edge in vertex.edges {
                 if let edgeRepresentation = edge.edgeRepresentation {
-                    self.layer.addSublayer(edgeRepresentation.layer)
-                    self.addSubview(edgeRepresentation.label)
+                    layer.addSublayer(edgeRepresentation.layer)
+                    addSubview(edgeRepresentation.label)
                 }
             }
         }
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             if let view = vertex.view {
-                self.addSubview(view)
+                addSubview(view)
             }
         }
     }
 
     private func setupVertexViews() {
         var level = 0
-        var buildViewQueue = [self.graph.startVertex!]
+        var buildViewQueue = [graph.startVertex!]
         let itemWidth: CGFloat = 40
         while !buildViewQueue.isEmpty {
             let levelItemsCount = CGFloat(buildViewQueue.count)
-            let xStep = (self.frame.width - levelItemsCount * itemWidth) / (levelItemsCount + 1)
+            let xStep = (frame.width - levelItemsCount * itemWidth) / (levelItemsCount + 1)
             var previousVertexMaxX: CGFloat = 0.0
             for vertex in buildViewQueue {
                 let x: CGFloat = previousVertexMaxX + xStep
@@ -84,12 +84,12 @@ public class GraphView: UIView {
                 vertexView.vertex = vertex
                 vertex.view?.setIdLabel(text: vertex.identifier)
                 vertex.view?.setPathLengthLabel(text: "\(vertex.pathLengthFromStart)")
-                vertex.view?.addTarget(self, action: #selector(self.didTapVertex(sender:)), for: .touchUpInside)
-                let panGesture = UIPanGestureRecognizer(target: self, action: #selector(self.handlePan(recognizer:)))
+                vertex.view?.addTarget(self, action: #selector(didTapVertex(sender:)), for: .touchUpInside)
+                let panGesture = UIPanGestureRecognizer(target: self, action: #selector(handlePan(recognizer:)))
                 vertex.view?.addGestureRecognizer(panGesture)
             }
             level += 1
-            buildViewQueue = self.graph.vertices.filter { $0.level == level }
+            buildViewQueue = graph.vertices.filter { $0.level == level }
         }
     }
 
@@ -100,8 +100,8 @@ public class GraphView: UIView {
         guard let vertexView = recognizer.view as? VertexView, let vertex = vertexView.vertex else {
             return
         }
-        if self.panningView != nil {
-            if self.panningView != vertexView {
+        if panningView != nil {
+            if panningView != vertexView {
                 return
             }
         }
@@ -122,39 +122,39 @@ public class GraphView: UIView {
                     }
                 }
             }
-            self.panningView = vertexView
+            panningView = vertexView
         case .changed:
-            if self.movingVertexOutputEdges.isEmpty && self.movingVertexInputEdges.isEmpty {
+            if movingVertexOutputEdges.isEmpty && movingVertexInputEdges.isEmpty {
                 return
             }
             let translation = recognizer.translation(in: self)
             if vertexView.frame.origin.x + translation.x <= 0
                 || vertexView.frame.origin.y + translation.y <= 0
-                || (vertexView.frame.origin.x + vertexView.frame.width + translation.x) >= self.frame.width
-                || (vertexView.frame.origin.y + vertexView.frame.height + translation.y) >= self.frame.height {
+                || (vertexView.frame.origin.x + vertexView.frame.width + translation.x) >= frame.width
+                || (vertexView.frame.origin.y + vertexView.frame.height + translation.y) >= frame.height {
                 break
             }
-            self.movingVertexInputEdges.forEach { edgeRepresentation in
+            movingVertexInputEdges.forEach { edgeRepresentation in
                 let originalLabelCenter = edgeRepresentation.label.center
                 edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.625,
                                                           y: originalLabelCenter.y + translation.y * 0.625)
 
                 CATransaction.begin()
                 CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
-                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: false)
+                let newPath = path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: false)
                 edgeRepresentation.layer.path = newPath
                 CATransaction.commit()
 
             }
 
-            self.movingVertexOutputEdges.forEach { edgeRepresentation in
+            movingVertexOutputEdges.forEach { edgeRepresentation in
                 let originalLabelCenter = edgeRepresentation.label.center
                 edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.375,
                                                           y: originalLabelCenter.y + translation.y * 0.375)
 
                 CATransaction.begin()
                 CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
-                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: true)
+                let newPath = path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: true)
                 edgeRepresentation.layer.path = newPath
                 CATransaction.commit()
             }
@@ -163,9 +163,9 @@ public class GraphView: UIView {
                                         y: vertexView.center.y + translation.y)
             recognizer.setTranslation(CGPoint.zero, in: self)
         case .ended:
-            self.movingVertexInputEdges = []
-            self.movingVertexOutputEdges = []
-            self.panningView = nil
+            movingVertexInputEdges = []
+            movingVertexOutputEdges = []
+            panningView = nil
         default:
             break
         }
@@ -223,7 +223,7 @@ public class GraphView: UIView {
     }
 
     private func setupEdgeRepresentations() {
-        var edgeQueue: [Vertex] = [self.graph.startVertex!]
+        var edgeQueue: [Vertex] = [graph.startVertex!]
 
         //BFS
         while !edgeQueue.isEmpty {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift
index c9270b0df..f18ec3114 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift	
@@ -1,10 +1,17 @@
 import UIKit
 
-public class Vertex: Hashable, Equatable {
+public class Vertex {
     private var graphColors: GraphColors = GraphColors.sharedInstance
 
+    public var view: VertexView?
+    
     public var identifier: String
     public var edges: [Edge] = []
+    public var pathVerticesFromStart: [Vertex] = []
+    public var level: Int = 0
+    public var levelChecked: Bool = false
+    public var haveAllEdges: Bool = false
+    public var visited: Bool = false
     public var pathLengthFromStart: Double = Double.infinity {
         didSet {
             DispatchQueue.main.async {
@@ -12,51 +19,45 @@ public class Vertex: Hashable, Equatable {
             }
         }
     }
-    public var pathVerticesFromStart: [Vertex] = []
-    public var level: Int = 0
-    public var levelChecked: Bool = false
-    public var haveAllEdges: Bool = false
-    public var visited: Bool = false
-
-    public var view: VertexView?
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-    public var hashValue: Int {
-        return self.identifier.hashValue
-    }
-
-    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
-        if lhs.hashValue == rhs.hashValue {
-            return true
-        }
-        return false
-    }
-
     public func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
-        self.visited = false
+        pathLengthFromStart = Double.infinity
+        pathVerticesFromStart = []
+        visited = false
     }
 
     public func clearLevelInfo() {
-        self.level = 0
-        self.levelChecked = false
+        level = 0
+        levelChecked = false
     }
 
     public func setVisitedColor() {
-        self.view?.backgroundColor = self.graphColors.visitedColor
-        self.view?.setLabelsTextColor(color: UIColor.white)
+        view?.backgroundColor = graphColors.visitedColor
+        view?.setLabelsTextColor(color: UIColor.white)
     }
 
     public func setCheckingPathColor() {
-        self.view?.backgroundColor = self.graphColors.checkingColor
+        view?.backgroundColor = graphColors.checkingColor
     }
 
     public func setDefaultColor() {
-        self.view?.backgroundColor = self.graphColors.defaultVertexColor
-        self.view?.setLabelsTextColor(color: UIColor.black)
+        view?.backgroundColor = graphColors.defaultVertexColor
+        view?.setLabelsTextColor(color: UIColor.black)
+    }
+}
+
+extension Vertex: Hashable {
+    public var hashValue: Int {
+        return identifier.hashValue
+    }
+}
+
+extension Vertex: Equatable {
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        return lhs.hashValue == rhs.hashValue
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
index e8aabad27..054b804c9 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -30,7 +30,7 @@ public class Window: UIView, GraphDelegate {
     public override init(frame: CGRect) {
         super.init(frame: frame)
         self.frame = frame
-        self.backgroundColor = self.graphColors.mainWindowBackgroundColor
+        backgroundColor = graphColors.mainWindowBackgroundColor
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -39,130 +39,130 @@ public class Window: UIView, GraphDelegate {
 
     public func configure(graph: Graph) {
         self.graph = graph
-        self.graph.createNewGraph()
-        self.graph.delegate = self
+        graph.createNewGraph()
+        graph.delegate = self
         let frame = CGRect(x: 10, y: 170, width: self.frame.width - 20, height: self.frame.height - 180)
-        self.graphView = GraphView(frame: frame)
-        self.graphView.layer.cornerRadius = 15
-
-        self.graphView.configure(graph: self.graph)
-        self.graphView.createNewGraph()
-        self.addSubview(self.graphView)
-
-        self.configureCreateGraphButton()
-        self.configureStartVisualizationButton()
-        self.configureStartInteractiveVisualizationButton()
-        self.configureStartButton()
-        self.configurePauseButton()
-        self.configureStopButton()
-        self.configureComparisonLabel()
-        self.configureActivityIndicator()
-
-        self.topView = UIView(frame: CGRect(x: 10, y: 10, width: self.frame.width - 20, height: 150))
-        self.topView.backgroundColor = self.graphColors.topViewBackgroundColor
-        self.topView.layer.cornerRadius = 15
-        self.addSubview(self.topView)
-
-        self.topView.addSubview(self.createGraphButton)
-        self.topView.addSubview(self.startVisualizationButton)
-        self.topView.addSubview(self.startInteractiveVisualizationButton)
-        self.topView.addSubview(self.startButton)
-        self.topView.addSubview(self.pauseButton)
-        self.topView.addSubview(self.stopButton)
-        self.topView.addSubview(self.comparisonLabel)
-        self.topView.addSubview(self.activityIndicator)
+        graphView = GraphView(frame: frame)
+        graphView.layer.cornerRadius = 15
+
+        graphView.configure(graph: graph)
+        graphView.createNewGraph()
+        addSubview(graphView)
+
+        configureCreateGraphButton()
+        configureStartVisualizationButton()
+        configureStartInteractiveVisualizationButton()
+        configureStartButton()
+        configurePauseButton()
+        configureStopButton()
+        configureComparisonLabel()
+        configureActivityIndicator()
+
+        topView = UIView(frame: CGRect(x: 10, y: 10, width: frame.width - 20, height: 150))
+        topView.backgroundColor = graphColors.topViewBackgroundColor
+        topView.layer.cornerRadius = 15
+        addSubview(topView)
+
+        topView.addSubview(createGraphButton)
+        topView.addSubview(startVisualizationButton)
+        topView.addSubview(startInteractiveVisualizationButton)
+        topView.addSubview(startButton)
+        topView.addSubview(pauseButton)
+        topView.addSubview(stopButton)
+        topView.addSubview(comparisonLabel)
+        topView.addSubview(activityIndicator)
     }
 
     private func configureCreateGraphButton() {
-        let frame = CGRect(x: self.center.x - 200, y: 12, width: 100, height: 34)
-        self.createGraphButton = RoundedButton(frame: frame)
-        self.createGraphButton.setTitle("New graph", for: .normal)
-        self.createGraphButton.addTarget(self, action: #selector(self.createGraphButtonTap), for: .touchUpInside)
+        let frame = CGRect(x: center.x - 200, y: 12, width: 100, height: 34)
+        createGraphButton = RoundedButton(frame: frame)
+        createGraphButton.setTitle("New graph", for: .normal)
+        createGraphButton.addTarget(self, action: #selector(createGraphButtonTap), for: .touchUpInside)
     }
 
     private func configureStartVisualizationButton() {
-        let frame = CGRect(x: self.center.x - 50, y: 12, width: 100, height: 34)
-        self.startVisualizationButton = RoundedButton(frame: frame)
-        self.startVisualizationButton.setTitle("Auto", for: .normal)
-        self.startVisualizationButton.addTarget(self, action: #selector(self.startVisualizationButtonDidTap), for: .touchUpInside)
+        let frame = CGRect(x: center.x - 50, y: 12, width: 100, height: 34)
+        startVisualizationButton = RoundedButton(frame: frame)
+        startVisualizationButton.setTitle("Auto", for: .normal)
+        startVisualizationButton.addTarget(self, action: #selector(startVisualizationButtonDidTap), for: .touchUpInside)
     }
 
     private func configureStartInteractiveVisualizationButton() {
-        let frame = CGRect(x: self.center.x + 100, y: 12, width: 100, height: 34)
-        self.startInteractiveVisualizationButton = RoundedButton(frame: frame)
-        self.startInteractiveVisualizationButton.setTitle("Interactive", for: .normal)
-        self.startInteractiveVisualizationButton.addTarget(self, action: #selector(self.startInteractiveVisualizationButtonDidTap), for: .touchUpInside)
+        let frame = CGRect(x: center.x + 100, y: 12, width: 100, height: 34)
+        startInteractiveVisualizationButton = RoundedButton(frame: frame)
+        startInteractiveVisualizationButton.setTitle("Interactive", for: .normal)
+        startInteractiveVisualizationButton.addTarget(self, action: #selector(startInteractiveVisualizationButtonDidTap), for: .touchUpInside)
     }
 
     private func configureStartButton() {
-        let frame = CGRect(x: self.center.x - 65, y: 56, width: 30, height: 30)
-        self.startButton = UIButton(frame: frame)
+        let frame = CGRect(x: center.x - 65, y: 56, width: 30, height: 30)
+        startButton = UIButton(frame: frame)
         let playImage = UIImage(named: "Start.png")
-        self.startButton.setImage(playImage, for: .normal)
-        self.startButton.isEnabled = false
-        self.startButton.addTarget(self, action: #selector(self.didTapStartButton), for: .touchUpInside)
+        startButton.setImage(playImage, for: .normal)
+        startButton.isEnabled = false
+        startButton.addTarget(self, action: #selector(didTapStartButton), for: .touchUpInside)
     }
 
     private func configurePauseButton() {
-        let frame = CGRect(x: self.center.x - 15, y: 56, width: 30, height: 30)
-        self.pauseButton = UIButton(frame: frame)
+        let frame = CGRect(x: center.x - 15, y: 56, width: 30, height: 30)
+        pauseButton = UIButton(frame: frame)
         let pauseImage = UIImage(named: "Pause.png")
-        self.pauseButton.setImage(pauseImage, for: .normal)
-        self.pauseButton.isEnabled = false
-        self.pauseButton.addTarget(self, action: #selector(self.didTapPauseButton), for: .touchUpInside)
+        pauseButton.setImage(pauseImage, for: .normal)
+        pauseButton.isEnabled = false
+        pauseButton.addTarget(self, action: #selector(didTapPauseButton), for: .touchUpInside)
     }
 
     private func configureStopButton() {
-        let frame = CGRect(x: self.center.x + 35, y: 56, width: 30, height: 30)
-        self.stopButton = UIButton(frame: frame)
+        let frame = CGRect(x: center.x + 35, y: 56, width: 30, height: 30)
+        stopButton = UIButton(frame: frame)
         let stopImage = UIImage(named: "Stop.png")
-        self.stopButton.setImage(stopImage, for: .normal)
-        self.stopButton.isEnabled = false
-        self.stopButton.addTarget(self, action: #selector(self.didTapStopButton), for: .touchUpInside)
+        stopButton.setImage(stopImage, for: .normal)
+        stopButton.isEnabled = false
+        stopButton.addTarget(self, action: #selector(didTapStopButton), for: .touchUpInside)
     }
 
     private func configureComparisonLabel() {
         let size = CGSize(width: 250, height: 42)
-        let origin = CGPoint(x: self.center.x - 125, y: 96)
+        let origin = CGPoint(x: center.x - 125, y: 96)
         let frame = CGRect(origin: origin, size: size)
-        self.comparisonLabel = UILabel(frame: frame)
-        self.comparisonLabel.textAlignment = .center
-        self.comparisonLabel.text = "Have fun!"
+        comparisonLabel = UILabel(frame: frame)
+        comparisonLabel.textAlignment = .center
+        comparisonLabel.text = "Have fun!"
     }
 
     private func configureActivityIndicator() {
         let size = CGSize(width: 50, height: 42)
-        let origin = CGPoint(x: self.center.x - 25, y: 100)
+        let origin = CGPoint(x: center.x - 25, y: 100)
         let activityIndicatorFrame = CGRect(origin: origin, size: size)
-        self.activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
-        self.activityIndicator.activityIndicatorViewStyle = .whiteLarge
+        activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
+        activityIndicator.activityIndicatorViewStyle = .whiteLarge
     }
 
     @objc private func createGraphButtonTap() {
-        self.comparisonLabel.text = ""
-        self.graphView.removeGraph()
-        self.graph.removeGraph()
-        self.graph.createNewGraph()
-        self.graphView.createNewGraph()
-        self.graph.state = .initial
+        comparisonLabel.text = ""
+        graphView.removeGraph()
+        graph.removeGraph()
+        graph.createNewGraph()
+        graphView.createNewGraph()
+        graph.state = .initial
     }
 
     @objc private func startVisualizationButtonDidTap() {
-        self.comparisonLabel.text = ""
-        self.pauseButton.isEnabled = true
-        self.stopButton.isEnabled = true
-        self.createGraphButton.isEnabled = false
-        self.startVisualizationButton.isEnabled = false
-        self.startInteractiveVisualizationButton.isEnabled = false
-        self.createGraphButton.alpha = 0.5
-        self.startVisualizationButton.alpha = 0.5
-        self.startInteractiveVisualizationButton.alpha = 0.5
-
-        if self.graph.state == .completed {
-            self.graphView.reset()
-            self.graph.reset()
+        comparisonLabel.text = ""
+        pauseButton.isEnabled = true
+        stopButton.isEnabled = true
+        createGraphButton.isEnabled = false
+        startVisualizationButton.isEnabled = false
+        startInteractiveVisualizationButton.isEnabled = false
+        createGraphButton.alpha = 0.5
+        startVisualizationButton.alpha = 0.5
+        startInteractiveVisualizationButton.alpha = 0.5
+
+        if graph.state == .completed {
+            graphView.reset()
+            graph.reset()
         }
-        self.graph.state = .autoVisualization
+        graph.state = .autoVisualization
         DispatchQueue.global(qos: .background).async {
             self.graph.findShortestPathsWithVisualization {
                 self.graph.state = .completed
@@ -184,25 +184,25 @@ public class Window: UIView, GraphDelegate {
     }
 
     @objc private func startInteractiveVisualizationButtonDidTap() {
-        self.comparisonLabel.text = ""
-        self.pauseButton.isEnabled = true
-        self.stopButton.isEnabled = true
-        self.createGraphButton.isEnabled = false
-        self.startVisualizationButton.isEnabled = false
-        self.startInteractiveVisualizationButton.isEnabled = false
-        self.createGraphButton.alpha = 0.5
-        self.startVisualizationButton.alpha = 0.5
-        self.startInteractiveVisualizationButton.alpha = 0.5
-
-        if self.graph.state == .completed {
-            self.graphView.reset()
-            self.graph.reset()
+        comparisonLabel.text = ""
+        pauseButton.isEnabled = true
+        stopButton.isEnabled = true
+        createGraphButton.isEnabled = false
+        startVisualizationButton.isEnabled = false
+        startInteractiveVisualizationButton.isEnabled = false
+        createGraphButton.alpha = 0.5
+        startVisualizationButton.alpha = 0.5
+        startInteractiveVisualizationButton.alpha = 0.5
+
+        if graph.state == .completed {
+            graphView.reset()
+            graph.reset()
         }
         
-        self.graph.startVertex.pathLengthFromStart = 0
-        self.graph.startVertex.pathVerticesFromStart.append(self.graph.startVertex)
-        self.graph.state = .parsing
-        self.graph.parseNeighborsFor(vertex: self.graph.startVertex) {
+        graph.startVertex.pathLengthFromStart = 0
+        graph.startVertex.pathVerticesFromStart.append(graph.startVertex)
+        graph.state = .parsing
+        graph.parseNeighborsFor(vertex: graph.startVertex) {
             self.graph.state = .interactiveVisualization
             DispatchQueue.main.async {
                 self.comparisonLabel.text = "Pick next vertex"
@@ -211,43 +211,43 @@ public class Window: UIView, GraphDelegate {
     }
 
     @objc private func didTapStartButton() {
-        self.startButton.isEnabled = false
-        self.pauseButton.isEnabled = true
+        startButton.isEnabled = false
+        pauseButton.isEnabled = true
         DispatchQueue.global(qos: .utility).async {
             self.graph.pauseVisualization = false
         }
     }
 
     @objc private func didTapPauseButton() {
-        self.startButton.isEnabled = true
-        self.pauseButton.isEnabled = false
+        startButton.isEnabled = true
+        pauseButton.isEnabled = false
         DispatchQueue.global(qos: .utility).async {
             self.graph.pauseVisualization = true
         }
     }
 
     @objc private func didTapStopButton() {
-        self.startButton.isEnabled = false
-        self.pauseButton.isEnabled = false
-        self.comparisonLabel.text = ""
-        self.activityIndicator.startAnimating()
-        if self.graph.state == .parsing || self.graph.state == .autoVisualization {
-            self.graph.stopVisualization = true
-        } else if self.graph.state == .interactiveVisualization {
-            self.didStop()
+        startButton.isEnabled = false
+        pauseButton.isEnabled = false
+        comparisonLabel.text = ""
+        activityIndicator.startAnimating()
+        if graph.state == .parsing || graph.state == .autoVisualization {
+            graph.stopVisualization = true
+        } else if graph.state == .interactiveVisualization {
+            didStop()
         }
     }
 
     private func setButtonsToInitialState() {
-        self.createGraphButton.isEnabled = true
-        self.startVisualizationButton.isEnabled = true
-        self.startInteractiveVisualizationButton.isEnabled = true
-        self.startButton.isEnabled = false
-        self.pauseButton.isEnabled = false
-        self.stopButton.isEnabled = false
-        self.createGraphButton.alpha = 1
-        self.startVisualizationButton.alpha = 1
-        self.startInteractiveVisualizationButton.alpha = 1
+        createGraphButton.isEnabled = true
+        startVisualizationButton.isEnabled = true
+        startInteractiveVisualizationButton.isEnabled = true
+        startButton.isEnabled = false
+        pauseButton.isEnabled = false
+        stopButton.isEnabled = false
+        createGraphButton.alpha = 1
+        startVisualizationButton.alpha = 1
+        startInteractiveVisualizationButton.alpha = 1
     }
 
     private func showError(error: String) {
@@ -268,14 +268,14 @@ public class Window: UIView, GraphDelegate {
 
     // MARK: GraphDelegate
     public func didCompleteGraphParsing() {
-        self.graph.state = .completed
-        self.setButtonsToInitialState()
-        self.comparisonLabel.text = "Completed!"
+        graph.state = .completed
+        setButtonsToInitialState()
+        comparisonLabel.text = "Completed!"
     }
 
     public func didTapWrongVertex() {
-        if !self.subviews.contains { $0 is ErrorView } {
-            self.showError(error: "You have picked wrong next vertex")
+        if !subviews.contains { $0 is ErrorView } {
+            showError(error: "You have picked wrong next vertex")
         }
     }
 
@@ -296,13 +296,13 @@ public class Window: UIView, GraphDelegate {
     }
 
     public func didStop() {
-        self.graph.state = .initial
-        self.graph.stopVisualization = false
-        self.graph.pauseVisualization = false
-        self.graphView.reset()
-        self.graph.reset()
-        self.setButtonsToInitialState()
-        self.activityIndicator.stopAnimating()
+        graph.state = .initial
+        graph.stopVisualization = false
+        graph.pauseVisualization = false
+        graphView.reset()
+        graph.reset()
+        setButtonsToInitialState()
+        activityIndicator.stopAnimating()
     }
 
     public func willStartVertexNeighborsChecking() {

From 900b7caf229697f5666627bd7cdc34c6f1143702 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:56:12 +0300
Subject: [PATCH 0936/1679] Replaced with optional

---
 .../Sources/Graph.swift                        | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
index 7c4a8e373..8bf2452cc 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -130,12 +130,12 @@ public class Graph {
         clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
-        var currentVertex: Vertex! = startVertex
+        var currentVertex: Vertex? = startVertex
 
         var totalVertices = _vertices
 
-        breakableLoop: while currentVertex != nil {
-            totalVertices.remove(currentVertex)
+        breakableLoop: while let vertex = currentVertex {
+            totalVertices.remove(vertex)
             while pauseVisualization == true {
                 if stopVisualization == true {
                     break breakableLoop
@@ -145,11 +145,11 @@ public class Graph {
                 break breakableLoop
             }
             DispatchQueue.main.async {
-                currentVertex.setVisitedColor()
+                vertex.setVisitedColor()
             }
             usleep(750000)
-            currentVertex.visited = true
-            let filteredEdges = currentVertex.edges.filter { !$0.neighbor.visited }
+            vertex.visited = true
+            let filteredEdges = vertex.edges.filter { !$0.neighbor.visited }
             for edge in filteredEdges {
                 let neighbor = edge.neighbor
                 let weight = edge.weight
@@ -166,14 +166,14 @@ public class Graph {
                 DispatchQueue.main.async {
                     edgeRepresentation?.setCheckingColor()
                     neighbor.setCheckingPathColor()
-                    self.delegate?.willCompareVertices(startVertexPathLength: currentVertex.pathLengthFromStart,
+                    self.delegate?.willCompareVertices(startVertexPathLength: vertex.pathLengthFromStart,
                                                        edgePathLength: weight,
                                                        endVertexPathLength: neighbor.pathLengthFromStart)
                 }
                 usleep(_visualizationOneSleepDuration)
 
 
-                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
 
                 if theoreticNewWeight < neighbor.pathLengthFromStart {
                     while pauseVisualization == true {
@@ -185,7 +185,7 @@ public class Graph {
                         break breakableLoop
                     }
                     neighbor.pathLengthFromStart = theoreticNewWeight
-                    neighbor.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighbor.pathVerticesFromStart = vertex.pathVerticesFromStart
                     neighbor.pathVerticesFromStart.append(neighbor)
                 }
                 usleep(_visualizationOneSleepDuration)

From 2a1a2a1a7bbdf738b8643d49775ccf7895d476b6 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 13:27:18 +0300
Subject: [PATCH 0937/1679] Refactored a bit

---
 .../Sources/Graph.swift                       | 14 ++++++++------
 .../Sources/GraphView.swift                   | 12 +++++-------
 .../Sources/Window.swift                      | 19 +++++++++++--------
 3 files changed, 24 insertions(+), 21 deletions(-)

diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
index 8bf2452cc..447b3dbe1 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -10,16 +10,14 @@ public enum GraphState {
 }
 
 public class Graph {
-    private init() { }
-
-    private var verticesCount: UInt!
+    private var verticesCount: UInt
     private var _vertices: Set<Vertex> = Set()
     public weak var delegate: GraphDelegate?
     public var nextVertices: [Vertex] = []
     public var state: GraphState = .initial
-    public var pauseVisualization: Bool = false
-    public var stopVisualization: Bool = false
-    public var startVertex: Vertex!
+    public var pauseVisualization = false
+    public var stopVisualization = false
+    public var startVertex: Vertex?
     public var interactiveNeighborCheckAnimationDuration: Double = 1.8 {
         didSet {
             _interactiveOneSleepDuration = UInt32(interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
@@ -127,6 +125,10 @@ public class Graph {
     }
 
     public func findShortestPathsWithVisualization(completion: () -> Void) {
+        guard let startVertex = self.startVertex else {
+            assertionFailure("start vertex is nil")
+            return
+        }
         clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
index bdeab7669..ec4f74705 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
@@ -1,13 +1,15 @@
 import UIKit
 
 public class GraphView: UIView {
-    private var graph: Graph!
+    private var graph: Graph
     private var panningView: VertexView? = nil
-    private var graphColors: GraphColors = GraphColors.sharedInstance
+    private var graphColors = GraphColors.sharedInstance
 
-    public override init(frame: CGRect) {
+    public init(frame: CGRect, graph: Graph) {
+        self.graph = graph
         super.init(frame: frame)
         backgroundColor = graphColors.graphBackgroundColor
+        layer.cornerRadius = 15
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -15,10 +17,6 @@ public class GraphView: UIView {
     
     }
 
-    public func configure(graph: Graph) {
-        self.graph = graph
-    }
-
     public func removeGraph() {
         for vertex in graph.vertices {
             if let view = vertex.view {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
index 054b804c9..73c512e6b 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -25,7 +25,7 @@ public class Window: UIView, GraphDelegate {
     private var activityIndicator: UIActivityIndicatorView!
     private var graph: Graph!
     private var numberOfVertices: UInt!
-    private var graphColors: GraphColors = GraphColors.sharedInstance
+    private var graphColors = GraphColors.sharedInstance
 
     public override init(frame: CGRect) {
         super.init(frame: frame)
@@ -42,10 +42,9 @@ public class Window: UIView, GraphDelegate {
         graph.createNewGraph()
         graph.delegate = self
         let frame = CGRect(x: 10, y: 170, width: self.frame.width - 20, height: self.frame.height - 180)
-        graphView = GraphView(frame: frame)
-        graphView.layer.cornerRadius = 15
+        graphView = GraphView(frame: frame, graph: graph)
+        
 
-        graphView.configure(graph: graph)
         graphView.createNewGraph()
         addSubview(graphView)
 
@@ -198,11 +197,15 @@ public class Window: UIView, GraphDelegate {
             graphView.reset()
             graph.reset()
         }
-        
-        graph.startVertex.pathLengthFromStart = 0
-        graph.startVertex.pathVerticesFromStart.append(graph.startVertex)
+
+        guard let startVertex = graph.startVertex else {
+            assertionFailure("startVertex is nil")
+            return
+        }
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
         graph.state = .parsing
-        graph.parseNeighborsFor(vertex: graph.startVertex) {
+        graph.parseNeighborsFor(vertex: startVertex) {
             self.graph.state = .interactiveVisualization
             DispatchQueue.main.async {
                 self.comparisonLabel.text = "Pick next vertex"

From 846101720981de86abf8fe8f372715fa50f12dcb Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:02:43 +0300
Subject: [PATCH 0938/1679] Updated description

---
 Dijkstra Algorithm/README.md | 38 ++++++++++++++++++++++++++----------
 1 file changed, 28 insertions(+), 10 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index bf158def9..2bbf74b87 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,21 +1,39 @@
 # Dijkstra-algorithm
 
-## About
-Dijkstra's algorithm is used for finding shortest paths from start vertex in graph(with weighted vertices) to all other vertices. 
-More algorithm's description can be found in playground or on wikipedia:
-[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
-
-To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
-
-If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
+## About this repository
+This repository contains to playgrounds:
+* To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
+* If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
 ## Demo video
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Screenshots
-
 <img src="Screenshots/screenshot1.jpg" height="400" />
 
+## Dijkstra's algorithm explanation
+
+Wikipedia's explanation:
+Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
+
+1. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.
+2. Set the initial node as current. Mark all other nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.
+3. For the current node, consider all of its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, keep the current value.
+4. When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.
+5. If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.
+6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new "current node", and go back to step 3.
+
+Explanation, that can be found in the **VisualizedDijkstra.playground**
+Algorithm's flow:
+First of all, this program randomly decides which vertex will be the start one, then the program assigns a zero value to the start vertex path length from the start.
+
+Then the algorithm repeats following cycle until all vertices are marked as visited.
+Cycle:
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+2. The algorithm marks picked vertex as visited.
+3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+
 ## Credits
-WWDC 2017 Scholarship Project
+WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From f7793cc6b6692000e4fd878afce62fd67d5b5f00 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:38:47 +0300
Subject: [PATCH 0939/1679] Added gif

---
 Dijkstra Algorithm/Images/Dijkstra_Animation.gif | Bin 0 -> 8561 bytes
 .../{Screenshots => Images}/screenshot1.jpg      | Bin
 Dijkstra Algorithm/README.md                     |   8 +++++++-
 3 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 Dijkstra Algorithm/Images/Dijkstra_Animation.gif
 rename Dijkstra Algorithm/{Screenshots => Images}/screenshot1.jpg (100%)

diff --git a/Dijkstra Algorithm/Images/Dijkstra_Animation.gif b/Dijkstra Algorithm/Images/Dijkstra_Animation.gif
new file mode 100644
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diff --git a/Dijkstra Algorithm/Screenshots/screenshot1.jpg b/Dijkstra Algorithm/Images/screenshot1.jpg
similarity index 100%
rename from Dijkstra Algorithm/Screenshots/screenshot1.jpg
rename to Dijkstra Algorithm/Images/screenshot1.jpg
diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 2bbf74b87..0ac4bc17e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,10 +9,12 @@ This repository contains to playgrounds:
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Screenshots
-<img src="Screenshots/screenshot1.jpg" height="400" />
+<img src="Images/screenshot1.jpg" height="400" />
 
 ## Dijkstra's algorithm explanation
 
+<img src="Images/Dijkstra_Animation.gif" height="250" />
+
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
 
@@ -34,6 +36,10 @@ Cycle:
 3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
+## Usage
+
+
+
 ## Credits
 WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From 3f6be33a1750d6f9122ca8ab38b70c3a9e4d123b Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:40:34 +0300
Subject: [PATCH 0940/1679] Added link

---
 Dijkstra Algorithm/README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 0ac4bc17e..b2606f0f9 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -13,7 +13,8 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Dijkstra's algorithm explanation
 
-<img src="Images/Dijkstra_Animation.gif" height="250" />
+GIF from Wikipedia
+<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From a153067e60fcd90d8a8b6448fbc5d9e0c5753076 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:41:35 +0300
Subject: [PATCH 0941/1679] Updated link

---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index b2606f0f9..cf939c7cc 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -14,7 +14,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Dijkstra's algorithm explanation
 
 GIF from Wikipedia
-<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
+<img src="https://commons.wikimedia.org/wiki/File:Dijkstra_Animation.gif#/media/File:Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From b59ffa53930e3021a22bee31923965a12f7031a3 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:42:10 +0300
Subject: [PATCH 0942/1679] Revert "Updated link"

This reverts commit a153067e60fcd90d8a8b6448fbc5d9e0c5753076.
---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index cf939c7cc..b2606f0f9 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -14,7 +14,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Dijkstra's algorithm explanation
 
 GIF from Wikipedia
-<img src="https://commons.wikimedia.org/wiki/File:Dijkstra_Animation.gif#/media/File:Dijkstra_Animation.gif" height="250" />
+<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From ef13b5076e1741023c6d014e32266044d8d63d7b Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:42:40 +0300
Subject: [PATCH 0943/1679] Revert "Added link"

This reverts commit 3f6be33a1750d6f9122ca8ab38b70c3a9e4d123b.
---
 Dijkstra Algorithm/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index b2606f0f9..0ac4bc17e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -13,8 +13,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Dijkstra's algorithm explanation
 
-GIF from Wikipedia
-<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
+<img src="Images/Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From aea01e8b68d7fefd06ccae2d3afeb253a43abba0 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:44:39 +0300
Subject: [PATCH 0944/1679] Added link to Wikipedia

This reverts commit a153067e60fcd90d8a8b6448fbc5d9e0c5753076.
---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 0ac4bc17e..325bab40f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -15,7 +15,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 <img src="Images/Dijkstra_Animation.gif" height="250" />
 
-Wikipedia's explanation:
+[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)'s explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
 
 1. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.

From edafd431fab46087ff805f6ad419b076a076bf82 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Mon, 17 Apr 2017 21:15:01 +0200
Subject: [PATCH 0945/1679] Add playground

---
 .../NaiveBayes.playground/Contents.swift      |  60 ++++++
 .../NaiveBayes.playground/Resources/wine.csv  | 177 ++++++++++++++++
 .../Sources/NaiveBayes.swift                  | 196 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Naive Bayes Classifier/NaiveBayes.swift       | 124 ++++-------
 6 files changed, 479 insertions(+), 89 deletions(-)
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
new file mode 100644
index 000000000..cb820272e
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -0,0 +1,60 @@
+import Foundation
+
+/*:
+ ## Naive Bayes Classifier
+ 
+ This playground uses the given algorithm and utilizes its features with some example datasets
+ 
+ ### Gaussian Naive Bayes
+ - Note:
+ When using Gaussian NB you have to have continuous features (Double). 
+ 
+ For this example we are going to use a famous dataset with different types of wine. The labels of the features can be viewed [here](https://gist.github.com/tijptjik/9408623)
+ */
+guard let wineCSV = Bundle.main.path(forResource: "wine", ofType: "csv") else {
+    print("Resource could not be found!")
+    exit(0)
+}
+
+guard let csv = try? String(contentsOfFile: wineCSV) else {
+    print("File could not be read!")
+    exit(0)
+}
+
+/*:
+ Reading the .csv file line per line
+ */
+let rows = csv.characters.split(separator: "\r\n").map { String($0) }
+/*:
+ Splitting on the ; sign and converting the value to a Double
+ 
+ - Important:
+ Do not force unwrap the mapped values in your real application. Carefully convert them! This is just for the sake of showing how the algorithm works.
+ */
+let wineData = rows.map { row -> [Double] in
+    let split = row.characters.split(separator: ";")
+    return split.map { Double(String($0))! }
+}
+
+/*:
+ The algorithm wants the classes and the data seperated since this gives a huge performance boost. Also I haven't implemented this in the NB class itself since it is not in the scope of it.
+ */
+let rowOfClasses = 0
+let classes = wineData.map { Int($0[rowOfClasses]) }
+let data = wineData.map { row in
+    return row.enumerated().filter { $0.offset != rowOfClasses }.map { $0.element }
+}
+
+/*:
+ Again use `guard` on the result of a `try?` or simply `do-try-catch` because this would crash your application if an error occured.
+ 
+ The array in the `classifyProba` method I passed is a former entry in the .csv file which I removed in order to classify it.
+ */
+let wineBayes = try! NaiveBayes(type: .gaussian, data: data, classes: classes).train()
+let result = wineBayes.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015])
+print(result)
+/*:
+ I can assure you that this is the correct result and as you can see the classifier thinks that its ***99.99%*** correct too.
+ 
+ ### Multinomial Naive Bayes
+ */
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv b/Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv
new file mode 100644
index 000000000..89e14fd02
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv	
@@ -0,0 +1,177 @@
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+2;13.03;.9;1.71;16;86;1.95;2.03;.24;1.46;4.6;1.19;2.48;392
+2;11.84;2.89;2.23;18;112;1.72;1.32;.43;.95;2.65;.96;2.52;500
+2;12.33;.99;1.95;14.8;136;1.9;1.85;.35;2.76;3.4;1.06;2.31;750
+2;12.7;3.87;2.4;23;101;2.83;2.55;.43;1.95;2.57;1.19;3.13;463
+2;12;.92;2;19;86;2.42;2.26;.3;1.43;2.5;1.38;3.12;278
+2;12.72;1.81;2.2;18.8;86;2.2;2.53;.26;1.77;3.9;1.16;3.14;714
+2;12.08;1.13;2.51;24;78;2;1.58;.4;1.4;2.2;1.31;2.72;630
+2;13.05;3.86;2.32;22.5;85;1.65;1.59;.61;1.62;4.8;.84;2.01;515
+2;11.84;.89;2.58;18;94;2.2;2.21;.22;2.35;3.05;.79;3.08;520
+2;12.67;.98;2.24;18;99;2.2;1.94;.3;1.46;2.62;1.23;3.16;450
+2;12.16;1.61;2.31;22.8;90;1.78;1.69;.43;1.56;2.45;1.33;2.26;495
+2;11.65;1.67;2.62;26;88;1.92;1.61;.4;1.34;2.6;1.36;3.21;562
+2;11.64;2.06;2.46;21.6;84;1.95;1.69;.48;1.35;2.8;1;2.75;680
+2;12.08;1.33;2.3;23.6;70;2.2;1.59;.42;1.38;1.74;1.07;3.21;625
+2;12.08;1.83;2.32;18.5;81;1.6;1.5;.52;1.64;2.4;1.08;2.27;480
+2;12;1.51;2.42;22;86;1.45;1.25;.5;1.63;3.6;1.05;2.65;450
+2;12.69;1.53;2.26;20.7;80;1.38;1.46;.58;1.62;3.05;.96;2.06;495
+2;12.29;2.83;2.22;18;88;2.45;2.25;.25;1.99;2.15;1.15;3.3;290
+2;11.62;1.99;2.28;18;98;3.02;2.26;.17;1.35;3.25;1.16;2.96;345
+2;12.47;1.52;2.2;19;162;2.5;2.27;.32;3.28;2.6;1.16;2.63;937
+2;11.81;2.12;2.74;21.5;134;1.6;.99;.14;1.56;2.5;.95;2.26;625
+2;12.29;1.41;1.98;16;85;2.55;2.5;.29;1.77;2.9;1.23;2.74;428
+2;12.37;1.07;2.1;18.5;88;3.52;3.75;.24;1.95;4.5;1.04;2.77;660
+2;12.29;3.17;2.21;18;88;2.85;2.99;.45;2.81;2.3;1.42;2.83;406
+2;12.08;2.08;1.7;17.5;97;2.23;2.17;.26;1.4;3.3;1.27;2.96;710
+2;12.6;1.34;1.9;18.5;88;1.45;1.36;.29;1.35;2.45;1.04;2.77;562
+2;12.34;2.45;2.46;21;98;2.56;2.11;.34;1.31;2.8;.8;3.38;438
+2;11.82;1.72;1.88;19.5;86;2.5;1.64;.37;1.42;2.06;.94;2.44;415
+2;12.51;1.73;1.98;20.5;85;2.2;1.92;.32;1.48;2.94;1.04;3.57;672
+2;12.42;2.55;2.27;22;90;1.68;1.84;.66;1.42;2.7;.86;3.3;315
+2;12.25;1.73;2.12;19;80;1.65;2.03;.37;1.63;3.4;1;3.17;510
+2;12.72;1.75;2.28;22.5;84;1.38;1.76;.48;1.63;3.3;.88;2.42;488
+2;12.22;1.29;1.94;19;92;2.36;2.04;.39;2.08;2.7;.86;3.02;312
+2;11.61;1.35;2.7;20;94;2.74;2.92;.29;2.49;2.65;.96;3.26;680
+2;11.46;3.74;1.82;19.5;107;3.18;2.58;.24;3.58;2.9;.75;2.81;562
+2;12.52;2.43;2.17;21;88;2.55;2.27;.26;1.22;2;.9;2.78;325
+2;11.76;2.68;2.92;20;103;1.75;2.03;.6;1.05;3.8;1.23;2.5;607
+2;11.41;.74;2.5;21;88;2.48;2.01;.42;1.44;3.08;1.1;2.31;434
+2;12.08;1.39;2.5;22.5;84;2.56;2.29;.43;1.04;2.9;.93;3.19;385
+2;11.03;1.51;2.2;21.5;85;2.46;2.17;.52;2.01;1.9;1.71;2.87;407
+2;11.82;1.47;1.99;20.8;86;1.98;1.6;.3;1.53;1.95;.95;3.33;495
+2;12.42;1.61;2.19;22.5;108;2;2.09;.34;1.61;2.06;1.06;2.96;345
+2;12.77;3.43;1.98;16;80;1.63;1.25;.43;.83;3.4;.7;2.12;372
+2;12;3.43;2;19;87;2;1.64;.37;1.87;1.28;.93;3.05;564
+2;11.45;2.4;2.42;20;96;2.9;2.79;.32;1.83;3.25;.8;3.39;625
+2;11.56;2.05;3.23;28.5;119;3.18;5.08;.47;1.87;6;.93;3.69;465
+2;12.42;4.43;2.73;26.5;102;2.2;2.13;.43;1.71;2.08;.92;3.12;365
+2;13.05;5.8;2.13;21.5;86;2.62;2.65;.3;2.01;2.6;.73;3.1;380
+2;11.87;4.31;2.39;21;82;2.86;3.03;.21;2.91;2.8;.75;3.64;380
+2;12.07;2.16;2.17;21;85;2.6;2.65;.37;1.35;2.76;.86;3.28;378
+2;12.43;1.53;2.29;21.5;86;2.74;3.15;.39;1.77;3.94;.69;2.84;352
+2;11.79;2.13;2.78;28.5;92;2.13;2.24;.58;1.76;3;.97;2.44;466
+2;12.37;1.63;2.3;24.5;88;2.22;2.45;.4;1.9;2.12;.89;2.78;342
+2;12.04;4.3;2.38;22;80;2.1;1.75;.42;1.35;2.6;.79;2.57;580
+3;12.86;1.35;2.32;18;122;1.51;1.25;.21;.94;4.1;.76;1.29;630
+3;12.88;2.99;2.4;20;104;1.3;1.22;.24;.83;5.4;.74;1.42;530
+3;12.81;2.31;2.4;24;98;1.15;1.09;.27;.83;5.7;.66;1.36;560
+3;12.7;3.55;2.36;21.5;106;1.7;1.2;.17;.84;5;.78;1.29;600
+3;12.51;1.24;2.25;17.5;85;2;.58;.6;1.25;5.45;.75;1.51;650
+3;12.6;2.46;2.2;18.5;94;1.62;.66;.63;.94;7.1;.73;1.58;695
+3;12.25;4.72;2.54;21;89;1.38;.47;.53;.8;3.85;.75;1.27;720
+3;12.53;5.51;2.64;25;96;1.79;.6;.63;1.1;5;.82;1.69;515
+3;13.49;3.59;2.19;19.5;88;1.62;.48;.58;.88;5.7;.81;1.82;580
+3;12.84;2.96;2.61;24;101;2.32;.6;.53;.81;4.92;.89;2.15;590
+3;12.93;2.81;2.7;21;96;1.54;.5;.53;.75;4.6;.77;2.31;600
+3;13.36;2.56;2.35;20;89;1.4;.5;.37;.64;5.6;.7;2.47;780
+3;13.52;3.17;2.72;23.5;97;1.55;.52;.5;.55;4.35;.89;2.06;520
+3;13.62;4.95;2.35;20;92;2;.8;.47;1.02;4.4;.91;2.05;550
+3;12.25;3.88;2.2;18.5;112;1.38;.78;.29;1.14;8.21;.65;2;855
+3;13.16;3.57;2.15;21;102;1.5;.55;.43;1.3;4;.6;1.68;830
+3;13.88;5.04;2.23;20;80;.98;.34;.4;.68;4.9;.58;1.33;415
+3;12.87;4.61;2.48;21.5;86;1.7;.65;.47;.86;7.65;.54;1.86;625
+3;13.32;3.24;2.38;21.5;92;1.93;.76;.45;1.25;8.42;.55;1.62;650
+3;13.08;3.9;2.36;21.5;113;1.41;1.39;.34;1.14;9.40;.57;1.33;550
+3;13.5;3.12;2.62;24;123;1.4;1.57;.22;1.25;8.60;.59;1.3;500
+3;12.79;2.67;2.48;22;112;1.48;1.36;.24;1.26;10.8;.48;1.47;480
+3;13.11;1.9;2.75;25.5;116;2.2;1.28;.26;1.56;7.1;.61;1.33;425
+3;13.23;3.3;2.28;18.5;98;1.8;.83;.61;1.87;10.52;.56;1.51;675
+3;12.58;1.29;2.1;20;103;1.48;.58;.53;1.4;7.6;.58;1.55;640
+3;13.17;5.19;2.32;22;93;1.74;.63;.61;1.55;7.9;.6;1.48;725
+3;13.84;4.12;2.38;19.5;89;1.8;.83;.48;1.56;9.01;.57;1.64;480
+3;12.45;3.03;2.64;27;97;1.9;.58;.63;1.14;7.5;.67;1.73;880
+3;14.34;1.68;2.7;25;98;2.8;1.31;.53;2.7;13;.57;1.96;660
+3;13.48;1.67;2.64;22.5;89;2.6;1.1;.52;2.29;11.75;.57;1.78;620
+3;12.36;3.83;2.38;21;88;2.3;.92;.5;1.04;7.65;.56;1.58;520
+3;13.69;3.26;2.54;20;107;1.83;.56;.5;.8;5.88;.96;1.82;680
+3;12.85;3.27;2.58;22;106;1.65;.6;.6;.96;5.58;.87;2.11;570
+3;12.96;3.45;2.35;18.5;106;1.39;.7;.4;.94;5.28;.68;1.75;675
+3;13.78;2.76;2.3;22;90;1.35;.68;.41;1.03;9.58;.7;1.68;615
+3;13.73;4.36;2.26;22.5;88;1.28;.47;.52;1.15;6.62;.78;1.75;520
+3;13.45;3.7;2.6;23;111;1.7;.92;.43;1.46;10.68;.85;1.56;695
+3;12.82;3.37;2.3;19.5;88;1.48;.66;.4;.97;10.26;.72;1.75;685
+3;13.58;2.58;2.69;24.5;105;1.55;.84;.39;1.54;8.66;.74;1.8;750
+3;13.4;4.6;2.86;25;112;1.98;.96;.27;1.11;8.5;.67;1.92;630
+3;12.2;3.03;2.32;19;96;1.25;.49;.4;.73;5.5;.66;1.83;510
+3;12.77;2.39;2.28;19.5;86;1.39;.51;.48;.64;9.899999;.57;1.63;470
+3;14.16;2.51;2.48;20;91;1.68;.7;.44;1.24;9.7;.62;1.71;660
+3;13.71;5.65;2.45;20.5;95;1.68;.61;.52;1.06;7.7;.64;1.74;740
+3;13.4;3.91;2.48;23;102;1.8;.75;.43;1.41;7.3;.7;1.56;750
+3;13.27;4.28;2.26;20;120;1.59;.69;.43;1.35;10.2;.59;1.56;835
+3;13.17;2.59;2.37;20;120;1.65;.68;.53;1.46;9.3;.6;1.62;840
+3;14.13;4.1;2.74;24.5;96;2.05;.76;.56;1.35;9.2;.61;1.6;560
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift
new file mode 100644
index 000000000..3af8102c7
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift	
@@ -0,0 +1,196 @@
+//
+//  NaiveBayes.swift
+//  NaiveBayes
+//
+//  Created by Philipp Gabriel on 14.04.17.
+//  Copyright © 2017 ph1ps. All rights reserved.
+//
+
+import Foundation
+
+extension String: Error {}
+
+extension Array where Element == Double {
+    
+    func mean() -> Double {
+        return self.reduce(0, +) / Double(count)
+    }
+    
+    func standardDeviation() -> Double {
+        let calculatedMean = mean()
+        
+        let sum = self.reduce(0.0) { (previous, next) in
+            return previous + pow(next - calculatedMean, 2)
+        }
+        
+        return sqrt(sum / Double(count - 1))
+    }
+}
+
+extension Array where Element == Int {
+    
+    func uniques() -> Set<Element> {
+        return Set(self)
+    }
+    
+}
+
+public enum NBType {
+    
+    case gaussian
+    case multinomial
+    //case bernoulli --> TODO
+    
+    func calcLikelihood(variables: [Any], input: Any) -> Double? {
+        
+        if case .gaussian = self {
+            
+            guard let input = input as? Double else {
+                return nil
+            }
+            
+            guard let mean = variables[0] as? Double else {
+                return nil
+            }
+            
+            guard let stDev = variables[1] as? Double else {
+                return nil
+            }
+            
+            let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
+            let distribution = eulerPart / sqrt(2 * .pi) / stDev
+            
+            return distribution
+            
+        } else if case .multinomial = self {
+            
+            guard let variables = variables as? [(category: Int, probability: Double)] else {
+                return nil
+            }
+            
+            guard let input = input as? Int else {
+                return nil
+            }
+            
+            return variables.first { variable in
+                return variable.category == input
+                }?.probability
+            
+        }
+        
+        return nil
+    }
+    
+    func train(values: [Any]) -> [Any]? {
+        
+        if case .gaussian = self {
+            
+            guard let values = values as? [Double] else {
+                return nil
+            }
+            
+            return [values.mean(), values.standardDeviation()]
+            
+        } else if case .multinomial = self {
+            
+            guard let values = values as? [Int] else {
+                return nil
+            }
+            
+            let count = values.count
+            let categoryProba = values.uniques().map { value -> (Int, Double) in
+                return (value, Double(values.filter { $0 == value }.count) / Double(count))
+            }
+            return categoryProba
+        }
+        
+        return nil
+    }
+}
+
+public class NaiveBayes<T> {
+    
+    var variables: [Int: [(feature: Int, variables: [Any])]]
+    var type: NBType
+    
+    var data: [[T]]
+    var classes: [Int]
+    
+    public init(type: NBType, data: [[T]], classes: [Int]) throws {
+        self.type = type
+        self.data = data
+        self.classes = classes
+        self.variables = [Int: [(Int, [Any])]]()
+        
+        if case .gaussian = type, T.self != Double.self {
+            throw "When using Gaussian NB you have to have continuous features (Double)"
+        } else if case .multinomial = type, T.self != Int.self {
+            throw "When using Multinomial NB you have to have categorical features (Int)"
+        }
+    }
+    
+    public func train() throws -> Self {
+        
+        for `class` in classes.uniques() {
+            variables[`class`] = [(Int, [Any])]()
+            
+            let classDependent = data.enumerated().filter { (offset, _) in
+                return classes[offset] == `class`
+            }
+            
+            for feature in 0..<data[0].count {
+                
+                let featureDependent = classDependent.map { $0.element[feature] }
+                
+                guard let trained = type.train(values: featureDependent) else {
+                    throw "Critical! Data could not be casted even though it was checked at init"
+                }
+                
+                variables[`class`]?.append((feature, trained))
+            }
+        }
+        
+        return self
+    }
+    
+    public func classify(with input: [T]) -> Int {
+        let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
+            return first.1 < second.1
+        }
+        
+        guard let `class` = likelihoods?.0 else {
+            return -1
+        }
+        
+        return `class`
+    }
+    
+    public func classifyProba(with input: [T]) -> [(Int, Double)] {
+        
+        var probaClass = [Int: Double]()
+        let amount = classes.count
+        
+        classes.forEach { `class` in
+            let individual = classes.filter { $0 == `class` }.count
+            probaClass[`class`] = Double(individual) / Double(amount)
+        }
+        
+        let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
+            let distribution = value.map { (feature, variables) -> Double in
+                return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
+            }
+            return (`class`, distribution)
+        }
+        
+        let likelihoods = classesAndFeatures.map { (`class`, distribution) in
+            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
+        }
+        
+        let sum = likelihoods.map { $0.1 }.reduce(0, +)
+        let normalized = likelihoods.map { (`class`, likelihood) in
+            return (`class`, likelihood / sum)
+        }
+        
+        return normalized
+    }
+}
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
new file mode 100644
index 000000000..b1148fc50
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos' display-mode='raw'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata b/Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index dbbf3cd9f..9b9ace86d 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -8,6 +8,8 @@
 
 import Foundation
 
+extension String: Error {}
+
 extension Array where Element == Double {
     
     func mean() -> Double {
@@ -35,29 +37,9 @@ extension Array where Element == Int {
 
 enum NBType {
     
-    case gaussian(data: [[Double]], classes: [Int])
-    case multinomial(data: [[Int]], classes: [Int])
-    //case bernoulli(data: [[Bool]], classes: [Int]) --> TODO
-    
-    var classes: [Int] {
-        if case .gaussian(_, let classes) = self {
-            return classes
-        } else if case .multinomial(_, let classes) = self {
-            return classes
-        }
-        
-        return []
-    }
-    
-    var data: [[Any]] {
-        if case .gaussian(let data, _) = self {
-            return data
-        } else if case .multinomial(let data, _) = self {
-            return data
-        }
-        
-        return []
-    }
+    case gaussian
+    case multinomial
+    //case bernoulli --> TODO
     
     func calcLikelihood(variables: [Any], input: Any) -> Double? {
         
@@ -86,12 +68,12 @@ enum NBType {
                 return nil
             }
             
-            guard let input = input as? Double else {
+            guard let input = input as? Int else {
                 return nil
             }
             
             return variables.first { variable in
-                return variable.category == Int(input)
+                return variable.category == input
                 }?.probability
             
         }
@@ -126,49 +108,52 @@ enum NBType {
     }
 }
 
-class NaiveBayes {
+class NaiveBayes<T> {
     
-    private var variables: [Int: [(feature: Int, variables: [Any])]]
-    private var type: NBType
+    var variables: [Int: [(feature: Int, variables: [Any])]]
+    var type: NBType
     
-    init(type: NBType) {
+    var data: [[T]]
+    var classes: [Int]
+    
+    init(type: NBType, data: [[T]], classes: [Int]) throws {
         self.type = type
+        self.data = data
+        self.classes = classes
         self.variables = [Int: [(Int, [Any])]]()
-    }
-    
-    static func convert<T: Any>(dataAndClasses: [[T]], rowOfClasses: Int) -> (data: [[T]], classes: [Int]) {
-        let classes = dataAndClasses.map { Int($0[rowOfClasses] as! Double) } //TODO
         
-        let data = dataAndClasses.map { row in
-            return row.enumerated().filter { $0.offset != rowOfClasses }.map { $0.element }
+        if case .gaussian = type, T.self != Double.self {
+            throw "When using Gaussian NB you have to have continuous features (Double)"
+        } else if case .multinomial = type, T.self != Int.self {
+            throw "When using Multinomial NB you have to have categorical features (Int)"
         }
-        
-        return (data, classes)
     }
     
-    //TODO remake pliss, i dont like this at all
-    func train() {
-        
-        var classes = type.classes
+    func train() throws -> Self {
         
         for `class` in classes.uniques() {
-            
             variables[`class`] = [(Int, [Any])]()
             
-            for feature in 0..<type.data[0].count {
+            let classDependent = data.enumerated().filter { (offset, _) in
+                return classes[offset] == `class`
+            }
+            
+            for feature in 0..<data[0].count {
                 
-                let values = type.data.map { $0[feature] }.enumerated().filter { (offset, _) in
-                    return classes[offset] == `class`
-                    }.map { $0.element }
+                let featureDependent = classDependent.map { $0.element[feature] }
                 
-                let trained = type.train(values: values) ?? [Any]()
+                guard let trained = type.train(values: featureDependent) else {
+                    throw "Critical! Data could not be casted even though it was checked at init"
+                }
                 
                 variables[`class`]?.append((feature, trained))
             }
         }
+        
+        return self
     }
     
-    func classify(with input: [Double]) -> Int {
+    func classify(with input: [T]) -> Int {
         let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
@@ -180,10 +165,8 @@ class NaiveBayes {
         return `class`
     }
     
-    //TODO fix this doesnt have to be a double
-    func classifyProba(with input: [Double]) -> [(Int, Double)] {
+    func classifyProba(with input: [T]) -> [(Int, Double)] {
         
-        let classes = type.classes
         var probaClass = [Int: Double]()
         let amount = classes.count
         
@@ -200,7 +183,7 @@ class NaiveBayes {
         }
         
         let likelihoods = classesAndFeatures.map { (`class`, distribution) in
-            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 1.0))
+            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
         }
         
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
@@ -211,40 +194,3 @@ class NaiveBayes {
         return normalized
     }
 }
-
-guard let csv = try? String(contentsOfFile: "/Users/ph1ps/Desktop/wine.csv") else {
-    print("file not found")
-    exit(0)
-}
-
-let rows = csv.characters.split(separator: "\r\n").map { String($0) }
-let wineData = rows.map { row -> [Double] in
-    let split = row.characters.split(separator: ";")
-    return split.map { Double(String($0))! }
-}
-
-let convertedWine = NaiveBayes.convert(dataAndClasses: wineData, rowOfClasses: 0)
-let wineNaive = NaiveBayes(type: .gaussian(data: convertedWine.data, classes: convertedWine.classes))
-wineNaive.train()
-print(wineNaive.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))
-
-let golfData = [
-    [0, 0, 0, 0],
-    [0, 0, 0, 1],
-    [1, 0, 0, 0],
-    [2, 1, 0, 0],
-    [2, 2, 1, 0],
-    [2, 2, 1, 1],
-    [1, 2, 1, 1],
-    [0, 1, 0, 0],
-    [0, 2, 1, 0],
-    [2, 1, 1, 0],
-    [0, 1, 1, 1],
-    [1, 1, 0, 1],
-    [1, 0, 1, 0],
-    [2, 1, 0, 1]
-]
-let golfClasses =  [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]
-let golfNaive = NaiveBayes(type: .multinomial(data: golfData, classes: golfClasses))
-golfNaive.train()
-print(golfNaive.classifyProba(with: [0, 2, 0, 1]))

From 8ac88ae7fe6134885956502bd9551e7b6cd0a083 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Mon, 17 Apr 2017 21:29:43 +0200
Subject: [PATCH 0946/1679] Change macOS playground to iOS

---
 .../NaiveBayes.playground/Contents.swift      | 51 +++++++++++++++++--
 .../contents.xcplayground                     |  2 +-
 .../NaiveBayes.playground/timeline.xctimeline | 21 ++++++++
 3 files changed, 70 insertions(+), 4 deletions(-)
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
index cb820272e..321e7a04a 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -7,7 +7,7 @@ import Foundation
  
  ### Gaussian Naive Bayes
  - Note:
- When using Gaussian NB you have to have continuous features (Double). 
+ When using Gaussian NB you have to have continuous features (Double).
  
  For this example we are going to use a famous dataset with different types of wine. The labels of the features can be viewed [here](https://gist.github.com/tijptjik/9408623)
  */
@@ -52,9 +52,54 @@ let data = wineData.map { row in
  */
 let wineBayes = try! NaiveBayes(type: .gaussian, data: data, classes: classes).train()
 let result = wineBayes.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015])
-print(result)
 /*:
- I can assure you that this is the correct result and as you can see the classifier thinks that its ***99.99%*** correct too.
+ I can assure you that ***class 1*** is the correct result and as you can see the classifier thinks that its ***99.99%*** likely too.
  
  ### Multinomial Naive Bayes
+ 
+ - Note:
+ When using Multinomial NB you have to have categorical features (Int).
+ 
+ Now this dataset is commonly used to describe the classification problem and it is categorical which means you don't have real values you just have categorical data as stated before. The structure of this dataset is as follows.
+ 
+ Outlook,Temperature,Humidity,Windy
+ 
+ ***Outlook***: 0 = rainy, 1 = overcast, 2 = sunny
+ 
+ ***Temperature***: 0 = hot, 1 = mild, 2 = cool
+ 
+ ***Humidity***: 0 = high, 1 = normal
+ 
+ ***Windy***: 0 = false, 1 = true
+ 
+ The classes are either he will play golf or not depending on the weather conditions. (0 = won't play, 1 = will play)
+ */
+
+let golfData = [
+    [0, 0, 0, 0],
+    [0, 0, 0, 1],
+    [1, 0, 0, 0],
+    [2, 1, 0, 0],
+    [2, 2, 1, 0],
+    [2, 2, 1, 1],
+    [1, 2, 1, 1],
+    [0, 1, 0, 0],
+    [0, 2, 1, 0],
+    [2, 1, 1, 0],
+    [0, 1, 1, 1],
+    [1, 1, 0, 1],
+    [1, 0, 1, 0],
+    [2, 1, 0, 1]
+]
+let golfClasses =  [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]
+
+let golfNaive = try! NaiveBayes(type: .multinomial, data: golfData, classes: golfClasses).train()
+
+/*:
+ The weather conditions is as follows now: Outlook=rainy, Temperature=cool, Humidity=high, Windy=true
+ */
+let golfResult = golfNaive.classifyProba(with: [0, 2, 0, 1])
+
+/*:
+ Naive Bayes tells us that the golf player will ***not*** play with a likelihood of almost ***80%***. Which is true of course.
  */
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
index b1148fc50..35968656f 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='macos' display-mode='raw'>
+<playground version='5.0' target-platform='ios' display-mode='raw'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline
new file mode 100644
index 000000000..b15fdda55
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline	
@@ -0,0 +1,21 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=2051&amp;EndingColumnNumber=14&amp;EndingLineNumber=53&amp;StartingColumnNumber=1&amp;StartingLineNumber=53&amp;Timestamp=514147811.827527"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=6&amp;CharacterRangeLoc=1936&amp;EndingColumnNumber=11&amp;EndingLineNumber=53&amp;StartingColumnNumber=5&amp;StartingLineNumber=53&amp;Timestamp=514147811.848778"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=10&amp;CharacterRangeLoc=3424&amp;EndingColumnNumber=15&amp;EndingLineNumber=100&amp;StartingColumnNumber=5&amp;StartingLineNumber=100&amp;Timestamp=514149150.852782"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>

From d9e36fa2800c2c67e07df17048424903ab5a7eb6 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 18 Apr 2017 13:43:41 +0200
Subject: [PATCH 0947/1679] Missing word

---
 Huffman Coding/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 69e105c87..7058096d0 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -1,6 +1,6 @@
 # Huffman Coding
 
-The idea: To encode objects that occur with a smaller number of bits than objects that occur less frequently.
+The idea: To encode objects that occur often with a smaller number of bits than objects that occur less frequently.
 
 Although any type of objects can be encoded with this scheme, it is common to compress a stream of bytes. Suppose you have the following text, where each character is one byte:
 

From 6c7e9de65cb84da86bb0a5de554f5d13fa6412e6 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 18 Apr 2017 13:45:16 +0200
Subject: [PATCH 0948/1679] Fix alignment

---
 Huffman Coding/README.markdown | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 7058096d0..d1181d215 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -9,13 +9,13 @@ Although any type of objects can be encoded with this scheme, it is common to co
 If you count how often each byte appears, you can see some bytes occur more than others:
 
 	space: 5                  u: 1
-	    o: 5	              h: 1
-	    s: 4	              d: 1
-	    m: 3	              a: 1
-	    w: 3	              y: 1
-	    c: 2	              p: 1
-	    r: 2	              e: 1
-	    n: 2	              i: 1
+	    o: 5                  h: 1
+	    s: 4                  d: 1
+	    m: 3                  a: 1
+	    w: 3                  y: 1
+	    c: 2                  p: 1
+	    r: 2                  e: 1
+	    n: 2                  i: 1
 
 We can assign bit strings to each of these bytes. The more common a byte is, the fewer bits we assign to it. We might get something like this:
 
@@ -23,10 +23,10 @@ We can assign bit strings to each of these bytes. The more common a byte is, the
 	    o: 5    000	          h: 1    10001
 	    s: 4    101	          d: 1    11010
 	    m: 3    111	          a: 1    11011
-	    w: 3    0010	      y: 1    01111
-	    c: 2    0011	      p: 1    11000
-	    r: 2    1001	      e: 1    01110
-	    n: 2    0110	      i: 1    10000
+	    w: 3    0010          y: 1    01111
+	    c: 2    0011          p: 1    11000
+	    r: 2    1001          e: 1    01110
+	    n: 2    0110          i: 1    10000
 
 Now if we replace the original bytes with these bit strings, the compressed output becomes:
 

From 9fafc9278d72240fda1117d010b1544ff106dccb Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Tue, 18 Apr 2017 13:47:17 +0200
Subject: [PATCH 0949/1679] Add README with explanation

---
 .../NaiveBayes.playground/Contents.swift      |  28 ++---
 .../Sources/NaiveBayes.swift                  | 100 +++++++++---------
 .../contents.xcplayground                     |   2 +-
 .../NaiveBayes.playground/timeline.xctimeline |  10 ++
 Naive Bayes Classifier/NaiveBayes.swift       | 100 +++++++++---------
 Naive Bayes Classifier/README.md              |  99 +++++++++++++++++
 Naive Bayes Classifier/images/bayes.gif       | Bin 0 -> 1095 bytes
 .../images/code_example.png                   | Bin 0 -> 122044 bytes
 Naive Bayes Classifier/images/mean.gif        | Bin 0 -> 590 bytes
 Naive Bayes Classifier/images/multinomial.gif | Bin 0 -> 703 bytes
 .../images/normal_distribution.gif            | Bin 0 -> 925 bytes
 .../images/standard_deviation.gif             | Bin 0 -> 1125 bytes
 .../images/tennis_dataset.png                 | Bin 0 -> 61477 bytes
 13 files changed, 224 insertions(+), 115 deletions(-)
 create mode 100644 Naive Bayes Classifier/images/bayes.gif
 create mode 100644 Naive Bayes Classifier/images/code_example.png
 create mode 100644 Naive Bayes Classifier/images/mean.gif
 create mode 100644 Naive Bayes Classifier/images/multinomial.gif
 create mode 100644 Naive Bayes Classifier/images/normal_distribution.gif
 create mode 100644 Naive Bayes Classifier/images/standard_deviation.gif
 create mode 100644 Naive Bayes Classifier/images/tennis_dataset.png

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
index 321e7a04a..66aefaa32 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -2,13 +2,13 @@ import Foundation
 
 /*:
  ## Naive Bayes Classifier
- 
+
  This playground uses the given algorithm and utilizes its features with some example datasets
- 
+
  ### Gaussian Naive Bayes
  - Note:
  When using Gaussian NB you have to have continuous features (Double).
- 
+
  For this example we are going to use a famous dataset with different types of wine. The labels of the features can be viewed [here](https://gist.github.com/tijptjik/9408623)
  */
 guard let wineCSV = Bundle.main.path(forResource: "wine", ofType: "csv") else {
@@ -27,7 +27,7 @@ guard let csv = try? String(contentsOfFile: wineCSV) else {
 let rows = csv.characters.split(separator: "\r\n").map { String($0) }
 /*:
  Splitting on the ; sign and converting the value to a Double
- 
+
  - Important:
  Do not force unwrap the mapped values in your real application. Carefully convert them! This is just for the sake of showing how the algorithm works.
  */
@@ -47,31 +47,31 @@ let data = wineData.map { row in
 
 /*:
  Again use `guard` on the result of a `try?` or simply `do-try-catch` because this would crash your application if an error occured.
- 
+
  The array in the `classifyProba` method I passed is a former entry in the .csv file which I removed in order to classify it.
  */
 let wineBayes = try! NaiveBayes(type: .gaussian, data: data, classes: classes).train()
 let result = wineBayes.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015])
 /*:
  I can assure you that ***class 1*** is the correct result and as you can see the classifier thinks that its ***99.99%*** likely too.
- 
+
  ### Multinomial Naive Bayes
- 
+
  - Note:
  When using Multinomial NB you have to have categorical features (Int).
- 
+
  Now this dataset is commonly used to describe the classification problem and it is categorical which means you don't have real values you just have categorical data as stated before. The structure of this dataset is as follows.
- 
+
  Outlook,Temperature,Humidity,Windy
- 
+
  ***Outlook***: 0 = rainy, 1 = overcast, 2 = sunny
- 
+
  ***Temperature***: 0 = hot, 1 = mild, 2 = cool
- 
+
  ***Humidity***: 0 = high, 1 = normal
- 
+
  ***Windy***: 0 = false, 1 = true
- 
+
  The classes are either he will play golf or not depending on the weather conditions. (0 = won't play, 1 = will play)
  */
 
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift
index 3af8102c7..6e6d7b4c0 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift	
@@ -11,186 +11,186 @@ import Foundation
 extension String: Error {}
 
 extension Array where Element == Double {
-    
+
     func mean() -> Double {
         return self.reduce(0, +) / Double(count)
     }
-    
+
     func standardDeviation() -> Double {
         let calculatedMean = mean()
-        
+
         let sum = self.reduce(0.0) { (previous, next) in
             return previous + pow(next - calculatedMean, 2)
         }
-        
+
         return sqrt(sum / Double(count - 1))
     }
 }
 
 extension Array where Element == Int {
-    
+
     func uniques() -> Set<Element> {
         return Set(self)
     }
-    
+
 }
 
 public enum NBType {
-    
+
     case gaussian
     case multinomial
     //case bernoulli --> TODO
-    
+
     func calcLikelihood(variables: [Any], input: Any) -> Double? {
-        
+
         if case .gaussian = self {
-            
+
             guard let input = input as? Double else {
                 return nil
             }
-            
+
             guard let mean = variables[0] as? Double else {
                 return nil
             }
-            
+
             guard let stDev = variables[1] as? Double else {
                 return nil
             }
-            
+
             let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
             let distribution = eulerPart / sqrt(2 * .pi) / stDev
-            
+
             return distribution
-            
+
         } else if case .multinomial = self {
-            
+
             guard let variables = variables as? [(category: Int, probability: Double)] else {
                 return nil
             }
-            
+
             guard let input = input as? Int else {
                 return nil
             }
-            
+
             return variables.first { variable in
                 return variable.category == input
                 }?.probability
-            
+
         }
-        
+
         return nil
     }
-    
+
     func train(values: [Any]) -> [Any]? {
-        
+
         if case .gaussian = self {
-            
+
             guard let values = values as? [Double] else {
                 return nil
             }
-            
+
             return [values.mean(), values.standardDeviation()]
-            
+
         } else if case .multinomial = self {
-            
+
             guard let values = values as? [Int] else {
                 return nil
             }
-            
+
             let count = values.count
             let categoryProba = values.uniques().map { value -> (Int, Double) in
                 return (value, Double(values.filter { $0 == value }.count) / Double(count))
             }
             return categoryProba
         }
-        
+
         return nil
     }
 }
 
 public class NaiveBayes<T> {
-    
+
     var variables: [Int: [(feature: Int, variables: [Any])]]
     var type: NBType
-    
+
     var data: [[T]]
     var classes: [Int]
-    
+
     public init(type: NBType, data: [[T]], classes: [Int]) throws {
         self.type = type
         self.data = data
         self.classes = classes
         self.variables = [Int: [(Int, [Any])]]()
-        
+
         if case .gaussian = type, T.self != Double.self {
             throw "When using Gaussian NB you have to have continuous features (Double)"
         } else if case .multinomial = type, T.self != Int.self {
             throw "When using Multinomial NB you have to have categorical features (Int)"
         }
     }
-    
+
     public func train() throws -> Self {
-        
+
         for `class` in classes.uniques() {
             variables[`class`] = [(Int, [Any])]()
-            
+
             let classDependent = data.enumerated().filter { (offset, _) in
                 return classes[offset] == `class`
             }
-            
+
             for feature in 0..<data[0].count {
-                
+
                 let featureDependent = classDependent.map { $0.element[feature] }
-                
+
                 guard let trained = type.train(values: featureDependent) else {
                     throw "Critical! Data could not be casted even though it was checked at init"
                 }
-                
+
                 variables[`class`]?.append((feature, trained))
             }
         }
-        
+
         return self
     }
-    
+
     public func classify(with input: [T]) -> Int {
         let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
-        
+
         guard let `class` = likelihoods?.0 else {
             return -1
         }
-        
+
         return `class`
     }
-    
+
     public func classifyProba(with input: [T]) -> [(Int, Double)] {
-        
+
         var probaClass = [Int: Double]()
         let amount = classes.count
-        
+
         classes.forEach { `class` in
             let individual = classes.filter { $0 == `class` }.count
             probaClass[`class`] = Double(individual) / Double(amount)
         }
-        
+
         let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
             let distribution = value.map { (feature, variables) -> Double in
                 return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
             }
             return (`class`, distribution)
         }
-        
+
         let likelihoods = classesAndFeatures.map { (`class`, distribution) in
             return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
         }
-        
+
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
         let normalized = likelihoods.map { (`class`, likelihood) in
             return (`class`, likelihood / sum)
         }
-        
+
         return normalized
     }
 }
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
index 35968656f..89da2d470 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios' display-mode='raw'>
+<playground version='5.0' target-platform='ios' display-mode='rendered'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline
index b15fdda55..7bc414f58 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline	
@@ -17,5 +17,15 @@
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=10&amp;CharacterRangeLoc=3410&amp;EndingColumnNumber=15&amp;EndingLineNumber=100&amp;StartingColumnNumber=5&amp;StartingLineNumber=100&amp;Timestamp=514208705.303681"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=6&amp;CharacterRangeLoc=1931&amp;EndingColumnNumber=11&amp;EndingLineNumber=53&amp;StartingColumnNumber=5&amp;StartingLineNumber=53&amp;Timestamp=514208705.303681"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
    </TimelineItems>
 </Timeline>
diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index 9b9ace86d..46a0bb4f5 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -11,186 +11,186 @@ import Foundation
 extension String: Error {}
 
 extension Array where Element == Double {
-    
+
     func mean() -> Double {
         return self.reduce(0, +) / Double(count)
     }
-    
+
     func standardDeviation() -> Double {
         let calculatedMean = mean()
-        
+
         let sum = self.reduce(0.0) { (previous, next) in
             return previous + pow(next - calculatedMean, 2)
         }
-        
+
         return sqrt(sum / Double(count - 1))
     }
 }
 
 extension Array where Element == Int {
-    
+
     func uniques() -> Set<Element> {
         return Set(self)
     }
-    
+
 }
 
 enum NBType {
-    
+
     case gaussian
     case multinomial
     //case bernoulli --> TODO
-    
+
     func calcLikelihood(variables: [Any], input: Any) -> Double? {
-        
+
         if case .gaussian = self {
-            
+
             guard let input = input as? Double else {
                 return nil
             }
-            
+
             guard let mean = variables[0] as? Double else {
                 return nil
             }
-            
+
             guard let stDev = variables[1] as? Double else {
                 return nil
             }
-            
+
             let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
             let distribution = eulerPart / sqrt(2 * .pi) / stDev
-            
+
             return distribution
-            
+
         } else if case .multinomial = self {
-            
+
             guard let variables = variables as? [(category: Int, probability: Double)] else {
                 return nil
             }
-            
+
             guard let input = input as? Int else {
                 return nil
             }
-            
+
             return variables.first { variable in
                 return variable.category == input
                 }?.probability
-            
+
         }
-        
+
         return nil
     }
-    
+
     func train(values: [Any]) -> [Any]? {
-        
+
         if case .gaussian = self {
-            
+
             guard let values = values as? [Double] else {
                 return nil
             }
-            
+
             return [values.mean(), values.standardDeviation()]
-            
+
         } else if case .multinomial = self {
-            
+
             guard let values = values as? [Int] else {
                 return nil
             }
-            
+
             let count = values.count
             let categoryProba = values.uniques().map { value -> (Int, Double) in
                 return (value, Double(values.filter { $0 == value }.count) / Double(count))
             }
             return categoryProba
         }
-        
+
         return nil
     }
 }
 
 class NaiveBayes<T> {
-    
+
     var variables: [Int: [(feature: Int, variables: [Any])]]
     var type: NBType
-    
+
     var data: [[T]]
     var classes: [Int]
-    
+
     init(type: NBType, data: [[T]], classes: [Int]) throws {
         self.type = type
         self.data = data
         self.classes = classes
         self.variables = [Int: [(Int, [Any])]]()
-        
+
         if case .gaussian = type, T.self != Double.self {
             throw "When using Gaussian NB you have to have continuous features (Double)"
         } else if case .multinomial = type, T.self != Int.self {
             throw "When using Multinomial NB you have to have categorical features (Int)"
         }
     }
-    
+
     func train() throws -> Self {
-        
+
         for `class` in classes.uniques() {
             variables[`class`] = [(Int, [Any])]()
-            
+
             let classDependent = data.enumerated().filter { (offset, _) in
                 return classes[offset] == `class`
             }
-            
+
             for feature in 0..<data[0].count {
-                
+
                 let featureDependent = classDependent.map { $0.element[feature] }
-                
+
                 guard let trained = type.train(values: featureDependent) else {
                     throw "Critical! Data could not be casted even though it was checked at init"
                 }
-                
+
                 variables[`class`]?.append((feature, trained))
             }
         }
-        
+
         return self
     }
-    
+
     func classify(with input: [T]) -> Int {
         let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
-        
+
         guard let `class` = likelihoods?.0 else {
             return -1
         }
-        
+
         return `class`
     }
-    
+
     func classifyProba(with input: [T]) -> [(Int, Double)] {
-        
+
         var probaClass = [Int: Double]()
         let amount = classes.count
-        
+
         classes.forEach { `class` in
             let individual = classes.filter { $0 == `class` }.count
             probaClass[`class`] = Double(individual) / Double(amount)
         }
-        
+
         let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
             let distribution = value.map { (feature, variables) -> Double in
                 return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
             }
             return (`class`, distribution)
         }
-        
+
         let likelihoods = classesAndFeatures.map { (`class`, distribution) in
             return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
         }
-        
+
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
         let normalized = likelihoods.map { (`class`, likelihood) in
             return (`class`, likelihood / sum)
         }
-        
+
         return normalized
     }
 }
diff --git a/Naive Bayes Classifier/README.md b/Naive Bayes Classifier/README.md
index e69de29bb..9c0f0082a 100644
--- a/Naive Bayes Classifier/README.md	
+++ b/Naive Bayes Classifier/README.md	
@@ -0,0 +1,99 @@
+# Naive Bayes Classifier
+
+> ***Disclaimer:*** Do not get scared of complicated formulas or terms, I will describe them right after I use them. Also the math skills you need to understand this are very basic.
+
+The goal of a classifier is to predict the class of a given data entry based on previously fed data and its features. 
+
+Now what is a class or a feature? The best I can do is to describe it with a table. 
+This is a dataset that uses height, weight and foot size of a person to illustrate the relationship between those values and the sex.
+
+| Sex       | height (feet)          | weight(lbs)  | foot size (inches) |
+| ------------- |:-------------:|:-----:|:---:|
+| male      | 6     | 180 | 12  |
+| male      | 5.92  | 190 | 11  |
+| male      | 5.58  | 170 | 12  |
+| male      | 5.92  | 165 | 10  |
+| female    | 5     | 100 | 6   |
+| female    | 5.5   | 150 | 8   |
+| female    | 5.42  | 130 | 7   |
+| female    | 5.75  | 150 | 9   |
+
+The ***classes*** of this table is the data in the sex column (male/female). You "classify" the rest of the data and bind them to a sex.
+
+The ***features*** of this table are the labels of the other columns (height, weight, foot size) and the numbers right under the labels.
+
+Now that I've told you what a classifier is I will tell you what exactly a ***Naive Bayes classifier*** is. There are a lot of other classifiers out there but what's so special about this specific is that it only needs a very small dataset to get good results. The others like Random Forests normally need a very large dataset.
+
+Why isn't this algorithm used more you might ask (or not). Because it is normally ***outperformed*** in accuracy by ***Random Forests*** or ***Boosted Trees***.
+
+## Theory
+
+The Naive Bayes classifier utilizes the ***Bayes Theorem*** (as its name suggests) which looks like this.
+
+![](images/bayes.gif)
+
+***P*** always means the probability of something.
+
+***A*** is the class, ***B*** is the data depending on a feature and the ***pipe*** symbol means given. 
+
+P(A | B) therefore is: probability of the class given the data (which is dependent on the feature).
+
+This is all you have to know about the Bayes Theorem. The important thing for us is now how to calculate all those variables, plug them into this formula and you are ready to classify data.
+
+### **P(A)**
+This is the probability of the class. To get back to the example I gave before: Let's say we want to classify this data entry:
+
+| height (feet)          | weight(lbs)  | foot size (inches) |
+|:-------------:|:-----:|:---:|
+| 6     | 130 | 8  |
+
+What Naive Bayes classifier now does: it checks the probability for every class possible which is in our case either male or female. Look back at the original table and count the male and the female entries. Then divide them by the overall count of data entries.
+
+P(male) = 4 / 8 = 0.5
+
+P(female) = 4 / 8 = 0.5
+
+This should be a very easy task to do. Basically just the probability of all classes.
+
+### **P(B)**
+This variable is not needed in a Naive Bayes classifier. It is the probability of the data. It does not change, therefore it is a constant. And what can you do with a constant? Exactly! Discard it. This saves time and code.
+
+### **P(B | A)**
+This is the probability of the data given the class. To calculate this I have to introduce you to the subtypes of NB. You have to decide which you use depending on your data which you want to classify.
+
+### **Gaussian Naive Bayes**
+If you have a dataset like the one I showed you before (continuous features -> `Double`s) you have to use this subtype. There are 3 formulas you need for Gaussian NB to calculate P(B | A).
+
+![mean](images/mean.gif)
+
+![standard deviation](images/standard_deviation.gif)
+
+![normal distribution](images/normal_distribution.gif)
+
+and **P(x | y) = P(B | A)**
+
+Again, very complicated looking formulas but they are very easy. The first formula with µ is just the mean of the data (adding all data points and dividing them by the count). The second with σ is the standard deviation. You might have heard of it somewhen in school. It is just the sum of all values minus the mean, squared and that divided by the count of the data minus 1 and a sqaure root around it. The third equation is the Gaussian or normal distribution if you want to read more about it I suggest reading [this](https://en.wikipedia.org/wiki/Normal_distribution).
+
+Why the Gaussian distribution? Because we assume that the continuous values associated with each class are distributed according to the Gaussian distribution. Simple as that.
+
+### **Multinomial Naive Bayes**
+
+What do we do if we have this for examples:
+
+![tennis or golf](images/tennis_dataset.png)
+
+We can't just calculate the mean of sunny, overcast and rainy. This is why we need the categorical model which is the multinomial NB. This is the last formula, I promise!
+
+![multinomial](images/multinomial.gif)
+
+Now this is the number of times feature **i** appears in a sample **N** of class **y** in the data set divided by the count of the sample just depending on the class **y**. That θ is also just a fancy way of writing P(B | A).
+
+You might have noticed that there is still the α in this formula. This solves a problem called "zero-frequency-problem". Because what happens if there is no sample with feature **i** and class **y**? The whole equation would result in 0 (because 0 / something is always 0). This is a huge problem but there is a simple solution to this. Just add 1 to any count of the sample (α = 1).
+
+## Those formulas in action
+
+Enough talking! This is the code. If you want a deeper explanation of how the code works just look at the Playground I provided.
+
+![code example](images/code_example.png)
+
+*Written for Swift Algorithm Club by Philipp Gabriel*
\ No newline at end of file
diff --git a/Naive Bayes Classifier/images/bayes.gif b/Naive Bayes Classifier/images/bayes.gif
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literal 0
HcmV?d00001


From 149515f17494f0a9c790fbfa84dca3e6b926887e Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 19 Apr 2017 16:44:55 +0300
Subject: [PATCH 0950/1679] Replaced _vertices with vertices

---
 .../Dijkstra.playground/Contents.swift          | 17 +++++++++--------
 1 file changed, 9 insertions(+), 8 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index cd08e26fb..1c12245bd 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,19 +1,19 @@
 //: Playground - noun: a place where people can play
 import Foundation
 
-var _vertices: Set<Vertex> = Set()
+var vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
     //change this value to increase or decrease amount of vertices in the graph
     let numberOfVerticesInGraph = 15
     for i in 0..<numberOfVerticesInGraph {
         let vertex = Vertex(identifier: "\(i)")
-        _vertices.insert(vertex)
+        vertices.insert(vertex)
     }
 }
 
 func setupConnections() {
-    for vertex in _vertices {
+    for vertex in vertices {
         let randomEdgesCount = arc4random_uniform(4) + 1
         for _ in 0..<randomEdgesCount {
             let randomWeight = Double(arc4random_uniform(10))
@@ -30,7 +30,7 @@ func setupConnections() {
 }
 
 func randomVertex(except vertex: Vertex) -> Vertex {
-    var newSet = _vertices
+    var newSet = vertices
     newSet.remove(vertex)
     let offset = Int(arc4random_uniform(UInt32(newSet.count)))
     let index = newSet.index(newSet.startIndex, offsetBy: offset)
@@ -38,9 +38,9 @@ func randomVertex(except vertex: Vertex) -> Vertex {
 }
 
 func randomVertex() -> Vertex {
-    let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
-    let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
-    return _vertices[index]
+    let offset = Int(arc4random_uniform(UInt32(vertices.count)))
+    let index = vertices.index(vertices.startIndex, offsetBy: offset)
+    return vertices[index]
 }
 
 //initialize random graph
@@ -48,7 +48,7 @@ createNotConnectedVertices()
 setupConnections()
 
 //initialize Dijkstra algorithm with graph vertices
-let dijkstra = Dijkstra(vertices: _vertices)
+let dijkstra = Dijkstra(vertices: vertices)
 
 //decide which vertex will be the starting one
 let startVertex = randomVertex()
@@ -63,6 +63,7 @@ var pathVerticesFromStartString: [String] = []
 for vertex in destinationVertex.pathVerticesFromStart {
     pathVerticesFromStartString.append(vertex.identifier)
 }
+
 print(pathVerticesFromStartString.joined(separator: "->"))
 
 

From 93aad5ea36a1f09d62c8c877675877097e9b29fc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 03:39:21 -0700
Subject: [PATCH 0951/1679] Added templates for the repository.

---
 .github/CONTRIBUTING.md          |  0
 .github/ISSUE_TEMPLATE.md        | 19 +++++++++++++++++++
 .github/PULL_REQUEST_TEMPLATE.md |  0
 3 files changed, 19 insertions(+)
 create mode 100644 .github/CONTRIBUTING.md
 create mode 100644 .github/ISSUE_TEMPLATE.md
 create mode 100644 .github/PULL_REQUEST_TEMPLATE.md

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
new file mode 100644
index 000000000..e69de29bb
diff --git a/.github/ISSUE_TEMPLATE.md b/.github/ISSUE_TEMPLATE.md
new file mode 100644
index 000000000..27a857ef5
--- /dev/null
+++ b/.github/ISSUE_TEMPLATE.md
@@ -0,0 +1,19 @@
+### Category
+
+- [ ] Bug
+- [ ] Feature Request
+- [ ] Question
+
+### Brief Intro
+
+> Describe this issue below in 1 sentence.
+
+### More Details
+
+> If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.
+
+[INSERT CODE HERE]
+
+> Describe the problem in more detail.
+
+[INSERT DETAILS HERE]
\ No newline at end of file
diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md
new file mode 100644
index 000000000..e69de29bb

From 5128bfa4dca199beeda930dacf0623d7f6e0e926 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:32:41 -0700
Subject: [PATCH 0952/1679] Updated contribution guidelines.

---
 .github/CONTRIBUTING.md | 57 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index e69de29bb..a1393a2e0 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -0,0 +1,57 @@
+# Contributing Guidelines
+
+Want to help out with the Swift Algorithm Club? Great! While we don't have strict templates on the format of each contribution, we do have a few guidelines that should be kept in mind:
+
+**Readability**
+
+The `README` file is the cake, and the sample code is the cherry on top. Readablity is really important for us. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
+
+**API Design Guidelines**
+
+A good contribution abides to the [Swift API Guidelines](https://swift.org/documentation/api-design-guidelines/). We review the pull requests with this in mind.
+
+**Swift Language Guidelines**
+
+We follow the following Swift [style guide](https://github.com/raywenderlich/swift-style-guide). 
+
+### Contribution Categories
+
+### Refinement
+
+Unit tests. Fixes for typos. No contribution is too small. :-)
+
+The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library is most welcomed. 
+
+### New Contributions
+
+Before writing about something new, you should do 2 things:
+
+1. Check the main page for existing implementations
+2. Check the [pull requests](https://github.com/raywenderlich/swift-algorithm-club/pulls) for "claimed" topics. More info on that below. 
+
+If what you have in mind is a new addition, please follow this process when submitting your contribution:
+
+1. Create a pull request to "claim" an algorithm or data structure. This is to avoid having multiple people working on the same thing.
+2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
+3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
+4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
+5. Add a playground and/or unit tests.
+
+For the unit tests:
+
+- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/raywenderlich/swift-algorithm-club). Add a line to `.travis.yml` like this:
+
+```
+- xctool test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
+```
+
+- Configure the Test project's scheme to run on Travis-CI:
+    - Open **Product -> Scheme -> Manage Schemes...**
+    - Uncheck **Autocreate schemes**
+    - Check **Shared**
+
+![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
+
+## Want to chat?
+
+This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!
\ No newline at end of file

From 1e149dc959731e16eb303396293e1e719f86d2ef Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:33:33 -0700
Subject: [PATCH 0953/1679] Fixed broken link.

---
 .github/CONTRIBUTING.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index a1393a2e0..fe8a23278 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -50,7 +50,7 @@ For the unit tests:
     - Uncheck **Autocreate schemes**
     - Check **Shared**
 
-![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
+![Screenshot of scheme settings](../Images/scheme-settings-for-travis.png)
 
 ## Want to chat?
 

From 1620a9cb811ecac68528c8f330f45762ec1beb6a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:34:11 -0700
Subject: [PATCH 0954/1679] Fixes another broken link in the readme.

---
 .github/CONTRIBUTING.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index fe8a23278..5b6f5d4dd 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -33,7 +33,7 @@ If what you have in mind is a new addition, please follow this process when subm
 
 1. Create a pull request to "claim" an algorithm or data structure. This is to avoid having multiple people working on the same thing.
 2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
-3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
+3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](../Quicksort/) to get an idea.
 4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
 5. Add a playground and/or unit tests.
 

From d83263cd7e2dcd13e7e2e8ad7c9f624fab337a00 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:43:55 -0700
Subject: [PATCH 0955/1679] Updated issue and pr template.

---
 .github/ISSUE_TEMPLATE.md        | 10 ++--------
 .github/PULL_REQUEST_TEMPLATE.md | 11 +++++++++++
 2 files changed, 13 insertions(+), 8 deletions(-)

diff --git a/.github/ISSUE_TEMPLATE.md b/.github/ISSUE_TEMPLATE.md
index 27a857ef5..416641261 100644
--- a/.github/ISSUE_TEMPLATE.md
+++ b/.github/ISSUE_TEMPLATE.md
@@ -6,14 +6,8 @@
 
 ### Brief Intro
 
-> Describe this issue below in 1 sentence.
+<!-- Describe the issue briefly.-->
 
 ### More Details
 
-> If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.
-
-[INSERT CODE HERE]
-
-> Describe the problem in more detail.
-
-[INSERT DETAILS HERE]
\ No newline at end of file
+<!-- If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.-->
\ No newline at end of file
diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md
index e69de29bb..c52564721 100644
--- a/.github/PULL_REQUEST_TEMPLATE.md
+++ b/.github/PULL_REQUEST_TEMPLATE.md
@@ -0,0 +1,11 @@
+<!-- Thanks for contributing to the SAC! Before you submit your pull request, please make sure to check the following boxes by putting an x in the [ ] -->
+
+### Checklist
+
+- [ ] I've looked at the [contribution guidelines](https://github.com/raywenderlich/swift-algorithm-club/blob/master/.github/CONTRIBUTING.md).
+- [ ] This pull request is complete and ready for review.
+
+### Description
+
+<!-- In a short paragraph, describe the PR --> 
+

From bb6c29fee3cf3549c56cf5fb351bf01b15301177 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:45:44 -0700
Subject: [PATCH 0956/1679] Fixes formatting.

---
 .github/CONTRIBUTING.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index 5b6f5d4dd..2b08e2633 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -14,7 +14,7 @@ A good contribution abides to the [Swift API Guidelines](https://swift.org/docum
 
 We follow the following Swift [style guide](https://github.com/raywenderlich/swift-style-guide). 
 
-### Contribution Categories
+## Contribution Categories
 
 ### Refinement
 

From aadae31ed56f8317eae20e94196b2c242994d1fb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:54:06 -0700
Subject: [PATCH 0957/1679] Updated readme with links to updated/new
 contributions.

---
 README.markdown | 19 +++++++------------
 1 file changed, 7 insertions(+), 12 deletions(-)

diff --git a/README.markdown b/README.markdown
index 29fc9d748..e0983f22e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,9 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Most code is compatible with **Xcode 8.2** and **Swift 3**. We'll keep this updated with the latest version of Swift.
-
-This is a work in progress. More algorithms will be added soon. :-)
+Most code is compatible with **Xcode 8.3** and **Swift 3**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 
@@ -24,9 +22,7 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 [Algorithm design techniques](Algorithm%20Design.markdown). How do you create your own algorithms?
 
-[How to contribute](How%20to%20Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
-
-[Under construction](Under%20Construction.markdown). Algorithms that are under construction.
+[How to contribute](https://github.com/raywenderlich/swift-algorithm-club/blob/master/.github/CONTRIBUTING.md). Report an issue to leave feedback, or submit a pull request.
 
 ## Where to start?
 
@@ -56,7 +52,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 
 - [Brute-Force String Search](Brute-Force%20String%20Search/). A naive method.
 - [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
-- Knuth-Morris-Pratt
+- [Knuth-Morris-Pratt](Knuth-Morris-Pratt/). A linear-time string algorithm that returns indexes of all occurrencies of a given pattern.
 - [Rabin-Karp](Rabin-Karp/)  Faster search by using hashing.
 - [Longest Common Subsequence](Longest%20Common%20Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
 - [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
@@ -103,7 +99,6 @@ Bad sorting algorithms (don't use these!):
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
 - [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
 - [Shunting Yard Algorithm](Shunting%20Yard/). Convert infix expressions to postfix.
-- Statistics
 - [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
 - [Strassen's Multiplication Matrix](Strassen%20Matrix%20Multiplication/). Efficient way to handle matrix multiplication.
@@ -112,7 +107,7 @@ Bad sorting algorithms (don't use these!):
 
 - [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
-- [Linear Regression](Linear%20Regression/)
+- [Linear Regression](Linear%20Regression/). A technique for creating a model of the relationship between two (or more) variable quantities.
 - Logistic Regression
 - Neural Networks
 - PageRank
@@ -153,9 +148,9 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Tree](Tree/). A general-purpose tree structure.
 - [Binary Tree](Binary%20Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary%20Search%20Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
-- Red-Black Tree
+- [Red-Black Tree](Red-Black%20Tree/). A self balancing binary search tree.
 - Splay Tree
-- Threaded Binary Tree
+- [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
@@ -226,7 +221,7 @@ Other algorithm repositories:
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
 
-It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka) and [Kelvin Lau](https://github.com/kelvinlauKL).
+It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL) and [Ross O'brien](https://www.raywenderlich.com/u/narrativium).
 
 The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How%20to%20Contribute.markdown)? :]
 

From 2ce23ca2b1059050be7c87cf45df184dd5090008 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:55:50 -0700
Subject: [PATCH 0958/1679] Removed old contribution guidelines.

---
 How to Contribute.markdown | 55 --------------------------------------
 1 file changed, 55 deletions(-)
 delete mode 100644 How to Contribute.markdown

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
deleted file mode 100644
index 1235f07ff..000000000
--- a/How to Contribute.markdown	
+++ /dev/null
@@ -1,55 +0,0 @@
-# How to contribute
-
-Want to help out with the Swift Algorithm Club? Great!
-
-## What sort of things can you contribute?
-
-Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
-
-Algorithms in the [Under construction](Under%20Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
-
-New algorithms and data structures are always welcome (even if they aren't on the list).
-
-We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library.
-
-Unit tests. Fixes for typos. No contribution is too small. :-)
-
-## Please follow this process
-
-To keep this a high quality repo, please follow this process when submitting your contribution:
-
-1. Create a pull request to "claim" an algorithm or data structure. Just so multiple people don't work on the same thing.
-2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
-3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
-4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
-5. Add a playground and/or unit tests.
-6. Run [SwiftLint](https://github.com/realm/SwiftLint)  
-  - [Install](https://github.com/realm/SwiftLint#installation)
-  - Open terminal and run the `swiftlint` command:
-
-```
-cd path/to/swift-algorithm-club
-swiftlint
-```
-
-
-Just so you know, I will probably edit your text and code for grammar etc, just to ensure a certain level of polish.
-
-For the unit tests:
-
-- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/raywenderlich/swift-algorithm-club). Add a line to `.travis.yml` like this:
-
-```
-- xctool test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
-```
-
-- Configure the Test project's scheme to run on Travis-CI:
-    - Open **Product -> Scheme -> Manage Schemes...**
-    - Uncheck **Autocreate schemes**
-    - Check **Shared**
-
-![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
-
-## Want to chat?
-
-This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!

From 37de447879960291131d97aecb3d56c89da77429 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:07:29 +0300
Subject: [PATCH 0959/1679] Updating

---
 Dijkstra Algorithm/README.md | 61 +++++++++++++++++++++++++++++++-----
 1 file changed, 53 insertions(+), 8 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 325bab40f..7ec9d352e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,19 +1,59 @@
 # Dijkstra-algorithm
 
-## About this repository
+This algorithm was invented in 1956 by Edsger W. Dijkstra. 
+
+This algorithm can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
+
+The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
+
+I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
+So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+When the algorithm starts to work initial graph looks like this:
+[image1.png all are non visited]
+Graph's array contains 5 vertices [A, B, C, D, E].
+Let's assume, that edge weight it is path length in kilometers between vertices.
+A vertex has neighbors: B(path from A: 5.0), C(path from A: 0.0), D(path from A: 0.0)
+And because algorithm has done nothing, then all vertices' path length from source vertex values are infinity (think about infinity as "I don't know, how long will it takes to get this vertex from source one")
+Finally we have to set source vertex path length from source vertex to 0.
+
+Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
+
+|                           |  A  |  B  |  C  |  D  |  E  |
+| ------------------------- | --- | --- | --- | --- | --- |
+| Visited                   |  F  |  F  |  F  |  F  |  F  |
+| Path Length From Start    | inf | inf | inf | inf | inf |
+| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
+
+But before we will go through all process side by side let me explain how algorithm works.
+The algorithm repeats following cycle until all vertices are marked as visited.
+Cycle:
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+2. The algorithm marks picked vertex as visited.
+3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+
+Okay, let's start!
+From now we will keep array which contains non visited vertices. Here they are:
+var nonVisitedVertices = [A, B, C, D, E]
+Let's follow the algorithm and pick the first vertex, which neighbors we want to check.
+Imagine that we have function, that returns vertex with smallest path length from start.
+var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
+Then we set this vertex as visited 
+checkingVertex.visited = true
+[image2.jpg visited first]
+Then we check all of its neighbors. 
+If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+[image3.jpg visited first with checked neighbors]
+
+
+
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-## Demo video
-Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
-
-## Screenshots
-<img src="Images/screenshot1.jpg" height="400" />
-
 ## Dijkstra's algorithm explanation
 
-<img src="Images/Dijkstra_Animation.gif" height="250" />
+
 
 [Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)'s explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
@@ -37,8 +77,13 @@ Cycle:
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
 ## Usage
+This algorithm is popular in routing. For example, biggest Russian IT company Yandex uses it in [Яндекс.Карты](https://yandex.ru/company/technologies/routes/)
 
+## Demo video
+Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
+## VisualizedDijkstra.playground Screenshots
+<img src="Images/screenshot1.jpg" height="400" />
 
 ## Credits
 WWDC 2017 Scholarship Project  

From f24ecc22436be2b71f6c840464d6826ddf9e258c Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:30:59 +0300
Subject: [PATCH 0960/1679] Still updating

---
 Dijkstra Algorithm/Images/image1.png | Bin 0 -> 61926 bytes
 Dijkstra Algorithm/Images/image2.png | Bin 0 -> 63758 bytes
 Dijkstra Algorithm/Images/image3.png | Bin 0 -> 65232 bytes
 Dijkstra Algorithm/Images/image4.png | Bin 0 -> 65286 bytes
 Dijkstra Algorithm/Images/image5.png | Bin 0 -> 66333 bytes
 Dijkstra Algorithm/Images/image6.png | Bin 0 -> 67070 bytes
 Dijkstra Algorithm/Images/image7.png | Bin 0 -> 66716 bytes
 Dijkstra Algorithm/README.md         |  66 +++++++++++++++++++++------
 8 files changed, 52 insertions(+), 14 deletions(-)
 create mode 100644 Dijkstra Algorithm/Images/image1.png
 create mode 100644 Dijkstra Algorithm/Images/image2.png
 create mode 100644 Dijkstra Algorithm/Images/image3.png
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diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 7ec9d352e..9a48bbeb3 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,7 +9,15 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[image1.png all are non visited]
+[image1.png]
+
+The table below will represent graph state
+|                           |  A  |  B  |  C  |  D  |  E  |
+| ------------------------- | --- | --- | --- | --- | --- |
+| Visited                   |  F  |  F  |  F  |  F  |  F  |
+| Path Length From Start    | inf | inf | inf | inf | inf |
+| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
+
 Graph's array contains 5 vertices [A, B, C, D, E].
 Let's assume, that edge weight it is path length in kilometers between vertices.
 A vertex has neighbors: B(path from A: 5.0), C(path from A: 0.0), D(path from A: 0.0)
@@ -18,12 +26,6 @@ Finally we have to set source vertex path length from source vertex to 0.
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 
-|                           |  A  |  B  |  C  |  D  |  E  |
-| ------------------------- | --- | --- | --- | --- | --- |
-| Visited                   |  F  |  F  |  F  |  F  |  F  |
-| Path Length From Start    | inf | inf | inf | inf | inf |
-| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
-
 But before we will go through all process side by side let me explain how algorithm works.
 The algorithm repeats following cycle until all vertices are marked as visited.
 Cycle:
@@ -39,13 +41,52 @@ Let's follow the algorithm and pick the first vertex, which neighbors we want to
 Imagine that we have function, that returns vertex with smallest path length from start.
 var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
 Then we set this vertex as visited 
+
+|                           |  A  |  B  |  C  |  D  |  E  |
+| ------------------------- | --- | --- | --- | --- | --- |
+| Visited                   |  T  |  F  |  F  |  F  |  F  |
+| Path Length From Start    |  0  | inf | inf | inf | inf |
+| Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
+
 checkingVertex.visited = true
-[image2.jpg visited first]
+[image2.jpg]
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[image3.jpg visited first with checked neighbors]
-
-
+[image3.jpg]
+
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     F      |     F      |     F      |     F      |
+| Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
+| Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
+
+[image4.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     F      |     F      |     T      |     F      |
+| Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
+
+[image5.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     F      |     F      |     T      |     T      |
+| Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
+
+[image6.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     T      |     F      |     T      |     T      |
+| Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
+
+[image7.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     T      |     T      |     T      |     T      |
+| Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
@@ -82,9 +123,6 @@ This algorithm is popular in routing. For example, biggest Russian IT company Ya
 ## Demo video
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
-## VisualizedDijkstra.playground Screenshots
-<img src="Images/screenshot1.jpg" height="400" />
-
 ## Credits
 WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From fb4c63bc92ac909159528e2e1c3f16d99eb9665a Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:32:05 +0300
Subject: [PATCH 0961/1679] Tables fix

---
 Dijkstra Algorithm/README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 9a48bbeb3..132f4e5bd 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -12,6 +12,7 @@ When the algorithm starts to work initial graph looks like this:
 [image1.png]
 
 The table below will represent graph state
+
 |                           |  A  |  B  |  C  |  D  |  E  |
 | ------------------------- | --- | --- | --- | --- | --- |
 | Visited                   |  F  |  F  |  F  |  F  |  F  |
@@ -61,6 +62,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
 [image4.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     F      |     F      |     T      |     F      |
@@ -68,6 +70,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
 [image5.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     F      |     F      |     T      |     T      |
@@ -75,6 +78,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
 [image6.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     T      |     F      |     T      |     T      |
@@ -82,6 +86,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
 [image7.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     T      |     T      |     T      |     T      |

From cce96e2694e71e473f30817a535a97a6d59591f3 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:34:16 +0300
Subject: [PATCH 0962/1679] Updating

---
 Dijkstra Algorithm/README.md | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 132f4e5bd..cb0683e5d 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,12 +9,12 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[image1.png]
+[images/image1.png]
 
 The table below will represent graph state
 
 |                           |  A  |  B  |  C  |  D  |  E  |
-| ------------------------- | --- | --- | --- | --- | --- |
+|:------------------------- |:---:|:---:|:---:|:---:|:---:|
 | Visited                   |  F  |  F  |  F  |  F  |  F  |
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
@@ -44,51 +44,51 @@ var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
 Then we set this vertex as visited 
 
 |                           |  A  |  B  |  C  |  D  |  E  |
-| ------------------------- | --- | --- | --- | --- | --- |
+|:------------------------- |:---:|:---:|:---:|:---:|:---:|
 | Visited                   |  T  |  F  |  F  |  F  |  F  |
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 checkingVertex.visited = true
-[image2.jpg]
+[images/image2.jpg]
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[image3.jpg]
+[images/image3.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     F      |     F      |
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-[image4.jpg]
+[images/image4.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     T      |     F      |
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-[image5.jpg]
+[images/image5.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-[image6.jpg]
+[images/image6.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     F      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-[image7.jpg]
+[images/image7.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     T      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |

From 142ff2e866c89259c576b03b025b500e655cf028 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:35:00 +0300
Subject: [PATCH 0963/1679] Fix folder references

---
 Dijkstra Algorithm/README.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index cb0683e5d..677c97447 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,7 +9,7 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[images/image1.png]
+[Images/image1.png]
 
 The table below will represent graph state
 
@@ -50,10 +50,10 @@ Then we set this vertex as visited
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 checkingVertex.visited = true
-[images/image2.jpg]
+[Images/image2.jpg]
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[images/image3.jpg]
+[Images/image3.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -61,7 +61,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-[images/image4.jpg]
+[Images/image4.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -69,7 +69,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-[images/image5.jpg]
+[Images/image5.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -77,7 +77,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-[images/image6.jpg]
+[Images/image6.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -85,7 +85,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-[images/image7.jpg]
+[Images/image7.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|

From 8e0d77ff9f99812bb8de307b66f1d211ef4ea785 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:37:15 +0300
Subject: [PATCH 0964/1679] Images

---
 Dijkstra Algorithm/README.md | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 677c97447..490b4de1d 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,7 +9,8 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[Images/image1.png]
+
+<img src="Images/image1.png" height="250" />
 
 The table below will represent graph state
 
@@ -50,10 +51,13 @@ Then we set this vertex as visited
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 checkingVertex.visited = true
-[Images/image2.jpg]
+
+<img src="Images/image2.png" height="250" />
+
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[Images/image3.jpg]
+
+<img src="Images/image3.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -61,7 +65,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-[Images/image4.jpg]
+<img src="Images/image4.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -69,7 +73,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-[Images/image5.jpg]
+<img src="Images/image5.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -77,7 +81,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-[Images/image6.jpg]
+<img src="Images/image6.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -85,7 +89,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-[Images/image7.jpg]
+<img src="Images/image7.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|

From 37550365f6db8b980cfe1792a3122efe24a1ed91 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:55:29 +0300
Subject: [PATCH 0965/1679] Still improving description

---
 Dijkstra Algorithm/README.md | 73 ++++++++++++++++++++++++++----------
 1 file changed, 54 insertions(+), 19 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 490b4de1d..5541276fc 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,4 +1,4 @@
-# Dijkstra-algorithm
+# Dijkstra's algorithm
 
 This algorithm was invented in 1956 by Edsger W. Dijkstra. 
 
@@ -6,13 +6,17 @@ This algorithm can be used, when you have one source vertex and want to find the
 
 The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
 
-I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
-So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+I have created **VisualizedDijkstra.playground** to help you to understand, how this algorithm works. Besides, I have described below step by step how does it works.
+
+So let's imagine, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+
+> Initialization
+
 When the algorithm starts to work initial graph looks like this:
 
 <img src="Images/image1.png" height="250" />
 
-The table below will represent graph state
+The table below represents graph state:
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -20,11 +24,17 @@ The table below will represent graph state
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
-Graph's array contains 5 vertices [A, B, C, D, E].
-Let's assume, that edge weight it is path length in kilometers between vertices.
-A vertex has neighbors: B(path from A: 5.0), C(path from A: 0.0), D(path from A: 0.0)
-And because algorithm has done nothing, then all vertices' path length from source vertex values are infinity (think about infinity as "I don't know, how long will it takes to get this vertex from source one")
-Finally we have to set source vertex path length from source vertex to 0.
+_inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one._
+_F states for False_
+_T states for True_
+
+To initialize out graph we have to set source vertex path length from source vertex to 0.
+
+|                           |  A  |  B  |  C  |  D  |  E  |
+|:------------------------- |:---:|:---:|:---:|:---:|:---:|
+| Visited                   |  F  |  F  |  F  |  F  |  F  |
+| Path Length From Start    |  0  | inf | inf | inf | inf |
+| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 
@@ -37,12 +47,15 @@ Cycle:
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
 Okay, let's start!
-From now we will keep array which contains non visited vertices. Here they are:
-var nonVisitedVertices = [A, B, C, D, E]
-Let's follow the algorithm and pick the first vertex, which neighbors we want to check.
-Imagine that we have function, that returns vertex with smallest path length from start.
-var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
-Then we set this vertex as visited 
+Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
+All our vertices are not visited, but there is only one have the smallest path length from start - A. This vertex is th first one, which neighbors we will check.
+First of all, set this vertex as visited 
+
+A.visited = true
+
+<img src="Images/image2.png" height="250" />
+
+After this step graph has this state:
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -50,21 +63,35 @@ Then we set this vertex as visited
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-checkingVertex.visited = true
-
-<img src="Images/image2.png" height="250" />
+> Step 1
 
 Then we check all of its neighbors. 
-If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+
+for clarity:
+```swift
+if (A.pathLengthFromStart + AB.weight) < B.pathLengthFromStart {
+    B.pathLengthFromStart = A.pathLengthFromStart + AB.weight
+    B.pathVerticesFromStart = A.pathVerticesFromStart
+    B.pathVerticesFromStart.append(B)
+}
+```
+And now our graph looks like this one:
 
 <img src="Images/image3.png" height="250" />
 
+And its state is here:
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     F      |     F      |
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
+> Step 2
+
+From now we repeat all actions again and fill our table with new info! 
+
 <img src="Images/image4.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
@@ -73,6 +100,8 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
+> Step 3
+
 <img src="Images/image5.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
@@ -81,6 +110,8 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
+> Step 4
+
 <img src="Images/image6.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
@@ -89,8 +120,12 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
+> Step 5
+
 <img src="Images/image7.png" height="250" />
 
+> Step 6
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     T      |     T      |     T      |

From 5e5e7a93188b79ee6693b19fd03d387635b87dbf Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:57:33 +0300
Subject: [PATCH 0966/1679] Description

---
 Dijkstra Algorithm/README.md | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 5541276fc..206507b7b 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -63,7 +63,7 @@ After this step graph has this state:
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-> Step 1
+## Step 1
 
 Then we check all of its neighbors. 
 If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
@@ -88,7 +88,7 @@ And its state is here:
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-> Step 2
+## Step 2
 
 From now we repeat all actions again and fill our table with new info! 
 
@@ -100,7 +100,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-> Step 3
+## Step 3
 
 <img src="Images/image5.png" height="250" />
 
@@ -110,7 +110,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-> Step 4
+## Step 4
 
 <img src="Images/image6.png" height="250" />
 
@@ -120,23 +120,23 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-> Step 5
+## Step 5
 
 <img src="Images/image7.png" height="250" />
 
-> Step 6
-
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     T      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
+## About
+
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-## Dijkstra's algorithm explanation
+
 
 
 

From 2e7c34c8d59c003dffe5f51a5f035a8c9b1141ba Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:58:50 +0300
Subject: [PATCH 0967/1679] Probably final updates

---
 Dijkstra Algorithm/README.md | 34 ++++------------------------------
 1 file changed, 4 insertions(+), 30 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 206507b7b..e73f95393 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -10,7 +10,7 @@ I have created **VisualizedDijkstra.playground** to help you to understand, how
 
 So let's imagine, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 
-> Initialization
+## Initialization
 
 When the algorithm starts to work initial graph looks like this:
 
@@ -130,43 +130,17 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-## About
+## About this repository
 
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-
-
-
-
-[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)'s explanation:
-Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
-
-1. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.
-2. Set the initial node as current. Mark all other nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.
-3. For the current node, consider all of its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, keep the current value.
-4. When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.
-5. If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.
-6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new "current node", and go back to step 3.
-
-Explanation, that can be found in the **VisualizedDijkstra.playground**
-Algorithm's flow:
-First of all, this program randomly decides which vertex will be the start one, then the program assigns a zero value to the start vertex path length from the start.
-
-Then the algorithm repeats following cycle until all vertices are marked as visited.
-Cycle:
-1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
-2. The algorithm marks picked vertex as visited.
-3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
-When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
-
-## Usage
-This algorithm is popular in routing. For example, biggest Russian IT company Yandex uses it in [Яндекс.Карты](https://yandex.ru/company/technologies/routes/)
-
 ## Demo video
+
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Credits
+
 WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From dd9e998e4482ff9665e3964829569a0c5489daf4 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 16:01:01 +0300
Subject: [PATCH 0968/1679] Added reference to wikipedia

---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index e73f95393..76cc4ca1d 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,6 +1,6 @@
 # Dijkstra's algorithm
 
-This algorithm was invented in 1956 by Edsger W. Dijkstra. 
+This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra. 
 
 This algorithm can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
 

From e2282045c04aeab0ff7eeb2c1df8edc33c92c76c Mon Sep 17 00:00:00 2001
From: Taras <crabman448@gmail.com>
Date: Thu, 20 Apr 2017 16:07:33 +0300
Subject: [PATCH 0969/1679] Update README.md

---
 Dijkstra Algorithm/README.md | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 76cc4ca1d..61b47e97f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -24,9 +24,11 @@ The table below represents graph state:
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
-_inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one._
-_F states for False_
-_T states for True_
+>inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one.
+
+>F states for False
+
+>T states for True
 
 To initialize out graph we have to set source vertex path length from source vertex to 0.
 

From b95331012e6fa880928b38a7606384e6b7a0db9a Mon Sep 17 00:00:00 2001
From: Taras <crabman448@gmail.com>
Date: Thu, 20 Apr 2017 16:09:14 +0300
Subject: [PATCH 0970/1679] Update README.md

---
 Dijkstra Algorithm/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 61b47e97f..9999e224e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -30,13 +30,13 @@ The table below represents graph state:
 
 >T states for True
 
-To initialize out graph we have to set source vertex path length from source vertex to 0.
+To initialize out graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices ffrom start.
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
 | Visited                   |  F  |  F  |  F  |  F  |  F  |
 | Path Length From Start    |  0  | inf | inf | inf | inf |
-| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
+| Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 

From a44f84ecad941273df7472ef1c7de7aa93b1d1c8 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 16:26:33 +0300
Subject: [PATCH 0971/1679] Removed unnecessary images

---
 .../Images/Dijkstra_Animation.gif              | Bin 8561 -> 0 bytes
 Dijkstra Algorithm/Images/screenshot1.jpg      | Bin 224243 -> 0 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Dijkstra Algorithm/Images/Dijkstra_Animation.gif
 delete mode 100644 Dijkstra Algorithm/Images/screenshot1.jpg

diff --git a/Dijkstra Algorithm/Images/Dijkstra_Animation.gif b/Dijkstra Algorithm/Images/Dijkstra_Animation.gif
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From 3395c01c00c80554be30f91310f2878d7faedcce Mon Sep 17 00:00:00 2001
From: darrellhz <zh0521@gmail.com>
Date: Fri, 21 Apr 2017 16:04:19 +0900
Subject: [PATCH 0972/1679] Update README.markdown

updated to Swift 3 syntax
---
 Linked List/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c5a752e13..c03023c42 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -364,7 +364,7 @@ What else do we need? Removing nodes, of course! First we'll do `removeAll()`, w
 
 If you had a tail pointer, you'd set it to `nil` here too.
 
-Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first.
+Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `remove()` is the most optimal because you don't need to iterate through the list to find the node first.
 
 ```swift
   public func remove(node: Node) -> T {

From b66e31825d9025916d9617073830f50284ebd488 Mon Sep 17 00:00:00 2001
From: Jacopo <jmangia@kywix.com>
Date: Fri, 21 Apr 2017 19:25:23 +0100
Subject: [PATCH 0973/1679] Filters the potential change arrays for only the
 ones which add up to the exact value

---
 MinimumCoinChange/Sources/MinimumCoinChange.swift | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index c995063ab..8b0da80ac 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -64,7 +64,10 @@ public struct MinimumCoinChange {
                 if value - coin >= 0 {
                     var potentialChange: [Int] = [coin]
                     potentialChange.append(contentsOf: _changeDynamic(value - coin))
-                    potentialChangeArray.append(potentialChange)
+
+                    if potentialChange.reduce(0, +) == value { 
+                        potentialChangeArray.append(potentialChange)
+                    } 
                 }
             }
             

From d5c9d179f63767cfad7dda48faad914f808ca68b Mon Sep 17 00:00:00 2001
From: Jacopo <jmangia@kywix.com>
Date: Fri, 21 Apr 2017 19:38:45 +0100
Subject: [PATCH 0974/1679] Optimisation: removed double check if the winner
 change is valid

---
 MinimumCoinChange/Sources/MinimumCoinChange.swift | 11 +++--------
 1 file changed, 3 insertions(+), 8 deletions(-)

diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index 8b0da80ac..55629d020 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -56,8 +56,6 @@ public struct MinimumCoinChange {
                 return cached
             }
             
-            var change: [Int] = []
-            
             var potentialChangeArray: [[Int]] = []
             
             for coin in sortedCoinSet {
@@ -73,14 +71,11 @@ public struct MinimumCoinChange {
             
             if potentialChangeArray.count > 0 {
                 let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
-                change = sortedPotentialChangeArray[0]
+                cache[value] = sortedPotentialChangeArray[0]
+                return sortedPotentialChangeArray[0]
             }
             
-            if change.reduce(0, +) == value { 
-                cache[value] = change
-            } 
-
-            return change
+            return []
         }
 
         let change: [Int] = _changeDynamic(value)

From 2ff26a1365cce2d47e7cf8cc341eadf3134cfdac Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Fri, 21 Apr 2017 23:07:00 -0700
Subject: [PATCH 0975/1679] prettify some syntax around optionals

---
 AVL Tree/AVLTree.swift | 28 +++++-----------------------
 1 file changed, 5 insertions(+), 23 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index cfcf114c0..4feb691e4 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -99,17 +99,11 @@ open class AVLTree<Key: Comparable, Payload> {
 
 extension TreeNode {
   public func minimum() -> TreeNode? {
-    if let leftChild = self.leftChild {
-      return leftChild.minimum()
-    }
-    return self
+    return leftChild?.minimum() ?? self
   }
 
   public func maximum() -> TreeNode? {
-    if let rightChild = self.rightChild {
-      return rightChild.maximum()
-    }
-    return self
+    return rightChild?.maximum() ?? self
   }
 }
 
@@ -120,11 +114,7 @@ extension AVLTree {
   }
 
   public func search(input: Key) -> Payload? {
-    if let result = search(key: input, node: root) {
-      return result.payload
-    } else {
-      return nil
-    }
+    return search(key: input, node: root)?.payload
   }
 
   fileprivate func search(key: Key, node: Node?) -> Node? {
@@ -385,11 +375,7 @@ extension TreeNode: CustomDebugStringConvertible {
 
 extension AVLTree: CustomDebugStringConvertible {
   public var debugDescription: String {
-    if let root = root {
-      return root.debugDescription
-    } else {
-      return "[]"
-    }
+    return root?.debugDescription ?? "[]"
   }
 }
 
@@ -409,10 +395,6 @@ extension TreeNode: CustomStringConvertible {
 
 extension AVLTree: CustomStringConvertible {
   public var description: String {
-    if let root = root {
-      return root.description
-    } else {
-      return "[]"
-    }
+    return root?.description ?? "[]"
   }
 }

From 7ecbb716fb9bd16f5f89bd491edc1fe81d3c85be Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Fri, 21 Apr 2017 23:15:30 -0700
Subject: [PATCH 0976/1679] prettify some syntax around optionals

---
 .../AVLTree.playground/Sources/AVLTree.swift  | 28 ++++---------------
 1 file changed, 5 insertions(+), 23 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index b4b97f0d6..56ba81608 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -99,17 +99,11 @@ open class AVLTree<Key: Comparable, Payload> {
 
 extension TreeNode {
   public func minimum() -> TreeNode? {
-    if let leftChild = self.leftChild {
-      return leftChild.minimum()
-    }
-    return self
+    return leftChild?.minimum() ?? self
   }
 
   public func maximum() -> TreeNode? {
-    if let rightChild = self.rightChild {
-      return rightChild.maximum()
-    }
-    return self
+    return rightChild?.maximum() ?? self
   }
 }
 
@@ -120,11 +114,7 @@ extension AVLTree {
   }
 
   public func search(input: Key) -> Payload? {
-    if let result = search(key: input, node: root) {
-      return result.payload
-    } else {
-      return nil
-    }
+    return search(key: input, node: root)?.payload
   }
 
   fileprivate func search(key: Key, node: Node?) -> Node? {
@@ -385,11 +375,7 @@ extension TreeNode: CustomDebugStringConvertible {
 
 extension AVLTree: CustomDebugStringConvertible {
   public var debugDescription: String {
-    if let root = root {
-      return root.debugDescription
-    } else {
-      return "[]"
-    }
+    return root?.debugDescription ?? "[]"
   }
 }
 
@@ -409,10 +395,6 @@ extension TreeNode: CustomStringConvertible {
 
 extension AVLTree: CustomStringConvertible {
   public var description: String {
-    if let root = root {
-      return root.description
-    } else {
-      return "[]"
-    }
+    return root?.description ?? "[]"
   }
 }

From 3d48ed411d872b5b3f03c114e6b1c074bb4293e8 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Sun, 23 Apr 2017 23:36:55 +0300
Subject: [PATCH 0977/1679] Credits

---
 Dijkstra Algorithm/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 9999e224e..086e60c55 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -144,5 +144,4 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Credits
 
-WWDC 2017 Scholarship Project  
-Created by [Taras Nikulin](https://github.com/crabman448)
+WWDC 2017 Scholarship Project (Rejected) created by [Taras Nikulin](https://github.com/crabman448)

From 83f7a32ccf0a2fe4b6223305bf89a7724b666a65 Mon Sep 17 00:00:00 2001
From: Antonio081014 <antonio081014@antonio081014.com>
Date: Mon, 24 Apr 2017 11:23:09 -0700
Subject: [PATCH 0978/1679] Add variety implementation with complexity
 analysis.

---
 Union-Find/README.markdown                    | 63 ++++++++++----
 .../UnionFind.playground/Contents.swift       | 82 ++++---------------
 .../Sources/UnionFindQuickFind.swift          | 50 +++++++++++
 .../Sources/UnionFindQuickUnion.swift         | 51 ++++++++++++
 .../Sources/UnionFindWeightedQuickFind.swift  | 59 +++++++++++++
 .../Sources/UnionFindWeightedQuickUnion.swift | 56 +++++++++++++
 ...indWeightedQuickUnionPathCompression.swift | 53 ++++++++++++
 .../UnionFind.playground/timeline.xctimeline  |  6 --
 Union-Find/UnionFind.swift                    | 59 -------------
 9 files changed, 330 insertions(+), 149 deletions(-)
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
 delete mode 100644 Union-Find/UnionFind.playground/timeline.xctimeline
 delete mode 100644 Union-Find/UnionFind.swift

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 5102f6b89..03e082507 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -23,7 +23,8 @@ The most common application of this data structure is keeping track of the conne
 
 ## Implementation
 
-Union-Find can be implemented in many ways but we'll look at the most efficient.
+Union-Find can be implemented in many ways but we'll look at an efficient and easy to understand implementation: Weighted Quick Union.
+> __PS: Variety implementation of Union-Find has been included in playground.__
 
 ```swift
 public struct UnionFind<T: Hashable> {
@@ -141,24 +142,24 @@ public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool
 
 Since this calls `setOf()` it also optimizes the tree.
 
-## Union
+## Union (Weighted)
 
 The final operation is **Union**, which combines two sets into one larger set.
 
 ```swift
-public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-  if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {  // 1
-    if firstSet != secondSet {               // 2
-      if size[firstSet] < size[secondSet] {  // 3
-        parent[firstSet] = secondSet         // 4
-        size[secondSet] += size[firstSet]    // 5
-      } else {
-        parent[secondSet] = firstSet
-        size[firstSet] += size[secondSet]
-      }
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) { // 1
+            if firstSet != secondSet {                // 2
+                if size[firstSet] < size[secondSet] { // 3
+                    parent[firstSet] = secondSet      // 4
+                    size[secondSet] += size[firstSet] // 5
+                } else {
+                    parent[secondSet] = firstSet
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
     }
-  }
-}
 ```
 
 Here is how it works:
@@ -167,7 +168,7 @@ Here is how it works:
 
 2. Check that the sets are not equal because if they are it makes no sense to union them.
 
-3. This is where the size optimization comes in. We want to keep the trees as shallow as possible so we always attach the smaller tree to the root of the larger tree. To determine which is the smaller tree we compare trees by their sizes.
+3. This is where the size optimization comes in (Weighting). We want to keep the trees as shallow as possible so we always attach the smaller tree to the root of the larger tree. To determine which is the smaller tree we compare trees by their sizes.
 
 4. Here we attach the smaller tree to the root of the larger tree.
 
@@ -185,10 +186,40 @@ Note that, because we call `setOf()` at the start of the method, the larger tree
 
 Union with optimizations also takes almost **O(1)** time.
 
+## Path Compression
+```swift
+private mutating func setByIndex(_ index: Int) -> Int {
+    if index != parent[index] {
+        // Updating parent index while looking up the index of parent.
+        parent[index] = setByIndex(parent[index])
+    }
+    return parent[index]
+}
+```
+Path Compression helps keep trees very flat, thus find operation could take __ALMOST__ in __O(1)__
+
+## Complexity Summary of Variety Implementation
+
+##### To process N objects
+| Data Structure | Union | Find |
+|---|---|---|
+|Quick Find|N|1|
+|Quick Union|Tree height|Tree height|
+|Weighted Quick Union|lgN|lgN|
+|Weighted Quick Union + Path Compression| very close, but not O(1)| very close, but not O(1) |
+
+##### To process M union commands on N objects
+| Algorithm | Worst-case time|
+|---|---|
+|Quick Find| M N |
+|Quick Union| M N |
+|Weighted Quick Union| N + M lgN |
+|Weighted Quick Union + Path Compression| (M + N) lgN |
+
 ## See also
 
 See the playground for more examples of how to use this handy data structure.
 
 [Union-Find at Wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
 
-*Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*
+*Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*, *modified by [Yi Ding](https://github.com/antonio081014).*
\ No newline at end of file
diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 09649b938..9ad5215b3 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,73 +1,19 @@
 //: Playground - noun: a place where people can play
 
-public struct UnionFind<T: Hashable> {
-  private var index = [T: Int]()
-  private var parent = [Int]()
-  private var size = [Int]()
-
-  public mutating func addSetWith(_ element: T) {
-    index[element] = parent.count
-    parent.append(parent.count)
-    size.append(1)
-  }
-
-  private mutating func setByIndex(_ index: Int) -> Int {
-    if parent[index] == index {
-      return index
-    } else {
-      parent[index] = setByIndex(parent[index])
-      return parent[index]
-    }
-  }
-
-  public mutating func setOf(_ element: T) -> Int? {
-    if let indexOfElement = index[element] {
-      return setByIndex(indexOfElement)
-    } else {
-      return nil
-    }
-  }
-
-  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      if firstSet != secondSet {
-        if size[firstSet] < size[secondSet] {
-          parent[firstSet] = secondSet
-          size[secondSet] += size[firstSet]
-        } else {
-          parent[secondSet] = firstSet
-          size[firstSet] += size[secondSet]
-        }
-      }
-    }
-  }
-
-  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      return firstSet == secondSet
-    } else {
-      return false
-    }
-  }
-}
-
-
-
-
-var dsu = UnionFind<Int>()
+var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {
-  dsu.addSetWith(i)
+    dsu.addSetWith(i)
 }
 // now our dsu contains 10 independent sets
 
 // let's divide our numbers into two sets by divisibility by 2
 for i in 3...10 {
-  if i % 2 == 0 {
-    dsu.unionSetsContaining(2, and: i)
-  } else {
-    dsu.unionSetsContaining(1, and: i)
-  }
+    if i % 2 == 0 {
+        dsu.unionSetsContaining(2, and: i)
+    } else {
+        dsu.unionSetsContaining(1, and: i)
+    }
 }
 
 // check our division
@@ -88,7 +34,7 @@ print(dsu.inSameSet(3, and: 6))
 
 
 
-var dsuForStrings = UnionFind<String>()
+var dsuForStrings = UnionFindQuickUnion<String>()
 let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
 
 dsuForStrings.addSetWith("a")
@@ -96,12 +42,12 @@ dsuForStrings.addSetWith("b")
 
 // In that example we divide strings by its first letter
 for word in words {
-  dsuForStrings.addSetWith(word)
-  if word.hasPrefix("a") {
-    dsuForStrings.unionSetsContaining("a", and: word)
-  } else if word.hasPrefix("b") {
-    dsuForStrings.unionSetsContaining("b", and: word)
-  }
+    dsuForStrings.addSetWith(word)
+    if word.hasPrefix("a") {
+        dsuForStrings.unionSetsContaining("a", and: word)
+    } else if word.hasPrefix("b") {
+        dsuForStrings.unionSetsContaining("b", and: word)
+    }
 }
 
 print(dsuForStrings.inSameSet("a", and: "all"))
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
new file mode 100644
index 000000000..25d7f5b5d
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
@@ -0,0 +1,50 @@
+import Foundation
+
+/// Quick-find algorithm may take ~MN steps
+/// to process M union commands on N objects
+public struct UnionFindQuickFind<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        return parent[index]
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                for index in 0..<parent.count {
+                    if parent[index] == firstSet {
+                        parent[index] = secondSet
+                    }
+                }
+                size[secondSet] += size[firstSet]
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
new file mode 100644
index 000000000..4c848e61d
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
@@ -0,0 +1,51 @@
+import Foundation
+
+/// Quick-Union algorithm may take ~MN steps
+/// to process M union commands on N objects
+public struct UnionFindQuickUnion<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        if parent[index] == index {
+            return index
+        } else {
+            parent[index] = setByIndex(parent[index])
+            return parent[index]
+        }
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                parent[firstSet] = secondSet
+                size[secondSet] += size[firstSet]
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
new file mode 100644
index 000000000..02bec94a8
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
@@ -0,0 +1,59 @@
+import Foundation
+
+/// Quick-find algorithm may take ~MN steps
+/// to process M union commands on N objects
+public struct UnionFindWeightedQuickFind<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        return parent[index]
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                if size[firstSet] < size[secondSet] {
+                    for index in 0..<parent.count {
+                        if parent[index] == firstSet {
+                            parent[index] = secondSet
+                        }
+                    }
+                    size[secondSet] += size[firstSet]
+                } else {
+                    for index in 0..<parent.count {
+                        if parent[index] == secondSet {
+                            parent[index] = firstSet
+                        }
+                    }
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
new file mode 100644
index 000000000..b3ac7445e
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
@@ -0,0 +1,56 @@
+import Foundation
+
+public struct UnionFindWeightedQuickUnion<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        if parent[index] == index {
+            return index
+        } else {
+            parent[index] = setByIndex(parent[index])
+            return parent[index]
+        }
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    /// Weighted, by comparing set size.
+    /// Merge small set into the large one.
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                if size[firstSet] < size[secondSet] {
+                    parent[firstSet] = secondSet
+                    size[secondSet] += size[firstSet]
+                } else {
+                    parent[secondSet] = firstSet
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
new file mode 100644
index 000000000..892f46a3c
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
@@ -0,0 +1,53 @@
+import Foundation
+
+public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    /// Path Compression.
+    private mutating func setByIndex(_ index: Int) -> Int {
+        if index != parent[index] {
+            parent[index] = setByIndex(parent[index])
+        }
+        return parent[index]
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                if size[firstSet] < size[secondSet] {
+                    parent[firstSet] = secondSet
+                    size[secondSet] += size[firstSet]
+                } else {
+                    parent[secondSet] = firstSet
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/timeline.xctimeline b/Union-Find/UnionFind.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Union-Find/UnionFind.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Union-Find/UnionFind.swift b/Union-Find/UnionFind.swift
deleted file mode 100644
index 506cdc1fe..000000000
--- a/Union-Find/UnionFind.swift
+++ /dev/null
@@ -1,59 +0,0 @@
-/*
-  Union-Find Data Structure
-
-  Performance:
-    adding new set is almost O(1)
-    finding set of element is almost O(1)
-    union sets is almost O(1)
-*/
-
-public struct UnionFind<T: Hashable> {
-  private var index = [T: Int]()
-  private var parent = [Int]()
-  private var size = [Int]()
-
-  public mutating func addSetWith(_ element: T) {
-    index[element] = parent.count
-    parent.append(parent.count)
-    size.append(1)
-  }
-
-  private mutating func setByIndex(_ index: Int) -> Int {
-    if parent[index] == index {
-      return index
-    } else {
-      parent[index] = setByIndex(parent[index])
-      return parent[index]
-    }
-  }
-
-  public mutating func setOf(_ element: T) -> Int? {
-    if let indexOfElement = index[element] {
-      return setByIndex(indexOfElement)
-    } else {
-      return nil
-    }
-  }
-
-  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      if firstSet != secondSet {
-        if size[firstSet] < size[secondSet] {
-          parent[firstSet] = secondSet
-          size[secondSet] += size[firstSet]
-        } else {
-          parent[secondSet] = firstSet
-          size[firstSet] += size[secondSet]
-        }
-      }
-    }
-  }
-
-  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      return firstSet == secondSet
-    } else {
-      return false
-    }
-  }
-}

From 0de6055763a91902d3a52ef4857930aec6dbd0d7 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 17:36:09 +0300
Subject: [PATCH 0979/1679] Added code description

---
 Dijkstra Algorithm/README.md | 138 +++++++++++++++++++++++++++++++++++
 1 file changed, 138 insertions(+)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 086e60c55..a72843e69 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -132,6 +132,144 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
+
+## Code implementation 
+First of all, lets create class, that will describe any Vertex in the graph.
+It is pretty simple
+```swift
+open class Vertex {
+
+	//Every vertex should be unique, that's why we set up identifier
+    open var identifier: String
+	
+	//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+    open var neighbors: [(Vertex, Double)] = []
+	
+	//As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
+	//It is var, because we will update it during algorithm execution.
+    open var pathLengthFromStart = Double.infinity
+	
+	//This array containt vertices, which we need to go through to reach this vertex from starting one
+	//As with path length from start, we will change this array during algorithm execution.
+    open var pathVerticesFromStart: [Vertex] = []
+
+    public init(identifier: String) {
+        self.identifier = identifier
+    }
+
+	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+    open func clearCache() {
+        pathLengthFromStart = Double.infinity
+        pathVerticesFromStart = []
+    }
+}
+```
+
+Because every vertex should be unique it is usefull to make them Hashable and according Equatable. We use identifier for this purposes.
+```swift
+extension Vertex: Hashable {
+    open var hashValue: Int {
+        return identifier.hashValue
+    }
+}
+
+extension Vertex: Equatable {
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        return lhs.hashValue == rhs.hashValue
+    }
+}
+```
+
+We've created a base for our algorithm. Now let's create a house :)
+Dijkstra's realization is really straightforward.
+```swift
+public class Dijkstra {
+	//It is a storage for vertices in the graph. 
+	//Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
+    private var totalVertices: Set<Vertex>
+
+    public init(vertices: Set<Vertex>) {
+        totalVertices = vertices
+    }
+
+	//Remember clearCache function in the Vertex class implementation? 
+	//This is just a wrapper that cleans cache for all stored vertices.
+    private func clearCache() {
+        totalVertices.forEach { $0.clearCache() }
+    }
+
+    public func findShortestPaths(from startVertex: Vertex) {
+		//Before we start searching shortes path from startVertex, 
+		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+		//Remember that every Vertex is a class and classes are passed by reference. 
+		//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
+        clearCache()
+		//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
+		
+		//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
+		
+		//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
+		//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
+        var currentVertex: Vertex? = startVertex
+		
+        while let vertex = currentVertex {
+			
+			//Nex line of code is an implementation of setting vertex as visited.
+			//As it has been said, we should check only unvisited vertices in the graph,
+			//So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
+            totalVertices.remove(vertex)
+			
+			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
+			
+			//Let's iterate through them
+            for neighbor in filteredNeighbors {
+				//These variable are more representative, than neighbor.0 or neighbor.1
+                let neighborVertex = neighbor.0
+                let weight = neighbor.1
+				
+				//Here we calculate new weight, that we can offer to neighbor. 
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
+				
+				//If it is smaller than neighbor's current pathLengthFromStart
+				//Then we perform this code
+                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+					
+					//set new pathLengthFromStart
+                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+					
+					//set new pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
+					
+					//append current vertex to neighbor's pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+                }
+            }
+			
+			//If totalVertices is empty, i.e. all vertices are visited
+			//Than break the loop
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+			
+			//If loop is not broken, than pick next vertex for checkin from not visited.
+			//Next vertex pathLengthFromStart should be the smallest one.
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+    }
+}
+```
+
+That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating random graph.
+
+Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm flow in real (slowed :)) time.  
+
 ## About this repository
 
 This repository contains to playgrounds:

From aac4f8fbf24f6996b70ea5c1f792ba7b81cd9e98 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 17:54:34 +0300
Subject: [PATCH 0980/1679] Fixed code comments

---
 Dijkstra Algorithm/README.md | 76 ++++++++++++++++++------------------
 1 file changed, 38 insertions(+), 38 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index a72843e69..2b6bc3875 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -139,28 +139,28 @@ It is pretty simple
 ```swift
 open class Vertex {
 
-	//Every vertex should be unique, that's why we set up identifier
+//Every vertex should be unique, that's why we set up identifier
     open var identifier: String
 	
-	//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
-	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
     open var neighbors: [(Vertex, Double)] = []
 	
-	//As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
-	//It is var, because we will update it during algorithm execution.
+//As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
+//It is var, because we will update it during algorithm execution.
     open var pathLengthFromStart = Double.infinity
 	
-	//This array containt vertices, which we need to go through to reach this vertex from starting one
-	//As with path length from start, we will change this array during algorithm execution.
+//This array containt vertices, which we need to go through to reach this vertex from starting one
+//As with path length from start, we will change this array during algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -187,79 +187,79 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realization is really straightforward.
 ```swift
 public class Dijkstra {
-	//It is a storage for vertices in the graph. 
-	//Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
+//It is a storage for vertices in the graph. 
+//Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
     private var totalVertices: Set<Vertex>
 
     public init(vertices: Set<Vertex>) {
         totalVertices = vertices
     }
 
-	//Remember clearCache function in the Vertex class implementation? 
-	//This is just a wrapper that cleans cache for all stored vertices.
+//Remember clearCache function in the Vertex class implementation? 
+//This is just a wrapper that cleans cache for all stored vertices.
     private func clearCache() {
         totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-		//Before we start searching shortes path from startVertex, 
-		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
-		//Remember that every Vertex is a class and classes are passed by reference. 
-		//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
+//Before we start searching shortes path from startVertex, 
+//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+//Remember that every Vertex is a class and classes are passed by reference. 
+//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
         clearCache()
-		//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
+//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
 		
-		//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
 		
-		//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
-		//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
+//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
+//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
         var currentVertex: Vertex? = startVertex
 		
         while let vertex = currentVertex {
 			
-			//Nex line of code is an implementation of setting vertex as visited.
-			//As it has been said, we should check only unvisited vertices in the graph,
-			//So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
+//Nex line of code is an implementation of setting vertex as visited.
+//As it has been said, we should check only unvisited vertices in the graph,
+//So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
             totalVertices.remove(vertex)
 			
-			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
 			
-			//Let's iterate through them
+//Let's iterate through them
             for neighbor in filteredNeighbors {
-				//These variable are more representative, than neighbor.0 or neighbor.1
+//These variable are more representative, than neighbor.0 or neighbor.1
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 				
-				//Here we calculate new weight, that we can offer to neighbor. 
+//Here we calculate new weight, that we can offer to neighbor. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-				//If it is smaller than neighbor's current pathLengthFromStart
-				//Then we perform this code
+//If it is smaller than neighbor's current pathLengthFromStart
+//Then we perform this code
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
 					
-					//set new pathLengthFromStart
+//set new pathLengthFromStart
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
 					
-					//set new pathVerticesFromStart
+//set new pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-					//append current vertex to neighbor's pathVerticesFromStart
+//append current vertex to neighbor's pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
 			
-			//If totalVertices is empty, i.e. all vertices are visited
-			//Than break the loop
+//If totalVertices is empty, i.e. all vertices are visited
+//Than break the loop
             if totalVertices.isEmpty {
                 currentVertex = nil
                 break
             }
 			
-			//If loop is not broken, than pick next vertex for checkin from not visited.
-			//Next vertex pathLengthFromStart should be the smallest one.
+//If loop is not broken, than pick next vertex for checkin from not visited.
+//Next vertex pathLengthFromStart should be the smallest one.
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
     }

From edbccd3b4fee79fe55ce2d741833dbef431bf466 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 17:57:12 +0300
Subject: [PATCH 0981/1679] Fixed comments again

---
 Dijkstra Algorithm/README.md | 76 ++++++++++++++++++------------------
 1 file changed, 38 insertions(+), 38 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 2b6bc3875..a8ed3c827 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -139,28 +139,28 @@ It is pretty simple
 ```swift
 open class Vertex {
 
-//Every vertex should be unique, that's why we set up identifier
+	//Every vertex should be unique, that's why we set up identifier
     open var identifier: String
 	
-//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
-//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+	//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
     open var neighbors: [(Vertex, Double)] = []
 	
-//As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
-//It is var, because we will update it during algorithm execution.
+	//As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
+	//It is var, because we will update it during algorithm execution.
     open var pathLengthFromStart = Double.infinity
 	
-//This array containt vertices, which we need to go through to reach this vertex from starting one
-//As with path length from start, we will change this array during algorithm execution.
+	//This array containt vertices, which we need to go through to reach this vertex from starting one
+	//As with path length from start, we will change this array during algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -187,79 +187,79 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realization is really straightforward.
 ```swift
 public class Dijkstra {
-//It is a storage for vertices in the graph. 
-//Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
+	//This is a storage for vertices in the graph. 
+	//Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
     private var totalVertices: Set<Vertex>
 
     public init(vertices: Set<Vertex>) {
         totalVertices = vertices
     }
 
-//Remember clearCache function in the Vertex class implementation? 
-//This is just a wrapper that cleans cache for all stored vertices.
+	//Remember clearCache function in the Vertex class implementation? 
+	//This is just a wrapper that cleans cache for all stored vertices.
     private func clearCache() {
         totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-//Before we start searching shortes path from startVertex, 
-//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
-//Remember that every Vertex is a class and classes are passed by reference. 
-//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
+		//Before we start searching shortes path from startVertex, 
+		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+		//Remember that every Vertex is a class and classes are passed by reference. 
+		//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
         clearCache()
-//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
+		//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
 		
-//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+		//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
 		
-//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
-//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
+		//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
+		//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
         var currentVertex: Vertex? = startVertex
 		
         while let vertex = currentVertex {
 			
-//Nex line of code is an implementation of setting vertex as visited.
-//As it has been said, we should check only unvisited vertices in the graph,
-//So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
+			//Nex line of code is an implementation of setting vertex as visited.
+			//As it has been said, we should check only unvisited vertices in the graph,
+			//So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
             totalVertices.remove(vertex)
 			
-//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
 			
-//Let's iterate through them
+			//Let's iterate through them
             for neighbor in filteredNeighbors {
-//These variable are more representative, than neighbor.0 or neighbor.1
+				//These variable are more representative, than neighbor.0 or neighbor.1
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 				
-//Here we calculate new weight, that we can offer to neighbor. 
+				//Here we calculate new weight, that we can offer to neighbor. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-//If it is smaller than neighbor's current pathLengthFromStart
-//Then we perform this code
+				//If it is smaller than neighbor's current pathLengthFromStart
+				//Then we perform this code
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
 					
-//set new pathLengthFromStart
+					//set new pathLengthFromStart
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
 					
-//set new pathVerticesFromStart
+					//set new pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-//append current vertex to neighbor's pathVerticesFromStart
+					//append current vertex to neighbor's pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
 			
-//If totalVertices is empty, i.e. all vertices are visited
-//Than break the loop
+			//If totalVertices is empty, i.e. all vertices are visited
+			//Than break the loop
             if totalVertices.isEmpty {
                 currentVertex = nil
                 break
             }
 			
-//If loop is not broken, than pick next vertex for checkin from not visited.
-//Next vertex pathLengthFromStart should be the smallest one.
+			//If loop is not broken, than pick next vertex for checkin from not visited.
+			//Next vertex pathLengthFromStart should be the smallest one.
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
     }

From b6c5b820be7506bbbfec04b230bbedcda1b6f5d0 Mon Sep 17 00:00:00 2001
From: Taras <crabman448@gmail.com>
Date: Tue, 25 Apr 2017 18:02:52 +0300
Subject: [PATCH 0982/1679] Update README.md

---
 Dijkstra Algorithm/README.md | 80 ++++++++++++++++++------------------
 1 file changed, 40 insertions(+), 40 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index a8ed3c827..f8ac37cf0 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -139,28 +139,28 @@ It is pretty simple
 ```swift
 open class Vertex {
 
-	//Every vertex should be unique, that's why we set up identifier
+    //Every vertex should be unique, that's why we set up identifier
     open var identifier: String
 	
-	//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
-	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+    //For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+    //when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+    //Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
     open var neighbors: [(Vertex, Double)] = []
 	
-	//As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
-	//It is var, because we will update it during algorithm execution.
+    //As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
+    //It is var, because we will update it during algorithm execution.
     open var pathLengthFromStart = Double.infinity
-	
-	//This array containt vertices, which we need to go through to reach this vertex from starting one
-	//As with path length from start, we will change this array during algorithm execution.
+
+    //This array containt vertices, which we need to go through to reach this vertex from starting one
+    //As with path length from start, we will change this array during algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+    //This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+    //When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -187,79 +187,79 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realization is really straightforward.
 ```swift
 public class Dijkstra {
-	//This is a storage for vertices in the graph. 
-	//Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
+    //This is a storage for vertices in the graph. 
+    //Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
     private var totalVertices: Set<Vertex>
 
     public init(vertices: Set<Vertex>) {
         totalVertices = vertices
     }
 
-	//Remember clearCache function in the Vertex class implementation? 
-	//This is just a wrapper that cleans cache for all stored vertices.
+    //Remember clearCache function in the Vertex class implementation? 
+    //This is just a wrapper that cleans cache for all stored vertices.
     private func clearCache() {
         totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-		//Before we start searching shortes path from startVertex, 
-		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
-		//Remember that every Vertex is a class and classes are passed by reference. 
-		//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
+	//Before we start searching shortes path from startVertex, 
+	//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+	//Remember that every Vertex is a class and classes are passed by reference. 
+	//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
         clearCache()
-		//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
+	//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
 		
-		//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+	//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
 		
-		//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
-		//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
+	//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
+	//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
         var currentVertex: Vertex? = startVertex
 		
         while let vertex = currentVertex {
-			
-			//Nex line of code is an implementation of setting vertex as visited.
-			//As it has been said, we should check only unvisited vertices in the graph,
-			//So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
+    			
+    	    //Nex line of code is an implementation of setting vertex as visited.
+    	    //As it has been said, we should check only unvisited vertices in the graph,
+	    //So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
             totalVertices.remove(vertex)
 			
-			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+	    //filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
 			
-			//Let's iterate through them
+	    //Let's iterate through them
             for neighbor in filteredNeighbors {
-				//These variable are more representative, than neighbor.0 or neighbor.1
+		//These variable are more representative, than neighbor.0 or neighbor.1
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 				
-				//Here we calculate new weight, that we can offer to neighbor. 
+		//Here we calculate new weight, that we can offer to neighbor. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-				//If it is smaller than neighbor's current pathLengthFromStart
-				//Then we perform this code
+		//If it is smaller than neighbor's current pathLengthFromStart
+		//Then we perform this code
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
 					
-					//set new pathLengthFromStart
+		    //set new pathLengthFromStart
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
 					
-					//set new pathVerticesFromStart
+		    //set new pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-					//append current vertex to neighbor's pathVerticesFromStart
+		    //append current vertex to neighbor's pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
 			
-			//If totalVertices is empty, i.e. all vertices are visited
-			//Than break the loop
+	    //If totalVertices is empty, i.e. all vertices are visited
+	    //Than break the loop
             if totalVertices.isEmpty {
                 currentVertex = nil
                 break
             }
 			
-			//If loop is not broken, than pick next vertex for checkin from not visited.
-			//Next vertex pathLengthFromStart should be the smallest one.
+	    //If loop is not broken, than pick next vertex for checkin from not visited.
+	    //Next vertex pathLengthFromStart should be the smallest one.
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
     }

From 9575a6745caa33bc5d864d6e406682af2f5f9515 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 18:22:00 +0300
Subject: [PATCH 0983/1679] Added some comments to playground

---
 Dijkstra Algorithm/Dijkstra.playground/Contents.swift | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 1c12245bd..7c7f1a4b0 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -14,13 +14,18 @@ func createNotConnectedVertices() {
 
 func setupConnections() {
     for vertex in vertices {
+        //the amount of edges each vertex can have
         let randomEdgesCount = arc4random_uniform(4) + 1
         for _ in 0..<randomEdgesCount {
+            //randomize weight value from 0 to 9
             let randomWeight = Double(arc4random_uniform(10))
             let neighborVertex = randomVertex(except: vertex)
+
+            //we need this check to set only one connection between two equal pairs of vertices
             if vertex.neighbors.contains(where: { $0.0 == neighborVertex }) {
                 continue
             }
+            //creating neighbors and setting them
             let neighbor1 = (neighborVertex, randomWeight)
             let neighbor2 = (vertex, randomWeight)
             vertex.neighbors.append(neighbor1)
@@ -53,9 +58,15 @@ let dijkstra = Dijkstra(vertices: vertices)
 //decide which vertex will be the starting one
 let startVertex = randomVertex()
 
+let startTime = Date()
+
 //ask algorithm to find shortest paths from start vertex to all others
 dijkstra.findShortestPaths(from: startVertex)
 
+let endTime = Date()
+
+print("calculation time is = \((endTime.timeIntervalSince(startTime))) sec")
+
 //printing results
 let destinationVertex = randomVertex(except: startVertex)
 print(destinationVertex.pathLengthFromStart)

From 9a8467fa24c780c3f4b2404989fa7a6616ea0946 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 26 Apr 2017 10:31:44 +0300
Subject: [PATCH 0984/1679] Final edits

---
 Dijkstra Algorithm/README.md | 16 +++++++++-------
 1 file changed, 9 insertions(+), 7 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index f8ac37cf0..db1726b1f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -2,13 +2,13 @@
 
 This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra. 
 
-This algorithm can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
+It can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
 
 The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
 
-I have created **VisualizedDijkstra.playground** to help you to understand, how this algorithm works. Besides, I have described below step by step how does it works.
+I have created **VisualizedDijkstra.playground** to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
-So let's imagine, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+Let's imagine, you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have graph, that connects your house with all these stores. So, you know what to do :)
 
 ## Initialization
 
@@ -30,7 +30,7 @@ The table below represents graph state:
 
 >T states for True
 
-To initialize out graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices ffrom start.
+To initialize our graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices from start.
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -40,7 +40,7 @@ To initialize out graph we have to set source vertex path length from source ver
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 
-But before we will go through all process side by side let me explain how algorithm works.
+But before we will go through all process side by side read this explanation.
 The algorithm repeats following cycle until all vertices are marked as visited.
 Cycle:
 1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
@@ -50,7 +50,7 @@ When all vertices are marked as visited, the algorithm's job is done. Now, you c
 
 Okay, let's start!
 Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
-All our vertices are not visited, but there is only one have the smallest path length from start - A. This vertex is th first one, which neighbors we will check.
+All our vertices are not visited, but there is only one has the smallest path length from start - A. This vertex is the first one, which neighbors we will check.
 First of all, set this vertex as visited 
 
 A.visited = true
@@ -268,7 +268,9 @@ public class Dijkstra {
 
 That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating random graph.
 
-Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm flow in real (slowed :)) time.  
+Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm's flow in real (slowed :)) time.
+
+It is up to you how to implement some specific parts of algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
 
 ## About this repository
 

From d79a076ea901657161392a4fc3b53b0e2df65cdd Mon Sep 17 00:00:00 2001
From: Lucy Jeong <yureka5345@gmail.com>
Date: Thu, 27 Apr 2017 11:31:57 +0900
Subject: [PATCH 0985/1679] Update README.markdown

changed enumerate() -> enumerated()
---
 Hash Table/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index bc9636195..8f1eaaf70 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -202,7 +202,7 @@ The code to insert a new element or update an existing element lives in `updateV
     let index = self.index(forKey: key)
     
     // Do we already have this key in the bucket?
-    for (i, element) in buckets[index].enumerate() {
+    for (i, element) in buckets[index].enumerated() {
       if element.key == key {
         let oldValue = element.value
         buckets[index][i].value = value

From 03393a86a3864221ff1f0b7137eefb619bf19698 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 06:17:13 +0500
Subject: [PATCH 0986/1679] Fix "found unknown escape character" while trying
 to run swiftlint 0.18.1

Also update the smiley face regex check to have a space before the colon so that it doesn't match: fatalError("init(coder:) has not been implemented")
---
 .swiftlint.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.swiftlint.yml b/.swiftlint.yml
index 1434bf637..6cb714110 100644
--- a/.swiftlint.yml
+++ b/.swiftlint.yml
@@ -17,8 +17,8 @@ disabled_rules:
 custom_rules:
   smiley_face:
     name: "Smiley Face"
-    regex: "(\:\))"
-    match_kinds: 
+    regex: '( :\))'
+    match_kinds:
       - comment
       - string
     message: "A closing parenthesis smiley :) creates a half-hearted smile, and thus is not preferred. Use :]"

From 018ddaccfc0276ac8740c093731b92aeae122a9d Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:42:15 +0500
Subject: [PATCH 0987/1679] [swiftlint] Fix: MARK comment should be in valid
 format.

---
 .../TST.playground/Sources/TernarySearchTree.swift            | 4 ++--
 Ternary Search Tree/TernarySearchTree.swift                   | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index fed8f9710..21b8f0dc3 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -15,7 +15,7 @@ public class TernarySearchTree<Element> {
 
     public init() {}
 
-    //MARK: - Insertion
+    // MARK: - Insertion
 
     public func insert(data: Element, withKey key: String) -> Bool {
         return insert(node: &root, withData: data, andKey: key, atIndex: 0)
@@ -59,7 +59,7 @@ public class TernarySearchTree<Element> {
     }
 
 
-    //MARK: - Finding
+    // MARK: - Finding
 
 
     public func find(key: String) -> Element? {
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 2e2ca2917..0fa6d9634 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -23,7 +23,7 @@ public class TernarySearchTree<Element> {
      */
     public init() {}
 
-    //MARK: - Insertion
+    // MARK: - Insertion
 
     /**
     Public insertion method.
@@ -85,7 +85,7 @@ public class TernarySearchTree<Element> {
     }
 
 
-    //MARK: - Finding
+    // MARK: - Finding
 
     /**
     Public find method.

From 29c5952fadf80e8ac3f0c717d7d7ae08620b0dcb Mon Sep 17 00:00:00 2001
From: Felipe Naranjo <fenaranjo42@gmail.com>
Date: Fri, 28 Apr 2017 10:57:48 -0400
Subject: [PATCH 0988/1679] Update README.markdown

Though "indexes" is grammatically correct, the word "indices" is used in Apple documentation.
---
 Union-Find/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 5102f6b89..68698f39e 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -119,7 +119,7 @@ Here's illustration of what I mean. Let's say the tree looks like this:
 
 ![BeforeFind](Images/BeforeFind.png)
 
-We call `setOf(4)`. To find the root node we have to first go to node `2` and then to node `7`. (The indexes of the elements are marked in red.)
+We call `setOf(4)`. To find the root node we have to first go to node `2` and then to node `7`. (The indices of the elements are marked in red.)
 
 During the call to `setOf(4)`, the tree is reorganized to look like this:
 

From 137c36051dff6a1e3965dad4959ad0a742fc01b4 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:46:49 +0500
Subject: [PATCH 0989/1679] [swiftlint] Fix: Else and catch should be on the
 same line

warning: Statement Position Violation: Else and catch should be on the same line, one space after the previous declaration.
---
 DiningPhilosophers/Sources/main.swift | 3 +--
 Skip-List/SkipList.swift              | 3 +--
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index 285402d53..338a9074d 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -22,8 +22,7 @@ struct ForkPair {
         if leftIndex > rightIndex {
             leftFork = ForkPair.forksSemaphore[leftIndex]
             rightFork = ForkPair.forksSemaphore[rightIndex]
-        }
-        else {
+        } else {
             leftFork = ForkPair.forksSemaphore[rightIndex]
             rightFork = ForkPair.forksSemaphore[leftIndex]
         }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 5fc61bf8e..c5fe2b821 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -118,8 +118,7 @@ extension SkipList {
           if value.key == key {
             isFound = true
             break
-          }
-          else {
+          } else {
             if key < value.key! {
               currentNode = node.down
             } else {

From c3a05c6bfe865554261fbb0b641651f7dcfffff4 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:49:54 +0500
Subject: [PATCH 0990/1679] [swiftlint] Fix: trailing_semicolon

warning: Trailing Semicolon Violation: Lines should not have trailing semicolons.
---
 Trie/Trie/TrieTests/TrieTests.swift | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index a75c35c62..50a30a552 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -175,21 +175,21 @@ class TrieTests: XCTestCase {
         trie.insert(word: "another")
         trie.insert(word: "exam")
         let wordsAll = trie.findWordsWithPrefix(prefix: "")
-        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"]);
+        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"])
         let words = trie.findWordsWithPrefix(prefix: "ex")
-        XCTAssertEqual(words, ["exam"]);
+        XCTAssertEqual(words, ["exam"])
         trie.insert(word: "examination")
         let words2 = trie.findWordsWithPrefix(prefix: "exam")
-        XCTAssertEqual(words2, ["exam", "examination"]);
+        XCTAssertEqual(words2, ["exam", "examination"])
         let noWords = trie.findWordsWithPrefix(prefix: "tee")
-        XCTAssertEqual(noWords, []);
+        XCTAssertEqual(noWords, [])
         let unicodeWord = "😬😎"
         trie.insert(word: unicodeWord)
         let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
-        XCTAssertEqual(wordsUnicode, [unicodeWord]);
+        XCTAssertEqual(wordsUnicode, [unicodeWord])
         trie.insert(word: "Team")
         let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
-        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"]);
+        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
 
     }
 }

From 4eb7ac1975dfbd2f3d9059d649af3ab6f90d97a2 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:52:12 +0500
Subject: [PATCH 0991/1679] [swiftlint] Fix control_statement  (i.e. parens
 around if statement)

warning: Control Statement Violation: if,for,while,do statements shouldn't wrap their conditionals in parentheses.
---
 Rootish Array Stack/Tests/RootishArrayStackTests.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index f73857d0f..9ffc4ebb9 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -4,7 +4,7 @@ fileprivate extension RootishArrayStack {
 	func equal(toArray array: Array<Int>) -> Bool{
 		for index in 0..<count {
 			guard let integerElement = self[index] as? Int else { return false }
-			if (array[index] != integerElement) {
+			if array[index] != integerElement {
 				return false
 			}
 		}

From 821bee3e76fa3520b38f12fc6c4147a3dba8d371 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:53:16 +0500
Subject: [PATCH 0992/1679] [swiftlint] Fix redundant_optional_initialization
 (i.e. don't need "= nil")

warning: Redundant Optional Initialization Violation: Initializing an optional variable with nil is redundant.
---
 Graph/Graph/AdjacencyListGraph.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index e5e9fc2db..edb754c97 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -12,7 +12,7 @@ import Foundation
 private class EdgeList<T> where T: Equatable, T: Hashable {
 
   var vertex: Vertex<T>
-  var edges: [Edge<T>]? = nil
+  var edges: [Edge<T>]?
 
   init(vertex: Vertex<T>) {
     self.vertex = vertex

From 55eba6e7d86e468b1cb0f114c25f5439cf2d4702 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:55:51 +0500
Subject: [PATCH 0993/1679] [swiftlint] Fix: closure_parameter_position

warning: Closure Parameter Position Violation: Closure parameters should be on the same line as opening brace.
---
 B-Tree/BTree.playground/Contents.swift                    | 3 +--
 Shunting Yard/ShuntingYard.playground/Sources/Stack.swift | 3 +--
 Skip-List/SkipList.swift                                  | 7 +++----
 Stack/Stack.swift                                         | 3 +--
 4 files changed, 6 insertions(+), 10 deletions(-)

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index 8238fe5a5..710ace701 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -14,8 +14,7 @@ bTree[3]
 
 bTree.remove(2)
 
-bTree.traverseKeysInOrder {
-  key in
+bTree.traverseKeysInOrder { key in
   print(key)
 }
 
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index a67bb9d64..27286fdbd 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -31,8 +31,7 @@ public struct Stack<T> {
 extension Stack: Sequence {
     public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyIterator {
-            _ -> T? in
+        return AnyIterator { _ -> T? in
             return curr.pop()
         }
     }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index c5fe2b821..1418656f3 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -52,10 +52,9 @@ public struct Stack<T> {
 extension Stack: Sequence {
   public func makeIterator() -> AnyIterator<T> {
     var curr = self
-    return AnyIterator {
-             _ -> T? in
-             return curr.pop()
-      }
+    return AnyIterator { _ -> T? in
+      return curr.pop()
+    }
   }
 }
 
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 974d5a443..c3f42ea44 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -30,8 +30,7 @@ public struct Stack<T> {
 extension Stack: Sequence {
     public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyIterator {
-            _ -> T? in
+        return AnyIterator { _ -> T? in
             return curr.pop()
         }
     }

From 6c3dcd4be40058e09875d4bcd3f6086e021380e4 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:57:19 +0500
Subject: [PATCH 0994/1679] [swiftlint] Fix: leading_whitespace

warning: Leading Whitespace Violation: File shouldn't start with whitespace.
---
 HaversineDistance/HaversineDistance.playground/Contents.swift   | 1 -
 QuadTree/QuadTree.playground/Contents.swift                     | 1 -
 QuadTree/QuadTree.playground/Sources/QuadTree.swift             | 1 -
 Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift | 1 -
 4 files changed, 4 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index f46d7c394..a6effb7b0 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,4 +1,3 @@
-
 import UIKit
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
index 41e73147f..ad8ee31f8 100644
--- a/QuadTree/QuadTree.playground/Contents.swift
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -1,4 +1,3 @@
-
 import Foundation
 
 let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))
diff --git a/QuadTree/QuadTree.playground/Sources/QuadTree.swift b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
index 65c55d49e..14d0dbba7 100644
--- a/QuadTree/QuadTree.playground/Sources/QuadTree.swift
+++ b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
@@ -1,4 +1,3 @@
-
 public struct Point {
   let x: Double
   let y: Double
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index 1735798d5..b0f440809 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -1,4 +1,3 @@
-
 private enum RBTColor {
     case red
     case black

From 932b453d5b0ce1b5ad058323bed79728f92dfd52 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:58:51 +0500
Subject: [PATCH 0995/1679] [swiftlint] Fix rule: trailing_newline

warning: Trailing Newline Violation: Files should have a single trailing newline.
---
 B-Tree/Tests/Tests/BTreeNodeTests.swift                         | 1 -
 Comb Sort/Comb Sort.playground/Contents.swift                   | 2 --
 Convex Hull/Convex Hull/AppDelegate.swift                       | 1 -
 Fixed Size Array/FixedSizeArray.playground/Contents.swift       | 1 -
 Insertion Sort/InsertionSort.playground/Contents.swift          | 2 +-
 Linked List/LinkedList.playground/Contents.swift                | 1 -
 .../MRPrimality.playground/Contents.swift                       | 2 +-
 Run-Length Encoding/RLE.playground/Contents.swift               | 2 +-
 Trie/Trie/Trie/AppDelegate.swift                                | 1 -
 Trie/Trie/Trie/ViewController.swift                             | 1 -
 10 files changed, 3 insertions(+), 11 deletions(-)

diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index da6ebe9f6..fd3ba10e8 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -51,4 +51,3 @@ class BTreeNodeTests: XCTestCase {
     XCTAssertEqual(root.children!.count, 2)
   }
 }
-
diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index d6add44f5..40176be9f 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -16,5 +16,3 @@ while i < 1000 {
   i += 1
 }
 combSort(bigArray)
-
-
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
index 1901083a8..4f8496cd5 100644
--- a/Convex Hull/Convex Hull/AppDelegate.swift	
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -54,4 +54,3 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
 
 
 }
-
diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index f1bc63315..4bc5d66df 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -53,4 +53,3 @@ array.append(2)
 array[1]
 array.removeAt(index: 0)
 array.removeAll()
-
diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index b25916b23..df1822b8f 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -16,4 +16,4 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 insertionSort(list, <)
-insertionSort(list, >)
\ No newline at end of file
+insertionSort(list, >)
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index b86fbf0b4..10677935a 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -389,4 +389,3 @@ let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
 listArrayLiteral2.count        // 3
 listArrayLiteral2[0]           // "Swift"
 listArrayLiteral2.removeLast()  // "Club"
-
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index 8d97dc409..98032bd59 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -21,4 +21,4 @@ mrPrimalityTest(178426363)
 mrPrimalityTest(32415187747)
 
 // With iteration
-mrPrimalityTest(32416190071, iteration: 10)
\ No newline at end of file
+mrPrimalityTest(32416190071, iteration: 10)
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 62b4ef437..11e177d0d 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -113,4 +113,4 @@ func runTests() -> Bool {
     return result
 }
 
-runTests()
\ No newline at end of file
+runTests()
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
index 4da9dc345..b2b4c0c5f 100644
--- a/Trie/Trie/Trie/AppDelegate.swift
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -23,4 +23,3 @@ class AppDelegate: NSObject, NSApplicationDelegate {
 
 
 }
-
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index b2e9d9105..e24a812cb 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -24,4 +24,3 @@ class ViewController: NSViewController {
 
 
 }
-

From a025c0cc27b3fa4b8bfa2255f59eceb8447ad9b3 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 10:00:27 +0500
Subject: [PATCH 0996/1679] [swiftlint] Fix rule: opening_brace

warning: Opening Brace Spacing Violation: Opening braces should be preceded by a single space and on the same line as the declaration.
---
 .../BruteForceStringSearch.playground/Contents.swift        | 2 +-
 Brute-Force String Search/BruteForceStringSearch.swift      | 2 +-
 .../KaratsubaMultiplication.playground/Contents.swift       | 6 +++---
 .../Red-Black Tree 2.playground/Sources/RBTree.swift        | 2 +-
 Rootish Array Stack/Tests/RootishArrayStackTests.swift      | 2 +-
 Shell Sort/ShellSortExample.swift                           | 2 +-
 Skip-List/SkipList.swift                                    | 2 +-
 .../Sources/Number.swift                                    | 2 +-
 8 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index 61064c698..00ac6da97 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -6,7 +6,7 @@ extension String {
     for i in self.characters.indices {
       var j = i
       var found = true
-      for p in pattern.characters.indices{
+      for p in pattern.characters.indices {
         if j == self.characters.endIndex || self[j] != pattern[p] {
           found = false
           break
diff --git a/Brute-Force String Search/BruteForceStringSearch.swift b/Brute-Force String Search/BruteForceStringSearch.swift
index 03a2dff13..016292304 100644
--- a/Brute-Force String Search/BruteForceStringSearch.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.swift	
@@ -6,7 +6,7 @@ extension String {
     for i in self.characters.indices {
         var j = i
         var found = true
-        for p in pattern.characters.indices{
+        for p in pattern.characters.indices {
             if j == self.characters.endIndex || self[j] != pattern[p] {
                 found = false
                 break
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index bde8fd9f9..3ac29301a 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -15,8 +15,8 @@ func ^^ (radix: Int, power: Int) -> Int {
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-  let num1Array = String(num1).characters.reversed().map{ Int(String($0))! }
-  let num2Array = String(num2).characters.reversed().map{ Int(String($0))! }
+  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
+  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
   
   var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
 
@@ -30,7 +30,7 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
     product[i + num2Array.count] += carry
   }
   
-  return Int(product.reversed().map{ String($0) }.reduce("", +))!
+  return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
 // Karatsuba Multiplication - O(n^log2(3))
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index b0f440809..0038494d3 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -22,7 +22,7 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
             // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
             if self.isRed {
                 nodeValue = "(\(self.value!))"
-            } else if self.isBlack{
+            } else if self.isBlack {
                 nodeValue = "|\(self.value!)|"
             } else {
                 nodeValue = "||\(self.value!)||"
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index 9ffc4ebb9..f0aaa8bca 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -1,7 +1,7 @@
 import XCTest
 
 fileprivate extension RootishArrayStack {
-	func equal(toArray array: Array<Int>) -> Bool{
+	func equal(toArray array: Array<Int>) -> Bool {
 		for index in 0..<count {
 			guard let integerElement = self[index] as? Int else { return false }
 			if array[index] != integerElement {
diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 9174b935b..aaf58cf4d 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -22,7 +22,7 @@ public func shellSort(_ list : inout [Int]) {
             
             guard sublistCount == 1 && index > 0 else { continue }
             
-            while list[index - 1] > list[index] && index - 1 > 0  {
+            while list[index - 1] > list[index] && index - 1 > 0 {
                 swap(&list[index - 1], &list[index])
                 index -= 1
             }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 1418656f3..52de1412e 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -283,7 +283,7 @@ extension SkipList {
 
 extension SkipList {
   
-  public func get(key:Key) -> Payload?{
+  public func get(key:Key) -> Payload? {
     return search(key: key)
   }
 }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 7da1eee60..69afe76e4 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -37,7 +37,7 @@ extension Array where Element: Number {
   public func dot(_ b: Array<Element>) -> Element {
     let a = self
     assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
-    let c = a.indices.map{ a[$0] * b[$0] }
+    let c = a.indices.map { a[$0] * b[$0] }
     return c.reduce(Element.zero, { $0 + $1 })
   }
 }

From 44adf5a8f6ac5e14ca74b761fbdd01083100ccf8 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 10:01:33 +0500
Subject: [PATCH 0997/1679] [swiftlint] Fix rule:
 empty_parentheses_with_trailing_closure

warning: Empty Parentheses with Trailing Closure Violation: When using trailing closures, empty parentheses should be avoided after the method call.
---
 All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift    | 2 +-
 Bloom Filter/BloomFilter.playground/Contents.swift        | 4 ++--
 Bloom Filter/BloomFilter.swift                            | 4 ++--
 Graph/Graph/AdjacencyListGraph.swift                      | 2 +-
 Graph/Graph/AdjacencyMatrixGraph.swift                    | 2 +-
 .../SSSP/BellmanFord.swift                                | 4 ++--
 Trie/Trie/TrieTests/TrieTests.swift                       | 8 ++++----
 7 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
index b1a870f2a..7bc78f326 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
@@ -175,7 +175,7 @@ public struct FloydWarshallResult<T>: APSPResult where T: Hashable {
   public func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
 
     if let path = recursePathFrom(fromVertex: from, toVertex: to, path: [ to ], inGraph: graph) {
-      let pathValues = path.map() { vertex in
+      let pathValues = path.map { vertex in
         vertex.data
       }
       return pathValues
diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index d5e7d2dc6..06022c9b3 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -10,7 +10,7 @@ public class BloomFilter<T> {
   }
 
   private func computeHashes(_ value: T) -> [Int] {
-    return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
+    return hashFunctions.map { hashFunc in abs(hashFunc(value) % array.count) }
   }
 
   public func insert(_ element: T) {
@@ -29,7 +29,7 @@ public class BloomFilter<T> {
     let hashValues = computeHashes(value)
 
     // Map hashes to indices in the Bloom Filter
-    let results = hashValues.map() { hashValue in array[hashValue] }
+    let results = hashValues.map { hashValue in array[hashValue] }
 
     // All values must be 'true' for the query to return true
 
diff --git a/Bloom Filter/BloomFilter.swift b/Bloom Filter/BloomFilter.swift
index 03b5333f1..56c3be328 100644
--- a/Bloom Filter/BloomFilter.swift	
+++ b/Bloom Filter/BloomFilter.swift	
@@ -8,7 +8,7 @@ public class BloomFilter<T> {
   }
 
   private func computeHashes(_ value: T) -> [Int] {
-    return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
+    return hashFunctions.map { hashFunc in abs(hashFunc(value) % array.count) }
   }
 
   public func insert(_ element: T) {
@@ -27,7 +27,7 @@ public class BloomFilter<T> {
     let hashValues = computeHashes(value)
 
     // Map hashes to indices in the Bloom Filter
-    let results = hashValues.map() { hashValue in array[hashValue] }
+    let results = hashValues.map { hashValue in array[hashValue] }
 
     // All values must be 'true' for the query to return true
 
diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index edb754c97..3d86c78f7 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -64,7 +64,7 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
 
   open override func createVertex(_ data: T) -> Vertex<T> {
     // check if the vertex already exists
-    let matchingVertices = vertices.filter() { vertex in
+    let matchingVertices = vertices.filter { vertex in
       return vertex.data == data
     }
 
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index 8f357bc8c..a9b43fb6d 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -46,7 +46,7 @@ open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hash
   // Performance: possibly O(n^2) because of the resizing of the matrix.
   open override func createVertex(_ data: T) -> Vertex<T> {
     // check if the vertex already exists
-    let matchingVertices = vertices.filter() { vertex in
+    let matchingVertices = vertices.filter { vertex in
       return vertex.data == data
     }
 
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift
index 5b6670806..41be9759b 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
@@ -41,7 +41,7 @@ extension BellmanFord: SSSPAlgorithm {
 
     for _ in 0 ..< vertices.count - 1 {
       var weightsUpdated = false
-      edges.forEach() { edge in
+      edges.forEach { edge in
         let weight = edge.weight!
         let relaxedDistance = weights[edge.from.index] + weight
         let nextVertexIdx = edge.to.index
@@ -116,7 +116,7 @@ extension BellmanFordResult: SSSPResult {
       return nil
     }
 
-    return path.map() { vertex in
+    return path.map { vertex in
       return vertex.data
     }
   }
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 50a30a552..960b65791 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -101,7 +101,7 @@ class TrieTests: XCTestCase {
 
     /// Tests the performance of the insert method.
     func testInsertPerformance() {
-        self.measure() {
+        self.measure {
             let trie = Trie()
             for word in self.wordArray! {
                 trie.insert(word: word)
@@ -114,7 +114,7 @@ class TrieTests: XCTestCase {
     /// Tests the performance of the insert method when the words are already
     /// present.
     func testInsertAgainPerformance() {
-        self.measure() {
+        self.measure {
             for word in self.wordArray! {
                 self.trie.insert(word: word)
             }
@@ -123,7 +123,7 @@ class TrieTests: XCTestCase {
 
     /// Tests the performance of the contains method.
     func testContainsPerformance() {
-        self.measure() {
+        self.measure {
             for word in self.wordArray! {
                 XCTAssertTrue(self.trie.contains(word: word))
             }
@@ -136,7 +136,7 @@ class TrieTests: XCTestCase {
         for word in self.wordArray! {
             self.trie.remove(word: word)
         }
-        self.measure() {
+        self.measure {
             self.insertWordsIntoTrie()
             for word in self.wordArray! {
                 self.trie.remove(word: word)

From 71c0e32fbc9794289199c3a8bbe0e1719a9b2ece Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 10:05:34 +0500
Subject: [PATCH 0998/1679] [swiftlint] Fix rule: colon (i.e. should be next to
 identifier)

warning: Colon Violation: Colons should be next to the identifier when specifying a type and next to the key in dictionary literals.
---
 .../BucketSort.playground/Sources/BucketSort.swift        | 2 +-
 Bucket Sort/BucketSort.swift                              | 2 +-
 Convex Hull/Convex Hull/View.swift                        | 2 +-
 Deque/Deque-Optimized.swift                               | 2 +-
 Linked List/LinkedList.playground/Contents.swift          | 2 +-
 Linked List/LinkedList.swift                              | 2 +-
 .../Red-Black Tree 2.playground/Sources/RBTree.swift      | 8 ++++----
 Skip-List/SkipList.swift                                  | 2 +-
 Topological Sort/Graph.swift                              | 4 ++--
 .../Topological Sort.playground/Sources/Graph.swift       | 4 ++--
 .../Sources/TopologicalSort1.swift                        | 2 +-
 Topological Sort/TopologicalSort1.swift                   | 2 +-
 12 files changed, 17 insertions(+), 17 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index e510e51b4..08962c0e1 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -122,7 +122,7 @@ public struct InsertionSorter: Sorter {
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
+public struct Bucket<T: Sortable> {
   var elements: [T]
   let capacity: Int
 
diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index ef72c67dc..ff36b372a 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -173,7 +173,7 @@ public struct InsertionSorter: Sorter {
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
+public struct Bucket<T: Sortable> {
     var elements: [T]
     let capacity: Int
 
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 2d7157e6f..f9f9f6ef4 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -150,7 +150,7 @@ class View: UIView {
         let context = UIGraphicsGetCurrentContext()
         
         // Draw hull
-        let lineWidth:CGFloat = 2.0
+        let lineWidth: CGFloat = 2.0
         
         context!.setFillColor(UIColor.black.cgColor)
         context!.setLineWidth(lineWidth)
diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index f565458c7..4eea01f1a 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -7,7 +7,7 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
-  private let originalCapacity:Int
+  private let originalCapacity: Int
 
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 10677935a..08e14ef70 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -177,7 +177,7 @@ public final class LinkedList<T> {
     if list.isEmpty { return }
     var (prev, next) = nodesBeforeAndAfter(index: index)
     var nodeToCopy = list.head
-    var newNode:Node?
+    var newNode: Node?
     while let node = nodeToCopy {
       newNode = Node(value: node.value)
       newNode?.previous = prev
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index a7ef9bf5e..783e650e8 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -129,7 +129,7 @@ public final class LinkedList<T> {
         if list.isEmpty { return }
         var (prev, next) = nodesBeforeAndAfter(index: index)
         var nodeToCopy = list.head
-        var newNode:Node?
+        var newNode: Node?
         while let node = nodeToCopy {
             newNode = Node(value: node.value)
             newNode?.previous = prev
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index 0038494d3..42a68237e 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -7,9 +7,9 @@ private enum RBTColor {
 public class RBTNode<T: Comparable>: CustomStringConvertible {
     fileprivate var color: RBTColor = .red
     public var value: T! = nil
-    public var right:  RBTNode<T>!
-    public var left:  RBTNode<T>!
-    public var parent:  RBTNode<T>!
+    public var right: RBTNode<T>!
+    public var left: RBTNode<T>!
+    public var parent: RBTNode<T>!
     
     public var description: String {
         if self.value == nil {
@@ -435,7 +435,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
     private func property3() {
         let bDepth = blackDepth(root: self.root)
         
-        let leaves:[RBTNode<T>] = getLeaves(n: self.root)
+        let leaves: [RBTNode<T>] = getLeaves(n: self.root)
         
         for leaflet in leaves {
             var leaf = leaflet
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 52de1412e..14b5a4076 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -283,7 +283,7 @@ extension SkipList {
 
 extension SkipList {
   
-  public func get(key:Key) -> Payload? {
+  public func get(key: Key) -> Payload? {
     return search(key: key)
   }
 }
diff --git a/Topological Sort/Graph.swift b/Topological Sort/Graph.swift
index 1e1be6919..5032ba1d1 100644
--- a/Topological Sort/Graph.swift	
+++ b/Topological Sort/Graph.swift	
@@ -4,7 +4,7 @@ public class Graph: CustomStringConvertible {
   private(set) public var adjacencyLists: [Node : [Node]]
 
   public init() {
-    adjacencyLists = [Node : [Node]]()
+    adjacencyLists = [Node: [Node]]()
   }
 
   public func addNode(_ value: Node) -> Node {
@@ -35,7 +35,7 @@ extension Graph {
   typealias InDegree = Int
 
   func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    var inDegrees = [Node : InDegree]()
+    var inDegrees = [Node: InDegree]()
 
     for (node, _) in adjacencyLists {
       inDegrees[node] = 0
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index 1e1be6919..5032ba1d1 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -4,7 +4,7 @@ public class Graph: CustomStringConvertible {
   private(set) public var adjacencyLists: [Node : [Node]]
 
   public init() {
-    adjacencyLists = [Node : [Node]]()
+    adjacencyLists = [Node: [Node]]()
   }
 
   public func addNode(_ value: Node) -> Node {
@@ -35,7 +35,7 @@ extension Graph {
   typealias InDegree = Int
 
   func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    var inDegrees = [Node : InDegree]()
+    var inDegrees = [Node: InDegree]()
 
     for (node, _) in adjacencyLists {
       inDegrees[node] = 0
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index 0f9566f6a..4d3717fe6 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -23,7 +23,7 @@ extension Graph {
       return node
     })
 
-    var visited = [Node : Bool]()
+    var visited = [Node: Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
     }
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 0f9566f6a..4d3717fe6 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -23,7 +23,7 @@ extension Graph {
       return node
     })
 
-    var visited = [Node : Bool]()
+    var visited = [Node: Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
     }

From c4fdd035df77487756eee2389d18c89f9dc652cd Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 00:52:39 -0700
Subject: [PATCH 0999/1679] switch removeFirst to dropFirst

we don't need a mutable copy of `array` to alter it, instead we can just drop the first element
---
 Select Minimum Maximum/Maximum.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index 991a0544e..c999504fb 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -3,13 +3,12 @@
  */
 
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-    var array = array
     guard !array.isEmpty else {
         return nil
     }
 
-    var maximum = array.removeFirst()
-    for element in array {
+    var maximum = array.first!
+    for element in array.dropFirst() {
         maximum = element > maximum ? element : maximum
     }
     return maximum

From 5e7fc5487f833fd96852d21d7f856c300956a62b Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 00:56:51 -0700
Subject: [PATCH 1000/1679] switch removeFirst to dropFirst

we don't need to alter a mutable copy of `array`, instead we can just drop the first element.
---
 Select Minimum Maximum/Minimum.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 90dfbd54b..88a562170 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -3,13 +3,12 @@
  */
 
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    var array = array
     guard !array.isEmpty else {
         return nil
     }
 
-    var minimum = array.removeFirst()
-    for element in array {
+    var minimum = array.first!
+    for element in array.dropFirst() {
         minimum = element < minimum ? element : minimum
     }
     return minimum

From e15e1330417dcbe2222d2606a35dd5462eac6b2c Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 18:14:37 -0700
Subject: [PATCH 1001/1679] switch from removeFirst to stride for pairing

We don't need to alter a local copy of `array` to generate each pair, instead use stride(from:to:by).  In my simple [tests](https://gist.github.com/TheIronBorn/cc0507b36fddad291aa34674eb52ad8f), this can be up to an order of magnitude faster.
---
 Select Minimum Maximum/MinimumMaximumPairs.swift | 13 +++++--------
 1 file changed, 5 insertions(+), 8 deletions(-)

diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index b7deb570a..2c7b5bb5f 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -3,7 +3,6 @@
  */
 
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-    var array = array
     guard !array.isEmpty else {
         return nil
     }
@@ -11,13 +10,11 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
     var minimum = array.first!
     var maximum = array.first!
 
+    // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
     let hasOddNumberOfItems = array.count % 2 != 0
-    if hasOddNumberOfItems {
-        array.removeFirst()
-    }
-
-    while !array.isEmpty {
-        let pair = (array.removeFirst(), array.removeFirst())
+    let start = hasOddNumberOfItems ? 1 : 0
+    for i in stride(from: start, to: array.count, by: 2) {
+        let pair = (array[i], array[i+1])
 
         if pair.0 > pair.1 {
             if pair.0 > maximum {
@@ -35,6 +32,6 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
             }
         }
     }
-    
+
     return (minimum, maximum)
 }

From b8d668d3883f79754aa83f5944a3e3d97e13d3a6 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 18:19:43 -0700
Subject: [PATCH 1002/1679] update to match source

---
 Select Minimum Maximum/README.markdown | 20 ++++++++------------
 1 file changed, 8 insertions(+), 12 deletions(-)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index fa0f8fed8..3c29b5764 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -24,26 +24,24 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
 
-  var minimum = array.removeFirst()
-  for element in array {
+  var minimum = array.first!
+  for element in array.dropFirst() {
     minimum = element < minimum ? element : minimum
   }
   return minimum
 }
 
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
 
-  var maximum = array.removeFirst()
-  for element in array {
+  var maximum = array.first!
+  for element in array.dropFirst() {
     maximum = element > maximum ? element : maximum
   }
   return maximum
@@ -99,7 +97,6 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
@@ -107,13 +104,12 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
   var minimum = array.first!
   var maximum = array.first!
 
+  // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
   let hasOddNumberOfItems = array.count % 2 != 0
-  if hasOddNumberOfItems {
-    array.removeFirst()
-  }
+  let start = hasOddNumberOfItems ? 1 : 0
+  for i in stride(from: start, to: array.count, by: 2) {
+    let pair = (array[i], array[i+1])
 
-  while !array.isEmpty {
-    let pair = (array.removeFirst(), array.removeFirst())
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0

From 5ddf933c48da612a9489c77b095496b0c80c1b66 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 18:21:35 -0700
Subject: [PATCH 1003/1679] update to match source

---
 .../Contents.swift                            | 33 ++++++++-----------
 1 file changed, 14 insertions(+), 19 deletions(-)

diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index 182060805..427ccdb9e 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -1,12 +1,11 @@
 // Compare each item to find minimum
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
-  
-  var minimum = array.removeFirst()
-  for element in array {
+
+  var minimum = array.first!
+  for element in array.dropFirst() {
     minimum = element < minimum ? element : minimum
   }
   return minimum
@@ -14,13 +13,12 @@ func minimum<T: Comparable>(_ array: [T]) -> T? {
 
 // Compare each item to find maximum
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
-  
-  var maximum = array.removeFirst()
-  for element in array {
+
+  var maximum = array.first!
+  for element in array.dropFirst() {
     maximum = element > maximum ? element : maximum
   }
   return maximum
@@ -28,22 +26,19 @@ func maximum<T: Comparable>(_ array: [T]) -> T? {
 
 // Compare in pairs to find minimum and maximum
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var minimum = array.first!
   var maximum = array.first!
-  
+
+  // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
   let hasOddNumberOfItems = array.count % 2 != 0
-  if hasOddNumberOfItems {
-    array.removeFirst()
-  }
-  
-  while !array.isEmpty {
-    let pair = (array.removeFirst(), array.removeFirst())
-    
+  let start = hasOddNumberOfItems ? 1 : 0
+  for i in stride(from: start, to: array.count, by: 2) {
+    let pair = (array[i], array[i+1])
+
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0
@@ -60,7 +55,7 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
       }
     }
   }
-  
+
   return (minimum, maximum)
 }
 

From 3f156498b0cb043f103eef22216f2e4e9df6edd6 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 1 May 2017 01:03:09 +0500
Subject: [PATCH 1004/1679] Fix alignment by adding an additional tab

---
 Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Tree/README.markdown b/Tree/README.markdown
index 440d9c9a4..566864a8f 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -153,7 +153,7 @@ tree.search("bubbly")   // nil
 
 It's also possible to describe a tree using nothing more than an array. The indices in the array then create the links between the different nodes. For example, if we have:
 
-	0 = beverage	5 = cocoa		9  = green
+	0 = beverage		5 = cocoa		9  = green
 	1 = hot			6 = soda		10 = chai
 	2 = cold		7 = milk		11 = ginger ale
 	3 = tea			8 = black		12 = bitter lemon

From 32457ce5aca5bcdee4acc1f8d6f6c0c6a075daba Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 1 May 2017 02:03:34 +0500
Subject: [PATCH 1005/1679] Fix misindented return statement

---
 Trie/ReadMe.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 7caa927a7..356f6887e 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -46,7 +46,7 @@ func contains(word: String) -> Bool {
 	if currentIndex == characters.count && currentNode.isTerminating {
 	  return true
 	} else {
-		return false
+	  return false
 	}
 }
 ```

From 09f2c8fb8564bd956beb1a067b6ad21255bad97c Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 1 May 2017 05:25:13 +0500
Subject: [PATCH 1006/1679] [swiftlint] Fix rule: force_cast (Force casts
 should be avoided)

---
 Trie/Trie/TrieTests/TrieTests.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 960b65791..b69c5666e 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -164,8 +164,8 @@ class TrieTests: XCTestCase {
         let fileName = "dictionary-archive"
         let filePath = resourcePath.appendingPathComponent(fileName)
         NSKeyedArchiver.archiveRootObject(trie, toFile: filePath)
-        let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as! Trie
-        XCTAssertEqual(trieCopy.count, trie.count)
+        let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
+        XCTAssertEqual(trieCopy?.count, trie.count)
 
     }
 

From b1319ce90d5288e20ee02b56390c61895d1d7765 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:23:06 +0500
Subject: [PATCH 1007/1679] [swiftlint] Fix violation: unused_closure_parameter

warning: Unused Closure Parameter Violation: Unused parameters in a closure should be replaced with _.
---
 B-Tree/Tests/Tests/BTreeTests.swift                             | 2 +-
 .../Topological Sort.playground/Sources/TopologicalSort1.swift  | 2 +-
 .../Topological Sort.playground/Sources/TopologicalSort2.swift  | 2 +-
 Topological Sort/TopologicalSort1.swift                         | 2 +-
 Topological Sort/TopologicalSort2.swift                         | 2 +-
 5 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index c8db17fa3..f2dac7511 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -31,7 +31,7 @@ class BTreeTests: XCTestCase {
   }
   
   func testInorderTraversalOfEmptyTree() {
-    bTree.traverseKeysInOrder { i in
+    bTree.traverseKeysInOrder { _ in
       XCTFail("Inorder travelsal fail.")
     }
   }
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index 4d3717fe6..2ad9b51a0 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -19,7 +19,7 @@ extension Graph {
 
     let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift
index f4c1cdd6f..589801d33 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
@@ -8,7 +8,7 @@ extension Graph {
     // topologically sorted list.
     var leaders = nodes.filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 4d3717fe6..2ad9b51a0 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -19,7 +19,7 @@ extension Graph {
 
     let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 
diff --git a/Topological Sort/TopologicalSort2.swift b/Topological Sort/TopologicalSort2.swift
index f4c1cdd6f..589801d33 100644
--- a/Topological Sort/TopologicalSort2.swift	
+++ b/Topological Sort/TopologicalSort2.swift	
@@ -8,7 +8,7 @@ extension Graph {
     // topologically sorted list.
     var leaders = nodes.filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 

From 9107542b7753210cef8eaf982373db377f6a8a62 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:25:35 +0500
Subject: [PATCH 1008/1679] [swiftlint] Fix violation:
 redundant_discardable_let

warning: Redundant Discardable Let Violation: Prefer `_ = foo()` over `let _ = foo()` when discarding a result from a function.
---
 Breadth-First Search/Tests/Graph.swift | 2 +-
 Palindromes/Test/Test/Test.swift       | 6 +++---
 Treap/TreapCollectionType.swift        | 2 +-
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Breadth-First Search/Tests/Graph.swift b/Breadth-First Search/Tests/Graph.swift
index 5e0837160..a8c34b3f6 100644
--- a/Breadth-First Search/Tests/Graph.swift	
+++ b/Breadth-First Search/Tests/Graph.swift	
@@ -86,7 +86,7 @@ public class Graph: CustomStringConvertible, Equatable {
     let duplicated = Graph()
 
     for node in nodes {
-      let _ = duplicated.addNode(node.label)
+      _ = duplicated.addNode(node.label)
     }
 
     for node in nodes {
diff --git a/Palindromes/Test/Test/Test.swift b/Palindromes/Test/Test/Test.swift
index e86a40cfb..1dd79ea97 100644
--- a/Palindromes/Test/Test/Test.swift
+++ b/Palindromes/Test/Test/Test.swift
@@ -29,9 +29,9 @@ class PalindromeTests: XCTestCase {
         // This is an example of a performance test case.
         self.measure {
             // Put the code you want to measure the time of here.
-            let _ = isPalindrome("abbcbba")
-            let _ = isPalindrome("asdkfaksjdfasjkdfhaslkjdfakjsdfhakljsdhflkjasdfhkasdjhfklajsdfhkljasdf")
-            let _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
+            _ = isPalindrome("abbcbba")
+            _ = isPalindrome("asdkfaksjdfasjkdfhaslkjdfakjsdfhakljsdhflkjasdfhkasdjhfklajsdfhkljasdf")
+            _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
         }
     }
     
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index de40464d1..9f7f81905 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -50,7 +50,7 @@ extension Treap: MutableCollection {
     
     mutating set {
       guard let value = newValue else {
-        let _ = try? self.delete(key: key)
+        _ = try? self.delete(key: key)
         return
       }
       

From c67a277487e3611ad51b0c88855540d3f56f58bb Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:34:24 +0500
Subject: [PATCH 1009/1679] [swiftlint] Fix violation: operator_whitespace

warning: Operator Function Whitespace Violation: Operators should be surrounded by a single whitespace when defining them.

Apple has also used spacing in The Swift Programming Language book
https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/AdvancedOperators.html#//apple_ref/doc/uid/TP40014097-CH27-ID42
---
 QuadTree/Tests/Tests/Tests.swift                            | 2 +-
 .../Sources/Matrix.swift                                    | 2 +-
 .../Sources/Number.swift                                    | 6 +++---
 Treap/TreapCollectionType.swift                             | 2 +-
 4 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/QuadTree/Tests/Tests/Tests.swift b/QuadTree/Tests/Tests/Tests.swift
index b7bcda4e6..b408c4f7e 100644
--- a/QuadTree/Tests/Tests/Tests.swift
+++ b/QuadTree/Tests/Tests/Tests.swift
@@ -12,7 +12,7 @@ extension Point: Equatable {
 
 }
 
-public func ==(lhs: Point, rhs: Point) -> Bool {
+public func == (lhs: Point, rhs: Point) -> Bool {
   return lhs.x == rhs.x && lhs.y == rhs.y
 }
 
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index c13b3eeee..ccfa58b09 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -19,7 +19,7 @@ public struct Matrix<T: Number> {
   public struct Size: Equatable {
     let rows: Int, columns: Int
     
-    public static func ==(lhs: Size, rhs: Size) -> Bool {
+    public static func == (lhs: Size, rhs: Size) -> Bool {
       return lhs.columns == rhs.columns && lhs.rows == rhs.rows
     }
   }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 69afe76e4..d53ef75bd 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -13,12 +13,12 @@ public protocol Number: Multipliable, Addable {
 }
 
 public protocol Addable {
-  static func +(lhs: Self, rhs: Self) -> Self
-  static func -(lhs: Self, rhs: Self) -> Self
+  static func + (lhs: Self, rhs: Self) -> Self
+  static func - (lhs: Self, rhs: Self) -> Self
 }
 
 public protocol Multipliable {
-  static func *(lhs: Self, rhs: Self) -> Self
+  static func * (lhs: Self, rhs: Self) -> Self
 }
 
 extension Int: Number {
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index 9f7f81905..7292c5f0a 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -85,7 +85,7 @@ extension Treap: MutableCollection {
 
 public struct TreapIndex<Key: Comparable>: Comparable {
   
-  public static func <(lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
+  public static func < (lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
     return lhs.keyIndex < rhs.keyIndex
   }
   

From 18c7b435cec0eafb657f28f7c80345d8a7aa513a Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:41:07 +0500
Subject: [PATCH 1010/1679] [swiftlint] Fix violation: Colons should be next to
 the identifier

warning: Colon Violation: Colons should be next to the identifier when specifying a type and next to the key in dictionary literals.
---
 Bucket Sort/BucketSort.swift |  4 ++--
 Skip-List/SkipList.swift     | 12 ++++++------
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index ff36b372a..5845819f2 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -23,7 +23,7 @@
 import Foundation
 // FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
 // Consider refactoring the code to use the non-optional operators.
-fileprivate func < <T : Comparable>(lhs: T?, rhs: T?) -> Bool {
+fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
   switch (lhs, rhs) {
   case let (l?, r?):
     return l < r
@@ -36,7 +36,7 @@ fileprivate func < <T : Comparable>(lhs: T?, rhs: T?) -> Bool {
 
 // FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
 // Consider refactoring the code to use the non-optional operators.
-fileprivate func >= <T : Comparable>(lhs: T?, rhs: T?) -> Bool {
+fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
   switch (lhs, rhs) {
   case let (l?, r?):
     return l >= r
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 14b5a4076..e844f9959 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -71,10 +71,10 @@ private func coinFlip() -> Bool {
 public class DataNode<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
   
-  var data            : Payload?  
-  fileprivate var key : Key?
-  var next            : Node?
-  var down            : Node?
+  var data: Payload?  
+  fileprivate var key: Key?
+  var next: Node?
+  var down: Node?
   
   public init(key: Key, data: Payload) {
     self.key  = key
@@ -102,8 +102,8 @@ open class SkipList<Key: Comparable, Payload> {
 extension SkipList {
   
   func findNode(key: Key) -> Node? {
-    var currentNode : Node? = head
-    var isFound     : Bool  = false
+    var currentNode: Node? = head
+    var isFound: Bool = false
 
     while !isFound {
       if let node = currentNode {

From e3a4494138ca4776aab23bed0428b3e4063395ca Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:47:57 +0500
Subject: [PATCH 1011/1679] [swiftlint] Fix violation: Computed properties
 should avoid using get

Rule: implicit_getter
warning: Implicit Getter Violation: Computed read-only properties should avoid using the get keyword.
---
 Graph/Graph/AdjacencyListGraph.swift   | 58 ++++++++++++--------------
 Graph/Graph/AdjacencyMatrixGraph.swift | 44 +++++++++----------
 Graph/Graph/Edge.swift                 | 19 ++++-----
 Graph/Graph/Graph.swift                | 12 ++----
 Graph/Graph/Vertex.swift               |  8 +---
 Treap/Treap.swift                      | 31 ++++++--------
 Treap/TreapMergeSplit.swift            |  4 +-
 7 files changed, 71 insertions(+), 105 deletions(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 3d86c78f7..57fd75fed 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -37,29 +37,25 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
   }
 
   open override var vertices: [Vertex<T>] {
-    get {
-      var vertices = [Vertex<T>]()
-      for edgeList in adjacencyList {
-        vertices.append(edgeList.vertex)
-      }
-      return vertices
+    var vertices = [Vertex<T>]()
+    for edgeList in adjacencyList {
+      vertices.append(edgeList.vertex)
     }
+    return vertices
   }
 
   open override var edges: [Edge<T>] {
-    get {
-      var allEdges = Set<Edge<T>>()
-      for edgeList in adjacencyList {
-        guard let edges = edgeList.edges else {
-          continue
-        }
+    var allEdges = Set<Edge<T>>()
+    for edgeList in adjacencyList {
+      guard let edges = edgeList.edges else {
+        continue
+      }
 
-        for edge in edges {
-          allEdges.insert(edge)
-        }
+      for edge in edges {
+        allEdges.insert(edge)
       }
-      return Array(allEdges)
     }
+    return Array(allEdges)
   }
 
   open override func createVertex(_ data: T) -> Vertex<T> {
@@ -114,27 +110,25 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
   }
 
   open override var description: String {
-    get {
-      var rows = [String]()
-      for edgeList in adjacencyList {
+    var rows = [String]()
+    for edgeList in adjacencyList {
 
-        guard let edges = edgeList.edges else {
-          continue
-        }
+      guard let edges = edgeList.edges else {
+        continue
+      }
 
-        var row = [String]()
-        for edge in edges {
-          var value = "\(edge.to.data)"
-          if edge.weight != nil {
-            value = "(\(value): \(edge.weight!))"
-          }
-          row.append(value)
+      var row = [String]()
+      for edge in edges {
+        var value = "\(edge.to.data)"
+        if edge.weight != nil {
+          value = "(\(value): \(edge.weight!))"
         }
-
-        rows.append("\(edgeList.vertex.data) -> [\(row.joined(separator: ", "))]")
+        row.append(value)
       }
 
-      return rows.joined(separator: "\n")
+      rows.append("\(edgeList.vertex.data) -> [\(row.joined(separator: ", "))]")
     }
+
+    return rows.joined(separator: "\n")
   }
 }
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index a9b43fb6d..1b12790d8 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -23,23 +23,19 @@ open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hash
   }
 
   open override var vertices: [Vertex<T>] {
-    get {
-      return _vertices
-    }
+    return _vertices
   }
 
   open override var edges: [Edge<T>] {
-    get {
-      var edges = [Edge<T>]()
-      for row in 0 ..< adjacencyMatrix.count {
-        for column in 0 ..< adjacencyMatrix.count {
-          if let weight = adjacencyMatrix[row][column] {
-            edges.append(Edge(from: vertices[row], to: vertices[column], weight: weight))
-          }
+    var edges = [Edge<T>]()
+    for row in 0 ..< adjacencyMatrix.count {
+      for column in 0 ..< adjacencyMatrix.count {
+        if let weight = adjacencyMatrix[row][column] {
+          edges.append(Edge(from: vertices[row], to: vertices[column], weight: weight))
         }
       }
-      return edges
     }
+    return edges
   }
 
   // Adds a new vertex to the matrix.
@@ -96,23 +92,21 @@ open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hash
   }
 
   open override var description: String {
-    get {
-      var grid = [String]()
-      let n = self.adjacencyMatrix.count
-      for i in 0..<n {
-        var row = ""
-        for j in 0..<n {
-          if let value = self.adjacencyMatrix[i][j] {
-            let number = NSString(format: "%.1f", value)
-            row += "\(value >= 0 ? " " : "")\(number) "
-          } else {
-            row += "  ø  "
-          }
+    var grid = [String]()
+    let n = self.adjacencyMatrix.count
+    for i in 0..<n {
+      var row = ""
+      for j in 0..<n {
+        if let value = self.adjacencyMatrix[i][j] {
+          let number = NSString(format: "%.1f", value)
+          row += "\(value >= 0 ? " " : "")\(number) "
+        } else {
+          row += "  ø  "
         }
-        grid.append(row)
       }
-      return (grid as NSArray).componentsJoined(by: "\n")
+      grid.append(row)
     }
+    return (grid as NSArray).componentsJoined(by: "\n")
   }
 
 }
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 03518da83..28ef91834 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -19,12 +19,10 @@ public struct Edge<T>: Equatable where T: Equatable, T: Hashable {
 extension Edge: CustomStringConvertible {
 
   public var description: String {
-    get {
-      guard let unwrappedWeight = weight else {
-        return "\(from.description) -> \(to.description)"
-      }
-      return "\(from.description) -(\(unwrappedWeight))-> \(to.description)"
+    guard let unwrappedWeight = weight else {
+      return "\(from.description) -> \(to.description)"
     }
+    return "\(from.description) -(\(unwrappedWeight))-> \(to.description)"
   }
 
 }
@@ -32,15 +30,12 @@ extension Edge: CustomStringConvertible {
 extension Edge: Hashable {
 
   public var hashValue: Int {
-    get {
-      var string = "\(from.description)\(to.description)"
-      if weight != nil {
-        string.append("\(weight!)")
-      }
-      return string.hashValue
+    var string = "\(from.description)\(to.description)"
+    if weight != nil {
+      string.append("\(weight!)")
     }
+    return string.hashValue
   }
-
 }
 
 public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
index 2ad91608b..13d6802b9 100644
--- a/Graph/Graph/Graph.swift
+++ b/Graph/Graph/Graph.swift
@@ -21,21 +21,15 @@ open class AbstractGraph<T>: CustomStringConvertible where T: Equatable, T: Hash
   }
 
   open var description: String {
-    get {
-      fatalError("abstract property accessed")
-    }
+    fatalError("abstract property accessed")
   }
 
   open var vertices: [Vertex<T>] {
-    get {
-      fatalError("abstract property accessed")
-    }
+    fatalError("abstract property accessed")
   }
 
   open var edges: [Edge<T>] {
-    get {
-      fatalError("abstract property accessed")
-    }
+    fatalError("abstract property accessed")
   }
 
   // Adds a new vertex to the matrix.
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 43cabcd1f..42a7dad7b 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -17,9 +17,7 @@ public struct Vertex<T>: Equatable where T: Equatable, T: Hashable {
 extension Vertex: CustomStringConvertible {
 
   public var description: String {
-    get {
-      return "\(index): \(data)"
-    }
+    return "\(index): \(data)"
   }
 
 }
@@ -27,9 +25,7 @@ extension Vertex: CustomStringConvertible {
 extension Vertex: Hashable {
 
   public var hashValue: Int {
-    get {
-      return "\(data)\(index)".hashValue
-    }
+    return "\(data)\(index)".hashValue
   }
 
 }
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 478f248df..6e80abfb2 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -63,27 +63,22 @@ public indirect enum Treap<Key: Comparable, Element> {
   }
   
   public var depth: Int {
-    get {
-      switch self {
-      case .empty:
-        return 0
-      case let .node(_, _, _, left, .empty):
-        return 1 + left.depth
-      case let .node(_, _, _, .empty, right):
-        return 1 + right.depth
-      case let .node(_, _, _, left, right):
-        let leftDepth = left.depth
-        let rightDepth = right.depth
-        return 1 + leftDepth > rightDepth ? leftDepth : rightDepth
-      }
-      
+    switch self {
+    case .empty:
+      return 0
+    case let .node(_, _, _, left, .empty):
+      return 1 + left.depth
+    case let .node(_, _, _, .empty, right):
+      return 1 + right.depth
+    case let .node(_, _, _, left, right):
+      let leftDepth = left.depth
+      let rightDepth = right.depth
+      return 1 + leftDepth > rightDepth ? leftDepth : rightDepth
     }
   }
-  
+
   public var count: Int {
-    get {
-      return Treap.countHelper(self)
-    }
+    return Treap.countHelper(self)
   }
   
   fileprivate static func countHelper(_ treap: Treap<Key, Element>) -> Int {
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index 660bd4932..34cfec3d2 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -94,9 +94,7 @@ internal func merge<Key: Comparable, Element>(_ left: Treap<Key, Element>, right
 
 extension Treap: CustomStringConvertible {
   public var description: String {
-    get {
-      return Treap.descHelper(self, indent: 0)
-    }
+    return Treap.descHelper(self, indent: 0)
   }
   
   fileprivate static func descHelper(_ treap: Treap<Key, Element>, indent: Int) -> String {

From 9af41f20ed8318739bd4f1d582a6789fe650e9b5 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:49:49 +0500
Subject: [PATCH 1012/1679] [swiftlint] Fix violation: trailing_whitespace

---
 Array2D/Array2D.playground/Contents.swift     |   4 +-
 Array2D/Array2D.swift                         |   4 +-
 B-Tree/BTree.playground/Sources/BTree.swift   | 108 +++++++-------
 B-Tree/BTree.swift                            | 108 +++++++-------
 B-Tree/Tests/Tests/BTreeNodeTests.swift       |  18 +--
 B-Tree/Tests/Tests/BTreeTests.swift           | 112 +++++++-------
 .../Contents.swift                            |   2 +-
 .../Sources/Comb Sort.swift                   |   4 +-
 Comb Sort/Comb Sort.swift                     |   4 +-
 Comb Sort/Tests/CombSortTests.swift           |   2 +-
 Convex Hull/Convex Hull/AppDelegate.swift     |   8 +-
 Convex Hull/Convex Hull/View.swift            |  80 +++++-----
 .../FixedSizeArray.playground/Contents.swift  |  10 +-
 Graph/Graph.playground/Contents.swift         |   2 +-
 .../HashSet.playground/Sources/HashSet.swift  |  16 +-
 .../Sources/HashTable.swift                   |  28 ++--
 .../Contents.swift                            |  10 +-
 Heap/Heap.swift                               |   4 +-
 Heap/Tests/HeapTests.swift                    |   4 +-
 Huffman Coding/Huffman.swift                  |  34 ++---
 Huffman Coding/NSData+Bits.swift              |   8 +-
 .../Contents.swift                            |  16 +-
 .../KaratsubaMultiplication.swift             |  12 +-
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     |  26 ++--
 .../LinkedList.playground/Contents.swift      |  62 ++++----
 Linked List/LinkedList.swift                  |  62 ++++----
 Linked List/Tests/LinkedListTests.swift       |  18 +--
 .../Sources/MRPrimality.swift                 |  28 ++--
 Miller-Rabin Primality Test/MRPrimality.swift |  28 ++--
 .../Contents.swift                            |   8 +-
 .../OrderedArray.playground/Contents.swift    |   2 +-
 .../Palindromes.playground/Contents.swift     |   8 +-
 Palindromes/Palindromes.swift                 |   8 +-
 Palindromes/Test/Palindromes.swift            |   8 +-
 Palindromes/Test/Test/Test.swift              |  18 +--
 .../Sources/QuadTree.swift                    |  88 +++++------
 QuadTree/Tests/Tests/Tests.swift              |  34 ++---
 .../Sources/radixSort.swift                   |  18 +--
 Radix Sort/RadixSortExample.swift             |  12 +-
 Radix Sort/radixSort.swift                    |  18 +--
 .../Contents.swift                            |   2 +-
 .../Sources/RBTree.swift                      | 138 +++++++++---------
 .../RLE.playground/Contents.swift             |  14 +-
 .../RLE.playground/Sources/RLE.swift          |  12 +-
 .../SegmentTree.playground/Contents.swift     |  18 +--
 Segment Tree/SegmentTree.swift                |  16 +-
 .../MinimumMaximumPairs.swift                 |   2 +-
 .../Contents.swift                            |  14 +-
 Shell Sort/ShellSortExample.swift             |  10 +-
 Shortest Path (Unweighted)/Tests/Graph.swift  |  32 ++--
 .../ShuntingYard.playground/Contents.swift    |  52 +++----
 .../Sources/Stack.swift                       |  14 +-
 Shunting Yard/ShuntingYard.swift              |  52 +++----
 Skip-List/SkipList.swift                      |  84 +++++------
 .../Sources/Matrix.swift                      |  88 +++++------
 .../TST.playground/Sources/Utils.swift        |   8 +-
 .../Tests/TernarySearchTreeTests.swift        |  18 +--
 Ternary Search Tree/Utils.swift               |   8 +-
 .../Sources/ThreadedBinaryTree.swift          |  52 +++----
 Treap/Treap.swift                             |  18 +--
 Treap/Treap/TreapTests/TreapTests.swift       |  12 +-
 Treap/TreapCollectionType.swift               |  34 ++---
 Treap/TreapMergeSplit.swift                   |  14 +-
 Trie/Trie/Trie/Trie.swift                     |  16 +-
 Trie/Trie/TrieUITests/TrieUITests.swift       |  12 +-
 Z-Algorithm/ZAlgorithm.swift                  |  22 +--
 .../ZetaAlgorithm.playground/Contents.swift   |  34 ++---
 Z-Algorithm/ZetaAlgorithm.swift               |  12 +-
 68 files changed, 926 insertions(+), 926 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index d088c99af..1a6a439bd 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -7,13 +7,13 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   fileprivate var array: [T]
-  
+
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(repeating: initialValue, count: rows*columns)
   }
-  
+
   public subscript(column: Int, row: Int) -> T {
     get {
       precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
diff --git a/Array2D/Array2D.swift b/Array2D/Array2D.swift
index df4822916..caff8373c 100644
--- a/Array2D/Array2D.swift
+++ b/Array2D/Array2D.swift
@@ -7,13 +7,13 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   fileprivate var array: [T]
-  
+
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(repeating: initialValue, count: rows*columns)
   }
-  
+
   public subscript(column: Int, row: Int) -> T {
     get {
       precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
diff --git a/B-Tree/BTree.playground/Sources/BTree.swift b/B-Tree/BTree.playground/Sources/BTree.swift
index 52cda4e43..2693eb308 100644
--- a/B-Tree/BTree.playground/Sources/BTree.swift
+++ b/B-Tree/BTree.playground/Sources/BTree.swift
@@ -33,23 +33,23 @@ class BTreeNode<Key: Comparable, Value> {
    * The tree that owns the node.
    */
   unowned var owner: BTree<Key, Value>
-  
+
   fileprivate var keys = [Key]()
   fileprivate var values = [Value]()
   var children: [BTreeNode]?
-  
+
   var isLeaf: Bool {
     return children == nil
   }
-  
+
   var numberOfKeys: Int {
     return keys.count
   }
-  
+
   init(owner: BTree<Key, Value>) {
     self.owner = owner
   }
-  
+
   convenience init(owner: BTree<Key, Value>, keys: [Key],
                    values: [Value], children: [BTreeNode]? = nil) {
     self.init(owner: owner)
@@ -62,7 +62,7 @@ class BTreeNode<Key: Comparable, Value> {
 // MARK: BTreeNode extesnion: Searching
 
 extension BTreeNode {
-  
+
   /**
    *  Returns the value for a given `key`, returns nil if the `key` is not found.
    *  
@@ -71,11 +71,11 @@ extension BTreeNode {
    */
   func value(for key: Key) -> Value? {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if key == keys[index] {
       return values[index]
     } else if key < keys[index] {
@@ -89,7 +89,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Travelsals
 
 extension BTreeNode {
-  
+
   /**
    *  Traverses the keys in order, executes `process` for every key.
    * 
@@ -101,7 +101,7 @@ extension BTreeNode {
       children?[i].traverseKeysInOrder(process)
       process(keys[i])
     }
-    
+
     children?.last?.traverseKeysInOrder(process)
   }
 }
@@ -109,7 +109,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Insertion
 
 extension BTreeNode {
-  
+
   /**
    *  Inserts `value` for `key` to the node, or to one if its descendants.
    *  
@@ -119,16 +119,16 @@ extension BTreeNode {
    */
   func insert(_ value: Value, for key: Key) {
     var index = keys.startIndex
-    
+
     while index < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if index < keys.endIndex && keys[index] == key {
       values[index] = value
       return
     }
-    
+
     if isLeaf {
       keys.insert(key, at: index)
       values.insert(value, at: index)
@@ -140,7 +140,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Splits `child` at `index`.
    *  The key-value pair at `index` gets moved up to the parent node,
@@ -156,7 +156,7 @@ extension BTreeNode {
     values.insert(child.values[middleIndex], at: index)
     child.keys.remove(at: middleIndex)
     child.values.remove(at: middleIndex)
-    
+
     let rightSibling = BTreeNode(
       owner: owner,
       keys: Array(child.keys[child.keys.indices.suffix(from: middleIndex)]),
@@ -164,9 +164,9 @@ extension BTreeNode {
     )
     child.keys.removeSubrange(child.keys.indices.suffix(from: middleIndex))
     child.values.removeSubrange(child.values.indices.suffix(from: middleIndex))
-    
+
     children!.insert(rightSibling, at: (index + 1))
-    
+
     if child.children != nil {
       rightSibling.children = Array(
         child.children![child.children!.indices.suffix(from: (middleIndex + 1))]
@@ -198,7 +198,7 @@ extension BTreeNode {
       return children!.last!.inorderPredecessor
     }
   }
-  
+
   /**
    *  Removes `key` and the value associated with it from the node
    *  or one of its descendants.
@@ -208,11 +208,11 @@ extension BTreeNode {
    */
   func remove(_ key: Key) {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if keys[index] == key {
       if isLeaf {
         keys.remove(at: index)
@@ -229,7 +229,7 @@ extension BTreeNode {
       }
     } else if key < keys[index] {
       // We should go to left child...
-      
+
       if let leftChild = children?[index] {
         leftChild.remove(key)
         if leftChild.numberOfKeys < owner.order {
@@ -240,7 +240,7 @@ extension BTreeNode {
       }
     } else {
       // We should go to right child...
-      
+
       if let rightChild = children?[(index + 1)] {
         rightChild.remove(key)
         if rightChild.numberOfKeys < owner.order {
@@ -251,7 +251,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Fixes `childWithTooFewKeys` by either moving a key to it from 
    *  one of its neighbouring nodes, or by merging.
@@ -264,7 +264,7 @@ extension BTreeNode {
    *    - index: the index of the child to be fixed in the current node
    */
   private func fix(childWithTooFewKeys child: BTreeNode, atIndex index: Int) {
-    
+
     if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
       move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
     } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
@@ -275,7 +275,7 @@ extension BTreeNode {
       merge(child: child, atIndex: index, to: .right)
     }
   }
-  
+
   /**
    *  Moves the key at the specified `index` from `node` to
    *  the `targetNode` at `position`
@@ -301,7 +301,7 @@ extension BTreeNode {
                                     at: targetNode.children!.startIndex)
         node.children!.removeLast()
       }
-      
+
     case .right:
       targetNode.keys.insert(keys[index], at: targetNode.keys.endIndex)
       targetNode.values.insert(values[index], at: targetNode.values.endIndex)
@@ -316,7 +316,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Merges `child` at `position` to the node at the `position`.
    *  
@@ -329,33 +329,33 @@ extension BTreeNode {
     switch position {
     case .left:
       // We can merge to the left sibling
-      
+
       children![(index - 1)].keys = children![(index - 1)].keys +
         [keys[(index - 1)]] + child.keys
-      
+
       children![(index - 1)].values = children![(index - 1)].values +
         [values[(index - 1)]] + child.values
-      
+
       keys.remove(at: (index - 1))
       values.remove(at: (index - 1))
-      
+
       if !child.isLeaf {
         children![(index - 1)].children =
           children![(index - 1)].children! + child.children!
       }
-      
+
     case .right:
       // We should merge to the right sibling
-      
+
       children![(index + 1)].keys = child.keys + [keys[index]] +
         children![(index + 1)].keys
-      
+
       children![(index + 1)].values = child.values + [values[index]] +
         children![(index + 1)].values
-      
+
       keys.remove(at: index)
       values.remove(at: index)
-      
+
       if !child.isLeaf {
         children![(index + 1)].children =
           child.children! + children![(index + 1)].children!
@@ -374,18 +374,18 @@ extension BTreeNode {
    */
   var inorderArrayFromKeys: [Key] {
     var array = [Key] ()
-    
+
     for i in 0..<numberOfKeys {
       if let returnedArray = children?[i].inorderArrayFromKeys {
         array += returnedArray
       }
       array += [keys[i]]
     }
-    
+
     if let returnedArray = children?.last?.inorderArrayFromKeys {
       array += returnedArray
     }
-    
+
     return array
   }
 }
@@ -398,13 +398,13 @@ extension BTreeNode: CustomStringConvertible {
    */
   var description: String {
     var str = "\(keys)"
-    
+
     if !isLeaf {
       for child in children! {
         str += child.description
       }
     }
-    
+
     return str
   }
 }
@@ -419,14 +419,14 @@ public class BTree<Key: Comparable, Value> {
    *  except the root node which is allowed to contain less keys than the value of order.
    */
   public let order: Int
-  
+
   /**
    *  The root node of the tree
    */
   var rootNode: BTreeNode<Key, Value>!
-  
+
   fileprivate(set) public var numberOfKeys = 0
-  
+
   /**
    *  Designated initializer for the tree
    *
@@ -484,7 +484,7 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
-    
+
     return rootNode.value(for: key)
   }
 }
@@ -501,12 +501,12 @@ extension BTree {
    */
   public func insert(_ value: Value, for key: Key) {
     rootNode.insert(value, for: key)
-    
+
     if rootNode.numberOfKeys > order * 2 {
       splitRoot()
     }
   }
-  
+
   /**
    *  Splits the root node of the tree.
    *  
@@ -515,7 +515,7 @@ extension BTree {
    */
   private func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
-    
+
     let newRoot = BTreeNode<Key, Value>(
       owner: self,
       keys: [rootNode.keys[middleIndexOfOldRoot]],
@@ -524,7 +524,7 @@ extension BTree {
     )
     rootNode.keys.remove(at: middleIndexOfOldRoot)
     rootNode.values.remove(at: middleIndexOfOldRoot)
-    
+
     let newRightChild = BTreeNode<Key, Value>(
       owner: self,
       keys: Array(rootNode.keys[rootNode.keys.indices.suffix(from: middleIndexOfOldRoot)]),
@@ -532,7 +532,7 @@ extension BTree {
     )
     rootNode.keys.removeSubrange(rootNode.keys.indices.suffix(from: middleIndexOfOldRoot))
     rootNode.values.removeSubrange(rootNode.values.indices.suffix(from: middleIndexOfOldRoot))
-    
+
     if rootNode.children != nil {
       newRightChild.children = Array(
         rootNode.children![rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))]
@@ -541,7 +541,7 @@ extension BTree {
         rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))
       )
     }
-    
+
     newRoot.children!.append(newRightChild)
     rootNode = newRoot
   }
@@ -560,9 +560,9 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
-    
+
     rootNode.remove(key)
-    
+
     if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
       rootNode = rootNode.children!.first!
     }
diff --git a/B-Tree/BTree.swift b/B-Tree/BTree.swift
index 52cda4e43..2693eb308 100644
--- a/B-Tree/BTree.swift
+++ b/B-Tree/BTree.swift
@@ -33,23 +33,23 @@ class BTreeNode<Key: Comparable, Value> {
    * The tree that owns the node.
    */
   unowned var owner: BTree<Key, Value>
-  
+
   fileprivate var keys = [Key]()
   fileprivate var values = [Value]()
   var children: [BTreeNode]?
-  
+
   var isLeaf: Bool {
     return children == nil
   }
-  
+
   var numberOfKeys: Int {
     return keys.count
   }
-  
+
   init(owner: BTree<Key, Value>) {
     self.owner = owner
   }
-  
+
   convenience init(owner: BTree<Key, Value>, keys: [Key],
                    values: [Value], children: [BTreeNode]? = nil) {
     self.init(owner: owner)
@@ -62,7 +62,7 @@ class BTreeNode<Key: Comparable, Value> {
 // MARK: BTreeNode extesnion: Searching
 
 extension BTreeNode {
-  
+
   /**
    *  Returns the value for a given `key`, returns nil if the `key` is not found.
    *  
@@ -71,11 +71,11 @@ extension BTreeNode {
    */
   func value(for key: Key) -> Value? {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if key == keys[index] {
       return values[index]
     } else if key < keys[index] {
@@ -89,7 +89,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Travelsals
 
 extension BTreeNode {
-  
+
   /**
    *  Traverses the keys in order, executes `process` for every key.
    * 
@@ -101,7 +101,7 @@ extension BTreeNode {
       children?[i].traverseKeysInOrder(process)
       process(keys[i])
     }
-    
+
     children?.last?.traverseKeysInOrder(process)
   }
 }
@@ -109,7 +109,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Insertion
 
 extension BTreeNode {
-  
+
   /**
    *  Inserts `value` for `key` to the node, or to one if its descendants.
    *  
@@ -119,16 +119,16 @@ extension BTreeNode {
    */
   func insert(_ value: Value, for key: Key) {
     var index = keys.startIndex
-    
+
     while index < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if index < keys.endIndex && keys[index] == key {
       values[index] = value
       return
     }
-    
+
     if isLeaf {
       keys.insert(key, at: index)
       values.insert(value, at: index)
@@ -140,7 +140,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Splits `child` at `index`.
    *  The key-value pair at `index` gets moved up to the parent node,
@@ -156,7 +156,7 @@ extension BTreeNode {
     values.insert(child.values[middleIndex], at: index)
     child.keys.remove(at: middleIndex)
     child.values.remove(at: middleIndex)
-    
+
     let rightSibling = BTreeNode(
       owner: owner,
       keys: Array(child.keys[child.keys.indices.suffix(from: middleIndex)]),
@@ -164,9 +164,9 @@ extension BTreeNode {
     )
     child.keys.removeSubrange(child.keys.indices.suffix(from: middleIndex))
     child.values.removeSubrange(child.values.indices.suffix(from: middleIndex))
-    
+
     children!.insert(rightSibling, at: (index + 1))
-    
+
     if child.children != nil {
       rightSibling.children = Array(
         child.children![child.children!.indices.suffix(from: (middleIndex + 1))]
@@ -198,7 +198,7 @@ extension BTreeNode {
       return children!.last!.inorderPredecessor
     }
   }
-  
+
   /**
    *  Removes `key` and the value associated with it from the node
    *  or one of its descendants.
@@ -208,11 +208,11 @@ extension BTreeNode {
    */
   func remove(_ key: Key) {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if keys[index] == key {
       if isLeaf {
         keys.remove(at: index)
@@ -229,7 +229,7 @@ extension BTreeNode {
       }
     } else if key < keys[index] {
       // We should go to left child...
-      
+
       if let leftChild = children?[index] {
         leftChild.remove(key)
         if leftChild.numberOfKeys < owner.order {
@@ -240,7 +240,7 @@ extension BTreeNode {
       }
     } else {
       // We should go to right child...
-      
+
       if let rightChild = children?[(index + 1)] {
         rightChild.remove(key)
         if rightChild.numberOfKeys < owner.order {
@@ -251,7 +251,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Fixes `childWithTooFewKeys` by either moving a key to it from 
    *  one of its neighbouring nodes, or by merging.
@@ -264,7 +264,7 @@ extension BTreeNode {
    *    - index: the index of the child to be fixed in the current node
    */
   private func fix(childWithTooFewKeys child: BTreeNode, atIndex index: Int) {
-    
+
     if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
       move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
     } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
@@ -275,7 +275,7 @@ extension BTreeNode {
       merge(child: child, atIndex: index, to: .right)
     }
   }
-  
+
   /**
    *  Moves the key at the specified `index` from `node` to
    *  the `targetNode` at `position`
@@ -301,7 +301,7 @@ extension BTreeNode {
                                     at: targetNode.children!.startIndex)
         node.children!.removeLast()
       }
-      
+
     case .right:
       targetNode.keys.insert(keys[index], at: targetNode.keys.endIndex)
       targetNode.values.insert(values[index], at: targetNode.values.endIndex)
@@ -316,7 +316,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Merges `child` at `position` to the node at the `position`.
    *  
@@ -329,33 +329,33 @@ extension BTreeNode {
     switch position {
     case .left:
       // We can merge to the left sibling
-      
+
       children![(index - 1)].keys = children![(index - 1)].keys +
         [keys[(index - 1)]] + child.keys
-      
+
       children![(index - 1)].values = children![(index - 1)].values +
         [values[(index - 1)]] + child.values
-      
+
       keys.remove(at: (index - 1))
       values.remove(at: (index - 1))
-      
+
       if !child.isLeaf {
         children![(index - 1)].children =
           children![(index - 1)].children! + child.children!
       }
-      
+
     case .right:
       // We should merge to the right sibling
-      
+
       children![(index + 1)].keys = child.keys + [keys[index]] +
         children![(index + 1)].keys
-      
+
       children![(index + 1)].values = child.values + [values[index]] +
         children![(index + 1)].values
-      
+
       keys.remove(at: index)
       values.remove(at: index)
-      
+
       if !child.isLeaf {
         children![(index + 1)].children =
           child.children! + children![(index + 1)].children!
@@ -374,18 +374,18 @@ extension BTreeNode {
    */
   var inorderArrayFromKeys: [Key] {
     var array = [Key] ()
-    
+
     for i in 0..<numberOfKeys {
       if let returnedArray = children?[i].inorderArrayFromKeys {
         array += returnedArray
       }
       array += [keys[i]]
     }
-    
+
     if let returnedArray = children?.last?.inorderArrayFromKeys {
       array += returnedArray
     }
-    
+
     return array
   }
 }
@@ -398,13 +398,13 @@ extension BTreeNode: CustomStringConvertible {
    */
   var description: String {
     var str = "\(keys)"
-    
+
     if !isLeaf {
       for child in children! {
         str += child.description
       }
     }
-    
+
     return str
   }
 }
@@ -419,14 +419,14 @@ public class BTree<Key: Comparable, Value> {
    *  except the root node which is allowed to contain less keys than the value of order.
    */
   public let order: Int
-  
+
   /**
    *  The root node of the tree
    */
   var rootNode: BTreeNode<Key, Value>!
-  
+
   fileprivate(set) public var numberOfKeys = 0
-  
+
   /**
    *  Designated initializer for the tree
    *
@@ -484,7 +484,7 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
-    
+
     return rootNode.value(for: key)
   }
 }
@@ -501,12 +501,12 @@ extension BTree {
    */
   public func insert(_ value: Value, for key: Key) {
     rootNode.insert(value, for: key)
-    
+
     if rootNode.numberOfKeys > order * 2 {
       splitRoot()
     }
   }
-  
+
   /**
    *  Splits the root node of the tree.
    *  
@@ -515,7 +515,7 @@ extension BTree {
    */
   private func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
-    
+
     let newRoot = BTreeNode<Key, Value>(
       owner: self,
       keys: [rootNode.keys[middleIndexOfOldRoot]],
@@ -524,7 +524,7 @@ extension BTree {
     )
     rootNode.keys.remove(at: middleIndexOfOldRoot)
     rootNode.values.remove(at: middleIndexOfOldRoot)
-    
+
     let newRightChild = BTreeNode<Key, Value>(
       owner: self,
       keys: Array(rootNode.keys[rootNode.keys.indices.suffix(from: middleIndexOfOldRoot)]),
@@ -532,7 +532,7 @@ extension BTree {
     )
     rootNode.keys.removeSubrange(rootNode.keys.indices.suffix(from: middleIndexOfOldRoot))
     rootNode.values.removeSubrange(rootNode.values.indices.suffix(from: middleIndexOfOldRoot))
-    
+
     if rootNode.children != nil {
       newRightChild.children = Array(
         rootNode.children![rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))]
@@ -541,7 +541,7 @@ extension BTree {
         rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))
       )
     }
-    
+
     newRoot.children!.append(newRightChild)
     rootNode = newRoot
   }
@@ -560,9 +560,9 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
-    
+
     rootNode.remove(key)
-    
+
     if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
       rootNode = rootNode.children!.first!
     }
diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index fd3ba10e8..8eff926b5 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -9,44 +9,44 @@
 import XCTest
 
 class BTreeNodeTests: XCTestCase {
-  
+
   let owner = BTree<Int, Int>(order: 2)!
   var root: BTreeNode<Int, Int>!
   var leftChild: BTreeNode<Int, Int>!
   var rightChild: BTreeNode<Int, Int>!
-  
+
   override func setUp() {
     super.setUp()
-    
+
     root = BTreeNode(owner: owner)
     leftChild = BTreeNode(owner: owner)
     rightChild = BTreeNode(owner: owner)
-    
+
     root.insert(1, for: 1)
     root.children = [leftChild, rightChild]
   }
-  
+
   func testIsLeafRoot() {
     XCTAssertFalse(root.isLeaf)
   }
-  
+
   func testIsLeafLeaf() {
     XCTAssertTrue(leftChild.isLeaf)
     XCTAssertTrue(rightChild.isLeaf)
   }
-  
+
   func testOwner() {
     XCTAssert(root.owner === owner)
     XCTAssert(leftChild.owner === owner)
     XCTAssert(rightChild.owner === owner)
   }
-  
+
   func testNumberOfKeys() {
     XCTAssertEqual(root.numberOfKeys, 1)
     XCTAssertEqual(leftChild.numberOfKeys, 0)
     XCTAssertEqual(rightChild.numberOfKeys, 0)
   }
-  
+
   func testChildren() {
     XCTAssertEqual(root.children!.count, 2)
   }
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index f2dac7511..1e94bfd7d 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -10,201 +10,201 @@ import XCTest
 
 class BTreeTests: XCTestCase {
   var bTree: BTree<Int, Int>!
-  
+
   override func setUp() {
     super.setUp()
     bTree = BTree<Int, Int>(order: 3)!
   }
-  
+
   // MARK: - Tests on empty tree
-  
+
   func testOrder() {
     XCTAssertEqual(bTree.order, 3)
   }
-  
+
   func testRootNode() {
     XCTAssertNotNil(bTree.rootNode)
   }
-  
+
   func testNumberOfNodesOnEmptyTree() {
     XCTAssertEqual(bTree.numberOfKeys, 0)
   }
-  
+
   func testInorderTraversalOfEmptyTree() {
     bTree.traverseKeysInOrder { _ in
       XCTFail("Inorder travelsal fail.")
     }
   }
-  
+
   func testSubscriptOnEmptyTree() {
     XCTAssertEqual(bTree[1], nil)
   }
-  
+
   func testSearchEmptyTree() {
     XCTAssertEqual(bTree.value(for: 1), nil)
   }
-  
+
   func testInsertToEmptyTree() {
     bTree.insert(1, for: 1)
-    
+
     XCTAssertEqual(bTree[1]!, 1)
   }
-  
+
   func testRemoveFromEmptyTree() {
     bTree.remove(1)
     XCTAssertEqual(bTree.description, "[]")
   }
-  
+
   func testInorderArrayFromEmptyTree() {
     XCTAssertEqual(bTree.inorderArrayFromKeys, [Int]())
   }
-  
+
   func testDescriptionOfEmptyTree() {
     XCTAssertEqual(bTree.description, "[]")
   }
-  
+
   // MARK: - Travelsal
-  
+
   func testInorderTravelsal() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     var j = 1
-    
+
     bTree.traverseKeysInOrder { i in
       XCTAssertEqual(i, j)
       j += 1
     }
   }
-  
+
   // MARK: - Searching
-  
+
   func testSearchForMaximum() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     XCTAssertEqual(bTree.value(for: 20)!, 20)
   }
-  
+
   func testSearchForMinimum() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     XCTAssertEqual(bTree.value(for: 1)!, 1)
   }
-  
+
   // MARK: - Insertion
-  
+
   func testInsertion() {
     bTree.insertKeysUpTo(20)
-    
+
     XCTAssertEqual(bTree.numberOfKeys, 20)
-    
+
     for i in 1...20 {
       XCTAssertNotNil(bTree[i])
     }
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   // MARK: - Removal
-  
+
   func testRemoveMaximum() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     bTree.remove(20)
-    
+
     XCTAssertNil(bTree[20])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveMinimum() {
     bTree.insertKeysUpTo(20)
-    
+
     bTree.remove(1)
-    
+
     XCTAssertNil(bTree[1])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveSome() {
     bTree.insertKeysUpTo(20)
-    
+
     bTree.remove(6)
     bTree.remove(9)
-    
+
     XCTAssertNil(bTree[6])
     XCTAssertNil(bTree[9])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveSomeFrom2ndOrder() {
     bTree = BTree<Int, Int>(order: 2)!
     bTree.insertKeysUpTo(20)
-    
+
     bTree.remove(6)
     bTree.remove(9)
-    
+
     XCTAssertNil(bTree[6])
     XCTAssertNil(bTree[9])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveAll() {
     bTree.insertKeysUpTo(20)
-    
+
     XCTAssertEqual(bTree.numberOfKeys, 20)
-    
+
     for i in (1...20).reversed() {
       bTree.remove(i)
     }
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
-    
+
     XCTAssertEqual(bTree.numberOfKeys, 0)
   }
-  
+
   // MARK: - InorderArray
-  
+
 	func testInorderArray() {
     bTree.insertKeysUpTo(20)
-		
+
 		let returnedArray = bTree.inorderArrayFromKeys
 		let targetArray = Array<Int>(1...20)
-		
+
 		XCTAssertEqual(returnedArray, targetArray)
 	}
 }
@@ -221,7 +221,7 @@ extension BTreeNode {
     } else if !root && numberOfKeys < owner.order {
       throw BTreeError.tooFewNodes
     }
-    
+
     if !isLeaf {
       for child in children! {
         try child.checkBalance(isRoot: false)
@@ -234,14 +234,14 @@ extension BTree where Key: SignedInteger, Value: SignedInteger {
   func insertKeysUpTo(_ to: Int) {
     var k: Key = 1
     var v: Value = 1
-    
+
     for _ in 1...to {
       insert(v, for: k)
       k = k + 1
       v = v + 1
     }
   }
-  
+
   func checkBalance() throws {
     try rootNode.checkBalance(isRoot: true)
   }
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index 00ac6da97..b9f2b1432 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -2,7 +2,7 @@
 
 extension String {
   func indexOf(_ pattern: String) -> String.Index? {
-    
+
     for i in self.characters.indices {
       var j = i
       var found = true
diff --git a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift
index b6e85fa2b..f7c4eec61 100644
--- a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
@@ -11,13 +11,13 @@ public func combSort<T: Comparable>(_ input: [T]) -> [T] {
     var copy: [T] = input
     var gap = copy.count
     let shrink = 1.3
-    
+
     while gap > 1 {
         gap = (Int)(Double(gap) / shrink)
         if gap < 1 {
             gap = 1
         }
-        
+
         var index = 0
         while !(index + gap >= copy.count) {
             if copy[index] > copy[index + gap] {
diff --git a/Comb Sort/Comb Sort.swift b/Comb Sort/Comb Sort.swift
index b6e85fa2b..f7c4eec61 100644
--- a/Comb Sort/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.swift	
@@ -11,13 +11,13 @@ public func combSort<T: Comparable>(_ input: [T]) -> [T] {
     var copy: [T] = input
     var gap = copy.count
     let shrink = 1.3
-    
+
     while gap > 1 {
         gap = (Int)(Double(gap) / shrink)
         if gap < 1 {
             gap = 1
         }
-        
+
         var index = 0
         while !(index + gap >= copy.count) {
             if copy[index] > copy[index + gap] {
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index 1bcc67fd0..b9287f84a 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -16,7 +16,7 @@ class CombSortTests: XCTestCase {
         super.setUp()
         sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
     }
-    
+
     override func tearDown() {
         super.tearDown()
     }
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
index 4f8496cd5..bfe15e1a7 100644
--- a/Convex Hull/Convex Hull/AppDelegate.swift	
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -17,16 +17,16 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
     func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
 
         let screenBounds = UIScreen.main.bounds
-        
+
         window = UIWindow(frame: screenBounds)
-        
+
         let viewController = UIViewController()
         viewController.view = View(frame: (window?.frame)!)
         viewController.view.backgroundColor = .white
-        
+
         window?.rootViewController = viewController
         window?.makeKeyAndVisible()
-        
+
         return true
     }
 
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index f9f9f6ef4..2f2c3e046 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -9,24 +9,24 @@
 import UIKit
 
 class View: UIView {
-    
+
     let MAX_POINTS = 100
-    
+
     var points = [CGPoint]()
-    
+
     var convexHull = [CGPoint]()
-    
+
     override init(frame: CGRect) {
         super.init(frame: frame)
-        
+
         generatePoints()
         quickHull(points: points)
     }
-    
+
     required init?(coder aDecoder: NSCoder) {
         fatalError("init(coder:) has not been implemented")
     }
-    
+
     func generatePoints() {
         for _ in 0..<MAX_POINTS {
             let offset: CGFloat = 50
@@ -35,101 +35,101 @@ class View: UIView {
             let point = CGPoint(x: xrand, y: yrand)
             points.append(point)
         }
-        
+
         points.sort { (a: CGPoint, b: CGPoint) -> Bool in
             return a.x < b.x
         }
     }
-    
+
     func quickHull(points: [CGPoint]) {
         var pts = points
-                
+
         // Assume points has at least 2 points
         // Assume list is ordered on x
-        
+
         // left most point
         let p1 = pts.removeFirst()
         // right most point
         let p2 = pts.removeLast()
-        
+
         // p1 and p2 are outer most points and thus are part of the hull
         convexHull.append(p1)
         convexHull.append(p2)
-        
+
         // points to the right of oriented line from p1 to p2
         var s1 = [CGPoint]()
-        
+
         // points to the right of oriented line from p2 to p1
         var s2 = [CGPoint]()
-        
+
         // p1 to p2 line
         let lineVec1 = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
-        
+
         for p in pts { // per point check if point is to right or left of p1 to p2 line
             let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y)
             let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // cross product to check on which side of the line point p is.
-            
+
             if sign1 > 0 { // right of p1 p2 line (in a normal xy coordinate system this would be < 0 but due to the weird iPhone screen coordinates this is > 0
                 s1.append(p)
             } else { // right of p2 p1 line
                 s2.append(p)
             }
         }
-        
+
         // find new hull points
         findHull(s1, p1, p2)
         findHull(s2, p2, p1)
     }
-    
+
     func findHull(_ points: [CGPoint], _ p1: CGPoint, _ p2: CGPoint) {
         // if set of points is empty there are no points to the right of this line so this line is part of the hull.
         if points.isEmpty {
             return
         }
-        
+
         var pts = points
-        
+
         // calculate parameters of general line equation y = a * x + b
         let a = (p1.y - p2.y) / (p1.x - p2.x)
         let b = p1.y - a * p1.x
-        
+
         // calculate normal line's growth factor
         let a1 = -1 / a
-        
+
         var maxDist: CGFloat = -1
         var maxPoint: CGPoint = pts.first!
-        
+
         for p in pts { // for every point check the distance from our line
             let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
             let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
             let y = a * x + b // calculate y value of this intersect point
-            
+
             let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
             if dist > maxDist { // if distance is larger than current maxDist remember new point p
                 maxDist = dist
                 maxPoint = p
             }
         }
-        
+
         convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
-        
+
         pts.remove(at: pts.index(of: maxPoint)!) // remove maxPoint from points array as we are going to split this array in points left and right of the line
-        
+
         // points to the right of oriented line from p1 to maxPoint
         var s1 = [CGPoint]()
-        
+
         // points to the right of oriented line from maxPoint to p2
         var s2 = [CGPoint]()
-        
+
         // p1 to maxPoint line
         let lineVec1 = CGPoint(x: maxPoint.x - p1.x, y: maxPoint.y - p1.y)
         // maxPoint to p2 line
         let lineVec2 = CGPoint(x: p2.x - maxPoint.x, y: p2.y - maxPoint.y)
-        
+
         for p in pts {
             let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y) // vector from p1 to p
             let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // sign to check is p is to the right or left of lineVec1
-            
+
             let pVec2 = CGPoint(x: p.x - maxPoint.x, y: p.y - maxPoint.y) // vector from p2 to p
             let sign2 = lineVec2.x * pVec2.y - pVec2.x * lineVec2.y // sign to check is p is to the right or left of lineVec2
 
@@ -139,34 +139,34 @@ class View: UIView {
                 s2.append(p)
             }
         }
-        
+
         // find new hull points
         findHull(s1, p1, maxPoint)
         findHull(s2, maxPoint, p2)
     }
 
     override func draw(_ rect: CGRect) {
-        
+
         let context = UIGraphicsGetCurrentContext()
-        
+
         // Draw hull
         let lineWidth: CGFloat = 2.0
-        
+
         context!.setFillColor(UIColor.black.cgColor)
         context!.setLineWidth(lineWidth)
         context!.setStrokeColor(UIColor.red.cgColor)
         context!.setFillColor(UIColor.black.cgColor)
-        
+
         let firstPoint = convexHull.first!
         context!.move(to: firstPoint)
-        
+
         for p in convexHull.dropFirst() {
             context!.addLine(to: p)
         }
         context!.addLine(to: firstPoint)
-        
+
         context!.strokePath()
-        
+
         // Draw points
         for p in points {
             let radius: CGFloat = 5
diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 4bc5d66df..8ef545e45 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -10,25 +10,25 @@ struct FixedSizeArray<T> {
   private var defaultValue: T
   private var array: [T]
   private (set) var count = 0
-  
+
   init(maxSize: Int, defaultValue: T) {
     self.maxSize = maxSize
     self.defaultValue = defaultValue
     self.array = [T](repeating: defaultValue, count: maxSize)
   }
-  
+
   subscript(index: Int) -> T {
     assert(index >= 0)
     assert(index < count)
     return array[index]
   }
-  
+
   mutating func append(_ newElement: T) {
     assert(count < maxSize)
     array[count] = newElement
     count += 1
   }
-  
+
   mutating func removeAt(index: Int) -> T {
     assert(index >= 0)
     assert(index < count)
@@ -38,7 +38,7 @@ struct FixedSizeArray<T> {
     array[count] = defaultValue
     return result
   }
-  
+
   mutating func removeAll() {
     for i in 0..<count {
       array[i] = defaultValue
diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index 77de8484b..fde396e64 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,7 +1,7 @@
 import Graph
 
 for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
-    
+
   let v1 = graph.createVertex(1)
   let v2 = graph.createVertex(2)
   let v3 = graph.createVertex(3)
diff --git a/Hash Set/HashSet.playground/Sources/HashSet.swift b/Hash Set/HashSet.playground/Sources/HashSet.swift
index c3365110b..3ccaa94ea 100644
--- a/Hash Set/HashSet.playground/Sources/HashSet.swift	
+++ b/Hash Set/HashSet.playground/Sources/HashSet.swift	
@@ -2,31 +2,31 @@
 
 public struct HashSet<T: Hashable> {
     fileprivate var dictionary = Dictionary<T, Bool>()
-    
+
     public init() {
-        
+
     }
-    
+
     public mutating func insert(_ element: T) {
         dictionary[element] = true
     }
-    
+
     public mutating func remove(_ element: T) {
         dictionary[element] = nil
     }
-    
+
     public func contains(_ element: T) -> Bool {
         return dictionary[element] != nil
     }
-    
+
     public func allElements() -> [T] {
         return Array(dictionary.keys)
     }
-    
+
     public var count: Int {
         return dictionary.count
     }
-    
+
     public var isEmpty: Bool {
         return dictionary.isEmpty
     }
diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
index 947737c32..2383b8192 100644
--- a/Hash Table/HashTable.playground/Sources/HashTable.swift	
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -34,19 +34,19 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
     private typealias Element = (key: Key, value: Value)
     private typealias Bucket = [Element]
     private var buckets: [Bucket]
-    
+
     /// The number of key-value pairs in the hash table.
     private(set) public var count = 0
-    
+
     /// A Boolean value that indicates whether the hash table is empty.
     public var isEmpty: Bool { return count == 0 }
-    
+
     /// A string that represents the contents of the hash table.
     public var description: String {
         let pairs = buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }
         return pairs.joined(separator: ", ")
     }
-    
+
     /// A string that represents the contents of
     /// the hash table, suitable for debugging.
     public var debugDescription: String {
@@ -57,7 +57,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         }
         return str
     }
-    
+
     /**
      Create a hash table with the given capacity.
      */
@@ -65,7 +65,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         assert(capacity > 0)
         buckets = Array<Bucket>(repeatElement([], count: capacity))
     }
-    
+
     /**
      Accesses the value associated with
      the given key for reading and writing.
@@ -82,7 +82,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
             }
         }
     }
-    
+
     /**
      Returns the value for the given key.
      */
@@ -95,14 +95,14 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         }
         return nil  // key not in hash table
     }
-    
+
     /**
      Updates the value stored in the hash table for the given key,
      or adds a new key-value pair if the key does not exist.
      */
     @discardableResult public mutating func updateValue(_ value: Value, forKey key: Key) -> Value? {
         let index = self.index(forKey: key)
-        
+
         // Do we already have this key in the bucket?
         for (i, element) in buckets[index].enumerated() {
             if element.key == key {
@@ -111,20 +111,20 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
                 return oldValue
             }
         }
-        
+
         // This key isn't in the bucket yet; add it to the chain.
         buckets[index].append((key: key, value: value))
         count += 1
         return nil
     }
-    
+
     /**
      Removes the given key and its
      associated value from the hash table.
      */
     @discardableResult public mutating func removeValue(forKey key: Key) -> Value? {
         let index = self.index(forKey: key)
-        
+
         // Find the element in the bucket's chain and remove it.
         for (i, element) in buckets[index].enumerated() {
             if element.key == key {
@@ -135,7 +135,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         }
         return nil  // key not in hash table
     }
-    
+
     /**
      Removes all key-value pairs from the hash table.
      */
@@ -143,7 +143,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         buckets = Array<Bucket>(repeatElement([], count: buckets.count))
         count = 0
     }
-    
+
     /**
      Returns the given key's array index.
      */
diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index a6effb7b0..449fa366d 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,25 +1,25 @@
 import UIKit
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
-    
+
     let haversin = { (angle: Double) -> Double in
         return (1 - cos(angle))/2
     }
-    
+
     let ahaversin = { (angle: Double) -> Double in
         return 2*asin(sqrt(angle))
     }
-    
+
     // Converts from degrees to radians
     let dToR = { (angle: Double) -> Double in
         return (angle / 360) * 2 * M_PI
     }
-    
+
     let lat1 = dToR(la1)
     let lon1 = dToR(lo1)
     let lat2 = dToR(la2)
     let lon2 = dToR(lo2)
-    
+
     return radius * ahaversin(haversin(lat2 - lat1) + cos(lat1) * cos(lat2) * haversin(lon2 - lon1))
 }
 
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index fa30df362..80b40c65f 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -113,7 +113,7 @@ public struct Heap<T> {
    */
   public mutating func replace(index i: Int, value: T) {
     guard i < elements.count else { return }
-    
+
     assert(isOrderedBefore(value, elements[i]))
     elements[i] = value
     shiftUp(i)
@@ -144,7 +144,7 @@ public struct Heap<T> {
    */
   public mutating func removeAt(_ index: Int) -> T? {
     guard index < elements.count else { return nil }
-    
+
     let size = elements.count - 1
     if index != size {
       swap(&elements[index], &elements[size])
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 0e6c504f3..cac934406 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -201,7 +201,7 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-    
+
     let v1 = h.removeAt(5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
@@ -314,7 +314,7 @@ class HeapTests: XCTestCase {
     h.replace(index: 5, value: 13)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-    
+
     //test index out of bounds
     h.replace(index: 20, value: 2)
     XCTAssertTrue(verifyMaxHeap(h))
diff --git a/Huffman Coding/Huffman.swift b/Huffman Coding/Huffman.swift
index 7e2961a2f..cad80327d 100644
--- a/Huffman Coding/Huffman.swift	
+++ b/Huffman Coding/Huffman.swift	
@@ -13,7 +13,7 @@ public class Huffman {
     /* Tree nodes don't use pointers to refer to each other, but simple integer
      indices. That allows us to use structs for the nodes. */
     typealias NodeIndex = Int
-    
+
     /* A node in the compression tree. Leaf nodes represent the actual bytes that
      are present in the input data. The count of an intermediary node is the sum
      of the counts of all nodes below it. The root node's count is the number of
@@ -25,15 +25,15 @@ public class Huffman {
         var left: NodeIndex = -1
         var right: NodeIndex = -1
     }
-    
+
     /* The tree structure. The first 256 entries are for the leaf nodes (not all
      of those may be used, depending on the input). We add additional nodes as
      we build the tree. */
     var tree = [Node](repeating: Node(), count: 256)
-    
+
     /* This is the last node we add to the tree. */
     var root: NodeIndex = -1
-    
+
     /* The frequency table describes how often a byte occurs in the input data.
      You need it to decompress the Huffman-encoded data. The frequency table
      should be serialized along with the compressed data. */
@@ -41,7 +41,7 @@ public class Huffman {
         var byte: UInt8 = 0
         var count = 0
     }
-    
+
     public init() { }
 }
 
@@ -59,7 +59,7 @@ extension Huffman {
             ptr = ptr.successor()
         }
     }
-    
+
     /* Takes a frequency table and rebuilds the tree. This is the first step of
      decompression. */
     fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
@@ -70,7 +70,7 @@ extension Huffman {
         }
         buildTree()
     }
-    
+
     /* Returns the frequency table. This is the first 256 nodes from the tree but
      only those that are actually used, without the parent/left/right pointers.
      You would serialize this along with the compressed file. */
@@ -91,13 +91,13 @@ extension Huffman {
         for node in tree where node.count > 0 {
             queue.enqueue(node)
         }
-        
+
         while queue.count > 1 {
             // Find the two nodes with the smallest frequencies that do not have
             // a parent node yet.
             let node1 = queue.dequeue()!
             let node2 = queue.dequeue()!
-            
+
             // Create a new intermediate node.
             var parentNode = Node()
             parentNode.count = node1.count + node2.count
@@ -105,15 +105,15 @@ extension Huffman {
             parentNode.right = node2.index
             parentNode.index = tree.count
             tree.append(parentNode)
-            
+
             // Link the two nodes into their new parent node.
             tree[node1.index].parent = parentNode.index
             tree[node2.index].parent = parentNode.index
-            
+
             // Put the intermediate node back into the queue.
             queue.enqueue(parentNode)
         }
-        
+
         // The final remaining node in the queue becomes the root of the tree.
         let rootNode = queue.dequeue()!
         root = rootNode.index
@@ -125,7 +125,7 @@ extension Huffman {
     public func compressData(data: NSData) -> NSData {
         countByteFrequency(inData: data)
         buildTree()
-        
+
         let writer = BitWriter()
         var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
         for _ in 0..<data.length {
@@ -137,7 +137,7 @@ extension Huffman {
         writer.flush()
         return writer.data
     }
-    
+
     /* Recursively walks the tree from a leaf node up to the root, and then back
      again. If a child is the right node, we emit a 0 bit; if it's the left node,
      we emit a 1 bit. */
@@ -159,11 +159,11 @@ extension Huffman {
     /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
     public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
         restoreTree(fromTable: frequencyTable)
-        
+
         let reader = BitReader(data: data)
         let outData = NSMutableData()
         let byteCount = tree[root].count
-        
+
         var i = 0
         while i < byteCount {
             var b = findLeafNode(reader: reader, nodeIndex: root)
@@ -172,7 +172,7 @@ extension Huffman {
         }
         return outData
     }
-    
+
     /* Walks the tree from the root down to the leaf node. At every node, read the
      next bit and use that to determine whether to step to the left or right.
      When we get to the leaf node, we simply return its index, which is equal to
diff --git a/Huffman Coding/NSData+Bits.swift b/Huffman Coding/NSData+Bits.swift
index 4ae3c5c6d..1f5333296 100644
--- a/Huffman Coding/NSData+Bits.swift	
+++ b/Huffman Coding/NSData+Bits.swift	
@@ -5,7 +5,7 @@ public class BitWriter {
     public var data = NSMutableData()
     var outByte: UInt8 = 0
     var outCount = 0
-    
+
     public func writeBit(bit: Bool) {
         if outCount == 8 {
             data.append(&outByte, length: 1)
@@ -14,7 +14,7 @@ public class BitWriter {
         outByte = (outByte << 1) | (bit ? 1 : 0)
         outCount += 1
     }
-    
+
     public func flush() {
         if outCount > 0 {
             if outCount < 8 {
@@ -31,11 +31,11 @@ public class BitReader {
     var ptr: UnsafePointer<UInt8>
     var inByte: UInt8 = 0
     var inCount = 8
-    
+
     public init(data: NSData) {
         ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
     }
-    
+
     public func readBit() -> Bool {
         if inCount == 8 {
             inByte = ptr.pointee    // load the next byte
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 3ac29301a..2d327fbac 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -17,7 +17,7 @@ func ^^ (radix: Int, power: Int) -> Int {
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
   let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
   let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
-  
+
   var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
 
   for i in num1Array.indices {
@@ -29,7 +29,7 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
     }
     product[i + num2Array.count] += carry
   }
-  
+
   return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
@@ -37,24 +37,24 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters
-  
+
   guard num1Array.count > 1 && num2Array.count > 1 else {
     return multiply(num1, by: num2)
   }
-  
+
   let n = max(num1Array.count, num2Array.count)
   let nBy2 = n / 2
-  
+
   let a = num1 / 10^^nBy2
   let b = num1 % 10^^nBy2
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
-  
+
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
   let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-  
+
   let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-  
+
   return product
 }
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index fb20a667d..0f0e8ed12 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -22,24 +22,24 @@ func ^^ (radix: Int, power: Int) -> Int {
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters
-  
+
   guard num1Array.count > 1 && num2Array.count > 1 else {
     return num1 * num2
   }
-  
+
   let n = max(num1Array.count, num2Array.count)
   let nBy2 = n / 2
-  
+
   let a = num1 / 10^^nBy2
   let b = num1 % 10^^nBy2
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
-  
+
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
   let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-  
+
   let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-  
+
   return product
 }
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 46a88c134..45d9812b7 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -9,54 +9,54 @@
 import Foundation
 
 extension String {
-    
+
     func indexesOf(ptnr: String) -> [Int]? {
-        
+
         let text = Array(self.characters)
         let pattern = Array(ptnr.characters)
-        
+
         let textLength: Int = text.count
         let patternLength: Int = pattern.count
-        
+
         guard patternLength > 0 else {
             return nil
         }
-        
+
         var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
         var textIndex: Int = 0
         var patternIndex: Int = 0
         var indexes: [Int] = [Int]()
-        
+
         /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
         let zeta = ZetaAlgorithm(ptnr: ptnr)
-        
+
         for patternIndex in (1 ..< patternLength).reversed() {
             textIndex = patternIndex + zeta![patternIndex] - 1
             suffixPrefix[textIndex] = zeta![patternIndex]
         }
-        
+
         /* Search stage: scanning the text for pattern matching */
         textIndex = 0
         patternIndex = 0
-        
+
         while textIndex + (patternLength - patternIndex - 1) < textLength {
-            
+
             while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
                 textIndex = textIndex + 1
                 patternIndex = patternIndex + 1
             }
-            
+
             if patternIndex == patternLength {
                 indexes.append(textIndex - patternIndex)
             }
-            
+
             if patternIndex == 0 {
                 textIndex = textIndex + 1
             } else {
                 patternIndex = suffixPrefix[patternIndex - 1]
             }
         }
-        
+
         guard !indexes.isEmpty else {
             return nil
         }
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 08e14ef70..9ee4cc4c4 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -4,37 +4,37 @@
 
 //: Linked List Class Declaration:
 public final class LinkedList<T> {
-  
+
   /// Linked List's Node Class Declaration
   public class LinkedListNode<T> {
     var value: T
     var next: LinkedListNode?
     weak var previous: LinkedListNode?
-    
+
     public init(value: T) {
       self.value = value
     }
   }
-  
+
   /// Typealiasing the node class to increase readability of code
   public typealias Node = LinkedListNode<T>
-  
+
   /// The head of the Linked List
   fileprivate var head: Node?
-  
+
   /// Default initializer
   public init() {}
-  
+
   /// Computed property to check if the linked list is empty
   public var isEmpty: Bool {
     return head == nil
   }
-  
+
   /// Computed property to get the first node in the linked list (if any)
   public var first: Node? {
     return head
   }
-  
+
   /// Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
     if var node = head {
@@ -46,7 +46,7 @@ public final class LinkedList<T> {
       return nil
     }
   }
-  
+
   /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
     if var node = head {
@@ -60,7 +60,7 @@ public final class LinkedList<T> {
       return 0
     }
   }
-  
+
   /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameter index: Integer value of the node's index to be returned
@@ -77,7 +77,7 @@ public final class LinkedList<T> {
     }
     return nil
   }
-  
+
   /// Subscript function to return the node at a specific index
   ///
   /// - Parameter index: Integer value of the requested value's index
@@ -86,7 +86,7 @@ public final class LinkedList<T> {
     assert(node != nil)
     return node!.value
   }
-  
+
   /// Append a value to the end of the list
   ///
   /// - Parameter value: The data value to be appended
@@ -94,7 +94,7 @@ public final class LinkedList<T> {
     let newNode = Node(value: value)
     self.append(newNode)
   }
-  
+
   /// Append a copy of a LinkedListNode to the end of the list.
   ///
   /// - Parameter node: The node containing the value to be appended
@@ -107,7 +107,7 @@ public final class LinkedList<T> {
       head = newNode
     }
   }
-  
+
   /// Append a copy of a LinkedList to the end of the list.
   ///
   /// - Parameter list: The list to be copied and appended.
@@ -118,28 +118,28 @@ public final class LinkedList<T> {
       nodeToCopy = node.next
     }
   }
-  
+
   /// A private helper funciton to find the nodes before and after a specified index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameter index: Integer value of the index between the nodes.
   /// - Returns: A tuple of 2 nodes before & after the specified index respectively.
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-    
+
     var i = index
     var next = head
     var prev: Node?
-    
+
     while next != nil && i > 0 {
       i -= 1
       prev = next
       next = next!.next
     }
     assert(i == 0)  // if > 0, then specified index was too large
-    
+
     return (prev, next)
   }
-  
+
   /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -149,7 +149,7 @@ public final class LinkedList<T> {
     let newNode = Node(value: value)
     self.insert(newNode, atIndex: index)
   }
-  
+
   /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -162,12 +162,12 @@ public final class LinkedList<T> {
     newNode.next = next
     prev?.next = newNode
     next?.previous = newNode
-    
+
     if prev == nil {
       head = newNode
     }
   }
-  
+
   /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -192,12 +192,12 @@ public final class LinkedList<T> {
     prev?.next = next
     next?.previous = prev
   }
-  
+
   /// Function to remove all nodes/value from the list
   public func removeAll() {
     head = nil
   }
-  
+
   /// Function to remove a specific node.
   ///
   /// - Parameter node: The node to be deleted
@@ -205,19 +205,19 @@ public final class LinkedList<T> {
   @discardableResult public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
-    
+
     if let prev = prev {
       prev.next = next
     } else {
       head = next
     }
     next?.previous = prev
-    
+
     node.previous = nil
     node.next = nil
     return node.value
   }
-  
+
   /// Function to remove the last node/value in the list. Crashes if the list is empty
   ///
   /// - Returns: The data value contained in the deleted node.
@@ -225,7 +225,7 @@ public final class LinkedList<T> {
     assert(!isEmpty)
     return remove(node: last!)
   }
-  
+
   /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameter index: Integer value of the index of the node to be removed
@@ -276,7 +276,7 @@ extension LinkedList {
     }
     return result
   }
-  
+
   public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
@@ -294,7 +294,7 @@ extension LinkedList {
 extension LinkedList {
   convenience init(array: Array<T>) {
     self.init()
-    
+
     for element in array {
       self.append(element)
     }
@@ -305,7 +305,7 @@ extension LinkedList {
 extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
     self.init()
-    
+
     for element in elements {
       self.append(element)
     }
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 783e650e8..94e978c07 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,29 +1,29 @@
 public final class LinkedList<T> {
-    
+
     public class LinkedListNode<T> {
         var value: T
         var next: LinkedListNode?
         weak var previous: LinkedListNode?
-        
+
         public init(value: T) {
             self.value = value
         }
     }
-  
+
     public typealias Node = LinkedListNode<T>
-    
+
     fileprivate var head: Node?
-    
+
     public init() {}
-    
+
     public var isEmpty: Bool {
         return head == nil
     }
-    
+
     public var first: Node? {
         return head
     }
-    
+
     public var last: Node? {
         if var node = head {
             while case let next? = node.next {
@@ -34,7 +34,7 @@ public final class LinkedList<T> {
             return nil
         }
     }
-    
+
     public var count: Int {
         if var node = head {
             var c = 1
@@ -47,7 +47,7 @@ public final class LinkedList<T> {
             return 0
         }
     }
-    
+
     public func node(atIndex index: Int) -> Node? {
         if index >= 0 {
             var node = head
@@ -60,18 +60,18 @@ public final class LinkedList<T> {
         }
         return nil
     }
-    
+
     public subscript(index: Int) -> T {
         let node = self.node(atIndex: index)
         assert(node != nil)
         return node!.value
     }
-    
+
     public func append(_ value: T) {
         let newNode = Node(value: value)
         self.append(newNode)
     }
-    
+
     public func append(_ node: Node) {
         let newNode = LinkedListNode(value: node.value)
         if let lastNode = last {
@@ -81,7 +81,7 @@ public final class LinkedList<T> {
             head = newNode
         }
     }
-    
+
     public func append(_ list: LinkedList) {
         var nodeToCopy = list.head
         while let node = nodeToCopy {
@@ -89,29 +89,29 @@ public final class LinkedList<T> {
             nodeToCopy = node.next
         }
     }
-    
+
     private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
         assert(index >= 0)
-        
+
         var i = index
         var next = head
         var prev: Node?
-        
+
         while next != nil && i > 0 {
             i -= 1
             prev = next
             next = next!.next
         }
         assert(i == 0)  // if > 0, then specified index was too large
-        
+
         return (prev, next)
     }
-    
+
     public func insert(_ value: T, atIndex index: Int) {
         let newNode = Node(value: value)
         self.insert(newNode, atIndex: index)
     }
-    
+
     public func insert(_ node: Node, atIndex index: Int) {
         let (prev, next) = nodesBeforeAndAfter(index: index)
         let newNode = LinkedListNode(value: node.value)
@@ -119,12 +119,12 @@ public final class LinkedList<T> {
         newNode.next = next
         prev?.next = newNode
         next?.previous = newNode
-        
+
         if prev == nil {
             head = newNode
         }
     }
-    
+
     public func insert(_ list: LinkedList, atIndex index: Int) {
         if list.isEmpty { return }
         var (prev, next) = nodesBeforeAndAfter(index: index)
@@ -144,32 +144,32 @@ public final class LinkedList<T> {
         prev?.next = next
         next?.previous = prev
     }
-    
+
     public func removeAll() {
         head = nil
     }
-    
+
     @discardableResult public func remove(node: Node) -> T {
         let prev = node.previous
         let next = node.next
-        
+
         if let prev = prev {
             prev.next = next
         } else {
             head = next
         }
         next?.previous = prev
-        
+
         node.previous = nil
         node.next = nil
         return node.value
     }
-    
+
     @discardableResult public func removeLast() -> T {
         assert(!isEmpty)
         return remove(node: last!)
     }
-    
+
     @discardableResult public func remove(atIndex index: Int) -> T {
         let node = self.node(atIndex: index)
         assert(node != nil)
@@ -211,7 +211,7 @@ extension LinkedList {
         }
         return result
     }
-    
+
     public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
         let result = LinkedList<T>()
         var node = head
@@ -228,7 +228,7 @@ extension LinkedList {
 extension LinkedList {
     convenience init(array: Array<T>) {
         self.init()
-        
+
         for element in array {
             self.append(element)
         }
@@ -238,7 +238,7 @@ extension LinkedList {
 extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
     self.init()
-    
+
     for element in elements {
       self.append(element)
     }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index ea063cacb..7fd31c2c7 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -165,7 +165,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertTrue(prev!.next === node)
     XCTAssertTrue(next!.previous === node)
   }
-  
+
   func testInsertListAtIndex() {
     let list = buildList()
     let list2 = LinkedList<Int>()
@@ -190,7 +190,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 1)?.value, 102)
     XCTAssertEqual(list.node(atIndex: 2)?.value, 8)
   }
-  
+
   func testInsertListAtLastIndex() {
     let list = buildList()
     let list2 = LinkedList<Int>()
@@ -202,7 +202,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
     XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
   }
-  
+
   func testAppendList() {
     let list = buildList()
     let list2 = LinkedList<Int>()
@@ -214,7 +214,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
     XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
   }
-  
+
   func testAppendListToEmptyList() {
     let list = LinkedList<Int>()
     let list2 = LinkedList<Int>()
@@ -225,7 +225,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 0)?.value, 5)
     XCTAssertEqual(list.node(atIndex: 1)?.value, 10)
   }
-  
+
   func testRemoveAtIndexOnListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)
@@ -308,10 +308,10 @@ class LinkedListTest: XCTestCase {
     XCTAssertTrue(last === list.first)
     XCTAssertEqual(nodeCount, list.count)
   }
-  
+
   func testArrayLiteralInitTypeInfer() {
     let arrayLiteralInitInfer: LinkedList = [1.0, 2.0, 3.0]
-    
+
     XCTAssertEqual(arrayLiteralInitInfer.count, 3)
     XCTAssertEqual(arrayLiteralInitInfer.first?.value, 1.0)
     XCTAssertEqual(arrayLiteralInitInfer.last?.value, 3.0)
@@ -319,10 +319,10 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(arrayLiteralInitInfer.removeLast(), 3.0)
     XCTAssertEqual(arrayLiteralInitInfer.count, 2)
   }
-  
+
   func testArrayLiteralInitExplicit() {
     let arrayLiteralInitExplicit: LinkedList<Int> = [1, 2, 3]
-    
+
     XCTAssertEqual(arrayLiteralInitExplicit.count, 3)
     XCTAssertEqual(arrayLiteralInitExplicit.first?.value, 1)
     XCTAssertEqual(arrayLiteralInitExplicit.last?.value, 3)
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
index 9dca23996..ee2ace8b9 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
@@ -23,38 +23,38 @@ import Foundation
  */
 public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
   guard n > 2 && n % 2 == 1 else { return false }
-  
+
   var d = n - 1
   var s = 0
-  
+
   while d % 2 == 0 {
     d /= 2
     s += 1
   }
-  
+
   let range = UInt64.max - UInt64.max % (n - 2)
   var r: UInt64 = 0
   repeat {
     arc4random_buf(&r, MemoryLayout.size(ofValue: r))
   } while r >= range
-  
+
   r = r % (n - 2) + 2
-  
+
   for _ in 1 ... k {
     var x = powmod64(r, d, n)
     if x == 1 || x == n - 1 { continue }
-    
+
     if s == 1 { s = 2 }
-    
+
     for _ in 1 ... s - 1 {
       x = powmod64(x, 2, n)
       if x == 1 { return false }
       if x == n - 1 { break }
     }
-    
+
     if x != n - 1 { return false }
   }
-  
+
   return true
 }
 
@@ -71,17 +71,17 @@ public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
  */
 private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
   if m == 1 { return 0 }
-  
+
   var result: UInt64 = 1
   var b = base % m
   var e = exp
-  
+
   while e > 0 {
     if e % 2 == 1 { result = mulmod64(result, b, m) }
     b = mulmod64(b, b, m)
     e >>= 1
   }
-  
+
   return result
 }
 
@@ -100,12 +100,12 @@ private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64
   var result: UInt64 = 0
   var a = first
   var b = second
-  
+
   while a != 0 {
     if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
     a >>= 1
     b = (b << 1) % m
   }
-  
+
   return result
 }
diff --git a/Miller-Rabin Primality Test/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.swift
index 9dca23996..ee2ace8b9 100644
--- a/Miller-Rabin Primality Test/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.swift	
@@ -23,38 +23,38 @@ import Foundation
  */
 public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
   guard n > 2 && n % 2 == 1 else { return false }
-  
+
   var d = n - 1
   var s = 0
-  
+
   while d % 2 == 0 {
     d /= 2
     s += 1
   }
-  
+
   let range = UInt64.max - UInt64.max % (n - 2)
   var r: UInt64 = 0
   repeat {
     arc4random_buf(&r, MemoryLayout.size(ofValue: r))
   } while r >= range
-  
+
   r = r % (n - 2) + 2
-  
+
   for _ in 1 ... k {
     var x = powmod64(r, d, n)
     if x == 1 || x == n - 1 { continue }
-    
+
     if s == 1 { s = 2 }
-    
+
     for _ in 1 ... s - 1 {
       x = powmod64(x, 2, n)
       if x == 1 { return false }
       if x == n - 1 { break }
     }
-    
+
     if x != n - 1 { return false }
   }
-  
+
   return true
 }
 
@@ -71,17 +71,17 @@ public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
  */
 private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
   if m == 1 { return 0 }
-  
+
   var result: UInt64 = 1
   var b = base % m
   var e = exp
-  
+
   while e > 0 {
     if e % 2 == 1 { result = mulmod64(result, b, m) }
     b = mulmod64(b, b, m)
     e >>= 1
   }
-  
+
   return result
 }
 
@@ -100,12 +100,12 @@ private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64
   var result: UInt64 = 0
   var a = first
   var b = second
-  
+
   while a != 0 {
     if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
     a >>= 1
     b = (b << 1) % m
   }
-  
+
   return result
 }
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
index d651ddf2e..238afeb9b 100755
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,21 +1,21 @@
 extension String {
-    
+
     public func minimumEditDistance(other: String) -> Int {
         let m = self.characters.count
         let n = other.characters.count
         var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
-        
+
         // initialize matrix
         for index in 1...m {
             // the distance of any first string to an empty second string
             matrix[index][0] = index
         }
-        
+
         for index in 1...n {
             // the distance of any second string to an empty first string
             matrix[0][index] = index
         }
-        
+
         // compute Levenshtein distance
         for (i, selfChar) in self.characters.enumerated() {
             for (j, otherChar) in other.characters.enumerated() {
diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 1a0320a65..5ca0d7d31 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -49,7 +49,7 @@ public struct OrderedArray<T: Comparable> {
   private func findInsertionPoint(_ newElement: T) -> Int {
     var startIndex = 0
     var endIndex = array.count
-    
+
     while startIndex < endIndex {
         let midIndex = startIndex + (endIndex - startIndex) / 2
         if array[midIndex] == newElement {
diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index e8562a367..b9e857dd0 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -10,7 +10,7 @@ import Foundation
 func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
     let length = strippedString.characters.count
-    
+
     if length > 1 {
         return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
     }
@@ -28,14 +28,14 @@ private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
     if left >= right {
         return true
     }
-    
+
     let lhs = str[str.index(str.startIndex, offsetBy: left)]
     let rhs = str[str.index(str.startIndex, offsetBy: right)]
-    
+
     if lhs != rhs {
         return false
     }
-    
+
     return palindrome(str, left: left + 1, right: right - 1)
 }
 
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Palindromes.swift
index 2760137ca..9ddd04c80 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -3,7 +3,7 @@ import Foundation
 func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
     let length = strippedString.characters.count
-    
+
     if length > 1 {
         return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
     }
@@ -14,13 +14,13 @@ private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
     if left >= right {
         return true
     }
-    
+
     let lhs = str[str.index(str.startIndex, offsetBy: left)]
     let rhs = str[str.index(str.startIndex, offsetBy: right)]
-    
+
     if lhs != rhs {
         return false
     }
-    
+
     return palindrome(str, left: left + 1, right: right - 1)
 }
diff --git a/Palindromes/Test/Palindromes.swift b/Palindromes/Test/Palindromes.swift
index 2760137ca..9ddd04c80 100644
--- a/Palindromes/Test/Palindromes.swift
+++ b/Palindromes/Test/Palindromes.swift
@@ -3,7 +3,7 @@ import Foundation
 func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
     let length = strippedString.characters.count
-    
+
     if length > 1 {
         return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
     }
@@ -14,13 +14,13 @@ private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
     if left >= right {
         return true
     }
-    
+
     let lhs = str[str.index(str.startIndex, offsetBy: left)]
     let rhs = str[str.index(str.startIndex, offsetBy: right)]
-    
+
     if lhs != rhs {
         return false
     }
-    
+
     return palindrome(str, left: left + 1, right: right - 1)
 }
diff --git a/Palindromes/Test/Test/Test.swift b/Palindromes/Test/Test/Test.swift
index 1dd79ea97..ddf970300 100644
--- a/Palindromes/Test/Test/Test.swift
+++ b/Palindromes/Test/Test/Test.swift
@@ -9,22 +9,22 @@
 import XCTest
 
 class PalindromeTests: XCTestCase {
-    
+
     override func setUp() {
         super.setUp()
         // Put setup code here. This method is called before the invocation of each test method in the class.
     }
-    
+
     override func tearDown() {
         // Put teardown code here. This method is called after the invocation of each test method in the class.
         super.tearDown()
     }
-    
+
     func testExample() {
         // This is an example of a functional test case.
         // Use XCTAssert and related functions to verify your tests produce the correct results.
     }
-    
+
     func testPerformanceExample() {
         // This is an example of a performance test case.
         self.measure {
@@ -34,12 +34,12 @@ class PalindromeTests: XCTestCase {
             _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
         }
     }
-    
+
     func testPalindromeWord() {
         XCTAssertTrue(isPalindrome("abbcbba"))
         XCTAssertTrue(isPalindrome("racecar"))
     }
-    
+
     func testPalindromeSentence() {
         XCTAssertTrue(isPalindrome("A man, a plan, a canal, Panama!"))
         XCTAssertTrue(isPalindrome("Madam, I'm Adam"))
@@ -47,17 +47,17 @@ class PalindromeTests: XCTestCase {
         XCTAssertTrue(isPalindrome("In girum imus nocte et consumimur igni"))
         XCTAssertTrue(isPalindrome("Never odd or even"))
     }
-    
+
     func testPalindromeNumber() {
         XCTAssertTrue(isPalindrome("5885"))
         XCTAssertTrue(isPalindrome("5 8 8 5"))
         XCTAssertTrue(isPalindrome("58 85"))
     }
-    
+
     func testSpecialCharacters() {
         XCTAssertTrue(isPalindrome("৯৯"))
     }
-    
+
     func testNonPalindromes() {
         XCTAssertFalse(isPalindrome("\\\\"))
         XCTAssertFalse(isPalindrome("desserts"))
diff --git a/QuadTree/QuadTree.playground/Sources/QuadTree.swift b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
index 14d0dbba7..7fd459e97 100644
--- a/QuadTree/QuadTree.playground/Sources/QuadTree.swift
+++ b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
@@ -1,7 +1,7 @@
 public struct Point {
   let x: Double
   let y: Double
-  
+
   public init(_ x: Double, _ y: Double) {
     self.x = x
     self.y = y
@@ -17,18 +17,18 @@ extension Point: CustomStringConvertible {
 public struct Size: CustomStringConvertible {
   var xLength: Double
   var yLength: Double
-  
+
   public init(xLength: Double, yLength: Double) {
     precondition(xLength >= 0, "xLength can not be negative")
     precondition(yLength >= 0, "yLength can not be negative")
     self.xLength = xLength
     self.yLength = yLength
   }
-  
+
   var half: Size {
     return Size(xLength: xLength / 2, yLength: yLength / 2)
   }
-  
+
   public var description: String {
     return "Size(\(xLength), \(yLength))"
   }
@@ -38,49 +38,49 @@ public struct Rect {
   // left top vertice
   var origin: Point
   var size: Size
-  
+
   public init(origin: Point, size: Size) {
     self.origin = origin
     self.size = size
   }
-  
+
   var minX: Double {
     return origin.x
   }
-  
+
   var minY: Double {
     return origin.y
   }
-  
+
   var maxX: Double {
     return origin.x + size.xLength
   }
-  
+
   var maxY: Double {
     return origin.y + size.yLength
   }
-  
+
   func containts(point: Point) -> Bool {
     return (minX <= point.x && point.x <= maxX) &&
       (minY <= point.y && point.y <= maxY)
   }
-  
+
   var leftTopRect: Rect {
     return Rect(origin: origin, size: size.half)
   }
-  
+
   var leftBottomRect: Rect {
     return Rect(origin: Point(origin.x, origin.y + size.half.yLength), size: size.half)
   }
-  
+
   var rightTopRect: Rect {
     return Rect(origin: Point(origin.x + size.half.xLength, origin.y), size: size.half)
   }
-  
+
   var rightBottomRect: Rect {
     return Rect(origin: Point(origin.x + size.half.xLength, origin.y + size.half.yLength), size: size.half)
   }
-  
+
   func intersects(rect: Rect) -> Bool {
 
     func lineSegmentsIntersect(lStart: Double, lEnd: Double, rStart: Double, rEnd: Double) -> Bool {
@@ -91,7 +91,7 @@ public struct Rect {
     if !lineSegmentsIntersect(lStart: minX, lEnd: maxX, rStart: rect.minX, rEnd: rect.maxX) {
       return false
     }
-    
+
     // vertical
     return lineSegmentsIntersect(lStart: minY, lEnd: maxY, rStart: rect.minY, rEnd: rect.maxY)
   }
@@ -109,37 +109,37 @@ protocol PointsContainer {
 }
 
 class QuadTreeNode {
-  
+
   enum NodeType {
     case leaf
     case `internal`(children: Children)
   }
-  
+
   struct Children: Sequence {
     let leftTop: QuadTreeNode
     let leftBottom: QuadTreeNode
     let rightTop: QuadTreeNode
     let rightBottom: QuadTreeNode
-    
+
     init(parentNode: QuadTreeNode) {
       leftTop = QuadTreeNode(rect: parentNode.rect.leftTopRect)
       leftBottom = QuadTreeNode(rect: parentNode.rect.leftBottomRect)
       rightTop = QuadTreeNode(rect: parentNode.rect.rightTopRect)
       rightBottom = QuadTreeNode(rect: parentNode.rect.rightBottomRect)
     }
-    
+
     struct ChildrenIterator: IteratorProtocol {
       private var index = 0
       private let children: Children
-      
+
       init(children: Children) {
         self.children = children
       }
-      
+
       mutating func next() -> QuadTreeNode? {
-        
+
         defer { index += 1 }
-        
+
         switch index {
         case 0: return children.leftTop
         case 1: return children.leftBottom
@@ -149,26 +149,26 @@ class QuadTreeNode {
         }
       }
     }
-    
+
     public func makeIterator() -> ChildrenIterator {
       return ChildrenIterator(children: self)
     }
   }
-  
+
   var points: [Point] = []
   let rect: Rect
   var type: NodeType = .leaf
-  
+
   static let maxPointCapacity = 3
-  
+
   init(rect: Rect) {
     self.rect = rect
   }
-  
+
   var recursiveDescription: String {
     return recursiveDescription(withTabCount: 0)
   }
-  
+
   private func recursiveDescription(withTabCount count: Int) -> String {
     let indent = String(repeating: "\t", count: count)
     var result = "\(indent)" + description + "\n"
@@ -185,13 +185,13 @@ class QuadTreeNode {
 }
 
 extension QuadTreeNode: PointsContainer {
-  
+
   @discardableResult
   func add(point: Point) -> Bool {
     if !rect.containts(point: point) {
       return false
     }
-    
+
     switch type {
     case .internal(let children):
       // pass the point to one of the children
@@ -200,7 +200,7 @@ extension QuadTreeNode: PointsContainer {
           return true
         }
       }
-      
+
       fatalError("rect.containts evaluted to true, but none of the children added the point")
     case .leaf:
       points.append(point)
@@ -211,7 +211,7 @@ extension QuadTreeNode: PointsContainer {
     }
     return true
   }
-  
+
   private func subdivide() {
     switch type {
     case .leaf:
@@ -220,25 +220,25 @@ extension QuadTreeNode: PointsContainer {
       preconditionFailure("Calling subdivide on an internal node")
     }
   }
-  
+
   func points(inRect rect: Rect) -> [Point] {
-    
+
     // if the node's rect and the given rect don't intersect, return an empty array,
     // because there can't be any points that lie the node's (or its children's) rect and
     // in the given rect
     if !self.rect.intersects(rect: rect) {
       return []
     }
-    
+
     var result: [Point] = []
-    
+
     // collect the node's points that lie in the rect
     for point in points {
       if rect.containts(point: point) {
         result.append(point)
       }
     }
-    
+
     switch type {
     case .leaf:
       break
@@ -248,7 +248,7 @@ extension QuadTreeNode: PointsContainer {
         result.append(contentsOf: childNode.points(inRect: rect))
       }
     }
-    
+
     return result
   }
 }
@@ -265,18 +265,18 @@ extension QuadTreeNode: CustomStringConvertible {
 }
 
 public class QuadTree: PointsContainer {
-  
+
   let root: QuadTreeNode
-  
+
   public init(rect: Rect) {
     self.root = QuadTreeNode(rect: rect)
   }
-  
+
   @discardableResult
   public func add(point: Point) -> Bool {
     return root.add(point: point)
   }
-  
+
   public func points(inRect rect: Rect) -> [Point] {
     return root.points(inRect: rect)
   }
diff --git a/QuadTree/Tests/Tests/Tests.swift b/QuadTree/Tests/Tests/Tests.swift
index b408c4f7e..9bd8ad28f 100644
--- a/QuadTree/Tests/Tests/Tests.swift
+++ b/QuadTree/Tests/Tests/Tests.swift
@@ -17,68 +17,68 @@ public func == (lhs: Point, rhs: Point) -> Bool {
 }
 
 class Tests: XCTestCase {
-  
+
   func testRectContains() {
     let rect = Rect(origin: Point(0, 0), size: Size(xLength: 3, yLength: 3))
-    
+
     XCTAssertTrue(rect.containts(point: Point(1, 1)))
     XCTAssertTrue(rect.containts(point: Point(0, 0)))
     XCTAssertTrue(rect.containts(point: Point(0, 3)))
     XCTAssertTrue(rect.containts(point: Point(3, 3)))
-    
+
     XCTAssertFalse(rect.containts(point: Point(-1, 1)))
     XCTAssertFalse(rect.containts(point: Point(-0.1, 0.1)))
     XCTAssertFalse(rect.containts(point: Point(0, 3.1)))
     XCTAssertFalse(rect.containts(point: Point(-4, 1)))
   }
-  
+
   func testIntersects() {
     let rect = Rect(origin: Point(0, 0), size: Size(xLength: 5, yLength: 5))
     let rect2 = Rect(origin: Point(1, 1), size: Size(xLength: 1, yLength: 1))
     XCTAssertTrue(rect.intersects(rect: rect2))
-    
+
     let rect3 = Rect(origin: Point(1, 0), size: Size(xLength: 1, yLength: 10))
     let rect4 = Rect(origin: Point(0, 1), size: Size(xLength: 10, yLength: 1))
     XCTAssertTrue(rect3.intersects(rect: rect4))
-    
+
     let rect5 = Rect(origin: Point(0, 0), size: Size(xLength: 4, yLength: 4))
     let rect6 = Rect(origin: Point(2, 2), size: Size(xLength: 4, yLength: 4))
     XCTAssertTrue(rect5.intersects(rect: rect6))
-    
+
     let rect7 = Rect(origin: Point(0, 0), size: Size(xLength: 4, yLength: 4))
     let rect8 = Rect(origin: Point(4, 4), size: Size(xLength: 1, yLength: 1))
     XCTAssertTrue(rect7.intersects(rect: rect8))
-    
+
     let rect9 = Rect(origin: Point(-1, -1), size: Size(xLength: 0.5, yLength: 0.5))
     let rect10 = Rect(origin: Point(0, 0), size: Size(xLength: 1, yLength: 1))
     XCTAssertFalse(rect9.intersects(rect: rect10))
-    
+
     let rect11 = Rect(origin: Point(0, 0), size: Size(xLength: 2, yLength: 1))
     let rect12 = Rect(origin: Point(3, 0), size: Size(xLength: 1, yLength: 1))
     XCTAssertFalse(rect11.intersects(rect: rect12))
   }
-  
+
   func testQuadTree() {
     let rect = Rect(origin: Point(0, 0), size: Size(xLength: 5, yLength: 5))
     let qt = QuadTree(rect: rect)
-    
+
     XCTAssertTrue(qt.points(inRect: rect) == [Point]())
-    
+
     XCTAssertFalse(qt.add(point: Point(-0.1, 0.1)))
-    
+
     XCTAssertTrue(qt.points(inRect: rect) == [Point]())
-    
+
     XCTAssertTrue(qt.add(point: Point(1, 1)))
     XCTAssertTrue(qt.add(point: Point(3, 3)))
     XCTAssertTrue(qt.add(point: Point(4, 4)))
     XCTAssertTrue(qt.add(point: Point(0.5, 0.5)))
-    
+
     XCTAssertFalse(qt.add(point: Point(5.5, 0)))
     XCTAssertFalse(qt.add(point: Point(5.5, 1)))
     XCTAssertFalse(qt.add(point: Point(5.5, 2)))
-    
+
     XCTAssertTrue(qt.add(point: Point(1.5, 1.5)))
-    
+
     let rect2 = Rect(origin: Point(0, 0), size: Size(xLength: 2, yLength: 2))
     XCTAssertTrue(qt.points(inRect: rect2) == [Point(1, 1), Point(0.5, 0.5), Point(1.5, 1.5)])
   }
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
index 136ede4fd..81c2479e8 100644
--- a/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -11,18 +11,18 @@ public func radixSort(_ array: inout [Int] ) {
   var done = false
   var index: Int
   var digit = 1  //Which digit are we on?
-  
-  
+
+
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
-    
+
     var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
-    
+
     for _ in 1...radix {
       buckets.append([])
     }
-    
-    
+
+
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
@@ -30,9 +30,9 @@ public func radixSort(_ array: inout [Int] ) {
         done = false
       }
     }
-    
+
     var i = 0
-    
+
     for j in 0..<radix {
       let bucket = buckets[j]
       for number in bucket {
@@ -40,7 +40,7 @@ public func radixSort(_ array: inout [Int] ) {
         i += 1
       }
     }
-    
+
     digit *= radix  //Move to the next digit
   }
 }
diff --git a/Radix Sort/RadixSortExample.swift b/Radix Sort/RadixSortExample.swift
index 7d9461c5c..f64dcfeb9 100644
--- a/Radix Sort/RadixSortExample.swift	
+++ b/Radix Sort/RadixSortExample.swift	
@@ -9,21 +9,21 @@
 import Foundation
 
 func radixSort1(_ arr: inout [Int]) {
-   
+
     var temp = [[Int]](repeating: [], count: 10)
-    
+
     for num in arr { temp[num % 10].append(num) }
-    
+
     for i in 1...Int(arr.max()!.description.characters.count) {
-        
+
         for index in 0..<temp.count {
-           
+
             for num in temp[index] {
                 temp[index].remove(at: temp[index].index(of: num)!)
                 temp[(num / Int(pow(10, Double(i)))) % 10].append(num)
             }
         }
     }
-    
+
     arr = temp[0]
 }
diff --git a/Radix Sort/radixSort.swift b/Radix Sort/radixSort.swift
index 24d4155d7..9e48093ef 100644
--- a/Radix Sort/radixSort.swift	
+++ b/Radix Sort/radixSort.swift	
@@ -11,18 +11,18 @@ func radixSort(_ array: inout [Int] ) {
   var done = false
   var index: Int
   var digit = 1  //Which digit are we on?
-  
-  
+
+
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
-    
+
     var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
-    
+
     for _ in 1...radix {
       buckets.append([])
     }
-    
-    
+
+
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
@@ -30,9 +30,9 @@ func radixSort(_ array: inout [Int] ) {
         done = false
       }
     }
-    
+
     var i = 0
-    
+
     for j in 0..<radix {
       let bucket = buckets[j]
       for number in bucket {
@@ -40,7 +40,7 @@ func radixSort(_ array: inout [Int] ) {
         i += 1
       }
     }
-    
+
     digit *= radix  //Move to the next digit
   }
 }
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
index d55c153d5..791ae822a 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift	
@@ -10,7 +10,7 @@ for _ in 0..<1000 {
     tree.insert(value)
 }
 tree.verify()
- 
+
 for _ in 0..<1000 {
     let rand = arc4random_uniform(UInt32(values.count))
     let index = Int(rand)
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index 42a68237e..97bb52422 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -10,13 +10,13 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
     public var right: RBTNode<T>!
     public var left: RBTNode<T>!
     public var parent: RBTNode<T>!
-    
+
     public var description: String {
         if self.value == nil {
             return "null"
         } else {
             var nodeValue: String
-            
+
             // If the value is encapsulated by parentheses it is red
             // If the value is encapsulated by pipes it is black
             // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
@@ -27,33 +27,33 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
             } else {
                 nodeValue = "||\(self.value!)||"
             }
-            
+
             return "(\(self.left.description)<-\(nodeValue)->\(self.right.description))"
         }
     }
-    
+
     init(tree: RBTree<T>) {
         right = tree.nullLeaf
         left = tree.nullLeaf
         parent = tree.nullLeaf
     }
-    
+
     init() {
         //This method is here to support the creation of a nullLeaf
     }
-    
+
     public var isLeftChild: Bool {
         return self.parent.left === self
     }
-    
+
     public var isRightChild: Bool {
         return self.parent.right === self
     }
-    
+
     public var grandparent: RBTNode<T> {
         return parent.parent
     }
-    
+
     public var sibling: RBTNode<T> {
         if isLeftChild {
             return self.parent.right
@@ -61,19 +61,19 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
             return self.parent.left
         }
     }
-    
+
     public var uncle: RBTNode<T> {
         return parent.sibling
     }
-    
+
     fileprivate var isRed: Bool {
         return color == .red
     }
-    
+
     fileprivate var isBlack: Bool {
         return color == .black
     }
-    
+
     fileprivate var isDoubleBlack: Bool {
         return color == .doubleBlack
     }
@@ -82,70 +82,70 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
 public class RBTree<T: Comparable>: CustomStringConvertible {
     public var root: RBTNode<T>
     fileprivate let nullLeaf: RBTNode<T>
-    
+
     public var description: String {
         return root.description
     }
-    
+
     public init() {
         nullLeaf = RBTNode<T>()
         nullLeaf.color = .black
         root = nullLeaf
     }
-    
+
     public convenience init(withValue value: T) {
         self.init()
         insert(value)
     }
-    
+
     public convenience init(withArray array: [T]) {
         self.init()
         insert(array)
     }
-    
+
     public func insert(_ value: T) {
         let newNode = RBTNode<T>(tree: self)
         newNode.value = value
         insertNode(n: newNode)
     }
-    
+
     public func insert(_ values: [T]) {
         for value in values {
             print(value)
             insert(value)
         }
     }
-    
+
     public func delete(_ value: T) {
         let nodeToDelete = find(value)
         if nodeToDelete !== nullLeaf {
             deleteNode(n: nodeToDelete)
         }
     }
-    
+
     public func find(_ value: T) -> RBTNode<T> {
         let foundNode = findNode(rootNode: root, value: value)
         return foundNode
     }
-    
+
     public func minimum(n: RBTNode<T>) -> RBTNode<T> {
         var min = n
         if n.left !== nullLeaf {
             min = minimum(n: n.left)
         }
-        
+
         return min
     }
-    
+
     public func maximum(n: RBTNode<T>) -> RBTNode<T> {
         var max = n
         if n.right !== nullLeaf {
             max = maximum(n: n.right)
         }
-        
+
         return max
     }
-    
+
     public func verify() {
         if self.root === nullLeaf {
             print("The tree is empty")
@@ -155,7 +155,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         property2(n: self.root)
         property3()
     }
-    
+
     private func findNode(rootNode: RBTNode<T>, value: T) -> RBTNode<T> {
         var nextNode = rootNode
         if rootNode !== nullLeaf && value != rootNode.value {
@@ -165,15 +165,15 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                 nextNode = findNode(rootNode: rootNode.right, value: value)
             }
         }
-        
+
         return nextNode
     }
-    
+
     private func insertNode(n: RBTNode<T>) {
         BSTInsertNode(n: n, parent: root)
         insertCase1(n: n)
     }
-    
+
     private func BSTInsertNode(n: RBTNode<T>, parent: RBTNode<T>) {
         if parent === nullLeaf {
             self.root = n
@@ -193,7 +193,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             }
         }
     }
-    
+
     // if node is root change color to black, else move on
     private func insertCase1(n: RBTNode<T>) {
         if n === root {
@@ -202,14 +202,14 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             insertCase2(n: n)
         }
     }
-    
+
     // if parent of node is not black, and node is not root move on
     private func insertCase2(n: RBTNode<T>) {
         if !n.parent.isBlack {
             insertCase3(n: n)
         }
     }
-    
+
     // if uncle is red do stuff otherwise move to 4
     private func insertCase3(n: RBTNode<T>) {
         if n.uncle.isRed { // node must have grandparent as children of root have a black parent
@@ -224,14 +224,14 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             insertCase4(n: n)
         }
     }
-    
+
     // parent is red, grandparent is black, uncle is black
     // There are 4 cases left:
     // - left left
     // - left right
     // - right right
     // - right left
-    
+
     // the cases "left right" and "right left" can be rotated into the other two
     // so if either of the two is detected we apply a rotation and then move on to
     // deal with the final two cases, if neither is detected we move on to those cases anyway
@@ -246,28 +246,28 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             insertCase5(n: n)
         }
     }
-    
+
     private func insertCase5(n: RBTNode<T>) {
         // swap color of parent and grandparent
         // parent is red grandparent is black
         n.parent.color = .black
         n.grandparent.color = .red
-        
+
         if n.isLeftChild { // left left case
             rightRotate(n: n.grandparent)
         } else { // right right case
             leftRotate(n: n.grandparent)
         }
     }
-    
+
     private func deleteNode(n: RBTNode<T>) {
         var toDel = n
-        
+
         if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.parent === nullLeaf {
             self.root = nullLeaf
             return
         }
-        
+
         if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.isRed {
             if toDel.isLeftChild {
                 toDel.parent.left = nullLeaf
@@ -276,38 +276,38 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             }
             return
         }
-        
+
         if toDel.left !== nullLeaf && toDel.right !== nullLeaf {
             let pred = maximum(n: toDel.left)
             toDel.value = pred.value
             toDel = pred
         }
-        
+
         // from here toDel has at most 1 non nullLeaf child
-        
+
         var child: RBTNode<T>
         if toDel.left !== nullLeaf {
             child = toDel.left
         } else {
             child = toDel.right
         }
-        
+
         if toDel.isRed || child.isRed {
             child.color = .black
-            
+
             if toDel.isLeftChild {
                 toDel.parent.left = child
             } else {
                 toDel.parent.right = child
             }
-            
+
             if child !== nullLeaf {
                 child.parent = toDel.parent
             }
         } else { // both toDel and child are black
-            
+
             var sibling = toDel.sibling
-            
+
             if toDel.isLeftChild {
                 toDel.parent.left = child
             } else {
@@ -317,10 +317,10 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                 child.parent = toDel.parent
             }
             child.color = .doubleBlack
-            
+
             while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
                 if sibling.isBlack {
-                    
+
                     var leftRedChild: RBTNode<T>! = nil
                     if sibling.left.isRed {
                         leftRedChild = sibling.left
@@ -329,7 +329,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                     if sibling.right.isRed {
                         rightRedChild = sibling.right
                     }
-                    
+
                     if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
                         child.color = .black
                         if sibling.isLeftChild {
@@ -389,7 +389,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                     }
                 } else { // sibling is red
                     sibling.color = .black
-                    
+
                     if sibling.isLeftChild { // left case
                         rightRotate(n: sibling.parent)
                         sibling = sibling.right.left
@@ -400,7 +400,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                         sibling.parent.color = .red
                     }
                 }
-                
+
                 // sibling check is here for when child is a nullLeaf and thus does not have a parent.
                 // child is here as sibling can become nil when child is the root
                 if (sibling.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
@@ -409,14 +409,14 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             }
         }
     }
-    
+
     private func property1() {
-        
+
         if self.root.isRed {
             print("Root is not black")
         }
     }
-    
+
     private func property2(n: RBTNode<T>) {
         if n === nullLeaf {
             return
@@ -431,48 +431,48 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         property2(n: n.left)
         property2(n: n.right)
     }
-    
+
     private func property3() {
         let bDepth = blackDepth(root: self.root)
-        
+
         let leaves: [RBTNode<T>] = getLeaves(n: self.root)
-        
+
         for leaflet in leaves {
             var leaf = leaflet
             var i = 0
-            
+
             while leaf !== nullLeaf {
                 if leaf.isBlack {
                     i = i + 1
                 }
                 leaf = leaf.parent
             }
-            
+
             if i != bDepth {
                 print("black depth: \(bDepth), is not equal (depth: \(i)) for leaf with value: \(leaflet.value)")
             }
         }
-        
+
     }
-    
+
     private func getLeaves(n: RBTNode<T>) -> [RBTNode<T>] {
         var leaves = [RBTNode<T>]()
-        
+
         if n !== nullLeaf {
             if n.left === nullLeaf && n.right === nullLeaf {
                 leaves.append(n)
             } else {
                 let leftLeaves = getLeaves(n: n.left)
                 let rightLeaves = getLeaves(n: n.right)
-                
+
                 leaves.append(contentsOf: leftLeaves)
                 leaves.append(contentsOf: rightLeaves)
             }
         }
-        
+
         return leaves
     }
-    
+
     private func blackDepth(root: RBTNode<T>) -> Int {
         if root === nullLeaf {
             return 0
@@ -481,7 +481,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             return returnValue + (max(blackDepth(root: root.left), blackDepth(root: root.right)))
         }
     }
-    
+
     private func leftRotate(n: RBTNode<T>) {
         let newRoot = n.right!
         n.right = newRoot.left!
@@ -499,7 +499,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         newRoot.left = n
         n.parent = newRoot
     }
-    
+
     private func rightRotate(n: RBTNode<T>) {
         let newRoot = n.left!
         n.left = newRoot.right!
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 11e177d0d..26f7dca48 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -12,16 +12,16 @@ originalString == restoredString
 
 func encodeAndDecode(_ bytes: [UInt8]) -> Bool {
     var bytes = bytes
-    
+
     var data1 = Data(bytes: &bytes, count: bytes.count)
     print("data1 is \(data1.count) bytes")
-    
+
     var rleData = data1.compressRLE()
     print("encoded data is \(rleData.count) bytes")
-    
+
     var data2 = rleData.decompressRLE()
     print("data2 is \(data2.count) bytes")
-    
+
     return data1 == data2
 }
 
@@ -66,10 +66,10 @@ func testBufferWithoutSpans() -> Bool {
 
 func testBufferWithSpans(_ spanSize: Int) -> Bool {
     print("span size \(spanSize)")
-    
+
     let length = spanSize * 32
     var bytes: [UInt8] = Array<UInt8>(repeating: 0, count: length)
-    
+
     for t in stride(from: 0, to: length, by: spanSize) {
         for i in 0..<spanSize {
             bytes[t + i] = UInt8(t % 256)
@@ -109,7 +109,7 @@ func runTests() -> Bool {
     for bool in tests {
         result = result && bool
     }
-    
+
     return result
 }
 
diff --git a/Run-Length Encoding/RLE.playground/Sources/RLE.swift b/Run-Length Encoding/RLE.playground/Sources/RLE.swift
index 5707e3d9d..0bb6fa00d 100644
--- a/Run-Length Encoding/RLE.playground/Sources/RLE.swift	
+++ b/Run-Length Encoding/RLE.playground/Sources/RLE.swift	
@@ -13,7 +13,7 @@ extension Data {
                 var count = 0
                 var byte = ptr.pointee
                 var next = byte
-                
+
                 // Is the next byte the same? Keep reading until we find a different
                 // value, or we reach the end of the data, or the run is 64 bytes.
                 while next == byte && ptr < end && count < 64 {
@@ -21,7 +21,7 @@ extension Data {
                     next = ptr.pointee
                     count += 1
                 }
-                
+
                 if count > 1 || byte >= 192 {       // byte run of up to 64 repeats
                     var size = 191 + UInt8(count)
                     data.append(&size, count: 1)
@@ -33,7 +33,7 @@ extension Data {
         }
         return data
     }
-    
+
     /*
      Converts a run-length encoded NSData back to the original.
      */
@@ -42,20 +42,20 @@ extension Data {
         self.withUnsafeBytes { (uPtr: UnsafePointer<UInt8>) in
             var ptr = uPtr
             let end = ptr + count
-            
+
             while ptr < end {
                 // Read the next byte. This is either a single value less than 192,
                 // or the start of a byte run.
                 var byte = ptr.pointee
                 ptr = ptr.advanced(by: 1)
-                
+
                 if byte < 192 {                     // single value
                     data.append(&byte, count: 1)
                 } else if ptr < end {               // byte run
                     // Read the actual data value.
                     var value = ptr.pointee
                     ptr = ptr.advanced(by: 1)
-                    
+
                     // And write it out repeatedly.
                     for _ in 0 ..< byte - 191 {
                         data.append(&value, count: 1)
diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 5bba56cc0..08474aee2 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -1,19 +1,19 @@
 //: Playground - noun: a place where people can play
 
 public class SegmentTree<T> {
-	
+
 	private var value: T
 	private var function: (T, T) -> T
 	private var leftBound: Int
 	private var rightBound: Int
 	private var leftChild: SegmentTree<T>?
 	private var rightChild: SegmentTree<T>?
-	
+
 	public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
 		self.leftBound = leftBound
 		self.rightBound = rightBound
 		self.function = function
-		
+
 		if leftBound == rightBound {
 			value = array[leftBound]
 		} else {
@@ -23,19 +23,19 @@ public class SegmentTree<T> {
 			value = function(leftChild!.value, rightChild!.value)
 		}
 	}
-	
+
 	public convenience init(array: [T], function: @escaping (T, T) -> T) {
 		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
 	}
-	
+
 	public func query(leftBound: Int, rightBound: Int) -> T {
 		if self.leftBound == leftBound && self.rightBound == rightBound {
 			return self.value
 		}
-		
+
 		guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
 		guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-		
+
 		if leftChild.rightBound < leftBound {
 			return rightChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else if rightChild.leftBound > rightBound {
@@ -46,7 +46,7 @@ public class SegmentTree<T> {
 			return function(leftResult, rightResult)
 		}
 	}
-	
+
 	public func replaceItem(at index: Int, withItem item: T) {
 		if leftBound == rightBound {
 			value = item
@@ -83,7 +83,7 @@ func gcd(_ m: Int, _ n: Int) -> Int {
 	var a = 0
 	var b = max(m, n)
 	var r = min(m, n)
-	
+
 	while r != 0 {
 		a = b
 		b = r
diff --git a/Segment Tree/SegmentTree.swift b/Segment Tree/SegmentTree.swift
index a3ec8b1bf..6f4edd306 100644
--- a/Segment Tree/SegmentTree.swift	
+++ b/Segment Tree/SegmentTree.swift	
@@ -8,19 +8,19 @@
 */
 
 public class SegmentTree<T> {
-	
+
 	private var value: T
 	private var function: (T, T) -> T
 	private var leftBound: Int
 	private var rightBound: Int
 	private var leftChild: SegmentTree<T>?
 	private var rightChild: SegmentTree<T>?
-	
+
 	public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
 		self.leftBound = leftBound
 		self.rightBound = rightBound
 		self.function = function
-		
+
 		if leftBound == rightBound {
 			value = array[leftBound]
 		} else {
@@ -30,19 +30,19 @@ public class SegmentTree<T> {
 			value = function(leftChild!.value, rightChild!.value)
 		}
 	}
-	
+
 	public convenience init(array: [T], function: @escaping (T, T) -> T) {
 		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
 	}
-	
+
 	public func query(leftBound: Int, rightBound: Int) -> T {
 		if self.leftBound == leftBound && self.rightBound == rightBound {
 			return self.value
 		}
-		
+
 		guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
 		guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-		
+
 		if leftChild.rightBound < leftBound {
 			return rightChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else if rightChild.leftBound > rightBound {
@@ -53,7 +53,7 @@ public class SegmentTree<T> {
 			return function(leftResult, rightResult)
 		}
 	}
-	
+
 	public func replaceItem(at index: Int, withItem item: T) {
 		if leftBound == rightBound {
 			value = item
diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index b7deb570a..81942b303 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -35,6 +35,6 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
             }
         }
     }
-    
+
     return (minimum, maximum)
 }
diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index 182060805..dbf3a7468 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -4,7 +4,7 @@ func minimum<T: Comparable>(_ array: [T]) -> T? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var minimum = array.removeFirst()
   for element in array {
     minimum = element < minimum ? element : minimum
@@ -18,7 +18,7 @@ func maximum<T: Comparable>(_ array: [T]) -> T? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var maximum = array.removeFirst()
   for element in array {
     maximum = element > maximum ? element : maximum
@@ -32,18 +32,18 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var minimum = array.first!
   var maximum = array.first!
-  
+
   let hasOddNumberOfItems = array.count % 2 != 0
   if hasOddNumberOfItems {
     array.removeFirst()
   }
-  
+
   while !array.isEmpty {
     let pair = (array.removeFirst(), array.removeFirst())
-    
+
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0
@@ -60,7 +60,7 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
       }
     }
   }
-  
+
   return (minimum, maximum)
 }
 
diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index aaf58cf4d..e9cee7543 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -10,18 +10,18 @@ import Foundation
 
 public func shellSort(_ list : inout [Int]) {
     var sublistCount = list.count / 2
-    
+
     while sublistCount > 0 {
         for var index in 0..<list.count {
-            
+
             guard index + sublistCount < list.count else { break }
-            
+
             if list[index] > list[index + sublistCount] {
                 swap(&list[index], &list[index + sublistCount])
             }
-            
+
             guard sublistCount == 1 && index > 0 else { continue }
-            
+
             while list[index - 1] > list[index] && index - 1 > 0 {
                 swap(&list[index - 1], &list[index])
                 index -= 1
diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index 8322ba0a9..4d2e59eab 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -2,7 +2,7 @@
 
 open class Edge: Equatable {
     open var neighbor: Node
-    
+
     public init(neighbor: Node) {
         self.neighbor = neighbor
     }
@@ -17,28 +17,28 @@ public func == (lhs: Edge, rhs: Edge) -> Bool {
 
 open class Node: CustomStringConvertible, Equatable {
     open var neighbors: [Edge]
-    
+
     open fileprivate(set) var label: String
     open var distance: Int?
     open var visited: Bool
-    
+
     public init(label: String) {
         self.label = label
         neighbors = []
         visited = false
     }
-    
+
     open var description: String {
         if let distance = distance {
             return "Node(label: \(label), distance: \(distance))"
         }
         return "Node(label: \(label), distance: infinity)"
     }
-    
+
     open var hasDistance: Bool {
         return distance != nil
     }
-    
+
     open func remove(_ edge: Edge) {
         neighbors.remove(at: neighbors.index { $0 === edge }!)
     }
@@ -52,25 +52,25 @@ public func == (lhs: Node, rhs: Node) -> Bool {
 
 open class Graph: CustomStringConvertible, Equatable {
     open fileprivate(set) var nodes: [Node]
-    
+
     public init() {
         self.nodes = []
     }
-    
+
     open func addNode(label: String) -> Node {
         let node = Node(label: label)
         nodes.append(node)
         return node
     }
-    
+
     open func addEdge(_ source: Node, neighbor: Node) {
         let edge = Edge(neighbor: neighbor)
         source.neighbors.append(edge)
     }
-    
+
     open var description: String {
         var description = ""
-        
+
         for node in nodes {
             if !node.neighbors.isEmpty {
                 description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
@@ -78,18 +78,18 @@ open class Graph: CustomStringConvertible, Equatable {
         }
         return description
     }
-    
+
     open func findNodeWithLabel(label: String) -> Node {
         return nodes.filter { $0.label == label }.first!
     }
-    
+
     open func duplicate() -> Graph {
         let duplicated = Graph()
-        
+
         for node in nodes {
             duplicated.addNode(label: node.label)
         }
-        
+
         for node in nodes {
             for edge in node.neighbors {
                 let source = duplicated.findNodeWithLabel(label: node.label)
@@ -97,7 +97,7 @@ open class Graph: CustomStringConvertible, Equatable {
                 duplicated.addEdge(source, neighbor: neighbour)
             }
         }
-        
+
         return duplicated
     }
 }
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index fa9f5745b..bd4d15515 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -12,7 +12,7 @@ public enum OperatorType: CustomStringConvertible {
   case multiply
   case percent
   case exponent
-  
+
   public var description: String {
     switch self {
     case .add:
@@ -36,7 +36,7 @@ public enum TokenType: CustomStringConvertible {
   case closeBracket
   case Operator(OperatorToken)
   case operand(Double)
-  
+
   public var description: String {
     switch self {
     case .openBracket:
@@ -53,11 +53,11 @@ public enum TokenType: CustomStringConvertible {
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-  
+
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-  
+
   var precedence: Int {
     switch operatorType {
     case .add, .subtract:
@@ -68,7 +68,7 @@ public struct OperatorToken: CustomStringConvertible {
       return 10
     }
   }
-  
+
   var associativity: OperatorAssociativity {
     switch operatorType {
     case .add, .subtract, .divide, .multiply, .percent:
@@ -77,7 +77,7 @@ public struct OperatorToken: CustomStringConvertible {
       return .rightAssociative
     }
   }
-  
+
   public var description: String {
     return operatorType.description
   }
@@ -93,19 +93,19 @@ func < (left: OperatorToken, right: OperatorToken) -> Bool {
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-  
+
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-  
+
   init(operand: Double) {
     tokenType = .operand(operand)
   }
-  
+
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-  
+
   var isOpenBracket: Bool {
     switch tokenType {
     case .openBracket:
@@ -114,7 +114,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var isOperator: Bool {
     switch tokenType {
     case .Operator(_):
@@ -123,7 +123,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var operatorToken: OperatorToken? {
     switch tokenType {
     case .Operator(let operatorToken):
@@ -132,7 +132,7 @@ public struct Token: CustomStringConvertible {
       return nil
     }
   }
-  
+
   public var description: String {
     return tokenType.description
   }
@@ -140,27 +140,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-  
+
   public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-  
+
   public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-  
+
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .openBracket))
     return self
   }
-  
+
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .closeBracket))
     return self
   }
-  
+
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -169,29 +169,29 @@ public class InfixExpressionBuilder {
 
 // This returns the result of the shunting yard algorithm
 public func reversePolishNotation(_ expression: [Token]) -> String {
-  
+
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-  
+
   for token in expression {
     switch token.tokenType {
     case .operand(_):
       reversePolishNotation.append(token)
-      
+
     case .openBracket:
       tokenStack.push(token)
-      
+
     case .closeBracket:
       while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
         reversePolishNotation.append(tempToken)
       }
-      
+
     case .Operator(let operatorToken):
       for tempToken in tokenStack.makeIterator() {
         if !tempToken.isOperator {
           break
         }
-        
+
         if let tempOperatorToken = tempToken.operatorToken {
           if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
             || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
@@ -204,11 +204,11 @@ public func reversePolishNotation(_ expression: [Token]) -> String {
       tokenStack.push(token)
     }
   }
-  
+
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-  
+
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
 
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index 27286fdbd..c54c5a600 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -2,27 +2,27 @@ import Foundation
 
 public struct Stack<T> {
     fileprivate var array = [T]()
-    
+
     public init() {
-        
+
     }
-    
+
     public var isEmpty: Bool {
         return array.isEmpty
     }
-    
+
     public var count: Int {
         return array.count
     }
-    
+
     public mutating func push(_ element: T) {
         array.append(element)
     }
-    
+
     public mutating func pop() -> T? {
         return array.popLast()
     }
-    
+
     public var top: T? {
         return array.last
     }
diff --git a/Shunting Yard/ShuntingYard.swift b/Shunting Yard/ShuntingYard.swift
index 97a72249d..201264650 100644
--- a/Shunting Yard/ShuntingYard.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -18,7 +18,7 @@ public enum OperatorType: CustomStringConvertible {
   case multiply
   case percent
   case exponent
-  
+
   public var description: String {
     switch self {
     case .add:
@@ -42,7 +42,7 @@ public enum TokenType: CustomStringConvertible {
   case closeBracket
   case Operator(OperatorToken)
   case operand(Double)
-  
+
   public var description: String {
     switch self {
     case .openBracket:
@@ -59,11 +59,11 @@ public enum TokenType: CustomStringConvertible {
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-  
+
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-  
+
   var precedence: Int {
     switch operatorType {
     case .add, .subtract:
@@ -74,7 +74,7 @@ public struct OperatorToken: CustomStringConvertible {
       return 10
     }
   }
-  
+
   var associativity: OperatorAssociativity {
     switch operatorType {
     case .add, .subtract, .divide, .multiply, .percent:
@@ -83,7 +83,7 @@ public struct OperatorToken: CustomStringConvertible {
       return .rightAssociative
     }
   }
-  
+
   public var description: String {
     return operatorType.description
   }
@@ -99,19 +99,19 @@ func < (left: OperatorToken, right: OperatorToken) -> Bool {
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-  
+
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-  
+
   init(operand: Double) {
     tokenType = .operand(operand)
   }
-  
+
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-  
+
   var isOpenBracket: Bool {
     switch tokenType {
     case .openBracket:
@@ -120,7 +120,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var isOperator: Bool {
     switch tokenType {
     case .Operator(_):
@@ -129,7 +129,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var operatorToken: OperatorToken? {
     switch tokenType {
     case .Operator(let operatorToken):
@@ -138,7 +138,7 @@ public struct Token: CustomStringConvertible {
       return nil
     }
   }
-  
+
   public var description: String {
     return tokenType.description
   }
@@ -146,27 +146,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-  
+
   public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-  
+
   public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-  
+
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .openBracket))
     return self
   }
-  
+
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .closeBracket))
     return self
   }
-  
+
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -175,29 +175,29 @@ public class InfixExpressionBuilder {
 
 // This returns the result of the shunting yard algorithm
 public func reversePolishNotation(_ expression: [Token]) -> String {
-  
+
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-  
+
   for token in expression {
     switch token.tokenType {
     case .operand(_):
       reversePolishNotation.append(token)
-      
+
     case .openBracket:
       tokenStack.push(token)
-      
+
     case .closeBracket:
       while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
         reversePolishNotation.append(tempToken)
       }
-      
+
     case .Operator(let operatorToken):
       for tempToken in tokenStack.makeIterator() {
         if !tempToken.isOperator {
           break
         }
-        
+
         if let tempOperatorToken = tempToken.operatorToken {
           if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
             || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
@@ -210,10 +210,10 @@ public func reversePolishNotation(_ expression: [Token]) -> String {
       tokenStack.push(token)
     }
   }
-  
+
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-  
+
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index e844f9959..cd832eef9 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -70,29 +70,29 @@ private func coinFlip() -> Bool {
 
 public class DataNode<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
-  
-  var data: Payload?  
+
+  var data: Payload?
   fileprivate var key: Key?
   var next: Node?
   var down: Node?
-  
+
   public init(key: Key, data: Payload) {
     self.key  = key
     self.data = data
   }
 
   public init(asHead head: Bool){}
-  
+
 }
 
 
 open class SkipList<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
-  
+
   fileprivate(set) var head: Node?
 
   public init() {}
-  
+
 }
 
 
@@ -100,18 +100,18 @@ open class SkipList<Key: Comparable, Payload> {
 // MARK: - Search lanes for a node with a given key
 
 extension SkipList {
-  
+
   func findNode(key: Key) -> Node? {
     var currentNode: Node? = head
     var isFound: Bool = false
 
     while !isFound {
       if let node = currentNode {
-        
+
         switch node.next {
         case .none:
-          
-          currentNode = node.down          
+
+          currentNode = node.down
         case .some(let value) where value.key != nil:
 
           if value.key == key {
@@ -122,14 +122,14 @@ extension SkipList {
               currentNode = node.down
             } else {
               currentNode = node.next
-            }            
+            }
           }
-          
+
         default:
           continue
         }
-        
-      } else { 
+
+      } else {
         break
       }
     }
@@ -139,7 +139,7 @@ extension SkipList {
     } else {
       return nil
     }
-    
+
   }
 
   func search(key: Key) -> Payload? {
@@ -147,9 +147,9 @@ extension SkipList {
       return nil
     }
 
-    return node.next!.data    
-  }    
-  
+    return node.next!.data
+  }
+
 }
 
 
@@ -157,12 +157,12 @@ extension SkipList {
 // MARK: - Insert a node into lanes depending on skip list status ( bootstrap base-layer if head is empty / start insertion from current head ).
 
 extension SkipList {
-  private func bootstrapBaseLayer(key: Key, data: Payload) {    
-    head       = Node(asHead: true)    
+  private func bootstrapBaseLayer(key: Key, data: Payload) {
+    head       = Node(asHead: true)
     var node   = Node(key: key, data: data)
 
     head!.next = node
-    
+
     var currentTopNode = node
 
     while coinFlip() {
@@ -174,7 +174,7 @@ extension SkipList {
       head           = newHead
       currentTopNode = node
     }
-    
+
   }
 
 
@@ -191,13 +191,13 @@ extension SkipList {
         } else {
           currentNode = nextNode
         }
-        
+
       } else {
         stack.push(currentNode!)
-        currentNode = currentNode!.down           
+        currentNode = currentNode!.down
       }
-      
-    }       
+
+    }
 
     let itemAtLayer    = stack.pop()
     var node           = Node(key: key, data: data)
@@ -208,24 +208,24 @@ extension SkipList {
     while coinFlip() {
       if stack.isEmpty {
         let newHead    = Node(asHead: true)
-        
+
         node           = Node(key: key, data: data)
         node.down      = currentTopNode
         newHead.next   = node
         newHead.down   = head
         head           = newHead
         currentTopNode = node
-        
-      } else {        
+
+      } else {
         let nextNode  = stack.pop()
-        
+
         node           = Node(key: key, data: data)
         node.down      = currentTopNode
         node.next      = nextNode!.next
         nextNode!.next = node
         currentTopNode = node
       }
-    }     
+    }
   }
 
 
@@ -233,7 +233,7 @@ extension SkipList {
     if head != nil {
       if let node = findNode(key: key) {
         // replace, in case of key already exists. 
-        var currentNode = node.next        
+        var currentNode = node.next
         while currentNode != nil && currentNode!.key == key {
           currentNode!.data = data
           currentNode       = currentNode!.down
@@ -241,12 +241,12 @@ extension SkipList {
       } else {
         insertItem(key: key, data: data)
       }
-      
+
     } else {
       bootstrapBaseLayer(key: key, data: data)
     }
   }
-  
+
 }
 
 
@@ -257,32 +257,32 @@ extension SkipList {
     guard let item = findNode(key: key) else {
       return
     }
-    
+
     var currentNode = Optional(item)
-    
+
     while currentNode != nil {
       let node   = currentNode!.next
-      
+
       if node!.key != key {
         currentNode = node
         continue
       }
 
       let nextNode      = node!.next
-      
+
       currentNode!.next = nextNode
       currentNode       = currentNode!.down
-      
+
     }
-    
-  }  
+
+  }
 }
 
 
 // MARK: - Get associated payload from a node with a given key.
 
 extension SkipList {
-  
+
   public func get(key: Key) -> Payload? {
     return search(key: key)
   }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index ccfa58b09..324e906ee 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -9,53 +9,53 @@
 import Foundation
 
 public struct Matrix<T: Number> {
-  
+
   // MARK: - Martix Objects
-  
+
   public enum Index {
     case row, column
   }
-  
+
   public struct Size: Equatable {
     let rows: Int, columns: Int
-    
+
     public static func == (lhs: Size, rhs: Size) -> Bool {
       return lhs.columns == rhs.columns && lhs.rows == rhs.rows
     }
   }
-  
+
   // MARK: - Variables
-  
+
   let rows: Int, columns: Int
   let size: Size
-  
+
   var grid: [T]
-  
+
   var isSquare: Bool {
     return rows == columns
   }
-  
+
   // MARK: - Init
-  
+
   public init(rows: Int, columns: Int, initialValue: T = T.zero) {
     self.rows = rows
     self.columns = columns
     self.size = Size(rows: rows, columns: columns)
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
-  
+
   public init(size: Int, initialValue: T = T.zero) {
     self.init(rows: size, columns: size, initialValue: initialValue)
   }
-  
+
   // MARK: - Private Functions
-  
+
   fileprivate func indexIsValid(row: Int, column: Int) -> Bool {
     return row >= 0 && row < rows && column >= 0 && column < columns
   }
-  
+
   // MARK: - Subscript
-  
+
   public subscript(row: Int, column: Int) -> T {
     get {
       assert(indexIsValid(row: row, column: column), "Index out of range")
@@ -65,7 +65,7 @@ public struct Matrix<T: Number> {
       grid[(row * columns) + column] = newValue
     }
   }
-  
+
   public subscript(type: Matrix.Index, value: Int) -> [T] {
     get {
       switch type {
@@ -95,24 +95,24 @@ public struct Matrix<T: Number> {
       }
     }
   }
-  
+
   // MARK: - Public Functions
-  
+
   public func row(for columnIndex: Int) -> [T] {
     assert(indexIsValid(row: columnIndex, column: 0), "Index out of range")
     return Array(grid[(columnIndex * columns)..<(columnIndex * columns) + columns])
   }
-  
+
   public func column(for rowIndex: Int) -> [T] {
     assert(indexIsValid(row: 0, column: rowIndex), "Index out of range")
-    
+
     let column = (0..<rows).map { (currentRow) -> T in
       let currentColumnIndex = currentRow * columns + rowIndex
       return grid[currentColumnIndex]
     }
     return column
   }
-  
+
   public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
     for row in 0..<rows {
       for column in 0..<columns {
@@ -128,15 +128,15 @@ extension Matrix {
   public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
+
     var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
+
     for i in 0..<A.rows {
       for j in 0..<B.columns {
         C[i, j] = A[.row, i].dot(B[.column, j])
       }
     }
-    
+
     return C
   }
 }
@@ -147,21 +147,21 @@ extension Matrix {
   public func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
+
     let n = max(A.rows, A.columns, B.rows, B.columns)
     let m = nextPowerOfTwo(after: n)
-    
+
     var APrep = Matrix(size: m)
     var BPrep = Matrix(size: m)
-    
+
     A.forEach { (i, j) in
       APrep[i,j] = A[i,j]
     }
-    
+
     B.forEach { (i, j) in
       BPrep[i,j] = B[i,j]
     }
-    
+
     let CPrep = APrep.strassenR(by: BPrep)
     var C = Matrix(rows: A.rows, columns: B.columns)
     for i in 0..<A.rows {
@@ -169,25 +169,25 @@ extension Matrix {
         C[i,j] = CPrep[i,j]
       }
     }
-    
+
     return C
   }
-  
+
   private func strassenR(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.isSquare && B.isSquare, "This function requires square matricies!")
     guard A.rows > 1 && B.rows > 1 else { return A * B }
-    
+
     let n    = A.rows
     let nBy2 = n / 2
-    
+
     /*
     Assume submatricies are allocated as follows
     
      matrix A = |a b|,    matrix B = |e f|
                 |c d|                |g h|
     */
-    
+
     var a = Matrix(size: nBy2)
     var b = Matrix(size: nBy2)
     var c = Matrix(size: nBy2)
@@ -196,7 +196,7 @@ extension Matrix {
     var f = Matrix(size: nBy2)
     var g = Matrix(size: nBy2)
     var h = Matrix(size: nBy2)
-    
+
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
         a[i,j] = A[i,j]
@@ -209,7 +209,7 @@ extension Matrix {
         h[i,j] = B[i+nBy2, j+nBy2]
       }
     }
-    
+
     let p1 = a.strassenR(by: f-h)       // a * (f - h)
     let p2 = (a+b).strassenR(by: h)     // (a + b) * h
     let p3 = (c+d).strassenR(by: e)     // (c + d) * e
@@ -217,12 +217,12 @@ extension Matrix {
     let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
     let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
     let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
-    
+
     let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
     let c12 = p1 + p2                   // p1 + p2
     let c21 = p3 + p4                   // p3 + p4
     let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
-    
+
     var C = Matrix(size: n)
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
@@ -232,10 +232,10 @@ extension Matrix {
         C[i+nBy2, j+nBy2] = c22[i,j]
       }
     }
-    
+
     return C
   }
-  
+
   private func nextPowerOfTwo(after n: Int) -> Int {
     return Int(pow(2, ceil(log2(Double(n)))))
   }
@@ -248,7 +248,7 @@ extension Matrix: Addable {
     assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
     let rows = lhs.rows
     let columns = lhs.columns
-    
+
     var newMatrix = Matrix<T>(rows: rows, columns: columns)
     for row in 0..<rows {
       for column in 0..<columns {
@@ -257,12 +257,12 @@ extension Matrix: Addable {
     }
     return newMatrix
   }
-  
+
   public static func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
     assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
     let rows = lhs.rows
     let columns = lhs.columns
-    
+
     var newMatrix = Matrix<T>(rows: rows, columns: columns)
     for row in 0..<rows {
       for column in 0..<columns {
@@ -278,7 +278,7 @@ extension Matrix: Multipliable {
     assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
     let rows = lhs.rows
     let columns = lhs.columns
-    
+
     var newMatrix = Matrix<T>(rows: rows, columns: columns)
     for row in 0..<rows {
       for column in 0..<columns {
diff --git a/Ternary Search Tree/TST.playground/Sources/Utils.swift b/Ternary Search Tree/TST.playground/Sources/Utils.swift
index cabfe1b68..97f09fdd2 100644
--- a/Ternary Search Tree/TST.playground/Sources/Utils.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/Utils.swift	
@@ -9,22 +9,22 @@
 import Foundation
 
 public struct Utils {
-    
+
     public static let shared = Utils()
-    
+
     let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     //Random string generator from:
     //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
     public func randomAlphaNumericString(withLength length: Int) -> String {
         let allowedCharsCount = UInt32(allowedChars.characters.count)
         var randomString = ""
-        
+
         for _ in (0..<length) {
             let randomNum = Int(arc4random_uniform(allowedCharsCount))
             let newCharacter = allowedChars[allowedChars.index(allowedChars.startIndex, offsetBy: randomNum)]
             randomString += String(newCharacter)
         }
-        
+
         return randomString
     }
 }
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index 40739c888..dfbbae9ca 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -9,19 +9,19 @@
 import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
-    
+
 
     let testCount = 30
-    
+
     func testCanFindStringInTree() {
         var testStrings: [(key: String, data: String)] = []
         let treeOfStrings = TernarySearchTree<String>()
 
         for _ in (1...testCount) {
             var randomLength = Int(arc4random_uniform(10))
-            
+
             var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            
+
             while testStrings.contains(where: { $0.key == key}) {
                 //That key is taken, so we generate a new one with another length
                 randomLength = Int(arc4random_uniform(10))
@@ -29,20 +29,20 @@ class TernarySearchTreeTests: XCTestCase {
             }
             let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
             //    print("Key: \(key) Data: \(data)")
-            
+
             if key != "" && data != "" {
                 testStrings.append((key, data))
                 treeOfStrings.insert(data: data, withKey: key)
             }
         }
-        
+
         for aTest in testStrings {
             let data = treeOfStrings.find(key: aTest.key)
             XCTAssertNotNil(data)
             XCTAssertEqual(data, aTest.data)
         }
     }
-    
+
     func testCanFindNumberInTree() {
         var testNums: [(key: String, data: Int)] = []
         let treeOfInts = TernarySearchTree<Int>()
@@ -55,13 +55,13 @@ class TernarySearchTreeTests: XCTestCase {
                 randomLength = Int(arc4random_uniform(10))
                 key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
             }
-            
+
             if key != "" {
                 testNums.append((key, randomNum))
                 treeOfInts.insert(data: randomNum, withKey: key)
             }
         }
-        
+
         for aTest in testNums {
             let data = treeOfInts.find(key: aTest.key)
             XCTAssertNotNil(data)
diff --git a/Ternary Search Tree/Utils.swift b/Ternary Search Tree/Utils.swift
index cabfe1b68..97f09fdd2 100644
--- a/Ternary Search Tree/Utils.swift	
+++ b/Ternary Search Tree/Utils.swift	
@@ -9,22 +9,22 @@
 import Foundation
 
 public struct Utils {
-    
+
     public static let shared = Utils()
-    
+
     let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     //Random string generator from:
     //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
     public func randomAlphaNumericString(withLength length: Int) -> String {
         let allowedCharsCount = UInt32(allowedChars.characters.count)
         var randomString = ""
-        
+
         for _ in (0..<length) {
             let randomNum = Int(arc4random_uniform(allowedCharsCount))
             let newCharacter = allowedChars[allowedChars.index(allowedChars.startIndex, offsetBy: randomNum)]
             randomString += String(newCharacter)
         }
-        
+
         return randomString
     }
 }
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index 6f438c0cf..c85f56a68 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -82,7 +82,7 @@ extension ThreadedBinaryTree {
   public func insert(_ value: T) {
     insert(value, parent: self)
   }
-    
+
   fileprivate func insert(_ value: T, parent: ThreadedBinaryTree) {
     if value < self.value {
       if let left = left {
@@ -123,13 +123,13 @@ extension ThreadedBinaryTree {
   @discardableResult public func remove(_ value: T) -> ThreadedBinaryTree? {
     return search(value)?.remove()
   }
-    
+
   /*
   Deletes "this" node from the tree.
   */
   public func remove() -> ThreadedBinaryTree? {
     let replacement: ThreadedBinaryTree?
-        
+
     if let left = left {
       if let right = right {
         replacement = removeNodeWithTwoChildren(left, right)
@@ -155,33 +155,33 @@ extension ThreadedBinaryTree {
         parent?.rightThread = rightThread
       }
     }
-        
+
     reconnectParentToNode(replacement)
-        
+
     // The current node is no longer part of the tree, so clean it up.
     parent = nil
     left = nil
     right = nil
     leftThread = nil
     rightThread = nil
-        
+
     return replacement
   }
-    
+
   private func removeNodeWithTwoChildren(_ left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
     // This node has two children. It must be replaced by the smallest
     // child that is larger than this node's value, which is the leftmost
     // descendent of the right child.
     let successor = right.minimum()
-        
+
     // If this in-order successor has a right child of its own (it cannot
     // have a left child by definition), then that must take its place.
     _ = successor.remove()
-        
+
     // Connect our left child with the new node.
     successor.left = left
     left.parent = successor
-        
+
     // Connect our right child with the new node. If the right child does
     // not have any left children of its own, then the in-order successor
     // *is* the right child.
@@ -191,11 +191,11 @@ extension ThreadedBinaryTree {
     } else {
       successor.right = nil
     }
-        
+
     // And finally, connect the successor node to our parent.
     return successor
   }
-    
+
   private func reconnectParentToNode(_ node: ThreadedBinaryTree?) {
     if let parent = parent {
       if isLeftChild {
@@ -228,7 +228,7 @@ extension ThreadedBinaryTree {
     }
     return nil
   }
-    
+
   /*
   // Recursive version of search
   // Educational but undesirable due to the overhead cost of recursion
@@ -242,11 +242,11 @@ extension ThreadedBinaryTree {
     }
   }
   */
-    
+
   public func contains(value: T) -> Bool {
     return search(value) != nil
   }
-    
+
   /*
   Returns the leftmost descendent. O(h) time.
   */
@@ -257,7 +257,7 @@ extension ThreadedBinaryTree {
     }
     return node
   }
-    
+
   /*
   Returns the rightmost descendent. O(h) time.
   */
@@ -268,7 +268,7 @@ extension ThreadedBinaryTree {
     }
     return node
   }
-    
+
   /*
   Calculates the depth of this node, i.e. the distance to the root.
   Takes O(h) time.
@@ -282,7 +282,7 @@ extension ThreadedBinaryTree {
     }
     return edges
   }
-    
+
   /*
   Calculates the height of this node, i.e. the distance to the lowest leaf.
   Since this looks at all children of this node, performance is O(n).
@@ -294,7 +294,7 @@ extension ThreadedBinaryTree {
       return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
     }
   }
-    
+
   /*
   Finds the node whose value precedes our value in sorted order.
   */
@@ -305,7 +305,7 @@ extension ThreadedBinaryTree {
       return leftThread
     }
   }
-    
+
   /*
   Finds the node whose value succeeds our value in sorted order.
   */
@@ -333,7 +333,7 @@ extension ThreadedBinaryTree {
       }
     }
   }
-    
+
   public func traverseInOrderBackward(_ visit: (T) -> Void) {
     var n: ThreadedBinaryTree
     n = maximum()
@@ -346,19 +346,19 @@ extension ThreadedBinaryTree {
       }
     }
   }
-    
+
   public func traversePreOrder(_ visit: (T) -> Void) {
     visit(value)
     left?.traversePreOrder(visit)
     right?.traversePreOrder(visit)
   }
-    
+
   public func traversePostOrder(_ visit: (T) -> Void) {
     left?.traversePostOrder(visit)
     right?.traversePostOrder(visit)
     visit(value)
   }
-    
+
   /*
   Performs an in-order traversal and collects the results in an array.
   */
@@ -390,7 +390,7 @@ extension ThreadedBinaryTree {
     let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
     return leftBST && rightBST
   }
-    
+
   /*
   Is this binary tree properly threaded?
   Either left or leftThread (but not both) must be nil (likewise for right).
@@ -452,7 +452,7 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     }
     return s
   }
-    
+
   public func toArray() -> [T] {
     return map { $0 }
   }
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 6e80abfb2..7038e843e 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -27,11 +27,11 @@ import Foundation
 public indirect enum Treap<Key: Comparable, Element> {
   case empty
   case node(key: Key, val: Element, p: Int, left: Treap, right: Treap)
-  
+
   public init() {
     self = .empty
   }
-  
+
   internal func get(_ key: Key) -> Element? {
     switch self {
     case .empty:
@@ -46,7 +46,7 @@ public indirect enum Treap<Key: Comparable, Element> {
       return nil
     }
   }
-  
+
   public func contains(_ key: Key) -> Bool {
     switch self {
     case .empty:
@@ -61,7 +61,7 @@ public indirect enum Treap<Key: Comparable, Element> {
       return false
     }
   }
-  
+
   public var depth: Int {
     switch self {
     case .empty:
@@ -80,12 +80,12 @@ public indirect enum Treap<Key: Comparable, Element> {
   public var count: Int {
     return Treap.countHelper(self)
   }
-  
+
   fileprivate static func countHelper(_ treap: Treap<Key, Element>) -> Int {
     if case let .node(_, _, _, left, right) = treap {
       return countHelper(left) + 1 + countHelper(right)
     }
-    
+
     return 0
   }
 }
@@ -121,7 +121,7 @@ public extension Treap {
       return .empty
     }
   }
-  
+
   fileprivate func insertAndBalance(_ nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap,
                                     _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
     let newChild: Treap<Key, Element>
@@ -141,14 +141,14 @@ public extension Treap {
       newNode = .empty
       return newNode
     }
-    
+
     if case let .node(_, _, newChildP, _, _) = newChild , newChildP < nodeP {
       return rotate(newNode)
     } else {
       return newNode
     }
   }
-  
+
   internal func delete(key: Key) throws -> Treap {
     switch self {
     case .empty:
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index f349e6ab8..d4fc4cfdb 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -27,17 +27,17 @@ THE SOFTWARE.*/
 import XCTest
 
 class TreapTests: XCTestCase {
-  
+
   override func setUp() {
     super.setUp()
     // Put setup code here. This method is called before the invocation of each test method in the class.
   }
-  
+
   override func tearDown() {
     // Put teardown code here. This method is called after the invocation of each test method in the class.
     super.tearDown()
   }
-  
+
   func testSanity() {
     var treap = Treap<Int, String>.empty
     treap = treap.set(key: 5, val: "a").set(key: 7, val: "b")
@@ -51,7 +51,7 @@ class TreapTests: XCTestCase {
     XCTAssert(!treap.contains(5))
     XCTAssert(treap.contains(7))
   }
-  
+
   func testFairlyBalanced() {
     var treap = Treap<Int, Int?>.empty
     for i in 0..<1000 {
@@ -60,7 +60,7 @@ class TreapTests: XCTestCase {
     let depth = treap.depth
     XCTAssert(depth < 30, "treap.depth was \(depth)")
   }
-  
+
   func testFairlyBalancedCollection() {
     var treap = Treap<Int, Int?>()
     for i in 0..<1000 {
@@ -69,5 +69,5 @@ class TreapTests: XCTestCase {
     let depth = treap.depth
     XCTAssert(depth > 0 && depth < 30)
   }
-  
+
 }
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index 7292c5f0a..eeee065fe 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -25,52 +25,52 @@ THE SOFTWARE.*/
 import Foundation
 
 extension Treap: MutableCollection {
-  
+
   public typealias Index = TreapIndex<Key>
-  
+
   public subscript(index: TreapIndex<Key>) -> Element {
     get {
       guard let result = self.get(index.keys[index.keyIndex]) else {
         fatalError("Invalid index!")
       }
-      
+
       return result
     }
-    
+
     mutating set {
       let key = index.keys[index.keyIndex]
       self = self.set(key: key, val: newValue)
     }
   }
-  
+
   public subscript(key: Key) -> Element? {
     get {
       return self.get(key)
     }
-    
+
     mutating set {
       guard let value = newValue else {
         _ = try? self.delete(key: key)
         return
       }
-      
+
       self = self.set(key: key, val: value)
     }
   }
-  
+
   public var startIndex: TreapIndex<Key> {
     return TreapIndex<Key>(keys: keys, keyIndex: 0)
   }
-  
+
   public var endIndex: TreapIndex<Key> {
     let keys = self.keys
     return TreapIndex<Key>(keys: keys, keyIndex: keys.count)
   }
-  
+
   public func index(after i: TreapIndex<Key>) -> TreapIndex<Key> {
     return i.successor()
   }
-  
+
   fileprivate var keys: [Key] {
     var results: [Key] = []
     if case let .node(key, _, _, left, right) = self {
@@ -78,28 +78,28 @@ extension Treap: MutableCollection {
       results.append(key)
       results.append(contentsOf: right.keys)
     }
-    
+
     return results
   }
 }
 
 public struct TreapIndex<Key: Comparable>: Comparable {
-  
+
   public static func < (lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
     return lhs.keyIndex < rhs.keyIndex
   }
-  
+
   fileprivate let keys: [Key]
   fileprivate let keyIndex: Int
-  
+
   public func successor() -> TreapIndex {
     return TreapIndex(keys: keys, keyIndex: keyIndex + 1)
   }
-  
+
   public func predecessor() -> TreapIndex {
     return TreapIndex(keys: keys, keyIndex: keyIndex - 1)
   }
-  
+
   fileprivate init(keys: [Key] = [], keyIndex: Int = 0) {
     self.keys = keys
     self.keyIndex = keyIndex
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index 34cfec3d2..62d18d16f 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -37,7 +37,7 @@ public extension Treap {
     } else {
       fatalError("No values in treap")
     }
-    
+
     switch self {
     case .node:
       if case let .node(_, _, _, left, right) = current.set(key: key, val: val, p: -1) {
@@ -49,7 +49,7 @@ public extension Treap {
       return (left: .empty, right: .empty)
     }
   }
-  
+
   internal var leastKey: Key? {
     switch self {
     case .empty:
@@ -60,7 +60,7 @@ public extension Treap {
       return left.leastKey
     }
   }
-  
+
   internal var mostKey: Key? {
     switch self {
     case .empty:
@@ -79,7 +79,7 @@ internal func merge<Key: Comparable, Element>(_ left: Treap<Key, Element>, right
     return right
   case (_, .empty):
     return left
-    
+
   case let (.node(leftKey, leftVal, leftP, leftLeft, leftRight), .node(rightKey, rightVal, rightP, rightLeft, rightRight)):
     if leftP < rightP {
       return .node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: merge(leftRight, right: right))
@@ -96,16 +96,16 @@ extension Treap: CustomStringConvertible {
   public var description: String {
     return Treap.descHelper(self, indent: 0)
   }
-  
+
   fileprivate static func descHelper(_ treap: Treap<Key, Element>, indent: Int) -> String {
     if case let .node(key, value, priority, left, right) = treap {
       var result = ""
       let tabs = String(repeating: "\t", count: indent)
-      
+
       result += descHelper(left, indent: indent + 1)
       result += "\n" + tabs + "\(key), \(value), \(priority)\n"
       result += descHelper(right, indent: indent + 1)
-      
+
       return result
     } else {
       return ""
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 4321479c3..7ff9638d7 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -18,8 +18,8 @@ class TrieNode<T: Hashable> {
   var isLeaf: Bool {
     return children.count == 0
   }
-  
-  
+
+
   /// Initializes a node.
   ///
   /// - Parameters:
@@ -29,7 +29,7 @@ class TrieNode<T: Hashable> {
     self.value = value
     self.parentNode = parentNode
   }
-  
+
   /// Adds a child node to self.  If the child is already present,
   /// do nothing.
   ///
@@ -92,7 +92,7 @@ class Trie: NSObject, NSCoding {
 
 // MARK: - Adds methods: insert, remove, contains
 extension Trie {
-  
+
   /// Inserts a word into the trie.  If the word is already present,
   /// there is no change.
   ///
@@ -117,7 +117,7 @@ extension Trie {
     wordCount += 1
     currentNode.isTerminating = true
   }
-  
+
   /// Determines whether a word is in the trie.
   ///
   /// - Parameter word: the word to check for
@@ -168,7 +168,7 @@ extension Trie {
     return nil
 
   }
-  
+
   /// Deletes a word from the trie by starting with the last letter
   /// and moving back, deleting nodes until either a non-leaf or a
   /// terminating node is found.
@@ -187,7 +187,7 @@ extension Trie {
       }
     }
   }
-  
+
   /// Removes a word from the trie.  If the word is not present or
   /// it is empty, just ignore it.  If the last node is a leaf,
   /// delete that node and higher nodes that are leaves until a
@@ -210,7 +210,7 @@ extension Trie {
     }
     wordCount -= 1
   }
-  
+
   /// Returns an array of words in a subtrie of the trie
   ///
   /// - Parameters:
diff --git a/Trie/Trie/TrieUITests/TrieUITests.swift b/Trie/Trie/TrieUITests/TrieUITests.swift
index f3da2a67f..acb3b1756 100644
--- a/Trie/Trie/TrieUITests/TrieUITests.swift
+++ b/Trie/Trie/TrieUITests/TrieUITests.swift
@@ -9,12 +9,12 @@
 import XCTest
 
 class TrieUITests: XCTestCase {
-        
+
     override func setUp() {
         super.setUp()
-        
+
         // Put setup code here. This method is called before the invocation of each test method in the class.
-        
+
         // In UI tests it is usually best to stop immediately when a failure occurs.
         continueAfterFailure = false
         // UI tests must launch the application that they test. Doing this in setup will make sure it happens for each test method.
@@ -22,15 +22,15 @@ class TrieUITests: XCTestCase {
 
         // In UI tests it’s important to set the initial state - such as interface orientation - required for your tests before they run. The setUp method is a good place to do this.
     }
-    
+
     override func tearDown() {
         // Put teardown code here. This method is called after the invocation of each test method in the class.
         super.tearDown()
     }
-    
+
     func testExample() {
         // Use recording to get started writing UI tests.
         // Use XCTAssert and related functions to verify your tests produce the correct results.
     }
-    
+
 }
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
index 9bef69687..969a3599b 100644
--- a/Z-Algorithm/ZAlgorithm.swift
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -9,34 +9,34 @@
 import Foundation
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-  
+
   let pattern = Array(ptrn.characters)
   let patternLength = pattern.count
-  
+
   guard patternLength > 0 else {
     return nil
   }
-  
+
   var zeta = [Int](repeating: 0, count: patternLength)
-  
+
   var left = 0
   var right = 0
   var k_1 = 0
   var betaLength = 0
   var textIndex = 0
   var patternIndex = 0
-  
+
   for k in 1 ..< patternLength {
     if k > right {
       patternIndex = 0
-      
+
       while k + patternIndex < patternLength  &&
         pattern[k + patternIndex] == pattern[patternIndex] {
           patternIndex = patternIndex + 1
       }
-      
+
       zeta[k] = patternIndex
-      
+
       if zeta[k] > 0 {
         left = k
         right = k + zeta[k] - 1
@@ -44,18 +44,18 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
     } else {
       k_1 = k - left + 1
       betaLength = right - k + 1
-      
+
       if zeta[k_1 - 1] < betaLength {
         zeta[k] = zeta[k_1 - 1]
       } else if zeta[k_1 - 1] >= betaLength {
         textIndex = betaLength
         patternIndex = right + 1
-        
+
         while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
           textIndex = textIndex + 1
           patternIndex = patternIndex + 1
         }
-        
+
         zeta[k] = patternIndex - k
         left = k
         right = patternIndex - 1
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index 395122af0..44faf6790 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -2,34 +2,34 @@
 
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-  
+
   let pattern = Array(ptrn.characters)
   let patternLength = pattern.count
-  
+
   guard patternLength > 0 else {
     return nil
   }
-  
+
   var zeta = [Int](repeating: 0, count: patternLength)
-  
+
   var left = 0
   var right = 0
   var k_1 = 0
   var betaLength = 0
   var textIndex = 0
   var patternIndex = 0
-  
+
   for k in 1 ..< patternLength {
     if k > right {
       patternIndex = 0
-      
+
       while k + patternIndex < patternLength  &&
         pattern[k + patternIndex] == pattern[patternIndex] {
           patternIndex = patternIndex + 1
       }
-      
+
       zeta[k] = patternIndex
-      
+
       if zeta[k] > 0 {
         left = k
         right = k + zeta[k] - 1
@@ -37,18 +37,18 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
     } else {
       k_1 = k - left + 1
       betaLength = right - k + 1
-      
+
       if zeta[k_1 - 1] < betaLength {
         zeta[k] = zeta[k_1 - 1]
       } else if zeta[k_1 - 1] >= betaLength {
         textIndex = betaLength
         patternIndex = right + 1
-        
+
         while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
           textIndex = textIndex + 1
           patternIndex = patternIndex + 1
         }
-        
+
         zeta[k] = patternIndex - k
         left = k
         right = patternIndex - 1
@@ -60,28 +60,28 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
 
 extension String {
-  
+
   func indexesOf(pattern: String) -> [Int]? {
     let patternLength = pattern.characters.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
-    
+
     guard zeta != nil else {
       return nil
     }
-    
+
     var indexes: [Int] = []
-    
+
     /* Scan the zeta array to find matched patterns */
     for i in 0 ..< zeta!.count {
       if zeta![i] == patternLength {
         indexes.append(i - patternLength - 1)
       }
     }
-    
+
     guard !indexes.isEmpty else {
       return nil
     }
-    
+
     return indexes
   }
 }
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
index c35703272..e60c1617f 100644
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -9,28 +9,28 @@
 import Foundation
 
 extension String {
-  
+
   func indexesOf(pattern: String) -> [Int]? {
     let patternLength = pattern.characters.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
-    
+
     guard zeta != nil else {
       return nil
     }
-    
+
     var indexes: [Int] = [Int]()
-    
+
     /* Scan the zeta array to find matched patterns */
     for i in 0 ..< zeta!.count {
       if zeta![i] == patternLength {
         indexes.append(i - patternLength - 1)
       }
     }
-    
+
     guard !indexes.isEmpty else {
       return nil
     }
-    
+
     return indexes
   }
 }

From b718f04b4be46ebe9d82cc1d18264d92b12be0a9 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:53:31 +0500
Subject: [PATCH 1013/1679] Fix violation: unused_optional_binding

warning: Unused Optional Binding Violation: Prefer `!= nil` over `let _ =` ()
---
 Graph/Graph/AdjacencyListGraph.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 57fd75fed..b58ef6417 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -78,7 +78,7 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
     // works
     let edge = Edge(from: from, to: to, weight: weight)
     let edgeList = adjacencyList[from.index]
-    if let _ = edgeList.edges {
+    if edgeList.edges != nil {
         edgeList.addEdge(edge)
     } else {
         edgeList.edges = [edge]

From 9a363c7082c2acbc6984864b67ac6c20ac911cdb Mon Sep 17 00:00:00 2001
From: Xiangxin <xiangxinsg@gmail.com>
Date: Fri, 17 Mar 2017 00:19:36 +0800
Subject: [PATCH 1014/1679] Minimum Spanning Tree (Kruskal's and Prim's)

---
 Minimum Spanning Tree/Images/kruskal.png      | Bin 0 -> 22083 bytes
 Minimum Spanning Tree/Images/prim.png         | Bin 0 -> 19053 bytes
 Minimum Spanning Tree/Kruskal.swift           |  31 +++
 .../Contents.swift                            |  93 +++++++
 .../Resources/mst.png                         | Bin 0 -> 19209 bytes
 .../Sources/Graph.swift                       |  55 +++++
 .../Sources/Heap.swift                        | 227 ++++++++++++++++++
 .../Sources/PriorityQueue.swift               |  58 +++++
 .../Sources/UnionFind.swift                   |  61 +++++
 .../contents.xcplayground                     |   4 +
 Minimum Spanning Tree/Prim.swift              |  45 ++++
 Minimum Spanning Tree/README.markdown         | 102 ++++++++
 README.markdown                               |   1 +
 .../contents.xcworkspacedata                  |  26 ++
 14 files changed, 703 insertions(+)
 create mode 100644 Minimum Spanning Tree/Images/kruskal.png
 create mode 100644 Minimum Spanning Tree/Images/prim.png
 create mode 100644 Minimum Spanning Tree/Kruskal.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/mst.png
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
 create mode 100644 Minimum Spanning Tree/Prim.swift
 create mode 100644 Minimum Spanning Tree/README.markdown

diff --git a/Minimum Spanning Tree/Images/kruskal.png b/Minimum Spanning Tree/Images/kruskal.png
new file mode 100644
index 0000000000000000000000000000000000000000..5172f180fda8dff8666a4a38f08e675311c515dd
GIT binary patch
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diff --git a/Minimum Spanning Tree/Kruskal.swift b/Minimum Spanning Tree/Kruskal.swift
new file mode 100644
index 000000000..bebd32602
--- /dev/null
+++ b/Minimum Spanning Tree/Kruskal.swift	
@@ -0,0 +1,31 @@
+//
+//  Kruskal.swift
+//  
+//
+//  Created by xiang xin on 16/3/17.
+//
+//
+
+
+func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+  var cost: Int = 0
+  var tree = Graph<T>()
+  let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
+
+  var unionFind = UnionFind<T>()
+  for vertex in graph.vertices {
+    unionFind.addSetWith(vertex)
+  }
+
+  for edge in sortedEdgeListByWeight {
+    let v1 = edge.vertex1
+    let v2 = edge.vertex2
+    if !unionFind.inSameSet(v1, and: v2) {
+      cost += edge.weight
+      tree.addEdge(edge)
+      unionFind.unionSetsContaining(v1, and: v2)
+    }
+  }
+
+  return (cost: cost, tree: tree)
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
new file mode 100644
index 000000000..99b5e859f
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -0,0 +1,93 @@
+/**
+ The following code demonstrates getting MST of the graph below by both
+ Kruskal's and Prim's algorithms.
+ */
+
+func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+  var cost: Int = 0
+  var tree = Graph<T>()
+  let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
+
+  var unionFind = UnionFind<T>()
+  for vertex in graph.vertices {
+    unionFind.addSetWith(vertex)
+  }
+
+  for edge in sortedEdgeListByWeight {
+    let v1 = edge.vertex1
+    let v2 = edge.vertex2
+    if !unionFind.inSameSet(v1, and: v2) {
+      cost += edge.weight
+      tree.addEdge(edge)
+      unionFind.unionSetsContaining(v1, and: v2)
+    }
+  }
+
+  return (cost: cost, tree: tree)
+}
+
+func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+  var cost: Int = 0
+  var tree = Graph<T>()
+
+  if graph.vertices.isEmpty {
+    return (cost: cost, tree: tree)
+  }
+
+  var visited = Set<T>()
+  var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
+    sort: { $0.weight < $1.weight })
+
+  priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+  while let head = priorityQueue.dequeue() {
+    let vertex = head.vertex
+    if visited.contains(vertex) {
+      continue
+    }
+    visited.insert(vertex)
+
+    cost += head.weight
+    if let prev = head.parent {
+      tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
+    }
+
+    if let neighbours = graph.adjList[vertex] {
+      for neighbour in neighbours {
+        let nextVertex = neighbour.vertex
+        if !visited.contains(nextVertex) {
+          priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+        }
+      }
+    }
+  }
+
+  return (cost: cost, tree: tree)
+}
+
+/*:
+ ![Graph](mst.png)
+ */
+
+var graph = Graph<Int>()
+graph.addEdge(vertex1: 1, vertex2: 2, weight: 6)
+graph.addEdge(vertex1: 1, vertex2: 3, weight: 1)
+graph.addEdge(vertex1: 1, vertex2: 4, weight: 5)
+graph.addEdge(vertex1: 2, vertex2: 3, weight: 5)
+graph.addEdge(vertex1: 2, vertex2: 5, weight: 3)
+graph.addEdge(vertex1: 3, vertex2: 4, weight: 5)
+graph.addEdge(vertex1: 3, vertex2: 5, weight: 6)
+graph.addEdge(vertex1: 3, vertex2: 6, weight: 4)
+graph.addEdge(vertex1: 4, vertex2: 6, weight: 2)
+graph.addEdge(vertex1: 5, vertex2: 6, weight: 6)
+
+print("===== Kruskal's =====")
+let result1 = minimumSpanningTreeKruskal(graph: graph)
+print("Minimum spanning tree total weight: \(result1.cost)")
+print("Minimum spanning tree:")
+print(result1.tree)
+
+print("===== Prim's =====")
+let result2 = minimumSpanningTreePrim(graph: graph)
+print("Minimum spanning tree total weight: \(result2.cost)")
+print("Minimum spanning tree:")
+print(result2.tree)
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/mst.png b/Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/mst.png
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diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
new file mode 100644
index 000000000..0ae996646
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -0,0 +1,55 @@
+
+// Undirected edge
+public struct Edge<T>: CustomStringConvertible {
+  public let vertex1: T
+  public let vertex2: T
+  public let weight: Int
+
+  public var description: String {
+    return "[\(vertex1)-\(vertex2), \(weight)]"
+  }
+}
+
+
+// Undirected weighted graph
+public struct Graph<T: Hashable>: CustomStringConvertible {
+
+  public private(set) var edgeList: [Edge<T>]
+  public private(set) var vertices: Set<T>
+  public private(set) var adjList: [T: [(vertex: T, weight: Int)]]
+
+  public init() {
+    edgeList = [Edge<T>]()
+    vertices = Set<T>()
+    adjList = [T: [(vertex: T, weight: Int)]]()
+  }
+
+  public var description: String {
+    var description = ""
+    for edge in edgeList {
+      description += edge.description + "\n"
+    }
+    return description
+  }
+
+  public mutating func addEdge(vertex1 v1: T, vertex2 v2: T, weight w: Int) {
+    edgeList.append(Edge(vertex1: v1, vertex2: v2, weight: w))
+    vertices.insert(v1)
+    vertices.insert(v2)
+    if adjList[v1] == nil {
+      adjList[v1] = [(vertex: v2, weight: w)]
+    } else {
+      adjList[v1]!.append((vertex: v2, weight: w))
+    }
+
+    if adjList[v2] == nil {
+      adjList[v2] = [(vertex: v1, weight: w)]
+    } else {
+      adjList[v2]!.append((vertex: v1, weight: w))
+    }
+  }
+
+  public mutating func addEdge(_ edge: Edge<T>) {
+    addEdge(vertex1: edge.vertex1, vertex2: edge.vertex2, weight: edge.weight)
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
new file mode 100644
index 000000000..fa30df362
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
@@ -0,0 +1,227 @@
+//
+//  Heap.swift
+//  Written for the Swift Algorithm Club by Kevin Randrup and Matthijs Hollemans
+//
+
+public struct Heap<T> {
+  /** The array that stores the heap's nodes. */
+  var elements = [T]()
+
+  /** Determines whether this is a max-heap (>) or min-heap (<). */
+  fileprivate var isOrderedBefore: (T, T) -> Bool
+
+  /**
+   * Creates an empty heap.
+   * The sort function determines whether this is a min-heap or max-heap.
+   * For integers, > makes a max-heap, < makes a min-heap.
+   */
+  public init(sort: @escaping (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+  }
+
+  /**
+   * Creates a heap from an array. The order of the array does not matter;
+   * the elements are inserted into the heap in the order determined by the
+   * sort function.
+   */
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+    buildHeap(fromArray: array)
+  }
+
+  /*
+  // This version has O(n log n) performance.
+  private mutating func buildHeap(array: [T]) {
+    elements.reserveCapacity(array.count)
+    for value in array {
+      insert(value)
+    }
+  }
+  */
+
+  /**
+   * Converts an array to a max-heap or min-heap in a bottom-up manner.
+   * Performance: This runs pretty much in O(n).
+   */
+  fileprivate mutating func buildHeap(fromArray array: [T]) {
+    elements = array
+    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+      shiftDown(i, heapSize: elements.count)
+    }
+  }
+
+  public var isEmpty: Bool {
+    return elements.isEmpty
+  }
+
+  public var count: Int {
+    return elements.count
+  }
+
+  /**
+   * Returns the index of the parent of the element at index i.
+   * The element at index 0 is the root of the tree and has no parent.
+   */
+  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+    return (i - 1) / 2
+  }
+
+  /**
+   * Returns the index of the left child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no left child.
+   */
+  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+    return 2*i + 1
+  }
+
+  /**
+   * Returns the index of the right child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no right child.
+   */
+  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+    return 2*i + 2
+  }
+
+  /**
+   * Returns the maximum value in the heap (for a max-heap) or the minimum
+   * value (for a min-heap).
+   */
+  public func peek() -> T? {
+    return elements.first
+  }
+
+  /**
+   * Adds a new value to the heap. This reorders the heap so that the max-heap
+   * or min-heap property still holds. Performance: O(log n).
+   */
+  public mutating func insert(_ value: T) {
+    elements.append(value)
+    shiftUp(elements.count - 1)
+  }
+
+  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+    for value in sequence {
+      insert(value)
+    }
+  }
+
+  /**
+   * Allows you to change an element. In a max-heap, the new element should be
+   * larger than the old one; in a min-heap it should be smaller.
+   */
+  public mutating func replace(index i: Int, value: T) {
+    guard i < elements.count else { return }
+    
+    assert(isOrderedBefore(value, elements[i]))
+    elements[i] = value
+    shiftUp(i)
+  }
+
+  /**
+   * Removes the root node from the heap. For a max-heap, this is the maximum
+   * value; for a min-heap it is the minimum value. Performance: O(log n).
+   */
+  @discardableResult public mutating func remove() -> T? {
+    if elements.isEmpty {
+      return nil
+    } else if elements.count == 1 {
+      return elements.removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = elements[0]
+      elements[0] = elements.removeLast()
+      shiftDown()
+      return value
+    }
+  }
+
+  /**
+   * Removes an arbitrary node from the heap. Performance: O(log n). You need
+   * to know the node's index, which may actually take O(n) steps to find.
+   */
+  public mutating func removeAt(_ index: Int) -> T? {
+    guard index < elements.count else { return nil }
+    
+    let size = elements.count - 1
+    if index != size {
+      swap(&elements[index], &elements[size])
+      shiftDown(index, heapSize: size)
+      shiftUp(index)
+    }
+    return elements.removeLast()
+  }
+
+  /**
+   * Takes a child node and looks at its parents; if a parent is not larger
+   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+   */
+  mutating func shiftUp(_ index: Int) {
+    var childIndex = index
+    let child = elements[childIndex]
+    var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+      elements[childIndex] = elements[parentIndex]
+      childIndex = parentIndex
+      parentIndex = self.parentIndex(ofIndex: childIndex)
+    }
+
+    elements[childIndex] = child
+  }
+
+  mutating func shiftDown() {
+    shiftDown(0, heapSize: elements.count)
+  }
+
+  /**
+   * Looks at a parent node and makes sure it is still larger (max-heap) or
+   * smaller (min-heap) than its childeren.
+   */
+  mutating func shiftDown(_ index: Int, heapSize: Int) {
+    var parentIndex = index
+
+    while true {
+      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+      let rightChildIndex = leftChildIndex + 1
+
+      // Figure out which comes first if we order them by the sort function:
+      // the parent, the left child, or the right child. If the parent comes
+      // first, we're done. If not, that element is out-of-place and we make
+      // it "float down" the tree until the heap property is restored.
+      var first = parentIndex
+      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+        first = leftChildIndex
+      }
+      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+        first = rightChildIndex
+      }
+      if first == parentIndex { return }
+
+      swap(&elements[parentIndex], &elements[first])
+      parentIndex = first
+    }
+  }
+}
+
+// MARK: - Searching
+
+extension Heap where T: Equatable {
+  /**
+   * Searches the heap for the given element. Performance: O(n).
+   */
+  public func index(of element: T) -> Int? {
+    return index(of: element, 0)
+  }
+
+  fileprivate func index(of element: T, _ i: Int) -> Int? {
+    if i >= count { return nil }
+    if isOrderedBefore(element, elements[i]) { return nil }
+    if element == elements[i] { return i }
+    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+    return nil
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift
new file mode 100644
index 000000000..92f7b6d3f
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift	
@@ -0,0 +1,58 @@
+/*
+  Priority Queue, a queue where the most "important" items are at the front of
+  the queue.
+
+  The heap is a natural data structure for a priority queue, so this object
+  simply wraps the Heap struct.
+
+  All operations are O(lg n).
+
+  Just like a heap can be a max-heap or min-heap, the queue can be a max-priority
+  queue (largest element first) or a min-priority queue (smallest element first).
+*/
+public struct PriorityQueue<T> {
+  fileprivate var heap: Heap<T>
+
+  /*
+    To create a max-priority queue, supply a > sort function. For a min-priority
+    queue, use <.
+  */
+  public init(sort: @escaping (T, T) -> Bool) {
+    heap = Heap(sort: sort)
+  }
+
+  public var isEmpty: Bool {
+    return heap.isEmpty
+  }
+
+  public var count: Int {
+    return heap.count
+  }
+
+  public func peek() -> T? {
+    return heap.peek()
+  }
+
+  public mutating func enqueue(_ element: T) {
+    heap.insert(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    return heap.remove()
+  }
+
+  /*
+    Allows you to change the priority of an element. In a max-priority queue,
+    the new priority should be larger than the old one; in a min-priority queue
+    it should be smaller.
+  */
+  public mutating func changePriority(index i: Int, value: T) {
+    return heap.replace(index: i, value: value)
+  }
+}
+
+extension PriorityQueue where T: Equatable {
+  public func index(of element: T) -> Int? {
+    return heap.index(of: element)
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift
new file mode 100644
index 000000000..29ea0a373
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift	
@@ -0,0 +1,61 @@
+/*
+ Union-Find Data Structure
+
+ Performance:
+ adding new set is almost O(1)
+ finding set of element is almost O(1)
+ union sets is almost O(1)
+ */
+
+public struct UnionFind<T: Hashable> {
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+
+  public init() {}
+
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = setByIndex(parent[index])
+      return parent[index]
+    }
+  }
+
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
+    }
+  }
+
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
+          size[secondSet] += size[firstSet]
+        } else {
+          parent[secondSet] = firstSet
+          size[firstSet] += size[secondSet]
+        }
+      }
+    }
+  }
+
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
+    }
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground b/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
new file mode 100644
index 000000000..89da2d470
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' display-mode='rendered'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
new file mode 100644
index 000000000..89c26cff0
--- /dev/null
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -0,0 +1,45 @@
+//
+//  Prim.swift
+//  
+//
+//  Created by xiang xin on 16/3/17.
+//
+//
+
+func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+  var cost: Int = 0
+  var tree = Graph<T>()
+
+  if graph.vertices.isEmpty {
+    return (cost: cost, tree: tree)
+  }
+
+  var visited = Set<T>()
+  var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
+    sort: { $0.weight < $1.weight })
+
+  priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+  while let head = priorityQueue.dequeue() {
+    let vertex = head.vertex
+    if visited.contains(vertex) {
+      continue
+    }
+    visited.insert(vertex)
+
+    cost += head.weight
+    if let prev = head.parent {
+      tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
+    }
+
+    if let neighbours = graph.adjList[vertex] {
+      for neighbour in neighbours {
+        let nextVertex = neighbour.vertex
+        if !visited.contains(nextVertex) {
+          priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+        }
+      }
+    }
+  }
+
+  return (cost: cost, tree: tree)
+}
diff --git a/Minimum Spanning Tree/README.markdown b/Minimum Spanning Tree/README.markdown
new file mode 100644
index 000000000..c47713701
--- /dev/null
+++ b/Minimum Spanning Tree/README.markdown	
@@ -0,0 +1,102 @@
+# Minimum Spanning Tree (Weighted Graph)
+
+A [minimum spanning tree](https://en.wikipedia.org/wiki/Minimum_spanning_tree) (MST) of a connected undirected weighted graph has a subset of the edges from the original graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. There can be more than one MSTs of a graph.
+
+There are two popular algorithms to calculate MST of a graph - [Kruskal's algorithm](https://en.wikipedia.org/wiki/Kruskal's_algorithm) and [Prim's algorithm](https://en.wikipedia.org/wiki/Prim's_algorithm). Both algorithms have a total time complexity of `O(ElogE)` where `E` is the number of edges from the original graph.
+
+### Kruskal's Algorithm
+Sort the edges base on weight. Greedily select the smallest one each time and add into the MST as long as it doesn't form a cycle.
+Kruskal's algoritm uses [Union Find](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Union-Find) data structure to check whether any additional edge causes a cycle. The logic is to put all connected vertices into the same set (in Union Find's concept). If the two vertices from a new edge do not belong to the same set, then it's safe to add that edge into the MST.
+
+The following graph demonstrates the steps:
+
+![Graph](Images/kruskal.png)
+
+Preparation
+```swift
+// Initialize the values to be returned and Union Find data structure.
+var cost: Int = 0
+var tree = Graph<T>()
+var unionFind = UnionFind<T>()
+for vertex in graph.vertices {
+
+// Initially all vertices are disconnected.
+// Each of them belongs to it's individual set.
+  unionFind.addSetWith(vertex)
+}
+```
+
+Sort the edges
+```swift
+let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
+```
+
+Take one edge at a time and try to insert it into the MST. 
+```swift
+for edge in sortedEdgeListByWeight {
+  let v1 = edge.vertex1
+  let v2 = edge.vertex2 
+  
+  // Same set means the two vertices of this edge were already connected in the MST.
+  // Adding this one will cause a cycle.
+  if !unionFind.inSameSet(v1, and: v2) {
+    // Add the edge into the MST and update the final cost.
+    cost += edge.weight
+    tree.addEdge(edge)
+    
+    // Put the two vertices into the same set.
+    unionFind.unionSetsContaining(v1, and: v2)
+  }
+}
+```
+### Prim's Algorithm
+Prim's algorithm doesn't pre-sort all edges. Instead, it uses a [Priority Queue](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Priority%20Queue) to maintain a running sorted next-possile vertices.
+Starting from one vertex, loop through all unvisited neighbours and enqueue a pair of values for each neighbour - the vertex and the weight of edge connecting current vertex to the neighbour. Each time it greedily select the top of the priority queue (the one with least weight value) and add the edge into the final MST if the enqueued neighbour hasn't been already visited.
+
+The following graph demonstrates the steps:
+
+![Graph](Images/prim.png)
+
+Preparation
+```swift
+// Initialize the values to be returned and Priority Queue data structure.
+var cost: Int = 0
+var tree = Graph<T>()
+var visited = Set<T>()
+
+// In addition to the (neighbour vertex, weight) pair, parent is added for the purpose of printing out the MST later.
+// parent is basically current vertex. aka. the previous vertex before neigbour vertex gets visited.
+var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(sort: { $0.weight < $1.weight })
+```
+
+Start from any vertex
+```swift
+priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+```
+
+```swift
+// Take from the top of the priority queue ensures getting the least weight edge.
+while let head = priorityQueue.dequeue() {
+  let vertex = head.vertex
+  if visited.contains(vertex) {
+    continue
+  }
+
+  // If the vertex hasn't been visited before, its edge (parent-vertex) is selected for MST.
+  visited.insert(vertex)
+  cost += head.weight
+  if let prev = head.parent { // The first vertex doesn't have a parent.
+    tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
+  }
+
+  // Add all unvisted neighbours into the priority queue.
+  if let neighbours = graph.adjList[vertex] {
+    for neighbour in neighbours {
+      let nextVertex = neighbour.vertex
+      if !visited.contains(nextVertex) {
+        priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+      }
+    }
+  }
+}
+```
diff --git a/README.markdown b/README.markdown
index e0983f22e..579ca0b4e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -178,6 +178,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Shortest Path](Shortest%20Path%20%28Unweighted%29/) on an unweighted tree
 - [Single-Source Shortest Paths](Single-Source%20Shortest%20Paths%20(Weighted)/)
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree%20%28Unweighted%29/) on an unweighted tree
+- [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 
 ## Puzzles
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index b2ffce836..c89ac0dfe 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1267,6 +1267,32 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "group:Minimum Spanning Tree"
+      name = "Minimum Spanning Tree">
+      <FileRef
+         location = "group:Kruskal.swift">
+      </FileRef>
+      <FileRef
+         location = "group:Prim.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:kruskal.png">
+         </FileRef>
+         <FileRef
+            location = "group:prim.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:MinimumSpanningTree.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Minimum Spanning Tree (Unweighted)"
       name = "Minimum Spanning Tree (Unweighted)">

From 6bc50e5f9a966738b8331d68de8ed421067d4f4e Mon Sep 17 00:00:00 2001
From: Xiangxin <xiangxinsg@gmail.com>
Date: Tue, 25 Apr 2017 15:29:45 +0800
Subject: [PATCH 1015/1679] Address comments and refactor

---
 .../MinimumSpanningTree.playground/Contents.swift   |  4 ++--
 .../Sources/Graph.swift                             | 13 +++++++------
 .../playground.xcworkspace/contents.xcworkspacedata |  7 +++++++
 Minimum Spanning Tree/Prim.swift                    |  5 +++--
 4 files changed, 19 insertions(+), 10 deletions(-)
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
index 99b5e859f..2981d30ea 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -30,7 +30,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var cost: Int = 0
   var tree = Graph<T>()
 
-  if graph.vertices.isEmpty {
+  guard let start = graph.vertices.first else {
     return (cost: cost, tree: tree)
   }
 
@@ -38,7 +38,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
     sort: { $0.weight < $1.weight })
 
-  priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+  priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
   while let head = priorityQueue.dequeue() {
     let vertex = head.vertex
     if visited.contains(vertex) {
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
index 0ae996646..a2f243202 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -36,16 +36,17 @@ public struct Graph<T: Hashable>: CustomStringConvertible {
     edgeList.append(Edge(vertex1: v1, vertex2: v2, weight: w))
     vertices.insert(v1)
     vertices.insert(v2)
-    if adjList[v1] == nil {
-      adjList[v1] = [(vertex: v2, weight: w)]
+
+    if let _ = adjList[v1] {
+      adjList[v1]?.append((vertex: v2, weight: w))
     } else {
-      adjList[v1]!.append((vertex: v2, weight: w))
+      adjList[v1] = [(vertex: v2, weight: w)]
     }
 
-    if adjList[v2] == nil {
-      adjList[v2] = [(vertex: v1, weight: w)]
+    if let _ = adjList[v2] {
+      adjList[v2]?.append((vertex: v1, weight: w))
     } else {
-      adjList[v2]!.append((vertex: v1, weight: w))
+      adjList[v2] = [(vertex: v1, weight: w)]
     }
   }
 
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
index 89c26cff0..d975fc430 100644
--- a/Minimum Spanning Tree/Prim.swift	
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -10,7 +10,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var cost: Int = 0
   var tree = Graph<T>()
 
-  if graph.vertices.isEmpty {
+  guard let start = graph.vertices.first else {
     return (cost: cost, tree: tree)
   }
 
@@ -18,7 +18,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
     sort: { $0.weight < $1.weight })
 
-  priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+  priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
   while let head = priorityQueue.dequeue() {
     let vertex = head.vertex
     if visited.contains(vertex) {
@@ -43,3 +43,4 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
 
   return (cost: cost, tree: tree)
 }
+

From ea777fb3bc861e4818c414a97eb72fb8b9e3b644 Mon Sep 17 00:00:00 2001
From: Xiangxin <xiangxinsg@gmail.com>
Date: Sat, 6 May 2017 13:08:41 +0800
Subject: [PATCH 1016/1679] refactor

---
 .../Sources/Graph.swift                            | 14 ++++----------
 1 file changed, 4 insertions(+), 10 deletions(-)

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
index a2f243202..5e74e14cb 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -37,17 +37,11 @@ public struct Graph<T: Hashable>: CustomStringConvertible {
     vertices.insert(v1)
     vertices.insert(v2)
 
-    if let _ = adjList[v1] {
-      adjList[v1]?.append((vertex: v2, weight: w))
-    } else {
-      adjList[v1] = [(vertex: v2, weight: w)]
-    }
+    adjList[v1] = adjList[v1] ?? []
+    adjList[v1]?.append((vertex: v2, weight: w))
 
-    if let _ = adjList[v2] {
-      adjList[v2]?.append((vertex: v1, weight: w))
-    } else {
-      adjList[v2] = [(vertex: v1, weight: w)]
-    }
+    adjList[v2] = adjList[v2] ?? []
+    adjList[v2]?.append((vertex: v1, weight: w))
   }
 
   public mutating func addEdge(_ edge: Edge<T>) {

From 12fac48235b369612be3a96b807e4e4ba2ad237c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 7 May 2017 04:45:19 -0700
Subject: [PATCH 1017/1679] Fixed spacing, and fixes some English.

---
 .../UnionFind.playground/Contents.swift       | 24 ++---
 .../Sources/UnionFindQuickFind.swift          | 80 ++++++++--------
 .../Sources/UnionFindQuickUnion.swift         | 82 ++++++++--------
 .../Sources/UnionFindWeightedQuickFind.swift  | 94 +++++++++----------
 .../Sources/UnionFindWeightedQuickUnion.swift | 92 +++++++++---------
 ...indWeightedQuickUnionPathCompression.swift | 86 ++++++++---------
 6 files changed, 229 insertions(+), 229 deletions(-)

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 9ad5215b3..0a50d1ba6 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -3,17 +3,17 @@
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {
-    dsu.addSetWith(i)
+  dsu.addSetWith(i)
 }
 // now our dsu contains 10 independent sets
 
 // let's divide our numbers into two sets by divisibility by 2
 for i in 3...10 {
-    if i % 2 == 0 {
-        dsu.unionSetsContaining(2, and: i)
-    } else {
-        dsu.unionSetsContaining(1, and: i)
-    }
+  if i % 2 == 0 {
+    dsu.unionSetsContaining(2, and: i)
+  } else {
+    dsu.unionSetsContaining(1, and: i)
+  }
 }
 
 // check our division
@@ -42,12 +42,12 @@ dsuForStrings.addSetWith("b")
 
 // In that example we divide strings by its first letter
 for word in words {
-    dsuForStrings.addSetWith(word)
-    if word.hasPrefix("a") {
-        dsuForStrings.unionSetsContaining("a", and: word)
-    } else if word.hasPrefix("b") {
-        dsuForStrings.unionSetsContaining("b", and: word)
-    }
+  dsuForStrings.addSetWith(word)
+  if word.hasPrefix("a") {
+    dsuForStrings.unionSetsContaining("a", and: word)
+  } else if word.hasPrefix("b") {
+    dsuForStrings.unionSetsContaining("b", and: word)
+  }
 }
 
 print(dsuForStrings.inSameSet("a", and: "all"))
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
index 25d7f5b5d..33e81832d 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
@@ -3,48 +3,48 @@ import Foundation
 /// Quick-find algorithm may take ~MN steps
 /// to process M union commands on N objects
 public struct UnionFindQuickFind<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    return parent[index]
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        return parent[index]
-    }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
-        } else {
-            return nil
-        }
-    }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                for index in 0..<parent.count {
-                    if parent[index] == firstSet {
-                        parent[index] = secondSet
-                    }
-                }
-                size[secondSet] += size[firstSet]
-            }
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        for index in 0..<parent.count {
+          if parent[index] == firstSet {
+            parent[index] = secondSet
+          }
         }
+        size[secondSet] += size[firstSet]
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
index 4c848e61d..9bff31616 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
@@ -3,49 +3,49 @@ import Foundation
 /// Quick-Union algorithm may take ~MN steps
 /// to process M union commands on N objects
 public struct UnionFindQuickUnion<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = setByIndex(parent[index])
+      return parent[index]
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        if parent[index] == index {
-            return index
-        } else {
-            parent[index] = setByIndex(parent[index])
-            return parent[index]
-        }
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
-        } else {
-            return nil
-        }
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        parent[firstSet] = secondSet
+        size[secondSet] += size[firstSet]
+      }
     }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                parent[firstSet] = secondSet
-                size[secondSet] += size[firstSet]
-            }
-        }
-    }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
index 02bec94a8..c89f2a457 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
@@ -3,57 +3,57 @@ import Foundation
 /// Quick-find algorithm may take ~MN steps
 /// to process M union commands on N objects
 public struct UnionFindWeightedQuickFind<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    return parent[index]
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        return parent[index]
-    }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          for index in 0..<parent.count {
+            if parent[index] == firstSet {
+              parent[index] = secondSet
+            }
+          }
+          size[secondSet] += size[firstSet]
         } else {
-            return nil
-        }
-    }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                if size[firstSet] < size[secondSet] {
-                    for index in 0..<parent.count {
-                        if parent[index] == firstSet {
-                            parent[index] = secondSet
-                        }
-                    }
-                    size[secondSet] += size[firstSet]
-                } else {
-                    for index in 0..<parent.count {
-                        if parent[index] == secondSet {
-                            parent[index] = firstSet
-                        }
-                    }
-                    size[firstSet] += size[secondSet]
-                }
+          for index in 0..<parent.count {
+            if parent[index] == secondSet {
+              parent[index] = firstSet
             }
+          }
+          size[firstSet] += size[secondSet]
         }
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
index b3ac7445e..cd33007bc 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
@@ -1,56 +1,56 @@
 import Foundation
 
 public struct UnionFindWeightedQuickUnion<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = setByIndex(parent[index])
+      return parent[index]
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        if parent[index] == index {
-            return index
-        } else {
-            parent[index] = setByIndex(parent[index])
-            return parent[index]
-        }
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
+  }
+  
+  /// Weighted, by comparing set size.
+  /// Merge small set into the large one.
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
+          size[secondSet] += size[firstSet]
         } else {
-            return nil
-        }
-    }
-    
-    /// Weighted, by comparing set size.
-    /// Merge small set into the large one.
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                if size[firstSet] < size[secondSet] {
-                    parent[firstSet] = secondSet
-                    size[secondSet] += size[firstSet]
-                } else {
-                    parent[secondSet] = firstSet
-                    size[firstSet] += size[secondSet]
-                }
-            }
+          parent[secondSet] = firstSet
+          size[firstSet] += size[secondSet]
         }
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
index 892f46a3c..7eb8fe209 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
@@ -1,53 +1,53 @@
 import Foundation
 
 public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  /// Path Compression.
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if index != parent[index] {
+      parent[index] = setByIndex(parent[index])
     }
-    
-    /// Path Compression.
-    private mutating func setByIndex(_ index: Int) -> Int {
-        if index != parent[index] {
-            parent[index] = setByIndex(parent[index])
-        }
-        return parent[index]
+    return parent[index]
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
+          size[secondSet] += size[firstSet]
         } else {
-            return nil
-        }
-    }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                if size[firstSet] < size[secondSet] {
-                    parent[firstSet] = secondSet
-                    size[secondSet] += size[firstSet]
-                } else {
-                    parent[secondSet] = firstSet
-                    size[firstSet] += size[secondSet]
-                }
-            }
+          parent[secondSet] = firstSet
+          size[firstSet] += size[secondSet]
         }
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }

From e560f60fc35889fefba95389ea53c6d02a9e22e9 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 8 May 2017 01:09:02 +0500
Subject: [PATCH 1018/1679] Fix a few typos in DiningPhilosophers Readme

an -> a
dinining -> dining
"no needs" -> "no need"
---
 DiningPhilosophers/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 0bf4f28ce..bc622e559 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -22,12 +22,12 @@ Eating is not limited by the remaining amounts of spaghetti or stomach space; an
 
 The problem is how to design a discipline of behavior (a concurrent algorithm) such that no philosopher will starve; i.e., each can forever continue to alternate between eating and thinking, assuming that no philosopher can know when others may want to eat or think.
 
-This is an illustration of an dinining table:
+This is an illustration of a dining table:
 
 ![Dining Philosophers table](https://upload.wikimedia.org/wikipedia/commons/7/7b/An_illustration_of_the_dining_philosophers_problem.png)
 
 # Solution
-There are different solutions for this classic algorithm, and this Swift implementation is based on the Chandy/Misra solution. This implementation allows agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
+There are different solutions for this classic algorithm, and this Swift implementation is based on the Chandy/Misra solution. This implementation allows agents to contend for an arbitrary number of resources in a completely distributed scenario with no need for a central authority to control the locking and serialization of resources. 
 
 However, this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
 

From 297b0d4679fbd8607edb5b59b87d273962354e84 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 8 May 2017 01:26:16 +0500
Subject: [PATCH 1019/1679] Fix minor grammar typo

---
 Graph/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index bc33b044a..d3c8b89e5 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -143,7 +143,7 @@ Here is an example of a simple graph:
 
 ![Demo](Images/Demo1.png)
 
-We can represent it as an adjacency matrix or adjacency list. The classes implementing those concept both inherit a common API from `AbstractGraph`, so they can be created in an identical fashion, with different optimized data structures behind the scenes.
+We can represent it as an adjacency matrix or adjacency list. The classes implementing those concepts both inherit a common API from `AbstractGraph`, so they can be created in an identical fashion, with different optimized data structures behind the scenes.
 
 Let's create some directed, weighted graphs, using each representation, to store the example:
 

From 24d5adeba873dc184e2fc28dcaf942b15c60b95e Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 8 May 2017 01:32:34 +0500
Subject: [PATCH 1020/1679] Fix broken links by replacing spaces with %20

---
 Heap/README.markdown | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 7beea4f34..a3b0038ab 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,11 +1,11 @@
 # Heap
 
-A heap is a [binary tree](../Binary Tree/) inside an array, so it does not use parent/child pointers. A heap is sorted based on the "heap property" that determines the order of the nodes in the tree.
+A heap is a [binary tree](../Binary%20Tree/) inside an array, so it does not use parent/child pointers. A heap is sorted based on the "heap property" that determines the order of the nodes in the tree.
 
 Common uses for heap:
 
-- To build [priority queues](../Priority Queue/).
-- To support [heap sorts](../Heap Sort/).
+- To build [priority queues](../Priority%20Queue/).
+- To support [heap sorts](../Heap%20Sort/).
 - To compute the minimum (or maximum) element of a collection quickly.
 - To impress your non-programmer friends.
 
@@ -21,7 +21,7 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority Queue/)to access the "most important" element quickly.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority%20Queue/)to access the "most important" element quickly.
 
 > **Note:** The root of the heap has the maximum or minimum element, but the sort order of other elements are not predictable. For example, the maximum element is always at index 0 in a max-heap, but the minimum element isn’t necessarily the last one. -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
@@ -30,11 +30,11 @@ As a result of this heap property, a max-heap always stores its largest item at
 A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
 
 
-**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must be smaller than its parent, and the right child must be greater. This is not true for a heap. In a max-heap both children must be smaller than the parent, while in a min-heap they both must be greater.
+**Order of the nodes.** In a [binary search tree (BST)](../Binary%20Search%20Tree/), the left child must be smaller than its parent, and the right child must be greater. This is not true for a heap. In a max-heap both children must be smaller than the parent, while in a min-heap they both must be greater.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL Tree/) or [red-black tree](../Red-Black Tree/), but with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
+**Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL%20Tree/) or [red-black tree](../Red-Black%20Tree/), but with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
 **Searching.** Whereas searching is fast in a binary tree, it is slow in a heap. Searching isn't a top priority in a heap since the purpose of a heap is to put the largest (or smallest) node at the front and to allow relatively fast inserts and deletes. 
 
@@ -112,7 +112,7 @@ Is this a valid heap? The answer is yes! A sorted array from low-to-high is a va
 
 The heap property holds for each node because a parent is always smaller than its children. (Verify for yourself that an array sorted from high-to-low is always a valid max-heap.)
 
-> **Note:** But not every min-heap is necessarily a sorted array! It only works one way. To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
+> **Note:** But not every min-heap is necessarily a sorted array! It only works one way. To turn a heap back into a sorted array, you need to use [heap sort](../Heap%20Sort/).
 
 ## More math!
 
@@ -162,7 +162,7 @@ All of the above take time **O(log n)** because shifting up or down is expensive
 
 - `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you are smart about this, it can be done in **O(n)** time.
 
-- [Heap sort](../Heap Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
+- [Heap sort](../Heap%20Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
 
 The heap also has a `peek()` function that returns the maximum (max-heap) or minimum (min-heap) element, without removing it from the heap. Time: **O(1)**.
 
@@ -289,7 +289,7 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 Heaps are not made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element. Searching is one way to do this, but it is slow.
 
-In a [binary search tree](../Binary Search Tree/), depending on the order of the nodes, a fast search can be guaranteed. Since a heap orders its nodes differently, a binary search will not work, and you need to check every node in the tree.
+In a [binary search tree](../Binary%20Search%20Tree/), depending on the order of the nodes, a fast search can be guaranteed. Since a heap orders its nodes differently, a binary search will not work, and you need to check every node in the tree.
 
 Let's take our example heap again:
 

From 1eb61c97a7949a0088834759bd9b1f40d884a9e9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 8 May 2017 05:16:23 -0700
Subject: [PATCH 1021/1679] Improves the wording for a few sentences.

---
 Union-Find/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index dfec7dbe6..a268f1d70 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -9,7 +9,7 @@ What do we mean by this? For example, the Union-Find data structure could be kee
 	[ g, d, c ]
 	[ i, j ]
 
-These sets are disjoint because they have no members in common.
+These sets are **disjoint** because they have no members in common.
 
 Union-Find supports three basic operations:
 
@@ -24,7 +24,7 @@ The most common application of this data structure is keeping track of the conne
 ## Implementation
 
 Union-Find can be implemented in many ways but we'll look at an efficient and easy to understand implementation: Weighted Quick Union.
-> __PS: Variety implementation of Union-Find has been included in playground.__
+> __PS: Multiple implementations of Union-Find has been included in playground.__
 
 ```swift
 public struct UnionFind<T: Hashable> {
@@ -198,7 +198,7 @@ private mutating func setByIndex(_ index: Int) -> Int {
 ```
 Path Compression helps keep trees very flat, thus find operation could take __ALMOST__ in __O(1)__
 
-## Complexity Summary of Variety Implementation
+## Complexity Summary
 
 ##### To process N objects
 | Data Structure | Union | Find |

From a087b19f146e32ac731fac5c4c989b1eff3c7401 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 8 May 2017 05:17:49 -0700
Subject: [PATCH 1022/1679] Fixes spelling.

---
 DiningPhilosophers/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 0bf4f28ce..e4db0d7e0 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -10,7 +10,7 @@ In computer science, the dining philosophers problem is often used in the concur
 
 It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.
 
-This Swift implementation is based on the Chandy/Misra solution, and it uses the GCD Dispatch and Semaphone on the Swift cross platform.
+This Swift implementation is based on the Chandy/Misra solution, and it uses the GCD Dispatch and Semaphores on the Swift cross platform.
 
 # Problem statement
 

From 988e354fed9122acb0b7b7ec8098b0a29c374070 Mon Sep 17 00:00:00 2001
From: Mike <perryao@users.noreply.github.com>
Date: Mon, 8 May 2017 18:54:43 -0400
Subject: [PATCH 1023/1679] Formatted headers in readme

Github seems to require spaces between "#" and headings .
---
 Radix Sort/ReadMe.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Radix Sort/ReadMe.md b/Radix Sort/ReadMe.md
index 5bdb931ca..ceb4459d7 100644
--- a/Radix Sort/ReadMe.md	
+++ b/Radix Sort/ReadMe.md	
@@ -2,19 +2,19 @@
 
 Radix sort is a sorting algorithm that takes as input an array of integers and uses a sorting subroutine( that is often another efficient sorting algorith) to sort the integers by their radix, or rather their digit.  Counting Sort, and Bucket Sort are often times used as the subroutine for Radix Sort.
 
-##Example
+## Example
 
 * Input Array: [170, 45, 75, 90, 802, 24, 2, 66]
 * Output Array (Sorted):  [2, 24, 45, 66, 75, 90, 170, 802]
 
-###Step 1:
+### Step 1:
 The first step in this algorithm is to define the digit or rather the "base" or radix that we will use to sort.
 For this example we will let radix = 10, since the integers we are working with in the example are of base 10.
 
-###Step 2:
+### Step 2:
 The next step is to simply iterate n times (where n is the number of digits in the largest integer in the input array), and upon each iteration perform a sorting subroutine on the current digit in question.
 
-###Algorithm in Action
+### Algorithm in Action
 
 Let's take a look at our example input array.
 

From 90730ade45d11947529e51acf15e09f1ef622596 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 16 May 2017 09:56:13 -0700
Subject: [PATCH 1024/1679] Fixes #464.

---
 Threaded Binary Tree/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 8a1c518f1..f631b86f9 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -267,9 +267,9 @@ something simple, like removing **7**, which has no children:
 Before we can just throw **7** away, we have to perform some clean-up.  In this
 case, because **7** is a `right` child and has no children itself, we can
 simply set the `rightThread` of **7**'s `parent`(**5**) to **7**'s (now
-outdated) `rightThread`.  Then we can just set **7**'s `parent`, `left`,
+outdated) `rightThread`. Then we can just set **7**'s `parent`, `left`,
 `right`, `leftThread`, and `rightThread` to `nil`, effectively removing it from
-the tree.
+the tree. We also set the parent's `rightChild` to `nil`, which completes the deletion of this right child. 
 
 Let's try something a little harder.  Say we remove **5** from the tree:
 

From cde6f854865d19c4cefb187894a4da09a0be4fee Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Wed, 17 May 2017 05:16:52 +0500
Subject: [PATCH 1025/1679] Fix a few typos in Heap/README

---
 Heap/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index a3b0038ab..bb7a785a5 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -21,7 +21,7 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority%20Queue/)to access the "most important" element quickly.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority%20Queue/) to access the "most important" element quickly.
 
 > **Note:** The root of the heap has the maximum or minimum element, but the sort order of other elements are not predictable. For example, the maximum element is always at index 0 in a max-heap, but the minimum element isn’t necessarily the last one. -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
@@ -124,7 +124,7 @@ This heap has height 3, so it has 4 levels:
 
 ![Large heap](Images/LargeHeap.png)
 
-A heap with *n* nodes has height *h = floor(log_2(n))*. This is because we always fill up the lowest level completely before we add a new level. The example has 15 nodes, so the height is `floor(log_2(15)) = floor(3.91) = 3`.
+A heap with *n* nodes has height *h = floor(log2(n))*. This is because we always fill up the lowest level completely before we add a new level. The example has 15 nodes, so the height is `floor(log2(15)) = floor(3.91) = 3`.
 
 If the lowest level is completely full, then that level contains *2^h* nodes. The rest of the tree above it contains *2^h - 1* nodes. Fill in the numbers from the example: the lowest level has 8 nodes, which indeed is `2^3 = 8`. The first three levels contain a total of 7 nodes, i.e. `2^3 - 1 = 8 - 1 = 7`.
 
@@ -303,7 +303,7 @@ Let's say we want to see if the heap contains the value `8` (it doesn't). We sta
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
-> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority%20Queue/) that's built on a heap.
+> **Note:** There is a way to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority%20Queue/) that's built on a heap.
 
 ## The code
 

From c014bd9a0823d6206fa18e915f6e4f01d5852beb Mon Sep 17 00:00:00 2001
From: Artur <gitkid@icloud.com>
Date: Wed, 17 May 2017 03:19:47 +0300
Subject: [PATCH 1026/1679] remove "countingSort" func throws

if you received empty array, just return empty array
---
 Counting Sort/CountingSort.swift | 10 ++--------
 1 file changed, 2 insertions(+), 8 deletions(-)

diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index abece0213..725a634a4 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -6,14 +6,8 @@
 //  Copyright © 2016 Ali Hafizji. All rights reserved.
 //
 
-enum CountingSortError: Error {
-  case arrayEmpty
-}
-
-func countingSort(_ array: [Int]) throws -> [Int] {
-  guard array.count > 0 else {
-    throw CountingSortError.arrayEmpty
-  }
+func countingSort(_ array: [Int])-> [Int] {
+  guard array.count > 0 else {return []}
 
   // Step 1
   // Create an array to store the count of each element

From d705414bbcf2eb62232d5c456befc193e397b208 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Wed, 17 May 2017 05:20:54 +0500
Subject: [PATCH 1027/1679] Update displayed code to use 2 space indentation

---
 Heap Sort/README.markdown | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index 7fdd8d2ca..a45dad6f9 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -48,13 +48,13 @@ Here's how you can implement heap sort in Swift:
 
 ```swift
 extension Heap {
-    public mutating func sort() -> [T] {
-        for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-            swap(&elements[0], &elements[i])
-            shiftDown(0, heapSize: i)
-        }
-    return elements
+  public mutating func sort() -> [T] {
+    for i in stride(from: (elements.count - 1), through: 1, by: -1) {
+      swap(&elements[0], &elements[i])
+      shiftDown(0, heapSize: i)
     }
+    return elements
+  }
 }
 ```
 
@@ -71,9 +71,9 @@ We can write a handy helper function for that:
 
 ```swift
 public func heapsort<T>(_ a: [T], _ sort: @escaping (T, T) -> Bool) -> [T] {
-    let reverseOrder = { i1, i2 in sort(i2, i1) }
-    var h = Heap(array: a, sort: reverseOrder)
-    return h.sort()
+  let reverseOrder = { i1, i2 in sort(i2, i1) }
+  var h = Heap(array: a, sort: reverseOrder)
+  return h.sort()
 }
 ```
 

From e311ee9b88a16d9dfaeacc7f2e7ea7825169fe8b Mon Sep 17 00:00:00 2001
From: Tobias Helmrich <helmrich@users.noreply.github.com>
Date: Thu, 18 May 2017 21:52:38 +0900
Subject: [PATCH 1028/1679] Fix typos and markdown formatting

---
 Linear Regression/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 1a1a1eb8b..29ac2e321 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -75,7 +75,7 @@ for n in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimse the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proprotional to `((slope.carAge + intercept) - carPrice)) ^ 2`.
+We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope.carAge + intercept) - carPrice)) ^ 2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 
@@ -98,7 +98,7 @@ Here is the same data shown as a graph. Each of the blue lines on the graph repr
 
 After 18,000 iterations it looks as if the line is getting closer to what we would expect (just by looking) to be the correct line of best fit. Also, each additional 2,000 iterations has less and less effect on the final result - the values of the intercept and the slope are converging on the correct values.
 
-##A closed form solution
+## A closed form solution
 
 There is another way we can calculate the line of best fit, without having to do multiple iterations. We can solve the equations describing the least squares minimisation and just work out the intercept and slope directly. 
 
@@ -139,7 +139,7 @@ This function takes as arguments two arrays of Doubles, and returns a function w
 Using this line, we would predict a price for our 4 year old car of £6952.
 
 
-##Summary
+## Summary
 We've seen two different ways to implement a simple linear regression in Swift. An obvious question is: why bother with the iterative approach at all? 
 
 Well, the line we've found doesn't fit the data perfectly. For one thing, the graph includes some negative values at high car ages! Possibly we would have to pay someone to tow away a very old car... but really these negative values just show that we have not modelled the real life situation very accurately. The relationship between the car age and the car price is not linear but instead is some other function. We also know that a car's price is not just related to its age but also other factors such as the make, model and engine size of the car. We would need to use additional variables to describe these other factors. 

From d2f02efd49d2367382c7a6fffc5fa1e3b74c8eff Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Sun, 21 May 2017 21:46:01 +0200
Subject: [PATCH 1029/1679] Initial Docs template and text

---
 Splay Tree/readme.md | 61 +++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 60 insertions(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 2282502fa..aa6bdd4db 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -1 +1,60 @@
-In progress
+# Splay Tree
+Splay tree is a data structure, structurally identitical to a Balanced Binary Search Tree. Every operation performed on a Splay Tree causes a readjustment in order to provide fast access to recently operated values. On every access, the tree is rearranged and the node accessed is moved to the root of the tree using a set of specific rotations, which together are referred to as **Splaying**.
+
+
+## Rotations
+
+### Zig-Zig
+
+Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* and *b* are left children or right children, a **Zig-Zig** is performed.
+
+### Zig-Zag
+
+Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
+
+### Zig
+
+A **Zig** is performed when the node *a* to be rotated has the root as parent.
+
+## Splaying
+
+## Operations
+
+### Insertion 
+
+### Deletion 
+
+### Search 
+
+## Examples 
+
+### Example 1
+
+### Example 2
+
+### Example 3
+
+## Advantages 
+
+Splay trees provide an efficient way to quickly access elements that are frequently requested. This characteristic makes then a good choice to implement, for exmaple, caches or garbage collection algorithms, or in any other problem involving frequent access to a certain numbers of elements from a data set.
+
+## Disadvantages
+
+Splay tree are not perfectly balanced always, so in case of accessing all the elements in the tree in an increasing order, the height of the tree becomes *n*.
+
+## Time complexity
+
+| Case        |    Performance        |
+| ------------- |:-------------:|
+| Average      | O(log n) |
+| Worst      | n |
+
+With *n* being the number of items in the tree.
+
+
+## See also
+
+[Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
+[Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
+
+*Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*

From 7f751918b92881d93aabce634a891b95f46a90f0 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 21 May 2017 22:03:23 +0200
Subject: [PATCH 1030/1679] images for documentation

---
 Splay Tree/Images /zig.png     | Bin 0 -> 7793 bytes
 Splay Tree/Images /zigzag1.png | Bin 0 -> 13964 bytes
 Splay Tree/Images /zigzag2.png | Bin 0 -> 13877 bytes
 Splay Tree/Images /zigzig1.png | Bin 0 -> 13855 bytes
 Splay Tree/Images /zigzig2.png | Bin 0 -> 15179 bytes
 5 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Splay Tree/Images /zig.png
 create mode 100644 Splay Tree/Images /zigzag1.png
 create mode 100644 Splay Tree/Images /zigzag2.png
 create mode 100644 Splay Tree/Images /zigzig1.png
 create mode 100644 Splay Tree/Images /zigzig2.png

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From 6c1c12651247ed73e3e727c0e7dc28e2a0b1e518 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 21 May 2017 22:17:44 +0200
Subject: [PATCH 1031/1679] Images for examples documentation

---
 Splay Tree/Images /example1-1.png     | Bin 0 -> 13964 bytes
 Splay Tree/Images /example1-2.png     | Bin 0 -> 15451 bytes
 Splay Tree/Images /example1-3.png     | Bin 0 -> 14778 bytes
 Splay Tree/Images /examplezig.svg     |   2 ++
 Splay Tree/Images /examplezig1.png    | Bin 0 -> 6583 bytes
 Splay Tree/Images /examplezig2.png    | Bin 0 -> 9317 bytes
 Splay Tree/Images /examplezigzig.svg  |   2 ++
 Splay Tree/Images /examplezigzig1.png | Bin 0 -> 13855 bytes
 Splay Tree/Images /examplezigzig2.png | Bin 0 -> 15247 bytes
 Splay Tree/Images /examplezigzig3.png | Bin 0 -> 18128 bytes
 10 files changed, 4 insertions(+)
 create mode 100644 Splay Tree/Images /example1-1.png
 create mode 100644 Splay Tree/Images /example1-2.png
 create mode 100644 Splay Tree/Images /example1-3.png
 create mode 100644 Splay Tree/Images /examplezig.svg
 create mode 100644 Splay Tree/Images /examplezig1.png
 create mode 100644 Splay Tree/Images /examplezig2.png
 create mode 100644 Splay Tree/Images /examplezigzig.svg
 create mode 100644 Splay Tree/Images /examplezigzig1.png
 create mode 100644 Splay Tree/Images /examplezigzig2.png
 create mode 100644 Splay Tree/Images /examplezigzig3.png

diff --git a/Splay Tree/Images /example1-1.png b/Splay Tree/Images /example1-1.png
new file mode 100644
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diff --git a/Splay Tree/Images /example1-2.png b/Splay Tree/Images /example1-2.png
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diff --git a/Splay Tree/Images /example1-3.png b/Splay Tree/Images /example1-3.png
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diff --git a/Splay Tree/Images /examplezigzig.svg b/Splay Tree/Images /examplezigzig.svg
new file mode 100644
index 000000000..7bd4dcf6f
--- /dev/null
+++ b/Splay Tree/Images /examplezigzig.svg	
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From 47a412279d3e05ae4edfacc8220f5d6050540783 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 21 May 2017 22:20:42 +0200
Subject: [PATCH 1032/1679] delete blank images space

---
 Splay Tree/{Images  => Images}/example1-1.png     | Bin
 Splay Tree/{Images  => Images}/example1-2.png     | Bin
 Splay Tree/{Images  => Images}/example1-3.png     | Bin
 Splay Tree/{Images  => Images}/examplezig.svg     |   0
 Splay Tree/{Images  => Images}/examplezig1.png    | Bin
 Splay Tree/{Images  => Images}/examplezig2.png    | Bin
 Splay Tree/{Images  => Images}/examplezigzig.svg  |   0
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 Splay Tree/{Images  => Images}/zig.png            | Bin
 Splay Tree/{Images  => Images}/zigzag1.png        | Bin
 Splay Tree/{Images  => Images}/zigzag2.png        | Bin
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 15 files changed, 0 insertions(+), 0 deletions(-)
 rename Splay Tree/{Images  => Images}/example1-1.png (100%)
 rename Splay Tree/{Images  => Images}/example1-2.png (100%)
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 rename Splay Tree/{Images  => Images}/examplezig.svg (100%)
 rename Splay Tree/{Images  => Images}/examplezig1.png (100%)
 rename Splay Tree/{Images  => Images}/examplezig2.png (100%)
 rename Splay Tree/{Images  => Images}/examplezigzig.svg (100%)
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 rename Splay Tree/{Images  => Images}/examplezigzig3.png (100%)
 rename Splay Tree/{Images  => Images}/zig.png (100%)
 rename Splay Tree/{Images  => Images}/zigzag1.png (100%)
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diff --git a/Splay Tree/Images /example1-1.png b/Splay Tree/Images/example1-1.png
similarity index 100%
rename from Splay Tree/Images /example1-1.png
rename to Splay Tree/Images/example1-1.png
diff --git a/Splay Tree/Images /example1-2.png b/Splay Tree/Images/example1-2.png
similarity index 100%
rename from Splay Tree/Images /example1-2.png
rename to Splay Tree/Images/example1-2.png
diff --git a/Splay Tree/Images /example1-3.png b/Splay Tree/Images/example1-3.png
similarity index 100%
rename from Splay Tree/Images /example1-3.png
rename to Splay Tree/Images/example1-3.png
diff --git a/Splay Tree/Images /examplezig.svg b/Splay Tree/Images/examplezig.svg
similarity index 100%
rename from Splay Tree/Images /examplezig.svg
rename to Splay Tree/Images/examplezig.svg
diff --git a/Splay Tree/Images /examplezig1.png b/Splay Tree/Images/examplezig1.png
similarity index 100%
rename from Splay Tree/Images /examplezig1.png
rename to Splay Tree/Images/examplezig1.png
diff --git a/Splay Tree/Images /examplezig2.png b/Splay Tree/Images/examplezig2.png
similarity index 100%
rename from Splay Tree/Images /examplezig2.png
rename to Splay Tree/Images/examplezig2.png
diff --git a/Splay Tree/Images /examplezigzig.svg b/Splay Tree/Images/examplezigzig.svg
similarity index 100%
rename from Splay Tree/Images /examplezigzig.svg
rename to Splay Tree/Images/examplezigzig.svg
diff --git a/Splay Tree/Images /examplezigzig1.png b/Splay Tree/Images/examplezigzig1.png
similarity index 100%
rename from Splay Tree/Images /examplezigzig1.png
rename to Splay Tree/Images/examplezigzig1.png
diff --git a/Splay Tree/Images /examplezigzig2.png b/Splay Tree/Images/examplezigzig2.png
similarity index 100%
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rename to Splay Tree/Images/examplezigzig2.png
diff --git a/Splay Tree/Images /examplezigzig3.png b/Splay Tree/Images/examplezigzig3.png
similarity index 100%
rename from Splay Tree/Images /examplezigzig3.png
rename to Splay Tree/Images/examplezigzig3.png
diff --git a/Splay Tree/Images /zig.png b/Splay Tree/Images/zig.png
similarity index 100%
rename from Splay Tree/Images /zig.png
rename to Splay Tree/Images/zig.png
diff --git a/Splay Tree/Images /zigzag1.png b/Splay Tree/Images/zigzag1.png
similarity index 100%
rename from Splay Tree/Images /zigzag1.png
rename to Splay Tree/Images/zigzag1.png
diff --git a/Splay Tree/Images /zigzag2.png b/Splay Tree/Images/zigzag2.png
similarity index 100%
rename from Splay Tree/Images /zigzag2.png
rename to Splay Tree/Images/zigzag2.png
diff --git a/Splay Tree/Images /zigzig1.png b/Splay Tree/Images/zigzig1.png
similarity index 100%
rename from Splay Tree/Images /zigzig1.png
rename to Splay Tree/Images/zigzig1.png
diff --git a/Splay Tree/Images /zigzig2.png b/Splay Tree/Images/zigzig2.png
similarity index 100%
rename from Splay Tree/Images /zigzig2.png
rename to Splay Tree/Images/zigzig2.png

From 5d15f553817310785fc0d5539c01508c86892250 Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Sun, 21 May 2017 22:27:24 +0200
Subject: [PATCH 1033/1679] Adding images for examples and rotation cases

---
 Splay Tree/readme.md | 26 ++++++++++++++++++++++++--
 1 file changed, 24 insertions(+), 2 deletions(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index aa6bdd4db..89444b2cc 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -8,14 +8,25 @@ Splay tree is a data structure, structurally identitical to a Balanced Binary Se
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* and *b* are left children or right children, a **Zig-Zig** is performed.
 
+![ZigZigCase1](Images/zigzig1.png)
+
+![ZigZigCase2](Images/zigzig2.png)
+
 ### Zig-Zag
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
 
+![ZigZagCase1](Images/zigzag1.png)
+
+![ZigZagCase2](Images/zigzag2.png)
+
 ### Zig
 
 A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
+![ZigCase](Images/zig.png)
+
+
 ## Splaying
 
 ## Operations
@@ -30,9 +41,20 @@ A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
 ### Example 1
 
+![ZigEx1](Images/examplezigzig1.png)
+
+![ZigEx2](Images/examplezigzig2.png)
+
+![ZigEx3](Images/examplezigzig3.png)
+
+
 ### Example 2
 
-### Example 3
+![ZigEx21](Images/example1-1.png)
+
+![ZigEx22](Images/example1-2.png)
+
+![ZigEx23](Images/example1-3.png)
 
 ## Advantages 
 
@@ -57,4 +79,4 @@ With *n* being the number of items in the tree.
 [Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
 [Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
 
-*Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*
+*Written for Swift Algorithm Club by Barbara Martina Rodeker*

From c4268801a9340b1776c6b4e0c452fe8a6388031b Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Tue, 23 May 2017 22:08:14 +0200
Subject: [PATCH 1034/1679] Update readme.md

---
 Splay Tree/readme.md | 64 +++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 63 insertions(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 89444b2cc..29f9dede5 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -4,22 +4,36 @@ Splay tree is a data structure, structurally identitical to a Balanced Binary Se
 
 ## Rotations
 
+There are 3 types of rotations that can form an **Splaying**:
+
+- ZigZig
+- ZigZag
+- Zig
+
 ### Zig-Zig
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* and *b* are left children or right children, a **Zig-Zig** is performed.
 
+### Case both nodes right children
 ![ZigZigCase1](Images/zigzig1.png)
 
+### Case both nodes left children
 ![ZigZigCase2](Images/zigzig2.png)
 
+**IMPORTANT** is to note that a *ZigZig* performs first the rotation of the middle node with its parent (call it the grandparent) and later the rotation of the remaining node (grandchild). Doing that helps to keep the trees balanced even if it was first created by inserted a sequence of increasing values (see below worst case scenario).
+
 ### Zig-Zag
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
 
+### Case right - left
 ![ZigZagCase1](Images/zigzag1.png)
 
+### Case left - right
 ![ZigZagCase2](Images/zigzag2.png)
 
+**IMPORTANT** A *ZigZag* performs first the rotation of the grandchild node and later the same node with its new parent again. 
+
 ### Zig
 
 A **Zig** is performed when the node *a* to be rotated has the root as parent.
@@ -29,7 +43,53 @@ A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
 ## Splaying
 
-## Operations
+A splaying consists in making so many rotations as needed until the node affected by the operation is at the top and becomes the root of the tree.
+
+```
+while (node.parent != nil) {
+            operation(forNode: node).apply(onNode: node)
+}
+```
+
+Where operation returns the required rotation to be applied. 
+
+```
+    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
+        
+        if let parent = node.parent, let _ = parent.parent {
+            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
+                return .zigZag
+            }
+            return .zigZig
+        }
+        return .zig
+    }
+```
+
+During the applying phase, the algorithms determines which nodes are involved depending on the rotation to be applied and proceeding to re-arrange the node with its parent.
+
+```
+    public func apply<T: Comparable>(onNode node: Node<T>) {
+        switch self {
+        case .zigZag:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node, parent: node.parent!)
+            rotate(child: node, parent: node.parent!)
+
+        case .zigZig:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node.parent!, parent: node.parent!.parent!)
+            rotate(child: node, parent: node.parent!)
+        
+        case .zig:
+            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+            rotate(child: node, parent: node.parent!)
+        }
+    }
+```
+
+
+## Operations on an Splay Tree
 
 ### Insertion 
 
@@ -73,6 +133,8 @@ Splay tree are not perfectly balanced always, so in case of accessing all the el
 
 With *n* being the number of items in the tree.
 
+# An example of the Worst Case Performance 
+
 
 ## See also
 

From 0a813ba0f16865323529e7de03ff9cb69eea378d Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 16:05:34 +0300
Subject: [PATCH 1035/1679] Code improvements

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index f4cd8503a..9c5961c71 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -13,11 +13,12 @@ public class Dijkstra {
 
     public func findShortestPaths(from startVertex: Vertex) {
         clearCache()
+        var currentVertices = self.totalVertices
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
         var currentVertex: Vertex? = startVertex
         while let vertex = currentVertex {
-            totalVertices.remove(vertex)
+            currentVertices.remove(vertex)
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
             for neighbor in filteredNeighbors {
                 let neighborVertex = neighbor.0

From 35db21bb212b56ab13a1ecf67b251727ca3718a9 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 17:54:49 +0300
Subject: [PATCH 1036/1679] Updated description

---
 Dijkstra Algorithm/Images/DirectedGraph.png   | Bin 0 -> 68702 bytes
 Dijkstra Algorithm/Images/Vertices.png        | Bin 0 -> 35896 bytes
 .../Images/WeightedDirectedGraph.png          | Bin 0 -> 70820 bytes
 .../Images/WeightedDirectedGraphFinal.png     | Bin 0 -> 76503 bytes
 .../Images/WeightedUndirectedGraph.png        | Bin 0 -> 78079 bytes
 Dijkstra Algorithm/README.md                  |  56 +++++++++++++-----
 6 files changed, 42 insertions(+), 14 deletions(-)
 create mode 100644 Dijkstra Algorithm/Images/DirectedGraph.png
 create mode 100644 Dijkstra Algorithm/Images/Vertices.png
 create mode 100644 Dijkstra Algorithm/Images/WeightedDirectedGraph.png
 create mode 100644 Dijkstra Algorithm/Images/WeightedDirectedGraphFinal.png
 create mode 100644 Dijkstra Algorithm/Images/WeightedUndirectedGraph.png

diff --git a/Dijkstra Algorithm/Images/DirectedGraph.png b/Dijkstra Algorithm/Images/DirectedGraph.png
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diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index db1726b1f..ddce51525 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,13 +1,50 @@
+#Weighted graph general cocepts
+
+Every weighted graph should contain: 
+1. Vertices/Nodes (I will use "vertex" in this readme).
+
+<img src="Images/Vertices.png" height="250" />
+
+2. Edges connecting vertices. Let's add some edges to our graph. For simplicity let's create directed graph for now. Directed means, that edge have a direction, i.e. vertex, where it starts and vertex, where it ends. But remember VERY IMPORTANT thing:
+    * All undirected graphs can be viewed as a directed graph.
+    * A directed graph is undirected if and only if every edge is paired with an edge going in the opposite direction.
+
+<img src="Images/DirectedGraph.png" height="250" />
+
+3. Weights for every edge. 
+
+<img src="Images/WeightedDirectedGraph.png" height="250" />
+
+Final result. 
+Directed weighted graph:
+
+<img src="Images/WeightedDirectedGraphFinal.png" height="250" />
+
+Undirected weighted graph:
+
+<img src="Images/WeightedUndirectedGraph.png" height="250" />
+
+And once again: An undireceted graph - it is a directed graph with every edge paired with an edge going in the opposite direction. This statement is clear on the image above.
+
+Great! Now we are familiar with general concepts about graphs.
+
 # Dijkstra's algorithm
+This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra.
 
-This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra. 
+It can be used, when you have one source vertex and want to find the shortest paths to ALL other vertices in the graph.
 
-It can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
+The best example is road network. If you wnat to find the shortest path from your house to your job, or if you want to find the closest store to your house, then it is time for the Dijkstra's algorithm.
 
-The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
+The algorithm repeats following cycle until all vertices are marked as visited.
+Cycle:
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+2. The algorithm marks picked vertex as visited.
+3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
-I have created **VisualizedDijkstra.playground** to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
+I have created **VisualizedDijkstra.playground** game/tutorial to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
+#Example 
 Let's imagine, you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have graph, that connects your house with all these stores. So, you know what to do :)
 
 ## Initialization
@@ -38,17 +75,8 @@ To initialize our graph we have to set source vertex path length from source ver
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
-
-But before we will go through all process side by side read this explanation.
-The algorithm repeats following cycle until all vertices are marked as visited.
-Cycle:
-1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
-2. The algorithm marks picked vertex as visited.
-3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
-When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm, let's start!
 
-Okay, let's start!
 Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
 All our vertices are not visited, but there is only one has the smallest path length from start - A. This vertex is the first one, which neighbors we will check.
 First of all, set this vertex as visited 

From e9017365a47a93a977dc0f26c42045d6fccd4b76 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 18:01:53 +0300
Subject: [PATCH 1037/1679] Fix

---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index ddce51525..5cf312acc 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,4 +1,4 @@
-#Weighted graph general cocepts
+# Weighted graph general cocepts
 
 Every weighted graph should contain: 
 1. Vertices/Nodes (I will use "vertex" in this readme).

From b1a50b492373dba7490e603975f9bec8e98c4725 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 18:04:09 +0300
Subject: [PATCH 1038/1679] fix

---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 5cf312acc..a9a898d80 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -44,7 +44,7 @@ When all vertices are marked as visited, the algorithm's job is done. Now, you c
 
 I have created **VisualizedDijkstra.playground** game/tutorial to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
-#Example 
+# Example 
 Let's imagine, you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have graph, that connects your house with all these stores. So, you know what to do :)
 
 ## Initialization

From bb8b2a7d480b6e9f3d5eeee87eaf4a7e01e2ba36 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 18:07:47 +0300
Subject: [PATCH 1039/1679] Fixes

---
 Dijkstra Algorithm/README.md | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index a9a898d80..7afc34094 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -44,10 +44,10 @@ When all vertices are marked as visited, the algorithm's job is done. Now, you c
 
 I have created **VisualizedDijkstra.playground** game/tutorial to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
-# Example 
+## Example 
 Let's imagine, you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have graph, that connects your house with all these stores. So, you know what to do :)
 
-## Initialization
+### Initialization
 
 When the algorithm starts to work initial graph looks like this:
 
@@ -93,7 +93,7 @@ After this step graph has this state:
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-## Step 1
+### Step 1
 
 Then we check all of its neighbors. 
 If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
@@ -118,7 +118,7 @@ And its state is here:
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-## Step 2
+### Step 2
 
 From now we repeat all actions again and fill our table with new info! 
 
@@ -130,7 +130,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-## Step 3
+### Step 3
 
 <img src="Images/image5.png" height="250" />
 
@@ -140,7 +140,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-## Step 4
+### Step 4
 
 <img src="Images/image6.png" height="250" />
 
@@ -150,7 +150,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-## Step 5
+### Step 5
 
 <img src="Images/image7.png" height="250" />
 
@@ -300,16 +300,16 @@ Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorith
 
 It is up to you how to implement some specific parts of algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
 
-## About this repository
+# About this repository
 
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-## Demo video
+# Demo video
 
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
-## Credits
+# Credits
 
 WWDC 2017 Scholarship Project (Rejected) created by [Taras Nikulin](https://github.com/crabman448)

From fbd5d6ea149cccd61c93530a772bad148e3a45e1 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Thu, 25 May 2017 14:04:49 +0200
Subject: [PATCH 1040/1679] Examples for documentation

---
 .../Images/SplayTreesWorstCaseExamples.svg      |   2 ++
 Splay Tree/Images/example-zigzig-1.png          | Bin 0 -> 32202 bytes
 Splay Tree/Images/example-zigzig-2.png          | Bin 0 -> 34485 bytes
 Splay Tree/Images/example-zigzig-3.png          | Bin 0 -> 29732 bytes
 Splay Tree/Images/example-zigzig-4.png          | Bin 0 -> 28709 bytes
 Splay Tree/Images/example-zigzig-5.png          | Bin 0 -> 25735 bytes
 Splay Tree/Images/worst-case-1.png              | Bin 0 -> 6795 bytes
 Splay Tree/Images/worst-case-2.png              | Bin 0 -> 7076 bytes
 Splay Tree/Images/worst-case-3.png              | Bin 0 -> 9049 bytes
 Splay Tree/Images/worst-case-4.png              | Bin 0 -> 10813 bytes
 Splay Tree/Images/worst-case-5.png              | Bin 0 -> 11827 bytes
 Splay Tree/Images/worst-case-6.png              | Bin 0 -> 35177 bytes
 Splay Tree/Images/zigzig-wrongrotated.png       | Bin 0 -> 38831 bytes
 13 files changed, 2 insertions(+)
 create mode 100644 Splay Tree/Images/SplayTreesWorstCaseExamples.svg
 create mode 100644 Splay Tree/Images/example-zigzig-1.png
 create mode 100644 Splay Tree/Images/example-zigzig-2.png
 create mode 100644 Splay Tree/Images/example-zigzig-3.png
 create mode 100644 Splay Tree/Images/example-zigzig-4.png
 create mode 100644 Splay Tree/Images/example-zigzig-5.png
 create mode 100644 Splay Tree/Images/worst-case-1.png
 create mode 100644 Splay Tree/Images/worst-case-2.png
 create mode 100644 Splay Tree/Images/worst-case-3.png
 create mode 100644 Splay Tree/Images/worst-case-4.png
 create mode 100644 Splay Tree/Images/worst-case-5.png
 create mode 100644 Splay Tree/Images/worst-case-6.png
 create mode 100644 Splay Tree/Images/zigzig-wrongrotated.png

diff --git a/Splay Tree/Images/SplayTreesWorstCaseExamples.svg b/Splay Tree/Images/SplayTreesWorstCaseExamples.svg
new file mode 100644
index 000000000..c07312af2
--- /dev/null
+++ b/Splay Tree/Images/SplayTreesWorstCaseExamples.svg	
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diff --git a/Splay Tree/Images/example-zigzig-3.png b/Splay Tree/Images/example-zigzig-3.png
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diff --git a/Splay Tree/Images/example-zigzig-4.png b/Splay Tree/Images/example-zigzig-4.png
new file mode 100644
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From 72b6ef68538b5021eae53d507f82a2e1a46a57ed Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Thu, 25 May 2017 14:29:27 +0200
Subject: [PATCH 1041/1679] Finishing documentation

---
 Splay Tree/readme.md | 144 ++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 137 insertions(+), 7 deletions(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 29f9dede5..c42cd87fb 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -20,7 +20,7 @@ Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* a
 ### Case both nodes left children
 ![ZigZigCase2](Images/zigzig2.png)
 
-**IMPORTANT** is to note that a *ZigZig* performs first the rotation of the middle node with its parent (call it the grandparent) and later the rotation of the remaining node (grandchild). Doing that helps to keep the trees balanced even if it was first created by inserted a sequence of increasing values (see below worst case scenario).
+**IMPORTANT** is to note that a *ZigZig* performs first the rotation of the middle node with its parent (call it the grandparent) and later the rotation of the remaining node (grandchild). Doing that helps to keep the trees balanced even if it was first created by inserted a sequence of increasing values (see below worst case scenario followed by an explanation about why ZigZig rotates first to the grandparent).
 
 ### Zig-Zag
 
@@ -93,28 +93,69 @@ During the applying phase, the algorithms determines which nodes are involved de
 
 ### Insertion 
 
+To insert a value:
+
+- Insert it as in a binary search tree
+- Splay the value to the root
+
 ### Deletion 
 
+To delete a value: 
+
+- Delete it as in a binary search tree 
+- Splay the parent of the removed node to the root 
+
 ### Search 
 
+To search a value: 
+
+- Search for it as in a binary search tree 
+- Splay the node containing the value to the root 
+- If not found splay the node that would had been the parent of the searched value 
+
+### Minimum and maximum 
+
+- Search the tree for the required value 
+- Splay the node to the root 
+
 ## Examples 
 
 ### Example 1
 
-![ZigEx1](Images/examplezigzig1.png)
+Lets suppose a *find(20)* operation was performed and now the values **20** needs to be splayed to the root. 
+The sequence of steps will be the following: 
+
 
-![ZigEx2](Images/examplezigzig2.png)
+1. Since we are in a *ZigZig* case, we need to rotate **9** to **4**
 
-![ZigEx3](Images/examplezigzig3.png)
+![ZiggEx1](Images/examplezigzig1.png)
+
+2. We got the following tree after the first rotation: 
+
+![ZiggEx2](Images/examplezigzig2.png)
+
+3. And finally the **20** is rotated to the **9**
+
+![ZiggEx3](Images/examplezigzig3.png)
 
 
 ### Example 2
 
-![ZigEx21](Images/example1-1.png)
+Now suppose a *insert(7)* operation was performed and we're in a *ZigZag* case.
+
+
+1. First **7** is rotated to **9**
+
+![ZigggEx21](Images/example1-1.png)
+
+2. And the result tree is: 
+
+![ZigggEx22](Images/example1-2.png)
 
-![ZigEx22](Images/example1-2.png)
+3. Finally **7** is rotated to **4**
+
+![ZigggEx23](Images/example1-3.png)
 
-![ZigEx23](Images/example1-3.png)
 
 ## Advantages 
 
@@ -135,10 +176,99 @@ With *n* being the number of items in the tree.
 
 # An example of the Worst Case Performance 
 
+Suppose the a sequence of consecutive values are inserted in an Splay Tree. 
+Let's take for example [1,2,3,4,5,6,7,8].
+
+The tree construction will be like following: 
+
+
+1. Insert the number **1**
+
+2. Insert **2** 
+
+
+![WorstCase1](Images/worst-case-1.png)
+
+
+3. Splay **2** to the root 
+
+
+![WorstCase2](Images/worst-case-2.png)
+
+
+4. Insert **3** 
+
+
+![WorstCase3](Images/worst-case-3.png)
+
+5. Splay **3** to the root 
+
+
+![WorstCase4](Images/worst-case-4.png)
+
+
+6. Insert **4** 
+
+
+![WorstCase5](Images/worst-case-5.png)
+
+
+7. After inserting the rest of the values the tree will look like this: 
+
+
+![WorstCase6](Images/worst-case-6.png)
+
+
+
+If we keep insert number following the same sequence, that tree becomes inbalanced and have a height of **n** with **n** being the numbers of values inserted. 
+After getting this tree, a *find(1)* operation for example will take **O(n)**
+
+## ZigZig rotation order: first grandparent
+
+But thanks to the properties of the **Splay Tree** and the *ZigZig* rotations after the *find(1)* operation the tree becomes balanced again. This only happens if we respect the order of the *ZigZig* rotation, and the rotation to the grandparent happens first. 
+
+The sequence of *ZigZigs* rotations will look like follows: 
+
+1. Rotate **2** to **3**
+
+![ZigZig1](Images/example-zigzig-1.png)
+
+2. Rotate **1** to **2** 
+
+![ZigZig2](Images/example-zigzig-2.png)
+
+3. Rotate **4** to **5**
+
+![ZigZig3](Images/example-zigzig-3.png)
+
+4. Rotate **1** to **4** 
+
+![ZigZig4](Images/example-zigzig-4.png)
+
+5. Finally after splaying **1** to the root the tree will look like this: 
+
+![ZigZig5](Images/example-zigzig-5.png)
+
+
+Based on the example above, we can see why it's important to rotate first to the grandparent. We got a tree of height = 6, from an initial tree of height = 8. If the tree would had been taller, we would have achieved almost half of the initial height after the splaying operation.
+
+## ZigZig wrong rotation order 
+
+If the rotations would had been taking first the parent and not the grandparent we would have finished with the following, yet unbalanced tree, just inverting the side of the elements.
+
+![ZigZigWrong](Images/zigzig-wrongrotated.png)
+
 
 ## See also
 
 [Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
+
 [Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
 
+
+----------------
+
 *Written for Swift Algorithm Club by Barbara Martina Rodeker*
+
+----------------
+

From 83745f236a3084a6fff50c1b12def18ffbdc7707 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Thu, 25 May 2017 21:46:56 +0200
Subject: [PATCH 1042/1679] Fix workspace structure

---
 .../contents.xcworkspacedata                  | 760 ++++++++++++++----
 1 file changed, 602 insertions(+), 158 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index c89ac0dfe..8ba66e153 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1,50 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Workspace
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-   </FileRef>
-   <FileRef
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-   </FileRef>
-   <FileRef
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-   </FileRef>
-   <FileRef
-      location = "group:How to Contribute.markdown">
-   </FileRef>
-   <FileRef
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-   </FileRef>
-   <FileRef
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-   </FileRef>
-   <FileRef
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-   <Group
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-      name = "Miller-Rabin Primality Test">
-      <Group
-         location = "container:Miller-Rabin Primality Test/Images"
-         name = "Images">
-         <FileRef
-            location = "group:img_pseudo.png">
-         </FileRef>
-      </Group>
-      <FileRef
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-      </FileRef>
-      <FileRef
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-      </FileRef>
-      <FileRef
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-      </FileRef>
-   </Group>
    <Group
       location = "group:All-Pairs Shortest Paths"
       name = "All-Pairs Shortest Paths">
@@ -193,6 +149,18 @@
          <FileRef
             location = "group:Height.png">
          </FileRef>
+         <FileRef
+            location = "group:RotationStep0.jpg">
+         </FileRef>
+         <FileRef
+            location = "group:RotationStep1.jpg">
+         </FileRef>
+         <FileRef
+            location = "group:RotationStep2.jpg">
+         </FileRef>
+         <FileRef
+            location = "group:RotationStep3.jpg">
+         </FileRef>
          <FileRef
             location = "group:Unbalanced.graffle">
          </FileRef>
@@ -220,6 +188,58 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:B-Tree"
+      name = "B-Tree">
+      <FileRef
+         location = "group:BTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:BTree.swift">
+      </FileRef>
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:BTree20.png">
+         </FileRef>
+         <FileRef
+            location = "group:InsertionSplit.png">
+         </FileRef>
+         <FileRef
+            location = "group:MergingNodes.png">
+         </FileRef>
+         <FileRef
+            location = "group:MovingKey.png">
+         </FileRef>
+         <FileRef
+            location = "group:Node.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <Group
+            location = "group:Tests"
+            name = "Tests">
+            <FileRef
+               location = "group:BTreeNodeTests.swift">
+            </FileRef>
+            <FileRef
+               location = "group:BTreeTests.swift">
+            </FileRef>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Binary Search"
       name = "Binary Search">
@@ -441,6 +461,22 @@
       <FileRef
          location = "group:README.markdown">
       </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:BoyerMooreHorspoolTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:BoyerMooreTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
    </Group>
    <Group
       location = "group:Breadth-First Search"
@@ -546,6 +582,32 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
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+      name = "Comb Sort">
+      <FileRef
+         location = "group:Comb Sort.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Comb Sort.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
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+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
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       name = "Combinatorics">
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-         location = "group:Combinatorics.swift">
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
+   <Group
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+      name = "Convex Hull">
+      <Group
+         location = "group:Convex Hull"
+         name = "Convex Hull">
+         <FileRef
+            location = "group:AppDelegate.swift">
+         </FileRef>
+         <Group
+            location = "group:Assets.xcassets"
+            name = "Assets.xcassets">
+            <Group
+               location = "group:AppIcon.appiconset"
+               name = "AppIcon.appiconset">
+               <FileRef
+                  location = "group:Contents.json">
+               </FileRef>
+            </Group>
+         </Group>
+         <Group
+            location = "group:Base.lproj"
+            name = "Base.lproj">
+            <FileRef
+               location = "group:LaunchScreen.storyboard">
+            </FileRef>
+         </Group>
+         <FileRef
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+         </FileRef>
+         <FileRef
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+         </FileRef>
+      </Group>
+      <FileRef
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+         location = "group:README.md">
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@@ -662,11 +762,34 @@
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    </Group>
+   <Group
+      location = "group:DiningPhilosophers"
+      name = "DiningPhilosophers">
+      <FileRef
+         location = "group:DiningPhilosophers.xcodeproj">
+      </FileRef>
+      <FileRef
+         location = "group:LICENSE">
+      </FileRef>
+      <FileRef
+         location = "group:Package.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Sources"
+         name = "Sources">
+         <FileRef
+            location = "group:main.swift">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
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       name = "Fixed Size Array">
       <FileRef
-         location = "group:FixedSizeArray.swift">
+         location = "group:FixedSizeArray.playground">
       </FileRef>
       <Group
          location = "group:Images"
@@ -889,6 +1012,16 @@
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    </Group>
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+      name = "HaversineDistance">
+      <FileRef
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+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+   </Group>
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       name = "Heap">
@@ -1033,13 +1166,6 @@
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       name = "Huffman Coding">
@@ -1162,6 +1288,32 @@
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+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:quadtree.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:QuadTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <Group
+            location = "group:Tests"
+            name = "Tests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:Tests.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Queue"
       name = "Queue">
@@ -1474,15 +1773,47 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Rabin-Karp"
+      name = "Rabin-Karp">
+      <FileRef
+         location = "group:Rabin-Karp.playground">
+      </FileRef>
+      <FileRef
+         location = "group:rabin-karp.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Radix Sort"
       name = "Radix Sort">
+      <FileRef
+         location = "group:RadixSort.playground">
+      </FileRef>
       <FileRef
          location = "group:radixSort.swift">
       </FileRef>
+      <FileRef
+         location = "group:RadixSortExample.swift">
+      </FileRef>
       <FileRef
          location = "group:ReadMe.md">
       </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:RadixSortTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
    </Group>
    <Group
       location = "group:Radix Tree"
@@ -1507,21 +1838,11 @@
    <Group
       location = "group:Red-Black Tree"
       name = "Red-Black Tree">
-      <Group
-         location = "group:files"
-         name = "files">
-         <FileRef
-            location = "group:fig1.png">
-         </FileRef>
-         <FileRef
-            location = "group:fig2.png">
-         </FileRef>
-      </Group>
       <FileRef
-         location = "group:RBTree.swift">
+         location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:README.md">
+         location = "group:Red-Black Tree 2.playground">
       </FileRef>
    </Group>
    <Group
@@ -1537,32 +1858,6 @@
          location = "group:RingBuffer.swift">
       </FileRef>
    </Group>
-   <Group
-      location = "group:Run-Length Encoding"
-      name = "Run-Length Encoding">
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:RLE.playground">
-      </FileRef>
-      <FileRef
-         location = "group:RLE.swift">
-      </FileRef>
-      <Group
-         location = "group:Tests"
-         name = "Tests">
-         <FileRef
-            location = "group:Info.plist">
-         </FileRef>
-         <FileRef
-            location = "group:RLETests.swift">
-         </FileRef>
-         <FileRef
-            location = "group:Tests.xcodeproj">
-         </FileRef>
-      </Group>
-   </Group>
    <Group
       location = "group:Rootish Array Stack"
       name = "Rootish Array Stack">
@@ -1579,6 +1874,15 @@
             location = "group:RootishArrayStackIntro.png">
          </FileRef>
       </Group>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:RootishArrayStack.playground">
+      </FileRef>
+      <FileRef
+         location = "group:RootishArrayStack.swift">
+      </FileRef>
       <Group
          location = "group:Tests"
          name = "Tests">
@@ -1586,23 +1890,24 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:RootishArrayStackTests.swift">
+            location = "group:RootishArrayStack.swift">
          </FileRef>
          <FileRef
-            location = "group:RootishArrayStack.swift">
+            location = "group:RootishArrayStackTests.swift">
          </FileRef>
          <FileRef
             location = "group:Tests.xcodeproj">
          </FileRef>
       </Group>
+   </Group>
+   <Group
+      location = "group:Run-Length Encoding"
+      name = "Run-Length Encoding">
       <FileRef
-         location = "group:README.md">
-      </FileRef>
-      <FileRef
-         location = "group:RootishArrayStack.swift">
+         location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:RootishArrayStack.playground">
+         location = "group:RLE.playground">
       </FileRef>
    </Group>
    <Group
@@ -1718,16 +2023,16 @@
       </Group>
    </Group>
    <Group
-      location = "container:"
+      location = "group:Set Cover (Unweighted)"
       name = "Set Cover (Unweighted)">
       <FileRef
-         location = "group:Set Cover (Unweighted)/README.markdown">
+         location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:Set Cover (Unweighted)/SetCover.playground">
+         location = "group:SetCover.playground">
       </FileRef>
       <FileRef
-         location = "group:Set Cover (Unweighted)/SetCover.swift">
+         location = "group:SetCover.swift">
       </FileRef>
    </Group>
    <Group
@@ -1739,6 +2044,9 @@
       <FileRef
          location = "group:shellsort.swift">
       </FileRef>
+      <FileRef
+         location = "group:ShellSortExample.swift">
+      </FileRef>
       <Group
          location = "group:Tests"
          name = "Tests">
@@ -1873,6 +2181,72 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Skip-List"
+      name = "Skip-List">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:Insert1.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert10.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert11.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert12.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert2.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert3.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert4.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert5.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert6.png">
+         </FileRef>
+         <FileRef
+            location = "group:insert7.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert8.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert9.png">
+         </FileRef>
+         <FileRef
+            location = "group:Intro.png">
+         </FileRef>
+         <FileRef
+            location = "group:Search1.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:SkipList.swift">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Slow Sort"
+      name = "Slow Sort">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:SlowSort.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Stack"
       name = "Stack">
@@ -1899,31 +2273,47 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Strassen Matrix Multiplication"
+      name = "Strassen Matrix Multiplication">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:StrassensMatrixMultiplication.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Ternary Search Tree"
       name = "Ternary Search Tree">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:TernarySearchTree.swift">
+      </FileRef>
       <Group
-         location = "container:Ternary Search Tree/Tests"
+         location = "group:Tests"
          name = "Tests">
          <FileRef
             location = "group:Info.plist">
          </FileRef>
+         <FileRef
+            location = "group:TernarySearchTreeTests.swift">
+         </FileRef>
          <FileRef
             location = "group:Tests.xcodeproj">
          </FileRef>
       </Group>
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:TernarySearchTree.swift">
-      </FileRef>
       <FileRef
          location = "group:TST.playground">
       </FileRef>
       <FileRef
          location = "group:TSTNode.swift">
       </FileRef>
+      <FileRef
+         location = "group:Utils.swift">
+      </FileRef>
    </Group>
    <Group
       location = "group:Threaded Binary Tree"
@@ -1966,10 +2356,7 @@
          location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:ThreadedBinaryTree.swift">
-      </FileRef>
-      <FileRef
-         location = "group:ThreadedBinaryTreeTests.swift">
+         location = "group:ThreadedBinaryTree.playground">
       </FileRef>
    </Group>
    <Group
@@ -2056,27 +2443,6 @@
          <Group
             location = "group:Treap"
             name = "Treap">
-            <FileRef
-               location = "group:AppDelegate.swift">
-            </FileRef>
-            <Group
-               location = "group:Assets.xcassets"
-               name = "Assets.xcassets">
-               <Group
-                  location = "group:AppIcon.appiconset"
-                  name = "AppIcon.appiconset">
-                  <FileRef
-                     location = "group:Contents.json">
-                  </FileRef>
-               </Group>
-            </Group>
-            <Group
-               location = "group:Base.lproj"
-               name = "Base.lproj">
-               <FileRef
-                  location = "group:MainMenu.xib">
-               </FileRef>
-            </Group>
             <FileRef
                location = "group:Info.plist">
             </FileRef>
@@ -2149,12 +2515,83 @@
    <Group
       location = "group:Trie"
       name = "Trie">
+      <Group
+         location = "group:images"
+         name = "images">
+         <FileRef
+            location = "group:trie.png">
+         </FileRef>
+      </Group>
       <FileRef
          location = "group:ReadMe.md">
       </FileRef>
-      <FileRef
-         location = "group:trie.swift">
-      </FileRef>
+      <Group
+         location = "group:Trie"
+         name = "Trie">
+         <Group
+            location = "group:Trie"
+            name = "Trie">
+            <FileRef
+               location = "group:AppDelegate.swift">
+            </FileRef>
+            <Group
+               location = "group:Assets.xcassets"
+               name = "Assets.xcassets">
+               <Group
+                  location = "group:AppIcon.appiconset"
+                  name = "AppIcon.appiconset">
+                  <FileRef
+                     location = "group:Contents.json">
+                  </FileRef>
+               </Group>
+            </Group>
+            <Group
+               location = "group:Base.lproj"
+               name = "Base.lproj">
+               <FileRef
+                  location = "group:Main.storyboard">
+               </FileRef>
+            </Group>
+            <FileRef
+               location = "group:dictionary.txt">
+            </FileRef>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:ReadMe.md">
+            </FileRef>
+            <FileRef
+               location = "group:Trie.swift">
+            </FileRef>
+            <FileRef
+               location = "group:ViewController.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Trie.xcodeproj">
+         </FileRef>
+         <Group
+            location = "group:TrieTests"
+            name = "TrieTests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:TrieTests.swift">
+            </FileRef>
+         </Group>
+         <Group
+            location = "group:TrieUITests"
+            name = "TrieUITests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:TrieUITests.swift">
+            </FileRef>
+         </Group>
+      </Group>
    </Group>
    <Group
       location = "group:Two-Sum Problem"
@@ -2168,9 +2605,6 @@
          <FileRef
             location = "group:2Sum.playground">
          </FileRef>
-         <FileRef
-            location = "group:2Sum.swift">
-         </FileRef>
       </Group>
       <Group
          location = "group:Solution 2"
@@ -2178,9 +2612,6 @@
          <FileRef
             location = "group:2Sum.playground">
          </FileRef>
-         <FileRef
-            location = "group:2Sum.swift">
-         </FileRef>
       </Group>
    </Group>
    <Group
@@ -2208,8 +2639,21 @@
       <FileRef
          location = "group:UnionFind.playground">
       </FileRef>
+   </Group>
+   <Group
+      location = "group:Z-Algorithm"
+      name = "Z-Algorithm">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:ZAlgorithm.swift">
+      </FileRef>
+      <FileRef
+         location = "group:ZetaAlgorithm.playground">
+      </FileRef>
       <FileRef
-         location = "group:UnionFind.swift">
+         location = "group:ZetaAlgorithm.swift">
       </FileRef>
    </Group>
 </Workspace>

From 613a420c92c2dc330506af0e3fdf8dbc5cac0ff4 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Thu, 25 May 2017 21:52:55 +0200
Subject: [PATCH 1043/1679] Swiftlint autocorrect

---
 .../AVLTree.playground/Sources/AVLTree.swift  |  5 ++-
 AVL Tree/AVLTree.swift                        |  5 ++-
 AVL Tree/Tests/TreeNodeTests.swift            |  1 -
 .../APSP/APSP/Helpers.swift                   |  1 -
 Array2D/Array2D.playground/Contents.swift     |  1 -
 .../BinaryTree.playground/Contents.swift      |  4 ---
 Bit Set/BitSet.playground/Contents.swift      |  9 -----
 .../BloomFilter.playground/Contents.swift     |  4 ---
 Bloom Filter/Tests/BloomFilterTests.swift     |  1 -
 .../Contents.swift                            |  6 ----
 .../Contents.swift                            |  3 --
 .../Contents.swift                            |  2 --
 .../Sources/BucketSort.swift                  |  2 --
 Bucket Sort/BucketSort.swift                  |  3 --
 Bucket Sort/Tests/Tests.swift                 |  1 -
 .../Combinatorics.playground/Contents.swift   | 12 -------
 Convex Hull/Convex Hull/AppDelegate.swift     |  2 --
 .../Contents.swift                            |  2 --
 .../CountingSort.playground/Contents.swift    |  1 -
 .../Contents.swift                            |  2 --
 DiningPhilosophers/Sources/main.swift         |  4 ---
 Graph/Graph/AdjacencyListGraph.swift          |  3 --
 .../Contents.swift                            |  1 -
 .../kthLargest.playground/Contents.swift      |  4 ---
 Kth Largest Element/kthLargest.swift          |  1 -
 .../Contents.swift                            |  2 +-
 .../LinkedList.playground/Contents.swift      |  2 --
 .../MergeSort.playground/Contents.swift       |  2 --
 .../Contents.swift                            |  2 --
 Minimum Spanning Tree/Kruskal.swift           |  1 -
 .../Sources/Graph.swift                       |  2 --
 .../Sources/Heap.swift                        |  4 +--
 Minimum Spanning Tree/Prim.swift              |  1 -
 .../Sources/MinimumCoinChange.swift           | 34 +++++++++----------
 .../MinimumCoinChangeTests.swift              |  3 +-
 .../OrderedArray.playground/Contents.swift    |  2 --
 Queue/Queue.playground/Contents.swift         |  3 --
 Quicksort/Quicksort.playground/Contents.swift |  9 -----
 .../Sources/radixSort.swift                   |  2 --
 Radix Sort/radixSort.swift                    |  3 --
 .../Contents.swift                            |  2 --
 .../Tests/RootishArrayStackTests.swift        |  1 -
 .../SegmentTree.playground/Contents.swift     |  6 ----
 .../Contents.swift                            |  3 --
 .../Contents.swift                            |  2 --
 Shortest Path (Unweighted)/Tests/Graph.swift  |  1 -
 Shuffle/Shuffle.playground/Contents.swift     |  4 ---
 .../ShuntingYard.playground/Contents.swift    |  1 -
 Skip-List/SkipList.swift                      | 15 +-------
 Slow Sort/SlowSort.swift                      | 11 +++---
 .../Contents.swift                            |  1 -
 .../Sources/Matrix.swift                      | 30 ++++++++--------
 .../TST.playground/Sources/TSTNode.swift      |  1 -
 .../Sources/TernarySearchTree.swift           |  3 --
 Ternary Search Tree/TernarySearchTree.swift   |  1 -
 .../Tests/TernarySearchTreeTests.swift        |  1 -
 .../Contents.swift                            |  5 ---
 .../Contents.swift                            |  2 --
 Treap/Treap.swift                             |  2 +-
 Tree/Tree.playground/Contents.swift           |  3 --
 Trie/Trie/Trie/AppDelegate.swift              |  3 --
 Trie/Trie/Trie/Trie.swift                     |  3 --
 Trie/Trie/Trie/ViewController.swift           |  1 -
 .../UnionFind.playground/Contents.swift       |  4 ---
 .../Sources/UnionFindQuickFind.swift          | 12 +++----
 .../Sources/UnionFindQuickUnion.swift         | 12 +++----
 .../Sources/UnionFindWeightedQuickFind.swift  | 12 +++----
 .../Sources/UnionFindWeightedQuickUnion.swift | 12 +++----
 ...indWeightedQuickUnionPathCompression.swift | 12 +++----
 .../ZetaAlgorithm.playground/Contents.swift   |  2 --
 70 files changed, 77 insertions(+), 243 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index 56ba81608..9f8695a83 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -341,11 +341,11 @@ extension AVLTree {
       }
     } else {
       // Handle stem cases
-      if let replacement = node.leftChild?.maximum() , replacement !== node {
+      if let replacement = node.leftChild?.maximum(), replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(node: replacement)
-      } else if let replacement = node.rightChild?.minimum() , replacement !== node {
+      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(node: replacement)
@@ -354,7 +354,6 @@ extension AVLTree {
   }
 }
 
-
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 4feb691e4..52ea082ce 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -341,11 +341,11 @@ extension AVLTree {
       }
     } else {
       // Handle stem cases
-      if let replacement = node.leftChild?.maximum() , replacement !== node {
+      if let replacement = node.leftChild?.maximum(), replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(node: replacement)
-      } else if let replacement = node.rightChild?.minimum() , replacement !== node {
+      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(node: replacement)
@@ -354,7 +354,6 @@ extension AVLTree {
   }
 }
 
-
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
diff --git a/AVL Tree/Tests/TreeNodeTests.swift b/AVL Tree/Tests/TreeNodeTests.swift
index 88b314e41..cac7e549b 100644
--- a/AVL Tree/Tests/TreeNodeTests.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -27,7 +27,6 @@ class TreeNodeTests: XCTestCase {
         super.tearDown()
     }
 
-
     func testSingleNodeCreationNOPayload() {
         let treeNode = TreeNode<String, String>(key: "Building")
         XCTAssertNil(treeNode.payload, "Payload for this case should be nil")
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift
index 3812b3f58..f590a6e50 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
@@ -7,7 +7,6 @@
 
 import Foundation
 
-
 /**
  Print a matrix, optionally specifying only the cells to display with the triplet (i, j, k) -> matrix[i][j], matrix[i][k], matrix[k][j]
  */
diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 1a6a439bd..d31d77540 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -28,7 +28,6 @@ public struct Array2D<T> {
   }
 }
 
-
 // initialization
 var matrix = Array2D(columns: 3, rows: 5, initialValue: 0)
 
diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index aa084e44d..b0bff577a 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -25,8 +25,6 @@ extension BinaryTree: CustomStringConvertible {
   }
 }
 
-
-
 // leaf nodes
 let node5 = BinaryTree.node(.empty, "5", .empty)
 let nodeA = BinaryTree.node(.empty, "a", .empty)
@@ -50,8 +48,6 @@ let tree = BinaryTree.node(timesLeft, "+", timesRight)
 print(tree)
 tree.count  // 12
 
-
-
 extension BinaryTree {
   public func traverseInOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 77d371420..d11b36e8c 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -29,9 +29,6 @@ print(bits)
 
 print("")
 
-
-
-
 // Bitwise operations
 
 var a = BitSet(size: 4)
@@ -69,9 +66,6 @@ print(~c)  // 0101110000000000000000000000000000000000000000000000000000000000
 (~b).cardinality  // 5
 (~c).cardinality  // 4
 
-
-
-
 var z = BitSet(size: 66)
 z.all0()        // true
 z.all1()        // false
@@ -93,8 +87,5 @@ z.all1()        // true
 z[65] = false
 z.all1()        // false
 
-
-
-
 //var bigBits = BitSet(size: 10000)
 //print(bigBits)
diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 06022c9b3..3dac76e8e 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -47,8 +47,6 @@ public class BloomFilter<T> {
   }
 }
 
-
-
 /* Two hash functions, adapted from http://www.cse.yorku.ca/~oz/hash.html */
 
 func djb2(x: String) -> Int {
@@ -67,8 +65,6 @@ func sdbm(x: String) -> Int {
   return Int(hash)
 }
 
-
-
 /* A simple test */
 
 let bloom = BloomFilter<String>(size: 17, hashFunctions: [djb2, sdbm])
diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 82bf4fb8f..55db71f3f 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -23,7 +23,6 @@ func sdbm(_ x: String) -> Int {
   return Int(hash)
 }
 
-
 class BloomFilterTests: XCTestCase {
 
   func testSingleHashFunction() {
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index 1bc678ccc..d6204abec 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -15,8 +15,6 @@ func < (m1: Message, m2: Message) -> Bool {
   return m1.priority < m2.priority
 }
 
-
-
 let queue = BoundedPriorityQueue<Message>(maxElements: 5)
 queue.count
 
@@ -48,8 +46,6 @@ print(queue)
 // At this point, the queue is:
 // <world:150, swift:110, hello:100, there:99, is:30, >
 
-
-
 // Try to insert an item with a really low priority. This should not get added.
 queue.enqueue(Message(name: "very", priority: -1))
 queue.count    // 5
@@ -70,8 +66,6 @@ queue.count
 queue.peek()
 print(queue)
 
-
-
 // Test dequeuing
 queue.dequeue()
 queue.count
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 0fb98e1c8..675be2203 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -19,8 +19,6 @@ func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   return nodesExplored
 }
 
-
-
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
@@ -42,6 +40,5 @@ graph.addEdge(nodeE, neighbor: nodeH)
 graph.addEdge(nodeE, neighbor: nodeF)
 graph.addEdge(nodeF, neighbor: nodeG)
 
-
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index b9f2b1432..fcee59a7b 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -22,8 +22,6 @@ extension String {
   }
 }
 
-
-
 // A few simple tests
 
 let s = "Hello, World"
diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index 08962c0e1..f16db3e67 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -26,7 +26,6 @@ import Foundation
 // MARK: Main algorithm
 //////////////////////////////////////
 
-
 public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: inout [Bucket<T>]) -> [T] {
   for elem in elements {
     distributor.distribute(element: elem, buckets: &buckets)
@@ -45,7 +44,6 @@ public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sor
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
   func distribute<T: Sortable>(element: T, buckets: inout [Bucket<T>])
 }
diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 5845819f2..f2aeaae99 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -45,12 +45,10 @@ fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
   }
 }
 
-
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
 
-
 /**
     Performs bucket sort algorithm on the given input elements.
     [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
@@ -96,7 +94,6 @@ private func enoughSpaceInBuckets<T: Sortable>(_ buckets: [Bucket<T>], elements:
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
     func distribute<T: Sortable>(_ element: T, buckets: inout [Bucket<T>])
 }
diff --git a/Bucket Sort/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
index b50789ed0..1a06c92b5 100644
--- a/Bucket Sort/Tests/Tests.swift	
+++ b/Bucket Sort/Tests/Tests.swift	
@@ -86,7 +86,6 @@ class TestTests: XCTestCase {
     }
 }
 
-
 //////////////////////////////////////
 // MARK: Extensions
 //////////////////////////////////////
diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 94951810f..9fbcc1c58 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -14,8 +14,6 @@ func factorial(_ n: Int) -> Int {
 factorial(5)
 factorial(20)
 
-
-
 /*
  Calculates P(n, k), the number of permutations of n distinct symbols
  in groups of size k.
@@ -34,8 +32,6 @@ permutations(5, 3)
 permutations(50, 6)
 permutations(9, 4)
 
-
-
 /*
  Prints out all the permutations of the given array.
  Original algorithm by Niklaus Wirth.
@@ -63,8 +59,6 @@ let xyz = [ "x", "y", "z" ]
 print("\nPermutations of \(xyz):")
 permuteWirth(xyz, 2)
 
-
-
 /*
  Prints out all the permutations of an n-element collection.
 
@@ -97,8 +91,6 @@ let numbers = [0, 0, 0, 0]  // must be all zeros
 var pos = -1
 permuteSedgewick(numbers, 0, &pos)
 
-
-
 /*
  Calculates C(n, k), or "n-choose-k", i.e. how many different selections
  of size k out of a total number of distinct elements (n) you can make.
@@ -115,8 +107,6 @@ for i in 1...20 {
     print("\(20)-choose-\(i) = \(combinations(20, choose: i))")
 }
 
-
-
 /*
  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
  k things out of n possibilities.
@@ -134,8 +124,6 @@ func quickBinomialCoefficient(_ n: Int, choose k: Int) -> Int {
 quickBinomialCoefficient(8, choose: 2)
 quickBinomialCoefficient(30, choose: 15)
 
-
-
 /* Supporting code because Swift doesn't have a built-in 2D array. */
 struct Array2D<T> {
   let columns: Int
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
index bfe15e1a7..9bc61ff96 100644
--- a/Convex Hull/Convex Hull/AppDelegate.swift	
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -13,7 +13,6 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
 
     var window: UIWindow?
 
-
     func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
 
         let screenBounds = UIScreen.main.bounds
@@ -52,5 +51,4 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
         // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
     }
 
-
 }
diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index cbb43c868..b4392d501 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -32,13 +32,11 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   return rightBoundary() - leftBoundary()
 }
 
-
 // Simple test
 
 let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 countOccurrencesOfKey(3, inArray: a)
 
-
 // Test with arrays of random size and contents (see debug output)
 
 import Foundation
diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 1d84f8132..dc375512a 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -37,5 +37,4 @@ func countingSort(array: [Int]) throws -> [Int] {
   return sortedArray
 }
 
-
 try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index b1d8494d6..1e32b4bbf 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -10,8 +10,6 @@ func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   return nodesExplored
 }
 
-
-
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index 338a9074d..32c3af979 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -6,7 +6,6 @@
 //
 //
 
-
 import Dispatch
 
 let numberOfPhilosophers = 4
@@ -41,7 +40,6 @@ struct ForkPair {
     }
 }
 
-
 struct Philosophers {
     let forkPair: ForkPair
     let philosopherIndex: Int
@@ -75,7 +73,6 @@ struct Philosophers {
     }
 }
 
-
 // Layout of the table (P = philosopher, f = fork) for 4 Philosophers
 //          P0
 //       f3    f0
@@ -99,6 +96,5 @@ for semaphore in ForkPair.forksSemaphore {
     semaphore.signal()
 }
 
-
 //Wait forever
 globalSem.wait()
diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index b58ef6417..4a84129df 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -7,8 +7,6 @@
 
 import Foundation
 
-
-
 private class EdgeList<T> where T: Equatable, T: Hashable {
 
   var vertex: Vertex<T>
@@ -90,7 +88,6 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
     addDirectedEdge(vertices.1, to: vertices.0, withWeight: weight)
   }
 
-
   open override func weightFrom(_ sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
     guard let edges = adjacencyList[sourceVertex.index].edges else {
       return nil
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index 35fb27ff8..a27726648 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -1,6 +1,5 @@
 //: Playground - noun: a place where people can play
 
-
 func ZetaAlgorithm(ptnr: String) -> [Int]? {
 
     let pattern = Array(ptnr.characters)
diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 9fba2b483..3e186760c 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -22,9 +22,6 @@ kthLargest(a, 6)
 kthLargest(a, 7)
 kthLargest(a, 8)
 
-
-
-
 import Foundation
 
 /* Returns a random integer in the range min...max, inclusive. */
@@ -84,7 +81,6 @@ public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   return randomizedSelect(&a, 0, a.count - 1, k)
 }
 
-
 randomizedSelect(a, order: 0)
 randomizedSelect(a, order: 1)
 randomizedSelect(a, order: 2)
diff --git a/Kth Largest Element/kthLargest.swift b/Kth Largest Element/kthLargest.swift
index 1f90b096f..16f6caf0c 100644
--- a/Kth Largest Element/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.swift	
@@ -14,7 +14,6 @@ func kthLargest(a: [Int], k: Int) -> Int? {
   }
 }
 
-
 // MARK: - Randomized selection
 
 /* Returns a random integer in the range min...max, inclusive. */
diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 8b579b3c1..8faf2b738 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -34,7 +34,7 @@ func average(_ input: [Double]) -> Double {
 }
 
 func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
-    return zip(a,b).map(*)
+    return zip(a, b).map(*)
 }
 
 func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 9ee4cc4c4..c7cd6265d 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -312,7 +312,6 @@ extension LinkedList: ExpressibleByArrayLiteral {
   }
 }
 
-
 //: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
@@ -352,7 +351,6 @@ list2.isEmpty                 // true
 list.removeLast()             // "World"
 list.remove(atIndex: 2)       // "Goodbye"
 
-
 list.insert("Swift", atIndex: 1)
 list[0]     // "Hello"
 list[1]     // "Swift"
diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index 137dd19e2..f5a1dbbcf 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -49,8 +49,6 @@ let sortedArray = mergeSort(array)
 let array2 = ["Tom", "Harry", "Ron", "Chandler", "Monica"]
 let sortedArray2 = mergeSort(array2)
 
-
-
 /* Bottom-up iterative version */
 
 func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 86fe27df8..8ad04379c 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -21,12 +21,10 @@ func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Grap
   return minimumSpanningTree
 }
 
-
 /*:
 ![Graph](Minimum_Spanning_Tree.png)
 */
 
-
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
diff --git a/Minimum Spanning Tree/Kruskal.swift b/Minimum Spanning Tree/Kruskal.swift
index bebd32602..5e6fc5fd2 100644
--- a/Minimum Spanning Tree/Kruskal.swift	
+++ b/Minimum Spanning Tree/Kruskal.swift	
@@ -6,7 +6,6 @@
 //
 //
 
-
 func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
   var cost: Int = 0
   var tree = Graph<T>()
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
index 5e74e14cb..f6e4d4fc1 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -1,4 +1,3 @@
-
 // Undirected edge
 public struct Edge<T>: CustomStringConvertible {
   public let vertex1: T
@@ -10,7 +9,6 @@ public struct Edge<T>: CustomStringConvertible {
   }
 }
 
-
 // Undirected weighted graph
 public struct Graph<T: Hashable>: CustomStringConvertible {
 
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
index fa30df362..80b40c65f 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
@@ -113,7 +113,7 @@ public struct Heap<T> {
    */
   public mutating func replace(index i: Int, value: T) {
     guard i < elements.count else { return }
-    
+
     assert(isOrderedBefore(value, elements[i]))
     elements[i] = value
     shiftUp(i)
@@ -144,7 +144,7 @@ public struct Heap<T> {
    */
   public mutating func removeAt(_ index: Int) -> T? {
     guard index < elements.count else { return nil }
-    
+
     let size = elements.count - 1
     if index != size {
       swap(&elements[index], &elements[size])
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
index d975fc430..d65d53f29 100644
--- a/Minimum Spanning Tree/Prim.swift	
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -43,4 +43,3 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
 
   return (cost: cost, tree: tree)
 }
-
diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index 55629d020..c83708dee 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -13,16 +13,16 @@ public enum MinimumCoinChangeError: Error {
 
 public struct MinimumCoinChange {
     internal let sortedCoinSet: [Int]
-    
+
     public init(coinSet: [Int]) {
-        self.sortedCoinSet = coinSet.sorted(by: { $0 > $1} )
+        self.sortedCoinSet = coinSet.sorted(by: { $0 > $1})
     }
 
     //Greedy Algorithm
     public func changeGreedy(_ value: Int) throws -> [Int] {
         guard value > 0 else { return [] }
 
-        var change:  [Int] = []
+        var change: [Int] = []
         var newValue = value
 
         for coin in sortedCoinSet {
@@ -35,10 +35,10 @@ public struct MinimumCoinChange {
                 break
             }
         }
-        
-        if newValue > 0 { 
-            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
-        } 
+
+        if newValue > 0 {
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue
+        }
 
         return change
     }
@@ -46,7 +46,7 @@ public struct MinimumCoinChange {
     //Dynamic Programming Algorithm
     public func changeDynamic(_ value: Int) throws -> [Int] {
         guard value > 0 else { return [] }
-        
+
         var cache: [Int : [Int]] = [:]
 
         func _changeDynamic(_ value: Int) -> [Int] {
@@ -55,34 +55,34 @@ public struct MinimumCoinChange {
             if let cached = cache[value] {
                 return cached
             }
-            
+
             var potentialChangeArray: [[Int]] = []
-            
+
             for coin in sortedCoinSet {
                 if value - coin >= 0 {
                     var potentialChange: [Int] = [coin]
                     potentialChange.append(contentsOf: _changeDynamic(value - coin))
 
-                    if potentialChange.reduce(0, +) == value { 
+                    if potentialChange.reduce(0, +) == value {
                         potentialChangeArray.append(potentialChange)
-                    } 
+                    }
                 }
             }
-            
+
             if potentialChangeArray.count > 0 {
                 let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
                 cache[value] = sortedPotentialChangeArray[0]
                 return sortedPotentialChangeArray[0]
             }
-            
+
             return []
         }
 
         let change: [Int] = _changeDynamic(value)
 
-        if change.reduce(0, +) != value { 
-            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
-        } 
+        if change.reduce(0, +) != value {
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue
+        }
 
         return change
     }
diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
index 705113e92..7c106eeb9 100644
--- a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -17,8 +17,7 @@ class MinimumCoinChangeTests: XCTestCase {
                     print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
                 }
             }
-        }
-        catch {
+        } catch {
             XCTFail("Test Failed: impossible to change with the given coin set")
         }
     }
diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 5ca0d7d31..4fe199f28 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -70,8 +70,6 @@ extension OrderedArray: CustomStringConvertible {
   }
 }
 
-
-
 var a = OrderedArray<Int>(array: [5, 1, 3, 9, 7, -1])
 a              // [-1, 1, 3, 5, 7, 9]
 
diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index a90fa647e..08327783f 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -39,9 +39,6 @@ public struct Queue<T> {
   }
 }
 
-
-
-
 // Create a queue and put some elements on it already.
 var queueOfNames = Queue(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index da02b69ce..972d0b5e1 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -2,7 +2,6 @@
 
 import Foundation
 
-
 // *** Simple but inefficient version of quicksort ***
 
 func quicksort<T: Comparable>(_ a: [T]) -> [T] {
@@ -23,8 +22,6 @@ func quicksort<T: Comparable>(_ a: [T]) -> [T] {
 let list1 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 quicksort(list1)
 
-
-
 // *** Using Lomuto partitioning ***
 
 /*
@@ -63,8 +60,6 @@ func quicksortLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
 
 quicksortLomuto(&list2, low: 0, high: list2.count - 1)
 
-
-
 // *** Hoare partitioning ***
 
 /*
@@ -106,8 +101,6 @@ func quicksortHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
 
 quicksortHoare(&list3, low: 0, high: list3.count - 1)
 
-
-
 // *** Randomized sorting ***
 
 /* Returns a random integer in the range min...max, inclusive. */
@@ -131,8 +124,6 @@ var list4 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 quicksortRandom(&list4, low: 0, high: list4.count - 1)
 list4
 
-
-
 // *** Dutch national flag partioning ***
 
 /*
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
index 81c2479e8..424d33fb9 100644
--- a/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -12,7 +12,6 @@ public func radixSort(_ array: inout [Int] ) {
   var index: Int
   var digit = 1  //Which digit are we on?
 
-
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
 
@@ -22,7 +21,6 @@ public func radixSort(_ array: inout [Int] ) {
       buckets.append([])
     }
 
-
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
diff --git a/Radix Sort/radixSort.swift b/Radix Sort/radixSort.swift
index 9e48093ef..302ea6056 100644
--- a/Radix Sort/radixSort.swift	
+++ b/Radix Sort/radixSort.swift	
@@ -4,7 +4,6 @@
 
 */
 
-
 // NOTE: This implementation does not handle negative numbers
 func radixSort(_ array: inout [Int] ) {
   let radix = 10  //Here we define our radix to be 10
@@ -12,7 +11,6 @@ func radixSort(_ array: inout [Int] ) {
   var index: Int
   var digit = 1  //Which digit are we on?
 
-
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
 
@@ -22,7 +20,6 @@ func radixSort(_ array: inout [Int] ) {
       buckets.append([])
     }
 
-
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
diff --git a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift
index 68ec0a53e..8b630528d 100644
--- a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
+++ b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
@@ -177,14 +177,12 @@ list[0]       // "Hello"
 list[1]       // "World"
 //list[2]     // crash!
 
-
 list.memoryDescription
 //	{
 //		[Optional("Hello")]
 //		[Optional("World"), nil]
 //	}
 
-
 list.insert(element: "Swift", atIndex: 1)
 list.isEmpty  // false
 list.first    // "Hello"
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index f0aaa8bca..9d5972a41 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -170,7 +170,6 @@ class RootishArrayStackTests: XCTestCase {
 		XCTAssertTrue(list.equal(toArray: array))
 	}
 
-
 	func testRemoveMiddle() {
 		var array = [0, 1, 2, 3]
 		var list = buildList(withNumbers: array)
diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 08474aee2..3a758981f 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -61,9 +61,6 @@ public class SegmentTree<T> {
 	}
 }
 
-
-
-
 let array = [1, 2, 3, 4]
 
 let sumSegmentTree = SegmentTree(array: array, function: +)
@@ -77,7 +74,6 @@ sumSegmentTree.replaceItem(at: 0, withItem: 2) //our array now is [2, 2, 3, 4]
 print(sumSegmentTree.query(leftBound: 0, rightBound: 0)) // 2 = 2
 print(sumSegmentTree.query(leftBound: 0, rightBound: 1)) // 2 + 2 = 4
 
-
 //you can use any associative function (i.e (a+b)+c == a+(b+c)) as function for segment tree
 func gcd(_ m: Int, _ n: Int) -> Int {
 	var a = 0
@@ -105,7 +101,6 @@ gcdSegmentTree.replaceItem(at: 3, withItem: 10) //gcdArray now is [2, 4, 6, 10,
 
 print(gcdSegmentTree.query(leftBound: 3, rightBound: 4)) // gcd(10, 5) = 5
 
-
 //example of segment tree which finds minimum on given range
 let minArray = [2, 4, 1, 5, 3]
 
@@ -118,7 +113,6 @@ minSegmentTree.replaceItem(at: 2, withItem: 10) // minArray now is [2, 4, 10, 5,
 
 print(minSegmentTree.query(leftBound: 0, rightBound: 4)) // min(2, 4, 10, 5, 3) = 2
 
-
 //type of elements in array can be any type which has some associative function
 let stringArray = ["a", "b", "c", "A", "B", "C"]
 
diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index df1bb2e32..4a2484162 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -44,7 +44,6 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   return b
 }
 
-
 let poem = [
   "there", "once", "was", "a", "man", "from", "nantucket",
   "who", "kept", "all", "of", "his", "cash", "in", "a", "bucket",
@@ -57,8 +56,6 @@ let output = select(from: poem, count: 10)
 print(output)
 output.count
 
-
-
 // Use this to verify that all input elements have the same probability
 // of being chosen. The "counts" dictionary should have a roughly equal
 // count for each input element.
diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index 2380ebb69..9f2eda4f3 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -19,8 +19,6 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   return shortestPathGraph
 }
 
-
-
 let graph = Graph()
 
 let nodeA = graph.addNode(label: "a")
diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index 4d2e59eab..cce697344 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -12,7 +12,6 @@ public func == (lhs: Edge, rhs: Edge) -> Bool {
     return lhs.neighbor == rhs.neighbor
 }
 
-
 // MARK: - Node
 
 open class Node: CustomStringConvertible, Equatable {
diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index e6d4f000d..704a94e7d 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -7,8 +7,6 @@ public func random(_ n: Int) -> Int {
   return Int(arc4random_uniform(UInt32(n)))
 }
 
-
-
 /* Fisher-Yates / Knuth shuffle */
 extension Array {
   public mutating func shuffle() {
@@ -26,8 +24,6 @@ list.shuffle()
 list.shuffle()
 list.shuffle()
 
-
-
 /* Create a new array of numbers that is already shuffled. */
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index bd4d15515..38431f5e2 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -212,7 +212,6 @@ public func reversePolishNotation(_ expression: [Token]) -> String {
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
 
-
 // Simple demo
 
 let expr = InfixExpressionBuilder()
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index cd832eef9..43173f236 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -20,10 +20,8 @@
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.
 
-
 import Foundation
 
-
 // Stack from : https://github.com/raywenderlich/swift-algorithm-club/tree/master/Stack
 public struct Stack<T> {
   fileprivate var array: [T] = []
@@ -58,7 +56,6 @@ extension Stack: Sequence {
   }
 }
 
-
 private func coinFlip() -> Bool {
   #if os(Linux)
       return random() % 2 == 0
@@ -67,7 +64,6 @@ private func coinFlip() -> Bool {
   #endif
 }
 
-
 public class DataNode<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
 
@@ -81,11 +77,10 @@ public class DataNode<Key: Comparable, Payload> {
     self.data = data
   }
 
-  public init(asHead head: Bool){}
+  public init(asHead head: Bool) {}
 
 }
 
-
 open class SkipList<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
 
@@ -95,8 +90,6 @@ open class SkipList<Key: Comparable, Payload> {
 
 }
 
-
-
 // MARK: - Search lanes for a node with a given key
 
 extension SkipList {
@@ -152,8 +145,6 @@ extension SkipList {
 
 }
 
-
-
 // MARK: - Insert a node into lanes depending on skip list status ( bootstrap base-layer if head is empty / start insertion from current head ).
 
 extension SkipList {
@@ -177,7 +168,6 @@ extension SkipList {
 
   }
 
-
   private func insertItem(key: Key, data: Payload) {
     var stack              = Stack<Node>()
     var currentNode: Node? = head
@@ -228,7 +218,6 @@ extension SkipList {
     }
   }
 
-
   func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
@@ -249,7 +238,6 @@ extension SkipList {
 
 }
 
-
 // MARK: - Remove a node with a given key. First, find its position in layers at the top, then remove it from each lane by traversing down to the base layer.
 
 extension SkipList {
@@ -278,7 +266,6 @@ extension SkipList {
   }
 }
 
-
 // MARK: - Get associated payload from a node with a given key.
 
 extension SkipList {
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index c21a77fd8..6396e8b38 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,23 +6,22 @@
 //
 //
 
-var numberList = [1,12,9,17,13,12]
+var numberList = [1, 12, 9, 17, 13, 12]
 
 public func slowsort(_ i: Int, _ j: Int) {
     if i>=j {
         return
     }
     let m = (i+j)/2
-    slowsort(i,m)
-    slowsort(m+1,j)
+    slowsort(i, m)
+    slowsort(m+1, j)
     if numberList[j] < numberList[m] {
         let temp = numberList[j]
         numberList[j] = numberList[m]
         numberList[m] = temp
     }
-    slowsort(i,j-1)
+    slowsort(i, j-1)
 }
 
-
-slowsort(0,numberList.count-1)
+slowsort(0, numberList.count-1)
 print(numberList)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 9e11cb6a1..6b9314557 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -11,7 +11,6 @@ print(B)
 B[.column, 0] = [3, 2, -1, 2]
 B[.column, 1] = [4, 1, 2, 7]
 
-
 let C = A.matrixMultiply(by: B)
 let D = A.strassenMatrixMultiply(by: B)
 let E = B.matrixMultiply(by: A)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index 324e906ee..da4b95a78 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -155,18 +155,18 @@ extension Matrix {
     var BPrep = Matrix(size: m)
 
     A.forEach { (i, j) in
-      APrep[i,j] = A[i,j]
+      APrep[i, j] = A[i, j]
     }
 
     B.forEach { (i, j) in
-      BPrep[i,j] = B[i,j]
+      BPrep[i, j] = B[i, j]
     }
 
     let CPrep = APrep.strassenR(by: BPrep)
     var C = Matrix(rows: A.rows, columns: B.columns)
     for i in 0..<A.rows {
       for j in 0..<B.columns {
-        C[i,j] = CPrep[i,j]
+        C[i, j] = CPrep[i, j]
       }
     }
 
@@ -199,14 +199,14 @@ extension Matrix {
 
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
-        a[i,j] = A[i,j]
-        b[i,j] = A[i, j+nBy2]
-        c[i,j] = A[i+nBy2, j]
-        d[i,j] = A[i+nBy2, j+nBy2]
-        e[i,j] = B[i,j]
-        f[i,j] = B[i, j+nBy2]
-        g[i,j] = B[i+nBy2, j]
-        h[i,j] = B[i+nBy2, j+nBy2]
+        a[i, j] = A[i, j]
+        b[i, j] = A[i, j+nBy2]
+        c[i, j] = A[i+nBy2, j]
+        d[i, j] = A[i+nBy2, j+nBy2]
+        e[i, j] = B[i, j]
+        f[i, j] = B[i, j+nBy2]
+        g[i, j] = B[i+nBy2, j]
+        h[i, j] = B[i+nBy2, j+nBy2]
       }
     }
 
@@ -226,10 +226,10 @@ extension Matrix {
     var C = Matrix(size: n)
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
-        C[i, j]           = c11[i,j]
-        C[i, j+nBy2]      = c12[i,j]
-        C[i+nBy2, j]      = c21[i,j]
-        C[i+nBy2, j+nBy2] = c22[i,j]
+        C[i, j]           = c11[i, j]
+        C[i, j+nBy2]      = c12[i, j]
+        C[i+nBy2, j]      = c21[i, j]
+        C[i+nBy2, j+nBy2] = c22[i, j]
       }
     }
 
diff --git a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift
index efdfd4299..7fea88d1d 100644
--- a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
@@ -17,7 +17,6 @@ class TSTNode<Element> {
     //Children
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
 
-
     init(key: Character, data: Element?) {
         self.key = key
         self.data = data
diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index 21b8f0dc3..9c4c860d8 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -8,7 +8,6 @@
 
 import Foundation
 
-
 public class TernarySearchTree<Element> {
 
     var root: TSTNode<Element>?
@@ -58,10 +57,8 @@ public class TernarySearchTree<Element> {
         }
     }
 
-
     // MARK: - Finding
 
-
     public func find(key: String) -> Element? {
         return find(node: root, withKey: key, atIndex: 0)
     }
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 0fa6d9634..761c75b6f 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -84,7 +84,6 @@ public class TernarySearchTree<Element> {
         }
     }
 
-
     // MARK: - Finding
 
     /**
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index dfbbae9ca..4a1816412 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -10,7 +10,6 @@ import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
 
-
     let testCount = 30
 
     func testCanFindStringInTree() {
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index e4b527664..ece1966e0 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,6 +1,5 @@
 //: Playground - noun: a place where people can play
 
-
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {
@@ -28,12 +27,10 @@ func check(_ tree: ThreadedBinaryTree<Int>?) {
     }
 }
 
-
 print("\nTree with Single Node")
 let emptyTree = ThreadedBinaryTree<Int>(value: 1)
 check(emptyTree)
 
-
 print("\nFull Balanced Binary Tree with 7 Nodes")
 let fullTree = ThreadedBinaryTree<Int>(value: 4)
 fullTree.insert(2)
@@ -44,7 +41,6 @@ fullTree.insert(3)
 fullTree.insert(7)
 check(fullTree)
 
-
 print("\n\nBase Binary Tree with 5 Nodes")
 let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
 check(tree)
@@ -81,5 +77,4 @@ print("\nRemove 12")
 newRoot?.remove(12)
 check(newRoot)
 
-
 print("\n\nDone with Tests!\n")
diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index d0ebe550d..8f78c388a 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -23,8 +23,6 @@ graph.addEdge(fromNode: node11, toNode: node9)
 graph.addEdge(fromNode: node11, toNode: node10)
 graph.addEdge(fromNode: node8, toNode: node9)
 
-
-
 // using depth-first search
 graph.topologicalSort()
 
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 7038e843e..d6cee2e70 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -142,7 +142,7 @@ public extension Treap {
       return newNode
     }
 
-    if case let .node(_, _, newChildP, _, _) = newChild , newChildP < nodeP {
+    if case let .node(_, _, newChildP, _, _) = newChild, newChildP < nodeP {
       return rotate(newNode)
     } else {
       return newNode
diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 77e8fd22e..d59b7eedb 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -26,9 +26,6 @@ extension TreeNode: CustomStringConvertible {
   }
 }
 
-
-
-
 let tree = TreeNode<String>(value: "beverages")
 
 let hotNode = TreeNode<String>(value: "hot")
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
index b2b4c0c5f..b2c46695b 100644
--- a/Trie/Trie/Trie/AppDelegate.swift
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -11,8 +11,6 @@ import Cocoa
 @NSApplicationMain
 class AppDelegate: NSObject, NSApplicationDelegate {
 
-
-
     func applicationDidFinishLaunching(_ aNotification: Notification) {
         // Insert code here to initialize your application
     }
@@ -21,5 +19,4 @@ class AppDelegate: NSObject, NSApplicationDelegate {
         // Insert code here to tear down your application
     }
 
-
 }
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 7ff9638d7..856384fff 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -8,7 +8,6 @@
 
 import Foundation
 
-
 /// A node in the trie
 class TrieNode<T: Hashable> {
   var value: T?
@@ -19,7 +18,6 @@ class TrieNode<T: Hashable> {
     return children.count == 0
   }
 
-
   /// Initializes a node.
   ///
   /// - Parameters:
@@ -136,7 +134,6 @@ extension Trie {
     return currentNode.isTerminating
   }
 
-
   /// Attempts to walk to the last node of a word.  The
   /// search will fail if the word is not present. Doesn't
   /// check if the node is terminating
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index e24a812cb..928b01f4c 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -22,5 +22,4 @@ class ViewController: NSViewController {
         }
     }
 
-
 }
diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 0a50d1ba6..b1f7fb4e1 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -22,18 +22,14 @@ print(dsu.inSameSet(4, and: 6))
 print(dsu.inSameSet(6, and: 8))
 print(dsu.inSameSet(8, and: 10))
 
-
 print(dsu.inSameSet(1, and: 3))
 print(dsu.inSameSet(3, and: 5))
 print(dsu.inSameSet(5, and: 7))
 print(dsu.inSameSet(7, and: 9))
 
-
 print(dsu.inSameSet(7, and: 4))
 print(dsu.inSameSet(3, and: 6))
 
-
-
 var dsuForStrings = UnionFindQuickUnion<String>()
 let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
 
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
index 33e81832d..2cd048de6 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
@@ -6,19 +6,19 @@ public struct UnionFindQuickFind<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     return parent[index]
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -26,7 +26,7 @@ public struct UnionFindQuickFind<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -39,7 +39,7 @@ public struct UnionFindQuickFind<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
index 9bff31616..2be8875eb 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
@@ -6,15 +6,15 @@ public struct UnionFindQuickUnion<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     if parent[index] == index {
       return index
@@ -23,7 +23,7 @@ public struct UnionFindQuickUnion<T: Hashable> {
       return parent[index]
     }
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -31,7 +31,7 @@ public struct UnionFindQuickUnion<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -40,7 +40,7 @@ public struct UnionFindQuickUnion<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
index c89f2a457..49a526fe3 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
@@ -6,19 +6,19 @@ public struct UnionFindWeightedQuickFind<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     return parent[index]
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -26,7 +26,7 @@ public struct UnionFindWeightedQuickFind<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -48,7 +48,7 @@ public struct UnionFindWeightedQuickFind<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
index cd33007bc..70217422f 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
@@ -4,15 +4,15 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     if parent[index] == index {
       return index
@@ -21,7 +21,7 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
       return parent[index]
     }
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -29,7 +29,7 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
       return nil
     }
   }
-  
+
   /// Weighted, by comparing set size.
   /// Merge small set into the large one.
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
@@ -45,7 +45,7 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
index 7eb8fe209..1c0bacd82 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
@@ -4,15 +4,15 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   /// Path Compression.
   private mutating func setByIndex(_ index: Int) -> Int {
     if index != parent[index] {
@@ -20,7 +20,7 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
     }
     return parent[index]
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -28,7 +28,7 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -42,7 +42,7 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index 44faf6790..b1d49eec7 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -1,6 +1,5 @@
 //: Playground - noun: a place where people can play
 
-
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
   let pattern = Array(ptrn.characters)
@@ -58,7 +57,6 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
   return zeta
 }
 
-
 extension String {
 
   func indexesOf(pattern: String) -> [Int]? {

From af2f370111a2b58bddcd6aed09d2edad1e5442ad Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Thu, 25 May 2017 22:28:45 +0200
Subject: [PATCH 1044/1679] Remove images group from workspace

---
 .../contents.xcworkspacedata                           | 10 ----------
 1 file changed, 10 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 8ba66e153..aa4529a48 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1213,16 +1213,6 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
-   <Group
-      location = "group:Images"
-      name = "Images">
-      <FileRef
-         location = "group:scheme-settings-for-travis.png">
-      </FileRef>
-      <FileRef
-         location = "group:SwiftAlgorithm-410-transp.png">
-      </FileRef>
-   </Group>
    <Group
       location = "group:Insertion Sort"
       name = "Insertion Sort">

From 5765dbf6448b15382e5c68cb1c2750c5b800a07d Mon Sep 17 00:00:00 2001
From: andmeics <396783795@qq.com>
Date: Sun, 28 May 2017 15:32:40 +0800
Subject: [PATCH 1045/1679] Remove "How to Contribute.markdown" from Workspace

Remove "How to Contribute.markdown" from Workspace,because file is not exist.
---
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index c89ac0dfe..a9c348d09 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -13,9 +13,6 @@
    <FileRef
       location = "group:Big-O Notation.markdown">
    </FileRef>
-   <FileRef
-      location = "group:How to Contribute.markdown">
-   </FileRef>
    <FileRef
       location = "group:Under Construction.markdown">
    </FileRef>

From c848c7e05c32362dc09384ee27c4f6ef1af7043f Mon Sep 17 00:00:00 2001
From: andmeics <396783795@qq.com>
Date: Sun, 28 May 2017 15:49:33 +0800
Subject: [PATCH 1046/1679] Add "CONTRIBUTING.md" file to Workspacedata

---
 .github/CONTRIBUTING.md                                   | 2 +-
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 3 +++
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index 2b08e2633..3bd5a1a91 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -54,4 +54,4 @@ For the unit tests:
 
 ## Want to chat?
 
-This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!
\ No newline at end of file
+This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index a9c348d09..d4b6645a9 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -13,6 +13,9 @@
    <FileRef
       location = "group:Big-O Notation.markdown">
    </FileRef>
+   <FileRef
+      location = "group:.github/CONTRIBUTING.md">
+   </FileRef>
    <FileRef
       location = "group:Under Construction.markdown">
    </FileRef>

From 919a5fe9a59564463720626a85938c3fdab9ecab Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 30 May 2017 16:09:04 -0700
Subject: [PATCH 1047/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 579ca0b4e..f4f10ef96 100644
--- a/README.markdown
+++ b/README.markdown
@@ -224,7 +224,7 @@ The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://
 
 It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL) and [Ross O'brien](https://www.raywenderlich.com/u/narrativium).
 
-The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](How%20to%20Contribute.markdown)? :]
+The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 
 ## License
 

From 5d378d52c6d455aae8f1c310dd6074fc7d084a7f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 31 May 2017 15:30:09 -0700
Subject: [PATCH 1048/1679] Update README.markdown

Addresses #477
---
 README.markdown | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/README.markdown b/README.markdown
index f4f10ef96..e81fe7932 100644
--- a/README.markdown
+++ b/README.markdown
@@ -93,6 +93,9 @@ Bad sorting algorithms (don't use these!):
 
 - [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
 - [Comb Sort](Comb%20Sort/). An improve upon the Bubble Sort algorithm.
+- [Convex Hull](Convex%20Hull/).
+- [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
+- [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 
 ### Mathematics
 
@@ -157,6 +160,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - Fibonacci Heap
 - [Trie](Trie/). A special type of tree used to store associative data structures.
 - [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
+- [QuadTree](QuadTree/). A tree with 4 children.
 
 ### Hashing
 

From 9bea75e527e666765a331737058317b4855953a6 Mon Sep 17 00:00:00 2001
From: Tobias Helmrich <me@tobias-helmrich.de>
Date: Sat, 3 Jun 2017 20:38:37 +0900
Subject: [PATCH 1049/1679] Fix minor typo

---
 Convex Hull/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index b73f66176..2e1fbe6a3 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -2,12 +2,12 @@
 
 There are multiple Convex Hull algorithms. This particular implementation uses the Quickhull algorithm.
 
-Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimention. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
+Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
 
 ## Quickhull
 
-The quickhull algorithm works as follows.
-The algorithm takes an input of a collection of points. These points should be ordered on their x coordinate value. We pick the two points A and B with the smallest(A) and the largest(B) x coordinate. These of course have to be part of the hull. Imagine a line from point A to point B. All points to the right of this line are grouped in an array S1. Imagine now a line from point B to point A. (this is of course the same line as before just with opposite direction) Again all points to the right of this line are grouped in an array, S2 this time.
+The quickhull algorithm works as follows:
+The algorithm takes an input of a collection of points. These points should be ordered on their x-coordinate value. We pick the two points A and B with the smallest(A) and the largest(B) x-coordinate. These of course have to be part of the hull. Imagine a line from point A to point B. All points to the right of this line are grouped in an array S1. Imagine now a line from point B to point A. (this is of course the same line as before just with opposite direction) Again all points to the right of this line are grouped in an array, S2 this time.
 We now define the following recursive function:
 
 `findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`

From 4e8614b84895240b6d7ae693ba07496a45df80de Mon Sep 17 00:00:00 2001
From: Tobias Helmrich <me@tobias-helmrich.de>
Date: Sat, 3 Jun 2017 20:51:47 +0900
Subject: [PATCH 1050/1679] Fix minor typo

---
 Selection Sampling/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index f8bd1c084..bf17d93bd 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -151,7 +151,7 @@ The random number is 0.346. The formula gives:
 	
 Just a tiny bit too high. We skip `"e"`. Only two candidates left...
 
-Note that now literally we're dealing with a toin coss: if the random number is less than 0.5 we select `"f"` and we're done. If it's greater than 0.5, we go on to the final element. Let's say we get 0.583:
+Note that now literally we're dealing with a coin toss: if the random number is less than 0.5 we select `"f"` and we're done. If it's greater than 0.5, we go on to the final element. Let's say we get 0.583:
 
 	2 * 0.583 = 1.166
 

From 519683761400c43236c29d1c39bac9cf313887da Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Sat, 3 Jun 2017 16:36:08 +0200
Subject: [PATCH 1051/1679] Incorporated reviews. changed isNullLeaf variable
 to a computed property

---
 .../RedBlackTree.playground/Contents.swift    | 14 +++-
 .../Sources/RedBlackTree.swift                | 65 +++++++++----------
 2 files changed, 43 insertions(+), 36 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
index 5b19f9bd1..50d61167d 100644
--- a/Red-Black Tree/RedBlackTree.playground/Contents.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -6,17 +6,25 @@ let redBlackTree = RedBlackTree<Double>()
 
 let randomMax = Double(0x10000000)
 var values = [Double]()
-for _ in 0..<1000 {
+for i in 0..<1000 {
   let value = Double(arc4random()) / randomMax
   values.append(value)
   redBlackTree.insert(key: value)
+  
+  if i % 100 == 0 {
+    redBlackTree.verify()
+  }
 }
 redBlackTree.verify()
 
-for _ in 0..<1000 {
+for i in 0..<1000 {
   let rand = arc4random_uniform(UInt32(values.count))
   let index = Int(rand)
   let value = values.remove(at: index)
   redBlackTree.delete(key: value)
+  
+  if i % 100 == 0 {
+    redBlackTree.verify()
+  }
 }
-redBlackTree.verify()
+redBlackTree.verify()
\ No newline at end of file
diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 351f89a9d..59633031d 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -32,17 +32,16 @@ private enum RotationDirection {
 
 // MARK: - RBNode
 
-public class RBTreeNode<Key: Comparable>: Equatable {
-  public typealias RBNode = RBTreeNode<Key>
+public class RBTreeNode<T: Comparable>: Equatable {
+  public typealias RBNode = RBTreeNode<T>
   
   fileprivate var color: RBTreeColor = .black
-  fileprivate var key: Key?
-  fileprivate var isNullLeaf = true
+  fileprivate var key: T?
   var leftChild: RBNode?
   var rightChild: RBNode?
   fileprivate weak var parent: RBNode?
   
-  public init(key: Key?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+  public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
     self.key = key
     self.leftChild = leftChild
     self.rightChild = rightChild
@@ -52,16 +51,14 @@ public class RBTreeNode<Key: Comparable>: Equatable {
     self.rightChild?.parent = self
   }
   
-  public convenience init(key: Key?) {
+  public convenience init(key: T?) {
     self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
-    self.isNullLeaf = false
   }
   
   // For initialising the nullLeaf
   public convenience init() {
     self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
     self.color = .black
-    self.isNullLeaf = true
   }
   
   var isRoot: Bool {
@@ -72,7 +69,11 @@ public class RBTreeNode<Key: Comparable>: Equatable {
     return rightChild == nil && leftChild == nil
   }
   
-  var isLeftCild: Bool {
+  var isNullLeaf: Bool {
+    return key == nil && isLeaf && color == .black
+  }
+  
+  var isLeftChild: Bool {
     return parent?.leftChild === self
   }
   
@@ -85,7 +86,7 @@ public class RBTreeNode<Key: Comparable>: Equatable {
   }
   
   var sibling: RBNode? {
-    if isLeftCild {
+    if isLeftChild {
       return parent?.rightChild
     } else {
       return parent?.leftChild
@@ -99,8 +100,8 @@ public class RBTreeNode<Key: Comparable>: Equatable {
 
 // MARK: - RedBlackTree
 
-public class RedBlackTree<Key: Comparable> {
-  public typealias RBNode = RBTreeNode<Key>
+public class RedBlackTree<T: Comparable> {
+  public typealias RBNode = RBTreeNode<T>
   
   fileprivate(set) var root: RBNode
   fileprivate(set) var size = 0
@@ -180,14 +181,14 @@ extension RedBlackTree {
   /*
    * Returns the node with the given key |input| if existing
    */
-  public func search(input: Key) -> RBNode? {
+  public func search(input: T) -> RBNode? {
     return search(key: input, node: root)
   }
   
   /*
    * Returns the node with given |key| in subtree of |node|
    */
-  fileprivate func search(key: Key, node: RBNode?) -> RBNode? {
+  fileprivate func search(key: T, node: RBNode?) -> RBNode? {
     // If node nil -> key not found
     guard let node = node else {
       return nil
@@ -215,23 +216,21 @@ extension RedBlackTree {
   /*
    * Returns the minimum key value of the whole tree
    */
-  public func minValue() -> Key? {
-    if let minNode = root.minimum() {
-       return minNode.key
-    } else {
+  public func minValue() -> T? {
+    guard let minNode = root.minimum() else {
       return nil
     }
+    return minNode.key
   }
   
   /*
    * Returns the maximum key value of the whole tree
    */
-  public func maxValue() -> Key? {
-      if let maxNode = root.maximum() {
-        return maxNode.key
-      } else {
-        return nil
+  public func maxValue() -> T? {
+    guard let maxNode = root.maximum() else {
+      return nil
     }
+    return maxNode.key
   }
 }
 
@@ -244,7 +243,7 @@ extension RedBlackTree {
    * 2. Fix red-black properties
    * Runntime: O(log n)
    */
-  public func insert(key: Key) {
+  public func insert(key: T) {
     if root.isNullLeaf {
       root = RBNode(key: key)
     } else {
@@ -332,10 +331,10 @@ extension RedBlackTree {
         else {
           var zNew = z
           // Case 2.a: z right child -> rotate
-          if parentZ.isLeftCild && z.isRightChild {
+          if parentZ.isLeftChild && z.isRightChild {
             zNew = parentZ
             leftRotate(node: zNew)
-          } else if parentZ.isRightChild && z.isLeftCild {
+          } else if parentZ.isRightChild && z.isLeftChild {
             zNew = parentZ
             rightRotate(node: zNew)
           }
@@ -343,7 +342,7 @@ extension RedBlackTree {
           zNew.parent?.color = .black
           if let grandparentZnew = zNew.grandparent {
             grandparentZnew.color = .red
-            if z.isLeftCild {
+            if z.isLeftChild {
               rightRotate(node: grandparentZnew)
             } else {
               leftRotate(node: grandparentZnew)
@@ -365,7 +364,7 @@ extension RedBlackTree {
    * 2. Fix red-black properties
    * Runntime: O(log n)
    */
-  public func delete(key: Key) {
+  public func delete(key: T) {
     if size == 1 {
       root = nullLeaf
       size -= 1
@@ -408,7 +407,7 @@ extension RedBlackTree {
       if parentY.isNullLeaf {
         root = nodeX
       } else {
-        if nodeY.isLeftCild {
+        if nodeY.isLeftChild {
           parentY.leftChild = nodeX
         } else {
           parentY.rightChild = nodeX
@@ -450,7 +449,7 @@ extension RedBlackTree {
         if let parentX = x.parent {
           parentX.color = .red
           // Rotation
-          if x.isLeftCild {
+          if x.isLeftChild {
             leftRotate(node: parentX)
           } else {
             rightRotate(node: parentX)
@@ -472,7 +471,7 @@ extension RedBlackTree {
         // We have a valid red-black-tree
       } else {
         // Case 3: a. Sibling black with one black child to the right
-        if x.isLeftCild && sibling.rightChild?.color == .black {
+        if x.isLeftChild && sibling.rightChild?.color == .black {
           // Recolor
           sibling.leftChild?.color = .black
           sibling.color = .red
@@ -501,7 +500,7 @@ extension RedBlackTree {
           sibling.color = parentX.color
           parentX.color = .black
           // a. x left and sibling with red right child
-          if x.isLeftCild {
+          if x.isLeftChild {
             sibling.rightChild?.color = .black
             // Rotate
             leftRotate(node: parentX)
@@ -581,7 +580,7 @@ extension RedBlackTree {
       if let node = nodeY {
         root = node
       }
-    } else if x.isLeftCild {
+    } else if x.isLeftChild {
       x.parent?.leftChild = nodeY
     } else if x.isRightChild {
       x.parent?.rightChild = nodeY

From ded16b8eea2a9243f8a948aaf5da806aa81cbc2b Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:47:29 -0700
Subject: [PATCH 1052/1679] implement gaurded array first

---
 Select Minimum Maximum/Maximum.swift | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index c999504fb..20c7d7c62 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -2,12 +2,9 @@
  Finds the maximum value in an array in O(n) time.
  */
 
-func maximum<T: Comparable>(_ array: [T]) -> T? {
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var maximum = array.first!
+func maximum1<T: Comparable>(_ array: [T]) -> T? {
+    guard var maximum = array.first else { return nil }
+    
     for element in array.dropFirst() {
         maximum = element > maximum ? element : maximum
     }

From 8e85522d34ce09f49430e9e7ee37465c52c2cbd2 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:48:29 -0700
Subject: [PATCH 1053/1679] Update Maximum.swift

---
 Select Minimum Maximum/Maximum.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index 20c7d7c62..82b76fd73 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -2,7 +2,7 @@
  Finds the maximum value in an array in O(n) time.
  */
 
-func maximum1<T: Comparable>(_ array: [T]) -> T? {
+func maximum<T: Comparable>(_ array: [T]) -> T? {
     guard var maximum = array.first else { return nil }
     
     for element in array.dropFirst() {

From 183815a72d83885fea57fb6fa8e316c6f43f5257 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:50:01 -0700
Subject: [PATCH 1054/1679] implement guarded array first

---
 Select Minimum Maximum/Minimum.swift | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 88a562170..891a69142 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -3,11 +3,8 @@
  */
 
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var minimum = array.first!
+    guard minimum = array.first else { return nil }
+ 
     for element in array.dropFirst() {
         minimum = element < minimum ? element : minimum
     }

From 87bde229ad8b63a1711552085ca0eb5cd6252a82 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:50:15 -0700
Subject: [PATCH 1055/1679] Update Minimum.swift

---
 Select Minimum Maximum/Minimum.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 891a69142..75ecfc3b1 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -3,7 +3,7 @@
  */
 
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    guard minimum = array.first else { return nil }
+    guard var minimum = array.first else { return nil }
  
     for element in array.dropFirst() {
         minimum = element < minimum ? element : minimum

From 5aef7034c482327a1a4c3a02e0474609ed6ffb2f Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:54:36 -0700
Subject: [PATCH 1056/1679] implement guarded array.first

---
 Select Minimum Maximum/MinimumMaximumPairs.swift | 11 +++--------
 1 file changed, 3 insertions(+), 8 deletions(-)

diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index 2c7b5bb5f..a19b037d1 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -3,16 +3,11 @@
  */
 
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var minimum = array.first!
-    var maximum = array.first!
+    guard var minimum = array.first else { return nil }
+    var maximum = minimum
 
     // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
-    let hasOddNumberOfItems = array.count % 2 != 0
-    let start = hasOddNumberOfItems ? 1 : 0
+    let start = array.count % 2 // 1 if odd, skipping the first element
     for i in stride(from: start, to: array.count, by: 2) {
         let pair = (array[i], array[i+1])
 

From a76ac65096e664e44a53c5c3fff6e11eca314ed1 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:58:10 -0700
Subject: [PATCH 1057/1679] implement guarded array first

---
 Select Minimum Maximum/README.markdown | 17 ++++++-----------
 1 file changed, 6 insertions(+), 11 deletions(-)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index 3c29b5764..c55272c63 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -24,11 +24,10 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-  guard !array.isEmpty else {
+  guard var minimum = array.first else {
     return nil
   }
 
-  var minimum = array.first!
   for element in array.dropFirst() {
     minimum = element < minimum ? element : minimum
   }
@@ -36,11 +35,10 @@ func minimum<T: Comparable>(_ array: [T]) -> T? {
 }
 
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-  guard !array.isEmpty else {
+  guard var maximum = array.first else {
     return nil
   }
 
-  var maximum = array.first!
   for element in array.dropFirst() {
     maximum = element > maximum ? element : maximum
   }
@@ -66,7 +64,7 @@ array.minElement()   // This will return 3
 array.maxElement()   // This will return 9
 ```
 
-```
+```swift
 let array = [ 8, 3, 9, 4, 6 ]
 //swift3
 array.min()   // This will return 3
@@ -97,16 +95,13 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-  guard !array.isEmpty else {
+  guard var minimum = array.first else {
     return nil
   }
-
-  var minimum = array.first!
-  var maximum = array.first!
+  var maximum = minimum
 
   // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
-  let hasOddNumberOfItems = array.count % 2 != 0
-  let start = hasOddNumberOfItems ? 1 : 0
+  let start = array.count % 2 // 1 if odd, skipping the first element
   for i in stride(from: start, to: array.count, by: 2) {
     let pair = (array[i], array[i+1])
 

From b2b88c03bd3944ef01d71ddc31bff9ae603e2bf7 Mon Sep 17 00:00:00 2001
From: Hassan Ahmed Khan <hassandotahmed@gmail.com>
Date: Fri, 9 Jun 2017 11:20:45 +0500
Subject: [PATCH 1058/1679] Divide and Conquer

Added description for Divide and Conquer section.
---
 Algorithm Design.markdown | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/Algorithm Design.markdown b/Algorithm Design.markdown
index 23f8ad70e..5d89cb05a 100644
--- a/Algorithm Design.markdown	
+++ b/Algorithm Design.markdown	
@@ -18,6 +18,13 @@ And if you only work with small datasets, then a brute force approach may actual
 
 ### Divide and conquer
 
-A big problem is often just a whole bunch of much smaller problems.
+>"When you change the way you look at things, the things you look at change."</br>
+>Max Planck, Quantum theorist and Nobel Prize Winner
 
-[More to come here]
+Divide and conquer is a way of dealing with a large problem by breaking it down into bits and pieces and working your way up towards the solution.
+
+Instead of seeing the whole problem as a single, huge and complex task you divide the problem in relatively smaller problems that are easier to understand and deal with.
+
+You solve smaller problems and aggregate the solution until you are left with the solution only. At each step the problem at hand shrinks and the solution gets mature until you have the final correct solution.
+
+Solving the smaller task and applying the same solution repetitively ( or often times recursively) to other chunks give you the result in less time.

From 1bc6990fe584080dcca0249bdb05d8a7c56907cd Mon Sep 17 00:00:00 2001
From: Darragh <Darraghk500@yahoo.ie>
Date: Sat, 10 Jun 2017 15:49:46 +0100
Subject: [PATCH 1059/1679] Create ShellSortExample.swift

Inner while loop was slightly incorrect - for example try array [64, 20, 50, 33, 72, 10, 23, -1, 4,-2,-3] with previous version.
---
 Shell Sort/ShellSortExample.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index e9cee7543..df0842770 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -22,7 +22,7 @@ public func shellSort(_ list : inout [Int]) {
 
             guard sublistCount == 1 && index > 0 else { continue }
 
-            while list[index - 1] > list[index] && index - 1 > 0 {
+            while index > 0 && list[index - 1] > list[index] {
                 swap(&list[index - 1], &list[index])
                 index -= 1
             }

From 5428e53eee961acc2d2dc7c0af0d6ef6a431f6e1 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman448@gmail.com>
Date: Mon, 12 Jun 2017 05:29:06 +0300
Subject: [PATCH 1060/1679] Language fixes

---
 Dijkstra Algorithm/README.md | 114 +++++++++++++++++------------------
 1 file changed, 57 insertions(+), 57 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 7afc34094..5f8a0ce07 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,11 +1,11 @@
-# Weighted graph general cocepts
+# Weighted graph general concepts
 
 Every weighted graph should contain: 
 1. Vertices/Nodes (I will use "vertex" in this readme).
 
 <img src="Images/Vertices.png" height="250" />
 
-2. Edges connecting vertices. Let's add some edges to our graph. For simplicity let's create directed graph for now. Directed means, that edge have a direction, i.e. vertex, where it starts and vertex, where it ends. But remember VERY IMPORTANT thing:
+2. Edges connecting vertices. Let's add some edges to our graph. For simplicity let's create directed graph for now. Directed means that edge has a direction, i.e. vertex, where it starts and vertex, where it ends. But remember a VERY IMPORTANT thing:
     * All undirected graphs can be viewed as a directed graph.
     * A directed graph is undirected if and only if every edge is paired with an edge going in the opposite direction.
 
@@ -24,30 +24,30 @@ Undirected weighted graph:
 
 <img src="Images/WeightedUndirectedGraph.png" height="250" />
 
-And once again: An undireceted graph - it is a directed graph with every edge paired with an edge going in the opposite direction. This statement is clear on the image above.
+And once again: An undirected graph it is a directed graph with every edge paired with an edge going in the opposite direction. This statement is clear on the image above.
 
 Great! Now we are familiar with general concepts about graphs.
 
-# Dijkstra's algorithm
+# The Dijkstra's algorithm
 This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra.
 
-It can be used, when you have one source vertex and want to find the shortest paths to ALL other vertices in the graph.
+It can be used when you have one source vertex and want to find the shortest paths to ALL other vertices in the graph.
 
-The best example is road network. If you wnat to find the shortest path from your house to your job, or if you want to find the closest store to your house, then it is time for the Dijkstra's algorithm.
+The best example is a road network. If you want to find the shortest path from your house to your job or if you want to find the closest store to your house then it is time for the Dijkstra's algorithm.
 
 The algorithm repeats following cycle until all vertices are marked as visited.
 Cycle:
-1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value then algorithm picks any of them)
 2. The algorithm marks picked vertex as visited.
-3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+3. The algorithm checks all of its neighbours. If the current vertex path length from the start plus an edge weight to a neighbour less than the neighbour current path length from the start than it assigns new path length from the start to the neighbour.
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
 I have created **VisualizedDijkstra.playground** game/tutorial to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
 ## Example 
-Let's imagine, you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have graph, that connects your house with all these stores. So, you know what to do :)
+Let's imagine that you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have a graph that connects your house with all these stores. So, you know what to do :)
 
-### Initialization
+### Initialisation
 
 When the algorithm starts to work initial graph looks like this:
 
@@ -61,13 +61,13 @@ The table below represents graph state:
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
->inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one.
+>inf is equal infinity which basically means that algorithm doesn't know how far away is this vertex from start one.
 
 >F states for False
 
 >T states for True
 
-To initialize our graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices from start.
+To initialize our graph we have to set source vertex path length from source vertex to 0 and append itself to path vertices from start.
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -75,11 +75,11 @@ To initialize our graph we have to set source vertex path length from source ver
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm, let's start!
+Great, now our graph is initialised and we can pass it to the Dijkstra's algorithm, let's start!
 
-Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
-All our vertices are not visited, but there is only one has the smallest path length from start - A. This vertex is the first one, which neighbors we will check.
-First of all, set this vertex as visited 
+Let's follow the algorithm's cycle and pick the first vertex which neighbours we want to check.
+All our vertices are not visited but there is only one has the smallest path length from start. It is A. This vertex is the first one which neighbors we will check.
+First of all, set this vertex as visited.
 
 A.visited = true
 
@@ -95,8 +95,8 @@ After this step graph has this state:
 
 ### Step 1
 
-Then we check all of its neighbors. 
-If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+Then we check all of its neighbours. 
+If checking vertex path length from start + edge weight is smaller than neighbour's path length from start then we set neighbour's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
 
 for clarity:
 ```swift
@@ -162,25 +162,25 @@ From now we repeat all actions again and fill our table with new info!
 
 
 ## Code implementation 
-First of all, lets create class, that will describe any Vertex in the graph.
+First of all, let’s create class that will describe any Vertex in the graph.
 It is pretty simple
 ```swift
 open class Vertex {
 
-    //Every vertex should be unique, that's why we set up identifier
+    //Every vertex should be unique that's why we set up identifier
     open var identifier: String
 	
-    //For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
-    //when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-    //Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
-    open var neighbors: [(Vertex, Double)] = []
+    //For Dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some usecases 
+    //when you firstly initialize all vertices without neighbours. And then on next iteration you set up their neighbours. So, initially neighbours is an empty array.
+    //Array contains tuples (Vertex, Double). Vertex is a neighbour and Double is as edge weight to that neighbour.
+    open var neighbours: [(Vertex, Double)] = []
 	
-    //As it was mentioned in algorithm description, default path length from start for all vertices should be as much as possible.
-    //It is var, because we will update it during algorithm execution.
+    //As it was mentioned in the algorithm description, default path length from start for all vertices should be as much as possible.
+    //It is var because we will update it during the algorithm execution.
     open var pathLengthFromStart = Double.infinity
 
-    //This array containt vertices, which we need to go through to reach this vertex from starting one
-    //As with path length from start, we will change this array during algorithm execution.
+    //This array contains vertices which we need to go through to reach this vertex from starting one
+    //As with path length from start, we will change this array during the algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
@@ -188,7 +188,7 @@ open class Vertex {
     }
 
     //This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-    //When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+    //When we will need to set new starting vertex and recalculate paths then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -196,7 +196,7 @@ open class Vertex {
 }
 ```
 
-Because every vertex should be unique it is usefull to make them Hashable and according Equatable. We use identifier for this purposes.
+As every vertex should be unique it is useful to make them Hashable and according Equatable. We use an identifier for this purposes.
 ```swift
 extension Vertex: Hashable {
     open var hashValue: Int {
@@ -212,11 +212,11 @@ extension Vertex: Equatable {
 ```
 
 We've created a base for our algorithm. Now let's create a house :)
-Dijkstra's realization is really straightforward.
+Dijkstra's realisation is really straightforward.
 ```swift
 public class Dijkstra {
     //This is a storage for vertices in the graph. 
-    //Assuming, that our vertices are unique, we can use Set instead of array. This approach will bring some benefits later.
+    //Assuming that our vertices are unique we can use Set instead of array. This approach will bring some benefits later.
     private var totalVertices: Set<Vertex>
 
     public init(vertices: Set<Vertex>) {
@@ -230,52 +230,52 @@ public class Dijkstra {
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-	//Before we start searching shortes path from startVertex, 
-	//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+	//Before we start searching the shortest path from startVertex, 
+	//we need to clear vertices cache just to be sure that out graph is clean.
 	//Remember that every Vertex is a class and classes are passed by reference. 
-	//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
+	//So whenever you change vertex outside of this class it will affect this vertex inside totalVertices Set
         clearCache()
-	//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
+	//Now all our vertices have Double.infinity pathLengthFromStart and an empty pathVerticesFromStart array.
 		
 	//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
 		
 	//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
-	//For this purpose we define currentVertex variable, which we will change in the end of each while cycle.
+	//For this purpose we define currentVertex variable which we will change in the end of each while cycle.
         var currentVertex: Vertex? = startVertex
 		
         while let vertex = currentVertex {
     			
-    	    //Nex line of code is an implementation of setting vertex as visited.
+    	    //Next line of code is an implementation of setting vertex as visited.
     	    //As it has been said, we should check only unvisited vertices in the graph,
 	    //So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
             totalVertices.remove(vertex)
 			
-	    //filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
-            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
+	    //filteredNeighbours is an array that contains current vertex neighbours which aren't yet visited
+            let filteredNeighbours = vertex.neighbours.filter { totalVertices.contains($0.0) }
 			
 	    //Let's iterate through them
-            for neighbor in filteredNeighbors {
-		//These variable are more representative, than neighbor.0 or neighbor.1
-                let neighborVertex = neighbor.0
-                let weight = neighbor.1
+            for neighbour in filteredNeighbours {
+		//These variable are more representative, than neighbour.0 or neighbour.1
+                let neighbourVertex = neighbour.0
+                let weight = neighbour.1
 				
-		//Here we calculate new weight, that we can offer to neighbor. 
+		//Here we calculate new weight, that we can offer to neighbour. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-		//If it is smaller than neighbor's current pathLengthFromStart
+		//If it is smaller than neighbour's current pathLengthFromStart
 		//Then we perform this code
-                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+                if theoreticNewWeight < neighbourVertex.pathLengthFromStart {
 					
 		    //set new pathLengthFromStart
-                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+                    neighbourVertex.pathLengthFromStart = theoreticNewWeight
 					
 		    //set new pathVerticesFromStart
-                    neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
+                    neighbourVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-		    //append current vertex to neighbor's pathVerticesFromStart
-                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+		    //append current vertex to neighbour's pathVerticesFromStart
+                    neighbourVertex.pathVerticesFromStart.append(neighbourVertex)
                 }
             }
 			
@@ -294,17 +294,17 @@ public class Dijkstra {
 }
 ```
 
-That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating random graph.
+That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating a random graph.
 
-Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm's flow in real (slowed :)) time.
+Also there is a **VisualizedDijkstra.playground**. Use it to figure out the algorithm's flow in real (slowed :)) time.
 
-It is up to you how to implement some specific parts of algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
+It is up to you how to implement some specific parts of the algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
 
 # About this repository
 
-This repository contains to playgrounds:
-* To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
-* If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
+This repository contains two playgrounds:
+* To understand how does this algorithm works, I created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover, there are play/pause/stop buttons.
+* If you need only realisation of the algorithm without visualisation then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
 # Demo video
 

From 8c34127f87850c2e1b378310c5a9c0a3a69c10f4 Mon Sep 17 00:00:00 2001
From: Ravi <imrvshah@gmail.com>
Date: Wed, 21 Jun 2017 21:27:51 -0500
Subject: [PATCH 1061/1679] Updated project settings to Swift4

---
 Graph/Graph.xcodeproj/project.pbxproj         | 22 +++++++++++++++----
 .../xcshareddata/xcschemes/Graph.xcscheme     |  2 +-
 .../xcschemes/GraphTests.xcscheme             |  2 +-
 3 files changed, 20 insertions(+), 6 deletions(-)

diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index ba07c3c26..4822d80bb 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -158,12 +158,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					49BFA2FC1CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 0900;
 					};
 					49BFA3061CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
@@ -247,14 +247,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -297,14 +303,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -349,7 +361,8 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -370,7 +383,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.Graph";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index c4750d846..a12d85dad 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index 42c83c5ad..28df1be50 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From b9ef916383a476f053fdc88fb2c86d04a6d7a2c8 Mon Sep 17 00:00:00 2001
From: Ravi <imrvshah@gmail.com>
Date: Wed, 21 Jun 2017 21:31:47 -0500
Subject: [PATCH 1062/1679] Fixed some warnings related to Redundant
 conformance

---
 Graph/Graph/AdjacencyListGraph.swift   | 4 ++--
 Graph/Graph/AdjacencyMatrixGraph.swift | 2 +-
 Graph/Graph/Edge.swift                 | 2 +-
 Graph/Graph/Graph.swift                | 2 +-
 Graph/Graph/Vertex.swift               | 4 ++--
 5 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 4a84129df..a24e732e7 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-private class EdgeList<T> where T: Equatable, T: Hashable {
+private class EdgeList<T> where T: Hashable {
 
   var vertex: Vertex<T>
   var edges: [Edge<T>]?
@@ -22,7 +22,7 @@ private class EdgeList<T> where T: Equatable, T: Hashable {
 
 }
 
-open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashable {
+open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Hashable {
 
   fileprivate var adjacencyList: [EdgeList<T>] = []
 
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index 1b12790d8..4d3ae9731 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashable {
+open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Hashable {
 
   // If adjacencyMatrix[i][j] is not nil, then there is an edge from
   // vertex i to vertex j.
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 28ef91834..ac5ed6a25 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public struct Edge<T>: Equatable where T: Equatable, T: Hashable {
+public struct Edge<T>: Equatable where T: Hashable {
 
   public let from: Vertex<T>
   public let to: Vertex<T>
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
index 13d6802b9..ddae4eddd 100644
--- a/Graph/Graph/Graph.swift
+++ b/Graph/Graph/Graph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-open class AbstractGraph<T>: CustomStringConvertible where T: Equatable, T: Hashable {
+open class AbstractGraph<T>: CustomStringConvertible where T: Hashable {
 
   public required init() {}
 
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 42a7dad7b..758a367bb 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public struct Vertex<T>: Equatable where T: Equatable, T: Hashable {
+public struct Vertex<T>: Equatable where T: Hashable {
 
   public var data: T
   public let index: Int
@@ -30,7 +30,7 @@ extension Vertex: Hashable {
 
 }
 
-public func ==<T: Equatable>(lhs: Vertex<T>, rhs: Vertex<T>) -> Bool {
+public func ==<T>(lhs: Vertex<T>, rhs: Vertex<T>) -> Bool {
   guard lhs.index == rhs.index else {
     return false
   }

From 89b337def3b3af1dea8a5d6223346dade373bb94 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 24 Jun 2017 09:06:34 -0700
Subject: [PATCH 1063/1679] Ordered Set - Apple Version

https://developer.apple.com/documentation/foundation/nsmutableorderedset

In this repo, the ordered set is actually not the right apple library ordered set. So, I write the one exactly the same as Apple one.
---
 .../AppleOrderedSet.playground/Contents.swift | 13 ++++
 .../Sources/AppleOrderedSet.swift             | 72 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 Ordered Set/AppleOrderedSet.swift             | 72 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  6 ++
 5 files changed, 167 insertions(+)
 create mode 100644 Ordered Set/AppleOrderedSet.playground/Contents.swift
 create mode 100644 Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
 create mode 100644 Ordered Set/AppleOrderedSet.playground/contents.xcplayground
 create mode 100644 Ordered Set/AppleOrderedSet.swift

diff --git a/Ordered Set/AppleOrderedSet.playground/Contents.swift b/Ordered Set/AppleOrderedSet.playground/Contents.swift
new file mode 100644
index 000000000..4388c664b
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.playground/Contents.swift	
@@ -0,0 +1,13 @@
+let s = AppleOrderedSet<Int>()
+
+s.add(1)
+s.add(2)
+s.add(-1)
+s.add(0)
+s.insert(4, at: 3)
+
+s.set(-1, at: 0)
+s.remove(-1)
+
+print(s.object(at: 1))
+
diff --git a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
new file mode 100644
index 000000000..3ff19cb8d
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
@@ -0,0 +1,72 @@
+public class AppleOrderedSet<T: Hashable> {
+    private var objects: [T] = []
+    private var indexOfKey: [T: Int] = [:]
+    
+    public init() {}
+    
+    // O(1)
+    public func add(_ object: T) {
+        guard indexOfKey[object] == nil else {
+            return
+        }
+        
+        objects.append(object)
+        indexOfKey[object] = objects.count - 1
+    }
+    
+    // O(n)
+    public func insert(_ object: T, at index: Int) {
+        assert(index < objects.count, "Index should be smaller than object count")
+        assert(index >= 0, "Index should be bigger than 0")
+        
+        guard indexOfKey[object] == nil else {
+            return
+        }
+        
+        objects.insert(object, at: index)
+        indexOfKey[object] = index
+        for i in index+1..<objects.count {
+            indexOfKey[objects[i]] = i
+        }
+    }
+    
+    // O(1)
+    public func object(at index: Int) -> T {
+        assert(index < objects.count, "Index should be smaller than object count")
+        assert(index >= 0, "Index should be bigger than 0")
+        
+        return objects[index]
+    }
+    
+    // O(1)
+    public func set(_ object: T, at index: Int) {
+        assert(index < objects.count, "Index should be smaller than object count")
+        assert(index >= 0, "Index should be bigger than 0")
+        
+        guard indexOfKey[object] == nil else {
+            return
+        }
+        
+        indexOfKey.removeValue(forKey: objects[index])
+        indexOfKey[object] = index
+        objects[index] = object
+    }
+    
+    // O(1)
+    public func indexOf(_ object: T) -> Int {
+        return indexOfKey[object] ?? -1
+    }
+    
+    // O(n)
+    public func remove(_ object: T) {
+        guard let index = indexOfKey[object] else {
+            return
+        }
+        
+        indexOfKey.removeValue(forKey: object)
+        objects.remove(at: index)
+        for i in index..<objects.count {
+            indexOfKey[objects[i]] = i
+        }
+    }
+}
diff --git a/Ordered Set/AppleOrderedSet.playground/contents.xcplayground b/Ordered Set/AppleOrderedSet.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Ordered Set/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.swift
new file mode 100644
index 000000000..3ff19cb8d
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.swift	
@@ -0,0 +1,72 @@
+public class AppleOrderedSet<T: Hashable> {
+    private var objects: [T] = []
+    private var indexOfKey: [T: Int] = [:]
+    
+    public init() {}
+    
+    // O(1)
+    public func add(_ object: T) {
+        guard indexOfKey[object] == nil else {
+            return
+        }
+        
+        objects.append(object)
+        indexOfKey[object] = objects.count - 1
+    }
+    
+    // O(n)
+    public func insert(_ object: T, at index: Int) {
+        assert(index < objects.count, "Index should be smaller than object count")
+        assert(index >= 0, "Index should be bigger than 0")
+        
+        guard indexOfKey[object] == nil else {
+            return
+        }
+        
+        objects.insert(object, at: index)
+        indexOfKey[object] = index
+        for i in index+1..<objects.count {
+            indexOfKey[objects[i]] = i
+        }
+    }
+    
+    // O(1)
+    public func object(at index: Int) -> T {
+        assert(index < objects.count, "Index should be smaller than object count")
+        assert(index >= 0, "Index should be bigger than 0")
+        
+        return objects[index]
+    }
+    
+    // O(1)
+    public func set(_ object: T, at index: Int) {
+        assert(index < objects.count, "Index should be smaller than object count")
+        assert(index >= 0, "Index should be bigger than 0")
+        
+        guard indexOfKey[object] == nil else {
+            return
+        }
+        
+        indexOfKey.removeValue(forKey: objects[index])
+        indexOfKey[object] = index
+        objects[index] = object
+    }
+    
+    // O(1)
+    public func indexOf(_ object: T) -> Int {
+        return indexOfKey[object] ?? -1
+    }
+    
+    // O(n)
+    public func remove(_ object: T) {
+        guard let index = indexOfKey[object] else {
+            return
+        }
+        
+        indexOfKey.removeValue(forKey: object)
+        objects.remove(at: index)
+        for i in index..<objects.count {
+            indexOfKey[objects[i]] = i
+        }
+    }
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ebc2fb33b..59852e045 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1645,6 +1645,12 @@
       <FileRef
          location = "group:OrderedSet.swift">
       </FileRef>
+      <FileRef
+         location = "group:AppleOrderedSet.swift">
+      </FileRef>
+      <FileRef
+         location = "group:AppleOrderedSet.playground">
+      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From 88e76dbb4e8fab288c683fc74505ab7c5b39f436 Mon Sep 17 00:00:00 2001
From: Brian Young <bdy-github@hiddentower.com>
Date: Sun, 9 Jul 2017 22:32:11 -0700
Subject: [PATCH 1064/1679] Add links to SortedArray Type

---
 Ordered Array/README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index 974a42cae..c40e5eff5 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -110,4 +110,6 @@ The big difference with a regular binary search is that this doesn't return `nil
 
 Note that using binary search doesn't change the worst-case running time complexity of `insert()`. The binary search itself takes only **O(log n)** time, but inserting a new object in the middle of an array still involves shifting all remaining elements in memory. So overall, the time complexity is still **O(n)**. But in practice this new version definitely is a lot faster, especially on large arrays.
 
+A more complete and production ready [SortedArray](https://github.com/ole/SortedArray) is avalible from [Ole Begemann](https://github.com/ole). The [accompanying article](https://oleb.net/blog/2017/02/sorted-array/) explains to advantages and tradeoffs.
+
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 6ee39fea58b47e0797401f81ee86c099bfc6fe57 Mon Sep 17 00:00:00 2001
From: Brian Young <bdy-github@hiddentower.com>
Date: Sun, 9 Jul 2017 22:33:19 -0700
Subject: [PATCH 1065/1679] typo fix

---
 Ordered Array/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index c40e5eff5..42c9880a3 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -110,6 +110,6 @@ The big difference with a regular binary search is that this doesn't return `nil
 
 Note that using binary search doesn't change the worst-case running time complexity of `insert()`. The binary search itself takes only **O(log n)** time, but inserting a new object in the middle of an array still involves shifting all remaining elements in memory. So overall, the time complexity is still **O(n)**. But in practice this new version definitely is a lot faster, especially on large arrays.
 
-A more complete and production ready [SortedArray](https://github.com/ole/SortedArray) is avalible from [Ole Begemann](https://github.com/ole). The [accompanying article](https://oleb.net/blog/2017/02/sorted-array/) explains to advantages and tradeoffs.
+A more complete and production ready [SortedArray](https://github.com/ole/SortedArray) is avalible from [Ole Begemann](https://github.com/ole). The [accompanying article](https://oleb.net/blog/2017/02/sorted-array/) explains the advantages and tradeoffs.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From df1440e2a74d37d7674efbd83c68fbcf9b680b95 Mon Sep 17 00:00:00 2001
From: Mayur <jhonmathews@gmail.com>
Date: Fri, 14 Jul 2017 11:39:18 +0530
Subject: [PATCH 1066/1679] Updated README for clarity

There was a typo in the line that has been changed. The sentence itself has been altered slightly to accommodate the fix for the typo and maintain clarity.
---
 Hash Table/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 8f1eaaf70..9c4065a51 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -103,7 +103,7 @@ it first hashes the key `"lastName"` to calculate the array index, which is 3. S
 
 Common ways to implement this chaining mechanism are to use a linked list or another array. Since the order of the items in the chain does not matter, you can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-Chains should not become long because the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
+Chains should not become long because looking up items in the hash table would become a slow process. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
 
 > **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. This approach has its own upsides and downsides.
 

From 4fc84eeecfc2238791e338dd8537745b39656791 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-MacBook-Pro.local>
Date: Sat, 15 Jul 2017 17:34:25 -0700
Subject: [PATCH 1067/1679] Adds reference to the Apple version of the ordered
 set.

---
 Ordered Set/README.markdown | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 1c0d5a8ac..bc5003a61 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -329,4 +329,9 @@ The right side did not contain the item, so we look at the left side:
 
 Finally, we've found `Player 2`, and return index 3.
 
+## See Also
+
+[Apple Ordered Set](AppleOrderedSet.playground)
+@remlostime added an Apple version of `OrderedSet`
+
 *Written By Zain Humayun*

From 5616f825c10be7bc0b81b538e7679fafab5d0f4f Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 17 Jul 2017 09:14:40 -0700
Subject: [PATCH 1068/1679] LRU Cache

Implement a simple LRU Cache algorithm.
---
 LRU Cache/LRUCache.playground/Contents.swift  |  10 +
 .../Sources/LRUCache.swift                    |  59 +++++
 .../Sources/LinkedList.swift                  | 246 ++++++++++++++++++
 .../LRUCache.playground/contents.xcplayground |   4 +
 LRU Cache/LRUCache.swift                      |  59 +++++
 LRU Cache/Readme.md                           |  50 ++++
 .../contents.xcworkspacedata                  |  13 +
 7 files changed, 441 insertions(+)
 create mode 100644 LRU Cache/LRUCache.playground/Contents.swift
 create mode 100644 LRU Cache/LRUCache.playground/Sources/LRUCache.swift
 create mode 100755 LRU Cache/LRUCache.playground/Sources/LinkedList.swift
 create mode 100644 LRU Cache/LRUCache.playground/contents.xcplayground
 create mode 100644 LRU Cache/LRUCache.swift
 create mode 100644 LRU Cache/Readme.md

diff --git a/LRU Cache/LRUCache.playground/Contents.swift b/LRU Cache/LRUCache.playground/Contents.swift
new file mode 100644
index 000000000..35dcc5d59
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/Contents.swift	
@@ -0,0 +1,10 @@
+let cache = LRUCache<String>(2)
+cache.set("a", val: 1)
+cache.set("b", val: 2)
+cache.get("a") // returns 1
+cache.set("c", val: 3) // evicts key "b"
+cache.get("b") // returns nil (not found)
+cache.set("d", val: 4) // evicts key "a"
+cache.get("a") // returns nil (not found)
+cache.get("c") // returns 3
+cache.get("d") // returns 4
diff --git a/LRU Cache/LRUCache.playground/Sources/LRUCache.swift b/LRU Cache/LRUCache.playground/Sources/LRUCache.swift
new file mode 100644
index 000000000..3b9ca1139
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/Sources/LRUCache.swift	
@@ -0,0 +1,59 @@
+//
+//  LRUCache.swift
+//  
+//
+//  Created by Kai Chen on 16/07/2017.
+//
+//
+
+import Foundation
+
+public class LRUCache<KeyType: Hashable> {
+    private let maxSize: Int
+    private var cache: [KeyType: Any] = [:]
+    private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+    private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+
+    public init(_ maxSize: Int) {
+        self.maxSize = maxSize
+    }
+
+    public func get(_ key: KeyType) -> Any? {
+        guard let val = cache[key] else {
+            return nil
+        }
+
+        remove(key)
+        insert(key, val: val)
+
+        return val
+    }
+
+    public func set(_ key: KeyType, val: Any) {
+        if cache[key] != nil {
+            remove(key)
+        } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
+            remove(keyToRemove)
+        }
+
+        insert(key, val: val)
+    }
+
+    private func remove(_ key: KeyType) {
+        cache.removeValue(forKey: key)
+        guard let node = key2node[key] else {
+            return
+        }
+        priority.remove(node: node)
+        key2node.removeValue(forKey: key)
+    }
+
+    private func insert(_ key: KeyType, val: Any) {
+        cache[key] = val
+        priority.insert(key, atIndex: 0)
+        guard let first = priority.first else {
+            return
+        }
+        key2node[key] = first
+    }
+}
diff --git a/LRU Cache/LRUCache.playground/Sources/LinkedList.swift b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift
new file mode 100755
index 000000000..94e978c07
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift	
@@ -0,0 +1,246 @@
+public final class LinkedList<T> {
+
+    public class LinkedListNode<T> {
+        var value: T
+        var next: LinkedListNode?
+        weak var previous: LinkedListNode?
+
+        public init(value: T) {
+            self.value = value
+        }
+    }
+
+    public typealias Node = LinkedListNode<T>
+
+    fileprivate var head: Node?
+
+    public init() {}
+
+    public var isEmpty: Bool {
+        return head == nil
+    }
+
+    public var first: Node? {
+        return head
+    }
+
+    public var last: Node? {
+        if var node = head {
+            while case let next? = node.next {
+                node = next
+            }
+            return node
+        } else {
+            return nil
+        }
+    }
+
+    public var count: Int {
+        if var node = head {
+            var c = 1
+            while case let next? = node.next {
+                node = next
+                c += 1
+            }
+            return c
+        } else {
+            return 0
+        }
+    }
+
+    public func node(atIndex index: Int) -> Node? {
+        if index >= 0 {
+            var node = head
+            var i = index
+            while node != nil {
+                if i == 0 { return node }
+                i -= 1
+                node = node!.next
+            }
+        }
+        return nil
+    }
+
+    public subscript(index: Int) -> T {
+        let node = self.node(atIndex: index)
+        assert(node != nil)
+        return node!.value
+    }
+
+    public func append(_ value: T) {
+        let newNode = Node(value: value)
+        self.append(newNode)
+    }
+
+    public func append(_ node: Node) {
+        let newNode = LinkedListNode(value: node.value)
+        if let lastNode = last {
+            newNode.previous = lastNode
+            lastNode.next = newNode
+        } else {
+            head = newNode
+        }
+    }
+
+    public func append(_ list: LinkedList) {
+        var nodeToCopy = list.head
+        while let node = nodeToCopy {
+            self.append(node.value)
+            nodeToCopy = node.next
+        }
+    }
+
+    private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
+        assert(index >= 0)
+
+        var i = index
+        var next = head
+        var prev: Node?
+
+        while next != nil && i > 0 {
+            i -= 1
+            prev = next
+            next = next!.next
+        }
+        assert(i == 0)  // if > 0, then specified index was too large
+
+        return (prev, next)
+    }
+
+    public func insert(_ value: T, atIndex index: Int) {
+        let newNode = Node(value: value)
+        self.insert(newNode, atIndex: index)
+    }
+
+    public func insert(_ node: Node, atIndex index: Int) {
+        let (prev, next) = nodesBeforeAndAfter(index: index)
+        let newNode = LinkedListNode(value: node.value)
+        newNode.previous = prev
+        newNode.next = next
+        prev?.next = newNode
+        next?.previous = newNode
+
+        if prev == nil {
+            head = newNode
+        }
+    }
+
+    public func insert(_ list: LinkedList, atIndex index: Int) {
+        if list.isEmpty { return }
+        var (prev, next) = nodesBeforeAndAfter(index: index)
+        var nodeToCopy = list.head
+        var newNode: Node?
+        while let node = nodeToCopy {
+            newNode = Node(value: node.value)
+            newNode?.previous = prev
+            if let previous = prev {
+                previous.next = newNode
+            } else {
+                self.head = newNode
+            }
+            nodeToCopy = nodeToCopy?.next
+            prev = newNode
+        }
+        prev?.next = next
+        next?.previous = prev
+    }
+
+    public func removeAll() {
+        head = nil
+    }
+
+    @discardableResult public func remove(node: Node) -> T {
+        let prev = node.previous
+        let next = node.next
+
+        if let prev = prev {
+            prev.next = next
+        } else {
+            head = next
+        }
+        next?.previous = prev
+
+        node.previous = nil
+        node.next = nil
+        return node.value
+    }
+
+    @discardableResult public func removeLast() -> T {
+        assert(!isEmpty)
+        return remove(node: last!)
+    }
+
+    @discardableResult public func remove(atIndex index: Int) -> T {
+        let node = self.node(atIndex: index)
+        assert(node != nil)
+        return remove(node: node!)
+    }
+}
+
+extension LinkedList: CustomStringConvertible {
+    public var description: String {
+        var s = "["
+        var node = head
+        while node != nil {
+            s += "\(node!.value)"
+            node = node!.next
+            if node != nil { s += ", " }
+        }
+        return s + "]"
+    }
+}
+
+extension LinkedList {
+    public func reverse() {
+        var node = head
+        while let currentNode = node {
+            node = currentNode.next
+            swap(&currentNode.next, &currentNode.previous)
+            head = currentNode
+        }
+    }
+}
+
+extension LinkedList {
+    public func map<U>(transform: (T) -> U) -> LinkedList<U> {
+        let result = LinkedList<U>()
+        var node = head
+        while node != nil {
+            result.append(transform(node!.value))
+            node = node!.next
+        }
+        return result
+    }
+
+    public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
+        let result = LinkedList<T>()
+        var node = head
+        while node != nil {
+            if predicate(node!.value) {
+                result.append(node!.value)
+            }
+            node = node!.next
+        }
+        return result
+    }
+}
+
+extension LinkedList {
+    convenience init(array: Array<T>) {
+        self.init()
+
+        for element in array {
+            self.append(element)
+        }
+    }
+}
+
+extension LinkedList: ExpressibleByArrayLiteral {
+  public convenience init(arrayLiteral elements: T...) {
+    self.init()
+
+    for element in elements {
+      self.append(element)
+    }
+  }
+}
diff --git a/LRU Cache/LRUCache.playground/contents.xcplayground b/LRU Cache/LRUCache.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/LRU Cache/LRUCache.swift b/LRU Cache/LRUCache.swift
new file mode 100644
index 000000000..4bfb3eabc
--- /dev/null
+++ b/LRU Cache/LRUCache.swift	
@@ -0,0 +1,59 @@
+//
+//  LRUCache.swift
+//
+//
+//  Created by Kai Chen on 16/07/2017.
+//
+//
+
+import Foundation
+
+public class LRUCache<KeyType: Hashable> {
+    private let maxSize: Int
+    private var cache: [KeyType: Any] = [:]
+    private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+    private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+
+    public init(_ maxSize: Int) {
+        self.maxSize = maxSize
+    }
+
+    public func get(_ key: KeyType) -> Any? {
+        guard let val = cache[key] else {
+            return nil
+        }
+
+        remove(key)
+        insert(key, val: val)
+
+        return val
+    }
+
+    public func set(_ key: KeyType, val: Any) {
+        if cache[key] != nil {
+            remove(key)
+        } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
+            remove(keyToRemove)
+        }
+
+        insert(key, val: val)
+    }
+
+    private func remove(_ key: KeyType) {
+        cache.removeValue(forKey: key)
+        guard let node = key2node[key] else {
+            return
+        }
+        priority.remove(node: node)
+        key2node.removeValue(forKey: key)
+    }
+
+    private func insert(_ key: KeyType, val: Any) {
+        cache[key] = val
+        priority.insert(key, atIndex: 0)
+        guard let first = priority.first else {
+            return
+        }
+        key2node[key] = first
+    }
+}
diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
new file mode 100644
index 000000000..c9a5de7a4
--- /dev/null
+++ b/LRU Cache/Readme.md	
@@ -0,0 +1,50 @@
+# LRU Cache
+
+[Least Recently Used][1] (LRU) is a popular algorithm in cache design. Here, we will try to write this algorithm ourselves.
+It should support the 2 operations: `get(key)` and `set(key, value)`.
+
+## Solution
+The key point in this algorithm is how to  maintain a priority queue when we do `get` and `set`.  Let’s say we have `priority` list, the priority is ranked from high to low. So, head has the highest priority and tail has the lowest priority. 
+
+There will be 2 key operations related to this queue. 
+* Remove element
+* Insert element
+
+Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. The `insert` operation will be look like this.
+
+```swift
+private func insert(_ key: KeyType, val: Any) {
+	cache[key] = val
+	priority.insert(key, atIndex: 0)
+	guard let first = priority.first else {
+		return
+	}
+	key2node[key]() = first
+}
+```
+
+Each time, when we `set`, the cache size maybe already full. In this case, we need to `remove` the lowest priority node. The operation is like this.
+
+```swift
+private func remove(_ key: KeyType) {
+	cache.removeValue(key)
+	guard let node = key2node[key] else {
+		return
+	}
+	priority.remove(node)
+	key2node.removeValue(key)
+}
+```
+
+
+Other hard part in this problem is usually find the element in the list will cost `O(n)` time. So, that's the bottleneck for `set` and `get` . It could slow down the whole cache alorightm. Is there a way to reduce this time complexity? The key idea here is to find a way to look up the element in the list fast. So, how about record the element position in the list. Then each time we just ask this record data structe to give us the element position in the list. So, that will be `O(1)` time, right? Aha, you got it. Which kind of data structe will have `O(1)` time? It's hash table. So, we use hash table to maintain the node's position. Here is the code.
+
+```swift
+private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+```
+
+
+
+
+[1]:	https://en.wikipedia.org/wiki/Cache_replacement_policies#LRU
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ebc2fb33b..d92007304 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -25,6 +25,19 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:"
+      name = "LRU Cache">
+      <FileRef
+         location = "group:LRU Cache/LRUCache.playground">
+      </FileRef>
+      <FileRef
+         location = "group:LRU Cache/LRUCache.swift">
+      </FileRef>
+      <FileRef
+         location = "group:LRU Cache/Readme.md">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"
       name = "Miller-Rabin Primality Test">

From 955bae283ab5d385f5bb62009b9af70aab301689 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:34:12 -0700
Subject: [PATCH 1069/1679] Fixes indentation of code to 2 spaces

---
 LRU Cache/LRUCache.swift | 86 ++++++++++++++++++++--------------------
 1 file changed, 43 insertions(+), 43 deletions(-)

diff --git a/LRU Cache/LRUCache.swift b/LRU Cache/LRUCache.swift
index 4bfb3eabc..4d15599de 100644
--- a/LRU Cache/LRUCache.swift	
+++ b/LRU Cache/LRUCache.swift	
@@ -9,51 +9,51 @@
 import Foundation
 
 public class LRUCache<KeyType: Hashable> {
-    private let maxSize: Int
-    private var cache: [KeyType: Any] = [:]
-    private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
-    private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
-
-    public init(_ maxSize: Int) {
-        self.maxSize = maxSize
+  private let maxSize: Int
+  private var cache: [KeyType: Any] = [:]
+  private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+  private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+  
+  public init(_ maxSize: Int) {
+    self.maxSize = maxSize
+  }
+  
+  public func get(_ key: KeyType) -> Any? {
+    guard let val = cache[key] else {
+      return nil
     }
-
-    public func get(_ key: KeyType) -> Any? {
-        guard let val = cache[key] else {
-            return nil
-        }
-
-        remove(key)
-        insert(key, val: val)
-
-        return val
+    
+    remove(key)
+    insert(key, val: val)
+    
+    return val
+  }
+  
+  public func set(_ key: KeyType, val: Any) {
+    if cache[key] != nil {
+      remove(key)
+    } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
+      remove(keyToRemove)
     }
-
-    public func set(_ key: KeyType, val: Any) {
-        if cache[key] != nil {
-            remove(key)
-        } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
-            remove(keyToRemove)
-        }
-
-        insert(key, val: val)
-    }
-
-    private func remove(_ key: KeyType) {
-        cache.removeValue(forKey: key)
-        guard let node = key2node[key] else {
-            return
-        }
-        priority.remove(node: node)
-        key2node.removeValue(forKey: key)
+    
+    insert(key, val: val)
+  }
+  
+  private func remove(_ key: KeyType) {
+    cache.removeValue(forKey: key)
+    guard let node = key2node[key] else {
+      return
     }
-
-    private func insert(_ key: KeyType, val: Any) {
-        cache[key] = val
-        priority.insert(key, atIndex: 0)
-        guard let first = priority.first else {
-            return
-        }
-        key2node[key] = first
+    priority.remove(node: node)
+    key2node.removeValue(forKey: key)
+  }
+  
+  private func insert(_ key: KeyType, val: Any) {
+    cache[key] = val
+    priority.insert(key, atIndex: 0)
+    guard let first = priority.first else {
+      return
     }
+    key2node[key] = first
+  }
 }

From 2cbed848bbeff4fe595658b532bb7e075af4cce3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:38:11 -0700
Subject: [PATCH 1070/1679] Refactors some of the readme files.

---
 LRU Cache/Readme.md | 15 +++++++--------
 1 file changed, 7 insertions(+), 8 deletions(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index c9a5de7a4..8c51cb6dc 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -1,14 +1,13 @@
 # LRU Cache
 
-[Least Recently Used][1] (LRU) is a popular algorithm in cache design. Here, we will try to write this algorithm ourselves.
-It should support the 2 operations: `get(key)` and `set(key, value)`.
+Caches are used to hold objects in memory. A caches size is finite; If the system doesn't have enough memory, the cache must be purged or the program will crash. [Least Recently Used][1] (LRU) is a popular algorithm in cache design. The idea is simple: In low memory situations, the oldest used member of the cache will be purged. A *priority queue* is used to enforce this behavior.
 
-## Solution
-The key point in this algorithm is how to  maintain a priority queue when we do `get` and `set`.  Let’s say we have `priority` list, the priority is ranked from high to low. So, head has the highest priority and tail has the lowest priority. 
+## The priority queue
 
-There will be 2 key operations related to this queue. 
-* Remove element
-* Insert element
+The key to the LRU cache is the priority queue. For simplicity, you'll model the queue using a linked list. All interactions with the LRU cache should respect this queue; Calling `get` and `set` should update the priority queue to reflect the most recently accessed element.
+
+
+### Operations
 
 Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. The `insert` operation will be look like this.
 
@@ -19,7 +18,7 @@ private func insert(_ key: KeyType, val: Any) {
 	guard let first = priority.first else {
 		return
 	}
-	key2node[key]() = first
+	key2node[key] = first
 }
 ```
 

From 87cae58bdc594217ca87c1e8b761bac74c5a7344 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:38:53 -0700
Subject: [PATCH 1071/1679] Added credits

---
 LRU Cache/Readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index 8c51cb6dc..ada2c9f9a 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -43,7 +43,7 @@ private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
 private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
 ```
 
-
+*Written for the Swift Algorithm Club by Kai Chen, with additions by Kelvin Lau*
 
 
 [1]:	https://en.wikipedia.org/wiki/Cache_replacement_policies#LRU

From 6c36ae77085b71932900cdc89bacbfcd2219e542 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:46:12 -0700
Subject: [PATCH 1072/1679] Updates wording for performance considerations
 paragraph.

---
 LRU Cache/Readme.md | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index ada2c9f9a..a268a667a 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -35,11 +35,13 @@ private func remove(_ key: KeyType) {
 }
 ```
 
+### Optimizing Performance
 
-Other hard part in this problem is usually find the element in the list will cost `O(n)` time. So, that's the bottleneck for `set` and `get` . It could slow down the whole cache alorightm. Is there a way to reduce this time complexity? The key idea here is to find a way to look up the element in the list fast. So, how about record the element position in the list. Then each time we just ask this record data structe to give us the element position in the list. So, that will be `O(1)` time, right? Aha, you got it. Which kind of data structe will have `O(1)` time? It's hash table. So, we use hash table to maintain the node's position. Here is the code.
+Removing elements from the priority queue is a frequent operation for the LRU cache. Since priority queue is modelled using a linked list, this is an expensive operation that costs `O(n)` time. This is the bottleneck for both the `set` and `get` methods.
 
-```swift
-private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+To help alleviate this problem, a hash table is used to store the references of each node:
+
+```
 private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
 ```
 

From 1de41865df6c9887c54b78bb35ede5847511f543 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:50:19 -0700
Subject: [PATCH 1073/1679] Refactors more of the readme.

---
 LRU Cache/Readme.md | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index a268a667a..580fed0d8 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -1,15 +1,19 @@
 # LRU Cache
 
-Caches are used to hold objects in memory. A caches size is finite; If the system doesn't have enough memory, the cache must be purged or the program will crash. [Least Recently Used][1] (LRU) is a popular algorithm in cache design. The idea is simple: In low memory situations, the oldest used member of the cache will be purged. A *priority queue* is used to enforce this behavior.
+Caches are used to hold objects in memory. A caches size is finite; If the system doesn't have enough memory, the cache must be purged or the program will crash. [Least Recently Used][1] (LRU) is a popular algorithm in cache design.
+
+In this implementation of the LRU Cache, a size is declared during instantiation, and any insertions that go beyond the size will purge the least recently used element of the cache. A *priority queue* is used to enforce this behavior.
 
 ## The priority queue
 
 The key to the LRU cache is the priority queue. For simplicity, you'll model the queue using a linked list. All interactions with the LRU cache should respect this queue; Calling `get` and `set` should update the priority queue to reflect the most recently accessed element.
 
+### Interesting tidbits
+
 
-### Operations
+#### Adding values
 
-Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. The `insert` operation will be look like this.
+Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. We use a helper method to handle this procedure:
 
 ```swift
 private func insert(_ key: KeyType, val: Any) {
@@ -22,7 +26,9 @@ private func insert(_ key: KeyType, val: Any) {
 }
 ```
 
-Each time, when we `set`, the cache size maybe already full. In this case, we need to `remove` the lowest priority node. The operation is like this.
+#### Purging the cache
+
+When the cahce is full, a purge must take place starting with the least recently used element. In this case, we need to `remove` the lowest priority node. The operation is like this:
 
 ```swift
 private func remove(_ key: KeyType) {

From e7a0002ed4c1e653bdfb2d4673fabd30a1cf2505 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 13:00:58 -0700
Subject: [PATCH 1074/1679] Fixes a spelling mistake.

---
 LRU Cache/Readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index 580fed0d8..8e2941991 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -28,7 +28,7 @@ private func insert(_ key: KeyType, val: Any) {
 
 #### Purging the cache
 
-When the cahce is full, a purge must take place starting with the least recently used element. In this case, we need to `remove` the lowest priority node. The operation is like this:
+When the cache is full, a purge must take place starting with the least recently used element. In this case, we need to `remove` the lowest priority node. The operation is like this:
 
 ```swift
 private func remove(_ key: KeyType) {

From 51ee1651fac832478d462396e7e4a82959c60c33 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 24 Jul 2017 17:37:41 -0700
Subject: [PATCH 1075/1679] Updated for Swift 4 Xcode 9b4

---
 Fizz Buzz/FizzBuzz.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index ba2f83b15..37acdab61 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
     var result = ""

From d745696bb7b9a8988b079e3e7cdbe8e2a7b28e0c Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 12:05:58 +0530
Subject: [PATCH 1076/1679] update Stack implementation to Swift 4 with Xcode
 9b4

---
 Stack/Stack.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 1eb705f20..e9e3e9a57 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,3 +1,9 @@
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*
   Stack
 

From 3f0d6971d3edd2cfaf7d69cf906ba0c61db03e37 Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 15:12:09 +0530
Subject: [PATCH 1077/1679] update palindrome implementation to Swift 4 with
 Xcode 9b4

---
 Palindromes/Palindromes.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index b9e857dd0..44662745a 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 /**

From 679f82ae0b5222caf36ee0aa044696b35fc05bec Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 15:28:12 +0530
Subject: [PATCH 1078/1679] update gcd implementation to Swift 4 with Xcode 9b4

---
 GCD/GCD.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 2e264be93..977b80f57 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Recursive version
 func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b

From 8073155a0a71665911e54aba21d4cd3ed24f6847 Mon Sep 17 00:00:00 2001
From: Benjamin Hendricks <hendricksbenjamin@gmail.com>
Date: Tue, 25 Jul 2017 13:31:25 +0100
Subject: [PATCH 1079/1679] claim TwoSum problem

---
 Two-Sum Problem/README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index a20666efd..4eeb99dcb 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,5 +1,7 @@
 # Two-Sum Problem
 
+### About to be edited for Swift 4 woohoo!
+
 You're given an array `a` with numbers. Write an algorithm that checks if there are any two entries in the array that add up to a given number `k`. In other words, is there any `a[i] + a[j] == k`?
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.

From b3e0dddc22cb26425a2075f67bf339cb1d46fe89 Mon Sep 17 00:00:00 2001
From: Benjamin Hendricks <hendricksbenjamin@gmail.com>
Date: Tue, 25 Jul 2017 18:07:17 +0100
Subject: [PATCH 1080/1679] no changes needed for twosum for swift 4

---
 Two-Sum Problem/README.markdown                           | 2 --
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift | 1 +
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift | 1 +
 3 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 4eeb99dcb..a20666efd 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,7 +1,5 @@
 # Two-Sum Problem
 
-### About to be edited for Swift 4 woohoo!
-
 You're given an array `a` with numbers. Write an algorithm that checks if there are any two entries in the array that add up to a given number `k`. In other words, is there any `a[i] + a[j] == k`?
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 00ce05136..9cc83c5ed 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,4 +1,5 @@
 //: Playground - noun: a place where people can play
+// Last checked with: Version 9.0 beta 4 (9M189t)
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index 9a555f0eb..b740dd3e6 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,4 +1,5 @@
 //: Playground - noun: a place where people can play
+// Last checked with: Version 9.0 beta 4 (9M189t)
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0

From efbc84a7cdfe979cda9ce2c09a8a05612bb87112 Mon Sep 17 00:00:00 2001
From: Benjamin Hendricks <hendricksbenjamin@gmail.com>
Date: Tue, 25 Jul 2017 18:41:47 +0100
Subject: [PATCH 1081/1679] add ifdef

---
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift   | 3 +++
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift   | 3 +++
 .../Solution 2/2Sum.playground/timeline.xctimeline          | 6 ------
 3 files changed, 6 insertions(+), 6 deletions(-)
 delete mode 100644 Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 9cc83c5ed..4de46128c 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
 // Last checked with: Version 9.0 beta 4 (9M189t)
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index b740dd3e6..4cb3d9283 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
 // Last checked with: Version 9.0 beta 4 (9M189t)
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline b/Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 49569597b19bc2c46277662a525163bd9d1979cd Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 23:49:54 +0530
Subject: [PATCH 1082/1679] update queue implementation to Swift 4 with Xcode
 9b4

---
 Queue/Queue.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 08327783f..22d2a84ca 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -1,3 +1,9 @@
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*
   Queue
 

From e30d68d8112ef069305d93dca33fede27e88e519 Mon Sep 17 00:00:00 2001
From: Vladimir Grigoriev <vladimir.grigoriev@appus.me>
Date: Wed, 26 Jul 2017 11:38:58 +0300
Subject: [PATCH 1083/1679] Correct typo

Algorithm doesn't work because of usage of incorrect vertices's set.
---
 .../Dijkstra.playground/Sources/Dijkstra.swift              | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index 9c5961c71..8cda797dd 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -19,7 +19,7 @@ public class Dijkstra {
         var currentVertex: Vertex? = startVertex
         while let vertex = currentVertex {
             currentVertices.remove(vertex)
-            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
+            let filteredNeighbors = vertex.neighbors.filter { currentVertices.contains($0.0) }
             for neighbor in filteredNeighbors {
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
@@ -31,11 +31,11 @@ public class Dijkstra {
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
-            if totalVertices.isEmpty {
+            if currentVertices.isEmpty {
                 currentVertex = nil
                 break
             }
-            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+            currentVertex = currentVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
     }
 }

From acc61b25e3af1f9180f73e49dbf388c1020c9854 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Wed, 26 Jul 2017 11:43:47 -0700
Subject: [PATCH 1084/1679] Count Occurrences to Swift 4

Tested Count Occurrences with Swift 4 and Xcode 9.0b4
---
 .../CountOccurrences.playground/Contents.swift              | 5 ++++-
 .../CountOccurrences.playground/timeline.xctimeline         | 6 ------
 2 files changed, 4 insertions(+), 7 deletions(-)
 delete mode 100644 Count Occurrences/CountOccurrences.playground/timeline.xctimeline

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index b4392d501..6138b74ac 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,4 +1,7 @@
-//: Playground - noun: a place where people can play
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
 
 func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {
diff --git a/Count Occurrences/CountOccurrences.playground/timeline.xctimeline b/Count Occurrences/CountOccurrences.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Count Occurrences/CountOccurrences.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From c679dcbd3fc856176f1d62e475110634934056b6 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Wed, 26 Jul 2017 12:24:25 -0700
Subject: [PATCH 1085/1679] Fixed Size Array to Swift 4

Tested Fixed Size Array with Swift 4 and Xcode 9.0b4
---
 Fixed Size Array/FixedSizeArray.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 8ef545e45..8b5bc1147 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
 /*
  An unordered array with a maximum size.
  
@@ -53,3 +58,4 @@ array.append(2)
 array[1]
 array.removeAt(index: 0)
 array.removeAll()
+

From aff5a595a3c3f8939496f2773995bc7b6ee0cdf8 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Wed, 26 Jul 2017 18:57:45 -0700
Subject: [PATCH 1086/1679] Boyer Moore to Swift 4

Updated Boyer Moore to Swift 4 and Xcode 9.0b4
---
 .../BoyerMoore.playground/Contents.swift      |  5 ++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 26 +++++++++++++++----
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 ++-
 3 files changed, 29 insertions(+), 6 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index f553e1a00..e88a1b93d 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 /*
   Boyer-Moore string search
 
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
index c4a005163..6fc005d43 100644
--- a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
@@ -16,7 +16,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreTests.swift; sourceTree = SOURCE_ROOT; };
-		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../../BoyerMoore.swift; sourceTree = "<group>"; };
+		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../BoyerMoore.swift; sourceTree = SOURCE_ROOT; };
 		9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreHorspoolTests.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -87,12 +87,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
@@ -162,14 +162,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -197,6 +203,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Debug;
 		};
@@ -208,14 +215,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -236,6 +249,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Release;
 		};
@@ -247,7 +261,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -259,7 +274,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..538a6f4fa 100644
--- a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 48eced4ff385e3829848cff2c3c3ad8f1c449638 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sat, 29 Jul 2017 21:04:30 -0700
Subject: [PATCH 1087/1679] [Swift 4] Update Shuffle to Swift 4

---
 Shuffle/Shuffle.playground/Contents.swift     | 35 ++----------
 .../Shuffle.playground/Sources/Shuffle.swift  | 39 ++++++++++++++
 .../Shuffle.playground/timeline.xctimeline    |  6 ---
 Shuffle/Shuffle.swift                         | 54 +++++++++++--------
 4 files changed, 75 insertions(+), 59 deletions(-)
 create mode 100644 Shuffle/Shuffle.playground/Sources/Shuffle.swift
 delete mode 100644 Shuffle/Shuffle.playground/timeline.xctimeline

diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index 704a94e7d..ac9181660 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -1,40 +1,15 @@
 //: Playground - noun: a place where people can play
 
-import Foundation
-
-/* Returns a random integer between 0 and n-1. */
-public func random(_ n: Int) -> Int {
-  return Int(arc4random_uniform(UInt32(n)))
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
-/* Fisher-Yates / Knuth shuffle */
-extension Array {
-  public mutating func shuffle() {
-    for i in stride(from: count - 1, through: 1, by: -1) {
-      let j = random(i + 1)
-      if i != j {
-        swap(&self[i], &self[j])
-      }
-    }
-  }
-}
+import Foundation
 
 var list = [ "a", "b", "c", "d", "e", "f", "g" ]
 list.shuffle()
 list.shuffle()
 list.shuffle()
 
-/* Create a new array of numbers that is already shuffled. */
-public func shuffledArray(_ n: Int) -> [Int] {
-  var a = [Int](repeating: 0, count: n)
-  for i in 0..<n {
-    let j = random(i + 1)
-    if i != j {
-      a[i] = a[j]
-    }
-    a[j] = i
-  }
-  return a
-}
-
 let numbers = shuffledArray(10)
diff --git a/Shuffle/Shuffle.playground/Sources/Shuffle.swift b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
new file mode 100644
index 000000000..63fea2899
--- /dev/null
+++ b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
@@ -0,0 +1,39 @@
+import Foundation
+
+/* Returns a random integer between 0 and n-1. */
+public func random(_ n: Int) -> Int {
+    return Int(arc4random_uniform(UInt32(n)))
+}
+
+extension Array {
+  /*
+    Randomly shuffles the array in-place
+    This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+    Time complexity: O(n)
+  */
+  public mutating func shuffle() {
+    for i in (1...count-1).reversed() {
+      let j = random(i + 1)
+      if i != j {
+        let t = self[i]
+        self[i] = self[j]
+        self[j] = t
+      }
+    }
+  }
+}
+
+/*
+  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
+*/
+public func shuffledArray(_ n: Int) -> [Int] {
+  var a = Array(repeating: 0, count: n)
+  for i in 0..<n {
+    let j = random(i + 1)
+    if i != j {
+      a[i] = a[j]
+    }
+    a[j] = i  // insert next number from the sequence
+  }
+  return a
+}
diff --git a/Shuffle/Shuffle.playground/timeline.xctimeline b/Shuffle/Shuffle.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Shuffle/Shuffle.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index 8fe8b4e87..19112fa37 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -1,32 +1,40 @@
 import Foundation
 
+/* Returns a random integer between 0 and n-1. */
+public func random(_ n: Int) -> Int {
+    return Int(arc4random_uniform(UInt32(n)))
+}
+
 extension Array {
-  /*
-    Randomly shuffles the array in-place
-    This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
-    Time complexity: O(n)
-  */
-  public mutating func shuffle() {
-    for i in (count - 1).stride(through: 1, by: -1) {
-      let j = random(i + 1)
-      if i != j {
-        swap(&self[i], &self[j])
-      }
+    /*
+     Randomly shuffles the array in-place
+     This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+     Time complexity: O(n)
+     */
+    public mutating func shuffle() {
+        for i in (1...count-1).reversed() {
+            let j = random(i + 1)
+            if i != j {
+                let t = self[i]
+                self[i] = self[j]
+                self[j] = t
+            }
+        }
     }
-  }
 }
 
 /*
-  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
-*/
-public func shuffledArray(n: Int) -> [Int] {
-  var a = [Int](count: n, repeatedValue: 0)
-  for i in 0..<n {
-    let j = random(i + 1)
-    if i != j {
-      a[i] = a[j]
+ Simultaneously initializes an array with the values 0...n-1 and shuffles it.
+ */
+public func shuffledArray(_ n: Int) -> [Int] {
+    var a = Array(repeating: 0, count: n)
+    for i in 0..<n {
+        let j = random(i + 1)
+        if i != j {
+            a[i] = a[j]
+        }
+        a[j] = i  // insert next number from the sequence
     }
-    a[j] = i  // insert next number from the sequence
-  }
-  return a
+    return a
 }
+

From 088b4347b6bdf84d42b456b2e09099ecf5ff1901 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:43:59 -0700
Subject: [PATCH 1088/1679] [Swift 4] Update Union Find

---
 Union-Find/UnionFind.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index b1f7fb4e1..6ac3b4c4e 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {

From c18e01c3fd1e8a2444e0967b8ce165926f82d3d7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:50:07 -0700
Subject: [PATCH 1089/1679] [Swift 4] Update Trie

---
 Trie/Trie/Trie/Trie.swift           | 5 +++++
 Trie/Trie/Trie/ViewController.swift | 5 +++++
 Trie/Trie/TrieTests/TrieTests.swift | 5 +++++
 3 files changed, 15 insertions(+)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 856384fff..1a7017c4c 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -6,6 +6,11 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 /// A node in the trie
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index 928b01f4c..9c5e66163 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -6,6 +6,11 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 import Cocoa
 
 class ViewController: NSViewController {
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index b69c5666e..45be03aad 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -6,6 +6,11 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 import XCTest
 @testable import Trie
 

From e36e7119714e164c0997eb1365334a4fa6979346 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:56:08 -0700
Subject: [PATCH 1090/1679] [Swift 4] Update Tree

---
 Tree/Tree.playground/Contents.swift      | 29 ++-----------
 Tree/Tree.playground/Sources/Tree.swift  | 39 +++++++++++++++++
 Tree/Tree.playground/timeline.xctimeline |  6 ---
 Tree/Tree.swift                          | 53 ++++++++++++------------
 4 files changed, 70 insertions(+), 57 deletions(-)
 create mode 100644 Tree/Tree.playground/Sources/Tree.swift
 delete mode 100644 Tree/Tree.playground/timeline.xctimeline

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index d59b7eedb..49cf41054 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -1,30 +1,9 @@
 //: Playground - noun: a place where people can play
 
-public class TreeNode<T> {
-  public var value: T
-
-  public weak var parent: TreeNode?
-  public var children = [TreeNode<T>]()
-
-  public init(value: T) {
-    self.value = value
-  }
-
-  public func addChild(_ node: TreeNode<T>) {
-    children.append(node)
-    node.parent = self
-  }
-}
-
-extension TreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = "\(value)"
-    if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
-    }
-    return s
-  }
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let tree = TreeNode<String>(value: "beverages")
 
diff --git a/Tree/Tree.playground/Sources/Tree.swift b/Tree/Tree.playground/Sources/Tree.swift
new file mode 100644
index 000000000..fa49f25e9
--- /dev/null
+++ b/Tree/Tree.playground/Sources/Tree.swift
@@ -0,0 +1,39 @@
+public class TreeNode<T> {
+  public var value: T
+
+  public weak var parent: TreeNode?
+  public var children = [TreeNode<T>]()
+
+  public init(value: T) {
+    self.value = value
+  }
+
+  public func addChild(_ node: TreeNode<T>) {
+    children.append(node)
+    node.parent = self
+  }
+}
+
+extension TreeNode: CustomStringConvertible {
+  public var description: String {
+    var s = "\(value)"
+    if !children.isEmpty {
+      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
+    }
+    return s
+  }
+}
+
+extension TreeNode where T: Equatable {
+  public func search(_ value: T) -> TreeNode? {
+    if value == self.value {
+      return self
+    }
+    for child in children {
+      if let found = child.search(value) {
+        return found
+      }
+    }
+    return nil
+  }
+}
diff --git a/Tree/Tree.playground/timeline.xctimeline b/Tree/Tree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Tree/Tree.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index fa49f25e9..08cb61eb5 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -1,39 +1,40 @@
 public class TreeNode<T> {
-  public var value: T
+    public var value: T
 
-  public weak var parent: TreeNode?
-  public var children = [TreeNode<T>]()
+    public weak var parent: TreeNode?
+    public var children = [TreeNode<T>]()
 
-  public init(value: T) {
-    self.value = value
-  }
+    public init(value: T) {
+        self.value = value
+    }
 
-  public func addChild(_ node: TreeNode<T>) {
-    children.append(node)
-    node.parent = self
-  }
+    public func addChild(_ node: TreeNode<T>) {
+        children.append(node)
+        node.parent = self
+    }
 }
 
 extension TreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = "\(value)"
-    if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
+    public var description: String {
+        var s = "\(value)"
+        if !children.isEmpty {
+            s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
+        }
+        return s
     }
-    return s
-  }
 }
 
 extension TreeNode where T: Equatable {
-  public func search(_ value: T) -> TreeNode? {
-    if value == self.value {
-      return self
+    public func search(_ value: T) -> TreeNode? {
+        if value == self.value {
+            return self
+        }
+        for child in children {
+            if let found = child.search(value) {
+                return found
+            }
+        }
+        return nil
     }
-    for child in children {
-      if let found = child.search(value) {
-        return found
-      }
-    }
-    return nil
-  }
 }
+

From 71a78276cdcaab0e1e7b7be57733caaf83757a57 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:58:36 -0700
Subject: [PATCH 1091/1679] [Swift 4] Update Topological Sort

---
 Topological Sort/Topological Sort.playground/Contents.swift | 5 +++++
 .../Topological Sort.playground/timeline.xctimeline         | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Topological Sort/Topological Sort.playground/timeline.xctimeline

diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index 8f78c388a..3921d37fc 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import UIKit
 
 let graph = Graph()
diff --git a/Topological Sort/Topological Sort.playground/timeline.xctimeline b/Topological Sort/Topological Sort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Topological Sort/Topological Sort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 207d7f916d59f05c9cc16c44bf8fbc7f93795638 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:08:51 -0700
Subject: [PATCH 1092/1679] [Swift 4] Update Selection Sort

---
 .../SelectionSort.playground/Contents.swift   | 20 +++---------
 .../Sources/SelectionSort.swift               | 21 ++++++++++++
 .../timeline.xctimeline                       |  6 ----
 Selection Sort/SelectionSort.swift            | 32 +++++++++----------
 .../contents.xcworkspacedata                  |  6 ++--
 5 files changed, 44 insertions(+), 41 deletions(-)
 create mode 100644 Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
 delete mode 100644 Selection Sort/SelectionSort.playground/timeline.xctimeline

diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index bd8c7cccf..e0bfdf259 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -1,21 +1,9 @@
 //: Playground - noun: a place where people can play
 
-func selectionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  guard array.count > 1 else { return array }
-  var a = array
-  for x in 0 ..< a.count - 1 {
-    var lowest = x
-    for y in x + 1 ..< a.count {
-      if isOrderedBefore(a[y], a[lowest]) {
-        lowest = y
-      }
-    }
-    if x != lowest {
-      swap(&a[x], &a[lowest])
-    }
-  }
-  return a
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 selectionSort(list, <)
diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
new file mode 100644
index 000000000..3015fde9b
--- /dev/null
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -0,0 +1,21 @@
+public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+  guard array.count > 1 else { return array }
+
+  var a = array
+  for x in 0 ..< a.count - 1 {
+
+    // Find the lowest value in the rest of the array.
+    var lowest = x
+    for y in x + 1 ..< a.count {
+      if isOrderedBefore(a[y], a[lowest]) {
+        lowest = y
+      }
+    }
+
+    // Swap the lowest value with the current array index.
+    if x != lowest {
+      a.swapAt(x, lowest)
+    }
+  }
+  return a
+}
diff --git a/Selection Sort/SelectionSort.playground/timeline.xctimeline b/Selection Sort/SelectionSort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Selection Sort/SelectionSort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Selection Sort/SelectionSort.swift b/Selection Sort/SelectionSort.swift
index e02c87259..943ae628d 100644
--- a/Selection Sort/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.swift	
@@ -1,21 +1,21 @@
-func selectionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  guard array.count > 1 else { return array }
+public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+    guard array.count > 1 else { return array }
 
-  var a = array
-  for x in 0 ..< a.count - 1 {
+    var a = array
+    for x in 0 ..< a.count - 1 {
 
-    // Find the lowest value in the rest of the array.
-    var lowest = x
-    for y in x + 1 ..< a.count {
-      if isOrderedBefore(a[y], a[lowest]) {
-        lowest = y
-      }
-    }
+        // Find the lowest value in the rest of the array.
+        var lowest = x
+        for y in x + 1 ..< a.count {
+            if isOrderedBefore(a[y], a[lowest]) {
+                lowest = y
+            }
+        }
 
-    // Swap the lowest value with the current array index.
-    if x != lowest {
-      swap(&a[x], &a[lowest])
+        // Swap the lowest value with the current array index.
+        if x != lowest {
+            a.swapAt(x, lowest)
+        }
     }
-  }
-  return a
+    return a
 }
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..db4691648 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -2058,9 +2058,6 @@
       <FileRef
          location = "group:SelectionSort.playground">
       </FileRef>
-      <FileRef
-         location = "group:SelectionSort.swift">
-      </FileRef>
       <Group
          location = "group:Tests"
          name = "Tests">
@@ -2074,6 +2071,9 @@
             location = "group:Tests.xcodeproj">
          </FileRef>
       </Group>
+      <FileRef
+         location = "group:SelectionSort.swift">
+      </FileRef>
    </Group>
    <Group
       location = "group:Set Cover (Unweighted)"

From fb5c1978dacaad89f4a83ce6dd00dff897e3f7e8 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:11:57 -0700
Subject: [PATCH 1093/1679] [Swift 4] Update Segment Tree

---
 Segment Tree/SegmentTree.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 3a758981f..25116c285 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public class SegmentTree<T> {
 
 	private var value: T

From a5ca2a8f9e887c61f7559ed7fc75e1e308a73e7f Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:16:03 -0700
Subject: [PATCH 1094/1679] [Swift 4] Update Merge Sort

---
 Merge Sort/MergeSort.playground/Contents.swift      | 5 +++++
 Merge Sort/MergeSort.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Merge Sort/MergeSort.playground/timeline.xctimeline

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index f5a1dbbcf..06fa3beaa 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 /* Top-down recursive version */
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
diff --git a/Merge Sort/MergeSort.playground/timeline.xctimeline b/Merge Sort/MergeSort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Merge Sort/MergeSort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From a5dc48eb316405d610c3547eb7c4d31c529065bf Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:34:12 -0700
Subject: [PATCH 1095/1679] [Swift 4] Update Heap

---
 Heap/Heap.swift                               | 430 ++++++------
 Heap/Tests/HeapTests.swift                    | 615 +++++++++---------
 Heap/Tests/Tests.xcodeproj/project.pbxproj    |   4 +-
 .../xcshareddata/xcschemes/Tests.xcscheme     |   2 +
 4 files changed, 530 insertions(+), 521 deletions(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 80b40c65f..18a350dca 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,224 +4,224 @@
 //
 
 public struct Heap<T> {
-  /** The array that stores the heap's nodes. */
-  var elements = [T]()
-
-  /** Determines whether this is a max-heap (>) or min-heap (<). */
-  fileprivate var isOrderedBefore: (T, T) -> Bool
-
-  /**
-   * Creates an empty heap.
-   * The sort function determines whether this is a min-heap or max-heap.
-   * For integers, > makes a max-heap, < makes a min-heap.
-   */
-  public init(sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-  }
-
-  /**
-   * Creates a heap from an array. The order of the array does not matter;
-   * the elements are inserted into the heap in the order determined by the
-   * sort function.
-   */
-  public init(array: [T], sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-    buildHeap(fromArray: array)
-  }
-
-  /*
-  // This version has O(n log n) performance.
-  private mutating func buildHeap(array: [T]) {
-    elements.reserveCapacity(array.count)
-    for value in array {
-      insert(value)
-    }
-  }
-  */
-
-  /**
-   * Converts an array to a max-heap or min-heap in a bottom-up manner.
-   * Performance: This runs pretty much in O(n).
-   */
-  fileprivate mutating func buildHeap(fromArray array: [T]) {
-    elements = array
-    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(i, heapSize: elements.count)
-    }
-  }
-
-  public var isEmpty: Bool {
-    return elements.isEmpty
-  }
-
-  public var count: Int {
-    return elements.count
-  }
-
-  /**
-   * Returns the index of the parent of the element at index i.
-   * The element at index 0 is the root of the tree and has no parent.
-   */
-  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
-    return (i - 1) / 2
-  }
-
-  /**
-   * Returns the index of the left child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no left child.
-   */
-  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 1
-  }
-
-  /**
-   * Returns the index of the right child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no right child.
-   */
-  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 2
-  }
-
-  /**
-   * Returns the maximum value in the heap (for a max-heap) or the minimum
-   * value (for a min-heap).
-   */
-  public func peek() -> T? {
-    return elements.first
-  }
-
-  /**
-   * Adds a new value to the heap. This reorders the heap so that the max-heap
-   * or min-heap property still holds. Performance: O(log n).
-   */
-  public mutating func insert(_ value: T) {
-    elements.append(value)
-    shiftUp(elements.count - 1)
-  }
-
-  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-    for value in sequence {
-      insert(value)
-    }
-  }
-
-  /**
-   * Allows you to change an element. In a max-heap, the new element should be
-   * larger than the old one; in a min-heap it should be smaller.
-   */
-  public mutating func replace(index i: Int, value: T) {
-    guard i < elements.count else { return }
-
-    assert(isOrderedBefore(value, elements[i]))
-    elements[i] = value
-    shiftUp(i)
-  }
-
-  /**
-   * Removes the root node from the heap. For a max-heap, this is the maximum
-   * value; for a min-heap it is the minimum value. Performance: O(log n).
-   */
-  @discardableResult public mutating func remove() -> T? {
-    if elements.isEmpty {
-      return nil
-    } else if elements.count == 1 {
-      return elements.removeLast()
-    } else {
-      // Use the last node to replace the first one, then fix the heap by
-      // shifting this new first node into its proper position.
-      let value = elements[0]
-      elements[0] = elements.removeLast()
-      shiftDown()
-      return value
-    }
-  }
-
-  /**
-   * Removes an arbitrary node from the heap. Performance: O(log n). You need
-   * to know the node's index, which may actually take O(n) steps to find.
-   */
-  public mutating func removeAt(_ index: Int) -> T? {
-    guard index < elements.count else { return nil }
-
-    let size = elements.count - 1
-    if index != size {
-      swap(&elements[index], &elements[size])
-      shiftDown(index, heapSize: size)
-      shiftUp(index)
-    }
-    return elements.removeLast()
-  }
-
-  /**
-   * Takes a child node and looks at its parents; if a parent is not larger
-   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
-   */
-  mutating func shiftUp(_ index: Int) {
-    var childIndex = index
-    let child = elements[childIndex]
-    var parentIndex = self.parentIndex(ofIndex: childIndex)
-
-    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-      elements[childIndex] = elements[parentIndex]
-      childIndex = parentIndex
-      parentIndex = self.parentIndex(ofIndex: childIndex)
-    }
-
-    elements[childIndex] = child
-  }
-
-  mutating func shiftDown() {
-    shiftDown(0, heapSize: elements.count)
-  }
-
-  /**
-   * Looks at a parent node and makes sure it is still larger (max-heap) or
-   * smaller (min-heap) than its childeren.
-   */
-  mutating func shiftDown(_ index: Int, heapSize: Int) {
-    var parentIndex = index
-
-    while true {
-      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-      let rightChildIndex = leftChildIndex + 1
-
-      // Figure out which comes first if we order them by the sort function:
-      // the parent, the left child, or the right child. If the parent comes
-      // first, we're done. If not, that element is out-of-place and we make
-      // it "float down" the tree until the heap property is restored.
-      var first = parentIndex
-      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-        first = leftChildIndex
-      }
-      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-        first = rightChildIndex
-      }
-      if first == parentIndex { return }
-
-      swap(&elements[parentIndex], &elements[first])
-      parentIndex = first
-    }
-  }
+    /** The array that stores the heap's nodes. */
+    var elements = [T]()
+
+    /** Determines whether this is a max-heap (>) or min-heap (<). */
+    fileprivate var isOrderedBefore: (T, T) -> Bool
+
+    /**
+     * Creates an empty heap.
+     * The sort function determines whether this is a min-heap or max-heap.
+     * For integers, > makes a max-heap, < makes a min-heap.
+     */
+    public init(sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+    }
+
+    /**
+     * Creates a heap from an array. The order of the array does not matter;
+     * the elements are inserted into the heap in the order determined by the
+     * sort function.
+     */
+    public init(array: [T], sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+        buildHeap(fromArray: array)
+    }
+
+    /*
+     // This version has O(n log n) performance.
+     private mutating func buildHeap(array: [T]) {
+     elements.reserveCapacity(array.count)
+     for value in array {
+     insert(value)
+     }
+     }
+     */
+
+    /**
+     * Converts an array to a max-heap or min-heap in a bottom-up manner.
+     * Performance: This runs pretty much in O(n).
+     */
+    fileprivate mutating func buildHeap(fromArray array: [T]) {
+        elements = array
+        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+            shiftDown(i, heapSize: elements.count)
+        }
+    }
+
+    public var isEmpty: Bool {
+        return elements.isEmpty
+    }
+
+    public var count: Int {
+        return elements.count
+    }
+
+    /**
+     * Returns the index of the parent of the element at index i.
+     * The element at index 0 is the root of the tree and has no parent.
+     */
+    @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+        return (i - 1) / 2
+    }
+
+    /**
+     * Returns the index of the left child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no left child.
+     */
+    @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 1
+    }
+
+    /**
+     * Returns the index of the right child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no right child.
+     */
+    @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 2
+    }
+
+    /**
+     * Returns the maximum value in the heap (for a max-heap) or the minimum
+     * value (for a min-heap).
+     */
+    public func peek() -> T? {
+        return elements.first
+    }
+
+    /**
+     * Adds a new value to the heap. This reorders the heap so that the max-heap
+     * or min-heap property still holds. Performance: O(log n).
+     */
+    public mutating func insert(_ value: T) {
+        elements.append(value)
+        shiftUp(elements.count - 1)
+    }
+
+    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+        for value in sequence {
+            insert(value)
+        }
+    }
+
+    /**
+     * Allows you to change an element. In a max-heap, the new element should be
+     * larger than the old one; in a min-heap it should be smaller.
+     */
+    public mutating func replace(index i: Int, value: T) {
+        guard i < elements.count else { return }
+
+        assert(isOrderedBefore(value, elements[i]))
+        elements[i] = value
+        shiftUp(i)
+    }
+
+    /**
+     * Removes the root node from the heap. For a max-heap, this is the maximum
+     * value; for a min-heap it is the minimum value. Performance: O(log n).
+     */
+    @discardableResult public mutating func remove() -> T? {
+        if elements.isEmpty {
+            return nil
+        } else if elements.count == 1 {
+            return elements.removeLast()
+        } else {
+            // Use the last node to replace the first one, then fix the heap by
+            // shifting this new first node into its proper position.
+            let value = elements[0]
+            elements[0] = elements.removeLast()
+            shiftDown()
+            return value
+        }
+    }
+
+    /**
+     * Removes an arbitrary node from the heap. Performance: O(log n). You need
+     * to know the node's index, which may actually take O(n) steps to find.
+     */
+    public mutating func removeAt(_ index: Int) -> T? {
+        guard index < elements.count else { return nil }
+
+        let size = elements.count - 1
+        if index != size {
+            elements.swapAt(index, size)
+            shiftDown(index, heapSize: size)
+            shiftUp(index)
+        }
+        return elements.removeLast()
+    }
+
+    /**
+     * Takes a child node and looks at its parents; if a parent is not larger
+     * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+     */
+    mutating func shiftUp(_ index: Int) {
+        var childIndex = index
+        let child = elements[childIndex]
+        var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+            elements[childIndex] = elements[parentIndex]
+            childIndex = parentIndex
+            parentIndex = self.parentIndex(ofIndex: childIndex)
+        }
+
+        elements[childIndex] = child
+    }
+
+    mutating func shiftDown() {
+        shiftDown(0, heapSize: elements.count)
+    }
+
+    /**
+     * Looks at a parent node and makes sure it is still larger (max-heap) or
+     * smaller (min-heap) than its childeren.
+     */
+    mutating func shiftDown(_ index: Int, heapSize: Int) {
+        var parentIndex = index
+
+        while true {
+            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let rightChildIndex = leftChildIndex + 1
+
+            // Figure out which comes first if we order them by the sort function:
+            // the parent, the left child, or the right child. If the parent comes
+            // first, we're done. If not, that element is out-of-place and we make
+            // it "float down" the tree until the heap property is restored.
+            var first = parentIndex
+            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+                first = leftChildIndex
+            }
+            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+                first = rightChildIndex
+            }
+            if first == parentIndex { return }
+
+            elements.swapAt(parentIndex, first)
+            parentIndex = first
+        }
+    }
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-  /**
-   * Searches the heap for the given element. Performance: O(n).
-   */
-  public func index(of element: T) -> Int? {
-    return index(of: element, 0)
-  }
-
-  fileprivate func index(of element: T, _ i: Int) -> Int? {
-    if i >= count { return nil }
-    if isOrderedBefore(element, elements[i]) { return nil }
-    if element == elements[i] { return i }
-    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
-    return nil
-  }
+    /**
+     * Searches the heap for the given element. Performance: O(n).
+     */
+    public func index(of element: T) -> Int? {
+        return index(of: element, 0)
+    }
+
+    fileprivate func index(of element: T, _ i: Int) -> Int? {
+        if i >= count { return nil }
+        if isOrderedBefore(element, elements[i]) { return nil }
+        if element == elements[i] { return i }
+        if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+        if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+        return nil
+    }
 }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index cac934406..0af3a14e0 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -7,317 +7,324 @@ import XCTest
 
 class HeapTests: XCTestCase {
 
-  fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
-    for i in 0..<h.count {
-      let left = h.leftChildIndex(ofIndex: i)
-      let right = h.rightChildIndex(ofIndex: i)
-      let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] < h.elements[left] { return false }
-      if right < h.count && h.elements[i] < h.elements[right] { return false }
-      if i > 0 && h.elements[parent] < h.elements[i] { return false }
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
     }
-    return true
-  }
-
-  fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
-    for i in 0..<h.count {
-      let left = h.leftChildIndex(ofIndex: i)
-      let right = h.rightChildIndex(ofIndex: i)
-      let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] > h.elements[left] { return false }
-      if right < h.count && h.elements[i] > h.elements[right] { return false }
-      if i > 0 && h.elements[parent] > h.elements[i] { return false }
+
+    fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
+        for i in 0..<h.count {
+            let left = h.leftChildIndex(ofIndex: i)
+            let right = h.rightChildIndex(ofIndex: i)
+            let parent = h.parentIndex(ofIndex: i)
+            if left < h.count && h.elements[i] < h.elements[left] { return false }
+            if right < h.count && h.elements[i] < h.elements[right] { return false }
+            if i > 0 && h.elements[parent] < h.elements[i] { return false }
+        }
+        return true
+    }
+
+    fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
+        for i in 0..<h.count {
+            let left = h.leftChildIndex(ofIndex: i)
+            let right = h.rightChildIndex(ofIndex: i)
+            let parent = h.parentIndex(ofIndex: i)
+            if left < h.count && h.elements[i] > h.elements[left] { return false }
+            if right < h.count && h.elements[i] > h.elements[right] { return false }
+            if i > 0 && h.elements[parent] > h.elements[i] { return false }
+        }
+        return true
+    }
+
+    fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
+        var a1 = array1
+        var a2 = array2
+        if a1.count != a2.count { return false }
+        while a1.count > 0 {
+            if let i = a2.index(of: a1[0]) {
+                a1.remove(at: 0)
+                a2.remove(at: i)
+            } else {
+                return false
+            }
+        }
+        return a2.count == 0
+    }
+
+    func testEmptyHeap() {
+        var heap = Heap<Int>(sort: <)
+        XCTAssertTrue(heap.isEmpty)
+        XCTAssertEqual(heap.count, 0)
+        XCTAssertNil(heap.peek())
+        XCTAssertNil(heap.remove())
+    }
+
+    func testIsEmpty() {
+        var heap = Heap<Int>(sort: >)
+        XCTAssertTrue(heap.isEmpty)
+        heap.insert(1)
+        XCTAssertFalse(heap.isEmpty)
+        heap.remove()
+        XCTAssertTrue(heap.isEmpty)
+    }
+
+    func testCount() {
+        var heap = Heap<Int>(sort: >)
+        XCTAssertEqual(0, heap.count)
+        heap.insert(1)
+        XCTAssertEqual(1, heap.count)
+    }
+
+    func testMaxHeapOneElement() {
+        let heap = Heap<Int>(array: [10], sort: >)
+        XCTAssertTrue(verifyMaxHeap(heap))
+        XCTAssertTrue(verifyMinHeap(heap))
+        XCTAssertFalse(heap.isEmpty)
+        XCTAssertEqual(heap.count, 1)
+        XCTAssertEqual(heap.peek()!, 10)
+    }
+
+    func testCreateMaxHeap() {
+        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h1))
+        XCTAssertFalse(verifyMinHeap(h1))
+        XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
+        XCTAssertFalse(h1.isEmpty)
+        XCTAssertEqual(h1.count, 7)
+        XCTAssertEqual(h1.peek()!, 7)
+
+        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h2))
+        XCTAssertFalse(verifyMinHeap(h2))
+        XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
+        XCTAssertFalse(h2.isEmpty)
+        XCTAssertEqual(h2.count, 7)
+        XCTAssertEqual(h2.peek()!, 7)
+
+        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h3))
+        XCTAssertFalse(verifyMinHeap(h3))
+        XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+        XCTAssertFalse(h3.isEmpty)
+        XCTAssertEqual(h3.count, 10)
+        XCTAssertEqual(h3.peek()!, 16)
+
+        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h4))
+        XCTAssertFalse(verifyMinHeap(h4))
+        XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
+        XCTAssertFalse(h4.isEmpty)
+        XCTAssertEqual(h4.count, 14)
+        XCTAssertEqual(h4.peek()!, 27)
+    }
+
+    func testCreateMinHeap() {
+        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
+        XCTAssertTrue(verifyMinHeap(h1))
+        XCTAssertFalse(verifyMaxHeap(h1))
+        XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
+        XCTAssertFalse(h1.isEmpty)
+        XCTAssertEqual(h1.count, 7)
+        XCTAssertEqual(h1.peek()!, 1)
+
+        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
+        XCTAssertTrue(verifyMinHeap(h2))
+        XCTAssertFalse(verifyMaxHeap(h2))
+        XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
+        XCTAssertFalse(h2.isEmpty)
+        XCTAssertEqual(h2.count, 7)
+        XCTAssertEqual(h2.peek()!, 1)
+
+        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
+        XCTAssertTrue(verifyMinHeap(h3))
+        XCTAssertFalse(verifyMaxHeap(h3))
+        XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
+        XCTAssertFalse(h3.isEmpty)
+        XCTAssertEqual(h3.count, 10)
+        XCTAssertEqual(h3.peek()!, 1)
+
+        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
+        XCTAssertTrue(verifyMinHeap(h4))
+        XCTAssertFalse(verifyMaxHeap(h4))
+        XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
+        XCTAssertFalse(h4.isEmpty)
+        XCTAssertEqual(h4.count, 14)
+        XCTAssertEqual(h4.peek()!, 0)
+    }
+
+    func testCreateMaxHeapEqualElements() {
+        let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(heap))
+        XCTAssertTrue(verifyMinHeap(heap))
+        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    }
+
+    func testCreateMinHeapEqualElements() {
+        let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
+        XCTAssertTrue(verifyMinHeap(heap))
+        XCTAssertTrue(verifyMaxHeap(heap))
+        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    }
+
+    fileprivate func randomArray(_ n: Int) -> [Int] {
+        var a = [Int]()
+        for _ in 0..<n {
+            a.append(Int(arc4random()))
+        }
+        return a
+    }
+
+    func testCreateRandomMaxHeap() {
+        for n in 1...40 {
+            let a = randomArray(n)
+            let h = Heap(array: a, sort: >)
+            XCTAssertTrue(verifyMaxHeap(h))
+            XCTAssertFalse(h.isEmpty)
+            XCTAssertEqual(h.count, n)
+            XCTAssertTrue(isPermutation(a, h.elements))
+        }
+    }
+
+    func testCreateRandomMinHeap() {
+        for n in 1...40 {
+            let a = randomArray(n)
+            let h = Heap(array: a, sort: <)
+            XCTAssertTrue(verifyMinHeap(h))
+            XCTAssertFalse(h.isEmpty)
+            XCTAssertEqual(h.count, n)
+            XCTAssertTrue(isPermutation(a, h.elements))
+        }
+    }
+
+    func testRemoving() {
+        var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+
+        //test index out of bounds
+        let v = h.removeAt(10)
+        XCTAssertEqual(v, nil)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+
+        let v1 = h.removeAt(5)
+        XCTAssertEqual(v1, 60)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
+
+        let v2 = h.removeAt(4)
+        XCTAssertEqual(v2, 20)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
+
+        let v3 = h.removeAt(4)
+        XCTAssertEqual(v3, 50)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 65, 70, 10])
+
+        let v4 = h.removeAt(0)
+        XCTAssertEqual(v4, 100)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [70, 65, 10])
+
+        XCTAssertEqual(h.peek()!, 70)
+        let v5 = h.remove()
+        XCTAssertEqual(v5, 70)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [65, 10])
+
+        XCTAssertEqual(h.peek()!, 65)
+        let v6 = h.remove()
+        XCTAssertEqual(v6, 65)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [10])
+
+        XCTAssertEqual(h.peek()!, 10)
+        let v7 = h.remove()
+        XCTAssertEqual(v7, 10)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [])
+
+        XCTAssertNil(h.peek())
     }
-    return true
-  }
-
-  fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
-    var a1 = array1
-    var a2 = array2
-    if a1.count != a2.count { return false }
-    while a1.count > 0 {
-      if let i = a2.index(of: a1[0]) {
-        a1.remove(at: 0)
-        a2.remove(at: i)
-      } else {
-        return false
-      }
+
+    func testRemoveEmpty() {
+        var heap = Heap<Int>(sort: >)
+        let removed = heap.remove()
+        XCTAssertNil(removed)
     }
-    return a2.count == 0
-  }
-
-  func testEmptyHeap() {
-    var heap = Heap<Int>(sort: <)
-    XCTAssertTrue(heap.isEmpty)
-    XCTAssertEqual(heap.count, 0)
-    XCTAssertNil(heap.peek())
-    XCTAssertNil(heap.remove())
-  }
-
-  func testIsEmpty() {
-    var heap = Heap<Int>(sort: >)
-    XCTAssertTrue(heap.isEmpty)
-    heap.insert(1)
-    XCTAssertFalse(heap.isEmpty)
-    heap.remove()
-    XCTAssertTrue(heap.isEmpty)
-  }
-
-  func testCount() {
-    var heap = Heap<Int>(sort: >)
-    XCTAssertEqual(0, heap.count)
-    heap.insert(1)
-    XCTAssertEqual(1, heap.count)
-  }
-
-  func testMaxHeapOneElement() {
-    let heap = Heap<Int>(array: [10], sort: >)
-    XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertFalse(heap.isEmpty)
-    XCTAssertEqual(heap.count, 1)
-    XCTAssertEqual(heap.peek()!, 10)
-  }
-
-  func testCreateMaxHeap() {
-    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h1))
-    XCTAssertFalse(verifyMinHeap(h1))
-    XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
-    XCTAssertFalse(h1.isEmpty)
-    XCTAssertEqual(h1.count, 7)
-    XCTAssertEqual(h1.peek()!, 7)
-
-    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h2))
-    XCTAssertFalse(verifyMinHeap(h2))
-    XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
-    XCTAssertFalse(h2.isEmpty)
-    XCTAssertEqual(h2.count, 7)
-    XCTAssertEqual(h2.peek()!, 7)
-
-    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h3))
-    XCTAssertFalse(verifyMinHeap(h3))
-    XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-    XCTAssertFalse(h3.isEmpty)
-    XCTAssertEqual(h3.count, 10)
-    XCTAssertEqual(h3.peek()!, 16)
-
-    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h4))
-    XCTAssertFalse(verifyMinHeap(h4))
-    XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
-    XCTAssertFalse(h4.isEmpty)
-    XCTAssertEqual(h4.count, 14)
-    XCTAssertEqual(h4.peek()!, 27)
-  }
-
-  func testCreateMinHeap() {
-    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
-    XCTAssertTrue(verifyMinHeap(h1))
-    XCTAssertFalse(verifyMaxHeap(h1))
-    XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
-    XCTAssertFalse(h1.isEmpty)
-    XCTAssertEqual(h1.count, 7)
-    XCTAssertEqual(h1.peek()!, 1)
-
-    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
-    XCTAssertTrue(verifyMinHeap(h2))
-    XCTAssertFalse(verifyMaxHeap(h2))
-    XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
-    XCTAssertFalse(h2.isEmpty)
-    XCTAssertEqual(h2.count, 7)
-    XCTAssertEqual(h2.peek()!, 1)
-
-    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
-    XCTAssertTrue(verifyMinHeap(h3))
-    XCTAssertFalse(verifyMaxHeap(h3))
-    XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
-    XCTAssertFalse(h3.isEmpty)
-    XCTAssertEqual(h3.count, 10)
-    XCTAssertEqual(h3.peek()!, 1)
-
-    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
-    XCTAssertTrue(verifyMinHeap(h4))
-    XCTAssertFalse(verifyMaxHeap(h4))
-    XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
-    XCTAssertFalse(h4.isEmpty)
-    XCTAssertEqual(h4.count, 14)
-    XCTAssertEqual(h4.peek()!, 0)
-  }
-
-  func testCreateMaxHeapEqualElements() {
-    let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-  }
-
-  func testCreateMinHeapEqualElements() {
-    let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
-    XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-  }
-
-  fileprivate func randomArray(_ n: Int) -> [Int] {
-    var a = [Int]()
-    for _ in 0..<n {
-      a.append(Int(arc4random()))
+
+    func testRemoveRoot() {
+        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+        XCTAssertEqual(h.peek()!, 15)
+        let v = h.remove()
+        XCTAssertEqual(v, 15)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
     }
-    return a
-  }
-
-  func testCreateRandomMaxHeap() {
-    for n in 1...40 {
-      let a = randomArray(n)
-      let h = Heap(array: a, sort: >)
-      XCTAssertTrue(verifyMaxHeap(h))
-      XCTAssertFalse(h.isEmpty)
-      XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+
+    func testRemoveRandomItems() {
+        for n in 1...40 {
+            var a = randomArray(n)
+            var h = Heap(array: a, sort: >)
+            XCTAssertTrue(verifyMaxHeap(h))
+            XCTAssertTrue(isPermutation(a, h.elements))
+
+            let m = (n + 1)/2
+            for k in 1...m {
+                let i = Int(arc4random_uniform(UInt32(n - k + 1)))
+                let v = h.removeAt(i)!
+                let j = a.index(of: v)!
+                a.remove(at: j)
+
+                XCTAssertTrue(verifyMaxHeap(h))
+                XCTAssertEqual(h.count, a.count)
+                XCTAssertEqual(h.count, n - k)
+                XCTAssertTrue(isPermutation(a, h.elements))
+            }
+        }
     }
-  }
-
-  func testCreateRandomMinHeap() {
-    for n in 1...40 {
-      let a = randomArray(n)
-      let h = Heap(array: a, sort: <)
-      XCTAssertTrue(verifyMinHeap(h))
-      XCTAssertFalse(h.isEmpty)
-      XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+
+    func testInsert() {
+        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+
+        h.insert(10)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
+    }
+
+    func testInsertArrayAndRemove() {
+        var heap = Heap<Int>(sort: >)
+        heap.insert([1, 3, 2, 7, 5, 9])
+        XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
+
+        XCTAssertEqual(9, heap.remove())
+        XCTAssertEqual(7, heap.remove())
+        XCTAssertEqual(5, heap.remove())
+        XCTAssertEqual(3, heap.remove())
+        XCTAssertEqual(2, heap.remove())
+        XCTAssertEqual(1, heap.remove())
+        XCTAssertNil(heap.remove())
     }
-  }
-
-  func testRemoving() {
-    var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-    //test index out of bounds
-    let v = h.removeAt(10)
-    XCTAssertEqual(v, nil)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-    let v1 = h.removeAt(5)
-    XCTAssertEqual(v1, 60)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
-
-    let v2 = h.removeAt(4)
-    XCTAssertEqual(v2, 20)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
-
-    let v3 = h.removeAt(4)
-    XCTAssertEqual(v3, 50)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10])
-
-    let v4 = h.removeAt(0)
-    XCTAssertEqual(v4, 100)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [70, 65, 10])
-
-    XCTAssertEqual(h.peek()!, 70)
-    let v5 = h.remove()
-    XCTAssertEqual(v5, 70)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [65, 10])
-
-    XCTAssertEqual(h.peek()!, 65)
-    let v6 = h.remove()
-    XCTAssertEqual(v6, 65)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [10])
-
-    XCTAssertEqual(h.peek()!, 10)
-    let v7 = h.remove()
-    XCTAssertEqual(v7, 10)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [])
-
-    XCTAssertNil(h.peek())
-  }
-
-  func testRemoveEmpty() {
-    var heap = Heap<Int>(sort: >)
-    let removed = heap.remove()
-    XCTAssertNil(removed)
-  }
-
-  func testRemoveRoot() {
-    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-    XCTAssertEqual(h.peek()!, 15)
-    let v = h.remove()
-    XCTAssertEqual(v, 15)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
-  }
-
-  func testRemoveRandomItems() {
-    for n in 1...40 {
-      var a = randomArray(n)
-      var h = Heap(array: a, sort: >)
-      XCTAssertTrue(verifyMaxHeap(h))
-      XCTAssertTrue(isPermutation(a, h.elements))
-
-      let m = (n + 1)/2
-      for k in 1...m {
-        let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        let v = h.removeAt(i)!
-        let j = a.index(of: v)!
-        a.remove(at: j)
 
+    func testReplace() {
+        var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+
+        h.replace(index: 5, value: 13)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+
+        //test index out of bounds
+        h.replace(index: 20, value: 2)
         XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.count, a.count)
-        XCTAssertEqual(h.count, n - k)
-        XCTAssertTrue(isPermutation(a, h.elements))
-      }
+        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
     }
-  }
-
-  func testInsert() {
-    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-
-    h.insert(10)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
-  }
-
-  func testInsertArrayAndRemove() {
-    var heap = Heap<Int>(sort: >)
-    heap.insert([1, 3, 2, 7, 5, 9])
-    XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
-
-    XCTAssertEqual(9, heap.remove())
-    XCTAssertEqual(7, heap.remove())
-    XCTAssertEqual(5, heap.remove())
-    XCTAssertEqual(3, heap.remove())
-    XCTAssertEqual(2, heap.remove())
-    XCTAssertEqual(1, heap.remove())
-    XCTAssertNil(heap.remove())
-  }
-
-  func testReplace() {
-    var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-
-    h.replace(index: 5, value: 13)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-
-    //test index out of bounds
-    h.replace(index: 20, value: 2)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-  }
 }
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
index 22112fa60..617e29f27 100644
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -226,7 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..80ed35600 100644
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 33b4078f41776ded597dbce39ff4ddcdf8f67bab Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:37:45 -0700
Subject: [PATCH 1096/1679] [Swift 4] Update Heap Sort

---
 Heap Sort/HeapSort.swift                      |   2 +-
 Heap Sort/Tests/HeapSortTests.swift           |  41 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     |   4 +-
 Heap/Heap.swift                               | 430 +++++++++---------
 4 files changed, 242 insertions(+), 235 deletions(-)

diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index 3fbaab14d..1e568f91f 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,7 +1,7 @@
 extension Heap {
   public mutating func sort() -> [T] {
     for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-      swap(&elements[0], &elements[i])
+        elements.swapAt(0, i)
       shiftDown(0, heapSize: i)
     }
     return elements
diff --git a/Heap Sort/Tests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
index e5e847a74..55f2f52b4 100644
--- a/Heap Sort/Tests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,26 +1,33 @@
 import XCTest
 
 class HeapSortTests: XCTestCase {
-  func testSort() {
-    var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
-    let a1 = h1.sort()
-    XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    
+    func testSort() {
+        var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
+        let a1 = h1.sort()
+        XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
 
-    let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
-    XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
+        let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
+        XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
 
-    var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
-    let a2 = h2.sort()
-    XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+        var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
+        let a2 = h2.sort()
+        XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
 
-    let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
-    XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+        let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
+        XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
 
-    var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
-    let a3 = h3.sort()
-    XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
+        var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
+        let a3 = h3.sort()
+        XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
 
-    let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
-    XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
-  }
+        let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
+        XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
+    }
 }
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index f7f101cd6..45b3f5821 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -230,7 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,7 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 80b40c65f..18a350dca 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,224 +4,224 @@
 //
 
 public struct Heap<T> {
-  /** The array that stores the heap's nodes. */
-  var elements = [T]()
-
-  /** Determines whether this is a max-heap (>) or min-heap (<). */
-  fileprivate var isOrderedBefore: (T, T) -> Bool
-
-  /**
-   * Creates an empty heap.
-   * The sort function determines whether this is a min-heap or max-heap.
-   * For integers, > makes a max-heap, < makes a min-heap.
-   */
-  public init(sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-  }
-
-  /**
-   * Creates a heap from an array. The order of the array does not matter;
-   * the elements are inserted into the heap in the order determined by the
-   * sort function.
-   */
-  public init(array: [T], sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-    buildHeap(fromArray: array)
-  }
-
-  /*
-  // This version has O(n log n) performance.
-  private mutating func buildHeap(array: [T]) {
-    elements.reserveCapacity(array.count)
-    for value in array {
-      insert(value)
-    }
-  }
-  */
-
-  /**
-   * Converts an array to a max-heap or min-heap in a bottom-up manner.
-   * Performance: This runs pretty much in O(n).
-   */
-  fileprivate mutating func buildHeap(fromArray array: [T]) {
-    elements = array
-    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(i, heapSize: elements.count)
-    }
-  }
-
-  public var isEmpty: Bool {
-    return elements.isEmpty
-  }
-
-  public var count: Int {
-    return elements.count
-  }
-
-  /**
-   * Returns the index of the parent of the element at index i.
-   * The element at index 0 is the root of the tree and has no parent.
-   */
-  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
-    return (i - 1) / 2
-  }
-
-  /**
-   * Returns the index of the left child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no left child.
-   */
-  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 1
-  }
-
-  /**
-   * Returns the index of the right child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no right child.
-   */
-  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 2
-  }
-
-  /**
-   * Returns the maximum value in the heap (for a max-heap) or the minimum
-   * value (for a min-heap).
-   */
-  public func peek() -> T? {
-    return elements.first
-  }
-
-  /**
-   * Adds a new value to the heap. This reorders the heap so that the max-heap
-   * or min-heap property still holds. Performance: O(log n).
-   */
-  public mutating func insert(_ value: T) {
-    elements.append(value)
-    shiftUp(elements.count - 1)
-  }
-
-  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-    for value in sequence {
-      insert(value)
-    }
-  }
-
-  /**
-   * Allows you to change an element. In a max-heap, the new element should be
-   * larger than the old one; in a min-heap it should be smaller.
-   */
-  public mutating func replace(index i: Int, value: T) {
-    guard i < elements.count else { return }
-
-    assert(isOrderedBefore(value, elements[i]))
-    elements[i] = value
-    shiftUp(i)
-  }
-
-  /**
-   * Removes the root node from the heap. For a max-heap, this is the maximum
-   * value; for a min-heap it is the minimum value. Performance: O(log n).
-   */
-  @discardableResult public mutating func remove() -> T? {
-    if elements.isEmpty {
-      return nil
-    } else if elements.count == 1 {
-      return elements.removeLast()
-    } else {
-      // Use the last node to replace the first one, then fix the heap by
-      // shifting this new first node into its proper position.
-      let value = elements[0]
-      elements[0] = elements.removeLast()
-      shiftDown()
-      return value
-    }
-  }
-
-  /**
-   * Removes an arbitrary node from the heap. Performance: O(log n). You need
-   * to know the node's index, which may actually take O(n) steps to find.
-   */
-  public mutating func removeAt(_ index: Int) -> T? {
-    guard index < elements.count else { return nil }
-
-    let size = elements.count - 1
-    if index != size {
-      swap(&elements[index], &elements[size])
-      shiftDown(index, heapSize: size)
-      shiftUp(index)
-    }
-    return elements.removeLast()
-  }
-
-  /**
-   * Takes a child node and looks at its parents; if a parent is not larger
-   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
-   */
-  mutating func shiftUp(_ index: Int) {
-    var childIndex = index
-    let child = elements[childIndex]
-    var parentIndex = self.parentIndex(ofIndex: childIndex)
-
-    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-      elements[childIndex] = elements[parentIndex]
-      childIndex = parentIndex
-      parentIndex = self.parentIndex(ofIndex: childIndex)
-    }
-
-    elements[childIndex] = child
-  }
-
-  mutating func shiftDown() {
-    shiftDown(0, heapSize: elements.count)
-  }
-
-  /**
-   * Looks at a parent node and makes sure it is still larger (max-heap) or
-   * smaller (min-heap) than its childeren.
-   */
-  mutating func shiftDown(_ index: Int, heapSize: Int) {
-    var parentIndex = index
-
-    while true {
-      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-      let rightChildIndex = leftChildIndex + 1
-
-      // Figure out which comes first if we order them by the sort function:
-      // the parent, the left child, or the right child. If the parent comes
-      // first, we're done. If not, that element is out-of-place and we make
-      // it "float down" the tree until the heap property is restored.
-      var first = parentIndex
-      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-        first = leftChildIndex
-      }
-      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-        first = rightChildIndex
-      }
-      if first == parentIndex { return }
-
-      swap(&elements[parentIndex], &elements[first])
-      parentIndex = first
-    }
-  }
+    /** The array that stores the heap's nodes. */
+    var elements = [T]()
+
+    /** Determines whether this is a max-heap (>) or min-heap (<). */
+    fileprivate var isOrderedBefore: (T, T) -> Bool
+
+    /**
+     * Creates an empty heap.
+     * The sort function determines whether this is a min-heap or max-heap.
+     * For integers, > makes a max-heap, < makes a min-heap.
+     */
+    public init(sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+    }
+
+    /**
+     * Creates a heap from an array. The order of the array does not matter;
+     * the elements are inserted into the heap in the order determined by the
+     * sort function.
+     */
+    public init(array: [T], sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+        buildHeap(fromArray: array)
+    }
+
+    /*
+     // This version has O(n log n) performance.
+     private mutating func buildHeap(array: [T]) {
+     elements.reserveCapacity(array.count)
+     for value in array {
+     insert(value)
+     }
+     }
+     */
+
+    /**
+     * Converts an array to a max-heap or min-heap in a bottom-up manner.
+     * Performance: This runs pretty much in O(n).
+     */
+    fileprivate mutating func buildHeap(fromArray array: [T]) {
+        elements = array
+        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+            shiftDown(i, heapSize: elements.count)
+        }
+    }
+
+    public var isEmpty: Bool {
+        return elements.isEmpty
+    }
+
+    public var count: Int {
+        return elements.count
+    }
+
+    /**
+     * Returns the index of the parent of the element at index i.
+     * The element at index 0 is the root of the tree and has no parent.
+     */
+    @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+        return (i - 1) / 2
+    }
+
+    /**
+     * Returns the index of the left child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no left child.
+     */
+    @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 1
+    }
+
+    /**
+     * Returns the index of the right child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no right child.
+     */
+    @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 2
+    }
+
+    /**
+     * Returns the maximum value in the heap (for a max-heap) or the minimum
+     * value (for a min-heap).
+     */
+    public func peek() -> T? {
+        return elements.first
+    }
+
+    /**
+     * Adds a new value to the heap. This reorders the heap so that the max-heap
+     * or min-heap property still holds. Performance: O(log n).
+     */
+    public mutating func insert(_ value: T) {
+        elements.append(value)
+        shiftUp(elements.count - 1)
+    }
+
+    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+        for value in sequence {
+            insert(value)
+        }
+    }
+
+    /**
+     * Allows you to change an element. In a max-heap, the new element should be
+     * larger than the old one; in a min-heap it should be smaller.
+     */
+    public mutating func replace(index i: Int, value: T) {
+        guard i < elements.count else { return }
+
+        assert(isOrderedBefore(value, elements[i]))
+        elements[i] = value
+        shiftUp(i)
+    }
+
+    /**
+     * Removes the root node from the heap. For a max-heap, this is the maximum
+     * value; for a min-heap it is the minimum value. Performance: O(log n).
+     */
+    @discardableResult public mutating func remove() -> T? {
+        if elements.isEmpty {
+            return nil
+        } else if elements.count == 1 {
+            return elements.removeLast()
+        } else {
+            // Use the last node to replace the first one, then fix the heap by
+            // shifting this new first node into its proper position.
+            let value = elements[0]
+            elements[0] = elements.removeLast()
+            shiftDown()
+            return value
+        }
+    }
+
+    /**
+     * Removes an arbitrary node from the heap. Performance: O(log n). You need
+     * to know the node's index, which may actually take O(n) steps to find.
+     */
+    public mutating func removeAt(_ index: Int) -> T? {
+        guard index < elements.count else { return nil }
+
+        let size = elements.count - 1
+        if index != size {
+            elements.swapAt(index, size)
+            shiftDown(index, heapSize: size)
+            shiftUp(index)
+        }
+        return elements.removeLast()
+    }
+
+    /**
+     * Takes a child node and looks at its parents; if a parent is not larger
+     * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+     */
+    mutating func shiftUp(_ index: Int) {
+        var childIndex = index
+        let child = elements[childIndex]
+        var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+            elements[childIndex] = elements[parentIndex]
+            childIndex = parentIndex
+            parentIndex = self.parentIndex(ofIndex: childIndex)
+        }
+
+        elements[childIndex] = child
+    }
+
+    mutating func shiftDown() {
+        shiftDown(0, heapSize: elements.count)
+    }
+
+    /**
+     * Looks at a parent node and makes sure it is still larger (max-heap) or
+     * smaller (min-heap) than its childeren.
+     */
+    mutating func shiftDown(_ index: Int, heapSize: Int) {
+        var parentIndex = index
+
+        while true {
+            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let rightChildIndex = leftChildIndex + 1
+
+            // Figure out which comes first if we order them by the sort function:
+            // the parent, the left child, or the right child. If the parent comes
+            // first, we're done. If not, that element is out-of-place and we make
+            // it "float down" the tree until the heap property is restored.
+            var first = parentIndex
+            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+                first = leftChildIndex
+            }
+            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+                first = rightChildIndex
+            }
+            if first == parentIndex { return }
+
+            elements.swapAt(parentIndex, first)
+            parentIndex = first
+        }
+    }
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-  /**
-   * Searches the heap for the given element. Performance: O(n).
-   */
-  public func index(of element: T) -> Int? {
-    return index(of: element, 0)
-  }
-
-  fileprivate func index(of element: T, _ i: Int) -> Int? {
-    if i >= count { return nil }
-    if isOrderedBefore(element, elements[i]) { return nil }
-    if element == elements[i] { return i }
-    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
-    return nil
-  }
+    /**
+     * Searches the heap for the given element. Performance: O(n).
+     */
+    public func index(of element: T) -> Int? {
+        return index(of: element, 0)
+    }
+
+    fileprivate func index(of element: T, _ i: Int) -> Int? {
+        if i >= count { return nil }
+        if isOrderedBefore(element, elements[i]) { return nil }
+        if element == elements[i] { return i }
+        if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+        if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+        return nil
+    }
 }

From 028b898af99b0979e0ea0d156f3dcb4ad45b4796 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 31 Jul 2017 16:09:43 +0900
Subject: [PATCH 1097/1679] Updates the indentation of the code to 2 spaces.

---
 Heap/Heap.swift            | 430 ++++++++++++-------------
 Heap/Tests/HeapTests.swift | 626 ++++++++++++++++++-------------------
 2 files changed, 528 insertions(+), 528 deletions(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 18a350dca..b0355da5d 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,224 +4,224 @@
 //
 
 public struct Heap<T> {
-    /** The array that stores the heap's nodes. */
-    var elements = [T]()
-
-    /** Determines whether this is a max-heap (>) or min-heap (<). */
-    fileprivate var isOrderedBefore: (T, T) -> Bool
-
-    /**
-     * Creates an empty heap.
-     * The sort function determines whether this is a min-heap or max-heap.
-     * For integers, > makes a max-heap, < makes a min-heap.
-     */
-    public init(sort: @escaping (T, T) -> Bool) {
-        self.isOrderedBefore = sort
-    }
-
-    /**
-     * Creates a heap from an array. The order of the array does not matter;
-     * the elements are inserted into the heap in the order determined by the
-     * sort function.
-     */
-    public init(array: [T], sort: @escaping (T, T) -> Bool) {
-        self.isOrderedBefore = sort
-        buildHeap(fromArray: array)
-    }
-
-    /*
-     // This version has O(n log n) performance.
-     private mutating func buildHeap(array: [T]) {
-     elements.reserveCapacity(array.count)
-     for value in array {
-     insert(value)
-     }
-     }
-     */
-
-    /**
-     * Converts an array to a max-heap or min-heap in a bottom-up manner.
-     * Performance: This runs pretty much in O(n).
-     */
-    fileprivate mutating func buildHeap(fromArray array: [T]) {
-        elements = array
-        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-            shiftDown(i, heapSize: elements.count)
-        }
-    }
-
-    public var isEmpty: Bool {
-        return elements.isEmpty
-    }
-
-    public var count: Int {
-        return elements.count
-    }
-
-    /**
-     * Returns the index of the parent of the element at index i.
-     * The element at index 0 is the root of the tree and has no parent.
-     */
-    @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
-        return (i - 1) / 2
-    }
-
-    /**
-     * Returns the index of the left child of the element at index i.
-     * Note that this index can be greater than the heap size, in which case
-     * there is no left child.
-     */
-    @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 1
-    }
-
-    /**
-     * Returns the index of the right child of the element at index i.
-     * Note that this index can be greater than the heap size, in which case
-     * there is no right child.
-     */
-    @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 2
-    }
-
-    /**
-     * Returns the maximum value in the heap (for a max-heap) or the minimum
-     * value (for a min-heap).
-     */
-    public func peek() -> T? {
-        return elements.first
-    }
-
-    /**
-     * Adds a new value to the heap. This reorders the heap so that the max-heap
-     * or min-heap property still holds. Performance: O(log n).
-     */
-    public mutating func insert(_ value: T) {
-        elements.append(value)
-        shiftUp(elements.count - 1)
-    }
-
-    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-        for value in sequence {
-            insert(value)
-        }
-    }
-
-    /**
-     * Allows you to change an element. In a max-heap, the new element should be
-     * larger than the old one; in a min-heap it should be smaller.
-     */
-    public mutating func replace(index i: Int, value: T) {
-        guard i < elements.count else { return }
-
-        assert(isOrderedBefore(value, elements[i]))
-        elements[i] = value
-        shiftUp(i)
-    }
-
-    /**
-     * Removes the root node from the heap. For a max-heap, this is the maximum
-     * value; for a min-heap it is the minimum value. Performance: O(log n).
-     */
-    @discardableResult public mutating func remove() -> T? {
-        if elements.isEmpty {
-            return nil
-        } else if elements.count == 1 {
-            return elements.removeLast()
-        } else {
-            // Use the last node to replace the first one, then fix the heap by
-            // shifting this new first node into its proper position.
-            let value = elements[0]
-            elements[0] = elements.removeLast()
-            shiftDown()
-            return value
-        }
-    }
-
-    /**
-     * Removes an arbitrary node from the heap. Performance: O(log n). You need
-     * to know the node's index, which may actually take O(n) steps to find.
-     */
-    public mutating func removeAt(_ index: Int) -> T? {
-        guard index < elements.count else { return nil }
-
-        let size = elements.count - 1
-        if index != size {
-            elements.swapAt(index, size)
-            shiftDown(index, heapSize: size)
-            shiftUp(index)
-        }
-        return elements.removeLast()
-    }
-
-    /**
-     * Takes a child node and looks at its parents; if a parent is not larger
-     * (max-heap) or not smaller (min-heap) than the child, we exchange them.
-     */
-    mutating func shiftUp(_ index: Int) {
-        var childIndex = index
-        let child = elements[childIndex]
-        var parentIndex = self.parentIndex(ofIndex: childIndex)
-
-        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-            elements[childIndex] = elements[parentIndex]
-            childIndex = parentIndex
-            parentIndex = self.parentIndex(ofIndex: childIndex)
-        }
-
-        elements[childIndex] = child
-    }
-
-    mutating func shiftDown() {
-        shiftDown(0, heapSize: elements.count)
-    }
-
-    /**
-     * Looks at a parent node and makes sure it is still larger (max-heap) or
-     * smaller (min-heap) than its childeren.
-     */
-    mutating func shiftDown(_ index: Int, heapSize: Int) {
-        var parentIndex = index
-
-        while true {
-            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-            let rightChildIndex = leftChildIndex + 1
-
-            // Figure out which comes first if we order them by the sort function:
-            // the parent, the left child, or the right child. If the parent comes
-            // first, we're done. If not, that element is out-of-place and we make
-            // it "float down" the tree until the heap property is restored.
-            var first = parentIndex
-            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-                first = leftChildIndex
-            }
-            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-                first = rightChildIndex
-            }
-            if first == parentIndex { return }
-
-            elements.swapAt(parentIndex, first)
-            parentIndex = first
-        }
-    }
+  /** The array that stores the heap's nodes. */
+  var elements = [T]()
+  
+  /** Determines whether this is a max-heap (>) or min-heap (<). */
+  fileprivate var isOrderedBefore: (T, T) -> Bool
+  
+  /**
+   * Creates an empty heap.
+   * The sort function determines whether this is a min-heap or max-heap.
+   * For integers, > makes a max-heap, < makes a min-heap.
+   */
+  public init(sort: @escaping (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+  }
+  
+  /**
+   * Creates a heap from an array. The order of the array does not matter;
+   * the elements are inserted into the heap in the order determined by the
+   * sort function.
+   */
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+    buildHeap(fromArray: array)
+  }
+  
+  /*
+   // This version has O(n log n) performance.
+   private mutating func buildHeap(array: [T]) {
+   elements.reserveCapacity(array.count)
+   for value in array {
+   insert(value)
+   }
+   }
+   */
+  
+  /**
+   * Converts an array to a max-heap or min-heap in a bottom-up manner.
+   * Performance: This runs pretty much in O(n).
+   */
+  fileprivate mutating func buildHeap(fromArray array: [T]) {
+    elements = array
+    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+      shiftDown(i, heapSize: elements.count)
+    }
+  }
+  
+  public var isEmpty: Bool {
+    return elements.isEmpty
+  }
+  
+  public var count: Int {
+    return elements.count
+  }
+  
+  /**
+   * Returns the index of the parent of the element at index i.
+   * The element at index 0 is the root of the tree and has no parent.
+   */
+  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+    return (i - 1) / 2
+  }
+  
+  /**
+   * Returns the index of the left child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no left child.
+   */
+  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+    return 2*i + 1
+  }
+  
+  /**
+   * Returns the index of the right child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no right child.
+   */
+  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+    return 2*i + 2
+  }
+  
+  /**
+   * Returns the maximum value in the heap (for a max-heap) or the minimum
+   * value (for a min-heap).
+   */
+  public func peek() -> T? {
+    return elements.first
+  }
+  
+  /**
+   * Adds a new value to the heap. This reorders the heap so that the max-heap
+   * or min-heap property still holds. Performance: O(log n).
+   */
+  public mutating func insert(_ value: T) {
+    elements.append(value)
+    shiftUp(elements.count - 1)
+  }
+  
+  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+    for value in sequence {
+      insert(value)
+    }
+  }
+  
+  /**
+   * Allows you to change an element. In a max-heap, the new element should be
+   * larger than the old one; in a min-heap it should be smaller.
+   */
+  public mutating func replace(index i: Int, value: T) {
+    guard i < elements.count else { return }
+    
+    assert(isOrderedBefore(value, elements[i]))
+    elements[i] = value
+    shiftUp(i)
+  }
+  
+  /**
+   * Removes the root node from the heap. For a max-heap, this is the maximum
+   * value; for a min-heap it is the minimum value. Performance: O(log n).
+   */
+  @discardableResult public mutating func remove() -> T? {
+    if elements.isEmpty {
+      return nil
+    } else if elements.count == 1 {
+      return elements.removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = elements[0]
+      elements[0] = elements.removeLast()
+      shiftDown()
+      return value
+    }
+  }
+  
+  /**
+   * Removes an arbitrary node from the heap. Performance: O(log n). You need
+   * to know the node's index, which may actually take O(n) steps to find.
+   */
+  public mutating func removeAt(_ index: Int) -> T? {
+    guard index < elements.count else { return nil }
+    
+    let size = elements.count - 1
+    if index != size {
+      elements.swapAt(index, size)
+      shiftDown(index, heapSize: size)
+      shiftUp(index)
+    }
+    return elements.removeLast()
+  }
+  
+  /**
+   * Takes a child node and looks at its parents; if a parent is not larger
+   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+   */
+  mutating func shiftUp(_ index: Int) {
+    var childIndex = index
+    let child = elements[childIndex]
+    var parentIndex = self.parentIndex(ofIndex: childIndex)
+    
+    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+      elements[childIndex] = elements[parentIndex]
+      childIndex = parentIndex
+      parentIndex = self.parentIndex(ofIndex: childIndex)
+    }
+    
+    elements[childIndex] = child
+  }
+  
+  mutating func shiftDown() {
+    shiftDown(0, heapSize: elements.count)
+  }
+  
+  /**
+   * Looks at a parent node and makes sure it is still larger (max-heap) or
+   * smaller (min-heap) than its childeren.
+   */
+  mutating func shiftDown(_ index: Int, heapSize: Int) {
+    var parentIndex = index
+    
+    while true {
+      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+      let rightChildIndex = leftChildIndex + 1
+      
+      // Figure out which comes first if we order them by the sort function:
+      // the parent, the left child, or the right child. If the parent comes
+      // first, we're done. If not, that element is out-of-place and we make
+      // it "float down" the tree until the heap property is restored.
+      var first = parentIndex
+      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+        first = leftChildIndex
+      }
+      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+        first = rightChildIndex
+      }
+      if first == parentIndex { return }
+      
+      elements.swapAt(parentIndex, first)
+      parentIndex = first
+    }
+  }
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-    /**
-     * Searches the heap for the given element. Performance: O(n).
-     */
-    public func index(of element: T) -> Int? {
-        return index(of: element, 0)
-    }
-
-    fileprivate func index(of element: T, _ i: Int) -> Int? {
-        if i >= count { return nil }
-        if isOrderedBefore(element, elements[i]) { return nil }
-        if element == elements[i] { return i }
-        if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-        if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
-        return nil
-    }
+  /**
+   * Searches the heap for the given element. Performance: O(n).
+   */
+  public func index(of element: T) -> Int? {
+    return index(of: element, 0)
+  }
+  
+  fileprivate func index(of element: T, _ i: Int) -> Int? {
+    if i >= count { return nil }
+    if isOrderedBefore(element, elements[i]) { return nil }
+    if element == elements[i] { return i }
+    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+    return nil
+  }
 }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 0af3a14e0..66be0931c 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -6,325 +6,325 @@
 import XCTest
 
 class HeapTests: XCTestCase {
-
-    func testSwift4() {
-        // last checked with Xcode 9.0b4
-        #if swift(>=4.0)
-            print("Hello, Swift 4!")
-        #endif
-    }
-
-    fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
-        for i in 0..<h.count {
-            let left = h.leftChildIndex(ofIndex: i)
-            let right = h.rightChildIndex(ofIndex: i)
-            let parent = h.parentIndex(ofIndex: i)
-            if left < h.count && h.elements[i] < h.elements[left] { return false }
-            if right < h.count && h.elements[i] < h.elements[right] { return false }
-            if i > 0 && h.elements[parent] < h.elements[i] { return false }
-        }
-        return true
-    }
-
-    fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
-        for i in 0..<h.count {
-            let left = h.leftChildIndex(ofIndex: i)
-            let right = h.rightChildIndex(ofIndex: i)
-            let parent = h.parentIndex(ofIndex: i)
-            if left < h.count && h.elements[i] > h.elements[left] { return false }
-            if right < h.count && h.elements[i] > h.elements[right] { return false }
-            if i > 0 && h.elements[parent] > h.elements[i] { return false }
-        }
-        return true
+  
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
+    for i in 0..<h.count {
+      let left = h.leftChildIndex(ofIndex: i)
+      let right = h.rightChildIndex(ofIndex: i)
+      let parent = h.parentIndex(ofIndex: i)
+      if left < h.count && h.elements[i] < h.elements[left] { return false }
+      if right < h.count && h.elements[i] < h.elements[right] { return false }
+      if i > 0 && h.elements[parent] < h.elements[i] { return false }
     }
-
-    fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
-        var a1 = array1
-        var a2 = array2
-        if a1.count != a2.count { return false }
-        while a1.count > 0 {
-            if let i = a2.index(of: a1[0]) {
-                a1.remove(at: 0)
-                a2.remove(at: i)
-            } else {
-                return false
-            }
-        }
-        return a2.count == 0
+    return true
+  }
+  
+  fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
+    for i in 0..<h.count {
+      let left = h.leftChildIndex(ofIndex: i)
+      let right = h.rightChildIndex(ofIndex: i)
+      let parent = h.parentIndex(ofIndex: i)
+      if left < h.count && h.elements[i] > h.elements[left] { return false }
+      if right < h.count && h.elements[i] > h.elements[right] { return false }
+      if i > 0 && h.elements[parent] > h.elements[i] { return false }
     }
-
-    func testEmptyHeap() {
-        var heap = Heap<Int>(sort: <)
-        XCTAssertTrue(heap.isEmpty)
-        XCTAssertEqual(heap.count, 0)
-        XCTAssertNil(heap.peek())
-        XCTAssertNil(heap.remove())
+    return true
+  }
+  
+  fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
+    var a1 = array1
+    var a2 = array2
+    if a1.count != a2.count { return false }
+    while a1.count > 0 {
+      if let i = a2.index(of: a1[0]) {
+        a1.remove(at: 0)
+        a2.remove(at: i)
+      } else {
+        return false
+      }
     }
-
-    func testIsEmpty() {
-        var heap = Heap<Int>(sort: >)
-        XCTAssertTrue(heap.isEmpty)
-        heap.insert(1)
-        XCTAssertFalse(heap.isEmpty)
-        heap.remove()
-        XCTAssertTrue(heap.isEmpty)
+    return a2.count == 0
+  }
+  
+  func testEmptyHeap() {
+    var heap = Heap<Int>(sort: <)
+    XCTAssertTrue(heap.isEmpty)
+    XCTAssertEqual(heap.count, 0)
+    XCTAssertNil(heap.peek())
+    XCTAssertNil(heap.remove())
+  }
+  
+  func testIsEmpty() {
+    var heap = Heap<Int>(sort: >)
+    XCTAssertTrue(heap.isEmpty)
+    heap.insert(1)
+    XCTAssertFalse(heap.isEmpty)
+    heap.remove()
+    XCTAssertTrue(heap.isEmpty)
+  }
+  
+  func testCount() {
+    var heap = Heap<Int>(sort: >)
+    XCTAssertEqual(0, heap.count)
+    heap.insert(1)
+    XCTAssertEqual(1, heap.count)
+  }
+  
+  func testMaxHeapOneElement() {
+    let heap = Heap<Int>(array: [10], sort: >)
+    XCTAssertTrue(verifyMaxHeap(heap))
+    XCTAssertTrue(verifyMinHeap(heap))
+    XCTAssertFalse(heap.isEmpty)
+    XCTAssertEqual(heap.count, 1)
+    XCTAssertEqual(heap.peek()!, 10)
+  }
+  
+  func testCreateMaxHeap() {
+    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h1))
+    XCTAssertFalse(verifyMinHeap(h1))
+    XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
+    XCTAssertFalse(h1.isEmpty)
+    XCTAssertEqual(h1.count, 7)
+    XCTAssertEqual(h1.peek()!, 7)
+    
+    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h2))
+    XCTAssertFalse(verifyMinHeap(h2))
+    XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
+    XCTAssertFalse(h2.isEmpty)
+    XCTAssertEqual(h2.count, 7)
+    XCTAssertEqual(h2.peek()!, 7)
+    
+    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h3))
+    XCTAssertFalse(verifyMinHeap(h3))
+    XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+    XCTAssertFalse(h3.isEmpty)
+    XCTAssertEqual(h3.count, 10)
+    XCTAssertEqual(h3.peek()!, 16)
+    
+    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h4))
+    XCTAssertFalse(verifyMinHeap(h4))
+    XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
+    XCTAssertFalse(h4.isEmpty)
+    XCTAssertEqual(h4.count, 14)
+    XCTAssertEqual(h4.peek()!, 27)
+  }
+  
+  func testCreateMinHeap() {
+    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
+    XCTAssertTrue(verifyMinHeap(h1))
+    XCTAssertFalse(verifyMaxHeap(h1))
+    XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
+    XCTAssertFalse(h1.isEmpty)
+    XCTAssertEqual(h1.count, 7)
+    XCTAssertEqual(h1.peek()!, 1)
+    
+    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
+    XCTAssertTrue(verifyMinHeap(h2))
+    XCTAssertFalse(verifyMaxHeap(h2))
+    XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
+    XCTAssertFalse(h2.isEmpty)
+    XCTAssertEqual(h2.count, 7)
+    XCTAssertEqual(h2.peek()!, 1)
+    
+    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
+    XCTAssertTrue(verifyMinHeap(h3))
+    XCTAssertFalse(verifyMaxHeap(h3))
+    XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
+    XCTAssertFalse(h3.isEmpty)
+    XCTAssertEqual(h3.count, 10)
+    XCTAssertEqual(h3.peek()!, 1)
+    
+    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
+    XCTAssertTrue(verifyMinHeap(h4))
+    XCTAssertFalse(verifyMaxHeap(h4))
+    XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
+    XCTAssertFalse(h4.isEmpty)
+    XCTAssertEqual(h4.count, 14)
+    XCTAssertEqual(h4.peek()!, 0)
+  }
+  
+  func testCreateMaxHeapEqualElements() {
+    let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(heap))
+    XCTAssertTrue(verifyMinHeap(heap))
+    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+  }
+  
+  func testCreateMinHeapEqualElements() {
+    let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
+    XCTAssertTrue(verifyMinHeap(heap))
+    XCTAssertTrue(verifyMaxHeap(heap))
+    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+  }
+  
+  fileprivate func randomArray(_ n: Int) -> [Int] {
+    var a = [Int]()
+    for _ in 0..<n {
+      a.append(Int(arc4random()))
     }
-
-    func testCount() {
-        var heap = Heap<Int>(sort: >)
-        XCTAssertEqual(0, heap.count)
-        heap.insert(1)
-        XCTAssertEqual(1, heap.count)
+    return a
+  }
+  
+  func testCreateRandomMaxHeap() {
+    for n in 1...40 {
+      let a = randomArray(n)
+      let h = Heap(array: a, sort: >)
+      XCTAssertTrue(verifyMaxHeap(h))
+      XCTAssertFalse(h.isEmpty)
+      XCTAssertEqual(h.count, n)
+      XCTAssertTrue(isPermutation(a, h.elements))
     }
-
-    func testMaxHeapOneElement() {
-        let heap = Heap<Int>(array: [10], sort: >)
-        XCTAssertTrue(verifyMaxHeap(heap))
-        XCTAssertTrue(verifyMinHeap(heap))
-        XCTAssertFalse(heap.isEmpty)
-        XCTAssertEqual(heap.count, 1)
-        XCTAssertEqual(heap.peek()!, 10)
+  }
+  
+  func testCreateRandomMinHeap() {
+    for n in 1...40 {
+      let a = randomArray(n)
+      let h = Heap(array: a, sort: <)
+      XCTAssertTrue(verifyMinHeap(h))
+      XCTAssertFalse(h.isEmpty)
+      XCTAssertEqual(h.count, n)
+      XCTAssertTrue(isPermutation(a, h.elements))
     }
-
-    func testCreateMaxHeap() {
-        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h1))
-        XCTAssertFalse(verifyMinHeap(h1))
-        XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
-        XCTAssertFalse(h1.isEmpty)
-        XCTAssertEqual(h1.count, 7)
-        XCTAssertEqual(h1.peek()!, 7)
-
-        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h2))
-        XCTAssertFalse(verifyMinHeap(h2))
-        XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
-        XCTAssertFalse(h2.isEmpty)
-        XCTAssertEqual(h2.count, 7)
-        XCTAssertEqual(h2.peek()!, 7)
-
-        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h3))
-        XCTAssertFalse(verifyMinHeap(h3))
-        XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-        XCTAssertFalse(h3.isEmpty)
-        XCTAssertEqual(h3.count, 10)
-        XCTAssertEqual(h3.peek()!, 16)
-
-        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h4))
-        XCTAssertFalse(verifyMinHeap(h4))
-        XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
-        XCTAssertFalse(h4.isEmpty)
-        XCTAssertEqual(h4.count, 14)
-        XCTAssertEqual(h4.peek()!, 27)
-    }
-
-    func testCreateMinHeap() {
-        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
-        XCTAssertTrue(verifyMinHeap(h1))
-        XCTAssertFalse(verifyMaxHeap(h1))
-        XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
-        XCTAssertFalse(h1.isEmpty)
-        XCTAssertEqual(h1.count, 7)
-        XCTAssertEqual(h1.peek()!, 1)
-
-        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
-        XCTAssertTrue(verifyMinHeap(h2))
-        XCTAssertFalse(verifyMaxHeap(h2))
-        XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
-        XCTAssertFalse(h2.isEmpty)
-        XCTAssertEqual(h2.count, 7)
-        XCTAssertEqual(h2.peek()!, 1)
-
-        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
-        XCTAssertTrue(verifyMinHeap(h3))
-        XCTAssertFalse(verifyMaxHeap(h3))
-        XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
-        XCTAssertFalse(h3.isEmpty)
-        XCTAssertEqual(h3.count, 10)
-        XCTAssertEqual(h3.peek()!, 1)
-
-        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
-        XCTAssertTrue(verifyMinHeap(h4))
-        XCTAssertFalse(verifyMaxHeap(h4))
-        XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
-        XCTAssertFalse(h4.isEmpty)
-        XCTAssertEqual(h4.count, 14)
-        XCTAssertEqual(h4.peek()!, 0)
-    }
-
-    func testCreateMaxHeapEqualElements() {
-        let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(heap))
-        XCTAssertTrue(verifyMinHeap(heap))
-        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-    }
-
-    func testCreateMinHeapEqualElements() {
-        let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
-        XCTAssertTrue(verifyMinHeap(heap))
-        XCTAssertTrue(verifyMaxHeap(heap))
-        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-    }
-
-    fileprivate func randomArray(_ n: Int) -> [Int] {
-        var a = [Int]()
-        for _ in 0..<n {
-            a.append(Int(arc4random()))
-        }
-        return a
-    }
-
-    func testCreateRandomMaxHeap() {
-        for n in 1...40 {
-            let a = randomArray(n)
-            let h = Heap(array: a, sort: >)
-            XCTAssertTrue(verifyMaxHeap(h))
-            XCTAssertFalse(h.isEmpty)
-            XCTAssertEqual(h.count, n)
-            XCTAssertTrue(isPermutation(a, h.elements))
-        }
-    }
-
-    func testCreateRandomMinHeap() {
-        for n in 1...40 {
-            let a = randomArray(n)
-            let h = Heap(array: a, sort: <)
-            XCTAssertTrue(verifyMinHeap(h))
-            XCTAssertFalse(h.isEmpty)
-            XCTAssertEqual(h.count, n)
-            XCTAssertTrue(isPermutation(a, h.elements))
-        }
-    }
-
-    func testRemoving() {
-        var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-        //test index out of bounds
-        let v = h.removeAt(10)
-        XCTAssertEqual(v, nil)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-        let v1 = h.removeAt(5)
-        XCTAssertEqual(v1, 60)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
-
-        let v2 = h.removeAt(4)
-        XCTAssertEqual(v2, 20)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
-
-        let v3 = h.removeAt(4)
-        XCTAssertEqual(v3, 50)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 65, 70, 10])
-
-        let v4 = h.removeAt(0)
-        XCTAssertEqual(v4, 100)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [70, 65, 10])
-
-        XCTAssertEqual(h.peek()!, 70)
-        let v5 = h.remove()
-        XCTAssertEqual(v5, 70)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [65, 10])
-
-        XCTAssertEqual(h.peek()!, 65)
-        let v6 = h.remove()
-        XCTAssertEqual(v6, 65)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [10])
-
-        XCTAssertEqual(h.peek()!, 10)
-        let v7 = h.remove()
-        XCTAssertEqual(v7, 10)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [])
-
-        XCTAssertNil(h.peek())
-    }
-
-    func testRemoveEmpty() {
-        var heap = Heap<Int>(sort: >)
-        let removed = heap.remove()
-        XCTAssertNil(removed)
-    }
-
-    func testRemoveRoot() {
-        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-        XCTAssertEqual(h.peek()!, 15)
-        let v = h.remove()
-        XCTAssertEqual(v, 15)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
-    }
-
-    func testRemoveRandomItems() {
-        for n in 1...40 {
-            var a = randomArray(n)
-            var h = Heap(array: a, sort: >)
-            XCTAssertTrue(verifyMaxHeap(h))
-            XCTAssertTrue(isPermutation(a, h.elements))
-
-            let m = (n + 1)/2
-            for k in 1...m {
-                let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-                let v = h.removeAt(i)!
-                let j = a.index(of: v)!
-                a.remove(at: j)
-
-                XCTAssertTrue(verifyMaxHeap(h))
-                XCTAssertEqual(h.count, a.count)
-                XCTAssertEqual(h.count, n - k)
-                XCTAssertTrue(isPermutation(a, h.elements))
-            }
-        }
-    }
-
-    func testInsert() {
-        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-
-        h.insert(10)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
-    }
-
-    func testInsertArrayAndRemove() {
-        var heap = Heap<Int>(sort: >)
-        heap.insert([1, 3, 2, 7, 5, 9])
-        XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
-
-        XCTAssertEqual(9, heap.remove())
-        XCTAssertEqual(7, heap.remove())
-        XCTAssertEqual(5, heap.remove())
-        XCTAssertEqual(3, heap.remove())
-        XCTAssertEqual(2, heap.remove())
-        XCTAssertEqual(1, heap.remove())
-        XCTAssertNil(heap.remove())
-    }
-
-    func testReplace() {
-        var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-
-        h.replace(index: 5, value: 13)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-
-        //test index out of bounds
-        h.replace(index: 20, value: 2)
+  }
+  
+  func testRemoving() {
+    var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    
+    //test index out of bounds
+    let v = h.removeAt(10)
+    XCTAssertEqual(v, nil)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    
+    let v1 = h.removeAt(5)
+    XCTAssertEqual(v1, 60)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
+    
+    let v2 = h.removeAt(4)
+    XCTAssertEqual(v2, 20)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
+    
+    let v3 = h.removeAt(4)
+    XCTAssertEqual(v3, 50)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 65, 70, 10])
+    
+    let v4 = h.removeAt(0)
+    XCTAssertEqual(v4, 100)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [70, 65, 10])
+    
+    XCTAssertEqual(h.peek()!, 70)
+    let v5 = h.remove()
+    XCTAssertEqual(v5, 70)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [65, 10])
+    
+    XCTAssertEqual(h.peek()!, 65)
+    let v6 = h.remove()
+    XCTAssertEqual(v6, 65)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [10])
+    
+    XCTAssertEqual(h.peek()!, 10)
+    let v7 = h.remove()
+    XCTAssertEqual(v7, 10)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [])
+    
+    XCTAssertNil(h.peek())
+  }
+  
+  func testRemoveEmpty() {
+    var heap = Heap<Int>(sort: >)
+    let removed = heap.remove()
+    XCTAssertNil(removed)
+  }
+  
+  func testRemoveRoot() {
+    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.peek()!, 15)
+    let v = h.remove()
+    XCTAssertEqual(v, 15)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
+  }
+  
+  func testRemoveRandomItems() {
+    for n in 1...40 {
+      var a = randomArray(n)
+      var h = Heap(array: a, sort: >)
+      XCTAssertTrue(verifyMaxHeap(h))
+      XCTAssertTrue(isPermutation(a, h.elements))
+      
+      let m = (n + 1)/2
+      for k in 1...m {
+        let i = Int(arc4random_uniform(UInt32(n - k + 1)))
+        let v = h.removeAt(i)!
+        let j = a.index(of: v)!
+        a.remove(at: j)
+        
         XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+        XCTAssertEqual(h.count, a.count)
+        XCTAssertEqual(h.count, n - k)
+        XCTAssertTrue(isPermutation(a, h.elements))
+      }
     }
+  }
+  
+  func testInsert() {
+    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    
+    h.insert(10)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
+  }
+  
+  func testInsertArrayAndRemove() {
+    var heap = Heap<Int>(sort: >)
+    heap.insert([1, 3, 2, 7, 5, 9])
+    XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
+    
+    XCTAssertEqual(9, heap.remove())
+    XCTAssertEqual(7, heap.remove())
+    XCTAssertEqual(5, heap.remove())
+    XCTAssertEqual(3, heap.remove())
+    XCTAssertEqual(2, heap.remove())
+    XCTAssertEqual(1, heap.remove())
+    XCTAssertNil(heap.remove())
+  }
+  
+  func testReplace() {
+    var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+    
+    h.replace(index: 5, value: 13)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+    
+    //test index out of bounds
+    h.replace(index: 20, value: 2)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+  }
 }

From 7077bc1d6df03c0c3dce224302207ba62f86c02b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 31 Jul 2017 16:10:56 +0900
Subject: [PATCH 1098/1679] Updates the indentation of the code and updated
 project settings for Xcode 9

---
 Heap Sort/HeapSort.swift                      |  8 +--
 Heap Sort/Tests/HeapSortTests.swift           | 56 +++++++++----------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 14 ++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +-
 4 files changed, 48 insertions(+), 34 deletions(-)

diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index 1e568f91f..6b5e91dc5 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,7 +1,7 @@
 extension Heap {
   public mutating func sort() -> [T] {
     for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-        elements.swapAt(0, i)
+      elements.swapAt(0, i)
       shiftDown(0, heapSize: i)
     }
     return elements
@@ -9,9 +9,9 @@ extension Heap {
 }
 
 /*
-  Sorts an array using a heap.
-  Heapsort can be performed in-place, but it is not a stable sort.
-*/
+ Sorts an array using a heap.
+ Heapsort can be performed in-place, but it is not a stable sort.
+ */
 public func heapsort<T>(_ a: [T], _ sort: @escaping (T, T) -> Bool) -> [T] {
   let reverseOrder = { i1, i2 in sort(i2, i1) }
   var h = Heap(array: a, sort: reverseOrder)
diff --git a/Heap Sort/Tests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
index 55f2f52b4..b36f605e3 100644
--- a/Heap Sort/Tests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,33 +1,33 @@
 import XCTest
 
 class HeapSortTests: XCTestCase {
-    func testSwift4() {
-        // last checked with Xcode 9.0b4
-        #if swift(>=4.0)
-            print("Hello, Swift 4!")
-        #endif
-    }
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  func testSort() {
+    var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
+    let a1 = h1.sort()
+    XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
     
-    func testSort() {
-        var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
-        let a1 = h1.sort()
-        XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
-
-        let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
-        XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
-
-        var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
-        let a2 = h2.sort()
-        XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
-
-        let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
-        XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
-
-        var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
-        let a3 = h3.sort()
-        XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
-
-        let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
-        XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
-    }
+    let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
+    XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
+    
+    var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
+    let a2 = h2.sort()
+    XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+    
+    let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
+    XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+    
+    var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
+    let a3 = h3.sort()
+    XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
+    
+    let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
+    XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
+  }
 }
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index 45b3f5821..ff1f4937f 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,7 +86,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -145,14 +145,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -191,14 +197,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index dfcf6de42..538a6f4fa 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 9f7c12a32410dc10f14dfa64f483c50444fb98c7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 07:46:30 -0700
Subject: [PATCH 1099/1679] [Swift 4] Update Array2D

---
 Array2D/Array2D.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index d31d77540..77c0b364c 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*
  Two-dimensional array with a fixed number of rows and columns.
  This is mostly handy for games that are played on a grid, such as chess.

From b49c81322f9d41b81ac1c70f5f452f0e1ebb8b1a Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 07:48:38 -0700
Subject: [PATCH 1100/1679] [Swift 4] Update Binary Search

---
 Binary Search/BinarySearch.playground/Contents.swift      | 5 +++++
 Binary Search/BinarySearch.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Binary Search/BinarySearch.playground/timeline.xctimeline

diff --git a/Binary Search/BinarySearch.playground/Contents.swift b/Binary Search/BinarySearch.playground/Contents.swift
index f673f25c4..715fb5dc2 100644
--- a/Binary Search/BinarySearch.playground/Contents.swift	
+++ b/Binary Search/BinarySearch.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // An unsorted array of numbers
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
diff --git a/Binary Search/BinarySearch.playground/timeline.xctimeline b/Binary Search/BinarySearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Search/BinarySearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 356c2fb881ed54e491a3b4c833dfb6f6d8a72742 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 07:50:34 -0700
Subject: [PATCH 1101/1679] [Swift 4] Update Binary Search Tree

---
 .../Solution 1/BinarySearchTree.playground/Contents.swift   | 5 +++++
 .../BinarySearchTree.playground/timeline.xctimeline         | 6 ------
 .../Solution 2/BinarySearchTree.playground/Contents.swift   | 5 +++++
 .../BinarySearchTree.playground/timeline.xctimeline         | 6 ------
 4 files changed, 10 insertions(+), 12 deletions(-)
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline
 delete mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index ec9902283..8c06ae9e1 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline b/Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 2b5dcc341..afa4338a9 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline b/Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From c37d8cb4fcae9add99622b7116a8b13b5fd4753c Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:36:07 -0700
Subject: [PATCH 1102/1679] [Swift 4] Update Binary Tree

---
 Binary Tree/BinaryTree.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index b0bff577a..9da194fed 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public indirect enum BinaryTree<T> {
   case node(BinaryTree<T>, T, BinaryTree<T>)
   case empty

From 0b7d673b61934812ac3bbf020b836eb8c6bd20e6 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:38:37 -0700
Subject: [PATCH 1103/1679] [Swift 4] Update DFS

---
 .../Pages/Simple Example.xcplaygroundpage/Contents.swift     | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 1e32b4bbf..5b1c1b3ee 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true

From 3fd8ebecfef9af9a641866d6fd5b3fa75c000d15 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:51:41 -0700
Subject: [PATCH 1104/1679] [Swift 4] Update Huffman Coding

---
 Huffman Coding/Huffman.playground/Contents.swift      | 5 +++++
 Huffman Coding/Huffman.playground/Sources/Heap.swift  | 4 ++--
 Huffman Coding/Huffman.playground/timeline.xctimeline | 4 ++--
 3 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index 2d59908e9..6242ad272 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 let s1 = "so much words wow many compression"
diff --git a/Huffman Coding/Huffman.playground/Sources/Heap.swift b/Huffman Coding/Huffman.playground/Sources/Heap.swift
index 5ace98a17..b578ef6e4 100644
--- a/Huffman Coding/Huffman.playground/Sources/Heap.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/Heap.swift	
@@ -143,7 +143,7 @@ public struct Heap<T> {
   public mutating func removeAtIndex(i: Int) -> T? {
     let size = elements.count - 1
     if i != size {
-      swap(&elements[i], &elements[size])
+      elements.swapAt(i, size)
       shiftDown(index: i, heapSize: size)
       shiftUp(index: i)
     }
@@ -196,7 +196,7 @@ public struct Heap<T> {
       }
       if first == parentIndex { return }
 
-      swap(&elements[parentIndex], &elements[first])
+      elements.swapAt(parentIndex, first)
       parentIndex = first
     }
   }
diff --git a/Huffman Coding/Huffman.playground/timeline.xctimeline b/Huffman Coding/Huffman.playground/timeline.xctimeline
index 2b2555bb1..5588b0fdd 100644
--- a/Huffman Coding/Huffman.playground/timeline.xctimeline	
+++ b/Huffman Coding/Huffman.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/peter/Programming/iOS/Workspace/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=19&amp;CharacterRangeLoc=678&amp;EndingLineNumber=21&amp;StartingLineNumber=21&amp;Timestamp=505135214.929897"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=752&amp;EndingColumnNumber=0&amp;EndingLineNumber=28&amp;StartingColumnNumber=0&amp;StartingLineNumber=28&amp;Timestamp=523212028.643394"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=14&amp;CharacterRangeLoc=350&amp;EndingColumnNumber=21&amp;EndingLineNumber=12&amp;StartingColumnNumber=7&amp;StartingLineNumber=12&amp;Timestamp=505138287.94525"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=14&amp;CharacterRangeLoc=433&amp;EndingColumnNumber=36&amp;EndingLineNumber=17&amp;StartingColumnNumber=22&amp;StartingLineNumber=17&amp;Timestamp=523212028.643973"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>

From f93b4c583d0401ec898444c58c29d671ed9d9925 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:53:46 -0700
Subject: [PATCH 1105/1679] [Swift 4] Update Deque

---
 Deque/Deque.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Deque/Deque.playground/Contents.swift b/Deque/Deque.playground/Contents.swift
index 9e7b22c02..df9b57a5e 100644
--- a/Deque/Deque.playground/Contents.swift
+++ b/Deque/Deque.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public struct Deque<T> {
   private var array = [T]()
 

From afcfa8028ca28bc37f35b0fccdd6d25a5fa33365 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:59:00 -0700
Subject: [PATCH 1106/1679] [Swift 4] Update Ordered Array

---
 Ordered Array/OrderedArray.playground/Contents.swift      | 5 +++++
 Ordered Array/OrderedArray.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Ordered Array/OrderedArray.playground/timeline.xctimeline

diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 4fe199f28..5b6be6420 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public struct OrderedArray<T: Comparable> {
   fileprivate var array = [T]()
 
diff --git a/Ordered Array/OrderedArray.playground/timeline.xctimeline b/Ordered Array/OrderedArray.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ordered Array/OrderedArray.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 9f38465199328cb708996f863492acc600c64498 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:05:59 -0700
Subject: [PATCH 1107/1679] Update Monty Hall Problem to Swift 4

Updated to work with Swift 4 and Xcode 9.0b4.
---
 Monty Hall Problem/MontyHall.playground/Contents.swift | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/Monty Hall Problem/MontyHall.playground/Contents.swift b/Monty Hall Problem/MontyHall.playground/Contents.swift
index bcdafd137..4bfff2340 100644
--- a/Monty Hall Problem/MontyHall.playground/Contents.swift	
+++ b/Monty Hall Problem/MontyHall.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 func random(_ n: Int) -> Int {
@@ -43,7 +48,7 @@ func playRound() {
 }
 
 // Run the simulation a large number of times.
-for i in 1...5000 {
+for _ in 1...5000 {
   playRound()
 }
 

From 0b097d82979cd624549154b39442860285923441 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:10:24 -0700
Subject: [PATCH 1108/1679] Update Minimum Edit Distance to Swift 4

Updated to work with Swift 4 and Xcode 9.0b4.
---
 .../MinimumEditDistance.playground/Contents.swift        | 9 ++++++++-
 .../MinimumEditDistance.playground/contents.xcplayground | 0
 Minimum Edit Distance/README.markdown                    | 2 +-
 3 files changed, 9 insertions(+), 2 deletions(-)
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground

diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
old mode 100755
new mode 100644
index 238afeb9b..479815df7
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,3 +1,10 @@
+// Minimum Edit Distance
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 extension String {
 
     public func minimumEditDistance(other: String) -> Int {
@@ -25,7 +32,7 @@ extension String {
                 } else {
                     // minimum of the cost of insertion, deletion, or substitution 
                     // added to the already computed costs in the corresponding cells
-                    matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+                    matrix[i + 1][j + 1] = Swift.min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
                 }
             }
         }
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground b/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground
old mode 100755
new mode 100644
diff --git a/Minimum Edit Distance/README.markdown b/Minimum Edit Distance/README.markdown
index 905b358ae..b8880b2d4 100755
--- a/Minimum Edit Distance/README.markdown	
+++ b/Minimum Edit Distance/README.markdown	
@@ -45,7 +45,7 @@ for (i, selfChar) in self.characters.enumerated() {
         } else {
             // minimum of the cost of insertion, deletion, or substitution 
             // added to the already computed costs in the corresponding cells
-            matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+            matrix[i + 1][j + 1] = Swift.min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
         } 
     }
 }

From 4c340abda42967ada0a272ff5cec4ae2fa065bd5 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:14:08 -0700
Subject: [PATCH 1109/1679] Update Ring Buffer to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Ring Buffer/RingBuffer.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index 29b9917a0..5c699f191 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public struct RingBuffer<T> {
   fileprivate var array: [T?]
   fileprivate var readIndex = 0

From b26a44ccead4c51f0c4b1d31e0a0192bb3cea6d6 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:16:45 -0700
Subject: [PATCH 1110/1679] Update Run-Length Encoding to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Run-Length Encoding/RLE.playground/Contents.swift      | 5 +++++
 Run-Length Encoding/RLE.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Run-Length Encoding/RLE.playground/timeline.xctimeline

diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 26f7dca48..fc2d82505 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 let originalString = "aaaaabbbcdeeeeeeef"
diff --git a/Run-Length Encoding/RLE.playground/timeline.xctimeline b/Run-Length Encoding/RLE.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Run-Length Encoding/RLE.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 21dc86c550e0be0155883255809038c522c5e290 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:20:29 -0700
Subject: [PATCH 1111/1679] Update Linear Search to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Linear Search/LinearSearch.playground/Contents.swift      | 5 +++++
 Linear Search/LinearSearch.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Linear Search/LinearSearch.playground/timeline.xctimeline

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 34e859fa3..dad9a77bd 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
   for (index, obj) in array.enumerated() where obj == object {
     return index
diff --git a/Linear Search/LinearSearch.playground/timeline.xctimeline b/Linear Search/LinearSearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Linear Search/LinearSearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From f10b1b19c290ce040a9cce25a35ec4974bd68e19 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:23:38 -0700
Subject: [PATCH 1112/1679] Update Selection Sampling to Swift 4

Update to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 .../SelectionSampling.playground/Contents.swift              | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index 4a2484162..f4aace0c7 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 /* Returns a random integer in the range min...max, inclusive. */

From d3dd6c8b1cf08fc2ecec0ed7039ef40f8236d319 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:26:46 -0700
Subject: [PATCH 1113/1679] Update Rabin-Karp to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Rabin-Karp/Rabin-Karp.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index 4956fabe3..c0a99339a 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Taking our rabin-karp algorithm for a walk
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import UIKit
 
 struct Constants {

From b6c7f6d922dc0fd35b2c4fdd4b3d90e731adb5bd Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:29:48 -0700
Subject: [PATCH 1114/1679] Update Radix Tree to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Radix Tree/RadixTree.playground/Contents.swift | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Radix Tree/RadixTree.playground/Contents.swift b/Radix Tree/RadixTree.playground/Contents.swift
index e161e48a2..a5e614849 100644
--- a/Radix Tree/RadixTree.playground/Contents.swift	
+++ b/Radix Tree/RadixTree.playground/Contents.swift	
@@ -1,3 +1,10 @@
+// Radix Tree
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 var radix = RadixTree()
 var radixWiki = RadixTree()
 

From 713bf52f2495203fb2806bd3944028f3e9718519 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:32:04 -0700
Subject: [PATCH 1115/1679] Updated SetCover to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Set Cover (Unweighted)/SetCover.playground/Contents.swift | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Set Cover (Unweighted)/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
index dcf998a66..d61b9c84a 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
@@ -1,3 +1,10 @@
+// SetCover
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let universe1 = Set(1...7)
 let array1 = randomArrayOfSets(covering: universe1)
 let cover1 = universe1.cover(within: array1)

From db1fc17de22adf7c4cc08117d02686abedb01149 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:37:54 -0700
Subject: [PATCH 1116/1679] Update Naive Bayes Classifier to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Naive Bayes Classifier/NaiveBayes.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
index 66aefaa32..6a2e01aab 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -1,5 +1,10 @@
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*:
  ## Naive Bayes Classifier
 

From b8d324e3309db84e2b0f645d864bccff90f44683 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 12:54:53 -0700
Subject: [PATCH 1117/1679] [Swift 4] Update All Pairs Shortest Paths

---
 .../APSP/APSP.playground/Contents.swift                    | 5 +++++
 .../APSP/APSP.playground/timeline.xctimeline               | 4 ++--
 .../APSP/APSP.xcodeproj/project.pbxproj                    | 4 ++--
 All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift    | 7 +++++++
 Graph/GraphTests/GraphTests.swift                          | 7 +++++++
 5 files changed, 23 insertions(+), 4 deletions(-)

diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
index 24c27cac8..b1b499b39 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Graph
 import APSP
 
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline
index 2c73a4e3e..c938ca857 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=888&amp;EndingColumnNumber=44&amp;EndingLineNumber=29&amp;StartingColumnNumber=3&amp;StartingLineNumber=28&amp;Timestamp=486844329.035763"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/All-Pairs%20Shortest%20Paths/APSP/APSP.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=971&amp;EndingColumnNumber=68&amp;EndingLineNumber=34&amp;StartingColumnNumber=68&amp;StartingLineNumber=34&amp;Timestamp=523221730.015692"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=4&amp;CharacterRangeLoc=825&amp;EndingColumnNumber=9&amp;EndingLineNumber=29&amp;StartingColumnNumber=5&amp;StartingLineNumber=29&amp;Timestamp=486844329.036018"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/All-Pairs%20Shortest%20Paths/APSP/APSP.playground#CharacterRangeLen=4&amp;CharacterRangeLoc=908&amp;EndingColumnNumber=9&amp;EndingLineNumber=34&amp;StartingColumnNumber=5&amp;StartingLineNumber=34&amp;Timestamp=523221730.015887"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index b2d93ea35..78df3fb76 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -388,7 +388,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -400,7 +400,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
index 9d026f680..c2f64e239 100644
--- a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -20,6 +20,13 @@ struct TestCase<T> where T: Hashable {
 
 class APSPTests: XCTestCase {
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   /**
    See Figure 25.1 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 690
    */
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 289d9aa64..92a4ce828 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -10,6 +10,13 @@ import XCTest
 
 class GraphTests: XCTestCase {
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()

From 1baaac856e5b3d99ece99594b8c0278f0c5be47b Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 12:58:32 -0700
Subject: [PATCH 1118/1679] [Swift 4] Update Brute Force String Search

---
 .../BruteForceStringSearch.playground/Contents.swift         | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index fcee59a7b..003a87e8f 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 extension String {
   func indexOf(_ pattern: String) -> String.Index? {
 

From 52802514df40566b0899dc54272649623da8b2af Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 13:00:14 -0700
Subject: [PATCH 1119/1679] [Swift 4] Update Insertion Sort

---
 Insertion Sort/InsertionSort.playground/Contents.swift      | 5 +++++
 Insertion Sort/InsertionSort.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Insertion Sort/InsertionSort.playground/timeline.xctimeline

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index df1822b8f..91e18640f 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   var a = array
   for x in 1..<a.count {
diff --git a/Insertion Sort/InsertionSort.playground/timeline.xctimeline b/Insertion Sort/InsertionSort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Insertion Sort/InsertionSort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From be012cc5df1acd178c770659dafa575d3c0b048d Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 01:43:58 +0500
Subject: [PATCH 1120/1679] Migrated to Swift 4

---
 AVL Tree/AVLTree.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 409dfdc49..04ef78d07 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let tree = AVLTree<Int, String>()
 
 tree.insert(key: 5, payload: "five")

From 190cc4e9a91a9fc28f14104b484ed72d6bca4136 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 01:51:23 +0500
Subject: [PATCH 1121/1679] Updated Test for Swift4

---
 AVL Tree/Tests/AVLTreeTests.swift              | 8 ++++++--
 AVL Tree/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 AVL Tree/Tests/TreeNodeTests.swift             | 9 +++++++--
 3 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 7765c6d29..a9e932117 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -7,11 +7,15 @@
 //
 
 import XCTest
-
 class AVLTreeTests: XCTestCase {
-
   var tree: AVLTree<Int, String>?
 
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
   override func setUp() {
     super.setUp()
 
diff --git a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj
index 64c244747..e7c6e2989 100644
--- a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -180,6 +180,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -230,7 +232,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,7 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/AVL Tree/Tests/TreeNodeTests.swift b/AVL Tree/Tests/TreeNodeTests.swift
index cac7e549b..dc393232c 100644
--- a/AVL Tree/Tests/TreeNodeTests.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -9,11 +9,16 @@
 import XCTest
 
 class TreeNodeTests: XCTestCase {
-
+   
     var root: TreeNode<String, String>?
     var left: TreeNode<String, String>?
     var right: TreeNode<String, String>?
-
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
     override func setUp() {
         super.setUp()
 

From aad5d28451f271dcf4f47e04613fe0e195e37a28 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 01:55:44 +0500
Subject: [PATCH 1122/1679] B-Tree Playground & Tests updated to Swift 4

---
 B-Tree/BTree.playground/Contents.swift       |  7 +-
 B-Tree/Tests/Tests.xcodeproj/project.pbxproj |  6 +-
 B-Tree/Tests/Tests/BTreeNodeTests.swift      | 87 +++++++++++---------
 B-Tree/Tests/Tests/BTreeTests.swift          |  7 ++
 4 files changed, 63 insertions(+), 44 deletions(-)

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index 710ace701..a0643586f 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -2,6 +2,11 @@
 
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let bTree = BTree<Int, Int>(order: 1)!
 
 bTree.insert(1, for: 1)
@@ -15,7 +20,7 @@ bTree[3]
 bTree.remove(2)
 
 bTree.traverseKeysInOrder { key in
-  print(key)
+    print(key)
 }
 
 bTree.numberOfKeys
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
index 79552bbe5..3e12b9ac3 100644
--- a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
+++ b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
@@ -179,6 +179,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -232,7 +234,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -245,7 +247,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index 8eff926b5..80de8b845 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -9,45 +9,50 @@
 import XCTest
 
 class BTreeNodeTests: XCTestCase {
-
-  let owner = BTree<Int, Int>(order: 2)!
-  var root: BTreeNode<Int, Int>!
-  var leftChild: BTreeNode<Int, Int>!
-  var rightChild: BTreeNode<Int, Int>!
-
-  override func setUp() {
-    super.setUp()
-
-    root = BTreeNode(owner: owner)
-    leftChild = BTreeNode(owner: owner)
-    rightChild = BTreeNode(owner: owner)
-
-    root.insert(1, for: 1)
-    root.children = [leftChild, rightChild]
-  }
-
-  func testIsLeafRoot() {
-    XCTAssertFalse(root.isLeaf)
-  }
-
-  func testIsLeafLeaf() {
-    XCTAssertTrue(leftChild.isLeaf)
-    XCTAssertTrue(rightChild.isLeaf)
-  }
-
-  func testOwner() {
-    XCTAssert(root.owner === owner)
-    XCTAssert(leftChild.owner === owner)
-    XCTAssert(rightChild.owner === owner)
-  }
-
-  func testNumberOfKeys() {
-    XCTAssertEqual(root.numberOfKeys, 1)
-    XCTAssertEqual(leftChild.numberOfKeys, 0)
-    XCTAssertEqual(rightChild.numberOfKeys, 0)
-  }
-
-  func testChildren() {
-    XCTAssertEqual(root.children!.count, 2)
-  }
+    
+    let owner = BTree<Int, Int>(order: 2)!
+    var root: BTreeNode<Int, Int>!
+    var leftChild: BTreeNode<Int, Int>!
+    var rightChild: BTreeNode<Int, Int>!
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    override func setUp() {
+        super.setUp()
+        
+        root = BTreeNode(owner: owner)
+        leftChild = BTreeNode(owner: owner)
+        rightChild = BTreeNode(owner: owner)
+        
+        root.insert(1, for: 1)
+        root.children = [leftChild, rightChild]
+    }
+    
+    func testIsLeafRoot() {
+        XCTAssertFalse(root.isLeaf)
+    }
+    
+    func testIsLeafLeaf() {
+        XCTAssertTrue(leftChild.isLeaf)
+        XCTAssertTrue(rightChild.isLeaf)
+    }
+    
+    func testOwner() {
+        XCTAssert(root.owner === owner)
+        XCTAssert(leftChild.owner === owner)
+        XCTAssert(rightChild.owner === owner)
+    }
+    
+    func testNumberOfKeys() {
+        XCTAssertEqual(root.numberOfKeys, 1)
+        XCTAssertEqual(leftChild.numberOfKeys, 0)
+        XCTAssertEqual(rightChild.numberOfKeys, 0)
+    }
+    
+    func testChildren() {
+        XCTAssertEqual(root.children!.count, 2)
+    }
 }
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index 1e94bfd7d..69d7ce55d 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -11,6 +11,13 @@ import XCTest
 class BTreeTests: XCTestCase {
   var bTree: BTree<Int, Int>!
 
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    
   override func setUp() {
     super.setUp()
     bTree = BTree<Int, Int>(order: 3)!

From efa7e4e5d33468b19d56b5aab43b5a215943038f Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 02:17:41 +0500
Subject: [PATCH 1123/1679] Updated Bloom Filter code & Test to Swift4

---
 Bloom Filter/BloomFilter.playground/Contents.swift | 5 ++++-
 Bloom Filter/Tests/BloomFilterTests.swift          | 7 ++++++-
 Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 3 files changed, 14 insertions(+), 4 deletions(-)

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 3dac76e8e..9e4a89351 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
-
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 public class BloomFilter<T> {
   fileprivate var array: [Bool]
   private var hashFunctions: [(T) -> Int]
diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 55db71f3f..30df702a7 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -24,7 +24,12 @@ func sdbm(_ x: String) -> Int {
 }
 
 class BloomFilterTests: XCTestCase {
-
+    func testSwift4(){
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
   func testSingleHashFunction() {
     let bloom = BloomFilter<String>(hashFunctions: [djb2])
 
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj
index 20998a80e..6493fd153 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
@@ -176,6 +176,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -215,6 +216,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -226,7 +228,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +240,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 85ff254cdda24448c2560aa21303fef603edabf1 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 02:39:03 +0500
Subject: [PATCH 1124/1679] Migrated Playground and Test to Swift 4

---
 Comb Sort/Comb Sort.playground/Contents.swift          | 4 ++++
 Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift | 2 +-
 Comb Sort/Comb Sort.swift                              | 6 +++---
 Comb Sort/Tests/CombSortTests.swift                    | 5 +++++
 Comb Sort/Tests/Tests.xcodeproj/project.pbxproj        | 6 ++++--
 5 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index 40176be9f..39e24248a 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -3,6 +3,10 @@
 // 7-16-2016
 
 import Cocoa
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 // Test Comb Sort with small array of ten values
 let array = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift
index f7c4eec61..559fe47e8 100644
--- a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
@@ -21,7 +21,7 @@ public func combSort<T: Comparable>(_ input: [T]) -> [T] {
         var index = 0
         while !(index + gap >= copy.count) {
             if copy[index] > copy[index + gap] {
-                swap(&copy[index], &copy[index + gap])
+               copy.swapAt(index, index + gap)
             }
             index += 1
         }
diff --git a/Comb Sort/Comb Sort.swift b/Comb Sort/Comb Sort.swift
index f7c4eec61..bd37fed42 100644
--- a/Comb Sort/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.swift	
@@ -11,17 +11,17 @@ public func combSort<T: Comparable>(_ input: [T]) -> [T] {
     var copy: [T] = input
     var gap = copy.count
     let shrink = 1.3
-
+    
     while gap > 1 {
         gap = (Int)(Double(gap) / shrink)
         if gap < 1 {
             gap = 1
         }
-
+        
         var index = 0
         while !(index + gap >= copy.count) {
             if copy[index] > copy[index + gap] {
-                swap(&copy[index], &copy[index + gap])
+                copy.swapAt(index, index + gap)
             }
             index += 1
         }
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index b9287f84a..e972c0a57 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -12,6 +12,11 @@ class CombSortTests: XCTestCase {
     var sequence: [Int]!
     let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
 
+    func testSwift4(){
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
     override func setUp() {
         super.setUp()
         sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
index 60039196c..7530acbdc 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -179,6 +179,7 @@
 				SDKROOT = macosx;
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -220,6 +221,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -233,7 +235,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -246,7 +248,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 05bf739ae9e0810633bcc14f48c4f46019e16c0f Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:04:04 -0700
Subject: [PATCH 1125/1679] [Swift 4] Update Counting Sort

---
 Counting Sort/CountingSort.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index dc375512a..4d918e384 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 enum CountingSortError: Error {
   case arrayEmpty
 }

From 47358d8ee427a5860a43ab0788045d91a6dcaba9 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:06:33 -0700
Subject: [PATCH 1126/1679] [Swift 4] Update Bounded PQ

---
 .../BoundedPriorityQueue.playground/Contents.swift           | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index d6204abec..f8e219c13 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 struct Message: Comparable, CustomStringConvertible {
   let name: String
   let priority: Int

From 649db39d6f7c1b7e1e080aa252c24a4b218cffd9 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:10:09 -0700
Subject: [PATCH 1127/1679] [Swift 4] Update BFS

---
 .../Pages/Simple example.xcplaygroundpage/Contents.swift     | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 675be2203..3986a0cee 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)

From c9afacb4e3be3ccca28614153b7727be6264e149 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:12:43 -0700
Subject: [PATCH 1128/1679] [Swift 4] Update Combinatorics

---
 Combinatorics/Combinatorics.playground/Contents.swift    | 9 +++++++--
 .../Combinatorics.playground/timeline.xctimeline         | 6 ------
 2 files changed, 7 insertions(+), 8 deletions(-)
 delete mode 100644 Combinatorics/Combinatorics.playground/timeline.xctimeline

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 9fbcc1c58..2daa5f22f 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /* Calculates n! */
 func factorial(_ n: Int) -> Int {
   var n = n
@@ -44,9 +49,9 @@ func permuteWirth<T>(_ a: [T], _ n: Int) {
     var a = a
     permuteWirth(a, n - 1)
     for i in 0..<n {
-      swap(&a[i], &a[n])
+      a.swapAt(i, n)
       permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
+      a.swapAt(i, n)
     }
   }
 }
diff --git a/Combinatorics/Combinatorics.playground/timeline.xctimeline b/Combinatorics/Combinatorics.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Combinatorics/Combinatorics.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From b9cbc739e862d847622d77bfbabfa3a09a5bcfa7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:17:02 -0700
Subject: [PATCH 1129/1679] [Swift 4] Update Convex Hull

---
 .../Convex Hull.xcodeproj/project.pbxproj     |   5 +-
 Convex Hull/Convex Hull/View.swift            | 255 +++++++++---------
 2 files changed, 133 insertions(+), 127 deletions(-)

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index 2f236b013..bb3189d64 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -254,7 +254,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -267,7 +267,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -290,6 +290,7 @@
 				8E6D68CA1E59989400161780 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 2f2c3e046..408689a13 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -10,168 +10,173 @@ import UIKit
 
 class View: UIView {
 
-    let MAX_POINTS = 100
-
-    var points = [CGPoint]()
-
-    var convexHull = [CGPoint]()
-
-    override init(frame: CGRect) {
-        super.init(frame: frame)
-
-        generatePoints()
-        quickHull(points: points)
-    }
-
-    required init?(coder aDecoder: NSCoder) {
-        fatalError("init(coder:) has not been implemented")
+  let MAX_POINTS = 100
+
+  var points = [CGPoint]()
+
+  var convexHull = [CGPoint]()
+
+  override init(frame: CGRect) {
+    super.init(frame: frame)
+
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+    
+    generatePoints()
+    quickHull(points: points)
+  }
+
+  required init?(coder aDecoder: NSCoder) {
+    fatalError("init(coder:) has not been implemented")
+  }
+
+  func generatePoints() {
+    for _ in 0..<MAX_POINTS {
+      let offset: CGFloat = 50
+      let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
+      let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
+      let point = CGPoint(x: xrand, y: yrand)
+      points.append(point)
     }
 
-    func generatePoints() {
-        for _ in 0..<MAX_POINTS {
-            let offset: CGFloat = 50
-            let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
-            let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
-            let point = CGPoint(x: xrand, y: yrand)
-            points.append(point)
-        }
-
-        points.sort { (a: CGPoint, b: CGPoint) -> Bool in
-            return a.x < b.x
-        }
+    points.sort { (a: CGPoint, b: CGPoint) -> Bool in
+      return a.x < b.x
     }
+  }
 
-    func quickHull(points: [CGPoint]) {
-        var pts = points
+  func quickHull(points: [CGPoint]) {
+    var pts = points
 
-        // Assume points has at least 2 points
-        // Assume list is ordered on x
+    // Assume points has at least 2 points
+    // Assume list is ordered on x
 
-        // left most point
-        let p1 = pts.removeFirst()
-        // right most point
-        let p2 = pts.removeLast()
+    // left most point
+    let p1 = pts.removeFirst()
+    // right most point
+    let p2 = pts.removeLast()
 
-        // p1 and p2 are outer most points and thus are part of the hull
-        convexHull.append(p1)
-        convexHull.append(p2)
+    // p1 and p2 are outer most points and thus are part of the hull
+    convexHull.append(p1)
+    convexHull.append(p2)
 
-        // points to the right of oriented line from p1 to p2
-        var s1 = [CGPoint]()
+    // points to the right of oriented line from p1 to p2
+    var s1 = [CGPoint]()
 
-        // points to the right of oriented line from p2 to p1
-        var s2 = [CGPoint]()
+    // points to the right of oriented line from p2 to p1
+    var s2 = [CGPoint]()
 
-        // p1 to p2 line
-        let lineVec1 = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
+    // p1 to p2 line
+    let lineVec1 = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
 
-        for p in pts { // per point check if point is to right or left of p1 to p2 line
-            let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y)
-            let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // cross product to check on which side of the line point p is.
+    for p in pts { // per point check if point is to right or left of p1 to p2 line
+      let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y)
+      let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // cross product to check on which side of the line point p is.
 
-            if sign1 > 0 { // right of p1 p2 line (in a normal xy coordinate system this would be < 0 but due to the weird iPhone screen coordinates this is > 0
-                s1.append(p)
-            } else { // right of p2 p1 line
-                s2.append(p)
-            }
-        }
-
-        // find new hull points
-        findHull(s1, p1, p2)
-        findHull(s2, p2, p1)
+      if sign1 > 0 { // right of p1 p2 line (in a normal xy coordinate system this would be < 0 but due to the weird iPhone screen coordinates this is > 0
+        s1.append(p)
+      } else { // right of p2 p1 line
+        s2.append(p)
+      }
     }
 
-    func findHull(_ points: [CGPoint], _ p1: CGPoint, _ p2: CGPoint) {
-        // if set of points is empty there are no points to the right of this line so this line is part of the hull.
-        if points.isEmpty {
-            return
-        }
+    // find new hull points
+    findHull(s1, p1, p2)
+    findHull(s2, p2, p1)
+  }
 
-        var pts = points
+  func findHull(_ points: [CGPoint], _ p1: CGPoint, _ p2: CGPoint) {
+    // if set of points is empty there are no points to the right of this line so this line is part of the hull.
+    if points.isEmpty {
+      return
+    }
 
-        // calculate parameters of general line equation y = a * x + b
-        let a = (p1.y - p2.y) / (p1.x - p2.x)
-        let b = p1.y - a * p1.x
+    var pts = points
 
-        // calculate normal line's growth factor
-        let a1 = -1 / a
+    // calculate parameters of general line equation y = a * x + b
+    let a = (p1.y - p2.y) / (p1.x - p2.x)
+    let b = p1.y - a * p1.x
 
-        var maxDist: CGFloat = -1
-        var maxPoint: CGPoint = pts.first!
+    // calculate normal line's growth factor
+    let a1 = -1 / a
 
-        for p in pts { // for every point check the distance from our line
-            let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
-            let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
-            let y = a * x + b // calculate y value of this intersect point
+    var maxDist: CGFloat = -1
+    var maxPoint: CGPoint = pts.first!
 
-            let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
-            if dist > maxDist { // if distance is larger than current maxDist remember new point p
-                maxDist = dist
-                maxPoint = p
-            }
-        }
+    for p in pts { // for every point check the distance from our line
+      let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
+      let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
+      let y = a * x + b // calculate y value of this intersect point
 
-        convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
+      let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
+      if dist > maxDist { // if distance is larger than current maxDist remember new point p
+        maxDist = dist
+        maxPoint = p
+      }
+    }
 
-        pts.remove(at: pts.index(of: maxPoint)!) // remove maxPoint from points array as we are going to split this array in points left and right of the line
+    convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
 
-        // points to the right of oriented line from p1 to maxPoint
-        var s1 = [CGPoint]()
+    pts.remove(at: pts.index(of: maxPoint)!) // remove maxPoint from points array as we are going to split this array in points left and right of the line
 
-        // points to the right of oriented line from maxPoint to p2
-        var s2 = [CGPoint]()
+    // points to the right of oriented line from p1 to maxPoint
+    var s1 = [CGPoint]()
 
-        // p1 to maxPoint line
-        let lineVec1 = CGPoint(x: maxPoint.x - p1.x, y: maxPoint.y - p1.y)
-        // maxPoint to p2 line
-        let lineVec2 = CGPoint(x: p2.x - maxPoint.x, y: p2.y - maxPoint.y)
+    // points to the right of oriented line from maxPoint to p2
+    var s2 = [CGPoint]()
 
-        for p in pts {
-            let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y) // vector from p1 to p
-            let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // sign to check is p is to the right or left of lineVec1
+    // p1 to maxPoint line
+    let lineVec1 = CGPoint(x: maxPoint.x - p1.x, y: maxPoint.y - p1.y)
+    // maxPoint to p2 line
+    let lineVec2 = CGPoint(x: p2.x - maxPoint.x, y: p2.y - maxPoint.y)
 
-            let pVec2 = CGPoint(x: p.x - maxPoint.x, y: p.y - maxPoint.y) // vector from p2 to p
-            let sign2 = lineVec2.x * pVec2.y - pVec2.x * lineVec2.y // sign to check is p is to the right or left of lineVec2
+    for p in pts {
+      let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y) // vector from p1 to p
+      let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // sign to check is p is to the right or left of lineVec1
 
-            if sign1 > 0 { // right of p1 maxPoint line
-                s1.append(p)
-            } else if sign2 > 0 { // right of maxPoint p2 line
-                s2.append(p)
-            }
-        }
+      let pVec2 = CGPoint(x: p.x - maxPoint.x, y: p.y - maxPoint.y) // vector from p2 to p
+      let sign2 = lineVec2.x * pVec2.y - pVec2.x * lineVec2.y // sign to check is p is to the right or left of lineVec2
 
-        // find new hull points
-        findHull(s1, p1, maxPoint)
-        findHull(s2, maxPoint, p2)
+      if sign1 > 0 { // right of p1 maxPoint line
+        s1.append(p)
+      } else if sign2 > 0 { // right of maxPoint p2 line
+        s2.append(p)
+      }
     }
 
-    override func draw(_ rect: CGRect) {
+    // find new hull points
+    findHull(s1, p1, maxPoint)
+    findHull(s2, maxPoint, p2)
+  }
 
-        let context = UIGraphicsGetCurrentContext()
+  override func draw(_ rect: CGRect) {
 
-        // Draw hull
-        let lineWidth: CGFloat = 2.0
+    let context = UIGraphicsGetCurrentContext()
 
-        context!.setFillColor(UIColor.black.cgColor)
-        context!.setLineWidth(lineWidth)
-        context!.setStrokeColor(UIColor.red.cgColor)
-        context!.setFillColor(UIColor.black.cgColor)
+    // Draw hull
+    let lineWidth: CGFloat = 2.0
 
-        let firstPoint = convexHull.first!
-        context!.move(to: firstPoint)
+    context!.setFillColor(UIColor.black.cgColor)
+    context!.setLineWidth(lineWidth)
+    context!.setStrokeColor(UIColor.red.cgColor)
+    context!.setFillColor(UIColor.black.cgColor)
 
-        for p in convexHull.dropFirst() {
-            context!.addLine(to: p)
-        }
-        context!.addLine(to: firstPoint)
+    let firstPoint = convexHull.first!
+    context!.move(to: firstPoint)
+
+    for p in convexHull.dropFirst() {
+      context!.addLine(to: p)
+    }
+    context!.addLine(to: firstPoint)
 
-        context!.strokePath()
+    context!.strokePath()
 
-        // Draw points
-        for p in points {
-            let radius: CGFloat = 5
-            let circleRect = CGRect(x: p.x - radius, y: p.y - radius, width: 2 * radius, height: 2 * radius)
-            context!.fillEllipse(in: circleRect)
-        }
+    // Draw points
+    for p in points {
+      let radius: CGFloat = 5
+      let circleRect = CGRect(x: p.x - radius, y: p.y - radius, width: 2 * radius, height: 2 * radius)
+      context!.fillEllipse(in: circleRect)
     }
+  }
 }

From 892f632c12cf46690a52f74320ff7bee7b8b4b65 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:21:09 -0700
Subject: [PATCH 1130/1679] [Swift 4] Update Dining Philosophers

---
 .../project.pbxproj                           | 469 +++++++++---------
 DiningPhilosophers/Sources/main.swift         |   5 +
 2 files changed, 227 insertions(+), 247 deletions(-)

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
index 9743ff7d1..ecb060026 100755
--- a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -1,250 +1,225 @@
 // !$*UTF8*$!
 {
-   archiveVersion = "1";
-   objectVersion = "46";
-   objects = {
-      OBJ_1 = {
-         isa = "PBXProject";
-         attributes = {
-            LastUpgradeCheck = "9999";
-         };
-         buildConfigurationList = OBJ_2;
-         compatibilityVersion = "Xcode 3.2";
-         developmentRegion = "English";
-         hasScannedForEncodings = "0";
-         knownRegions = (
-            "en",
-         );
-         mainGroup = OBJ_5;
-         productRefGroup = OBJ_11;
-         projectDirPath = ".";
-         targets = (
-            OBJ_13,
-         );
-      };
-      OBJ_10 = {
-         isa = "PBXGroup";
-         children = (
-         );
-         path = "Tests";
-         sourceTree = "<group>";
-      };
-      OBJ_11 = {
-         isa = "PBXGroup";
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-         };
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-         sourceTree = "SOURCE_ROOT";
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-         isa = "PBXFileReference";
-         path = "main.swift";
-         sourceTree = "<group>";
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-   };
-   rootObject = OBJ_1;
+	archiveVersion = 1;
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+	};
+	objectVersion = 46;
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+
+/* Begin PBXBuildFile section */
+		OBJ_18 /* main.swift in Sources */ = {isa = PBXBuildFile; fileRef = OBJ_9 /* main.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		OBJ_12 /* DiningPhilosophers */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; path = DiningPhilosophers; sourceTree = BUILT_PRODUCTS_DIR; };
+		OBJ_6 /* Package.swift */ = {isa = PBXFileReference; explicitFileType = sourcecode.swift; path = Package.swift; sourceTree = "<group>"; };
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+
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+			);
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+/* End PBXFrameworksBuildPhase section */
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+		OBJ_10 /* Tests */ = {
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+			);
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+		};
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+				OBJ_12 /* DiningPhilosophers */,
+			);
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+				OBJ_8 /* DiningPhilosophers */,
+			);
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+			children = (
+				OBJ_9 /* main.swift */,
+			);
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+		};
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+				OBJ_17 /* Sources */,
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+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
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+			isa = PBXProject;
+			attributes = {
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+			buildConfigurationList = OBJ_2 /* Build configuration list for PBXProject "DiningPhilosophers" */;
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+				OBJ_18 /* main.swift in Sources */,
+			);
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+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
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+			isa = XCBuildConfiguration;
+			buildSettings = {
+				FRAMEWORK_SEARCH_PATHS = "$(PLATFORM_DIR)/Developer/Library/Frameworks";
+				HEADER_SEARCH_PATHS = "";
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+				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
+				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
+				SWIFT_VERSION = 4.0;
+				TARGET_NAME = DiningPhilosophers;
+			};
+			name = Debug;
+		};
+		OBJ_16 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				FRAMEWORK_SEARCH_PATHS = "$(PLATFORM_DIR)/Developer/Library/Frameworks";
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+				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
+				SWIFT_VERSION = 4.0;
+				TARGET_NAME = DiningPhilosophers;
+			};
+			name = Release;
+		};
+		OBJ_3 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
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+				ENABLE_NS_ASSERTIONS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				MACOSX_DEPLOYMENT_TARGET = 10.10;
+				ONLY_ACTIVE_ARCH = YES;
+				OTHER_SWIFT_FLAGS = "-DXcode";
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+				SUPPORTED_PLATFORMS = "macosx iphoneos iphonesimulator appletvos appletvsimulator watchos watchsimulator";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
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+			name = Debug;
+		};
+		OBJ_4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = YES;
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+				SUPPORTED_PLATFORMS = "macosx iphoneos iphonesimulator appletvos appletvsimulator watchos watchsimulator";
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
+				USE_HEADERMAP = NO;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		OBJ_14 /* Build configuration list for PBXNativeTarget "DiningPhilosophers" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				OBJ_15 /* Debug */,
+				OBJ_16 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Debug;
+		};
+		OBJ_2 /* Build configuration list for PBXProject "DiningPhilosophers" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				OBJ_3 /* Debug */,
+				OBJ_4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Debug;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = OBJ_1 /* Project object */;
 }
diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index 32c3af979..f473e76fb 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -6,6 +6,11 @@
 //
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
 import Dispatch
 
 let numberOfPhilosophers = 4

From e3e8a34a2f48322c4e567450cd8563460380601e Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:26:43 -0700
Subject: [PATCH 1131/1679] [Swift 4] Update KMeans

---
 K-Means/Tests/KMeansTests.swift               | 7 +++++++
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index 7e0c93004..e6f4b08a1 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,6 +10,13 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func genPoints(_ numPoints: Int, numDimensions: Int) -> [Vector] {
     var points = [Vector]()
     for _ in 0..<numPoints {
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 08b64a8f9..139f6baf5 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -229,7 +229,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -271,7 +271,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From b0e6897fff17688018ab50ed3dd402ebff21a509 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:35:14 -0700
Subject: [PATCH 1132/1679] [Swift 4] Update Kth Largest Element

---
 .../kthLargest.playground/Contents.swift      | 72 ++-----------------
 .../Sources}/kthLargest.swift                 | 30 +++-----
 .../contents.xcworkspacedata                  |  3 -
 3 files changed, 14 insertions(+), 91 deletions(-)
 rename Kth Largest Element/{ => kthLargest.playground/Sources}/kthLargest.swift (65%)

diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 3e186760c..e6fca2ceb 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -1,14 +1,9 @@
 //: Playground - noun: a place where people can play
 
-func kthLargest(_ a: [Int], _ k: Int) -> Int? {
-  let len = a.count
-  if k > 0 && k <= len {
-    let sorted = a.sorted()
-    return sorted[len - k]
-  } else {
-    return nil
-  }
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let a = [5, 1, 3, 2, 7, 6, 4]
 
@@ -22,65 +17,6 @@ kthLargest(a, 6)
 kthLargest(a, 7)
 kthLargest(a, 8)
 
-import Foundation
-
-/* Returns a random integer in the range min...max, inclusive. */
-public func random( min: Int, max: Int) -> Int {
-  assert(min < max)
-  return min + Int(arc4random_uniform(UInt32(max - min + 1)))
-}
-
-/*
-  Swift's swap() doesn't like it if the items you're trying to swap refer to
-  the same memory location. This little wrapper simply ignores such swaps.
-*/
-public func swap<T>(_ a:inout [T], _ i: Int, _ j: Int) {
-  if i != j {
-    swap(&a[i], &a[j])
-  }
-}
-
-public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
-  var a = array
-
-  func randomPivot<T: Comparable>(_ a: inout[T], _ low: Int, _ high: Int) -> T {
-    let pivotIndex = random(min: low, max: high)
-    swap(&a, pivotIndex, high)
-    return a[high]
-  }
-
-  func randomizedPartition<T: Comparable>(_ a: inout[T], _ low: Int, _ high: Int) -> Int {
-    let pivot = randomPivot(&a, low, high)
-    var i = low
-    for j in low..<high {
-      if a[j] <= pivot {
-        swap(&a, i, j)
-        i += 1
-      }
-    }
-    swap(&a, i, high)
-    return i
-  }
-
-  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
-    if low < high {
-      let p = randomizedPartition(&a, low, high)
-      if k == p {
-        return a[p]
-      } else if k < p {
-        return randomizedSelect(&a, low, p - 1, k)
-      } else {
-        return randomizedSelect(&a, p + 1, high, k)
-      }
-    } else {
-      return a[low]
-    }
-  }
-
-  precondition(a.count > 0)
-  return randomizedSelect(&a, 0, a.count - 1, k)
-}
-
 randomizedSelect(a, order: 0)
 randomizedSelect(a, order: 1)
 randomizedSelect(a, order: 2)
diff --git a/Kth Largest Element/kthLargest.swift b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift
similarity index 65%
rename from Kth Largest Element/kthLargest.swift
rename to Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift
index 16f6caf0c..397c43a38 100644
--- a/Kth Largest Element/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift	
@@ -4,10 +4,10 @@ import Foundation
   Returns the k-th largest value inside of an array a.
   This is an O(n log n) solution since we sort the array.
 */
-func kthLargest(a: [Int], k: Int) -> Int? {
+public func kthLargest(_ a: [Int], _ k: Int) -> Int? {
   let len = a.count
   if k > 0 && k <= len {
-    let sorted = a.sort()
+    let sorted = a.sorted()
     return sorted[len - k]
   } else {
     return nil
@@ -17,21 +17,11 @@ func kthLargest(a: [Int], k: Int) -> Int? {
 // MARK: - Randomized selection
 
 /* Returns a random integer in the range min...max, inclusive. */
-public func random(min min: Int, max: Int) -> Int {
+public func random(min: Int, max: Int) -> Int {
   assert(min < max)
   return min + Int(arc4random_uniform(UInt32(max - min + 1)))
 }
 
-/*
-  Swift's swap() doesn't like it if the items you're trying to swap refer to
-  the same memory location. This little wrapper simply ignores such swaps.
-*/
-public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
-  if i != j {
-    swap(&a[i], &a[j])
-  }
-}
-
 /*
   Returns the i-th smallest element from the array.
 
@@ -45,29 +35,29 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
 
   Expected running time: O(n) if the elements are distinct.
 */
-public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
+public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
-  func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
+  func randomPivot<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
-    swap(&a, pivotIndex, high)
+    a.swapAt(pivotIndex, high)
     return a[high]
   }
 
-  func randomizedPartition<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> Int {
+  func randomizedPartition<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> Int {
     let pivot = randomPivot(&a, low, high)
     var i = low
     for j in low..<high {
       if a[j] <= pivot {
-        swap(&a, i, j)
+        a.swapAt(i, j)
         i += 1
       }
     }
-    swap(&a, i, high)
+    a.swapAt(i, high)
     return i
   }
 
-  func randomizedSelect<T: Comparable>(inout a: [T], _ low: Int, _ high: Int, _ k: Int) -> T {
+  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
     if low < high {
       let p = randomizedPartition(&a, low, high)
       if k == p {
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..eaa1e1167 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1367,9 +1367,6 @@
       <FileRef
          location = "group:kthLargest.playground">
       </FileRef>
-      <FileRef
-         location = "group:kthLargest.swift">
-      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From 4f4b09dcb465882ceb43dd88ae50a59a2a0da381 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 12:38:49 +0500
Subject: [PATCH 1133/1679] Updated Code & Test to Swift4

---
 .../Contents.swift                            |   6 +
 .../Tests/DepthFirstSearchTests.swift         | 168 +++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |   6 +-
 3 files changed, 97 insertions(+), 83 deletions(-)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 1e32b4bbf..dd98e87dc 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,9 @@
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index 2cb2556ce..afff5f62f 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -1,85 +1,91 @@
 import XCTest
 
 class DepthFirstSearchTests: XCTestCase {
-
-  func testExploringTree() {
-    let tree = Graph()
-
-    let nodeA = tree.addNode("a")
-    let nodeB = tree.addNode("b")
-    let nodeC = tree.addNode("c")
-    let nodeD = tree.addNode("d")
-    let nodeE = tree.addNode("e")
-    let nodeF = tree.addNode("f")
-    let nodeG = tree.addNode("g")
-    let nodeH = tree.addNode("h")
-
-    tree.addEdge(nodeA, neighbor: nodeB)
-    tree.addEdge(nodeA, neighbor: nodeC)
-    tree.addEdge(nodeB, neighbor: nodeD)
-    tree.addEdge(nodeB, neighbor: nodeE)
-    tree.addEdge(nodeC, neighbor: nodeF)
-    tree.addEdge(nodeC, neighbor: nodeG)
-    tree.addEdge(nodeE, neighbor: nodeH)
-
-    let nodesExplored = depthFirstSearch(tree, source: nodeA)
-
-    XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
-  }
-
-  func testExploringGraph() {
-    let graph = Graph()
-
-    let nodeA = graph.addNode("a")
-    let nodeB = graph.addNode("b")
-    let nodeC = graph.addNode("c")
-    let nodeD = graph.addNode("d")
-    let nodeE = graph.addNode("e")
-    let nodeF = graph.addNode("f")
-    let nodeG = graph.addNode("g")
-    let nodeH = graph.addNode("h")
-    let nodeI = graph.addNode("i")
-
-    graph.addEdge(nodeA, neighbor: nodeB)
-    graph.addEdge(nodeA, neighbor: nodeH)
-    graph.addEdge(nodeB, neighbor: nodeA)
-    graph.addEdge(nodeB, neighbor: nodeC)
-    graph.addEdge(nodeB, neighbor: nodeH)
-    graph.addEdge(nodeC, neighbor: nodeB)
-    graph.addEdge(nodeC, neighbor: nodeD)
-    graph.addEdge(nodeC, neighbor: nodeF)
-    graph.addEdge(nodeC, neighbor: nodeI)
-    graph.addEdge(nodeD, neighbor: nodeC)
-    graph.addEdge(nodeD, neighbor: nodeE)
-    graph.addEdge(nodeD, neighbor: nodeF)
-    graph.addEdge(nodeE, neighbor: nodeD)
-    graph.addEdge(nodeE, neighbor: nodeF)
-    graph.addEdge(nodeF, neighbor: nodeC)
-    graph.addEdge(nodeF, neighbor: nodeD)
-    graph.addEdge(nodeF, neighbor: nodeE)
-    graph.addEdge(nodeF, neighbor: nodeG)
-    graph.addEdge(nodeG, neighbor: nodeF)
-    graph.addEdge(nodeG, neighbor: nodeH)
-    graph.addEdge(nodeG, neighbor: nodeI)
-    graph.addEdge(nodeH, neighbor: nodeA)
-    graph.addEdge(nodeH, neighbor: nodeB)
-    graph.addEdge(nodeH, neighbor: nodeG)
-    graph.addEdge(nodeH, neighbor: nodeI)
-    graph.addEdge(nodeI, neighbor: nodeC)
-    graph.addEdge(nodeI, neighbor: nodeG)
-    graph.addEdge(nodeI, neighbor: nodeH)
-
-    let nodesExplored = depthFirstSearch(graph, source: nodeA)
-
-    XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
-  }
-
-  func testExploringGraphWithASingleNode() {
-    let graph = Graph()
-    let node = graph.addNode("a")
-
-    let nodesExplored = depthFirstSearch(graph, source: node)
-
-    XCTAssertEqual(nodesExplored, ["a"])
-  }
+    
+    func testSwift4(){
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    func testExploringTree() {
+        let tree = Graph()
+        
+        let nodeA = tree.addNode("a")
+        let nodeB = tree.addNode("b")
+        let nodeC = tree.addNode("c")
+        let nodeD = tree.addNode("d")
+        let nodeE = tree.addNode("e")
+        let nodeF = tree.addNode("f")
+        let nodeG = tree.addNode("g")
+        let nodeH = tree.addNode("h")
+        
+        tree.addEdge(nodeA, neighbor: nodeB)
+        tree.addEdge(nodeA, neighbor: nodeC)
+        tree.addEdge(nodeB, neighbor: nodeD)
+        tree.addEdge(nodeB, neighbor: nodeE)
+        tree.addEdge(nodeC, neighbor: nodeF)
+        tree.addEdge(nodeC, neighbor: nodeG)
+        tree.addEdge(nodeE, neighbor: nodeH)
+        
+        let nodesExplored = depthFirstSearch(tree, source: nodeA)
+        
+        XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
+    }
+    
+    func testExploringGraph() {
+        let graph = Graph()
+        
+        let nodeA = graph.addNode("a")
+        let nodeB = graph.addNode("b")
+        let nodeC = graph.addNode("c")
+        let nodeD = graph.addNode("d")
+        let nodeE = graph.addNode("e")
+        let nodeF = graph.addNode("f")
+        let nodeG = graph.addNode("g")
+        let nodeH = graph.addNode("h")
+        let nodeI = graph.addNode("i")
+        
+        graph.addEdge(nodeA, neighbor: nodeB)
+        graph.addEdge(nodeA, neighbor: nodeH)
+        graph.addEdge(nodeB, neighbor: nodeA)
+        graph.addEdge(nodeB, neighbor: nodeC)
+        graph.addEdge(nodeB, neighbor: nodeH)
+        graph.addEdge(nodeC, neighbor: nodeB)
+        graph.addEdge(nodeC, neighbor: nodeD)
+        graph.addEdge(nodeC, neighbor: nodeF)
+        graph.addEdge(nodeC, neighbor: nodeI)
+        graph.addEdge(nodeD, neighbor: nodeC)
+        graph.addEdge(nodeD, neighbor: nodeE)
+        graph.addEdge(nodeD, neighbor: nodeF)
+        graph.addEdge(nodeE, neighbor: nodeD)
+        graph.addEdge(nodeE, neighbor: nodeF)
+        graph.addEdge(nodeF, neighbor: nodeC)
+        graph.addEdge(nodeF, neighbor: nodeD)
+        graph.addEdge(nodeF, neighbor: nodeE)
+        graph.addEdge(nodeF, neighbor: nodeG)
+        graph.addEdge(nodeG, neighbor: nodeF)
+        graph.addEdge(nodeG, neighbor: nodeH)
+        graph.addEdge(nodeG, neighbor: nodeI)
+        graph.addEdge(nodeH, neighbor: nodeA)
+        graph.addEdge(nodeH, neighbor: nodeB)
+        graph.addEdge(nodeH, neighbor: nodeG)
+        graph.addEdge(nodeH, neighbor: nodeI)
+        graph.addEdge(nodeI, neighbor: nodeC)
+        graph.addEdge(nodeI, neighbor: nodeG)
+        graph.addEdge(nodeI, neighbor: nodeH)
+        
+        let nodesExplored = depthFirstSearch(graph, source: nodeA)
+        
+        XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
+    }
+    
+    func testExploringGraphWithASingleNode() {
+        let graph = Graph()
+        let node = graph.addNode("a")
+        
+        let nodesExplored = depthFirstSearch(graph, source: node)
+        
+        XCTAssertEqual(nodesExplored, ["a"])
+    }
 }
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index dbc44ecd4..8f6058600 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -180,6 +180,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -232,7 +234,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -245,7 +247,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From e1c0189ad8951acbecb6a71d32a85ef039ea00fc Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 12:44:48 +0500
Subject: [PATCH 1134/1679] HashSet Code updated to Swift4

---
 Hash Set/HashSet.playground/Contents.swift      | 4 ++++
 Hash Set/HashSet.playground/timeline.xctimeline | 6 ------
 2 files changed, 4 insertions(+), 6 deletions(-)
 delete mode 100644 Hash Set/HashSet.playground/timeline.xctimeline

diff --git a/Hash Set/HashSet.playground/Contents.swift b/Hash Set/HashSet.playground/Contents.swift
index 551c6dc86..5edb76bb4 100644
--- a/Hash Set/HashSet.playground/Contents.swift	
+++ b/Hash Set/HashSet.playground/Contents.swift	
@@ -1,4 +1,8 @@
 //: Playground - noun: a place where people can play
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 var set = HashSet<String>()
 
diff --git a/Hash Set/HashSet.playground/timeline.xctimeline b/Hash Set/HashSet.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Hash Set/HashSet.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 403e11cfcb0f5063415cd24c1df7960afcc8c650 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 1 Aug 2017 18:04:26 +0900
Subject: [PATCH 1135/1679] Updated files for 2 spaced-indentations

---
 .../Shuffle.playground/Sources/Shuffle.swift  | 14 +++---
 Shuffle/Shuffle.swift                         | 46 +++++++++----------
 2 files changed, 30 insertions(+), 30 deletions(-)

diff --git a/Shuffle/Shuffle.playground/Sources/Shuffle.swift b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
index 63fea2899..553832d43 100644
--- a/Shuffle/Shuffle.playground/Sources/Shuffle.swift
+++ b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
@@ -2,15 +2,15 @@ import Foundation
 
 /* Returns a random integer between 0 and n-1. */
 public func random(_ n: Int) -> Int {
-    return Int(arc4random_uniform(UInt32(n)))
+  return Int(arc4random_uniform(UInt32(n)))
 }
 
 extension Array {
   /*
-    Randomly shuffles the array in-place
-    This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
-    Time complexity: O(n)
-  */
+   Randomly shuffles the array in-place
+   This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+   Time complexity: O(n)
+   */
   public mutating func shuffle() {
     for i in (1...count-1).reversed() {
       let j = random(i + 1)
@@ -24,8 +24,8 @@ extension Array {
 }
 
 /*
-  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
-*/
+ Simultaneously initializes an array with the values 0...n-1 and shuffles it.
+ */
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index 19112fa37..3e4292d56 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -2,39 +2,39 @@ import Foundation
 
 /* Returns a random integer between 0 and n-1. */
 public func random(_ n: Int) -> Int {
-    return Int(arc4random_uniform(UInt32(n)))
+  return Int(arc4random_uniform(UInt32(n)))
 }
 
 extension Array {
-    /*
-     Randomly shuffles the array in-place
-     This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
-     Time complexity: O(n)
-     */
-    public mutating func shuffle() {
-        for i in (1...count-1).reversed() {
-            let j = random(i + 1)
-            if i != j {
-                let t = self[i]
-                self[i] = self[j]
-                self[j] = t
-            }
-        }
+  /*
+   Randomly shuffles the array in-place
+   This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+   Time complexity: O(n)
+   */
+  public mutating func shuffle() {
+    for i in (1...count-1).reversed() {
+      let j = random(i + 1)
+      if i != j {
+        let t = self[i]
+        self[i] = self[j]
+        self[j] = t
+      }
     }
+  }
 }
 
 /*
  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
  */
 public func shuffledArray(_ n: Int) -> [Int] {
-    var a = Array(repeating: 0, count: n)
-    for i in 0..<n {
-        let j = random(i + 1)
-        if i != j {
-            a[i] = a[j]
-        }
-        a[j] = i  // insert next number from the sequence
+  var a = Array(repeating: 0, count: n)
+  for i in 0..<n {
+    let j = random(i + 1)
+    if i != j {
+      a[i] = a[j]
     }
-    return a
+    a[j] = i  // insert next number from the sequence
+  }
+  return a
 }
 

From d6e59a4204f8ea77ca5febfe975adc921282649c Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 07:13:17 -0700
Subject: [PATCH 1136/1679] [Swift 4] Update Treap

---
 Treap/Treap/Treap.xcodeproj/project.pbxproj | 4 ++--
 Treap/Treap/TreapTests/TreapTests.swift     | 7 +++++++
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/Treap/Treap/Treap.xcodeproj/project.pbxproj b/Treap/Treap/Treap.xcodeproj/project.pbxproj
index df9a0d6ee..d8393e1c5 100644
--- a/Treap/Treap/Treap.xcodeproj/project.pbxproj
+++ b/Treap/Treap/Treap.xcodeproj/project.pbxproj
@@ -243,7 +243,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -255,7 +255,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index d4fc4cfdb..a5d156ec9 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -38,6 +38,13 @@ class TreapTests: XCTestCase {
     super.tearDown()
   }
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func testSanity() {
     var treap = Treap<Int, String>.empty
     treap = treap.set(key: 5, val: "a").set(key: 7, val: "b")

From fec536468ce17e1b044296e2957b07ded5b51912 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 07:19:26 -0700
Subject: [PATCH 1137/1679] [Swift 4] Update Graph

---
 Graph/Graph.playground/Contents.swift      | 6 ++++++
 Graph/Graph.playground/timeline.xctimeline | 2 +-
 Graph/GraphTests/GraphTests.swift          | 8 ++++++++
 3 files changed, 15 insertions(+), 1 deletion(-)

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index fde396e64..0410942f8 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,5 +1,11 @@
 import Graph
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+
 for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 
   let v1 = graph.createVertex(1)
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph.playground/timeline.xctimeline
index 688276d32..6afe06b6f 100644
--- a/Graph/Graph.playground/timeline.xctimeline
+++ b/Graph/Graph.playground/timeline.xctimeline
@@ -3,7 +3,7 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=12&amp;CharacterRangeLoc=1238&amp;EndingColumnNumber=15&amp;EndingLineNumber=38&amp;StartingColumnNumber=3&amp;StartingLineNumber=38&amp;Timestamp=498745868.545441"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Graph/Graph.playground#CharacterRangeLen=12&amp;CharacterRangeLoc=1322&amp;EndingColumnNumber=4&amp;EndingLineNumber=45&amp;StartingColumnNumber=7&amp;StartingLineNumber=44&amp;Timestamp=523289935.918656"
          selectedRepresentationIndex = "1"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 289d9aa64..a2f43f9bf 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -10,6 +10,14 @@ import XCTest
 
 class GraphTests: XCTestCase {
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+
+  }
+
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()

From e7b8f970b08d2c6df4aaeff129de003ef6a290e4 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:20:38 +0500
Subject: [PATCH 1138/1679] Hash Table migrated to Swift4

---
 Hash Table/HashTable.playground/Contents.swift | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index 121fb6032..67d082094 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
-
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 // Playing with hash values
 
 "firstName".hashValue

From df5b59ea03f3c067890419a84551163052504d71 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:24:54 +0500
Subject: [PATCH 1139/1679] Hash Table updated to Swift4

---
 Hash Table/HashTable.playground/Contents.swift | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index 121fb6032..29cbfd6a9 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,5 +1,7 @@
 //: Playground - noun: a place where people can play
-
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 // Playing with hash values
 
 "firstName".hashValue

From fbcf17b573aa99da235591464c46f4490c85390b Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:29:06 +0500
Subject: [PATCH 1140/1679] Haversine Distance updated to Swift4

---
 .../HaversineDistance.playground/Contents.swift    | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 449fa366d..5b3f591d6 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,25 +1,29 @@
 import UIKit
+// last checked with Xcode 9.04
+#if swift(>=4)
+print("Hello, Swift 4!")
+#endif
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
-
+    
     let haversin = { (angle: Double) -> Double in
         return (1 - cos(angle))/2
     }
-
+    
     let ahaversin = { (angle: Double) -> Double in
         return 2*asin(sqrt(angle))
     }
-
+    
     // Converts from degrees to radians
     let dToR = { (angle: Double) -> Double in
         return (angle / 360) * 2 * M_PI
     }
-
+    
     let lat1 = dToR(la1)
     let lon1 = dToR(lo1)
     let lat2 = dToR(la2)
     let lon2 = dToR(lo2)
-
+    
     return radius * ahaversin(haversin(lat2 - lat1) + cos(lat1) * cos(lat2) * haversin(lon2 - lon1))
 }
 

From 8bc4e9a920cf3a1526bf61714fb8c9eac2da73db Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:33:51 +0500
Subject: [PATCH 1141/1679] Karatsuba Multiplication updated to Swift4

---
 .../Contents.swift                            | 87 ++++++++++---------
 1 file changed, 45 insertions(+), 42 deletions(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 2d327fbac..6b1b0bca2 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -1,60 +1,63 @@
 //: Playground - noun: a place where people can play
 
 import Foundation
-
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4")
+#endif
 precedencegroup ExponentiativePrecedence {
-  higherThan: MultiplicationPrecedence
-  lowerThan: BitwiseShiftPrecedence
-  associativity: left
+    higherThan: MultiplicationPrecedence
+    lowerThan: BitwiseShiftPrecedence
+    associativity: left
 }
 
 infix operator ^^: ExponentiativePrecedence
 func ^^ (radix: Int, power: Int) -> Int {
-  return Int(pow(Double(radix), Double(power)))
+    return Int(pow(Double(radix), Double(power)))
 }
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
-  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
-
-  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
-
-  for i in num1Array.indices {
-    var carry = 0
-    for j in num2Array.indices {
-      product[i + j] += carry + num1Array[i] * num2Array[j]
-      carry = product[i + j] / base
-      product[i + j] %= base
+    let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
+    let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
+    
+    var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+    
+    for i in num1Array.indices {
+        var carry = 0
+        for j in num2Array.indices {
+            product[i + j] += carry + num1Array[i] * num2Array[j]
+            carry = product[i + j] / base
+            product[i + j] %= base
+        }
+        product[i + num2Array.count] += carry
     }
-    product[i + num2Array.count] += carry
-  }
-
-  return Int(product.reversed().map { String($0) }.reduce("", +))!
+    
+    return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
 // Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
-
-  guard num1Array.count > 1 && num2Array.count > 1 else {
-    return multiply(num1, by: num2)
-  }
-
-  let n = max(num1Array.count, num2Array.count)
-  let nBy2 = n / 2
-
-  let a = num1 / 10^^nBy2
-  let b = num1 % 10^^nBy2
-  let c = num2 / 10^^nBy2
-  let d = num2 % 10^^nBy2
-
-  let ac = karatsuba(a, by: c)
-  let bd = karatsuba(b, by: d)
-  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-
-  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-
-  return product
+    let num1Array = String(num1).characters
+    let num2Array = String(num2).characters
+    
+    guard num1Array.count > 1 && num2Array.count > 1 else {
+        return multiply(num1, by: num2)
+    }
+    
+    let n = max(num1Array.count, num2Array.count)
+    let nBy2 = n / 2
+    
+    let a = num1 / 10^^nBy2
+    let b = num1 % 10^^nBy2
+    let c = num2 / 10^^nBy2
+    let d = num2 % 10^^nBy2
+    
+    let ac = karatsuba(a, by: c)
+    let bd = karatsuba(b, by: d)
+    let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
+    
+    let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
+    
+    return product
 }

From be7832327db0b0e20db5c6d829f0bac16ac347bc Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:46:09 +0500
Subject: [PATCH 1142/1679] Knuth-Morris-Pratt updated to Swift 4

---
 .../Contents.swift                            | 53 ++++++++++---------
 1 file changed, 29 insertions(+), 24 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index a27726648..b47cf1257 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -1,34 +1,39 @@
 //: Playground - noun: a place where people can play
 
-func ZetaAlgorithm(ptnr: String) -> [Int]? {
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift4!")
+#endif
 
+func ZetaAlgorithm(ptnr: String) -> [Int]? {
+    
     let pattern = Array(ptnr.characters)
     let patternLength: Int = pattern.count
-
+    
     guard patternLength > 0 else {
         return nil
     }
-
+    
     var zeta: [Int] = [Int](repeating: 0, count: patternLength)
-
+    
     var left: Int = 0
     var right: Int = 0
     var k_1: Int = 0
     var betaLength: Int = 0
     var textIndex: Int = 0
     var patternIndex: Int = 0
-
+    
     for k in 1 ..< patternLength {
         if k > right {
             patternIndex = 0
-
+            
             while k + patternIndex < patternLength  &&
                 pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
+                    patternIndex = patternIndex + 1
             }
-
+            
             zeta[k] = patternIndex
-
+            
             if zeta[k] > 0 {
                 left = k
                 right = k + zeta[k] - 1
@@ -36,13 +41,13 @@ func ZetaAlgorithm(ptnr: String) -> [Int]? {
         } else {
             k_1 = k - left + 1
             betaLength = right - k + 1
-
+            
             if zeta[k_1 - 1] < betaLength {
                 zeta[k] = zeta[k_1 - 1]
             } else if zeta[k_1 - 1] >= betaLength {
                 textIndex = betaLength
                 patternIndex = right + 1
-
+                
                 while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
                     textIndex = textIndex + 1
                     patternIndex = patternIndex + 1
@@ -57,54 +62,54 @@ func ZetaAlgorithm(ptnr: String) -> [Int]? {
 }
 
 extension String {
-
+    
     func indexesOf(ptnr: String) -> [Int]? {
-
+        
         let text = Array(self.characters)
         let pattern = Array(ptnr.characters)
-
+        
         let textLength: Int = text.count
         let patternLength: Int = pattern.count
-
+        
         guard patternLength > 0 else {
             return nil
         }
-
+        
         var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
         var textIndex: Int = 0
         var patternIndex: Int = 0
         var indexes: [Int] = [Int]()
-
+        
         /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
         let zeta = ZetaAlgorithm(ptnr: ptnr)
-
+        
         for patternIndex in (1 ..< patternLength).reversed() {
             textIndex = patternIndex + zeta![patternIndex] - 1
             suffixPrefix[textIndex] = zeta![patternIndex]
         }
-
+        
         /* Search stage: scanning the text for pattern matching */
         textIndex = 0
         patternIndex = 0
-
+        
         while textIndex + (patternLength - patternIndex - 1) < textLength {
-
+            
             while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
                 textIndex = textIndex + 1
                 patternIndex = patternIndex + 1
             }
-
+            
             if patternIndex == patternLength {
                 indexes.append(textIndex - patternIndex)
             }
-
+            
             if patternIndex == 0 {
                 textIndex = textIndex + 1
             } else {
                 patternIndex = suffixPrefix[patternIndex - 1]
             }
         }
-
+        
         guard !indexes.isEmpty else {
             return nil
         }

From 554dfa47a2c1f73415630f79b49c64d145e36f50 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:49:14 +0500
Subject: [PATCH 1143/1679] Linear Regression updated to Swift 4

---
 Linear Regression/LinearRegression.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 8faf2b738..3e4135794 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -2,6 +2,11 @@
 
 import Foundation
 
+// last checked with Xcode 4.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let carAge: [Double] = [10, 8, 3, 3, 2, 1]
 let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
 var intercept = 0.0

From e390f5995fd62c27be4c6085dad43b800b381bd3 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:51:44 +0500
Subject: [PATCH 1144/1679] Linear Search updated to Swift 4

---
 .../LinearSearch.playground/Contents.swift          | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 34e859fa3..436af2eda 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,10 +1,15 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 4.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
-  for (index, obj) in array.enumerated() where obj == object {
-    return index
-  }
-  return nil
+    for (index, obj) in array.enumerated() where obj == object {
+        return index
+    }
+    return nil
 }
 
 let array = [5, 2, 4, 7]

From b7b6130e0e062cfbef47cde923c270690cb8b758 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:53:47 +0500
Subject: [PATCH 1145/1679] code update

---
 Linear Search/LinearSearch.playground/timeline.xctimeline | 6 ------
 1 file changed, 6 deletions(-)
 delete mode 100644 Linear Search/LinearSearch.playground/timeline.xctimeline

diff --git a/Linear Search/LinearSearch.playground/timeline.xctimeline b/Linear Search/LinearSearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Linear Search/LinearSearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 6cf3900a186c16aa4ab8e8cc17f9474cc9ea4433 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Wed, 2 Aug 2017 00:00:20 +0500
Subject: [PATCH 1146/1679] Miller-Rabin Primality Test updated to Swift 4

---
 .../MRPrimality.playground/Contents.swift                    | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index 98032bd59..d8fd7fad8 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Real primes
 mrPrimalityTest(5)
 mrPrimalityTest(439)

From 99d955a1804fedfcd80c60af7224caceb8b9154b Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Wed, 2 Aug 2017 00:04:23 +0500
Subject: [PATCH 1147/1679] Minimum Edit Distance updated to Swift 4

---
 .../MinimumEditDistance.playground/Contents.swift | 15 ++++++++++-----
 .../contents.xcplayground                         |  0
 2 files changed, 10 insertions(+), 5 deletions(-)
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground

diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
old mode 100755
new mode 100644
index 238afeb9b..ad4f2dd8d
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,21 +1,26 @@
-extension String {
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
+extension String {
+    
     public func minimumEditDistance(other: String) -> Int {
         let m = self.characters.count
         let n = other.characters.count
         var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
-
+        
         // initialize matrix
         for index in 1...m {
             // the distance of any first string to an empty second string
             matrix[index][0] = index
         }
-
+        
         for index in 1...n {
             // the distance of any second string to an empty first string
             matrix[0][index] = index
         }
-
+        
         // compute Levenshtein distance
         for (i, selfChar) in self.characters.enumerated() {
             for (j, otherChar) in other.characters.enumerated() {
@@ -25,7 +30,7 @@ extension String {
                 } else {
                     // minimum of the cost of insertion, deletion, or substitution 
                     // added to the already computed costs in the corresponding cells
-                    matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+                    matrix[i + 1][j + 1] = Swift.min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
                 }
             }
         }
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground b/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground
old mode 100755
new mode 100644

From 9bd6c97f3ebf2a00f128fc2e2e41892895d3b337 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Wed, 2 Aug 2017 00:14:50 +0500
Subject: [PATCH 1148/1679] Minimum Spanning Tree updated to Swift4

---
 .../Contents.swift                            | 107 +++++++++---------
 .../Sources/Heap.swift                        |   4 +-
 2 files changed, 58 insertions(+), 53 deletions(-)

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
index 2981d30ea..c4f0a811b 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -3,65 +3,70 @@
  Kruskal's and Prim's algorithms.
  */
 
-func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
-  var cost: Int = 0
-  var tree = Graph<T>()
-  let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
-
-  var unionFind = UnionFind<T>()
-  for vertex in graph.vertices {
-    unionFind.addSetWith(vertex)
-  }
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
-  for edge in sortedEdgeListByWeight {
-    let v1 = edge.vertex1
-    let v2 = edge.vertex2
-    if !unionFind.inSameSet(v1, and: v2) {
-      cost += edge.weight
-      tree.addEdge(edge)
-      unionFind.unionSetsContaining(v1, and: v2)
+func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+    var cost: Int = 0
+    var tree = Graph<T>()
+    let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
+    
+    var unionFind = UnionFind<T>()
+    for vertex in graph.vertices {
+        unionFind.addSetWith(vertex)
     }
-  }
-
-  return (cost: cost, tree: tree)
+    
+    for edge in sortedEdgeListByWeight {
+        let v1 = edge.vertex1
+        let v2 = edge.vertex2
+        if !unionFind.inSameSet(v1, and: v2) {
+            cost += edge.weight
+            tree.addEdge(edge)
+            unionFind.unionSetsContaining(v1, and: v2)
+        }
+    }
+    
+    return (cost: cost, tree: tree)
 }
 
 func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
-  var cost: Int = 0
-  var tree = Graph<T>()
-
-  guard let start = graph.vertices.first else {
-    return (cost: cost, tree: tree)
-  }
-
-  var visited = Set<T>()
-  var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
-    sort: { $0.weight < $1.weight })
-
-  priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
-  while let head = priorityQueue.dequeue() {
-    let vertex = head.vertex
-    if visited.contains(vertex) {
-      continue
+    var cost: Int = 0
+    var tree = Graph<T>()
+    
+    guard let start = graph.vertices.first else {
+        return (cost: cost, tree: tree)
     }
-    visited.insert(vertex)
-
-    cost += head.weight
-    if let prev = head.parent {
-      tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
-    }
-
-    if let neighbours = graph.adjList[vertex] {
-      for neighbour in neighbours {
-        let nextVertex = neighbour.vertex
-        if !visited.contains(nextVertex) {
-          priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+    
+    var visited = Set<T>()
+    var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
+        sort: { $0.weight < $1.weight })
+    
+    priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
+    while let head = priorityQueue.dequeue() {
+        let vertex = head.vertex
+        if visited.contains(vertex) {
+            continue
+        }
+        visited.insert(vertex)
+        
+        cost += head.weight
+        if let prev = head.parent {
+            tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
+        }
+        
+        if let neighbours = graph.adjList[vertex] {
+            for neighbour in neighbours {
+                let nextVertex = neighbour.vertex
+                if !visited.contains(nextVertex) {
+                    priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+                }
+            }
         }
-      }
     }
-  }
-
-  return (cost: cost, tree: tree)
+    
+    return (cost: cost, tree: tree)
 }
 
 /*:
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
index 80b40c65f..8a2c2aa07 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
@@ -147,7 +147,7 @@ public struct Heap<T> {
 
     let size = elements.count - 1
     if index != size {
-      swap(&elements[index], &elements[size])
+      elements.swapAt(index,size)
       shiftDown(index, heapSize: size)
       shiftUp(index)
     }
@@ -200,7 +200,7 @@ public struct Heap<T> {
       }
       if first == parentIndex { return }
 
-      swap(&elements[parentIndex], &elements[first])
+      elements.swapAt(parentIndex,first)
       parentIndex = first
     }
   }

From 9f85804ce36d56e328cc01f07ef58d75368a8496 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Tue, 1 Aug 2017 22:13:16 -0400
Subject: [PATCH 1149/1679] Update travis to xcode 9

Update travis to use xcode 9 for swift 4 migration.
---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index d413140fc..1515be04f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 language: objective-c
-osx_image: xcode8.3
+osx_image: xcode9
 # sudo: false
 
 install:

From eb798f2d905c5d5c15555bb47be1854765562cac Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 21:55:11 -0700
Subject: [PATCH 1150/1679] [Swift 4] Update Z Algorithm

---
 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index b1d49eec7..d057080a1 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
   let pattern = Array(ptrn.characters)

From 0b558063e41f37a7ddb7cadb6ae7ac9959d90137 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:01:52 -0700
Subject: [PATCH 1151/1679] [Swift 4] Update Threaded Binary Tree

---
 .../ThreadedBinaryTree.playground/Contents.swift             | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index ece1966e0..4ce9d8157 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {

From 82d8f3dc7d106ddfada053a0a20b2ff5bcf6ff72 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:05:53 -0700
Subject: [PATCH 1152/1679] [Swift 4] Update Ternary Search Tree

---
 .../TST.playground/Contents.swift             |  5 +
 .../Tests/TernarySearchTreeTests.swift        | 99 ++++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  4 +-
 .../contents.xcworkspacedata                  |  7 ++
 4 files changed, 67 insertions(+), 48 deletions(-)
 create mode 100644 Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata

diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index bacf56aee..0f576835b 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -3,6 +3,11 @@
 import Cocoa
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let treeOfStrings = TernarySearchTree<String>()
 
 var testStrings: [(key: String, data: String)] = []
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index 4a1816412..a595e40a3 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -10,61 +10,68 @@ import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
 
-    let testCount = 30
+  let testCount = 30
 
-    func testCanFindStringInTree() {
-        var testStrings: [(key: String, data: String)] = []
-        let treeOfStrings = TernarySearchTree<String>()
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 
-        for _ in (1...testCount) {
-            var randomLength = Int(arc4random_uniform(10))
+  func testCanFindStringInTree() {
+    var testStrings: [(key: String, data: String)] = []
+    let treeOfStrings = TernarySearchTree<String>()
 
-            var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+    for _ in (1...testCount) {
+      var randomLength = Int(arc4random_uniform(10))
 
-            while testStrings.contains(where: { $0.key == key}) {
-                //That key is taken, so we generate a new one with another length
-                randomLength = Int(arc4random_uniform(10))
-                key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            }
-            let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            //    print("Key: \(key) Data: \(data)")
+      var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
 
-            if key != "" && data != "" {
-                testStrings.append((key, data))
-                treeOfStrings.insert(data: data, withKey: key)
-            }
-        }
+      while testStrings.contains(where: { $0.key == key}) {
+        //That key is taken, so we generate a new one with another length
+        randomLength = Int(arc4random_uniform(10))
+        key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      }
+      let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      //    print("Key: \(key) Data: \(data)")
 
-        for aTest in testStrings {
-            let data = treeOfStrings.find(key: aTest.key)
-            XCTAssertNotNil(data)
-            XCTAssertEqual(data, aTest.data)
-        }
+      if key != "" && data != "" {
+        testStrings.append((key, data))
+        treeOfStrings.insert(data: data, withKey: key)
+      }
     }
 
-    func testCanFindNumberInTree() {
-        var testNums: [(key: String, data: Int)] = []
-        let treeOfInts = TernarySearchTree<Int>()
-        for _ in (1...testCount) {
-            let randomNum = Int(arc4random_uniform(UInt32.max))
-            var randomLength = Int(arc4random_uniform(10))
-            var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            while testNums.contains(where: { $0.key == key}) {
-                //That key is taken, so we generate a new one with another length
-                randomLength = Int(arc4random_uniform(10))
-                key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            }
+    for aTest in testStrings {
+      let data = treeOfStrings.find(key: aTest.key)
+      XCTAssertNotNil(data)
+      XCTAssertEqual(data, aTest.data)
+    }
+  }
+
+  func testCanFindNumberInTree() {
+    var testNums: [(key: String, data: Int)] = []
+    let treeOfInts = TernarySearchTree<Int>()
+    for _ in (1...testCount) {
+      let randomNum = Int(arc4random_uniform(UInt32.max))
+      var randomLength = Int(arc4random_uniform(10))
+      var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      while testNums.contains(where: { $0.key == key}) {
+        //That key is taken, so we generate a new one with another length
+        randomLength = Int(arc4random_uniform(10))
+        key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      }
 
-            if key != "" {
-                testNums.append((key, randomNum))
-                treeOfInts.insert(data: randomNum, withKey: key)
-            }
-        }
+      if key != "" {
+        testNums.append((key, randomNum))
+        treeOfInts.insert(data: randomNum, withKey: key)
+      }
+    }
 
-        for aTest in testNums {
-            let data = treeOfInts.find(key: aTest.key)
-            XCTAssertNotNil(data)
-            XCTAssertEqual(data, aTest.data)
-        }
+    for aTest in testNums {
+      let data = treeOfInts.find(key: aTest.key)
+      XCTAssertNotNil(data)
+      XCTAssertEqual(data, aTest.data)
     }
+  }
 }
diff --git a/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj b/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj
index 7afaca944..1d48e705a 100644
--- a/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -220,7 +220,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -233,7 +233,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From fe933ee784f8e25408ead1fdc483b4a4ff9f147a Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:08:54 -0700
Subject: [PATCH 1153/1679] [Swift 4] Update Strassen Matrix Multiplication

---
 .../StrassensMatrixMultiplication.playground/Contents.swift  | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 6b9314557..409e28c52 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 var A = Matrix(rows: 2, columns: 4, initialValue: 0)

From 5f9a11c95b1271dac89ed11f3ebdcb819302cfef Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:23:58 -0700
Subject: [PATCH 1154/1679] [Swift 4] Update Slow Sort

---
 Slow Sort/SlowSort.playground/Contents.swift  |  9 ++++++
 .../Sources/SlowSort.swift                    | 16 ++++++++++
 .../SlowSort.playground/contents.xcplayground |  4 +++
 .../contents.xcworkspacedata                  |  7 +++++
 Slow Sort/SlowSort.swift                      | 31 +++++++++----------
 .../contents.xcworkspacedata                  |  3 ++
 6 files changed, 53 insertions(+), 17 deletions(-)
 create mode 100644 Slow Sort/SlowSort.playground/Contents.swift
 create mode 100644 Slow Sort/SlowSort.playground/Sources/SlowSort.swift
 create mode 100644 Slow Sort/SlowSort.playground/contents.xcplayground
 create mode 100644 Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Slow Sort/SlowSort.playground/Contents.swift b/Slow Sort/SlowSort.playground/Contents.swift
new file mode 100644
index 000000000..95bf80739
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/Contents.swift	
@@ -0,0 +1,9 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+var numberList = [1, 12, 9, 17, 13, 12]
+
+slowsort(0, numberList.count-1, &numberList)
+print(numberList)
diff --git a/Slow Sort/SlowSort.playground/Sources/SlowSort.swift b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift
new file mode 100644
index 000000000..32bb38505
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift	
@@ -0,0 +1,16 @@
+import Foundation
+
+public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  if i>=j {
+    return
+  }
+  let m = (i+j)/2
+  slowsort(i, m, &numberList)
+  slowsort(m+1, j, &numberList)
+  if numberList[j] < numberList[m] {
+    let temp = numberList[j]
+    numberList[j] = numberList[m]
+    numberList[m] = temp
+  }
+  slowsort(i, j-1, &numberList)
+}
diff --git a/Slow Sort/SlowSort.playground/contents.xcplayground b/Slow Sort/SlowSort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 6396e8b38..9f264a057 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,22 +6,19 @@
 //
 //
 
-var numberList = [1, 12, 9, 17, 13, 12]
+import Foundation
 
-public func slowsort(_ i: Int, _ j: Int) {
-    if i>=j {
-        return
-    }
-    let m = (i+j)/2
-    slowsort(i, m)
-    slowsort(m+1, j)
-    if numberList[j] < numberList[m] {
-        let temp = numberList[j]
-        numberList[j] = numberList[m]
-        numberList[m] = temp
-    }
-    slowsort(i, j-1)
+public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  if i>=j {
+    return
+  }
+  let m = (i+j)/2
+  slowsort(i, m, &numberList)
+  slowsort(m+1, j, &numberList)
+  if numberList[j] < numberList[m] {
+    let temp = numberList[j]
+    numberList[j] = numberList[m]
+    numberList[m] = temp
+  }
+  slowsort(i, j-1, &numberList)
 }
-
-slowsort(0, numberList.count-1)
-print(numberList)
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..883185e49 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -2293,6 +2293,9 @@
    <Group
       location = "group:Slow Sort"
       name = "Slow Sort">
+      <FileRef
+         location = "group:SlowSort.playground">
+      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From ef52311487a7123cd71c34f9df0af2f2a68a7372 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:33:01 -0700
Subject: [PATCH 1155/1679] [Swift 4] Update Skip List

---
 Skip-List/SkipList.playground/Contents.swift  |   7 +
 .../Sources/SkipList.swift                    | 270 ++++++++++++++++++
 .../SkipList.playground/contents.xcplayground |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Skip-List/SkipList.swift                      |  13 +-
 .../contents.xcworkspacedata                  |   3 +
 6 files changed, 295 insertions(+), 9 deletions(-)
 create mode 100644 Skip-List/SkipList.playground/Contents.swift
 create mode 100644 Skip-List/SkipList.playground/Sources/SkipList.swift
 create mode 100644 Skip-List/SkipList.playground/contents.xcplayground
 create mode 100644 Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Skip-List/SkipList.playground/Contents.swift b/Skip-List/SkipList.playground/Contents.swift
new file mode 100644
index 000000000..1b4847c0e
--- /dev/null
+++ b/Skip-List/SkipList.playground/Contents.swift
@@ -0,0 +1,7 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+// SkipList is ready for Swift 4.
+// TODO: Add Test
diff --git a/Skip-List/SkipList.playground/Sources/SkipList.swift b/Skip-List/SkipList.playground/Sources/SkipList.swift
new file mode 100644
index 000000000..f626da0f8
--- /dev/null
+++ b/Skip-List/SkipList.playground/Sources/SkipList.swift
@@ -0,0 +1,270 @@
+// The MIT License (MIT)
+
+// Copyright (c) 2016 Mike Taghavi (mitghi[at]me.com)
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+import Foundation
+
+// Stack from : https://github.com/raywenderlich/swift-algorithm-club/tree/master/Stack
+public struct Stack<T> {
+  fileprivate var array: [T] = []
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
+
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
+
+  public func peek() -> T? {
+    return array.last
+  }
+}
+
+extension Stack: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator { curr.pop() }
+  }
+}
+
+private func coinFlip() -> Bool {
+  return arc4random_uniform(2) == 1
+}
+
+public class DataNode<Key: Comparable, Payload> {
+  public typealias Node = DataNode<Key, Payload>
+
+  var data: Payload?
+  fileprivate var key: Key?
+  var next: Node?
+  var down: Node?
+
+  public init(key: Key, data: Payload) {
+    self.key  = key
+    self.data = data
+  }
+
+  public init(asHead head: Bool) {}
+
+}
+
+open class SkipList<Key: Comparable, Payload> {
+  public typealias Node = DataNode<Key, Payload>
+
+  fileprivate(set) var head: Node?
+
+  public init() {}
+
+}
+
+// MARK: - Search lanes for a node with a given key
+
+extension SkipList {
+
+  func findNode(key: Key) -> Node? {
+    var currentNode: Node? = head
+    var isFound: Bool = false
+
+    while !isFound {
+      if let node = currentNode {
+
+        switch node.next {
+        case .none:
+
+          currentNode = node.down
+        case .some(let value) where value.key != nil:
+
+          if value.key == key {
+            isFound = true
+            break
+          } else {
+            if key < value.key! {
+              currentNode = node.down
+            } else {
+              currentNode = node.next
+            }
+          }
+
+        default:
+          continue
+        }
+
+      } else {
+        break
+      }
+    }
+
+    if isFound {
+      return currentNode
+    } else {
+      return nil
+    }
+
+  }
+
+  func search(key: Key) -> Payload? {
+    guard let node = findNode(key: key) else {
+      return nil
+    }
+
+    return node.next!.data
+  }
+
+}
+
+// MARK: - Insert a node into lanes depending on skip list status ( bootstrap base-layer if head is empty / start insertion from current head ).
+
+extension SkipList {
+  private func bootstrapBaseLayer(key: Key, data: Payload) {
+    head       = Node(asHead: true)
+    var node   = Node(key: key, data: data)
+
+    head!.next = node
+
+    var currentTopNode = node
+
+    while coinFlip() {
+      let newHead    = Node(asHead: true)
+      node           = Node(key: key, data: data)
+      node.down      = currentTopNode
+      newHead.next   = node
+      newHead.down   = head
+      head           = newHead
+      currentTopNode = node
+    }
+
+  }
+
+  private func insertItem(key: Key, data: Payload) {
+    var stack              = Stack<Node>()
+    var currentNode: Node? = head
+
+    while currentNode != nil {
+
+      if let nextNode = currentNode!.next {
+        if nextNode.key! > key {
+          stack.push(currentNode!)
+          currentNode = currentNode!.down
+        } else {
+          currentNode = nextNode
+        }
+
+      } else {
+        stack.push(currentNode!)
+        currentNode = currentNode!.down
+      }
+
+    }
+
+    let itemAtLayer    = stack.pop()
+    var node           = Node(key: key, data: data)
+    node.next          = itemAtLayer!.next
+    itemAtLayer!.next  = node
+    var currentTopNode = node
+
+    while coinFlip() {
+      if stack.isEmpty {
+        let newHead    = Node(asHead: true)
+
+        node           = Node(key: key, data: data)
+        node.down      = currentTopNode
+        newHead.next   = node
+        newHead.down   = head
+        head           = newHead
+        currentTopNode = node
+
+      } else {
+        let nextNode  = stack.pop()
+
+        node           = Node(key: key, data: data)
+        node.down      = currentTopNode
+        node.next      = nextNode!.next
+        nextNode!.next = node
+        currentTopNode = node
+      }
+    }
+  }
+
+  func insert(key: Key, data: Payload) {
+    if head != nil {
+      if let node = findNode(key: key) {
+        // replace, in case of key already exists.
+        var currentNode = node.next
+        while currentNode != nil && currentNode!.key == key {
+          currentNode!.data = data
+          currentNode       = currentNode!.down
+        }
+      } else {
+        insertItem(key: key, data: data)
+      }
+
+    } else {
+      bootstrapBaseLayer(key: key, data: data)
+    }
+  }
+
+}
+
+// MARK: - Remove a node with a given key. First, find its position in layers at the top, then remove it from each lane by traversing down to the base layer.
+
+extension SkipList {
+  public func remove(key: Key) {
+    guard let item = findNode(key: key) else {
+      return
+    }
+
+    var currentNode = Optional(item)
+
+    while currentNode != nil {
+      let node   = currentNode!.next
+
+      if node!.key != key {
+        currentNode = node
+        continue
+      }
+
+      let nextNode      = node!.next
+
+      currentNode!.next = nextNode
+      currentNode       = currentNode!.down
+
+    }
+
+  }
+}
+
+// MARK: - Get associated payload from a node with a given key.
+
+extension SkipList {
+
+  public func get(key: Key) -> Payload? {
+    return search(key: key)
+  }
+}
diff --git a/Skip-List/SkipList.playground/contents.xcplayground b/Skip-List/SkipList.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Skip-List/SkipList.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata b/Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 43173f236..fc635d0f2 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -50,18 +50,12 @@ public struct Stack<T> {
 extension Stack: Sequence {
   public func makeIterator() -> AnyIterator<T> {
     var curr = self
-    return AnyIterator { _ -> T? in
-      return curr.pop()
-    }
+    return AnyIterator { curr.pop() }
   }
 }
 
 private func coinFlip() -> Bool {
-  #if os(Linux)
-      return random() % 2 == 0
-  #elseif os(OSX)
-      return arc4random_uniform(2) == 1
-  #endif
+  return arc4random_uniform(2) == 1
 }
 
 public class DataNode<Key: Comparable, Payload> {
@@ -221,7 +215,7 @@ extension SkipList {
   func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
-        // replace, in case of key already exists. 
+        // replace, in case of key already exists.
         var currentNode = node.next
         while currentNode != nil && currentNode!.key == key {
           currentNode!.data = data
@@ -274,3 +268,4 @@ extension SkipList {
     return search(key: key)
   }
 }
+
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..5b78bd25a 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -2237,6 +2237,9 @@
    <Group
       location = "group:Skip-List"
       name = "Skip-List">
+      <FileRef
+         location = "group:SkipList.playground">
+      </FileRef>
       <Group
          location = "group:Images"
          name = "Images">

From 691b5566cf32b55dddd7015d897b769971d37542 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:35:09 -0700
Subject: [PATCH 1156/1679] [Swift 4] Update Shunting Yard

---
 .../ShuntingYard.playground/Contents.swift    |  5 ++
 .../Sources/Stack.swift                       | 60 +++++++++----------
 2 files changed, 34 insertions(+), 31 deletions(-)

diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index 38431f5e2..ddd73de59 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 internal enum OperatorAssociativity {
   case leftAssociative
   case rightAssociative
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index c54c5a600..54ffe02ce 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -1,38 +1,36 @@
 import Foundation
 
 public struct Stack<T> {
-    fileprivate var array = [T]()
-
-    public init() {
-
-    }
-
-    public var isEmpty: Bool {
-        return array.isEmpty
-    }
-
-    public var count: Int {
-        return array.count
-    }
-
-    public mutating func push(_ element: T) {
-        array.append(element)
-    }
-
-    public mutating func pop() -> T? {
-        return array.popLast()
-    }
-
-    public var top: T? {
-        return array.last
-    }
+  fileprivate var array = [T]()
+  
+  public init() {
+    
+  }
+  
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+  
+  public var count: Int {
+    return array.count
+  }
+  
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
+  
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
+  
+  public var top: T? {
+    return array.last
+  }
 }
 
 extension Stack: Sequence {
-    public func makeIterator() -> AnyIterator<T> {
-        var curr = self
-        return AnyIterator { _ -> T? in
-            return curr.pop()
-        }
-    }
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator { curr.pop() }
+  }
 }

From 4a85e17c6733d9bb27fa8d3d7c29fbd1b1af2470 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:38:19 -0700
Subject: [PATCH 1157/1679] [Swift 4] Update Rootish Array Stack

---
 .../RootishArrayStack.playground/Contents.swift            | 5 +++++
 Rootish Array Stack/Tests/RootishArrayStackTests.swift     | 7 +++++++
 Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj  | 4 ++--
 3 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift
index 8b630528d..ade32a3e7 100644
--- a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
+++ b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Darwin
 
 public struct RootishArrayStack<T> {
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index 9d5972a41..fc045faf4 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -205,4 +205,11 @@ class RootishArrayStackTests: XCTestCase {
 		XCTAssertEqual(list.first, 0)
 		XCTAssertTrue(list.equal(toArray: array))
 	}
+
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 }
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj
index cdfd35f71..bbc3967e5 100644
--- a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
@@ -226,7 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 08cf693ea36bbd313bddc3a649a1dbf6223f7517 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Thu, 3 Aug 2017 09:26:29 +0500
Subject: [PATCH 1158/1679] Fixed Indent issue

---
 .../Contents.swift                            | 16 +++++++--------
 .../Sources/Edge.swift                        | 12 +++++------
 .../Sources/Graph.swift                       | 20 +++++++++----------
 .../Sources/Node.swift                        | 10 +++++-----
 4 files changed, 29 insertions(+), 29 deletions(-)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index dd98e87dc..8a1338dbd 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -5,15 +5,15 @@ print("Hello, Swift 4!")
 #endif
 
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
-  var nodesExplored = [source.label]
-  source.visited = true
-
-  for edge in source.neighbors {
-    if !edge.neighbor.visited {
-      nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
+    var nodesExplored = [source.label]
+    source.visited = true
+    
+    for edge in source.neighbors {
+        if !edge.neighbor.visited {
+            nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
+        }
     }
-  }
-  return nodesExplored
+    return nodesExplored
 }
 
 let graph = Graph()
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift
index 7c841be30..40e769aae 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
@@ -1,11 +1,11 @@
 public class Edge: Equatable {
-  public var neighbor: Node
-
-  public init(_ neighbor: Node) {
-    self.neighbor = neighbor
-  }
+    public var neighbor: Node
+    
+    public init(_ neighbor: Node) {
+        self.neighbor = neighbor
+    }
 }
 
 public func == (_ lhs: Edge, rhs: Edge) -> Bool {
-  return lhs.neighbor == rhs.neighbor
+    return lhs.neighbor == rhs.neighbor
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index 87e21897c..34ee2fa3a 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -1,24 +1,24 @@
 public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
-
+  
   public init() {
     self.nodes = []
   }
-
+  
   public func addNode(_ label: String) -> Node {
     let node = Node(label)
     nodes.append(node)
     return node
   }
-
+  
   public func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor)
     source.neighbors.append(edge)
   }
-
+  
   public var description: String {
     var description = ""
-
+    
     for node in nodes {
       if !node.neighbors.isEmpty {
         description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
@@ -26,18 +26,18 @@ public class Graph: CustomStringConvertible, Equatable {
     }
     return description
   }
-
+  
   public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
-
+  
   public func duplicate() -> Graph {
     let duplicated = Graph()
-
+    
     for node in nodes {
       duplicated.addNode(node.label)
     }
-
+    
     for node in nodes {
       for edge in node.neighbors {
         let source = duplicated.findNodeWithLabel(node.label)
@@ -45,7 +45,7 @@ public class Graph: CustomStringConvertible, Equatable {
         duplicated.addEdge(source, neighbor: neighbour)
       }
     }
-
+    
     return duplicated
   }
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift
index 48fc952e3..bab55c371 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
@@ -1,27 +1,27 @@
 public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-
+  
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
-
+  
   public init(_ label: String) {
     self.label = label
     neighbors = []
     visited = false
   }
-
+  
   public var description: String {
     if let distance = distance {
       return "Node(label: \(label), distance: \(distance))"
     }
     return "Node(label: \(label), distance: infinity)"
   }
-
+  
   public var hasDistance: Bool {
     return distance != nil
   }
-
+  
   public func remove(_ edge: Edge) {
     neighbors.remove(at: neighbors.index { $0 === edge }!)
   }

From 19433a0d39ddd33a6cc5f3fd617daeeb58629ba8 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Thu, 3 Aug 2017 09:41:50 +0500
Subject: [PATCH 1159/1679] Fixed Indents

---
 Minimum Spanning Tree/Kruskal.swift |  6 +++---
 Minimum Spanning Tree/Prim.swift    | 12 ++++++------
 2 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/Minimum Spanning Tree/Kruskal.swift b/Minimum Spanning Tree/Kruskal.swift
index 5e6fc5fd2..7db4aeb2d 100644
--- a/Minimum Spanning Tree/Kruskal.swift	
+++ b/Minimum Spanning Tree/Kruskal.swift	
@@ -10,12 +10,12 @@ func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T
   var cost: Int = 0
   var tree = Graph<T>()
   let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
-
+  
   var unionFind = UnionFind<T>()
   for vertex in graph.vertices {
     unionFind.addSetWith(vertex)
   }
-
+  
   for edge in sortedEdgeListByWeight {
     let v1 = edge.vertex1
     let v2 = edge.vertex2
@@ -25,6 +25,6 @@ func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T
       unionFind.unionSetsContaining(v1, and: v2)
     }
   }
-
+  
   return (cost: cost, tree: tree)
 }
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
index d65d53f29..b05fc1b1f 100644
--- a/Minimum Spanning Tree/Prim.swift	
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -9,15 +9,15 @@
 func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
   var cost: Int = 0
   var tree = Graph<T>()
-
+  
   guard let start = graph.vertices.first else {
     return (cost: cost, tree: tree)
   }
-
+  
   var visited = Set<T>()
   var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
     sort: { $0.weight < $1.weight })
-
+  
   priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
   while let head = priorityQueue.dequeue() {
     let vertex = head.vertex
@@ -25,12 +25,12 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
       continue
     }
     visited.insert(vertex)
-
+    
     cost += head.weight
     if let prev = head.parent {
       tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
     }
-
+    
     if let neighbours = graph.adjList[vertex] {
       for neighbour in neighbours {
         let nextVertex = neighbour.vertex
@@ -40,6 +40,6 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
       }
     }
   }
-
+  
   return (cost: cost, tree: tree)
 }

From d54829d5017c0bd193b562338ab4f3cb73d1d223 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:14:07 -0700
Subject: [PATCH 1160/1679] [Swift 4] Update Linked List

---
 Linked List/LinkedList.playground/Contents.swift  | 5 +++++
 Linked List/Tests/LinkedListTests.swift           | 7 +++++++
 Linked List/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 3 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index c7cd6265d..b78ee4809 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,6 +3,11 @@
 // For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
 //: Linked List Class Declaration:
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public final class LinkedList<T> {
 
   /// Linked List's Node Class Declaration
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 7fd31c2c7..0b2b116df 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -11,6 +11,13 @@ class LinkedListTest: XCTestCase {
     return list
   }
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func testEmptyList() {
     let list = LinkedList<Int>()
     XCTAssertTrue(list.isEmpty)
diff --git a/Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Linked List/Tests/Tests.xcodeproj/project.pbxproj
index 3a29f5677..388dcd96c 100644
--- a/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -221,7 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -233,7 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 449b14b904c6cee06460c3933b7b73f60104593a Mon Sep 17 00:00:00 2001
From: Daniel Stokowski <daniel.stokowski@gmail.com>
Date: Sat, 5 Aug 2017 09:44:55 +0200
Subject: [PATCH 1161/1679] Update to Swift 4 - applied XCode fixes in
 Quicksort.swift and Quicsort playgrund - renamed "Tests" project to
 "Tests(quicksort)" and recreated scheme - to be easier pickable in schemes
 list - applied swift 4 settings

---
 .travis.yml                                   |  2 +-
 Quicksort/Quicksort.playground/Contents.swift |  9 +++-
 Quicksort/Quicksort.swift                     |  4 +-
 .../project.pbxproj                           | 44 +++++++++++++------
 .../contents.xcworkspacedata                  |  0
 .../xcschemes/Tests(quicksort).xcscheme}      | 44 +++----------------
 .../contents.xcworkspacedata                  |  2 +-
 7 files changed, 47 insertions(+), 58 deletions(-)
 rename Quicksort/Tests/{Tests.xcodeproj => Tests(quicksort).xcodeproj}/project.pbxproj (86%)
 rename Quicksort/Tests/{Tests.xcodeproj => Tests(quicksort).xcodeproj}/project.xcworkspace/contents.xcworkspacedata (100%)
 rename Quicksort/Tests/{Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme => Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme} (53%)

diff --git a/.travis.yml b/.travis.yml
index 1515be04f..6efcbd42b 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -32,7 +32,7 @@ script:
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Quicksort/Tests/Tests(quicksort).xcodeproj -scheme Tests(quicksort)
 - xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 972d0b5e1..94d9f8e45 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 // *** Simple but inefficient version of quicksort ***
@@ -80,7 +85,7 @@ func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
     repeat { i += 1 } while a[i] < pivot
 
     if i < j {
-      swap(&a[i], &a[j])
+        a.swapAt(i, j)
     } else {
       return j
     }
@@ -132,7 +137,7 @@ list4
 */
 public func swap<T>(_ a: inout [T], _ i: Int, _ j: Int) {
   if i != j {
-    swap(&a[i], &a[j])
+    a.swapAt(i, j)
   }
 }
 
diff --git a/Quicksort/Quicksort.swift b/Quicksort/Quicksort.swift
index 39fa27b66..a67122723 100644
--- a/Quicksort/Quicksort.swift
+++ b/Quicksort/Quicksort.swift
@@ -90,7 +90,7 @@ func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
     repeat { i += 1 } while a[i] < pivot
 
     if i < j {
-      swap(&a[i], &a[j])
+        a.swapAt(i, j)
     } else {
       return j
     }
@@ -144,7 +144,7 @@ func quicksortRandom<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
 */
 public func swap<T>(_ a: inout [T], _ i: Int, _ j: Int) {
   if i != j {
-    swap(&a[i], &a[j])
+    a.swapAt(i, j)
   }
 }
 
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj b/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
similarity index 86%
rename from Quicksort/Tests/Tests.xcodeproj/project.pbxproj
rename to Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
index 2d8ee18ff..70deb0c74 100644
--- a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
@@ -13,7 +13,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Tests(quicksort).xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3E51C77A4CA003CECC7 /* Quicksort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Quicksort.swift; path = ../Quicksort.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3E71C77A4D0003CECC7 /* QuicksortTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = QuicksortTests.swift; sourceTree = SOURCE_ROOT; };
@@ -42,7 +42,7 @@
 		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC801C779D720067B71D /* Tests.xctest */,
+				7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -62,9 +62,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* Tests */ = {
+		7B2BBC7F1C779D720067B71D /* Tests(quicksort) */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */;
 			buildPhases = (
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
@@ -74,9 +74,9 @@
 			);
 			dependencies = (
 			);
-			name = Tests;
+			name = "Tests(quicksort)";
 			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productReference = 7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -86,16 +86,16 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
-			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -108,7 +108,7 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				7B2BBC7F1C779D720067B71D /* Tests */,
+				7B2BBC7F1C779D720067B71D /* Tests(quicksort) */,
 			);
 		};
 /* End PBXProject section */
@@ -145,14 +145,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -180,6 +186,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
 			};
 			name = Debug;
 		};
@@ -191,14 +198,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -219,6 +232,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
 			};
 			name = Release;
 		};
@@ -230,7 +244,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,14 +257,15 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC871C779D720067B71D /* Debug */,
@@ -258,7 +274,7 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC8D1C779D720067B71D /* Debug */,
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
similarity index 53%
rename from Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
index dfcf6de42..ac3eafc78 100644
--- a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
@@ -1,31 +1,16 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
-      <BuildActionEntries>
-         <BuildActionEntry
-            buildForTesting = "YES"
-            buildForRunning = "YES"
-            buildForProfiling = "NO"
-            buildForArchiving = "NO"
-            buildForAnalyzing = "NO">
-            <BuildableReference
-               BuildableIdentifier = "primary"
-               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
-            </BuildableReference>
-         </BuildActionEntry>
-      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -33,9 +18,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
+               BuildableName = "Tests(quicksort).xctest"
+               BlueprintName = "Tests(quicksort)"
+               ReferencedContainer = "container:Tests(quicksort).xcodeproj">
             </BuildableReference>
          </TestableReference>
       </Testables>
@@ -46,21 +31,13 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
-      <MacroExpansion>
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "Tests.xctest"
-            BlueprintName = "Tests"
-            ReferencedContainer = "container:Tests.xcodeproj">
-         </BuildableReference>
-      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -70,15 +47,6 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
-      <MacroExpansion>
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "Tests.xctest"
-            BlueprintName = "Tests"
-            ReferencedContainer = "container:Tests.xcodeproj">
-         </BuildableReference>
-      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index db4691648..3fa8aef62 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1822,7 +1822,7 @@
             location = "group:SortingTestHelpers.swift">
          </FileRef>
          <FileRef
-            location = "group:Tests.xcodeproj">
+            location = "group:/Users/danielstokowski/Documents/GitHub/swift-algorithm-club/Quicksort/Tests/Tests(quicksort).xcodeproj">
          </FileRef>
       </Group>
    </Group>

From 038347d1ce7d72b40c9f7dc4010094068447ee8c Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sat, 5 Aug 2017 14:34:45 -0700
Subject: [PATCH 1162/1679] Add hashed heap data structure

---
 Hashed Heap/HashedHeap.swift                  | 239 ++++++++++++++++
 Hashed Heap/README.markdown                   |  11 +
 .../project.pbxproj                           | 268 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcschemes/Hashed Heap Tests.xcscheme      |  67 +++++
 Hashed Heap/Tests/HashedHeapTests.swift       |  88 ++++++
 Hashed Heap/Tests/Info.plist                  |  24 ++
 .../contents.xcworkspacedata                  |  23 ++
 8 files changed, 727 insertions(+)
 create mode 100644 Hashed Heap/HashedHeap.swift
 create mode 100644 Hashed Heap/README.markdown
 create mode 100644 Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
 create mode 100644 Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme
 create mode 100755 Hashed Heap/Tests/HashedHeapTests.swift
 create mode 100644 Hashed Heap/Tests/Info.plist

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
new file mode 100644
index 000000000..f123bbc54
--- /dev/null
+++ b/Hashed Heap/HashedHeap.swift	
@@ -0,0 +1,239 @@
+// Written by Alejandro Isaza. Adapted from heap implementation written by Kevin Randrup and Matthijs Hollemans.
+
+/// Heap with an index hash map (dictionary) to speed up lookups by value.
+///
+/// A heap keeps elements ordered in a binary tree without the use of pointers. A hashed heap does that as well as
+/// having amortized constant lookups by value. This is used in the A* and other heuristic search alogirhtms to achieve
+/// optimal perfomrance.
+public struct HashedHeap<T: Hashable> {
+    /// The array that stores the heap's nodes.
+    private(set) var elements = [T]()
+
+    /// Hash mapping from elements to indices in the `elements` array.
+    private(set) var indices = [T: Int]()
+
+    /// Determines whether this is a max-heap (>) or min-heap (<).
+    fileprivate var isOrderedBefore: (T, T) -> Bool
+
+    /// Creates an empty hashed heap.
+    ///
+    /// The sort function determines whether this is a min-heap or max-heap. For integers, > makes a max-heap, < makes
+    /// a min-heap.
+    public init(sort: @escaping (T, T) -> Bool) {
+        isOrderedBefore = sort
+    }
+
+    /// Creates a hashed heap from an array.
+    ///
+    /// The order of the array does not matter; the elements are inserted into the heap in the order determined by the
+    /// sort function.
+    ///
+    /// - Complexity: O(n)
+    public init(array: [T], sort: @escaping (T, T) -> Bool) {
+        isOrderedBefore = sort
+        buildHeap(fromArray: array)
+    }
+
+    /// Converts an array to a max-heap or min-heap in a bottom-up manner.
+    ///
+    /// - Complexity: O(n)
+    private mutating func buildHeap(fromArray array: [T]) {
+        elements = array
+        for index in elements.indices {
+            indices[elements[index]] = index
+        }
+
+        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+            shiftDown(i, heapSize: elements.count)
+        }
+    }
+
+    /// Whether the heap is empty.
+    public var isEmpty: Bool {
+        return elements.isEmpty
+    }
+
+    /// The number of elements in the heap.
+    public var count: Int {
+        return elements.count
+    }
+
+    /// Returns the index of the given element.
+    ///
+    /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
+    /// would take O(n), but for the hashed heap this takes amortized constatn time.
+    ///
+    /// - Complexity: Amortized constant
+    public func index(of element: T) -> Int? {
+        return indices[element]
+    }
+
+    /// Returns the maximum value in the heap (for a max-heap) or the minimum value (for a min-heap).
+    ///
+    /// - Complexity: O(1)
+    public func peek() -> T? {
+        return elements.first
+    }
+
+    /// Adds a new value to the heap.
+    ///
+    /// This reorders the heap so that the max-heap or min-heap property still holds.
+    ///
+    /// - Complexity: O(log n)
+    public mutating func insert(_ value: T) {
+        elements.append(value)
+        indices[value] = elements.count - 1
+        shiftUp(elements.count - 1)
+    }
+
+    /// Adds new values to the heap.
+    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+        for value in sequence {
+            insert(value)
+        }
+    }
+
+    /// Replaces an element in the hash.
+    ///
+    /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
+    public mutating func replace(index i: Int, value: T) {
+        guard i < elements.count else { return }
+
+        assert(isOrderedBefore(value, elements[i]))
+        set(value, at: i)
+        shiftUp(i)
+    }
+
+    /// Removes the root node from the heap.
+    ///
+    /// For a max-heap, this is the maximum value; for a min-heap it is the minimum value.
+    ///
+    /// - Complexity: O(log n)
+    @discardableResult
+    public mutating func remove() -> T? {
+        if elements.isEmpty {
+            return nil
+        } else if elements.count == 1 {
+            return removeLast()
+        } else {
+            // Use the last node to replace the first one, then fix the heap by
+            // shifting this new first node into its proper position.
+            let value = elements[0]
+            set(removeLast(), at: 0)
+            shiftDown()
+            return value
+        }
+    }
+
+    /// Removes an arbitrary node from the heap.
+    ///
+    /// You need to know the node's index, which may actually take O(n) steps to find.
+    ///
+    /// - Complexity: O(log n).
+    public mutating func removeAt(_ index: Int) -> T? {
+        guard index < elements.count else { return nil }
+
+        let size = elements.count - 1
+        if index != size {
+            swapAt(index, size)
+            shiftDown(index, heapSize: size)
+            shiftUp(index)
+        }
+        return removeLast()
+    }
+
+    /// Removes the last element from the heap.
+    ///
+    /// - Complexity: O(1)
+    public mutating func removeLast() -> T {
+        guard let value = elements.last else {
+            preconditionFailure("Trying to remove element from empty heap")
+        }
+        indices[value] = nil
+        return elements.removeLast()
+    }
+
+    /// Takes a child node and looks at its parents; if a parent is not larger (max-heap) or not smaller (min-heap)
+    /// than the child, we exchange them.
+    mutating func shiftUp(_ index: Int) {
+        var childIndex = index
+        let child = elements[childIndex]
+        var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+            set(elements[parentIndex], at: childIndex)
+            childIndex = parentIndex
+            parentIndex = self.parentIndex(ofIndex: childIndex)
+        }
+
+        set(child, at: childIndex)
+    }
+
+    mutating func shiftDown() {
+        shiftDown(0, heapSize: elements.count)
+    }
+
+    /// Looks at a parent node and makes sure it is still larger (max-heap) or smaller (min-heap) than its childeren.
+    mutating func shiftDown(_ index: Int, heapSize: Int) {
+        var parentIndex = index
+
+        while true {
+            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let rightChildIndex = leftChildIndex + 1
+
+            // Figure out which comes first if we order them by the sort function:
+            // the parent, the left child, or the right child. If the parent comes
+            // first, we're done. If not, that element is out-of-place and we make
+            // it "float down" the tree until the heap property is restored.
+            var first = parentIndex
+            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+                first = leftChildIndex
+            }
+            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+                first = rightChildIndex
+            }
+            if first == parentIndex { return }
+
+            swapAt(parentIndex, first)
+            parentIndex = first
+        }
+    }
+
+    /// Replaces an element in the heap and updates the indices hash.
+    private mutating func set(_ newValue: T, at index: Int) {
+        indices[elements[index]] = nil
+        elements[index] = newValue
+        indices[newValue] = index
+    }
+
+    /// Swap two elements in the heap and update the indices hash.
+    private mutating func swapAt(_ i: Int, _ j: Int) {
+        swap(&elements[i], &elements[j])
+        indices[elements[i]] = i
+        indices[elements[j]] = j
+    }
+
+    /// Returns the index of the parent of the element at index i.
+    ///
+    /// - Note: The element at index 0 is the root of the tree and has no parent.
+    @inline(__always)
+    func parentIndex(ofIndex i: Int) -> Int {
+        return (i - 1) / 2
+    }
+
+    /// Returns the index of the left child of the element at index i.
+    ///
+    /// - Note: this index can be greater than the heap size, in which case there is no left child.
+    @inline(__always)
+    func leftChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 1
+    }
+
+    /// Returns the index of the right child of the element at index i.
+    ///
+    /// - Note: this index can be greater than the heap size, in which case there is no right child.
+    @inline(__always)
+    func rightChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 2
+    }
+}
diff --git a/Hashed Heap/README.markdown b/Hashed Heap/README.markdown
new file mode 100644
index 000000000..48fe312ab
--- /dev/null
+++ b/Hashed Heap/README.markdown	
@@ -0,0 +1,11 @@
+# Hashed Heap
+
+A hashed heap is a [heap](../Heap/) with a hash map (also known as a dictionary) to speed up lookup of elements by value. This combination doesn't compromize on time performance but requires extra storage for the hash map. This is mainly used for heuristic search algorihms, in particular A*.
+
+## The code
+
+See [HashedHeap.swift](HashedHeap.swift) for the implementation. See [Heap](../Heap/) for a detailed explanation of the basic heap implementation.
+
+## See also
+
+[Heap on Wikipedia](https://en.wikipedia.org/wiki/Heap_%28data_structure%29)
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..87791f04d
--- /dev/null
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,268 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3FC1C77A658003CECC7 /* HashedHeap.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FB1C77A658003CECC7 /* HashedHeap.swift */; };
+		7B80C3FE1C77A65E003CECC7 /* HashedHeapTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FD1C77A65E003CECC7 /* HashedHeapTests.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Hashed Heap Tests.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C3FB1C77A658003CECC7 /* HashedHeap.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = HashedHeap.swift; path = ../HashedHeap.swift; sourceTree = SOURCE_ROOT; };
+		7B80C3FD1C77A65E003CECC7 /* HashedHeapTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = HashedHeapTests.swift; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B80C3FB1C77A658003CECC7 /* HashedHeap.swift */,
+				7B80C3FD1C77A65E003CECC7 /* HashedHeapTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Hashed Heap Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Hashed Heap Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = "Hashed Heap Tests";
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0800;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Hashed Heap Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Hashed Heap Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C3FE1C77A65E003CECC7 /* HashedHeapTests.swift in Sources */,
+				7B80C3FC1C77A658003CECC7 /* HashedHeap.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Hashed Heap Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Hashed Heap Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme
new file mode 100644
index 000000000..406c8dd2e
--- /dev/null
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme	
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0800"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Hashed Heap Tests.xctest"
+               BlueprintName = "Hashed Heap Tests"
+               ReferencedContainer = "container:Hashed Heap Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Hashed Heap/Tests/HashedHeapTests.swift b/Hashed Heap/Tests/HashedHeapTests.swift
new file mode 100755
index 000000000..6badb4ec5
--- /dev/null
+++ b/Hashed Heap/Tests/HashedHeapTests.swift	
@@ -0,0 +1,88 @@
+import Foundation
+import XCTest
+
+private struct Message: Hashable {
+    let text: String
+    let priority: Int
+
+    var hashValue: Int {
+        return text.hashValue
+    }
+
+    static func == (lhs: Message, rhs: Message) -> Bool {
+        return lhs.text == rhs.text
+    }
+
+    static func < (m1: Message, m2: Message) -> Bool {
+        return m1.priority < m2.priority
+    }
+}
+
+class HashedHeapTest: XCTestCase {
+    func testEmpty() {
+        var queue = HashedHeap<Message>(sort: <)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+        XCTAssertNil(queue.remove())
+    }
+
+    func testOneElement() {
+        var queue = HashedHeap<Message>(sort: <)
+
+        queue.insert(Message(text: "hello", priority: 100))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()!.priority, 100)
+
+        let result = queue.remove()
+        XCTAssertEqual(result!.priority, 100)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+    }
+
+    func testTwoElementsInOrder() {
+        var queue = HashedHeap<Message>(sort: <)
+
+        queue.insert(Message(text: "hello", priority: 100))
+        queue.insert(Message(text: "world", priority: 200))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 2)
+        XCTAssertEqual(queue.peek()!.priority, 100)
+
+        let result1 = queue.remove()
+        XCTAssertEqual(result1!.priority, 100)
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()!.priority, 200)
+
+        let result2 = queue.remove()
+        XCTAssertEqual(result2!.priority, 200)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+    }
+
+    func testTwoElementsOutOfOrder() {
+        var queue = HashedHeap<Message>(sort: <)
+
+        queue.insert(Message(text: "world", priority: 200))
+        queue.insert(Message(text: "hello", priority: 100))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 2)
+        XCTAssertEqual(queue.peek()!.priority, 100)
+
+        let result1 = queue.remove()
+        XCTAssertEqual(result1!.priority, 100)
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()!.priority, 200)
+
+        let result2 = queue.remove()
+        XCTAssertEqual(result2!.priority, 200)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+    }
+}
diff --git a/Hashed Heap/Tests/Info.plist b/Hashed Heap/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Hashed Heap/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index db4691648..e2afda53b 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1069,6 +1069,29 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "group:Hashed Heap"
+      name = "Hashed Heap">
+      <FileRef
+         location = "group:HashedHeap.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:HashedHeapTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:/Users/al/dev/swift-algorithm-club/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:HaversineDistance"
       name = "HaversineDistance">

From e0b58f68943724a52c0bfd843cb8e2f349bb88c0 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 08:08:27 +0100
Subject: [PATCH 1163/1679] [Swift 4] Singly Linked List with value semantics,
 copy-on-write and collection protocol conformance.

---
 .travis.yml                                   |   1 +
 .../Images/CopiedIndirectStorage.png          | Bin 0 -> 44765 bytes
 .../Images/SharedIndirectStorage.png          | Bin 0 -> 40994 bytes
 Singly Linked List/KeyValuePair.swift         |  77 ++
 Singly Linked List/Queue.swift                |  28 +
 Singly Linked List/README.markdown            | 140 ++++
 .../Contents.swift                            | 744 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Singly Linked List/SinglyLinkedList.swift     | 581 ++++++++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 284 +++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++
 Singly Linked List/Tests/Tests/Info.plist     |  22 +
 .../Tests/Tests/SinglyLinkedListTests.swift   | 329 ++++++++
 .../contents.xcworkspacedata                  |  46 ++
 16 files changed, 2326 insertions(+)
 create mode 100644 Singly Linked List/Images/CopiedIndirectStorage.png
 create mode 100644 Singly Linked List/Images/SharedIndirectStorage.png
 create mode 100644 Singly Linked List/KeyValuePair.swift
 create mode 100644 Singly Linked List/Queue.swift
 create mode 100644 Singly Linked List/README.markdown
 create mode 100644 Singly Linked List/SinglyLinkedList.playground/Contents.swift
 create mode 100644 Singly Linked List/SinglyLinkedList.playground/contents.xcplayground
 create mode 100644 Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Singly Linked List/SinglyLinkedList.swift
 create mode 100644 Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Singly Linked List/Tests/Tests/Info.plist
 create mode 100644 Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift

diff --git a/.travis.yml b/.travis.yml
index 1515be04f..7954c48b1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -28,6 +28,7 @@ script:
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Singly Linked List/Images/CopiedIndirectStorage.png b/Singly Linked List/Images/CopiedIndirectStorage.png
new file mode 100644
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diff --git a/Singly Linked List/KeyValuePair.swift b/Singly Linked List/KeyValuePair.swift
new file mode 100644
index 000000000..2751503c2
--- /dev/null
+++ b/Singly Linked List/KeyValuePair.swift	
@@ -0,0 +1,77 @@
+/// Conformers of this protocol represent a pair of comparable values
+/// This can be useful in many data structures and algorithms where items
+/// stored contain a value, but are ordered or retrieved according to a key.
+public protocol KeyValuePair : Comparable {
+    
+    associatedtype K : Comparable, Hashable
+    associatedtype V : Comparable, Hashable
+    
+    // Identifier used in many algorithms to search by, order by, etc
+    var key : K {get set}
+    
+    // A data container
+    var value : V {get set}
+    
+    
+    /// Initializer
+    ///
+    /// - Parameters:
+    ///   - key: Identifier used in many algorithms to search by, order by, etc.
+    ///   - value: A data container.
+    init(key: K, value: V)
+    
+    
+    /// Creates a copy
+    ///
+    /// - Abstract: Conformers of this class can be either value or reference types.
+    ///   Some algorithms might need to guarantee that a conformer instance gets copied.
+    ///   This will perform an innecessary in the case of value types.
+    ///   TODO: is there a better way?
+    /// - Returns: A new instance with the old one's values copied.
+    func copy() -> Self
+}
+
+
+/// Conformance to Equatable and Comparable protocols
+extension KeyValuePair {
+    
+    // MARK: - Equatable protocol
+    public static func ==(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key == rhs.key
+    }
+    
+    
+    
+    // MARK: - Comparable protocol
+    
+    public static func <(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key < rhs.key
+    }
+    
+    public static func <=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key <= rhs.key
+    }
+    
+    public static func >=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key >= rhs.key
+    }
+    
+    public static func >(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key > rhs.key
+    }
+}
+
+
+
+/// Concrete impletation of a KeyValuePair where  both the key and the value
+/// are Integers.
+struct IntegerPair : KeyValuePair {
+    
+    // MARK - KeyValuePair protocol
+    var key : Int
+    var value : Int
+    
+    func copy() -> IntegerPair {
+        return IntegerPair(key: self.key, value: self.value)
+    }
+}
diff --git a/Singly Linked List/Queue.swift b/Singly Linked List/Queue.swift
new file mode 100644
index 000000000..68fda9f99
--- /dev/null
+++ b/Singly Linked List/Queue.swift	
@@ -0,0 +1,28 @@
+import Foundation
+
+
+/// Data structure that provides FIFO access
+protocol Queue
+{
+    associatedtype Item
+    
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: Item) throws
+    
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> Item?
+    
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> Item?
+    
+}
diff --git a/Singly Linked List/README.markdown b/Singly Linked List/README.markdown
new file mode 100644
index 000000000..b3c8b8b2d
--- /dev/null
+++ b/Singly Linked List/README.markdown	
@@ -0,0 +1,140 @@
+# Singly-Linked List
+
+#### How is this different to the Linked List implementation?
+The existing Linked list implementation represents the same concept. However, the existing implementation has reference semantics and does not conform to the Collection protocol implemented in the Swift's standard Library. What SinglyLinkedList aims to contribute is a more idiomatic Swift implementation, that uses value semantics and copy-on-write as well as conforms to the collection protocol.
+
+#### Conceptual representation
+A Singly linked list is a non-contiguous sequence of data items in memory. Each element links to the next via a memory reference. Additionally, this implementation keeps track of the last element, which can be retrived in order O(1). However, the list can only be traversed from head to tail.
+
+    +--------+    +--------+    +--------+    +--------+
+    |        |    |        |    |        |    |        |
+    | node 0 |--->| node 1 |--->| node 2 |--->| node 3 |---> nil
+    |        |    |        |    |        |    |        |
+    +--------+    +--------+    +--------+    +--------+
+    ^                                         ^
+    |                                         |
+    Head                                      Tail
+
+Each element in the list is represented with an instance of SinglyLinkedListNode class, which basically contains some data and a reference of optional type to the next node, which means that the last node's next reference is `nil`.
+
+#### In-memory representation
+In Swift, data types can have value or reference semantics. This implementation of a singly-linked list uses value semantics. Support for copy-on-write has been added in order to improve performance and delay copying the elements of the array until strictly necessary.
+
+The image below shows how initially, after variable `l2` is assigned `l1`, a new instance of the struct SinglyLinkedList is created. Nevertheless, the indirect storage is still shared as indicated by the references that both l1 and l2 have pointing to a common area in memory.
+
+![alt text](Images/SharedIndirectStorage.png "Two linked lists sharing the indirect storage")
+
+Once a mutating operation happens --for example on `l2` to append a new element--, then the indirect storage and all nodes in the list is actually copied and the references from `l1` and `l2` are updated. This is ilustrated in the following figure.
+
+![alt text](Images/CopiedIndirectStorage.png "A copy is created after editing one of the lists")
+
+#### Implementation details
+1. Direct access to the tail in O(1) by keeping a reference that gets updated only when an operation to the list modifies the tail.
+2. Value semantics. This implementation of a singly-linked list uses a struct. When the list struct is assigned into another variable or passed as an argument to a function, a copy of the struct is made.
+3. Copy-on write. Instances of SinglyLinkedList have an internal reference to an indirect storage allocated in the heap. When a copy of the list is made (according to its value semantics) the indirect storage is initialy shared between the copies. This means that a potentially large list can be accessed to read values in it without an expensive copy having to take place. However, as soon as there is a write access to the indirect storage when there are more than one instances referencing to it, a copy will be performed to guarantee value semantics.
+4. Conformance to the Collection protocol.
+
+
+
+
+
+## Performance of linked lists
+
+EDITION
+- *append*: Appends a new node to the end of the list. This method will modify the list's tail. If the list is empty, it will also modify the head. This operation's time complexity is *O(1)* since there's a reference to the tail node in this implementation.
+- *prepend*: Inserts a new node at the start of the list. If the list is empty, it will also modify the head. This operation's time complexity is *O(1)* since there's a reference to the head node.
+- *delete*: Finds a node in the list and deletes it. This operation's time complexity has an upper bound described by a linear function; O(n).
+
+SEARCH
+- find k-th to last element. Given a list with `n` number of elements and `k` being the passed parameter with `0` <= `k` <= `n`, this method has *O(k)*.
+
+## Conforming to the Collection protocol
+Collections are sequences, therefore the first step is to conform to the Sequence protocol.
+
+```
+extension SinglyLinkedList : Sequence
+{
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
+    {
+        return SinglyLinkedListForwardIterator(head: self.storage.head)
+    }
+}
+```
+
+We have used `SinglyLinkedListForwardIterator` an iterator class to keep track of the progress while iterating the structure:
+
+```
+public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
+
+    public typealias Element = T
+
+    private(set) var head: SinglyLinkedListNode<T>?
+
+    mutating public func next() -> T?
+    {
+        let result = self.head?.value
+        self.head = self.head?.next
+        return result
+    }
+}
+```
+
+Next, a collection needs to be indexable. Indexes are implemented by the data structure class. We have encapsulated this knowledge in instances of the class `SinglyLinkedListIndex`. 
+
+```
+public struct SinglyLinkedListIndex<T> : Comparable
+{
+    fileprivate let node: SinglyLinkedListNode<T>?
+    fileprivate let tag: Int
+
+    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+
+    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
+}
+```
+
+Finally, the methods in the collection to manipulate indexes are implemented below:
+- startIndex: Index of the first element. Can be calculated with O(1).
+- endIndex: Index that follows the last valid index in the collection. That is, the index that follows the tail's index. Can be calculated with O(1) if the count of elements is kept internally. However, the implementation below is O(n) with `n` being the number of elements in the list. 
+
+```
+extension SinglyLinkedList : Collection {
+
+    public typealias Index = SinglyLinkedListIndex<T>
+
+    public var startIndex: Index {
+        get {
+            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+        }
+    }
+
+public var endIndex: Index {
+    get {
+        if let h = self.storage.head {
+        let (_, numberOfElements) = findTail(in: h)
+            return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+        } else {
+            return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+        }
+    }
+}
+
+public subscript(position: Index) -> T {
+    get {
+        return position.node!.value
+    }
+}
+
+public func index(after idx: Index) -> Index {
+    return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+    }
+}
+```
+
+Conforming to the Collection protocol allows our class SinglyLinkedList to take adventage of all the collection methods included in the Stardard Library.
+
+*Written by Borja Arias Drake*
diff --git a/Singly Linked List/SinglyLinkedList.playground/Contents.swift b/Singly Linked List/SinglyLinkedList.playground/Contents.swift
new file mode 100644
index 000000000..fc6acf9dc
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
@@ -0,0 +1,744 @@
+//: # Linked Lists
+
+// For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
+
+//: Linked List Class Declaration:
+// last checked with Xcode 9M136h
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+//: We will start by defining a protocol that elements inserted into this implementation of a List will conform to. This is useful, because many algorithms are only interested in a key that all elements have.
+
+/// Conformers of this protocol represent a pair of comparable values
+/// This can be useful in many data structures and algorithms where items
+/// stored contain a value, but are ordered or retrieved according to a key.
+public protocol KeyValuePair : Comparable {
+    
+    associatedtype K : Comparable, Hashable
+    associatedtype V : Comparable, Hashable
+    
+    // Identifier used in many algorithms to search by, order by, etc
+    var key : K {get set}
+    
+    // A data container
+    var value : V {get set}
+    
+    
+    /// Initializer
+    ///
+    /// - Parameters:
+    ///   - key: Identifier used in many algorithms to search by, order by, etc.
+    ///   - value: A data container.
+    init(key: K, value: V)
+    
+    
+    /// Creates a copy
+    ///
+    /// - Abstract: Conformers of this class can be either value or reference types.
+    ///   Some algorithms might need to guarantee that a conformer instance gets copied.
+    ///   This will perform an innecessary in the case of value types.
+    ///   TODO: is there a better way?
+    /// - Returns: A new instance with the old one's values copied.
+    func copy() -> Self
+}
+
+
+/// Conformance to Equatable and Comparable protocols
+extension KeyValuePair {
+    
+    // MARK: - Equatable protocol
+    public static func ==(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key == rhs.key
+    }
+    
+    
+    
+    // MARK: - Comparable protocol
+    
+    public static func <(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key < rhs.key
+    }
+    
+    public static func <=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key <= rhs.key
+    }
+    
+    public static func >=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key >= rhs.key
+    }
+    
+    public static func >(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key > rhs.key
+    }
+}
+
+//: Concrete impletation of a KeyValuePair where  both the key and the value that we'll use in the examples in this playground
+
+struct IntegerPair : KeyValuePair {
+    
+    // MARK - KeyValuePair protocol
+    var key : Int
+    var value : Int
+    
+    func copy() -> IntegerPair {
+        return IntegerPair(key: self.key, value: self.value)
+    }
+}
+
+//: Lists are usually used as queues. As an example, we'll define these expectations in a protocol and we'll make the the SinglyLinkedList class conform to it.
+
+/// Data structure that provides FIFO access
+protocol Queue
+{
+    associatedtype Item
+    
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: Item) throws
+    
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> Item?
+    
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> Item?
+}
+
+
+//: Next, we are going to implement a list that has value semantics. Value semantics imply that the values will be copied when assigned and passed as a parameter to functions and methods. In order to prevent unnecesasry copies, Swift uses a technique called copy-on-write; copies are only performed when a mutating operation is performed on an instance that is referenced by more than one objects. In Swift, this is ahieved with an additional level of indirection, an internal class instance, therefore with reference semantics, that will be shared, until a mutating operation occurs.
+
+
+/// Helper class to implement copy-on-write
+fileprivate class IndirectStorage<T> {
+    
+    var head: SinglyLinkedListNode<T>?
+    
+    var tail: SinglyLinkedListNode<T>?
+    
+    init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
+        self.head = head
+        self.tail = tail
+    }
+    
+    convenience init() {
+        self.init(head: nil, tail: nil)
+    }
+}
+
+
+//: Node of the list
+
+
+// MARK: - NODE -
+
+/// A node is the building block of a linked list.
+/// It can be used on its own to create linked lists. However users of this class,
+/// will need to manipulate references directly.
+public class SinglyLinkedListNode<T> {
+    
+    /// Data container
+    public var value: T
+    
+    /// Link to the next node
+    public var next: SinglyLinkedListNode<T>?
+    
+    /// Designated initializer
+    ///
+    /// - Parameter value: A value
+    public init(value: T) {
+        self.value = value
+    }
+}
+
+//: The list with value semantics
+
+// MARK: - LINKED LIST -
+
+/// Data structure to hold a collection of items.
+/// Each nodes contains a reference to the next node.
+/// The last node does not reference any other node.
+/// This class implements value semantics based on copy-on-write.
+///
+/// However, the elements contained in the list, will be shallow copied if they
+/// implement reference semantics.
+public struct SinglyLinkedList<T>
+{
+    // MARK: PROPERTIES
+    
+    // A level of inderiction, with reference semantics to allow easy
+    // detection of when there are more than one references of the storage.
+    private var storage: IndirectStorage<T>
+    
+    /// Whenever there's a change that potentially can change the value, this reference to the
+    /// storage should be used to guarantee that a new copy is created and written on.
+    private var storageForWritting: IndirectStorage<T> {
+        
+        mutating get {
+            if !isKnownUniquelyReferenced(&self.storage) {
+                self.storage = self.copyStorage()
+            }
+            return self.storage
+        }
+    }
+    
+    /// Returns the last element in the collection
+    public var last: T? {
+        get {
+            return self.storage.tail?.value
+        }
+    }
+    
+    
+    
+    // MARK: INITIALIZERS
+    
+    /// Creates a list with the given node.
+    /// NOTE: This method can break value semantics by accepting a node.
+    ///
+    /// - Parameter head: First node
+    internal init(head: SinglyLinkedListNode<T>)
+    {
+        self.storage = IndirectStorage()
+        self.append(node: head)
+    }
+    
+    
+    /// Creates a list with a single element
+    ///
+    /// - Parameter value: element to populate the list with
+    public init(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.init(head: node)
+    }
+    
+    
+    /// Creates an empty list
+    public init()
+    {
+        self.storage = IndirectStorage()
+    }
+    
+    
+    // MARK: EDITION
+    
+    /// Convenience method to append a value directly to the list
+    ///
+    /// - Parameter value: value to be added
+    public mutating func append(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.append(node: node)
+    }
+    
+    
+    /// Convenience method to prepend a value directly to the list
+    ///
+    /// - Parameter value: value to be added as the new head of the list
+    public mutating func prepend(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.prepend(node: node)
+    }
+    
+    
+    public mutating func deleteItem(at index:Int) -> T
+    {
+        precondition((index >= 0) && (index < self.count))
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storageForWritting.head
+        var i = 0
+        var elementToDelete: SinglyLinkedListNode<T>
+        
+        while (i < index) {
+            previous = current
+            current = current?.next
+            i += 1
+        }
+        
+        // Current is now the element to delete (at index position.tag)
+        elementToDelete = current!
+        if (self.storage.head === current) {
+            self.storageForWritting.head = current?.next
+        }
+        
+        if (self.storage.tail === current) {
+            self.storageForWritting.tail = previous
+        }
+        
+        previous?.next = current?.next
+        
+        return elementToDelete.value
+    }
+    
+    
+    
+    // MARK: SEARCH
+    
+    /// Returns the node located at the k-th to last position
+    ///
+    /// - Parameter kthToLast: 1 <= k <= N
+    private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>?
+    {
+        guard kthToLast <= count else {
+            return nil
+        }
+        
+        guard (node != nil) else {
+            return nil
+        }
+        
+        let i = (count - kthToLast)
+        
+        if (i == 0) {
+            return node
+        }
+        
+        return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+    }
+    
+    
+    /// Returns the kth-to-last element in the list
+    ///
+    /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
+    public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
+    {
+        return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
+    }
+    
+    
+    
+    // MARK: LOOP DETECTION
+    
+    /// A singly linked list contains a loop if one node references back to a previous node.
+    ///
+    /// - Returns: Whether the linked list contains a loop
+    public func containsLoop() -> Bool
+    {
+        /// Advances a node at a time
+        var current = self.storage.head
+        
+        /// Advances twice as fast
+        var runner = self.storage.head
+        
+        while (runner != nil) && (runner?.next != nil) {
+            
+            current = current?.next
+            runner = runner?.next?.next
+            
+            if runner === current {
+                return true
+            }
+        }
+        
+        return false
+    }
+    
+}
+
+
+
+// MARK:- Private Methods
+
+private extension SinglyLinkedList {
+    
+    /// Adds a new node to the current head. This method can easily break value semantics. It is left
+    /// for internal use.
+    ///
+    /// - Parameter node: the node that will be the new head of the list.
+    private mutating func prepend(node: SinglyLinkedListNode<T>)
+    {
+        let (tailFromNewNode, _) = findTail(in: node)
+        tailFromNewNode.next = self.storageForWritting.head
+        self.storageForWritting.head = node
+        
+        if self.storage.tail == nil {
+            self.storageForWritting.tail = tailFromNewNode
+        }
+    }
+    
+    /// Appends a new node to the list. This method can easily break value semantics. It is left
+    /// for internal use.
+    /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
+    ///   This is a private method, therefore this can only happen directly under the control of this class.
+    /// - Parameter node: node to be appended. (It can be a list, even contain loops).
+    private mutating func append(node: SinglyLinkedListNode<T>)
+    {
+        if self.storage.tail != nil
+        {
+            // Copy on write: we are about to modify next a property in
+            // a potentially shared node. Make sure it's new if necessary.
+            self.storageForWritting.tail?.next = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+        else
+        {
+            // This also means that there's no head.
+            // Otherwise the state would be inconsistent.
+            // This will be checked when adding and deleting nodes.
+            self.storageForWritting.head = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+    }
+    
+    /// Creates a copy of the linked list in a diffent memory location.
+    ///
+    /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
+    private func copyStorage() -> IndirectStorage<T> {
+        // If the list is empty, next time an item will be created, it won't affect
+        // other instances of the list that came from copies derived from value types.
+        // like assignments or parameters
+        guard (self.storage.head != nil) && (self.storage.tail != nil) else {
+            return IndirectStorage(head: nil, tail: nil)
+        }
+        
+        // Create a new position in memory.
+        // Note that we are shallow copying the value. If it was reference type
+        // we just make a copy of the reference.
+        let copiedHead = SinglyLinkedListNode<T>(value: self.storage.head!.value)
+        var previousCopied: SinglyLinkedListNode<T> = copiedHead
+        
+        // Iterate through current list of nodes and copy them.
+        var current: SinglyLinkedListNode<T>? = self.storage.head?.next
+        
+        while (current != nil) {
+            // Create a copy
+            let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
+            
+            // Create links
+            previousCopied.next = currentCopy
+            
+            // Update pointers
+            current = current?.next
+            previousCopied = currentCopy
+        }
+        
+        return IndirectStorage(head: copiedHead, tail: previousCopied)
+    }
+}
+
+
+
+// MARK:- Extensions when comparable
+
+extension SinglyLinkedList where T: Comparable
+{
+    /// Deletes node containing a given value
+    ///
+    /// - Parameter v: value of the node to be deleted.
+    public mutating func deleteNode(withValue v: T) {
+        
+        guard self.storage.head != nil else {
+            return
+        }
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storage.head
+        
+        while (current != nil) && (current?.value != v) {
+            previous = current
+            current = current?.next
+        }
+        
+        if let foundNode = current {
+            
+            if (self.storage.head === foundNode) {
+                self.storageForWritting.head = foundNode.next
+            }
+            
+            if (self.storage.tail === foundNode) {
+                self.storage.tail = previous
+            }
+            
+            previous?.next = foundNode.next
+            foundNode.next = nil
+        }
+    }
+    
+    
+    /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
+    /// - Complexity: O(N^2)
+    public mutating func deleteDuplicatesInPlace()
+    {
+        // Copy on write: this updates self.storage if necessary.
+        var current = self.storageForWritting.head
+        
+        while (current != nil)
+        {
+            var previous: SinglyLinkedListNode<T>? = current
+            var next = current?.next
+            
+            while (next != nil)
+            {
+                if (current?.value == next?.value) {
+                    
+                    if (self.storage.head === next) {
+                        self.storage.head = next?.next
+                    }
+                    
+                    if (self.storage.tail === next) {
+                        self.storage.tail = previous
+                    }
+                    
+                    // Delete next
+                    previous?.next = next?.next
+                }
+                previous = next
+                next = next?.next
+            }
+            current = current?.next
+        }
+    }
+}
+
+
+
+// MARK: - ITERATOR -
+
+public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
+    
+    public typealias Element = T
+    
+    private(set) var head: SinglyLinkedListNode<T>?
+    
+    mutating public func next() -> T?
+    {
+        let result = self.head?.value
+        self.head = self.head?.next
+        return result
+    }
+}
+
+
+
+// MARK: - SEQUENCE -
+
+extension SinglyLinkedList : Sequence
+{
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
+    {
+        return SinglyLinkedListForwardIterator(head: self.storage.head)
+    }
+}
+
+
+
+// MARK: - COLLECTION -
+
+extension SinglyLinkedList : Collection {
+    
+    public typealias Index = SinglyLinkedListIndex<T>
+    
+    public var startIndex: Index {
+        get {
+            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+        }
+    }
+    
+    public var endIndex: Index {
+        get {
+            if let h = self.storage.head {
+                let (_, numberOfElements) = findTail(in: h)
+                return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+            } else {
+                return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+            }
+        }
+    }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
+    }
+    
+    public func index(after idx: Index) -> Index {
+        return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+    }
+}
+
+
+
+// MARK: - QUEUE -
+
+extension SinglyLinkedList : Queue
+{
+    typealias Item = T
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> T? {
+        return self.storage.head?.value
+    }
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: T) throws {
+        self.append(node: SinglyLinkedListNode<T>(value: item))
+    }
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> T?
+    {
+        guard self.count > 0 else {
+            return nil
+        }
+        
+        return self.deleteItem(at: 0)
+    }
+}
+
+
+
+// MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
+
+extension SinglyLinkedList : ExpressibleByArrayLiteral
+{
+    public typealias Element = T
+    
+    public init(arrayLiteral elements: Element...)
+    {
+        var headSet = false
+        var current : SinglyLinkedListNode<T>?
+        var numberOfElements = 0
+        self.storage = IndirectStorage()
+        
+        for element in elements {
+            
+            numberOfElements += 1
+            
+            if headSet == false {
+                self.storage.head = SinglyLinkedListNode<T>(value: element)
+                current = self.storage.head
+                headSet = true
+            } else {
+                let newNode = SinglyLinkedListNode<T>(value: element)
+                current?.next = newNode
+                current = newNode
+            }
+        }
+        self.storage.tail = current
+    }
+}
+
+
+
+// MARK: - FORWARD-INDEX -
+
+public struct SinglyLinkedListIndex<T> : Comparable
+{
+    fileprivate let node: SinglyLinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
+}
+
+
+extension SinglyLinkedList where T : KeyValuePair {
+    
+    public func find(elementWithKey key: T.K) -> T? {
+        let searchResults = self.filter { (keyValuePair) -> Bool in
+            return keyValuePair.key == key
+        }
+        
+        return searchResults.first
+    }
+}
+
+// MARK: - HELPERS -
+
+func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int)
+{
+    // Assign the tail
+    // Note that the passed node can already be linking to other nodes,
+    // so the tail needs to be calculated.
+    var current: SinglyLinkedListNode<T>? = node
+    var count = 1
+    
+    while (current?.next != nil) {
+        current = current?.next
+        count += 1
+    }
+    
+    if current != nil {
+        return (tail: current!, count: count)
+    } else {
+        return (tail: node, count: 1)
+    }
+}
+
+
+
+//: EXAMPLES
+//: Let's create a list
+
+var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7]
+
+//: Because it has value semantics, if we assign it, a new value will be created. However, internally the storage is shared.
+
+var l2 = l1
+
+//: If we modify l2, l1 will remain unaffected.
+l2.append(value: 67)
+
+assert(l1.count == 7)
+assert(l1.contains(67) == false)
+
+//: However, as expected, l2 has changed
+assert(l2.count == 8)
+assert(l2.contains(67) == true)
+
+
+//: Notice that becuase our implementation conforms to the Collection protocol, we can use a lot of methods already implemented for us in Swift's standard library, for example, contains, dropLast, etc.
+
+let l3 = l2.dropLast()
+assert(l3.count == 7)
+assert(l3.contains(67) == false)
+
+//: We can use this class as a queue.
+
+func empty<Q: Queue>(queue: inout Q) {
+    while let _ = queue.dequeue() {}
+}
+
+var q: SinglyLinkedList<Int> = [5,1,2,3]
+empty(queue: &q)
+assert(q.count == 0)
+
+try? q.enqueue(item: 1)
+try? q.enqueue(item: 3)
+try? q.enqueue(item: 5)
+assert(q.count == 3)
+
+
diff --git a/Singly Linked List/SinglyLinkedList.playground/contents.xcplayground b/Singly Linked List/SinglyLinkedList.playground/contents.xcplayground
new file mode 100644
index 000000000..fd676d5b4
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx' display-mode='raw'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata b/Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
new file mode 100644
index 000000000..b05526b35
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -0,0 +1,581 @@
+import Foundation
+
+
+/// Helper class to implement copy-on-write
+fileprivate class IndirectStorage<T> {
+    
+    var head: SinglyLinkedListNode<T>?
+    
+    var tail: SinglyLinkedListNode<T>?
+    
+    init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
+        self.head = head
+        self.tail = tail
+    }
+    
+    convenience init() {
+        self.init(head: nil, tail: nil)
+    }
+}
+
+
+
+// MARK: - NODE -
+
+/// A node is the building block of a linked list.
+/// It can be used on its own to create linked lists. However users of this class,
+/// will need to manipulate references directly.
+public class SinglyLinkedListNode<T> {
+    
+    /// Data container
+    public var value: T
+    
+    /// Link to the next node
+    public var next: SinglyLinkedListNode<T>?
+    
+    /// Designated initializer
+    ///
+    /// - Parameter value: A value
+    public init(value: T) {
+        self.value = value
+    }
+}
+
+
+
+// MARK: - LINKED LIST -
+
+/// Data structure to hold a collection of items.
+/// Each nodes contains a reference to the next node.
+/// The last node does not reference any other node.
+/// This class implements value semantics based on copy-on-write.
+///
+/// However, the elements contained in the list, will be shallow copied if they
+/// implement reference semantics.
+public struct SinglyLinkedList<T>
+{
+    // MARK: PROPERTIES
+    
+    // A level of inderiction, with reference semantics to allow easy
+    // detection of when there are more than one references of the storage.
+    private var storage: IndirectStorage<T>
+    
+    /// Whenever there's a change that potentially can change the value, this reference to the
+    /// storage should be used to guarantee that a new copy is created and written on.
+    private var storageForWritting: IndirectStorage<T> {
+        
+        mutating get {
+            if !isKnownUniquelyReferenced(&self.storage) {
+                self.storage = self.copyStorage()
+            }
+            return self.storage
+        }
+    }
+    
+    /// Returns the last element in the collection
+    public var last: T? {
+        get {
+            return self.storage.tail?.value
+        }
+    }
+    
+    
+    
+    // MARK: INITIALIZERS
+    
+    /// Creates a list with the given node.
+    /// NOTE: This method can break value semantics by accepting a node.
+    ///
+    /// - Parameter head: First node
+    internal init(head: SinglyLinkedListNode<T>)
+    {
+        self.storage = IndirectStorage()
+        self.append(node: head)
+    }
+    
+    
+    /// Creates a list with a single element
+    ///
+    /// - Parameter value: element to populate the list with
+    public init(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.init(head: node)
+    }
+    
+    
+    /// Creates an empty list
+    public init()
+    {
+        self.storage = IndirectStorage()
+    }
+    
+    
+    // MARK: EDITION
+    
+    /// Convenience method to append a value directly to the list
+    ///
+    /// - Parameter value: value to be added
+    public mutating func append(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.append(node: node)
+    }
+    
+    
+    /// Convenience method to prepend a value directly to the list
+    ///
+    /// - Parameter value: value to be added as the new head of the list
+    public mutating func prepend(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.prepend(node: node)
+    }
+    
+    
+    public mutating func deleteItem(at index:Int) -> T
+    {
+        precondition((index >= 0) && (index < self.count))
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storageForWritting.head
+        var i = 0
+        var elementToDelete: SinglyLinkedListNode<T>
+        
+        while (i < index) {
+            previous = current
+            current = current?.next
+            i += 1
+        }
+        
+        // Current is now the element to delete (at index position.tag)
+        elementToDelete = current!
+        if (self.storage.head === current) {
+            self.storageForWritting.head = current?.next
+        }
+        
+        if (self.storage.tail === current) {
+            self.storageForWritting.tail = previous
+        }
+        
+        previous?.next = current?.next
+        
+        return elementToDelete.value
+    }
+    
+    
+    
+    // MARK: SEARCH
+    
+    /// Returns the node located at the k-th to last position
+    ///
+    /// - Parameter kthToLast: 1 <= k <= N
+    private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>?
+    {
+        guard kthToLast <= count else {
+            return nil
+        }
+        
+        guard (node != nil) else {
+            return nil
+        }
+        
+        let i = (count - kthToLast)
+        
+        if (i == 0) {
+            return node
+        }
+        
+        return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+    }
+    
+    
+    /// Returns the kth-to-last element in the list
+    ///
+    /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
+    public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
+    {
+        return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
+    }
+    
+    
+    
+    // MARK: LOOP DETECTION
+    
+    /// A singly linked list contains a loop if one node references back to a previous node.
+    ///
+    /// - Returns: Whether the linked list contains a loop
+    public func containsLoop() -> Bool
+    {
+        /// Advances a node at a time
+        var current = self.storage.head
+        
+        /// Advances twice as fast
+        var runner = self.storage.head
+        
+        while (runner != nil) && (runner?.next != nil) {
+            
+            current = current?.next
+            runner = runner?.next?.next
+            
+            if runner === current {
+                return true
+            }
+        }
+        
+        return false
+    }
+    
+}
+
+
+
+// MARK:- Private Methods
+
+private extension SinglyLinkedList {
+    
+    /// Adds a new node to the current head. This method can easily break value semantics. It is left
+    /// for internal use.
+    ///
+    /// - Parameter node: the node that will be the new head of the list.
+    private mutating func prepend(node: SinglyLinkedListNode<T>)
+    {
+        let (tailFromNewNode, _) = findTail(in: node)
+        tailFromNewNode.next = self.storageForWritting.head
+        self.storageForWritting.head = node
+        
+        if self.storage.tail == nil {
+            self.storageForWritting.tail = tailFromNewNode
+        }
+    }
+    
+    /// Appends a new node to the list. This method can easily break value semantics. It is left
+    /// for internal use.
+    /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
+    ///   This is a private method, therefore this can only happen directly under the control of this class.
+    /// - Parameter node: node to be appended. (It can be a list, even contain loops).
+    private mutating func append(node: SinglyLinkedListNode<T>)
+    {
+        if self.storage.tail != nil
+        {
+            // Copy on write: we are about to modify next a property in
+            // a potentially shared node. Make sure it's new if necessary.
+            self.storageForWritting.tail?.next = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+        else
+        {
+            // This also means that there's no head.
+            // Otherwise the state would be inconsistent.
+            // This will be checked when adding and deleting nodes.
+            self.storageForWritting.head = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+    }
+    
+    /// Creates a copy of the linked list in a diffent memory location.
+    ///
+    /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
+    private func copyStorage() -> IndirectStorage<T> {
+        // If the list is empty, next time an item will be created, it won't affect
+        // other instances of the list that came from copies derived from value types.
+        // like assignments or parameters
+        guard (self.storage.head != nil) && (self.storage.tail != nil) else {
+            return IndirectStorage(head: nil, tail: nil)
+        }
+        
+        // Create a new position in memory.
+        // Note that we are shallow copying the value. If it was reference type
+        // we just make a copy of the reference.
+        let copiedHead = SinglyLinkedListNode<T>(value: self.storage.head!.value)
+        var previousCopied: SinglyLinkedListNode<T> = copiedHead
+        
+        // Iterate through current list of nodes and copy them.
+        var current: SinglyLinkedListNode<T>? = self.storage.head?.next
+        
+        while (current != nil) {
+            // Create a copy
+            let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
+            
+            // Create links
+            previousCopied.next = currentCopy
+            
+            // Update pointers
+            current = current?.next
+            previousCopied = currentCopy
+        }
+        
+        return IndirectStorage(head: copiedHead, tail: previousCopied)
+    }
+}
+
+
+
+// MARK:- Extensions when comparable
+
+extension SinglyLinkedList where T: Comparable
+{
+    /// Deletes node containing a given value
+    ///
+    /// - Parameter v: value of the node to be deleted.
+    public mutating func deleteNode(withValue v: T) {
+        
+        guard self.storage.head != nil else {
+            return
+        }
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storage.head
+        
+        while (current != nil) && (current?.value != v) {
+            previous = current
+            current = current?.next
+        }
+        
+        if let foundNode = current {
+            
+            if (self.storage.head === foundNode) {
+                self.storageForWritting.head = foundNode.next
+            }
+            
+            if (self.storage.tail === foundNode) {
+                self.storage.tail = previous
+            }
+            
+            previous?.next = foundNode.next
+            foundNode.next = nil
+        }
+    }
+    
+    
+    /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
+    /// - Complexity: O(N^2)
+    public mutating func deleteDuplicatesInPlace()
+    {
+        // Copy on write: this updates self.storage if necessary.
+        var current = self.storageForWritting.head
+        
+        while (current != nil)
+        {
+            var previous: SinglyLinkedListNode<T>? = current
+            var next = current?.next
+            
+            while (next != nil)
+            {
+                if (current?.value == next?.value) {
+                    
+                    if (self.storage.head === next) {
+                        self.storage.head = next?.next
+                    }
+                    
+                    if (self.storage.tail === next) {
+                        self.storage.tail = previous
+                    }
+                    
+                    // Delete next
+                    previous?.next = next?.next
+                }
+                previous = next
+                next = next?.next
+            }
+            current = current?.next
+        }
+    }
+}
+
+
+
+// MARK: - ITERATOR -
+
+public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
+    
+    public typealias Element = T
+    
+    private(set) var head: SinglyLinkedListNode<T>?
+    
+    mutating public func next() -> T?
+    {
+        let result = self.head?.value
+        self.head = self.head?.next
+        return result
+    }
+}
+
+
+
+// MARK: - SEQUENCE -
+
+extension SinglyLinkedList : Sequence
+{
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
+    {
+        return SinglyLinkedListForwardIterator(head: self.storage.head)
+    }
+}
+
+
+
+// MARK: - COLLECTION -
+
+extension SinglyLinkedList : Collection {
+    
+    public typealias Index = SinglyLinkedListIndex<T>
+    
+    public var startIndex: Index {
+        get {
+            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+        }
+    }
+    
+    public var endIndex: Index {
+        get {
+            if let h = self.storage.head {
+                let (_, numberOfElements) = findTail(in: h)
+                return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+            } else {
+                return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+            }
+        }
+    }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
+    }
+    
+    public func index(after idx: Index) -> Index {
+        return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+    }
+}
+
+
+
+// MARK: - QUEUE -
+
+extension SinglyLinkedList : Queue
+{
+    typealias Item = T
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> T? {
+        return self.storage.head?.value
+    }
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: T) throws {
+        self.append(node: SinglyLinkedListNode<T>(value: item))
+    }
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> T?
+    {
+        guard self.count > 0 else {
+            return nil
+        }
+        
+        return self.deleteItem(at: 0)
+    }
+}
+
+
+
+// MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
+
+extension SinglyLinkedList : ExpressibleByArrayLiteral
+{
+    public typealias Element = T
+    
+    public init(arrayLiteral elements: Element...)
+    {
+        var headSet = false
+        var current : SinglyLinkedListNode<T>?
+        var numberOfElements = 0
+        self.storage = IndirectStorage()
+        
+        for element in elements {
+            
+            numberOfElements += 1
+            
+            if headSet == false {
+                self.storage.head = SinglyLinkedListNode<T>(value: element)
+                current = self.storage.head
+                headSet = true
+            } else {
+                let newNode = SinglyLinkedListNode<T>(value: element)
+                current?.next = newNode
+                current = newNode
+            }
+        }
+        self.storage.tail = current
+    }
+}
+
+
+
+// MARK: - FORWARD-INDEX -
+
+public struct SinglyLinkedListIndex<T> : Comparable
+{
+    fileprivate let node: SinglyLinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
+}
+
+
+extension SinglyLinkedList where T : KeyValuePair {
+    
+    public func find(elementWithKey key: T.K) -> T? {
+        let searchResults = self.filter { (keyValuePair) -> Bool in
+            return keyValuePair.key == key
+        }
+        
+        return searchResults.first
+    }
+}
+
+// MARK: - HELPERS -
+
+func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int)
+{
+    // Assign the tail
+    // Note that the passed node can already be linking to other nodes,
+    // so the tail needs to be calculated.
+    var current: SinglyLinkedListNode<T>? = node
+    var count = 1
+    
+    while (current?.next != nil) {
+        current = current?.next
+        count += 1
+    }
+    
+    if current != nil {
+        return (tail: current!, count: count)
+    } else {
+        return (tail: node, count: 1)
+    }
+}
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new file mode 100644
index 000000000..27d922edf
--- /dev/null
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+		006104751F361359007A6F50 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		006104661F36104C007A6F50 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				006104671F36104C007A6F50 /* Debug */,
+				006104681F36104C007A6F50 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		006104731F361359007A6F50 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				006104741F361359007A6F50 /* Debug */,
+				006104751F361359007A6F50 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 006104631F36104C007A6F50 /* Project object */;
+}
diff --git a/Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..a3659d5ab
--- /dev/null
+++ b/Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0830"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "0061046C1F361359007A6F50"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Singly Linked List/Tests/Tests/Info.plist b/Singly Linked List/Tests/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Singly Linked List/Tests/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
new file mode 100644
index 000000000..11b63f251
--- /dev/null
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -0,0 +1,329 @@
+import XCTest
+
+
+class FindTailInNodeTests: XCTestCase {
+    
+    func testExample() {
+        let n1 = SinglyLinkedListNode<Int>(value: 34)
+        let n2 = SinglyLinkedListNode<Int>(value: 35)
+        let n3 = SinglyLinkedListNode<Int>(value: 36)
+        let n4 = SinglyLinkedListNode<Int>(value: 37)
+        
+        n1.next = n2
+        n2.next = n3
+        n3.next = n4
+        
+        XCTAssertTrue(findTail(in: n1).tail === n4)
+        XCTAssertTrue(findTail(in: n2).tail === n4)
+        XCTAssertTrue(findTail(in: n4).tail === n4)
+        XCTAssertTrue(findTail(in: n4).tail === n4)
+    }
+    
+}
+
+class SinglyLinkedListTests: XCTestCase {
+    
+    func testAppendOneNodeFromEmptyList() {
+        var list = SinglyLinkedList<Int>()
+        list.append(value: 34)
+        XCTAssertTrue(list.first == 34)
+        XCTAssertTrue(list.count == 1, "Found \(list.count)")
+    }
+    
+    func testAppendMultipleNodesFromEmptyList() {
+        var list = SinglyLinkedList<Int>()
+        list.append(value: 34)
+        list.append(value: 35)
+        list.append(value: 36)
+        list.append(value: 34)
+        XCTAssertTrue(list.first == 34)
+        let second = list.index(list.startIndex, offsetBy: 1)
+        let third = list.index(list.startIndex, offsetBy: 2)
+        let fouth = list.index(list.startIndex, offsetBy: 3)
+        XCTAssertTrue(list[second] == 35)
+        XCTAssertTrue(list[third] == 36)
+        XCTAssertTrue(list[fouth] == 34)
+        XCTAssertTrue(list.count == 4, "Found \(list.count)")
+    }
+    
+    func testDelete() {
+        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        list.append(value: 2)
+        list.append(value: 3)
+        list.append(value: 4)
+        list.append(value: 5)
+        
+        list.deleteNode(withValue: 1)
+        var second = list.index(list.startIndex, offsetBy: 1)
+        var third = list.index(list.startIndex, offsetBy: 2)
+        XCTAssertTrue(list.first == 2)
+        XCTAssertTrue(list[second] == 3)
+        XCTAssertTrue(list[third] == 4)
+        XCTAssertTrue(list.last == 5)
+        XCTAssertTrue(list.count == 4)
+        
+        list.deleteNode(withValue: 5)
+        second = list.index(list.startIndex, offsetBy: 1)
+        third = list.index(list.startIndex, offsetBy: 2)
+        XCTAssertTrue(list.first == 2)
+        XCTAssertTrue(list[second] == 3)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 3)
+        
+        list.deleteNode(withValue: 3)
+        XCTAssertTrue(list.first == 2)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 2)
+        
+        list.deleteNode(withValue: 2)
+        XCTAssertTrue(list.first == 4)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 1)
+        
+        list.deleteNode(withValue: 4)
+        XCTAssertTrue(list.first == nil)
+        XCTAssertTrue(list.last == nil)
+        XCTAssertTrue(list.count == 0)
+    }
+    
+    func testDeleteDuplicatesInPlace() {
+        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        list.append(value: 2)
+        list.append(value: 2)
+        list.append(value: 3)
+        list.append(value: 5)
+        list.append(value: 2)
+        list.append(value: 4)
+        list.append(value: 2)
+        list.append(value: 5)
+        
+        list.deleteDuplicatesInPlace()
+        let second = list.index(list.startIndex, offsetBy: 1)
+        let third = list.index(list.startIndex, offsetBy: 2)
+        let fourth = list.index(list.startIndex, offsetBy: 3)
+        XCTAssertTrue(list.first == 1)
+        XCTAssertTrue(list[second] == 2)
+        XCTAssertTrue(list[third] == 3)
+        XCTAssertTrue(list[fourth] == 5)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 5)
+    }
+    
+    func testFindKthToLast() {
+        let list: SinglyLinkedList<Int> = [2,2,3,5,2,4,2,5]
+        XCTAssertTrue(list.find(kthToLast: 1)?.value == 5)
+        XCTAssertTrue(list.find(kthToLast: 2)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 3)?.value == 4)
+        XCTAssertTrue(list.find(kthToLast: 4)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 5)?.value == 5)
+        XCTAssertTrue(list.find(kthToLast: 6)?.value == 3)
+        XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
+        XCTAssertFalse(list.containsLoop())
+    }
+    
+    func testContainsLoop() {
+        let n1 = SinglyLinkedListNode<Int>(value: 1)
+        let n2 = SinglyLinkedListNode<Int>(value: 2)
+        let n3 = SinglyLinkedListNode<Int>(value: 3)
+        let n4 = SinglyLinkedListNode<Int>(value: 4)
+        let n5 = SinglyLinkedListNode<Int>(value: 5)
+        let n6 = SinglyLinkedListNode<Int>(value: 6)
+        let n7 = SinglyLinkedListNode<Int>(value: 7)
+        let n8 = SinglyLinkedListNode<Int>(value: 8)
+        n1.next = n2
+        n2.next = n3
+        n3.next = n4
+        n4.next = n5
+        n5.next = n6
+        n6.next = n7
+        n7.next = n8
+        n8.next = n2
+        
+        let list = SinglyLinkedList<Int>(head: n1)
+        XCTAssertTrue(list.containsLoop())
+        XCTAssertTrue(list.last == nil)
+    }
+    
+    func testContainsLoopFalseWithLiterals() {
+        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
+        XCTAssertFalse(list.containsLoop())
+    }
+    
+    func testContainsLoopFalseWithNodes() {
+        let n1 = SinglyLinkedListNode<Int>(value: 1)
+        let n2 = SinglyLinkedListNode<Int>(value: 2)
+        let n3 = SinglyLinkedListNode<Int>(value: 3)
+        n1.next = n2
+        n2.next = n3
+        
+        let list = SinglyLinkedList<Int>(head: n1)
+        XCTAssertFalse(list.containsLoop())
+        
+    }
+    
+    func testConstructorFromArrayLiteralWhenEmpty() {
+        let list: SinglyLinkedList<Int> = []
+        XCTAssertTrue(list.first == nil)
+        XCTAssertTrue(list.last == nil)
+        XCTAssertTrue(list.count == 0, "Found \(list.count)")
+    }
+    
+    func testConstructorFromArrayLiteralWithSingleElement() {
+        let list: SinglyLinkedList<Int> = [5]
+        XCTAssertTrue(list.first == 5)
+        XCTAssertTrue(list.last == 5)
+        XCTAssertTrue(list.count == 1, "Found \(list.count)")
+    }
+    
+    
+    func testAppendValue() {
+        var list = SinglyLinkedList<Int>()
+        list.append(value: 1)
+        list.append(value: 1)
+        list.append(value: 2)
+        list.append(value: 2)
+        list.append(value: 4)
+        
+        let result = string(from: list)
+        XCTAssertTrue(result == "11224", "Found \(result)")
+        XCTAssertTrue(list.count == 5, "Found \(list.count)")
+        XCTAssertTrue(list.last == 4, "Found \(String(describing: list.last))")
+    }
+    
+    func testPrependValue() {
+        var list = SinglyLinkedList<Int>()
+        list.prepend(value: 1)
+        list.prepend(value: 2)
+        list.prepend(value: 3)
+        list.prepend(value: 4)
+        list.prepend(value: 5)
+        list.prepend(value: 6)
+        
+        let result = string(from: list)
+        XCTAssertTrue(result == "654321", "Found \(result)")
+        XCTAssertTrue(list.count == 6, "Found \(list.count)")
+        XCTAssertTrue(list.last == 1, "Found \(String(describing: list.last))")
+    }
+    
+    func testDeleteHeadInListWithMultipleItems() {
+        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        
+        let _ = list.deleteItem(at: 0)
+        let result = string(from: list)
+        XCTAssertTrue(result == "2345678", "Found \(result)")
+        XCTAssertTrue(list.first == 2, "Found \(String(describing: list.first))")
+        XCTAssertTrue(list.count == 7, "Found \(list.count)")
+    }
+    
+    func testDeleteTailInListWithMultipleItems() {
+        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        
+        let _ = list.deleteItem(at: 7)
+        let result = string(from: list)
+        XCTAssertTrue(result == "1234567", "Found \(result)")
+        XCTAssertTrue(list.last == 7, "Found \(String(describing: list.last))")
+        XCTAssertTrue(list.count == 7, "Found \(list.count)")
+    }
+    
+    func testDeleteItemInListWithMultipleItems() {
+        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        
+        let _ = list.deleteItem(at: 4)
+        let result = string(from: list)
+        XCTAssertTrue(result == "1234678", "Found \(result)")
+        XCTAssertTrue(list.first == 1, "Found \(String(describing: list.first))")
+        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
+        XCTAssertTrue(list.count == 7, "Found \(list.count)")
+    }
+    
+    func testDeleteHeadInListWithSingleElement() {
+        var list: SinglyLinkedList<Int> = [1]
+        
+        let _ = list.deleteItem(at: 0)
+        let result = string(from: list)
+        XCTAssertTrue(result == "", "Found \(result)")
+        XCTAssertTrue(list.first == nil, "Found \(String(describing: list.first))")
+        XCTAssertTrue(list.last == nil, "Found \(String(describing: list.last))")
+        XCTAssertTrue(list.count == 0, "Found \(list.count)")
+    }
+    
+    func testDirectIndexAccess() {
+        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        let fifthElementIndex = list.index(list.startIndex, offsetBy: 5)
+        XCTAssertTrue(list[fifthElementIndex] == 6 ,  "Found \(list.count)")
+    }
+    
+    
+    func string(from list: SinglyLinkedList<Int>) -> String {
+        var result = ""
+        var iterator = list.makeIterator()
+        while let current = iterator.next() {
+            result += String(describing: current)
+        }
+        
+        return result
+    }
+    
+    func testCopyOnWriteUsingLiterals() {
+        var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        l1.append(value: 0)
+        var l2 = l1
+        
+        _ = l2.deleteItem(at: 3)
+        XCTAssertTrue(l1.count == 9)
+        XCTAssertTrue(l2.count == 8)
+        
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        
+        XCTAssertTrue(l1.count == 0)
+        XCTAssertTrue(l2.count == 8)
+    }
+    
+}
+
+class SinglyLinkedListQueueTests: XCTestCase {
+    
+    func testQueue() {
+        var queue = SinglyLinkedList<Int>()
+        
+        try! queue.enqueue(item: 1)
+        XCTAssertTrue(queue.getFirst()! == 1)
+        XCTAssertTrue(queue.count == 1)
+        
+        try! queue.enqueue(item: 2)
+        XCTAssertTrue(queue.getFirst()! == 1)
+        XCTAssertTrue(queue.count == 2)
+        
+        try! queue.enqueue(item: 3)
+        XCTAssertTrue(queue.getFirst()! == 1)
+        XCTAssertTrue(queue.count == 3)
+        
+        XCTAssertTrue(queue.dequeue() == 1)
+        XCTAssertTrue(queue.count == 2)
+        
+        XCTAssertTrue(queue.dequeue() == 2)
+        XCTAssertTrue(queue.count == 1)
+        
+        XCTAssertTrue(queue.dequeue() == 3)
+        XCTAssertTrue(queue.count == 0)
+        
+        XCTAssertTrue(queue.dequeue() == nil)
+        XCTAssertTrue(queue.count == 0)
+        
+        try! queue.enqueue(item: 9)
+        XCTAssertTrue(queue.getFirst()! == 9)
+        XCTAssertTrue(queue.count == 1)
+        
+    }
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index db4691648..d56db7d12 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1436,6 +1436,52 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Singly Linked List"
+      name = "Singly Linked List">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:CopiedIndirectStorage.png">
+         </FileRef>
+         <FileRef
+            location = "group:SharedIndirectStorage.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:KeyValuePair.swift">
+      </FileRef>
+      <FileRef
+         location = "group:Queue.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:SinglyLinkedList.playground">
+      </FileRef>
+      <FileRef
+         location = "group:SinglyLinkedList.swift">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <Group
+            location = "group:Tests"
+            name = "Tests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:SinglyLinkedListTests.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Longest Common Subsequence"
       name = "Longest Common Subsequence">

From be11f6bcf44cf435b66647faa51a7be07ae0c0e7 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:00:25 +0100
Subject: [PATCH 1164/1679] Remove loop-detection logic and tests.

---
 Singly Linked List/SinglyLinkedList.swift     | 44 ++-----------------
 .../Tests/Tests/SinglyLinkedListTests.swift   | 43 ------------------
 2 files changed, 4 insertions(+), 83 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index b05526b35..bdc544079 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -198,34 +198,6 @@ public struct SinglyLinkedList<T>
         return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
     }
     
-    
-    
-    // MARK: LOOP DETECTION
-    
-    /// A singly linked list contains a loop if one node references back to a previous node.
-    ///
-    /// - Returns: Whether the linked list contains a loop
-    public func containsLoop() -> Bool
-    {
-        /// Advances a node at a time
-        var current = self.storage.head
-        
-        /// Advances twice as fast
-        var runner = self.storage.head
-        
-        while (runner != nil) && (runner?.next != nil) {
-            
-            current = current?.next
-            runner = runner?.next?.next
-            
-            if runner === current {
-                return true
-            }
-        }
-        
-        return false
-    }
-    
 }
 
 
@@ -261,12 +233,8 @@ private extension SinglyLinkedList {
             // Copy on write: we are about to modify next a property in
             // a potentially shared node. Make sure it's new if necessary.
             self.storageForWritting.tail?.next = node
-            if !self.containsLoop() {
-                let (tail, _) = findTail(in: node)
-                self.storageForWritting.tail = tail // There
-            } else {
-                self.storageForWritting.tail = nil
-            }
+            let (tail, _) = findTail(in: node)
+            self.storageForWritting.tail = tail // There
         }
         else
         {
@@ -274,12 +242,8 @@ private extension SinglyLinkedList {
             // Otherwise the state would be inconsistent.
             // This will be checked when adding and deleting nodes.
             self.storageForWritting.head = node
-            if !self.containsLoop() {
-                let (tail, _) = findTail(in: node)
-                self.storageForWritting.tail = tail // There
-            } else {
-                self.storageForWritting.tail = nil
-            }
+            let (tail, _) = findTail(in: node)
+            self.storageForWritting.tail = tail // There
         }
     }
     
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index 11b63f251..2efa7b8d0 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -120,48 +120,6 @@ class SinglyLinkedListTests: XCTestCase {
         XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
         XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
         XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
-        XCTAssertFalse(list.containsLoop())
-    }
-    
-    func testContainsLoop() {
-        let n1 = SinglyLinkedListNode<Int>(value: 1)
-        let n2 = SinglyLinkedListNode<Int>(value: 2)
-        let n3 = SinglyLinkedListNode<Int>(value: 3)
-        let n4 = SinglyLinkedListNode<Int>(value: 4)
-        let n5 = SinglyLinkedListNode<Int>(value: 5)
-        let n6 = SinglyLinkedListNode<Int>(value: 6)
-        let n7 = SinglyLinkedListNode<Int>(value: 7)
-        let n8 = SinglyLinkedListNode<Int>(value: 8)
-        n1.next = n2
-        n2.next = n3
-        n3.next = n4
-        n4.next = n5
-        n5.next = n6
-        n6.next = n7
-        n7.next = n8
-        n8.next = n2
-        
-        let list = SinglyLinkedList<Int>(head: n1)
-        XCTAssertTrue(list.containsLoop())
-        XCTAssertTrue(list.last == nil)
-    }
-    
-    func testContainsLoopFalseWithLiterals() {
-        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
-        XCTAssertFalse(list.containsLoop())
-    }
-    
-    func testContainsLoopFalseWithNodes() {
-        let n1 = SinglyLinkedListNode<Int>(value: 1)
-        let n2 = SinglyLinkedListNode<Int>(value: 2)
-        let n3 = SinglyLinkedListNode<Int>(value: 3)
-        n1.next = n2
-        n2.next = n3
-        
-        let list = SinglyLinkedList<Int>(head: n1)
-        XCTAssertFalse(list.containsLoop())
-        
     }
     
     func testConstructorFromArrayLiteralWhenEmpty() {
@@ -178,7 +136,6 @@ class SinglyLinkedListTests: XCTestCase {
         XCTAssertTrue(list.count == 1, "Found \(list.count)")
     }
     
-    
     func testAppendValue() {
         var list = SinglyLinkedList<Int>()
         list.append(value: 1)

From 0041be6c0bfc54912127add7c4c1168adebe8e41 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:07:15 +0100
Subject: [PATCH 1165/1679] Remove internal initializer method that takes a
 node as a parameter to prevent misuse that could break value semantics.

---
 Singly Linked List/SinglyLinkedList.swift         | 15 ++-------------
 .../Tests/Tests/SinglyLinkedListTests.swift       |  4 ++--
 2 files changed, 4 insertions(+), 15 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index bdc544079..bdf7d248b 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -83,24 +83,13 @@ public struct SinglyLinkedList<T>
     
     // MARK: INITIALIZERS
     
-    /// Creates a list with the given node.
-    /// NOTE: This method can break value semantics by accepting a node.
-    ///
-    /// - Parameter head: First node
-    internal init(head: SinglyLinkedListNode<T>)
-    {
-        self.storage = IndirectStorage()
-        self.append(node: head)
-    }
-    
-    
     /// Creates a list with a single element
     ///
     /// - Parameter value: element to populate the list with
     public init(value: T)
     {
-        let node = SinglyLinkedListNode<T>(value: value)
-        self.init(head: node)
+        self.init()
+        self.append(value: value)
     }
     
     
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index 2efa7b8d0..ee8f989c3 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -47,7 +47,7 @@ class SinglyLinkedListTests: XCTestCase {
     }
     
     func testDelete() {
-        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        var list: SinglyLinkedList<Int> = [1]
         list.append(value: 2)
         list.append(value: 3)
         list.append(value: 4)
@@ -87,7 +87,7 @@ class SinglyLinkedListTests: XCTestCase {
     }
     
     func testDeleteDuplicatesInPlace() {
-        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        var list: SinglyLinkedList<Int> = [1]
         list.append(value: 2)
         list.append(value: 2)
         list.append(value: 3)

From 74fb0ecb9558a4a26fd8af53f89b3254b6429768 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:11:22 +0100
Subject: [PATCH 1166/1679] Remove SinglyLinedList's conformance to Queue
 protocol.

---
 Singly Linked List/Queue.swift                | 28 ---------------
 Singly Linked List/SinglyLinkedList.swift     | 36 -------------------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  4 ---
 .../Tests/Tests/SinglyLinkedListTests.swift   | 36 -------------------
 4 files changed, 104 deletions(-)
 delete mode 100644 Singly Linked List/Queue.swift

diff --git a/Singly Linked List/Queue.swift b/Singly Linked List/Queue.swift
deleted file mode 100644
index 68fda9f99..000000000
--- a/Singly Linked List/Queue.swift	
+++ /dev/null
@@ -1,28 +0,0 @@
-import Foundation
-
-
-/// Data structure that provides FIFO access
-protocol Queue
-{
-    associatedtype Item
-    
-    
-    /// Adds an element to the queue
-    ///
-    /// - Parameter item: Item to be added
-    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
-    mutating func enqueue(item: Item) throws
-    
-    
-    /// Returns the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue. It does not dequeue it.
-    func getFirst() -> Item?
-    
-    
-    /// Dequeues the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue, which gets removed from it.
-    mutating func dequeue() -> Item?
-    
-}
diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index bdf7d248b..db8cc0229 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -414,42 +414,6 @@ extension SinglyLinkedList : Collection {
 
 
 
-// MARK: - QUEUE -
-
-extension SinglyLinkedList : Queue
-{
-    typealias Item = T
-    
-    /// Returns the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue. It does not dequeue it.
-    func getFirst() -> T? {
-        return self.storage.head?.value
-    }
-    
-    /// Adds an element to the queue
-    ///
-    /// - Parameter item: Item to be added
-    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
-    mutating func enqueue(item: T) throws {
-        self.append(node: SinglyLinkedListNode<T>(value: item))
-    }
-    
-    /// Dequeues the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue, which gets removed from it.
-    mutating func dequeue() -> T?
-    {
-        guard self.count > 0 else {
-            return nil
-        }
-        
-        return self.deleteItem(at: 0)
-    }
-}
-
-
-
 // MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
 
 extension SinglyLinkedList : ExpressibleByArrayLiteral
diff --git a/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj
index 27d922edf..8dddf6498 100644
--- a/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -9,7 +9,6 @@
 /* Begin PBXBuildFile section */
 		006104711F361359007A6F50 /* SinglyLinkedListTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104701F361359007A6F50 /* SinglyLinkedListTests.swift */; };
 		006104791F36144E007A6F50 /* KeyValuePair.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104761F36144E007A6F50 /* KeyValuePair.swift */; };
-		0061047A1F36144E007A6F50 /* Queue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104771F36144E007A6F50 /* Queue.swift */; };
 		0061047B1F36144E007A6F50 /* SinglyLinkedList.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104781F36144E007A6F50 /* SinglyLinkedList.swift */; };
 /* End PBXBuildFile section */
 
@@ -18,7 +17,6 @@
 		006104701F361359007A6F50 /* SinglyLinkedListTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = SinglyLinkedListTests.swift; sourceTree = "<group>"; };
 		006104721F361359007A6F50 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		006104761F36144E007A6F50 /* KeyValuePair.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = KeyValuePair.swift; path = ../../KeyValuePair.swift; sourceTree = "<group>"; };
-		006104771F36144E007A6F50 /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Queue.swift; path = ../../Queue.swift; sourceTree = "<group>"; };
 		006104781F36144E007A6F50 /* SinglyLinkedList.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = SinglyLinkedList.swift; path = ../../SinglyLinkedList.swift; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
@@ -54,7 +52,6 @@
 			children = (
 				006104701F361359007A6F50 /* SinglyLinkedListTests.swift */,
 				006104761F36144E007A6F50 /* KeyValuePair.swift */,
-				006104771F36144E007A6F50 /* Queue.swift */,
 				006104781F36144E007A6F50 /* SinglyLinkedList.swift */,
 				006104721F361359007A6F50 /* Info.plist */,
 			);
@@ -130,7 +127,6 @@
 			buildActionMask = 2147483647;
 			files = (
 				006104711F361359007A6F50 /* SinglyLinkedListTests.swift in Sources */,
-				0061047A1F36144E007A6F50 /* Queue.swift in Sources */,
 				0061047B1F36144E007A6F50 /* SinglyLinkedList.swift in Sources */,
 				006104791F36144E007A6F50 /* KeyValuePair.swift in Sources */,
 			);
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index ee8f989c3..50d354808 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -248,39 +248,3 @@ class SinglyLinkedListTests: XCTestCase {
     }
     
 }
-
-class SinglyLinkedListQueueTests: XCTestCase {
-    
-    func testQueue() {
-        var queue = SinglyLinkedList<Int>()
-        
-        try! queue.enqueue(item: 1)
-        XCTAssertTrue(queue.getFirst()! == 1)
-        XCTAssertTrue(queue.count == 1)
-        
-        try! queue.enqueue(item: 2)
-        XCTAssertTrue(queue.getFirst()! == 1)
-        XCTAssertTrue(queue.count == 2)
-        
-        try! queue.enqueue(item: 3)
-        XCTAssertTrue(queue.getFirst()! == 1)
-        XCTAssertTrue(queue.count == 3)
-        
-        XCTAssertTrue(queue.dequeue() == 1)
-        XCTAssertTrue(queue.count == 2)
-        
-        XCTAssertTrue(queue.dequeue() == 2)
-        XCTAssertTrue(queue.count == 1)
-        
-        XCTAssertTrue(queue.dequeue() == 3)
-        XCTAssertTrue(queue.count == 0)
-        
-        XCTAssertTrue(queue.dequeue() == nil)
-        XCTAssertTrue(queue.count == 0)
-        
-        try! queue.enqueue(item: 9)
-        XCTAssertTrue(queue.getFirst()! == 9)
-        XCTAssertTrue(queue.count == 1)
-        
-    }
-}

From 70781ec072f2cf84c40379b6497f1fa2a6eb9e37 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:19:29 +0100
Subject: [PATCH 1167/1679] Remove needless self references to follow the
 repository's Swift style guidelines.

---
 Singly Linked List/SinglyLinkedList.swift | 96 +++++++++++------------
 1 file changed, 48 insertions(+), 48 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index db8cc0229..cb05914f7 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -65,17 +65,17 @@ public struct SinglyLinkedList<T>
     private var storageForWritting: IndirectStorage<T> {
         
         mutating get {
-            if !isKnownUniquelyReferenced(&self.storage) {
-                self.storage = self.copyStorage()
+            if !isKnownUniquelyReferenced(&storage) {
+                storage = copyStorage()
             }
-            return self.storage
+            return storage
         }
     }
     
     /// Returns the last element in the collection
     public var last: T? {
         get {
-            return self.storage.tail?.value
+            return storage.tail?.value
         }
     }
     
@@ -108,7 +108,7 @@ public struct SinglyLinkedList<T>
     public mutating func append(value: T)
     {
         let node = SinglyLinkedListNode<T>(value: value)
-        self.append(node: node)
+        append(node: node)
     }
     
     
@@ -118,16 +118,16 @@ public struct SinglyLinkedList<T>
     public mutating func prepend(value: T)
     {
         let node = SinglyLinkedListNode<T>(value: value)
-        self.prepend(node: node)
+        prepend(node: node)
     }
     
     
     public mutating func deleteItem(at index:Int) -> T
     {
-        precondition((index >= 0) && (index < self.count))
+        precondition((index >= 0) && (index < count))
         
         var previous: SinglyLinkedListNode<T>? = nil
-        var current = self.storageForWritting.head
+        var current = storageForWritting.head
         var i = 0
         var elementToDelete: SinglyLinkedListNode<T>
         
@@ -139,12 +139,12 @@ public struct SinglyLinkedList<T>
         
         // Current is now the element to delete (at index position.tag)
         elementToDelete = current!
-        if (self.storage.head === current) {
-            self.storageForWritting.head = current?.next
+        if (storage.head === current) {
+            storageForWritting.head = current?.next
         }
         
-        if (self.storage.tail === current) {
-            self.storageForWritting.tail = previous
+        if (storage.tail === current) {
+            storageForWritting.tail = previous
         }
         
         previous?.next = current?.next
@@ -184,7 +184,7 @@ public struct SinglyLinkedList<T>
     /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
     public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
     {
-        return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
+        return find(kthToLast: kthToLast, startingAt: storage.head, count: UInt(count))
     }
     
 }
@@ -202,11 +202,11 @@ private extension SinglyLinkedList {
     private mutating func prepend(node: SinglyLinkedListNode<T>)
     {
         let (tailFromNewNode, _) = findTail(in: node)
-        tailFromNewNode.next = self.storageForWritting.head
-        self.storageForWritting.head = node
+        tailFromNewNode.next = storageForWritting.head
+        storageForWritting.head = node
         
-        if self.storage.tail == nil {
-            self.storageForWritting.tail = tailFromNewNode
+        if storage.tail == nil {
+            storageForWritting.tail = tailFromNewNode
         }
     }
     
@@ -217,22 +217,22 @@ private extension SinglyLinkedList {
     /// - Parameter node: node to be appended. (It can be a list, even contain loops).
     private mutating func append(node: SinglyLinkedListNode<T>)
     {
-        if self.storage.tail != nil
+        if storage.tail != nil
         {
             // Copy on write: we are about to modify next a property in
             // a potentially shared node. Make sure it's new if necessary.
-            self.storageForWritting.tail?.next = node
+            storageForWritting.tail?.next = node
             let (tail, _) = findTail(in: node)
-            self.storageForWritting.tail = tail // There
+            storageForWritting.tail = tail // There
         }
         else
         {
             // This also means that there's no head.
             // Otherwise the state would be inconsistent.
             // This will be checked when adding and deleting nodes.
-            self.storageForWritting.head = node
+            storageForWritting.head = node
             let (tail, _) = findTail(in: node)
-            self.storageForWritting.tail = tail // There
+            storageForWritting.tail = tail // There
         }
     }
     
@@ -243,18 +243,18 @@ private extension SinglyLinkedList {
         // If the list is empty, next time an item will be created, it won't affect
         // other instances of the list that came from copies derived from value types.
         // like assignments or parameters
-        guard (self.storage.head != nil) && (self.storage.tail != nil) else {
+        guard (storage.head != nil) && (storage.tail != nil) else {
             return IndirectStorage(head: nil, tail: nil)
         }
         
         // Create a new position in memory.
         // Note that we are shallow copying the value. If it was reference type
         // we just make a copy of the reference.
-        let copiedHead = SinglyLinkedListNode<T>(value: self.storage.head!.value)
+        let copiedHead = SinglyLinkedListNode<T>(value: storage.head!.value)
         var previousCopied: SinglyLinkedListNode<T> = copiedHead
         
         // Iterate through current list of nodes and copy them.
-        var current: SinglyLinkedListNode<T>? = self.storage.head?.next
+        var current: SinglyLinkedListNode<T>? = storage.head?.next
         
         while (current != nil) {
             // Create a copy
@@ -283,12 +283,12 @@ extension SinglyLinkedList where T: Comparable
     /// - Parameter v: value of the node to be deleted.
     public mutating func deleteNode(withValue v: T) {
         
-        guard self.storage.head != nil else {
+        guard storage.head != nil else {
             return
         }
         
         var previous: SinglyLinkedListNode<T>? = nil
-        var current = self.storage.head
+        var current = storage.head
         
         while (current != nil) && (current?.value != v) {
             previous = current
@@ -297,12 +297,12 @@ extension SinglyLinkedList where T: Comparable
         
         if let foundNode = current {
             
-            if (self.storage.head === foundNode) {
-                self.storageForWritting.head = foundNode.next
+            if (storage.head === foundNode) {
+                storageForWritting.head = foundNode.next
             }
             
-            if (self.storage.tail === foundNode) {
-                self.storage.tail = previous
+            if (storage.tail === foundNode) {
+                storage.tail = previous
             }
             
             previous?.next = foundNode.next
@@ -315,8 +315,8 @@ extension SinglyLinkedList where T: Comparable
     /// - Complexity: O(N^2)
     public mutating func deleteDuplicatesInPlace()
     {
-        // Copy on write: this updates self.storage if necessary.
-        var current = self.storageForWritting.head
+        // Copy on write: this updates storage if necessary.
+        var current = storageForWritting.head
         
         while (current != nil)
         {
@@ -327,12 +327,12 @@ extension SinglyLinkedList where T: Comparable
             {
                 if (current?.value == next?.value) {
                     
-                    if (self.storage.head === next) {
-                        self.storage.head = next?.next
+                    if (storage.head === next) {
+                        storage.head = next?.next
                     }
                     
-                    if (self.storage.tail === next) {
-                        self.storage.tail = previous
+                    if (storage.tail === next) {
+                        storage.tail = previous
                     }
                     
                     // Delete next
@@ -358,8 +358,8 @@ public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
     
     mutating public func next() -> T?
     {
-        let result = self.head?.value
-        self.head = self.head?.next
+        let result = head?.value
+        head = head?.next
         return result
     }
 }
@@ -372,7 +372,7 @@ extension SinglyLinkedList : Sequence
 {
     public func makeIterator() -> SinglyLinkedListForwardIterator<T>
     {
-        return SinglyLinkedListForwardIterator(head: self.storage.head)
+        return SinglyLinkedListForwardIterator(head: storage.head)
     }
 }
 
@@ -386,17 +386,17 @@ extension SinglyLinkedList : Collection {
     
     public var startIndex: Index {
         get {
-            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+            return SinglyLinkedListIndex<T>(node: storage.head, tag: 0)
         }
     }
     
     public var endIndex: Index {
         get {
-            if let h = self.storage.head {
+            if let h = storage.head {
                 let (_, numberOfElements) = findTail(in: h)
                 return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
             } else {
-                return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+                return SinglyLinkedListIndex<T>(node: nil, tag: startIndex.tag)
             }
         }
     }
@@ -425,15 +425,15 @@ extension SinglyLinkedList : ExpressibleByArrayLiteral
         var headSet = false
         var current : SinglyLinkedListNode<T>?
         var numberOfElements = 0
-        self.storage = IndirectStorage()
+        storage = IndirectStorage()
         
         for element in elements {
             
             numberOfElements += 1
             
             if headSet == false {
-                self.storage.head = SinglyLinkedListNode<T>(value: element)
-                current = self.storage.head
+                storage.head = SinglyLinkedListNode<T>(value: element)
+                current = storage.head
                 headSet = true
             } else {
                 let newNode = SinglyLinkedListNode<T>(value: element)
@@ -441,7 +441,7 @@ extension SinglyLinkedList : ExpressibleByArrayLiteral
                 current = newNode
             }
         }
-        self.storage.tail = current
+        storage.tail = current
     }
 }
 
@@ -467,7 +467,7 @@ public struct SinglyLinkedListIndex<T> : Comparable
 extension SinglyLinkedList where T : KeyValuePair {
     
     public func find(elementWithKey key: T.K) -> T? {
-        let searchResults = self.filter { (keyValuePair) -> Bool in
+        let searchResults = filter { (keyValuePair) -> Bool in
             return keyValuePair.key == key
         }
         

From 11fcad75d64fe194fd7f884b87f2679b043fc060 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:47:22 +0100
Subject: [PATCH 1168/1679] Replace spacing from 4 to 2 spaces to follow the
 repository's Swift Style guide.

---
 Singly Linked List/KeyValuePair.swift         | 114 +--
 Singly Linked List/SinglyLinkedList.swift     | 736 +++++++++---------
 .../Tests/Tests/SinglyLinkedListTests.swift   | 477 ++++++------
 3 files changed, 651 insertions(+), 676 deletions(-)

diff --git a/Singly Linked List/KeyValuePair.swift b/Singly Linked List/KeyValuePair.swift
index 2751503c2..9c6cacea4 100644
--- a/Singly Linked List/KeyValuePair.swift	
+++ b/Singly Linked List/KeyValuePair.swift	
@@ -3,62 +3,62 @@
 /// stored contain a value, but are ordered or retrieved according to a key.
 public protocol KeyValuePair : Comparable {
     
-    associatedtype K : Comparable, Hashable
-    associatedtype V : Comparable, Hashable
-    
-    // Identifier used in many algorithms to search by, order by, etc
-    var key : K {get set}
-    
-    // A data container
-    var value : V {get set}
-    
-    
-    /// Initializer
-    ///
-    /// - Parameters:
-    ///   - key: Identifier used in many algorithms to search by, order by, etc.
-    ///   - value: A data container.
-    init(key: K, value: V)
-    
-    
-    /// Creates a copy
-    ///
-    /// - Abstract: Conformers of this class can be either value or reference types.
-    ///   Some algorithms might need to guarantee that a conformer instance gets copied.
-    ///   This will perform an innecessary in the case of value types.
-    ///   TODO: is there a better way?
-    /// - Returns: A new instance with the old one's values copied.
-    func copy() -> Self
+  associatedtype K : Comparable, Hashable
+  associatedtype V : Comparable, Hashable
+  
+  // Identifier used in many algorithms to search by, order by, etc
+  var key : K {get set}
+  
+  // A data container
+  var value : V {get set}
+  
+  
+  /// Initializer
+  ///
+  /// - Parameters:
+  ///   - key: Identifier used in many algorithms to search by, order by, etc.
+  ///   - value: A data container.
+  init(key: K, value: V)
+  
+  
+  /// Creates a copy
+  ///
+  /// - Abstract: Conformers of this class can be either value or reference types.
+  ///   Some algorithms might need to guarantee that a conformer instance gets copied.
+  ///   This will perform an innecessary in the case of value types.
+  ///   TODO: is there a better way?
+  /// - Returns: A new instance with the old one's values copied.
+  func copy() -> Self
 }
 
 
 /// Conformance to Equatable and Comparable protocols
 extension KeyValuePair {
     
-    // MARK: - Equatable protocol
-    public static func ==(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key == rhs.key
-    }
-    
-    
-    
-    // MARK: - Comparable protocol
-    
-    public static func <(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key < rhs.key
-    }
-    
-    public static func <=(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key <= rhs.key
-    }
-    
-    public static func >=(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key >= rhs.key
-    }
-    
-    public static func >(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key > rhs.key
-    }
+  // MARK: - Equatable protocol
+  public static func ==(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key == rhs.key
+  }
+  
+  
+  
+  // MARK: - Comparable protocol
+  
+  public static func <(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key < rhs.key
+  }
+  
+  public static func <=(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key <= rhs.key
+  }
+  
+  public static func >=(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key >= rhs.key
+  }
+  
+  public static func >(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key > rhs.key
+  }
 }
 
 
@@ -67,11 +67,11 @@ extension KeyValuePair {
 /// are Integers.
 struct IntegerPair : KeyValuePair {
     
-    // MARK - KeyValuePair protocol
-    var key : Int
-    var value : Int
-    
-    func copy() -> IntegerPair {
-        return IntegerPair(key: self.key, value: self.value)
-    }
+  // MARK - KeyValuePair protocol
+  var key : Int
+  var value : Int
+  
+  func copy() -> IntegerPair {
+    return IntegerPair(key: self.key, value: self.value)
+  }
 }
diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index cb05914f7..4e088e195 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -4,18 +4,18 @@ import Foundation
 /// Helper class to implement copy-on-write
 fileprivate class IndirectStorage<T> {
     
-    var head: SinglyLinkedListNode<T>?
-    
-    var tail: SinglyLinkedListNode<T>?
-    
-    init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
-        self.head = head
-        self.tail = tail
-    }
-    
-    convenience init() {
-        self.init(head: nil, tail: nil)
-    }
+  var head: SinglyLinkedListNode<T>?
+    
+  var tail: SinglyLinkedListNode<T>?
+  
+  init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
+    self.head = head
+    self.tail = tail
+  }
+  
+  convenience init() {
+    self.init(head: nil, tail: nil)
+  }
 }
 
 
@@ -27,18 +27,18 @@ fileprivate class IndirectStorage<T> {
 /// will need to manipulate references directly.
 public class SinglyLinkedListNode<T> {
     
-    /// Data container
-    public var value: T
-    
-    /// Link to the next node
-    public var next: SinglyLinkedListNode<T>?
-    
-    /// Designated initializer
-    ///
-    /// - Parameter value: A value
-    public init(value: T) {
-        self.value = value
-    }
+  /// Data container
+  public var value: T
+  
+  /// Link to the next node
+  public var next: SinglyLinkedListNode<T>?
+  
+  /// Designated initializer
+  ///
+  /// - Parameter value: A value
+  public init(value: T) {
+    self.value = value
+  }
 }
 
 
@@ -52,140 +52,132 @@ public class SinglyLinkedListNode<T> {
 ///
 /// However, the elements contained in the list, will be shallow copied if they
 /// implement reference semantics.
-public struct SinglyLinkedList<T>
-{
-    // MARK: PROPERTIES
-    
-    // A level of inderiction, with reference semantics to allow easy
-    // detection of when there are more than one references of the storage.
-    private var storage: IndirectStorage<T>
-    
-    /// Whenever there's a change that potentially can change the value, this reference to the
-    /// storage should be used to guarantee that a new copy is created and written on.
-    private var storageForWritting: IndirectStorage<T> {
-        
-        mutating get {
-            if !isKnownUniquelyReferenced(&storage) {
-                storage = copyStorage()
-            }
-            return storage
-        }
+public struct SinglyLinkedList<T> {
+  // MARK: PROPERTIES
+  
+  // A level of inderiction, with reference semantics to allow easy
+  // detection of when there are more than one references of the storage.
+  private var storage: IndirectStorage<T>
+  
+  /// Whenever there's a change that potentially can change the value, this reference to the
+  /// storage should be used to guarantee that a new copy is created and written on.
+  private var storageForWritting: IndirectStorage<T> {
+    
+    mutating get {
+      if !isKnownUniquelyReferenced(&storage) {
+          storage = copyStorage()
+      }
+      return storage
     }
-    
-    /// Returns the last element in the collection
-    public var last: T? {
-        get {
-            return storage.tail?.value
-        }
+  }
+  
+  /// Returns the last element in the collection
+  public var last: T? {
+    get {
+      return storage.tail?.value
     }
-    
-    
-    
-    // MARK: INITIALIZERS
-    
-    /// Creates a list with a single element
-    ///
-    /// - Parameter value: element to populate the list with
-    public init(value: T)
-    {
-        self.init()
-        self.append(value: value)
+  }
+  
+  
+  
+  // MARK: INITIALIZERS
+  
+  /// Creates a list with a single element
+  ///
+  /// - Parameter value: element to populate the list with
+  public init(value: T) {
+    self.init()
+    self.append(value: value)
+  }
+  
+  
+  /// Creates an empty list
+  public init() {
+    self.storage = IndirectStorage()
+  }
+  
+  
+  // MARK: EDITION
+  
+  /// Convenience method to append a value directly to the list
+  ///
+  /// - Parameter value: value to be added
+  public mutating func append(value: T) {
+    let node = SinglyLinkedListNode<T>(value: value)
+    append(node: node)
+  }
+  
+  
+  /// Convenience method to prepend a value directly to the list
+  ///
+  /// - Parameter value: value to be added as the new head of the list
+  public mutating func prepend(value: T) {
+    let node = SinglyLinkedListNode<T>(value: value)
+    prepend(node: node)
+  }
+  
+  
+  public mutating func deleteItem(at index:Int) -> T {
+    precondition((index >= 0) && (index < count))
+    
+    var previous: SinglyLinkedListNode<T>? = nil
+    var current = storageForWritting.head
+    var i = 0
+    var elementToDelete: SinglyLinkedListNode<T>
+    
+    while (i < index) {
+      previous = current
+      current = current?.next
+      i += 1
     }
     
-    
-    /// Creates an empty list
-    public init()
-    {
-        self.storage = IndirectStorage()
+    // Current is now the element to delete (at index position.tag)
+    elementToDelete = current!
+    if (storage.head === current) {
+      storageForWritting.head = current?.next
     }
     
-    
-    // MARK: EDITION
-    
-    /// Convenience method to append a value directly to the list
-    ///
-    /// - Parameter value: value to be added
-    public mutating func append(value: T)
-    {
-        let node = SinglyLinkedListNode<T>(value: value)
-        append(node: node)
+    if (storage.tail === current) {
+      storageForWritting.tail = previous
     }
     
-    
-    /// Convenience method to prepend a value directly to the list
-    ///
-    /// - Parameter value: value to be added as the new head of the list
-    public mutating func prepend(value: T)
-    {
-        let node = SinglyLinkedListNode<T>(value: value)
-        prepend(node: node)
+    previous?.next = current?.next
+    
+    return elementToDelete.value
+  }
+  
+  
+  
+  // MARK: SEARCH
+  
+  /// Returns the node located at the k-th to last position
+  ///
+  /// - Parameter kthToLast: 1 <= k <= N
+  private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>? {
+    guard kthToLast <= count else {
+      return nil
     }
     
-    
-    public mutating func deleteItem(at index:Int) -> T
-    {
-        precondition((index >= 0) && (index < count))
-        
-        var previous: SinglyLinkedListNode<T>? = nil
-        var current = storageForWritting.head
-        var i = 0
-        var elementToDelete: SinglyLinkedListNode<T>
-        
-        while (i < index) {
-            previous = current
-            current = current?.next
-            i += 1
-        }
-        
-        // Current is now the element to delete (at index position.tag)
-        elementToDelete = current!
-        if (storage.head === current) {
-            storageForWritting.head = current?.next
-        }
-        
-        if (storage.tail === current) {
-            storageForWritting.tail = previous
-        }
-        
-        previous?.next = current?.next
-        
-        return elementToDelete.value
+    guard (node != nil) else {
+      return nil
     }
     
+    let i = (count - kthToLast)
     
-    
-    // MARK: SEARCH
-    
-    /// Returns the node located at the k-th to last position
-    ///
-    /// - Parameter kthToLast: 1 <= k <= N
-    private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>?
-    {
-        guard kthToLast <= count else {
-            return nil
-        }
-        
-        guard (node != nil) else {
-            return nil
-        }
-        
-        let i = (count - kthToLast)
-        
-        if (i == 0) {
-            return node
-        }
-        
-        return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+    if (i == 0) {
+      return node
     }
     
-    
-    /// Returns the kth-to-last element in the list
-    ///
-    /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
-    public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
-    {
-        return find(kthToLast: kthToLast, startingAt: storage.head, count: UInt(count))
-    }
+    return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+  }
+  
+  
+  /// Returns the kth-to-last element in the list
+  ///
+  /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
+  public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>? {
+    return find(kthToLast: kthToLast, startingAt: storage.head, count: UInt(count))
+  }
     
 }
 
@@ -195,155 +187,146 @@ public struct SinglyLinkedList<T>
 
 private extension SinglyLinkedList {
     
-    /// Adds a new node to the current head. This method can easily break value semantics. It is left
-    /// for internal use.
-    ///
-    /// - Parameter node: the node that will be the new head of the list.
-    private mutating func prepend(node: SinglyLinkedListNode<T>)
-    {
-        let (tailFromNewNode, _) = findTail(in: node)
-        tailFromNewNode.next = storageForWritting.head
-        storageForWritting.head = node
-        
-        if storage.tail == nil {
-            storageForWritting.tail = tailFromNewNode
-        }
+  /// Adds a new node to the current head. This method can easily break value semantics. It is left
+  /// for internal use.
+  ///
+  /// - Parameter node: the node that will be the new head of the list.
+  private mutating func prepend(node: SinglyLinkedListNode<T>) {
+    let (tailFromNewNode, _) = findTail(in: node)
+    tailFromNewNode.next = storageForWritting.head
+    storageForWritting.head = node
+    
+    if storage.tail == nil {
+      storageForWritting.tail = tailFromNewNode
     }
-    
-    /// Appends a new node to the list. This method can easily break value semantics. It is left
-    /// for internal use.
-    /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
-    ///   This is a private method, therefore this can only happen directly under the control of this class.
-    /// - Parameter node: node to be appended. (It can be a list, even contain loops).
-    private mutating func append(node: SinglyLinkedListNode<T>)
-    {
-        if storage.tail != nil
-        {
-            // Copy on write: we are about to modify next a property in
-            // a potentially shared node. Make sure it's new if necessary.
-            storageForWritting.tail?.next = node
-            let (tail, _) = findTail(in: node)
-            storageForWritting.tail = tail // There
-        }
-        else
-        {
-            // This also means that there's no head.
-            // Otherwise the state would be inconsistent.
-            // This will be checked when adding and deleting nodes.
-            storageForWritting.head = node
-            let (tail, _) = findTail(in: node)
-            storageForWritting.tail = tail // There
-        }
+  }
+  
+  /// Appends a new node to the list. This method can easily break value semantics. It is left
+  /// for internal use.
+  /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
+  ///   This is a private method, therefore this can only happen directly under the control of this class.
+  /// - Parameter node: node to be appended. (It can be a list, even contain loops).
+  private mutating func append(node: SinglyLinkedListNode<T>) {
+    if storage.tail != nil {
+      // Copy on write: we are about to modify next a property in
+      // a potentially shared node. Make sure it's new if necessary.
+      storageForWritting.tail?.next = node
+      let (tail, _) = findTail(in: node)
+      storageForWritting.tail = tail // There
+    } else {
+      // This also means that there's no head.
+      // Otherwise the state would be inconsistent.
+      // This will be checked when adding and deleting nodes.
+      storageForWritting.head = node
+      let (tail, _) = findTail(in: node)
+      storageForWritting.tail = tail // There
+    }
+  }
+  
+  /// Creates a copy of the linked list in a diffent memory location.
+  ///
+  /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
+  private func copyStorage() -> IndirectStorage<T> {
+    // If the list is empty, next time an item will be created, it won't affect
+    // other instances of the list that came from copies derived from value types.
+    // like assignments or parameters
+    guard (storage.head != nil) && (storage.tail != nil) else {
+      return IndirectStorage(head: nil, tail: nil)
     }
     
-    /// Creates a copy of the linked list in a diffent memory location.
-    ///
-    /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
-    private func copyStorage() -> IndirectStorage<T> {
-        // If the list is empty, next time an item will be created, it won't affect
-        // other instances of the list that came from copies derived from value types.
-        // like assignments or parameters
-        guard (storage.head != nil) && (storage.tail != nil) else {
-            return IndirectStorage(head: nil, tail: nil)
-        }
-        
-        // Create a new position in memory.
-        // Note that we are shallow copying the value. If it was reference type
-        // we just make a copy of the reference.
-        let copiedHead = SinglyLinkedListNode<T>(value: storage.head!.value)
-        var previousCopied: SinglyLinkedListNode<T> = copiedHead
-        
-        // Iterate through current list of nodes and copy them.
-        var current: SinglyLinkedListNode<T>? = storage.head?.next
-        
-        while (current != nil) {
-            // Create a copy
-            let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
-            
-            // Create links
-            previousCopied.next = currentCopy
-            
-            // Update pointers
-            current = current?.next
-            previousCopied = currentCopy
-        }
-        
-        return IndirectStorage(head: copiedHead, tail: previousCopied)
+    // Create a new position in memory.
+    // Note that we are shallow copying the value. If it was reference type
+    // we just make a copy of the reference.
+    let copiedHead = SinglyLinkedListNode<T>(value: storage.head!.value)
+    var previousCopied: SinglyLinkedListNode<T> = copiedHead
+    
+    // Iterate through current list of nodes and copy them.
+    var current: SinglyLinkedListNode<T>? = storage.head?.next
+    
+    while (current != nil) {
+      // Create a copy
+      let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
+      
+      // Create links
+      previousCopied.next = currentCopy
+      
+      // Update pointers
+      current = current?.next
+      previousCopied = currentCopy
     }
+    
+    return IndirectStorage(head: copiedHead, tail: previousCopied)
+  }
 }
 
 
 
 // MARK:- Extensions when comparable
 
-extension SinglyLinkedList where T: Comparable
-{
-    /// Deletes node containing a given value
-    ///
-    /// - Parameter v: value of the node to be deleted.
-    public mutating func deleteNode(withValue v: T) {
-        
-        guard storage.head != nil else {
-            return
-        }
-        
-        var previous: SinglyLinkedListNode<T>? = nil
-        var current = storage.head
-        
-        while (current != nil) && (current?.value != v) {
-            previous = current
-            current = current?.next
-        }
-        
-        if let foundNode = current {
-            
-            if (storage.head === foundNode) {
-                storageForWritting.head = foundNode.next
-            }
-            
-            if (storage.tail === foundNode) {
-                storage.tail = previous
-            }
-            
-            previous?.next = foundNode.next
-            foundNode.next = nil
-        }
+extension SinglyLinkedList where T: Comparable {
+  /// Deletes node containing a given value
+  ///
+  /// - Parameter v: value of the node to be deleted.
+  public mutating func deleteNode(withValue v: T) {
+    
+    guard storage.head != nil else {
+      return
     }
     
+    var previous: SinglyLinkedListNode<T>? = nil
+    var current = storage.head
+    
+    while (current != nil) && (current?.value != v) {
+      previous = current
+      current = current?.next
+    }
     
-    /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
-    /// - Complexity: O(N^2)
-    public mutating func deleteDuplicatesInPlace()
-    {
-        // Copy on write: this updates storage if necessary.
-        var current = storageForWritting.head
-        
-        while (current != nil)
-        {
-            var previous: SinglyLinkedListNode<T>? = current
-            var next = current?.next
-            
-            while (next != nil)
-            {
-                if (current?.value == next?.value) {
-                    
-                    if (storage.head === next) {
-                        storage.head = next?.next
-                    }
-                    
-                    if (storage.tail === next) {
-                        storage.tail = previous
-                    }
-                    
-                    // Delete next
-                    previous?.next = next?.next
-                }
-                previous = next
-                next = next?.next
-            }
-            current = current?.next
+    if let foundNode = current {
+      
+      if (storage.head === foundNode) {
+        storageForWritting.head = foundNode.next
+      }
+      
+      if (storage.tail === foundNode) {
+        storage.tail = previous
+      }
+      
+      previous?.next = foundNode.next
+      foundNode.next = nil
+    }
+  }
+  
+  
+  /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
+  /// - Complexity: O(N^2)
+  public mutating func deleteDuplicatesInPlace() {
+    // Copy on write: this updates storage if necessary.
+    var current = storageForWritting.head
+    
+    while (current != nil) {
+      var previous: SinglyLinkedListNode<T>? = current
+      var next = current?.next
+      
+      while (next != nil) {
+        if (current?.value == next?.value) {
+          
+          if (storage.head === next) {
+            storage.head = next?.next
+          }
+          
+          if (storage.tail === next) {
+            storage.tail = previous
+          }
+          
+          // Delete next
+          previous?.next = next?.next
         }
+        previous = next
+        next = next?.next
+      }
+      current = current?.next
     }
+  }
 }
 
 
@@ -352,28 +335,25 @@ extension SinglyLinkedList where T: Comparable
 
 public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
     
-    public typealias Element = T
-    
-    private(set) var head: SinglyLinkedListNode<T>?
-    
-    mutating public func next() -> T?
-    {
-        let result = head?.value
-        head = head?.next
-        return result
-    }
+  public typealias Element = T
+  
+  private(set) var head: SinglyLinkedListNode<T>?
+  
+  mutating public func next() -> T? {
+    let result = head?.value
+    head = head?.next
+    return result
+  }
 }
 
 
 
 // MARK: - SEQUENCE -
 
-extension SinglyLinkedList : Sequence
-{
-    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
-    {
-        return SinglyLinkedListForwardIterator(head: storage.head)
-    }
+extension SinglyLinkedList : Sequence {
+  public func makeIterator() -> SinglyLinkedListForwardIterator<T> {
+    return SinglyLinkedListForwardIterator(head: storage.head)
+  }
 }
 
 
@@ -382,117 +362,113 @@ extension SinglyLinkedList : Sequence
 
 extension SinglyLinkedList : Collection {
     
-    public typealias Index = SinglyLinkedListIndex<T>
-    
-    public var startIndex: Index {
-        get {
-            return SinglyLinkedListIndex<T>(node: storage.head, tag: 0)
-        }
-    }
-    
-    public var endIndex: Index {
-        get {
-            if let h = storage.head {
-                let (_, numberOfElements) = findTail(in: h)
-                return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
-            } else {
-                return SinglyLinkedListIndex<T>(node: nil, tag: startIndex.tag)
-            }
-        }
+  public typealias Index = SinglyLinkedListIndex<T>
+  
+  public var startIndex: Index {
+    get {
+      return SinglyLinkedListIndex<T>(node: storage.head, tag: 0)
     }
-    
-    public subscript(position: Index) -> T {
-        get {
-            return position.node!.value
-        }
+  }
+  
+  public var endIndex: Index {
+    get {
+      if let h = storage.head {
+        let (_, numberOfElements) = findTail(in: h)
+        return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+      } else {
+        return SinglyLinkedListIndex<T>(node: nil, tag: startIndex.tag)
+      }
     }
-    
-    public func index(after idx: Index) -> Index {
-        return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
+  
+  public subscript(position: Index) -> T {
+    get {
+      return position.node!.value
     }
+  }
+  
+  public func index(after idx: Index) -> Index {
+    return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
 }
 
 
 
 // MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
 
-extension SinglyLinkedList : ExpressibleByArrayLiteral
-{
-    public typealias Element = T
-    
-    public init(arrayLiteral elements: Element...)
-    {
-        var headSet = false
-        var current : SinglyLinkedListNode<T>?
-        var numberOfElements = 0
-        storage = IndirectStorage()
-        
-        for element in elements {
-            
-            numberOfElements += 1
-            
-            if headSet == false {
-                storage.head = SinglyLinkedListNode<T>(value: element)
-                current = storage.head
-                headSet = true
-            } else {
-                let newNode = SinglyLinkedListNode<T>(value: element)
-                current?.next = newNode
-                current = newNode
-            }
-        }
-        storage.tail = current
+extension SinglyLinkedList : ExpressibleByArrayLiteral {
+  public typealias Element = T
+  
+  public init(arrayLiteral elements: Element...) {
+    var headSet = false
+    var current : SinglyLinkedListNode<T>?
+    var numberOfElements = 0
+    storage = IndirectStorage()
+    
+    for element in elements {
+      
+      numberOfElements += 1
+      
+      if headSet == false {
+        storage.head = SinglyLinkedListNode<T>(value: element)
+        current = storage.head
+        headSet = true
+      } else {
+        let newNode = SinglyLinkedListNode<T>(value: element)
+        current?.next = newNode
+        current = newNode
+      }
     }
+    storage.tail = current
+  }
 }
 
 
 
 // MARK: - FORWARD-INDEX -
 
-public struct SinglyLinkedListIndex<T> : Comparable
-{
-    fileprivate let node: SinglyLinkedListNode<T>?
-    fileprivate let tag: Int
-    
-    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
-        return (lhs.tag == rhs.tag)
-    }
-    
-    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
-        return (lhs.tag < rhs.tag)
-    }
+public struct SinglyLinkedListIndex<T> : Comparable {
+  fileprivate let node: SinglyLinkedListNode<T>?
+  fileprivate let tag: Int
+  
+  public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+  
+  public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
 }
 
 
 extension SinglyLinkedList where T : KeyValuePair {
     
-    public func find(elementWithKey key: T.K) -> T? {
-        let searchResults = filter { (keyValuePair) -> Bool in
-            return keyValuePair.key == key
-        }
-        
-        return searchResults.first
+  public func find(elementWithKey key: T.K) -> T? {
+    let searchResults = filter { (keyValuePair) -> Bool in
+      return keyValuePair.key == key
     }
+    
+    return searchResults.first
+  }
 }
 
 // MARK: - HELPERS -
 
-func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int)
-{
-    // Assign the tail
-    // Note that the passed node can already be linking to other nodes,
-    // so the tail needs to be calculated.
-    var current: SinglyLinkedListNode<T>? = node
-    var count = 1
-    
-    while (current?.next != nil) {
-        current = current?.next
-        count += 1
-    }
-    
-    if current != nil {
-        return (tail: current!, count: count)
-    } else {
-        return (tail: node, count: 1)
-    }
+func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int) {
+  // Assign the tail
+  // Note that the passed node can already be linking to other nodes,
+  // so the tail needs to be calculated.
+  var current: SinglyLinkedListNode<T>? = node
+  var count = 1
+  
+  while (current?.next != nil) {
+    current = current?.next
+    count += 1
+  }
+  
+  if current != nil {
+    return (tail: current!, count: count)
+  } else {
+    return (tail: node, count: 1)
+  }
 }
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index 50d354808..5ad8ffcc4 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -3,248 +3,247 @@ import XCTest
 
 class FindTailInNodeTests: XCTestCase {
     
-    func testExample() {
-        let n1 = SinglyLinkedListNode<Int>(value: 34)
-        let n2 = SinglyLinkedListNode<Int>(value: 35)
-        let n3 = SinglyLinkedListNode<Int>(value: 36)
-        let n4 = SinglyLinkedListNode<Int>(value: 37)
-        
-        n1.next = n2
-        n2.next = n3
-        n3.next = n4
-        
-        XCTAssertTrue(findTail(in: n1).tail === n4)
-        XCTAssertTrue(findTail(in: n2).tail === n4)
-        XCTAssertTrue(findTail(in: n4).tail === n4)
-        XCTAssertTrue(findTail(in: n4).tail === n4)
-    }
-    
+  func testExample() {
+    let n1 = SinglyLinkedListNode<Int>(value: 34)
+    let n2 = SinglyLinkedListNode<Int>(value: 35)
+    let n3 = SinglyLinkedListNode<Int>(value: 36)
+    let n4 = SinglyLinkedListNode<Int>(value: 37)
+    
+    n1.next = n2
+    n2.next = n3
+    n3.next = n4
+    
+    XCTAssertTrue(findTail(in: n1).tail === n4)
+    XCTAssertTrue(findTail(in: n2).tail === n4)
+    XCTAssertTrue(findTail(in: n4).tail === n4)
+    XCTAssertTrue(findTail(in: n4).tail === n4)
+  }
 }
 
 class SinglyLinkedListTests: XCTestCase {
     
-    func testAppendOneNodeFromEmptyList() {
-        var list = SinglyLinkedList<Int>()
-        list.append(value: 34)
-        XCTAssertTrue(list.first == 34)
-        XCTAssertTrue(list.count == 1, "Found \(list.count)")
-    }
-    
-    func testAppendMultipleNodesFromEmptyList() {
-        var list = SinglyLinkedList<Int>()
-        list.append(value: 34)
-        list.append(value: 35)
-        list.append(value: 36)
-        list.append(value: 34)
-        XCTAssertTrue(list.first == 34)
-        let second = list.index(list.startIndex, offsetBy: 1)
-        let third = list.index(list.startIndex, offsetBy: 2)
-        let fouth = list.index(list.startIndex, offsetBy: 3)
-        XCTAssertTrue(list[second] == 35)
-        XCTAssertTrue(list[third] == 36)
-        XCTAssertTrue(list[fouth] == 34)
-        XCTAssertTrue(list.count == 4, "Found \(list.count)")
-    }
-    
-    func testDelete() {
-        var list: SinglyLinkedList<Int> = [1]
-        list.append(value: 2)
-        list.append(value: 3)
-        list.append(value: 4)
-        list.append(value: 5)
-        
-        list.deleteNode(withValue: 1)
-        var second = list.index(list.startIndex, offsetBy: 1)
-        var third = list.index(list.startIndex, offsetBy: 2)
-        XCTAssertTrue(list.first == 2)
-        XCTAssertTrue(list[second] == 3)
-        XCTAssertTrue(list[third] == 4)
-        XCTAssertTrue(list.last == 5)
-        XCTAssertTrue(list.count == 4)
-        
-        list.deleteNode(withValue: 5)
-        second = list.index(list.startIndex, offsetBy: 1)
-        third = list.index(list.startIndex, offsetBy: 2)
-        XCTAssertTrue(list.first == 2)
-        XCTAssertTrue(list[second] == 3)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 3)
-        
-        list.deleteNode(withValue: 3)
-        XCTAssertTrue(list.first == 2)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 2)
-        
-        list.deleteNode(withValue: 2)
-        XCTAssertTrue(list.first == 4)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 1)
-        
-        list.deleteNode(withValue: 4)
-        XCTAssertTrue(list.first == nil)
-        XCTAssertTrue(list.last == nil)
-        XCTAssertTrue(list.count == 0)
-    }
-    
-    func testDeleteDuplicatesInPlace() {
-        var list: SinglyLinkedList<Int> = [1]
-        list.append(value: 2)
-        list.append(value: 2)
-        list.append(value: 3)
-        list.append(value: 5)
-        list.append(value: 2)
-        list.append(value: 4)
-        list.append(value: 2)
-        list.append(value: 5)
-        
-        list.deleteDuplicatesInPlace()
-        let second = list.index(list.startIndex, offsetBy: 1)
-        let third = list.index(list.startIndex, offsetBy: 2)
-        let fourth = list.index(list.startIndex, offsetBy: 3)
-        XCTAssertTrue(list.first == 1)
-        XCTAssertTrue(list[second] == 2)
-        XCTAssertTrue(list[third] == 3)
-        XCTAssertTrue(list[fourth] == 5)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 5)
-    }
-    
-    func testFindKthToLast() {
-        let list: SinglyLinkedList<Int> = [2,2,3,5,2,4,2,5]
-        XCTAssertTrue(list.find(kthToLast: 1)?.value == 5)
-        XCTAssertTrue(list.find(kthToLast: 2)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 3)?.value == 4)
-        XCTAssertTrue(list.find(kthToLast: 4)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 5)?.value == 5)
-        XCTAssertTrue(list.find(kthToLast: 6)?.value == 3)
-        XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
-    }
-    
-    func testConstructorFromArrayLiteralWhenEmpty() {
-        let list: SinglyLinkedList<Int> = []
-        XCTAssertTrue(list.first == nil)
-        XCTAssertTrue(list.last == nil)
-        XCTAssertTrue(list.count == 0, "Found \(list.count)")
-    }
-    
-    func testConstructorFromArrayLiteralWithSingleElement() {
-        let list: SinglyLinkedList<Int> = [5]
-        XCTAssertTrue(list.first == 5)
-        XCTAssertTrue(list.last == 5)
-        XCTAssertTrue(list.count == 1, "Found \(list.count)")
-    }
-    
-    func testAppendValue() {
-        var list = SinglyLinkedList<Int>()
-        list.append(value: 1)
-        list.append(value: 1)
-        list.append(value: 2)
-        list.append(value: 2)
-        list.append(value: 4)
-        
-        let result = string(from: list)
-        XCTAssertTrue(result == "11224", "Found \(result)")
-        XCTAssertTrue(list.count == 5, "Found \(list.count)")
-        XCTAssertTrue(list.last == 4, "Found \(String(describing: list.last))")
-    }
-    
-    func testPrependValue() {
-        var list = SinglyLinkedList<Int>()
-        list.prepend(value: 1)
-        list.prepend(value: 2)
-        list.prepend(value: 3)
-        list.prepend(value: 4)
-        list.prepend(value: 5)
-        list.prepend(value: 6)
-        
-        let result = string(from: list)
-        XCTAssertTrue(result == "654321", "Found \(result)")
-        XCTAssertTrue(list.count == 6, "Found \(list.count)")
-        XCTAssertTrue(list.last == 1, "Found \(String(describing: list.last))")
-    }
-    
-    func testDeleteHeadInListWithMultipleItems() {
-        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        
-        let _ = list.deleteItem(at: 0)
-        let result = string(from: list)
-        XCTAssertTrue(result == "2345678", "Found \(result)")
-        XCTAssertTrue(list.first == 2, "Found \(String(describing: list.first))")
-        XCTAssertTrue(list.count == 7, "Found \(list.count)")
-    }
-    
-    func testDeleteTailInListWithMultipleItems() {
-        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        
-        let _ = list.deleteItem(at: 7)
-        let result = string(from: list)
-        XCTAssertTrue(result == "1234567", "Found \(result)")
-        XCTAssertTrue(list.last == 7, "Found \(String(describing: list.last))")
-        XCTAssertTrue(list.count == 7, "Found \(list.count)")
-    }
-    
-    func testDeleteItemInListWithMultipleItems() {
-        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        
-        let _ = list.deleteItem(at: 4)
-        let result = string(from: list)
-        XCTAssertTrue(result == "1234678", "Found \(result)")
-        XCTAssertTrue(list.first == 1, "Found \(String(describing: list.first))")
-        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
-        XCTAssertTrue(list.count == 7, "Found \(list.count)")
-    }
-    
-    func testDeleteHeadInListWithSingleElement() {
-        var list: SinglyLinkedList<Int> = [1]
-        
-        let _ = list.deleteItem(at: 0)
-        let result = string(from: list)
-        XCTAssertTrue(result == "", "Found \(result)")
-        XCTAssertTrue(list.first == nil, "Found \(String(describing: list.first))")
-        XCTAssertTrue(list.last == nil, "Found \(String(describing: list.last))")
-        XCTAssertTrue(list.count == 0, "Found \(list.count)")
-    }
-    
-    func testDirectIndexAccess() {
-        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        let fifthElementIndex = list.index(list.startIndex, offsetBy: 5)
-        XCTAssertTrue(list[fifthElementIndex] == 6 ,  "Found \(list.count)")
-    }
-    
-    
-    func string(from list: SinglyLinkedList<Int>) -> String {
-        var result = ""
-        var iterator = list.makeIterator()
-        while let current = iterator.next() {
-            result += String(describing: current)
-        }
-        
-        return result
-    }
-    
-    func testCopyOnWriteUsingLiterals() {
-        var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        l1.append(value: 0)
-        var l2 = l1
-        
-        _ = l2.deleteItem(at: 3)
-        XCTAssertTrue(l1.count == 9)
-        XCTAssertTrue(l2.count == 8)
-        
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        
-        XCTAssertTrue(l1.count == 0)
-        XCTAssertTrue(l2.count == 8)
-    }
+  func testAppendOneNodeFromEmptyList() {
+    var list = SinglyLinkedList<Int>()
+    list.append(value: 34)
+    XCTAssertTrue(list.first == 34)
+    XCTAssertTrue(list.count == 1, "Found \(list.count)")
+  }
+    
+  func testAppendMultipleNodesFromEmptyList() {
+    var list = SinglyLinkedList<Int>()
+    list.append(value: 34)
+    list.append(value: 35)
+    list.append(value: 36)
+    list.append(value: 34)
+    XCTAssertTrue(list.first == 34)
+    let second = list.index(list.startIndex, offsetBy: 1)
+    let third = list.index(list.startIndex, offsetBy: 2)
+    let fouth = list.index(list.startIndex, offsetBy: 3)
+    XCTAssertTrue(list[second] == 35)
+    XCTAssertTrue(list[third] == 36)
+    XCTAssertTrue(list[fouth] == 34)
+    XCTAssertTrue(list.count == 4, "Found \(list.count)")
+  }
+    
+  func testDelete() {
+    var list: SinglyLinkedList<Int> = [1]
+    list.append(value: 2)
+    list.append(value: 3)
+    list.append(value: 4)
+    list.append(value: 5)
+    
+    list.deleteNode(withValue: 1)
+    var second = list.index(list.startIndex, offsetBy: 1)
+    var third = list.index(list.startIndex, offsetBy: 2)
+    XCTAssertTrue(list.first == 2)
+    XCTAssertTrue(list[second] == 3)
+    XCTAssertTrue(list[third] == 4)
+    XCTAssertTrue(list.last == 5)
+    XCTAssertTrue(list.count == 4)
+    
+    list.deleteNode(withValue: 5)
+    second = list.index(list.startIndex, offsetBy: 1)
+    third = list.index(list.startIndex, offsetBy: 2)
+    XCTAssertTrue(list.first == 2)
+    XCTAssertTrue(list[second] == 3)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 3)
+    
+    list.deleteNode(withValue: 3)
+    XCTAssertTrue(list.first == 2)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 2)
+    
+    list.deleteNode(withValue: 2)
+    XCTAssertTrue(list.first == 4)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 1)
+    
+    list.deleteNode(withValue: 4)
+    XCTAssertTrue(list.first == nil)
+    XCTAssertTrue(list.last == nil)
+    XCTAssertTrue(list.count == 0)
+  }
+    
+  func testDeleteDuplicatesInPlace() {
+    var list: SinglyLinkedList<Int> = [1]
+    list.append(value: 2)
+    list.append(value: 2)
+    list.append(value: 3)
+    list.append(value: 5)
+    list.append(value: 2)
+    list.append(value: 4)
+    list.append(value: 2)
+    list.append(value: 5)
+    
+    list.deleteDuplicatesInPlace()
+    let second = list.index(list.startIndex, offsetBy: 1)
+    let third = list.index(list.startIndex, offsetBy: 2)
+    let fourth = list.index(list.startIndex, offsetBy: 3)
+    XCTAssertTrue(list.first == 1)
+    XCTAssertTrue(list[second] == 2)
+    XCTAssertTrue(list[third] == 3)
+    XCTAssertTrue(list[fourth] == 5)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 5)
+  }
+    
+  func testFindKthToLast() {
+    let list: SinglyLinkedList<Int> = [2,2,3,5,2,4,2,5]
+    XCTAssertTrue(list.find(kthToLast: 1)?.value == 5)
+    XCTAssertTrue(list.find(kthToLast: 2)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 3)?.value == 4)
+    XCTAssertTrue(list.find(kthToLast: 4)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 5)?.value == 5)
+    XCTAssertTrue(list.find(kthToLast: 6)?.value == 3)
+    XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
+  }
+    
+  func testConstructorFromArrayLiteralWhenEmpty() {
+    let list: SinglyLinkedList<Int> = []
+    XCTAssertTrue(list.first == nil)
+    XCTAssertTrue(list.last == nil)
+    XCTAssertTrue(list.count == 0, "Found \(list.count)")
+  }
+    
+  func testConstructorFromArrayLiteralWithSingleElement() {
+    let list: SinglyLinkedList<Int> = [5]
+    XCTAssertTrue(list.first == 5)
+    XCTAssertTrue(list.last == 5)
+    XCTAssertTrue(list.count == 1, "Found \(list.count)")
+  }
+  
+  func testAppendValue() {
+    var list = SinglyLinkedList<Int>()
+    list.append(value: 1)
+    list.append(value: 1)
+    list.append(value: 2)
+    list.append(value: 2)
+    list.append(value: 4)
+    
+    let result = string(from: list)
+    XCTAssertTrue(result == "11224", "Found \(result)")
+    XCTAssertTrue(list.count == 5, "Found \(list.count)")
+    XCTAssertTrue(list.last == 4, "Found \(String(describing: list.last))")
+  }
+    
+  func testPrependValue() {
+    var list = SinglyLinkedList<Int>()
+    list.prepend(value: 1)
+    list.prepend(value: 2)
+    list.prepend(value: 3)
+    list.prepend(value: 4)
+    list.prepend(value: 5)
+    list.prepend(value: 6)
+    
+    let result = string(from: list)
+    XCTAssertTrue(result == "654321", "Found \(result)")
+    XCTAssertTrue(list.count == 6, "Found \(list.count)")
+    XCTAssertTrue(list.last == 1, "Found \(String(describing: list.last))")
+  }
+    
+  func testDeleteHeadInListWithMultipleItems() {
+    var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    
+    let _ = list.deleteItem(at: 0)
+    let result = string(from: list)
+    XCTAssertTrue(result == "2345678", "Found \(result)")
+    XCTAssertTrue(list.first == 2, "Found \(String(describing: list.first))")
+    XCTAssertTrue(list.count == 7, "Found \(list.count)")
+  }
+    
+  func testDeleteTailInListWithMultipleItems() {
+    var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    
+    let _ = list.deleteItem(at: 7)
+    let result = string(from: list)
+    XCTAssertTrue(result == "1234567", "Found \(result)")
+    XCTAssertTrue(list.last == 7, "Found \(String(describing: list.last))")
+    XCTAssertTrue(list.count == 7, "Found \(list.count)")
+  }
+    
+  func testDeleteItemInListWithMultipleItems() {
+    var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    
+    let _ = list.deleteItem(at: 4)
+    let result = string(from: list)
+    XCTAssertTrue(result == "1234678", "Found \(result)")
+    XCTAssertTrue(list.first == 1, "Found \(String(describing: list.first))")
+    XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
+    XCTAssertTrue(list.count == 7, "Found \(list.count)")
+  }
+    
+  func testDeleteHeadInListWithSingleElement() {
+    var list: SinglyLinkedList<Int> = [1]
+    
+    let _ = list.deleteItem(at: 0)
+    let result = string(from: list)
+    XCTAssertTrue(result == "", "Found \(result)")
+    XCTAssertTrue(list.first == nil, "Found \(String(describing: list.first))")
+    XCTAssertTrue(list.last == nil, "Found \(String(describing: list.last))")
+    XCTAssertTrue(list.count == 0, "Found \(list.count)")
+  }
+    
+  func testDirectIndexAccess() {
+    let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    let fifthElementIndex = list.index(list.startIndex, offsetBy: 5)
+    XCTAssertTrue(list[fifthElementIndex] == 6 ,  "Found \(list.count)")
+  }
+  
+  
+  func string(from list: SinglyLinkedList<Int>) -> String {
+    var result = ""
+    var iterator = list.makeIterator()
+    while let current = iterator.next() {
+        result += String(describing: current)
+    }
+    
+    return result
+  }
+  
+  func testCopyOnWriteUsingLiterals() {
+    var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    l1.append(value: 0)
+    var l2 = l1
+  
+    _ = l2.deleteItem(at: 3)
+    XCTAssertTrue(l1.count == 9)
+    XCTAssertTrue(l2.count == 8)
+  
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+  
+    XCTAssertTrue(l1.count == 0)
+    XCTAssertTrue(l2.count == 8)
+  }
     
 }

From 15d277849385433a0cfdd2dff71eaaee5e0a9bda Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:50:27 +0100
Subject: [PATCH 1169/1679] Remove needless parenthesis in conditional
 statements to follow the repository's Swift Style Guide.

---
 Singly Linked List/SinglyLinkedList.swift | 26 +++++++++++------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index 4e088e195..e8fdfa32c 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -125,7 +125,7 @@ public struct SinglyLinkedList<T> {
     var i = 0
     var elementToDelete: SinglyLinkedListNode<T>
     
-    while (i < index) {
+    while i < index {
       previous = current
       current = current?.next
       i += 1
@@ -133,11 +133,11 @@ public struct SinglyLinkedList<T> {
     
     // Current is now the element to delete (at index position.tag)
     elementToDelete = current!
-    if (storage.head === current) {
+    if storage.head === current {
       storageForWritting.head = current?.next
     }
     
-    if (storage.tail === current) {
+    if storage.tail === current {
       storageForWritting.tail = previous
     }
     
@@ -164,7 +164,7 @@ public struct SinglyLinkedList<T> {
     
     let i = (count - kthToLast)
     
-    if (i == 0) {
+    if i == 0 {
       return node
     }
     
@@ -243,7 +243,7 @@ private extension SinglyLinkedList {
     // Iterate through current list of nodes and copy them.
     var current: SinglyLinkedListNode<T>? = storage.head?.next
     
-    while (current != nil) {
+    while current != nil {
       // Create a copy
       let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
       
@@ -283,11 +283,11 @@ extension SinglyLinkedList where T: Comparable {
     
     if let foundNode = current {
       
-      if (storage.head === foundNode) {
+      if storage.head === foundNode {
         storageForWritting.head = foundNode.next
       }
       
-      if (storage.tail === foundNode) {
+      if storage.tail === foundNode {
         storage.tail = previous
       }
       
@@ -303,18 +303,18 @@ extension SinglyLinkedList where T: Comparable {
     // Copy on write: this updates storage if necessary.
     var current = storageForWritting.head
     
-    while (current != nil) {
+    while current != nil {
       var previous: SinglyLinkedListNode<T>? = current
       var next = current?.next
       
-      while (next != nil) {
-        if (current?.value == next?.value) {
+      while next != nil {
+        if current?.value == next?.value {
           
-          if (storage.head === next) {
+          if storage.head === next {
             storage.head = next?.next
           }
           
-          if (storage.tail === next) {
+          if storage.tail === next {
             storage.tail = previous
           }
           
@@ -461,7 +461,7 @@ func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNod
   var current: SinglyLinkedListNode<T>? = node
   var count = 1
   
-  while (current?.next != nil) {
+  while current?.next != nil {
     current = current?.next
     count += 1
   }

From 06d29b77f9399c813e08bc7ae2d65514779c37fc Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:53:38 +0100
Subject: [PATCH 1170/1679] Remove custom iterator
 SinglyLinkedListForwardIterator to rely on the default implementation
 provided by Collection.

---
 Singly Linked List/SinglyLinkedList.swift | 27 -----------------------
 1 file changed, 27 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index e8fdfa32c..faf25b255 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -331,33 +331,6 @@ extension SinglyLinkedList where T: Comparable {
 
 
 
-// MARK: - ITERATOR -
-
-public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
-    
-  public typealias Element = T
-  
-  private(set) var head: SinglyLinkedListNode<T>?
-  
-  mutating public func next() -> T? {
-    let result = head?.value
-    head = head?.next
-    return result
-  }
-}
-
-
-
-// MARK: - SEQUENCE -
-
-extension SinglyLinkedList : Sequence {
-  public func makeIterator() -> SinglyLinkedListForwardIterator<T> {
-    return SinglyLinkedListForwardIterator(head: storage.head)
-  }
-}
-
-
-
 // MARK: - COLLECTION -
 
 extension SinglyLinkedList : Collection {

From 745cc1a87adc21fc99de34b4c19a0f5ad2cc24e6 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:56:24 +0100
Subject: [PATCH 1171/1679] Remove SinglyLinkedList's initializer that takes a
 value as an argument, to rely exclusively on mutating methods to edit the
 list.

---
 Singly Linked List/SinglyLinkedList.swift | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index faf25b255..67e30eb7d 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -82,15 +82,6 @@ public struct SinglyLinkedList<T> {
   
   // MARK: INITIALIZERS
   
-  /// Creates a list with a single element
-  ///
-  /// - Parameter value: element to populate the list with
-  public init(value: T) {
-    self.init()
-    self.append(value: value)
-  }
-  
-  
   /// Creates an empty list
   public init() {
     self.storage = IndirectStorage()

From d01e3b312fcbafc26f6ac96b6ee9d80fad00a948 Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sun, 6 Aug 2017 10:45:25 -0700
Subject: [PATCH 1172/1679] Style fixes

---
 Hashed Heap/HashedHeap.swift | 36 ++++++++++++++++++------------------
 1 file changed, 18 insertions(+), 18 deletions(-)

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index f123bbc54..db4278a36 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -31,13 +31,13 @@ public struct HashedHeap<T: Hashable> {
     /// - Complexity: O(n)
     public init(array: [T], sort: @escaping (T, T) -> Bool) {
         isOrderedBefore = sort
-        buildHeap(fromArray: array)
+        build(from: array)
     }
 
     /// Converts an array to a max-heap or min-heap in a bottom-up manner.
     ///
     /// - Complexity: O(n)
-    private mutating func buildHeap(fromArray array: [T]) {
+    private mutating func build(from array: [T]) {
         elements = array
         for index in elements.indices {
             indices[elements[index]] = index
@@ -96,12 +96,12 @@ public struct HashedHeap<T: Hashable> {
     /// Replaces an element in the hash.
     ///
     /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
-    public mutating func replace(index i: Int, value: T) {
-        guard i < elements.count else { return }
+    public mutating func replace(_ value: T, at index: Int) {
+        guard index < elements.count else { return }
 
-        assert(isOrderedBefore(value, elements[i]))
-        set(value, at: i)
-        shiftUp(i)
+        assert(isOrderedBefore(value, elements[index]))
+        set(value, at: index)
+        shiftUp(index)
     }
 
     /// Removes the root node from the heap.
@@ -130,7 +130,7 @@ public struct HashedHeap<T: Hashable> {
     /// You need to know the node's index, which may actually take O(n) steps to find.
     ///
     /// - Complexity: O(log n).
-    public mutating func removeAt(_ index: Int) -> T? {
+    public mutating func remove(at index: Int) -> T? {
         guard index < elements.count else { return nil }
 
         let size = elements.count - 1
@@ -158,12 +158,12 @@ public struct HashedHeap<T: Hashable> {
     mutating func shiftUp(_ index: Int) {
         var childIndex = index
         let child = elements[childIndex]
-        var parentIndex = self.parentIndex(ofIndex: childIndex)
+        var parentIndex = self.parentIndex(of: childIndex)
 
         while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
             set(elements[parentIndex], at: childIndex)
             childIndex = parentIndex
-            parentIndex = self.parentIndex(ofIndex: childIndex)
+            parentIndex = self.parentIndex(of: childIndex)
         }
 
         set(child, at: childIndex)
@@ -178,7 +178,7 @@ public struct HashedHeap<T: Hashable> {
         var parentIndex = index
 
         while true {
-            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let leftChildIndex = self.leftChildIndex(of: parentIndex)
             let rightChildIndex = leftChildIndex + 1
 
             // Figure out which comes first if we order them by the sort function:
@@ -208,7 +208,7 @@ public struct HashedHeap<T: Hashable> {
 
     /// Swap two elements in the heap and update the indices hash.
     private mutating func swapAt(_ i: Int, _ j: Int) {
-        swap(&elements[i], &elements[j])
+        elements.swapAt(i, j)
         indices[elements[i]] = i
         indices[elements[j]] = j
     }
@@ -217,23 +217,23 @@ public struct HashedHeap<T: Hashable> {
     ///
     /// - Note: The element at index 0 is the root of the tree and has no parent.
     @inline(__always)
-    func parentIndex(ofIndex i: Int) -> Int {
-        return (i - 1) / 2
+    func parentIndex(of index: Int) -> Int {
+        return (index - 1) / 2
     }
 
     /// Returns the index of the left child of the element at index i.
     ///
     /// - Note: this index can be greater than the heap size, in which case there is no left child.
     @inline(__always)
-    func leftChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 1
+    func leftChildIndex(of index: Int) -> Int {
+        return 2*index + 1
     }
 
     /// Returns the index of the right child of the element at index i.
     ///
     /// - Note: this index can be greater than the heap size, in which case there is no right child.
     @inline(__always)
-    func rightChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 2
+    func rightChildIndex(of index: Int) -> Int {
+        return 2*index + 2
     }
 }

From 3ef6ef4a520b62bea0aa713be96eba0eb1d490b2 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:14:49 +0100
Subject: [PATCH 1173/1679] Add conformance to Collection protocol for
 LinkedList class.

---
 .../LinkedList.playground/Contents.swift      | 63 ++++++++++++++++++
 Linked List/LinkedList.swift                  | 54 +++++++++++++++
 Linked List/README.markdown                   | 66 +++++++++++++++++++
 Linked List/Tests/LinkedListTests.swift       |  8 +++
 4 files changed, 191 insertions(+)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index b78ee4809..ed3de41be 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -317,6 +317,61 @@ extension LinkedList: ExpressibleByArrayLiteral {
   }
 }
 
+// MARK: - Collection
+extension LinkedList : Collection {
+  
+  public typealias Index = LinkedListIndex<T>
+  
+  /// The position of the first element in a nonempty collection.
+  ///
+  /// If the collection is empty, `startIndex` is equal to `endIndex`.
+  /// - Complexity: O(1)
+  public var startIndex: Index {
+    get {
+      return LinkedListIndex<T>(node: head, tag: 0)
+    }
+  }
+  
+  /// The collection's "past the end" position---that is, the position one
+  /// greater than the last valid subscript argument.
+  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+  ///   to the last node in the collection.
+  public var endIndex: Index {
+    get {
+      if let h = self.head {
+        return LinkedListIndex<T>(node: h, tag: count)
+      } else {
+        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+      }
+    }
+  }
+  
+  public subscript(position: Index) -> T {
+    get {
+      return position.node!.value
+    }
+  }
+  
+  public func index(after idx: Index) -> Index {
+    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
+}
+
+// MARK: - Collection Index
+/// Custom index type that contains a reference to the node at index 'tag'
+public struct LinkedListIndex<T> : Comparable
+{
+  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+  fileprivate let tag: Int
+  
+  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+  
+  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
+}
 //: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
@@ -392,3 +447,11 @@ let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
 listArrayLiteral2.count        // 3
 listArrayLiteral2[0]           // "Swift"
 listArrayLiteral2.removeLast()  // "Club"
+
+
+// Conformance to the Collection protocol
+let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
+let index2 = collection.index(collection.startIndex, offsetBy: 2)
+let value = collection[index2] // 3
+
+
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 94e978c07..f51064e01 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -244,3 +244,57 @@ extension LinkedList: ExpressibleByArrayLiteral {
     }
   }
 }
+
+extension LinkedList : Collection {
+  
+  public typealias Index = LinkedListIndex<T>
+  
+  /// The position of the first element in a nonempty collection.
+  ///
+  /// If the collection is empty, `startIndex` is equal to `endIndex`.
+  /// - Complexity: O(1)
+  public var startIndex: Index {
+    get {
+      return LinkedListIndex<T>(node: head, tag: 0)
+    }
+  }
+  
+  /// The collection's "past the end" position---that is, the position one
+  /// greater than the last valid subscript argument.
+  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+  ///   to the last node in the collection.
+  public var endIndex: Index {
+    get {
+      if let h = self.head {
+        return LinkedListIndex<T>(node: h, tag: count)
+      } else {
+        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+      }
+    }
+  }
+  
+  public subscript(position: Index) -> T {
+    get {
+      return position.node!.value
+    }
+  }
+  
+  public func index(after idx: Index) -> Index {
+    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
+}
+
+/// Custom index type that contains a reference to the node at index 'tag'
+public struct LinkedListIndex<T> : Comparable
+{
+  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+  fileprivate let tag: Int
+  
+  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+  
+  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
+}
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c03023c42..f1b1a2480 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -535,6 +535,72 @@ The big difference with the class-based version is that any modification you mak
 
 [I might fill out this section in more detail if there's a demand for it.]
 
+## Conforming to the Collection protocol
+Types that conform to the Sequence protocol, whose elements can be traversed multiple times, nondestructively, and accessed by indexed subscript should conform to the Collection protocol defined in Swift's Standard Library.
+
+Doing so grants access to a very large number of properties and operations that are common when dealing collections of data. In addition to this, it lets custom types follow the patterns that are common to Swift developers.
+
+In order to conform to this protocol, classes need to provide:
+  1 `startIndex` and `endIndex` properties.
+  2 Subscript access to elements as O(1). Diversions of this time complexity need to be documented.
+  
+```swift
+/// The position of the first element in a nonempty collection.
+public var startIndex: Index {
+  get {
+    return LinkedListIndex<T>(node: head, tag: 0)
+  }
+}
+  
+/// The collection's "past the end" position---that is, the position one
+/// greater than the last valid subscript argument.
+/// - Complexity: O(n), where n is the number of elements in the list.
+///   This diverts from the protocol's expectation.
+public var endIndex: Index {
+  get {
+    if let h = self.head {
+      return LinkedListIndex<T>(node: h, tag: count)
+    } else {
+      return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+    }
+  }
+}
+```
+
+```swift
+public subscript(position: Index) -> T {
+  get {
+    return position.node!.value
+  }
+}
+```
+
+Becuase collections are responsible for managing their own indexes, the implementation below keeps a reference to a node in the list. A tag property in the index represents the position of the node in the list.
+
+```swift
+/// Custom index type that contains a reference to the node at index 'tag'
+public struct LinkedListIndex<T> : Comparable
+{
+  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+  fileprivate let tag: Int
+
+  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+
+  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
+}
+```
+
+Finally, the linked is is able to calculate the index after a given one with the following implementation.
+```swift
+public func index(after idx: Index) -> Index {
+  return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+}
+```
+
 ## Some things to keep in mind
 
 Linked lists are flexible but many operations are **O(n)**.
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 0b2b116df..bc9831a41 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -337,4 +337,12 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
     XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
   }
+  
+  func testConformanceToCollectionProtocol() {
+    let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
+    let index2 = collection.index(collection.startIndex, offsetBy: 2)
+    let value = collection[index2]
+    
+    XCTAssertTrue(value == 3)
+  }
 }

From c76252a5b5dfeccaf7f96bbbf99583e2a08b3980 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:17:21 +0100
Subject: [PATCH 1174/1679] Remove queue example from playground as
 implementation was removed.

---
 .../SinglyLinkedList.playground/Contents.swift  | 17 -----------------
 1 file changed, 17 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.playground/Contents.swift b/Singly Linked List/SinglyLinkedList.playground/Contents.swift
index fc6acf9dc..d9104ebe7 100644
--- a/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
+++ b/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
@@ -725,20 +725,3 @@ assert(l2.contains(67) == true)
 let l3 = l2.dropLast()
 assert(l3.count == 7)
 assert(l3.contains(67) == false)
-
-//: We can use this class as a queue.
-
-func empty<Q: Queue>(queue: inout Q) {
-    while let _ = queue.dequeue() {}
-}
-
-var q: SinglyLinkedList<Int> = [5,1,2,3]
-empty(queue: &q)
-assert(q.count == 0)
-
-try? q.enqueue(item: 1)
-try? q.enqueue(item: 3)
-try? q.enqueue(item: 5)
-assert(q.count == 3)
-
-

From f5678857ca24a9c1403a5f721d62e73ef90e64c3 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:23:17 +0100
Subject: [PATCH 1175/1679] Fix styling issue; Parentheses on new line.

---
 Linked List/LinkedList.playground/Contents.swift | 3 +--
 Linked List/LinkedList.swift                     | 3 +--
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index ed3de41be..7805d4a37 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -359,8 +359,7 @@ extension LinkedList : Collection {
 
 // MARK: - Collection Index
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable
-{
+public struct LinkedListIndex<T> : Comparable {
   fileprivate let node: LinkedList<T>.LinkedListNode<T>?
   fileprivate let tag: Int
   
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index f51064e01..e7e2c714e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -285,8 +285,7 @@ extension LinkedList : Collection {
 }
 
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable
-{
+public struct LinkedListIndex<T> : Comparable {
   fileprivate let node: LinkedList<T>.LinkedListNode<T>?
   fileprivate let tag: Int
   

From 5570a711df3d1bc79ce921bd94fe2b9365e141ad Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:32:55 +0100
Subject: [PATCH 1176/1679] Add two examples of Sequence methods gained through
 the conformance to Collection protocol.

---
 Linked List/LinkedList.playground/Contents.swift | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 7805d4a37..ef70c561b 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -453,4 +453,16 @@ let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
 let index2 = collection.index(collection.startIndex, offsetBy: 2)
 let value = collection[index2] // 3
 
+// Iterating in a for loop, since the Sequence protocol allows this.
+var sum = 0
+for element in collection {
+  sum += element
+}
+// sum is 15
+
+// Another way of achieving the same result though 'reduce', another method defined in an extension of Sequence. Collections are Sequences.
+let result = collection.reduce(0) {$0 + $1} // 15
+
+
+
 

From 18a46e78b7e8cb37bf9643368ac5cb5173565832 Mon Sep 17 00:00:00 2001
From: Alessandro Martin <martin.acg@gmail.com>
Date: Sun, 6 Aug 2017 21:28:31 +0100
Subject: [PATCH 1177/1679] Added array private extension to wrap indexes,
 added Sequence conformance, simplified read and write implementations,
 nilling out value when reading.

---
 .../RingBuffer.playground/Contents.swift      | 48 +++++++++++++------
 Ring Buffer/RingBuffer.swift                  | 48 ++++++++++++-------
 2 files changed, 65 insertions(+), 31 deletions(-)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index 29b9917a0..d1195e102 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -9,24 +9,20 @@ public struct RingBuffer<T> {
     array = [T?](repeating: nil, count: count)
   }
 
+  /* Returns false if out of space. */
+  @discardableResult
   public mutating func write(_ element: T) -> Bool {
-    if !isFull {
-      array[writeIndex % array.count] = element
-      writeIndex += 1
-      return true
-    } else {
-      return false
-    }
+    guard !isFull else { return false }
+    defer { writeIndex += 1 }
+    array[wrapped: writeIndex] = element
+    return true
   }
-
+    
+  /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
-    if !isEmpty {
-      let element = array[readIndex % array.count]
-      readIndex += 1
-      return element
-    } else {
-      return nil
-    }
+    guard !isEmpty else { return nil }
+    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    return array[wrapped: readIndex]
   }
 
   fileprivate var availableSpaceForReading: Int {
@@ -46,6 +42,28 @@ public struct RingBuffer<T> {
   }
 }
 
+extension RingBuffer: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var index = readIndex
+    return AnyIterator {
+      guard index < self.writeIndex else { return nil }
+      defer { index += 1 }
+      return self.array[wrapped: index]
+    }
+  }
+}
+
+private extension Array {
+  subscript (wrapped index: Int) -> Element {
+    get {
+      return self[index % count]
+    }
+    set {
+      self[index % count] = newValue
+    }
+  }
+}
+
 var buffer = RingBuffer<Int>(count: 5)
 buffer.array          // [nil, nil, nil, nil, nil]
 buffer.readIndex      // 0
diff --git a/Ring Buffer/RingBuffer.swift b/Ring Buffer/RingBuffer.swift
index 7e845aa74..7dd0d6fc3 100644
--- a/Ring Buffer/RingBuffer.swift	
+++ b/Ring Buffer/RingBuffer.swift	
@@ -16,29 +16,23 @@ public struct RingBuffer<T> {
   private var writeIndex = 0
 
   public init(count: Int) {
-    array = [T?](count: count, repeatedValue: nil)
+    array = [T?](repeating: nil, count: count)
   }
 
   /* Returns false if out of space. */
-  public mutating func write(element: T) -> Bool {
-    if !isFull {
-      array[writeIndex % array.count] = element
-      writeIndex += 1
-      return true
-    } else {
-      return false
-    }
+  @discardableResult
+  public mutating func write(_ element: T) -> Bool {
+    guard !isFull else { return false }
+    defer { writeIndex += 1 }
+    array[wrapped: writeIndex] = element
+    return true
   }
 
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
-    if !isEmpty {
-      let element = array[readIndex % array.count]
-      readIndex += 1
-      return element
-    } else {
-      return nil
-    }
+    guard !isEmpty else { return nil }
+    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    return array[wrapped: readIndex]
   }
 
   private var availableSpaceForReading: Int {
@@ -57,3 +51,25 @@ public struct RingBuffer<T> {
     return availableSpaceForWriting == 0
   }
 }
+
+public extension RingBuffer: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var index = readIndex
+    return AnyIterator {
+        guard index < self.writeIndex else { return nil }
+        defer { index += 1 }
+        return self.array[wrapped: index]
+    }
+  }
+}
+
+private extension Array {
+  subscript (wrapped index: Int) -> Element {
+    get {
+      return self[index % count]
+    }
+    set {
+      self[index % count] = newValue
+    }
+  }
+}

From a40da8c0424635da3f8ea393668fe08f44cc268e Mon Sep 17 00:00:00 2001
From: Ishaan Sejwal <ishaan211991@gmail.com>
Date: Tue, 8 Aug 2017 17:23:05 +0530
Subject: [PATCH 1178/1679] Improved description [skip ci]

---
 Array2D/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 88f25c99a..cf00638e1 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -33,7 +33,7 @@ You can also create the array in a single line of code:
 var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 ```
 
-This looks complicated, but can simplfy it in a helper function:
+This looks complicated, but you can simplify it with a helper function:
 
 ```swift
 func dim<T>(_ count: Int, _ value: T) -> [T] {

From f5a8485b5fb3f4588306e7efb5c95cd9957c9931 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:19:46 +0900
Subject: [PATCH 1179/1679] Applies Xcode 9 b4 changes to Hashed Heap test
 xcodeproj

---
 .../project.pbxproj                           | 22 +++++++++++++++----
 .../xcschemes/Hashed Heap Tests.xcscheme      |  2 +-
 2 files changed, 19 insertions(+), 5 deletions(-)

diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
index 87791f04d..ae1904884 100644
--- a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
@@ -82,12 +82,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
@@ -140,14 +140,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -186,14 +192,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -225,7 +237,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -237,7 +250,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme
index 406c8dd2e..3f298101d 100644
--- a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme	
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 15ca8aff43cde029018a70675059ba26e6966398 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:27:40 +0900
Subject: [PATCH 1180/1679] Turns automatic objc inference to default (off) for
 the Hashed Heap.

---
 .../Tests/Hashed Heap Tests.xcodeproj/project.pbxproj       | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
index ae1904884..01f5fae50 100644
--- a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
@@ -181,6 +181,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Debug;
 		};
@@ -226,6 +227,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Release;
 		};
@@ -237,7 +239,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
@@ -250,7 +252,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.0;
 			};
 			name = Release;

From 864c16cd6a79877fda59440109ab190432f132bd Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:28:38 +0900
Subject: [PATCH 1181/1679] Fixes some spelling errors.

---
 Hashed Heap/HashedHeap.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index db4278a36..ac8035057 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -3,8 +3,8 @@
 /// Heap with an index hash map (dictionary) to speed up lookups by value.
 ///
 /// A heap keeps elements ordered in a binary tree without the use of pointers. A hashed heap does that as well as
-/// having amortized constant lookups by value. This is used in the A* and other heuristic search alogirhtms to achieve
-/// optimal perfomrance.
+/// having amortized constant lookups by value. This is used in the A* and other heuristic search algorithms to achieve
+/// optimal performance.
 public struct HashedHeap<T: Hashable> {
     /// The array that stores the heap's nodes.
     private(set) var elements = [T]()

From 0a73a1402a3675f6268a0e0eaf3c19b64f30ce6c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:31:19 +0900
Subject: [PATCH 1182/1679] Adds credit footer.

---
 Hashed Heap/README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Hashed Heap/README.markdown b/Hashed Heap/README.markdown
index 48fe312ab..8a4fece02 100644
--- a/Hashed Heap/README.markdown	
+++ b/Hashed Heap/README.markdown	
@@ -9,3 +9,5 @@ See [HashedHeap.swift](HashedHeap.swift) for the implementation. See [Heap](../H
 ## See also
 
 [Heap on Wikipedia](https://en.wikipedia.org/wiki/Heap_%28data_structure%29)
+
+*Written for the Swift Algorithm Club by [Alejandro Isaza](https://github.com/aleph7)*

From 0055ab0e88e95200ba45c8b07f9e0946c3e7bdd3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:33:34 +0900
Subject: [PATCH 1183/1679] Added if check for Swift 4

---
 Hashed Heap/Tests/HashedHeapTests.swift | 168 +++++++++++++-----------
 1 file changed, 88 insertions(+), 80 deletions(-)

diff --git a/Hashed Heap/Tests/HashedHeapTests.swift b/Hashed Heap/Tests/HashedHeapTests.swift
index 6badb4ec5..895a21c63 100755
--- a/Hashed Heap/Tests/HashedHeapTests.swift	
+++ b/Hashed Heap/Tests/HashedHeapTests.swift	
@@ -2,87 +2,95 @@ import Foundation
 import XCTest
 
 private struct Message: Hashable {
-    let text: String
-    let priority: Int
-
-    var hashValue: Int {
-        return text.hashValue
-    }
-
-    static func == (lhs: Message, rhs: Message) -> Bool {
-        return lhs.text == rhs.text
-    }
-
-    static func < (m1: Message, m2: Message) -> Bool {
-        return m1.priority < m2.priority
-    }
+  let text: String
+  let priority: Int
+  
+  var hashValue: Int {
+    return text.hashValue
+  }
+  
+  static func == (lhs: Message, rhs: Message) -> Bool {
+    return lhs.text == rhs.text
+  }
+  
+  static func < (m1: Message, m2: Message) -> Bool {
+    return m1.priority < m2.priority
+  }
 }
 
 class HashedHeapTest: XCTestCase {
-    func testEmpty() {
-        var queue = HashedHeap<Message>(sort: <)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-        XCTAssertNil(queue.remove())
-    }
-
-    func testOneElement() {
-        var queue = HashedHeap<Message>(sort: <)
-
-        queue.insert(Message(text: "hello", priority: 100))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()!.priority, 100)
-
-        let result = queue.remove()
-        XCTAssertEqual(result!.priority, 100)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-    }
-
-    func testTwoElementsInOrder() {
-        var queue = HashedHeap<Message>(sort: <)
-
-        queue.insert(Message(text: "hello", priority: 100))
-        queue.insert(Message(text: "world", priority: 200))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 2)
-        XCTAssertEqual(queue.peek()!.priority, 100)
-
-        let result1 = queue.remove()
-        XCTAssertEqual(result1!.priority, 100)
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()!.priority, 200)
-
-        let result2 = queue.remove()
-        XCTAssertEqual(result2!.priority, 200)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-    }
-
-    func testTwoElementsOutOfOrder() {
-        var queue = HashedHeap<Message>(sort: <)
-
-        queue.insert(Message(text: "world", priority: 200))
-        queue.insert(Message(text: "hello", priority: 100))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 2)
-        XCTAssertEqual(queue.peek()!.priority, 100)
-
-        let result1 = queue.remove()
-        XCTAssertEqual(result1!.priority, 100)
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()!.priority, 200)
-
-        let result2 = queue.remove()
-        XCTAssertEqual(result2!.priority, 200)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-    }
+  override func setUp() {
+    super.setUp()
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  func testEmpty() {
+    var queue = HashedHeap<Message>(sort: <)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+    XCTAssertNil(queue.remove())
+  }
+  
+  func testOneElement() {
+    var queue = HashedHeap<Message>(sort: <)
+    
+    queue.insert(Message(text: "hello", priority: 100))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()!.priority, 100)
+    
+    let result = queue.remove()
+    XCTAssertEqual(result!.priority, 100)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+  }
+  
+  func testTwoElementsInOrder() {
+    var queue = HashedHeap<Message>(sort: <)
+    
+    queue.insert(Message(text: "hello", priority: 100))
+    queue.insert(Message(text: "world", priority: 200))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 2)
+    XCTAssertEqual(queue.peek()!.priority, 100)
+    
+    let result1 = queue.remove()
+    XCTAssertEqual(result1!.priority, 100)
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()!.priority, 200)
+    
+    let result2 = queue.remove()
+    XCTAssertEqual(result2!.priority, 200)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+  }
+  
+  func testTwoElementsOutOfOrder() {
+    var queue = HashedHeap<Message>(sort: <)
+    
+    queue.insert(Message(text: "world", priority: 200))
+    queue.insert(Message(text: "hello", priority: 100))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 2)
+    XCTAssertEqual(queue.peek()!.priority, 100)
+    
+    let result1 = queue.remove()
+    XCTAssertEqual(result1!.priority, 100)
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()!.priority, 200)
+    
+    let result2 = queue.remove()
+    XCTAssertEqual(result2!.priority, 200)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+  }
 }

From 9971ae6f22f0690e7565001ec3969cd42566ae79 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:33:56 +0900
Subject: [PATCH 1184/1679] Fixes indentation to 2 spaces.

---
 Hashed Heap/HashedHeap.swift | 460 +++++++++++++++++------------------
 1 file changed, 230 insertions(+), 230 deletions(-)

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index ac8035057..be7d9ab78 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -6,234 +6,234 @@
 /// having amortized constant lookups by value. This is used in the A* and other heuristic search algorithms to achieve
 /// optimal performance.
 public struct HashedHeap<T: Hashable> {
-    /// The array that stores the heap's nodes.
-    private(set) var elements = [T]()
-
-    /// Hash mapping from elements to indices in the `elements` array.
-    private(set) var indices = [T: Int]()
-
-    /// Determines whether this is a max-heap (>) or min-heap (<).
-    fileprivate var isOrderedBefore: (T, T) -> Bool
-
-    /// Creates an empty hashed heap.
-    ///
-    /// The sort function determines whether this is a min-heap or max-heap. For integers, > makes a max-heap, < makes
-    /// a min-heap.
-    public init(sort: @escaping (T, T) -> Bool) {
-        isOrderedBefore = sort
-    }
-
-    /// Creates a hashed heap from an array.
-    ///
-    /// The order of the array does not matter; the elements are inserted into the heap in the order determined by the
-    /// sort function.
-    ///
-    /// - Complexity: O(n)
-    public init(array: [T], sort: @escaping (T, T) -> Bool) {
-        isOrderedBefore = sort
-        build(from: array)
-    }
-
-    /// Converts an array to a max-heap or min-heap in a bottom-up manner.
-    ///
-    /// - Complexity: O(n)
-    private mutating func build(from array: [T]) {
-        elements = array
-        for index in elements.indices {
-            indices[elements[index]] = index
-        }
-
-        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-            shiftDown(i, heapSize: elements.count)
-        }
-    }
-
-    /// Whether the heap is empty.
-    public var isEmpty: Bool {
-        return elements.isEmpty
-    }
-
-    /// The number of elements in the heap.
-    public var count: Int {
-        return elements.count
-    }
-
-    /// Returns the index of the given element.
-    ///
-    /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
-    /// would take O(n), but for the hashed heap this takes amortized constatn time.
-    ///
-    /// - Complexity: Amortized constant
-    public func index(of element: T) -> Int? {
-        return indices[element]
-    }
-
-    /// Returns the maximum value in the heap (for a max-heap) or the minimum value (for a min-heap).
-    ///
-    /// - Complexity: O(1)
-    public func peek() -> T? {
-        return elements.first
-    }
-
-    /// Adds a new value to the heap.
-    ///
-    /// This reorders the heap so that the max-heap or min-heap property still holds.
-    ///
-    /// - Complexity: O(log n)
-    public mutating func insert(_ value: T) {
-        elements.append(value)
-        indices[value] = elements.count - 1
-        shiftUp(elements.count - 1)
-    }
-
-    /// Adds new values to the heap.
-    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-        for value in sequence {
-            insert(value)
-        }
-    }
-
-    /// Replaces an element in the hash.
-    ///
-    /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
-    public mutating func replace(_ value: T, at index: Int) {
-        guard index < elements.count else { return }
-
-        assert(isOrderedBefore(value, elements[index]))
-        set(value, at: index)
-        shiftUp(index)
-    }
-
-    /// Removes the root node from the heap.
-    ///
-    /// For a max-heap, this is the maximum value; for a min-heap it is the minimum value.
-    ///
-    /// - Complexity: O(log n)
-    @discardableResult
-    public mutating func remove() -> T? {
-        if elements.isEmpty {
-            return nil
-        } else if elements.count == 1 {
-            return removeLast()
-        } else {
-            // Use the last node to replace the first one, then fix the heap by
-            // shifting this new first node into its proper position.
-            let value = elements[0]
-            set(removeLast(), at: 0)
-            shiftDown()
-            return value
-        }
-    }
-
-    /// Removes an arbitrary node from the heap.
-    ///
-    /// You need to know the node's index, which may actually take O(n) steps to find.
-    ///
-    /// - Complexity: O(log n).
-    public mutating func remove(at index: Int) -> T? {
-        guard index < elements.count else { return nil }
-
-        let size = elements.count - 1
-        if index != size {
-            swapAt(index, size)
-            shiftDown(index, heapSize: size)
-            shiftUp(index)
-        }
-        return removeLast()
-    }
-
-    /// Removes the last element from the heap.
-    ///
-    /// - Complexity: O(1)
-    public mutating func removeLast() -> T {
-        guard let value = elements.last else {
-            preconditionFailure("Trying to remove element from empty heap")
-        }
-        indices[value] = nil
-        return elements.removeLast()
-    }
-
-    /// Takes a child node and looks at its parents; if a parent is not larger (max-heap) or not smaller (min-heap)
-    /// than the child, we exchange them.
-    mutating func shiftUp(_ index: Int) {
-        var childIndex = index
-        let child = elements[childIndex]
-        var parentIndex = self.parentIndex(of: childIndex)
-
-        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-            set(elements[parentIndex], at: childIndex)
-            childIndex = parentIndex
-            parentIndex = self.parentIndex(of: childIndex)
-        }
-
-        set(child, at: childIndex)
-    }
-
-    mutating func shiftDown() {
-        shiftDown(0, heapSize: elements.count)
-    }
-
-    /// Looks at a parent node and makes sure it is still larger (max-heap) or smaller (min-heap) than its childeren.
-    mutating func shiftDown(_ index: Int, heapSize: Int) {
-        var parentIndex = index
-
-        while true {
-            let leftChildIndex = self.leftChildIndex(of: parentIndex)
-            let rightChildIndex = leftChildIndex + 1
-
-            // Figure out which comes first if we order them by the sort function:
-            // the parent, the left child, or the right child. If the parent comes
-            // first, we're done. If not, that element is out-of-place and we make
-            // it "float down" the tree until the heap property is restored.
-            var first = parentIndex
-            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-                first = leftChildIndex
-            }
-            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-                first = rightChildIndex
-            }
-            if first == parentIndex { return }
-
-            swapAt(parentIndex, first)
-            parentIndex = first
-        }
-    }
-
-    /// Replaces an element in the heap and updates the indices hash.
-    private mutating func set(_ newValue: T, at index: Int) {
-        indices[elements[index]] = nil
-        elements[index] = newValue
-        indices[newValue] = index
-    }
-
-    /// Swap two elements in the heap and update the indices hash.
-    private mutating func swapAt(_ i: Int, _ j: Int) {
-        elements.swapAt(i, j)
-        indices[elements[i]] = i
-        indices[elements[j]] = j
-    }
-
-    /// Returns the index of the parent of the element at index i.
-    ///
-    /// - Note: The element at index 0 is the root of the tree and has no parent.
-    @inline(__always)
-    func parentIndex(of index: Int) -> Int {
-        return (index - 1) / 2
-    }
-
-    /// Returns the index of the left child of the element at index i.
-    ///
-    /// - Note: this index can be greater than the heap size, in which case there is no left child.
-    @inline(__always)
-    func leftChildIndex(of index: Int) -> Int {
-        return 2*index + 1
-    }
-
-    /// Returns the index of the right child of the element at index i.
-    ///
-    /// - Note: this index can be greater than the heap size, in which case there is no right child.
-    @inline(__always)
-    func rightChildIndex(of index: Int) -> Int {
-        return 2*index + 2
-    }
+  /// The array that stores the heap's nodes.
+  private(set) var elements = [T]()
+  
+  /// Hash mapping from elements to indices in the `elements` array.
+  private(set) var indices = [T: Int]()
+  
+  /// Determines whether this is a max-heap (>) or min-heap (<).
+  fileprivate var isOrderedBefore: (T, T) -> Bool
+  
+  /// Creates an empty hashed heap.
+  ///
+  /// The sort function determines whether this is a min-heap or max-heap. For integers, > makes a max-heap, < makes
+  /// a min-heap.
+  public init(sort: @escaping (T, T) -> Bool) {
+    isOrderedBefore = sort
+  }
+  
+  /// Creates a hashed heap from an array.
+  ///
+  /// The order of the array does not matter; the elements are inserted into the heap in the order determined by the
+  /// sort function.
+  ///
+  /// - Complexity: O(n)
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
+    isOrderedBefore = sort
+    build(from: array)
+  }
+  
+  /// Converts an array to a max-heap or min-heap in a bottom-up manner.
+  ///
+  /// - Complexity: O(n)
+  private mutating func build(from array: [T]) {
+    elements = array
+    for index in elements.indices {
+      indices[elements[index]] = index
+    }
+    
+    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+      shiftDown(i, heapSize: elements.count)
+    }
+  }
+  
+  /// Whether the heap is empty.
+  public var isEmpty: Bool {
+    return elements.isEmpty
+  }
+  
+  /// The number of elements in the heap.
+  public var count: Int {
+    return elements.count
+  }
+  
+  /// Returns the index of the given element.
+  ///
+  /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
+  /// would take O(n), but for the hashed heap this takes amortized constatn time.
+  ///
+  /// - Complexity: Amortized constant
+  public func index(of element: T) -> Int? {
+    return indices[element]
+  }
+  
+  /// Returns the maximum value in the heap (for a max-heap) or the minimum value (for a min-heap).
+  ///
+  /// - Complexity: O(1)
+  public func peek() -> T? {
+    return elements.first
+  }
+  
+  /// Adds a new value to the heap.
+  ///
+  /// This reorders the heap so that the max-heap or min-heap property still holds.
+  ///
+  /// - Complexity: O(log n)
+  public mutating func insert(_ value: T) {
+    elements.append(value)
+    indices[value] = elements.count - 1
+    shiftUp(elements.count - 1)
+  }
+  
+  /// Adds new values to the heap.
+  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+    for value in sequence {
+      insert(value)
+    }
+  }
+  
+  /// Replaces an element in the hash.
+  ///
+  /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
+  public mutating func replace(_ value: T, at index: Int) {
+    guard index < elements.count else { return }
+    
+    assert(isOrderedBefore(value, elements[index]))
+    set(value, at: index)
+    shiftUp(index)
+  }
+  
+  /// Removes the root node from the heap.
+  ///
+  /// For a max-heap, this is the maximum value; for a min-heap it is the minimum value.
+  ///
+  /// - Complexity: O(log n)
+  @discardableResult
+  public mutating func remove() -> T? {
+    if elements.isEmpty {
+      return nil
+    } else if elements.count == 1 {
+      return removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = elements[0]
+      set(removeLast(), at: 0)
+      shiftDown()
+      return value
+    }
+  }
+  
+  /// Removes an arbitrary node from the heap.
+  ///
+  /// You need to know the node's index, which may actually take O(n) steps to find.
+  ///
+  /// - Complexity: O(log n).
+  public mutating func remove(at index: Int) -> T? {
+    guard index < elements.count else { return nil }
+    
+    let size = elements.count - 1
+    if index != size {
+      swapAt(index, size)
+      shiftDown(index, heapSize: size)
+      shiftUp(index)
+    }
+    return removeLast()
+  }
+  
+  /// Removes the last element from the heap.
+  ///
+  /// - Complexity: O(1)
+  public mutating func removeLast() -> T {
+    guard let value = elements.last else {
+      preconditionFailure("Trying to remove element from empty heap")
+    }
+    indices[value] = nil
+    return elements.removeLast()
+  }
+  
+  /// Takes a child node and looks at its parents; if a parent is not larger (max-heap) or not smaller (min-heap)
+  /// than the child, we exchange them.
+  mutating func shiftUp(_ index: Int) {
+    var childIndex = index
+    let child = elements[childIndex]
+    var parentIndex = self.parentIndex(of: childIndex)
+    
+    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+      set(elements[parentIndex], at: childIndex)
+      childIndex = parentIndex
+      parentIndex = self.parentIndex(of: childIndex)
+    }
+    
+    set(child, at: childIndex)
+  }
+  
+  mutating func shiftDown() {
+    shiftDown(0, heapSize: elements.count)
+  }
+  
+  /// Looks at a parent node and makes sure it is still larger (max-heap) or smaller (min-heap) than its childeren.
+  mutating func shiftDown(_ index: Int, heapSize: Int) {
+    var parentIndex = index
+    
+    while true {
+      let leftChildIndex = self.leftChildIndex(of: parentIndex)
+      let rightChildIndex = leftChildIndex + 1
+      
+      // Figure out which comes first if we order them by the sort function:
+      // the parent, the left child, or the right child. If the parent comes
+      // first, we're done. If not, that element is out-of-place and we make
+      // it "float down" the tree until the heap property is restored.
+      var first = parentIndex
+      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+        first = leftChildIndex
+      }
+      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+        first = rightChildIndex
+      }
+      if first == parentIndex { return }
+      
+      swapAt(parentIndex, first)
+      parentIndex = first
+    }
+  }
+  
+  /// Replaces an element in the heap and updates the indices hash.
+  private mutating func set(_ newValue: T, at index: Int) {
+    indices[elements[index]] = nil
+    elements[index] = newValue
+    indices[newValue] = index
+  }
+  
+  /// Swap two elements in the heap and update the indices hash.
+  private mutating func swapAt(_ i: Int, _ j: Int) {
+    elements.swapAt(i, j)
+    indices[elements[i]] = i
+    indices[elements[j]] = j
+  }
+  
+  /// Returns the index of the parent of the element at index i.
+  ///
+  /// - Note: The element at index 0 is the root of the tree and has no parent.
+  @inline(__always)
+  func parentIndex(of index: Int) -> Int {
+    return (index - 1) / 2
+  }
+  
+  /// Returns the index of the left child of the element at index i.
+  ///
+  /// - Note: this index can be greater than the heap size, in which case there is no left child.
+  @inline(__always)
+  func leftChildIndex(of index: Int) -> Int {
+    return 2*index + 1
+  }
+  
+  /// Returns the index of the right child of the element at index i.
+  ///
+  /// - Note: this index can be greater than the heap size, in which case there is no right child.
+  @inline(__always)
+  func rightChildIndex(of index: Int) -> Int {
+    return 2*index + 2
+  }
 }

From aa8081e56c66499fce86c55116a16abc7359fd43 Mon Sep 17 00:00:00 2001
From: Vui Nguyen <vui_engineer@yahoo.com>
Date: Wed, 9 Aug 2017 14:55:29 -0600
Subject: [PATCH 1185/1679] Updated to Swift 4 & Xcode 9.0b5.No code changes
 needed,only minor spelling change to README

---
 QuadTree/QuadTree.playground/Contents.swift | 5 +++++
 QuadTree/README.md                          | 2 +-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
index ad8ee31f8..f0d8cb2ef 100644
--- a/QuadTree/QuadTree.playground/Contents.swift
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b5
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))
diff --git a/QuadTree/README.md b/QuadTree/README.md
index 3fc682547..ff71a66f0 100644
--- a/QuadTree/README.md
+++ b/QuadTree/README.md
@@ -152,7 +152,7 @@ Both adding a point and searching can still take up to O(n) in the worst case, s
 
 ### See also
 
-Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Atricle](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
+Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Article](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
 
 More info on [Wiki](https://en.wikipedia.org/wiki/Quadtree)
 

From aa900e36d75cd669ab85cb5afd64c4388252f12b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=82=B8=E3=83=A5=E3=83=A9=E3=82=AD=E3=83=A5=E3=83=BC?=
 =?UTF-8?q?=E3=83=AB=E3=83=BB=E3=83=9F=E3=83=9B=E3=83=BC=E3=82=AF?=
 <dkhuong291@gmail.com>
Date: Thu, 17 Aug 2017 23:05:21 +0700
Subject: [PATCH 1186/1679] Update reverse function in LinkedList

Add `tail = node` to update tail.
---
 Linked List/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c03023c42..9aaecc206 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -451,6 +451,7 @@ How about reversing a list, so that the head becomes the tail and vice versa? Th
 ```swift
   public func reverse() {
     var node = head
+    tail = node // If you had a tail pointer
     while let currentNode = node {
       node = currentNode.next
       swap(&currentNode.next, &currentNode.previous)

From 06d3ef364bde2462e2ee31055124f69e466ab9b5 Mon Sep 17 00:00:00 2001
From: Yeral <YYamil24@gmail.com>
Date: Thu, 17 Aug 2017 18:07:08 -0400
Subject: [PATCH 1187/1679] [Swift 4] Update Bucket Search

---
 Bucket Sort/BucketSort.swift                  | 47 ++++++++++++++-----
 Bucket Sort/Tests/Tests.swift                 |  9 ++--
 .../Tests/Tests.xcodeproj/project.pbxproj     | 24 +++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +-
 4 files changed, 64 insertions(+), 20 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 8363fd867..108073288 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -21,12 +21,34 @@
 //
 
 import Foundation
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+  switch (lhs, rhs) {
+  case let (l?, r?):
+    return l < r
+  case (nil, _?):
+    return true
+  default:
+    return false
+  }
+}
+
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+  switch (lhs, rhs) {
+  case let (l?, r?):
+    return l >= r
+  default:
+    return !(lhs < rhs)
+  }
+}
 
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
 
-
 /**
     Performs bucket sort algorithm on the given input elements.
     [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
@@ -39,7 +61,7 @@ import Foundation
     - Returns: A new array with sorted elements
  */
 
-public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+public func bucketSort<T>(_ elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
     precondition(allPositiveNumbers(elements))
     precondition(enoughSpaceInBuckets(buckets, elements: elements))
 
@@ -57,12 +79,12 @@ public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sor
     return results
 }
 
-private func allPositiveNumbers<T: Sortable>(array: [T]) -> Bool {
+private func allPositiveNumbers<T: Sortable>(_ array: [T]) -> Bool {
     return array.filter { $0.toInt() >= 0 }.count > 0
 }
 
-private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [T]) -> Bool {
-    let maximumValue = elements.maxElement()?.toInt()
+private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> Bool {
+    let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
 
     return totalCapacity >= maximumValue
@@ -72,9 +94,8 @@ private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
-    func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
+    func distribute<T>(_ element: T, buckets: inout [Bucket<T>])
 }
 
 /*
@@ -96,7 +117,7 @@ public struct RangeDistributor: Distributor {
 
     public init() {}
 
-    public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
+    public func distribute<T>(_ element: T, buckets: inout [Bucket<T>]) {
         let value = element.toInt()
         let bucketCapacity = buckets.first!.capacity
 
@@ -121,14 +142,14 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-    func sort<T: Sortable>(items: [T]) -> [T]
+    func sort<T: Sortable>(_ items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
 
     public init() {}
 
-    public func sort<T: Sortable>(items: [T]) -> [T] {
+    public func sort<T: Sortable>(_ items: [T]) -> [T] {
         var results = items
         for i in 0 ..< results.count {
             var j = i
@@ -149,7 +170,7 @@ public struct InsertionSorter: Sorter {
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
+public struct Bucket<T: Sortable> {
     var elements: [T]
     let capacity: Int
 
@@ -158,13 +179,13 @@ public struct Bucket<T:Sortable> {
         elements = [T]()
     }
 
-    public mutating func add(item: T) {
+    public mutating func add(_ item: T) {
         if elements.count < capacity {
             elements.append(item)
         }
     }
 
-    public func sort(algorithm: Sorter) -> [T] {
+    public func sort(_ algorithm: Sorter) -> [T] {
         return algorithm.sort(elements)
     }
 }
diff --git a/Bucket Sort/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
index 22ac751de..1a06c92b5 100644
--- a/Bucket Sort/Tests/Tests.swift	
+++ b/Bucket Sort/Tests/Tests.swift	
@@ -25,7 +25,7 @@ class TestTests: XCTestCase {
 
         largeArray = [Int]()
         for _ in 0..<total {
-            largeArray!.append( random() % maximum )
+            largeArray!.append( Int(arc4random_uniform( UInt32( maximum ) ) ) )
         }
 
         sparsedArray = [Int]()
@@ -57,9 +57,9 @@ class TestTests: XCTestCase {
 
     // MARK: Private functions
 
-    private func performBucketSort(elements: [Int], totalBuckets: Int) -> [Int] {
+    fileprivate func performBucketSort(_ elements: [Int], totalBuckets: Int) -> [Int] {
 
-        let value = (elements.maxElement()?.toInt())! + 1
+        let value = (elements.max()?.toInt())! + 1
         let capacityRequired = Int( ceil( Double(value) / Double(totalBuckets) ) )
 
         var buckets = [Bucket<Int>]()
@@ -71,7 +71,7 @@ class TestTests: XCTestCase {
         return results
     }
 
-    func isSorted(array: [Int]) -> Bool {
+    func isSorted(_ array: [Int]) -> Bool {
 
         var index = 0
         var sorted = true
@@ -86,7 +86,6 @@ class TestTests: XCTestCase {
     }
 }
 
-
 //////////////////////////////////////
 // MARK: Extensions
 //////////////////////////////////////
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 9a42afa4b..84a305784 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,11 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
@@ -140,13 +141,21 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -184,13 +193,21 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +226,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -222,6 +240,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -234,6 +254,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..538a6f4fa 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 689efb386ed0e227659cc7363da4efb8b11f6cc0 Mon Sep 17 00:00:00 2001
From: Yeral <YYamil24@gmail.com>
Date: Thu, 17 Aug 2017 22:59:41 -0400
Subject: [PATCH 1188/1679] [Swift 4] Update Bucket Search

---
 .../Sources/BucketSort.swift                  | 166 +++++++++++-------
 1 file changed, 107 insertions(+), 59 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index c93b96cb2..bafd216fa 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -21,34 +21,81 @@
 //
 
 import Foundation
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+    switch (lhs, rhs) {
+    case let (l?, r?):
+        return l < r
+    case (nil, _?):
+        return true
+    default:
+        return false
+    }
+}
+
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+    switch (lhs, rhs) {
+    case let (l?, r?):
+        return l >= r
+    default:
+        return !(lhs < rhs)
+    }
+}
 
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
 
+/**
+ Performs bucket sort algorithm on the given input elements.
+ [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
+ 
+ - Parameter elements:     Array of Sortable elements
+ - Parameter distributor:  Performs the distribution of each element of a bucket
+ - Parameter sorter:       Performs the sorting inside each bucket, after all the elements are distributed
+ - Parameter buckets:      An array of buckets
+ 
+ - Returns: A new array with sorted elements
+ */
 
-public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
-  var bucketsCopy = buckets
-  for elem in elements {
-    distributor.distribute(elem, buckets: &bucketsCopy)
-  }
-
-  var results = [T]()
+public func bucketSort<T>(_ elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+    precondition(allPositiveNumbers(elements))
+    precondition(enoughSpaceInBuckets(buckets, elements: elements))
+    
+    var bucketsCopy = buckets
+    for elem in elements {
+        distributor.distribute(elem, buckets: &bucketsCopy)
+    }
+    
+    var results = [T]()
+    
+    for bucket in bucketsCopy {
+        results += bucket.sort(sorter)
+    }
+    
+    return results
+}
 
-  for bucket in buckets {
-    results += bucket.sort(sorter)
-  }
+private func allPositiveNumbers<T: Sortable>(_ array: [T]) -> Bool {
+    return array.filter { $0.toInt() >= 0 }.count > 0
+}
 
-  return results
+private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> Bool {
+    let maximumValue = elements.max()?.toInt()
+    let totalCapacity = buckets.count * (buckets.first?.capacity)!
+    
+    return totalCapacity >= maximumValue
 }
 
 //////////////////////////////////////
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
-  func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
+    func distribute<T>(_ element: T, buckets: inout [Bucket<T>])
 }
 
 /*
@@ -67,16 +114,16 @@ public protocol Distributor {
  * By following the formula: element / capacity = #ofBucket
  */
 public struct RangeDistributor: Distributor {
-
-  public init() {}
-
-  public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
-    let value = element.toInt()
-    let bucketCapacity = buckets.first!.capacity
-
-    let bucketIndex = value / bucketCapacity
-    buckets[bucketIndex].add(element)
-  }
+    
+    public init() {}
+    
+    public func distribute<T>(_ element: T, buckets: inout [Bucket<T>]) {
+        let value = element.toInt()
+        let bucketCapacity = buckets.first!.capacity
+        
+        let bucketIndex = value / bucketCapacity
+        buckets[bucketIndex].add(element)
+    }
 }
 
 //////////////////////////////////////
@@ -84,7 +131,7 @@ public struct RangeDistributor: Distributor {
 //////////////////////////////////////
 
 public protocol IntConvertible {
-  func toInt() -> Int
+    func toInt() -> Int
 }
 
 public protocol Sortable: IntConvertible, Comparable {
@@ -95,50 +142,51 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-  func sort<T: Sortable>(items: [T]) -> [T]
+    func sort<T: Sortable>(_ items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
-
-  public init() {}
-
-  public func sort<T: Sortable>(items: [T]) -> [T] {
-    var results = items
-    for i in 0 ..< results.count {
-      var j = i
-      while j > 0 && results[j-i] > results[j] {
-
-        let auxiliar = results[i]
-        results[i] = results[j]
-        results[j] = auxiliar
-
-        j -= 1
-      }
+    
+    public init() {}
+    
+    public func sort<T: Sortable>(_ items: [T]) -> [T] {
+        var results = items
+        for i in 0 ..< results.count {
+            var j = i
+            while j > 0 && results[j-1] > results[j] {
+                
+                let auxiliar = results[j-1]
+                results[j-1] = results[j]
+                results[j] = auxiliar
+                
+                j -= 1
+            }
+        }
+        return results
     }
-    return results
-  }
 }
 
 //////////////////////////////////////
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
-  var elements: [T]
-  let capacity: Int
-
-  public init(capacity: Int) {
-    self.capacity = capacity
-    elements = [T]()
-  }
-
-  public mutating func add(item: T) {
-    if elements.count < capacity {
-      elements.append(item)
+public struct Bucket<T: Sortable> {
+    var elements: [T]
+    let capacity: Int
+    
+    public init(capacity: Int) {
+        self.capacity = capacity
+        elements = [T]()
+    }
+    
+    public mutating func add(_ item: T) {
+        if elements.count < capacity {
+            elements.append(item)
+        }
+    }
+    
+    public func sort(_ algorithm: Sorter) -> [T] {
+        return algorithm.sort(elements)
     }
-  }
-
-  public func sort(algorithm: Sorter) -> [T] {
-    return algorithm.sort(elements)
-  }
 }
+

From 69edcb4830ead3e51fd21b1a3c65998413670588 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Sat, 19 Aug 2017 11:27:59 +0500
Subject: [PATCH 1189/1679] Fix indentation to 2 spaces

---
 .../Contents.swift                            | 82 +++++++++----------
 .../KaratsubaMultiplication.swift             | 12 +--
 2 files changed, 47 insertions(+), 47 deletions(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 6b1b0bca2..04aff1ec4 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -6,58 +6,58 @@ import Foundation
 print("Hello, Swift 4")
 #endif
 precedencegroup ExponentiativePrecedence {
-    higherThan: MultiplicationPrecedence
-    lowerThan: BitwiseShiftPrecedence
-    associativity: left
+  higherThan: MultiplicationPrecedence
+  lowerThan: BitwiseShiftPrecedence
+  associativity: left
 }
 
 infix operator ^^: ExponentiativePrecedence
 func ^^ (radix: Int, power: Int) -> Int {
-    return Int(pow(Double(radix), Double(power)))
+  return Int(pow(Double(radix), Double(power)))
 }
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-    let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
-    let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
-    
-    var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
-    
-    for i in num1Array.indices {
-        var carry = 0
-        for j in num2Array.indices {
-            product[i + j] += carry + num1Array[i] * num2Array[j]
-            carry = product[i + j] / base
-            product[i + j] %= base
-        }
-        product[i + num2Array.count] += carry
+  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
+  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
+  
+  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+  
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
     }
-    
-    return Int(product.reversed().map { String($0) }.reduce("", +))!
+    product[i + num2Array.count] += carry
+  }
+  
+  return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
 // Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-    let num1Array = String(num1).characters
-    let num2Array = String(num2).characters
-    
-    guard num1Array.count > 1 && num2Array.count > 1 else {
-        return multiply(num1, by: num2)
-    }
-    
-    let n = max(num1Array.count, num2Array.count)
-    let nBy2 = n / 2
-    
-    let a = num1 / 10^^nBy2
-    let b = num1 % 10^^nBy2
-    let c = num2 / 10^^nBy2
-    let d = num2 % 10^^nBy2
-    
-    let ac = karatsuba(a, by: c)
-    let bd = karatsuba(b, by: d)
-    let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-    
-    let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-    
-    return product
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return multiply(num1, by: num2)
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, by: c)
+  let bd = karatsuba(b, by: d)
+  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
+  
+  return product
 }
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index 0f0e8ed12..fb20a667d 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -22,24 +22,24 @@ func ^^ (radix: Int, power: Int) -> Int {
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters
-
+  
   guard num1Array.count > 1 && num2Array.count > 1 else {
     return num1 * num2
   }
-
+  
   let n = max(num1Array.count, num2Array.count)
   let nBy2 = n / 2
-
+  
   let a = num1 / 10^^nBy2
   let b = num1 % 10^^nBy2
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
-
+  
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
   let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-
+  
   let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-
+  
   return product
 }

From a6c3e9f32d68c595150db11b274e4908cee20928 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Sat, 19 Aug 2017 11:33:45 +0500
Subject: [PATCH 1190/1679] Fix indentation to 2 spaces

---
 .../Contents.swift                            | 192 +++++++++---------
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     | 116 +++++------
 2 files changed, 154 insertions(+), 154 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index b47cf1257..6609c9abe 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -6,115 +6,115 @@ print("Hello, Swift4!")
 #endif
 
 func ZetaAlgorithm(ptnr: String) -> [Int]? {
+  
+  let pattern = Array(ptnr.characters)
+  let patternLength: Int = pattern.count
+  
+  guard patternLength > 0 else {
+    return nil
+  }
+  
+  var zeta: [Int] = [Int](repeating: 0, count: patternLength)
+  
+  var left: Int = 0
+  var right: Int = 0
+  var k_1: Int = 0
+  var betaLength: Int = 0
+  var textIndex: Int = 0
+  var patternIndex: Int = 0
+  
+  for k in 1 ..< patternLength {
+    if k > right {
+      patternIndex = 0
+      
+      while k + patternIndex < patternLength  &&
+        pattern[k + patternIndex] == pattern[patternIndex] {
+          patternIndex = patternIndex + 1
+      }
+      
+      zeta[k] = patternIndex
+      
+      if zeta[k] > 0 {
+        left = k
+        right = k + zeta[k] - 1
+      }
+    } else {
+      k_1 = k - left + 1
+      betaLength = right - k + 1
+      
+      if zeta[k_1 - 1] < betaLength {
+        zeta[k] = zeta[k_1 - 1]
+      } else if zeta[k_1 - 1] >= betaLength {
+        textIndex = betaLength
+        patternIndex = right + 1
+        
+        while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+          textIndex = textIndex + 1
+          patternIndex = patternIndex + 1
+        }
+        zeta[k] = patternIndex - k
+        left = k
+        right = patternIndex - 1
+      }
+    }
+  }
+  return zeta
+}
+
+extension String {
+  
+  func indexesOf(ptnr: String) -> [Int]? {
     
+    let text = Array(self.characters)
     let pattern = Array(ptnr.characters)
+    
+    let textLength: Int = text.count
     let patternLength: Int = pattern.count
     
     guard patternLength > 0 else {
-        return nil
+      return nil
     }
     
-    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
-    
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
+    var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
     var textIndex: Int = 0
     var patternIndex: Int = 0
+    var indexes: [Int] = [Int]()
     
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-            
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                    patternIndex = patternIndex + 1
-            }
-            
-            zeta[k] = patternIndex
-            
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-            
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-                
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
-        }
+    /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+    let zeta = ZetaAlgorithm(ptnr: ptnr)
+    
+    for patternIndex in (1 ..< patternLength).reversed() {
+      textIndex = patternIndex + zeta![patternIndex] - 1
+      suffixPrefix[textIndex] = zeta![patternIndex]
     }
-    return zeta
-}
-
-extension String {
     
-    func indexesOf(ptnr: String) -> [Int]? {
-        
-        let text = Array(self.characters)
-        let pattern = Array(ptnr.characters)
-        
-        let textLength: Int = text.count
-        let patternLength: Int = pattern.count
-        
-        guard patternLength > 0 else {
-            return nil
-        }
-        
-        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
-        var textIndex: Int = 0
-        var patternIndex: Int = 0
-        var indexes: [Int] = [Int]()
-        
-        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr: ptnr)
-        
-        for patternIndex in (1 ..< patternLength).reversed() {
-            textIndex = patternIndex + zeta![patternIndex] - 1
-            suffixPrefix[textIndex] = zeta![patternIndex]
-        }
-        
-        /* Search stage: scanning the text for pattern matching */
-        textIndex = 0
-        patternIndex = 0
-        
-        while textIndex + (patternLength - patternIndex - 1) < textLength {
-            
-            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
-                textIndex = textIndex + 1
-                patternIndex = patternIndex + 1
-            }
-            
-            if patternIndex == patternLength {
-                indexes.append(textIndex - patternIndex)
-            }
-            
-            if patternIndex == 0 {
-                textIndex = textIndex + 1
-            } else {
-                patternIndex = suffixPrefix[patternIndex - 1]
-            }
-        }
-        
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        return indexes
+    /* Search stage: scanning the text for pattern matching */
+    textIndex = 0
+    patternIndex = 0
+    
+    while textIndex + (patternLength - patternIndex - 1) < textLength {
+      
+      while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+        textIndex = textIndex + 1
+        patternIndex = patternIndex + 1
+      }
+      
+      if patternIndex == patternLength {
+        indexes.append(textIndex - patternIndex)
+      }
+      
+      if patternIndex == 0 {
+        textIndex = textIndex + 1
+      } else {
+        patternIndex = suffixPrefix[patternIndex - 1]
+      }
+    }
+    
+    guard !indexes.isEmpty else {
+      return nil
     }
+    return indexes
+  }
 }
 
 /* Examples */
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 45d9812b7..81bc65278 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -1,65 +1,65 @@
 /*  Knuth-Morris-Pratt algorithm for pattern/string matching
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
+ 
+ The code is based on the book:
+ "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+ by Dan Gusfield
+ Cambridge University Press, 1997
+ */
 
 import Foundation
 
 extension String {
-
-    func indexesOf(ptnr: String) -> [Int]? {
-
-        let text = Array(self.characters)
-        let pattern = Array(ptnr.characters)
-
-        let textLength: Int = text.count
-        let patternLength: Int = pattern.count
-
-        guard patternLength > 0 else {
-            return nil
-        }
-
-        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
-        var textIndex: Int = 0
-        var patternIndex: Int = 0
-        var indexes: [Int] = [Int]()
-
-        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr: ptnr)
-
-        for patternIndex in (1 ..< patternLength).reversed() {
-            textIndex = patternIndex + zeta![patternIndex] - 1
-            suffixPrefix[textIndex] = zeta![patternIndex]
-        }
-
-        /* Search stage: scanning the text for pattern matching */
-        textIndex = 0
-        patternIndex = 0
-
-        while textIndex + (patternLength - patternIndex - 1) < textLength {
-
-            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
-                textIndex = textIndex + 1
-                patternIndex = patternIndex + 1
-            }
-
-            if patternIndex == patternLength {
-                indexes.append(textIndex - patternIndex)
-            }
-
-            if patternIndex == 0 {
-                textIndex = textIndex + 1
-            } else {
-                patternIndex = suffixPrefix[patternIndex - 1]
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        return indexes
+  
+  func indexesOf(ptnr: String) -> [Int]? {
+    
+    let text = Array(self.characters)
+    let pattern = Array(ptnr.characters)
+    
+    let textLength: Int = text.count
+    let patternLength: Int = pattern.count
+    
+    guard patternLength > 0 else {
+      return nil
+    }
+    
+    var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+    var indexes: [Int] = [Int]()
+    
+    /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+    let zeta = ZetaAlgorithm(ptnr: ptnr)
+    
+    for patternIndex in (1 ..< patternLength).reversed() {
+      textIndex = patternIndex + zeta![patternIndex] - 1
+      suffixPrefix[textIndex] = zeta![patternIndex]
+    }
+    
+    /* Search stage: scanning the text for pattern matching */
+    textIndex = 0
+    patternIndex = 0
+    
+    while textIndex + (patternLength - patternIndex - 1) < textLength {
+      
+      while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+        textIndex = textIndex + 1
+        patternIndex = patternIndex + 1
+      }
+      
+      if patternIndex == patternLength {
+        indexes.append(textIndex - patternIndex)
+      }
+      
+      if patternIndex == 0 {
+        textIndex = textIndex + 1
+      } else {
+        patternIndex = suffixPrefix[patternIndex - 1]
+      }
+    }
+    
+    guard !indexes.isEmpty else {
+      return nil
     }
+    return indexes
+  }
 }

From dd1ed39fca150d4fa2905b902736f12a49f3efb1 Mon Sep 17 00:00:00 2001
From: Alessandro Martin <martin.acg@gmail.com>
Date: Thu, 24 Aug 2017 22:19:06 +0100
Subject: [PATCH 1191/1679] Code Review comments addressed

---
 Ring Buffer/RingBuffer.playground/Contents.swift | 13 ++++++++++---
 Ring Buffer/RingBuffer.swift                     | 13 ++++++++++---
 2 files changed, 20 insertions(+), 6 deletions(-)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index d1195e102..adcf146b4 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -13,7 +13,9 @@ public struct RingBuffer<T> {
   @discardableResult
   public mutating func write(_ element: T) -> Bool {
     guard !isFull else { return false }
-    defer { writeIndex += 1 }
+    defer {
+        writeIndex += 1
+    }
     array[wrapped: writeIndex] = element
     return true
   }
@@ -21,7 +23,10 @@ public struct RingBuffer<T> {
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
     guard !isEmpty else { return nil }
-    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    defer {
+        array[wrapped: readIndex] = nil
+        readIndex += 1
+    }
     return array[wrapped: readIndex]
   }
 
@@ -47,7 +52,9 @@ extension RingBuffer: Sequence {
     var index = readIndex
     return AnyIterator {
       guard index < self.writeIndex else { return nil }
-      defer { index += 1 }
+      defer {
+        index += 1
+        }
       return self.array[wrapped: index]
     }
   }
diff --git a/Ring Buffer/RingBuffer.swift b/Ring Buffer/RingBuffer.swift
index 7dd0d6fc3..0006afea6 100644
--- a/Ring Buffer/RingBuffer.swift	
+++ b/Ring Buffer/RingBuffer.swift	
@@ -23,7 +23,9 @@ public struct RingBuffer<T> {
   @discardableResult
   public mutating func write(_ element: T) -> Bool {
     guard !isFull else { return false }
-    defer { writeIndex += 1 }
+    defer {
+        writeIndex += 1
+    }
     array[wrapped: writeIndex] = element
     return true
   }
@@ -31,7 +33,10 @@ public struct RingBuffer<T> {
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
     guard !isEmpty else { return nil }
-    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    defer {
+        array[wrapped: readIndex] = nil
+        readIndex += 1
+    }
     return array[wrapped: readIndex]
   }
 
@@ -57,7 +62,9 @@ public extension RingBuffer: Sequence {
     var index = readIndex
     return AnyIterator {
         guard index < self.writeIndex else { return nil }
-        defer { index += 1 }
+        defer {
+            index += 1
+        }
         return self.array[wrapped: index]
     }
   }

From 9b6ca04034f7dfc2c5eec2ba885a88d828d46468 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Thu, 24 Aug 2017 22:55:19 -0700
Subject: [PATCH 1192/1679] [Swift 4] Update LRU Cache

---
 LRU Cache/LRUCache.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/LRU Cache/LRUCache.playground/Contents.swift b/LRU Cache/LRUCache.playground/Contents.swift
index 35dcc5d59..2ebc03242 100644
--- a/LRU Cache/LRUCache.playground/Contents.swift	
+++ b/LRU Cache/LRUCache.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let cache = LRUCache<String>(2)
 cache.set("a", val: 1)
 cache.set("b", val: 2)

From 975709d99f1304d66c1d7b3b7c98734aeac83ee0 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Thu, 24 Aug 2017 22:57:23 -0700
Subject: [PATCH 1193/1679] [Swift 4] Update Ordered Set

---
 .../Pages/Example 1.xcplaygroundpage/Contents.swift         | 5 +++++
 .../Pages/Example 1.xcplaygroundpage/timeline.xctimeline    | 6 +++---
 2 files changed, 8 insertions(+), 3 deletions(-)

diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index 2420019fc..c12dadf0f 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 //: # Example 1 with type Int
 
 var mySet = OrderedSet<Int>()
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
index 454d1011b..53114d22e 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=21&amp;CharacterRangeLoc=288&amp;EndingColumnNumber=22&amp;EndingLineNumber=18&amp;StartingColumnNumber=1&amp;StartingLineNumber=18&amp;Timestamp=496197876.557751"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=21&amp;CharacterRangeLoc=371&amp;EndingColumnNumber=0&amp;EndingLineNumber=24&amp;StartingColumnNumber=1&amp;StartingLineNumber=23&amp;Timestamp=525333424.593074"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=24&amp;CharacterRangeLoc=329&amp;EndingColumnNumber=27&amp;EndingLineNumber=20&amp;StartingColumnNumber=3&amp;StartingLineNumber=20&amp;Timestamp=496197876.557751"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=24&amp;CharacterRangeLoc=412&amp;EndingColumnNumber=0&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=25&amp;Timestamp=525333424.593234"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=25&amp;CharacterRangeLoc=428&amp;EndingColumnNumber=28&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=26&amp;Timestamp=496197876.557751"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=25&amp;CharacterRangeLoc=511&amp;EndingColumnNumber=0&amp;EndingLineNumber=32&amp;StartingColumnNumber=3&amp;StartingLineNumber=31&amp;Timestamp=525333424.593352"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>

From c03c0a558e12156b543be7482e649e571e89c6ac Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:33:30 -0700
Subject: [PATCH 1194/1679] [Swift 4] Update Longest Common Subsequence

---
 .../LongestCommonSubsequence.playground/Contents.swift       | 5 +++++
 .../contents.xcplayground                                    | 2 +-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index 0fc9ec325..c8d413e7f 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 extension String {
   public func longestCommonSubsequence(_ other: String) -> String {
 
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground
index fc5b4ab70..5da2641c9 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
 <playground version='5.0' target-platform='ios'>
     <timeline fileName='timeline.xctimeline'/>
-</playground>
+</playground>
\ No newline at end of file

From c7d25842a6eb11d8fee32d6ebfddb0a9fb4d53ed Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:36:59 -0700
Subject: [PATCH 1195/1679] [Swift 4] Update Minimum Spanning Tree(unweighted)

---
 .../Contents.swift                                           | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 8ad04379c..65aa9fbc4 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 

From c66f3c361b47c263b4bde9cbf076129fa5fb64bd Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:42:58 -0700
Subject: [PATCH 1196/1679] [Swift 4] Update Minimum Coin Change

---
 .../MinimumCoinChangeTests.swift              | 47 +++++++++++--------
 1 file changed, 27 insertions(+), 20 deletions(-)

diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
index 7c106eeb9..45beff775 100644
--- a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -2,27 +2,34 @@ import XCTest
 @testable import MinimumCoinChange
 
 class MinimumCoinChangeTests: XCTestCase {
-    func testExample() {
-        let mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
-        print("Coin set: \(mcc.sortedCoinSet)")
-
-        do {
-            for i in 0..<100 {
-                let greedy = try mcc.changeGreedy(i)
-                let dynamic = try mcc.changeDynamic(i)
-
-                XCTAssertEqual(greedy.reduce(0, +), dynamic.reduce(0, +), "Greedy and Dynamic return two different changes")
-
-                if greedy.count != dynamic.count {
-                    print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
-                }
-            }
-        } catch {
-            XCTFail("Test Failed: impossible to change with the given coin set")
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  func testExample() {
+    let mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+    print("Coin set: \(mcc.sortedCoinSet)")
+    
+    do {
+      for i in 0..<100 {
+        let greedy = try mcc.changeGreedy(i)
+        let dynamic = try mcc.changeDynamic(i)
+        
+        XCTAssertEqual(greedy.reduce(0, +), dynamic.reduce(0, +), "Greedy and Dynamic return two different changes")
+        
+        if greedy.count != dynamic.count {
+          print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
         }
+      }
+    } catch {
+      XCTFail("Test Failed: impossible to change with the given coin set")
     }
-
-    static var allTests = [
-        ("testExample", testExample),
+  }
+  
+  static var allTests = [
+    ("testExample", testExample),
     ]
 }

From d8e0bf5eb18a6ac9e4bd281c6b3fc207afeb4b56 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:52:25 -0700
Subject: [PATCH 1197/1679] [Swift 4] Update Priority Queue

---
 Priority Queue/Tests/PriorityQueueTests.swift        | 7 +++++++
 Priority Queue/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/Priority Queue/Tests/PriorityQueueTests.swift b/Priority Queue/Tests/PriorityQueueTests.swift
index 56536310d..e31fa3d07 100755
--- a/Priority Queue/Tests/PriorityQueueTests.swift	
+++ b/Priority Queue/Tests/PriorityQueueTests.swift	
@@ -11,6 +11,13 @@ private func < (m1: Message, m2: Message) -> Bool {
 }
 
 class PriorityQueueTest: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testEmpty() {
     var queue = PriorityQueue<Message>(sort: <)
     XCTAssertTrue(queue.isEmpty)
diff --git a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 0f7d84be9..5ddfd574d 100644
--- a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -180,6 +180,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -230,7 +232,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,7 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From b85438e81864b29acce71a49186475c69719f2ac Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:56:36 -0700
Subject: [PATCH 1198/1679] [Swift 4] Update Radix Sort

---
 Radix Sort/RadixSort.playground/Contents.swift   | 5 +++++
 Radix Sort/Tests/RadixSortTests.swift            | 7 +++++++
 Radix Sort/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 3 files changed, 16 insertions(+), 2 deletions(-)

diff --git a/Radix Sort/RadixSort.playground/Contents.swift b/Radix Sort/RadixSort.playground/Contents.swift
index a4f7e3527..941723c37 100644
--- a/Radix Sort/RadixSort.playground/Contents.swift	
+++ b/Radix Sort/RadixSort.playground/Contents.swift	
@@ -2,6 +2,11 @@
 
 import Cocoa
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Test Radix Sort with small array of ten values
 var array: [Int] = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
 radixSort(&array)
diff --git a/Radix Sort/Tests/RadixSortTests.swift b/Radix Sort/Tests/RadixSortTests.swift
index 688bcdcb8..9b881318a 100644
--- a/Radix Sort/Tests/RadixSortTests.swift	
+++ b/Radix Sort/Tests/RadixSortTests.swift	
@@ -9,6 +9,13 @@
 import XCTest
 
 class RadixSortTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testCombSort() {
     let expectedSequence: [Int] = [2, 9, 19, 32, 55, 67, 89, 101, 912, 4242]
     var sequence = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
diff --git a/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj b/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj
index 4b32f71b5..bef4ead9b 100644
--- a/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -179,6 +179,7 @@
 				SDKROOT = macosx;
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -220,6 +221,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -233,7 +235,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -246,7 +248,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From acd52410739a05bf63c7773e1397170fb566e7b0 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 09:00:31 -0700
Subject: [PATCH 1199/1679] [Swift 4] Update Red Black Tree

---
 Red-Black Tree/RedBlackTree.playground/Contents.swift     | 7 ++++++-
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 4 ++--
 2 files changed, 8 insertions(+), 3 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
index 50d61167d..f14f18e58 100644
--- a/Red-Black Tree/RedBlackTree.playground/Contents.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -2,6 +2,11 @@
 // Test for  the RedBlackTree implementation provided in the Source folder of this Playground
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let redBlackTree = RedBlackTree<Double>()
 
 let randomMax = Double(0x10000000)
@@ -27,4 +32,4 @@ for i in 0..<1000 {
     redBlackTree.verify()
   }
 }
-redBlackTree.verify()
\ No newline at end of file
+redBlackTree.verify()
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7fd89d5f2..f8f58fd7c 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1912,10 +1912,10 @@
       location = "group:Red-Black Tree"
       name = "Red-Black Tree">
       <FileRef
-         location = "group:README.markdown">
+         location = "group:RedBlackTree.playground">
       </FileRef>
       <FileRef
-         location = "group:Red-Black Tree 2.playground">
+         location = "group:README.markdown">
       </FileRef>
    </Group>
    <Group

From f03f5ecc42b7fa5a4c37b6f43b8429a40c849986 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 17:43:39 -0700
Subject: [PATCH 1200/1679] [Swift 4] Update Select Minimum Maximum

---
 .../SelectMinimumMaximum.playground/Contents.swift           | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index c30bf2fa4..e1101a864 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Compare each item to find minimum
 func minimum<T: Comparable>(_ array: [T]) -> T? {
   guard var minimum = array.first else {

From 5286469928e5c24de3a05404060e11f5473278b2 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 17:46:46 -0700
Subject: [PATCH 1201/1679] [Swift 4] Update Shell Sort

---
 Shell Sort/Tests/ShellSortTests.swift            | 7 +++++++
 Shell Sort/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/Shell Sort/Tests/ShellSortTests.swift b/Shell Sort/Tests/ShellSortTests.swift
index f9404b781..494d6841e 100644
--- a/Shell Sort/Tests/ShellSortTests.swift	
+++ b/Shell Sort/Tests/ShellSortTests.swift	
@@ -1,6 +1,13 @@
 import XCTest
 
 class ShellSortTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testShellSort() {
     checkSortAlgorithm { (a: [Int]) -> [Int] in
       var b = a
diff --git a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj
index 1de1c7213..c2966af46 100644
--- a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -178,6 +178,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -214,6 +215,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -225,7 +227,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -237,7 +239,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From d1542eb5b57c87545a98d17b9edbbb961e8a54d8 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 17:54:35 -0700
Subject: [PATCH 1202/1679] [Swift 4] Update Shortest Path (Unweighted)

---
 .../Shortest path example.xcplaygroundpage/Contents.swift  | 5 +++++
 Shortest Path (Unweighted)/Tests/ShortestPathTests.swift   | 7 +++++++
 .../Tests/Tests.xcodeproj/project.pbxproj                  | 6 ++++--
 3 files changed, 16 insertions(+), 2 deletions(-)

diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index 9f2eda4f3..2404f5b8c 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
diff --git a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift
index 71b9f88ab..4d79eeaa7 100644
--- a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
+++ b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
@@ -1,6 +1,13 @@
 import XCTest
 
 class ShortestPathTests: XCTestCase {
+  
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 
   func testShortestPathWhenGivenTree() {
     let tree = Graph()
diff --git a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
index f1744fcf1..b601a1665 100644
--- a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
@@ -182,6 +182,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -218,6 +219,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -231,7 +233,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -244,7 +246,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 23ff396398e9ea3f4985c3bac25348c3a33c501e Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 18:00:40 -0700
Subject: [PATCH 1203/1679] [Swift 4] Update Single-Source Shortest Paths
 (Weighted)

---
 Graph/Graph.xcodeproj/project.pbxproj                |  2 ++
 .../SSSP.playground/Contents.swift                   |  5 +++++
 .../SSSP.xcodeproj/project.pbxproj                   | 12 ++++++------
 .../SSSPTests/SSSPTests.swift                        |  7 +++++++
 4 files changed, 20 insertions(+), 6 deletions(-)

diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index 4822d80bb..17a5a7d6b 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -289,6 +289,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -338,6 +339,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift
index 652b558b1..e897ada4a 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
@@ -1,6 +1,11 @@
 import Graph
 import SSSP
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let graph = AdjacencyMatrixGraph<String>()
 let s = graph.createVertex("s")
 let t = graph.createVertex("t")
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj
index fb425a73e..44365e5aa 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
@@ -334,7 +334,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -378,7 +378,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -401,7 +401,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -421,7 +421,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -433,7 +433,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -445,7 +445,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift
index 04584dfeb..924a487f5 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
@@ -10,6 +10,13 @@ import XCTest
 @testable import SSSP
 
 class SSSPTests: XCTestCase {
+  
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 
   /**
    See Figure 24.4 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 652

From 4c796cca9566e888ac6c3871f068c00f0a3a2b5e Mon Sep 17 00:00:00 2001
From: "Carlos A. King" <carlos.king70@gmail.com>
Date: Sat, 26 Aug 2017 22:22:54 -0400
Subject: [PATCH 1204/1679] [Swift 4] Update Shell Sort

---
 .../Shell Sort.playground/Contents.swift      | 34 +++++++++++++++++++
 .../contents.xcplayground                     |  4 +++
 2 files changed, 38 insertions(+)
 create mode 100644 Shell Sort/Shell Sort.playground/Contents.swift
 create mode 100644 Shell Sort/Shell Sort.playground/contents.xcplayground

diff --git a/Shell Sort/Shell Sort.playground/Contents.swift b/Shell Sort/Shell Sort.playground/Contents.swift
new file mode 100644
index 000000000..9e2153f88
--- /dev/null
+++ b/Shell Sort/Shell Sort.playground/Contents.swift	
@@ -0,0 +1,34 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
+public func insertionSort(_ list: inout [Int], start: Int, gap: Int) {
+    for i in stride(from: (start + gap), to: list.count, by: gap) {
+        let currentValue = list[i]
+        var pos = i
+        while pos >= gap && list[pos - gap] > currentValue {
+            list[pos] = list[pos - gap]
+            pos -= gap
+        }
+        list[pos] = currentValue
+    }
+}
+
+public func shellSort(_ list: inout [Int]) {
+    var sublistCount = list.count / 2
+    while sublistCount > 0 {
+        for pos in 0..<sublistCount {
+            insertionSort(&list, start: pos, gap: sublistCount)
+        }
+        sublistCount = sublistCount / 2
+    }
+}
+
+var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
+
+shellSort(&arr)
diff --git a/Shell Sort/Shell Sort.playground/contents.xcplayground b/Shell Sort/Shell Sort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Shell Sort/Shell Sort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From 1df06b2a962c63e44cf90aae513c149511d69a19 Mon Sep 17 00:00:00 2001
From: "Carlos A. King" <carlos.king70@gmail.com>
Date: Sat, 26 Aug 2017 22:55:08 -0400
Subject: [PATCH 1205/1679] Update README.markdown

---
 Shell Sort/README.markdown | 18 ++----------------
 1 file changed, 2 insertions(+), 16 deletions(-)

diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index c21c29685..72375e51b 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -117,24 +117,10 @@ Here is an implementation of Shell Sort in Swift:
 var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
 
 public func shellSort(_ list: inout [Int]) {
-    
     var sublistCount = list.count / 2
-   
     while sublistCount > 0 {
-        
-        for index in 0..<list.count {
-           
-            guard index + sublistCount < list.count else { break }
-            
-            if list[index] > list[index + sublistCount] {
-                swap(&list[index], &list[index + sublistCount])
-            }
-            
-            guard sublistCount == 1 && index > 0 else { continue }
-            
-            if list[index - 1] > list[index] {
-                swap(&list[index - 1], &list[index])
-            }
+        for pos in 0..<sublistCount {
+            insertionSort(&list, start: pos, gap: sublistCount)
         }
         sublistCount = sublistCount / 2
     }

From da7b056a139cff811a607dff953d3e51718fc3ed Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 18:31:49 -0700
Subject: [PATCH 1206/1679] [Bug] Fix build error

---
 .travis.yml                                   |  2 +-
 Quicksort/Tests/QuicksortTests.swift          |  7 ++++++
 .../project.pbxproj                           | 22 ++++++++++---------
 .../contents.xcworkspacedata                  |  2 +-
 .../xcschemes/Tests-Quicksort.xcscheme}       |  6 ++---
 .../contents.xcworkspacedata                  |  3 ---
 6 files changed, 24 insertions(+), 18 deletions(-)
 rename Quicksort/Tests/{Tests(quicksort).xcodeproj => Tests-Quicksort.xcodeproj}/project.pbxproj (93%)
 rename Quicksort/Tests/{Tests(quicksort).xcodeproj => Tests-Quicksort.xcodeproj}/project.xcworkspace/contents.xcworkspacedata (50%)
 rename Quicksort/Tests/{Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme => Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme} (90%)

diff --git a/.travis.yml b/.travis.yml
index 6efcbd42b..244b8819d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -32,7 +32,7 @@ script:
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests(quicksort).xcodeproj -scheme Tests(quicksort)
+- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Tests-Quicksort
 - xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Quicksort/Tests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
index c8d9a62e6..0a8f1a2a8 100644
--- a/Quicksort/Tests/QuicksortTests.swift
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -1,6 +1,13 @@
 import XCTest
 
 class QuicksortTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testQuicksort() {
     checkSortAlgorithm(quicksort)
   }
diff --git a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
similarity index 93%
rename from Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
rename to Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
index 70deb0c74..c1b14e727 100644
--- a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
@@ -13,7 +13,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Tests(quicksort).xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC801C779D720067B71D /* Tests-Quicksort.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Tests-Quicksort.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3E51C77A4CA003CECC7 /* Quicksort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Quicksort.swift; path = ../Quicksort.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3E71C77A4D0003CECC7 /* QuicksortTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = QuicksortTests.swift; sourceTree = SOURCE_ROOT; };
@@ -42,7 +42,7 @@
 		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */,
+				7B2BBC801C779D720067B71D /* Tests-Quicksort.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -62,9 +62,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* Tests(quicksort) */ = {
+		7B2BBC7F1C779D720067B71D /* Tests-Quicksort */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests-Quicksort" */;
 			buildPhases = (
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
@@ -74,9 +74,9 @@
 			);
 			dependencies = (
 			);
-			name = "Tests(quicksort)";
+			name = "Tests-Quicksort";
 			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */;
+			productReference = 7B2BBC801C779D720067B71D /* Tests-Quicksort.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -95,7 +95,7 @@
 					};
 				};
 			};
-			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests-Quicksort" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -108,7 +108,7 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				7B2BBC7F1C779D720067B71D /* Tests(quicksort) */,
+				7B2BBC7F1C779D720067B71D /* Tests-Quicksort */,
 			);
 		};
 /* End PBXProject section */
@@ -187,6 +187,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -233,6 +234,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -265,7 +267,7 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests-Quicksort" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC871C779D720067B71D /* Debug */,
@@ -274,7 +276,7 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests-Quicksort" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC8D1C779D720067B71D /* Debug */,
diff --git a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 50%
rename from Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Quicksort/Tests/Tests-Quicksort.xcodeproj/project.xcworkspace/contents.xcworkspacedata
index 6c0ea8493..c948249d9 100644
--- a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -2,6 +2,6 @@
 <Workspace
    version = "1.0">
    <FileRef
-      location = "self:Tests.xcodeproj">
+      location = "self:/Users/kaichen/src/swift-algorithm-club/Quicksort/Tests/Tests-Quicksort.xcodeproj">
    </FileRef>
 </Workspace>
diff --git a/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
similarity index 90%
rename from Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
rename to Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
index ac3eafc78..5b67c6f70 100644
--- a/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
@@ -18,9 +18,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests(quicksort).xctest"
-               BlueprintName = "Tests(quicksort)"
-               ReferencedContainer = "container:Tests(quicksort).xcodeproj">
+               BuildableName = "Tests-Quicksort.xctest"
+               BlueprintName = "Tests-Quicksort"
+               ReferencedContainer = "container:Tests-Quicksort.xcodeproj">
             </BuildableReference>
          </TestableReference>
       </Testables>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7fd89d5f2..e1b09e0b2 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1841,9 +1841,6 @@
          <FileRef
             location = "group:SortingTestHelpers.swift">
          </FileRef>
-         <FileRef
-            location = "group:/Users/danielstokowski/Documents/GitHub/swift-algorithm-club/Quicksort/Tests/Tests(quicksort).xcodeproj">
-         </FileRef>
       </Group>
    </Group>
    <Group

From a5cf6b71c4dab7f6e1dfbf8c28687eb8b0b563f3 Mon Sep 17 00:00:00 2001
From: Mac Bellingrath <mbellingrath@weddingwire.com>
Date: Tue, 29 Aug 2017 09:19:42 -0400
Subject: [PATCH 1207/1679] removes redundant case let ? statements from
 workspace

---
 Binary Search Tree/README.markdown                   | 12 ++++++------
 .../Sources/BinarySearchTree.swift                   | 12 ++++++------
 .../LRUCache.playground/Sources/LinkedList.swift     |  4 ++--
 Linked List/LinkedList.swift                         |  4 ++--
 Linked List/README.markdown                          |  6 +++---
 .../Sources/ThreadedBinaryTree.swift                 |  8 ++++----
 6 files changed, 23 insertions(+), 23 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 80c2df7df..340a58655 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -267,7 +267,7 @@ Searching is a recursive process, but you can also implement it with a simple lo
 ```swift
   public func search(value: T) -> BinarySearchTree? {
     var node: BinarySearchTree? = self
-    while case let n? = node {
+    while let n = node {
       if value < n.value {
         node = n.left
       } else if value > n.value {
@@ -391,7 +391,7 @@ We also need a function that returns the minimum and maximum of a node:
 ```swift
   public func minimum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.left {
+    while let next = node.left {
       node = next
     }
     return node
@@ -399,7 +399,7 @@ We also need a function that returns the minimum and maximum of a node:
 
   public func maximum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.right {
+    while let next = node.right {
       node = next
     }
     return node
@@ -471,7 +471,7 @@ You can also calculate the *depth* of a node, which is the distance to the root.
   public func depth() -> Int {
     var node = self
     var edges = 0
-    while case let parent? = node.parent {
+    while let parent = node.parent {
       node = parent
       edges += 1
     }
@@ -503,7 +503,7 @@ The `predecessor()` function returns the node whose value precedes the current v
       return left.maximum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value < value { return parent }
         node = parent
       }
@@ -524,7 +524,7 @@ The code for `successor()` works the same way but mirrored:
       return right.minimum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value > value { return parent }
         node = parent
       }
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 8a126e950..34ade3896 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -155,7 +155,7 @@ extension BinarySearchTree {
   */
   public func search(value: T) -> BinarySearchTree? {
     var node: BinarySearchTree? = self
-    while case let n? = node {
+    while let n = node {
       if value < n.value {
         node = n.left
       } else if value > n.value {
@@ -189,7 +189,7 @@ extension BinarySearchTree {
   */
   public func minimum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.left {
+    while let next = node.left {
       node = next
     }
     return node
@@ -200,7 +200,7 @@ extension BinarySearchTree {
   */
   public func maximum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.right {
+    while let next = node.right {
       node = next
     }
     return node
@@ -213,7 +213,7 @@ extension BinarySearchTree {
   public func depth() -> Int {
     var node = self
     var edges = 0
-    while case let parent? = node.parent {
+    while let parent = node.parent {
       node = parent
       edges += 1
     }
@@ -240,7 +240,7 @@ extension BinarySearchTree {
       return left.maximum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value < value { return parent }
         node = parent
       }
@@ -256,7 +256,7 @@ extension BinarySearchTree {
       return right.minimum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value > value { return parent }
         node = parent
       }
diff --git a/LRU Cache/LRUCache.playground/Sources/LinkedList.swift b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift
index 94e978c07..a5594eb31 100755
--- a/LRU Cache/LRUCache.playground/Sources/LinkedList.swift	
+++ b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift	
@@ -26,7 +26,7 @@ public final class LinkedList<T> {
 
     public var last: Node? {
         if var node = head {
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
             }
             return node
@@ -38,7 +38,7 @@ public final class LinkedList<T> {
     public var count: Int {
         if var node = head {
             var c = 1
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
                 c += 1
             }
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 94e978c07..a5594eb31 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -26,7 +26,7 @@ public final class LinkedList<T> {
 
     public var last: Node? {
         if var node = head {
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
             }
             return node
@@ -38,7 +38,7 @@ public final class LinkedList<T> {
     public var count: Int {
         if var node = head {
             var c = 1
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
                 c += 1
             }
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 9aaecc206..240d3fbba 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -109,7 +109,7 @@ Let's also add a property that gives you the last node in the list. This is wher
 ```swift
   public var last: Node? {
     if var node = head {
-      while case let next? = node.next {
+      while let next = node.next {
         node = next
       }
       return node
@@ -121,7 +121,7 @@ Let's also add a property that gives you the last node in the list. This is wher
 
 If you're new to Swift, you've probably seen `if let` but maybe not `if var`. It does the same thing -- it unwraps the `head` optional and puts the result in a new local variable named `node`. The difference is that `node` is not a constant but an actual variable, so we can change it inside the loop.
 
-The loop also does some Swift magic. The `while case let next? = node.next` bit keeps looping until `node.next` is nil. You could have written this as follows:
+The loop also does some Swift magic. The `while let next = node.next` bit keeps looping until `node.next` is nil. You could have written this as follows:
 
 ```swift
       var node: Node? = head
@@ -198,7 +198,7 @@ Let's add a method to count how many nodes are in the list. This will look very
   public var count: Int {
     if var node = head {
       var c = 1
-      while case let next? = node.next {
+      while let next = node.next {
         node = next
         c += 1
       }
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index c85f56a68..5c7671688 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -217,7 +217,7 @@ extension ThreadedBinaryTree {
   */
   public func search(_ value: T) -> ThreadedBinaryTree? {
     var node: ThreadedBinaryTree? = self
-    while case let n? = node {
+    while let n = node {
       if value < n.value {
         node = n.left
       } else if value > n.value {
@@ -252,7 +252,7 @@ extension ThreadedBinaryTree {
   */
   public func minimum() -> ThreadedBinaryTree {
     var node = self
-    while case let next? = node.left {
+    while let next = node.left {
       node = next
     }
     return node
@@ -263,7 +263,7 @@ extension ThreadedBinaryTree {
   */
   public func maximum() -> ThreadedBinaryTree {
     var node = self
-    while case let next? = node.right {
+    while let next = node.right {
       node = next
     }
     return node
@@ -276,7 +276,7 @@ extension ThreadedBinaryTree {
   public func depth() -> Int {
     var node = self
     var edges = 0
-    while case let parent? = node.parent {
+    while let parent = node.parent {
       node = parent
       edges += 1
     }

From 23770dd5dc49948534961b93c4dbdecc72d14e7c Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Mon, 4 Sep 2017 18:16:29 +0100
Subject: [PATCH 1208/1679] Add Multiset

---
 Multiset/Multiset.playground/Contents.swift   | 19 +++++
 .../Sources/Multiset.swift                    | 82 +++++++++++++++++++
 .../Multiset.playground/contents.xcplayground |  4 +
 Multiset/README.markdown                      | 12 +++
 README.markdown                               |  2 +-
 .../contents.xcworkspacedata                  | 10 +++
 6 files changed, 128 insertions(+), 1 deletion(-)
 create mode 100644 Multiset/Multiset.playground/Contents.swift
 create mode 100644 Multiset/Multiset.playground/Sources/Multiset.swift
 create mode 100644 Multiset/Multiset.playground/contents.xcplayground
 create mode 100644 Multiset/README.markdown

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
new file mode 100644
index 000000000..e99d12b01
--- /dev/null
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -0,0 +1,19 @@
+//: Playground - noun: a place where people can play
+
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
+import Cocoa
+
+var set = Multiset<String>()
+
+set.add("Foo")
+set.add("Foo")
+set.add("Bar")
+set.add("Baz")
+
+set.count
+set.count(for: "Foo")
+
+set.allItems()
\ No newline at end of file
diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
new file mode 100644
index 000000000..ac393e8dd
--- /dev/null
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -0,0 +1,82 @@
+//
+//  Multiset.swift
+//  Multiset
+//
+//  Created by Simon Whitaker on 28/08/2017.
+//
+
+import Foundation
+
+public struct Multiset<T: Hashable> {
+  fileprivate var storage: Dictionary<T, Int>
+  private var _count: Int = 0
+
+  public init() {
+    storage = Dictionary<T, Int>()
+  }
+
+  public mutating func add (_ elem: T) {
+    if let currentCount = self.storage[elem] {
+      self.storage[elem] = currentCount + 1;
+    } else {
+      self.storage[elem] = 1
+    }
+    _count += 1
+  }
+
+  public mutating func remove (_ elem: T) {
+    if let currentCount = self.storage[elem] {
+      if currentCount > 1 {
+        self.storage[elem] = currentCount - 1
+      } else {
+        self.storage.removeValue(forKey: elem)
+      }
+      _count -= 1
+    }
+  }
+
+  public func isSubSet (of superset: Multiset<T>) -> Bool {
+    for (key, count) in self.storage {
+      let supersetcount = superset.storage[key] ?? 0
+      if count > supersetcount {
+        return false
+      }
+    }
+    return true
+  }
+
+  public var count: Int {
+    get {
+      return _count
+    }
+  }
+
+  public func count(for key: T) -> Int {
+    return self.storage[key] ?? 0
+  }
+
+  public func allItems() -> [T] {
+    var result = Array<T>()
+    for (key, count) in self.storage {
+      for _ in 0 ..< count {
+        result.append(key)
+      }
+    }
+    return result
+  }
+}
+
+extension Multiset: Equatable {
+  public static func == (lhs: Multiset<T>, rhs: Multiset<T>) -> Bool {
+    if lhs.storage.count != rhs.storage.count {
+      return false
+    }
+    for (lkey, lcount) in lhs.storage {
+      let rcount = rhs.storage[lkey] ?? 0
+      if lcount != rcount {
+        return false
+      }
+    }
+    return true
+  }
+}
diff --git a/Multiset/Multiset.playground/contents.xcplayground b/Multiset/Multiset.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Multiset/Multiset.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Multiset/README.markdown b/Multiset/README.markdown
new file mode 100644
index 000000000..a6e7c7391
--- /dev/null
+++ b/Multiset/README.markdown
@@ -0,0 +1,12 @@
+# An implementation of the multiset data stucture
+
+## Usage
+
+``` swift
+var b = Multiset<Character>();
+for c in "hello".characters {
+    b.add(c)
+}
+let count = b.count // count is 5
+let lcount = b.count(for: "l") // lcount is 2
+```
diff --git a/README.markdown b/README.markdown
index 3c25a4bb3..464c6b199 100644
--- a/README.markdown
+++ b/README.markdown
@@ -172,7 +172,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Bloom Filter](Bloom%20Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash%20Set/). A set implemented using a hash table.
-- Multiset
+- [Multiset](Multiset/). A set where the number of times an element is added matters. (Also known as a bag.)
 - [Ordered Set](Ordered%20Set/). A set where the order of items matters.
 
 ### Graphs
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index e1b09e0b2..d27e01804 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1656,6 +1656,16 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "container:"
+      name = "Multiset">
+      <FileRef
+         location = "group:Multiset/Multiset.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Multiset/README.markdown">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Ordered Array"
       name = "Ordered Array">

From 8fcb7e4cd9fbf68a3d2afec558ad816428f7dcca Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Mon, 4 Sep 2017 18:22:47 +0100
Subject: [PATCH 1209/1679] Make allItems a var

---
 Multiset/Multiset.playground/Contents.swift        |  3 ++-
 .../Multiset.playground/Sources/Multiset.swift     | 14 ++++++++------
 2 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index e99d12b01..59abb7f30 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -16,4 +16,5 @@ set.add("Baz")
 set.count
 set.count(for: "Foo")
 
-set.allItems()
\ No newline at end of file
+set.allItems
+
diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index ac393e8dd..32bc0db92 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -55,14 +55,16 @@ public struct Multiset<T: Hashable> {
     return self.storage[key] ?? 0
   }
 
-  public func allItems() -> [T] {
-    var result = Array<T>()
-    for (key, count) in self.storage {
-      for _ in 0 ..< count {
-        result.append(key)
+  public var allItems: [T] {
+    get {
+      var result = Array<T>()
+      for (key, count) in self.storage {
+        for _ in 0 ..< count {
+          result.append(key)
+        }
       }
+      return result
     }
-    return result
   }
 }
 

From 4fbe62b0f0511b9c7a7f2c250d57c962d532ca8b Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Mon, 4 Sep 2017 18:38:40 +0100
Subject: [PATCH 1210/1679] Adopt Ray Wenderlich Swift coding style

https://github.com/raywenderlich/swift-style-guide
---
 .../Sources/Multiset.swift                    | 53 +++++++++----------
 1 file changed, 25 insertions(+), 28 deletions(-)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index 32bc0db92..67a8851c6 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -7,36 +7,36 @@
 
 import Foundation
 
-public struct Multiset<T: Hashable> {
-  fileprivate var storage: Dictionary<T, Int>
-  private var _count: Int = 0
+public struct Multiset<Element: Hashable> {
+  fileprivate var storage: [Element: Int]
+  private var _count = 0
 
   public init() {
-    storage = Dictionary<T, Int>()
+    storage = [:]
   }
 
-  public mutating func add (_ elem: T) {
-    if let currentCount = self.storage[elem] {
-      self.storage[elem] = currentCount + 1;
+  public mutating func add (_ elem: Element) {
+    if let currentCount = storage[elem] {
+      storage[elem] = currentCount + 1;
     } else {
-      self.storage[elem] = 1
+      storage[elem] = 1
     }
     _count += 1
   }
 
-  public mutating func remove (_ elem: T) {
-    if let currentCount = self.storage[elem] {
+  public mutating func remove (_ elem: Element) {
+    if let currentCount = storage[elem] {
       if currentCount > 1 {
-        self.storage[elem] = currentCount - 1
+        storage[elem] = currentCount - 1
       } else {
-        self.storage.removeValue(forKey: elem)
+        storage.removeValue(forKey: elem)
       }
       _count -= 1
     }
   }
 
-  public func isSubSet (of superset: Multiset<T>) -> Bool {
-    for (key, count) in self.storage {
+  public func isSubSet (of superset: Multiset<Element>) -> Bool {
+    for (key, count) in storage {
       let supersetcount = superset.storage[key] ?? 0
       if count > supersetcount {
         return false
@@ -46,30 +46,27 @@ public struct Multiset<T: Hashable> {
   }
 
   public var count: Int {
-    get {
-      return _count
-    }
+    return _count
   }
 
-  public func count(for key: T) -> Int {
-    return self.storage[key] ?? 0
+  public func count(for key: Element) -> Int {
+    return storage[key] ?? 0
   }
 
-  public var allItems: [T] {
-    get {
-      var result = Array<T>()
-      for (key, count) in self.storage {
-        for _ in 0 ..< count {
-          result.append(key)
-        }
+  public var allItems: [Element] {
+    var result = Array<Element>()
+    for (key, count) in storage {
+      for _ in 0 ..< count {
+        result.append(key)
       }
-      return result
     }
+    return result
   }
 }
 
+// MARK: - Equatable
 extension Multiset: Equatable {
-  public static func == (lhs: Multiset<T>, rhs: Multiset<T>) -> Bool {
+  public static func == (lhs: Multiset<Element>, rhs: Multiset<Element>) -> Bool {
     if lhs.storage.count != rhs.storage.count {
       return false
     }

From 6fda1b763408c4ba35977e3f8f9cfea28d96802d Mon Sep 17 00:00:00 2001
From: Simon Whitaker <sw@netcetera.org>
Date: Mon, 4 Sep 2017 21:41:09 +0100
Subject: [PATCH 1211/1679] Add isSubSet examples

---
 Multiset/Multiset.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index 59abb7f30..e9c64a74b 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -18,3 +18,9 @@ set.count(for: "Foo")
 
 set.allItems
 
+var set2 = Multiset<String>()
+set2.add("Foo")
+set2.add("Foo")
+
+set2.isSubSet(of: set) // true
+set.isSubSet(of: set2) // false

From 0490426d16ca4a52e798674f873a36d5dd7332cf Mon Sep 17 00:00:00 2001
From: Simon Whitaker <sw@netcetera.org>
Date: Mon, 4 Sep 2017 21:41:52 +0100
Subject: [PATCH 1212/1679] Make count type UInt

---
 Multiset/Multiset.playground/Sources/Multiset.swift | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index 67a8851c6..b4d309e24 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -8,8 +8,8 @@
 import Foundation
 
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: Int]
-  private var _count = 0
+  fileprivate var storage: [Element: UInt]
+  private var _count: UInt = 0
 
   public init() {
     storage = [:]
@@ -45,16 +45,16 @@ public struct Multiset<Element: Hashable> {
     return true
   }
 
-  public var count: Int {
+  public var count: UInt {
     return _count
   }
 
-  public func count(for key: Element) -> Int {
+  public func count(for key: Element) -> UInt {
     return storage[key] ?? 0
   }
 
   public var allItems: [Element] {
-    var result = Array<Element>()
+    var result = [Element]()
     for (key, count) in storage {
       for _ in 0 ..< count {
         result.append(key)

From d5c14d3735882e8ee3ca46696ec6d30757a0bf79 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <sw@netcetera.org>
Date: Mon, 4 Sep 2017 21:42:02 +0100
Subject: [PATCH 1213/1679] Improve README

---
 Multiset/README.markdown | 91 ++++++++++++++++++++++++++++++++++++----
 1 file changed, 84 insertions(+), 7 deletions(-)

diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index a6e7c7391..eb28e3eea 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -1,12 +1,89 @@
-# An implementation of the multiset data stucture
+# Multiset
 
-## Usage
+A multiset (also known as a bag) is a data structure similar to a regular set, but it can store multiple instances of the same element.
+
+The following all represent the same *set*, but do not represent the same *multiset*.
+
+```
+[1, 3, 2]
+[1, 3, 2, 2]
+```
+
+In this multiset implementation, ordering is unimportant. So these two multisets are identical:
+
+```
+[1, 2, 2]
+[2, 1, 2]
+```
+
+Typical operations on a multiset are:
+
+- Add an element
+- Remove an element
+- Get the count for an element (the number of times it's been added)
+- Get the count for the whole set (the number of items that have been added)
+- Check whether it is a subset of another multiset
+
+## Implementation
+
+Under the hood, this implementation of Multiset uses a dictionary to store a mapping of elements to the number of times they've been added.
+
+Here's the essence of it:
+
+``` swift
+public struct Multiset<Element: Hashable> {
+  fileprivate var storage: [Element: UInt]
+  
+  public init() {
+    storage = [:]
+  }
+```
+
+And here's how you'd use this class to create a multiset of strings:
+
+``` swift
+var set = Multiset<String>()
+```
+
+Adding an element is a case of incrementing the counter for that element, or setting it to 1 if it doesn't already exist:
+
+``` swift
+public mutating func add (_ elem: Element) {
+  if let currentCount = storage[elem] {
+    storage[elem] = currentCount + 1;
+  } else {
+    storage[elem] = 1
+  }
+}
+```
+
+Here's how you'd use this method to add to the set we created earlier:
+
+```swift
+set.add("foo")
+set.add("foo") 
+```
+
+Our set now contains two elements, both the string "foo".
+
+Removing an element works much the same way as adding; decrement the counter for the element, or remove it from the underlying dictionary if its value is 1 before removal.
+
+``` swift
+public mutating func remove (_ elem: Element) {
+  if let currentCount = storage[elem] {
+    if currentCount > 1 {
+      storage[elem] = currentCount - 1
+    } else {
+      storage.removeValue(forKey: elem)
+    }
+  }
+}
+```
+
+Getting the count for an item is simple: we just return the value for the given item in the internal dictionary.
 
 ``` swift
-var b = Multiset<Character>();
-for c in "hello".characters {
-    b.add(c)
+public func count(for key: Element) -> UInt {
+  return storage[key] ?? 0
 }
-let count = b.count // count is 5
-let lcount = b.count(for: "l") // lcount is 2
 ```

From 6c7eb0c3f1936dfe782da74a4ab325eed5ac92cd Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 06:19:31 +0100
Subject: [PATCH 1214/1679] Address review comments

---
 .../Sources/Multiset.swift                    | 22 +++++--------------
 Multiset/README.markdown                      |  2 ++
 2 files changed, 8 insertions(+), 16 deletions(-)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index b4d309e24..71bc78fa9 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -8,20 +8,14 @@
 import Foundation
 
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: UInt]
-  private var _count: UInt = 0
+  private var storage: [Element: UInt] = [:]
+  public private(set) var count: UInt = 0
 
-  public init() {
-    storage = [:]
-  }
+  public init() {}
 
   public mutating func add (_ elem: Element) {
-    if let currentCount = storage[elem] {
-      storage[elem] = currentCount + 1;
-    } else {
-      storage[elem] = 1
-    }
-    _count += 1
+    storage[elem, default: 0] += 1
+    count += 1
   }
 
   public mutating func remove (_ elem: Element) {
@@ -31,7 +25,7 @@ public struct Multiset<Element: Hashable> {
       } else {
         storage.removeValue(forKey: elem)
       }
-      _count -= 1
+      count -= 1
     }
   }
 
@@ -45,10 +39,6 @@ public struct Multiset<Element: Hashable> {
     return true
   }
 
-  public var count: UInt {
-    return _count
-  }
-
   public func count(for key: Element) -> UInt {
     return storage[key] ?? 0
   }
diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index eb28e3eea..fd72d269c 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -87,3 +87,5 @@ public func count(for key: Element) -> UInt {
   return storage[key] ?? 0
 }
 ```
+
+*Written for the Swift Algorithm Club by Simon Whitaker*

From ecaf749467a2966474ab94bca7bf8e386fb53f4c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 4 Sep 2017 22:36:45 -0700
Subject: [PATCH 1215/1679] Fixed readme to match code.

---
 Multiset/README.markdown | 12 +++---------
 1 file changed, 3 insertions(+), 9 deletions(-)

diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index fd72d269c..85538d870 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -32,11 +32,9 @@ Here's the essence of it:
 
 ``` swift
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: UInt]
+  public private(set) var storage: [Element: UInt] = [:]
   
-  public init() {
-    storage = [:]
-  }
+  public init() {}
 ```
 
 And here's how you'd use this class to create a multiset of strings:
@@ -49,11 +47,7 @@ Adding an element is a case of incrementing the counter for that element, or set
 
 ``` swift
 public mutating func add (_ elem: Element) {
-  if let currentCount = storage[elem] {
-    storage[elem] = currentCount + 1;
-  } else {
-    storage[elem] = 1
-  }
+  storage[elem, default: 0] += 1
 }
 ```
 

From fb523d64407e9f2e51cec1dbf48aaf4634255c88 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 08:03:57 +0100
Subject: [PATCH 1216/1679] Add ctor for instantiating with a collection of
 Hashables

---
 Multiset/Multiset.playground/Contents.swift   |  5 +++
 .../Sources/Multiset.swift                    | 24 +++++++----
 Multiset/README.markdown                      | 43 ++++++++++++-------
 3 files changed, 47 insertions(+), 25 deletions(-)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index e9c64a74b..f8b05d2b0 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -24,3 +24,8 @@ set2.add("Foo")
 
 set2.isSubSet(of: set) // true
 set.isSubSet(of: set2) // false
+
+var cacti = Multiset<Character>("cacti")
+var tactical = Multiset<Character>("tactical")
+cacti.isSubSet(of: tactical) // true
+tactical.isSubSet(of: cacti) // false
diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index 71bc78fa9..f77983f8c 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -7,18 +7,24 @@
 
 import Foundation
 
-public struct Multiset<Element: Hashable> {
-  private var storage: [Element: UInt] = [:]
+public struct Multiset<T: Hashable> {
+  private var storage: [T: UInt] = [:]
   public private(set) var count: UInt = 0
 
   public init() {}
 
-  public mutating func add (_ elem: Element) {
+  public init<C: Collection>(_ collection: C) where C.Element == T {
+    for element in collection {
+      self.add(element)
+    }
+  }
+
+  public mutating func add (_ elem: T) {
     storage[elem, default: 0] += 1
     count += 1
   }
 
-  public mutating func remove (_ elem: Element) {
+  public mutating func remove (_ elem: T) {
     if let currentCount = storage[elem] {
       if currentCount > 1 {
         storage[elem] = currentCount - 1
@@ -29,7 +35,7 @@ public struct Multiset<Element: Hashable> {
     }
   }
 
-  public func isSubSet (of superset: Multiset<Element>) -> Bool {
+  public func isSubSet (of superset: Multiset<T>) -> Bool {
     for (key, count) in storage {
       let supersetcount = superset.storage[key] ?? 0
       if count > supersetcount {
@@ -39,12 +45,12 @@ public struct Multiset<Element: Hashable> {
     return true
   }
 
-  public func count(for key: Element) -> UInt {
+  public func count(for key: T) -> UInt {
     return storage[key] ?? 0
   }
 
-  public var allItems: [Element] {
-    var result = [Element]()
+  public var allItems: [T] {
+    var result = [T]()
     for (key, count) in storage {
       for _ in 0 ..< count {
         result.append(key)
@@ -56,7 +62,7 @@ public struct Multiset<Element: Hashable> {
 
 // MARK: - Equatable
 extension Multiset: Equatable {
-  public static func == (lhs: Multiset<Element>, rhs: Multiset<Element>) -> Bool {
+  public static func == (lhs: Multiset<T>, rhs: Multiset<T>) -> Bool {
     if lhs.storage.count != rhs.storage.count {
       return false
     }
diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index fd72d269c..6296a1538 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -2,20 +2,30 @@
 
 A multiset (also known as a bag) is a data structure similar to a regular set, but it can store multiple instances of the same element.
 
-The following all represent the same *set*, but do not represent the same *multiset*.
+For example, if I added the elements 1, 2, 2 to a regular set, the set would only contain two items, since adding 2 a second time has no effect.
 
 ```
-[1, 3, 2]
-[1, 3, 2, 2]
+var set = Set<Int>()
+set.add(1) // set is now [1]
+set.add(2) // set is now [1, 2]
+set.add(2) // set is still [1, 2]
 ```
 
-In this multiset implementation, ordering is unimportant. So these two multisets are identical:
+By comparison, after adding the elements 1, 2, 2 to a multiset, it would contain three items.
 
 ```
-[1, 2, 2]
-[2, 1, 2]
+var set = Multiset<Int>()
+set.add(1) // set is now [1]
+set.add(2) // set is now [1, 2]
+set.add(2) // set is now [1, 2, 2]
 ```
 
+You might be thinking that this looks an awful lot like an array. So why would you use a multiset? Let's consider the differences between the two…
+
+- Ordering: arrays maintain the order of items added to them, multisets do not
+- Testing for membership: testing whether an element is a member of the collection is O(N) for arrays, O(1) for multisets.
+- Testing for subset: testing whether collection X is a subset of collection Y is a simple operation for a multiset, but complex for arrays
+
 Typical operations on a multiset are:
 
 - Add an element
@@ -24,6 +34,14 @@ Typical operations on a multiset are:
 - Get the count for the whole set (the number of items that have been added)
 - Check whether it is a subset of another multiset
 
+One real-world use of multisets is to determine whether one string is a partial anagram of another. For example, the word "cacti" is a partial anagrams of "tactical". (In other words, I can rearrange the letters of "tactical" to make "cacti", with some letters left over.)
+
+``` swift
+var cacti = Multiset<Character>("cacti")
+var tactical = Multiset<Character>("tactical")
+cacti.isSubSet(of: tactical) // true!
+```
+
 ## Implementation
 
 Under the hood, this implementation of Multiset uses a dictionary to store a mapping of elements to the number of times they've been added.
@@ -32,11 +50,7 @@ Here's the essence of it:
 
 ``` swift
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: UInt]
-  
-  public init() {
-    storage = [:]
-  }
+  private var storage: [Element: UInt] = [:]
 ```
 
 And here's how you'd use this class to create a multiset of strings:
@@ -49,11 +63,7 @@ Adding an element is a case of incrementing the counter for that element, or set
 
 ``` swift
 public mutating func add (_ elem: Element) {
-  if let currentCount = storage[elem] {
-    storage[elem] = currentCount + 1;
-  } else {
-    storage[elem] = 1
-  }
+  storage[elem, default: 0] += 1
 }
 ```
 
@@ -62,6 +72,7 @@ Here's how you'd use this method to add to the set we created earlier:
 ```swift
 set.add("foo")
 set.add("foo") 
+set.allItems // returns ["foo", "foo"]
 ```
 
 Our set now contains two elements, both the string "foo".

From b4533bffdf2537773deb2c0edbba6a69c283fdf2 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 19:34:18 +0100
Subject: [PATCH 1217/1679] Implement ExpressibleByArrayLiteral protocol

---
 Multiset/Multiset.playground/Sources/Multiset.swift | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index f77983f8c..5dba5d32c 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -75,3 +75,10 @@ extension Multiset: Equatable {
     return true
   }
 }
+
+// MARK: - ExpressibleByArrayLiteral
+extension Multiset: ExpressibleByArrayLiteral {
+  public init(arrayLiteral elements: T...) {
+    self.init(elements)
+  }
+}

From e7bce0ddcc03ac933f69f18b1115bb242cd2ddd3 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 19:34:47 +0100
Subject: [PATCH 1218/1679] Add more toys to the playground

---
 Multiset/Multiset.playground/Contents.swift | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index f8b05d2b0..b4f64ee1f 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -25,7 +25,18 @@ set2.add("Foo")
 set2.isSubSet(of: set) // true
 set.isSubSet(of: set2) // false
 
+// Convenience constructor: pass a Collection of Hashables to the constructor
 var cacti = Multiset<Character>("cacti")
+cacti.allItems
 var tactical = Multiset<Character>("tactical")
 cacti.isSubSet(of: tactical) // true
 tactical.isSubSet(of: cacti) // false
+
+// Test ExpressibleByArrayLiteral protocol
+let set3: Multiset<String> = ["foo", "bar"]
+set3.count(for: "foo")
+
+// Test Equatable protocol
+let set4 = Multiset<String>(set3.allItems)
+set4 == set3 // true
+set4 == set // false

From 10d90da2d16a46bb5183448be7c39a5720d50c23 Mon Sep 17 00:00:00 2001
From: Harry Twan <gua@desgard.com>
Date: Wed, 6 Sep 2017 15:40:57 +0800
Subject: [PATCH 1219/1679] Update the Segment Tree: add Lazy Propagation for
 interval update

Signed-off-by: Harry Twan <gua@desgard.com>
---
 .../LazyPropagation/Images/Segment-tree.png   | Bin 0 -> 34257 bytes
 .../LazyPropagation/Images/lazy-sample-2.png  | Bin 0 -> 80206 bytes
 .../LazyPropagation/Images/pushUp.png         | Bin 0 -> 30566 bytes
 .../LazyPropagation/Images/pushdown.png       | Bin 0 -> 32410 bytes
 .../LazyPropagation.playground/Contents.swift | 147 ++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Segment Tree/LazyPropagation/README.markdown  | 269 ++++++++++++++++++
 8 files changed, 427 insertions(+)
 create mode 100644 Segment Tree/LazyPropagation/Images/Segment-tree.png
 create mode 100644 Segment Tree/LazyPropagation/Images/lazy-sample-2.png
 create mode 100644 Segment Tree/LazyPropagation/Images/pushUp.png
 create mode 100644 Segment Tree/LazyPropagation/Images/pushdown.png
 create mode 100644 Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
 create mode 100644 Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground
 create mode 100644 Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Segment Tree/LazyPropagation/README.markdown

diff --git a/Segment Tree/LazyPropagation/Images/Segment-tree.png b/Segment Tree/LazyPropagation/Images/Segment-tree.png
new file mode 100644
index 0000000000000000000000000000000000000000..283bcca5d0a356323acf277f4266ae08c4eb09fd
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diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
new file mode 100644
index 000000000..d576be254
--- /dev/null
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -0,0 +1,147 @@
+//: Playground - noun: a place where people can play
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+//protocol SegmentTree<T> {
+//    func pushUp(lson: T, rson: T)
+//    func pushDown(round: Int, lson: T, rson: T)
+//}
+
+public class LazySegmentTree {
+    
+    private var value: Int
+    
+    private var leftBound: Int
+    
+    private var rightBound: Int
+    
+    private var leftChild: LazySegmentTree?
+    
+    private var rightChild: LazySegmentTree?
+    
+    // Interval Update Lazy Element
+    private var lazyValue: Int
+    
+    // MARK: - Push Up Operation
+    // Description: 这里是 push up 操作，用来对 Segment Tree 向上更新
+    private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
+        self.value = lson.value + rson.value
+    }
+    
+    // MARK: - Push Down Operation
+    // Description: 这里是 push down 操作，用来对 Segment Tree 向下更新
+    // Open Interface Function: 此处应该开放方法对齐进行 Override
+    private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
+        if lazyValue != 0 {
+            lson.lazyValue += lazyValue
+            rson.lazyValue += lazyValue
+            lson.value += lazyValue * (round - (round >> 1))
+            rson.value += lazyValue * (round >> 1)
+            lazyValue = 0
+        }
+    }
+    
+    public init(array: [Int], leftBound: Int, rightBound: Int) {
+        self.leftBound = leftBound
+        self.rightBound = rightBound
+        self.value = 0
+        self.lazyValue = 0
+        
+        if leftBound == rightBound {
+            value = array[leftBound]
+            return
+        }
+        
+        let middle = (leftBound + rightBound) / 2
+        leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
+        rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
+        pushUp(lson: leftChild!, rson: rightChild!)
+        
+    }
+    
+    public convenience init(array: [Int]) {
+        self.init(array: array, leftBound: 0, rightBound: array.count - 1)
+    }
+    
+    public func query(leftBound: Int, rightBound: Int) -> Int {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            return value
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result: Int = 0
+        
+        if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
+        if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
+        
+        return result
+    }
+    
+    // MARK: - One Item Update
+    public func update(index: Int, incremental: Int) {
+        if self.leftBound == self.rightBound {
+            self.value += incremental
+            return
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        
+        let middle = (self.leftBound + self.rightBound) / 2
+        
+        if index <= middle { leftChild.update(index: index, incremental: incremental) }
+        else { rightChild.update(index: index, incremental: incremental) }
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+    
+    // MARK: - Interval Item Update
+    public func update(leftBound: Int, rightBound: Int, incremental: Int) {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            self.lazyValue += incremental
+            self.value += incremental * (self.rightBound - self.leftBound + 1)
+            return 
+        }
+        
+        guard let leftChild = leftChild else { fatalError() }
+        guard let rightChild = rightChild else { fatalError() }
+        
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        
+        let middle = (self.leftBound + self.rightBound) / 2
+        
+        if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+    
+}
+
+let array = [1, 2, 3, 4, 1, 3, 2]
+
+let sumSegmentTree = LazySegmentTree(array: array)
+
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 10 = 1 + 2 + 3 + 4
+sumSegmentTree.update(index: 1, incremental: 2)
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 12 = 1 + 4 + 3 + 4
+sumSegmentTree.update(leftBound: 0, rightBound: 2, incremental: 2)
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 18 = 3 + 6 + 5 + 4
+
+for index in 2 ... 5 {
+    sumSegmentTree.update(index: index, incremental: 3)
+}
+
+
+sumSegmentTree.update(leftBound: 0, rightBound: 5, incremental: 2)
+print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
+
+
+
+
+
diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground b/Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground
new file mode 100644
index 000000000..16f9952aa
--- /dev/null
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx' last-migration='0800'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata b/Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
new file mode 100644
index 000000000..49987c14e
--- /dev/null
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -0,0 +1,269 @@
+# Lazy Propagation in Segment Tree
+
+In previous implement about the Segment Tree by **Artur Antonov**, it's a strong data structure with *Generic* `<T>`. And we can pass a closure parameter `function: (T, T) -> T` to reflect the relationship between parent and child node. And in particular, Generic can solve multiple strings stitching problem. It's just like the sample in Playground:
+
+```swift
+stringSegmentTree.replaceItem(at: 0, withItem: "I")
+stringSegmentTree.replaceItem(at: 1, withItem: " like")
+stringSegmentTree.replaceItem(at: 2, withItem: " algorithms")
+stringSegmentTree.replaceItem(at: 3, withItem: " and")
+stringSegmentTree.replaceItem(at: 4, withItem: " swift")
+stringSegmentTree.replaceItem(at: 5, withItem: "!")
+print(stringSegmentTree.query(leftBound: 0, rightBound: 5))
+// "I like algorithms and swift!"
+```
+
+The use of `<T>` is so exciting. But we seldom use the Segment Tree to solve string problem instead of *Suffix Array*. And the Segment Tree is a kind of *Interval Tree* to solve the Interval Problem in mathemtics and statistics, which is a structure for storing intervals, or segments, and allows querying which of the stored segments contain a given point. A segment tree for a set *I* of n intervals uses `O(nlogn)` storage and can be built in `O(nlogn)` time. Segment trees support searching for all the intervals that contain a query point in O(log n+k), k being the number of retrieved intervals or segments.
+
+But that is common Segment Tree. By **Lazy Propagation**, we can implement to modify an interval in `O(nlogn)` time. Let's explore together in following:
+
+## `PushUp` - update to the top
+
+At first, we reference the implement of **Artur Antonov** about Segment Tree. This code contained *build*, *single update* and *interval query* three operation. The implement of *build* and *single update* operation is following:
+
+```swift
+public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
+	self.leftBound = leftBound
+	self.rightBound = rightBound
+	self.function = function
+	// ①
+	if leftBound == rightBound {
+		value = array[leftBound]
+	} 
+	// ②
+	else {
+		let middle = (leftBound + rightBound) / 2
+		leftChild = SegmentTree<T>(array: array, leftBound: leftBound, rightBound: middle, function: function)
+		rightChild = SegmentTree<T>(array: array, leftBound: middle+1, rightBound: rightBound, function: function)
+		value = function(leftChild!.value, rightChild!.value)
+	}
+}
+```
+
+In position ①, it means the current node is *leaf* because its left bound data is equal to the right. So we assign a value to it directly. In position ②, it means the current node is *parent* (which has one or more children), and we need to recursion down and update current node's data in the follow-up process.
+
+And then, we have a look for *interval query* operation:
+
+```swift
+public func query(leftBound: Int, rightBound: Int) -> T {
+	if self.leftBound == leftBound && self.rightBound == rightBound {
+		return self.value
+	}
+	guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
+	guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+	// ①
+	if leftChild.rightBound < leftBound {
+		return rightChild.query(leftBound: leftBound, rightBound: rightBound)
+	} 
+	// ②
+	else if rightChild.leftBound > rightBound {
+		return leftChild.query(leftBound: leftBound, rightBound: rightBound)
+	}
+	// ③ 
+	else {
+		let leftResult = leftChild.query(leftBound: leftBound, rightBound: leftChild.rightBound)
+		let rightResult = rightChild.query(leftBound:rightChild.leftBound, rightBound: rightBound)
+		return function(leftResult, rightResult)
+	}
+}
+```
+
+Position ① means that the left bound of current query interval is on the  right of this right bound, so recurs to right direction. Position ② is opposite of position ①, recurs to left direction. Position ③ means our check interval is included the interval we need, so recurs deeply.
+
+![pushUp](Images/pushUp.png)
+There are common part from the two parts of code above - **recurs deeply below, and update data up**. So we can decouple this operation named `func pushUp(lson: LazySegmentTree, rson: LazySegmentTree)`:
+
+```swift
+// MARK: - Push Up Operation
+private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
+    self.value = lson.value + rson.value
+}
+```
+
+(This code only describe the *Sum Segment Tree*)
+
+And then, we can update the implement before:
+
+```swift
+public init(array: [Int], leftBound: Int, rightBound: Int) {
+    self.leftBound = leftBound
+    self.rightBound = rightBound
+    self.value = 0
+    self.lazyValue = 0
+    if leftBound == rightBound {
+        value = array[leftBound]
+        return
+    }
+    let middle = (leftBound + rightBound) / 2
+    leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
+    rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
+    pushUp(lson: leftChild!, rson: rightChild!)
+}
+// MARK: - One Item Update
+public func update(index: Int, newValue: Int) {
+    if self.leftBound == self.rightBound {
+        self.value = newValue
+        return
+    }
+    guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+    guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+    let middle = (self.leftBound + self.rightBound) / 2
+    if index <= middle { leftChild.update(index: index, newValue: newValue) }
+    else { rightChild.update(index: index, newValue: newValue) }
+    pushUp(lson: leftChild, rson: rightChild)
+}
+```
+
+## `PushDown` - Lazy Propagation 
+
+You may feel that the `pushUp` is so simple. In fact, this's just to lead `pushDown` this function.
+
+Before this, I want to talk about the topic about **interval operation**. The interval operation is a way to update all elements of a continuous subset. But these isn't in the version of **Artur Antonov**. You might disdain with this, because it's solved with a `for` loop:
+
+```swift
+// Sample: update the elements with subscript [2, 5] 
+for index in 2 ... 5 {
+    sumSegmentTree.update(index: index, incremental: 3)
+}
+```
+
+It is a `O(n)` time operation, which make the interval operation uses `O(nlogn)` time to update these elements. We need a `O(logn)` way to maintain the elegance of Segment Tree. 
+
+ Check the data structure of Segment Tree again:
+ 
+ ![Segment-tree](Images/Segment-tree.png)
+We only catch the root node in programming. If we want to explore the bottom of the tree, and use `pushUp` to update every node, the task will be reached. So it asked us to traverse the tree, that spent `O(n)` time to do this with any way. This can't conform our expectations.  
+
+Then we started to think about `pushDown` to update down from the root. **After we update the parent, the data continued to distributed to its children according to law.** But it still need `O(n)` time to do this. Keep thinking, we **only update the parent, and to update the children when `query` time**. Yeah, that's the key of **lazy propagation**. Because the recursing direct of the `query` and `update interval` is same. So we got it! 😁 Let's check this sample:
+
+![lazy-sample-2](Images/lazy-sample-2.png)
+`update` make the subscript 1...3 elements plus 2, so we make the 1st node in 2 depth and 3rd in 3 depth get a *lazy mark*, which means these node need to be updated. And we shouldn't add a *lazy mark* for root node, because it was updated before the `pushDown` in the first recursing. 
+
+In `query` operation, we accord to the original method to recurs the tree, and find the 1st node held *lazy mark* in 2 depth, so to update it. It's the same situation about the 1st node in 3 depth.
+
+Do you understand the **lazy propagation**? **In short, we only update the wide range node data and add it a lazy mark. Then they will be update when we need to query them.** And the *Update Down* operation is the function of `pushDown`.
+
+This is the complete implementation about the Sum Segment Tree with interval update operation:
+
+```swift
+public class LazySegmentTree {
+    private var value: Int
+    private var leftBound: Int
+    private var rightBound: Int
+    private var leftChild: LazySegmentTree?
+    private var rightChild: LazySegmentTree?
+    // Interval Update Lazy Element
+    private var lazyValue: Int
+    // MARK: - Push Up Operation
+    private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
+        self.value = lson.value + rson.value
+    }
+    // MARK: - Push Down Operation
+    private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
+        if lazyValue != 0 {
+            lson.lazyValue += lazyValue
+            rson.lazyValue += lazyValue
+            lson.value += lazyValue * (round - (round >> 1))
+            rson.value += lazyValue * (round >> 1)
+            lazyValue = 0
+        }
+    }
+    public init(array: [Int], leftBound: Int, rightBound: Int) {
+        self.leftBound = leftBound
+        self.rightBound = rightBound
+        self.value = 0
+        self.lazyValue = 0
+        if leftBound == rightBound {
+            value = array[leftBound]
+            return
+        }
+        let middle = (leftBound + rightBound) / 2
+        leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
+        rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
+        pushUp(lson: leftChild!, rson: rightChild!)
+    }
+    public convenience init(array: [Int]) {
+        self.init(array: array, leftBound: 0, rightBound: array.count - 1)
+    }
+    public func query(leftBound: Int, rightBound: Int) -> Int {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            return value
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result: Int = 0
+        if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
+        if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
+        return result
+    }
+    // MARK: - One Item Update
+    public func update(index: Int, incremental: Int) {
+        if self.leftBound == self.rightBound {
+            self.value += incremental
+            return
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        let middle = (self.leftBound + self.rightBound) / 2
+        if index <= middle { leftChild.update(index: index, incremental: incremental) }
+        else { rightChild.update(index: index, incremental: incremental) }
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+    // MARK: - Interval Item Update
+    public func update(leftBound: Int, rightBound: Int, incremental: Int) {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            self.lazyValue += incremental
+            self.value += incremental * (self.rightBound - self.leftBound + 1)
+            return 
+        }
+        guard let leftChild = leftChild else { fatalError() }
+        guard let rightChild = rightChild else { fatalError() }
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        let middle = (self.leftBound + self.rightBound) / 2
+        if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+}
+```
+
+Explain some sample snippets:
+
+```swift
+private var lazyValue: Int
+```
+
+Here we add a new property for Segment Tree to represent *lazy mark*. And it is a incremental value for Sum Segment Tree. If the `lazyValue` isn't equal to zero, the current node need to be updated. And its real value is equal to `value + lazyValue * (rightBound - leftBound + 1)`.
+
+```swift
+// MARK: - Push Down Operation
+private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
+    if lazyValue != 0 {
+        lson.lazyValue += lazyValue
+        rson.lazyValue += lazyValue
+        lson.value += lazyValue * (round - (round >> 1))
+        rson.value += lazyValue * (round >> 1)
+        lazyValue = 0
+    }
+}
+```
+
+![pushdown](Images/pushdown.png)
+
+At first we check whether the node needs to be updated. If the `lazyValue` isn't equal to zero, we need to `pushDown`. And the update rules are the `lazyValue * (rightBound - leftBound + 1)`. At last, reset the `lazyValue` to zero.
+
+## Conclusion
+
+This is the introduce of the Lazy Propagation in Segment Tree. You can also learn **Functional Segment Tree** to understand the Lazy Propagation deeply. In addition, I learn from the *notonlysuccess*'s code about Segment Tree described by C, this is the [link](http://www.cnblogs.com/Destiny-Gem/articles/3875243.html).
+
+In fact, the operation of Segment Tree is far more than that. It can also be used to handle problems between collections. I want to implement it with Swift in the future and make the Swift Segment Tree stronger and stronger. 😁
+
+---
+
+*Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
+
+
+
+

From 891a700361267067f0db4d9ba6b828119230edc3 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 9 Sep 2017 08:04:31 -0700
Subject: [PATCH 1220/1679] [Swift 4] Update Bit Set

---
 Bit Set/BitSet.playground/Contents.swift      |  5 ++
 .../BitSet.playground/Sources/BitSet.swift    |  4 +-
 Bit Set/BitSet.playground/timeline.xctimeline |  6 --
 Bit Set/BitSet.swift                          | 75 ++++++++++---------
 4 files changed, 45 insertions(+), 45 deletions(-)
 delete mode 100644 Bit Set/BitSet.playground/timeline.xctimeline

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index d11b36e8c..95253ea27 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
 
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index d8985bd13..59306f5a5 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -41,7 +41,7 @@ public struct BitSet {
       // Set the highest bit that's still valid.
       let mask = 1 << Word(63 - diff)
       // Subtract 1 to turn it into a mask, and add the high bit back in.
-      return mask | (mask - 1)
+      return (Word)(mask | (mask - 1))
     } else {
       return allOnes
     }
@@ -167,7 +167,7 @@ extension BitSet: Hashable {
 
 // MARK: - Bitwise operations
 
-extension BitSet: BitwiseOperations {
+extension BitSet {
   public static var allZeros: BitSet {
     return BitSet(size: 64)
   }
diff --git a/Bit Set/BitSet.playground/timeline.xctimeline b/Bit Set/BitSet.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Bit Set/BitSet.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index d8985bd13..cfe8517b5 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -1,30 +1,30 @@
 /*
-  A fixed-size sequence of n bits. Bits have indices 0 to n-1.
-*/
+ A fixed-size sequence of n bits. Bits have indices 0 to n-1.
+ */
 public struct BitSet {
   /* How many bits this object can hold. */
   private(set) public var size: Int
-
+  
   /*
-    We store the bits in a list of unsigned 64-bit integers.
-    The first entry, `words[0]`, is the least significant word.
-  */
+   We store the bits in a list of unsigned 64-bit integers.
+   The first entry, `words[0]`, is the least significant word.
+   */
   private let N = 64
   public typealias Word = UInt64
   fileprivate(set) public var words: [Word]
-
+  
   private let allOnes = ~Word()
-
+  
   /* Creates a bit set that can hold `size` bits. All bits are initially 0. */
   public init(size: Int) {
     precondition(size > 0)
     self.size = size
-
+    
     // Round up the count to the next multiple of 64.
     let n = (size + (N-1)) / N
     words = [Word](repeating: 0, count: n)
   }
-
+  
   /* Converts a bit index into an array index and a mask inside the word. */
   private func indexOf(_ i: Int) -> (Int, Word) {
     precondition(i >= 0)
@@ -33,7 +33,7 @@ public struct BitSet {
     let m = Word(i - o*N)
     return (o, 1 << m)
   }
-
+  
   /* Returns a mask that has 1s for all bits that are in the last word. */
   private func lastWordMask() -> Word {
     let diff = words.count*N - size
@@ -41,33 +41,33 @@ public struct BitSet {
       // Set the highest bit that's still valid.
       let mask = 1 << Word(63 - diff)
       // Subtract 1 to turn it into a mask, and add the high bit back in.
-      return mask | (mask - 1)
+      return (Word)(mask | (mask - 1))
     } else {
       return allOnes
     }
   }
-
+  
   /*
-    If the size is not a multiple of N, then we have to clear out the bits
-    that we're not using, or bitwise operations between two differently sized
-    BitSets will go wrong.
-  */
+   If the size is not a multiple of N, then we have to clear out the bits
+   that we're not using, or bitwise operations between two differently sized
+   BitSets will go wrong.
+   */
   fileprivate mutating func clearUnusedBits() {
     words[words.count - 1] &= lastWordMask()
   }
-
+  
   /* So you can write bitset[99] = ... */
   public subscript(i: Int) -> Bool {
     get { return isSet(i) }
     set { if newValue { set(i) } else { clear(i) } }
   }
-
+  
   /* Sets the bit at the specified index to 1. */
   public mutating func set(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] |= m
   }
-
+  
   /* Sets all the bits to 1. */
   public mutating func setAll() {
     for i in 0..<words.count {
@@ -75,37 +75,37 @@ public struct BitSet {
     }
     clearUnusedBits()
   }
-
+  
   /* Sets the bit at the specified index to 0. */
   public mutating func clear(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] &= ~m
   }
-
+  
   /* Sets all the bits to 0. */
   public mutating func clearAll() {
     for i in 0..<words.count {
       words[i] = 0
     }
   }
-
+  
   /* Changes 0 into 1 and 1 into 0. Returns the new value of the bit. */
   public mutating func flip(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     words[j] ^= m
     return (words[j] & m) != 0
   }
-
+  
   /* Determines whether the bit at the specific index is 1 (true) or 0 (false). */
   public func isSet(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     return (words[j] & m) != 0
   }
-
+  
   /*
-    Returns the number of bits that are 1. Time complexity is O(s) where s is
-    the number of 1-bits.
-  */
+   Returns the number of bits that are 1. Time complexity is O(s) where s is
+   the number of 1-bits.
+   */
   public var cardinality: Int {
     var count = 0
     for var x in words {
@@ -117,7 +117,7 @@ public struct BitSet {
     }
     return count
   }
-
+  
   /* Checks if all the bits are set. */
   public func all1() -> Bool {
     for i in 0..<words.count - 1 {
@@ -125,7 +125,7 @@ public struct BitSet {
     }
     return words[words.count - 1] == lastWordMask()
   }
-
+  
   /* Checks if any of the bits are set. */
   public func any1() -> Bool {
     for x in words {
@@ -133,7 +133,7 @@ public struct BitSet {
     }
     return false
   }
-
+  
   /* Checks if none of the bits are set. */
   public func all0() -> Bool {
     for x in words {
@@ -167,7 +167,7 @@ extension BitSet: Hashable {
 
 // MARK: - Bitwise operations
 
-extension BitSet: BitwiseOperations {
+extension BitSet {
   public static var allZeros: BitSet {
     return BitSet(size: 64)
   }
@@ -178,11 +178,11 @@ private func copyLargest(_ lhs: BitSet, _ rhs: BitSet) -> BitSet {
 }
 
 /*
-  Note: In all of these bitwise operations, lhs and rhs are allowed to have a
-  different number of bits. The new BitSet always has the larger size.
-  The extra bits that get added to the smaller BitSet are considered to be 0.
-  That will strip off the higher bits from the larger BitSet when doing &.
-*/
+ Note: In all of these bitwise operations, lhs and rhs are allowed to have a
+ different number of bits. The new BitSet always has the larger size.
+ The extra bits that get added to the smaller BitSet are considered to be 0.
+ That will strip off the higher bits from the larger BitSet when doing &.
+ */
 
 public func & (lhs: BitSet, rhs: BitSet) -> BitSet {
   let m = max(lhs.size, rhs.size)
@@ -245,3 +245,4 @@ extension BitSet: CustomStringConvertible {
     return s
   }
 }
+

From 557d208a90873cfb0fc8dcaa90a2ed2c26c3ff31 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 9 Sep 2017 08:14:39 -0700
Subject: [PATCH 1221/1679] [Swift 4] Update Dijkstra

---
 .../Dijkstra.playground/Contents.swift        |  5 ++
 .../Contents.swift                            |  6 +++
 .../timeline.xctimeline                       |  6 ---
 .../contents.xcworkspacedata                  | 53 +++++++++++++++++++
 4 files changed, 64 insertions(+), 6 deletions(-)
 delete mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 7c7f1a4b0..1cd1254b1 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,6 +1,11 @@
 //: Playground - noun: a place where people can play
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 var vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
index e4b3e6732..8e61ef49b 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
@@ -8,6 +8,12 @@
  */
 import UIKit
 import PlaygroundSupport
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*:
  First of all, let's set up colors for our window and graph. The visited color will be applied to visited vertices. The checking color will be applied to an edge and an edge neighbor every time the algorithm is checking some vertex neighbors. And default colors are just initial colors for elements.
  */
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline b/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index dfa422074..975e8e21c 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -25,6 +25,59 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:"
+      name = "Dijkstra">
+      <Group
+         location = "group:Dijkstra Algorithm/Images"
+         name = "Images">
+         <FileRef
+            location = "group:DirectedGraph.png">
+         </FileRef>
+         <FileRef
+            location = "group:image1.png">
+         </FileRef>
+         <FileRef
+            location = "group:image2.png">
+         </FileRef>
+         <FileRef
+            location = "group:image3.png">
+         </FileRef>
+         <FileRef
+            location = "group:image4.png">
+         </FileRef>
+         <FileRef
+            location = "group:image5.png">
+         </FileRef>
+         <FileRef
+            location = "group:image6.png">
+         </FileRef>
+         <FileRef
+            location = "group:image7.png">
+         </FileRef>
+         <FileRef
+            location = "group:Vertices.png">
+         </FileRef>
+         <FileRef
+            location = "group:WeightedDirectedGraph.png">
+         </FileRef>
+         <FileRef
+            location = "group:WeightedDirectedGraphFinal.png">
+         </FileRef>
+         <FileRef
+            location = "group:WeightedUndirectedGraph.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:Dijkstra Algorithm/README.md">
+      </FileRef>
+      <FileRef
+         location = "group:Dijkstra Algorithm/VisualizedDijkstra.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Dijkstra Algorithm/Dijkstra.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "container:"
       name = "LRU Cache">

From 5bdfb5d034d770d12d60dc070d3da394e03157cb Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Sat, 9 Sep 2017 23:30:28 +0800
Subject: [PATCH 1222/1679] Update README.markdown

---
 Segment Tree/LazyPropagation/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 49987c14e..6f85f47bd 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -15,7 +15,7 @@ print(stringSegmentTree.query(leftBound: 0, rightBound: 5))
 
 The use of `<T>` is so exciting. But we seldom use the Segment Tree to solve string problem instead of *Suffix Array*. And the Segment Tree is a kind of *Interval Tree* to solve the Interval Problem in mathemtics and statistics, which is a structure for storing intervals, or segments, and allows querying which of the stored segments contain a given point. A segment tree for a set *I* of n intervals uses `O(nlogn)` storage and can be built in `O(nlogn)` time. Segment trees support searching for all the intervals that contain a query point in O(log n+k), k being the number of retrieved intervals or segments.
 
-But that is common Segment Tree. By **Lazy Propagation**, we can implement to modify an interval in `O(nlogn)` time. Let's explore together in following:
+But that is common Segment Tree. By **Lazy Propagation**, we can implement to modify an interval in `O(logn)` time. Let's explore together in following:
 
 ## `PushUp` - update to the top
 

From 22984bbad346431d7887f939ea4f1fb353fe0873 Mon Sep 17 00:00:00 2001
From: Yeral <YYamil24@gmail.com>
Date: Sat, 9 Sep 2017 11:51:39 -0400
Subject: [PATCH 1223/1679] Fix playground compilation error

---
 Bucket Sort/BucketSort.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Contents.swift b/Bucket Sort/BucketSort.playground/Contents.swift
index c111c3961..e862f8bb1 100644
--- a/Bucket Sort/BucketSort.playground/Contents.swift	
+++ b/Bucket Sort/BucketSort.playground/Contents.swift	
@@ -34,9 +34,9 @@ extension Int: IntConvertible, Sortable {
 // MARK: Playing code
 //////////////////////////////////////
 
-let input = [1, 2, 4, 6, 10]
+let input = [1, 2, 4, 6, 10, 5]
 var buckets = [Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15)]
 
-let sortedElements = bucketSort(elements: input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: &buckets)
+let sortedElements = bucketSort(input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
 
 print(sortedElements)

From 433d1f909846f168307830cf0f1e982eaf5daf99 Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 11 Sep 2017 09:08:56 +0800
Subject: [PATCH 1224/1679] Update Contents.swift

---
 .../LazyPropagation.playground/Contents.swift | 52 ++++++-------------
 1 file changed, 17 insertions(+), 35 deletions(-)

diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
index d576be254..79b791431 100644
--- a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -1,15 +1,3 @@
-//: Playground - noun: a place where people can play
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
-//protocol SegmentTree<T> {
-//    func pushUp(lson: T, rson: T)
-//    func pushDown(round: Int, lson: T, rson: T)
-//}
-
 public class LazySegmentTree {
     
     private var value: Int
@@ -26,22 +14,20 @@ public class LazySegmentTree {
     private var lazyValue: Int
     
     // MARK: - Push Up Operation
-    // Description: 这里是 push up 操作，用来对 Segment Tree 向上更新
+    // Description: pushUp() - update items to the top
     private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
         self.value = lson.value + rson.value
     }
     
     // MARK: - Push Down Operation
-    // Description: 这里是 push down 操作，用来对 Segment Tree 向下更新
-    // Open Interface Function: 此处应该开放方法对齐进行 Override
+    // Description: pushDown() - update items to the bottom
     private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
-        if lazyValue != 0 {
-            lson.lazyValue += lazyValue
-            rson.lazyValue += lazyValue
-            lson.value += lazyValue * (round - (round >> 1))
-            rson.value += lazyValue * (round >> 1)
-            lazyValue = 0
-        }
+        guard lazyValue != 0 else { return }
+        lson.lazyValue += lazyValue
+        rson.lazyValue += lazyValue
+        lson.value += lazyValue * (round - (round >> 1))
+        rson.value += lazyValue * (round >> 1)
+        lazyValue = 0
     }
     
     public init(array: [Int], leftBound: Int, rightBound: Int) {
@@ -50,16 +36,17 @@ public class LazySegmentTree {
         self.value = 0
         self.lazyValue = 0
         
-        if leftBound == rightBound {
+        guard leftBound != rightBound else {
             value = array[leftBound]
             return
         }
         
-        let middle = (leftBound + rightBound) / 2
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
-        pushUp(lson: leftChild!, rson: rightChild!)
-        
+        if let leftChild = leftChild, let rightChild = rightChild {
+            pushUp(lson: leftChild, rson: rightChild)
+        }
     }
     
     public convenience init(array: [Int]) {
@@ -75,7 +62,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result: Int = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -86,14 +73,14 @@ public class LazySegmentTree {
     
     // MARK: - One Item Update
     public func update(index: Int, incremental: Int) {
-        if self.leftBound == self.rightBound {
+        guard self.leftBound != self.rightBound else {
             self.value += incremental
             return
         }
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -113,7 +100,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -140,8 +127,3 @@ for index in 2 ... 5 {
 
 sumSegmentTree.update(leftBound: 0, rightBound: 5, incremental: 2)
 print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
-
-
-
-
-

From a9fa8db3a017bd6ad2c680e7d99c9ea1cfe32fd4 Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 11 Sep 2017 09:14:54 +0800
Subject: [PATCH 1225/1679] Update README.markdown

After code review to update readme.md
---
 Segment Tree/LazyPropagation/README.markdown | 101 +++++++++++++------
 1 file changed, 70 insertions(+), 31 deletions(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 6f85f47bd..4aaa41d93 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -71,6 +71,7 @@ public func query(leftBound: Int, rightBound: Int) -> T {
 Position ① means that the left bound of current query interval is on the  right of this right bound, so recurs to right direction. Position ② is opposite of position ①, recurs to left direction. Position ③ means our check interval is included the interval we need, so recurs deeply.
 
 ![pushUp](Images/pushUp.png)
+
 There are common part from the two parts of code above - **recurs deeply below, and update data up**. So we can decouple this operation named `func pushUp(lson: LazySegmentTree, rson: LazySegmentTree)`:
 
 ```swift
@@ -90,26 +91,32 @@ public init(array: [Int], leftBound: Int, rightBound: Int) {
     self.rightBound = rightBound
     self.value = 0
     self.lazyValue = 0
-    if leftBound == rightBound {
+    
+    guard leftBound != rightBound else {
         value = array[leftBound]
         return
     }
-    let middle = (leftBound + rightBound) / 2
+    
+    let middle = leftBound + (rightBound - leftBound) / 2
     leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
     rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
-    pushUp(lson: leftChild!, rson: rightChild!)
+    if let leftChild = leftChild, let rightChild = rightChild {
+        pushUp(lson: leftChild, rson: rightChild)
+    }
 }
 // MARK: - One Item Update
-public func update(index: Int, newValue: Int) {
-    if self.leftBound == self.rightBound {
-        self.value = newValue
+public func update(index: Int, incremental: Int) {
+    guard self.leftBound != self.rightBound else {
+        self.value += incremental
         return
     }
     guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-    let middle = (self.leftBound + self.rightBound) / 2
-    if index <= middle { leftChild.update(index: index, newValue: newValue) }
-    else { rightChild.update(index: index, newValue: newValue) }
+    
+    let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+    
+    if index <= middle { leftChild.update(index: index, incremental: incremental) }
+    else { rightChild.update(index: index, incremental: incremental) }
     pushUp(lson: leftChild, rson: rightChild)
 }
 ```
@@ -132,11 +139,13 @@ It is a `O(n)` time operation, which make the interval operation uses `O(nlogn)`
  Check the data structure of Segment Tree again:
  
  ![Segment-tree](Images/Segment-tree.png)
+ 
 We only catch the root node in programming. If we want to explore the bottom of the tree, and use `pushUp` to update every node, the task will be reached. So it asked us to traverse the tree, that spent `O(n)` time to do this with any way. This can't conform our expectations.  
 
 Then we started to think about `pushDown` to update down from the root. **After we update the parent, the data continued to distributed to its children according to law.** But it still need `O(n)` time to do this. Keep thinking, we **only update the parent, and to update the children when `query` time**. Yeah, that's the key of **lazy propagation**. Because the recursing direct of the `query` and `update interval` is same. So we got it! 😁 Let's check this sample:
 
 ![lazy-sample-2](Images/lazy-sample-2.png)
+
 `update` make the subscript 1...3 elements plus 2, so we make the 1st node in 2 depth and 3rd in 3 depth get a *lazy mark*, which means these node need to be updated. And we shouldn't add a *lazy mark* for root node, because it was updated before the `pushDown` in the first recursing. 
 
 In `query` operation, we accord to the original method to recurs the tree, and find the 1st node held *lazy mark* in 2 depth, so to update it. It's the same situation about the 1st node in 3 depth.
@@ -147,70 +156,94 @@ This is the complete implementation about the Sum Segment Tree with interval upd
 
 ```swift
 public class LazySegmentTree {
+    
     private var value: Int
+    
     private var leftBound: Int
+    
     private var rightBound: Int
+    
     private var leftChild: LazySegmentTree?
+    
     private var rightChild: LazySegmentTree?
+    
     // Interval Update Lazy Element
     private var lazyValue: Int
+    
     // MARK: - Push Up Operation
+    // Description: pushUp() - update items to the top
     private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
         self.value = lson.value + rson.value
     }
+    
     // MARK: - Push Down Operation
+    // Description: pushDown() - update items to the bottom
     private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
-        if lazyValue != 0 {
-            lson.lazyValue += lazyValue
-            rson.lazyValue += lazyValue
-            lson.value += lazyValue * (round - (round >> 1))
-            rson.value += lazyValue * (round >> 1)
-            lazyValue = 0
-        }
+        guard lazyValue != 0 else { return }
+        lson.lazyValue += lazyValue
+        rson.lazyValue += lazyValue
+        lson.value += lazyValue * (round - (round >> 1))
+        rson.value += lazyValue * (round >> 1)
+        lazyValue = 0
     }
+    
     public init(array: [Int], leftBound: Int, rightBound: Int) {
         self.leftBound = leftBound
         self.rightBound = rightBound
         self.value = 0
         self.lazyValue = 0
-        if leftBound == rightBound {
+        
+        guard leftBound != rightBound else {
             value = array[leftBound]
             return
         }
-        let middle = (leftBound + rightBound) / 2
+        
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
-        pushUp(lson: leftChild!, rson: rightChild!)
+        if let leftChild = leftChild, let rightChild = rightChild {
+            pushUp(lson: leftChild, rson: rightChild)
+        }
     }
+    
     public convenience init(array: [Int]) {
         self.init(array: array, leftBound: 0, rightBound: array.count - 1)
     }
+    
     public func query(leftBound: Int, rightBound: Int) -> Int {
         if leftBound <= self.leftBound && self.rightBound <= rightBound {
             return value
         }
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
-        let middle = (self.leftBound + self.rightBound) / 2
+        
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result: Int = 0
+        
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
         if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
+        
         return result
     }
+    
     // MARK: - One Item Update
     public func update(index: Int, incremental: Int) {
-        if self.leftBound == self.rightBound {
+        guard self.leftBound != self.rightBound else {
             self.value += incremental
             return
         }
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-        let middle = (self.leftBound + self.rightBound) / 2
+        
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
         pushUp(lson: leftChild, rson: rightChild)
     }
+    
     // MARK: - Interval Item Update
     public func update(leftBound: Int, rightBound: Int, incremental: Int) {
         if leftBound <= self.leftBound && self.rightBound <= rightBound {
@@ -218,14 +251,20 @@ public class LazySegmentTree {
             self.value += incremental * (self.rightBound - self.leftBound + 1)
             return 
         }
+        
         guard let leftChild = leftChild else { fatalError() }
         guard let rightChild = rightChild else { fatalError() }
+        
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
-        let middle = (self.leftBound + self.rightBound) / 2
+        
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        
         pushUp(lson: leftChild, rson: rightChild)
     }
+    
 }
 ```
 
@@ -238,15 +277,15 @@ private var lazyValue: Int
 Here we add a new property for Segment Tree to represent *lazy mark*. And it is a incremental value for Sum Segment Tree. If the `lazyValue` isn't equal to zero, the current node need to be updated. And its real value is equal to `value + lazyValue * (rightBound - leftBound + 1)`.
 
 ```swift
-// MARK: - Push Down Operation
+    // MARK: - Push Down Operation
+    // Description: pushDown() - update items to the bottom
 private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
-    if lazyValue != 0 {
-        lson.lazyValue += lazyValue
-        rson.lazyValue += lazyValue
-        lson.value += lazyValue * (round - (round >> 1))
-        rson.value += lazyValue * (round >> 1)
-        lazyValue = 0
-    }
+    guard lazyValue != 0 else { return }
+    lson.lazyValue += lazyValue
+    rson.lazyValue += lazyValue
+    lson.value += lazyValue * (round - (round >> 1))
+    rson.value += lazyValue * (round >> 1)
+    lazyValue = 0
 }
 ```
 

From 643828a6f3087c180f5a52663d129744200fd623 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 11 Sep 2017 17:02:55 -0700
Subject: [PATCH 1226/1679] Updates Splay tree to Swift 4

---
 Splay Tree/SplayTree.playground/Contents.swift         |  4 ++++
 .../SplayTree.playground/Sources/SplayTree.swift       | 10 +++++-----
 2 files changed, 9 insertions(+), 5 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
index 4406a759d..a8a0bc5c6 100644
--- a/Splay Tree/SplayTree.playground/Contents.swift	
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -1,5 +1,9 @@
 //: Playground - Splay Tree Implementation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let splayTree = SplayTree(value: 1)
 splayTree.insert(value: 2)
diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index a4feda7ef..9e484129c 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -28,7 +28,7 @@ public enum SplayOperation {
      - Parameters:
      - node      SplayTree node to move up to the root
      */
-    public static func splay<T: Comparable>(node: Node<T>) {
+    public static func splay<T>(node: Node<T>) {
         
         while (node.parent != nil) {
             operation(forNode: node).apply(onNode: node)
@@ -44,7 +44,7 @@ public enum SplayOperation {
      - Returns
      - Operation     Case zigZag - zigZig - zig
      */
-    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
+    public static func operation<T>(forNode node: Node<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -62,7 +62,7 @@ public enum SplayOperation {
      - Parameters:
      - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    public func apply<T: Comparable>(onNode node: Node<T>) {
+    public func apply<T>(onNode node: Node<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,7 +84,7 @@ public enum SplayOperation {
      Performs a single rotation from a node to its parent
      re-arranging the children properly
      */
-    public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
+    public func rotate<T>(child: Node<T>, parent: Node<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
@@ -610,7 +610,7 @@ extension SplayTree: CustomStringConvertible {
 
 extension Node: CustomDebugStringConvertible {
     public var debugDescription: String {
-        var s = "value: \(value)"
+      var s = "value: \(String(describing: value))"
         if let parent = parent, let v = parent.value {
             s += ", parent: \(v)"
         }

From bedaaac782478eddeff7ede9fde6957fcf6c9999 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 11 Sep 2017 17:06:40 -0700
Subject: [PATCH 1227/1679] Updated readme for splay trees for Swift 4.

---
 Splay Tree/readme.md | 56 ++++++++++++++++++++++----------------------
 1 file changed, 28 insertions(+), 28 deletions(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index c42cd87fb..2c5e87ed7 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -1,5 +1,5 @@
 # Splay Tree
-Splay tree is a data structure, structurally identitical to a Balanced Binary Search Tree. Every operation performed on a Splay Tree causes a readjustment in order to provide fast access to recently operated values. On every access, the tree is rearranged and the node accessed is moved to the root of the tree using a set of specific rotations, which together are referred to as **Splaying**.
+Splay tree is a data structure, structurally identitical to a balanced binary search tree. Every operation performed on a Splay Tree causes a readjustment in order to provide fast access to recently operated values. On every access, the tree is rearranged and the node accessed is moved to the root of the tree using a set of specific rotations, which together are referred to as **Splaying**.
 
 
 ## Rotations
@@ -24,7 +24,7 @@ Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* a
 
 ### Zig-Zag
 
-Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
+Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opposite), a **Zig-Zag** is performed.
 
 ### Case right - left
 ![ZigZagCase1](Images/zigzag1.png)
@@ -43,49 +43,49 @@ A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
 ## Splaying
 
-A splaying consists in making so many rotations as needed until the node affected by the operation is at the top and becomes the root of the tree.
+Splaying consists in making so many rotations as needed until the node affected by the operation is at the top and becomes the root of the tree.
 
 ```
 while (node.parent != nil) {
-            operation(forNode: node).apply(onNode: node)
+    operation(forNode: node).apply(onNode: node)
 }
 ```
 
 Where operation returns the required rotation to be applied. 
 
 ```
-    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
-        
-        if let parent = node.parent, let _ = parent.parent {
-            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
-                return .zigZag
-            }
-            return .zigZig
+public static func operation<T>(forNode node: Node<T>) -> SplayOperation {
+    
+    if let parent = node.parent, let _ = parent.parent {
+        if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
+            return .zigZag
         }
-        return .zig
+        return .zigZig
     }
+    return .zig
+}
 ```
 
 During the applying phase, the algorithms determines which nodes are involved depending on the rotation to be applied and proceeding to re-arrange the node with its parent.
 
 ```
-    public func apply<T: Comparable>(onNode node: Node<T>) {
-        switch self {
-        case .zigZag:
-            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
-            rotate(child: node, parent: node.parent!)
-            rotate(child: node, parent: node.parent!)
-
-        case .zigZig:
-            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
-            rotate(child: node.parent!, parent: node.parent!.parent!)
-            rotate(child: node, parent: node.parent!)
-        
-        case .zig:
-            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
-            rotate(child: node, parent: node.parent!)
-        }
+public func apply<T>(onNode node: Node<T>) {
+    switch self {
+    case .zigZag:
+        assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+        rotate(child: node, parent: node.parent!)
+        rotate(child: node, parent: node.parent!)
+
+    case .zigZig:
+        assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+        rotate(child: node.parent!, parent: node.parent!.parent!)
+        rotate(child: node, parent: node.parent!)
+    
+    case .zig:
+        assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+        rotate(child: node, parent: node.parent!)
     }
+}
 ```
 
 

From 08abb81fc0616f29d5064145597e2a3558eca523 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 11 Sep 2017 17:08:10 -0700
Subject: [PATCH 1228/1679] Added splay trees to main readme.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 464c6b199..0494e749d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -153,7 +153,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary%20Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary%20Search%20Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [Red-Black Tree](Red-Black%20Tree/). A self balancing binary search tree.
-- Splay Tree
+- [Splay Tree](Splay%20Tree/). A self balancing binary search tree that enables fast retrieval of recently updated elements.
 - [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree

From 45889d79c0aac7d1889aeb6839041f518e6d5247 Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Sun, 17 Sep 2017 12:05:36 -0700
Subject: [PATCH 1229/1679] Syntax Updates

Minor update due to Swift changed in the makeIterator function.
---
 Stack/Stack.swift | 51 +++++++++++++++++++++++------------------------
 1 file changed, 25 insertions(+), 26 deletions(-)

diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index c3f42ea44..a9e8fb7a4 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -1,36 +1,35 @@
 /*
-  Last-in first-out stack (LIFO)
-
-  Push and pop are O(1) operations.
-*/
+ Last-in first-out stack (LIFO)
+ Push and pop are O(1) operations.
+ */
 public struct Stack<T> {
-  fileprivate var array = [T]()
-
-  public var isEmpty: Bool {
-    return array.isEmpty
-  }
-
-  public var count: Int {
-    return array.count
-  }
-
-  public mutating func push(_ element: T) {
-    array.append(element)
-  }
-
-  public mutating func pop() -> T? {
-    return array.popLast()
-  }
-
-  public var top: T? {
-    return array.last
-  }
+    fileprivate var array = [T]()
+    
+    public var isEmpty: Bool {
+        return array.isEmpty
+    }
+    
+    public var count: Int {
+        return array.count
+    }
+    
+    public mutating func push(_ element: T) {
+        array.append(element)
+    }
+    
+    public mutating func pop() -> T? {
+        return array.popLast()
+    }
+    
+    public var top: T? {
+        return array.last
+    }
 }
 
 extension Stack: Sequence {
     public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyIterator { _ -> T? in
+        return AnyIterator {
             return curr.pop()
         }
     }

From 0d5d8d38ed681a18d2951875545a5882df686a71 Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Sun, 17 Sep 2017 12:09:21 -0700
Subject: [PATCH 1230/1679] Swap changes

Swap changed from swap(&a[y - 1], &a[y])  ->  a.swapAt(y - 1, y)
---
 Insertion Sort/README.markdown | 16 +++++++++++++++-
 1 file changed, 15 insertions(+), 1 deletion(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 286d92ed1..91dfd18ad 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -91,7 +91,7 @@ Here is an implementation of insertion sort in Swift:
 
 ```swift
 func insertionSort(_ array: [Int]) -> [Int] {
-  var a = array                             // 1
+  var a = array                            
   for x in 1..<a.count {                    // 2
     var y = x
     while y > 0 && a[y] < a[y - 1] {        // 3
@@ -101,6 +101,20 @@ func insertionSort(_ array: [Int]) -> [Int] {
   }
   return a
 }
+
+func insertionSort(_ array: [Int]) -> [Int] {
+    var a = array			 // 1
+    for x in 1..<a.count {		 // 2
+        var y = x
+        while y > 0 && a[y] < a[y - 1] { // 3
+            a.swapAt(y - 1, y)
+            y -= 1
+        }
+    }
+    return a
+}
+
+
 ```
 
 Put this code in a playground and test it like so:

From 28f1fc3d70c318394a3944a4e206d25149160450 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 17 Sep 2017 20:19:44 -0700
Subject: [PATCH 1231/1679] Reverts indentation to 2 spaces.

---
 Stack/Stack.swift | 52 +++++++++++++++++++++++------------------------
 1 file changed, 26 insertions(+), 26 deletions(-)

diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index a9e8fb7a4..b12f713f5 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -3,34 +3,34 @@
  Push and pop are O(1) operations.
  */
 public struct Stack<T> {
-    fileprivate var array = [T]()
-    
-    public var isEmpty: Bool {
-        return array.isEmpty
-    }
-    
-    public var count: Int {
-        return array.count
-    }
-    
-    public mutating func push(_ element: T) {
-        array.append(element)
-    }
-    
-    public mutating func pop() -> T? {
-        return array.popLast()
-    }
-    
-    public var top: T? {
-        return array.last
-    }
+  fileprivate var array = [T]()
+  
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+  
+  public var count: Int {
+    return array.count
+  }
+  
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
+  
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
+  
+  public var top: T? {
+    return array.last
+  }
 }
 
 extension Stack: Sequence {
-    public func makeIterator() -> AnyIterator<T> {
-        var curr = self
-        return AnyIterator {
-            return curr.pop()
-        }
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator {
+      return curr.pop()
     }
+  }
 }

From d27354e096f73c9a078fc956099eefbf80e0468b Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 18 Sep 2017 11:26:05 +0800
Subject: [PATCH 1232/1679] Update Contents.swift

---
 .../LazyPropagation.playground/Contents.swift      | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
index 79b791431..5def3df33 100644
--- a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -41,7 +41,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = leftBound + (rightBound - leftBound) / 2
+        let middle = (leftBound + rightBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -62,8 +62,8 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
-        var result: Int = 0
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
         if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -80,7 +80,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -95,12 +95,12 @@ public class LazySegmentTree {
             return 
         }
         
-        guard let leftChild = leftChild else { fatalError() }
-        guard let rightChild = rightChild else { fatalError() }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }

From 5e8840787066ede9bcdbf32b338c5a50b8d4a3a2 Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 18 Sep 2017 12:46:02 +0800
Subject: [PATCH 1233/1679] Update README.markdown

---
 Segment Tree/LazyPropagation/README.markdown | 22 ++++++++------------
 1 file changed, 9 insertions(+), 13 deletions(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 4aaa41d93..bcfb890fd 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -97,7 +97,7 @@ public init(array: [Int], leftBound: Int, rightBound: Int) {
         return
     }
     
-    let middle = leftBound + (rightBound - leftBound) / 2
+    let middle = (leftBound + rightBound) / 2
     leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
     rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
     if let leftChild = leftChild, let rightChild = rightChild {
@@ -113,7 +113,7 @@ public func update(index: Int, incremental: Int) {
     guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
     
-    let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+    let middle = (self.leftBound + self.rightBound) / 2
     
     if index <= middle { leftChild.update(index: index, incremental: incremental) }
     else { rightChild.update(index: index, incremental: incremental) }
@@ -198,7 +198,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = leftBound + (rightBound - leftBound) / 2
+        let middle = (leftBound + rightBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -219,8 +219,8 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
-        var result: Int = 0
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
         if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -237,7 +237,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -252,12 +252,12 @@ public class LazySegmentTree {
             return 
         }
         
-        guard let leftChild = leftChild else { fatalError() }
-        guard let rightChild = rightChild else { fatalError() }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -302,7 +302,3 @@ In fact, the operation of Segment Tree is far more than that. It can also be use
 ---
 
 *Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
-
-
-
-

From c4952f9fbdcb00801167ac28327a56ab7cd97aee Mon Sep 17 00:00:00 2001
From: Harry Twan <gua@desgard.com>
Date: Mon, 18 Sep 2017 12:54:18 +0800
Subject: [PATCH 1234/1679] Update the pushUp image

---
 .../LazyPropagation/Images/pushUp.png         | Bin 30566 -> 28125 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/Segment Tree/LazyPropagation/Images/pushUp.png b/Segment Tree/LazyPropagation/Images/pushUp.png
index b45589b7213104195dbc4da6c74114cf427e6a2c..ae868037f133fc62a66abccd4eb740280d07fac0 100644
GIT binary patch
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From aef1bb7092e6dd05190fb32b66d148792385ebca Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 19 Sep 2017 20:42:45 -0700
Subject: [PATCH 1235/1679] Removes old implementation

---
 Insertion Sort/README.markdown | 12 ------------
 1 file changed, 12 deletions(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 91dfd18ad..4bad29aa1 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -90,18 +90,6 @@ This was a description of the inner loop of the insertion sort algorithm, which
 Here is an implementation of insertion sort in Swift:
 
 ```swift
-func insertionSort(_ array: [Int]) -> [Int] {
-  var a = array                            
-  for x in 1..<a.count {                    // 2
-    var y = x
-    while y > 0 && a[y] < a[y - 1] {        // 3
-      swap(&a[y - 1], &a[y])
-      y -= 1
-    }
-  }
-  return a
-}
-
 func insertionSort(_ array: [Int]) -> [Int] {
     var a = array			 // 1
     for x in 1..<a.count {		 // 2

From ba27b0bd6624234d42dd60c36115a7b6f9933607 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 20 Sep 2017 00:21:27 -0700
Subject: [PATCH 1236/1679] Updates the preamble and description of the readme

---
 Egg Drop Problem/README.markdown | 23 ++++++++++++++++-------
 1 file changed, 16 insertions(+), 7 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 82543502d..7c15bcf62 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -1,18 +1,27 @@
-# Egg Drop Dynamic Problem
+# Egg Drop
 
-## Problem Description 
+The *egg drop* problem is an interview question popularized by Google. The premise is simple; You're given a task to evaluate the *shatter resistance* of unknown objects by dropping them at a certain height. For simplicity, you test this by going inside a multi-story building and performing tests by dropping the objects out the window and onto the ground:
 
-Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
+![building with eggs being dropped](images/eggdrop.png)
 
-Suppose that we wish to know which stories in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing. We make a few assumptions:
+Your goal is to find out the **minimum** height that causes the object to shatter. Consider the trivial case you're given **1** object to obtain the results with. Since you've only got one sample for testing, you need to play it safe by performing drop tests starting with the bottom floor and working your way up:
+
+![dropping from first floor](images/eggdrop2.png)
+
+If the object is incredibly resilient, and you may need to do the testing on the world's tallest building - the [Burj Khalifa](https://en.wikipedia.org/wiki/Burj_Khalifa). With **163** floors, that's a lot of climbing. Let's assume you complain, and your employer hears your plight. You are now given *several* samples to work with. How can you make use of these extra samples to expedite your testing process? The problem for this situation is popularized as the **egg drop** problem.
+
+## Description
+
+You're in a building with **m** floors and you are given **n** eggs. What is the minimum number attempts it will take to find out the lowest floor that breaks the egg?
+
+For convenience, here are a few rules to keep in mind:
 
 - An egg that survives a fall can be used again.
 - A broken egg must be discarded.
 - The effect of a fall is the same for all eggs.
-- If an egg breaks when dropped, then it would break if dropped from a higher floor.
-- If an egg survives a fall then it would survive a shorter fall.
+- If an egg breaks, then it would break if dropped from a higher floor.
+- If an egg survives, then it would survive a shorter fall.
 
-If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
 ## Solution

From 4ace4c5c9b35fcc0839eaf00ba0ec388a23767eb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 20 Sep 2017 00:23:42 -0700
Subject: [PATCH 1237/1679] Adds images to egg drop problem

---
 Egg Drop Problem/images/eggdrop.png  | Bin 0 -> 312712 bytes
 Egg Drop Problem/images/eggdrop2.png | Bin 0 -> 368811 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Egg Drop Problem/images/eggdrop.png
 create mode 100644 Egg Drop Problem/images/eggdrop2.png

diff --git a/Egg Drop Problem/images/eggdrop.png b/Egg Drop Problem/images/eggdrop.png
new file mode 100644
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HcmV?d00001


From ea4b20857955ae00d425604a159ee0ab67dd4fa3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 20 Sep 2017 01:24:45 -0700
Subject: [PATCH 1238/1679] Updates code to Swift 4. Refactored a bit of the
 readme.

---
 .../EggDrop.playground/Contents.swift         | 17 +++---
 .../EggDrop.playground/Sources/EggDrop.swift  | 60 ++++++++-----------
 .../contents.xcworkspacedata                  |  7 +++
 Egg Drop Problem/README.markdown              |  5 +-
 4 files changed, 43 insertions(+), 46 deletions(-)
 create mode 100644 Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
index d452e7f9f..0b707da98 100644
--- a/Egg Drop Problem/EggDrop.playground/Contents.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -1,9 +1,12 @@
- //: Playground - noun: a place where people can play
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
 
-import Cocoa
+drop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
+drop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
+drop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
+drop(numberOfEggs: 5, numberOfFloors: 5) //expected answer: 2
+drop(numberOfEggs: 5, numberOfFloors: 20) //expected answer: 4
 
-eggDrop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
-eggDrop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
-eggDrop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
-eggDrop(numberOfEggs: 5, numberOfFloors: 5) //expected answer: 2
-eggDrop(numberOfEggs: 5, numberOfFloors: 20) //expected answer: 4
\ No newline at end of file
+drop(numberOfEggs: 2, numberOfFloors: 36)
+drop(numberOfEggs: 2, numberOfFloors: 10)
diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
index db1e48b95..f8bb0a420 100644
--- a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -1,39 +1,27 @@
-public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
-        return 0
-    }
-    if numberOfEggs == 1 || numberOfFloors == 1{ //edge case: When either number of eggs or number of floors is 1, answer is 1
-        return 1
-    }
-    
-    var eggFloor = [[Int]](repeating: [Int](repeating: 0, count: numberOfFloors+1), count: numberOfEggs+1) //egg(rows) floor(cols) array to store the solutions
-    var attempts: Int = 0
-    
-    for var floorNumber in (0..<(numberOfFloors+1)){
-        eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
-    }
-    eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
-    
-    for var eggNumber in (2..<(numberOfEggs+1)){
-        for var floorNumber in (2..<(numberOfFloors+1)){
-            eggFloor[eggNumber][floorNumber] = Int.max   //setting the final result a high number to find out minimum
-            for var visitingFloor in (1..<(floorNumber+1)){
-                //there are two cases
-                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
-                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floorNumber-visitingFloor
-                attempts = 1 + max(eggFloor[eggNumber-1][visitingFloor-1], eggFloor[eggNumber][floorNumber-visitingFloor])//we add one taking into account the attempt we're taking at the moment
-                
-                if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
-                    eggFloor[eggNumber][floorNumber] = attempts;
-                }
-            }
+public func drop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
+  guard numberOfEggs != 0 && numberOfFloors != 0 else { return 0 }
+  guard numberOfEggs != 1 && numberOfFloors != 1 else { return 1 }
+  
+  var eggFloor: [[Int]] = .init(repeating: .init(repeating: 0, count: numberOfFloors + 1), count: numberOfEggs + 1)
+  var attempts = 0
+  
+  for floorNumber in stride(from: 0, through: numberOfFloors, by: 1) {
+    eggFloor[1][floorNumber] = floorNumber
+  }
+  eggFloor[2][1] = 1
+  
+  for eggNumber in stride(from: 2, through: numberOfEggs, by: 1) {
+    for floorNumber in stride(from: 2, through: numberOfFloors, by: 1) {
+      eggFloor[eggNumber][floorNumber] = Int.max
+      for visitingFloor in stride(from: 1, through: floorNumber, by: 1) {
+        attempts = 1 + max(eggFloor[eggNumber - 1][visitingFloor - 1], eggFloor[eggNumber][floorNumber - visitingFloor])
+        
+        if attempts < eggFloor[eggNumber][floorNumber] {
+          eggFloor[eggNumber][floorNumber] = attempts
         }
+      }
     }
-    
-    return eggFloor[numberOfEggs][numberOfFloors]
-}
-
-//Helper function to find max of two integers
-public func max(_ x1: Int, _ x2: Int) -> Int{
-    return x1 > x2 ? x1 : x2
+  }
+  
+  return eggFloor[numberOfEggs][numberOfFloors]
 }
diff --git a/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 7c15bcf62..dd7ed4104 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -12,7 +12,7 @@ If the object is incredibly resilient, and you may need to do the testing on the
 
 ## Description
 
-You're in a building with **m** floors and you are given **n** eggs. What is the minimum number attempts it will take to find out the lowest floor that breaks the egg?
+You're in a building with **m** floors and you are given **n** eggs. What is the maximum number of attempts it will take to find out the floor that breaks the egg?
 
 For convenience, here are a few rules to keep in mind:
 
@@ -22,9 +22,8 @@ For convenience, here are a few rules to keep in mind:
 - If an egg breaks, then it would break if dropped from a higher floor.
 - If an egg survives, then it would survive a shorter fall.
 
-The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
-
 ## Solution
+
 - eggNumber -> Number of eggs at the moment
 - floorNumber -> Floor number at the moment
 - visitingFloor -> Floor being visited at the moment

From 19acc0096a4d106b06dcd6fc8f240f96990ba6e5 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 20 Sep 2017 01:26:06 -0700
Subject: [PATCH 1239/1679] Added credits footer.

---
 Egg Drop Problem/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index dd7ed4104..b2f45d09e 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -69,4 +69,4 @@ Let's assume we have 2 eggs and 2 floors.
 3) Finding the minimum of 2 and 2 gives us 2, so the answer is 2. 
    2 is the minimum number of attempts it will take to find out from which floor egg will break.
 
-
+*Written for the Swift Algorithm Club by Arkalyk Akash. Revisions and additions by Kelvin Lau*

From eb8edb19c446070806ae335b3b3522f97d9003be Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 20 Sep 2017 01:28:23 -0700
Subject: [PATCH 1240/1679] Adds egg drop problem to the main README file.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 0494e749d..c28d37f7a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -196,7 +196,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Monty Hall Problem](Monty%20Hall%20Problem/)
 - [Finding Palindromes](Palindromes/)
 - [Dining Philosophers](DiningPhilosophers/)
-
+- [Egg Drop Problem](Egg%20Drop%20Problem/)
 ## Learn more!
 
 For more information, check out these great books:

From 16775c6b7b26a838d4b7a5d42bf231bb983607fc Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Wed, 20 Sep 2017 11:48:46 -0700
Subject: [PATCH 1241/1679] Minor Change

Updated the sort() function to sorted() based on Swift syntax changes.
---
 Kth Largest Element/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index 53bec1c1c..aba2d9c29 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -12,7 +12,7 @@ The following solution is semi-naive. Its time complexity is **O(n log n)** sinc
 func kthLargest(a: [Int], k: Int) -> Int? {
   let len = a.count
   if k > 0 && k <= len {
-    let sorted = a.sort()
+    let sorted = a.sorted()
     return sorted[len - k]
   } else {
     return nil

From 37594584bdadf5290dd11afe2e0f56090f05130f Mon Sep 17 00:00:00 2001
From: Harry Twan <gua@desgard.com>
Date: Thu, 21 Sep 2017 09:23:17 +0800
Subject: [PATCH 1242/1679] Update mid is `l + (r + l) / 2`

---
 .../LazyPropagation.playground/Contents.swift    | 10 +++++-----
 Segment Tree/LazyPropagation/README.markdown     | 16 ++++++++++------
 2 files changed, 15 insertions(+), 11 deletions(-)

diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
index 5def3df33..38dd51859 100644
--- a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -41,7 +41,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = (leftBound + rightBound) / 2
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -62,7 +62,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -80,7 +80,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -100,7 +100,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -126,4 +126,4 @@ for index in 2 ... 5 {
 
 
 sumSegmentTree.update(leftBound: 0, rightBound: 5, incremental: 2)
-print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
+print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
\ No newline at end of file
diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index bcfb890fd..21f6a7868 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -22,6 +22,7 @@ But that is common Segment Tree. By **Lazy Propagation**, we can implement to mo
 At first, we reference the implement of **Artur Antonov** about Segment Tree. This code contained *build*, *single update* and *interval query* three operation. The implement of *build* and *single update* operation is following:
 
 ```swift
+// Author: Artur Antonov
 public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
 	self.leftBound = leftBound
 	self.rightBound = rightBound
@@ -45,6 +46,7 @@ In position ①, it means the current node is *leaf* because its left bound data
 And then, we have a look for *interval query* operation:
 
 ```swift
+// Author: Artur Antonov
 public func query(leftBound: Int, rightBound: Int) -> T {
 	if self.leftBound == leftBound && self.rightBound == rightBound {
 		return self.value
@@ -97,7 +99,7 @@ public init(array: [Int], leftBound: Int, rightBound: Int) {
         return
     }
     
-    let middle = (leftBound + rightBound) / 2
+    let middle = leftBound + (rightBound - leftBound) / 2
     leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
     rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
     if let leftChild = leftChild, let rightChild = rightChild {
@@ -113,7 +115,7 @@ public func update(index: Int, incremental: Int) {
     guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
     
-    let middle = (self.leftBound + self.rightBound) / 2
+    let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
     
     if index <= middle { leftChild.update(index: index, incremental: incremental) }
     else { rightChild.update(index: index, incremental: incremental) }
@@ -198,7 +200,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = (leftBound + rightBound) / 2
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -219,7 +221,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -237,7 +239,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -257,7 +259,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -302,3 +304,5 @@ In fact, the operation of Segment Tree is far more than that. It can also be use
 ---
 
 *Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
+
+

From bf50772cec8a64eab3e219994046f3d15cb29b5c Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Thu, 21 Sep 2017 09:24:46 +0800
Subject: [PATCH 1243/1679] Update README.markdown

---
 Segment Tree/LazyPropagation/README.markdown | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 21f6a7868..c625a7dc8 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -304,5 +304,3 @@ In fact, the operation of Segment Tree is far more than that. It can also be use
 ---
 
 *Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
-
-

From 7f7270dc5c25dae5251e7914c10fa2ef18b96c44 Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Wed, 20 Sep 2017 21:13:30 -0700
Subject: [PATCH 1244/1679] Missing a curly Brace, opps.

Missing a curly Brace, opps.
---
 Run-Length Encoding/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Run-Length Encoding/README.markdown b/Run-Length Encoding/README.markdown
index f7d196161..b29a49dd1 100644
--- a/Run-Length Encoding/README.markdown	
+++ b/Run-Length Encoding/README.markdown	
@@ -51,6 +51,7 @@ extension Data {
         }
         return data
     }
+ }
 ```
 
 How it works:

From 9f1f467648a84f0997d69757fb0b03e5cd6461de Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 21 Sep 2017 03:39:36 -0700
Subject: [PATCH 1245/1679] Updated solution 1 for clarity.

---
 Two-Sum Problem/README.markdown               | 20 +++++++-------
 .../Solution 1/2Sum.playground/Contents.swift | 27 ++++++++-----------
 2 files changed, 21 insertions(+), 26 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index a20666efd..e99902167 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,24 +1,24 @@
 # Two-Sum Problem
 
-You're given an array `a` with numbers. Write an algorithm that checks if there are any two entries in the array that add up to a given number `k`. In other words, is there any `a[i] + a[j] == k`?
+You're given an array of numbers. Write an algorithm that checks if there are any two elements in the array that add up to a given number.
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.
 
 # Solution 1
 
-This solution uses a dictionary to store differences between each element in the array and the sum `k` that we're looking for. The dictionary also stores the indices of each element.
+This solution uses a dictionary to store differences between each element in the array and the sum that we're looking for. The dictionary also stores the indices of each element.
 
-With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum to `k`.
+With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum.
 
 ```swift
-func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
-  var dict = [Int: Int]()
-
-  for i in 0 ..< a.count {
-    if let newK = dict[a[i]] {
-      return (newK, i)
+func twoSumProblem(_ numbers: [Int], sum: Int) -> (Int, Int)? {
+  var dict: [Int: Int] = [:]
+  
+  for (index, number) in numbers.enumerated() {
+    if let otherIndex = dict[number] {
+      return (index, otherIndex)
     } else {
-      dict[k - a[i]] =  i
+      dict[sum - number] = index
     }
   }
 
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 4de46128c..4b6db5d51 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -4,26 +4,21 @@
 print("Hello, Swift 4!")
 #endif
 
-func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
-  var map = [Int: Int]()
-
-  for i in 0 ..< a.count {
-    if let newK = map[a[i]] {
-      return (newK, i)
+func twoSum(_ numbers: [Int], target: Int) -> (Int, Int)? {
+  var dict: [Int: Int] = [:]
+  
+  for (index, number) in numbers.enumerated() {
+    if let otherIndex = dict[number] {
+      return (index, otherIndex)
     } else {
-      map[k - a[i]] =  i
+      dict[target - number] = index
     }
   }
+  
   return nil
 }
 
-let a = [7, 100, 2, 21, 12, 10, 22, 14, 3, 4, 8, 4, 9]
-if let (i, j) = twoSumProblem(a, k: 33) {
-  i            // 3
-  a[i]         // 21
-  j            // 4
-  a[j]         // 12
-  a[i] + a[j]  // 33
-}
+let numbers = [3, 2, 4]
+let target = 6
 
-twoSumProblem(a, k: 37)  // nil
+twoSum(numbers, target: target) // expected output: indices 2 and 1

From d757cbe04c88ab9ef8065ac240fd04db0e5d0e4a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 21 Sep 2017 03:40:58 -0700
Subject: [PATCH 1246/1679] Fixes a typo.

---
 Two-Sum Problem/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index e99902167..6fb05d316 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -11,14 +11,14 @@ This solution uses a dictionary to store differences between each element in the
 With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum.
 
 ```swift
-func twoSumProblem(_ numbers: [Int], sum: Int) -> (Int, Int)? {
+func twoSumProblem(_ numbers: [Int], target: Int) -> (Int, Int)? {
   var dict: [Int: Int] = [:]
   
   for (index, number) in numbers.enumerated() {
     if let otherIndex = dict[number] {
       return (index, otherIndex)
     } else {
-      dict[sum - number] = index
+      dict[target - number] = index
     }
   }
 

From c93cc36debd8f0965575a330a3d531fa6e09a954 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 21 Sep 2017 03:46:05 -0700
Subject: [PATCH 1247/1679] Fixes the explanation to match the code.

---
 Two-Sum Problem/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 6fb05d316..dacf5a40a 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -26,7 +26,7 @@ func twoSumProblem(_ numbers: [Int], target: Int) -> (Int, Int)? {
 }
 ```
 
-The `twoSumProblem()` function takes two parameters: the array `a` with the numbers, and `k`, the sum we're looking for. It returns the first set of indices `(i, j)` where `a[i] + a[j] == k`, or `nil` if no two numbers add up to `k`.
+The `twoSumProble` function takes two parameters: the `numbers` array and the target sum you're looking for. It returns the 2 indices with elements that sums up to the target, or `nil` if it can't be found.
 
 Let's take a look at an example and run through the algorithm to see how it works. Given is the array:
 
@@ -38,7 +38,7 @@ Let's find out if there exist two entries whose sum is equal to 10.
 
 Initially, our dictionary is empty. We begin looping through each element:
 
-- **i = 0**: Is `7` in the dictionary? No. We add the difference between the target `k` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
+- **i = 0**: Is `7` in the dictionary? No. We add the difference between the `target` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
 
 ```swift
 [ 3: 0 ]

From a75e7047a92005649f547d2e3d212318473e0c71 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 23 Sep 2017 23:14:14 -0700
Subject: [PATCH 1248/1679] Update readme for swift 4 and Xcode 9

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index c28d37f7a..48e1a90f0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Most code is compatible with **Xcode 8.3** and **Swift 3**. We'll keep this updated with the latest version of Swift.
+All code are compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From b521470d82f9c9fbb54d3ec9ccfc7a84dea6dc34 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 24 Sep 2017 07:45:19 -0700
Subject: [PATCH 1249/1679] Updated readme for Swift 4

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 48e1a90f0..dd001f75a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-All code are compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
+Code is compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From 0d17a67abfa28dd093189ad1af581ffb2a6d5c7d Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Mon, 25 Sep 2017 17:09:08 +0900
Subject: [PATCH 1250/1679] Code Refactoring

Modifying the merge method in Merge Sort:
* empty array definition.
* unifying the while loop.
---
 .../MergeSort.playground/Contents.swift       | 27 +++++-------
 Merge Sort/MergeSort.swift                    | 41 ++++++++-----------
 2 files changed, 28 insertions(+), 40 deletions(-)

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index 06fa3beaa..b05332bfe 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -21,31 +21,24 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
     orderedPile.reserveCapacity(leftPile.count + rightPile.count)
   }
 
-  while leftIndex < leftPile.count && rightIndex < rightPile.count {
+  while true {
+    guard leftIndex < leftPile.endIndex else {
+      orderedPile.append(contentsOf: rightPile[rightIndex..<rightPile.endIndex])
+      break
+    }
+    guard rightIndex < rightPile.endIndex else {
+      orderedPile.append(contentsOf: leftPile[leftIndex..<leftPile.endIndex])
+      break
+    }
+    
     if leftPile[leftIndex] < rightPile[rightIndex] {
       orderedPile.append(leftPile[leftIndex])
       leftIndex += 1
-    } else if leftPile[leftIndex] > rightPile[rightIndex] {
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
     } else {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
       orderedPile.append(rightPile[rightIndex])
       rightIndex += 1
     }
   }
-
-  while leftIndex < leftPile.count {
-    orderedPile.append(leftPile[leftIndex])
-    leftIndex += 1
-  }
-
-  while rightIndex < rightPile.count {
-    orderedPile.append(rightPile[rightIndex])
-    rightIndex += 1
-  }
-
   return orderedPile
 }
 
diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index 990c432fa..00e35f498 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -17,35 +17,30 @@ func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
 func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var leftIndex = 0
   var rightIndex = 0
-  var orderedPile = [T]()
+  var orderedPile: [T] = []
   if orderedPile.capacity < leftPile.count + rightPile.count {
     orderedPile.reserveCapacity(leftPile.count + rightPile.count)
   }
 
-  while leftIndex < leftPile.count && rightIndex < rightPile.count {
-    if leftPile[leftIndex] < rightPile[rightIndex] {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
-    } else if leftPile[leftIndex] > rightPile[rightIndex] {
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
-    } else {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
-    }
-  }
-
-  while leftIndex < leftPile.count {
-    orderedPile.append(leftPile[leftIndex])
-    leftIndex += 1
+  while true {
+      guard leftIndex < leftPile.endIndex else {
+          orderedPile.append(contentsOf: rightPile[rightIndex..<rightPile.endIndex])
+          break
+      }
+      guard rightIndex < rightPile.endIndex else {
+          orderedPile.append(contentsOf: leftPile[leftIndex..<leftPile.endIndex])
+          break
+      }
+      
+      if leftPile[leftIndex] < rightPile[rightIndex] {
+          orderedPile.append(leftPile[leftIndex])
+          leftIndex += 1
+      } else {
+          orderedPile.append(rightPile[rightIndex])
+          rightIndex += 1
+      }
   }
 
-  while rightIndex < rightPile.count {
-    orderedPile.append(rightPile[rightIndex])
-    rightIndex += 1
-  }
 
   return orderedPile
 }

From 71ab3f8eb62bea0886536f2fd12b7b703ea0cb2e Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine@appirio.com>
Date: Tue, 26 Sep 2017 15:34:03 -0700
Subject: [PATCH 1251/1679] algorithm proposal

---
 Genetic/README.markdown |   2 +
 Genetic/gen.swift       | 179 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 181 insertions(+)
 create mode 100644 Genetic/README.markdown
 create mode 100644 Genetic/gen.swift

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
new file mode 100644
index 000000000..7cad649cb
--- /dev/null
+++ b/Genetic/README.markdown
@@ -0,0 +1,2 @@
+# todo
+refactoring https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba for swift 4. Creating a tutorial and writing in more playground friendly format
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
new file mode 100644
index 000000000..72830b8a7
--- /dev/null
+++ b/Genetic/gen.swift
@@ -0,0 +1,179 @@
+/*
+  base .. to be refactored
+*/
+
+import Foundation
+
+// HELPERS
+/*
+    String extension to convert a string to ascii value
+*/
+extension String {
+    var asciiArray: [UInt8] {
+        return unicodeScalars.filter{$0.isASCII}.map{UInt8($0.value)}
+    }
+}
+
+/*
+    helper function to return a random character string
+*/
+func randomChar() -> UInt8 {
+    
+    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+    let len = UInt32(letters.count-1)
+    
+    let rand = Int(arc4random_uniform(len))
+    return letters[rand]
+}
+
+// END HELPERS
+
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+let DNA_SIZE = OPTIMAL.count
+let POP_SIZE = 50
+let GENERATIONS = 5000
+let MUTATION_CHANCE = 100
+
+/*
+    calculated the fitness based on approximate string matching
+    compares each character ascii value difference and adds that to a total fitness
+    optimal string comparsion = 0
+*/
+func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+    
+    var fitness = 0
+    for c in 0...dna.count-1 {
+        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    }
+    return fitness
+}
+
+/*
+    randomly mutate the string
+*/
+func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
+    var outputDna = dna
+    
+    for i in 0..<dnaSize {
+        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        if rand == 1 {
+            outputDna[i] = randomChar()
+        }
+    }
+
+    return outputDna
+}
+
+/*
+    combine two parents to create an offspring
+    parent = xy & yx, offspring = xx, yy
+*/
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
+    
+    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+    
+    return (
+        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
+        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
+    )
+}
+
+
+/*
+returns a random population, used to start the evolution
+*/
+func randomPopulation(populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+    
+    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+    let len = UInt32(letters.count)
+
+    var pop = [[UInt8]]()
+    
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let rand = arc4random_uniform(len)
+            let nextChar = letters[Int(rand)]
+            dna.append(nextChar)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+
+
+/*
+function to return random canidate of a population randomally, but weight on fitness.
+*/
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+    var weightTotal = 0.0
+    for itemTuple in items {
+        weightTotal += itemTuple.weight;
+    }
+    
+    var n = Double(arc4random_uniform(UInt32(weightTotal * 1000000.0))) / 1000000.0
+
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+
+func main() {
+
+    // generate the starting random population
+    var population:[[UInt8]] = randomPopulation(populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+    // print("population: \(population), dnaSize: \(DNA_SIZE) ")
+    var fittest = [UInt8]()
+
+    for generation in 0...GENERATIONS {
+        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        
+        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        
+        // calulcated the fitness of each individual in the population
+        // and add it to the weight population (weighted = 1.0/fitness)
+        for individual in population {
+            let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+            
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            
+            weightedPopulation.append(pair)
+        }
+        
+        population = []
+        
+        // create a new generation using the individuals in the origional population
+        for _ in 0...POP_SIZE/2 {
+            let ind1 = weightedChoice(items: weightedPopulation)
+            let ind2 = weightedChoice(items: weightedPopulation)
+            
+            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+
+            // append to the population and mutate
+            population.append(mutate(dna: offspring.dna1, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
+            population.append(mutate(dna: offspring.dna2, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
+        }
+        
+        fittest = population[0]
+        var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
+        
+        // parse the population for the fittest string
+        for indv in population {
+            let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+            if indvFitness < minFitness {
+                fittest = indv
+                minFitness = indvFitness
+            }
+        }
+        if minFitness == 0 { break; }
+    }
+    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+}
+
+main()

From 08543ed89a5b2e2275f037f01970544199b66397 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 3 Oct 2017 18:40:21 -0300
Subject: [PATCH 1252/1679] Aditions to AVLTree

---
 AVL Tree/AVLTree.swift | 704 ++++++++++++++++++++++-------------------
 1 file changed, 384 insertions(+), 320 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 52ea082ce..ddc8e7892 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -21,379 +21,443 @@
 // SOFTWARE.
 
 public class TreeNode<Key: Comparable, Payload> {
-  public typealias Node = TreeNode<Key, Payload>
-
-  var payload: Payload?
-
-  fileprivate var key: Key
-  internal var leftChild: Node?
-  internal var rightChild: Node?
-  fileprivate var height: Int
-  fileprivate weak var parent: Node?
-
-  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
-    self.key = key
-    self.payload = payload
-    self.leftChild = leftChild
-    self.rightChild = rightChild
-    self.parent = parent
-    self.height = height
-
-    self.leftChild?.parent = self
-    self.rightChild?.parent = self
-  }
-
-  public convenience init(key: Key, payload: Payload?) {
-    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
-  }
-
-  public convenience init(key: Key) {
-    self.init(key: key, payload: nil)
-  }
-
-  var isRoot: Bool {
-    return parent == nil
-  }
-
-  var isLeaf: Bool {
-    return rightChild == nil && leftChild == nil
-  }
-
-  var isLeftChild: Bool {
-    return parent?.leftChild === self
-  }
-
-  var isRightChild: Bool {
-    return parent?.rightChild === self
-  }
-
-  var hasLeftChild: Bool {
-    return leftChild != nil
-  }
-
-  var hasRightChild: Bool {
-    return rightChild != nil
-  }
-
-  var hasAnyChild: Bool {
-    return leftChild != nil || rightChild != nil
-  }
-
-  var hasBothChildren: Bool {
-    return leftChild != nil && rightChild != nil
-  }
+    public typealias Node = TreeNode<Key, Payload>
+    
+    var payload: Payload?   // Value held by the node
+    
+    fileprivate var key: Key    // Node's name
+    internal var leftChild: Node?
+    internal var rightChild: Node?
+    fileprivate var height: Int
+    weak fileprivate var parent: Node?
+    
+    public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
+        self.key = key
+        self.payload = payload
+        self.leftChild = leftChild
+        self.rightChild = rightChild
+        self.parent = parent
+        self.height = height
+        
+        self.leftChild?.parent = self
+        self.rightChild?.parent = self
+    }
+    
+    public convenience init(key: Key, payload: Payload?) {
+        self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
+    }
+    
+    public convenience init(key: Key) {
+        self.init(key: key, payload: nil)
+    }
+    
+    var isRoot: Bool {
+        return parent == nil
+    }
+    
+    var isLeaf: Bool {
+        return rightChild == nil && leftChild == nil
+    }
+    
+    var isLeftChild: Bool {
+        return parent?.leftChild === self
+    }
+    
+    var isRightChild: Bool {
+        return parent?.rightChild === self
+    }
+    
+    var hasLeftChild: Bool {
+        return leftChild != nil
+    }
+    
+    var hasRightChild: Bool {
+        return rightChild != nil
+    }
+    
+    var hasAnyChild: Bool {
+        return leftChild != nil || rightChild != nil
+    }
+    
+    var hasBothChildren: Bool {
+        return leftChild != nil && rightChild != nil
+    }
 }
 
 // MARK: - The AVL tree
 
 open class AVLTree<Key: Comparable, Payload> {
-  public typealias Node = TreeNode<Key, Payload>
-
-  fileprivate(set) var root: Node?
-  fileprivate(set) var size = 0
-
-  public init() { }
+    public typealias Node = TreeNode<Key, Payload>
+    
+    fileprivate(set) var root: Node?
+    fileprivate(set) var size = 0
+    
+    public init() { }
 }
 
 // MARK: - Searching
 
 extension TreeNode {
-  public func minimum() -> TreeNode? {
-    return leftChild?.minimum() ?? self
-  }
-
-  public func maximum() -> TreeNode? {
-    return rightChild?.maximum() ?? self
-  }
+    public func minimum() -> TreeNode? {
+        return leftChild?.minimum() ?? self
+    }
+    
+    public func maximum() -> TreeNode? {
+        return rightChild?.maximum() ?? self
+    }
 }
 
 extension AVLTree {
-  subscript(key: Key) -> Payload? {
-    get { return search(input: key) }
-    set { insert(key: key, payload: newValue) }
-  }
-
-  public func search(input: Key) -> Payload? {
-    return search(key: input, node: root)?.payload
-  }
-
-  fileprivate func search(key: Key, node: Node?) -> Node? {
-    if let node = node {
-      if key == node.key {
-        return node
-      } else if key < node.key {
-        return search(key: key, node: node.leftChild)
-      } else {
-        return search(key: key, node: node.rightChild)
-      }
-    }
-    return nil
-  }
+    subscript(key: Key) -> Payload? {
+        get { return search(input: key) }
+        set { insert(key: key, payload: newValue) }
+    }
+    
+    public func search(input: Key) -> Payload? {
+        return search(key: input, node: root)?.payload
+    }
+    
+    fileprivate func search(key: Key, node: Node?) -> Node? {
+        if let node = node {
+            if key == node.key {
+                return node
+            } else if key < node.key {
+                return search(key: key, node: node.leftChild)
+            } else {
+                return search(key: key, node: node.rightChild)
+            }
+        }
+        return nil
+    }
 }
 
 // MARK: - Inserting new items
 
 extension AVLTree {
-  public func insert(key: Key, payload: Payload? = nil) {
-    if let root = root {
-      insert(input: key, payload: payload, node: root)
-    } else {
-      root = Node(key: key, payload: payload)
-    }
-    size += 1
-  }
-
-  private func insert(input: Key, payload: Payload?, node: Node) {
-    if input < node.key {
-      if let child = node.leftChild {
-        insert(input: input, payload: payload, node: child)
-      } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-        node.leftChild = child
-        balance(node: child)
-      }
-    } else {
-      if let child = node.rightChild {
-        insert(input: input, payload: payload, node: child)
-      } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-        node.rightChild = child
-        balance(node: child)
-      }
-    }
-  }
+    public func insert(key: Key, payload: Payload? = nil) {
+        if let root = root {
+            insert(input: key, payload: payload, node: root)
+        } else {
+            root = Node(key: key, payload: payload)
+        }
+        size += 1
+    }
+    
+    private func insert(input: Key, payload: Payload?, node: Node) {
+        if input < node.key {
+            if let child = node.leftChild {
+                insert(input: input, payload: payload, node: child)
+            } else {
+                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+                node.leftChild = child
+                balance(node: child)
+            }
+        } else if input != node.key {
+            if let child = node.rightChild {
+                insert(input: input, payload: payload, node: child)
+            } else {
+                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+                node.rightChild = child
+                balance(node: child)
+            }
+        }
+    }
 }
 
 // MARK: - Balancing tree
 
 extension AVLTree {
-  fileprivate func updateHeightUpwards(node: Node?) {
-    if let node = node {
-      let lHeight = node.leftChild?.height ?? 0
-      let rHeight = node.rightChild?.height ?? 0
-      node.height = max(lHeight, rHeight) + 1
-      updateHeightUpwards(node: node.parent)
-    }
-  }
-
-  fileprivate func lrDifference(node: Node?) -> Int {
-    let lHeight = node?.leftChild?.height ?? 0
-    let rHeight = node?.rightChild?.height ?? 0
-    return lHeight - rHeight
-  }
-
-  fileprivate func balance(node: Node?) {
-    guard let node = node else {
-      return
+    fileprivate func updateHeightUpwards(node: Node?) {
+        if let node = node {
+            let lHeight = node.leftChild?.height ?? 0
+            let rHeight = node.rightChild?.height ?? 0
+            node.height = max(lHeight, rHeight) + 1
+            updateHeightUpwards(node: node.parent)
+        }
     }
-
-    updateHeightUpwards(node: node.leftChild)
-    updateHeightUpwards(node: node.rightChild)
-
-    var nodes = [Node?](repeating: nil, count: 3)
-    var subtrees = [Node?](repeating: nil, count: 4)
-    let nodeParent = node.parent
-
-    let lrFactor = lrDifference(node: node)
-    if lrFactor > 1 {
-      // left-left or left-right
-      if lrDifference(node: node.leftChild) > 0 {
-        // left-left
-        nodes[0] = node
-        nodes[2] = node.leftChild
-        nodes[1] = nodes[2]?.leftChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[1]?.rightChild
-        subtrees[2] = nodes[2]?.rightChild
-        subtrees[3] = nodes[0]?.rightChild
-      } else {
-        // left-right
-        nodes[0] = node
-        nodes[1] = node.leftChild
-        nodes[2] = nodes[1]?.rightChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[2]?.leftChild
-        subtrees[2] = nodes[2]?.rightChild
-        subtrees[3] = nodes[0]?.rightChild
-      }
-    } else if lrFactor < -1 {
-      // right-left or right-right
-      if lrDifference(node: node.rightChild) < 0 {
-        // right-right
-        nodes[1] = node
-        nodes[2] = node.rightChild
-        nodes[0] = nodes[2]?.rightChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[2]?.leftChild
-        subtrees[2] = nodes[0]?.leftChild
-        subtrees[3] = nodes[0]?.rightChild
-      } else {
-        // right-left
-        nodes[1] = node
-        nodes[0] = node.rightChild
-        nodes[2] = nodes[0]?.leftChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[2]?.leftChild
-        subtrees[2] = nodes[2]?.rightChild
-        subtrees[3] = nodes[0]?.rightChild
-      }
-    } else {
-      // Don't need to balance 'node', go for parent
-      balance(node: node.parent)
-      return
+    
+    fileprivate func lrDifference(node: Node?) -> Int {
+        let lHeight = node?.leftChild?.height ?? 0
+        let rHeight = node?.rightChild?.height ?? 0
+        return lHeight - rHeight
     }
-
-    // nodes[2] is always the head
-
-    if node.isRoot {
-      root = nodes[2]
-      root?.parent = nil
-    } else if node.isLeftChild {
-      nodeParent?.leftChild = nodes[2]
-      nodes[2]?.parent = nodeParent
-    } else if node.isRightChild {
-      nodeParent?.rightChild = nodes[2]
-      nodes[2]?.parent = nodeParent
+    
+    fileprivate func balance(node: Node?) {
+        guard let node = node else {
+            return
+        }
+        
+        updateHeightUpwards(node: node.leftChild)
+        updateHeightUpwards(node: node.rightChild)
+        
+        var nodes = [Node?](repeating: nil, count: 3)
+        var subtrees = [Node?](repeating: nil, count: 4)
+        let nodeParent = node.parent
+        
+        let lrFactor = lrDifference(node: node)
+        if lrFactor > 1 {
+            // left-left or left-right
+            if lrDifference(node: node.leftChild) > 0 {
+                // left-left
+                nodes[0] = node
+                nodes[2] = node.leftChild
+                nodes[1] = nodes[2]?.leftChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[1]?.rightChild
+                subtrees[2] = nodes[2]?.rightChild
+                subtrees[3] = nodes[0]?.rightChild
+            } else {
+                // left-right
+                nodes[0] = node
+                nodes[1] = node.leftChild
+                nodes[2] = nodes[1]?.rightChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[2]?.leftChild
+                subtrees[2] = nodes[2]?.rightChild
+                subtrees[3] = nodes[0]?.rightChild
+            }
+        } else if lrFactor < -1 {
+            // right-left or right-right
+            if lrDifference(node: node.rightChild) < 0 {
+                // right-right
+                nodes[1] = node
+                nodes[2] = node.rightChild
+                nodes[0] = nodes[2]?.rightChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[2]?.leftChild
+                subtrees[2] = nodes[0]?.leftChild
+                subtrees[3] = nodes[0]?.rightChild
+            } else {
+                // right-left
+                nodes[1] = node
+                nodes[0] = node.rightChild
+                nodes[2] = nodes[0]?.leftChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[2]?.leftChild
+                subtrees[2] = nodes[2]?.rightChild
+                subtrees[3] = nodes[0]?.rightChild
+            }
+        } else {
+            // Don't need to balance 'node', go for parent
+            balance(node: node.parent)
+            return
+        }
+        
+        // nodes[2] is always the head
+        
+        if node.isRoot {
+            root = nodes[2]
+            root?.parent = nil
+        } else if node.isLeftChild {
+            nodeParent?.leftChild = nodes[2]
+            nodes[2]?.parent = nodeParent
+        } else if node.isRightChild {
+            nodeParent?.rightChild = nodes[2]
+            nodes[2]?.parent = nodeParent
+        }
+        
+        nodes[2]?.leftChild = nodes[1]
+        nodes[1]?.parent = nodes[2]
+        nodes[2]?.rightChild = nodes[0]
+        nodes[0]?.parent = nodes[2]
+        
+        nodes[1]?.leftChild = subtrees[0]
+        subtrees[0]?.parent = nodes[1]
+        nodes[1]?.rightChild = subtrees[1]
+        subtrees[1]?.parent = nodes[1]
+        
+        nodes[0]?.leftChild = subtrees[2]
+        subtrees[2]?.parent = nodes[0]
+        nodes[0]?.rightChild = subtrees[3]
+        subtrees[3]?.parent = nodes[0]
+        
+        updateHeightUpwards(node: nodes[1])    // Update height from left
+        updateHeightUpwards(node: nodes[0])    // Update height from right
+        
+        balance(node: nodes[2]?.parent)
     }
-
-    nodes[2]?.leftChild = nodes[1]
-    nodes[1]?.parent = nodes[2]
-    nodes[2]?.rightChild = nodes[0]
-    nodes[0]?.parent = nodes[2]
-
-    nodes[1]?.leftChild = subtrees[0]
-    subtrees[0]?.parent = nodes[1]
-    nodes[1]?.rightChild = subtrees[1]
-    subtrees[1]?.parent = nodes[1]
-
-    nodes[0]?.leftChild = subtrees[2]
-    subtrees[2]?.parent = nodes[0]
-    nodes[0]?.rightChild = subtrees[3]
-    subtrees[3]?.parent = nodes[0]
-
-    updateHeightUpwards(node: nodes[1])    // Update height from left
-    updateHeightUpwards(node: nodes[0])    // Update height from right
-
-    balance(node: nodes[2]?.parent)
-  }
 }
 
 // MARK: - Displaying tree
 
 extension AVLTree {
-  fileprivate func display(node: Node?, level: Int) {
-    if let node = node {
-      display(node: node.rightChild, level: level + 1)
-      print("")
-      if node.isRoot {
-        print("Root -> ", terminator: "")
-      }
-      for _ in 0..<level {
-        print("        ", terminator:  "")
-      }
-      print("(\(node.key):\(node.height))", terminator: "")
-      display(node: node.leftChild, level: level + 1)
-    }
-  }
-
-  public func display(node: Node) {
-    display(node: node, level: 0)
-    print("")
-  }
+    fileprivate func display(node: Node?, level: Int) {
+        if let node = node {
+            display(node: node.rightChild, level: level + 1)
+            print("")
+            if node.isRoot {
+                print("Root -> ", terminator: "")
+            }
+            for _ in 0..<level {
+                print("        ", terminator:  "")
+            }
+            print("(\(node.key):\(node.height))", terminator: "")
+            display(node: node.leftChild, level: level + 1)
+        }
+    }
+    
+    public func display(node: Node) {
+        display(node: node, level: 0)
+        print("")
+    }
+    
+    public func inorder(node: Node?) -> String {
+        var output = ""
+        if let node = node {
+            output = "\(inorder(node: node.leftChild)) \(print("\(node.key) ")) \(inorder(node: node.rightChild))"
+        }
+        return output
+    }
+    
+    public func preorder(node: Node?) -> String {
+        var output = ""
+        if let node = node {
+            output = "\(preorder(node: node.leftChild)) \(print("\(node.key) ")) \(preorder(node: node.rightChild))"
+        }
+        return output
+    }
+    
+    public func postorder(node: Node?) -> String {
+        var output = ""
+        if let node = node {
+            output = "\(postorder(node: node.leftChild)) \(print("\(node.key) ")) \(postorder(node: node.rightChild))"
+        }
+        return output
+    }
 }
 
 // MARK: - Delete node
 
 extension AVLTree {
-  public func delete(key: Key) {
-    if size == 1 {
-      root = nil
-      size -= 1
-    } else if let node = search(key: key, node: root) {
-      delete(node: node)
-      size -= 1
-    }
-  }
-
-  private func delete(node: Node) {
-    if node.isLeaf {
-      // Just remove and balance up
-      if let parent = node.parent {
-        guard node.isLeftChild || node.isRightChild else {
-          // just in case
-          fatalError("Error: tree is invalid.")
+    public func delete(key: Key) {
+        if size == 1 {
+            root = nil
+            size -= 1
+        } else if let node = search(key: key, node: root) {
+            delete(node: node)
+            size -= 1
         }
-
-        if node.isLeftChild {
-          parent.leftChild = nil
-        } else if node.isRightChild {
-          parent.rightChild = nil
+    }
+    
+    private func delete(node: Node) {
+        if node.isLeaf {
+            // Just remove and balance up
+            if let parent = node.parent {
+                guard node.isLeftChild || node.isRightChild else {
+                    // just in case
+                    fatalError("Error: tree is invalid.")
+                }
+                
+                if node.isLeftChild {
+                    parent.leftChild = nil
+                } else if node.isRightChild {
+                    parent.rightChild = nil
+                }
+                
+                balance(node: parent)
+            } else {
+                // at root
+                root = nil
+            }
+        } else {
+            // Handle stem cases
+            if let replacement = node.leftChild?.maximum(), replacement !== node {
+                node.key = replacement.key
+                node.payload = replacement.payload
+                delete(node: replacement)
+            } else if let replacement = node.rightChild?.minimum(), replacement !== node {
+                node.key = replacement.key
+                node.payload = replacement.payload
+                delete(node: replacement)
+            }
         }
+    }
+}
 
-        balance(node: parent)
-      } else {
-        // at root
-        root = nil
-      }
-    } else {
-      // Handle stem cases
-      if let replacement = node.leftChild?.maximum(), replacement !== node {
-        node.key = replacement.key
-        node.payload = replacement.payload
-        delete(node: replacement)
-      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
-        node.key = replacement.key
-        node.payload = replacement.payload
-        delete(node: replacement)
-      }
-    }
-  }
+// MARK: - Advanced Stuff
+
+extension AVLTree {
+    public func doInOrder(node: Node?, _ completion: (Node) -> Void) {
+        if let node = node {
+            doInOrder(node: node.leftChild) { lnode in
+                completion(lnode)
+            }
+            completion(node)
+            doInOrder(node: node.rightChild) { rnode in
+                completion(rnode)
+            }
+        }
+    }
+    
+    public func doInPreOrder(node: Node?, _ completion: (Node) -> Void) {
+        if let node = node {
+            completion(node)
+            doInPreOrder(node: node.leftChild) { lnode in
+                completion(lnode)
+            }
+            doInPreOrder(node: node.rightChild) { rnode in
+                completion(rnode)
+            }
+        }
+    }
+    
+    public func doInPostOrder(node: Node?, _ completion: (Node) -> Void) {
+        if let node = node {
+            doInPostOrder(node: node.leftChild) { lnode in
+                completion(lnode)
+            }
+            doInPostOrder(node: node.rightChild) { rnode in
+                completion(rnode)
+            }
+            completion(node)
+        }
+    }
 }
 
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = "key: \(key), payload: \(payload), height: \(height)"
-    if let parent = parent {
-      s += ", parent: \(parent.key)"
-    }
-    if let left = leftChild {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = rightChild {
-      s += ", right = [" + right.debugDescription + "]"
+    public var debugDescription: String {
+        var s = "key: \(key), payload: \(payload), height: \(height)"
+        if let parent = parent {
+            s += ", parent: \(parent.key)"
+        }
+        if let left = leftChild {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = rightChild {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
     }
-    return s
-  }
 }
 
 extension AVLTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    return root?.debugDescription ?? "[]"
-  }
+    public var debugDescription: String {
+        return root?.debugDescription ?? "[]"
+    }
 }
 
 extension TreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if let left = leftChild {
-      s += "(\(left.description)) <- "
-    }
-    s += "\(key)"
-    if let right = rightChild {
-      s += " -> (\(right.description))"
+    public var description: String {
+        var s = ""
+        if let left = leftChild {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(key)"
+        if let right = rightChild {
+            s += " -> (\(right.description))"
+        }
+        return s
     }
-    return s
-  }
 }
 
 extension AVLTree: CustomStringConvertible {
-  public var description: String {
-    return root?.description ?? "[]"
-  }
+    public var description: String {
+        return root?.description ?? "[]"
+    }
 }

From fbfd2062cd53b51effc66b414121f1818e217a3d Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 6 Oct 2017 20:23:19 -0700
Subject: [PATCH 1253/1679] Added a note concerning brevity in CONTRIBUTING

---
 .github/CONTRIBUTING.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index 3bd5a1a91..e5d00c17b 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -4,7 +4,9 @@ Want to help out with the Swift Algorithm Club? Great! While we don't have stric
 
 **Readability**
 
-The `README` file is the cake, and the sample code is the cherry on top. Readablity is really important for us. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
+Our repo is all about learning. The `README` file is the cake, and the sample code is the cherry on top. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
+
+> When choosing between brievity and performance, err to the side of brievity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things. 
 
 **API Design Guidelines**
 

From d32c5e7476cdc77d84c13d79cae37e3d63131c5b Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:23:37 +0100
Subject: [PATCH 1254/1679] Deleted old version

---
 t.txt | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 t.txt

diff --git a/t.txt b/t.txt
new file mode 100644
index 000000000..d5f75df13
--- /dev/null
+++ b/t.txt
@@ -0,0 +1 @@
+wer

From a792197665757a73fea960d9ef739375c5dcfe65 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 15 Jul 2017 20:35:33 -0700
Subject: [PATCH 1255/1679] 3Sum and 4Sum
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Follow up 2Sum problem. How to solve 3Sum and 4Sum problem? What’s their relationships? Could we get some generic idea to solve this kind of problems? I give the explanation here.
---
 3Sum and 4Sum/3Sum.playground/Contents.swift  | 53 ++++++++++++++++
 .../3Sum.playground/contents.xcplayground     |  4 ++
 3Sum and 4Sum/4Sum.playground/Contents.swift  | 61 +++++++++++++++++++
 .../4Sum.playground/contents.xcplayground     |  4 ++
 3Sum and 4Sum/README.md                       | 48 +++++++++++++++
 .../contents.xcworkspacedata                  |  9 +++
 6 files changed, 179 insertions(+)
 create mode 100644 3Sum and 4Sum/3Sum.playground/Contents.swift
 create mode 100644 3Sum and 4Sum/3Sum.playground/contents.xcplayground
 create mode 100644 3Sum and 4Sum/4Sum.playground/Contents.swift
 create mode 100644 3Sum and 4Sum/4Sum.playground/contents.xcplayground
 create mode 100644 3Sum and 4Sum/README.md

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
new file mode 100644
index 000000000..7091ab789
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -0,0 +1,53 @@
+func ThreeSum(_ nums: [Int], targetSum: Int) -> [[Int]] {
+    var a = nums.sorted()
+    var ret: [[Int]] = []
+    
+    for i in 0..<a.count {
+        if i != 0 && a[i] == a[i-1] {
+            continue
+        }
+        
+        var j = i + 1
+        var k = nums.count - 1
+        
+        while j < k {
+            let sum = a[i] + a[j] + a[k]
+            
+            if sum == targetSum {
+                ret.append([a[i], a[j], a[k]])
+                j += 1
+            } else if sum < targetSum {
+                j += 1
+            } else {
+                k -= 1
+            }
+            
+            if sum == targetSum {
+                while j < k {
+                    var flag = false
+                    if j != 0 && a[j] == a[j-1] {
+                        j += 1
+                        flag = true
+                    }
+                    
+                    if (k != a.count - 1) && a[k] == a[k+1] {
+                        k -= 1
+                        flag = true
+                    }
+                    
+                    if (!flag) {
+                        break
+                    }
+                }
+            }
+        }
+    }
+    
+    return ret
+}
+
+// Answer: [[-1, 0, 1], [-1, -1, 2]]
+ThreeSum([-1, 0, 1, 2, -1, -4], targetSum: 0)
+
+// Answer: [[-1, -1, 1]]
+ThreeSum([-1, 1, 1, -1], targetSum: 1)
diff --git a/3Sum and 4Sum/3Sum.playground/contents.xcplayground b/3Sum and 4Sum/3Sum.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
new file mode 100644
index 000000000..b86dd42f5
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -0,0 +1,61 @@
+func FourSum(_ nums: [Int], target: Int) -> [[Int]] {
+    let a = nums.sorted()
+    var ret: [[Int]] = []
+    
+    for i in 0..<nums.count {
+        if i != 0 && a[i] == a[i-1] {
+            continue
+        }
+        for j in i+1..<nums.count {
+            if j != i+1 && a[j] == a[j-1] {
+                continue
+            }
+            
+            var k = j + 1
+            var t = nums.count - 1
+            
+            while k < t {
+                let sum = a[i] + a[j] + a[k] + a[t]
+                
+                if sum == target {
+                    ret.append([a[i], a[j], a[k], a[t]])
+                    k += 1
+                } else if sum < target {
+                    k += 1
+                } else {
+                    t -= 1
+                }
+                
+                if sum == target {
+                    while k < t {
+                        var flag = true
+                        if k != j + 1 && a[k] == a[k-1] {
+                            k += 1
+                            flag = false
+                        }
+                        
+                        if t != nums.count - 1 && a[t] == a[t+1] {
+                            t -= 1
+                            flag = false
+                        }
+                        
+                        if flag {
+                            break
+                        }
+                    }
+                }
+            }
+        }
+    }
+    
+    return ret
+}
+
+/* Answer
+[
+    [-1,  0, 0, 1],
+    [-2, -1, 1, 2],
+    [-2,  0, 0, 2]
+]
+*/
+FourSum([1, 0, -1, 0, -2, 2], target: 0)
diff --git a/3Sum and 4Sum/4Sum.playground/contents.xcplayground b/3Sum and 4Sum/4Sum.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
new file mode 100644
index 000000000..e8ae4f2e1
--- /dev/null
+++ b/3Sum and 4Sum/README.md	
@@ -0,0 +1,48 @@
+# 3Sum and 4Sum
+
+## 3Sum
+Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? 
+Find all unique triplets in the array which gives the sum of zero.
+
+**Note**: The solution set must not contain duplicate triplets.
+
+> For example, given array S = [-1, 0, 1, 2, -1, -4](),
+> A solution set is:
+> [
+> ]()>  [-1, 0, 1](),
+>  [-1, -1, 2]()
+> ]
+
+### Solution
+Like [2Sum][5], we can sort the array first, then use 2 pointers method to solve the problem. But here, we need 3 numbers, so we need add one more pointer. But how to play with 3 pointers?
+
+The key idea here is we split the array into 2 parts, if we have a pointer `i`, let’s assume we got `i` position already. What’ next? Actually, next is just a 2Sum problem right? We can just apply 2 pointers method in 2Sum. But what’s 2Sum’s target sum? Is it `target2Sum = target3Sum - nums[i]` ? That’s awesome! 
+
+How we figure out `i`? We can loop i from `0` to `nums.count - 1`.
+
+How we avoid duplicate triplets? Since the array has been sorted, we just need to check if `a[i] == a[i-1]`. Why? Because if `a[i] == a[i-1]`, it means that `a[i-1]` already covers all `a[i]` solutions, we should not do it, otherwise it will have duplicate answers. The same for `j` and `k` which runs for 2Sum.
+
+So, we successfully downgrade 3Sum to 2Sum problem with some tricks. Next, you will see how we downgrade 4Sum to 3Sum.
+
+## 4Sum
+Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.
+
+**Note**: The solution set must not contain duplicate quadruplets.
+
+### Solution
+After 3Sum, you should have feeling actually we just need a same idea to downgrade it to 3Sum, and then 2Sum, and then solve it.
+
+How? I will leave it as a challenge for you to figure out first and see if you really master the idea behind this kind of problems.
+
+Feel free to check out the solution if you are blocked.
+
+## Where to go next?
+If it’s a KSum, and `K` is a big number, do we need to create `K` pointers and solve it?
+
+I will write another topic to present how we will solve this KSum problem with a generic way soon.
+
+
+
+
+
+[5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 1e3c20224..2d9123248 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -103,6 +103,15 @@
       <FileRef
          location = "group:LRU Cache/Readme.md">
       </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/README.md">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/3Sum.playground">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/4Sum.playground">
+      </FileRef>
    </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"

From 936bf5bfc115c79cff4bb667a4aa1820b88d2bb2 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 15 Jul 2017 20:35:33 -0700
Subject: [PATCH 1256/1679] 3Sum and 4Sum
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Follow up 2Sum problem. How to solve 3Sum and 4Sum problem? What’s their relationships? Could we get some generic idea to solve this kind of problems? I give the explanation here.
---
 3Sum and 4Sum/README.md | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index e8ae4f2e1..caac3f37e 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -6,12 +6,8 @@ Find all unique triplets in the array which gives the sum of zero.
 
 **Note**: The solution set must not contain duplicate triplets.
 
-> For example, given array S = [-1, 0, 1, 2, -1, -4](),
-> A solution set is:
-> [
-> ]()>  [-1, 0, 1](),
->  [-1, -1, 2]()
-> ]
+> For example, given array S = [-1, 0, 1, 2, -1, -4],
+> A solution set is: [[-1, 0, 1], [-1, -1, 2]]
 
 ### Solution
 Like [2Sum][5], we can sort the array first, then use 2 pointers method to solve the problem. But here, we need 3 numbers, so we need add one more pointer. But how to play with 3 pointers?
@@ -45,4 +41,4 @@ I will write another topic to present how we will solve this KSum problem with a
 
 
 
-[5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
\ No newline at end of file
+[5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem

From 00994544ebbf59a27876b3d8ec21c02ef1645e64 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 28 Sep 2017 01:47:37 -0700
Subject: [PATCH 1257/1679] Update README.md

Work in progress, not done yet!
---
 3Sum and 4Sum/README.md | 125 ++++++++++++++++++++++++++++++++++++----
 1 file changed, 114 insertions(+), 11 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index caac3f37e..3d311f650 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -1,24 +1,127 @@
 # 3Sum and 4Sum
 
+3Sum and 4Sum are extensions of a popular algorithm question, the [2Sum][5]. This article will talk about the problem and describe possible solutions.
+
 ## 3Sum
-Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? 
-Find all unique triplets in the array which gives the sum of zero.
 
-**Note**: The solution set must not contain duplicate triplets.
+Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
 
-> For example, given array S = [-1, 0, 1, 2, -1, -4],
-> A solution set is: [[-1, 0, 1], [-1, -1, 2]]
+**Note**: The solution subsets must not contain duplicate triplets. (Each element in the array can only be used once)
 
-### Solution
-Like [2Sum][5], we can sort the array first, then use 2 pointers method to solve the problem. But here, we need 3 numbers, so we need add one more pointer. But how to play with 3 pointers?
+> For example, given the array [-1, 0, 1, 2, -1, -4], and the target **0**:
+> The solution set is: [[-1, 0, 1], [-1, -1, 2]] // The two **-1** values in the array are considered to be distinct
+
+### Example
+
+Consider the following array of integers, and a target sum of **0**:
+
+```
+[-1, 0, 1, 2, -1, -4]
+```
+
+#### 1. Sorting
+
+You'll first sort the array in ascending order:
+
+```
+[-4, -1, -1, 0, 1, 2]
+```
+
+#### 2. Two Sum's Methodology
+
+The 3Sum problem can be solved by augmenting the 2Sum solution, so let's begin by doing a quick explanation on how 2Sum handles the solution. 2Sum begins by comparing the left and right most values:
+
+```
+[-4, -1, -1, 0, 1, 2]
+  l                r
+```
+
+Your target sum is **0**. Given the current left and right values, you won't be able to make the target number. However, you've gained a valuable hint for your next step. 
+
+```
+-4 + 2 = -2 // too small!
+```
+
+The result of `l + r` gave you a value that is smaller than the target number. Thus, you have two options:
+
+1. Increase the lower number. 
+2. Increase the higher number.
+
+Because your array is sorted, you can quickly identify that you cannot pick option **2**, since the rightmost number is already the biggest number. Thus, you have no choice but to try for a different number from the left end of the array:
+
+```
+[-4, -1, -1, 0, 1, 2]
+      l            r
+```
+
+This time, you'll get the following result from summing `l` and `r`:
+
+```
+-1 + 2 = 1 // too big!
+```
+
+This time, the value is too big! I hope you see where it goes from here. Since the array is already sorted, you can only decrease the value on the right side in an attempt to balance things out. Hence, the next iteration of your algorithm will look like this:
+
+```
+[-4, -1, -1, 0, 1, 2]
+      l         r 
+```
+
+And then you've found a match :]
+
+```
+-1 + 1 = 0
+```
+
+#### Augmenting 2Sum
+
+Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
+
+```
+[-4, -1, -1, 0, 1, 2]
+  l                r
+```
+
+Your goal this time is the following equation:
+
+```
+l + r + m = 0
+```
+
+You have the values of `l` and `r`:
+
+```
+-4 + 2 + m = 0
+
+// in other words
+m = 4 - 2 = 2
+```
+
+For the current values of `l` and `r`, you need to find a value of **2** in the array to satisfy your target sum...
+
+#### Finding `m`
+
+```
+         m -- where?
+[-4, -1, -1, 0, 1, 2]
+  l                r 
+```
+
+There are slight optimizations you can do to find `m`, but to keep things simple, you'll just iterate through the array from `l` index to the `r` index. Once you find a value where `l + r + m = target`, you've found your first match! 
+
+#### Avoiding Duplicates
+
+// TODO: Work in progress
 
-The key idea here is we split the array into 2 parts, if we have a pointer `i`, let’s assume we got `i` position already. What’ next? Actually, next is just a 2Sum problem right? We can just apply 2 pointers method in 2Sum. But what’s 2Sum’s target sum? Is it `target2Sum = target3Sum - nums[i]` ? That’s awesome! 
+Avoiding duplicate values is fairly straightforward if you've understood everything so far. Let's consider a sample array that has a few duplicates:
 
-How we figure out `i`? We can loop i from `0` to `nums.count - 1`.
+```
+target = 0
 
-How we avoid duplicate triplets? Since the array has been sorted, we just need to check if `a[i] == a[i-1]`. Why? Because if `a[i] == a[i-1]`, it means that `a[i-1]` already covers all `a[i]` solutions, we should not do it, otherwise it will have duplicate answers. The same for `j` and `k` which runs for 2Sum.
+[-1, -1, -1, -1, 0, 1, 1, 1]
+```
 
-So, we successfully downgrade 3Sum to 2Sum problem with some tricks. Next, you will see how we downgrade 4Sum to 3Sum.
+One possible subset is `[-1, 0, 1]`, and in fact is the only subset for 3Sum. 
 
 ## 4Sum
 Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.

From 5632cae5ed1d7255c799252ccc5a2fd8a0f1f741 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 30 Sep 2017 08:56:22 -0700
Subject: [PATCH 1258/1679] address comment

---
 3Sum and 4Sum/README.md                       | 41 +++++++++++++------
 .../contents.xcworkspacedata                  | 22 ++++++----
 t.txt                                         |  1 -
 3 files changed, 42 insertions(+), 22 deletions(-)
 delete mode 100644 t.txt

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 3d311f650..486c45c92 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -111,8 +111,6 @@ There are slight optimizations you can do to find `m`, but to keep things simple
 
 #### Avoiding Duplicates
 
-// TODO: Work in progress
-
 Avoiding duplicate values is fairly straightforward if you've understood everything so far. Let's consider a sample array that has a few duplicates:
 
 ```
@@ -123,25 +121,44 @@ target = 0
 
 One possible subset is `[-1, 0, 1]`, and in fact is the only subset for 3Sum. 
 
-## 4Sum
-Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.
+The easiet way is using set. We can maintain a solution set, then we can check if the triplets is in the set or not to determine whether it's duplicate.
 
-**Note**: The solution set must not contain duplicate quadruplets.
+Set introduces space complexity. So we still want to avoid extra space using. Let's change an angle consider, we can loop the array first find `m` then next thing is to find `l` and `r`. 
 
-### Solution
-After 3Sum, you should have feeling actually we just need a same idea to downgrade it to 3Sum, and then 2Sum, and then solve it.
+For example
 
-How? I will leave it as a challenge for you to figure out first and see if you really master the idea behind this kind of problems.
+```
+​```
+[-1, 0, 1, 2, -1, -4] // unsorted
 
-Feel free to check out the solution if you are blocked.
+1)
+[-4, -1, -1, 0, 1, 2]
+      m   l        r
 
-## Where to go next?
-If it’s a KSum, and `K` is a big number, do we need to create `K` pointers and solve it?
+2)
+[-4, -1, -1, 0, 1, 2]
+          m  l     r
 
-I will write another topic to present how we will solve this KSum problem with a generic way soon.
+3)
+[-4, -1, -1, 0, 1, 2]
+      m      l     r
+​```
+
+We loop `m` in `0..<n`. We will do another inner loop at the same time, `l..r` loops in `i+1..<n`. 
+In 1), we will check if `a[i] == a[i-1]`? It's not in this case, then the problem is 2sum (`l..r`).
+In 2), Since `a[i] == a[i-1]`, it means `a[i-1]` covers `a[i]` case. Because case 3) contains case 2) solutions.
+```
 
 
 
+## 4Sum
+Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
+
+**Note**: The solution set must not contain duplicate quadruplets.
+
+### Solution
+After 3Sum, we already have the idea to change to a problem to a familiar problem we solved before. So, the idea here is straightforward. We just need to downgrade 4Sum to 3Sum. Then we can solve 4Sum.
 
+It's easy to think that we loop the array and get the first the element, then the rest array is 3Sum problem. Since the code is pretty simple, I will avoid duplicate introducation here.
 
 [5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 2d9123248..4cab8e2d4 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -38,6 +38,19 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:"
+      name = "3Sum and 4Sum">
+      <FileRef
+         location = "group:3Sum and 4Sum/README.md">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/3Sum.playground">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/4Sum.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "container:"
       name = "Dijkstra">
@@ -103,15 +116,6 @@
       <FileRef
          location = "group:LRU Cache/Readme.md">
       </FileRef>
-      <FileRef
-         location = "group:3Sum and 4Sum/README.md">
-      </FileRef>
-      <FileRef
-         location = "group:3Sum and 4Sum/3Sum.playground">
-      </FileRef>
-      <FileRef
-         location = "group:3Sum and 4Sum/4Sum.playground">
-      </FileRef>
    </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"
diff --git a/t.txt b/t.txt
deleted file mode 100644
index d5f75df13..000000000
--- a/t.txt
+++ /dev/null
@@ -1 +0,0 @@
-wer

From ca6bd9f1c0c851e0561443c9b5bffdb926f38929 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Fri, 6 Oct 2017 22:51:55 -0700
Subject: [PATCH 1259/1679] address comments

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 36 ++++++++++++--------
 1 file changed, 21 insertions(+), 15 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 7091ab789..ec79ba787 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -2,36 +2,36 @@ func ThreeSum(_ nums: [Int], targetSum: Int) -> [[Int]] {
     var a = nums.sorted()
     var ret: [[Int]] = []
     
-    for i in 0..<a.count {
-        if i != 0 && a[i] == a[i-1] {
+    for m in 0..<a.count {
+        if m != 0 && a[m] == a[m-1] {
             continue
         }
         
-        var j = i + 1
-        var k = nums.count - 1
+        var l = m + 1
+        var r = nums.count - 1
         
-        while j < k {
-            let sum = a[i] + a[j] + a[k]
+        while l < r {
+            let sum = a[m] + a[l] + a[r]
             
             if sum == targetSum {
-                ret.append([a[i], a[j], a[k]])
-                j += 1
+                ret.append([a[m], a[l], a[r]])
+                l += 1
             } else if sum < targetSum {
-                j += 1
+                l += 1
             } else {
-                k -= 1
+                r -= 1
             }
             
             if sum == targetSum {
-                while j < k {
+                while l < r {
                     var flag = false
-                    if j != 0 && a[j] == a[j-1] {
-                        j += 1
+                    if l != 0 && a[l] == a[l-1] {
+                        l += 1
                         flag = true
                     }
                     
-                    if (k != a.count - 1) && a[k] == a[k+1] {
-                        k -= 1
+                    if (r != a.count - 1) && a[r] == a[r+1] {
+                        r -= 1
                         flag = true
                     }
                     
@@ -51,3 +51,9 @@ ThreeSum([-1, 0, 1, 2, -1, -4], targetSum: 0)
 
 // Answer: [[-1, -1, 1]]
 ThreeSum([-1, 1, 1, -1], targetSum: 1)
+
+// Answer: [[-1, -1, 2], [-1, 0, 1]]
+ThreeSum([-1, -1, -1, -1, 2, 1, -4, 0], targetSum: 0)
+
+// Answer: [[-1, -1, 2]]
+ThreeSum([-1, -1, -1, -1, -1, -1, 2], targetSum: 0)

From a47ddd704b70b6a4e7e93fedf8d4b1032c0f70a2 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 12:15:39 -0500
Subject: [PATCH 1260/1679] fix: convex hull no longer produces concave shapes

- removed a division by zero in the point-to-line distance formula
---
 .../Convex Hull.xcodeproj/project.pbxproj     | 146 +++++++++++++++++-
 Convex Hull/Convex Hull/View.swift            |  30 ++--
 .../Convex HullTests/Convex_HullTests.swift   |  34 ++++
 Convex Hull/Convex HullTests/Info.plist       |  22 +++
 4 files changed, 218 insertions(+), 14 deletions(-)
 create mode 100644 Convex Hull/Convex HullTests/Convex_HullTests.swift
 create mode 100644 Convex Hull/Convex HullTests/Info.plist

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index bb3189d64..4eec69f7d 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -7,13 +7,28 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
+		1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1CB614201F893A3800A14493 /* Convex_HullTests.swift */; };
+		1CB614281F893ACA00A14493 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
 		8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68B91E59989400161780 /* AppDelegate.swift */; };
 		8E6D68C11E59989400161780 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C01E59989400161780 /* Assets.xcassets */; };
 		8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C21E59989400161780 /* LaunchScreen.storyboard */; };
 		8E6D68CC1E599CF100161780 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
 /* End PBXBuildFile section */
 
+/* Begin PBXContainerItemProxy section */
+		1CB614231F893A3800A14493 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 8E6D68AE1E59989400161780 /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = 8E6D68B51E59989400161780;
+			remoteInfo = "Convex Hull";
+		};
+/* End PBXContainerItemProxy section */
+
 /* Begin PBXFileReference section */
+		1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Convex HullTests.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
+		1CB614201F893A3800A14493 /* Convex_HullTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Convex_HullTests.swift; sourceTree = "<group>"; };
+		1CB614221F893A3800A14493 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		8E6D68B61E59989400161780 /* Convex Hull.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = "Convex Hull.app"; sourceTree = BUILT_PRODUCTS_DIR; };
 		8E6D68B91E59989400161780 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
 		8E6D68C01E59989400161780 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
@@ -23,6 +38,13 @@
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
+		1CB6141B1F893A3800A14493 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
 		8E6D68B31E59989400161780 /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
@@ -33,10 +55,20 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
+		1CB6141F1F893A3800A14493 /* Convex HullTests */ = {
+			isa = PBXGroup;
+			children = (
+				1CB614201F893A3800A14493 /* Convex_HullTests.swift */,
+				1CB614221F893A3800A14493 /* Info.plist */,
+			);
+			path = "Convex HullTests";
+			sourceTree = "<group>";
+		};
 		8E6D68AD1E59989400161780 = {
 			isa = PBXGroup;
 			children = (
 				8E6D68B81E59989400161780 /* Convex Hull */,
+				1CB6141F1F893A3800A14493 /* Convex HullTests */,
 				8E6D68B71E59989400161780 /* Products */,
 			);
 			sourceTree = "<group>";
@@ -45,6 +77,7 @@
 			isa = PBXGroup;
 			children = (
 				8E6D68B61E59989400161780 /* Convex Hull.app */,
+				1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -64,6 +97,24 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
+		1CB6141D1F893A3800A14493 /* Convex HullTests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */;
+			buildPhases = (
+				1CB6141A1F893A3800A14493 /* Sources */,
+				1CB6141B1F893A3800A14493 /* Frameworks */,
+				1CB6141C1F893A3800A14493 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				1CB614241F893A3800A14493 /* PBXTargetDependency */,
+			);
+			name = "Convex HullTests";
+			productName = "Convex HullTests";
+			productReference = 1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
 		8E6D68B51E59989400161780 /* Convex Hull */ = {
 			isa = PBXNativeTarget;
 			buildConfigurationList = 8E6D68C81E59989400161780 /* Build configuration list for PBXNativeTarget "Convex Hull" */;
@@ -87,10 +138,15 @@
 		8E6D68AE1E59989400161780 /* Project object */ = {
 			isa = PBXProject;
 			attributes = {
-				LastSwiftUpdateCheck = 0820;
+				LastSwiftUpdateCheck = 0900;
 				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = Workmoose;
 				TargetAttributes = {
+					1CB6141D1F893A3800A14493 = {
+						CreatedOnToolsVersion = 9.0;
+						ProvisioningStyle = Automatic;
+						TestTargetID = 8E6D68B51E59989400161780;
+					};
 					8E6D68B51E59989400161780 = {
 						CreatedOnToolsVersion = 8.2.1;
 						DevelopmentTeam = 7C4LVS3ZVC;
@@ -112,11 +168,19 @@
 			projectRoot = "";
 			targets = (
 				8E6D68B51E59989400161780 /* Convex Hull */,
+				1CB6141D1F893A3800A14493 /* Convex HullTests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
+		1CB6141C1F893A3800A14493 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
 		8E6D68B41E59989400161780 /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
@@ -129,6 +193,15 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
+		1CB6141A1F893A3800A14493 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				1CB614281F893ACA00A14493 /* View.swift in Sources */,
+				1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
 		8E6D68B21E59989400161780 /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
@@ -140,6 +213,14 @@
 		};
 /* End PBXSourcesBuildPhase section */
 
+/* Begin PBXTargetDependency section */
+		1CB614241F893A3800A14493 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			target = 8E6D68B51E59989400161780 /* Convex Hull */;
+			targetProxy = 1CB614231F893A3800A14493 /* PBXContainerItemProxy */;
+		};
+/* End PBXTargetDependency section */
+
 /* Begin PBXVariantGroup section */
 		8E6D68C21E59989400161780 /* LaunchScreen.storyboard */ = {
 			isa = PBXVariantGroup;
@@ -152,6 +233,60 @@
 /* End PBXVariantGroup section */
 
 /* Begin XCBuildConfiguration section */
+		1CB614251F893A3800A14493 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++14";
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CODE_SIGN_IDENTITY = "iPhone Developer";
+				CODE_SIGN_STYLE = Automatic;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+				TARGETED_DEVICE_FAMILY = "1,2";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
+			};
+			name = Debug;
+		};
+		1CB614261F893A3800A14493 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++14";
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CODE_SIGN_IDENTITY = "iPhone Developer";
+				CODE_SIGN_STYLE = Automatic;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+				TARGETED_DEVICE_FAMILY = "1,2";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
+			};
+			name = Release;
+		};
 		8E6D68C61E59989400161780 /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
@@ -274,6 +409,15 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
+		1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				1CB614251F893A3800A14493 /* Debug */,
+				1CB614261F893A3800A14493 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
 		8E6D68B11E59989400161780 /* Build configuration list for PBXProject "Convex Hull" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 408689a13..a50cc247a 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -93,23 +93,11 @@ class View: UIView {
     }
 
     var pts = points
-
-    // calculate parameters of general line equation y = a * x + b
-    let a = (p1.y - p2.y) / (p1.x - p2.x)
-    let b = p1.y - a * p1.x
-
-    // calculate normal line's growth factor
-    let a1 = -1 / a
-
     var maxDist: CGFloat = -1
     var maxPoint: CGPoint = pts.first!
 
     for p in pts { // for every point check the distance from our line
-      let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
-      let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
-      let y = a * x + b // calculate y value of this intersect point
-
-      let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
+      let dist = distance(from: p, to: (p1, p2))
       if dist > maxDist { // if distance is larger than current maxDist remember new point p
         maxDist = dist
         maxPoint = p
@@ -150,6 +138,22 @@ class View: UIView {
     findHull(s2, maxPoint, p2)
   }
 
+  func distance(from p: CGPoint, to line: (CGPoint, CGPoint)) -> CGFloat {
+    // If line.0 and line.1 are the same point, they don't define a line (and, besides,
+    // would cause division by zero in the distance formula). Return the distance between
+    // line.0 and point p instead.
+    if line.0 == line.1 {
+      return sqrt(pow(p.x - line.0.x, 2) + pow(p.y - line.0.y, 2))
+    }
+
+    // from Deza, Michel Marie; Deza, Elena (2013), Encyclopedia of Distances (2nd ed.), Springer, p. 86, ISBN 9783642309588
+    return abs((line.1.y - line.0.y) * p.x
+      - (line.1.x - line.0.x) * p.y
+      + line.1.x * line.0.y
+      - line.1.y * line.0.x)
+      / sqrt(pow(line.1.y - line.0.y, 2) + pow(line.1.x - line.0.x, 2))
+  }
+
   override func draw(_ rect: CGRect) {
 
     let context = UIGraphicsGetCurrentContext()
diff --git a/Convex Hull/Convex HullTests/Convex_HullTests.swift b/Convex Hull/Convex HullTests/Convex_HullTests.swift
new file mode 100644
index 000000000..40f6def07
--- /dev/null
+++ b/Convex Hull/Convex HullTests/Convex_HullTests.swift	
@@ -0,0 +1,34 @@
+//
+//  Convex_HullTests.swift
+//  Convex HullTests
+//
+//  Created by Matthew Nespor on 10/7/17.
+//  Copyright © 2017 Workmoose. All rights reserved.
+//
+
+import XCTest
+
+class Convex_HullTests: XCTestCase {
+  func testHorizontalInitialLine() {
+    let view = View()
+    let excludedPoint = CGPoint(x: 146, y: 284)
+    let includedPoints = [
+      CGPoint(x: 353, y: 22),
+      CGPoint(x: 22, y: 22),
+      CGPoint(x: 157, y: 447),
+    ]
+
+    view.points.append(contentsOf: includedPoints)
+    view.points.append(excludedPoint)
+    view.points.sort { (a: CGPoint, b: CGPoint) -> Bool in
+      return a.x < b.x
+    }
+
+    view.quickHull(points: view.points)
+
+    assert(includedPoints.filter({ view.convexHull.contains($0) }).count == 3,
+           "\(includedPoints) should have been included")
+    assert(!view.convexHull.contains(excludedPoint),
+           "\(excludedPoint) should have been excluded")
+    }
+}
diff --git a/Convex Hull/Convex HullTests/Info.plist b/Convex Hull/Convex HullTests/Info.plist
new file mode 100644
index 000000000..6c40a6cd0
--- /dev/null
+++ b/Convex Hull/Convex HullTests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>$(DEVELOPMENT_LANGUAGE)</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>

From dad84159ddd2af73945b8a2da85c987151042007 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 12:34:10 -0500
Subject: [PATCH 1261/1679] test: configure convex hull tests for travis ci

---
 .travis.yml                                   |  1 +
 .../Convex Hull.xcodeproj/project.pbxproj     | 78 +++++++++----------
 .../xcshareddata/xcschemes/Tests.xcscheme     | 58 ++++++++++++++
 .../{Convex HullTests => Tests}/Info.plist    |  0
 .../Tests.swift}                              |  8 +-
 5 files changed, 103 insertions(+), 42 deletions(-)
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 rename Convex Hull/{Convex HullTests => Tests}/Info.plist (100%)
 rename Convex Hull/{Convex HullTests/Convex_HullTests.swift => Tests/Tests.swift} (87%)

diff --git a/.travis.yml b/.travis.yml
index 16f1934d1..977ff6774 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,6 +20,7 @@ script:
 - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests
 - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index 4eec69f7d..651a5bed3 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -7,8 +7,8 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1CB614201F893A3800A14493 /* Convex_HullTests.swift */; };
-		1CB614281F893ACA00A14493 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
+		1CB614301F89456C00A14493 /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1CB6142F1F89456C00A14493 /* Tests.swift */; };
+		1CB614371F8945B300A14493 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
 		8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68B91E59989400161780 /* AppDelegate.swift */; };
 		8E6D68C11E59989400161780 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C01E59989400161780 /* Assets.xcassets */; };
 		8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C21E59989400161780 /* LaunchScreen.storyboard */; };
@@ -16,7 +16,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
-		1CB614231F893A3800A14493 /* PBXContainerItemProxy */ = {
+		1CB614321F89456C00A14493 /* PBXContainerItemProxy */ = {
 			isa = PBXContainerItemProxy;
 			containerPortal = 8E6D68AE1E59989400161780 /* Project object */;
 			proxyType = 1;
@@ -26,9 +26,9 @@
 /* End PBXContainerItemProxy section */
 
 /* Begin PBXFileReference section */
-		1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Convex HullTests.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
-		1CB614201F893A3800A14493 /* Convex_HullTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Convex_HullTests.swift; sourceTree = "<group>"; };
-		1CB614221F893A3800A14493 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		1CB6142D1F89456C00A14493 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		1CB6142F1F89456C00A14493 /* Tests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Tests.swift; sourceTree = "<group>"; };
+		1CB614311F89456C00A14493 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		8E6D68B61E59989400161780 /* Convex Hull.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = "Convex Hull.app"; sourceTree = BUILT_PRODUCTS_DIR; };
 		8E6D68B91E59989400161780 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
 		8E6D68C01E59989400161780 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
@@ -38,7 +38,7 @@
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
-		1CB6141B1F893A3800A14493 /* Frameworks */ = {
+		1CB6142A1F89456C00A14493 /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -55,20 +55,20 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
-		1CB6141F1F893A3800A14493 /* Convex HullTests */ = {
+		1CB6142E1F89456C00A14493 /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				1CB614201F893A3800A14493 /* Convex_HullTests.swift */,
-				1CB614221F893A3800A14493 /* Info.plist */,
+				1CB6142F1F89456C00A14493 /* Tests.swift */,
+				1CB614311F89456C00A14493 /* Info.plist */,
 			);
-			path = "Convex HullTests";
+			path = Tests;
 			sourceTree = "<group>";
 		};
 		8E6D68AD1E59989400161780 = {
 			isa = PBXGroup;
 			children = (
 				8E6D68B81E59989400161780 /* Convex Hull */,
-				1CB6141F1F893A3800A14493 /* Convex HullTests */,
+				1CB6142E1F89456C00A14493 /* Tests */,
 				8E6D68B71E59989400161780 /* Products */,
 			);
 			sourceTree = "<group>";
@@ -77,7 +77,7 @@
 			isa = PBXGroup;
 			children = (
 				8E6D68B61E59989400161780 /* Convex Hull.app */,
-				1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */,
+				1CB6142D1F89456C00A14493 /* Tests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -97,22 +97,22 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		1CB6141D1F893A3800A14493 /* Convex HullTests */ = {
+		1CB6142C1F89456C00A14493 /* Tests */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */;
+			buildConfigurationList = 1CB614341F89456C00A14493 /* Build configuration list for PBXNativeTarget "Tests" */;
 			buildPhases = (
-				1CB6141A1F893A3800A14493 /* Sources */,
-				1CB6141B1F893A3800A14493 /* Frameworks */,
-				1CB6141C1F893A3800A14493 /* Resources */,
+				1CB614291F89456C00A14493 /* Sources */,
+				1CB6142A1F89456C00A14493 /* Frameworks */,
+				1CB6142B1F89456C00A14493 /* Resources */,
 			);
 			buildRules = (
 			);
 			dependencies = (
-				1CB614241F893A3800A14493 /* PBXTargetDependency */,
+				1CB614331F89456C00A14493 /* PBXTargetDependency */,
 			);
-			name = "Convex HullTests";
-			productName = "Convex HullTests";
-			productReference = 1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */;
+			name = Tests;
+			productName = Tests;
+			productReference = 1CB6142D1F89456C00A14493 /* Tests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 		8E6D68B51E59989400161780 /* Convex Hull */ = {
@@ -142,7 +142,7 @@
 				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = Workmoose;
 				TargetAttributes = {
-					1CB6141D1F893A3800A14493 = {
+					1CB6142C1F89456C00A14493 = {
 						CreatedOnToolsVersion = 9.0;
 						ProvisioningStyle = Automatic;
 						TestTargetID = 8E6D68B51E59989400161780;
@@ -168,13 +168,13 @@
 			projectRoot = "";
 			targets = (
 				8E6D68B51E59989400161780 /* Convex Hull */,
-				1CB6141D1F893A3800A14493 /* Convex HullTests */,
+				1CB6142C1F89456C00A14493 /* Tests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
-		1CB6141C1F893A3800A14493 /* Resources */ = {
+		1CB6142B1F89456C00A14493 /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -193,12 +193,12 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
-		1CB6141A1F893A3800A14493 /* Sources */ = {
+		1CB614291F89456C00A14493 /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				1CB614281F893ACA00A14493 /* View.swift in Sources */,
-				1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */,
+				1CB614371F8945B300A14493 /* View.swift in Sources */,
+				1CB614301F89456C00A14493 /* Tests.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -214,10 +214,10 @@
 /* End PBXSourcesBuildPhase section */
 
 /* Begin PBXTargetDependency section */
-		1CB614241F893A3800A14493 /* PBXTargetDependency */ = {
+		1CB614331F89456C00A14493 /* PBXTargetDependency */ = {
 			isa = PBXTargetDependency;
 			target = 8E6D68B51E59989400161780 /* Convex Hull */;
-			targetProxy = 1CB614231F893A3800A14493 /* PBXContainerItemProxy */;
+			targetProxy = 1CB614321F89456C00A14493 /* PBXContainerItemProxy */;
 		};
 /* End PBXTargetDependency section */
 
@@ -233,7 +233,7 @@
 /* End PBXVariantGroup section */
 
 /* Begin XCBuildConfiguration section */
-		1CB614251F893A3800A14493 /* Debug */ = {
+		1CB614351F89456C00A14493 /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "$(TEST_HOST)";
@@ -249,10 +249,10 @@
 				CODE_SIGN_IDENTITY = "iPhone Developer";
 				CODE_SIGN_STYLE = Automatic;
 				GCC_C_LANGUAGE_STANDARD = gnu11;
-				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				INFOPLIST_FILE = Tests/Info.plist;
 				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_VERSION = 4.0;
 				TARGETED_DEVICE_FAMILY = "1,2";
@@ -260,7 +260,7 @@
 			};
 			name = Debug;
 		};
-		1CB614261F893A3800A14493 /* Release */ = {
+		1CB614361F89456C00A14493 /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "$(TEST_HOST)";
@@ -276,10 +276,10 @@
 				CODE_SIGN_IDENTITY = "iPhone Developer";
 				CODE_SIGN_STYLE = Automatic;
 				GCC_C_LANGUAGE_STANDARD = gnu11;
-				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				INFOPLIST_FILE = Tests/Info.plist;
 				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_VERSION = 4.0;
 				TARGETED_DEVICE_FAMILY = "1,2";
@@ -409,11 +409,11 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */ = {
+		1CB614341F89456C00A14493 /* Build configuration list for PBXNativeTarget "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
-				1CB614251F893A3800A14493 /* Debug */,
-				1CB614261F893A3800A14493 /* Release */,
+				1CB614351F89456C00A14493 /* Debug */,
+				1CB614361F89456C00A14493 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
diff --git a/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..1f93a0c4f
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,58 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0900"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "1CB6142C1F89456C00A14493"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Convex Hull.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Convex Hull/Convex HullTests/Info.plist b/Convex Hull/Tests/Info.plist
similarity index 100%
rename from Convex Hull/Convex HullTests/Info.plist
rename to Convex Hull/Tests/Info.plist
diff --git a/Convex Hull/Convex HullTests/Convex_HullTests.swift b/Convex Hull/Tests/Tests.swift
similarity index 87%
rename from Convex Hull/Convex HullTests/Convex_HullTests.swift
rename to Convex Hull/Tests/Tests.swift
index 40f6def07..411424479 100644
--- a/Convex Hull/Convex HullTests/Convex_HullTests.swift	
+++ b/Convex Hull/Tests/Tests.swift	
@@ -1,6 +1,6 @@
 //
-//  Convex_HullTests.swift
-//  Convex HullTests
+//  Tests.swift
+//  Tests
 //
 //  Created by Matthew Nespor on 10/7/17.
 //  Copyright © 2017 Workmoose. All rights reserved.
@@ -8,7 +8,7 @@
 
 import XCTest
 
-class Convex_HullTests: XCTestCase {
+class Tests: XCTestCase {
   func testHorizontalInitialLine() {
     let view = View()
     let excludedPoint = CGPoint(x: 146, y: 284)
@@ -18,6 +18,8 @@ class Convex_HullTests: XCTestCase {
       CGPoint(x: 157, y: 447),
     ]
 
+    view.points = [CGPoint]()
+    view.convexHull = [CGPoint]()
     view.points.append(contentsOf: includedPoints)
     view.points.append(excludedPoint)
     view.points.sort { (a: CGPoint, b: CGPoint) -> Bool in

From a1d0e3fd3008d1c17c37aee32d3d8ab39bab669c Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 12:48:13 -0500
Subject: [PATCH 1262/1679] edit Selection Sampling for clarity as described in
 #475

---
 .../SelectionSampling.playground/Contents.swift           | 8 ++++----
 Selection Sampling/SelectionSampling.swift                | 8 ++++----
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index f4aace0c7..7443db67c 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -32,19 +32,19 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var b = [T]()
 
   while selected < requested {
-    examined += 1
-
     // Calculate random variable 0.0 <= r < 1.0 (exclusive!).
     let r = Double(arc4random()) / 0x100000000
 
-    let leftToExamine = a.count - examined + 1
+    let leftToExamine = a.count - examined
     let leftToAdd = requested - selected
 
     // Decide whether to use the next record from the input.
     if Double(leftToExamine) * r < Double(leftToAdd) {
       selected += 1
-      b.append(a[examined - 1])
+      b.append(a[examined])
     }
+
+    examined += 1
   }
   return b
 }
diff --git a/Selection Sampling/SelectionSampling.swift b/Selection Sampling/SelectionSampling.swift
index 1e6257908..52aa5988b 100644
--- a/Selection Sampling/SelectionSampling.swift	
+++ b/Selection Sampling/SelectionSampling.swift	
@@ -61,19 +61,19 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var b = [T]()
 
   while selected < requested {
-    examined += 1
-
     // Calculate random variable 0.0 <= r < 1.0 (exclusive!).
     let r = Double(arc4random()) / 0x100000000
 
-    let leftToExamine = a.count - examined + 1
+    let leftToExamine = a.count - examined
     let leftToAdd = requested - selected
 
     // Decide whether to use the next record from the input.
     if Double(leftToExamine) * r < Double(leftToAdd) {
       selected += 1
-      b.append(a[examined - 1])
+      b.append(a[examined])
     }
+
+    examined += 1
   }
   return b
 }

From 6d816c24b159b591ddbe11d9ececa1e1ac8b2c42 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 14:08:34 -0500
Subject: [PATCH 1263/1679] specify simulator for convex hull tests on travis

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 977ff6774..d70eb74b6 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,7 +20,7 @@ script:
 - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests
+- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0'
 - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests

From cc32ec58d921793b97d203bc60994b406ea91bb3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 13:29:39 -0700
Subject: [PATCH 1264/1679] Deleted the checkboxes in favour of using labels

---
 .github/ISSUE_TEMPLATE.md | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/.github/ISSUE_TEMPLATE.md b/.github/ISSUE_TEMPLATE.md
index 416641261..5c72ed5a5 100644
--- a/.github/ISSUE_TEMPLATE.md
+++ b/.github/ISSUE_TEMPLATE.md
@@ -1,13 +1,7 @@
-### Category
-
-- [ ] Bug
-- [ ] Feature Request
-- [ ] Question
-
 ### Brief Intro
 
 <!-- Describe the issue briefly.-->
 
 ### More Details
 
-<!-- If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.-->
\ No newline at end of file
+<!-- If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.-->

From bed042cc2e8ceec0fa1ca1aa592038e050b3eea7 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 15:44:30 -0500
Subject: [PATCH 1265/1679] update Selection Sampling readme to match code

---
 Selection Sampling/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index bf17d93bd..ff80791e1 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -89,17 +89,17 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var b = [T]()
   
   while selected < requested {                          // 1
-    examined += 1
-    
     let r = Double(arc4random()) / 0x100000000          // 2
     
-    let leftToExamine = a.count - examined + 1          // 3
+    let leftToExamine = a.count - examined              // 3
     let leftToAdd = requested - selected
 
     if Double(leftToExamine) * r < Double(leftToAdd) {  // 4
       selected += 1
-      b.append(a[examined - 1])
+      b.append(a[examined])
     }
+
+    examined += 1
   }
   return b
 }

From be2785025b67b813bd1afc3a7d6aeda87c816ca9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 16:25:16 -0700
Subject: [PATCH 1266/1679] Fixed a section header to emphasize 3Sum

---
 3Sum and 4Sum/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 486c45c92..129555061 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -73,7 +73,7 @@ And then you've found a match :]
 -1 + 1 = 0
 ```
 
-#### Augmenting 2Sum
+# Augmenting 2Sum
 
 Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
 

From 4567dd1e49d079b5761d8349cbef3966e8231f05 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 16:25:47 -0700
Subject: [PATCH 1267/1679] Fixed a typo

---
 3Sum and 4Sum/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 129555061..a34d2f49e 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -73,7 +73,7 @@ And then you've found a match :]
 -1 + 1 = 0
 ```
 
-# Augmenting 2Sum
+# 3Sum
 
 Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
 

From d7ebac3d898e931719de3611fbcf410552fbd8fa Mon Sep 17 00:00:00 2001
From: Nishtha Bhatia <nbhatia329@gmail.com>
Date: Sun, 8 Oct 2017 09:52:50 +0530
Subject: [PATCH 1268/1679] Updated Big-O Notation.markdown

---
 Big-O Notation.markdown | 108 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 107 insertions(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 746cba8a3..2bb0d77db 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -15,8 +15,114 @@ Big-O | Name | Description
 **O(n^2)** | quadratic | **Kinda slow.** If you have 100 items, this does 100^2 = 10,000 units of work. Doubling the number of items makes it four times slower (because 2 squared equals 4). Example: algorithms using nested loops, such as insertion sort.
 **O(n^3)** | cubic | **Poor performance.** If you have 100 items, this does 100^3 = 1,000,000 units of work. Doubling the input size makes it eight times slower. Example: matrix multiplication.
 **O(2^n)** | exponential | **Very poor performance.** You want to avoid these kinds of algorithms, but sometimes you have no choice. Adding just one bit to the input doubles the running time. Example: traveling salesperson problem.
-**O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.
+**O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
+  
 
+Some examples to better understand the Big(O) notation:
+
+**O(1)**
+
+  The most common example with O(1) complexity is accessing an array index.
+  
+  ```c++
+  int i = a[5];
+  ```
+    
+  Another example of O(1) is Pushing and Popping from Stack.
+  
+ 
+**O(log n)**
+
+  ```c++
+  for(int i=0; i<n; i *= 2){
+      cout<<i<<endl;  // instead of simply incrementing, 'i' is increased by 2 times itself in each run.
+  }
+  ```
+  Binary Search Algorithm is an example of O(log n) complexity.
+  
+  
+**O(n)**
+
+  ```c++
+  for(int i=0; i<n; i++){
+      cout<<a[i]<<endl;
+  } 
+  ```
+  
+  Array Traversal and Linear Search are examples of O(n) complexity.  
+  
+  
+**O(n log n)**
+
+  ```c++
+  for(int i = 0; i < n; i++) { //linear
+    for(int j = 1; j < n; j *= 2){ // log (n)
+        //do constant time stuff
+    }
+  }
+```
+  
+  Merge Sort and Heap Sort are examples of O(n log n) complexity.  
+  
+  
+**O(n^2)**
+
+  ```c++
+  for(int i = 0; i < n; i++) { 
+    for(int j = 1; j < n; j++){ 
+        //do constant time stuff
+    }
+  }  
+  ```
+  
+  Traversing a simple 2-D array and Bubble Sort are examples of O(n^2) complexity.
+  
+  
+**O(n^3)**
+
+  ```c++
+  for(int i = 0; i < n; i++) { 
+    for(int j = 1; j < n; j++){ 
+      for(int k = 1; k < n; k++){
+        //do constant time stuff
+      }
+    }
+  }  
+  ```  
+  
+**O(2^n)**
+
+  Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1.
+  The following example prints all the moves necessary to solve the famous "Towers of Hanoi" problem for N disks.
+
+  ```c++
+  void solve_hanoi(int N, string from, string to, string spare) {
+    if (N<1) {
+        return;
+    }
+    if (N>1) {
+        solve_hanoi(N-1, from, spare, to);
+    }
+    print "move from " + from + " to " + to;
+    if (N>1) {
+        solve_hanoi(N-1, spare, to, from);
+    }
+  } 
+  ```
+  
+  
+**O(n!)**
+
+  The most trivial example of function that takes O(n!) time is given below.
+
+  ```c++
+    void nFacFunc(int n) {
+      for(int i=0; i<n; i++) {
+        nFacFunc(n-1);
+      }
+    } 
+  ``` 
+  
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
 
 Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge%20Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!

From d7589aa68e46d1bdc4402dce754fab5a5b654744 Mon Sep 17 00:00:00 2001
From: Nishtha Bhatia <nbhatia329@gmail.com>
Date: Sun, 8 Oct 2017 10:50:00 +0530
Subject: [PATCH 1269/1679] Replaces the code snippets with swift equivalents

---
 Big-O Notation.markdown | 104 +++++++++++++++++++++++-----------------
 1 file changed, 60 insertions(+), 44 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 2bb0d77db..6819e17de 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -24,8 +24,8 @@ Some examples to better understand the Big(O) notation:
 
   The most common example with O(1) complexity is accessing an array index.
   
-  ```c++
-  int i = a[5];
+  ```swift
+  let value = array[5]
   ```
     
   Another example of O(1) is Pushing and Popping from Stack.
@@ -33,20 +33,25 @@ Some examples to better understand the Big(O) notation:
  
 **O(log n)**
 
-  ```c++
-  for(int i=0; i<n; i *= 2){
-      cout<<i<<endl;  // instead of simply incrementing, 'i' is increased by 2 times itself in each run.
+  ```swift
+  var j = 1
+  while j < n {
+    // do constant time stuff
+    j *= 2
   }
-  ```
+  ```  
+  
+  Instead of simply incrementing, 'j' is increased by 2 times itself in each run.
+  
   Binary Search Algorithm is an example of O(log n) complexity.
   
   
 **O(n)**
 
-  ```c++
-  for(int i=0; i<n; i++){
-      cout<<a[i]<<endl;
-  } 
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+    print(array[i])
+  }
   ```
   
   Array Traversal and Linear Search are examples of O(n) complexity.  
@@ -54,25 +59,40 @@ Some examples to better understand the Big(O) notation:
   
 **O(n log n)**
 
-  ```c++
-  for(int i = 0; i < n; i++) { //linear
-    for(int j = 1; j < n; j *= 2){ // log (n)
-        //do constant time stuff
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+  var j = 1
+    while j < n {
+      j *= 2
+      // do constant time stuff
+    }
+  }
+  ```
+  
+  OR
+  
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+    func index(after i: Int) -> Int? { // multiplies `i` by 2 until `i` >= `n`
+      return i < n ? i * 2 : nil 
+    }
+    for j in sequence(first: 1, next: index(after:)) {
+      // do constant time stuff
     }
   }
-```
+  ```
   
   Merge Sort and Heap Sort are examples of O(n log n) complexity.  
   
   
 **O(n^2)**
 
-  ```c++
-  for(int i = 0; i < n; i++) { 
-    for(int j = 1; j < n; j++){ 
-        //do constant time stuff
+  ```swift
+  for i  in stride(from: 0, to: n, by: 1) {
+    for j in stride(from: 1, to: n, by: 1) {
+      // do constant time stuff
     }
-  }  
+  }
   ```
   
   Traversing a simple 2-D array and Bubble Sort are examples of O(n^2) complexity.
@@ -80,14 +100,14 @@ Some examples to better understand the Big(O) notation:
   
 **O(n^3)**
 
-  ```c++
-  for(int i = 0; i < n; i++) { 
-    for(int j = 1; j < n; j++){ 
-      for(int k = 1; k < n; k++){
-        //do constant time stuff
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+    for j in stride(from: 1, to: n, by: 1) {
+      for k in stride(from: 1, to: n, by: 1) {
+        // do constant time stuff
       }
     }
-  }  
+  }
   ```  
   
 **O(2^n)**
@@ -95,19 +115,15 @@ Some examples to better understand the Big(O) notation:
   Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1.
   The following example prints all the moves necessary to solve the famous "Towers of Hanoi" problem for N disks.
 
-  ```c++
-  void solve_hanoi(int N, string from, string to, string spare) {
-    if (N<1) {
-        return;
-    }
-    if (N>1) {
-        solve_hanoi(N-1, from, spare, to);
+  ```swift
+  func solveHanoi(N: Int, from: String, to: String, spare: String) {
+    guard n >= 1 else { return }
+    if N > 1 {
+      solveHanoi(N: N - 1, from: from, to: spare, spare: to)
+    } else {
+      solveHanoi(N: N-1, from: spare, to: to, spare: from)
     }
-    print "move from " + from + " to " + to;
-    if (N>1) {
-        solve_hanoi(N-1, spare, to, from);
-    }
-  } 
+  }
   ```
   
   
@@ -115,12 +131,12 @@ Some examples to better understand the Big(O) notation:
 
   The most trivial example of function that takes O(n!) time is given below.
 
-  ```c++
-    void nFacFunc(int n) {
-      for(int i=0; i<n; i++) {
-        nFacFunc(n-1);
-      }
-    } 
+  ```swift
+  func nFacFunc(n: Int) {
+    for i in stride(from: 0, to: n, by: 1) {
+      nFactFunc(n - 1)
+    }
+  }
   ``` 
   
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.

From 8ea6fb23654c44fc9d5f5accac9d091bf220a142 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 22:40:10 -0700
Subject: [PATCH 1270/1679] Fixes grammar.

---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 6819e17de..acb9b0a36 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -28,7 +28,7 @@ Some examples to better understand the Big(O) notation:
   let value = array[5]
   ```
     
-  Another example of O(1) is Pushing and Popping from Stack.
+  Another example of O(1) is pushing and popping from Stack.
   
  
 **O(log n)**

From 6cfff2fa0b8cfcdf8bd8ed889423236340eaf951 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 22:42:02 -0700
Subject: [PATCH 1271/1679] Grammar fixes.

---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index acb9b0a36..78b1808e6 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -18,7 +18,7 @@ Big-O | Name | Description
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
   
 
-Some examples to better understand the Big(O) notation:
+Below are some examples for each category of performance:
 
 **O(1)**
 

From 69b7eeed4e29313e0e1b9e4af0b34ba620e0db0b Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 9 Oct 2017 09:50:41 -0300
Subject: [PATCH 1272/1679] Changed tabs width

changed it back to two spaces
---
 AVL Tree/AVLTree.swift | 748 ++++++++++++++++++++---------------------
 1 file changed, 374 insertions(+), 374 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index ddc8e7892..04763f03b 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -21,443 +21,443 @@
 // SOFTWARE.
 
 public class TreeNode<Key: Comparable, Payload> {
-    public typealias Node = TreeNode<Key, Payload>
+  public typealias Node = TreeNode<Key, Payload>
+  
+  var payload: Payload?   // Value held by the node
+  
+  fileprivate var key: Key    // Node's name
+  internal var leftChild: Node?
+  internal var rightChild: Node?
+  fileprivate var height: Int
+  weak fileprivate var parent: Node?
+  
+  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
+    self.key = key
+    self.payload = payload
+    self.leftChild = leftChild
+    self.rightChild = rightChild
+    self.parent = parent
+    self.height = height
     
-    var payload: Payload?   // Value held by the node
-    
-    fileprivate var key: Key    // Node's name
-    internal var leftChild: Node?
-    internal var rightChild: Node?
-    fileprivate var height: Int
-    weak fileprivate var parent: Node?
-    
-    public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
-        self.key = key
-        self.payload = payload
-        self.leftChild = leftChild
-        self.rightChild = rightChild
-        self.parent = parent
-        self.height = height
-        
-        self.leftChild?.parent = self
-        self.rightChild?.parent = self
-    }
-    
-    public convenience init(key: Key, payload: Payload?) {
-        self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
-    }
-    
-    public convenience init(key: Key) {
-        self.init(key: key, payload: nil)
-    }
-    
-    var isRoot: Bool {
-        return parent == nil
-    }
-    
-    var isLeaf: Bool {
-        return rightChild == nil && leftChild == nil
-    }
-    
-    var isLeftChild: Bool {
-        return parent?.leftChild === self
-    }
-    
-    var isRightChild: Bool {
-        return parent?.rightChild === self
-    }
-    
-    var hasLeftChild: Bool {
-        return leftChild != nil
-    }
-    
-    var hasRightChild: Bool {
-        return rightChild != nil
-    }
-    
-    var hasAnyChild: Bool {
-        return leftChild != nil || rightChild != nil
-    }
-    
-    var hasBothChildren: Bool {
-        return leftChild != nil && rightChild != nil
-    }
+    self.leftChild?.parent = self
+    self.rightChild?.parent = self
+  }
+  
+  public convenience init(key: Key, payload: Payload?) {
+    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
+  }
+  
+  public convenience init(key: Key) {
+    self.init(key: key, payload: nil)
+  }
+  
+  var isRoot: Bool {
+    return parent == nil
+  }
+  
+  var isLeaf: Bool {
+    return rightChild == nil && leftChild == nil
+  }
+  
+  var isLeftChild: Bool {
+    return parent?.leftChild === self
+  }
+  
+  var isRightChild: Bool {
+    return parent?.rightChild === self
+  }
+  
+  var hasLeftChild: Bool {
+    return leftChild != nil
+  }
+  
+  var hasRightChild: Bool {
+    return rightChild != nil
+  }
+  
+  var hasAnyChild: Bool {
+    return leftChild != nil || rightChild != nil
+  }
+  
+  var hasBothChildren: Bool {
+    return leftChild != nil && rightChild != nil
+  }
 }
 
 // MARK: - The AVL tree
 
 open class AVLTree<Key: Comparable, Payload> {
-    public typealias Node = TreeNode<Key, Payload>
-    
-    fileprivate(set) var root: Node?
-    fileprivate(set) var size = 0
-    
-    public init() { }
+  public typealias Node = TreeNode<Key, Payload>
+  
+  fileprivate(set) var root: Node?
+  fileprivate(set) var size = 0
+  
+  public init() { }
 }
 
 // MARK: - Searching
 
 extension TreeNode {
-    public func minimum() -> TreeNode? {
-        return leftChild?.minimum() ?? self
-    }
-    
-    public func maximum() -> TreeNode? {
-        return rightChild?.maximum() ?? self
-    }
+  public func minimum() -> TreeNode? {
+    return leftChild?.minimum() ?? self
+  }
+  
+  public func maximum() -> TreeNode? {
+    return rightChild?.maximum() ?? self
+  }
 }
 
 extension AVLTree {
-    subscript(key: Key) -> Payload? {
-        get { return search(input: key) }
-        set { insert(key: key, payload: newValue) }
-    }
-    
-    public func search(input: Key) -> Payload? {
-        return search(key: input, node: root)?.payload
-    }
-    
-    fileprivate func search(key: Key, node: Node?) -> Node? {
-        if let node = node {
-            if key == node.key {
-                return node
-            } else if key < node.key {
-                return search(key: key, node: node.leftChild)
-            } else {
-                return search(key: key, node: node.rightChild)
-            }
-        }
-        return nil
-    }
+  subscript(key: Key) -> Payload? {
+    get { return search(input: key) }
+    set { insert(key: key, payload: newValue) }
+  }
+  
+  public func search(input: Key) -> Payload? {
+    return search(key: input, node: root)?.payload
+  }
+  
+  fileprivate func search(key: Key, node: Node?) -> Node? {
+    if let node = node {
+      if key == node.key {
+        return node
+      } else if key < node.key {
+        return search(key: key, node: node.leftChild)
+      } else {
+        return search(key: key, node: node.rightChild)
+      }
+    }
+    return nil
+  }
 }
 
 // MARK: - Inserting new items
 
 extension AVLTree {
-    public func insert(key: Key, payload: Payload? = nil) {
-        if let root = root {
-            insert(input: key, payload: payload, node: root)
-        } else {
-            root = Node(key: key, payload: payload)
-        }
-        size += 1
-    }
-    
-    private func insert(input: Key, payload: Payload?, node: Node) {
-        if input < node.key {
-            if let child = node.leftChild {
-                insert(input: input, payload: payload, node: child)
-            } else {
-                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-                node.leftChild = child
-                balance(node: child)
-            }
-        } else if input != node.key {
-            if let child = node.rightChild {
-                insert(input: input, payload: payload, node: child)
-            } else {
-                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-                node.rightChild = child
-                balance(node: child)
-            }
-        }
-    }
+  public func insert(key: Key, payload: Payload? = nil) {
+    if let root = root {
+      insert(input: key, payload: payload, node: root)
+    } else {
+      root = Node(key: key, payload: payload)
+    }
+    size += 1
+  }
+  
+  private func insert(input: Key, payload: Payload?, node: Node) {
+    if input < node.key {
+      if let child = node.leftChild {
+        insert(input: input, payload: payload, node: child)
+      } else {
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+        node.leftChild = child
+        balance(node: child)
+      }
+    } else if input != node.key {
+      if let child = node.rightChild {
+        insert(input: input, payload: payload, node: child)
+      } else {
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+        node.rightChild = child
+        balance(node: child)
+      }
+    }
+  }
 }
 
 // MARK: - Balancing tree
 
 extension AVLTree {
-    fileprivate func updateHeightUpwards(node: Node?) {
-        if let node = node {
-            let lHeight = node.leftChild?.height ?? 0
-            let rHeight = node.rightChild?.height ?? 0
-            node.height = max(lHeight, rHeight) + 1
-            updateHeightUpwards(node: node.parent)
-        }
+  fileprivate func updateHeightUpwards(node: Node?) {
+    if let node = node {
+      let lHeight = node.leftChild?.height ?? 0
+      let rHeight = node.rightChild?.height ?? 0
+      node.height = max(lHeight, rHeight) + 1
+      updateHeightUpwards(node: node.parent)
+    }
+  }
+  
+  fileprivate func lrDifference(node: Node?) -> Int {
+    let lHeight = node?.leftChild?.height ?? 0
+    let rHeight = node?.rightChild?.height ?? 0
+    return lHeight - rHeight
+  }
+  
+  fileprivate func balance(node: Node?) {
+    guard let node = node else {
+      return
     }
     
-    fileprivate func lrDifference(node: Node?) -> Int {
-        let lHeight = node?.leftChild?.height ?? 0
-        let rHeight = node?.rightChild?.height ?? 0
-        return lHeight - rHeight
-    }
+    updateHeightUpwards(node: node.leftChild)
+    updateHeightUpwards(node: node.rightChild)
     
-    fileprivate func balance(node: Node?) {
-        guard let node = node else {
-            return
-        }
-        
-        updateHeightUpwards(node: node.leftChild)
-        updateHeightUpwards(node: node.rightChild)
-        
-        var nodes = [Node?](repeating: nil, count: 3)
-        var subtrees = [Node?](repeating: nil, count: 4)
-        let nodeParent = node.parent
-        
-        let lrFactor = lrDifference(node: node)
-        if lrFactor > 1 {
-            // left-left or left-right
-            if lrDifference(node: node.leftChild) > 0 {
-                // left-left
-                nodes[0] = node
-                nodes[2] = node.leftChild
-                nodes[1] = nodes[2]?.leftChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[1]?.rightChild
-                subtrees[2] = nodes[2]?.rightChild
-                subtrees[3] = nodes[0]?.rightChild
-            } else {
-                // left-right
-                nodes[0] = node
-                nodes[1] = node.leftChild
-                nodes[2] = nodes[1]?.rightChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[2]?.leftChild
-                subtrees[2] = nodes[2]?.rightChild
-                subtrees[3] = nodes[0]?.rightChild
-            }
-        } else if lrFactor < -1 {
-            // right-left or right-right
-            if lrDifference(node: node.rightChild) < 0 {
-                // right-right
-                nodes[1] = node
-                nodes[2] = node.rightChild
-                nodes[0] = nodes[2]?.rightChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[2]?.leftChild
-                subtrees[2] = nodes[0]?.leftChild
-                subtrees[3] = nodes[0]?.rightChild
-            } else {
-                // right-left
-                nodes[1] = node
-                nodes[0] = node.rightChild
-                nodes[2] = nodes[0]?.leftChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[2]?.leftChild
-                subtrees[2] = nodes[2]?.rightChild
-                subtrees[3] = nodes[0]?.rightChild
-            }
-        } else {
-            // Don't need to balance 'node', go for parent
-            balance(node: node.parent)
-            return
-        }
-        
-        // nodes[2] is always the head
-        
-        if node.isRoot {
-            root = nodes[2]
-            root?.parent = nil
-        } else if node.isLeftChild {
-            nodeParent?.leftChild = nodes[2]
-            nodes[2]?.parent = nodeParent
-        } else if node.isRightChild {
-            nodeParent?.rightChild = nodes[2]
-            nodes[2]?.parent = nodeParent
-        }
-        
-        nodes[2]?.leftChild = nodes[1]
-        nodes[1]?.parent = nodes[2]
-        nodes[2]?.rightChild = nodes[0]
-        nodes[0]?.parent = nodes[2]
+    var nodes = [Node?](repeating: nil, count: 3)
+    var subtrees = [Node?](repeating: nil, count: 4)
+    let nodeParent = node.parent
+    
+    let lrFactor = lrDifference(node: node)
+    if lrFactor > 1 {
+      // left-left or left-right
+      if lrDifference(node: node.leftChild) > 0 {
+        // left-left
+        nodes[0] = node
+        nodes[2] = node.leftChild
+        nodes[1] = nodes[2]?.leftChild
         
-        nodes[1]?.leftChild = subtrees[0]
-        subtrees[0]?.parent = nodes[1]
-        nodes[1]?.rightChild = subtrees[1]
-        subtrees[1]?.parent = nodes[1]
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[1]?.rightChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
+      } else {
+        // left-right
+        nodes[0] = node
+        nodes[1] = node.leftChild
+        nodes[2] = nodes[1]?.rightChild
         
-        nodes[0]?.leftChild = subtrees[2]
-        subtrees[2]?.parent = nodes[0]
-        nodes[0]?.rightChild = subtrees[3]
-        subtrees[3]?.parent = nodes[0]
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
+      }
+    } else if lrFactor < -1 {
+      // right-left or right-right
+      if lrDifference(node: node.rightChild) < 0 {
+        // right-right
+        nodes[1] = node
+        nodes[2] = node.rightChild
+        nodes[0] = nodes[2]?.rightChild
         
-        updateHeightUpwards(node: nodes[1])    // Update height from left
-        updateHeightUpwards(node: nodes[0])    // Update height from right
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[0]?.leftChild
+        subtrees[3] = nodes[0]?.rightChild
+      } else {
+        // right-left
+        nodes[1] = node
+        nodes[0] = node.rightChild
+        nodes[2] = nodes[0]?.leftChild
         
-        balance(node: nodes[2]?.parent)
-    }
-}
-
-// MARK: - Displaying tree
-
-extension AVLTree {
-    fileprivate func display(node: Node?, level: Int) {
-        if let node = node {
-            display(node: node.rightChild, level: level + 1)
-            print("")
-            if node.isRoot {
-                print("Root -> ", terminator: "")
-            }
-            for _ in 0..<level {
-                print("        ", terminator:  "")
-            }
-            print("(\(node.key):\(node.height))", terminator: "")
-            display(node: node.leftChild, level: level + 1)
-        }
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
+      }
+    } else {
+      // Don't need to balance 'node', go for parent
+      balance(node: node.parent)
+      return
     }
     
-    public func display(node: Node) {
-        display(node: node, level: 0)
-        print("")
-    }
+    // nodes[2] is always the head
     
-    public func inorder(node: Node?) -> String {
-        var output = ""
-        if let node = node {
-            output = "\(inorder(node: node.leftChild)) \(print("\(node.key) ")) \(inorder(node: node.rightChild))"
-        }
-        return output
+    if node.isRoot {
+      root = nodes[2]
+      root?.parent = nil
+    } else if node.isLeftChild {
+      nodeParent?.leftChild = nodes[2]
+      nodes[2]?.parent = nodeParent
+    } else if node.isRightChild {
+      nodeParent?.rightChild = nodes[2]
+      nodes[2]?.parent = nodeParent
     }
     
-    public func preorder(node: Node?) -> String {
-        var output = ""
-        if let node = node {
-            output = "\(preorder(node: node.leftChild)) \(print("\(node.key) ")) \(preorder(node: node.rightChild))"
-        }
-        return output
-    }
+    nodes[2]?.leftChild = nodes[1]
+    nodes[1]?.parent = nodes[2]
+    nodes[2]?.rightChild = nodes[0]
+    nodes[0]?.parent = nodes[2]
     
-    public func postorder(node: Node?) -> String {
-        var output = ""
-        if let node = node {
-            output = "\(postorder(node: node.leftChild)) \(print("\(node.key) ")) \(postorder(node: node.rightChild))"
-        }
-        return output
-    }
+    nodes[1]?.leftChild = subtrees[0]
+    subtrees[0]?.parent = nodes[1]
+    nodes[1]?.rightChild = subtrees[1]
+    subtrees[1]?.parent = nodes[1]
+    
+    nodes[0]?.leftChild = subtrees[2]
+    subtrees[2]?.parent = nodes[0]
+    nodes[0]?.rightChild = subtrees[3]
+    subtrees[3]?.parent = nodes[0]
+    
+    updateHeightUpwards(node: nodes[1])    // Update height from left
+    updateHeightUpwards(node: nodes[0])    // Update height from right
+    
+    balance(node: nodes[2]?.parent)
+  }
+}
+
+// MARK: - Displaying tree
+
+extension AVLTree {
+  fileprivate func display(node: Node?, level: Int) {
+    if let node = node {
+      display(node: node.rightChild, level: level + 1)
+      print("")
+      if node.isRoot {
+        print("Root -> ", terminator: "")
+      }
+      for _ in 0..<level {
+        print("        ", terminator:  "")
+      }
+      print("(\(node.key):\(node.height))", terminator: "")
+      display(node: node.leftChild, level: level + 1)
+    }
+  }
+  
+  public func display(node: Node) {
+    display(node: node, level: 0)
+    print("")
+  }
+  
+  public func inorder(node: Node?) -> String {
+    var output = ""
+    if let node = node {
+      output = "\(inorder(node: node.leftChild)) \(print("\(node.key) ")) \(inorder(node: node.rightChild))"
+    }
+    return output
+  }
+  
+  public func preorder(node: Node?) -> String {
+    var output = ""
+    if let node = node {
+      output = "\(preorder(node: node.leftChild)) \(print("\(node.key) ")) \(preorder(node: node.rightChild))"
+    }
+    return output
+  }
+  
+  public func postorder(node: Node?) -> String {
+    var output = ""
+    if let node = node {
+      output = "\(postorder(node: node.leftChild)) \(print("\(node.key) ")) \(postorder(node: node.rightChild))"
+    }
+    return output
+  }
 }
 
 // MARK: - Delete node
 
 extension AVLTree {
-    public func delete(key: Key) {
-        if size == 1 {
-            root = nil
-            size -= 1
-        } else if let node = search(key: key, node: root) {
-            delete(node: node)
-            size -= 1
+  public func delete(key: Key) {
+    if size == 1 {
+      root = nil
+      size -= 1
+    } else if let node = search(key: key, node: root) {
+      delete(node: node)
+      size -= 1
+    }
+  }
+  
+  private func delete(node: Node) {
+    if node.isLeaf {
+      // Just remove and balance up
+      if let parent = node.parent {
+        guard node.isLeftChild || node.isRightChild else {
+          // just in case
+          fatalError("Error: tree is invalid.")
         }
-    }
-    
-    private func delete(node: Node) {
-        if node.isLeaf {
-            // Just remove and balance up
-            if let parent = node.parent {
-                guard node.isLeftChild || node.isRightChild else {
-                    // just in case
-                    fatalError("Error: tree is invalid.")
-                }
-                
-                if node.isLeftChild {
-                    parent.leftChild = nil
-                } else if node.isRightChild {
-                    parent.rightChild = nil
-                }
-                
-                balance(node: parent)
-            } else {
-                // at root
-                root = nil
-            }
-        } else {
-            // Handle stem cases
-            if let replacement = node.leftChild?.maximum(), replacement !== node {
-                node.key = replacement.key
-                node.payload = replacement.payload
-                delete(node: replacement)
-            } else if let replacement = node.rightChild?.minimum(), replacement !== node {
-                node.key = replacement.key
-                node.payload = replacement.payload
-                delete(node: replacement)
-            }
+        
+        if node.isLeftChild {
+          parent.leftChild = nil
+        } else if node.isRightChild {
+          parent.rightChild = nil
         }
-    }
+        
+        balance(node: parent)
+      } else {
+        // at root
+        root = nil
+      }
+    } else {
+      // Handle stem cases
+      if let replacement = node.leftChild?.maximum(), replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(node: replacement)
+      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(node: replacement)
+      }
+    }
+  }
 }
 
 // MARK: - Advanced Stuff
 
 extension AVLTree {
-    public func doInOrder(node: Node?, _ completion: (Node) -> Void) {
-        if let node = node {
-            doInOrder(node: node.leftChild) { lnode in
-                completion(lnode)
-            }
-            completion(node)
-            doInOrder(node: node.rightChild) { rnode in
-                completion(rnode)
-            }
-        }
-    }
-    
-    public func doInPreOrder(node: Node?, _ completion: (Node) -> Void) {
-        if let node = node {
-            completion(node)
-            doInPreOrder(node: node.leftChild) { lnode in
-                completion(lnode)
-            }
-            doInPreOrder(node: node.rightChild) { rnode in
-                completion(rnode)
-            }
-        }
-    }
-    
-    public func doInPostOrder(node: Node?, _ completion: (Node) -> Void) {
-        if let node = node {
-            doInPostOrder(node: node.leftChild) { lnode in
-                completion(lnode)
-            }
-            doInPostOrder(node: node.rightChild) { rnode in
-                completion(rnode)
-            }
-            completion(node)
-        }
-    }
+  public func doInOrder(node: Node?, _ completion: (Node) -> Void) {
+    if let node = node {
+      doInOrder(node: node.leftChild) { lnode in
+        completion(lnode)
+      }
+      completion(node)
+      doInOrder(node: node.rightChild) { rnode in
+        completion(rnode)
+      }
+    }
+  }
+  
+  public func doInPreOrder(node: Node?, _ completion: (Node) -> Void) {
+    if let node = node {
+      completion(node)
+      doInPreOrder(node: node.leftChild) { lnode in
+        completion(lnode)
+      }
+      doInPreOrder(node: node.rightChild) { rnode in
+        completion(rnode)
+      }
+    }
+  }
+  
+  public func doInPostOrder(node: Node?, _ completion: (Node) -> Void) {
+    if let node = node {
+      doInPostOrder(node: node.leftChild) { lnode in
+        completion(lnode)
+      }
+      doInPostOrder(node: node.rightChild) { rnode in
+        completion(rnode)
+      }
+      completion(node)
+    }
+  }
 }
 
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
-    public var debugDescription: String {
-        var s = "key: \(key), payload: \(payload), height: \(height)"
-        if let parent = parent {
-            s += ", parent: \(parent.key)"
-        }
-        if let left = leftChild {
-            s += ", left = [" + left.debugDescription + "]"
-        }
-        if let right = rightChild {
-            s += ", right = [" + right.debugDescription + "]"
-        }
-        return s
+  public var debugDescription: String {
+    var s = "key: \(key), payload: \(payload), height: \(height)"
+    if let parent = parent {
+      s += ", parent: \(parent.key)"
+    }
+    if let left = leftChild {
+      s += ", left = [" + left.debugDescription + "]"
     }
+    if let right = rightChild {
+      s += ", right = [" + right.debugDescription + "]"
+    }
+    return s
+  }
 }
 
 extension AVLTree: CustomDebugStringConvertible {
-    public var debugDescription: String {
-        return root?.debugDescription ?? "[]"
-    }
+  public var debugDescription: String {
+    return root?.debugDescription ?? "[]"
+  }
 }
 
 extension TreeNode: CustomStringConvertible {
-    public var description: String {
-        var s = ""
-        if let left = leftChild {
-            s += "(\(left.description)) <- "
-        }
-        s += "\(key)"
-        if let right = rightChild {
-            s += " -> (\(right.description))"
-        }
-        return s
+  public var description: String {
+    var s = ""
+    if let left = leftChild {
+      s += "(\(left.description)) <- "
+    }
+    s += "\(key)"
+    if let right = rightChild {
+      s += " -> (\(right.description))"
     }
+    return s
+  }
 }
 
 extension AVLTree: CustomStringConvertible {
-    public var description: String {
-        return root?.description ?? "[]"
-    }
+  public var description: String {
+    return root?.description ?? "[]"
+  }
 }

From 952a064d4acf96c452169e4d1c4634e895432db6 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 9 Oct 2017 10:38:10 -0300
Subject: [PATCH 1273/1679] further corrections

---
 .../Tests/DepthFirstSearchTests.swift         | 90 +++++++++----------
 1 file changed, 45 insertions(+), 45 deletions(-)

diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index afff5f62f..abf1c19c6 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -9,7 +9,7 @@ class DepthFirstSearchTests: XCTestCase {
         #endif
     }
     func testExploringTree() {
-        let tree = Graph()
+        let tree = Digraph()
         
         let nodeA = tree.addNode("a")
         let nodeB = tree.addNode("b")
@@ -33,58 +33,58 @@ class DepthFirstSearchTests: XCTestCase {
         XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
     }
     
-    func testExploringGraph() {
-        let graph = Graph()
+    func testExploringDigraph() {
+        let digraph = Digraph()
         
-        let nodeA = graph.addNode("a")
-        let nodeB = graph.addNode("b")
-        let nodeC = graph.addNode("c")
-        let nodeD = graph.addNode("d")
-        let nodeE = graph.addNode("e")
-        let nodeF = graph.addNode("f")
-        let nodeG = graph.addNode("g")
-        let nodeH = graph.addNode("h")
-        let nodeI = graph.addNode("i")
+        let nodeA = digraph.addNode("a")
+        let nodeB = digraph.addNode("b")
+        let nodeC = digraph.addNode("c")
+        let nodeD = digraph.addNode("d")
+        let nodeE = digraph.addNode("e")
+        let nodeF = digraph.addNode("f")
+        let nodeG = digraph.addNode("g")
+        let nodeH = digraph.addNode("h")
+        let nodeI = digraph.addNode("i")
         
-        graph.addEdge(nodeA, neighbor: nodeB)
-        graph.addEdge(nodeA, neighbor: nodeH)
-        graph.addEdge(nodeB, neighbor: nodeA)
-        graph.addEdge(nodeB, neighbor: nodeC)
-        graph.addEdge(nodeB, neighbor: nodeH)
-        graph.addEdge(nodeC, neighbor: nodeB)
-        graph.addEdge(nodeC, neighbor: nodeD)
-        graph.addEdge(nodeC, neighbor: nodeF)
-        graph.addEdge(nodeC, neighbor: nodeI)
-        graph.addEdge(nodeD, neighbor: nodeC)
-        graph.addEdge(nodeD, neighbor: nodeE)
-        graph.addEdge(nodeD, neighbor: nodeF)
-        graph.addEdge(nodeE, neighbor: nodeD)
-        graph.addEdge(nodeE, neighbor: nodeF)
-        graph.addEdge(nodeF, neighbor: nodeC)
-        graph.addEdge(nodeF, neighbor: nodeD)
-        graph.addEdge(nodeF, neighbor: nodeE)
-        graph.addEdge(nodeF, neighbor: nodeG)
-        graph.addEdge(nodeG, neighbor: nodeF)
-        graph.addEdge(nodeG, neighbor: nodeH)
-        graph.addEdge(nodeG, neighbor: nodeI)
-        graph.addEdge(nodeH, neighbor: nodeA)
-        graph.addEdge(nodeH, neighbor: nodeB)
-        graph.addEdge(nodeH, neighbor: nodeG)
-        graph.addEdge(nodeH, neighbor: nodeI)
-        graph.addEdge(nodeI, neighbor: nodeC)
-        graph.addEdge(nodeI, neighbor: nodeG)
-        graph.addEdge(nodeI, neighbor: nodeH)
+        digraph.addEdge(nodeA, neighbor: nodeB)
+        digraph.addEdge(nodeA, neighbor: nodeH)
+        digraph.addEdge(nodeB, neighbor: nodeA)
+        digraph.addEdge(nodeB, neighbor: nodeC)
+        digraph.addEdge(nodeB, neighbor: nodeH)
+        digraph.addEdge(nodeC, neighbor: nodeB)
+        digraph.addEdge(nodeC, neighbor: nodeD)
+        digraph.addEdge(nodeC, neighbor: nodeF)
+        digraph.addEdge(nodeC, neighbor: nodeI)
+        digraph.addEdge(nodeD, neighbor: nodeC)
+        digraph.addEdge(nodeD, neighbor: nodeE)
+        digraph.addEdge(nodeD, neighbor: nodeF)
+        digraph.addEdge(nodeE, neighbor: nodeD)
+        digraph.addEdge(nodeE, neighbor: nodeF)
+        digraph.addEdge(nodeF, neighbor: nodeC)
+        digraph.addEdge(nodeF, neighbor: nodeD)
+        digraph.addEdge(nodeF, neighbor: nodeE)
+        digraph.addEdge(nodeF, neighbor: nodeG)
+        digraph.addEdge(nodeG, neighbor: nodeF)
+        digraph.addEdge(nodeG, neighbor: nodeH)
+        digraph.addEdge(nodeG, neighbor: nodeI)
+        digraph.addEdge(nodeH, neighbor: nodeA)
+        digraph.addEdge(nodeH, neighbor: nodeB)
+        digraph.addEdge(nodeH, neighbor: nodeG)
+        digraph.addEdge(nodeH, neighbor: nodeI)
+        digraph.addEdge(nodeI, neighbor: nodeC)
+        digraph.addEdge(nodeI, neighbor: nodeG)
+        digraph.addEdge(nodeI, neighbor: nodeH)
         
-        let nodesExplored = depthFirstSearch(graph, source: nodeA)
+        let nodesExplored = depthFirstSearch(digraph, source: nodeA)
         
         XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
     }
     
-    func testExploringGraphWithASingleNode() {
-        let graph = Graph()
-        let node = graph.addNode("a")
+    func testExploringDigraphWithASingleNode() {
+        let digraph = Digraph()
+        let node = digraph.addNode("a")
         
-        let nodesExplored = depthFirstSearch(graph, source: node)
+        let nodesExplored = depthFirstSearch(digraph, source: node)
         
         XCTAssertEqual(nodesExplored, ["a"])
     }

From f71c10d104247d239a9d4fb238ed195e687f0eac Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Mon, 9 Oct 2017 17:30:42 +0200
Subject: [PATCH 1274/1679] create octree algorithm

---
 Octree/Octree.playground/Contents.swift       |  33 ++
 Octree/Octree.playground/Sources/Octree.swift | 372 ++++++++++++++++++
 .../Octree.playground/contents.xcplayground   |   4 +
 Octree/Octree.playground/timeline.xctimeline  |  16 +
 4 files changed, 425 insertions(+)
 create mode 100644 Octree/Octree.playground/Contents.swift
 create mode 100644 Octree/Octree.playground/Sources/Octree.swift
 create mode 100644 Octree/Octree.playground/contents.xcplayground
 create mode 100644 Octree/Octree.playground/timeline.xctimeline

diff --git a/Octree/Octree.playground/Contents.swift b/Octree/Octree.playground/Contents.swift
new file mode 100644
index 000000000..cdcd2df0f
--- /dev/null
+++ b/Octree/Octree.playground/Contents.swift
@@ -0,0 +1,33 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+import simd
+
+let boxMin = vector_double3(0, 2, 6)
+let boxMax = vector_double3(5, 10, 9)
+let box = Box(boxMin: boxMin, boxMax: boxMax)
+var octree = Octree<Int>(boundingBox: box, minimumCellSize: 5.0)
+var five = octree.add(5, at: vector_double3(3,4,8))
+octree.add(8, at: vector_double3(3,4,8.2))
+octree.add(10, at: vector_double3(3,4,8.2))
+octree.add(7, at: vector_double3(2,5,8))
+octree.add(2, at: vector_double3(1,6,7))
+
+var cont = octree.elements(at: vector_double3(3,4,8.2))
+octree.remove(8)
+octree.elements(at: vector_double3(3,4,8))
+
+let boxMin2 = vector_double3(1,3,7)
+let boxMax2 = vector_double3(4,9,8)
+let box2 = Box(boxMin: boxMin2, boxMax: boxMax2)
+box.isContained(in: box2)
+box.intersects(box2)
+
+let boxMin3 = vector_double3(3,8,8)
+let boxMax3 = vector_double3(10,12,20)
+let box3 = Box(boxMin: boxMin3, boxMax: boxMax3)
+box3.intersects(box3)
+
+octree.elements(in: box)
+octree.elements(in: box2)
+print(octree)
diff --git a/Octree/Octree.playground/Sources/Octree.swift b/Octree/Octree.playground/Sources/Octree.swift
new file mode 100644
index 000000000..72863fb7c
--- /dev/null
+++ b/Octree/Octree.playground/Sources/Octree.swift
@@ -0,0 +1,372 @@
+import Foundation
+import simd
+
+public struct Box: CustomStringConvertible {
+    public var boxMin: vector_double3
+    public var boxMax: vector_double3
+    
+    public init(boxMin: vector_double3, boxMax: vector_double3) {
+        self.boxMin = boxMin
+        self.boxMax = boxMax
+    }
+    
+    public var boxSize: vector_double3 {
+        return boxMax - boxMin
+    }
+    
+    var halfBoxSize: vector_double3 {
+        return boxSize/2
+    }
+    
+    var frontLeftTop: Box {
+        let boxMin = self.boxMin + vector_double3(0, halfBoxSize.y, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, 0, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var frontLeftBottom: Box {
+        let boxMin = self.boxMin + vector_double3(0, 0, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, halfBoxSize.y, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var frontRightTop: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, halfBoxSize.y, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(0, 0, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var frontRightBottom: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, 0, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(0, halfBoxSize.y, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backLeftTop: Box {
+        let boxMin = self.boxMin + vector_double3(0, halfBoxSize.y, 0)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, 0, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backLeftBottom: Box {
+        let boxMin = self.boxMin + vector_double3(0, 0, 0)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, halfBoxSize.y, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backRightTop: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, halfBoxSize.y, 0)
+        let boxMax = self.boxMax - vector_double3(0, 0, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backRightBottom: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, 0, 0)
+        let boxMax = self.boxMax - vector_double3(0, halfBoxSize.y, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    
+    public func contains(_ point: vector_double3) -> Bool {
+        return (boxMin.x <= point.x && point.x <= boxMax.x) && (boxMin.y <= point.y && point.y <= boxMax.y) && (boxMin.z <= point.z && point.z <= boxMax.z)
+    }
+    
+    public func contains(_ box: Box) -> Bool {
+        return
+            self.boxMin.x <= box.boxMin.x &&
+                self.boxMin.y <= box.boxMin.y &&
+                self.boxMin.z <= box.boxMin.z &&
+                self.boxMax.x >= box.boxMax.x &&
+                self.boxMax.y >= box.boxMax.y &&
+                self.boxMax.z >= box.boxMax.z
+    }
+    
+    public func isContained(in box: Box) -> Bool {
+        return
+            self.boxMin.x >= box.boxMin.x &&
+                self.boxMin.y >= box.boxMin.y &&
+                self.boxMin.z >= box.boxMin.z &&
+                self.boxMax.x <= box.boxMax.x &&
+                self.boxMax.y <= box.boxMax.y &&
+                self.boxMax.z <= box.boxMax.z
+    }
+    
+    /* This intersect function does not handle all possibilities such as two beams
+     of different diameter crossing each other half way. But it does cover all cases
+     needed for an octree as the bounding box has to contain the given intersect box */
+    public func intersects(_ box: Box) -> Bool {
+        let corners = [
+            vector_double3(boxMin.x, boxMax.y, boxMax.z), //frontLeftTop
+            vector_double3(boxMin.x, boxMin.y, boxMax.z), //frontLeftBottom
+            vector_double3(boxMax.x, boxMax.y, boxMax.z), //frontRightTop
+            vector_double3(boxMax.x, boxMin.y, boxMax.z), //frontRightBottom
+            vector_double3(boxMin.x, boxMax.y, boxMin.z), //backLeftTop
+            vector_double3(boxMin.x, boxMin.y, boxMin.z), //backLeftBottom
+            vector_double3(boxMax.x, boxMax.y, boxMin.z), //backRightTop
+            vector_double3(boxMax.x, boxMin.y, boxMin.z)  //backRightBottom
+        ]
+        for corner in corners {
+            if box.contains(corner) {
+                return true
+            }
+        }
+        return false
+    }
+    
+    public var description: String {
+        return "Box from:\(boxMin) to:\(boxMax)"
+    }
+}
+
+public class OctreeNode<T: Equatable>: CustomStringConvertible {
+    let box: Box
+    var point: vector_double3!
+    var elements: [T]!
+    var type: NodeType = .leaf
+    
+    enum NodeType {
+        case leaf
+        case `internal`(children: Children)
+    }
+    
+    public var description: String {
+        switch type {
+        case .leaf:
+            return "leaf node with \(box) elements: \(elements)"
+        case .internal:
+            return "internal node with \(box)"
+        }
+    }
+    
+    var recursiveDescription: String {
+        return recursiveDescription(withTabCount: 0)
+    }
+    
+    private func recursiveDescription(withTabCount count: Int) -> String {
+        let indent = String(repeating: "\t", count: count)
+        var result = "\(indent)" + description + "\n"
+        switch type {
+        case .internal(let children):
+            for child in children {
+                result += child.recursiveDescription(withTabCount: count + 1)
+            }
+        default:
+            break
+        }
+        return result
+    }
+    
+    struct Children: Sequence {
+        let frontLeftTop: OctreeNode
+        let frontLeftBottom: OctreeNode
+        let frontRightTop: OctreeNode
+        let frontRightBottom: OctreeNode
+        let backLeftTop: OctreeNode
+        let backLeftBottom: OctreeNode
+        let backRightTop: OctreeNode
+        let backRightBottom: OctreeNode
+        
+        init(parentNode: OctreeNode) {
+            frontLeftTop = OctreeNode(box: parentNode.box.frontLeftTop)
+            frontLeftBottom = OctreeNode(box: parentNode.box.frontLeftBottom)
+            frontRightTop = OctreeNode(box: parentNode.box.frontRightTop)
+            frontRightBottom = OctreeNode(box: parentNode.box.frontRightBottom)
+            backLeftTop = OctreeNode(box: parentNode.box.backLeftTop)
+            backLeftBottom = OctreeNode(box: parentNode.box.backLeftBottom)
+            backRightTop = OctreeNode(box: parentNode.box.backRightTop)
+            backRightBottom = OctreeNode(box: parentNode.box.backRightBottom)
+        }
+        
+        struct ChildrenIterator: IteratorProtocol {
+            var index = 0
+            let children: Children
+            
+            init(children: Children) {
+                self.children = children
+            }
+            
+            mutating func next() -> OctreeNode? {
+                defer { index += 1 }
+                switch index {
+                case 0: return children.frontLeftTop
+                case 1: return children.frontLeftBottom
+                case 2: return children.frontRightTop
+                case 3: return children.frontRightBottom
+                case 4: return children.backLeftTop
+                case 5: return children.backLeftBottom
+                case 6: return children.backRightTop
+                case 7: return children.backRightBottom
+                default: return nil
+                }
+            }
+        }
+        
+        func makeIterator() -> ChildrenIterator {
+            return ChildrenIterator(children: self)
+        }
+    }
+    
+    init(box: Box) {
+        self.box = box
+    }
+    
+    @discardableResult
+    func add(_ element: T, at point: vector_double3) -> OctreeNode {
+        return tryAdd(element, at: point)!
+    }
+    
+    private func tryAdd(_ element: T, at point: vector_double3) -> OctreeNode? {
+        if !box.contains(point) {
+            return nil
+        }
+        
+        switch type {
+        case .internal(let children):
+            // pass the point to one of the children
+            for child in children {
+                if let child = child.tryAdd(element, at: point) {
+                    return child
+                }
+            }
+            
+            fatalError("box.contains evaluted to true, but none of the children added the point")
+        case .leaf:
+            if self.point != nil {
+                // leaf already has an asigned point
+                if self.point == point {
+                    self.elements.append(element)
+                    return self
+                } else {
+                    return subdivide(adding: element, at: point)
+                }
+            } else {
+                self.elements = [element]
+                self.point = point
+                return self
+            }
+        }
+    }
+    
+    func add(_ elements: [T], at point: vector_double3) {
+        for element in elements {
+            self.add(element, at: point)
+        }
+    }
+    
+    @discardableResult
+    func remove(_ element: T) -> Bool {
+        switch type {
+        case .leaf:
+            if let elements = self.elements {
+                // leaf contains one ore more elements
+                if let index = elements.index(of: element) {
+                    // leaf contains the element we want to remove
+                    self.elements.remove(at: index)
+                    // if elements is now empty remove it
+                    if self.elements.isEmpty {
+                        self.elements = nil
+                    }
+                    return true
+                }
+            }
+            return false
+        case .internal(let children):
+            for child in children  {
+                if child.remove(element) {
+                    return true
+                }
+            }
+            return false
+        }
+    }
+    
+    func elements(at point: vector_double3) -> [T]? {
+        switch type {
+        case .leaf:
+            if self.point == point {
+                return self.elements
+            }
+        case .internal(let children):
+            for child in children {
+                if child.box.contains(point) {
+                    return child.elements(at: point)
+                }
+            }
+        }
+        // tree does not contain given point
+        return nil
+    }
+    
+    func elements(in box: Box) -> [T]? {
+        var values: [T] = []
+        switch type {
+        case .leaf:
+            // check if leaf has an assigned point
+            if let point = self.point {
+                // check if point is inside given box
+                if box.contains(point) {
+                    values += elements ?? []
+                }
+            }
+        case .internal(let children):
+            for child in children {
+                if child.box.isContained(in: box) {
+                    // child is contained in box
+                    // add all children of child
+                    values += child.elements(in: child.box) ?? []
+                } else if child.box.contains(box) || child.box.intersects(box) {
+                    // child contains at least part of box
+                    values += child.elements(in: box) ?? []
+                }
+                // child does not contain any part of given box
+            }
+        }
+        if values.isEmpty { return nil }
+        return values
+    }
+    
+    private func subdivide(adding element: T, at point: vector_double3) -> OctreeNode? {
+        precondition(self.elements != nil, "Subdividing while leaf does not contain a element")
+        precondition(self.point != nil, "Subdividing while leaf does not contain a point")
+        switch type {
+        case .leaf:
+            type = .internal(children: Children(parentNode: self))
+            // add element previously contained in leaf to children
+            self.add(self.elements, at: self.point)
+            self.elements = nil
+            self.point = nil
+            // add new element to children
+            return self.add(element, at: point)
+        case .internal:
+            preconditionFailure("Calling subdivide on an internal node")
+        }
+    }
+}
+
+public class Octree<T: Equatable>: CustomStringConvertible {
+    var root: OctreeNode<T>
+    
+    public var description: String {
+        return "Octree\n" + root.recursiveDescription
+    }
+    
+    public init(boundingBox: Box, minimumCellSize: Double) {
+        root = OctreeNode<T>(box: boundingBox)
+    }
+    
+    @discardableResult
+    public func add(_ element: T, at point: vector_double3) -> OctreeNode<T> {
+        return root.add(element, at: point)
+    }
+    
+    @discardableResult
+    public func remove(_ element: T, using node: OctreeNode<T>) -> Bool {
+        return node.remove(element)
+    }
+    
+    @discardableResult
+    public func remove(_ element: T) -> Bool {
+        return root.remove(element)
+    }
+    
+    public func elements(at point: vector_double3) -> [T]? {
+        return root.elements(at: point)
+    }
+    
+    public func elements(in box: Box) -> [T]? {
+        precondition(root.box.contains(box), "box is outside of octree bounds")
+        return root.elements(in: box)
+    }
+}
diff --git a/Octree/Octree.playground/contents.xcplayground b/Octree/Octree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Octree/Octree.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Octree/Octree.playground/timeline.xctimeline b/Octree/Octree.playground/timeline.xctimeline
new file mode 100644
index 000000000..783cc6694
--- /dev/null
+++ b/Octree/Octree.playground/timeline.xctimeline
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/jaap/code/swift-algorithm-club/Octree/Octree.playground#CharacterRangeLen=17&amp;CharacterRangeLoc=968&amp;EndingColumnNumber=13&amp;EndingLineNumber=32&amp;StartingColumnNumber=22&amp;StartingLineNumber=31&amp;Timestamp=529255572.908338"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/jaap/code/swift-algorithm-club/Octree/Octree.playground#CharacterRangeLen=32&amp;CharacterRangeLoc=455&amp;EndingColumnNumber=0&amp;EndingLineNumber=14&amp;StartingColumnNumber=9&amp;StartingLineNumber=13&amp;Timestamp=529255572.908505"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>

From 33e5572b5f3891bb600724d32b8ec5079ffaeba6 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Mon, 9 Oct 2017 17:42:54 +0200
Subject: [PATCH 1275/1679] add readme

---
 Octree/README.md | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 Octree/README.md

diff --git a/Octree/README.md b/Octree/README.md
new file mode 100644
index 000000000..12b8cff39
--- /dev/null
+++ b/Octree/README.md
@@ -0,0 +1,27 @@
+# OcTree
+
+An octree is a [tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Tree) in which each internal (not leaf) node has eight children. Often used for collision detection in games for example.
+
+### Problem
+
+Consider the following problem: your need to store a number of objects in 3D space (each at a certain location with `X`, `Y` and `Z` coordinates) and then you need to answer which objects lie in a certain 3D region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though.
+
+### A Better Approach
+
+Octrees are most commonly used to partition a three-dimensional space by recursively subdividing it into 8 regions. Let's see how we can use an Octree to store some values.
+
+Each node in the tree represents a box-like region. Leaf nodes store a single point in that region with an array of objects assigned to that point.
+
+Once an object within the same region (but at a different point) is added the leaf node turns into an internal node and 8 child nodes (leaves) are added to it. All points previously contained in the node are passed to its corresponding children and stored. Thus only leaves contain actual points and values.
+
+To find the points that lie in a given region we can now traverse the tree from top to bottom and collect the suitable points from nodes.
+
+Both adding a point and searching can still take up to O(n) in the worst case, since the tree isn't balanced in any way. However, on average it runs significantly faster (something comparable to O(log n)).
+
+### See also
+
+More info on [Wiki](https://en.wikipedia.org/wiki/Octree)
+Apple's implementation of [GKOctree](https://developer.apple.com/documentation/gameplaykit/gkoctree)
+
+*Written for Swift Algorithm Club by Jaap Wijnen*
+*Heavily inspired by Timur Galimov's Quadtree implementation and Apple's GKOctree implementation

From d7cc4b6a625427271ce8c744369e6eedbcab4c31 Mon Sep 17 00:00:00 2001
From: Paige Sun <paige.sun.dev@gmail.com>
Date: Mon, 9 Oct 2017 16:42:03 -0400
Subject: [PATCH 1276/1679] Simplify twoSum logic by using (n) instead of the
 (target - n) as the dictionary key.

---
 .../Solution 1/2Sum.playground/Contents.swift | 28 ++++++++++---------
 1 file changed, 15 insertions(+), 13 deletions(-)

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 4b6db5d51..7ce0ba07d 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -4,21 +4,23 @@
 print("Hello, Swift 4!")
 #endif
 
-func twoSum(_ numbers: [Int], target: Int) -> (Int, Int)? {
-  var dict: [Int: Int] = [:]
-  
-  for (index, number) in numbers.enumerated() {
-    if let otherIndex = dict[number] {
-      return (index, otherIndex)
-    } else {
-      dict[target - number] = index
+func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
+    var dict = [Int: Int]()
+    
+    for (currentIndex, n) in nums.enumerated() {
+        let complement = target - n
+        
+        if let complementIndex = dict[complement] {
+            return (complementIndex, currentIndex)
+        }
+        
+        dict[n] = currentIndex
     }
-  }
-  
-  return nil
+    
+    return nil
 }
 
-let numbers = [3, 2, 4]
+let numbers = [3, 2, 8, 4]
 let target = 6
 
-twoSum(numbers, target: target) // expected output: indices 2 and 1
+twoSum(numbers, target: target) // expected output: indices 1 and 3

From 5eb53e0479061402f35cd9bcf3a9ecab98183206 Mon Sep 17 00:00:00 2001
From: Paige Sun <paige.sun.dev@gmail.com>
Date: Mon, 9 Oct 2017 16:48:58 -0400
Subject: [PATCH 1277/1679] Update title, Xcode version. Minor refactor.

---
 .../Solution 1/2Sum.playground/Contents.swift            | 9 +++------
 .../Solution 1/2Sum.playground/contents.xcplayground     | 2 +-
 2 files changed, 4 insertions(+), 7 deletions(-)

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 7ce0ba07d..e89e52c94 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,5 +1,5 @@
-//: Playground - noun: a place where people can play
-// Last checked with: Version 9.0 beta 4 (9M189t)
+//: Two Sum
+// Last checked with: Version 9.0 (9A235)
 #if swift(>=4.0)
 print("Hello, Swift 4!")
 #endif
@@ -20,7 +20,4 @@ func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
     return nil
 }
 
-let numbers = [3, 2, 8, 4]
-let target = 6
-
-twoSum(numbers, target: target) // expected output: indices 1 and 3
+twoSum([3, 2, 8, 4], target: 6) // expected output: indices 1 and 3
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground b/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground
index 06828af92..3de2b51ba 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' display-mode='rendered'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 38e284f12cd61a0b6ad87196778b005ab9cbb7fe Mon Sep 17 00:00:00 2001
From: Paige Sun <paige.sun.dev@gmail.com>
Date: Mon, 9 Oct 2017 17:55:55 -0400
Subject: [PATCH 1278/1679] =?UTF-8?q?Update=20twoSum=E2=80=99s=20README=20?=
 =?UTF-8?q?with=20a=20simpler=20dictionary.?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Two-Sum Problem/README.markdown               | 70 ++++++++++++-------
 .../Solution 1/2Sum.playground/Contents.swift |  2 +-
 2 files changed, 44 insertions(+), 28 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index dacf5a40a..b2f126595 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,66 +1,82 @@
 # Two-Sum Problem
 
-You're given an array of numbers. Write an algorithm that checks if there are any two elements in the array that add up to a given number.
+Given an array of integers and an integer target, return the indices of two numbers that add up to the target.
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.
 
 # Solution 1
 
-This solution uses a dictionary to store differences between each element in the array and the sum that we're looking for. The dictionary also stores the indices of each element.
+This solution looks at one number at a time, storing each number in the dictionary. It uses the number as the key and the number's index in the array as the value.
 
-With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum.
+For each number n, we know the complementing number to sum up to the target is `target - n`. By looking up the complement in the dictionary, we'd know whether we've seen the complement before and what its index is.
 
 ```swift
-func twoSumProblem(_ numbers: [Int], target: Int) -> (Int, Int)? {
-  var dict: [Int: Int] = [:]
-  
-  for (index, number) in numbers.enumerated() {
-    if let otherIndex = dict[number] {
-      return (index, otherIndex)
-    } else {
-      dict[target - number] = index
+func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
+    var dict = [Int: Int]()
+    
+    // For every number n,
+    for (currentIndex, n) in nums.enumerated() {
+        // Find the complement to n that would sum up to the target.
+        let complement = target - n
+        
+        // Check if the complement is in the dictionary.
+        if let complementIndex = dict[complement] {
+            return (complementIndex, currentIndex)
+        }
+        
+        // Store n and its index into the dictionary.
+        dict[n] = currentIndex
     }
-  }
-
-  return nil  // if empty array or no entries sum to target k
+    
+    return nil
 }
 ```
 
-The `twoSumProble` function takes two parameters: the `numbers` array and the target sum you're looking for. It returns the 2 indices with elements that sums up to the target, or `nil` if it can't be found.
+The `twoSum` function takes two parameters: the `numbers` array and the target sum. It returns the two indicies of the pair of elements that sums up to the target, or `nil` if they can't be found.
 
-Let's take a look at an example and run through the algorithm to see how it works. Given is the array:
+Let's run through the algorithm to see how it works. Given the array:
 
 ```swift
-[ 7, 2, 23, 8, -1, 0, 11, 6  ]
+[3, 2, 9, 8]
 ```
 
-Let's find out if there exist two entries whose sum is equal to 10.
+Let's find out if there exist two entries whose sum is 10.
 
 Initially, our dictionary is empty. We begin looping through each element:
 
-- **i = 0**: Is `7` in the dictionary? No. We add the difference between the `target` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
+- **currentIndex = 0** | n = nums[0] = 3 | complement = 10 - 3 = 7
+
+Is the complement `7` in the dictionary? No, so we add `3` and its index `0` to the dictionary.
 
 ```swift
-[ 3: 0 ]
+[3: 0]
 ```
 
-- **i = 1:** Is `2` in the dictionary? No. Let's do as above and add the difference (`10 - 2 = 8`) and the array index (`1`). The dictionary is:
+- **currentIndex = 1** | n = 2 | complement = 10 - 2 = 8
+
+Is the complement `8` in the dictionary? No, so we add `2` and its index `1` to the dictionary.
 
 ```swift
-[ 3: 0, 8: 1 ]
+[3: 0, 2: 1]
 ```
 
-- **i = 2:** Is `23` in the dictionary? No. Again, we add it to the dictionary. The difference is `10 - 23 = -13` and the index is `2`:
+- **currentIndex = 2** | n = 9 | complement = 10 - 9 = 1
+
+Is the complement `1` in the dictionary? No, so we add `9` and its index `2` to the dictionary.:
 
 ```swift
-[ 3: 0, 8: 1, -13: 2 ]
+[3: 0, 2: 1, 9: 2]
 ```
 
-- **i = 3:** Is `8` in the dictionary? Yes! That means that we have found a pair of entries that sum to our target. Namely the current number `8` and `array[dict[8]]` because `dict[8] = 1`, `array[1] = 2`, and `8 + 2 = 10`. Therefore, we return the corresponding indices of these numbers. For `8` that is the current loop index, `3`. For `2` that is `dict[8]` or `1`. The tuple we return is `(1, 3)`.
+- **currentIndex = 3** | n = 8 | complement = 10 - 8 = 2
+
+Is the complement `2` in the dictionary? Yes! That means that we have found a pair of entries that sum to the target!
+
+Therefore, the `complementIndex = dict[2] = 1` and the `currentIndex = 3`. The tuple we return is `(1, 3)`.
 
-The given array actually has multiple solutions: `(1, 3)` and `(4, 6)`. However, only the first solution is returned.
+If the given array has multiple solutions, only the first solution is returned.
 
-The running time of this algorithm is **O(n)** because it potentially may need to look at all array elements. It also requires **O(n)** additional storage space for the dictionary.
+The running time of this algorithm is **O(n)** because it may look at every element in the array. It also requires **O(n)** additional storage space for the dictionary.
 
 # Solution 2
 
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index e89e52c94..26bfae449 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -20,4 +20,4 @@ func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
     return nil
 }
 
-twoSum([3, 2, 8, 4], target: 6) // expected output: indices 1 and 3
+twoSum([3, 2, 9, 8], target: 10) // expected output: indices 1 and 3

From eca6517dc5dafd3d39901160d8ae9c3589652a87 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:33:09 -0700
Subject: [PATCH 1279/1679] Added links to the topic on Lazy Propagation

---
 Segment Tree/README.markdown | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 9897c9c3b..97d7f7d92 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -1,5 +1,7 @@
 # Segment Tree
 
+> For an example on lazy propagation, see this [article](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation).
+
 I'm pleased to present to you Segment Tree. It's actually one of my favorite data structures because it's very flexible and simple in realization.
 
 Let's suppose that you have an array **a** of some type and some associative function **f**. For example, the function can be sum, multiplication, min, max, [gcd](../GCD/), and so on.
@@ -199,6 +201,7 @@ See the playground for more examples of how to use the segment tree.
 
 ## See also
 
+[Lazy Propagation]((https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 [Segment tree at PEGWiki](http://wcipeg.com/wiki/Segment_tree)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From cfb4f9bc05a6f7a8c50c42ae97bb116e5cd2ce4e Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:33:28 -0700
Subject: [PATCH 1280/1679] Fixed formatting

---
 Segment Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 97d7f7d92..e3010b1fe 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -201,7 +201,7 @@ See the playground for more examples of how to use the segment tree.
 
 ## See also
 
-[Lazy Propagation]((https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
+[Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 [Segment tree at PEGWiki](http://wcipeg.com/wiki/Segment_tree)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From cefb1c1ea2e9e998a5c12a95c789345e500a7a51 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:34:25 -0700
Subject: [PATCH 1281/1679] Added a few extra words describing lazy
 propagation.

---
 Segment Tree/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index e3010b1fe..99ec85cd8 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -201,7 +201,8 @@ See the playground for more examples of how to use the segment tree.
 
 ## See also
 
-[Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
+[Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation) implementation and explanation.
+
 [Segment tree at PEGWiki](http://wcipeg.com/wiki/Segment_tree)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From 70bae5bee70aaea80dd5fe7d74824098f8107f4b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:35:33 -0700
Subject: [PATCH 1282/1679] Added lazy propagation to main README.

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index dd001f75a..fa3483657 100644
--- a/README.markdown
+++ b/README.markdown
@@ -156,6 +156,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Splay Tree](Splay%20Tree/). A self balancing binary search tree that enables fast retrieval of recently updated elements.
 - [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
+  - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation) 
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap

From 4d92bfc5fd05c72fc5e35f45c17dbadb637b9db1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:36:00 -0700
Subject: [PATCH 1283/1679] Updates the avoiding duplicates section.

---
 3Sum and 4Sum/README.md | 82 ++++++++++++++++++++++-------------------
 1 file changed, 44 insertions(+), 38 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index a34d2f49e..f9a121fab 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -111,45 +111,51 @@ There are slight optimizations you can do to find `m`, but to keep things simple
 
 #### Avoiding Duplicates
 
-Avoiding duplicate values is fairly straightforward if you've understood everything so far. Let's consider a sample array that has a few duplicates:
-
-```
-target = 0
-
-[-1, -1, -1, -1, 0, 1, 1, 1]
-```
-
-One possible subset is `[-1, 0, 1]`, and in fact is the only subset for 3Sum. 
-
-The easiet way is using set. We can maintain a solution set, then we can check if the triplets is in the set or not to determine whether it's duplicate.
-
-Set introduces space complexity. So we still want to avoid extra space using. Let's change an angle consider, we can loop the array first find `m` then next thing is to find `l` and `r`. 
-
-For example
-
+Since you pre-sort the array, duplicates will be adjacent to each other. You just need to skip over duplicates by comparing adjacent values:
+
+```
+extension Collection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  func uniqueIndex(after index: Index) -> Index? {
+    guard index < endIndex else { return nil }
+    var index = index
+    var nextIndex = self.index(after: index)
+    while nextIndex < endIndex && self[index] == self[nextIndex] {
+      formIndex(after: &index)
+      formIndex(after: &nextIndex)
+    }
+    
+    if nextIndex == endIndex {
+      return nil
+    } else {
+      return nextIndex
+    }
+  }
+}
+```
+
+A similar implementation is used to get the unique index *before* a given index:
+
+```
+extension BidirectionalCollection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  func uniqueIndex(before index: Index) -> Index? {
+    return indices[..<index].reversed().first { index -> Bool in
+      let nextIndex = self.index(after: index)
+      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
+      return true
+    }
+  }
+}
 ```
-​```
-[-1, 0, 1, 2, -1, -4] // unsorted
-
-1)
-[-4, -1, -1, 0, 1, 2]
-      m   l        r
-
-2)
-[-4, -1, -1, 0, 1, 2]
-          m  l     r
-
-3)
-[-4, -1, -1, 0, 1, 2]
-      m      l     r
-​```
-
-We loop `m` in `0..<n`. We will do another inner loop at the same time, `l..r` loops in `i+1..<n`. 
-In 1), we will check if `a[i] == a[i-1]`? It's not in this case, then the problem is 2sum (`l..r`).
-In 2), Since `a[i] == a[i-1]`, it means `a[i-1]` covers `a[i]` case. Because case 3) contains case 2) solutions.
-```
-
-
 
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 

From 8a51e9730e31b8d1e824a18c663e949df46b406d Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:45:25 -0700
Subject: [PATCH 1284/1679] Removes unnecessary explanations.

---
 3Sum and 4Sum/README.md | 104 ++++------------------------------------
 1 file changed, 8 insertions(+), 96 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index f9a121fab..c808e5e26 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -4,110 +4,20 @@
 
 ## 3Sum
 
-Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
+> Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
 
-**Note**: The solution subsets must not contain duplicate triplets. (Each element in the array can only be used once)
+> **Note**: The solution subsets must not contain duplicate triplets.
 
 > For example, given the array [-1, 0, 1, 2, -1, -4], and the target **0**:
 > The solution set is: [[-1, 0, 1], [-1, -1, 2]] // The two **-1** values in the array are considered to be distinct
 
-### Example
+There are 3 key procedures in solving this algorithm:
 
-Consider the following array of integers, and a target sum of **0**:
+1. Sort the array in ascending order. This allows you to make smart decisions when moving indexes around (since duplicates will be adjacent to each other).
 
-```
-[-1, 0, 1, 2, -1, -4]
-```
-
-#### 1. Sorting
-
-You'll first sort the array in ascending order:
-
-```
-[-4, -1, -1, 0, 1, 2]
-```
-
-#### 2. Two Sum's Methodology
-
-The 3Sum problem can be solved by augmenting the 2Sum solution, so let's begin by doing a quick explanation on how 2Sum handles the solution. 2Sum begins by comparing the left and right most values:
-
-```
-[-4, -1, -1, 0, 1, 2]
-  l                r
-```
-
-Your target sum is **0**. Given the current left and right values, you won't be able to make the target number. However, you've gained a valuable hint for your next step. 
-
-```
--4 + 2 = -2 // too small!
-```
-
-The result of `l + r` gave you a value that is smaller than the target number. Thus, you have two options:
-
-1. Increase the lower number. 
-2. Increase the higher number.
-
-Because your array is sorted, you can quickly identify that you cannot pick option **2**, since the rightmost number is already the biggest number. Thus, you have no choice but to try for a different number from the left end of the array:
-
-```
-[-4, -1, -1, 0, 1, 2]
-      l            r
-```
-
-This time, you'll get the following result from summing `l` and `r`:
-
-```
--1 + 2 = 1 // too big!
-```
-
-This time, the value is too big! I hope you see where it goes from here. Since the array is already sorted, you can only decrease the value on the right side in an attempt to balance things out. Hence, the next iteration of your algorithm will look like this:
+2. Ignoring duplicate values
 
-```
-[-4, -1, -1, 0, 1, 2]
-      l         r 
-```
-
-And then you've found a match :]
-
-```
--1 + 1 = 0
-```
-
-# 3Sum
-
-Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
-
-```
-[-4, -1, -1, 0, 1, 2]
-  l                r
-```
-
-Your goal this time is the following equation:
-
-```
-l + r + m = 0
-```
-
-You have the values of `l` and `r`:
-
-```
--4 + 2 + m = 0
-
-// in other words
-m = 4 - 2 = 2
-```
-
-For the current values of `l` and `r`, you need to find a value of **2** in the array to satisfy your target sum...
-
-#### Finding `m`
-
-```
-         m -- where?
-[-4, -1, -1, 0, 1, 2]
-  l                r 
-```
-
-There are slight optimizations you can do to find `m`, but to keep things simple, you'll just iterate through the array from `l` index to the `r` index. Once you find a value where `l + r + m = target`, you've found your first match! 
+3. Clever adjustment of indices for each pass. 
 
 #### Avoiding Duplicates
 
@@ -157,6 +67,8 @@ extension BidirectionalCollection where Element: Equatable {
 }
 ```
 
+### 
+
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From 63cae2538e12b358f7b0c514d2b5a2df7bb1fcf1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:56:55 -0700
Subject: [PATCH 1285/1679] Summarizes technique for solving the problem.

---
 3Sum and 4Sum/README.md | 17 +++++++++--------
 1 file changed, 9 insertions(+), 8 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index c808e5e26..26b007668 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -5,19 +5,22 @@
 ## 3Sum
 
 > Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
-
+>
 > **Note**: The solution subsets must not contain duplicate triplets.
-
+>
 > For example, given the array [-1, 0, 1, 2, -1, -4], and the target **0**:
 > The solution set is: [[-1, 0, 1], [-1, -1, 2]] // The two **-1** values in the array are considered to be distinct
 
-There are 3 key procedures in solving this algorithm:
+There are 2 key procedures in solving this algorithm. Sorting the array, and avoiding duplicates.
 
-1. Sort the array in ascending order. This allows you to make smart decisions when moving indexes around (since duplicates will be adjacent to each other).
+### Pre-sorting
 
-2. Ignoring duplicate values
+Sorting your input array allows for powerful assumptions:
 
-3. Clever adjustment of indices for each pass. 
+* duplicates are always adjacent to each other
+* moving an index to the right increases the value, while moving an index to the left decreases the value
+
+You'll make use of these two rules to create an efficient algorithm.
 
 #### Avoiding Duplicates
 
@@ -67,8 +70,6 @@ extension BidirectionalCollection where Element: Equatable {
 }
 ```
 
-### 
-
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From a7ab5dae00c799d292845169940653a26070eb40 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:57:28 -0700
Subject: [PATCH 1286/1679] Removes a pointless sentence.

---
 3Sum and 4Sum/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 26b007668..f37d18d9c 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -1,6 +1,6 @@
 # 3Sum and 4Sum
 
-3Sum and 4Sum are extensions of a popular algorithm question, the [2Sum][5]. This article will talk about the problem and describe possible solutions.
+3Sum and 4Sum are extensions of a popular algorithm question, the [2Sum][5]. 
 
 ## 3Sum
 

From 0bf83f16b7eafcb5dea84fe97cb4cbc10755bb14 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:58:09 -0700
Subject: [PATCH 1287/1679] Updates a header.

---
 3Sum and 4Sum/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index f37d18d9c..9a5124637 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -13,7 +13,7 @@
 
 There are 2 key procedures in solving this algorithm. Sorting the array, and avoiding duplicates.
 
-### Pre-sorting
+### Sorting
 
 Sorting your input array allows for powerful assumptions:
 
@@ -22,7 +22,7 @@ Sorting your input array allows for powerful assumptions:
 
 You'll make use of these two rules to create an efficient algorithm.
 
-#### Avoiding Duplicates
+### Avoiding Duplicates
 
 Since you pre-sort the array, duplicates will be adjacent to each other. You just need to skip over duplicates by comparing adjacent values:
 

From 1fc26da0fa18a6134428dc14bef7a767fbd3c5c0 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 02:12:20 -0700
Subject: [PATCH 1288/1679] Added solution to 3Sum

---
 3Sum and 4Sum/README.md | 47 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 9a5124637..42732fda9 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -70,6 +70,53 @@ extension BidirectionalCollection where Element: Equatable {
 }
 ```
 
+### Assembling the Subsets
+
+You'll keep track of 3 indices to represent the 3 numbers. The sum at any given moment is `array[l] + array[m] + array[r]`:
+
+```
+      m ->      <- r
+[-4, -1, -1, 0, 1, 2]
+  l   
+```
+
+The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
+
+```
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+    var m = sorted.index(after: l)
+    var r = sorted.index(before: sorted.endIndex)
+
+    while m < r {
+      let sum = sorted[l] + sorted[m] + sorted[r]
+      switch target {
+      case sum:
+        ret.append([sorted[l], sorted[m], sorted[r]])
+        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
+        m = nextMid
+        r = nextRight
+      case ..<target:
+        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
+        m = nextMid
+      case target...:
+        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
+        r = nextRight
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+      }
+    }
+  }
+  
+  return ret
+}
+```
+
+
+
+
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From 1279b3791e37c3531c9400524420cd3befd055cd Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 02:13:48 -0700
Subject: [PATCH 1289/1679] Updates implementation.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 117 +++++++++++--------
 1 file changed, 67 insertions(+), 50 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index ec79ba787..fad2bf76d 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -1,59 +1,76 @@
-func ThreeSum(_ nums: [Int], targetSum: Int) -> [[Int]] {
-    var a = nums.sorted()
-    var ret: [[Int]] = []
-    
-    for m in 0..<a.count {
-        if m != 0 && a[m] == a[m-1] {
-            continue
-        }
-        
-        var l = m + 1
-        var r = nums.count - 1
-        
-        while l < r {
-            let sum = a[m] + a[l] + a[r]
-            
-            if sum == targetSum {
-                ret.append([a[m], a[l], a[r]])
-                l += 1
-            } else if sum < targetSum {
-                l += 1
-            } else {
-                r -= 1
-            }
-            
-            if sum == targetSum {
-                while l < r {
-                    var flag = false
-                    if l != 0 && a[l] == a[l-1] {
-                        l += 1
-                        flag = true
-                    }
-                    
-                    if (r != a.count - 1) && a[r] == a[r+1] {
-                        r -= 1
-                        flag = true
-                    }
-                    
-                    if (!flag) {
-                        break
-                    }
-                }
-            }
-        }
+extension Collection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  func uniqueIndex(after index: Index) -> Index? {
+    guard index < endIndex else { return nil }
+    var index = index
+    var nextIndex = self.index(after: index)
+    while nextIndex < endIndex && self[index] == self[nextIndex] {
+      formIndex(after: &index)
+      formIndex(after: &nextIndex)
     }
     
-    return ret
+    if nextIndex == endIndex {
+      return nil
+    } else {
+      return nextIndex
+    }
+  }
 }
 
-// Answer: [[-1, 0, 1], [-1, -1, 2]]
-ThreeSum([-1, 0, 1, 2, -1, -4], targetSum: 0)
+extension BidirectionalCollection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  func uniqueIndex(before index: Index) -> Index? {
+    return indices[..<index].reversed().first { index -> Bool in
+      let nextIndex = self.index(after: index)
+      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
+      return true
+    }
+  }
+}
 
-// Answer: [[-1, -1, 1]]
-ThreeSum([-1, 1, 1, -1], targetSum: 1)
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+    var m = sorted.index(after: l)
+    var r = sorted.index(before: sorted.endIndex)
+
+    while m < r {
+      let sum = sorted[l] + sorted[m] + sorted[r]
+      switch target {
+      case sum:
+        ret.append([sorted[l], sorted[m], sorted[r]])
+        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
+        m = nextMid
+        r = nextRight
+      case ..<target:
+        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
+        m = nextMid
+      case target...:
+        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
+        r = nextRight
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+      }
+    }
+  }
+  
+  return ret
+}
+
+// Answer: [[-1, 0, 1], [-1, -1, 2]]
+threeSum([-1, 0, 1, 2, -1, -4], target: 0)
 
 // Answer: [[-1, -1, 2], [-1, 0, 1]]
-ThreeSum([-1, -1, -1, -1, 2, 1, -4, 0], targetSum: 0)
+threeSum([-1, -1, -1, -1, 2, 1, -4, 0], target: 0)
 
 // Answer: [[-1, -1, 2]]
-ThreeSum([-1, -1, -1, -1, -1, -1, 2], targetSum: 0)
+threeSum([-1, -1, -1, -1, -1, -1, 2], target: 0)

From 5aa6e17acc7224857ff5b5e27b55b6daf1ef56e6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 14:53:22 -0700
Subject: [PATCH 1290/1679] Downgraded from BinaryInteger to Numeric. Fixes
 documentation.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 14 +++++---------
 1 file changed, 5 insertions(+), 9 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index fad2bf76d..1a2f2933f 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -3,7 +3,7 @@ extension Collection where Element: Equatable {
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
   /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
   func uniqueIndex(after index: Index) -> Index? {
     guard index < endIndex else { return nil }
     var index = index
@@ -13,11 +13,7 @@ extension Collection where Element: Equatable {
       formIndex(after: &nextIndex)
     }
     
-    if nextIndex == endIndex {
-      return nil
-    } else {
-      return nextIndex
-    }
+    return nextIndex != endIndex ? nextIndex : nil
   }
 }
 
@@ -25,8 +21,8 @@ extension BidirectionalCollection where Element: Equatable {
   
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  /// - Parameter index: The current index.
+  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
   func uniqueIndex(before index: Index) -> Index? {
     return indices[..<index].reversed().first { index -> Bool in
       let nextIndex = self.index(after: index)
@@ -36,7 +32,7 @@ extension BidirectionalCollection where Element: Equatable {
   }
 }
 
-func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
   

From 7d1d83ee2c74b3dded13e191ba23ed08d155d544 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 14:57:38 -0700
Subject: [PATCH 1291/1679] Adds loop labeling for better visibility

Easier to understand which parts of the code is borrowed using TwoSum.
---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 1a2f2933f..8730a9b39 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -36,23 +36,23 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
   
-  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+  ThreeSum: for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
 
-    while m < r {
+    TwoSum: while m < r {
       let sum = sorted[l] + sorted[m] + sorted[r]
       switch target {
       case sum:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
+        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
         m = nextMid
         r = nextRight
       case ..<target:
-        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
+        guard let nextMid = sorted.uniqueIndex(after: m) else { break TwoSum }
         m = nextMid
       case target...:
-        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
+        guard let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
         r = nextRight
       default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }

From 26052e77e4747eb060780cfa369648c1885e736a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 14:58:03 -0700
Subject: [PATCH 1292/1679] Removes extra line.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 8730a9b39..c5680d345 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -12,7 +12,6 @@ extension Collection where Element: Equatable {
       formIndex(after: &index)
       formIndex(after: &nextIndex)
     }
-    
     return nextIndex != endIndex ? nextIndex : nil
   }
 }

From 48d83f2cbe1d813adb5519de31990b54a0c65e20 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 15:00:10 -0700
Subject: [PATCH 1293/1679] Updates readme based on changes to playground code.

---
 3Sum and 4Sum/README.md | 41 ++++++++++++++++++-----------------------
 1 file changed, 18 insertions(+), 23 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 42732fda9..9fdc0277a 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -31,8 +31,8 @@ extension Collection where Element: Equatable {
   
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  /// - Parameter index: The current index.
+  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
   func uniqueIndex(after index: Index) -> Index? {
     guard index < endIndex else { return nil }
     var index = index
@@ -41,12 +41,7 @@ extension Collection where Element: Equatable {
       formIndex(after: &index)
       formIndex(after: &nextIndex)
     }
-    
-    if nextIndex == endIndex {
-      return nil
-    } else {
-      return nextIndex
-    }
+    return nextIndex != endIndex ? nextIndex : nil
   }
 }
 ```
@@ -58,8 +53,8 @@ extension BidirectionalCollection where Element: Equatable {
   
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  /// - Parameter index: The current index.
+  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
   func uniqueIndex(before index: Index) -> Index? {
     return indices[..<index].reversed().first { index -> Bool in
       let nextIndex = self.index(after: index)
@@ -83,29 +78,29 @@ You'll keep track of 3 indices to represent the 3 numbers. The sum at any given
 The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
 
 ```
-func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
-  let sorted = collection.sorted()
+func threeSum<T: BidirectionalCollection>(_ c: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = c.sorted()
   var ret: [[T.Element]] = []
   
   for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
-
+    
     while m < r {
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch target {
-      case sum:
+      switch sum {
+      case target:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
-        m = nextMid
-        r = nextRight
+        guard let nextM = sorted.uniqueIndex(after: m), let nextR = sorted.uniqueIndex(before: r) else { break }
+        m = nextM
+        r = nextR
       case ..<target:
-        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
-        m = nextMid
+        guard let nextM = sorted.uniqueIndex(after: m) else { break }
+        m = nextM
       case target...:
-        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
-        r = nextRight
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+        guard let nextR = sorted.uniqueIndex(before: m) else { break }
+        r = nextR
+      default: fatalError()
       }
     }
   }

From f9b6a2f3059b258ffeff1fa11342d1652cd8a5a0 Mon Sep 17 00:00:00 2001
From: Semen Zhydenko <simeon.zhidenko@gmail.com>
Date: Sat, 14 Oct 2017 21:27:16 +0200
Subject: [PATCH 1294/1679] becuase -> because

---
 Singly Linked List/SinglyLinkedList.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Singly Linked List/SinglyLinkedList.playground/Contents.swift b/Singly Linked List/SinglyLinkedList.playground/Contents.swift
index d9104ebe7..8c62f9e78 100644
--- a/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
+++ b/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
@@ -720,7 +720,7 @@ assert(l2.count == 8)
 assert(l2.contains(67) == true)
 
 
-//: Notice that becuase our implementation conforms to the Collection protocol, we can use a lot of methods already implemented for us in Swift's standard library, for example, contains, dropLast, etc.
+//: Notice that because our implementation conforms to the Collection protocol, we can use a lot of methods already implemented for us in Swift's standard library, for example, contains, dropLast, etc.
 
 let l3 = l2.dropLast()
 assert(l3.count == 7)

From 3402103956c96bfd03af5a1345aa8cfce05fda3c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:38:08 -0700
Subject: [PATCH 1295/1679] Simplifies algorithm via in-place index traversals

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 57 +++++++++-----------
 1 file changed, 26 insertions(+), 31 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index c5680d345..d16492689 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -1,61 +1,56 @@
+
 extension Collection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
-  func uniqueIndex(after index: Index) -> Index? {
-    guard index < endIndex else { return nil }
-    var index = index
-    var nextIndex = self.index(after: index)
-    while nextIndex < endIndex && self[index] == self[nextIndex] {
+  /// - Parameter index: A valid index of the collection. `index` must be less than `endIndex`
+  func formUniqueIndex(after index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
       formIndex(after: &index)
-      formIndex(after: &nextIndex)
-    }
-    return nextIndex != endIndex ? nextIndex : nil
+    } while index < endIndex && self[prev] == self[index]
   }
 }
 
 extension BidirectionalCollection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
   ///
-  /// - Parameter index: The current index.
-  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
-  func uniqueIndex(before index: Index) -> Index? {
-    return indices[..<index].reversed().first { index -> Bool in
-      let nextIndex = self.index(after: index)
-      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
-      return true
-    }
+  /// - Parameter index: A valid index of the collection. `index` must be greater than `startIndex`.
+  func formUniqueIndex(before index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(before: &index)
+    } while index > startIndex && self[prev] == self[index]
   }
 }
 
 func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
+  var l = sorted.startIndex
   
-  ThreeSum: for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+  while l < sorted.endIndex {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
-
-    TwoSum: while m < r {
+    
+    while m < r && r < sorted.endIndex {
       let sum = sorted[l] + sorted[m] + sorted[r]
       switch target {
       case sum:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
-        m = nextMid
-        r = nextRight
+        sorted.formUniqueIndex(after: &m)
+        sorted.formUniqueIndex(before: &r)
       case ..<target:
-        guard let nextMid = sorted.uniqueIndex(after: m) else { break TwoSum }
-        m = nextMid
+        sorted.formUniqueIndex(after: &m)
       case target...:
-        guard let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
-        r = nextRight
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+        sorted.formUniqueIndex(before: &r)
+      default: fatalError("Sw ift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
+    sorted.formUniqueIndex(after: &l)
   }
   
   return ret

From e4d1faec77b123b60cb975302fcc5701f54484e0 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:38:57 -0700
Subject: [PATCH 1296/1679] Removes a needless whitespace in string.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index d16492689..dfc4d12f8 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -47,7 +47,7 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
         sorted.formUniqueIndex(after: &m)
       case target...:
         sorted.formUniqueIndex(before: &r)
-      default: fatalError("Sw ift isn't smart enough to detect that this switch statement is exhausive")
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
     sorted.formUniqueIndex(after: &l)

From 1c4ce41440cfd34f38993dfb82853130c953c07b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:42:19 -0700
Subject: [PATCH 1297/1679] Updated readme based on code changes.

---
 3Sum and 4Sum/README.md | 65 ++++++++++++++++++-----------------------
 1 file changed, 28 insertions(+), 37 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 9fdc0277a..781c1f52b 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -29,19 +29,15 @@ Since you pre-sort the array, duplicates will be adjacent to each other. You jus
 ```
 extension Collection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
   ///
-  /// - Parameter index: The current index.
-  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
-  func uniqueIndex(after index: Index) -> Index? {
-    guard index < endIndex else { return nil }
-    var index = index
-    var nextIndex = self.index(after: index)
-    while nextIndex < endIndex && self[index] == self[nextIndex] {
+  /// - Parameter index: A valid index of the collection. `index` must be less than `endIndex`
+  func formUniqueIndex(after index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
       formIndex(after: &index)
-      formIndex(after: &nextIndex)
-    }
-    return nextIndex != endIndex ? nextIndex : nil
+    } while index < endIndex && self[prev] == self[index]
   }
 }
 ```
@@ -51,16 +47,15 @@ A similar implementation is used to get the unique index *before* a given index:
 ```
 extension BidirectionalCollection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
   ///
-  /// - Parameter index: The current index.
-  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
-  func uniqueIndex(before index: Index) -> Index? {
-    return indices[..<index].reversed().first { index -> Bool in
-      let nextIndex = self.index(after: index)
-      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
-      return true
-    }
+  /// - Parameter index: A valid index of the collection. `index` must be greater than `startIndex`.
+  func formUniqueIndex(before index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(before: &index)
+    } while index > startIndex && self[prev] == self[index]
   }
 }
 ```
@@ -78,40 +73,36 @@ You'll keep track of 3 indices to represent the 3 numbers. The sum at any given
 The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
 
 ```
-func threeSum<T: BidirectionalCollection>(_ c: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
-  let sorted = c.sorted()
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = collection.sorted()
   var ret: [[T.Element]] = []
+  var l = sorted.startIndex
   
-  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+  while l < sorted.endIndex {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r {
+    while m < r && r < sorted.endIndex {
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch sum {
-      case target:
+      switch target {
+      case sum:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextM = sorted.uniqueIndex(after: m), let nextR = sorted.uniqueIndex(before: r) else { break }
-        m = nextM
-        r = nextR
+        sorted.formUniqueIndex(after: &m)
+        sorted.formUniqueIndex(before: &r)
       case ..<target:
-        guard let nextM = sorted.uniqueIndex(after: m) else { break }
-        m = nextM
+        sorted.formUniqueIndex(after: &m)
       case target...:
-        guard let nextR = sorted.uniqueIndex(before: m) else { break }
-        r = nextR
-      default: fatalError()
+        sorted.formUniqueIndex(before: &r)
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
+    sorted.formUniqueIndex(after: &l)
   }
   
   return ret
 }
 ```
 
-
-
-
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From 8c10fbddd1c44b4ecfeb13a666a6a17ab5f1d762 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:48:31 -0700
Subject: [PATCH 1298/1679] Repositions index traversal of `l`

Seems like a good use case for `defer`... giving the index traversal more visibility by putting it next to the `while` loop. Reads a bit more like for loops now, where exit condition and traversal procedure can be understood in 1 line.
---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index dfc4d12f8..ec021a75c 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -32,11 +32,11 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex {
+  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex {
+    while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
       switch target {
       case sum:
@@ -50,7 +50,6 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
       default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
-    sorted.formUniqueIndex(after: &l)
   }
   
   return ret

From 676fbbe9d096daa6916504e36acbfce60fdc73c7 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:49:02 -0700
Subject: [PATCH 1299/1679] Updates README based on code updates

---
 3Sum and 4Sum/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 781c1f52b..c2374507f 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -78,7 +78,7 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex {
+  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
@@ -96,7 +96,6 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
       default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
-    sorted.formUniqueIndex(after: &l)
   }
   
   return ret

From da9e823f7b486c088a7d5f0134abe008b794b0f6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 22:07:09 -0700
Subject: [PATCH 1300/1679] Simplified switch statement to if-else loop

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index ec021a75c..6c9a81f50 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -38,16 +38,14 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
     
     while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch target {
-      case sum:
+      if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])
         sorted.formUniqueIndex(after: &m)
         sorted.formUniqueIndex(before: &r)
-      case ..<target:
+      } else if sum < target {
         sorted.formUniqueIndex(after: &m)
-      case target...:
+      } else {
         sorted.formUniqueIndex(before: &r)
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
   }

From c76072464c603b348ffa183de4ee36ae060ffece Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 22:08:12 -0700
Subject: [PATCH 1301/1679] Updated readme for new code.

---
 3Sum and 4Sum/README.md | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index c2374507f..77e7ff854 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -82,18 +82,16 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex {
+    while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch target {
-      case sum:
+      if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])
         sorted.formUniqueIndex(after: &m)
         sorted.formUniqueIndex(before: &r)
-      case ..<target:
+      } else if sum < target {
         sorted.formUniqueIndex(after: &m)
-      case target...:
+      } else {
         sorted.formUniqueIndex(before: &r)
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
   }

From 30d168445a17ec1b16b24f9ccbb1fc8c3fd35c5c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:24:31 -0700
Subject: [PATCH 1302/1679] Updated implementation of 4Sum

---
 3Sum and 4Sum/4Sum.playground/Contents.swift | 111 +++++++++----------
 1 file changed, 54 insertions(+), 57 deletions(-)

diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index b86dd42f5..4c26bbf07 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -1,61 +1,58 @@
-func FourSum(_ nums: [Int], target: Int) -> [[Int]] {
-    let a = nums.sorted()
-    var ret: [[Int]] = []
-    
-    for i in 0..<nums.count {
-        if i != 0 && a[i] == a[i-1] {
-            continue
-        }
-        for j in i+1..<nums.count {
-            if j != i+1 && a[j] == a[j-1] {
-                continue
-            }
-            
-            var k = j + 1
-            var t = nums.count - 1
-            
-            while k < t {
-                let sum = a[i] + a[j] + a[k] + a[t]
-                
-                if sum == target {
-                    ret.append([a[i], a[j], a[k], a[t]])
-                    k += 1
-                } else if sum < target {
-                    k += 1
-                } else {
-                    t -= 1
-                }
-                
-                if sum == target {
-                    while k < t {
-                        var flag = true
-                        if k != j + 1 && a[k] == a[k-1] {
-                            k += 1
-                            flag = false
-                        }
-                        
-                        if t != nums.count - 1 && a[t] == a[t+1] {
-                            t -= 1
-                            flag = false
-                        }
-                        
-                        if flag {
-                            break
-                        }
-                    }
-                }
-            }
+extension Collection where Element: Equatable {
+  
+  /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
+  ///
+  /// - Parameter index: A valid index of the collection. `index` must be less than `endIndex`
+  func formUniqueIndex(after index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(after: &index)
+    } while index < endIndex && self[prev] == self[index]
+  }
+}
+
+extension BidirectionalCollection where Element: Equatable {
+  
+  /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
+  ///
+  /// - Parameter index: A valid index of the collection. `index` must be greater than `startIndex`.
+  func formUniqueIndex(before index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(before: &index)
+    } while index > startIndex && self[prev] == self[index]
+  }
+}
+
+func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  var l = sorted.startIndex
+  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+    var ml = sorted.index(after: l)
+    while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
+      var mr = sorted.index(after: ml)
+      var r = sorted.index(before: sorted.endIndex)
+      
+      while mr < r && r < sorted.endIndex {
+        let sum = sorted[l] + sorted[ml] + sorted[mr] + sorted[r]
+        if sum == target {
+          ret.append([sorted[l], sorted[ml], sorted[mr], sorted[r]])
+          sorted.formUniqueIndex(after: &mr)
+          sorted.formUniqueIndex(before: &r)
+        } else if sum < target {
+          sorted.formUniqueIndex(after: &mr)
+        } else {
+          sorted.formUniqueIndex(before: &r)
         }
+      }
     }
-    
-    return ret
+  }
+  return ret
 }
 
-/* Answer
-[
-    [-1,  0, 0, 1],
-    [-2, -1, 1, 2],
-    [-2,  0, 0, 2]
-]
-*/
-FourSum([1, 0, -1, 0, -2, 2], target: 0)
+// answer: [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]
+fourSum([1, 0, -1, 0, -2, 2], target: 0)

From d7b2c1a60e03970cb998cce5ad5e44c6865565f9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:25:03 -0700
Subject: [PATCH 1303/1679] Labeled while loops for clarity.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 6c9a81f50..2581da6e7 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -32,11 +32,11 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+  ThreeSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex { 
+    TwoSum: while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
       if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])

From 67d4c9d306719e79612875c36759c9c9e19a3ef1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:25:35 -0700
Subject: [PATCH 1304/1679] Labelled while loops for clarity.

---
 3Sum and 4Sum/4Sum.playground/Contents.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index 4c26bbf07..100534b28 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -31,13 +31,13 @@ func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   
   var l = sorted.startIndex
-  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+  FourSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var ml = sorted.index(after: l)
-    while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
+    ThreeSum: while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
       var mr = sorted.index(after: ml)
       var r = sorted.index(before: sorted.endIndex)
       
-      while mr < r && r < sorted.endIndex {
+      TwoSum: while mr < r && r < sorted.endIndex {
         let sum = sorted[l] + sorted[ml] + sorted[mr] + sorted[r]
         if sum == target {
           ret.append([sorted[l], sorted[ml], sorted[mr], sorted[r]])

From 97911efc8216f439df075c3842d57340a7a972ee Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:26:11 -0700
Subject: [PATCH 1305/1679] Added new line between loops

---
 3Sum and 4Sum/4Sum.playground/Contents.swift | 1 +
 1 file changed, 1 insertion(+)

diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index 100534b28..86b530224 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -33,6 +33,7 @@ func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var l = sorted.startIndex
   FourSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var ml = sorted.index(after: l)
+                                      
     ThreeSum: while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
       var mr = sorted.index(after: ml)
       var r = sorted.index(before: sorted.endIndex)

From 38b32d28c2f61e8ec3eb3e75516ee2bad2d0c3fb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:31:58 -0700
Subject: [PATCH 1306/1679] Updated for FourSum.

---
 3Sum and 4Sum/README.md | 55 ++++++++++++++++++++++++++++++++++++++---
 1 file changed, 51 insertions(+), 4 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 77e7ff854..af998a4a7 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -78,11 +78,11 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+  ThreeSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex { 
+    TwoSum: while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
       if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])
@@ -101,13 +101,60 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 ```
 
 ## 4Sum
+
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 
 **Note**: The solution set must not contain duplicate quadruplets.
 
 ### Solution
-After 3Sum, we already have the idea to change to a problem to a familiar problem we solved before. So, the idea here is straightforward. We just need to downgrade 4Sum to 3Sum. Then we can solve 4Sum.
 
-It's easy to think that we loop the array and get the first the element, then the rest array is 3Sum problem. Since the code is pretty simple, I will avoid duplicate introducation here.
+Foursum is a very straightforward extension to the threeSum algorithm. In threeSum, you kept track of 3 indices:
+
+```
+      m ->      <- r
+[-4, -1, -1, 0, 1, 2]
+  l   
+```
+
+For fourSum, you'll keep track of 4:
+
+```
+         mr ->  <- r
+[-4, -1, -1, 0, 1, 2]
+  l  ml -> 
+```
+
+Here's the code for it (notice it is very similar to 3Sum):
+
+```
+func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  var l = sorted.startIndex
+  FourSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+    var ml = sorted.index(after: l)
+    
+    ThreeSum: while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
+      var mr = sorted.index(after: ml)
+      var r = sorted.index(before: sorted.endIndex)
+      
+      TwoSum: while mr < r && r < sorted.endIndex {
+        let sum = sorted[l] + sorted[ml] + sorted[mr] + sorted[r]
+        if sum == target {
+          ret.append([sorted[l], sorted[ml], sorted[mr], sorted[r]])
+          sorted.formUniqueIndex(after: &mr)
+          sorted.formUniqueIndex(before: &r)
+        } else if sum < target {
+          sorted.formUniqueIndex(after: &mr)
+        } else {
+          sorted.formUniqueIndex(before: &r)
+        }
+      }
+    }
+  }
+  return ret
+}
+```
 
 [5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem

From 3c0612a467c362a6ef882a6b39f91b7f8375dce7 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:46:46 -0700
Subject: [PATCH 1307/1679] Fixes a bit of formatting.

---
 3Sum and 4Sum/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index af998a4a7..4a51b00f0 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -102,9 +102,9 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 
 ## 4Sum
 
-Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
-
-**Note**: The solution set must not contain duplicate quadruplets.
+> Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
+>
+> **Note**: The solution set must not contain duplicate quadruplets.
 
 ### Solution
 

From 7dcfdf41cccb5c7ea1ede852cebf72a2c9f4a503 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:51:15 -0700
Subject: [PATCH 1308/1679] Added link to 3sum/4sum

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index fa3483657..e874a8190 100644
--- a/README.markdown
+++ b/README.markdown
@@ -193,6 +193,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see [here](http://elementsofprogramminginterviews.com/) and [here](http://www.crackingthecodinginterview.com).
 
 - [Two-Sum Problem](Two-Sum%20Problem/)
+- [Three-Sum/Four-Sum Problem](3Sum%20and%204Sum/)
 - [Fizz Buzz](Fizz%20Buzz/)
 - [Monty Hall Problem](Monty%20Hall%20Problem/)
 - [Finding Palindromes](Palindromes/)

From 4213b0892ec878609b114d0f34f9417164f56e1e Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:51:58 -0700
Subject: [PATCH 1309/1679] Added credits.

---
 3Sum and 4Sum/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 4a51b00f0..5547789c7 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -158,3 +158,5 @@ func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 ```
 
 [5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
+
+*Written for the Swift Algorithm Club by Kai Chen and Kelvin Lau*

From dfc1246b4f5a489f8e5bf76fb208e2684c9f7fc5 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:52:49 -0700
Subject: [PATCH 1310/1679] Added reference to 3sum/4sum

---
 Two-Sum Problem/README.markdown | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index b2f126595..4d8ffcd95 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -164,4 +164,8 @@ It's possible, of course, that there are no values for `a[i] + a[j]` that sum to
 
 I'm quite enamored by this little algorithm. It shows that with some basic preprocessing on the input data -- sorting it from low to high -- you can turn a tricky problem into a very simple and beautiful algorithm.
 
+## Additional Reading
+
+* [3Sum / 4Sum](https://github.com/raywenderlich/swift-algorithm-club/tree/master/3Sum%20and%204Sum)
+
 *Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser*

From 829cf17379477f4ac085f8d80ecb4b68ca020e51 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 18:50:28 -0700
Subject: [PATCH 1311/1679] Adds Octree to the main toc

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index e874a8190..42cd23739 100644
--- a/README.markdown
+++ b/README.markdown
@@ -163,6 +163,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Trie](Trie/). A special type of tree used to store associative data structures.
 - [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
 - [QuadTree](QuadTree/). A tree with 4 children.
+- [Octree](Octree/). A tree with 8 children. 
 
 ### Hashing
 

From 97acdd38f33fdf682a2c56a52501b738054e8a85 Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Sun, 15 Oct 2017 21:32:04 -0700
Subject: [PATCH 1312/1679] Fix typos

---
 All-Pairs Shortest Paths/README.markdown | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/All-Pairs Shortest Paths/README.markdown b/All-Pairs Shortest Paths/README.markdown
index 8a75c8b73..bbef6c64e 100644
--- a/All-Pairs Shortest Paths/README.markdown	
+++ b/All-Pairs Shortest Paths/README.markdown	
@@ -1,14 +1,14 @@
 # All-Pairs Shortest Paths
 
-The All-Pairs shortest path problem simultaneously computes the shortest path from each node in the graph to each other node, provded a path exists for each pair. In the naive approach, we could simply compute a single-source shortest path from each node to each other node. The number of shortest paths computed is then bound by `O(V^2)`, where `V` is the number of vertices in the graph. Because SSSP is also bounded by `O(V^2)`, the total running time for the naive approach would be `O(V^4)`.
+The All-Pairs shortest path problem simultaneously computes the shortest path from each node in the graph to each other node, provided a path exists for each pair. In the naive approach, we could simply compute a single-source shortest path from each node to each other node. The number of shortest paths computed is then bound by `O(V^2)`, where `V` is the number of vertices in the graph. Because SSSP is also bounded by `O(V^2)`, the total running time for the naive approach would be `O(V^4)`.
 
-However, by applying a dynamic approach on the adjacency matrix of the graph, a running time of `Θ(V^3)` is achievable, using the `Floyd-Warshall` algorithm. Floyd-Warshall iterates through an adjacency matrix, and for each pair of start(`i`) and end(`j`) vertices it considers if the current distance between them is greater than a path taken through another vertex(`k`) in the graph (if paths `i` ~> `k` and `k` ~> `j` exist). It moves through an adjacency matrix for every vertex `k` applying its comparison for each pair (`i`, `j`), so for each `k` a new adjacency matrix `D(k)` is derived, where each value `d(k)[i][j]` is defined as:
+However, by applying a dynamic approach on the adjacency matrix of the graph, a running time of `O(V^3)` is achievable, using the `Floyd-Warshall` algorithm. Floyd-Warshall iterates through an adjacency matrix, and for each pair of start(`i`) and end(`j`) vertices it considers if the current distance between them is greater than a path taken through another vertex(`k`) in the graph (if paths `i` ~> `k` and `k` ~> `j` exist). It moves through an adjacency matrix for every vertex `k` applying its comparison for each pair (`i`, `j`), so for each `k` a new adjacency matrix `D(k)` is derived, where each value `d(k)[i][j]` is defined as:
 
 <img src="img/weight_comparison_formula.png" width="400px" />
 
-where `w[i][j]` is the weight of the edge connecting vertex `i` to vertex `j` in the graph's original adjacency matrix. 
+where `w[i][j]` is the weight of the edge connecting vertex `i` to vertex `j` in the graph's original adjacency matrix.
 
-When the algorithm memoizes each refined adjacency and predecessor matrix, its space complexity is `Θ(V^3)`, which can be optimised to `Θ(V^2)` by only memoizing the latest refinements. Reconstructing paths is a recursive procedure which requires `Θ(V)` time and `Θ(V^2)` space.
+When the algorithm memoizes each refined adjacency and predecessor matrix, its space complexity is `O(V^3)`, which can be optimised to `O(V^2)` by only memoizing the latest refinements. Reconstructing paths is a recursive procedure which requires `O(V)` time and `O(V^2)` space.
 
 # Example
 
@@ -22,9 +22,9 @@ the adjacency matrix representation `w` is
 
 ### Calculating shortest paths' weights
 
-At the beginning of the algorithm, `D(0)` is the same as `w`, with the following exceptions to accomodate the comparison function:
+At the beginning of the algorithm, `D(0)` is the same as `w`, with the following exceptions to accommodate the comparison function:
 
-1. vertices with no path connecting them have the `ø` replaced with `∞` 
+1. vertices with no path connecting them have the `ø` replaced with `∞`
 2. the diagonal has all `0`s
 
 Here are all the adjacency matrices derived when perform Floyd-Warshall on the above graph:
@@ -56,7 +56,7 @@ This algorithm finds only the lengths of the shortest paths between all pairs of
 
 # Project Structure
 
-The provided xcworkspace allows working in the playground, which imports the APSP framework target from the xcodeproj. Build the framework target and rerun the playground to get started. There is also a test target in the xcodeproj. 
+The provided xcworkspace allows working in the playground, which imports the APSP framework target from the xcodeproj. Build the framework target and rerun the playground to get started. There is also a test target in the xcodeproj.
 
 In the framework:
 
@@ -65,7 +65,7 @@ In the framework:
 
 # TODO
 
-- Implement naive `Θ(V^4)` method for comparison
+- Implement naive `O(V^4)` method for comparison
 - Implement Johnson's algorithm for sparse graphs
 - Implement other cool optimized versions
 
@@ -73,4 +73,4 @@ In the framework:
 
 Chapter 25 of Introduction to Algorithms, Third Edition by Cormen, Leiserson, Rivest and Stein [https://mitpress.mit.edu/books/introduction-algorithms](https://mitpress.mit.edu/books/introduction-algorithms)
 
-*Written for Swift Algorithm Club by [Andrew McKnight](https://github.com/armcknight)*
\ No newline at end of file
+*Written for Swift Algorithm Club by [Andrew McKnight](https://github.com/armcknight)*

From 07563e0cdb87bd0efc1e359bdaae5f13ac932075 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 19 Oct 2017 00:22:35 +0200
Subject: [PATCH 1313/1679] add astar reference in readme

---
 Dijkstra Algorithm/README.md | 58 +++++++++++++++++++-----------------
 1 file changed, 30 insertions(+), 28 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 5f8a0ce07..4bc719598 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,6 +1,6 @@
 # Weighted graph general concepts
 
-Every weighted graph should contain: 
+Every weighted graph should contain:
 1. Vertices/Nodes (I will use "vertex" in this readme).
 
 <img src="Images/Vertices.png" height="250" />
@@ -11,11 +11,11 @@ Every weighted graph should contain:
 
 <img src="Images/DirectedGraph.png" height="250" />
 
-3. Weights for every edge. 
+3. Weights for every edge.
 
 <img src="Images/WeightedDirectedGraph.png" height="250" />
 
-Final result. 
+Final result.
 Directed weighted graph:
 
 <img src="Images/WeightedDirectedGraphFinal.png" height="250" />
@@ -44,7 +44,9 @@ When all vertices are marked as visited, the algorithm's job is done. Now, you c
 
 I have created **VisualizedDijkstra.playground** game/tutorial to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
-## Example 
+A short sidenote. The Swift Algorithm Club also contains the A* algorithm, which essentially is a faster version of Dijkstra's algorithm for which the only extra prerequisite is you have to know where the destination is located.
+
+## Example
 Let's imagine that you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have a graph that connects your house with all these stores. So, you know what to do :)
 
 ### Initialisation
@@ -95,7 +97,7 @@ After this step graph has this state:
 
 ### Step 1
 
-Then we check all of its neighbours. 
+Then we check all of its neighbours.
 If checking vertex path length from start + edge weight is smaller than neighbour's path length from start then we set neighbour's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
 
 for clarity:
@@ -120,7 +122,7 @@ And its state is here:
 
 ### Step 2
 
-From now we repeat all actions again and fill our table with new info! 
+From now we repeat all actions again and fill our table with new info!
 
 <img src="Images/image4.png" height="250" />
 
@@ -161,7 +163,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
 
-## Code implementation 
+## Code implementation
 First of all, let’s create class that will describe any Vertex in the graph.
 It is pretty simple
 ```swift
@@ -169,12 +171,12 @@ open class Vertex {
 
     //Every vertex should be unique that's why we set up identifier
     open var identifier: String
-	
-    //For Dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some usecases 
+
+    //For Dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some usecases
     //when you firstly initialize all vertices without neighbours. And then on next iteration you set up their neighbours. So, initially neighbours is an empty array.
     //Array contains tuples (Vertex, Double). Vertex is a neighbour and Double is as edge weight to that neighbour.
     open var neighbours: [(Vertex, Double)] = []
-	
+
     //As it was mentioned in the algorithm description, default path length from start for all vertices should be as much as possible.
     //It is var because we will update it during the algorithm execution.
     open var pathLengthFromStart = Double.infinity
@@ -215,7 +217,7 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realisation is really straightforward.
 ```swift
 public class Dijkstra {
-    //This is a storage for vertices in the graph. 
+    //This is a storage for vertices in the graph.
     //Assuming that our vertices are unique we can use Set instead of array. This approach will bring some benefits later.
     private var totalVertices: Set<Vertex>
 
@@ -223,69 +225,69 @@ public class Dijkstra {
         totalVertices = vertices
     }
 
-    //Remember clearCache function in the Vertex class implementation? 
+    //Remember clearCache function in the Vertex class implementation?
     //This is just a wrapper that cleans cache for all stored vertices.
     private func clearCache() {
         totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-	//Before we start searching the shortest path from startVertex, 
+	//Before we start searching the shortest path from startVertex,
 	//we need to clear vertices cache just to be sure that out graph is clean.
-	//Remember that every Vertex is a class and classes are passed by reference. 
+	//Remember that every Vertex is a class and classes are passed by reference.
 	//So whenever you change vertex outside of this class it will affect this vertex inside totalVertices Set
         clearCache()
 	//Now all our vertices have Double.infinity pathLengthFromStart and an empty pathVerticesFromStart array.
-		
+
 	//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
-		
+
 	//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
 	//For this purpose we define currentVertex variable which we will change in the end of each while cycle.
         var currentVertex: Vertex? = startVertex
-		
+
         while let vertex = currentVertex {
-    			
+
     	    //Next line of code is an implementation of setting vertex as visited.
     	    //As it has been said, we should check only unvisited vertices in the graph,
 	    //So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
             totalVertices.remove(vertex)
-			
+
 	    //filteredNeighbours is an array that contains current vertex neighbours which aren't yet visited
             let filteredNeighbours = vertex.neighbours.filter { totalVertices.contains($0.0) }
-			
+
 	    //Let's iterate through them
             for neighbour in filteredNeighbours {
 		//These variable are more representative, than neighbour.0 or neighbour.1
                 let neighbourVertex = neighbour.0
                 let weight = neighbour.1
-				
-		//Here we calculate new weight, that we can offer to neighbour. 
+
+		//Here we calculate new weight, that we can offer to neighbour.
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
-				
+
 		//If it is smaller than neighbour's current pathLengthFromStart
 		//Then we perform this code
                 if theoreticNewWeight < neighbourVertex.pathLengthFromStart {
-					
+
 		    //set new pathLengthFromStart
                     neighbourVertex.pathLengthFromStart = theoreticNewWeight
-					
+
 		    //set new pathVerticesFromStart
                     neighbourVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
-					
+
 		    //append current vertex to neighbour's pathVerticesFromStart
                     neighbourVertex.pathVerticesFromStart.append(neighbourVertex)
                 }
             }
-			
+
 	    //If totalVertices is empty, i.e. all vertices are visited
 	    //Than break the loop
             if totalVertices.isEmpty {
                 currentVertex = nil
                 break
             }
-			
+
 	    //If loop is not broken, than pick next vertex for checkin from not visited.
 	    //Next vertex pathLengthFromStart should be the smallest one.
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }

From 54d4ef15ed6d624e2028795ab3214060e897f380 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 19 Oct 2017 03:28:12 +0200
Subject: [PATCH 1314/1679] rename boyer-moore to boyer-moore-horspool

---
 .../BoyerMooreHorspool.playground}/Contents.swift                 | 0
 .../BoyerMooreHorspool.playground}/contents.xcplayground          | 0
 .../playground.xcworkspace/contents.xcworkspacedata               | 0
 .../BoyerMooreHorspool.playground}/timeline.xctimeline            | 0
 .../BoyerMooreHorspool.swift                                      | 0
 {Boyer-Moore => Boyer-Moore-Horspool}/README.markdown             | 0
 .../Tests/BoyerMooreHorspoolTests.swift                           | 0
 {Boyer-Moore => Boyer-Moore-Horspool}/Tests/BoyerMooreTests.swift | 0
 {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Info.plist            | 0
 .../Tests/Tests.xcodeproj/project.pbxproj                         | 0
 .../Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata  | 0
 .../project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings | 0
 .../Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme   | 0
 13 files changed, 0 insertions(+), 0 deletions(-)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/Contents.swift (100%)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/contents.xcplayground (100%)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/playground.xcworkspace/contents.xcworkspacedata (100%)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/timeline.xctimeline (100%)
 rename Boyer-Moore/BoyerMoore.swift => Boyer-Moore-Horspool/BoyerMooreHorspool.swift (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/README.markdown (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/BoyerMooreHorspoolTests.swift (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/BoyerMooreTests.swift (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Info.plist (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/project.pbxproj (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme (100%)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/Contents.swift
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
diff --git a/Boyer-Moore/BoyerMoore.playground/contents.xcplayground b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/contents.xcplayground
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/contents.xcplayground
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/contents.xcplayground
diff --git a/Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/contents.xcworkspacedata
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
similarity index 100%
rename from Boyer-Moore/BoyerMoore.swift
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.swift
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore-Horspool/README.markdown
similarity index 100%
rename from Boyer-Moore/README.markdown
rename to Boyer-Moore-Horspool/README.markdown
diff --git a/Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift b/Boyer-Moore-Horspool/Tests/BoyerMooreHorspoolTests.swift
similarity index 100%
rename from Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift
rename to Boyer-Moore-Horspool/Tests/BoyerMooreHorspoolTests.swift
diff --git a/Boyer-Moore/Tests/BoyerMooreTests.swift b/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
similarity index 100%
rename from Boyer-Moore/Tests/BoyerMooreTests.swift
rename to Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
diff --git a/Boyer-Moore/Tests/Info.plist b/Boyer-Moore-Horspool/Tests/Info.plist
similarity index 100%
rename from Boyer-Moore/Tests/Info.plist
rename to Boyer-Moore-Horspool/Tests/Info.plist
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

From 453dcba01ef0c10212ae70f4b02607a258d84f6f Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Fri, 20 Oct 2017 12:26:07 +0200
Subject: [PATCH 1315/1679] fix tests

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 23 ++++++-------------
 1 file changed, 7 insertions(+), 16 deletions(-)

diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
index 6fc005d43..ab93d46a0 100644
--- a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
@@ -8,7 +8,7 @@
 
 /* Begin PBXBuildFile section */
 		7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */; };
-		9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */; };
+		8ED7591C1F9A064A00440D89 /* BoyerMooreHorspool.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8ED7591B1F9A064A00440D89 /* BoyerMooreHorspool.swift */; };
 		9AED56801E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */; };
 /* End PBXBuildFile section */
 
@@ -16,7 +16,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreTests.swift; sourceTree = SOURCE_ROOT; };
-		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../BoyerMoore.swift; sourceTree = SOURCE_ROOT; };
+		8ED7591B1F9A064A00440D89 /* BoyerMooreHorspool.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMooreHorspool.swift; path = ../BoyerMooreHorspool.swift; sourceTree = "<group>"; };
 		9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreHorspoolTests.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -34,7 +34,10 @@
 		7B2BBC681C779D710067B71D = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC831C779D720067B71D /* Tests */,
+				8ED7591B1F9A064A00440D89 /* BoyerMooreHorspool.swift */,
+				7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+				9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */,
 				7B2BBC721C779D710067B71D /* Products */,
 			);
 			sourceTree = "<group>";
@@ -47,18 +50,6 @@
 			name = Products;
 			sourceTree = "<group>";
 		};
-		7B2BBC831C779D720067B71D /* Tests */ = {
-			isa = PBXGroup;
-			children = (
-				9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */,
-				7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */,
-				7B2BBC941C779E7B0067B71D /* Info.plist */,
-				9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */,
-			);
-			name = Tests;
-			path = TestsTests;
-			sourceTree = "<group>";
-		};
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
@@ -145,8 +136,8 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				8ED7591C1F9A064A00440D89 /* BoyerMooreHorspool.swift in Sources */,
 				9AED56801E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift in Sources */,
-				9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */,
 				7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;

From 1376007baed57cf196abf92b239f12bcca44869d Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Fri, 20 Oct 2017 13:30:44 +0200
Subject: [PATCH 1316/1679] change test command for boyer-moore-horspool

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index d70eb74b6..5d2a05848 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -12,7 +12,7 @@ script:
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Boyer-Moore/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests

From 4c9c04e9686c2147fe6a6ff3fafacd488406a758 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sat, 21 Oct 2017 08:52:25 -0700
Subject: [PATCH 1317/1679] Add syntax color for code

---
 3Sum and 4Sum/README.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 5547789c7..188f89109 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -26,7 +26,7 @@ You'll make use of these two rules to create an efficient algorithm.
 
 Since you pre-sort the array, duplicates will be adjacent to each other. You just need to skip over duplicates by comparing adjacent values:
 
-```
+```swift
 extension Collection where Element: Equatable {
   
   /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
@@ -44,7 +44,7 @@ extension Collection where Element: Equatable {
 
 A similar implementation is used to get the unique index *before* a given index:
 
-```
+```swift
 extension BidirectionalCollection where Element: Equatable {
   
   /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
@@ -64,7 +64,7 @@ extension BidirectionalCollection where Element: Equatable {
 
 You'll keep track of 3 indices to represent the 3 numbers. The sum at any given moment is `array[l] + array[m] + array[r]`:
 
-```
+```swift
       m ->      <- r
 [-4, -1, -1, 0, 1, 2]
   l   
@@ -72,7 +72,7 @@ You'll keep track of 3 indices to represent the 3 numbers. The sum at any given
 
 The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
 
-```
+```swift
 func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
@@ -110,7 +110,7 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 
 Foursum is a very straightforward extension to the threeSum algorithm. In threeSum, you kept track of 3 indices:
 
-```
+```swift
       m ->      <- r
 [-4, -1, -1, 0, 1, 2]
   l   
@@ -118,7 +118,7 @@ Foursum is a very straightforward extension to the threeSum algorithm. In threeS
 
 For fourSum, you'll keep track of 4:
 
-```
+```swift
          mr ->  <- r
 [-4, -1, -1, 0, 1, 2]
   l  ml -> 
@@ -126,7 +126,7 @@ For fourSum, you'll keep track of 4:
 
 Here's the code for it (notice it is very similar to 3Sum):
 
-```
+```swift
 func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []

From 2be222849f4dfeb35fd69335fa120965d7dec227 Mon Sep 17 00:00:00 2001
From: Egor Zhdan <egor.zhdan@gmail.com>
Date: Sun, 22 Oct 2017 00:50:15 +0300
Subject: [PATCH 1318/1679] Fix integer overflow in LCM algorithm

---
 GCD/GCD.playground/Contents.swift | 2 +-
 GCD/GCD.swift                     | 2 +-
 GCD/README.markdown               | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 977b80f57..f0fceb0da 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -32,7 +32,7 @@ func gcd(m: Int, _ n: Int) -> Int {
 */
 
 func lcm(_ m: Int, _ n: Int) -> Int {
-  return m*n / gcd(m, n)
+  return m / gcd(m, n) * n // we divide before multiplying to avoid integer overflow
 }
 
 gcd(52, 39)       // 13
diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index ce7e7fa78..bd903e58a 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -30,5 +30,5 @@ func gcd(_ a: Int, _ b: Int) -> Int {
   Returns the least common multiple of two numbers.
 */
 func lcm(_ m: Int, _ n: Int) -> Int {
-  return m*n / gcd(m, n)
+  return m / gcd(m, n) * n
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index 07d2de1ca..d7e9304bd 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -102,7 +102,7 @@ In code:
 
 ```swift
 func lcm(_ m: Int, _ n: Int) -> Int {
-  return m*n / gcd(m, n)
+  return m / gcd(m, n) * n
 }
 ```
 

From b8d20e6287e25cc9f60acc50c93266f437834fd2 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sat, 21 Oct 2017 22:06:09 -0700
Subject: [PATCH 1319/1679] Adds links to written tutorials on
 raywenderlich.com

---
 Binary Search Tree/README.markdown    | 3 +++
 Boyer-Moore-Horspool/README.markdown  | 3 +++
 Breadth-First Search/README.markdown  | 3 +++
 Depth-First Search/README.markdown    | 2 ++
 Graph/README.markdown                 | 3 +++
 Heap/README.markdown                  | 2 ++
 Linked List/README.markdown           | 2 ++
 Merge Sort/README.markdown            | 2 ++
 Minimum Spanning Tree/README.markdown | 2 ++
 Queue/README.markdown                 | 2 ++
 Stack/README.markdown                 | 2 ++
 Tree/README.markdown                  | 3 +++
 Trie/ReadMe.md                        | 2 ++
 13 files changed, 31 insertions(+)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 340a58655..1d9321591 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -1,5 +1,8 @@
 # Binary Search Tree (BST)
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/139821/swift-algorithm-club-swift-binary-search-tree-data-structure)
+
+
 A binary search tree is a special kind of [binary tree](../Binary%20Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
 
 For more information about a tree, [read this first](../Tree/).
diff --git a/Boyer-Moore-Horspool/README.markdown b/Boyer-Moore-Horspool/README.markdown
index 5b3841eca..f5e21ea41 100644
--- a/Boyer-Moore-Horspool/README.markdown
+++ b/Boyer-Moore-Horspool/README.markdown
@@ -1,5 +1,8 @@
 # Boyer-Moore String Search
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/163964/swift-algorithm-club-booyer-moore-string-search-algorithm)
+
+
 Goal: Write a string search algorithm in pure Swift without importing Foundation or using `NSString`'s `rangeOfString()` method.
 
 In other words, we want to implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 2ef92fd73..b2298822f 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,5 +1,8 @@
 # Breadth-First Search
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/155801/swift-algorithm-club-swift-breadth-first-search)
+
+
 Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors.
 
 Breadth-first search can be used on both directed and undirected graphs.
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index 98a19e0cb..67030346b 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -1,5 +1,7 @@
 # Depth-First Search
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/157949/swift-algorithm-club-depth-first-search)
+
 Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores as far as possible along each branch before backtracking.
 
 Depth-first search can be used on both directed and undirected graphs.
diff --git a/Graph/README.markdown b/Graph/README.markdown
index d3c8b89e5..1331a07d3 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,5 +1,8 @@
 # Graph
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/152046/swift-algorithm-club-graphs-adjacency-list)
+
+
 A graph looks like the following picture:
 
 ![A graph](Images/Graph.png)
diff --git a/Heap/README.markdown b/Heap/README.markdown
index bb7a785a5..49031dcc3 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,5 +1,7 @@
 # Heap
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/160631/swift-algorithm-club-heap-and-priority-queue-data-structure)
+
 A heap is a [binary tree](../Binary%20Tree/) inside an array, so it does not use parent/child pointers. A heap is sorted based on the "heap property" that determines the order of the nodes in the tree.
 
 Common uses for heap:
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 240d3fbba..2e1f03ece 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -1,5 +1,7 @@
 # Linked List
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/144083/swift-algorithm-club-swift-linked-list-data-structure)
+
 A linked list is a sequence of data items, just like an array. But where an array allocates a big block of memory to store the objects, the elements in a linked list are totally separate objects in memory and are connected through links:
 
 	+--------+    +--------+    +--------+    +--------+
diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 05b90f166..140cfe48f 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -1,5 +1,7 @@
 # Merge Sort
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/154256/swift-algorithm-club-swift-merge-sort)
+
 Goal: Sort an array from low to high (or high to low)
 
 Invented in 1945 by John von Neumann, merge-sort is an efficient algorithm with a best, worst, and average time complexity of **O(n log n)**.
diff --git a/Minimum Spanning Tree/README.markdown b/Minimum Spanning Tree/README.markdown
index c47713701..6ae7a89d9 100644
--- a/Minimum Spanning Tree/README.markdown	
+++ b/Minimum Spanning Tree/README.markdown	
@@ -1,5 +1,7 @@
 # Minimum Spanning Tree (Weighted Graph)
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/169392/swift-algorithm-club-minimum-spanning-tree-with-prims-algorithm)
+
 A [minimum spanning tree](https://en.wikipedia.org/wiki/Minimum_spanning_tree) (MST) of a connected undirected weighted graph has a subset of the edges from the original graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. There can be more than one MSTs of a graph.
 
 There are two popular algorithms to calculate MST of a graph - [Kruskal's algorithm](https://en.wikipedia.org/wiki/Kruskal's_algorithm) and [Prim's algorithm](https://en.wikipedia.org/wiki/Prim's_algorithm). Both algorithms have a total time complexity of `O(ElogE)` where `E` is the number of edges from the original graph.
diff --git a/Queue/README.markdown b/Queue/README.markdown
index 8938e0cf1..ca55f0f28 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -1,5 +1,7 @@
 # Queue
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/148141/swift-algorithm-club-swift-queue-data-structure)
+
 A queue is a list where you can only insert new items at the back and remove items from the front. This ensures that the first item you enqueue is also the first item you dequeue. First come, first serve!
 
 Why would you need this? Well, in many algorithms you want to add objects to a temporary list and pull them off this list later. Often the order in which you add and remove these objects matters.
diff --git a/Stack/README.markdown b/Stack/README.markdown
index 1a3ca2638..b84b585df 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -1,5 +1,7 @@
 # Stack
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/149213/swift-algorithm-club-swift-stack-data-structure)
+
 A stack is like an array but with limited functionality. You can only *push* to add a new element to the top of the stack, *pop* to remove the element from the top, and *peek* at the top element without popping it off.
 
 Why would you want to do this? Well, in many algorithms you want to add objects to a temporary list at some point and then pull them off this list again at a later time. Often the order in which you add and remove these objects matters.
diff --git a/Tree/README.markdown b/Tree/README.markdown
index 566864a8f..40129cab5 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -1,5 +1,8 @@
 # Trees
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/138190/swift-algorithm-club-swift-tree-data-structure)
+
+
 A tree represents hierarchical relationships between objects. This is a tree:
 
 ![A tree](Images/Tree.png)
diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 356f6887e..34b9beb9c 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,5 +1,7 @@
 # Trie
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/139410/swift-algorithm-club-swift-trie-data-structure)
+
 ## What is a Trie?
 
 A `Trie`, (also known as a prefix tree, or radix tree in some other implementations) is a special type of tree used to store associative data structures. A `Trie` for a dictionary might look like this:

From 575bacaa6176f0edc84fac83e935c02a627fa677 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 25 Oct 2017 13:24:30 -0700
Subject: [PATCH 1320/1679] Fixes the tests.

---
 Depth-First Search/Tests/DepthFirstSearchTests.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index abf1c19c6..5fb450190 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -9,7 +9,7 @@ class DepthFirstSearchTests: XCTestCase {
         #endif
     }
     func testExploringTree() {
-        let tree = Digraph()
+        let tree = Graph()
         
         let nodeA = tree.addNode("a")
         let nodeB = tree.addNode("b")
@@ -34,7 +34,7 @@ class DepthFirstSearchTests: XCTestCase {
     }
     
     func testExploringDigraph() {
-        let digraph = Digraph()
+        let digraph = Graph()
         
         let nodeA = digraph.addNode("a")
         let nodeB = digraph.addNode("b")
@@ -81,7 +81,7 @@ class DepthFirstSearchTests: XCTestCase {
     }
     
     func testExploringDigraphWithASingleNode() {
-        let digraph = Digraph()
+        let digraph = Graph()
         let node = digraph.addNode("a")
         
         let nodesExplored = depthFirstSearch(digraph, source: node)

From 4b73295140df7cb645431aeb01b867f944725ef8 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 26 Oct 2017 02:21:17 +0200
Subject: [PATCH 1321/1679] initial points lines planes commit

---
 .../project.pbxproj                           | 296 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../Points Lines Planes/2D/Line2D.swift       | 161 ++++++++++
 .../Points Lines Planes/2D/Point2D.swift      |  40 +++
 .../Points Lines Planes/main.swift            |  24 ++
 Points Lines Planes/README.md                 |  34 ++
 6 files changed, 562 insertions(+)
 create mode 100644 Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj
 create mode 100644 Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Points Lines Planes/Points Lines Planes/2D/Line2D.swift
 create mode 100644 Points Lines Planes/Points Lines Planes/2D/Point2D.swift
 create mode 100644 Points Lines Planes/Points Lines Planes/main.swift
 create mode 100644 Points Lines Planes/README.md

diff --git a/Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj b/Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..aeba4777b
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj	
@@ -0,0 +1,296 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 48;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		8EA8A3BB1F9F7B6300FD8BC0 /* Point2D.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8EA8A3BA1F9F7B6300FD8BC0 /* Point2D.swift */; };
+		8EA8A3BD1F9F7B7100FD8BC0 /* Line2D.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */; };
+		8EF612481F9E00E000267358 /* main.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8EF612471F9E00E000267358 /* main.swift */; };
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+
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+			);
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+		};
+/* End PBXCopyFilesBuildPhase section */
+
+/* Begin PBXFileReference section */
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+		8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Line2D.swift; sourceTree = "<group>"; };
+		8EF612441F9E00E000267358 /* Points Lines Planes */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; includeInIndex = 0; path = "Points Lines Planes"; sourceTree = BUILT_PRODUCTS_DIR; };
+		8EF612471F9E00E000267358 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = "<group>"; };
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+
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+			);
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+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
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+			isa = PBXGroup;
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+				8EA8A3BA1F9F7B6300FD8BC0 /* Point2D.swift */,
+				8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */,
+			);
+			path = 2D;
+			sourceTree = "<group>";
+		};
+		8EF6123B1F9E00DF00267358 = {
+			isa = PBXGroup;
+			children = (
+				8EF612461F9E00E000267358 /* Points Lines Planes */,
+				8EF612451F9E00E000267358 /* Products */,
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+				8EF612441F9E00E000267358 /* Points Lines Planes */,
+			);
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+			isa = PBXGroup;
+			children = (
+				8EF612471F9E00E000267358 /* main.swift */,
+				8EA8A3C21F9F7C9000FD8BC0 /* 2D */,
+			);
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+			sourceTree = "<group>";
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+			productType = "com.apple.product-type.tool";
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+
+/* Begin PBXProject section */
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+			isa = PBXProject;
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+				LastSwiftUpdateCheck = 0900;
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+			buildConfigurationList = 8EF6123F1F9E00DF00267358 /* Build configuration list for PBXProject "Points Lines Planes" */;
+			compatibilityVersion = "Xcode 8.0";
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+
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+				8EA8A3BD1F9F7B7100FD8BC0 /* Line2D.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
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+				CLANG_ANALYZER_NONNULL = YES;
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+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
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+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "Mac Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.13;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		8EF6124A1F9E00E000267358 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++14";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "Mac Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.13;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		8EF6124C1F9E00E000267358 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CODE_SIGN_STYLE = Automatic;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+			};
+			name = Debug;
+		};
+		8EF6124D1F9E00E000267358 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CODE_SIGN_STYLE = Automatic;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		8EF6123F1F9E00DF00267358 /* Build configuration list for PBXProject "Points Lines Planes" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8EF612491F9E00E000267358 /* Debug */,
+				8EF6124A1F9E00E000267358 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		8EF6124B1F9E00E000267358 /* Build configuration list for PBXNativeTarget "Points Lines Planes" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8EF6124C1F9E00E000267358 /* Debug */,
+				8EF6124D1F9E00E000267358 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 8EF6123C1F9E00DF00267358 /* Project object */;
+}
diff --git a/Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..82bfe2b7d
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Points Lines Planes.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Points Lines Planes/Points Lines Planes/2D/Line2D.swift b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift
new file mode 100644
index 000000000..c92cbdbed
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift	
@@ -0,0 +1,161 @@
+//
+//  Line2D.swift
+//  Points Lines Planes
+//
+//  Created by Jaap Wijnen on 24-10-17.
+//
+
+struct Line2D: Equatable {
+    
+    var slope: Slope
+    var offset: Double
+    var direction: Direction
+    
+    enum Slope: Equatable {
+        case finite(slope: Double)
+        case infinite(offset: Double)
+        
+        static func ==(lhs: Slope, rhs: Slope) -> Bool {
+            switch (lhs, rhs) {
+            case (.finite(let slope1), .finite(let slope2)): return slope1 == slope2
+            case (.infinite(let offset1), .infinite(let offset2)): return offset1 == offset2
+            default: return false
+            }
+        }
+    }
+    
+    enum Direction: Equatable {
+        case increasing
+        case decreasing
+        
+        static func ==(lhs: Direction, rhs: Direction) -> Bool {
+            switch (lhs, rhs) {
+            case (.increasing, .increasing): return true
+            case (.decreasing, .decreasing): return true
+            default: return false
+            }
+        }
+    }
+    
+    init(from p1: Point2D, to p2: Point2D) {
+        if p1 == p2 { fatalError("Points can not be equal when creating a line between them") }
+        if p1.x == p2.x {
+            self.slope = .infinite(offset: p1.x)
+            self.offset = 0
+            self.direction = p1.y < p2.y ? .increasing : .decreasing
+            
+            return
+        }
+        
+        let slope = (p1.y - p2.y)/(p1.x - p2.x)
+        self.slope = .finite(slope: slope)
+        offset = (p1.y + p2.y - slope * (p1.x + p2.x))/2
+        if slope >= 0 {
+            // so a horizontal line going left to right is called increasing
+            self.direction = p1.x < p2.x ? .increasing : .decreasing
+        } else {
+            self.direction = p1.x < p2.x ? .decreasing : .increasing
+        }
+    }
+    
+    fileprivate init(slope: Slope, offset: Double, direction: Direction) {
+        self.slope = slope
+        self.offset = offset
+        self.direction = direction
+    }
+    
+    // returns y coordinate on line for given x
+    func y(at x: Double) -> Double {
+        switch self.slope {
+        case .finite(let slope):
+            return slope * x + self.offset
+        case .infinite:
+            fatalError("y can be anywhere on vertical line")
+        }
+    }
+    
+    // returns x coordinate on line for given y
+    func x(at y: Double) -> Double {
+        switch self.slope {
+        case .finite(let slope):
+            if slope == 0 {
+                fatalError("x can be anywhere on horizontal line")
+            }
+            return (y - self.offset)/slope
+        case .infinite(let offset):
+            return offset
+        }
+    }
+    
+    // finds intersection point between two lines. returns nil when lines don't intersect or lie on top of each other.
+    func intersect(with line: Line2D) -> Point2D? {
+        if self == line { return nil }
+        switch (self.slope, line.slope) {
+        case (.infinite, .infinite):
+            // lines are either parallel or on top of each other.
+            return nil
+        case (.finite(let slope1), .finite(let slope2)):
+            if slope1 == slope2 { return nil } // lines are parallel
+            // lines are not parallel calculate intersection point
+            let x = (line.offset - self.offset)/(slope1 - slope2)
+            let y = (slope1 + slope2) * x + self.offset + line.offset
+            return Point2D(x: x, y: y)
+        case (.infinite(let offset), .finite):
+            // one line is vertical so we only check what y value the other line has at that point
+            let x = offset
+            let y = line.y(at: x)
+            return Point2D(x: x, y: y)
+        case (.finite, .infinite(let offset)):
+            // one line is vertical so we only check what y value the other line has at that point
+            // lines are switched with respect to case above this one
+            let x = offset
+            let y = self.y(at: x)
+            return Point2D(x: x, y: y)
+        }
+    }
+    
+    // returns a line perpendicular to self at the given y coordinate
+    // direction of perpendicular lines always changes clockwise
+    func perpendicularLineAt(y: Double) -> Line2D {
+        return perpendicularLineAt(p: Point2D(x: self.x(at: y), y: y))
+    }
+    
+    // returns a line perpendicular to self at the given x coordinate
+    // direction of perpendicular lines always changes clockwise
+    func perpendicularLineAt(x: Double) -> Line2D {
+        return perpendicularLineAt(p: Point2D(x: x, y: self.y(at: x)))
+    }
+    
+    private func perpendicularLineAt(p: Point2D) -> Line2D {
+        switch self.slope {
+        case .finite(let slope):
+            if slope == 0 {
+                // line is horizontal so new line will be vertical
+                let dir: Direction = self.direction == .increasing ? .decreasing : .increasing
+                return Line2D(slope: .infinite(offset: p.x), offset: 0, direction: dir)
+            }
+            
+            // line is neither horizontal nor vertical
+            // we make a new line through the point p with new slope -1/slope
+            let offset = (slope + 1/slope)*p.x + self.offset
+            
+            // determine direction of new line based on direction of the old line and its slope
+            let dir: Direction
+            switch self.direction {
+            case .increasing:
+                dir = slope > 0 ? .decreasing : .increasing
+            case .decreasing:
+                dir = slope > 0 ? .increasing : .decreasing
+            }
+            return Line2D(slope: .finite(slope: -1/slope), offset: offset, direction: dir)
+        case .infinite:
+            // line is vertical so new line will be horizontal
+            let dir: Direction = self.direction == .increasing ? .increasing : .decreasing
+            return Line2D(slope: .finite(slope: 0), offset: p.y, direction: dir)
+        }
+    }
+    
+    static func ==(lhs: Line2D, rhs: Line2D) -> Bool {
+        return lhs.slope == rhs.slope && lhs.offset == rhs.offset && lhs.direction == rhs.direction
+    }
+}
diff --git a/Points Lines Planes/Points Lines Planes/2D/Point2D.swift b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift
new file mode 100644
index 000000000..f51ffd64d
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift	
@@ -0,0 +1,40 @@
+//
+//  Point2D.swift
+//  Points Lines Planes
+//
+//  Created by Jaap Wijnen on 24-10-17.
+//
+
+struct Point2D: Equatable {
+    var x: Double
+    var y: Double
+    
+    static func ==(lhs: Point2D, rhs: Point2D) -> Bool {
+        return lhs.x == rhs.x && lhs.y == rhs.y
+    }
+    
+    // returns true if point is on or right of line
+    func isRight(of line: Line2D) -> Bool {
+        switch line.slope {
+        case .finite:
+            let y = line.y(at: self.x)
+            switch line.direction {
+            case .increasing:
+                return y >= self.y
+            case .decreasing:
+                return y <= self.y
+            }
+        case .infinite(let offset):
+            switch line.direction {
+            case .increasing:
+                return self.x >= offset
+            case .decreasing:
+                return self.x <= offset
+            }
+        }
+    }
+    
+    func isLeft(of line: Line2D) -> Bool {
+        return !self.isRight(of: line)
+    }
+}
diff --git a/Points Lines Planes/Points Lines Planes/main.swift b/Points Lines Planes/Points Lines Planes/main.swift
new file mode 100644
index 000000000..02137fc9d
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes/main.swift	
@@ -0,0 +1,24 @@
+//
+//  main.swift
+//  Points Lines Planes
+//
+//  Created by Jaap Wijnen on 23-10-17.
+//
+
+let p0 = Point2D(x: 0, y: 2)
+let p1 = Point2D(x: 1, y: 1)
+let p2 = Point2D(x: 1, y: 3)
+let p3 = Point2D(x: 3, y: 1)
+let p4 = Point2D(x: 3, y: 3)
+
+let horLine = Line2D(from: p1, to: p3)
+let verLine = Line2D(from: p1, to: p2)
+let line45 = Line2D(from: p1, to: p4)
+
+print(horLine.intersect(with: verLine))
+print(p0.isRight(of: line45))
+print(p0.isRight(of: horLine))
+print(p0.isRight(of: verLine))
+let lineperp = horLine.perpendicularLineAt(x: 2)
+print(lineperp)
+
diff --git a/Points Lines Planes/README.md b/Points Lines Planes/README.md
new file mode 100644
index 000000000..23c965978
--- /dev/null
+++ b/Points Lines Planes/README.md	
@@ -0,0 +1,34 @@
+# Points Lines (Planes)
+This implements data structures for points lines and planes(not yet) in (for now) 2D space and a few functions to play around with them. This was originally written to improve on the Convex Hull algorithm but I thought it might be a nice addition in itself. Im planning to add 3D implementations as well.
+
+# implementation
+Two `struct`s are implemented the `Point2D` and `Line2D`.
+
+```
+struct Point2D: {
+  var x: Double
+  var y: double
+}
+```
+
+```
+struct Line2D {
+  var slope: Slope
+  var offset: Double
+  var direction: Direction
+}
+```
+Here `Slope` is an enum to account for vertical lines.
+slope is infinite for vertical lines, offset is the x coordinate where the line crosses the line `y=0`.
+slope is finite for any other line and contains a double with the actual value of the slope.
+```
+enum Slope {
+  case finite(slope: Double)
+  case infinite(offset: Double)
+}
+```
+`Line2D` also contains a `Direction` enum. This is introduced in order to make lines directional in order to be able to determine what is left and right of a certain line. It is `.increasing` if the line points in positive y direction and `.decreasing` if it points in the negative y direction.
+
+`Line2D`'s offset is the the y-coordinate where the line crosses the vertical x=0 line
+
+*Written for the Swift Algorithm Club by Jaap Wijnen.*

From 7f6f5a5a56baa1a1bb6854dd2a29699f1be2c558 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 26 Oct 2017 02:40:29 +0200
Subject: [PATCH 1322/1679] typo

---
 Points Lines Planes/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Points Lines Planes/README.md b/Points Lines Planes/README.md
index 23c965978..2d36667ec 100644
--- a/Points Lines Planes/README.md	
+++ b/Points Lines Planes/README.md	
@@ -29,6 +29,6 @@ enum Slope {
 ```
 `Line2D` also contains a `Direction` enum. This is introduced in order to make lines directional in order to be able to determine what is left and right of a certain line. It is `.increasing` if the line points in positive y direction and `.decreasing` if it points in the negative y direction.
 
-`Line2D`'s offset is the the y-coordinate where the line crosses the vertical x=0 line
+`Line2D`'s offset is the the y-coordinate where the line crosses the vertical `x=0` line.
 
 *Written for the Swift Algorithm Club by Jaap Wijnen.*

From 6ca1ad1da1e6c629e164a23c6b5759225f61962e Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Sat, 21 Oct 2017 10:02:08 -0700
Subject: [PATCH 1323/1679] Add .gfm-render.sh

---
 .travis.yml   |  82 +++++++++++++++++++-------------------
 gfm-render.sh | 106 ++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 149 insertions(+), 39 deletions(-)
 create mode 100755 gfm-render.sh

diff --git a/.travis.yml b/.travis.yml
index 5d2a05848..7cd02c9bc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,46 +4,50 @@ osx_image: xcode9
 
 install:
 
+- gem install xcpretty-travis-formatter
 # - ./install_swiftlint.sh
 
 script:
 
-- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0'
-- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
-- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Tests-Quicksort
-- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
-- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test
-- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0' | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Test-Quicksort | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+
+after_success:
+- if [[ "$TRAVIS_BRANCH" == "master" ]]; then ./gfm-render.sh; fi
diff --git a/gfm-render.sh b/gfm-render.sh
new file mode 100755
index 000000000..09c026d55
--- /dev/null
+++ b/gfm-render.sh
@@ -0,0 +1,106 @@
+#!/usr/bin/env bash
+
+# $1 - readme
+function render_markdown_to_html {
+  # escape escaping characters
+  if [[ $(uname) == "Darwin" ]]; then
+    content=$(
+      cat "$1"                                          \
+        | sed 's/\\/\\\\/g'                             \
+        | sed 's/"/\\"/g'                               \
+        | sed $'s/\t/\\\\t/g'                           \
+        | sed -e ':a' -e 'N' -e '$!ba' -e 's/\n/\\\n/g' \
+    )
+  else
+    content=$(
+      cat "$1"                          \
+        | sed 's/\\/\\\\/g'             \
+        | sed 's/"/\\"/g'               \
+        | sed 's/\t/\\t/g'              \
+        | sed ':a;N;$!ba;s/\n/\\n/g'    \
+    )
+  fi
+
+  # network call to GitHub API
+  json="{\"text\":\"$content\",\"mode\":\"gfm\",\"context\":\"$USERNAME/swift-algorithm-club\"}"
+  echo -e "$(curl -s --data "$json" -u $USERNAME:$TOKEN https://api.github.com/markdown)"
+}
+
+# $1 - comment
+function push_to_gh_pages {
+  git checkout -b gh-pages
+  git add .
+  git commit -m "$1"
+  git push -f https://$TOKEN@github.com/$USERNAME/swift-algorithm-club.git gh-pages
+}
+
+# download github systax highlight stylesheet
+echo "> Downloading github-light.css..."
+curl -s -O https://raw.githubusercontent.com/primer/github-syntax-light/master/lib/github-light.css
+
+# if index.html does not exist, create one;
+# otherwise, empty its content.
+if [[ -z index.html ]]; then
+  touch index.html
+else
+  > index.html
+fi
+
+# iterate immediate directories
+find . -maxdepth 1 -type d | while read folder; do
+  readme=''
+
+  # get the right extension for the README file if there is one
+  if [[ -f $folder/README.md ]]; then readme="$folder/README.md"; fi
+  if [[ -f $folder/README.markdown ]]; then readme="$folder/README.markdown"; fi
+
+  # exclude the repository's README
+  if [[ !(-z $readme) && ($readme != "./README.markdown") ]]; then
+    name=$(basename "$folder")
+    echo "> Generating $name/index.html..."
+
+    cat > "$folder/index.html" << EOF
+<!DOCTYPE html>
+<head>
+  <link rel="stylesheet" type="text/css" href="../github-light.css">
+  <style>
+    body {
+      font-size: 18px;
+    }
+    code {
+        padding: 0.2em;
+        margin: 0;
+        font-size: 85%;
+        background-color: #f6f8fa;
+        line-height: 1.45;
+        border-radius: 3px
+    }
+    pre code {
+        padding: 0px;
+        background-color: transparent;
+    }
+    .highlight {
+      margin: 0px;
+      padding: 0px 16px;
+      font-size: 85%;
+      line-height: 1.45;
+      overflow: auto;
+      background-color: #f6f8fa;
+      border-radius: 3px;
+    }
+  </style>
+</head>
+<body>
+    $(render_markdown_to_html "$readme")
+</body>
+</html>
+EOF
+    # temporarily write the list of HTML filenames to the main index.html
+    echo "$lists<li><a href=\"$name/index.html\">$name</a></li>" >> index.html
+  fi
+done
+
+echo "<!DOCTYPE html><body><h1>Swift Algorithm</h1><ul>$(echo -n $(cat index.html))</ul></body></html>" > index.html
+
+# push to gh-pages
+if [[ $CI = true ]]; then push_to_gh_pages "Generated by TravisCI on $(date +%D)"; fi

From b687ab17a53a08bfd5b7cc9814c655be094acef5 Mon Sep 17 00:00:00 2001
From: Volkan Bicer <vlknbcr@gmail.com>
Date: Tue, 31 Oct 2017 23:47:18 +0200
Subject: [PATCH 1324/1679] Update README.markdown

Boyer-Moore path is wrong.
---
 README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.markdown b/README.markdown
index 42cd23739..b15bd1527 100644
--- a/README.markdown
+++ b/README.markdown
@@ -33,7 +33,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Insertion Sort](Insertion%20Sort/)
 - [Binary Search](Binary%20Search/) and [Binary Search Tree](Binary%20Search%20Tree/)
 - [Merge Sort](Merge%20Sort/)
-- [Boyer-Moore string search](Boyer-Moore/)
+- [Boyer-Moore string search](Boyer-Moore-Horspool/)
 
 ## The algorithms
 
@@ -51,7 +51,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 ### String Search
 
 - [Brute-Force String Search](Brute-Force%20String%20Search/). A naive method.
-- [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
+- [Boyer-Moore](Boyer-Moore-Horspool/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
 - [Knuth-Morris-Pratt](Knuth-Morris-Pratt/). A linear-time string algorithm that returns indexes of all occurrencies of a given pattern.
 - [Rabin-Karp](Rabin-Karp/)  Faster search by using hashing.
 - [Longest Common Subsequence](Longest%20Common%20Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.

From e466249391a1b7c8e4a009593eefc45fc14bf5ca Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 9 Nov 2017 00:21:30 +0500
Subject: [PATCH 1325/1679] Fix the position of the opening brace to conform to
 the style guide

---
 Singly Linked List/README.markdown | 12 ++++--------
 1 file changed, 4 insertions(+), 8 deletions(-)

diff --git a/Singly Linked List/README.markdown b/Singly Linked List/README.markdown
index b3c8b8b2d..6d896db88 100644
--- a/Singly Linked List/README.markdown	
+++ b/Singly Linked List/README.markdown	
@@ -52,10 +52,8 @@ SEARCH
 Collections are sequences, therefore the first step is to conform to the Sequence protocol.
 
 ```
-extension SinglyLinkedList : Sequence
-{
-    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
-    {
+extension SinglyLinkedList: Sequence {
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T> {
         return SinglyLinkedListForwardIterator(head: self.storage.head)
     }
 }
@@ -70,8 +68,7 @@ public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
 
     private(set) var head: SinglyLinkedListNode<T>?
 
-    mutating public func next() -> T?
-    {
+    mutating public func next() -> T? {
         let result = self.head?.value
         self.head = self.head?.next
         return result
@@ -82,8 +79,7 @@ public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
 Next, a collection needs to be indexable. Indexes are implemented by the data structure class. We have encapsulated this knowledge in instances of the class `SinglyLinkedListIndex`. 
 
 ```
-public struct SinglyLinkedListIndex<T> : Comparable
-{
+public struct SinglyLinkedListIndex<T>: Comparable {
     fileprivate let node: SinglyLinkedListNode<T>?
     fileprivate let tag: Int
 

From 02395b8cc0a32b7b11dd0cddfc8c4c74360edaff Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 10:27:30 +0400
Subject: [PATCH 1326/1679] Fix nonconventional parameter naming in Big-O
 notation article

---
 Big-O Notation.markdown | 60 ++++++++++++++++++++---------------------
 1 file changed, 30 insertions(+), 30 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 78b1808e6..33cdf9465 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -16,21 +16,21 @@ Big-O | Name | Description
 **O(n^3)** | cubic | **Poor performance.** If you have 100 items, this does 100^3 = 1,000,000 units of work. Doubling the input size makes it eight times slower. Example: matrix multiplication.
 **O(2^n)** | exponential | **Very poor performance.** You want to avoid these kinds of algorithms, but sometimes you have no choice. Adding just one bit to the input doubles the running time. Example: traveling salesperson problem.
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
-  
+
 
 Below are some examples for each category of performance:
 
 **O(1)**
 
   The most common example with O(1) complexity is accessing an array index.
-  
+
   ```swift
   let value = array[5]
   ```
-    
+
   Another example of O(1) is pushing and popping from Stack.
-  
- 
+
+
 **O(log n)**
 
   ```swift
@@ -40,12 +40,12 @@ Below are some examples for each category of performance:
     j *= 2
   }
   ```  
-  
+
   Instead of simply incrementing, 'j' is increased by 2 times itself in each run.
-  
+
   Binary Search Algorithm is an example of O(log n) complexity.
-  
-  
+
+
 **O(n)**
 
   ```swift
@@ -53,10 +53,10 @@ Below are some examples for each category of performance:
     print(array[i])
   }
   ```
-  
+
   Array Traversal and Linear Search are examples of O(n) complexity.  
-  
-  
+
+
 **O(n log n)**
 
   ```swift
@@ -68,23 +68,23 @@ Below are some examples for each category of performance:
     }
   }
   ```
-  
+
   OR
-  
+
   ```swift
   for i in stride(from: 0, to: n, by: 1) {
     func index(after i: Int) -> Int? { // multiplies `i` by 2 until `i` >= `n`
-      return i < n ? i * 2 : nil 
+      return i < n ? i * 2 : nil
     }
     for j in sequence(first: 1, next: index(after:)) {
       // do constant time stuff
     }
   }
   ```
-  
+
   Merge Sort and Heap Sort are examples of O(n log n) complexity.  
-  
-  
+
+
 **O(n^2)**
 
   ```swift
@@ -94,10 +94,10 @@ Below are some examples for each category of performance:
     }
   }
   ```
-  
+
   Traversing a simple 2-D array and Bubble Sort are examples of O(n^2) complexity.
-  
-  
+
+
 **O(n^3)**
 
   ```swift
@@ -109,24 +109,24 @@ Below are some examples for each category of performance:
     }
   }
   ```  
-  
+
 **O(2^n)**
 
   Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1.
   The following example prints all the moves necessary to solve the famous "Towers of Hanoi" problem for N disks.
 
   ```swift
-  func solveHanoi(N: Int, from: String, to: String, spare: String) {
+  func solveHanoi(n: Int, from: String, to: String, spare: String) {
     guard n >= 1 else { return }
-    if N > 1 {
-      solveHanoi(N: N - 1, from: from, to: spare, spare: to)
+    if n > 1 {
+      solveHanoi(n: n - 1, from: from, to: spare, spare: to)
     } else {
-      solveHanoi(N: N-1, from: spare, to: to, spare: from)
+      solveHanoi(n: n-1, from: spare, to: to, spare: from)
     }
   }
   ```
-  
-  
+
+
 **O(n!)**
 
   The most trivial example of function that takes O(n!) time is given below.
@@ -137,8 +137,8 @@ Below are some examples for each category of performance:
       nFactFunc(n - 1)
     }
   }
-  ``` 
-  
+  ```
+
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
 
 Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge%20Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!

From d38c428e7f10010562af5500322ca843ddd54e25 Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 10:38:25 +0400
Subject: [PATCH 1327/1679] Fix spacing in Big-O notation article

---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 33cdf9465..19a1ddbde 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -121,7 +121,7 @@ Below are some examples for each category of performance:
     if n > 1 {
       solveHanoi(n: n - 1, from: from, to: spare, spare: to)
     } else {
-      solveHanoi(n: n-1, from: spare, to: to, spare: from)
+      solveHanoi(n: n - 1, from: spare, to: to, spare: from)
     }
   }
   ```

From b49331f0d8e387cf21b6be2e4f1e6ebd023c8248 Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 15:06:25 +0400
Subject: [PATCH 1328/1679] Fix typos in Merge Sort article

---
 Merge Sort/README.markdown | 38 +++++++++++++++++++-------------------
 1 file changed, 19 insertions(+), 19 deletions(-)

diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 140cfe48f..7ad6fd95e 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -6,7 +6,7 @@ Goal: Sort an array from low to high (or high to low)
 
 Invented in 1945 by John von Neumann, merge-sort is an efficient algorithm with a best, worst, and average time complexity of **O(n log n)**.
 
-The merge-sort algorithm uses the **divide and conquer** approach which is to divide a big problem into smaller problems and solve them. I think of the merge-sort algorithm as **split first** and **merge after**. 
+The merge-sort algorithm uses the **divide and conquer** approach which is to divide a big problem into smaller problems and solve them. I think of the merge-sort algorithm as **split first** and **merge after**.
 
 Assume you need to sort an array of *n* numbers in the right order. The merge-sort algorithm works as follows:
 
@@ -19,13 +19,13 @@ Assume you need to sort an array of *n* numbers in the right order. The merge-so
 
 ### Splitting
 
-Assume you are given an array of *n* numbers as`[2, 1, 5, 4, 9]`. This is an unsorted pile. The goal is to keep splitting the pile until you cannot split anymore. 
+Assume you are given an array of *n* numbers as`[2, 1, 5, 4, 9]`. This is an unsorted pile. The goal is to keep splitting the pile until you cannot split anymore.
 
 First, split the array into two halves: `[2, 1]` and `[5, 4, 9]`. Can you keep splitting them? Yes, you can!
 
 Focus on the left pile. Split`[2, 1]` into `[2]` and `[1]`. Can you keep splitting them? No. Time to check the other pile.
 
-Split `[5, 4, 9]` into `[5]` and `[4, 9]`. Unsurprisingly, `[5]` cannot be split anymore, but `[4, 9]` can be split into `[4]` and `[9]`. 
+Split `[5, 4, 9]` into `[5]` and `[4, 9]`. Unsurprisingly, `[5]` cannot be split anymore, but `[4, 9]` can be split into `[4]` and `[9]`.
 
 The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9]`. Notice that each pile consists of just one element.
 
@@ -33,11 +33,11 @@ The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9
 
 Now that you have split the array, you should **merge** the piles together **while sorting them**. Remember, the idea is to solve many small problems rather than a big one. For each merge iteration, you must be concerned at merging one pile with another.
 
-Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1, 2]` and `[4, 5]` and `[9]`. Since `[9]` is the odd one out, you cannot merge it with anything during this pass. 
+Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1, 2]` and `[4, 5]` and `[9]`. Since `[9]` is the odd one out, you cannot merge it with anything during this pass.
 
-The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again because it is the odd one out. 
+The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again because it is the odd one out.
 
-You are left with only two piles and `[9]`, finally gets its chance to merge, resulting in the sorted array as `[1, 2, 4, 5, 9]`. 
+You are left with only two piles `[1, 2, 4, 5]` and `[9]`, finally gets its chance to merge, resulting in the sorted array as `[1, 2, 4, 5, 9]`.
 
 ## Top-down implementation
 
@@ -61,7 +61,7 @@ A step-by-step explanation of how the code works:
 
 1. If the array is empty or contains a single element, there is no way to split it into smaller pieces. You must just return the array.
 
-2. Find the middle index. 
+2. Find the middle index.
 
 3. Using the middle index from the previous step, recursively split the left side of the array.
 
@@ -77,7 +77,7 @@ func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
   var leftIndex = 0
   var rightIndex = 0
 
-  // 2 
+  // 2
   var orderedPile = [Int]()
 
   // 3
@@ -144,16 +144,16 @@ This process repeats. At each step, we pick the smallest item from either the `l
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6 ]
          l              -->r
-	
+
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6, 7 ]
          -->l              r
-	
+
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6, 7, 8 ]
             -->l           r
 
-Now, there are no more items in the left pile. We simply add the remaining items from the right pile, and we are done. The merged pile is `[ 1, 3, 6, 7, 8, 9 ]`. 
+Now, there are no more items in the left pile. We simply add the remaining items from the right pile, and we are done. The merged pile is `[ 1, 3, 6, 7, 8, 9 ]`.
 
 Notice that, this algorithm is very simple: it moves from left-to-right through the two piles and at every step picks the smallest item. This works because we guarantee that each of the piles is already sorted.
 
@@ -169,20 +169,20 @@ func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
   var z = [a, a]      // 1
   var d = 0
-    
+
   var width = 1
   while width < n {   // 2
-  
+
     var i = 0
     while i < n {     // 3
 
       var j = i
       var l = i
       var r = i + width
-      
+
       let lmax = min(l + width, n)
       let rmax = min(r + width, n)
-      
+
       while l < lmax && r < rmax {                // 4
         if isOrderedBefore(z[d][l], z[d][r]) {
           z[1 - d][j] = z[d][l]
@@ -206,7 +206,7 @@ func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
       i += width*2
     }
-    
+
     width *= 2
     d = 1 - d      // 5
   }
@@ -239,11 +239,11 @@ mergeSortBottomUp(array, <)   // [1, 2, 4, 5, 9]
 
 ## Performance
 
-The speed of the merge-sort algorithm is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do. 
+The speed of the merge-sort algorithm is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do.
 
-Whether or not the initial array is sorted already doesnot affect the speed of the merge-sort algorithm since you will be doing the same amount splits and comparisons regardless of the initial order of the elements.
+Whether or not the initial array is sorted already does not affect the speed of the merge-sort algorithm since you will be doing the same amount splits and comparisons regardless of the initial order of the elements.
 
-Therefore, the time complexity for the best, worst, and average case will always be **O(n log n)**. 
+Therefore, the time complexity for the best, worst, and average case will always be **O(n log n)**.
 
 A disadvantage of the merge-sort algorithm is that it needs a temporary "working" array equal in size to the array being sorted. It is not an **in-place** sort, unlike for example [quicksort](../Quicksort/).
 

From bdedbff97fd610e27ae41c0137e7bdb057e3611f Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 16:26:17 +0400
Subject: [PATCH 1329/1679] Fix a typo in Selection Sort article

---
 Selection Sort/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index daebc64f4..cbcf5d352 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -19,7 +19,7 @@ It works as follows:
 - Find the lowest number in the rest of the array, starting from index 2, and swap it with the one at index 2. Now, the array is sorted from index 0 to 2; this range contains the three lowest numbers in the array.
 - And continue until no numbers remain to be sorted.
 
-It nis called a "selection" sort because at every step you search through the rest of the array to select the next lowest number.
+It is called a "selection" sort because at every step you search through the rest of the array to select the next lowest number.
 
 ## An example
 
@@ -108,7 +108,7 @@ The source file [SelectionSort.swift](SelectionSort.swift) has a version of this
 
 ## Performance
 
-The selection sort is easy to understand but it performs slow as **O(n^2)**. It is worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). Finding the lowest element in the rest of the array is slow, especially since the inner loop will be performed repeatedly .
+The selection sort is easy to understand but it performs slow as **O(n^2)**. It is worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). Finding the lowest element in the rest of the array is slow, especially since the inner loop will be performed repeatedly.
 
 The [Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a fast method for finding the minimum value in the rest of the array. The heap sort' performance is **O(n log n)**.
 

From 5a6e1a70151e0770f20db9412595795cc3a8eec1 Mon Sep 17 00:00:00 2001
From: Jacek Lampart <jlampa@gmail.com>
Date: Sat, 11 Nov 2017 19:25:42 +0000
Subject: [PATCH 1330/1679] Update README.markdown

---
 Heap/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 49031dcc3..4344d9e7c 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -27,7 +27,7 @@ As a result of this heap property, a max-heap always stores its largest item at
 
 > **Note:** The root of the heap has the maximum or minimum element, but the sort order of other elements are not predictable. For example, the maximum element is always at index 0 in a max-heap, but the minimum element isn’t necessarily the last one. -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
-## How does a heap can be compared to regular trees?
+## How does a heap compare to regular trees?
 
 A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
 

From 02d583e8be5267707a8d37a8e2b3cc68d6bae1c5 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 29 Jul 2017 08:58:05 -0700
Subject: [PATCH 1331/1679] Improvement of Red Black Tree

* Add count(), allElements(), isEmpty() functions
* Make the config right for RBTree in workspace
* Create a separate class for RBTree
---
 .../Sources/RedBlackTree.swift                | 1347 +++++++++--------
 Red-Black Tree/RedBlackTree.swift             |  795 ++++++++++
 2 files changed, 1491 insertions(+), 651 deletions(-)
 create mode 100644 Red-Black Tree/RedBlackTree.swift

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 59633031d..fc0411b42 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -21,730 +21,775 @@
 import Foundation
 
 private enum RBTreeColor {
-  case red
-  case black
+    case red
+    case black
 }
 
 private enum RotationDirection {
-  case left
-  case right
+    case left
+    case right
 }
 
 // MARK: - RBNode
 
 public class RBTreeNode<T: Comparable>: Equatable {
-  public typealias RBNode = RBTreeNode<T>
-  
-  fileprivate var color: RBTreeColor = .black
-  fileprivate var key: T?
-  var leftChild: RBNode?
-  var rightChild: RBNode?
-  fileprivate weak var parent: RBNode?
-  
-  public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
-    self.key = key
-    self.leftChild = leftChild
-    self.rightChild = rightChild
-    self.parent = parent
-    
-    self.leftChild?.parent = self
-    self.rightChild?.parent = self
-  }
-  
-  public convenience init(key: T?) {
-    self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
-  }
-  
-  // For initialising the nullLeaf
-  public convenience init() {
-    self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
-    self.color = .black
-  }
-  
-  var isRoot: Bool {
-    return parent == nil
-  }
-  
-  var isLeaf: Bool {
-    return rightChild == nil && leftChild == nil
-  }
-  
-  var isNullLeaf: Bool {
-    return key == nil && isLeaf && color == .black
-  }
-  
-  var isLeftChild: Bool {
-    return parent?.leftChild === self
-  }
-  
-  var isRightChild: Bool {
-    return parent?.rightChild === self
-  }
-  
-  var grandparent: RBNode? {
-    return parent?.parent
-  }
-  
-  var sibling: RBNode? {
-    if isLeftChild {
-      return parent?.rightChild
-    } else {
-      return parent?.leftChild
-    }
-  }
-  
-  var uncle: RBNode? {
-    return parent?.sibling
-  }
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate var color: RBTreeColor = .black
+    fileprivate var key: T?
+    var leftChild: RBNode?
+    var rightChild: RBNode?
+    fileprivate weak var parent: RBNode?
+    
+    public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+        self.key = key
+        self.leftChild = leftChild
+        self.rightChild = rightChild
+        self.parent = parent
+        
+        self.leftChild?.parent = self
+        self.rightChild?.parent = self
+    }
+    
+    public convenience init(key: T?) {
+        self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
+    }
+    
+    // For initialising the nullLeaf
+    public convenience init() {
+        self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
+        self.color = .black
+    }
+    
+    var isRoot: Bool {
+        return parent == nil
+    }
+    
+    var isLeaf: Bool {
+        return rightChild == nil && leftChild == nil
+    }
+    
+    var isNullLeaf: Bool {
+        return key == nil && isLeaf && color == .black
+    }
+    
+    var isLeftChild: Bool {
+        return parent?.leftChild === self
+    }
+    
+    var isRightChild: Bool {
+        return parent?.rightChild === self
+    }
+    
+    var grandparent: RBNode? {
+        return parent?.parent
+    }
+    
+    var sibling: RBNode? {
+        if isLeftChild {
+            return parent?.rightChild
+        } else {
+            return parent?.leftChild
+        }
+    }
+    
+    var uncle: RBNode? {
+        return parent?.sibling
+    }
 }
 
 // MARK: - RedBlackTree
 
 public class RedBlackTree<T: Comparable> {
-  public typealias RBNode = RBTreeNode<T>
-  
-  fileprivate(set) var root: RBNode
-  fileprivate(set) var size = 0
-  fileprivate let nullLeaf = RBNode()
-  
-  public init() {
-    root = nullLeaf
-  }
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate(set) var root: RBNode
+    fileprivate(set) var size = 0
+    fileprivate let nullLeaf = RBNode()
+    fileprivate let allowDuplicateNode: Bool
+    
+    public init(_ allowDuplicateNode: Bool = false) {
+        root = nullLeaf
+        self.allowDuplicateNode = allowDuplicateNode
+    }
+}
+
+// MARK: - Size
+
+extension RedBlackTree {
+    public func count() -> Int {
+        return size
+    }
+    
+    public func isEmpty() -> Bool {
+        return size == 0
+    }
+    
+    public func allElements() -> [T] {
+        var nodes: [T] = []
+        
+        getAllElements(node: root, nodes: &nodes)
+        
+        return nodes
+    }
+    
+    private func getAllElements(node: RBTreeNode<T>, nodes: inout [T]) {
+        guard !node.isNullLeaf else {
+            return
+        }
+        
+        if let left = node.leftChild {
+            getAllElements(node: left, nodes: &nodes)
+        }
+        
+        if let key = node.key {
+            nodes.append(key)
+        }
+        
+        if let right = node.rightChild {
+            getAllElements(node: right, nodes: &nodes)
+        }
+    }
 }
 
 // MARK: - Equatable protocol
 
 extension RBTreeNode {
-  static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
-    return lhs.key == rhs.key
-  }
+    static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+        return lhs.key == rhs.key
+    }
 }
 
 // MARK: - Finding a nodes successor
 
 extension RBTreeNode {
-  /*
-   * Returns the inorder successor node of a node
-   * The successor is a node with the next larger key value of the current node
-   */
-  public func getSuccessor() -> RBNode? {
-    // If node has right child: successor min of this right tree
-    if let rightChild = self.rightChild {
-      if !rightChild.isNullLeaf {
-        return rightChild.minimum()
-      }
-    }
-    // Else go upward until node left child
-    var currentNode = self
-    var parent = currentNode.parent
-    while currentNode.isRightChild {
-      if let parent = parent {
-        currentNode = parent
-      }
-      parent = currentNode.parent
-    }
-    return parent
-  }
+    /*
+     * Returns the inorder successor node of a node
+     * The successor is a node with the next larger key value of the current node
+     */
+    public func getSuccessor() -> RBNode? {
+        // If node has right child: successor min of this right tree
+        if let rightChild = self.rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.minimum()
+            }
+        }
+        // Else go upward until node left child
+        var currentNode = self
+        var parent = currentNode.parent
+        while currentNode.isRightChild {
+            if let parent = parent {
+                currentNode = parent
+            }
+            parent = currentNode.parent
+        }
+        return parent
+    }
 }
 
 // MARK: - Searching
 
 extension RBTreeNode {
-  /*
-   * Returns the node with the minimum key of the current subtree
-   */
-  public func minimum() -> RBNode? {
-    if let leftChild = leftChild {
-      if !leftChild.isNullLeaf {
-        return leftChild.minimum()
-      }
-      return self
-    }
-    return self
-  }
-  
-  /*
-   * Returns the node with the maximum key of the current subtree
-   */
-  public func maximum() -> RBNode? {
-    if let rightChild = rightChild {
-      if !rightChild.isNullLeaf {
-        return rightChild.maximum()
-      }
-      return self
-    }
-    return self
-  }
+    /*
+     * Returns the node with the minimum key of the current subtree
+     */
+    public func minimum() -> RBNode? {
+        if let leftChild = leftChild {
+            if !leftChild.isNullLeaf {
+                return leftChild.minimum()
+            }
+            return self
+        }
+        return self
+    }
+    
+    /*
+     * Returns the node with the maximum key of the current subtree
+     */
+    public func maximum() -> RBNode? {
+        if let rightChild = rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.maximum()
+            }
+            return self
+        }
+        return self
+    }
 }
 
 extension RedBlackTree {
-  /*
-   * Returns the node with the given key |input| if existing
-   */
-  public func search(input: T) -> RBNode? {
-    return search(key: input, node: root)
-  }
-  
-  /*
-   * Returns the node with given |key| in subtree of |node|
-   */
-  fileprivate func search(key: T, node: RBNode?) -> RBNode? {
-    // If node nil -> key not found
-    guard let node = node else {
-      return nil
-    }
-    // If node is nullLeaf == semantically same as if nil
-    if !node.isNullLeaf {
-      if let nodeKey = node.key {
-        // Node found
-        if key == nodeKey {
-          return node
-        } else if key < nodeKey {
-          return search(key: key, node: node.leftChild)
-        } else {
-          return search(key: key, node: node.rightChild)
+    /*
+     * Returns the node with the given key |input| if existing
+     */
+    public func search(input: T) -> RBNode? {
+        return search(key: input, node: root)
+    }
+    
+    /*
+     * Returns the node with given |key| in subtree of |node|
+     */
+    fileprivate func search(key: T, node: RBNode?) -> RBNode? {
+        // If node nil -> key not found
+        guard let node = node else {
+            return nil
+        }
+        // If node is nullLeaf == semantically same as if nil
+        if !node.isNullLeaf {
+            if let nodeKey = node.key {
+                // Node found
+                if key == nodeKey {
+                    return node
+                } else if key < nodeKey {
+                    return search(key: key, node: node.leftChild)
+                } else {
+                    return search(key: key, node: node.rightChild)
+                }
+            }
         }
-      }
+        return nil
     }
-    return nil
-  }
 }
 
 // MARK: - Finding maximum and minimum value
 
 extension RedBlackTree {
-  /*
-   * Returns the minimum key value of the whole tree
-   */
-  public func minValue() -> T? {
-    guard let minNode = root.minimum() else {
-      return nil
-    }
-    return minNode.key
-  }
-  
-  /*
-   * Returns the maximum key value of the whole tree
-   */
-  public func maxValue() -> T? {
-    guard let maxNode = root.maximum() else {
-      return nil
-    }
-    return maxNode.key
-  }
+    /*
+     * Returns the minimum key value of the whole tree
+     */
+    public func minValue() -> T? {
+        guard let minNode = root.minimum() else {
+            return nil
+        }
+        return minNode.key
+    }
+    
+    /*
+     * Returns the maximum key value of the whole tree
+     */
+    public func maxValue() -> T? {
+        guard let maxNode = root.maximum() else {
+            return nil
+        }
+        return maxNode.key
+    }
 }
 
 // MARK: - Inserting new nodes
 
 extension RedBlackTree {
-  /*
-   * Insert a node with key |key| into the tree
-   * 1. Perform normal insert operation as in a binary search tree
-   * 2. Fix red-black properties
-   * Runntime: O(log n)
-   */
-  public func insert(key: T) {
-    if root.isNullLeaf {
-      root = RBNode(key: key)
-    } else {
-      insert(input: RBNode(key: key), node: root)
-    }
-    
-    size += 1
-  }
-  
-  /*
-   * Nearly identical insert operation as in a binary search tree
-   * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
-   * after inserting we call insertFixup to maintain the red-black properties
-   */
-  private func insert(input: RBNode, node: RBNode) {
-    guard let inputKey = input.key, let nodeKey = node.key else {
-        return
-    }
-    if inputKey < nodeKey {
-      guard let child = node.leftChild else {
-        addAsLeftChild(child: input, parent: node)
-        return
-      }
-      if child.isNullLeaf {
-        addAsLeftChild(child: input, parent: node)
-      } else {
-        insert(input: input, node: child)
-      }
-    } else {
-      guard let child = node.rightChild else {
-        addAsRightChild(child: input, parent: node)
-        return
-      }
-      if child.isNullLeaf {
-        addAsRightChild(child: input, parent: node)
-      } else {
-        insert(input: input, node: child)
-      }
-    }
-  }
-  
-  private func addAsLeftChild(child: RBNode, parent: RBNode) {
-    parent.leftChild = child
-    child.parent = parent
-    child.color = .red
-    insertFixup(node: child)
-  }
-  
-  private func addAsRightChild(child: RBNode, parent: RBNode) {
-    parent.rightChild = child
-    child.parent = parent
-    child.color = .red
-    insertFixup(node: child)
-  }
-  
-  /*
-   * Fixes possible violations of the red-black property after insertion
-   * Only violation of red-black properties occurs at inserted node |z| and z.parent
-   * We have 3 distinct cases: case 1, 2a and 2b
-   * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
-   * - case 2a -> case 2b -> red-black tree
-   * - case 2b -> red-black tree
-   */
-  private func insertFixup(node z: RBNode) {
-    if !z.isNullLeaf {
-      guard let parentZ = z.parent else {
-        return
-      }
-      // If both |z| and his parent are red -> violation of red-black property -> need to fix it
-      if parentZ.color == .red {
-        guard let uncle = z.uncle else {
-          return
-        }
-        // Case 1: Uncle red -> recolor + move z
-        if uncle.color == .red {
-          parentZ.color = .black
-          uncle.color = .black
-          if let grandparentZ = parentZ.parent {
-            grandparentZ.color = .red
-            // Move z to grandparent and check again
-            insertFixup(node: grandparentZ)
-          }
-        }
-        // Case 2: Uncle black
-        else {
-          var zNew = z
-          // Case 2.a: z right child -> rotate
-          if parentZ.isLeftChild && z.isRightChild {
-            zNew = parentZ
-            leftRotate(node: zNew)
-          } else if parentZ.isRightChild && z.isLeftChild {
-            zNew = parentZ
-            rightRotate(node: zNew)
-          }
-          // Case 2.b: z left child -> recolor + rotate
-          zNew.parent?.color = .black
-          if let grandparentZnew = zNew.grandparent {
-            grandparentZnew.color = .red
-            if z.isLeftChild {
-              rightRotate(node: grandparentZnew)
+    /*
+     * Insert a node with key |key| into the tree
+     * 1. Perform normal insert operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func insert(key: T) {
+        // If key must be unique and find the key already existed, quit
+        if search(input: key) != nil && !allowDuplicateNode {
+            return
+        }
+        
+        if root.isNullLeaf {
+            root = RBNode(key: key)
+        } else {
+            insert(input: RBNode(key: key), node: root)
+        }
+        
+        size += 1
+    }
+    
+    /*
+     * Nearly identical insert operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
+     * after inserting we call insertFixup to maintain the red-black properties
+     */
+    private func insert(input: RBNode, node: RBNode) {
+        guard let inputKey = input.key, let nodeKey = node.key else {
+            return
+        }
+        if inputKey < nodeKey {
+            guard let child = node.leftChild else {
+                addAsLeftChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsLeftChild(child: input, parent: node)
+            } else {
+                insert(input: input, node: child)
+            }
+        } else {
+            guard let child = node.rightChild else {
+                addAsRightChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsRightChild(child: input, parent: node)
             } else {
-              leftRotate(node: grandparentZnew)
+                insert(input: input, node: child)
             }
-            // We have a valid red-black-tree
-          }
         }
-      }
     }
-    root.color = .black
-  }
+    
+    private func addAsLeftChild(child: RBNode, parent: RBNode) {
+        parent.leftChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    private func addAsRightChild(child: RBNode, parent: RBNode) {
+        parent.rightChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after insertion
+     * Only violation of red-black properties occurs at inserted node |z| and z.parent
+     * We have 3 distinct cases: case 1, 2a and 2b
+     * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
+     * - case 2a -> case 2b -> red-black tree
+     * - case 2b -> red-black tree
+     */
+    private func insertFixup(node z: RBNode) {
+        if !z.isNullLeaf {
+            guard let parentZ = z.parent else {
+                return
+            }
+            // If both |z| and his parent are red -> violation of red-black property -> need to fix it
+            if parentZ.color == .red {
+                guard let uncle = z.uncle else {
+                    return
+                }
+                // Case 1: Uncle red -> recolor + move z
+                if uncle.color == .red {
+                    parentZ.color = .black
+                    uncle.color = .black
+                    if let grandparentZ = parentZ.parent {
+                        grandparentZ.color = .red
+                        // Move z to grandparent and check again
+                        insertFixup(node: grandparentZ)
+                    }
+                }
+                    // Case 2: Uncle black
+                else {
+                    var zNew = z
+                    // Case 2.a: z right child -> rotate
+                    if parentZ.isLeftChild && z.isRightChild {
+                        zNew = parentZ
+                        leftRotate(node: zNew)
+                    } else if parentZ.isRightChild && z.isLeftChild {
+                        zNew = parentZ
+                        rightRotate(node: zNew)
+                    }
+                    // Case 2.b: z left child -> recolor + rotate
+                    zNew.parent?.color = .black
+                    if let grandparentZnew = zNew.grandparent {
+                        grandparentZnew.color = .red
+                        if z.isLeftChild {
+                            rightRotate(node: grandparentZnew)
+                        } else {
+                            leftRotate(node: grandparentZnew)
+                        }
+                        // We have a valid red-black-tree
+                    }
+                }
+            }
+        }
+        root.color = .black
+    }
 }
 
 // MARK: - Deleting a node
 extension RedBlackTree {
-  /*
-   * Delete a node with key |key| from the tree
-   * 1. Perform standard delete operation as in a binary search tree
-   * 2. Fix red-black properties
-   * Runntime: O(log n)
-   */
-  public func delete(key: T) {
-    if size == 1 {
-      root = nullLeaf
-      size -= 1
-    } else if let node = search(key: key, node: root) {
-      if !node.isNullLeaf {
-        delete(node: node)
-        size -= 1
-      }
-    }
-  }
-  
-  /*
-   * Nearly identical delete operation as in a binary search tree
-   * Differences: All nil pointers are replaced by the nullLeaf,
-   * after deleting we call insertFixup to maintain the red-black properties if the delted node was
-   * black (as if it was red -> no violation of red-black properties)
-   */
-  private func delete(node z: RBNode) {
-    var nodeY = RBNode()
-    var nodeX = RBNode()
-    if let leftChild = z.leftChild, let rightChild = z.rightChild {
-      if leftChild.isNullLeaf || rightChild.isNullLeaf {
-        nodeY = z
-      } else {
-        if let successor = z.getSuccessor() {
-          nodeY = successor
-        }
-      }
-    }
-    if let leftChild = nodeY.leftChild {
-      if !leftChild.isNullLeaf {
-        nodeX = leftChild
-      } else if let rightChild = nodeY.rightChild {
-        nodeX = rightChild
-      }
-    }
-    nodeX.parent = nodeY.parent
-    if let parentY = nodeY.parent {
-      // Should never be the case, as parent of root = nil
-      if parentY.isNullLeaf {
-        root = nodeX
-      } else {
-        if nodeY.isLeftChild {
-          parentY.leftChild = nodeX
+    /*
+     * Delete a node with key |key| from the tree
+     * 1. Perform standard delete operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func delete(key: T) {
+        if size == 1 {
+            root = nullLeaf
+            size -= 1
+        } else if let node = search(key: key, node: root) {
+            if !node.isNullLeaf {
+                delete(node: node)
+                size -= 1
+            }
+        }
+    }
+    
+    /*
+     * Nearly identical delete operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf,
+     * after deleting we call insertFixup to maintain the red-black properties if the delted node was
+     * black (as if it was red -> no violation of red-black properties)
+     */
+    private func delete(node z: RBNode) {
+        var nodeY = RBNode()
+        var nodeX = RBNode()
+        if let leftChild = z.leftChild, let rightChild = z.rightChild {
+            if leftChild.isNullLeaf || rightChild.isNullLeaf {
+                nodeY = z
+            } else {
+                if let successor = z.getSuccessor() {
+                    nodeY = successor
+                }
+            }
+        }
+        if let leftChild = nodeY.leftChild {
+            if !leftChild.isNullLeaf {
+                nodeX = leftChild
+            } else if let rightChild = nodeY.rightChild {
+                nodeX = rightChild
+            }
+        }
+        nodeX.parent = nodeY.parent
+        if let parentY = nodeY.parent {
+            // Should never be the case, as parent of root = nil
+            if parentY.isNullLeaf {
+                root = nodeX
+            } else {
+                if nodeY.isLeftChild {
+                    parentY.leftChild = nodeX
+                } else {
+                    parentY.rightChild = nodeX
+                }
+            }
         } else {
-          parentY.rightChild = nodeX
-        }
-      }
-    } else {
-      root = nodeX
-    }
-    if nodeY != z {
-      z.key = nodeY.key
-    }
-    // If sliced out node was red -> nothing to do as red-black-property holds
-    // If it was black -> fix red-black-property
-    if nodeY.color == .black {
-      deleteFixup(node: nodeX)
-    }
-  }
-  
-  /*
-   * Fixes possible violations of the red-black property after deletion
-   * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height 
-   * of the tree
-   * - case 1 -> case 2 -> red-black tree
-   *   case 1 -> case 3 -> case 4 -> red-black tree
-   *   case 1 -> case 4 -> red-black tree
-   * - case 3 -> case 4 -> red-black tree
-   * - case 4 -> red-black tree
-   */
-  private func deleteFixup(node x: RBNode) {
-    var xTmp = x
-    if !x.isRoot && x.color == .black {
-      guard var sibling = x.sibling else {
-        return
-      }
-      // Case 1: Sibling of x is red
-      if sibling.color == .red {
-        // Recolor
-        sibling.color = .black
-        if let parentX = x.parent {
-          parentX.color = .red
-          // Rotation
-          if x.isLeftChild {
-            leftRotate(node: parentX)
-          } else {
-            rightRotate(node: parentX)
-          }
-          // Update sibling
-          if let sibl = x.sibling {
-            sibling = sibl
-          }
-        }
-      }
-      // Case 2: Sibling is black with two black children
-      if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
-        // Recolor
-        sibling.color = .red
-        // Move fake black unit upwards
-        if let parentX = x.parent {
-          deleteFixup(node: parentX)
-        }
-        // We have a valid red-black-tree
-      } else {
-        // Case 3: a. Sibling black with one black child to the right
-        if x.isLeftChild && sibling.rightChild?.color == .black {
-          // Recolor
-          sibling.leftChild?.color = .black
-          sibling.color = .red
-          // Rotate
-          rightRotate(node: sibling)
-          // Update sibling of x
-          if let sibl = x.sibling {
-            sibling = sibl
-          }
-        }
-        // Still case 3: b. One black child to the left
-        else if x.isRightChild && sibling.leftChild?.color == .black {
-          // Recolor
-          sibling.rightChild?.color = .black
-          sibling.color = .red
-          // Rotate
-          leftRotate(node: sibling)
-          // Update sibling of x
-          if let sibl = x.sibling {
-            sibling = sibl
-          }
-        }
-        // Case 4: Sibling is black with red right child
-        // Recolor
-        if let parentX = x.parent {
-          sibling.color = parentX.color
-          parentX.color = .black
-          // a. x left and sibling with red right child
-          if x.isLeftChild {
-            sibling.rightChild?.color = .black
-            // Rotate
-            leftRotate(node: parentX)
-          }
-          // b. x right and sibling with red left child
-          else {
-            sibling.leftChild?.color = .black
-            //Rotate
-            rightRotate(node: parentX)
-          }
-          // We have a valid red-black-tree
-          xTmp = root
-        }
-      }
-    }
-    xTmp.color = .black
-  }
+            root = nodeX
+        }
+        if nodeY != z {
+            z.key = nodeY.key
+        }
+        // If sliced out node was red -> nothing to do as red-black-property holds
+        // If it was black -> fix red-black-property
+        if nodeY.color == .black {
+            deleteFixup(node: nodeX)
+        }
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after deletion
+     * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height
+     * of the tree
+     * - case 1 -> case 2 -> red-black tree
+     *   case 1 -> case 3 -> case 4 -> red-black tree
+     *   case 1 -> case 4 -> red-black tree
+     * - case 3 -> case 4 -> red-black tree
+     * - case 4 -> red-black tree
+     */
+    private func deleteFixup(node x: RBNode) {
+        var xTmp = x
+        if !x.isRoot && x.color == .black {
+            guard var sibling = x.sibling else {
+                return
+            }
+            // Case 1: Sibling of x is red
+            if sibling.color == .red {
+                // Recolor
+                sibling.color = .black
+                if let parentX = x.parent {
+                    parentX.color = .red
+                    // Rotation
+                    if x.isLeftChild {
+                        leftRotate(node: parentX)
+                    } else {
+                        rightRotate(node: parentX)
+                    }
+                    // Update sibling
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+            }
+            // Case 2: Sibling is black with two black children
+            if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
+                // Recolor
+                sibling.color = .red
+                // Move fake black unit upwards
+                if let parentX = x.parent {
+                    deleteFixup(node: parentX)
+                }
+                // We have a valid red-black-tree
+            } else {
+                // Case 3: a. Sibling black with one black child to the right
+                if x.isLeftChild && sibling.rightChild?.color == .black {
+                    // Recolor
+                    sibling.leftChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    rightRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                    // Still case 3: b. One black child to the left
+                else if x.isRightChild && sibling.leftChild?.color == .black {
+                    // Recolor
+                    sibling.rightChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    leftRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                // Case 4: Sibling is black with red right child
+                // Recolor
+                if let parentX = x.parent {
+                    sibling.color = parentX.color
+                    parentX.color = .black
+                    // a. x left and sibling with red right child
+                    if x.isLeftChild {
+                        sibling.rightChild?.color = .black
+                        // Rotate
+                        leftRotate(node: parentX)
+                    }
+                        // b. x right and sibling with red left child
+                    else {
+                        sibling.leftChild?.color = .black
+                        //Rotate
+                        rightRotate(node: parentX)
+                    }
+                    // We have a valid red-black-tree
+                    xTmp = root
+                }
+            }
+        }
+        xTmp.color = .black
+    }
 }
 
 // MARK: - Rotation
 extension RedBlackTree {
-  /*
-   * Left rotation around node x
-   * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
-   * makes y the new root of the subtree with x as y's left child and y's left child as x's right 
-   * child, where n = a node, [n] = a subtree
-   *     |                |
-   *     x                y
-   *   /   \     ~>     /   \
-   * [A]    y          x    [C]
-   *       / \        / \
-   *     [B] [C]    [A] [B]
-   */
-  fileprivate func leftRotate(node x: RBNode) {
-    rotate(node: x, direction: .left)
-  }
-  
-  /*
-   * Right rotation around node y
-   * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
-   * makes x the new root of the subtree with y as x's right child and x's right child as y's left
-   * child, where n = a node, [n] = a subtree
-   *     |                |
-   *     x                y
-   *   /   \     <~     /   \
-   * [A]    y          x    [C]
-   *       / \        / \
-   *     [B] [C]    [A] [B]
-   */
-  fileprivate func rightRotate(node x: RBNode) {
-    rotate(node: x, direction: .right)
-  }
-  
-  /*
-   * Rotation around a node x
-   * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
-   * Runntime: O(1)
-   */
-  private func rotate(node x: RBNode, direction: RotationDirection) {
-    var nodeY: RBNode? = RBNode()
-    
-    // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
-    switch direction {
-    case .left:
-      nodeY = x.rightChild
-      x.rightChild = nodeY?.leftChild
-      x.rightChild?.parent = x
-    case .right:
-      nodeY = x.leftChild
-      x.leftChild = nodeY?.rightChild
-      x.leftChild?.parent = x
-    }
-    
-    // Link |x|'s parent to nodeY
-    nodeY?.parent = x.parent
-    if x.isRoot {
-      if let node = nodeY {
-        root = node
-      }
-    } else if x.isLeftChild {
-      x.parent?.leftChild = nodeY
-    } else if x.isRightChild {
-      x.parent?.rightChild = nodeY
-    }
-    
-    // Put |x| on |nodeY|'s left
-    switch direction {
-    case .left:
-      nodeY?.leftChild = x
-    case .right:
-      nodeY?.rightChild = x
-    }
-    x.parent = nodeY
-  }
+    /*
+     * Left rotation around node x
+     * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
+     * makes y the new root of the subtree with x as y's left child and y's left child as x's right
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     ~>     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func leftRotate(node x: RBNode) {
+        rotate(node: x, direction: .left)
+    }
+    
+    /*
+     * Right rotation around node y
+     * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
+     * makes x the new root of the subtree with y as x's right child and x's right child as y's left
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     <~     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func rightRotate(node x: RBNode) {
+        rotate(node: x, direction: .right)
+    }
+    
+    /*
+     * Rotation around a node x
+     * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
+     * Runntime: O(1)
+     */
+    private func rotate(node x: RBNode, direction: RotationDirection) {
+        var nodeY: RBNode? = RBNode()
+        
+        // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
+        switch direction {
+        case .left:
+            nodeY = x.rightChild
+            x.rightChild = nodeY?.leftChild
+            x.rightChild?.parent = x
+        case .right:
+            nodeY = x.leftChild
+            x.leftChild = nodeY?.rightChild
+            x.leftChild?.parent = x
+        }
+        
+        // Link |x|'s parent to nodeY
+        nodeY?.parent = x.parent
+        if x.isRoot {
+            if let node = nodeY {
+                root = node
+            }
+        } else if x.isLeftChild {
+            x.parent?.leftChild = nodeY
+        } else if x.isRightChild {
+            x.parent?.rightChild = nodeY
+        }
+        
+        // Put |x| on |nodeY|'s left
+        switch direction {
+        case .left:
+            nodeY?.leftChild = x
+        case .right:
+            nodeY?.rightChild = x
+        }
+        x.parent = nodeY
+    }
 }
 
 // MARK: - Verify
 extension RedBlackTree {
-  /*
-   * Verifies that the existing tree fulfills all red-black properties
-   * Returns true if the tree is a valid red-black tree, false otherwise
-   */
-  public func verify() -> Bool {
-    if root.isNullLeaf {
-      print("The tree is empty")
-      return true
-    }
-    return property2() && property4() && property5()
-  }
-  
-  // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
-  // RBTreeColor
-  
-  // Property 2: The root is black
-  private func property2() -> Bool {
-    if root.color == .red {
-      print("Property-Error: Root is red")
-      return false
-    }
-    return true
-  }
-  
-  // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
-  
-  // Property 4: If a node is red, then both its children are black
-  private func property4() -> Bool {
-    return property4(node: root)
-  }
-  
-  private func property4(node: RBNode) -> Bool {
-    if node.isNullLeaf {
-      return true
-    }
-    if let leftChild = node.leftChild, let rightChild = node.rightChild {
-      if node.color == .red {
-        if !leftChild.isNullLeaf && leftChild.color == .red {
-            print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
-          return false
-        }
-        if !rightChild.isNullLeaf && rightChild.color == .red {
-          print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
-          return false
-        }
-      }
-      return property4(node: leftChild) && property4(node: rightChild)
-    }
-    return false
-  }
-  
-  // Property 5: For each node, all paths from the node to descendant leaves contain the same number
-  // of black nodes (same blackheight)
-  private func property5() -> Bool {
-    if property5(node: root) == -1 {
-      return false
-    } else {
-      return true
-    }
-  }
-  
-  private func property5(node: RBNode) -> Int {
-    if node.isNullLeaf {
-      return 0
-    }
-    guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
-      return -1
-    }
-    let left = property5(node: leftChild)
-    let right = property5(node: rightChild)
-    
-    if left == -1 || right == -1 {
-      return -1
-    } else if left == right {
-      let addedHeight = node.color == .black ? 1 : 0
-      return left + addedHeight
-    } else {
-      print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
-      return -1
-    }
-  }
+    /*
+     * Verifies that the existing tree fulfills all red-black properties
+     * Returns true if the tree is a valid red-black tree, false otherwise
+     */
+    public func verify() -> Bool {
+        if root.isNullLeaf {
+            print("The tree is empty")
+            return true
+        }
+        return property2() && property4() && property5()
+    }
+    
+    // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
+    // RBTreeColor
+    
+    // Property 2: The root is black
+    private func property2() -> Bool {
+        if root.color == .red {
+            print("Property-Error: Root is red")
+            return false
+        }
+        return true
+    }
+    
+    // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
+    
+    // Property 4: If a node is red, then both its children are black
+    private func property4() -> Bool {
+        return property4(node: root)
+    }
+    
+    private func property4(node: RBNode) -> Bool {
+        if node.isNullLeaf {
+            return true
+        }
+        if let leftChild = node.leftChild, let rightChild = node.rightChild {
+            if node.color == .red {
+                if !leftChild.isNullLeaf && leftChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
+                    return false
+                }
+                if !rightChild.isNullLeaf && rightChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
+                    return false
+                }
+            }
+            return property4(node: leftChild) && property4(node: rightChild)
+        }
+        return false
+    }
+    
+    // Property 5: For each node, all paths from the node to descendant leaves contain the same number
+    // of black nodes (same blackheight)
+    private func property5() -> Bool {
+        if property5(node: root) == -1 {
+            return false
+        } else {
+            return true
+        }
+    }
+    
+    private func property5(node: RBNode) -> Int {
+        if node.isNullLeaf {
+            return 0
+        }
+        guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
+            return -1
+        }
+        let left = property5(node: leftChild)
+        let right = property5(node: rightChild)
+        
+        if left == -1 || right == -1 {
+            return -1
+        } else if left == right {
+            let addedHeight = node.color == .black ? 1 : 0
+            return left + addedHeight
+        } else {
+            print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
+            return -1
+        }
+    }
 }
 
 // MARK: - Debugging
 
 extension RBTreeNode: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = ""
-    if isNullLeaf {
-      s = "nullLeaf"
-    } else {
-      if let key = key {
-        s = "key: \(key)"
-      } else {
-        s = "key: nil"
-      }
-      if let parent = parent {
-        s += ", parent: \(String(describing: parent.key))"
-      }
-      if let left = leftChild {
-        s += ", left = [" + left.debugDescription + "]"
-      }
-      if let right = rightChild {
-        s += ", right = [" + right.debugDescription + "]"
-      }
-      s += ", color = \(color)"
-    }
-    return s
-  }
+    public var debugDescription: String {
+        var s = ""
+        if isNullLeaf {
+            s = "nullLeaf"
+        } else {
+            if let key = key {
+                s = "key: \(key)"
+            } else {
+                s = "key: nil"
+            }
+            if let parent = parent {
+                s += ", parent: \(String(describing: parent.key))"
+            }
+            if let left = leftChild {
+                s += ", left = [" + left.debugDescription + "]"
+            }
+            if let right = rightChild {
+                s += ", right = [" + right.debugDescription + "]"
+            }
+            s += ", color = \(color)"
+        }
+        return s
+    }
 }
 
 extension RedBlackTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    return root.debugDescription
-  }
+    public var debugDescription: String {
+        return root.debugDescription
+    }
 }
 
 extension RBTreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if isNullLeaf {
-      s += "nullLeaf"
-    } else {
-      if let left = leftChild {
-        s += "(\(left.description)) <- "
-      }
-      if let key = key {
-        s += "\(key)"
-      } else {
-        s += "nil"
-      }
-      s += ", \(color)"
-      if let right = rightChild {
-        s += " -> (\(right.description))"
-      }
-    }
-    return s
-  }
+    public var description: String {
+        var s = ""
+        if isNullLeaf {
+            s += "nullLeaf"
+        } else {
+            if let left = leftChild {
+                s += "(\(left.description)) <- "
+            }
+            if let key = key {
+                s += "\(key)"
+            } else {
+                s += "nil"
+            }
+            s += ", \(color)"
+            if let right = rightChild {
+                s += " -> (\(right.description))"
+            }
+        }
+        return s
+    }
 }
 
 extension RedBlackTree: CustomStringConvertible {
-  public var description: String {
-    if root.isNullLeaf {
-      return "[]"
-    } else {
-      return root.description
+    public var description: String {
+        if root.isNullLeaf {
+            return "[]"
+        } else {
+            return root.description
+        }
     }
-  }
 }
diff --git a/Red-Black Tree/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.swift
new file mode 100644
index 000000000..fc0411b42
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.swift	
@@ -0,0 +1,795 @@
+//Copyright (c) 2016 Matthijs Hollemans and contributors
+//
+//Permission is hereby granted, free of charge, to any person obtaining a copy
+//of this software and associated documentation files (the "Software"), to deal
+//in the Software without restriction, including without limitation the rights
+//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//copies of the Software, and to permit persons to whom the Software is
+//furnished to do so, subject to the following conditions:
+//
+//The above copyright notice and this permission notice shall be included in
+//all copies or substantial portions of the Software.
+//
+//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+//THE SOFTWARE.
+
+import Foundation
+
+private enum RBTreeColor {
+    case red
+    case black
+}
+
+private enum RotationDirection {
+    case left
+    case right
+}
+
+// MARK: - RBNode
+
+public class RBTreeNode<T: Comparable>: Equatable {
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate var color: RBTreeColor = .black
+    fileprivate var key: T?
+    var leftChild: RBNode?
+    var rightChild: RBNode?
+    fileprivate weak var parent: RBNode?
+    
+    public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+        self.key = key
+        self.leftChild = leftChild
+        self.rightChild = rightChild
+        self.parent = parent
+        
+        self.leftChild?.parent = self
+        self.rightChild?.parent = self
+    }
+    
+    public convenience init(key: T?) {
+        self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
+    }
+    
+    // For initialising the nullLeaf
+    public convenience init() {
+        self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
+        self.color = .black
+    }
+    
+    var isRoot: Bool {
+        return parent == nil
+    }
+    
+    var isLeaf: Bool {
+        return rightChild == nil && leftChild == nil
+    }
+    
+    var isNullLeaf: Bool {
+        return key == nil && isLeaf && color == .black
+    }
+    
+    var isLeftChild: Bool {
+        return parent?.leftChild === self
+    }
+    
+    var isRightChild: Bool {
+        return parent?.rightChild === self
+    }
+    
+    var grandparent: RBNode? {
+        return parent?.parent
+    }
+    
+    var sibling: RBNode? {
+        if isLeftChild {
+            return parent?.rightChild
+        } else {
+            return parent?.leftChild
+        }
+    }
+    
+    var uncle: RBNode? {
+        return parent?.sibling
+    }
+}
+
+// MARK: - RedBlackTree
+
+public class RedBlackTree<T: Comparable> {
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate(set) var root: RBNode
+    fileprivate(set) var size = 0
+    fileprivate let nullLeaf = RBNode()
+    fileprivate let allowDuplicateNode: Bool
+    
+    public init(_ allowDuplicateNode: Bool = false) {
+        root = nullLeaf
+        self.allowDuplicateNode = allowDuplicateNode
+    }
+}
+
+// MARK: - Size
+
+extension RedBlackTree {
+    public func count() -> Int {
+        return size
+    }
+    
+    public func isEmpty() -> Bool {
+        return size == 0
+    }
+    
+    public func allElements() -> [T] {
+        var nodes: [T] = []
+        
+        getAllElements(node: root, nodes: &nodes)
+        
+        return nodes
+    }
+    
+    private func getAllElements(node: RBTreeNode<T>, nodes: inout [T]) {
+        guard !node.isNullLeaf else {
+            return
+        }
+        
+        if let left = node.leftChild {
+            getAllElements(node: left, nodes: &nodes)
+        }
+        
+        if let key = node.key {
+            nodes.append(key)
+        }
+        
+        if let right = node.rightChild {
+            getAllElements(node: right, nodes: &nodes)
+        }
+    }
+}
+
+// MARK: - Equatable protocol
+
+extension RBTreeNode {
+    static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+        return lhs.key == rhs.key
+    }
+}
+
+// MARK: - Finding a nodes successor
+
+extension RBTreeNode {
+    /*
+     * Returns the inorder successor node of a node
+     * The successor is a node with the next larger key value of the current node
+     */
+    public func getSuccessor() -> RBNode? {
+        // If node has right child: successor min of this right tree
+        if let rightChild = self.rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.minimum()
+            }
+        }
+        // Else go upward until node left child
+        var currentNode = self
+        var parent = currentNode.parent
+        while currentNode.isRightChild {
+            if let parent = parent {
+                currentNode = parent
+            }
+            parent = currentNode.parent
+        }
+        return parent
+    }
+}
+
+// MARK: - Searching
+
+extension RBTreeNode {
+    /*
+     * Returns the node with the minimum key of the current subtree
+     */
+    public func minimum() -> RBNode? {
+        if let leftChild = leftChild {
+            if !leftChild.isNullLeaf {
+                return leftChild.minimum()
+            }
+            return self
+        }
+        return self
+    }
+    
+    /*
+     * Returns the node with the maximum key of the current subtree
+     */
+    public func maximum() -> RBNode? {
+        if let rightChild = rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.maximum()
+            }
+            return self
+        }
+        return self
+    }
+}
+
+extension RedBlackTree {
+    /*
+     * Returns the node with the given key |input| if existing
+     */
+    public func search(input: T) -> RBNode? {
+        return search(key: input, node: root)
+    }
+    
+    /*
+     * Returns the node with given |key| in subtree of |node|
+     */
+    fileprivate func search(key: T, node: RBNode?) -> RBNode? {
+        // If node nil -> key not found
+        guard let node = node else {
+            return nil
+        }
+        // If node is nullLeaf == semantically same as if nil
+        if !node.isNullLeaf {
+            if let nodeKey = node.key {
+                // Node found
+                if key == nodeKey {
+                    return node
+                } else if key < nodeKey {
+                    return search(key: key, node: node.leftChild)
+                } else {
+                    return search(key: key, node: node.rightChild)
+                }
+            }
+        }
+        return nil
+    }
+}
+
+// MARK: - Finding maximum and minimum value
+
+extension RedBlackTree {
+    /*
+     * Returns the minimum key value of the whole tree
+     */
+    public func minValue() -> T? {
+        guard let minNode = root.minimum() else {
+            return nil
+        }
+        return minNode.key
+    }
+    
+    /*
+     * Returns the maximum key value of the whole tree
+     */
+    public func maxValue() -> T? {
+        guard let maxNode = root.maximum() else {
+            return nil
+        }
+        return maxNode.key
+    }
+}
+
+// MARK: - Inserting new nodes
+
+extension RedBlackTree {
+    /*
+     * Insert a node with key |key| into the tree
+     * 1. Perform normal insert operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func insert(key: T) {
+        // If key must be unique and find the key already existed, quit
+        if search(input: key) != nil && !allowDuplicateNode {
+            return
+        }
+        
+        if root.isNullLeaf {
+            root = RBNode(key: key)
+        } else {
+            insert(input: RBNode(key: key), node: root)
+        }
+        
+        size += 1
+    }
+    
+    /*
+     * Nearly identical insert operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
+     * after inserting we call insertFixup to maintain the red-black properties
+     */
+    private func insert(input: RBNode, node: RBNode) {
+        guard let inputKey = input.key, let nodeKey = node.key else {
+            return
+        }
+        if inputKey < nodeKey {
+            guard let child = node.leftChild else {
+                addAsLeftChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsLeftChild(child: input, parent: node)
+            } else {
+                insert(input: input, node: child)
+            }
+        } else {
+            guard let child = node.rightChild else {
+                addAsRightChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsRightChild(child: input, parent: node)
+            } else {
+                insert(input: input, node: child)
+            }
+        }
+    }
+    
+    private func addAsLeftChild(child: RBNode, parent: RBNode) {
+        parent.leftChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    private func addAsRightChild(child: RBNode, parent: RBNode) {
+        parent.rightChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after insertion
+     * Only violation of red-black properties occurs at inserted node |z| and z.parent
+     * We have 3 distinct cases: case 1, 2a and 2b
+     * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
+     * - case 2a -> case 2b -> red-black tree
+     * - case 2b -> red-black tree
+     */
+    private func insertFixup(node z: RBNode) {
+        if !z.isNullLeaf {
+            guard let parentZ = z.parent else {
+                return
+            }
+            // If both |z| and his parent are red -> violation of red-black property -> need to fix it
+            if parentZ.color == .red {
+                guard let uncle = z.uncle else {
+                    return
+                }
+                // Case 1: Uncle red -> recolor + move z
+                if uncle.color == .red {
+                    parentZ.color = .black
+                    uncle.color = .black
+                    if let grandparentZ = parentZ.parent {
+                        grandparentZ.color = .red
+                        // Move z to grandparent and check again
+                        insertFixup(node: grandparentZ)
+                    }
+                }
+                    // Case 2: Uncle black
+                else {
+                    var zNew = z
+                    // Case 2.a: z right child -> rotate
+                    if parentZ.isLeftChild && z.isRightChild {
+                        zNew = parentZ
+                        leftRotate(node: zNew)
+                    } else if parentZ.isRightChild && z.isLeftChild {
+                        zNew = parentZ
+                        rightRotate(node: zNew)
+                    }
+                    // Case 2.b: z left child -> recolor + rotate
+                    zNew.parent?.color = .black
+                    if let grandparentZnew = zNew.grandparent {
+                        grandparentZnew.color = .red
+                        if z.isLeftChild {
+                            rightRotate(node: grandparentZnew)
+                        } else {
+                            leftRotate(node: grandparentZnew)
+                        }
+                        // We have a valid red-black-tree
+                    }
+                }
+            }
+        }
+        root.color = .black
+    }
+}
+
+// MARK: - Deleting a node
+extension RedBlackTree {
+    /*
+     * Delete a node with key |key| from the tree
+     * 1. Perform standard delete operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func delete(key: T) {
+        if size == 1 {
+            root = nullLeaf
+            size -= 1
+        } else if let node = search(key: key, node: root) {
+            if !node.isNullLeaf {
+                delete(node: node)
+                size -= 1
+            }
+        }
+    }
+    
+    /*
+     * Nearly identical delete operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf,
+     * after deleting we call insertFixup to maintain the red-black properties if the delted node was
+     * black (as if it was red -> no violation of red-black properties)
+     */
+    private func delete(node z: RBNode) {
+        var nodeY = RBNode()
+        var nodeX = RBNode()
+        if let leftChild = z.leftChild, let rightChild = z.rightChild {
+            if leftChild.isNullLeaf || rightChild.isNullLeaf {
+                nodeY = z
+            } else {
+                if let successor = z.getSuccessor() {
+                    nodeY = successor
+                }
+            }
+        }
+        if let leftChild = nodeY.leftChild {
+            if !leftChild.isNullLeaf {
+                nodeX = leftChild
+            } else if let rightChild = nodeY.rightChild {
+                nodeX = rightChild
+            }
+        }
+        nodeX.parent = nodeY.parent
+        if let parentY = nodeY.parent {
+            // Should never be the case, as parent of root = nil
+            if parentY.isNullLeaf {
+                root = nodeX
+            } else {
+                if nodeY.isLeftChild {
+                    parentY.leftChild = nodeX
+                } else {
+                    parentY.rightChild = nodeX
+                }
+            }
+        } else {
+            root = nodeX
+        }
+        if nodeY != z {
+            z.key = nodeY.key
+        }
+        // If sliced out node was red -> nothing to do as red-black-property holds
+        // If it was black -> fix red-black-property
+        if nodeY.color == .black {
+            deleteFixup(node: nodeX)
+        }
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after deletion
+     * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height
+     * of the tree
+     * - case 1 -> case 2 -> red-black tree
+     *   case 1 -> case 3 -> case 4 -> red-black tree
+     *   case 1 -> case 4 -> red-black tree
+     * - case 3 -> case 4 -> red-black tree
+     * - case 4 -> red-black tree
+     */
+    private func deleteFixup(node x: RBNode) {
+        var xTmp = x
+        if !x.isRoot && x.color == .black {
+            guard var sibling = x.sibling else {
+                return
+            }
+            // Case 1: Sibling of x is red
+            if sibling.color == .red {
+                // Recolor
+                sibling.color = .black
+                if let parentX = x.parent {
+                    parentX.color = .red
+                    // Rotation
+                    if x.isLeftChild {
+                        leftRotate(node: parentX)
+                    } else {
+                        rightRotate(node: parentX)
+                    }
+                    // Update sibling
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+            }
+            // Case 2: Sibling is black with two black children
+            if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
+                // Recolor
+                sibling.color = .red
+                // Move fake black unit upwards
+                if let parentX = x.parent {
+                    deleteFixup(node: parentX)
+                }
+                // We have a valid red-black-tree
+            } else {
+                // Case 3: a. Sibling black with one black child to the right
+                if x.isLeftChild && sibling.rightChild?.color == .black {
+                    // Recolor
+                    sibling.leftChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    rightRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                    // Still case 3: b. One black child to the left
+                else if x.isRightChild && sibling.leftChild?.color == .black {
+                    // Recolor
+                    sibling.rightChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    leftRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                // Case 4: Sibling is black with red right child
+                // Recolor
+                if let parentX = x.parent {
+                    sibling.color = parentX.color
+                    parentX.color = .black
+                    // a. x left and sibling with red right child
+                    if x.isLeftChild {
+                        sibling.rightChild?.color = .black
+                        // Rotate
+                        leftRotate(node: parentX)
+                    }
+                        // b. x right and sibling with red left child
+                    else {
+                        sibling.leftChild?.color = .black
+                        //Rotate
+                        rightRotate(node: parentX)
+                    }
+                    // We have a valid red-black-tree
+                    xTmp = root
+                }
+            }
+        }
+        xTmp.color = .black
+    }
+}
+
+// MARK: - Rotation
+extension RedBlackTree {
+    /*
+     * Left rotation around node x
+     * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
+     * makes y the new root of the subtree with x as y's left child and y's left child as x's right
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     ~>     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func leftRotate(node x: RBNode) {
+        rotate(node: x, direction: .left)
+    }
+    
+    /*
+     * Right rotation around node y
+     * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
+     * makes x the new root of the subtree with y as x's right child and x's right child as y's left
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     <~     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func rightRotate(node x: RBNode) {
+        rotate(node: x, direction: .right)
+    }
+    
+    /*
+     * Rotation around a node x
+     * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
+     * Runntime: O(1)
+     */
+    private func rotate(node x: RBNode, direction: RotationDirection) {
+        var nodeY: RBNode? = RBNode()
+        
+        // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
+        switch direction {
+        case .left:
+            nodeY = x.rightChild
+            x.rightChild = nodeY?.leftChild
+            x.rightChild?.parent = x
+        case .right:
+            nodeY = x.leftChild
+            x.leftChild = nodeY?.rightChild
+            x.leftChild?.parent = x
+        }
+        
+        // Link |x|'s parent to nodeY
+        nodeY?.parent = x.parent
+        if x.isRoot {
+            if let node = nodeY {
+                root = node
+            }
+        } else if x.isLeftChild {
+            x.parent?.leftChild = nodeY
+        } else if x.isRightChild {
+            x.parent?.rightChild = nodeY
+        }
+        
+        // Put |x| on |nodeY|'s left
+        switch direction {
+        case .left:
+            nodeY?.leftChild = x
+        case .right:
+            nodeY?.rightChild = x
+        }
+        x.parent = nodeY
+    }
+}
+
+// MARK: - Verify
+extension RedBlackTree {
+    /*
+     * Verifies that the existing tree fulfills all red-black properties
+     * Returns true if the tree is a valid red-black tree, false otherwise
+     */
+    public func verify() -> Bool {
+        if root.isNullLeaf {
+            print("The tree is empty")
+            return true
+        }
+        return property2() && property4() && property5()
+    }
+    
+    // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
+    // RBTreeColor
+    
+    // Property 2: The root is black
+    private func property2() -> Bool {
+        if root.color == .red {
+            print("Property-Error: Root is red")
+            return false
+        }
+        return true
+    }
+    
+    // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
+    
+    // Property 4: If a node is red, then both its children are black
+    private func property4() -> Bool {
+        return property4(node: root)
+    }
+    
+    private func property4(node: RBNode) -> Bool {
+        if node.isNullLeaf {
+            return true
+        }
+        if let leftChild = node.leftChild, let rightChild = node.rightChild {
+            if node.color == .red {
+                if !leftChild.isNullLeaf && leftChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
+                    return false
+                }
+                if !rightChild.isNullLeaf && rightChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
+                    return false
+                }
+            }
+            return property4(node: leftChild) && property4(node: rightChild)
+        }
+        return false
+    }
+    
+    // Property 5: For each node, all paths from the node to descendant leaves contain the same number
+    // of black nodes (same blackheight)
+    private func property5() -> Bool {
+        if property5(node: root) == -1 {
+            return false
+        } else {
+            return true
+        }
+    }
+    
+    private func property5(node: RBNode) -> Int {
+        if node.isNullLeaf {
+            return 0
+        }
+        guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
+            return -1
+        }
+        let left = property5(node: leftChild)
+        let right = property5(node: rightChild)
+        
+        if left == -1 || right == -1 {
+            return -1
+        } else if left == right {
+            let addedHeight = node.color == .black ? 1 : 0
+            return left + addedHeight
+        } else {
+            print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
+            return -1
+        }
+    }
+}
+
+// MARK: - Debugging
+
+extension RBTreeNode: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = ""
+        if isNullLeaf {
+            s = "nullLeaf"
+        } else {
+            if let key = key {
+                s = "key: \(key)"
+            } else {
+                s = "key: nil"
+            }
+            if let parent = parent {
+                s += ", parent: \(String(describing: parent.key))"
+            }
+            if let left = leftChild {
+                s += ", left = [" + left.debugDescription + "]"
+            }
+            if let right = rightChild {
+                s += ", right = [" + right.debugDescription + "]"
+            }
+            s += ", color = \(color)"
+        }
+        return s
+    }
+}
+
+extension RedBlackTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        return root.debugDescription
+    }
+}
+
+extension RBTreeNode: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if isNullLeaf {
+            s += "nullLeaf"
+        } else {
+            if let left = leftChild {
+                s += "(\(left.description)) <- "
+            }
+            if let key = key {
+                s += "\(key)"
+            } else {
+                s += "nil"
+            }
+            s += ", \(color)"
+            if let right = rightChild {
+                s += " -> (\(right.description))"
+            }
+        }
+        return s
+    }
+}
+
+extension RedBlackTree: CustomStringConvertible {
+    public var description: String {
+        if root.isNullLeaf {
+            return "[]"
+        } else {
+            return root.description
+        }
+    }
+}

From a642a929ae4ce72ba0f00fc037c292a02db0fc9a Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Thu, 16 Nov 2017 22:37:27 -0500
Subject: [PATCH 1332/1679] Add username as test

---
 gfm-render.sh | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/gfm-render.sh b/gfm-render.sh
index 09c026d55..88970dd15 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,5 +1,7 @@
 #!/usr/bin/env bash
 
+USERNAME="raywenderlich"
+
 # $1 - readme
 function render_markdown_to_html {
   # escape escaping characters

From 7cb8185679cdc3acf38e9123ef7503fba5b4d116 Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sat, 7 Oct 2017 15:50:19 -0700
Subject: [PATCH 1333/1679] Add A* algorithm

---
 A-Star/AStar.swift                            | 153 +++++++++
 A-Star/README.md                              |   7 +
 A-Star/Tests/AStarTests.swift                 |  57 ++++
 .../AStarTests.xcodeproj/project.pbxproj      | 291 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 A-Star/Tests/Info.plist                       |  24 ++
 Hashed Heap/HashedHeap.swift                  |  13 +-
 .../contents.xcworkspacedata                  |  23 ++
 8 files changed, 574 insertions(+), 1 deletion(-)
 create mode 100644 A-Star/AStar.swift
 create mode 100644 A-Star/README.md
 create mode 100755 A-Star/Tests/AStarTests.swift
 create mode 100644 A-Star/Tests/AStarTests.xcodeproj/project.pbxproj
 create mode 100644 A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 A-Star/Tests/Info.plist

diff --git a/A-Star/AStar.swift b/A-Star/AStar.swift
new file mode 100644
index 000000000..41a9fac6c
--- /dev/null
+++ b/A-Star/AStar.swift
@@ -0,0 +1,153 @@
+// Written by Alejandro Isaza.
+
+import Foundation
+
+public protocol Graph {
+    associatedtype Vertex: Hashable
+    associatedtype Edge: WeightedEdge where Edge.Vertex == Vertex
+
+    /// Lists all edges going out from a vertex.
+    func edgesOutgoing(from vertex: Vertex) -> [Edge]
+}
+
+public protocol WeightedEdge {
+    associatedtype Vertex
+
+    /// The edge's cost.
+    var cost: Double { get }
+
+    /// The target vertex.
+    var target: Vertex { get }
+}
+
+public final class AStar<G: Graph> {
+    /// The graph to search on.
+    public let graph: G
+
+    /// The heuristic cost function that estimates the cost between two vertices.
+    ///
+    /// - Note: The heuristic function needs to always return a value that is lower-than or equal to the actual
+    ///         cost for the resulting path of the A* search to be optimal.
+    public let heuristic: (G.Vertex, G.Vertex) -> Double
+
+    /// Open list of nodes to expand.
+    private var open: HashedHeap<Node<G.Vertex>>
+
+    /// Closed list of vertices already expanded.
+    private var closed = Set<G.Vertex>()
+
+    /// Actual vertex cost for vertices we already encountered (refered to as `g` on the literature).
+    private var costs = Dictionary<G.Vertex, Double>()
+
+    /// Store the previous node for each expanded node to recreate the path.
+    private var parents = Dictionary<G.Vertex, G.Vertex>()
+
+    /// Initializes `AStar` with a graph and a heuristic cost function.
+    public init(graph: G, heuristic: @escaping (G.Vertex, G.Vertex) -> Double) {
+        self.graph = graph
+        self.heuristic = heuristic
+        open = HashedHeap(sort: <)
+    }
+
+    /// Finds an optimal path between `source` and `target`.
+    ///
+    /// - Precondition: both `source` and `target` belong to `graph`.
+    public func path(start: G.Vertex, target: G.Vertex) -> [G.Vertex] {
+        open.insert(Node<G.Vertex>(vertex: start, cost: 0, estimate: heuristic(start, target)))
+        while !open.isEmpty {
+            guard let node = open.remove() else {
+                break
+            }
+            costs[node.vertex] = node.cost
+
+            if (node.vertex == target) {
+                let path = buildPath(start: start, target: target)
+                cleanup()
+                return path
+            }
+
+            if !closed.contains(node.vertex) {
+                expand(node: node, target: target)
+                closed.insert(node.vertex)
+            }
+        }
+
+        // No path found
+        return []
+    }
+
+    private func expand(node: Node<G.Vertex>, target: G.Vertex) {
+        let edges = graph.edgesOutgoing(from: node.vertex)
+        for edge in edges {
+            let g = cost(node.vertex) + edge.cost
+            if g < cost(edge.target) {
+                open.insert(Node<G.Vertex>(vertex: edge.target, cost: g, estimate: heuristic(edge.target, target)))
+                parents[edge.target] = node.vertex
+            }
+        }
+    }
+
+    private func cost(_ vertex: G.Edge.Vertex) -> Double {
+        if let c = costs[vertex] {
+            return c
+        }
+
+        let node = Node(vertex: vertex, cost: Double.greatestFiniteMagnitude, estimate: 0)
+        if let index = open.index(of: node) {
+            return open[index].cost
+        }
+
+        return Double.greatestFiniteMagnitude
+    }
+
+    private func buildPath(start: G.Vertex, target: G.Vertex) -> [G.Vertex] {
+        var path = Array<G.Vertex>()
+        path.append(target)
+
+        var current = target
+        while current != start {
+            guard let parent = parents[current] else {
+                return [] // no path found
+            }
+            current = parent
+            path.append(current)
+        }
+
+        return path.reversed()
+    }
+
+    private func cleanup() {
+        open.removeAll()
+        closed.removeAll()
+        parents.removeAll()
+    }
+}
+
+private struct Node<V: Hashable>: Hashable, Comparable {
+    /// The graph vertex.
+    var vertex: V
+
+    /// The actual cost between the start vertex and this vertex.
+    var cost: Double
+
+    /// Estimated (heuristic) cost betweent this vertex and the target vertex.
+    var estimate: Double
+
+    public init(vertex: V, cost: Double, estimate: Double) {
+        self.vertex = vertex
+        self.cost = cost
+        self.estimate = estimate
+    }
+
+    static func < (lhs: Node<V>, rhs: Node<V>) -> Bool {
+        return lhs.cost + lhs.estimate < rhs.cost + rhs.estimate
+    }
+
+    static func == (lhs: Node<V>, rhs: Node<V>) -> Bool {
+        return lhs.vertex == rhs.vertex
+    }
+
+    var hashValue: Int {
+        return vertex.hashValue
+    }
+}
diff --git a/A-Star/README.md b/A-Star/README.md
new file mode 100644
index 000000000..cafd5027a
--- /dev/null
+++ b/A-Star/README.md
@@ -0,0 +1,7 @@
+# A*
+
+A* (pronounced "ay star") is a heuristic best-first search algorithm. A* minimizes node expansions, therefore minimizing the search time, by using a heuristic function. The heuristic function gives an estimate of the distance between two vertices. For instance if you are searching for a path between two points in a city, you can estimate the actual street distance with the straight-line distance.
+
+A* works by expanding the most promising nodes first, according to the heuristic function. In the city example it would choose streets which go in the general direction of the target first and, only if those are dead ends, backtrack and try other streets. This speeds up search in most sitations.
+
+A* is optimal (it always find the shortest path) if the heuristic function is admissible. A heuristic function is admissible if it never overestimates the cost of reaching the goal. In the extreme case of the heuristic function always retuning `0` A* acts exactly the same as [Dijkstra's Algorithm](../Dijkstra). The closer the heuristic function is the the actual distance the faster the search.
diff --git a/A-Star/Tests/AStarTests.swift b/A-Star/Tests/AStarTests.swift
new file mode 100755
index 000000000..87f674cd5
--- /dev/null
+++ b/A-Star/Tests/AStarTests.swift
@@ -0,0 +1,57 @@
+import Foundation
+import XCTest
+
+struct GridGraph: Graph {
+    struct Vertex: Hashable {
+        var x: Int
+        var y: Int
+
+        static func == (lhs: Vertex, rhs: Vertex) -> Bool {
+            return lhs.x == rhs.x && lhs.y == rhs.y
+        }
+
+        public var hashValue: Int {
+            return x.hashValue ^ y.hashValue
+        }
+    }
+
+    struct Edge: WeightedEdge {
+        var cost: Double
+        var target: Vertex
+    }
+
+    func edgesOutgoing(from vertex: Vertex) -> [Edge] {
+        return [
+            Edge(cost: 1, target: Vertex(x: vertex.x - 1, y: vertex.y)),
+            Edge(cost: 1, target: Vertex(x: vertex.x + 1, y: vertex.y)),
+            Edge(cost: 1, target: Vertex(x: vertex.x, y: vertex.y - 1)),
+            Edge(cost: 1, target: Vertex(x: vertex.x, y: vertex.y + 1)),
+        ]
+    }
+}
+
+class AStarTests: XCTestCase {
+    func testSameStartAndEnd() {
+        let graph = GridGraph()
+        let astar = AStar(graph: graph, heuristic: manhattanDistance)
+        let path = astar.path(start: GridGraph.Vertex(x: 0, y: 0), target: GridGraph.Vertex(x: 0, y: 0))
+        XCTAssertEqual(path.count, 1)
+        XCTAssertEqual(path[0].x, 0)
+        XCTAssertEqual(path[0].y, 0)
+    }
+
+    func testDiagonal() {
+        let graph = GridGraph()
+        let astar = AStar(graph: graph, heuristic: manhattanDistance)
+        let path = astar.path(start: GridGraph.Vertex(x: 0, y: 0), target: GridGraph.Vertex(x: 10, y: 10))
+        XCTAssertEqual(path.count, 21)
+        XCTAssertEqual(path[0].x, 0)
+        XCTAssertEqual(path[0].y, 0)
+        XCTAssertEqual(path[20].x, 10)
+        XCTAssertEqual(path[20].y, 10)
+    }
+
+    func manhattanDistance(_ s: GridGraph.Vertex, _ t: GridGraph.Vertex) -> Double {
+        return Double(abs(s.x - t.x) + abs(s.y - t.y))
+    }
+}
diff --git a/A-Star/Tests/AStarTests.xcodeproj/project.pbxproj b/A-Star/Tests/AStarTests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..cacd1e5ae
--- /dev/null
+++ b/A-Star/Tests/AStarTests.xcodeproj/project.pbxproj
@@ -0,0 +1,291 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		611D099C1F8978AB00C7092B /* AStarTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 611D099B1F8978AB00C7092B /* AStarTests.swift */; };
+		611D099E1F8978BC00C7092B /* AStar.swift in Sources */ = {isa = PBXBuildFile; fileRef = 611D099D1F8978BB00C7092B /* AStar.swift */; };
+		611D09A01F89795100C7092B /* HashedHeap.swift in Sources */ = {isa = PBXBuildFile; fileRef = 611D099F1F89795100C7092B /* HashedHeap.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		611D099B1F8978AB00C7092B /* AStarTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = AStarTests.swift; sourceTree = "<group>"; };
+		611D099D1F8978BB00C7092B /* AStar.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = AStar.swift; path = ../AStar.swift; sourceTree = "<group>"; };
+		611D099F1F89795100C7092B /* HashedHeap.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = HashedHeap.swift; path = "../../Hashed Heap/HashedHeap.swift"; sourceTree = "<group>"; };
+		7B2BBC801C779D720067B71D /* AStarTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = AStarTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* AStarTests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				611D099F1F89795100C7092B /* HashedHeap.swift */,
+				611D099D1F8978BB00C7092B /* AStar.swift */,
+				611D099B1F8978AB00C7092B /* AStarTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* AStarTests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "AStarTests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = AStarTests;
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* AStarTests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0900;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0900;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "AStarTests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* AStarTests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				611D099C1F8978AB00C7092B /* AStarTests.swift in Sources */,
+				611D099E1F8978BC00C7092B /* AStar.swift in Sources */,
+				611D09A01F89795100C7092B /* HashedHeap.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "AStarTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "AStarTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/A-Star/Tests/Info.plist b/A-Star/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/A-Star/Tests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index be7d9ab78..106cdacb0 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -57,7 +57,12 @@ public struct HashedHeap<T: Hashable> {
   public var count: Int {
     return elements.count
   }
-  
+
+  /// Accesses an element by its index.
+  public subscript(index: Int) -> T {
+    return elements[index]
+  }
+
   /// Returns the index of the given element.
   ///
   /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
@@ -141,6 +146,12 @@ public struct HashedHeap<T: Hashable> {
     }
     return removeLast()
   }
+
+  /// Removes all elements from the heap.
+  public mutating func removeAll() {
+    elements.removeAll()
+    indices.removeAll()
+  }
   
   /// Removes the last element from the heap.
   ///
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4cab8e2d4..28fb4f1a7 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -38,6 +38,29 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:A-Star"
+      name = "A-Star">
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:AStar.swift">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:AStarTests.xcodeproj">
+         </FileRef>
+         <FileRef
+            location = "group:AStarTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "container:"
       name = "3Sum and 4Sum">

From cb26964f1ea032be9fbe7b64f1f6e849d1fda5d5 Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sat, 7 Oct 2017 15:53:59 -0700
Subject: [PATCH 1334/1679] Add to .travis.yml

---
 .travis.yml                                   |  1 +
 .../xcschemes/AStarTests.xcscheme             | 67 +++++++++++++++++++
 2 files changed, 68 insertions(+)
 create mode 100644 A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme

diff --git a/.travis.yml b/.travis.yml
index 7cd02c9bc..30b54f140 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,6 +9,7 @@ install:
 
 script:
 
+- xcodebuild test -project ./A-Star/Tests/AStarTests.xcodeproj -scheme AStarTests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
diff --git a/A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme b/A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme
new file mode 100644
index 000000000..5473b4c0c
--- /dev/null
+++ b/A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0900"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "AStarTests.xctest"
+               BlueprintName = "AStarTests"
+               ReferencedContainer = "container:AStarTests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 2c2ec49e225861e9aa0da42b54e35c90f81ddbed Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Thu, 16 Nov 2017 22:17:19 -0800
Subject: [PATCH 1335/1679] Add example to README

---
 A-Star/Images/graph.dot |  12 ++++++++++++
 A-Star/Images/graph.png | Bin 0 -> 20882 bytes
 A-Star/Images/step1.dot |  12 ++++++++++++
 A-Star/Images/step1.png | Bin 0 -> 28753 bytes
 A-Star/Images/step2.dot |  12 ++++++++++++
 A-Star/Images/step2.png | Bin 0 -> 29088 bytes
 A-Star/Images/step3.dot |  12 ++++++++++++
 A-Star/Images/step3.png | Bin 0 -> 30158 bytes
 A-Star/Images/step4.dot |  12 ++++++++++++
 A-Star/Images/step4.png | Bin 0 -> 30130 bytes
 A-Star/Images/step5.dot |  12 ++++++++++++
 A-Star/Images/step5.png | Bin 0 -> 29802 bytes
 A-Star/Images/step6.dot |  12 ++++++++++++
 A-Star/Images/step6.png | Bin 0 -> 29596 bytes
 A-Star/Images/step7.dot |  12 ++++++++++++
 A-Star/Images/step7.png | Bin 0 -> 30012 bytes
 A-Star/README.md        |  38 +++++++++++++++++++++++++++++++++++++-
 17 files changed, 133 insertions(+), 1 deletion(-)
 create mode 100644 A-Star/Images/graph.dot
 create mode 100644 A-Star/Images/graph.png
 create mode 100644 A-Star/Images/step1.dot
 create mode 100644 A-Star/Images/step1.png
 create mode 100644 A-Star/Images/step2.dot
 create mode 100644 A-Star/Images/step2.png
 create mode 100644 A-Star/Images/step3.dot
 create mode 100644 A-Star/Images/step3.png
 create mode 100644 A-Star/Images/step4.dot
 create mode 100644 A-Star/Images/step4.png
 create mode 100644 A-Star/Images/step5.dot
 create mode 100644 A-Star/Images/step5.png
 create mode 100644 A-Star/Images/step6.dot
 create mode 100644 A-Star/Images/step6.png
 create mode 100644 A-Star/Images/step7.dot
 create mode 100644 A-Star/Images/step7.png

diff --git a/A-Star/Images/graph.dot b/A-Star/Images/graph.dot
new file mode 100644
index 000000000..941d66232
--- /dev/null
+++ b/A-Star/Images/graph.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "h = 3" ] }
+    { rank = same; B [ label = "h = 2" ]; C [ label = "h = 2" ]; D [ label = "h = 2" ] }
+    { rank = same; E [ label = "h = 1" ]; F [ label = "h = 1" ]; G [ label = "h = 1" ] }
+    { H  [ label = "h = 0", style = filled, color = green ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/graph.png b/A-Star/Images/graph.png
new file mode 100644
index 0000000000000000000000000000000000000000..c0a4b1cc8fd31a372f6843f858703950a0adee4a
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diff --git a/A-Star/Images/step1.dot b/A-Star/Images/step1.dot
new file mode 100644
index 000000000..5785aea4c
--- /dev/null
+++ b/A-Star/Images/step1.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = deepskyblue1 ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; C [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
+    { rank = same; E [ label = "g = \?\nh = 1" ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step1.png b/A-Star/Images/step1.png
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diff --git a/A-Star/Images/step2.dot b/A-Star/Images/step2.dot
new file mode 100644
index 000000000..0c8a9d53d
--- /dev/null
+++ b/A-Star/Images/step2.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ]; C [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step2.png b/A-Star/Images/step2.png
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diff --git a/A-Star/Images/step3.dot b/A-Star/Images/step3.dot
new file mode 100644
index 000000000..32a75891d
--- /dev/null
+++ b/A-Star/Images/step3.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step3.png b/A-Star/Images/step3.png
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diff --git a/A-Star/Images/step4.dot b/A-Star/Images/step4.dot
new file mode 100644
index 000000000..16db76796
--- /dev/null
+++ b/A-Star/Images/step4.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = 2\nh = 1", style = filled, color = lightgrey ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step4.png b/A-Star/Images/step4.png
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diff --git a/A-Star/Images/step5.dot b/A-Star/Images/step5.dot
new file mode 100644
index 000000000..2986b6a90
--- /dev/null
+++ b/A-Star/Images/step5.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = deepskyblue1 ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = lightgrey ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step5.png b/A-Star/Images/step5.png
new file mode 100644
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diff --git a/A-Star/Images/step6.dot b/A-Star/Images/step6.dot
new file mode 100644
index 000000000..b5e3179b6
--- /dev/null
+++ b/A-Star/Images/step6.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightblue ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = deepskyblue1 ] }
+    { H  [ label = "g = 3\nh = 0", style = filled, color = lightgrey ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step6.png b/A-Star/Images/step6.png
new file mode 100644
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diff --git a/A-Star/Images/step7.dot b/A-Star/Images/step7.dot
new file mode 100644
index 000000000..c5b26b6b3
--- /dev/null
+++ b/A-Star/Images/step7.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightblue ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = lightblue ] }
+    { H  [ label = "g = 3\nh = 0", style = filled, color = deepskyblue1 ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step7.png b/A-Star/Images/step7.png
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diff --git a/A-Star/README.md b/A-Star/README.md
index cafd5027a..f362bb61e 100644
--- a/A-Star/README.md
+++ b/A-Star/README.md
@@ -4,4 +4,40 @@ A* (pronounced "ay star") is a heuristic best-first search algorithm. A* minimiz
 
 A* works by expanding the most promising nodes first, according to the heuristic function. In the city example it would choose streets which go in the general direction of the target first and, only if those are dead ends, backtrack and try other streets. This speeds up search in most sitations.
 
-A* is optimal (it always find the shortest path) if the heuristic function is admissible. A heuristic function is admissible if it never overestimates the cost of reaching the goal. In the extreme case of the heuristic function always retuning `0` A* acts exactly the same as [Dijkstra's Algorithm](../Dijkstra). The closer the heuristic function is the the actual distance the faster the search.
+A* is optimal (it always find the shortest path) if the heuristic function is admissible. A heuristic function is admissible if it never overestimates the cost of reaching the goal. In the extreme case of the heuristic function always retuning `0` A* acts exactly the same as [Dijkstra's Algorithm](../Dijkstra). The closer the heuristic function is to the actual distance the faster the search.
+
+## Example
+
+Let's run through an example on this simple directed graph. We are going to assume that all edges have a cost of 1 and the heuristic function is going to be the column starting at goal and going back:
+
+![Graph](Images/graph.png)
+
+On the first step we expand the root node on the left (blue). We set the cost `g` to zero and add all neighbors to the open list (grey). 
+
+![Step 1](Images/step1.png)
+
+We put the first not in the closed list (light blue) so that we don't try expanding it again if there were to be loops in the graph. Next we take the node on the open list with the smallest value of `g + h` where `g` is the current cost (0) plus the edge cost (1). Since all nodes in the open list have the same value we choose the top one.
+
+![Step 2](Images/step2.png)
+
+We repeat the process and pick the next node from the open list. In this case there are no new nodes to add to the open list.
+
+![Step 3](Images/step3.png)
+
+We expand the next node. One more node on the open list, but nothing exciting yet.
+
+![Step 4](Images/step4.png)
+
+Sicne the top and the bottom nodes have the same value we choose the top one. This is not a great choice but we could do better if we had a better heuristic function.
+
+![Step 5](Images/step5.png)
+
+Now we expand the bottom node because it has a smaller value than the middle node (2 + 1 < 3 + 1).
+
+![Step 6](Images/step6.png)
+
+And we finally reach the goal! We never even expanded that middle node. We didn't have to because its value is 4, which is equal to the total lenght of our solution and therefore guaranteed to not be part of the optimal solution.
+
+![Step 7](Images/step7.png)
+
+The final step is to backtrack from the goal node to buld the optimal path.

From 58245be3842c9c5f428fc63f35e637da6a551f63 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Fri, 17 Nov 2017 16:51:17 -0500
Subject: [PATCH 1336/1679] Add Token for gfm render

---
 gfm-render.sh | 1 +
 1 file changed, 1 insertion(+)

diff --git a/gfm-render.sh b/gfm-render.sh
index 88970dd15..7a3df636c 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,6 +1,7 @@
 #!/usr/bin/env bash
 
 USERNAME="raywenderlich"
+TOKEN="e64530973ec12f12c94ac26cce8c93caf466fc89"
 
 # $1 - readme
 function render_markdown_to_html {

From 0c2aa34b5a93e4e5ecf18b451ecae932f480d8ad Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Fri, 17 Nov 2017 17:45:19 -0500
Subject: [PATCH 1337/1679] revoke token

---
 gfm-render.sh | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/gfm-render.sh b/gfm-render.sh
index 7a3df636c..09c026d55 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,8 +1,5 @@
 #!/usr/bin/env bash
 
-USERNAME="raywenderlich"
-TOKEN="e64530973ec12f12c94ac26cce8c93caf466fc89"
-
 # $1 - readme
 function render_markdown_to_html {
   # escape escaping characters

From d7f172a8db597a7c699679b9b9977bede7469487 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sun, 23 Jul 2017 13:13:39 -0700
Subject: [PATCH 1338/1679] Improvement of Apple Ordered Set

Add explaination for apple ordered set
---
 .../AppleOrderedSet.playground/Contents.swift |  13 +-
 .../Sources/AppleOrderedSet.swift             |   4 +
 Ordered Set/AppleOrderedSet.swift             |   4 +
 Ordered Set/README.markdown                   | 126 +++++++++++++++++-
 .../contents.xcworkspacedata                  |   8 +-
 5 files changed, 144 insertions(+), 11 deletions(-)

diff --git a/Ordered Set/AppleOrderedSet.playground/Contents.swift b/Ordered Set/AppleOrderedSet.playground/Contents.swift
index 4388c664b..c5548c2c2 100644
--- a/Ordered Set/AppleOrderedSet.playground/Contents.swift	
+++ b/Ordered Set/AppleOrderedSet.playground/Contents.swift	
@@ -6,8 +6,17 @@ s.add(-1)
 s.add(0)
 s.insert(4, at: 3)
 
-s.set(-1, at: 0)
+print(s.all()) // [1, 2, -1, 4, 0]
+
+s.set(-1, at: 0) // We already have -1 in index: 2, so we will do nothing here
+
+print(s.all()) // [1, 2, -1, 4, 0]
+
 s.remove(-1)
 
-print(s.object(at: 1))
+print(s.all()) // [1, 2, 4, 0]
+
+print(s.object(at: 1)) // 2
+
+print(s.object(at: 2)) // 4
 
diff --git a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
index 3ff19cb8d..6bd8f94a0 100644
--- a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
+++ b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
@@ -69,4 +69,8 @@ public class AppleOrderedSet<T: Hashable> {
             indexOfKey[objects[i]] = i
         }
     }
+    
+    public func all() -> [T] {
+        return objects
+    }
 }
diff --git a/Ordered Set/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.swift
index 3ff19cb8d..6bd8f94a0 100644
--- a/Ordered Set/AppleOrderedSet.swift	
+++ b/Ordered Set/AppleOrderedSet.swift	
@@ -69,4 +69,8 @@ public class AppleOrderedSet<T: Hashable> {
             indexOfKey[objects[i]] = i
         }
     }
+    
+    public func all() -> [T] {
+        return objects
+    }
 }
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index bc5003a61..11096d5bb 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -1,5 +1,7 @@
 # Ordered Set
 
+## Sorted Array Version
+
 An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
 
 The Ordered Set data type is a hybrid of:
@@ -323,15 +325,129 @@ The right side did not contain the item, so we look at the left side:
 
 	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
 	                              *        mid        
-
+	
 	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
 	                    *                  mid        
 
 Finally, we've found `Player 2`, and return index 3.
 
-## See Also
+## Apple's Ordered Set
+Below the ordered set is based on sorted array. But [Apple's version](https://developer.apple.com/documentation/foundation/nsorderedset), it's pretty different. Now, let's look into how to implement apple's ordered set.
+
+Here is the example about how it works
+
+```swift
+let s = AppleOrderedSet<Int>()
+
+s.add(1)
+s.add(2)
+s.add(-1)
+s.add(0)
+s.insert(4, at: 3)
+
+print(s.all()) // [1, 2, -1, 4, 0]
+
+s.set(-1, at: 0) // We already have -1 in index: 2, so we will do nothing here
+
+print(s.all()) // [1, 2, -1, 4, 0]
+
+s.remove(-1)
+
+print(s.all()) // [1, 2, 4, 0]
+
+print(s.object(at: 1)) // 2
+
+print(s.object(at: 2)) // 4
+```
+
+The significant difference is the the array is not sorted. The elements in the array are the same when insert them. Image the array without duplicates and with `O(logn)` or `O(1)` search time.
+
+The idea here is using a data structure to provide `O(1)` or `O(logn)` time complexity, so it's easy to think about hash table.
+
+```swift
+var indexOfKey: [T: Int]
+var objects: [T]
+```
+
+`indexOfKey` is used to track the index of the element. `objects` is array holding elements.
+
+We will go through some key functions details here.
+
+### Add
 
-[Apple Ordered Set](AppleOrderedSet.playground)
-@remlostime added an Apple version of `OrderedSet`
+Update `indexOfKey` and insert element in the end of `objects`
+
+```swift
+// O(1)
+public func add(_ object: T) {
+	guard indexOfKey[object] == nil else {
+		return
+	}
+
+	objects.append(object)
+	indexOfKey[object] = objects.count - 1
+}
+```
+
+### Insert
+
+Insert in a random place of the array will cost `O(n)` time.
+
+```swift
+// O(n)
+public func insert(_ object: T, at index: Int) {
+	assert(index < objects.count, "Index should be smaller than object count")
+	assert(index >= 0, "Index should be bigger than 0")
+
+	guard indexOfKey[object] == nil else {
+		return
+	}
+
+	objects.insert(object, at: index)
+	indexOfKey[object] = index
+	for i in index+1..<objects.count {
+		indexOfKey[objects[i]] = i
+	}
+}
+```
+
+###  Set
+
+If the `object` already existed in the `OrderedSet`, do nothing. Otherwise, we need to update the `indexOfkey` and `objects`.
+
+```swift
+// O(1)
+public func set(_ object: T, at index: Int) {
+	assert(index < objects.count, "Index should be smaller than object count")
+	assert(index >= 0, "Index should be bigger than 0")
+
+	guard indexOfKey[object] == nil else {
+		return
+	}
+
+	indexOfKey.removeValue(forKey: objects[index])
+	indexOfKey[object] = index
+	objects[index] = object
+}
+```
+
+### Remove
+
+Remove element in the array will cost `O(n)`. At the same time, we need to update all elements's index after the removed element.
+
+```swift
+// O(n)
+public func remove(_ object: T) {
+	guard let index = indexOfKey[object] else {
+		return 
+	}
+
+	indexOfKey.removeValue(forKey: object)
+	objects.remove(at: index)
+	for i in index..<objects.count {
+		indexOfKey[objects[i]] = i
+	}
+}
+```
 
-*Written By Zain Humayun*
+*Ordered Set is Written By Zain Humayun, Apple Ordered Set is Written By Kai Chen*
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4cab8e2d4..fbaa4cd54 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1808,16 +1808,16 @@
       location = "group:Ordered Set"
       name = "Ordered Set">
       <FileRef
-         location = "group:OrderedSet.playground">
+         location = "group:AppleOrderedSet.playground">
       </FileRef>
       <FileRef
-         location = "group:OrderedSet.swift">
+         location = "group:AppleOrderedSet.swift">
       </FileRef>
       <FileRef
-         location = "group:AppleOrderedSet.swift">
+         location = "group:OrderedSet.playground">
       </FileRef>
       <FileRef
-         location = "group:AppleOrderedSet.playground">
+         location = "group:OrderedSet.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">

From 95b45f038bfaba63fac2621c24dd3bd0bd9d59be Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 18 Nov 2017 20:08:36 -0800
Subject: [PATCH 1339/1679] Split sorted set and ordered set

---
 .../Sources/AppleOrderedSet.swift             |  76 ----
 .../contents.xcplayground                     |   4 -
 Ordered Set/AppleOrderedSet.swift             |  76 ----
 .../Contents.swift                            |   2 +-
 .../timeline.xctimeline                       |   6 -
 .../Sources/OrderedSet.swift                  | 171 ++++-----
 .../contents.xcplayground                     |   8 +-
 Ordered Set/OrderedSet.swift                  | 172 ++++-----
 Ordered Set/README.markdown                   | 336 +-----------------
 Sorted Set/README.markdown                    | 334 +++++++++++++++++
 .../Example 1.xcplaygroundpage/Contents.swift |   2 +-
 .../timeline.xctimeline                       |   6 +-
 .../Example 2.xcplaygroundpage/Contents.swift |   2 +-
 .../Example 3.xcplaygroundpage/Contents.swift |   2 +-
 .../Sources/Player.swift                      |   6 +-
 .../Sources/Random.swift                      |   4 +-
 .../Sources/SortedSet.swift                   | 118 ++++++
 .../contents.xcplayground                     |   8 +
 .../contents.xcworkspacedata                  |   0
 Sorted Set/SortedSet.swift                    | 118 ++++++
 .../contents.xcworkspacedata                  |  19 +-
 21 files changed, 738 insertions(+), 732 deletions(-)
 delete mode 100644 Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
 delete mode 100644 Ordered Set/AppleOrderedSet.playground/contents.xcplayground
 delete mode 100644 Ordered Set/AppleOrderedSet.swift
 rename Ordered Set/{AppleOrderedSet.playground => OrderedSet.playground}/Contents.swift (91%)
 delete mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Sorted Set/README.markdown
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 1.xcplaygroundpage/Contents.swift (94%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 1.xcplaygroundpage/timeline.xctimeline (50%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 2.xcplaygroundpage/Contents.swift (95%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 3.xcplaygroundpage/Contents.swift (95%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Sources/Player.swift (95%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Sources/Random.swift (88%)
 create mode 100644 Sorted Set/SortedSet.playground/Sources/SortedSet.swift
 create mode 100644 Sorted Set/SortedSet.playground/contents.xcplayground
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/playground.xcworkspace/contents.xcworkspacedata (100%)
 create mode 100644 Sorted Set/SortedSet.swift

diff --git a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
deleted file mode 100644
index 6bd8f94a0..000000000
--- a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
+++ /dev/null
@@ -1,76 +0,0 @@
-public class AppleOrderedSet<T: Hashable> {
-    private var objects: [T] = []
-    private var indexOfKey: [T: Int] = [:]
-    
-    public init() {}
-    
-    // O(1)
-    public func add(_ object: T) {
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.append(object)
-        indexOfKey[object] = objects.count - 1
-    }
-    
-    // O(n)
-    public func insert(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.insert(object, at: index)
-        indexOfKey[object] = index
-        for i in index+1..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    // O(1)
-    public func object(at index: Int) -> T {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        return objects[index]
-    }
-    
-    // O(1)
-    public func set(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: objects[index])
-        indexOfKey[object] = index
-        objects[index] = object
-    }
-    
-    // O(1)
-    public func indexOf(_ object: T) -> Int {
-        return indexOfKey[object] ?? -1
-    }
-    
-    // O(n)
-    public func remove(_ object: T) {
-        guard let index = indexOfKey[object] else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: object)
-        objects.remove(at: index)
-        for i in index..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    public func all() -> [T] {
-        return objects
-    }
-}
diff --git a/Ordered Set/AppleOrderedSet.playground/contents.xcplayground b/Ordered Set/AppleOrderedSet.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Ordered Set/AppleOrderedSet.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Ordered Set/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.swift
deleted file mode 100644
index 6bd8f94a0..000000000
--- a/Ordered Set/AppleOrderedSet.swift	
+++ /dev/null
@@ -1,76 +0,0 @@
-public class AppleOrderedSet<T: Hashable> {
-    private var objects: [T] = []
-    private var indexOfKey: [T: Int] = [:]
-    
-    public init() {}
-    
-    // O(1)
-    public func add(_ object: T) {
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.append(object)
-        indexOfKey[object] = objects.count - 1
-    }
-    
-    // O(n)
-    public func insert(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.insert(object, at: index)
-        indexOfKey[object] = index
-        for i in index+1..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    // O(1)
-    public func object(at index: Int) -> T {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        return objects[index]
-    }
-    
-    // O(1)
-    public func set(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: objects[index])
-        indexOfKey[object] = index
-        objects[index] = object
-    }
-    
-    // O(1)
-    public func indexOf(_ object: T) -> Int {
-        return indexOfKey[object] ?? -1
-    }
-    
-    // O(n)
-    public func remove(_ object: T) {
-        guard let index = indexOfKey[object] else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: object)
-        objects.remove(at: index)
-        for i in index..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    public func all() -> [T] {
-        return objects
-    }
-}
diff --git a/Ordered Set/AppleOrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
similarity index 91%
rename from Ordered Set/AppleOrderedSet.playground/Contents.swift
rename to Ordered Set/OrderedSet.playground/Contents.swift
index c5548c2c2..6a2415231 100644
--- a/Ordered Set/AppleOrderedSet.playground/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -1,4 +1,4 @@
-let s = AppleOrderedSet<Int>()
+let s = OrderedSet<Int>()
 
 s.add(1)
 s.add(2)
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
index 8490a3320..5508c3637 100644
--- a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
@@ -1,117 +1,76 @@
-/*
-  An Ordered Set is a collection where all items in the set follow an ordering,
-  usually ordered from 'least' to 'most'. The way you value and compare items
-  can be user-defined.
-*/
-public struct OrderedSet<T: Comparable> {
-  private var internalSet = [T]()
-
-  public init() { }
-
-  // Returns the number of elements in the OrderedSet.
-  public var count: Int {
-    return internalSet.count
-  }
-
-  // Inserts an item. Performance: O(n)
-  public mutating func insert(_ item: T) {
-    if exists(item) {
-      return  // don't add an item if it already exists
-    }
-
-    // Insert new the item just before the one that is larger.
-    for i in 0..<count {
-      if internalSet[i] > item {
-        internalSet.insert(item, at: i)
-        return
-      }
+public class OrderedSet<T: Hashable> {
+  private var objects: [T] = []
+  private var indexOfKey: [T: Int] = [:]
+  
+  public init() {}
+  
+  // O(1)
+  public func add(_ object: T) {
+    guard indexOfKey[object] == nil else {
+      return
     }
-
-    // Append to the back if the new item is greater than any other in the set.
-    internalSet.append(item)
+    
+    objects.append(object)
+    indexOfKey[object] = objects.count - 1
   }
-
-  // Removes an item if it exists. Performance: O(n)
-  public mutating func remove(_ item: T) {
-    if let index = index(of: item) {
-      internalSet.remove(at: index)
+  
+  // O(n)
+  public func insert(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
     }
-  }
-
-  // Returns true if and only if the item exists somewhere in the set.
-  public func exists(_ item: T) -> Bool {
-    return index(of: item) != nil
-  }
-
-  // Returns the index of an item if it exists, or -1 otherwise.
-  public func index(of item: T) -> Int? {
-    var leftBound = 0
-    var rightBound = count - 1
-
-    while leftBound <= rightBound {
-      let mid = leftBound + ((rightBound - leftBound) / 2)
-
-      if internalSet[mid] > item {
-        rightBound = mid - 1
-      } else if internalSet[mid] < item {
-        leftBound = mid + 1
-      } else if internalSet[mid] == item {
-        return mid
-      } else {
-        // When we get here, we've landed on an item whose value is equal to the
-        // value of the item we're looking for, but the items themselves are not
-        // equal. We need to check the items with the same value to the right
-        // and to the left in order to find an exact match.
-
-        // Check to the right.
-        for j in stride(from: mid, to: count - 1, by: 1) {
-          if internalSet[j + 1] == item {
-            return j + 1
-          } else if internalSet[j] < internalSet[j + 1] {
-            break
-          }
-        }
-
-        // Check to the left.
-        for j in stride(from: mid, to: 0, by: -1) {
-          if internalSet[j - 1] == item {
-            return j - 1
-          } else if internalSet[j] > internalSet[j - 1] {
-            break
-          }
-        }
-        return nil
-      }
+    
+    objects.insert(object, at: index)
+    indexOfKey[object] = index
+    for i in index+1..<objects.count {
+      indexOfKey[objects[i]] = i
     }
-    return nil
   }
-
-  // Returns the item at the given index.
-  // Assertion fails if the index is out of the range of [0, count).
-  public subscript(index: Int) -> T {
-    assert(index >= 0 && index < count)
-    return internalSet[index]
+  
+  // O(1)
+  public func object(at index: Int) -> T {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    return objects[index]
   }
-
-  // Returns the 'maximum' or 'largest' value in the set.
-  public func max() -> T? {
-    return count == 0 ? nil : internalSet[count - 1]
+  
+  // O(1)
+  public func set(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: objects[index])
+    indexOfKey[object] = index
+    objects[index] = object
   }
-
-  // Returns the 'minimum' or 'smallest' value in the set.
-  public func min() -> T? {
-    return count == 0 ? nil : internalSet[0]
+  
+  // O(1)
+  public func indexOf(_ object: T) -> Int {
+    return indexOfKey[object] ?? -1
   }
-
-  // Returns the k-th largest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kLargest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[count - k]
+  
+  // O(n)
+  public func remove(_ object: T) {
+    guard let index = indexOfKey[object] else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: object)
+    objects.remove(at: index)
+    for i in index..<objects.count {
+      indexOfKey[objects[i]] = i
+    }
   }
-
-  // Returns the k-th smallest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kSmallest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  
+  public func all() -> [T] {
+    return objects
   }
 }
diff --git a/Ordered Set/OrderedSet.playground/contents.xcplayground b/Ordered Set/OrderedSet.playground/contents.xcplayground
index 18c02c912..5da2641c9 100644
--- a/Ordered Set/OrderedSet.playground/contents.xcplayground	
+++ b/Ordered Set/OrderedSet.playground/contents.xcplayground	
@@ -1,8 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='6.0' target-platform='ios' display-mode='raw' executeOnSourceChanges='false'>
-    <pages>
-        <page name='Example 1'/>
-        <page name='Example 2'/>
-        <page name='Example 3'/>
-    </pages>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index a8b3b0966..8b6df7d3e 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -1,117 +1,77 @@
-/*
-  An Ordered Set is a collection where all items in the set follow an ordering,
-  usually ordered from 'least' to 'most'. The way you value and compare items
-  can be user-defined.
-*/
-public struct OrderedSet<T: Comparable> {
-  private var internalSet = [T]()
-
-  public init() { }
-
-  // Returns the number of elements in the OrderedSet.
-  public var count: Int {
-    return internalSet.count
-  }
-
-  // Inserts an item. Performance: O(n)
-  public mutating func insert(item: T) {
-    if exists(item) {
-      return  // don't add an item if it already exists
+public class OrderedSet<T: Hashable> {
+  private var objects: [T] = []
+  private var indexOfKey: [T: Int] = [:]
+  
+  public init() {}
+  
+  // O(1)
+  public func add(_ object: T) {
+    guard indexOfKey[object] == nil else {
+      return
     }
-
-    // Insert new the item just before the one that is larger.
-    for i in 0..<count {
-      if internalSet[i] > item {
-        internalSet.insert(item, atIndex: i)
-        return
-      }
-    }
-
-    // Append to the back if the new item is greater than any other in the set.
-    internalSet.append(item)
+    
+    objects.append(object)
+    indexOfKey[object] = objects.count - 1
   }
-
-  // Removes an item if it exists. Performance: O(n)
-  public mutating func remove(item: T) {
-    if let index = indexOf(item) {
-      internalSet.removeAtIndex(index)
+  
+  // O(n)
+  public func insert(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
     }
-  }
-
-  // Returns true if and only if the item exists somewhere in the set.
-  public func exists(item: T) -> Bool {
-    return indexOf(item) != nil
-  }
-
-  // Returns the index of an item if it exists, or -1 otherwise.
-  public func indexOf(item: T) -> Int? {
-    var leftBound = 0
-    var rightBound = count - 1
-
-    while leftBound <= rightBound {
-      let mid = leftBound + ((rightBound - leftBound) / 2)
-
-      if internalSet[mid] > item {
-        rightBound = mid - 1
-      } else if internalSet[mid] < item {
-        leftBound = mid + 1
-      } else if internalSet[mid] == item {
-        return mid
-      } else {
-        // When we get here, we've landed on an item whose value is equal to the
-        // value of the item we're looking for, but the items themselves are not
-        // equal. We need to check the items with the same value to the right
-        // and to the left in order to find an exact match.
-
-        // Check to the right.
-        for j in mid.stride(to: count - 1, by: 1) {
-          if internalSet[j + 1] == item {
-            return j + 1
-          } else if internalSet[j] < internalSet[j + 1] {
-            break
-          }
-        }
-
-        // Check to the left.
-        for j in mid.stride(to: 0, by: -1) {
-          if internalSet[j - 1] == item {
-            return j - 1
-          } else if internalSet[j] > internalSet[j - 1] {
-            break
-          }
-        }
-        return nil
-      }
+    
+    objects.insert(object, at: index)
+    indexOfKey[object] = index
+    for i in index+1..<objects.count {
+      indexOfKey[objects[i]] = i
     }
-    return nil
   }
-
-  // Returns the item at the given index.
-  // Assertion fails if the index is out of the range of [0, count).
-  public subscript(index: Int) -> T {
-    assert(index >= 0 && index < count)
-    return internalSet[index]
+  
+  // O(1)
+  public func object(at index: Int) -> T {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    return objects[index]
   }
-
-  // Returns the 'maximum' or 'largest' value in the set.
-  public func max() -> T? {
-    return count == 0 ? nil : internalSet[count - 1]
+  
+  // O(1)
+  public func set(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: objects[index])
+    indexOfKey[object] = index
+    objects[index] = object
   }
-
-  // Returns the 'minimum' or 'smallest' value in the set.
-  public func min() -> T? {
-    return count == 0 ? nil : internalSet[0]
+  
+  // O(1)
+  public func indexOf(_ object: T) -> Int {
+    return indexOfKey[object] ?? -1
   }
-
-  // Returns the k-th largest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kLargest(k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[count - k]
+  
+  // O(n)
+  public func remove(_ object: T) {
+    guard let index = indexOfKey[object] else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: object)
+    objects.remove(at: index)
+    for i in index..<objects.count {
+      indexOfKey[objects[i]] = i
+    }
   }
-
-  // Returns the k-th smallest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kSmallest(k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  
+  public func all() -> [T] {
+    return objects
   }
 }
+
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 11096d5bb..82d736731 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -1,338 +1,6 @@
 # Ordered Set
 
-## Sorted Array Version
-
-An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
-
-The Ordered Set data type is a hybrid of:
-
-- a [Set](https://en.wikipedia.org/wiki/Set_%28mathematics%29), a collection of unique items where the order does not matter, and
-- a [Sequence](https://en.wikipedia.org/wiki/Sequence), an ordered list of items where each item may appear more than once.
-
-It's important to keep in mind that two items can have the same *value* but still may not be equal. For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
-
-## Why use an ordered set?
-
-Ordered Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Ordered Set are **O(1)**.
-
-A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below).
-
-#### These are ordered sets
-
-A set of integers:
-
-	[1, 2, 3, 6, 8, 10, 1000]
-
-A set of strings:
-
-	["a", "is", "set", "this"]
-
-The "value" of these strings could be their text content, but also for example their length.
-
-#### These are not ordered sets
-
-This set violates the property of uniqueness:
-
-	[1, 1, 2, 3, 5, 8]
-
-This set violates the sorted property:
-
-	[1, 11, 2, 3]
-
-## The code
-
-We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep the set sorted, we need to be able to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
-
-```swift
-public struct OrderedSet<T: Comparable> {
-  private var internalSet = [T]()
-
-  // Returns the number of elements in the OrderedSet.
-  public var count: Int {
-    return internalSet.count
-  }
-  ...
-```
-
-Lets take a look at the `insert()` function first. This first checks if the item already exists in the collection. If so, it returns and does not insert the item.  Otherwise, it will insert the item through straightforward iteration.
-
-```swift
-  public mutating func insert(_ item: T){
-    if exists(item) {
-      return  // don't add an item if it already exists
-    }
-
-    // Insert new the item just before the one that is larger.
-    for i in 0..<count {
-      if internalSet[i] > item {
-        internalSet.insert(item, at: i)
-        return
-      }
-    }
-
-    // Append to the back if the new item is greater than any other in the set.
-    internalSet.append(item)
-  }
-```
-
-As we'll see later on, checking if the item is already in the set has an efficiency of **O(log(n) + k)** where **k** is the number of items with the same value as the item we are inserting.
-
-To insert the new item, the `for` loop starts from the beginning of the array, and checks to see if each item is larger than the item we want to insert. Once we find such an item, we insert the new one into its place. This shifts the rest of the array over to the right by 1 position. This loop is at worst **O(n)**.
-
-The total performance of the `insert()` function is therefore **O(n)**.
-
-Next up is the `remove()` function:
-
-```swift
-  public mutating func remove(_ item: T) {
-    if let index = index(of: item) {
-      internalSet.remove(at: index)
-    }
-  }
-```
-
-First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n)**.
-
-The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item.
-
-```swift
-  public func index(of item: T) -> Int? {
-    var leftBound = 0
-    var rightBound = count - 1
-
-    while leftBound <= rightBound {
-      let mid = leftBound + ((rightBound - leftBound) / 2)
-
-      if internalSet[mid] > item {
-        rightBound = mid - 1
-      } else if internalSet[mid] < item {
-        leftBound = mid + 1
-      } else if internalSet[mid] == item {
-        return mid
-      } else {
-      	// see below
-      }
-    }
-    return nil
-  }
-```
-
-> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary%20Search).
-
-However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item.
-
-For example, consider this ordered set of `Player` objects. Each `Player` has a name and a number of points:
-
-	[ ("Bill", 50), ("Ada", 50), ("Jony", 50), ("Steve", 200), ("Jean-Louis", 500), ("Woz", 1000) ]
-
-We want the set to be ordered by points, from low to high. Multiple players can have the same number of points. The name of the player is not important for this ordering. However, the name *is* important for retrieving the correct item.
-
-Let's say we do `indexOf(bill)` where `bill` is player object `("Bill", 50)`. If we did a traditional binary search we'd land on index 2, which is the object `("Jony", 50)`. The value 50 matches, but it's not the object we're looking for!
-
-Therefore, we also need to check the items with the same value to the right and left of the midpoint. The code to check the left and right side looks like this:
-
-```swift
-        // Check to the right.
-        for j in mid.stride(to: count - 1, by: 1) {
-          if internalSet[j + 1] == item {
-            return j + 1
-          } else if internalSet[j] < internalSet[j + 1] {
-            break
-          }
-        }
-
-        // Check to the left.
-        for j in mid.stride(to: 0, by: -1) {
-          if internalSet[j - 1] == item {
-            return j - 1
-          } else if internalSet[j] > internalSet[j - 1] {
-            break
-          }
-        }
-
-        return nil
-```
-
-These loops start at the current `mid` value and then look at the neighboring values until we've found the correct object.
-
-The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for.
-
-Since the set is sorted, the following operations are all **O(1)**:
-
-```swift
-  // Returns the 'maximum' or 'largest' value in the set.
-  public func max() -> T? {
-    return count == 0 ? nil : internalSet[count - 1]
-  }
-
-  // Returns the 'minimum' or 'smallest' value in the set.
-  public func min() -> T? {
-    return count == 0 ? nil : internalSet[0]
-  }
-
-  // Returns the k-th largest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kLargest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[count - k]
-  }
-
-  // Returns the k-th smallest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kSmallest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[k - 1]
-  }
-```
-
-## Examples
-
-Below are a few examples that can be found in the playground file.
-
-### Example 1
-
-Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
-
-```swift
-// Example 1 with type Int
-var mySet = OrderedSet<Int>()
-
-// Insert random numbers into the set
-for _ in 0..<50 {
-  mySet.insert(randomNum(50, max: 500))
-}
-
-print(mySet)
-
-print(mySet.max())
-print(mySet.min())
-
-// Print the 5 largest values
-for k in 1...5 {
-  print(mySet.kLargest(k))
-}
-
-// Print the 5 lowest values
-for k in 1...5 {
-  print(mySet.kSmallest(k))
-}
-```
-
-### Example 2
-
-In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
-
-```swift
-public struct Player: Comparable {
-  public var name: String
-  public var points: Int
-}
-```
-
-The `Player` also gets its own `==` and `<` operators. The `<` operator is used to determine the sort order of the set, while `==` determines whether two objects are really equal.
-
-Note that `==` compares both the name and the points:  
-
-```swifr
-func ==(x: Player, y: Player) -> Bool {
-  return x.name == y.name && x.points == y.points
-}
-```
-
-But `<` only compares the points:
-
-```swift
-func <(x: Player, y: Player) -> Bool {
-  return x.points < y.points
-}
-```
-
-Therefore, two `Player`s can each have the same value (the number of points), but are not guaranteed to be equal (they can have different names).
-
-We create a new set and insert 20 random players. The `Player()` constructor gives each player a random name and score:
-
-```swift
-var playerSet = OrderedSet<Player>()
-
-// Populate the set with random players.
-for _ in 0..<20 {
-  playerSet.insert(Player())
-}
-```
-
-Insert another player:
-
-```swift
-var anotherPlayer = Player()
-playerSet.insert(anotherPlayer)
-```
-
-Now we use the `indexOf()` function to find out what rank `anotherPlayer` is.
-
-```swift
-let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
-print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
-```
-
-### Example 3
-
-The final example demonstrates the need to look for the right item even after the binary search has completed.
-
-We insert 9 players into the set:
-
-```swift
-var repeatedSet = OrderedSet<Player>()
-
-repeatedSet.insert(Player(name: "Player 1", points: 100))
-repeatedSet.insert(Player(name: "Player 2", points: 100))
-repeatedSet.insert(Player(name: "Player 3", points: 100))
-repeatedSet.insert(Player(name: "Player 4", points: 100))
-repeatedSet.insert(Player(name: "Player 5", points: 100))
-repeatedSet.insert(Player(name: "Player 6", points: 50))
-repeatedSet.insert(Player(name: "Player 7", points: 200))
-repeatedSet.insert(Player(name: "Player 8", points: 250))
-repeatedSet.insert(Player(name: "Player 9", points: 25))
-```
-
-Notice how several of these players have the same value of 100 points.
-
-The set looks something like this:
-
-	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
-
-The next line looks for `Player 2`:
-
-```swift
-print(repeatedSet.index(of: Player(name: "Player 2", points: 100)))
-```
-
-After the binary search finishes, the value of `mid` is at index 5:
-
-	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
-	                                                      mid
-
-However, this is not `Player 2`. Both `Player 4` and `Player 2` have the same points, but a different name. The binary search only looked at the points, not the name.
-
-But we do know that `Player 2` must be either to the immediate left or the right of `Player 4`, so we check both sides of `mid`. We only need to look at the objects with the same value as `Player 4`. The others are replaced by `X`:
-
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                                       mid
-
-The code then first checks on the right of `mid` (where the `*` is):
-
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                                       mid        *
-
-The right side did not contain the item, so we look at the left side:
-
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                              *        mid        
-	
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                    *                  mid        
-
-Finally, we've found `Player 2`, and return index 3.
-
-## Apple's Ordered Set
-Below the ordered set is based on sorted array. But [Apple's version](https://developer.apple.com/documentation/foundation/nsorderedset), it's pretty different. Now, let's look into how to implement apple's ordered set.
+Let's look into how to implement [Ordered Set](https://developer.apple.com/documentation/foundation/nsorderedset).
 
 Here is the example about how it works
 
@@ -450,4 +118,4 @@ public func remove(_ object: T) {
 }
 ```
 
-*Ordered Set is Written By Zain Humayun, Apple Ordered Set is Written By Kai Chen*
+*Written By Kai Chen*
diff --git a/Sorted Set/README.markdown b/Sorted Set/README.markdown
new file mode 100644
index 000000000..a8b5ad1ea
--- /dev/null
+++ b/Sorted Set/README.markdown	
@@ -0,0 +1,334 @@
+# Sorted Set
+
+## Sorted Array Version
+
+An Sorted Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
+
+The Sorted Set data type is a hybrid of:
+
+- a [Set](https://en.wikipedia.org/wiki/Set_%28mathematics%29), a collection of unique items where the order does not matter, and
+- a [Sequence](https://en.wikipedia.org/wiki/Sequence), an sorted list of items where each item may appear more than once.
+
+It's important to keep in mind that two items can have the same *value* but still may not be equal. For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
+
+## Why use an sorted set?
+
+Sorted Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Sorted Set are **O(1)**.
+
+A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below).
+
+#### These are sorted sets
+
+A set of integers:
+
+	[1, 2, 3, 6, 8, 10, 1000]
+
+A set of strings:
+
+	["a", "is", "set", "this"]
+
+The "value" of these strings could be their text content, but also for example their length.
+
+#### These are not sorted sets
+
+This set violates the property of uniqueness:
+
+	[1, 1, 2, 3, 5, 8]
+
+This set violates the sorted property:
+
+	[1, 11, 2, 3]
+
+## The code
+
+We'll start by creating our internal representation for the Sorted Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep the set sorted, we need to be able to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
+
+```swift
+public struct SortedSet<T: Comparable> {
+  private var internalSet = [T]()
+
+  // Returns the number of elements in the SortedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  ...
+```
+
+Lets take a look at the `insert()` function first. This first checks if the item already exists in the collection. If so, it returns and does not insert the item.  Otherwise, it will insert the item through straightforward iteration.
+
+```swift
+  public mutating func insert(_ item: T){
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, at: i)
+        return
+      }
+    }
+
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+```
+
+As we'll see later on, checking if the item is already in the set has an efficiency of **O(log(n) + k)** where **k** is the number of items with the same value as the item we are inserting.
+
+To insert the new item, the `for` loop starts from the beginning of the array, and checks to see if each item is larger than the item we want to insert. Once we find such an item, we insert the new one into its place. This shifts the rest of the array over to the right by 1 position. This loop is at worst **O(n)**.
+
+The total performance of the `insert()` function is therefore **O(n)**.
+
+Next up is the `remove()` function:
+
+```swift
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
+    }
+  }
+```
+
+First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n)**.
+
+The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item.
+
+```swift
+  public func index(of item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+      	// see below
+      }
+    }
+    return nil
+  }
+```
+
+> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary%20Search).
+
+However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item.
+
+For example, consider this sorted set of `Player` objects. Each `Player` has a name and a number of points:
+
+	[ ("Bill", 50), ("Ada", 50), ("Jony", 50), ("Steve", 200), ("Jean-Louis", 500), ("Woz", 1000) ]
+
+We want the set to be sorted by points, from low to high. Multiple players can have the same number of points. The name of the player is not important for this ordering. However, the name *is* important for retrieving the correct item.
+
+Let's say we do `indexOf(bill)` where `bill` is player object `("Bill", 50)`. If we did a traditional binary search we'd land on index 2, which is the object `("Jony", 50)`. The value 50 matches, but it's not the object we're looking for!
+
+Therefore, we also need to check the items with the same value to the right and left of the midpoint. The code to check the left and right side looks like this:
+
+```swift
+        // Check to the right.
+        for j in mid.stride(to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+
+        // Check to the left.
+        for j in mid.stride(to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+
+        return nil
+```
+
+These loops start at the current `mid` value and then look at the neighboring values until we've found the correct object.
+
+The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for.
+
+Since the set is sorted, the following operations are all **O(1)**:
+
+```swift
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+
+  // Returns the k-th largest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+```
+
+## Examples
+
+Below are a few examples that can be found in the playground file.
+
+### Example 1
+
+Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
+
+```swift
+// Example 1 with type Int
+var mySet = SortedSet<Int>()
+
+// Insert random numbers into the set
+for _ in 0..<50 {
+  mySet.insert(randomNum(50, max: 500))
+}
+
+print(mySet)
+
+print(mySet.max())
+print(mySet.min())
+
+// Print the 5 largest values
+for k in 1...5 {
+  print(mySet.kLargest(k))
+}
+
+// Print the 5 lowest values
+for k in 1...5 {
+  print(mySet.kSmallest(k))
+}
+```
+
+### Example 2
+
+In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
+
+```swift
+public struct Player: Comparable {
+  public var name: String
+  public var points: Int
+}
+```
+
+The `Player` also gets its own `==` and `<` operators. The `<` operator is used to determine the sort order of the set, while `==` determines whether two objects are really equal.
+
+Note that `==` compares both the name and the points:  
+
+```swifr
+func ==(x: Player, y: Player) -> Bool {
+  return x.name == y.name && x.points == y.points
+}
+```
+
+But `<` only compares the points:
+
+```swift
+func <(x: Player, y: Player) -> Bool {
+  return x.points < y.points
+}
+```
+
+Therefore, two `Player`s can each have the same value (the number of points), but are not guaranteed to be equal (they can have different names).
+
+We create a new set and insert 20 random players. The `Player()` constructor gives each player a random name and score:
+
+```swift
+var playerSet = SortedSet<Player>()
+
+// Populate the set with random players.
+for _ in 0..<20 {
+  playerSet.insert(Player())
+}
+```
+
+Insert another player:
+
+```swift
+var anotherPlayer = Player()
+playerSet.insert(anotherPlayer)
+```
+
+Now we use the `indexOf()` function to find out what rank `anotherPlayer` is.
+
+```swift
+let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
+print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
+```
+
+### Example 3
+
+The final example demonstrates the need to look for the right item even after the binary search has completed.
+
+We insert 9 players into the set:
+
+```swift
+var repeatedSet = SortedSet<Player>()
+
+repeatedSet.insert(Player(name: "Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 2", points: 100))
+repeatedSet.insert(Player(name: "Player 3", points: 100))
+repeatedSet.insert(Player(name: "Player 4", points: 100))
+repeatedSet.insert(Player(name: "Player 5", points: 100))
+repeatedSet.insert(Player(name: "Player 6", points: 50))
+repeatedSet.insert(Player(name: "Player 7", points: 200))
+repeatedSet.insert(Player(name: "Player 8", points: 250))
+repeatedSet.insert(Player(name: "Player 9", points: 25))
+```
+
+Notice how several of these players have the same value of 100 points.
+
+The set looks something like this:
+
+	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+
+The next line looks for `Player 2`:
+
+```swift
+print(repeatedSet.index(of: Player(name: "Player 2", points: 100)))
+```
+
+After the binary search finishes, the value of `mid` is at index 5:
+
+	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+	                                                      mid
+
+However, this is not `Player 2`. Both `Player 4` and `Player 2` have the same points, but a different name. The binary search only looked at the points, not the name.
+
+But we do know that `Player 2` must be either to the immediate left or the right of `Player 4`, so we check both sides of `mid`. We only need to look at the objects with the same value as `Player 4`. The others are replaced by `X`:
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                                       mid
+
+The code then first checks on the right of `mid` (where the `*` is):
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                                       mid        *
+
+The right side did not contain the item, so we look at the left side:
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                              *        mid        
+	
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                    *                  mid        
+
+Finally, we've found `Player 2`, and return index 3.
+
+*Written By Zain Humayun*
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
similarity index 94%
rename from Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
rename to Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index c12dadf0f..45af5f99d 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -5,7 +5,7 @@ print("Hello, Swift 4!")
 
 //: # Example 1 with type Int
 
-var mySet = OrderedSet<Int>()
+var mySet = SortedSet<Int>()
 
 // Insert random numbers into the set
 for _ in 0..<50 {
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
similarity index 50%
rename from Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
rename to Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
index 53114d22e..dffc42643 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=21&amp;CharacterRangeLoc=371&amp;EndingColumnNumber=0&amp;EndingLineNumber=24&amp;StartingColumnNumber=1&amp;StartingLineNumber=23&amp;Timestamp=525333424.593074"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Sorted%20Set/SortedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=21&amp;CharacterRangeLoc=370&amp;EndingColumnNumber=0&amp;EndingLineNumber=24&amp;StartingColumnNumber=1&amp;StartingLineNumber=23&amp;Timestamp=532757103.131521"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=24&amp;CharacterRangeLoc=412&amp;EndingColumnNumber=0&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=25&amp;Timestamp=525333424.593234"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Sorted%20Set/SortedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=24&amp;CharacterRangeLoc=411&amp;EndingColumnNumber=0&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=25&amp;Timestamp=532757103.131695"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=25&amp;CharacterRangeLoc=511&amp;EndingColumnNumber=0&amp;EndingLineNumber=32&amp;StartingColumnNumber=3&amp;StartingLineNumber=31&amp;Timestamp=525333424.593352"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Sorted%20Set/SortedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=25&amp;CharacterRangeLoc=510&amp;EndingColumnNumber=0&amp;EndingLineNumber=32&amp;StartingColumnNumber=3&amp;StartingLineNumber=31&amp;Timestamp=532757103.131826"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
similarity index 95%
rename from Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
rename to Sorted Set/SortedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
index c30260fff..2408d35d2 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
@@ -2,7 +2,7 @@
 
 //: # Example 2 with Player objects
 
-var playerSet = OrderedSet<Player>()
+var playerSet = SortedSet<Player>()
 
 // Populate the set with random players.
 for _ in 0..<20 {
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
similarity index 95%
rename from Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
rename to Sorted Set/SortedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
index 52f154c05..63edd11d2 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
@@ -2,7 +2,7 @@
 
 //: # Example 3: multiple entries with the same value
 
-var repeatedSet = OrderedSet<Player>()
+var repeatedSet = SortedSet<Player>()
 
 repeatedSet.insert(Player(name: "Player 1", points: 100))
 repeatedSet.insert(Player(name: "Player 2", points: 100))
diff --git a/Ordered Set/OrderedSet.playground/Sources/Player.swift b/Sorted Set/SortedSet.playground/Sources/Player.swift
similarity index 95%
rename from Ordered Set/OrderedSet.playground/Sources/Player.swift
rename to Sorted Set/SortedSet.playground/Sources/Player.swift
index 26835b0a8..0960b2400 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Player.swift	
+++ b/Sorted Set/SortedSet.playground/Sources/Player.swift	
@@ -3,12 +3,12 @@
 public struct Player: Comparable {
   public var name: String
   public var points: Int
-
+  
   public init() {
     self.name = String.random()
     self.points = random(min: 0, max: 5000)
   }
-
+  
   public init(name: String, points: Int) {
     self.name = name
     self.points = points
@@ -31,7 +31,7 @@ public func print(player: Player) {
   print("Player: \(player.name) | Points: \(player.points)")
 }
 
-public func print(set: OrderedSet<Player>) {
+public func print(set: SortedSet<Player>) {
   for i in 0..<set.count {
     print(set[set.count - i - 1])
   }
diff --git a/Ordered Set/OrderedSet.playground/Sources/Random.swift b/Sorted Set/SortedSet.playground/Sources/Random.swift
similarity index 88%
rename from Ordered Set/OrderedSet.playground/Sources/Random.swift
rename to Sorted Set/SortedSet.playground/Sources/Random.swift
index eccd65df6..3f6c7536d 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Random.swift	
+++ b/Sorted Set/SortedSet.playground/Sources/Random.swift	
@@ -10,9 +10,9 @@ extension String {
   public static func random(length: Int = 8) -> String {
     let base = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     var randomString: String = ""
-
+    
     for _ in 0..<length {
-      let randomValue = arc4random_uniform(UInt32(base.characters.count))
+      let randomValue = arc4random_uniform(UInt32(base.count))
       randomString += "\(base[base.index(base.startIndex, offsetBy: Int(randomValue))])"
     }
     return randomString
diff --git a/Sorted Set/SortedSet.playground/Sources/SortedSet.swift b/Sorted Set/SortedSet.playground/Sources/SortedSet.swift
new file mode 100644
index 000000000..69546da0d
--- /dev/null
+++ b/Sorted Set/SortedSet.playground/Sources/SortedSet.swift	
@@ -0,0 +1,118 @@
+/*
+ An Sorted Set is a collection where all items in the set follow an ordering,
+ usually sorted from 'least' to 'most'. The way you value and compare items
+ can be user-defined.
+ */
+public struct SortedSet<T: Comparable> {
+  private var internalSet = [T]()
+  
+  public init() { }
+  
+  // Returns the number of elements in the SortedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  
+  // Inserts an item. Performance: O(n)
+  public mutating func insert(_ item: T) {
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+    
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, at: i)
+        return
+      }
+    }
+    
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+  
+  // Removes an item if it exists. Performance: O(n)
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
+    }
+  }
+  
+  // Returns true if and only if the item exists somewhere in the set.
+  public func exists(_ item: T) -> Bool {
+    return index(of: item) != nil
+  }
+  
+  // Returns the index of an item if it exists, or -1 otherwise.
+  public func index(of item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+    
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+      
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+        // When we get here, we've landed on an item whose value is equal to the
+        // value of the item we're looking for, but the items themselves are not
+        // equal. We need to check the items with the same value to the right
+        // and to the left in order to find an exact match.
+        
+        // Check to the right.
+        for j in stride(from: mid, to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+        
+        // Check to the left.
+        for j in stride(from: mid, to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+        return nil
+      }
+    }
+    return nil
+  }
+  
+  // Returns the item at the given index.
+  // Assertion fails if the index is out of the range of [0, count).
+  public subscript(index: Int) -> T {
+    assert(index >= 0 && index < count)
+    return internalSet[index]
+  }
+  
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+  
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+  
+  // Returns the k-th largest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+  
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+}
+
diff --git a/Sorted Set/SortedSet.playground/contents.xcplayground b/Sorted Set/SortedSet.playground/contents.xcplayground
new file mode 100644
index 000000000..18c02c912
--- /dev/null
+++ b/Sorted Set/SortedSet.playground/contents.xcplayground	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='6.0' target-platform='ios' display-mode='raw' executeOnSourceChanges='false'>
+    <pages>
+        <page name='Example 1'/>
+        <page name='Example 2'/>
+        <page name='Example 3'/>
+    </pages>
+</playground>
\ No newline at end of file
diff --git a/Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata b/Sorted Set/SortedSet.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Sorted Set/SortedSet.playground/playground.xcworkspace/contents.xcworkspacedata
diff --git a/Sorted Set/SortedSet.swift b/Sorted Set/SortedSet.swift
new file mode 100644
index 000000000..69546da0d
--- /dev/null
+++ b/Sorted Set/SortedSet.swift	
@@ -0,0 +1,118 @@
+/*
+ An Sorted Set is a collection where all items in the set follow an ordering,
+ usually sorted from 'least' to 'most'. The way you value and compare items
+ can be user-defined.
+ */
+public struct SortedSet<T: Comparable> {
+  private var internalSet = [T]()
+  
+  public init() { }
+  
+  // Returns the number of elements in the SortedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  
+  // Inserts an item. Performance: O(n)
+  public mutating func insert(_ item: T) {
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+    
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, at: i)
+        return
+      }
+    }
+    
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+  
+  // Removes an item if it exists. Performance: O(n)
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
+    }
+  }
+  
+  // Returns true if and only if the item exists somewhere in the set.
+  public func exists(_ item: T) -> Bool {
+    return index(of: item) != nil
+  }
+  
+  // Returns the index of an item if it exists, or -1 otherwise.
+  public func index(of item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+    
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+      
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+        // When we get here, we've landed on an item whose value is equal to the
+        // value of the item we're looking for, but the items themselves are not
+        // equal. We need to check the items with the same value to the right
+        // and to the left in order to find an exact match.
+        
+        // Check to the right.
+        for j in stride(from: mid, to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+        
+        // Check to the left.
+        for j in stride(from: mid, to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+        return nil
+      }
+    }
+    return nil
+  }
+  
+  // Returns the item at the given index.
+  // Assertion fails if the index is out of the range of [0, count).
+  public subscript(index: Int) -> T {
+    assert(index >= 0 && index < count)
+    return internalSet[index]
+  }
+  
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+  
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+  
+  // Returns the k-th largest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+  
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+}
+
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index fbaa4cd54..3c7134d72 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1,6 +1,19 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Workspace
    version = "1.0">
+   <Group
+      location = "container:"
+      name = "Sorted Set">
+      <FileRef
+         location = "group:Sorted Set/README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:Sorted Set/SortedSet.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Sorted Set/SortedSet.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Egg Drop Problem"
       name = "Egg Drop Problem">
@@ -1807,12 +1820,6 @@
    <Group
       location = "group:Ordered Set"
       name = "Ordered Set">
-      <FileRef
-         location = "group:AppleOrderedSet.playground">
-      </FileRef>
-      <FileRef
-         location = "group:AppleOrderedSet.swift">
-      </FileRef>
       <FileRef
          location = "group:OrderedSet.playground">
       </FileRef>

From c284df5882a11ad0c882ef32f32ac1e0759ff184 Mon Sep 17 00:00:00 2001
From: Emmanuoel Haroutunian <emmanuoel.h@gmail.com>
Date: Wed, 22 Nov 2017 23:55:30 -0800
Subject: [PATCH 1340/1679] Update README code to Swift 4

---
 Selection Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index cbcf5d352..b958da927 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -74,7 +74,7 @@ func selectionSort(_ array: [Int]) -> [Int] {
     }
 
     if x != lowest {               // 5
-      swap(&a[x], &a[lowest])
+      a.swapAt(x, lowest)
     }
   }
   return a

From ec6d34dd662eb42857d3d82197f358d4b7e64fb3 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 00:33:57 +0900
Subject: [PATCH 1341/1679] Fixed LinkedList as follows: * Modified
 node(atIndex:) method not to return nil, and code refactoring. * Deleted
 nodesBeforeAndAfter(index:) method, and modified insert methods.

---
 .../LinkedList.playground/Contents.swift      | 169 +++++++++---------
 Linked List/LinkedList.swift                  | 118 ++++++------
 Linked List/Tests/LinkedListTests.swift       |  59 +++---
 3 files changed, 166 insertions(+), 180 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index b78ee4809..559e652bb 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -42,45 +42,50 @@ public final class LinkedList<T> {
 
   /// Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
-    if var node = head {
-      while case let next? = node.next {
-        node = next
-      }
-      return node
-    } else {
+    guard let head = head else {
       return nil
     }
+    var node = head
+    while let next = node.next {
+      node = next
+    }
+    return node
   }
 
   /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
-    if var node = head {
-      var c = 1
-      while case let next? = node.next {
-        node = next
-        c += 1
-      }
-      return c
-    } else {
+    guard let head = head else {
       return 0
     }
+    var node = head
+    var count = 1
+    while let next = node.next {
+      node = next
+      count += 1
+    }
+    return count
   }
 
   /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameter index: Integer value of the node's index to be returned
   /// - Returns: Optional LinkedListNode
-  public func node(atIndex index: Int) -> Node? {
-    if index >= 0 {
-      var node = head
-      var i = index
-      while node != nil {
-        if i == 0 { return node }
-        i -= 1
-        node = node!.next
-      }
+  public func node(atIndex index: Int) -> Node {
+    assert(head != nil, "List is empty")
+    if index == 0 {
+        return head!
+    } else {
+        var node = head!.next
+        for _ in 1..<index {
+            node = node?.next
+            if node == nil {
+                break
+            }
+        }
+        
+        assert(node != nil, "index is out of bounds.")
+        return node!
     }
-    return nil
   }
 
   /// Subscript function to return the node at a specific index
@@ -88,8 +93,7 @@ public final class LinkedList<T> {
   /// - Parameter index: Integer value of the requested value's index
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
-    assert(node != nil)
-    return node!.value
+    return node.value
   }
 
   /// Append a value to the end of the list
@@ -104,7 +108,7 @@ public final class LinkedList<T> {
   ///
   /// - Parameter node: The node containing the value to be appended
   public func append(_ node: Node) {
-    let newNode = LinkedListNode(value: node.value)
+    let newNode = node
     if let lastNode = last {
       newNode.previous = lastNode
       lastNode.next = newNode
@@ -124,27 +128,6 @@ public final class LinkedList<T> {
     }
   }
 
-  /// A private helper funciton to find the nodes before and after a specified index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameter index: Integer value of the index between the nodes.
-  /// - Returns: A tuple of 2 nodes before & after the specified index respectively.
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-    assert(index >= 0)
-
-    var i = index
-    var next = head
-    var prev: Node?
-
-    while next != nil && i > 0 {
-      i -= 1
-      prev = next
-      next = next!.next
-    }
-    assert(i == 0)  // if > 0, then specified index was too large
-
-    return (prev, next)
-  }
-
   /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -161,18 +144,20 @@ public final class LinkedList<T> {
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
   public func insert(_ node: Node, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index: index)
     let newNode = LinkedListNode(value: node.value)
-    newNode.previous = prev
-    newNode.next = next
-    prev?.next = newNode
-    next?.previous = newNode
-
-    if prev == nil {
+    if index == 0 {
+      newNode.next = head
+      head?.previous = newNode
       head = newNode
+    } else {
+      let separator = self.node(atIndex: index-1)
+      newNode.previous = separator
+      newNode.next = separator.next
+      separator.next?.previous = newNode
+      separator.next = newNode
     }
   }
-
+    
   /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -180,22 +165,21 @@ public final class LinkedList<T> {
   ///   - index: Integer value of the index to be inserted at
   public func insert(_ list: LinkedList, atIndex index: Int) {
     if list.isEmpty { return }
-    var (prev, next) = nodesBeforeAndAfter(index: index)
-    var nodeToCopy = list.head
-    var newNode: Node?
-    while let node = nodeToCopy {
-      newNode = Node(value: node.value)
-      newNode?.previous = prev
-      if let previous = prev {
-        previous.next = newNode
-      } else {
-        self.head = newNode
-      }
-      nodeToCopy = nodeToCopy?.next
-      prev = newNode
+    
+    if index == 0 {
+      let temp = head
+      head = list.head
+      list.last?.next = temp
+    } else {
+      let separate = self.node(atIndex: index-1)
+      let temp = separate.next
+
+      separate.next = list.head
+      list.head?.previous = separate
+
+      list.last?.next = temp
+      temp?.previous = list.last?.next
     }
-    prev?.next = next
-    next?.previous = prev
   }
 
   /// Function to remove all nodes/value from the list
@@ -237,8 +221,7 @@ public final class LinkedList<T> {
   /// - Returns: The data value contained in the deleted node
   @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
-    assert(node != nil)
-    return remove(node: node!)
+    return remove(node: node)
   }
 }
 
@@ -324,7 +307,7 @@ list.first                    // nil
 list.last                     // nil
 
 list.append("Hello")
-list.isEmpty
+list.isEmpty                  // false
 list.first!.value             // "Hello"
 list.last!.value              // "Hello"
 list.count                    // 1
@@ -339,9 +322,9 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.node(atIndex: 0)!.value    // "Hello"
-list.node(atIndex: 1)!.value    // "World"
-list.node(atIndex: 2)           // nil
+list.node(atIndex: 0).value    // "Hello"
+list.node(atIndex: 1).value    // "World"
+//list.node(atIndex: 2)           // crash!
 
 list[0]     // "Hello"
 list[1]     // "World"
@@ -364,11 +347,11 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.node(atIndex: 0)!.value = "Universe"
-list.node(atIndex: 1)!.value = "Swifty"
-let m = list.map { s in s.characters.count }
+list.node(atIndex: 0).value = "Universe"
+list.node(atIndex: 1).value = "Swifty"
+let m = list.map { s in s.count }
 m    // [8, 6, 5]
-let f = list.filter { s in s.characters.count > 5 }
+let f = list.filter { s in s.count > 5 }
 f    // [Universe, Swifty]
 
 list.remove(node: list.first!) // "Universe"
@@ -376,13 +359,37 @@ list.count                     // 2
 list[0]                        // "Swifty"
 list[1]                        // "Hello"
 
+list.count                     // 2
 list.removeLast()              // "Hello"
+list.head?.value
 list.count                     // 1
 list[0]                        // "Swifty"
 
 list.remove(atIndex: 0)        // "Swifty"
 list.count                     // 0
 
+let list3 = LinkedList<String>()
+list3.insert("2", atIndex: 0) // [2]
+list3.count                   // 1
+list3.insert("4", atIndex: 1) // [2,4]
+list3.count                   // 2
+list3.insert("5", atIndex: 2) // [2,4,5]
+list3.count                   // 3
+list3.insert("3", atIndex: 1) // [2,3,4,5]
+list3.insert("1", atIndex: 0) // [1,2,3,4,5]
+
+let list4 = LinkedList<String>()
+list4.insert(list3, atIndex: 0) // [1,2,3,4,5]
+list4.count                     // 5
+
+let list5 = LinkedList<String>()
+list5.append("0")                // [0]
+list5.insert("End", atIndex:1)   // [0,End]
+list5.count                      // 2
+list5.insert(list4, atIndex: 1)  // [0,1,2,3,4,5,End]
+list5.count                      // 7
+
+
 let linkedList: LinkedList<Int> = [1, 2, 3, 4] // [1, 2, 3, 4]
 linkedList.count               // 4
 linkedList[0]                  // 1
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index a5594eb31..cef6670de 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -36,35 +36,40 @@ public final class LinkedList<T> {
     }
 
     public var count: Int {
-        if var node = head {
-            var c = 1
-            while let next = node.next {
-                node = next
-                c += 1
-            }
-            return c
-        } else {
+        guard let head = head else {
             return 0
         }
-    }
-
-    public func node(atIndex index: Int) -> Node? {
-        if index >= 0 {
-            var node = head
-            var i = index
-            while node != nil {
-                if i == 0 { return node }
-                i -= 1
-                node = node!.next
+        var node = head
+        var count = 1
+        while let next = node.next {
+            node = next
+            count += 1
+        }
+        return count
+    }
+    
+    public func node(atIndex index: Int) -> Node {
+        assert(head != nil, "List is empty")
+        assert(index >= 0, "index must be greater than 0")
+        if index == 0 {
+            return head!
+        } else {
+            var node = head!.next
+            for _ in 1..<index {
+                node = node?.next
+                if node == nil {
+                    break
+                }
             }
+            
+            assert(node != nil, "index is out of bounds.")
+            return node!
         }
-        return nil
     }
 
     public subscript(index: Int) -> T {
         let node = self.node(atIndex: index)
-        assert(node != nil)
-        return node!.value
+        return node.value
     }
 
     public func append(_ value: T) {
@@ -73,7 +78,7 @@ public final class LinkedList<T> {
     }
 
     public func append(_ node: Node) {
-        let newNode = LinkedListNode(value: node.value)
+        let newNode = node
         if let lastNode = last {
             newNode.previous = lastNode
             lastNode.next = newNode
@@ -90,61 +95,45 @@ public final class LinkedList<T> {
         }
     }
 
-    private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-        assert(index >= 0)
-
-        var i = index
-        var next = head
-        var prev: Node?
-
-        while next != nil && i > 0 {
-            i -= 1
-            prev = next
-            next = next!.next
-        }
-        assert(i == 0)  // if > 0, then specified index was too large
-
-        return (prev, next)
-    }
-
     public func insert(_ value: T, atIndex index: Int) {
         let newNode = Node(value: value)
         self.insert(newNode, atIndex: index)
     }
 
     public func insert(_ node: Node, atIndex index: Int) {
-        let (prev, next) = nodesBeforeAndAfter(index: index)
         let newNode = LinkedListNode(value: node.value)
-        newNode.previous = prev
-        newNode.next = next
-        prev?.next = newNode
-        next?.previous = newNode
-
-        if prev == nil {
+        if index == 0 {
+            newNode.next = head
+            head?.previous = newNode
             head = newNode
+        } else {
+            let separator = self.node(atIndex: index-1)
+            newNode.previous = separator
+            newNode.next = separator.next
+            separator.next?.previous = newNode
+            separator.next = newNode
         }
     }
-
+    
     public func insert(_ list: LinkedList, atIndex index: Int) {
         if list.isEmpty { return }
-        var (prev, next) = nodesBeforeAndAfter(index: index)
-        var nodeToCopy = list.head
-        var newNode: Node?
-        while let node = nodeToCopy {
-            newNode = Node(value: node.value)
-            newNode?.previous = prev
-            if let previous = prev {
-                previous.next = newNode
-            } else {
-                self.head = newNode
-            }
-            nodeToCopy = nodeToCopy?.next
-            prev = newNode
+        
+        if index == 0 {
+            let temp = head
+            head = list.head
+            list.last?.next = temp
+        } else {
+            let separate = self.node(atIndex: index-1)
+            let temp = separate.next
+            
+            separate.next = list.head
+            list.head?.previous = separate
+            
+            list.last?.next = temp
+            temp?.previous = list.last?.next
         }
-        prev?.next = next
-        next?.previous = prev
     }
-
+    
     public func removeAll() {
         head = nil
     }
@@ -172,8 +161,7 @@ public final class LinkedList<T> {
 
     @discardableResult public func remove(atIndex index: Int) -> T {
         let node = self.node(atIndex: index)
-        assert(node != nil)
-        return remove(node: node!)
+        return remove(node: node)
     }
 }
 
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 0b2b116df..5bc27b23d 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -93,19 +93,13 @@ class LinkedListTest: XCTestCase {
     XCTAssertNil(list.last!.next)
   }
 
-  func testNodeAtIndexInEmptyList() {
-    let list = LinkedList<Int>()
-    let node = list.node(atIndex: 0)
-    XCTAssertNil(node)
-  }
-
   func testNodeAtIndexInListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)
 
     let node = list.node(atIndex: 0)
     XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 123)
+    XCTAssertEqual(node.value, 123)
     XCTAssertTrue(node === list.first)
   }
 
@@ -115,23 +109,20 @@ class LinkedListTest: XCTestCase {
     let nodeCount = list.count
     XCTAssertEqual(nodeCount, numbers.count)
 
-    XCTAssertNil(list.node(atIndex: -1))
-    XCTAssertNil(list.node(atIndex: nodeCount))
-
     let first = list.node(atIndex: 0)
     XCTAssertNotNil(first)
     XCTAssertTrue(first === list.first)
-    XCTAssertEqual(first!.value, numbers[0])
+    XCTAssertEqual(first.value, numbers[0])
 
     let last = list.node(atIndex: nodeCount - 1)
     XCTAssertNotNil(last)
     XCTAssertTrue(last === list.last)
-    XCTAssertEqual(last!.value, numbers[nodeCount - 1])
+    XCTAssertEqual(last.value, numbers[nodeCount - 1])
 
     for i in 0..<nodeCount {
       let node = list.node(atIndex: i)
       XCTAssertNotNil(node)
-      XCTAssertEqual(node!.value, numbers[i])
+      XCTAssertEqual(node.value, numbers[i])
     }
   }
 
@@ -151,7 +142,7 @@ class LinkedListTest: XCTestCase {
 
     let node = list.node(atIndex: 0)
     XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 123)
+    XCTAssertEqual(node.value, 123)
   }
 
   func testInsertAtIndex() {
@@ -164,13 +155,13 @@ class LinkedListTest: XCTestCase {
 
     let node = list.node(atIndex: 3)
     XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 444)
+    XCTAssertEqual(node.value, 444)
     XCTAssertEqual(nodeCount + 1, list.count)
 
     XCTAssertFalse(prev === node)
     XCTAssertFalse(next === node)
-    XCTAssertTrue(prev!.next === node)
-    XCTAssertTrue(next!.previous === node)
+    XCTAssertTrue(prev.next === node)
+    XCTAssertTrue(next.previous === node)
   }
 
   func testInsertListAtIndex() {
@@ -180,10 +171,10 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.insert(list2, atIndex: 2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 1)?.value, 2)
-    XCTAssertEqual(list.node(atIndex: 2)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 3)?.value, 102)
-    XCTAssertEqual(list.node(atIndex: 4)?.value, 10)
+    XCTAssertEqual(list.node(atIndex: 1).value, 2)
+    XCTAssertEqual(list.node(atIndex: 2).value, 99)
+    XCTAssertEqual(list.node(atIndex: 3).value, 102)
+    XCTAssertEqual(list.node(atIndex: 4).value, 10)
   }
 
   func testInsertListAtFirstIndex() {
@@ -193,9 +184,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.insert(list2, atIndex: 0)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 0)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 1)?.value, 102)
-    XCTAssertEqual(list.node(atIndex: 2)?.value, 8)
+    XCTAssertEqual(list.node(atIndex: 0).value, 99)
+    XCTAssertEqual(list.node(atIndex: 1).value, 102)
+    XCTAssertEqual(list.node(atIndex: 2).value, 8)
   }
 
   func testInsertListAtLastIndex() {
@@ -205,9 +196,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.insert(list2, atIndex: list.count)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5)?.value, 5)
-    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
+    XCTAssertEqual(list.node(atIndex: 5).value, 5)
+    XCTAssertEqual(list.node(atIndex: 6).value, 99)
+    XCTAssertEqual(list.node(atIndex: 7).value, 102)
   }
 
   func testAppendList() {
@@ -217,9 +208,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.append(list2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5)?.value, 5)
-    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
+    XCTAssertEqual(list.node(atIndex: 5).value, 5)
+    XCTAssertEqual(list.node(atIndex: 6).value, 99)
+    XCTAssertEqual(list.node(atIndex: 7).value, 102)
   }
 
   func testAppendListToEmptyList() {
@@ -229,8 +220,8 @@ class LinkedListTest: XCTestCase {
     list2.append(10)
     list.append(list2)
     XCTAssertTrue(list.count == 2)
-    XCTAssertEqual(list.node(atIndex: 0)?.value, 5)
-    XCTAssertEqual(list.node(atIndex: 1)?.value, 10)
+    XCTAssertEqual(list.node(atIndex: 0).value, 5)
+    XCTAssertEqual(list.node(atIndex: 1).value, 10)
   }
 
   func testRemoveAtIndexOnListWithOneElement() {
@@ -259,8 +250,8 @@ class LinkedListTest: XCTestCase {
 
     let node = list.node(atIndex: 3)
     XCTAssertTrue(next === node)
-    XCTAssertTrue(prev!.next === node)
-    XCTAssertTrue(node!.previous === prev)
+    XCTAssertTrue(prev.next === node)
+    XCTAssertTrue(node.previous === prev)
     XCTAssertEqual(nodeCount, list.count)
   }
 

From dc810d2a08c7f2d619a43626b1e9883e897f6f16 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 11:39:40 +0900
Subject: [PATCH 1342/1679] Modified last and count method after review.

---
 Linked List/LinkedList.playground/Contents.swift |  8 ++++----
 Linked List/LinkedList.swift                     | 16 ++++++++--------
 2 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 559e652bb..167e55b56 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -42,10 +42,10 @@ public final class LinkedList<T> {
 
   /// Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
-    guard let head = head else {
+    guard var node = head else {
       return nil
     }
-    var node = head
+    
     while let next = node.next {
       node = next
     }
@@ -54,10 +54,10 @@ public final class LinkedList<T> {
 
   /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
-    guard let head = head else {
+    guard var node = head else {
       return 0
     }
-    var node = head
+    
     var count = 1
     while let next = node.next {
       node = next
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index cef6670de..e29bee86b 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -25,21 +25,21 @@ public final class LinkedList<T> {
     }
 
     public var last: Node? {
-        if var node = head {
-            while let next = node.next {
-                node = next
-            }
-            return node
-        } else {
+        guard var node = head else {
             return nil
         }
+        
+        while let next = node.next {
+            node = next
+        }
+        return node
     }
 
     public var count: Int {
-        guard let head = head else {
+        guard var node = head else {
             return 0
         }
-        var node = head
+        
         var count = 1
         while let next = node.next {
             node = next

From 71ae5a3bfb18cba13314593cad2a5da8d0906873 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 11:57:13 +0900
Subject: [PATCH 1343/1679] Renamed variables in insert methods and code
 refactoring.

---
 .../LinkedList.playground/Contents.swift      | 20 +++++++++----------
 Linked List/LinkedList.swift                  | 20 +++++++++----------
 2 files changed, 20 insertions(+), 20 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 167e55b56..f8216fc6f 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -144,17 +144,17 @@ public final class LinkedList<T> {
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
   public func insert(_ node: Node, atIndex index: Int) {
-    let newNode = LinkedListNode(value: node.value)
+    let newNode = node
     if index == 0 {
       newNode.next = head
       head?.previous = newNode
       head = newNode
     } else {
-      let separator = self.node(atIndex: index-1)
-      newNode.previous = separator
-      newNode.next = separator.next
-      separator.next?.previous = newNode
-      separator.next = newNode
+      let prev = self.node(atIndex: index-1)
+      newNode.previous = prev
+      newNode.next = prev.next
+      prev.next?.previous = newNode
+      prev.next = newNode
     }
   }
     
@@ -171,11 +171,11 @@ public final class LinkedList<T> {
       head = list.head
       list.last?.next = temp
     } else {
-      let separate = self.node(atIndex: index-1)
-      let temp = separate.next
+      let prev = self.node(atIndex: index-1)
+      let temp = prev.next
 
-      separate.next = list.head
-      list.head?.previous = separate
+      prev.next = list.head
+      list.head?.previous = prev
 
       list.last?.next = temp
       temp?.previous = list.last?.next
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index e29bee86b..c0331bc0e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -101,17 +101,17 @@ public final class LinkedList<T> {
     }
 
     public func insert(_ node: Node, atIndex index: Int) {
-        let newNode = LinkedListNode(value: node.value)
+        let newNode = node
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let separator = self.node(atIndex: index-1)
-            newNode.previous = separator
-            newNode.next = separator.next
-            separator.next?.previous = newNode
-            separator.next = newNode
+            let prev = self.node(atIndex: index-1)
+            newNode.previous = prev
+            newNode.next = prev.next
+            prev.next?.previous = newNode
+            prev.next = newNode
         }
     }
     
@@ -123,11 +123,11 @@ public final class LinkedList<T> {
             head = list.head
             list.last?.next = temp
         } else {
-            let separate = self.node(atIndex: index-1)
-            let temp = separate.next
+            let prev = self.node(atIndex: index-1)
+            let temp = prev.next
             
-            separate.next = list.head
-            list.head?.previous = separate
+            prev.next = list.head
+            list.head?.previous = prev
             
             list.last?.next = temp
             temp?.previous = list.last?.next

From bd7e4b1ef7a3d0c787aa74e06bc54750cf140805 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 12:09:43 +0900
Subject: [PATCH 1344/1679] Fixed node(atIndex:) method to be the same in
 LinkedList.swift file.

---
 Linked List/LinkedList.playground/Contents.swift | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index f8216fc6f..af27f63a0 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -72,6 +72,8 @@ public final class LinkedList<T> {
   /// - Returns: Optional LinkedListNode
   public func node(atIndex index: Int) -> Node {
     assert(head != nil, "List is empty")
+    assert(index >= 0, "index must be greater than 0")
+    
     if index == 0 {
         return head!
     } else {

From b68e1fd411e8698c5de39bccb240fd6649acd3f7 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:12:52 +0500
Subject: [PATCH 1345/1679] Fix a few typos in QuadTree/README.md

Quadrees -> Quadtrees
containts -> contains
Wiki -> Wikipedia

Also my editor automatically removed trailing spaces from empty lines
---
 QuadTree/README.md | 33 ++++++++++++++++-----------------
 1 file changed, 16 insertions(+), 17 deletions(-)

diff --git a/QuadTree/README.md b/QuadTree/README.md
index ff71a66f0..ff660f852 100644
--- a/QuadTree/README.md
+++ b/QuadTree/README.md
@@ -6,11 +6,11 @@ A quadtree is a [tree](https://github.com/raywenderlich/swift-algorithm-club/tre
 
 ### Problem
 
-Consider the following problem: your need to store a number of points (each point is a pair of `X` and `Y` coordinates) and then you need to answer which points lie in a certain rectangular region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though. 
+Consider the following problem: your need to store a number of points (each point is a pair of `X` and `Y` coordinates) and then you need to answer which points lie in a certain rectangular region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though.
 
 ### A Better Approach
 
-Quadrees are most commonly used to partition a two-dimensional space by recursively subdividing it into four regions(quadrants). Let's see how we can use a Quadtree to store the points.
+Quadtrees are most commonly used to partition a two-dimensional space by recursively subdividing it into four regions(quadrants). Let's see how we can use a Quadtree to store the points.
 
 Each node in the tree represents a rectangular region and stores a limited number(`maxPointCapacity`) of points that all lie in its region.
 
@@ -40,7 +40,7 @@ class QuadTreeNode {
   init(rect: Rect) {
     self.rect = rect
   }
-  
+
   ...
 }
 
@@ -52,11 +52,11 @@ extension QuadTreeNode {
 
   @discardableResult
   func add(point: Point) -> Bool {
-    
-    if !rect.containts(point: point) {
+
+    if !rect.contains(point: point) {
       return false
     }
-    
+
     switch type {
     case .internal(let children):
       // pass the point to one of the children
@@ -75,7 +75,7 @@ extension QuadTreeNode {
     }
     return true
   }
-  
+
   private func subdivide() {
     switch type {
     case .leaf:
@@ -105,9 +105,9 @@ To find the points that lie in a given region we can now traverse the tree from
 class QuadTree {
 
   ...
-  
+
   let root: QuadTreeNode
-  
+
    public func points(inRect rect: Rect) -> [Point] {
     return root.points(inRect: rect)
   }
@@ -115,23 +115,23 @@ class QuadTree {
 
 extension QuadTreeNode {
   func points(inRect rect: Rect) -> [Point] {
-    
+
     // if the node's rect and the given rect don't intersect, return an empty array,
     // because there can't be any points that lie the node's (or its children's) rect and
     // in the given rect
     if !self.rect.intersects(rect: rect) {
       return []
     }
-    
+
     var result: [Point] = []
-    
+
     // collect the node's points that lie in the rect
     for point in points {
-      if rect.containts(point: point) {
+      if rect.contains(point: point) {
         result.append(point)
       }
     }
-    
+
     switch type {
     case .leaf:
       break
@@ -141,7 +141,7 @@ extension QuadTreeNode {
         result.append(contentsOf: childNode.points(inRect: rect))
       }
     }
-    
+
     return result
   }
 }
@@ -154,7 +154,6 @@ Both adding a point and searching can still take up to O(n) in the worst case, s
 
 Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Article](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
 
-More info on [Wiki](https://en.wikipedia.org/wiki/Quadtree)
+More info on [Wikipedia](https://en.wikipedia.org/wiki/Quadtree)
 
 *Written for Swift Algorithm Club by Timur Galimov*
-

From fcf235ce42ae0bc281e78b48a79fa6e5174b2109 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:27:27 +0500
Subject: [PATCH 1346/1679] Fix typos

alogrithm -> algorithm
collison -> collison

Also added a "to" to improved grammar and added newline to the file
---
 Rabin-Karp/README.markdown | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Rabin-Karp/README.markdown b/Rabin-Karp/README.markdown
index 79699caa8..4470c7f75 100644
--- a/Rabin-Karp/README.markdown
+++ b/Rabin-Karp/README.markdown
@@ -1,6 +1,6 @@
 # Rabin-Karp string search algorithm
 
-The Rabin-Karp string search alogrithm is used to search text for a pattern.
+The Rabin-Karp string search algorithm is used to search text for a pattern.
 
 A practical application of the algorithm is detecting plagiarism. Given source material, the algorithm can rapidly search through a paper for instances of sentences from the source material, ignoring details such as case and punctuation. Because of the abundance of the sought strings, single-string searching algorithms are impractical.
 
@@ -12,10 +12,10 @@ at a time (e.g. "he ") and subtracts out the previous hash from the "T".
 
 ## Algorithm
 
-The Rabin-Karp alogrithm uses a sliding window the size of the search pattern.  It starts by hashing the search pattern, then
+The Rabin-Karp algorithm uses a sliding window the size of the search pattern.  It starts by hashing the search pattern, then
 hashing the first x characters of the text string where x is the length of the search pattern.  It then slides the window one character over and uses
 the previous hash value to calculate the new hash faster.  Only when it finds a hash that matches the hash of the search pattern will it compare
-the two strings it see if they are the same (prevent a hash collision from producing a false positive)
+the two strings it see if they are the same (to prevent a hash collision from producing a false positive).
 
 ## The code
 
@@ -37,7 +37,7 @@ public func search(text: String , pattern: String) -> Int {
     let firstHash = hash(array: firstChars)
 
     if (patternHash == firstHash) {
-        // Verify this was not a hash collison
+        // Verify this was not a hash collision
         if firstChars == patternArray {
             return 0
         }
@@ -76,4 +76,4 @@ This will return 13 since ump is in the 13 position of the zero based string.
 [Rabin-Karp Wikipedia](https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm)
 
 
-*Written by [Bill Barbour](https://github.com/brbatwork)*
\ No newline at end of file
+*Written by [Bill Barbour](https://github.com/brbatwork)*

From 7e75d1086ee7c0dbac5ee2096eb294ef14c30324 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:27:47 +0500
Subject: [PATCH 1347/1679] Fix warning: 'characters' is deprecated: Please use
 String or Substring directly

---
 Rabin-Karp/README.markdown                      | 4 ++--
 Rabin-Karp/Rabin-Karp.playground/Contents.swift | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Rabin-Karp/README.markdown b/Rabin-Karp/README.markdown
index 4470c7f75..a618d3981 100644
--- a/Rabin-Karp/README.markdown
+++ b/Rabin-Karp/README.markdown
@@ -24,8 +24,8 @@ The major search method is next.  More implementation details are in rabin-karp.
 ```swift
 public func search(text: String , pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.characters.flatMap { $0.asInt }
-    let textArray = text.characters.flatMap { $0.asInt }
+    let patternArray = pattern.flatMap { $0.asInt }
+    let textArray = text.flatMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1
diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index c0a99339a..739b74e2a 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -30,8 +30,8 @@ extension Character {
 // Find first position of pattern in the text using Rabin Karp algorithm
 public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.characters.flatMap { $0.asInt }
-    let textArray = text.characters.flatMap { $0.asInt }
+    let patternArray = pattern.flatMap { $0.asInt }
+    let textArray = text.flatMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1

From 885d9d3d650296e15fa8b12eba734c36afb9069a Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:48:57 +0500
Subject: [PATCH 1348/1679] Fix warning: Result of call to 'addNode' is unused

---
 .../DepthFirstSearch.playground/Sources/Graph.swift              | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index 34ee2fa3a..48b8feed5 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -5,6 +5,7 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
   
+  @discardableResult
   public func addNode(_ label: String) -> Node {
     let node = Node(label)
     nodes.append(node)

From 0b129e8894ec9699f5ebee60c2bcddddc256b770 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Tue, 28 Nov 2017 00:56:30 +0900
Subject: [PATCH 1349/1679] Modified readme file in LinkedList.

---
 Linked List/README.markdown | 227 ++++++++++++++++++++----------------
 1 file changed, 124 insertions(+), 103 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 2e1f03ece..55b61e910 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -110,14 +110,14 @@ Let's also add a property that gives you the last node in the list. This is wher
 
 ```swift
   public var last: Node? {
-    if var node = head {
-      while let next = node.next {
-        node = next
-      }
-      return node
-    } else {
+    guard var node = head else {
       return nil
     }
+  
+    while let next = node.next {
+      node = next
+    }
+    return node
   }
 ```
 
@@ -198,16 +198,16 @@ Let's add a method to count how many nodes are in the list. This will look very
 
 ```swift
   public var count: Int {
-    if var node = head {
-      var c = 1
-      while let next = node.next {
-        node = next
-        c += 1
-      }
-      return c
-    } else {
+    guard var node = head else {
       return 0
     }
+  
+    var count = 1
+    while let next = node.next {
+      node = next
+      count += 1
+    }
+    return count
   }
 ```
 
@@ -218,37 +218,43 @@ It loops through the list in the same manner but this time increments a counter
 What if we wanted to find the node at a specific index in the list? With an array we can just write `array[index]` and it's an **O(1)** operation. It's a bit more involved with linked lists, but again the code follows a similar pattern:
 
 ```swift
-  public func nodeAt(_ index: Int) -> Node? {
-    if index >= 0 {
-      var node = head
-      var i = index
-      while node != nil {
-        if i == 0 { return node }
-        i -= 1
-        node = node!.next
+  public func node(atIndex index: Int) -> Node {
+    if index == 0 {
+      return head!
+    } else {
+      var node = head!.next
+      for _ in 1..<index {
+        node = node?.next
+        if node == nil { //(*1)
+          break
+        }
       }
+      return node!
     }
-    return nil
   }
 ```
 
-The loop looks a little different but it does the same thing: it starts at `head` and then keeps following the `node.next` pointers to step through the list. We're done when we've seen `index` nodes, i.e. when the counter has reached 0.
+First we check whether the given index is 0 or not. Because if it is 0, it returns the head as it is.
+However, when the given index is greater than 0, it starts at head then keeps following the node.next pointers to step through the list.
+The difference from count method at this time is that there are two termination conditions.
+One is when the for-loop statement reaches index, and we were able to acquire the node of the given index.
+The second is when `node.next` in for-loop statement returns nil and cause break. (*1)
+This means that the given index is out of bounds and it causes a crash.
 
 Try it out:
 
 ```swift
 list.nodeAt(0)!.value    // "Hello"
 list.nodeAt(1)!.value    // "World"
-list.nodeAt(2)           // nil
+// list.nodeAt(2)           // crash
 ```
 
 For fun we can implement a `subscript` method too:
 
 ```swift
   public subscript(index: Int) -> T {
-    let node = nodeAt(index)
-    assert(node != nil)
-    return node!.value
+    let node = node(atIndex: index)
+    return node.value
   }
 ```
 
@@ -264,84 +270,100 @@ It crashes on `list[2]` because there is no node at that index.
 
 So far we've written code to add new nodes to the end of the list, but that's slow because you need to find the end of the list first. (It would be fast if we used a tail pointer.) For this reason, if the order of the items in the list doesn't matter, you should insert at the front of the list instead. That's always an **O(1)** operation.
 
-Let's write a method that lets you insert a new node at any index in the list. First, we'll define a helper function:
-
-```swift
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-    assert(index >= 0)
-
-    var i = index
-    var next = head
-    var prev: Node?
-
-    while next != nil && i > 0 {
-      i -= 1
-      prev = next
-      next = next!.next
-    }
-    assert(i == 0)
-
-    return (prev, next)
-  }
-```
-
-This returns a tuple containing the node currently at the specified index and the node that immediately precedes it, if any. The loop is very similar to `nodeAtIndex()`, except that here we also keep track of what the previous node is as we iterate through the list.
-
-Let's look at an example. Suppose we have the following list:
 
-	head --> A --> B --> C --> D --> E --> nil
-
-We want to find the nodes before and after index 3. As we start the loop, `i = 3`, `next` points at `"A"`, and `prev` is nil.
-
-	head --> A --> B --> C --> D --> E --> nil
-	        next
-
-We decrement `i`, make `prev` point to `"A"`, and move `next` to the next node, `"B"`:
-
-	head --> A --> B --> C --> D --> E --> F --> nil
-	        prev  next
-
-Again, we decrement `i` and update the pointers. Now `prev` points to `"B"`, and `next` points to `"C"`:
-
-	head --> A --> B --> C --> D --> E --> F --> nil
-	              prev  next
-
-As you can see, `prev` always follows one behind `next`. We do this one more time and then `i` equals 0 and we exit the loop:
-
-	head --> A --> B --> C --> D --> E --> F --> nil
-	                    prev  next
-
-The `assert()` after the loop checks whether there really were enough nodes in the list. If `i > 0` at this point, then the specified index was too large.
-
-> **Note:** If any of the loops in this article don't make much sense to you, then draw a linked list on a piece of paper and step through the loop by hand, just like what we did here.
-
-For this example, the function returns `("C", "D")` because `"D"` is the node at index 3 and `"C"` is the one right before that.
-
-Now that we have this helper function, we can write the method for inserting nodes:
+Let's write a method that lets you insert a new node at any index in the list.
 
 ```swift
-  public func insert(value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index)     // 1
-
-    let newNode = Node(value: value)    // 2
-    newNode.previous = prev
-    newNode.next = next
-    prev?.next = newNode
-    next?.previous = newNode
-
-    if prev == nil {                    // 3
-      head = newNode
-    }
-  }
+  public func insert(_ node: Node, atIndex index: Int) {
+   let newNode = node
+   if index == 0 {
+     newNode.next = head                      
+     head?.previous = newNode
+     head = newNode
+   } else {
+     let prev = self.node(atIndex: index-1)
+     let next = prev.next
+
+     newNode.previous = prev
+     newNode.next = prev.next
+     prev.next = newNode
+     next?.previous = newNode
+   }
+}
 ```
 
-Some remarks about this method:
-
-1. First, we need to find where to insert this node. After calling the helper method, `prev` points to the previous node and `next` is the node currently at the given index. We'll insert the new node in between these two. Note that `prev` can be nil (index is 0), `next` can be nil (index equals size of the list), or both can be nil if the list is empty.
+As with node(atIndex :) method, insert(_: at:) method also branches depending on whether the given index is 0 or not.
+First let's look at the former case. Suppose we have the following list and the new node(C).
+
+             +---------+     +---------+
+    head --->|         |---->|         |-----//----->
+             |    A    |     |    B    |
+     nil <---|         |<----|         |<----//------
+             +---------+     +---------+ 
+                 [0]             [1]
+                  
+                  
+             +---------+ 
+     new --->|         |----> nil
+             |    C    |
+             |         |
+             +---------+
+    
+Now put the new node before the first node. In this way: 
+
+    new.next = head
+    head.previous = new
+    
+             +---------+            +---------+     +---------+
+     new --->|         |--> head -->|         |---->|         |-----//----->
+             |    C    |            |    A    |     |    B    |
+             |         |<-----------|         |<----|         |<----//------
+             +---------+            +---------+     +---------+ 
+
+
+Finally, replace the head with the new node.
+
+    head = new
+    
+             +---------+    +---------+     +---------+
+    head --->|         |--->|         |---->|         |-----//----->
+             |    C    |    |    A    |     |    B    |
+     nil <---|         |<---|         |<----|         |<----//------
+             +---------+    +---------+     +---------+ 
+                 [0]            [1]
+
+
+However, when the given index is greater than 0, it is necessary to get the node previous and next index and insert between them.
+You can also obtain the previous and next node using node(atIndex:) as follows:
+
+             +---------+         +---------+     +---------+    
+    head --->|         |---//--->|         |---->|         |----
+             |    0    |         |    A    |     |    B    |    
+     nil <---|         |---//<---|         |<----|         |<---
+             +---------+         +---------+     +---------+    
+                                  [index-1]        [index]      
+                                      ^               ^ 
+                                      |               | 
+                                     prev            next
+    
+    prev = node(at: index-1)
+    next = prev.next
+
+Now insert new node between the prev and the next.
+
+    new.prev = prev; prev.next = new  // connect prev and new.
+    new.next = next; next.prev = new  // connect new and next.
+
+             +---------+         +---------+     +---------+     +---------+
+    head --->|         |---//--->|         |---->|         |---->|         |
+             |    0    |         |    A    |     |    C    |     |    B    |
+     nil <---|         |---//<---|         |<----|         |<----|         |
+             +---------+         +---------+     +---------+     +---------+
+                                  [index-1]        [index]        [index+1]
+                                      ^               ^               ^
+                                      |               |               |
+                                     prev            new             next
 
-2. Create the new node and connect the `previous` and `next` pointers. Because the local `prev` and `next` variables are optionals and may be nil, so we use optional chaining here.
-
-3. If the new node is being inserted at the front of the list, we need to update the `head` pointer. (Note: If the list had a tail pointer, you'd also need to update that pointer here if `next == nil`, because that means the last element has changed.)
 
 Try it out:
 
@@ -353,8 +375,7 @@ list[2]     // "World"
 ```
 
 Also try adding new nodes to the front and back of the list, to verify that this works properly.
-
-> **Note:** The `nodesBeforeAndAfter()` and `insert(atIndex)` functions can also be used with a singly linked list because we don't depend on the node's `previous` pointer to find the previous element.
+> **Note:** The `node(atIndex:)` and `insert(_: atIndex:)` functions can also be used with a singly linked list because we don't depend on the node's `previous` pointer to find the previous element.
 
 What else do we need? Removing nodes, of course! First we'll do `removeAll()`, which is really simple:
 
@@ -515,7 +536,7 @@ And here's filter:
 And a silly example:
 
 ```swift
-let f = list.filter { s in s.characters.count > 5 }
+let f = list.filter { s in s.count > 5 }
 f    // [Universe, Swifty]
 ```
 

From 3de5a1bfc49f9019badd6ba32fa23b0452e30d71 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Wed, 29 Nov 2017 13:12:47 +0900
Subject: [PATCH 1350/1679] Fixed insert method and some related files.

---
 .../LinkedList.playground/Contents.swift      | 21 +++++++++----------
 Linked List/LinkedList.swift                  | 19 ++++++++---------
 Linked List/README.markdown                   | 10 ++++-----
 3 files changed, 24 insertions(+), 26 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index af27f63a0..2b7d2873b 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -145,17 +145,17 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
-  public func insert(_ node: Node, atIndex index: Int) {
-    let newNode = node
+  public func insert(_ newNode: Node, atIndex index: Int) {
     if index == 0 {
       newNode.next = head
       head?.previous = newNode
       head = newNode
     } else {
-      let prev = self.node(atIndex: index-1)
+      let prev = node(atIndex: index-1)
+      let next = prev.next
       newNode.previous = prev
-      newNode.next = prev.next
-      prev.next?.previous = newNode
+      newNode.next = next
+      next?.previous = newNode
       prev.next = newNode
     }
   }
@@ -169,18 +169,17 @@ public final class LinkedList<T> {
     if list.isEmpty { return }
     
     if index == 0 {
-      let temp = head
+      list.last?.next = head
       head = list.head
-      list.last?.next = temp
     } else {
-      let prev = self.node(atIndex: index-1)
-      let temp = prev.next
+      let prev = node(atIndex: index-1)
+      let next = prev.next
 
       prev.next = list.head
       list.head?.previous = prev
 
-      list.last?.next = temp
-      temp?.previous = list.last?.next
+      list.last?.next = next
+      next?.previous = list.last?.next
     }
   }
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index c0331bc0e..a9848328d 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -100,17 +100,17 @@ public final class LinkedList<T> {
         self.insert(newNode, atIndex: index)
     }
 
-    public func insert(_ node: Node, atIndex index: Int) {
-        let newNode = node
+    public func insert(_ newNode: Node, atIndex index: Int) {
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let prev = self.node(atIndex: index-1)
+            let prev = node(atIndex: index-1)
+            let next = prev.next
             newNode.previous = prev
-            newNode.next = prev.next
-            prev.next?.previous = newNode
+            newNode.next = next
+            next?.previous = newNode
             prev.next = newNode
         }
     }
@@ -119,18 +119,17 @@ public final class LinkedList<T> {
         if list.isEmpty { return }
         
         if index == 0 {
-            let temp = head
+            list.last?.next = head
             head = list.head
-            list.last?.next = temp
         } else {
             let prev = self.node(atIndex: index-1)
-            let temp = prev.next
+            let next = prev.next
             
             prev.next = list.head
             list.head?.previous = prev
             
-            list.last?.next = temp
-            temp?.previous = list.last?.next
+            list.last?.next = next
+            next?.previous = list.last?.next
         }
     }
     
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 55b61e910..52e30261a 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -330,7 +330,7 @@ Finally, replace the head with the new node.
              |    C    |    |    A    |     |    B    |
      nil <---|         |<---|         |<----|         |<----//------
              +---------+    +---------+     +---------+ 
-                 [0]            [1]
+                 [0]            [1]             [2]
 
 
 However, when the given index is greater than 0, it is necessary to get the node previous and next index and insert between them.
@@ -338,10 +338,10 @@ You can also obtain the previous and next node using node(atIndex:) as follows:
 
              +---------+         +---------+     +---------+    
     head --->|         |---//--->|         |---->|         |----
-             |    0    |         |    A    |     |    B    |    
+             |         |         |    A    |     |    B    |    
      nil <---|         |---//<---|         |<----|         |<---
              +---------+         +---------+     +---------+    
-                                  [index-1]        [index]      
+                 [0]              [index-1]        [index]      
                                       ^               ^ 
                                       |               | 
                                      prev            next
@@ -356,10 +356,10 @@ Now insert new node between the prev and the next.
 
              +---------+         +---------+     +---------+     +---------+
     head --->|         |---//--->|         |---->|         |---->|         |
-             |    0    |         |    A    |     |    C    |     |    B    |
+             |         |         |    A    |     |    C    |     |    B    |
      nil <---|         |---//<---|         |<----|         |<----|         |
              +---------+         +---------+     +---------+     +---------+
-                                  [index-1]        [index]        [index+1]
+                 [0]              [index-1]        [index]        [index+1]
                                       ^               ^               ^
                                       |               |               |
                                      prev            new             next

From bb21f61b53dc08af0e5d5081951c683d0f57a979 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Thu, 30 Nov 2017 15:40:48 +0900
Subject: [PATCH 1351/1679] [Code refactoring] Renamed `atIndex` label in
 method to `at`.

---
 .../LinkedList.playground/Contents.swift      | 52 +++++++-------
 Linked List/LinkedList.swift                  | 20 +++---
 Linked List/Tests/LinkedListTests.swift       | 68 +++++++++----------
 3 files changed, 70 insertions(+), 70 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 2b7d2873b..b215bb3c7 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -70,7 +70,7 @@ public final class LinkedList<T> {
   ///
   /// - Parameter index: Integer value of the node's index to be returned
   /// - Returns: Optional LinkedListNode
-  public func node(atIndex index: Int) -> Node {
+  public func node(at index: Int) -> Node {
     assert(head != nil, "List is empty")
     assert(index >= 0, "index must be greater than 0")
     
@@ -94,7 +94,7 @@ public final class LinkedList<T> {
   ///
   /// - Parameter index: Integer value of the requested value's index
   public subscript(index: Int) -> T {
-    let node = self.node(atIndex: index)
+    let node = self.node(at: index)
     return node.value
   }
 
@@ -135,9 +135,9 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - value: The data value to be inserted
   ///   - index: Integer value of the index to be insterted at
-  public func insert(_ value: T, atIndex index: Int) {
+  public func insert(_ value: T, at index: Int) {
     let newNode = Node(value: value)
-    self.insert(newNode, atIndex: index)
+    self.insert(newNode, at: index)
   }
 
   /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
@@ -145,13 +145,13 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
-  public func insert(_ newNode: Node, atIndex index: Int) {
+  public func insert(_ newNode: Node, at index: Int) {
     if index == 0 {
       newNode.next = head
       head?.previous = newNode
       head = newNode
     } else {
-      let prev = node(atIndex: index-1)
+      let prev = node(at: index-1)
       let next = prev.next
       newNode.previous = prev
       newNode.next = next
@@ -165,14 +165,14 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - list: The LinkedList to be copied and inserted
   ///   - index: Integer value of the index to be inserted at
-  public func insert(_ list: LinkedList, atIndex index: Int) {
+  public func insert(_ list: LinkedList, at index: Int) {
     if list.isEmpty { return }
     
     if index == 0 {
       list.last?.next = head
       head = list.head
     } else {
-      let prev = node(atIndex: index-1)
+      let prev = node(at: index-1)
       let next = prev.next
 
       prev.next = list.head
@@ -220,8 +220,8 @@ public final class LinkedList<T> {
   ///
   /// - Parameter index: Integer value of the index of the node to be removed
   /// - Returns: The data value contained in the deleted node
-  @discardableResult public func remove(atIndex index: Int) -> T {
-    let node = self.node(atIndex: index)
+  @discardableResult public func remove(at index: Int) -> T {
+    let node = self.node(at: index)
     return remove(node: node)
   }
 }
@@ -323,9 +323,9 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.node(atIndex: 0).value    // "Hello"
-list.node(atIndex: 1).value    // "World"
-//list.node(atIndex: 2)           // crash!
+list.node(at: 0).value    // "Hello"
+list.node(at: 1).value    // "World"
+//list.node(at: 2)           // crash!
 
 list[0]     // "Hello"
 list[1]     // "World"
@@ -338,9 +338,9 @@ list.append(list2)            // [Hello, World, Goodbye, World]
 list2.removeAll()             // [ ]
 list2.isEmpty                 // true
 list.removeLast()             // "World"
-list.remove(atIndex: 2)       // "Goodbye"
+list.remove(at: 2)       // "Goodbye"
 
-list.insert("Swift", atIndex: 1)
+list.insert("Swift", at: 1)
 list[0]     // "Hello"
 list[1]     // "Swift"
 list[2]     // "World"
@@ -348,8 +348,8 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.node(atIndex: 0).value = "Universe"
-list.node(atIndex: 1).value = "Swifty"
+list.node(at: 0).value = "Universe"
+list.node(at: 1).value = "Swifty"
 let m = list.map { s in s.count }
 m    // [8, 6, 5]
 let f = list.filter { s in s.count > 5 }
@@ -366,28 +366,28 @@ list.head?.value
 list.count                     // 1
 list[0]                        // "Swifty"
 
-list.remove(atIndex: 0)        // "Swifty"
+list.remove(at: 0)        // "Swifty"
 list.count                     // 0
 
 let list3 = LinkedList<String>()
-list3.insert("2", atIndex: 0) // [2]
+list3.insert("2", at: 0) // [2]
 list3.count                   // 1
-list3.insert("4", atIndex: 1) // [2,4]
+list3.insert("4", at: 1) // [2,4]
 list3.count                   // 2
-list3.insert("5", atIndex: 2) // [2,4,5]
+list3.insert("5", at: 2) // [2,4,5]
 list3.count                   // 3
-list3.insert("3", atIndex: 1) // [2,3,4,5]
-list3.insert("1", atIndex: 0) // [1,2,3,4,5]
+list3.insert("3", at: 1) // [2,3,4,5]
+list3.insert("1", at: 0) // [1,2,3,4,5]
 
 let list4 = LinkedList<String>()
-list4.insert(list3, atIndex: 0) // [1,2,3,4,5]
+list4.insert(list3, at: 0) // [1,2,3,4,5]
 list4.count                     // 5
 
 let list5 = LinkedList<String>()
 list5.append("0")                // [0]
-list5.insert("End", atIndex:1)   // [0,End]
+list5.insert("End", at:1)   // [0,End]
 list5.count                      // 2
-list5.insert(list4, atIndex: 1)  // [0,1,2,3,4,5,End]
+list5.insert(list4, at: 1)  // [0,1,2,3,4,5,End]
 list5.count                      // 7
 
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index a9848328d..14f2ffe29 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -48,7 +48,7 @@ public final class LinkedList<T> {
         return count
     }
     
-    public func node(atIndex index: Int) -> Node {
+    public func node(at index: Int) -> Node {
         assert(head != nil, "List is empty")
         assert(index >= 0, "index must be greater than 0")
         if index == 0 {
@@ -68,7 +68,7 @@ public final class LinkedList<T> {
     }
 
     public subscript(index: Int) -> T {
-        let node = self.node(atIndex: index)
+        let node = self.node(at: index)
         return node.value
     }
 
@@ -95,18 +95,18 @@ public final class LinkedList<T> {
         }
     }
 
-    public func insert(_ value: T, atIndex index: Int) {
+    public func insert(_ value: T, at index: Int) {
         let newNode = Node(value: value)
-        self.insert(newNode, atIndex: index)
+        self.insert(newNode, at: index)
     }
 
-    public func insert(_ newNode: Node, atIndex index: Int) {
+    public func insert(_ newNode: Node, at index: Int) {
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let prev = node(atIndex: index-1)
+            let prev = node(at: index-1)
             let next = prev.next
             newNode.previous = prev
             newNode.next = next
@@ -115,14 +115,14 @@ public final class LinkedList<T> {
         }
     }
     
-    public func insert(_ list: LinkedList, atIndex index: Int) {
+    public func insert(_ list: LinkedList, at index: Int) {
         if list.isEmpty { return }
         
         if index == 0 {
             list.last?.next = head
             head = list.head
         } else {
-            let prev = self.node(atIndex: index-1)
+            let prev = self.node(at: index-1)
             let next = prev.next
             
             prev.next = list.head
@@ -158,8 +158,8 @@ public final class LinkedList<T> {
         return remove(node: last!)
     }
 
-    @discardableResult public func remove(atIndex index: Int) -> T {
-        let node = self.node(atIndex: index)
+    @discardableResult public func remove(at index: Int) -> T {
+        let node = self.node(at: index)
         return remove(node: node)
     }
 }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 5bc27b23d..969ee5e08 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -97,7 +97,7 @@ class LinkedListTest: XCTestCase {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let node = list.node(atIndex: 0)
+    let node = list.node(at: 0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node.value, 123)
     XCTAssertTrue(node === list.first)
@@ -109,18 +109,18 @@ class LinkedListTest: XCTestCase {
     let nodeCount = list.count
     XCTAssertEqual(nodeCount, numbers.count)
 
-    let first = list.node(atIndex: 0)
+    let first = list.node(at: 0)
     XCTAssertNotNil(first)
     XCTAssertTrue(first === list.first)
     XCTAssertEqual(first.value, numbers[0])
 
-    let last = list.node(atIndex: nodeCount - 1)
+    let last = list.node(at: nodeCount - 1)
     XCTAssertNotNil(last)
     XCTAssertTrue(last === list.last)
     XCTAssertEqual(last.value, numbers[nodeCount - 1])
 
     for i in 0..<nodeCount {
-      let node = list.node(atIndex: i)
+      let node = list.node(at: i)
       XCTAssertNotNil(node)
       XCTAssertEqual(node.value, numbers[i])
     }
@@ -135,25 +135,25 @@ class LinkedListTest: XCTestCase {
 
   func testInsertAtIndexInEmptyList() {
     let list = LinkedList<Int>()
-    list.insert(123, atIndex: 0)
+    list.insert(123, at: 0)
 
     XCTAssertFalse(list.isEmpty)
     XCTAssertEqual(list.count, 1)
 
-    let node = list.node(atIndex: 0)
+    let node = list.node(at: 0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node.value, 123)
   }
 
   func testInsertAtIndex() {
     let list = buildList()
-    let prev = list.node(atIndex: 2)
-    let next = list.node(atIndex: 3)
+    let prev = list.node(at: 2)
+    let next = list.node(at: 3)
     let nodeCount = list.count
 
-    list.insert(444, atIndex: 3)
+    list.insert(444, at: 3)
 
-    let node = list.node(atIndex: 3)
+    let node = list.node(at: 3)
     XCTAssertNotNil(node)
     XCTAssertEqual(node.value, 444)
     XCTAssertEqual(nodeCount + 1, list.count)
@@ -169,12 +169,12 @@ class LinkedListTest: XCTestCase {
     let list2 = LinkedList<Int>()
     list2.append(99)
     list2.append(102)
-    list.insert(list2, atIndex: 2)
+    list.insert(list2, at: 2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 1).value, 2)
-    XCTAssertEqual(list.node(atIndex: 2).value, 99)
-    XCTAssertEqual(list.node(atIndex: 3).value, 102)
-    XCTAssertEqual(list.node(atIndex: 4).value, 10)
+    XCTAssertEqual(list.node(at: 1).value, 2)
+    XCTAssertEqual(list.node(at: 2).value, 99)
+    XCTAssertEqual(list.node(at: 3).value, 102)
+    XCTAssertEqual(list.node(at: 4).value, 10)
   }
 
   func testInsertListAtFirstIndex() {
@@ -182,11 +182,11 @@ class LinkedListTest: XCTestCase {
     let list2 = LinkedList<Int>()
     list2.append(99)
     list2.append(102)
-    list.insert(list2, atIndex: 0)
+    list.insert(list2, at: 0)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 0).value, 99)
-    XCTAssertEqual(list.node(atIndex: 1).value, 102)
-    XCTAssertEqual(list.node(atIndex: 2).value, 8)
+    XCTAssertEqual(list.node(at: 0).value, 99)
+    XCTAssertEqual(list.node(at: 1).value, 102)
+    XCTAssertEqual(list.node(at: 2).value, 8)
   }
 
   func testInsertListAtLastIndex() {
@@ -194,11 +194,11 @@ class LinkedListTest: XCTestCase {
     let list2 = LinkedList<Int>()
     list2.append(99)
     list2.append(102)
-    list.insert(list2, atIndex: list.count)
+    list.insert(list2, at: list.count)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5).value, 5)
-    XCTAssertEqual(list.node(atIndex: 6).value, 99)
-    XCTAssertEqual(list.node(atIndex: 7).value, 102)
+    XCTAssertEqual(list.node(at: 5).value, 5)
+    XCTAssertEqual(list.node(at: 6).value, 99)
+    XCTAssertEqual(list.node(at: 7).value, 102)
   }
 
   func testAppendList() {
@@ -208,9 +208,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.append(list2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5).value, 5)
-    XCTAssertEqual(list.node(atIndex: 6).value, 99)
-    XCTAssertEqual(list.node(atIndex: 7).value, 102)
+    XCTAssertEqual(list.node(at: 5).value, 5)
+    XCTAssertEqual(list.node(at: 6).value, 99)
+    XCTAssertEqual(list.node(at: 7).value, 102)
   }
 
   func testAppendListToEmptyList() {
@@ -220,15 +220,15 @@ class LinkedListTest: XCTestCase {
     list2.append(10)
     list.append(list2)
     XCTAssertTrue(list.count == 2)
-    XCTAssertEqual(list.node(atIndex: 0).value, 5)
-    XCTAssertEqual(list.node(atIndex: 1).value, 10)
+    XCTAssertEqual(list.node(at: 0).value, 5)
+    XCTAssertEqual(list.node(at: 1).value, 10)
   }
 
   func testRemoveAtIndexOnListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let value = list.remove(atIndex: 0)
+    let value = list.remove(at: 0)
     XCTAssertEqual(value, 123)
 
     XCTAssertTrue(list.isEmpty)
@@ -239,16 +239,16 @@ class LinkedListTest: XCTestCase {
 
   func testRemoveAtIndex() {
     let list = buildList()
-    let prev = list.node(atIndex: 2)
-    let next = list.node(atIndex: 3)
+    let prev = list.node(at: 2)
+    let next = list.node(at: 3)
     let nodeCount = list.count
 
-    list.insert(444, atIndex: 3)
+    list.insert(444, at: 3)
 
-    let value = list.remove(atIndex: 3)
+    let value = list.remove(at: 3)
     XCTAssertEqual(value, 444)
 
-    let node = list.node(atIndex: 3)
+    let node = list.node(at: 3)
     XCTAssertTrue(next === node)
     XCTAssertTrue(prev.next === node)
     XCTAssertTrue(node.previous === prev)

From aa6e2bf750322666722c8fdea77b2dae4476cc5b Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Sat, 2 Dec 2017 14:43:05 -0800
Subject: [PATCH 1352/1679] GitHub Pages Script Updates (#670)

* Move inline css to the main stylesheet - github-light.css & parse the repo README to
html instead of generating one.

* Minor clean up

* Fix image link

* Parse other markdown files
---
 .travis.yml     |   1 +
 README.markdown |   8 +--
 gfm-render.sh   | 175 +++++++++++++++++++++++++++++-------------------
 3 files changed, 110 insertions(+), 74 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 7cd02c9bc..edf1cf89f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -50,4 +50,5 @@ script:
 - xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 
 after_success:
+
 - if [[ "$TRAVIS_BRANCH" == "master" ]]; then ./gfm-render.sh; fi
diff --git a/README.markdown b/README.markdown
index b15bd1527..46544682e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,4 +1,4 @@
-![Swift Algorithm Club](/Images/SwiftAlgorithm-410-transp.png)
+![Swift Algorithm Club](Images/SwiftAlgorithm-410-transp.png)
 
 # Welcome to the Swift Algorithm Club!
 
@@ -156,14 +156,14 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Splay Tree](Splay%20Tree/). A self balancing binary search tree that enables fast retrieval of recently updated elements.
 - [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
-  - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation) 
+  - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - [Trie](Trie/). A special type of tree used to store associative data structures.
 - [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
 - [QuadTree](QuadTree/). A tree with 4 children.
-- [Octree](Octree/). A tree with 8 children. 
+- [Octree](Octree/). A tree with 8 children.
 
 ### Hashing
 
@@ -208,7 +208,7 @@ For more information, check out these great books:
 - [The Algorithm Design Manual](http://www.algorist.com) by Skiena
 - [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
 - [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
-- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava 
+- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava
 
 The following books are available for free online:
 
diff --git a/gfm-render.sh b/gfm-render.sh
index 09c026d55..4e18c8560 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,50 +1,108 @@
 #!/usr/bin/env bash
 
-# $1 - readme
+set -e
+
+# $1 - readme file name
 function render_markdown_to_html {
-  # escape escaping characters
-  if [[ $(uname) == "Darwin" ]]; then
-    content=$(
-      cat "$1"                                          \
-        | sed 's/\\/\\\\/g'                             \
-        | sed 's/"/\\"/g'                               \
-        | sed $'s/\t/\\\\t/g'                           \
-        | sed -e ':a' -e 'N' -e '$!ba' -e 's/\n/\\\n/g' \
-    )
-  else
-    content=$(
-      cat "$1"                          \
-        | sed 's/\\/\\\\/g'             \
-        | sed 's/"/\\"/g'               \
-        | sed 's/\t/\\t/g'              \
-        | sed ':a;N;$!ba;s/\n/\\n/g'    \
-    )
-  fi
+  # escape escaping characters on Darwin only
+  content=$(
+    cat "$1"                                          \
+      | sed 's/\\/\\\\/g'                             \
+      | sed 's/"/\\"/g'                               \
+      | sed $'s/\t/\\\\t/g'                           \
+      | sed -e ':a' -e 'N' -e '$!ba' -e 's/\n/\\\n/g' \
+  )
 
   # network call to GitHub API
   json="{\"text\":\"$content\",\"mode\":\"gfm\",\"context\":\"$USERNAME/swift-algorithm-club\"}"
   echo -e "$(curl -s --data "$json" -u $USERNAME:$TOKEN https://api.github.com/markdown)"
 }
 
-# $1 - comment
-function push_to_gh_pages {
-  git checkout -b gh-pages
-  git add .
-  git commit -m "$1"
-  git push -f https://$TOKEN@github.com/$USERNAME/swift-algorithm-club.git gh-pages
-}
-
 # download github systax highlight stylesheet
 echo "> Downloading github-light.css..."
 curl -s -O https://raw.githubusercontent.com/primer/github-syntax-light/master/lib/github-light.css
 
+# slightly modify the main stylesheet
+echo "> Modifying github-light.css..."
+cat >> github-light.css << EOF
+#container {
+  margin: 0 auto;
+  width: 75%;
+  min-width: 768px;
+  max-width: 896px;
+  position: relative;
+}
+
+body {
+  font-size: 18px;
+}
+
+code {
+    padding: 0.2em;
+    margin: 0;
+    font-size: 85%;
+    background-color: #f6f8fa;
+    line-height: 1.45;
+    border-radius: 3px
+}
+
+pre code {
+    padding: 0px;
+    background-color: transparent;
+}
+
+.highlight {
+  margin: 0px;
+  padding: 0px 16px;
+  font-size: 85%;
+  line-height: 1.45;
+  overflow: auto;
+  background-color: #f6f8fa;
+  border-radius: 3px;
+}
+
+@media (max-width: 768px) {
+  #container {
+    position: absolute;
+    margin: 0;
+    width: 100%;
+    height: 100%;
+    min-width: 100%;
+  }
+}
+EOF
+
+# other markdown articles
+for title in "What are Algorithms" "Big-O Notation" "Algorithm Design" "Why Algorithms"; do
+  echo "> Generating $title.html..."
+
+  cat > "$title.html" << EOF
+<!DOCTYPE html>
+<head>
+  <title>$title</title>
+  <link rel="stylesheet" type="text/css" href="github-light.css">
+</head>
+<body>
+  <div id="container">$(render_markdown_to_html "$title.markdown")</div>
+</body>
+</html>
+EOF
+done
+
 # if index.html does not exist, create one;
 # otherwise, empty its content.
-if [[ -z index.html ]]; then
-  touch index.html
-else
-  > index.html
-fi
+echo "> Generating index.html..."
+cat > index.html << EOF
+<!DOCTYPE html>
+<head>
+  <title>Swift Algorithm Club</title>
+  <link rel="stylesheet" type="text/css" href="github-light.css">
+</head>
+<body>
+  <div id="container">$(render_markdown_to_html README.markdown | sed 's/.markdown/.html/g')</div>
+</body>
+</html>
+EOF
 
 # iterate immediate directories
 find . -maxdepth 1 -type d | while read folder; do
@@ -54,53 +112,30 @@ find . -maxdepth 1 -type d | while read folder; do
   if [[ -f $folder/README.md ]]; then readme="$folder/README.md"; fi
   if [[ -f $folder/README.markdown ]]; then readme="$folder/README.markdown"; fi
 
-  # exclude the repository's README
-  if [[ !(-z $readme) && ($readme != "./README.markdown") ]]; then
-    name=$(basename "$folder")
-    echo "> Generating $name/index.html..."
+  # skip if there is no README or it it the README of the repository
+  if [[ (-z $readme) || $readme == "./README.markdown" ]]; then continue; fi
+
+  # render README to HTML
+  name=$(basename "$folder")
+  echo "> Generating $name/index.html..."
 
-    cat > "$folder/index.html" << EOF
+  cat > "$folder/index.html" << EOF
 <!DOCTYPE html>
 <head>
+  <title>$name</title>
   <link rel="stylesheet" type="text/css" href="../github-light.css">
-  <style>
-    body {
-      font-size: 18px;
-    }
-    code {
-        padding: 0.2em;
-        margin: 0;
-        font-size: 85%;
-        background-color: #f6f8fa;
-        line-height: 1.45;
-        border-radius: 3px
-    }
-    pre code {
-        padding: 0px;
-        background-color: transparent;
-    }
-    .highlight {
-      margin: 0px;
-      padding: 0px 16px;
-      font-size: 85%;
-      line-height: 1.45;
-      overflow: auto;
-      background-color: #f6f8fa;
-      border-radius: 3px;
-    }
-  </style>
 </head>
 <body>
-    $(render_markdown_to_html "$readme")
+  <div id="container">$(render_markdown_to_html "$readme")</div>
 </body>
 </html>
 EOF
-    # temporarily write the list of HTML filenames to the main index.html
-    echo "$lists<li><a href=\"$name/index.html\">$name</a></li>" >> index.html
-  fi
 done
 
-echo "<!DOCTYPE html><body><h1>Swift Algorithm</h1><ul>$(echo -n $(cat index.html))</ul></body></html>" > index.html
-
 # push to gh-pages
-if [[ $CI = true ]]; then push_to_gh_pages "Generated by TravisCI on $(date +%D)"; fi
+if [[ $CI = true ]]; then
+  git checkout -b gh-pages
+  git add .
+  git commit -m "$Generated by TravisCI on $(date +%D)"
+  git push -f https://$TOKEN@github.com/$USERNAME/swift-algorithm-club.git gh-pages
+fi

From aa1c3f799020bc854a934b3b107ff97a8412ae5f Mon Sep 17 00:00:00 2001
From: n0an <nantog@gmail.com>
Date: Wed, 20 Dec 2017 13:49:51 +0300
Subject: [PATCH 1353/1679] RadixTree syntax updated to Swift 4

Characters removed (deprecated in Swift 4). Substring removed (deprecated in Swift 4). String slicing subscript used for substrings creation.
---
 .../Sources/RadixTree.swift                   | 46 +++++++++----------
 Radix Tree/RadixTree.swift                    | 46 +++++++++----------
 2 files changed, 46 insertions(+), 46 deletions(-)

diff --git a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift
index 1914f57bc..77e289f7d 100644
--- a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
+++ b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
@@ -181,10 +181,10 @@ public class RadixTree {
 				else if shared == e.label {
 					currEdge = e
 					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = searchStr.characters.index(after: tempIndex)
+					for _ in 1...shared.count {
+						tempIndex = searchStr.index(after: tempIndex)
 					}
-                    searchStr = searchStr.substring(from: tempIndex)
+                    searchStr = String(searchStr[tempIndex...])
 					found = true
 					break
 				}
@@ -192,18 +192,18 @@ public class RadixTree {
 				// If the child's label and the search string share a partial prefix,
 				// then both the label and the search string need to be substringed
 				// and a new branch needs to be created
-				else if shared.characters.count > 0 {
-					var labelIndex = e.label.characters.startIndex
+				else if shared.count > 0 {
+					var labelIndex = e.label.startIndex
 
 					// Create index objects and move them to after the shared prefix
-					for _ in 1...shared.characters.count {
-                        index = searchStr.characters.index(after: index)
-						labelIndex = e.label.characters.index(after: labelIndex)
+					for _ in 1...shared.count {
+                        index = searchStr.index(after: index)
+						labelIndex = e.label.index(after: labelIndex)
 					}
 
 					// Substring both the search string and the label from the shared prefix
-                    searchStr = searchStr.substring(from: index)
-                    e.label = e.label.substring(from: labelIndex)
+                    searchStr = String(searchStr[index...])
+                    e.label = String(e.label[labelIndex...])
 
 					// Create 2 new edges and update parent/children values
 					let newEdge = Edge(e.label)
@@ -266,16 +266,16 @@ public class RadixTree {
 				if shared == c.label {
 					currEdge = c
 					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = searchStr.characters.index(after: tempIndex)
+					for _ in 1...shared.count {
+						tempIndex = searchStr.index(after: tempIndex)
 					}
-					searchStr = searchStr.substring(from: tempIndex)
+					searchStr = String(searchStr[tempIndex...])
 					found = true
 					break
 				}
 
 				// If the shared string is empty, go to the next child
-				else if shared.characters.count == 0 {
+				else if shared.count == 0 {
 					continue
 				}
 
@@ -287,7 +287,7 @@ public class RadixTree {
 				// If the search string and the child's label only share some characters,
 				// the string is not in the tree, return false
 				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-				  shared.characters.count < c.label.characters.count {
+				  shared.count < c.label.count {
 				  	return false
 				}
 			}
@@ -340,10 +340,10 @@ public class RadixTree {
 				if shared == currEdge.children[c].label {
 					currEdge = currEdge.children[c]
 					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = searchStr.characters.index(after: tempIndex)
+					for _ in 1...shared.count {
+						tempIndex = searchStr.index(after: tempIndex)
 					}
-					searchStr = searchStr.substring(from: tempIndex)
+					searchStr = String(searchStr[tempIndex...])
 					found = true
 					break
 				}
@@ -366,13 +366,13 @@ public class RadixTree {
 // i.e. sharedPrefix("court", "coral") -> "co"
 public func sharedPrefix(_ str1: String, _ str2: String) -> String {
 	var temp = ""
-	var c1 = str1.characters.startIndex
-	var c2 = str2.characters.startIndex
-	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+	var c1 = str1.startIndex
+	var c2 = str2.startIndex
+	for _ in 0...min(str1.count-1, str2.count-1) {
 		if str1[c1] == str2[c2] {
 			temp.append( str1[c1] )
-            c1 = str1.characters.index(after:c1)
-            c2 = str2.characters.index(after:c2)
+            c1 = str1.index(after:c1)
+            c2 = str2.index(after:c2)
 		} else {
 			return temp
 		}
diff --git a/Radix Tree/RadixTree.swift b/Radix Tree/RadixTree.swift
index 958ffb4e6..943000dd3 100644
--- a/Radix Tree/RadixTree.swift	
+++ b/Radix Tree/RadixTree.swift	
@@ -181,10 +181,10 @@ public class RadixTree {
         else if shared == e.label {
           currEdge = e
           var tempIndex = searchStr.startIndex
-          for _ in 1...shared.characters.count {
-            tempIndex = searchStr.characters.index(after: tempIndex)
+          for _ in 1...shared.count {
+            tempIndex = searchStr.index(after: tempIndex)
           }
-          searchStr = searchStr.substring(from: tempIndex)
+          searchStr = String(searchStr[tempIndex...])
           found = true
           break
         }
@@ -192,18 +192,18 @@ public class RadixTree {
           // If the child's label and the search string share a partial prefix,
           // then both the label and the search string need to be substringed
           // and a new branch needs to be created
-        else if shared.characters.count > 0 {
-          var labelIndex = e.label.characters.startIndex
+        else if shared.count > 0 {
+          var labelIndex = e.label.startIndex
 
           // Create index objects and move them to after the shared prefix
-          for _ in 1...shared.characters.count {
-            index = searchStr.characters.index(after: index)
-            labelIndex = e.label.characters.index(after: labelIndex)
+          for _ in 1...shared.count {
+            index = searchStr.index(after: index)
+            labelIndex = e.label.index(after: labelIndex)
           }
 
           // Substring both the search string and the label from the shared prefix
-          searchStr = searchStr.substring(from: index)
-          e.label = e.label.substring(from: labelIndex)
+          searchStr = String(searchStr[index...])
+          e.label = String(e.label[labelIndex...])
 
           // Create 2 new edges and update parent/children values
           let newEdge = Edge(e.label)
@@ -266,16 +266,16 @@ public class RadixTree {
         if shared == c.label {
           currEdge = c
           var tempIndex = searchStr.startIndex
-          for _ in 1...shared.characters.count {
-            tempIndex = searchStr.characters.index(after: tempIndex)
+          for _ in 1...shared.count {
+            tempIndex = searchStr.index(after: tempIndex)
           }
-          searchStr = searchStr.substring(from: tempIndex)
+          searchStr = String(searchStr[tempIndex...])
           found = true
           break
         }
 
           // If the shared string is empty, go to the next child
-        else if shared.characters.count == 0 {
+        else if shared.count == 0 {
           continue
         }
 
@@ -287,7 +287,7 @@ public class RadixTree {
           // If the search string and the child's label only share some characters,
           // the string is not in the tree, return false
         else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-          shared.characters.count < c.label.characters.count {
+          shared.count < c.label.count {
           return false
         }
       }
@@ -340,10 +340,10 @@ public class RadixTree {
         if shared == currEdge.children[c].label {
           currEdge = currEdge.children[c]
           var tempIndex = searchStr.startIndex
-          for _ in 1...shared.characters.count {
-            tempIndex = searchStr.characters.index(after: tempIndex)
+          for _ in 1...shared.count {
+            tempIndex = searchStr.index(after: tempIndex)
           }
-          searchStr = searchStr.substring(from: tempIndex)
+          searchStr = String(searchStr[tempIndex...])
           found = true
           break
         }
@@ -366,13 +366,13 @@ public class RadixTree {
 // i.e. sharedPrefix("court", "coral") -> "co"
 public func sharedPrefix(_ str1: String, _ str2: String) -> String {
   var temp = ""
-  var c1 = str1.characters.startIndex
-  var c2 = str2.characters.startIndex
-  for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+  var c1 = str1.startIndex
+  var c2 = str2.startIndex
+  for _ in 0...min(str1.count-1, str2.count-1) {
     if str1[c1] == str2[c2] {
       temp.append( str1[c1] )
-      c1 = str1.characters.index(after:c1)
-      c2 = str2.characters.index(after:c2)
+      c1 = str1.index(after:c1)
+      c2 = str2.index(after:c2)
     } else {
       return temp
     }

From f035a25111c9d87335a187afcedda77afd4d7ee4 Mon Sep 17 00:00:00 2001
From: Aamir Anwar <aamir.anwar021193@gmail.com>
Date: Fri, 22 Dec 2017 16:02:39 +0530
Subject: [PATCH 1354/1679] Fixed typo in the README for the word 'example'

---
 Splay Tree/readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 2c5e87ed7..f3b852f22 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -159,7 +159,7 @@ Now suppose a *insert(7)* operation was performed and we're in a *ZigZag* case.
 
 ## Advantages 
 
-Splay trees provide an efficient way to quickly access elements that are frequently requested. This characteristic makes then a good choice to implement, for exmaple, caches or garbage collection algorithms, or in any other problem involving frequent access to a certain numbers of elements from a data set.
+Splay trees provide an efficient way to quickly access elements that are frequently requested. This characteristic makes then a good choice to implement, for example, caches or garbage collection algorithms, or in any other problem involving frequent access to a certain numbers of elements from a data set.
 
 ## Disadvantages
 

From bcd0896b446c91c76a2e758bd8add3b882fa5126 Mon Sep 17 00:00:00 2001
From: Hemang <hemangshah.in@gmail.com>
Date: Wed, 3 Jan 2018 12:06:27 +0530
Subject: [PATCH 1355/1679] Update README.markdown

Corrected the Written by (Author) URL for Palindrome algorithm.
---
 Palindromes/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 18518adbe..69520a132 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -104,4 +104,4 @@ racecar -> left index == right index -> return true
 [Palindrome Wikipedia](https://en.wikipedia.org/wiki/Palindrome)
 
 
-*Written by [Joshua Alvarado](https://github.com/https://github.com/lostatseajoshua)*
+*Written by [Joshua Alvarado](https://github.com/lostatseajoshua)*

From a51f98aa0737063e5dc882c19df22b9de388bccf Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Thu, 4 Jan 2018 16:29:14 +0800
Subject: [PATCH 1356/1679] Fix a spelling mistake

change the `probablistic` to `probabilistic`
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 46544682e..7c9482d0c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -145,7 +145,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 ### Lists
 
 - [Linked List](Linked%20List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
-- [Skip-List](Skip-List/). Skip List is a probablistic data-structure with same logarithmic time bound and efficiency as AVL/ or Red-Black tree and provides a clever compromise to efficiently support search and update operations.
+- [Skip-List](Skip-List/). Skip List is a probabilistic data-structure with same logarithmic time bound and efficiency as AVL/ or Red-Black tree and provides a clever compromise to efficiently support search and update operations.
 
 ### Trees
 

From 677e3cefa18c9a815d7d2509e1198553c7a63468 Mon Sep 17 00:00:00 2001
From: Giuseppe Lanza <giuseppe@getdrop.com>
Date: Thu, 4 Jan 2018 14:48:07 +0000
Subject: [PATCH 1357/1679] IntroSort playground implementation

---
 Introsort/Introsort.playground/Contents.swift | 41 +++++++++++++++
 .../Sources/HeapSort.swift                    | 50 +++++++++++++++++++
 .../Sources/InsertionSort.swift               | 28 +++++++++++
 .../Sources/Partition.swift                   | 43 ++++++++++++++++
 .../Sources/Randomize.swift                   |  9 ++++
 .../Introsort.playground/Sources/Sort3.swift  | 21 ++++++++
 .../contents.xcplayground                     |  4 ++
 7 files changed, 196 insertions(+)
 create mode 100644 Introsort/Introsort.playground/Contents.swift
 create mode 100644 Introsort/Introsort.playground/Sources/HeapSort.swift
 create mode 100644 Introsort/Introsort.playground/Sources/InsertionSort.swift
 create mode 100644 Introsort/Introsort.playground/Sources/Partition.swift
 create mode 100644 Introsort/Introsort.playground/Sources/Randomize.swift
 create mode 100644 Introsort/Introsort.playground/Sources/Sort3.swift
 create mode 100644 Introsort/Introsort.playground/contents.xcplayground

diff --git a/Introsort/Introsort.playground/Contents.swift b/Introsort/Introsort.playground/Contents.swift
new file mode 100644
index 000000000..43ee02e3f
--- /dev/null
+++ b/Introsort/Introsort.playground/Contents.swift
@@ -0,0 +1,41 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+func introsort<T>(_ array: inout [T],  by areInIncreasingOrder: (T, T) -> Bool) {
+    //The depth limit is as best practice 2 * log( n )
+    let depthLimit = 2 * floor(log2(Double(array.count)))
+    
+    introSortImplementation(for: &array, range: 0..<array.count, depthLimit: Int(depthLimit), by: areInIncreasingOrder)
+}
+
+///This method is recursively executed for each partition result of the quicksort part of the algorithm
+private func introSortImplementation<T>(for array: inout [T], range: Range<Int>, depthLimit: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    if array.distance(from: range.lowerBound, to: range.upperBound) < 20 {
+        //if the partition count is less than 20 we can sort it using insertion sort. This algorithm in fact performs well on collections
+        //of this size, plus, at this point is quite probable that the quisksort part of the algorithm produced a partition which is
+        //nearly sorted. As we knoe insertion sort tends to O( n ) if this is the case.
+        insertionSort(for: &array, range: range, by: areInIncreasingOrder)
+    } else if depthLimit == 0 {
+        //If we reached the depth limit for this recursion branch, it's possible that we are hitting quick sort's worst case.
+        //Since quicksort degrades to O( n^2 ) in its worst case we stop using quicksort for this recursion branch and we switch to heapsort.
+        //Our preference remains quicksort, and we hope to be rare to see this condition to be true
+        heapsort(for: &array, range: range, by: areInIncreasingOrder)
+    } else {
+        //By default we use quicksort to sort our collection. The partition index method chose a pivot, and puts all the
+        //elements less than pivot on the left, and the ones bigger than pivot on the right. At the end of the operation the
+        //position of the pivot in the array is returned so that we can form the two partitions.
+        let partIdx = partitionIndex(for: &array, subRange: range, by: areInIncreasingOrder)
+        
+        //We can recursively call introsort implementation, decreasing the depthLimit for the left partition and the right partition.
+        introSortImplementation(for: &array, range: range.lowerBound..<partIdx, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+        introSortImplementation(for: &array, range: partIdx..<range.upperBound, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+    }
+}
+
+var unsorted = randomize(n: 1000)
+
+let swiftSorted = unsorted.sorted()
+introsort(&unsorted, by: <)
+
+print("does it work? \(unsorted == swiftSorted)")
diff --git a/Introsort/Introsort.playground/Sources/HeapSort.swift b/Introsort/Introsort.playground/Sources/HeapSort.swift
new file mode 100644
index 000000000..f5bc466da
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/HeapSort.swift
@@ -0,0 +1,50 @@
+import Foundation
+
+private func shiftDown<T>(_ elements: inout [T], _ index: Int, _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let countToIndex = elements.distance(from: range.lowerBound, to: index)
+    let countFromIndex = elements.distance(from: index, to: range.upperBound)
+    
+    guard countToIndex + 1 < countFromIndex else { return }
+    
+    let left = elements.index(index, offsetBy: countToIndex + 1)
+    var largest = index
+    if areInIncreasingOrder(elements[largest], elements[left]) {
+        largest = left
+    }
+    
+    if countToIndex + 2 < countFromIndex {
+        let right = elements.index(after: left)
+        if areInIncreasingOrder(elements[largest], elements[right]) {
+            largest = right
+        }
+    }
+
+    if largest != index {
+        elements.swapAt(index, largest)
+        shiftDown(&elements, largest, range, by: areInIncreasingOrder)
+    }
+    
+}
+
+private func heapify<T>(_ list: inout [T], _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let root = range.lowerBound
+    var node = list.index(root, offsetBy: list.distance(from: range.lowerBound, to: range.upperBound)/2)
+    
+    while node != root {
+        list.formIndex(before: &node)
+        shiftDown(&list, node, range, by: areInIncreasingOrder)
+    }
+}
+
+public func heapsort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    var hi = range.upperBound
+    let lo = range.lowerBound
+    heapify(&array, range, by: areInIncreasingOrder)
+    array.formIndex(before: &hi)
+    
+    while hi != lo {
+        array.swapAt(lo, hi)
+        shiftDown(&array, lo, lo..<hi, by: areInIncreasingOrder)
+        array.formIndex(before: &hi)
+    }
+}
diff --git a/Introsort/Introsort.playground/Sources/InsertionSort.swift b/Introsort/Introsort.playground/Sources/InsertionSort.swift
new file mode 100644
index 000000000..36887ea06
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/InsertionSort.swift
@@ -0,0 +1,28 @@
+import Foundation
+
+public func insertionSort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    guard !range.isEmpty else { return }
+    
+    let start = range.lowerBound
+    var sortedEnd = start
+    
+    array.formIndex(after: &sortedEnd)
+    while sortedEnd != range.upperBound {
+        let x = array[sortedEnd]
+        
+        var i = sortedEnd
+        repeat {
+            let predecessor = array[array.index(before: i)]
+            
+            guard areInIncreasingOrder(x, predecessor) else { break }
+            array[i] = predecessor
+            array.formIndex(before: &i)
+        } while i != start
+        
+        if i != sortedEnd {
+            array[i] = x
+        }
+        array.formIndex(after: &sortedEnd)
+    }
+    
+}
diff --git a/Introsort/Introsort.playground/Sources/Partition.swift b/Introsort/Introsort.playground/Sources/Partition.swift
new file mode 100644
index 000000000..e24636da7
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/Partition.swift
@@ -0,0 +1,43 @@
+import Foundation
+
+public func partitionIndex<T>(for elements: inout [T], subRange range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) -> Int {
+    var lo = range.lowerBound
+    var hi = elements.index(before: range.upperBound)
+    
+    // Sort the first, middle, and last elements, then use the middle value
+    // as the pivot for the partition.
+    let half = elements.distance(from: lo, to: hi) / 2
+    let mid = elements.index(lo, offsetBy: half)
+    
+    sort3(in: &elements, a: lo, b: mid, c: hi, by: areInIncreasingOrder)
+    let pivot = elements[mid]
+    
+    while true {
+        elements.formIndex(after: &lo)
+        guard findLo(in: elements, pivot: pivot, from: &lo, to: hi, by: areInIncreasingOrder) else { break }
+        elements.formIndex(before: &hi)
+        guard findHi(in: elements, pivot: pivot, from: lo, to: &hi, by: areInIncreasingOrder) else { break }
+        elements.swapAt(lo, hi)
+    }
+
+    
+    return lo
+}
+
+private func findLo<T>(in array: [T], pivot: T, from lo: inout Int, to hi: Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while lo != hi {
+        if !areInIncreasingOrder(array[lo], pivot) {
+            return true
+        }
+        array.formIndex(after: &lo)
+    }
+    return false
+}
+
+private func findHi<T>(in array: [T], pivot: T, from lo: Int, to hi: inout Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while hi != lo {
+        if areInIncreasingOrder(array[hi], pivot) { return true }
+        array.formIndex(before: &hi)
+    }
+    return false
+}
diff --git a/Introsort/Introsort.playground/Sources/Randomize.swift b/Introsort/Introsort.playground/Sources/Randomize.swift
new file mode 100644
index 000000000..6d1d57132
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/Randomize.swift
@@ -0,0 +1,9 @@
+import Foundation
+
+public func randomize(n: Int) -> [Int] {
+    var unsorted = [Int]()
+    for _ in 0..<n {
+        unsorted.append(Int(arc4random()))
+    }
+    return unsorted
+}
diff --git a/Introsort/Introsort.playground/Sources/Sort3.swift b/Introsort/Introsort.playground/Sources/Sort3.swift
new file mode 100644
index 000000000..04d20a6a6
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/Sort3.swift
@@ -0,0 +1,21 @@
+import Foundation
+
+public func sort3<T>(in array: inout [T], a: Int, b: Int, c: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    switch (areInIncreasingOrder(array[b], array[a]),
+            areInIncreasingOrder(array[c], array[b])) {
+    case (false, false): break
+    case (true, true): array.swapAt(a, c)
+    case (true, false):
+        array.swapAt(a, b)
+        
+        if areInIncreasingOrder(array[c], array[b]) {
+            array.swapAt(b, c)
+        }
+    case (false, true):
+        array.swapAt(b, c)
+        
+        if areInIncreasingOrder(array[b], array[a]) {
+            array.swapAt(a, b)
+        }
+    }
+}
diff --git a/Introsort/Introsort.playground/contents.xcplayground b/Introsort/Introsort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Introsort/Introsort.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From 717ba94933686ea00068b5fc4ea0bc223c93cf38 Mon Sep 17 00:00:00 2001
From: Giuseppe Lanza <giuseppe@getdrop.com>
Date: Thu, 4 Jan 2018 15:49:29 +0000
Subject: [PATCH 1358/1679] Added readme file

---
 Introsort/HeapSort.swift      |  50 ++++++++++++++++
 Introsort/InsertionSort.swift |  28 +++++++++
 Introsort/IntroSort.swift     |  32 ++++++++++
 Introsort/Partition.swift     |  43 +++++++++++++
 Introsort/README.markdown     | 110 ++++++++++++++++++++++++++++++++++
 Introsort/Randomize.swift     |   9 +++
 Introsort/Sort3.swift         |  21 +++++++
 README.markdown               |   4 ++
 8 files changed, 297 insertions(+)
 create mode 100644 Introsort/HeapSort.swift
 create mode 100644 Introsort/InsertionSort.swift
 create mode 100644 Introsort/IntroSort.swift
 create mode 100644 Introsort/Partition.swift
 create mode 100644 Introsort/README.markdown
 create mode 100644 Introsort/Randomize.swift
 create mode 100644 Introsort/Sort3.swift

diff --git a/Introsort/HeapSort.swift b/Introsort/HeapSort.swift
new file mode 100644
index 000000000..f5bc466da
--- /dev/null
+++ b/Introsort/HeapSort.swift
@@ -0,0 +1,50 @@
+import Foundation
+
+private func shiftDown<T>(_ elements: inout [T], _ index: Int, _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let countToIndex = elements.distance(from: range.lowerBound, to: index)
+    let countFromIndex = elements.distance(from: index, to: range.upperBound)
+    
+    guard countToIndex + 1 < countFromIndex else { return }
+    
+    let left = elements.index(index, offsetBy: countToIndex + 1)
+    var largest = index
+    if areInIncreasingOrder(elements[largest], elements[left]) {
+        largest = left
+    }
+    
+    if countToIndex + 2 < countFromIndex {
+        let right = elements.index(after: left)
+        if areInIncreasingOrder(elements[largest], elements[right]) {
+            largest = right
+        }
+    }
+
+    if largest != index {
+        elements.swapAt(index, largest)
+        shiftDown(&elements, largest, range, by: areInIncreasingOrder)
+    }
+    
+}
+
+private func heapify<T>(_ list: inout [T], _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let root = range.lowerBound
+    var node = list.index(root, offsetBy: list.distance(from: range.lowerBound, to: range.upperBound)/2)
+    
+    while node != root {
+        list.formIndex(before: &node)
+        shiftDown(&list, node, range, by: areInIncreasingOrder)
+    }
+}
+
+public func heapsort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    var hi = range.upperBound
+    let lo = range.lowerBound
+    heapify(&array, range, by: areInIncreasingOrder)
+    array.formIndex(before: &hi)
+    
+    while hi != lo {
+        array.swapAt(lo, hi)
+        shiftDown(&array, lo, lo..<hi, by: areInIncreasingOrder)
+        array.formIndex(before: &hi)
+    }
+}
diff --git a/Introsort/InsertionSort.swift b/Introsort/InsertionSort.swift
new file mode 100644
index 000000000..36887ea06
--- /dev/null
+++ b/Introsort/InsertionSort.swift
@@ -0,0 +1,28 @@
+import Foundation
+
+public func insertionSort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    guard !range.isEmpty else { return }
+    
+    let start = range.lowerBound
+    var sortedEnd = start
+    
+    array.formIndex(after: &sortedEnd)
+    while sortedEnd != range.upperBound {
+        let x = array[sortedEnd]
+        
+        var i = sortedEnd
+        repeat {
+            let predecessor = array[array.index(before: i)]
+            
+            guard areInIncreasingOrder(x, predecessor) else { break }
+            array[i] = predecessor
+            array.formIndex(before: &i)
+        } while i != start
+        
+        if i != sortedEnd {
+            array[i] = x
+        }
+        array.formIndex(after: &sortedEnd)
+    }
+    
+}
diff --git a/Introsort/IntroSort.swift b/Introsort/IntroSort.swift
new file mode 100644
index 000000000..866b2603f
--- /dev/null
+++ b/Introsort/IntroSort.swift
@@ -0,0 +1,32 @@
+import Foundation
+
+public func introsort<T>(_ array: inout [T],  by areInIncreasingOrder: (T, T) -> Bool) {
+    //The depth limit is as best practice 2 * log( n )
+    let depthLimit = 2 * floor(log2(Double(array.count)))
+    
+    introSortImplementation(for: &array, range: 0..<array.count, depthLimit: Int(depthLimit), by: areInIncreasingOrder)
+}
+
+///This method is recursively executed for each partition result of the quicksort part of the algorithm
+private func introSortImplementation<T>(for array: inout [T], range: Range<Int>, depthLimit: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    if array.distance(from: range.lowerBound, to: range.upperBound) < 20 {
+        //if the partition count is less than 20 we can sort it using insertion sort. This algorithm in fact performs well on collections
+        //of this size, plus, at this point is quite probable that the quisksort part of the algorithm produced a partition which is
+        //nearly sorted. As we knoe insertion sort tends to O( n ) if this is the case.
+        insertionSort(for: &array, range: range, by: areInIncreasingOrder)
+    } else if depthLimit == 0 {
+        //If we reached the depth limit for this recursion branch, it's possible that we are hitting quick sort's worst case.
+        //Since quicksort degrades to O( n^2 ) in its worst case we stop using quicksort for this recursion branch and we switch to heapsort.
+        //Our preference remains quicksort, and we hope to be rare to see this condition to be true
+        heapsort(for: &array, range: range, by: areInIncreasingOrder)
+    } else {
+        //By default we use quicksort to sort our collection. The partition index method chose a pivot, and puts all the
+        //elements less than pivot on the left, and the ones bigger than pivot on the right. At the end of the operation the
+        //position of the pivot in the array is returned so that we can form the two partitions.
+        let partIdx = partitionIndex(for: &array, subRange: range, by: areInIncreasingOrder)
+        
+        //We can recursively call introsort implementation, decreasing the depthLimit for the left partition and the right partition.
+        introSortImplementation(for: &array, range: range.lowerBound..<partIdx, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+        introSortImplementation(for: &array, range: partIdx..<range.upperBound, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+    }
+}
diff --git a/Introsort/Partition.swift b/Introsort/Partition.swift
new file mode 100644
index 000000000..e24636da7
--- /dev/null
+++ b/Introsort/Partition.swift
@@ -0,0 +1,43 @@
+import Foundation
+
+public func partitionIndex<T>(for elements: inout [T], subRange range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) -> Int {
+    var lo = range.lowerBound
+    var hi = elements.index(before: range.upperBound)
+    
+    // Sort the first, middle, and last elements, then use the middle value
+    // as the pivot for the partition.
+    let half = elements.distance(from: lo, to: hi) / 2
+    let mid = elements.index(lo, offsetBy: half)
+    
+    sort3(in: &elements, a: lo, b: mid, c: hi, by: areInIncreasingOrder)
+    let pivot = elements[mid]
+    
+    while true {
+        elements.formIndex(after: &lo)
+        guard findLo(in: elements, pivot: pivot, from: &lo, to: hi, by: areInIncreasingOrder) else { break }
+        elements.formIndex(before: &hi)
+        guard findHi(in: elements, pivot: pivot, from: lo, to: &hi, by: areInIncreasingOrder) else { break }
+        elements.swapAt(lo, hi)
+    }
+
+    
+    return lo
+}
+
+private func findLo<T>(in array: [T], pivot: T, from lo: inout Int, to hi: Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while lo != hi {
+        if !areInIncreasingOrder(array[lo], pivot) {
+            return true
+        }
+        array.formIndex(after: &lo)
+    }
+    return false
+}
+
+private func findHi<T>(in array: [T], pivot: T, from lo: Int, to hi: inout Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while hi != lo {
+        if areInIncreasingOrder(array[hi], pivot) { return true }
+        array.formIndex(before: &hi)
+    }
+    return false
+}
diff --git a/Introsort/README.markdown b/Introsort/README.markdown
new file mode 100644
index 000000000..c4ee6f804
--- /dev/null
+++ b/Introsort/README.markdown
@@ -0,0 +1,110 @@
+# IntroSort
+
+Goal: Sort an array from low to high (or high to low).
+
+IntroSort is the algorithm used by swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
+
+The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
+
+Here's an implementation in Pseudocode:
+
+```
+procedure sort(A : array):
+    let maxdepth = ⌊log(length(A))⌋ × 2
+    introSort(A, maxdepth)
+
+procedure introsort(A, maxdepth):
+    n ← length(A)
+    if n < 20:
+        insertionsort(A)
+    else if maxdepth = 0:
+        heapsort(A)
+    else:
+        p ← partition(A)  // the pivot is selected using median of 3
+        introsort(A[0:p], maxdepth - 1)
+        introsort(A[p+1:n], maxdepth - 1)
+```
+
+## An example
+
+Let's walk through the example. The array is initially:
+
+	[ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
+
+
+for this example let's assume that `maxDepth` is **2** and that the size of the partition for the insertionSort to kick in is **5**
+
+At the first iteration we run introSort on the full collection that counts 13 elements. the maxDepth is 2, therefore we fall in the else case where quicksort acts.
+
+The `partition`  method picks the first element, the median and the last, it sorts them and uses the new median as pivot.
+
+    [ 10, 8, 26 ] -> [ 8, 10, 26 ]
+    
+Our array is now
+
+    [ 8, 0, 3, 9, 2, 14, 10, 27, 1, 5, 8, -1, 26 ]
+
+**10** is the pivot. After the choice of the pivot, the `partition` method swaps elements to get all the elements less than pivot on the left, and all the elements more or equal than pivot on the right.
+
+    [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10, 27, 14, 26 ]
+    
+Because of the swaps, the index of of pivot is now changed and returned. The next step of introsort is to call recursively itself for the two sub arrays:
+
+    less: [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10 ]
+    greater: [ 27, 14, 26 ]
+
+## maxDepth: 1, branch: less
+
+    [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10 ]
+
+The count of the array is still more than 5 so we don't meet yet the conditions for insertion sort to kick in. At this iteration maxDepth is decreased by one but it is still more than zero, so heapsort will not act.
+
+Just like in the previous iteration quicksort wins and the `partition` method choses a pivot and sorts the elemets less than pivot on the left and the elements more or equeal than pivot on the right.
+
+    array: [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10 ]
+    pivot candidates: [ 8, 1, 10] -> [ 1, 8, 10]
+    pivot: 8
+    before partition: [ 1, 0, 3, 9, 2, 8, 5, 8, -1, 10 ]
+    after partition: [ 1, 0, 3, -1, 2, 5, 8, 8, 9, 10 ]
+    
+    less: [ 1, 0, 3, -1, 2, 5, 8 ]
+    greater: [ 8, 9, 10 ]
+    
+## maxDepth: 0, branch: less
+
+    [ 1, 0, 3, -1, 2, 5, 8 ]
+    
+Just like before, introsort is recursively executed for `less` and greater. This time `less`has a count more than **5** so it will not be sorted with insertion sort, but the maxDepth decreased again by 1 is now 0 and heapsort takes over sorting the array.
+
+    heapsort -> [ -1, 0, 1, 2, 3, 5, 8 ]
+    
+## maxDepth: 0, branch: greater
+
+    [ 8, 9, 10 ]
+
+following greater in this recursion, the count of elements is 3, which is less than 5, so this partition is sorted using insertionSort.
+
+    insertionSort -> [ 8, 9 , 10]
+    
+
+## back to maxDepth = 1, branch: greater
+
+    [ 27, 14, 26 ]
+
+At this point the original array has mutated to be
+
+    [ -1, 0, 1, 2, 3, 5, 8, 8, 9, 10, 27, 14, 26 ]
+    
+now the `less` partition is sorted  and since the count of the `greater` partition is 3 it will be sorted with insertion sort  `[ 14, 26, 27 ]`
+
+The array is now successfully sorted
+
+    [ -1, 0, 1, 2, 3, 5, 8, 8, 9, 10, 14, 26, 27 ]
+
+
+## See also
+
+[Introsort on Wikipedia](https://en.wikipedia.org/wiki/Introsort)
+[Introsort comparison with other sorting algorithms](http://agostini.tech/2017/12/18/swift-sorting-algorithm/)
+
+*Written for Swift Algorithm Club by Giuseppe Lanza*
diff --git a/Introsort/Randomize.swift b/Introsort/Randomize.swift
new file mode 100644
index 000000000..6d1d57132
--- /dev/null
+++ b/Introsort/Randomize.swift
@@ -0,0 +1,9 @@
+import Foundation
+
+public func randomize(n: Int) -> [Int] {
+    var unsorted = [Int]()
+    for _ in 0..<n {
+        unsorted.append(Int(arc4random()))
+    }
+    return unsorted
+}
diff --git a/Introsort/Sort3.swift b/Introsort/Sort3.swift
new file mode 100644
index 000000000..04d20a6a6
--- /dev/null
+++ b/Introsort/Sort3.swift
@@ -0,0 +1,21 @@
+import Foundation
+
+public func sort3<T>(in array: inout [T], a: Int, b: Int, c: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    switch (areInIncreasingOrder(array[b], array[a]),
+            areInIncreasingOrder(array[c], array[b])) {
+    case (false, false): break
+    case (true, true): array.swapAt(a, c)
+    case (true, false):
+        array.swapAt(a, b)
+        
+        if areInIncreasingOrder(array[c], array[b]) {
+            array.swapAt(b, c)
+        }
+    case (false, true):
+        array.swapAt(b, c)
+        
+        if areInIncreasingOrder(array[b], array[a]) {
+            array.swapAt(a, b)
+        }
+    }
+}
diff --git a/README.markdown b/README.markdown
index 46544682e..beac173d6 100644
--- a/README.markdown
+++ b/README.markdown
@@ -73,6 +73,10 @@ Fast sorts:
 - [Merge Sort](Merge%20Sort/)
 - [Heap Sort](Heap%20Sort/)
 
+Hybrid sorts:
+
+- [Introsort](Introsort/)
+
 Special-purpose sorts:
 
 - [Counting Sort](Counting%20Sort/)

From e30467bcc9a9681780cee9d7206f4e2bda776ac6 Mon Sep 17 00:00:00 2001
From: Davis Riedel <mail@davis-riedel.de>
Date: Sat, 6 Jan 2018 22:47:22 +0100
Subject: [PATCH 1359/1679] Improvements to Heap

- renamed "elements" to "nodes" to clarify the difference between array and heap. This also unifies code and comments, which were sometimes referring to the array as "nodes".
- made nodes publicly readable but only settable within the heap itself. To change the nodes/operate on the heap, the provided functions should be used, to guarantee the heaps structure.
- renamed isOrderedBefore to orderCriteria. The variable name isOrderedBefore did not clearly explain what the variable is for/what the closure stored within does
- added method to get node at a specific index
- replace method should not force the replaced value to be higher/lower than its parent. Instead replace should remove the node to be replaced and insert the given value as a new one in order to preserve the heap's structure. Asserting crashes the whole program.
- added @discardableResult to removeAt. If remove is @discardableResult removeAt should be as well in for consistency.
- replaced while true in shiftDown with a recursive call. while true is bad programming style.
- simplified indexOf method
- added a removeNode method for heaps with equatable data type
- improved, adjusted and added descriptions
- made functions private where fileprivate was not needed
- added tests for new functions and tested everything
- updated README where necessary (to conform to new code, only a few changes)
---
 Heap/Heap.swift                               | 187 +++++++++---------
 Heap/README.markdown                          |  12 +-
 Heap/Tests/HeapTests.swift                    |  97 +++++----
 Heap/Tests/Tests.xcodeproj/project.pbxproj    |  14 +-
 .../contents.xcworkspacedata                  |   0
 .../xcshareddata/xcschemes/Tests.xcscheme     |   2 +-
 6 files changed, 172 insertions(+), 140 deletions(-)
 mode change 100644 => 100755 Heap/Heap.swift
 mode change 100644 => 100755 Heap/README.markdown
 mode change 100644 => 100755 Heap/Tests/HeapTests.swift
 mode change 100644 => 100755 Heap/Tests/Tests.xcodeproj/project.pbxproj
 mode change 100644 => 100755 Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 mode change 100644 => 100755 Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
old mode 100644
new mode 100755
index b0355da5d..a33fc0b94
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,58 +4,55 @@
 //
 
 public struct Heap<T> {
+  
   /** The array that stores the heap's nodes. */
-  var elements = [T]()
+  private(set) var nodes = [T]()
   
-  /** Determines whether this is a max-heap (>) or min-heap (<). */
-  fileprivate var isOrderedBefore: (T, T) -> Bool
+  /**
+   * Determines how to compare two nodes in the heap.
+   * Use '>' for a max-heap or '<' for a min-heap,
+   * or provide a comparing method if the heap is made
+   * of custom elements, for example tuples.
+   */
+  private var orderCriteria: (T, T) -> Bool
   
   /**
    * Creates an empty heap.
    * The sort function determines whether this is a min-heap or max-heap.
-   * For integers, > makes a max-heap, < makes a min-heap.
+   * For comparable data types, > makes a max-heap, < makes a min-heap.
    */
   public init(sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
+    self.orderCriteria = sort
   }
   
   /**
    * Creates a heap from an array. The order of the array does not matter;
    * the elements are inserted into the heap in the order determined by the
-   * sort function.
+   * sort function. For comparable data types, '>' makes a max-heap,
+   * '<' makes a min-heap.
    */
   public init(array: [T], sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
+    self.orderCriteria = sort
     buildHeap(fromArray: array)
   }
   
-  /*
-   // This version has O(n log n) performance.
-   private mutating func buildHeap(array: [T]) {
-   elements.reserveCapacity(array.count)
-   for value in array {
-   insert(value)
-   }
-   }
-   */
-  
   /**
-   * Converts an array to a max-heap or min-heap in a bottom-up manner.
+   * Creates the max-heap or min-heap from an array, in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
    */
-  fileprivate mutating func buildHeap(fromArray array: [T]) {
-    elements = array
-    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(i, heapSize: elements.count)
+  private mutating func buildHeap(fromArray array: [T]) {
+    nodes = array
+    for i in stride(from: (nodes.count/2-1), through: 0, by: -1) {
+      shiftDown(i)
     }
   }
   
   public var isEmpty: Bool {
-    return elements.isEmpty
+    return nodes.isEmpty
   }
   
   public var count: Int {
-    return elements.count
+    return nodes.count
   }
   
   /**
@@ -89,7 +86,13 @@ public struct Heap<T> {
    * value (for a min-heap).
    */
   public func peek() -> T? {
-    return elements.first
+    return nodes.first
+  }
+  
+  /** Returns the node at given index */
+  public func node(at i: Int) -> T? {
+    guard i < nodes.count else { return nil }
+    return nodes[i]
   }
   
   /**
@@ -97,10 +100,14 @@ public struct Heap<T> {
    * or min-heap property still holds. Performance: O(log n).
    */
   public mutating func insert(_ value: T) {
-    elements.append(value)
-    shiftUp(elements.count - 1)
+    nodes.append(value)
+    shiftUp(nodes.count - 1)
   }
   
+  /**
+   * Adds a sequence of values to the heap. This reorders the heap so that
+   * the max-heap or min-heap property still holds. Performance: O(log n).
+   */
   public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
     for value in sequence {
       insert(value)
@@ -108,15 +115,14 @@ public struct Heap<T> {
   }
   
   /**
-   * Allows you to change an element. In a max-heap, the new element should be
-   * larger than the old one; in a min-heap it should be smaller.
+   * Allows you to change an element. This reorders the heap so that
+   * the max-heap or min-heap property still holds.
    */
   public mutating func replace(index i: Int, value: T) {
-    guard i < elements.count else { return }
+    guard i < nodes.count else { return }
     
-    assert(isOrderedBefore(value, elements[i]))
-    elements[i] = value
-    shiftUp(i)
+    removeAt(i)
+    insert(value)
   }
   
   /**
@@ -124,34 +130,35 @@ public struct Heap<T> {
    * value; for a min-heap it is the minimum value. Performance: O(log n).
    */
   @discardableResult public mutating func remove() -> T? {
-    if elements.isEmpty {
-      return nil
-    } else if elements.count == 1 {
-      return elements.removeLast()
-    } else {
-      // Use the last node to replace the first one, then fix the heap by
-      // shifting this new first node into its proper position.
-      let value = elements[0]
-      elements[0] = elements.removeLast()
-      shiftDown()
-      return value
+    if !nodes.isEmpty {
+      if nodes.count == 1 {
+        return nodes.removeLast()
+      } else {
+        // Use the last node to replace the first one, then fix the heap by
+        // shifting this new first node into its proper position.
+        let value = nodes[0]
+        nodes[0] = nodes.removeLast()
+        shiftDown(0)
+        return value
+      }
     }
+    return nil
   }
   
   /**
-   * Removes an arbitrary node from the heap. Performance: O(log n). You need
-   * to know the node's index, which may actually take O(n) steps to find.
+   * Removes an arbitrary node from the heap. Performance: O(log n).
+   * Note that you need to know the node's index.
    */
-  public mutating func removeAt(_ index: Int) -> T? {
-    guard index < elements.count else { return nil }
+  @discardableResult public mutating func removeAt(_ index: Int) -> T? {
+    guard index < nodes.count else { return nil }
     
-    let size = elements.count - 1
+    let size = nodes.count - 1
     if index != size {
-      elements.swapAt(index, size)
-      shiftDown(index, heapSize: size)
+      nodes.swapAt(index, size)
+      shiftDown(from: index, until: size)
       shiftUp(index)
     }
-    return elements.removeLast()
+    return nodes.removeLast()
   }
   
   /**
@@ -160,68 +167,64 @@ public struct Heap<T> {
    */
   mutating func shiftUp(_ index: Int) {
     var childIndex = index
-    let child = elements[childIndex]
+    let child = nodes[childIndex]
     var parentIndex = self.parentIndex(ofIndex: childIndex)
     
-    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-      elements[childIndex] = elements[parentIndex]
+    while childIndex > 0 && orderCriteria(child, nodes[parentIndex]) {
+      nodes[childIndex] = nodes[parentIndex]
       childIndex = parentIndex
       parentIndex = self.parentIndex(ofIndex: childIndex)
     }
     
-    elements[childIndex] = child
-  }
-  
-  mutating func shiftDown() {
-    shiftDown(0, heapSize: elements.count)
+    nodes[childIndex] = child
   }
   
   /**
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  mutating func shiftDown(_ index: Int, heapSize: Int) {
-    var parentIndex = index
+  private mutating func shiftDown(from index: Int, until endIndex: Int) {
+    let leftChildIndex = self.leftChildIndex(ofIndex: index)
+    let rightChildIndex = leftChildIndex + 1
     
-    while true {
-      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-      let rightChildIndex = leftChildIndex + 1
-      
-      // Figure out which comes first if we order them by the sort function:
-      // the parent, the left child, or the right child. If the parent comes
-      // first, we're done. If not, that element is out-of-place and we make
-      // it "float down" the tree until the heap property is restored.
-      var first = parentIndex
-      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-        first = leftChildIndex
-      }
-      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-        first = rightChildIndex
-      }
-      if first == parentIndex { return }
-      
-      elements.swapAt(parentIndex, first)
-      parentIndex = first
+    // Figure out which comes first if we order them by the sort function:
+    // the parent, the left child, or the right child. If the parent comes
+    // first, we're done. If not, that element is out-of-place and we make
+    // it "float down" the tree until the heap property is restored.
+    var first = index
+    if leftChildIndex < endIndex && orderCriteria(nodes[leftChildIndex], nodes[first]) {
+      first = leftChildIndex
+    }
+    if rightChildIndex < endIndex && orderCriteria(nodes[rightChildIndex], nodes[first]) {
+      first = rightChildIndex
     }
+    if first == index { return }
+    
+    nodes.swapAt(index, first)
+    shiftDown(from: first, until: endIndex)
+  }
+  
+  private mutating func shiftDown(_ index: Int) {
+    shiftDown(from: index, until: nodes.count)
   }
+  
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-  /**
-   * Searches the heap for the given element. Performance: O(n).
-   */
-  public func index(of element: T) -> Int? {
-    return index(of: element, 0)
+  
+  /** Get the index of a node in the heap. Performance: O(n). */
+  public func index(of node: T) -> Int? {
+    return nodes.index(where: { $0 == node })
   }
   
-  fileprivate func index(of element: T, _ i: Int) -> Int? {
-    if i >= count { return nil }
-    if isOrderedBefore(element, elements[i]) { return nil }
-    if element == elements[i] { return i }
-    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+  /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
+  @discardableResult public mutating func remove(node: T) -> T? {
+    if let index = index(of: node) {
+      return removeAt(index)
+    }
     return nil
   }
+  
 }
diff --git a/Heap/README.markdown b/Heap/README.markdown
old mode 100644
new mode 100755
index 4344d9e7c..76d2bee39
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -38,7 +38,7 @@ A heap is not a replacement for a binary search tree, and there are similarities
 
 **Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL%20Tree/) or [red-black tree](../Red-Black%20Tree/), but with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
-**Searching.** Whereas searching is fast in a binary tree, it is slow in a heap. Searching isn't a top priority in a heap since the purpose of a heap is to put the largest (or smallest) node at the front and to allow relatively fast inserts and deletes. 
+**Searching.** Whereas searching is fast in a binary tree, it is slow in a heap. Searching isn't a top priority in a heap since the purpose of a heap is to put the largest (or smallest) node at the front and to allow relatively fast inserts and deletes.
 
 ## The tree inside an array
 
@@ -148,7 +148,7 @@ There are two primitive operations necessary to make sure the heap is a valid ma
 
 Shifting up or down is a recursive procedure that takes **O(log n)** time.
 
-Here are other operations that are built on primitive operations: 
+Here are other operations that are built on primitive operations:
 
 - `insert(value)`: Adds the new element to the end of the heap and then uses `shiftUp()` to fix the heap.
 
@@ -190,7 +190,7 @@ The `(16)` was added to the first available space on the last row.
 
 Unfortunately, the heap property is no longer satisfied because `(2)` is above `(16)`, and we want higher numbers above lower numbers. (This is a max-heap.)
 
-To restore the heap property, we swap `(16)` and `(2)`. 
+To restore the heap property, we swap `(16)` and `(2)`.
 
 ![The heap before insertion](Images/Insert2.png)
 
@@ -214,7 +214,7 @@ What happens to the empty spot at the top?
 
 ![The root is gone](Images/Remove1.png)
 
-When inserting, we put the new value at the end of the array. Here, we do the opposite: we take the last object we have, stick it up on top of the tree, and restore the heap property. 
+When inserting, we put the new value at the end of the array. Here, we do the opposite: we take the last object we have, stick it up on top of the tree, and restore the heap property.
 
 ![The last node goes to the root](Images/Remove2.png)
 
@@ -226,7 +226,7 @@ Keep shifting down until the node does not have any children or it is larger tha
 
 ![The last node goes to the root](Images/Remove4.png)
 
-The time required for shifting all the way down is proportional to the height of the tree which takes **O(log n)** time. 
+The time required for shifting all the way down is proportional to the height of the tree which takes **O(log n)** time.
 
 > **Note:** `shiftUp()` and `shiftDown()` can only fix one out-of-place element at a time. If there are multiple elements in the wrong place, you need to call these functions once for each of those elements.
 
@@ -279,7 +279,7 @@ In code:
 ```swift
   private mutating func buildHeap(fromArray array: [T]) {
     elements = array
-    for i in (elements.count/2 - 1).stride(through: 0, by: -1) {
+    for i in stride(from: (nodes.count/2-1), through: 0, by: -1) {
       shiftDown(index: i, heapSize: elements.count)
     }
   }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
old mode 100644
new mode 100755
index 66be0931c..36035fe93
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -19,9 +19,9 @@ class HeapTests: XCTestCase {
       let left = h.leftChildIndex(ofIndex: i)
       let right = h.rightChildIndex(ofIndex: i)
       let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] < h.elements[left] { return false }
-      if right < h.count && h.elements[i] < h.elements[right] { return false }
-      if i > 0 && h.elements[parent] < h.elements[i] { return false }
+      if left < h.count && h.nodes[i] < h.nodes[left] { return false }
+      if right < h.count && h.nodes[i] < h.nodes[right] { return false }
+      if i > 0 && h.nodes[parent] < h.nodes[i] { return false }
     }
     return true
   }
@@ -31,9 +31,9 @@ class HeapTests: XCTestCase {
       let left = h.leftChildIndex(ofIndex: i)
       let right = h.rightChildIndex(ofIndex: i)
       let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] > h.elements[left] { return false }
-      if right < h.count && h.elements[i] > h.elements[right] { return false }
-      if i > 0 && h.elements[parent] > h.elements[i] { return false }
+      if left < h.count && h.nodes[i] > h.nodes[left] { return false }
+      if right < h.count && h.nodes[i] > h.nodes[right] { return false }
+      if i > 0 && h.nodes[parent] > h.nodes[i] { return false }
     }
     return true
   }
@@ -90,7 +90,7 @@ class HeapTests: XCTestCase {
     let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
     XCTAssertTrue(verifyMaxHeap(h1))
     XCTAssertFalse(verifyMinHeap(h1))
-    XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
+    XCTAssertEqual(h1.nodes, [7, 5, 6, 4, 2, 1, 3])
     XCTAssertFalse(h1.isEmpty)
     XCTAssertEqual(h1.count, 7)
     XCTAssertEqual(h1.peek()!, 7)
@@ -98,7 +98,7 @@ class HeapTests: XCTestCase {
     let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h2))
     XCTAssertFalse(verifyMinHeap(h2))
-    XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
+    XCTAssertEqual(h2.nodes, [7, 6, 5, 4, 3, 2, 1])
     XCTAssertFalse(h2.isEmpty)
     XCTAssertEqual(h2.count, 7)
     XCTAssertEqual(h2.peek()!, 7)
@@ -106,7 +106,7 @@ class HeapTests: XCTestCase {
     let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
     XCTAssertTrue(verifyMaxHeap(h3))
     XCTAssertFalse(verifyMinHeap(h3))
-    XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+    XCTAssertEqual(h3.nodes, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
     XCTAssertFalse(h3.isEmpty)
     XCTAssertEqual(h3.count, 10)
     XCTAssertEqual(h3.peek()!, 16)
@@ -114,7 +114,7 @@ class HeapTests: XCTestCase {
     let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
     XCTAssertTrue(verifyMaxHeap(h4))
     XCTAssertFalse(verifyMinHeap(h4))
-    XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
+    XCTAssertEqual(h4.nodes, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
     XCTAssertFalse(h4.isEmpty)
     XCTAssertEqual(h4.count, 14)
     XCTAssertEqual(h4.peek()!, 27)
@@ -124,7 +124,7 @@ class HeapTests: XCTestCase {
     let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
     XCTAssertTrue(verifyMinHeap(h1))
     XCTAssertFalse(verifyMaxHeap(h1))
-    XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
+    XCTAssertEqual(h1.nodes, [1, 2, 3, 4, 5, 6, 7])
     XCTAssertFalse(h1.isEmpty)
     XCTAssertEqual(h1.count, 7)
     XCTAssertEqual(h1.peek()!, 1)
@@ -132,7 +132,7 @@ class HeapTests: XCTestCase {
     let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
     XCTAssertTrue(verifyMinHeap(h2))
     XCTAssertFalse(verifyMaxHeap(h2))
-    XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
+    XCTAssertEqual(h2.nodes, [1, 3, 2, 4, 6, 7, 5])
     XCTAssertFalse(h2.isEmpty)
     XCTAssertEqual(h2.count, 7)
     XCTAssertEqual(h2.peek()!, 1)
@@ -140,7 +140,7 @@ class HeapTests: XCTestCase {
     let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
     XCTAssertTrue(verifyMinHeap(h3))
     XCTAssertFalse(verifyMaxHeap(h3))
-    XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
+    XCTAssertEqual(h3.nodes, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
     XCTAssertFalse(h3.isEmpty)
     XCTAssertEqual(h3.count, 10)
     XCTAssertEqual(h3.peek()!, 1)
@@ -148,7 +148,7 @@ class HeapTests: XCTestCase {
     let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
     XCTAssertTrue(verifyMinHeap(h4))
     XCTAssertFalse(verifyMaxHeap(h4))
-    XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
+    XCTAssertEqual(h4.nodes, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
     XCTAssertFalse(h4.isEmpty)
     XCTAssertEqual(h4.count, 14)
     XCTAssertEqual(h4.peek()!, 0)
@@ -158,14 +158,14 @@ class HeapTests: XCTestCase {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(heap))
     XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    XCTAssertEqual(heap.nodes, [1, 1, 1, 1, 1])
   }
   
   func testCreateMinHeapEqualElements() {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
     XCTAssertTrue(verifyMinHeap(heap))
     XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    XCTAssertEqual(heap.nodes, [1, 1, 1, 1, 1])
   }
   
   fileprivate func randomArray(_ n: Int) -> [Int] {
@@ -183,7 +183,7 @@ class HeapTests: XCTestCase {
       XCTAssertTrue(verifyMaxHeap(h))
       XCTAssertFalse(h.isEmpty)
       XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+      XCTAssertTrue(isPermutation(a, h.nodes))
     }
   }
   
@@ -194,58 +194,58 @@ class HeapTests: XCTestCase {
       XCTAssertTrue(verifyMinHeap(h))
       XCTAssertFalse(h.isEmpty)
       XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+      XCTAssertTrue(isPermutation(a, h.nodes))
     }
   }
   
-  func testRemoving() {
+  func testRemovingAtIndex() {
     var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
     //test index out of bounds
     let v = h.removeAt(10)
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
     let v1 = h.removeAt(5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
+    XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 65])
     
     let v2 = h.removeAt(4)
     XCTAssertEqual(v2, 20)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
+    XCTAssertEqual(h.nodes, [100, 65, 70, 10, 50])
     
     let v3 = h.removeAt(4)
     XCTAssertEqual(v3, 50)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10])
+    XCTAssertEqual(h.nodes, [100, 65, 70, 10])
     
     let v4 = h.removeAt(0)
     XCTAssertEqual(v4, 100)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [70, 65, 10])
+    XCTAssertEqual(h.nodes, [70, 65, 10])
     
     XCTAssertEqual(h.peek()!, 70)
     let v5 = h.remove()
     XCTAssertEqual(v5, 70)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [65, 10])
+    XCTAssertEqual(h.nodes, [65, 10])
     
     XCTAssertEqual(h.peek()!, 65)
     let v6 = h.remove()
     XCTAssertEqual(v6, 65)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [10])
+    XCTAssertEqual(h.nodes, [10])
     
     XCTAssertEqual(h.peek()!, 10)
     let v7 = h.remove()
     XCTAssertEqual(v7, 10)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [])
+    XCTAssertEqual(h.nodes, [])
     
     XCTAssertNil(h.peek())
   }
@@ -259,12 +259,23 @@ class HeapTests: XCTestCase {
   func testRemoveRoot() {
     var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
     XCTAssertEqual(h.peek()!, 15)
     let v = h.remove()
     XCTAssertEqual(v, 15)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
+    XCTAssertEqual(h.nodes, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
+  }
+  
+  func testRemoveNode() {
+    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.node(at: 3)!, 5)
+    let v = h.remove(node: 5)
+    XCTAssertEqual(v, 5)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertFalse(h.nodes.contains(5))
   }
   
   func testRemoveRandomItems() {
@@ -272,19 +283,27 @@ class HeapTests: XCTestCase {
       var a = randomArray(n)
       var h = Heap(array: a, sort: >)
       XCTAssertTrue(verifyMaxHeap(h))
-      XCTAssertTrue(isPermutation(a, h.elements))
+      XCTAssertTrue(isPermutation(a, h.nodes))
       
       let m = (n + 1)/2
       for k in 1...m {
         let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        let v = h.removeAt(i)!
-        let j = a.index(of: v)!
+        
+        var v: Int? = nil
+        if k == 2 || k == m {
+          v = h.remove(node: h.node(at: i)!)
+        } else {
+          v = h.removeAt(i)
+        }
+        XCTAssertNotNil(v)
+        
+        let j = a.index(of: v!)!
         a.remove(at: j)
         
         XCTAssertTrue(verifyMaxHeap(h))
         XCTAssertEqual(h.count, a.count)
         XCTAssertEqual(h.count, n - k)
-        XCTAssertTrue(isPermutation(a, h.elements))
+        XCTAssertTrue(isPermutation(a, h.nodes))
       }
     }
   }
@@ -292,17 +311,17 @@ class HeapTests: XCTestCase {
   func testInsert() {
     var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
     
     h.insert(10)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
+    XCTAssertEqual(h.nodes, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
   }
   
   func testInsertArrayAndRemove() {
     var heap = Heap<Int>(sort: >)
     heap.insert([1, 3, 2, 7, 5, 9])
-    XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
+    XCTAssertEqual(heap.nodes, [9, 5, 7, 1, 3, 2])
     
     XCTAssertEqual(9, heap.remove())
     XCTAssertEqual(7, heap.remove())
@@ -316,15 +335,13 @@ class HeapTests: XCTestCase {
   func testReplace() {
     var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
     
     h.replace(index: 5, value: 13)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
     
     //test index out of bounds
     h.replace(index: 20, value: 2)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
   }
+  
 }
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
old mode 100644
new mode 100755
index 617e29f27..51433ee64
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,7 +83,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0920;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -141,14 +141,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -187,14 +193,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
diff --git a/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
old mode 100644
new mode 100755
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
old mode 100644
new mode 100755
index 80ed35600..77d01bebc
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0920"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 92f67b5136fb4623cb9c0cfb9826b72562455534 Mon Sep 17 00:00:00 2001
From: Davis Riedel <mail@davis-riedel.de>
Date: Mon, 8 Jan 2018 10:47:59 +0100
Subject: [PATCH 1360/1679] - Adopted discussed improvements - Made nodes and
 some other methods internal, so that extensions like HeapSort can use them.
 This fixes the HeapSort algorithm as well as the tests for both.

---
 Heap Sort/HeapSort.swift   |  8 +++---
 Heap/Heap.swift            | 55 +++++++++++++++++---------------------
 Heap/Tests/HeapTests.swift | 39 +++++++--------------------
 3 files changed, 38 insertions(+), 64 deletions(-)

diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index 6b5e91dc5..0354817a6 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,10 +1,10 @@
 extension Heap {
   public mutating func sort() -> [T] {
-    for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-      elements.swapAt(0, i)
-      shiftDown(0, heapSize: i)
+    for i in stride(from: (nodes.count - 1), through: 1, by: -1) {
+      nodes.swapAt(0, i)
+      shiftDown(from: 0, until: i)
     }
-    return elements
+    return nodes
   }
 }
 
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index a33fc0b94..ae392d448 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -6,7 +6,7 @@
 public struct Heap<T> {
   
   /** The array that stores the heap's nodes. */
-  private(set) var nodes = [T]()
+  internal var nodes = [T]()
   
   /**
    * Determines how to compare two nodes in the heap.
@@ -33,14 +33,14 @@ public struct Heap<T> {
    */
   public init(array: [T], sort: @escaping (T, T) -> Bool) {
     self.orderCriteria = sort
-    buildHeap(fromArray: array)
+    configureHeap(from: array)
   }
   
   /**
-   * Creates the max-heap or min-heap from an array, in a bottom-up manner.
+   * Configures the max-heap or min-heap from an array, in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
    */
-  private mutating func buildHeap(fromArray array: [T]) {
+  private mutating func configureHeap(from array: [T]) {
     nodes = array
     for i in stride(from: (nodes.count/2-1), through: 0, by: -1) {
       shiftDown(i)
@@ -59,7 +59,7 @@ public struct Heap<T> {
    * Returns the index of the parent of the element at index i.
    * The element at index 0 is the root of the tree and has no parent.
    */
-  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+  @inline(__always) internal func parentIndex(ofIndex i: Int) -> Int {
     return (i - 1) / 2
   }
   
@@ -68,7 +68,7 @@ public struct Heap<T> {
    * Note that this index can be greater than the heap size, in which case
    * there is no left child.
    */
-  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+  @inline(__always) internal func leftChildIndex(ofIndex i: Int) -> Int {
     return 2*i + 1
   }
   
@@ -77,7 +77,7 @@ public struct Heap<T> {
    * Note that this index can be greater than the heap size, in which case
    * there is no right child.
    */
-  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+  @inline(__always) internal func rightChildIndex(ofIndex i: Int) -> Int {
     return 2*i + 2
   }
   
@@ -89,12 +89,6 @@ public struct Heap<T> {
     return nodes.first
   }
   
-  /** Returns the node at given index */
-  public func node(at i: Int) -> T? {
-    guard i < nodes.count else { return nil }
-    return nodes[i]
-  }
-  
   /**
    * Adds a new value to the heap. This reorders the heap so that the max-heap
    * or min-heap property still holds. Performance: O(log n).
@@ -121,7 +115,7 @@ public struct Heap<T> {
   public mutating func replace(index i: Int, value: T) {
     guard i < nodes.count else { return }
     
-    removeAt(i)
+    remove(at: i)
     insert(value)
   }
   
@@ -130,26 +124,25 @@ public struct Heap<T> {
    * value; for a min-heap it is the minimum value. Performance: O(log n).
    */
   @discardableResult public mutating func remove() -> T? {
-    if !nodes.isEmpty {
-      if nodes.count == 1 {
-        return nodes.removeLast()
-      } else {
-        // Use the last node to replace the first one, then fix the heap by
-        // shifting this new first node into its proper position.
-        let value = nodes[0]
-        nodes[0] = nodes.removeLast()
-        shiftDown(0)
-        return value
-      }
+    guard !nodes.isEmpty else { return nil }
+    
+    if nodes.count == 1 {
+      return nodes.removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = nodes[0]
+      nodes[0] = nodes.removeLast()
+      shiftDown(0)
+      return value
     }
-    return nil
   }
   
   /**
    * Removes an arbitrary node from the heap. Performance: O(log n).
    * Note that you need to know the node's index.
    */
-  @discardableResult public mutating func removeAt(_ index: Int) -> T? {
+  @discardableResult public mutating func remove(at index: Int) -> T? {
     guard index < nodes.count else { return nil }
     
     let size = nodes.count - 1
@@ -165,7 +158,7 @@ public struct Heap<T> {
    * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
-  mutating func shiftUp(_ index: Int) {
+  internal mutating func shiftUp(_ index: Int) {
     var childIndex = index
     let child = nodes[childIndex]
     var parentIndex = self.parentIndex(ofIndex: childIndex)
@@ -183,7 +176,7 @@ public struct Heap<T> {
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  private mutating func shiftDown(from index: Int, until endIndex: Int) {
+  internal mutating func shiftDown(from index: Int, until endIndex: Int) {
     let leftChildIndex = self.leftChildIndex(ofIndex: index)
     let rightChildIndex = leftChildIndex + 1
     
@@ -204,7 +197,7 @@ public struct Heap<T> {
     shiftDown(from: first, until: endIndex)
   }
   
-  private mutating func shiftDown(_ index: Int) {
+  internal mutating func shiftDown(_ index: Int) {
     shiftDown(from: index, until: nodes.count)
   }
   
@@ -222,7 +215,7 @@ extension Heap where T: Equatable {
   /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
   @discardableResult public mutating func remove(node: T) -> T? {
     if let index = index(of: node) {
-      return removeAt(index)
+      return remove(at: index)
     }
     return nil
   }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 36035fe93..1ed15c726 100755
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -154,14 +154,14 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(h4.peek()!, 0)
   }
   
-  func testCreateMaxHeapEqualElements() {
+  func testCreateMaxHeapEqualnodes() {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(heap))
     XCTAssertTrue(verifyMinHeap(heap))
     XCTAssertEqual(heap.nodes, [1, 1, 1, 1, 1])
   }
   
-  func testCreateMinHeapEqualElements() {
+  func testCreateMinHeapEqualnodes() {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
     XCTAssertTrue(verifyMinHeap(heap))
     XCTAssertTrue(verifyMaxHeap(heap))
@@ -198,33 +198,33 @@ class HeapTests: XCTestCase {
     }
   }
   
-  func testRemovingAtIndex() {
+  func testRemoving() {
     var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
     //test index out of bounds
-    let v = h.removeAt(10)
+    let v = h.remove(at: 10)
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
-    let v1 = h.removeAt(5)
+    let v1 = h.remove(at: 5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 65])
     
-    let v2 = h.removeAt(4)
+    let v2 = h.remove(at: 4)
     XCTAssertEqual(v2, 20)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 65, 70, 10, 50])
     
-    let v3 = h.removeAt(4)
+    let v3 = h.remove(at: 4)
     XCTAssertEqual(v3, 50)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 65, 70, 10])
     
-    let v4 = h.removeAt(0)
+    let v4 = h.remove(at: 0)
     XCTAssertEqual(v4, 100)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [70, 65, 10])
@@ -267,17 +267,6 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(h.nodes, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
   }
   
-  func testRemoveNode() {
-    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-    XCTAssertEqual(h.node(at: 3)!, 5)
-    let v = h.remove(node: 5)
-    XCTAssertEqual(v, 5)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertFalse(h.nodes.contains(5))
-  }
-  
   func testRemoveRandomItems() {
     for n in 1...40 {
       var a = randomArray(n)
@@ -288,16 +277,8 @@ class HeapTests: XCTestCase {
       let m = (n + 1)/2
       for k in 1...m {
         let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        
-        var v: Int? = nil
-        if k == 2 || k == m {
-          v = h.remove(node: h.node(at: i)!)
-        } else {
-          v = h.removeAt(i)
-        }
-        XCTAssertNotNil(v)
-        
-        let j = a.index(of: v!)!
+        let v = h.remove(at: i)!
+        let j = a.index(of: v)!
         a.remove(at: j)
         
         XCTAssertTrue(verifyMaxHeap(h))

From 39b7311ec6fe68af0fb83b6322d7121a6d9c8f62 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 8 Jan 2018 17:47:10 -0800
Subject: [PATCH 1361/1679] Removes redundant `internal` modifier.

---
 Heap/Heap.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index ae392d448..cf39fb8a5 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -6,7 +6,7 @@
 public struct Heap<T> {
   
   /** The array that stores the heap's nodes. */
-  internal var nodes = [T]()
+  var nodes = [T]()
   
   /**
    * Determines how to compare two nodes in the heap.

From d4d471ba02dfcca3c58221a35159f650d15eb570 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Wed, 10 Jan 2018 11:28:05 +0800
Subject: [PATCH 1362/1679] Update README.markdown

fix Code syntax error
---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 1d9321591..84e278f5c 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -268,7 +268,7 @@ If there are no more nodes to look at -- when `left` or `right` is nil -- then w
 Searching is a recursive process, but you can also implement it with a simple loop instead:
 
 ```swift
-  public func search(value: T) -> BinarySearchTree? {
+  public func search(_ value: T) -> BinarySearchTree? {
     var node: BinarySearchTree? = self
     while let n = node {
       if value < n.value {

From b36304c7ae0ae92dacf59f9d8c96f7fe7f4b5315 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Wed, 10 Jan 2018 22:18:14 -0800
Subject: [PATCH 1363/1679] add update to readme

---
 Red-Black Tree/README.markdown | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 74fffa415..6db827ea6 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -39,6 +39,9 @@ Tree:
 * `insert(key:)` Inserts the key value into the tree
 * `delete(key:)` Delete the node with the respective key value from the tree
 * `verify()` Verifies that the given tree fulfills the red-black tree properties
+* `count()` Returns how many nodes in the tree
+* `isEmpty()` Returns if the tree has no nodes
+* `allElements()` Returns an array containing all nodes (in-order traversal) in the tree.
 
 The rotation, insertion and deletion algorithms are implemented based on the pseudo-code provided in [CLRS]
 

From adf606599050c8eaf4b63a0c8e18a5b52a4892b7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Wed, 19 Jul 2017 15:47:40 -0700
Subject: [PATCH 1364/1679] Encode and Decode A Binary Tree

Encode and Decode A Binary Tree
---
 .../Contents.swift                            |  49 +++++++++
 .../Sources/EncodeAndDecodeTree.swift         | 104 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../EncodeAndDecodeTree.swift                 | 104 ++++++++++++++++++
 Encode and Decode Tree/readme.md              |  27 +++++
 .../contents.xcworkspacedata                  |  10 ++
 6 files changed, 298 insertions(+)
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.swift
 create mode 100644 Encode and Decode Tree/readme.md

diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift
new file mode 100644
index 000000000..dbd2fd180
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift	
@@ -0,0 +1,49 @@
+//: Playground - noun: a place where people can play
+
+
+func printTree(_ root: TreeNode?) {
+    guard let root = root else {
+        return
+    }
+
+    var pointer = root
+
+    let leftVal = root.left == nil ? "nil" : root.left!.val
+    let rightVal = root.right == nil ? "nil" : root.right!.val
+
+    print("val: \(root.val) left: \(leftVal) right: \(rightVal)")
+
+    printTree(root.left)
+    printTree(root.right)
+}
+
+let s = EncodeAndDecodeTree()
+
+let node1 = TreeNode("a")
+let node2 = TreeNode("b")
+let node3 = TreeNode("c")
+let node4 = TreeNode("d")
+let node5 = TreeNode("e")
+
+node1.left = node2
+node1.right = node3
+node3.left = node4
+node3.right = node5
+
+let encodeStr = s.encode(node1)
+print(encodeStr)
+// "a b # # c d # # e # #"
+
+
+let root = s.decode(encodeStr)
+print("Tree:")
+printTree(root)
+/*
+ Tree:
+ val: a left: b right: c
+ val: b left: nil right: nil
+ val: c left: d right: e
+ val: d left: nil right: nil
+ val: e left: nil right: nil
+ */
+
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift
new file mode 100644
index 000000000..e9d22f8a9
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift	
@@ -0,0 +1,104 @@
+//
+//  EncodeAndDecodeTree.swift
+//  
+//
+//  Created by Kai Chen on 19/07/2017.
+//
+//
+
+import Foundation
+
+public class TreeNode {
+    public var val: String
+    public var left: TreeNode?
+    public var right: TreeNode?
+
+    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
+        self.val = val
+        self.left = left
+        self.right = right
+    }
+}
+
+public class EncodeAndDecodeTree {
+    private var encodeStr = ""
+    private var ret: [String] = []
+
+    public init() {}
+
+    public func encode(_ root: TreeNode?) -> String {
+        encodeIt(root)
+
+        return encodeStr
+    }
+
+    public func decode(_ data: String) -> TreeNode? {
+        var s = data
+        while (s.contains(" ")) {
+            let index = s.index(of: " ")
+            let endIndex = s.index(before: index)
+            let element = s[s.startIndex...endIndex]
+            ret.append(element)
+            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
+            s.removeSubrange(range)
+        }
+
+        if ret.count == 0 {
+            return nil
+        }
+
+        var dep = 0
+        let root = decodeIt(&dep)
+
+        return root
+    }
+
+    private func getNode(_ element: String) -> TreeNode? {
+        if element == "#" {
+            return nil
+        }
+
+        return TreeNode(element)
+    }
+
+    private func decodeIt(_ dep: inout Int) -> TreeNode? {
+        guard let currentNode = getNode(ret[dep]) else {
+            return nil
+        }
+
+        dep += 1
+        let left = decodeIt(&dep)
+        dep += 1
+        let right = decodeIt(&dep)
+
+        currentNode.left = left
+        currentNode.right = right
+
+        return currentNode
+    }
+
+    private func encodeIt(_ root: TreeNode?) {
+        guard let root = root else {
+            encodeStr += "# "
+            return
+        }
+
+        encodeStr += root.val + " "
+        encodeIt(root.left)
+        encodeIt(root.right)
+    }
+}
+
+extension String {
+    func index(of target: Character) -> String.Index {
+        var i = 0
+        for c in self.characters {
+            if c == target {
+                return self.index(self.startIndex, offsetBy: i)
+            }
+            i += 1
+        }
+
+        return self.endIndex
+    }
+}
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground b/Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.swift
new file mode 100644
index 000000000..daa3c3ea2
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.swift	
@@ -0,0 +1,104 @@
+//
+//  EncodeAndDecodeTree.swift
+//
+//
+//  Created by Kai Chen on 19/07/2017.
+//
+//
+
+import Foundation
+
+public class TreeNode {
+    public var val: String
+    public var left: TreeNode?
+    public var right: TreeNode?
+
+    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
+        self.val = val
+        self.left = left
+        self.right = right
+    }
+}
+
+public class EncodeAndDecodeTree {
+    private var encodeStr = ""
+    private var ret: [String] = []
+
+    public init() {}
+
+    public func encode(_ root: TreeNode?) -> String {
+        encodeIt(root)
+
+        return encodeStr
+    }
+
+    public func decode(_ data: String) -> TreeNode? {
+        var s = data
+        while (s.contains(" ")) {
+            let index = s.index(of: " ")
+            let endIndex = s.index(before: index)
+            let element = s[s.startIndex...endIndex]
+            ret.append(element)
+            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
+            s.removeSubrange(range)
+        }
+
+        if ret.count == 0 {
+            return nil
+        }
+
+        var dep = 0
+        let root = decodeIt(&dep)
+
+        return root
+    }
+
+    private func getNode(_ element: String) -> TreeNode? {
+        if element == "#" {
+            return nil
+        }
+
+        return TreeNode(element)
+    }
+
+    private func decodeIt(_ dep: inout Int) -> TreeNode? {
+        guard let currentNode = getNode(ret[dep]) else {
+            return nil
+        }
+
+        dep += 1
+        let left = decodeIt(&dep)
+        dep += 1
+        let right = decodeIt(&dep)
+
+        currentNode.left = left
+        currentNode.right = right
+
+        return currentNode
+    }
+
+    private func encodeIt(_ root: TreeNode?) {
+        guard let root = root else {
+            encodeStr += "# "
+            return
+        }
+
+        encodeStr += root.val + " "
+        encodeIt(root.left)
+        encodeIt(root.right)
+    }
+}
+
+extension String {
+    func index(of target: Character) -> String.Index {
+        var i = 0
+        for c in self.characters {
+            if c == target {
+                return self.index(self.startIndex, offsetBy: i)
+            }
+            i += 1
+        }
+        
+        return self.endIndex
+    }
+}
diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
new file mode 100644
index 000000000..c986d9147
--- /dev/null
+++ b/Encode and Decode Tree/readme.md	
@@ -0,0 +1,27 @@
+# Encode and Decode Binary Tree
+
+We need to design an algorithm to encode and decode a binary tree. 
+* **Encode**: Convert a tree into a string that can be stored in the disk.
+* **Decode**: Given the encoded string, you need to convert it into a Tree.
+
+For example, you may serialize the following tree
+
+
+as "[1,2,3,null,null,4,5]", just the same as how LeetCode OJ serializes a binary tree. You do not necessarily need to follow this format, so please be creative and come up with different approaches yourself.
+Note: Do not use class member/global/static variables to store states. Your serialize and deserialize algorithms should be stateless.
+
+## Solution
+For example, given a tree like this
+>       a
+>      /  \\
+>
+>    b     c
+>
+>    ​      /  \\
+>    ​    d    e
+
+We can use inorder traversal to convert the tree into the string like this `a b # # c d # # e # #`
+
+So, the idea is for the empty node, we use `#` to represent.
+
+For the decode process, we can still use inorder to convert the string back to a tree.
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4cab8e2d4..77f124fc3 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -117,6 +117,16 @@
          location = "group:LRU Cache/Readme.md">
       </FileRef>
    </Group>
+   <Group
+      location = "container:"
+      name = "Encode and Decode Tree">
+      <FileRef
+         location = "group:Encode and Decode Tree/EncodeAndDecodeTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Encode and Decode Tree/EncodeAndDecodeTree.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"
       name = "Miller-Rabin Primality Test">

From f5c74b9aa9f34e7e57fc16059ee3076642abcdc9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 16 Nov 2017 09:13:20 -0800
Subject: [PATCH 1365/1679] Refactor in progress

---
 Encode and Decode Tree/readme.md | 58 ++++++++++++++++++++++----------
 1 file changed, 40 insertions(+), 18 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index c986d9147..7f3e5538d 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -1,27 +1,49 @@
 # Encode and Decode Binary Tree
 
-We need to design an algorithm to encode and decode a binary tree. 
-* **Encode**: Convert a tree into a string that can be stored in the disk.
-* **Decode**: Given the encoded string, you need to convert it into a Tree.
+> **Note**: The prerequisite for this article is an understanding of how [binary trees](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Tree) work.
 
-For example, you may serialize the following tree
+Trees are complex structures. Unlike linear collections such as arrays or linked lists, trees are *non-linear* and each element in a tree has positional information such as the *parent-child* relationship between nodes. When you want to send a tree structure to your backend, you need to send the data of each node, and a way to represent the parent-child relationship for each node.
 
+Your strategy in how you choose to represent this information is called your **encoding** strategy. The opposite of that - changing your encoded data back to its original form - is your **decoding** strategy. 
 
-as "[1,2,3,null,null,4,5]", just the same as how LeetCode OJ serializes a binary tree. You do not necessarily need to follow this format, so please be creative and come up with different approaches yourself.
-Note: Do not use class member/global/static variables to store states. Your serialize and deserialize algorithms should be stateless.
+There are many ways to encode a tree and decode a tree. The important thing to keep in mind is that encoding and decoding strategies are closely related. The way you choose to encode a tree directly affects how you might decode a tree. 
 
-## Solution
-For example, given a tree like this
->       a
->      /  \\
->
->    b     c
->
->    ​      /  \\
->    ​    d    e
+Encoding and decoding are synonyms to *serializing* and *deserializing* trees. 
 
-We can use inorder traversal to convert the tree into the string like this `a b # # c d # # e # #`
+As a reference, the following code represents the typical `Node` type of a binary tree:
 
-So, the idea is for the empty node, we use `#` to represent.
+```swift
+class BinaryNode<Element: Comparable> {
+  var data: Element
+  var leftChild: BinaryNode?
+  var rightChild: BinaryNode?
+
+  // ... (rest of the implementation)
+}
+```
+
+## Encoding
+
+As mentioned before, there are different ways to do encoding. For no particular reason, you'll opt for the following rules:
+
+1. The result of the encoding will be a `String` object.
+2. You'll encode using *pre-order* traversal.
+
+Here's an example of this operation in code:
+
+```swift
+extension BinaryNode {
+  var encodedString: String {
+    var str = ""
+    preOrderTraversal { str.append($0) }
+    return str
+  }
+  
+  func preOrderTraversal(visit: (T) -> ()) {
+    visit(data)
+    leftChild?.preOrderTraversal(visit: visit)
+    rightChild?.preOrderTraversal(visit: visit)
+  }
+}
+```
 
-For the decode process, we can still use inorder to convert the string back to a tree.
\ No newline at end of file

From b772141951fe32729c6976d9a082b5c2f3eef203 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 16 Nov 2017 10:06:14 -0800
Subject: [PATCH 1366/1679] More progress

---
 Encode and Decode Tree/readme.md | 77 ++++++++++++++++++++++++++++++--
 1 file changed, 73 insertions(+), 4 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index 7f3e5538d..3b2281224 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -33,17 +33,86 @@ Here's an example of this operation in code:
 
 ```swift
 extension BinaryNode {
+  // 1
+  private var splitter: String { return "," }
+  private var nilNode: String { return "nil" }
+  
+  // 2
   var encodedString: String {
     var str = ""
-    preOrderTraversal { str.append($0) }
+    preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(splitter)
+    }
     return str
   }
   
-  func preOrderTraversal(visit: (T) -> ()) {
+  // 3
+  func preOrderTraversal(visit: (T?) -> ()) {
     visit(data)
-    leftChild?.preOrderTraversal(visit: visit)
-    rightChild?.preOrderTraversal(visit: visit)
+    
+    if let leftChild = leftChild {
+      leftChild.preOrderTraversal(visit: visit)
+    } else {
+      visit(nil)
+    }
+    
+    if let rightChild = rightChild {
+      rightChild.preOrderTraversal(visit: visit)
+    } else {
+      visit(nil)
+    }
   }
 }
 ```
 
+Here's a high level overview of the above code:
+
+1. `splitter` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `splitter`, you can't tell.
+
+2. `encodedString` is the result of the encoding process. Returns a string representation of the tree. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
+
+3. It is interesting to note that this pre-order traversal implementation also emits `nil` values in place of absent children.
+
+## Decoding
+
+Your decoding strategy is the exact opposite of your encoding strategy. You'll take an encoded string, and turn it back into your binary tree.
+
+Your encoding strategy followed the following rules:
+
+1. The result of the encoding will be a `String` object.
+2. You'll encode using *pre-order* traversal.
+
+The implementation also added a few important details:
+
+* node values are separated by `,` 
+* `nil` children are denoted by the `nil` string
+
+These details will shape your `decode` operation. Here's a possible implementation:
+
+```swift
+extension BinaryTree {
+  
+  static func decode<Element>(from string: String) -> BinaryNode<Element>? {
+    let array = string.split(separator: ",")
+    let deque: Deque<String> = array
+    return decode(from: deque)
+  }
+  
+  static func decode<Elements: RangeReplaceableCollection>(from deque: RangeReplaceableCollection) 
+    -> BinaryNode<Elements.Element>? {
+    
+  }
+}
+```
+
+
+
+
+
+

From 959aaafe2d16b9e82f830381c6856c396590c51f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 16 Nov 2017 10:22:28 -0800
Subject: [PATCH 1367/1679] More progress.

---
 Encode and Decode Tree/readme.md | 23 ++++++++++++++++++-----
 1 file changed, 18 insertions(+), 5 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index 3b2281224..506bfbe05 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -34,8 +34,8 @@ Here's an example of this operation in code:
 ```swift
 extension BinaryNode {
   // 1
-  private var splitter: String { return "," }
-  private var nilNode: String { return "nil" }
+  fileprivate var splitter: String { return "," }
+  fileprivate var nilNode: String { return "nil" }
   
   // 2
   var encodedString: String {
@@ -98,19 +98,32 @@ These details will shape your `decode` operation. Here's a possible implementati
 ```swift
 extension BinaryTree {
   
+  // 1
   static func decode<Element>(from string: String) -> BinaryNode<Element>? {
     let array = string.split(separator: ",")
-    let deque: Deque<String> = array
-    return decode(from: deque)
+    return decode(from: array)
   }
   
-  static func decode<Elements: RangeReplaceableCollection>(from deque: RangeReplaceableCollection) 
+  // 2
+  static func decode<Elements: Sequence>(from sequence: Sequence) 
     -> BinaryNode<Elements.Element>? {
     
+    guard let value = sequence.first else { return nil }
+    if value == nilNode {
+      return nil
+    } else {
+      let node = BinaryNode<Elements.Element>(value: value)
+      node.leftChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
+      node.rightChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
+    }    
   }
 }
 ```
 
+Here's a high level overview of the above code:
+
+1. Takes a `String`, and uses `split` to partition the contents of `string` into an array based on the `","` character. 
+2. Takes any `Sequence` type and recursively creates a binary tree based on the rules declared in the encoding operation.
 
 
 

From e1599029f885de746bb8b7626246d57f7bdbd664 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 18 Nov 2017 01:45:12 -0800
Subject: [PATCH 1368/1679] More progress

---
 Encode and Decode Tree/readme.md | 60 +++++++++++++++++---------------
 1 file changed, 31 insertions(+), 29 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index 506bfbe05..e0c38531c 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -34,8 +34,8 @@ Here's an example of this operation in code:
 ```swift
 extension BinaryNode {
   // 1
-  fileprivate var splitter: String { return "," }
-  fileprivate var nilNode: String { return "nil" }
+  fileprivate var separator: String { return "," }
+  fileprivate var nilNode: String { return "X" }
   
   // 2
   var encodedString: String {
@@ -47,25 +47,25 @@ extension BinaryNode {
       } else {
         str.append(nilNode)
       }
-      str.append(splitter)
+      str.append(separator)
     }
     return str
   }
   
   // 3
-  func preOrderTraversal(visit: (T?) -> ()) {
-    visit(data)
+  func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
+    try visit(data)
     
     if let leftChild = leftChild {
-      leftChild.preOrderTraversal(visit: visit)
+      try leftChild.preOrderTraversal(visit: visit)
     } else {
-      visit(nil)
+      try visit(nil)
     }
     
     if let rightChild = rightChild {
-      rightChild.preOrderTraversal(visit: visit)
+      try rightChild.preOrderTraversal(visit: visit)
     } else {
-      visit(nil)
+      try visit(nil)
     }
   }
 }
@@ -73,7 +73,7 @@ extension BinaryNode {
 
 Here's a high level overview of the above code:
 
-1. `splitter` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `splitter`, you can't tell.
+1. `separator` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `separator`, you can't tell.
 
 2. `encodedString` is the result of the encoding process. Returns a string representation of the tree. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
 
@@ -96,34 +96,36 @@ The implementation also added a few important details:
 These details will shape your `decode` operation. Here's a possible implementation:
 
 ```swift
-extension BinaryTree {
-  
+extension BinaryNode {
+
   // 1
-  static func decode<Element>(from string: String) -> BinaryNode<Element>? {
-    let array = string.split(separator: ",")
-    return decode(from: array)
+  public static func decode(from str: String) -> AVLNode<String>? {
+    let components = encoded.lazy.split(separator: separator).reversed().map(String.init)
+    return decode(from: components)
   }
-  
-  // 2
-  static func decode<Elements: Sequence>(from sequence: Sequence) 
-    -> BinaryNode<Elements.Element>? {
+
+  public static func decode(from array: inout [String])
+    -> AVLNode<String>? {
     
-    guard let value = sequence.first else { return nil }
-    if value == nilNode {
-      return nil
-    } else {
-      let node = BinaryNode<Elements.Element>(value: value)
-      node.leftChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
-      node.rightChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
-    }    
+      guard !array.isEmpty else { return nil }
+      let value = array.removeLast()
+      guard value != "\(nilNode)" else { return nil }
+      
+      let node = AVLNode<String>(value: value)
+      node.leftChild = decode(from: &array)
+      node.rightChild = decode(from: &array)
+      return node
   }
 }
 ```
 
 Here's a high level overview of the above code:
 
-1. Takes a `String`, and uses `split` to partition the contents of `string` into an array based on the `","` character. 
-2. Takes any `Sequence` type and recursively creates a binary tree based on the rules declared in the encoding operation.
+1. Takes a `String`, and uses `split` to partition the contents of `string` into an array based on the `separator` defined in the encoding step. The result is first `reversed`, and then mapped to a `String`. The `reverse` step is an optimization for the next function, allowing us to use `array.removeLast()` instead of `array.removeFirst()`.
+
+2. Using an array as a stack, you recursively decode each node. The array keeps track of sequence of nodes and progress.
+
+
 
 
 

From 8bc6ab70c45d36d55466046d613509f64ca8ee59 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 18 Nov 2017 01:51:20 -0800
Subject: [PATCH 1369/1679] Added example case.

---
 Encode and Decode Tree/readme.md | 42 ++++++++++++++++++++++++++++++--
 1 file changed, 40 insertions(+), 2 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index e0c38531c..d7dd89424 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -125,9 +125,47 @@ Here's a high level overview of the above code:
 
 2. Using an array as a stack, you recursively decode each node. The array keeps track of sequence of nodes and progress.
 
+Here's an example output of a tree undergoing the encoding and decoding process:
 
-
-
+```
+Original Tree
+
+  ┌──8423
+ ┌──8391
+ │ └──nil
+┌──7838
+│ │ ┌──4936
+│ └──3924
+│  └──2506
+830
+│ ┌──701
+└──202
+ └──169
+
+Encoded tree: 830,202,169,X,X,701,X,X,7838,3924,2506,X,X,4936,X,X,8391,X,8423,X,X,
+
+Decoded tree
+
+  ┌──8423
+ ┌──8391
+ │ └──nil
+┌──7838
+│ │ ┌──4936
+│ └──3924
+│  └──2506
+830
+│ ┌──701
+└──202
+ └──169
+ ```
+
+Notice the original tree and decoded tree are identical. 
+
+## Further Reading & References
+
+- [LeetCode](https://leetcode.com/problems/serialize-and-deserialize-binary-tree/description/)
+
+*Written for the Swift Algorithm Club by Kai Chen & Kelvin Lau*
 
 
 

From eeea2027fe024dcf7a553f6c3c3479e39942045f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 21 Nov 2017 22:32:03 -0800
Subject: [PATCH 1370/1679] Updates readme to reference new class to handle
 encoding and decoding operations

---
 Encode and Decode Tree/readme.md | 103 +++++++++++++++++++------------
 1 file changed, 65 insertions(+), 38 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index d7dd89424..d60075e63 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -13,7 +13,7 @@ Encoding and decoding are synonyms to *serializing* and *deserializing* trees.
 As a reference, the following code represents the typical `Node` type of a binary tree:
 
 ```swift
-class BinaryNode<Element: Comparable> {
+class BinaryNode<Element: Comparable & Encodable> {
   var data: Element
   var leftChild: BinaryNode?
   var rightChild: BinaryNode?
@@ -22,6 +22,24 @@ class BinaryNode<Element: Comparable> {
 }
 ```
 
+Your encoding and decoding methods will reside in the `BinaryNodeEncoder` and `BinaryNodeDecoder` classes:
+
+```swift
+class BinaryNodeCoder {
+ 
+  // transforms nodes into string representation
+  func encode<T>(_ node: BinaryNode<T>) throws -> String where T: Encodable {
+    
+  }
+  
+  // transforms string into `BinaryNode` representation
+  func decode<T>(_ node: BinaryNode<T>Type, from string: String) 
+    throws -> BinaryNode<T> where T: Decodable {
+  
+  }
+}
+```
+
 ## Encoding
 
 As mentioned before, there are different ways to do encoding. For no particular reason, you'll opt for the following rules:
@@ -32,27 +50,9 @@ As mentioned before, there are different ways to do encoding. For no particular
 Here's an example of this operation in code:
 
 ```swift
-extension BinaryNode {
-  // 1
-  fileprivate var separator: String { return "," }
-  fileprivate var nilNode: String { return "X" }
-  
-  // 2
-  var encodedString: String {
-    var str = ""
-    preOrderTraversal { data in
-      if let data = data {
-        let string = String(describing: data)
-        str.append(string)
-      } else {
-        str.append(nilNode)
-      }
-      str.append(separator)
-    }
-    return str
-  }
+fileprivate extension BinaryNode {
   
-  // 3
+  // 1
   func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
     try visit(data)
     
@@ -69,15 +69,41 @@ extension BinaryNode {
     }
   }
 }
+
+class BinaryNodeCoder {
+
+  // 2
+  private var separator: String { return "," }
+  
+  // 3
+  private var nilNode: String { return "X" }
+  
+  // 4
+  func encode<T: Encodable>(_ node: BinaryNode<T>) -> String {
+    var str = ""
+    node.preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(separator)
+    }
+    return str
+  }
+  
+  // ...
+}
 ```
 
 Here's a high level overview of the above code:
 
-1. `separator` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `separator`, you can't tell.
+2. `separator` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `separator`, you can't tell.
 
-2. `encodedString` is the result of the encoding process. Returns a string representation of the tree. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
+3. `nilNode` is used to identify empty children. This a necesssary piece of information to retain in order to rebuild the tree later.
 
-3. It is interesting to note that this pre-order traversal implementation also emits `nil` values in place of absent children.
+4. `encode` returns a `String` representation of the `BinaryNode`. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
 
 ## Decoding
 
@@ -96,28 +122,29 @@ The implementation also added a few important details:
 These details will shape your `decode` operation. Here's a possible implementation:
 
 ```swift
-extension BinaryNode {
 
+class BinaryNodeCoder {
+
+  // ...
+  
   // 1
-  public static func decode(from str: String) -> AVLNode<String>? {
+  func decode<T: Decodable>(_ string: String) -> BinaryNode<T>? {
     let components = encoded.lazy.split(separator: separator).reversed().map(String.init)
     return decode(from: components)
   }
-
-  public static func decode(from array: inout [String])
-    -> AVLNode<String>? {
+  
+  // 2
+  private func decode(from array: inout [String]) -> AVLNode<String>? {
+    guard !array.isEmpty else { return nil }
+    let value = array.removeLast()
+    guard value != "\(nilNode)" else { return nil }
     
-      guard !array.isEmpty else { return nil }
-      let value = array.removeLast()
-      guard value != "\(nilNode)" else { return nil }
-      
-      let node = AVLNode<String>(value: value)
-      node.leftChild = decode(from: &array)
-      node.rightChild = decode(from: &array)
-      return node
+    let node = AVLNode<String>(value: value)
+    node.leftChild = decode(from: &array)
+    node.rightChild = decode(from: &array)
+    return node
   }
 }
-```
 
 Here's a high level overview of the above code:
 

From 4187a9af9f6b316479562589fd78c7685b633f22 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 23 Nov 2017 01:54:56 -0800
Subject: [PATCH 1371/1679] Fixed some formatting.

---
 Encode and Decode Tree/readme.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index d60075e63..ce5b45aaf 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -33,7 +33,7 @@ class BinaryNodeCoder {
   }
   
   // transforms string into `BinaryNode` representation
-  func decode<T>(_ node: BinaryNode<T>Type, from string: String) 
+  func decode<T>(from string: String) 
     throws -> BinaryNode<T> where T: Decodable {
   
   }
@@ -145,6 +145,7 @@ class BinaryNodeCoder {
     return node
   }
 }
+```
 
 Here's a high level overview of the above code:
 

From 25e6a190af8d13ee4e72bd41087fe593d49eba0f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 23 Nov 2017 23:34:24 -0800
Subject: [PATCH 1372/1679] Removed mentions of Encodable and Decodable
 protocol. Fixed a typo.

---
 Encode and Decode Tree/readme.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index ce5b45aaf..b60e0a504 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -13,7 +13,7 @@ Encoding and decoding are synonyms to *serializing* and *deserializing* trees.
 As a reference, the following code represents the typical `Node` type of a binary tree:
 
 ```swift
-class BinaryNode<Element: Comparable & Encodable> {
+class BinaryNode<Element: Comparable> {
   var data: Element
   var leftChild: BinaryNode?
   var rightChild: BinaryNode?
@@ -79,7 +79,7 @@ class BinaryNodeCoder {
   private var nilNode: String { return "X" }
   
   // 4
-  func encode<T: Encodable>(_ node: BinaryNode<T>) -> String {
+  func encode<T>(_ node: BinaryNode<T>) -> String {
     var str = ""
     node.preOrderTraversal { data in
       if let data = data {
@@ -128,13 +128,13 @@ class BinaryNodeCoder {
   // ...
   
   // 1
-  func decode<T: Decodable>(_ string: String) -> BinaryNode<T>? {
+  func decode<T>(_ string: String) -> BinaryNode<T>? {
     let components = encoded.lazy.split(separator: separator).reversed().map(String.init)
     return decode(from: components)
   }
   
   // 2
-  private func decode(from array: inout [String]) -> AVLNode<String>? {
+  private func decode(from array: inout [String]) -> BinaryNode<String>? {
     guard !array.isEmpty else { return nil }
     let value = array.removeLast()
     guard value != "\(nilNode)" else { return nil }

From 074dac29084d235f93edb68e58d2deb92ffc0bbf Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 14 Jan 2018 18:16:35 -0800
Subject: [PATCH 1373/1679] Address comments and update the code to sync up
 with readme

---
 .../Contents.swift                            |  21 ++-
 .../Sources/EncodeAndDecodeTree.swift         | 137 ++++++++----------
 .../EncodeAndDecodeTree.swift                 | 137 ++++++++----------
 3 files changed, 137 insertions(+), 158 deletions(-)

diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift
index dbd2fd180..44c2440d5 100644
--- a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift	
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift	
@@ -1,13 +1,10 @@
 //: Playground - noun: a place where people can play
 
-
-func printTree(_ root: TreeNode?) {
+func printTree(_ root: BinaryNode<String>?) {
     guard let root = root else {
         return
     }
 
-    var pointer = root
-
     let leftVal = root.left == nil ? "nil" : root.left!.val
     let rightVal = root.right == nil ? "nil" : root.right!.val
 
@@ -17,25 +14,25 @@ func printTree(_ root: TreeNode?) {
     printTree(root.right)
 }
 
-let s = EncodeAndDecodeTree()
+let coder = BinaryNodeCoder<String>()
 
-let node1 = TreeNode("a")
-let node2 = TreeNode("b")
-let node3 = TreeNode("c")
-let node4 = TreeNode("d")
-let node5 = TreeNode("e")
+let node1 = BinaryNode("a")
+let node2 = BinaryNode("b")
+let node3 = BinaryNode("c")
+let node4 = BinaryNode("d")
+let node5 = BinaryNode("e")
 
 node1.left = node2
 node1.right = node3
 node3.left = node4
 node3.right = node5
 
-let encodeStr = s.encode(node1)
+let encodeStr = try coder.encode(node1)
 print(encodeStr)
 // "a b # # c d # # e # #"
 
 
-let root = s.decode(encodeStr)
+let root: BinaryNode<String> = coder.decode(from: encodeStr)!
 print("Tree:")
 printTree(root)
 /*
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift
index e9d22f8a9..10bb277f5 100644
--- a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift	
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift	
@@ -8,97 +8,88 @@
 
 import Foundation
 
-public class TreeNode {
-    public var val: String
-    public var left: TreeNode?
-    public var right: TreeNode?
-
-    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
-        self.val = val
-        self.left = left
-        self.right = right
-    }
+protocol BinaryNodeEncoder {
+  func encode<T>(_ node: BinaryNode<T>?) throws -> String
 }
 
-public class EncodeAndDecodeTree {
-    private var encodeStr = ""
-    private var ret: [String] = []
+protocol BinaryNodeDecoder {
+  func decode<T>(from string: String) -> BinaryNode<T>?
+}
 
-    public init() {}
+public class BinaryNodeCoder<T: Comparable>: BinaryNodeEncoder, BinaryNodeDecoder {
 
-    public func encode(_ root: TreeNode?) -> String {
-        encodeIt(root)
+  // MARK: Private
 
-        return encodeStr
-    }
+  private let separator: Character = ","
+  private let nilNode = "X"
 
-    public func decode(_ data: String) -> TreeNode? {
-        var s = data
-        while (s.contains(" ")) {
-            let index = s.index(of: " ")
-            let endIndex = s.index(before: index)
-            let element = s[s.startIndex...endIndex]
-            ret.append(element)
-            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
-            s.removeSubrange(range)
-        }
-
-        if ret.count == 0 {
-            return nil
-        }
-
-        var dep = 0
-        let root = decodeIt(&dep)
-
-        return root
+  private func decode<T>(from array: inout [String]) -> BinaryNode<T>? {
+    guard !array.isEmpty else {
+      return nil
     }
 
-    private func getNode(_ element: String) -> TreeNode? {
-        if element == "#" {
-            return nil
-        }
+    let value = array.removeLast()
 
-        return TreeNode(element)
+    guard value != nilNode, let val = value as? T else {
+      return nil
     }
 
-    private func decodeIt(_ dep: inout Int) -> TreeNode? {
-        guard let currentNode = getNode(ret[dep]) else {
-            return nil
-        }
+    let node = BinaryNode<T>(val)
+    node.left = decode(from: &array)
+    node.right = decode(from: &array)
 
-        dep += 1
-        let left = decodeIt(&dep)
-        dep += 1
-        let right = decodeIt(&dep)
+    return node
+  }
 
-        currentNode.left = left
-        currentNode.right = right
+  // MARK: Public
 
-        return currentNode
+  public init() {}
+
+  public func encode<T>(_ node: BinaryNode<T>?) throws -> String {
+    var str = ""
+    node?.preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(separator)
     }
 
-    private func encodeIt(_ root: TreeNode?) {
-        guard let root = root else {
-            encodeStr += "# "
-            return
-        }
+    return str
+  }
 
-        encodeStr += root.val + " "
-        encodeIt(root.left)
-        encodeIt(root.right)
-    }
+  public func decode<T>(from string: String) -> BinaryNode<T>? {
+    var components = string.split(separator: separator).reversed().map(String.init)
+    return decode(from: &components)
+  }
 }
 
-extension String {
-    func index(of target: Character) -> String.Index {
-        var i = 0
-        for c in self.characters {
-            if c == target {
-                return self.index(self.startIndex, offsetBy: i)
-            }
-            i += 1
-        }
-
-        return self.endIndex
+public class BinaryNode<Element: Comparable> {
+  public var val: Element
+  public var left: BinaryNode?
+  public var right: BinaryNode?
+
+  public init(_ val: Element, left: BinaryNode? = nil, right: BinaryNode? = nil) {
+    self.val = val
+    self.left = left
+    self.right = right
+  }
+
+  public func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
+    try visit(val)
+
+    if let left = left {
+      try left.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
+    }
+
+    if let right = right {
+      try right.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
     }
+  }
 }
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.swift
index daa3c3ea2..6ec8a3046 100644
--- a/Encode and Decode Tree/EncodeAndDecodeTree.swift	
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.swift	
@@ -8,97 +8,88 @@
 
 import Foundation
 
-public class TreeNode {
-    public var val: String
-    public var left: TreeNode?
-    public var right: TreeNode?
-
-    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
-        self.val = val
-        self.left = left
-        self.right = right
-    }
+protocol BinaryNodeEncoder {
+  func encode<T>(_ node: BinaryNode<T>?) throws -> String
 }
 
-public class EncodeAndDecodeTree {
-    private var encodeStr = ""
-    private var ret: [String] = []
+protocol BinaryNodeDecoder {
+  func decode<T>(from string: String) -> BinaryNode<T>?
+}
 
-    public init() {}
+public class BinaryNodeCoder<T: Comparable>: BinaryNodeEncoder, BinaryNodeDecoder {
 
-    public func encode(_ root: TreeNode?) -> String {
-        encodeIt(root)
+  // MARK: Private
 
-        return encodeStr
-    }
+  private let separator: Character = ","
+  private let nilNode = "X"
 
-    public func decode(_ data: String) -> TreeNode? {
-        var s = data
-        while (s.contains(" ")) {
-            let index = s.index(of: " ")
-            let endIndex = s.index(before: index)
-            let element = s[s.startIndex...endIndex]
-            ret.append(element)
-            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
-            s.removeSubrange(range)
-        }
-
-        if ret.count == 0 {
-            return nil
-        }
-
-        var dep = 0
-        let root = decodeIt(&dep)
-
-        return root
+  private func decode<T>(from array: inout [String]) -> BinaryNode<T>? {
+    guard !array.isEmpty else {
+      return nil
     }
 
-    private func getNode(_ element: String) -> TreeNode? {
-        if element == "#" {
-            return nil
-        }
+    let value = array.removeLast()
 
-        return TreeNode(element)
+    guard value != nilNode, let val = value as? T else {
+      return nil
     }
 
-    private func decodeIt(_ dep: inout Int) -> TreeNode? {
-        guard let currentNode = getNode(ret[dep]) else {
-            return nil
-        }
+    let node = BinaryNode<T>(val)
+    node.left = decode(from: &array)
+    node.right = decode(from: &array)
 
-        dep += 1
-        let left = decodeIt(&dep)
-        dep += 1
-        let right = decodeIt(&dep)
+    return node
+  }
 
-        currentNode.left = left
-        currentNode.right = right
+  // MARK: Public
 
-        return currentNode
+  public init() {}
+
+  public func encode<T>(_ node: BinaryNode<T>?) throws -> String {
+    var str = ""
+    node?.preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(separator)
     }
 
-    private func encodeIt(_ root: TreeNode?) {
-        guard let root = root else {
-            encodeStr += "# "
-            return
-        }
+    return str
+  }
 
-        encodeStr += root.val + " "
-        encodeIt(root.left)
-        encodeIt(root.right)
-    }
+  public func decode<T>(from string: String) -> BinaryNode<T>? {
+    var components = string.split(separator: separator).reversed().map(String.init)
+    return decode(from: &components)
+  }
 }
 
-extension String {
-    func index(of target: Character) -> String.Index {
-        var i = 0
-        for c in self.characters {
-            if c == target {
-                return self.index(self.startIndex, offsetBy: i)
-            }
-            i += 1
-        }
-        
-        return self.endIndex
+public class BinaryNode<Element: Comparable> {
+  public var val: Element
+  public var left: BinaryNode?
+  public var right: BinaryNode?
+
+  public init(_ val: Element, left: BinaryNode? = nil, right: BinaryNode? = nil) {
+    self.val = val
+    self.left = left
+    self.right = right
+  }
+
+  public func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
+    try visit(val)
+
+    if let left = left {
+      try left.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
+    }
+
+    if let right = right {
+      try right.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
     }
+  }
 }

From 90ac6b3b8cc3b341bc3e691998dc02a2cfd9de18 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 22 Jan 2018 08:09:08 -0800
Subject: [PATCH 1374/1679] Updates link to new contribution

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 7c9482d0c..6169b07b1 100644
--- a/README.markdown
+++ b/README.markdown
@@ -200,6 +200,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Finding Palindromes](Palindromes/)
 - [Dining Philosophers](DiningPhilosophers/)
 - [Egg Drop Problem](Egg%20Drop%20Problem/)
+- [Encoding and Decoding Binary Tree](Encode%20and%20Decode%20Tree/)
 ## Learn more!
 
 For more information, check out these great books:

From 5ff583027979d8826d2a9328f84534a1e5712323 Mon Sep 17 00:00:00 2001
From: Chris <cconover@gmail.com>
Date: Fri, 26 Jan 2018 10:54:10 -0800
Subject: [PATCH 1375/1679] Fix typo: bottom-left -> bottom-right

---
 Longest Common Subsequence/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index 4cd2c2fcb..a62c562a6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -99,7 +99,7 @@ And so on... this is how `lcsLength(_:)` fills in the entire matrix.
 
 ## Backtracking to find the actual subsequence
 
-So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-left corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
+So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-right corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
 
 Having the length of every combination of substrings makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
 

From 157431e2a6f5615a70495c045d6f21a1f86d4f14 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Sun, 28 Jan 2018 07:06:45 +0800
Subject: [PATCH 1376/1679] Update README.markdown

Find a kth smallest element should use a[k-1]
---
 Kth Largest Element/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index aba2d9c29..f1721df96 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -40,7 +40,7 @@ Now, all we must do is take the value at index `a.count - k`:
 a[a.count - k] = a[8 - 4] = a[4] = 9
 ```
 
-Of course, if you were looking for the k-th *smallest* element, you'd use `a[k]`.
+Of course, if you were looking for the k-th *smallest* element, you'd use `a[k-1]`.
 
 ## A faster solution
 

From e14a46f35964c4d1c0d41a90fd7b1ddbda5ad0bd Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Mon, 29 Jan 2018 09:04:10 +0800
Subject: [PATCH 1377/1679] Update README.markdown

update the code in the article same as source code
---
 Kth Largest Element/README.markdown | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index f1721df96..b23d22b74 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -84,29 +84,29 @@ The index of pivot `9` is 4, and that's exactly the *k* we're looking for. We're
 The following function implements these ideas:
 
 ```swift
-public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
+public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
-  func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
+  func randomPivot<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
-    swap(&a, pivotIndex, high)
+    a.swapAt(pivotIndex, high)
     return a[high]
   }
 
-  func randomizedPartition<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> Int {
+  func randomizedPartition<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> Int {
     let pivot = randomPivot(&a, low, high)
     var i = low
     for j in low..<high {
       if a[j] <= pivot {
-        swap(&a, i, j)
+        a.swapAt(i, j)
         i += 1
       }
     }
-    swap(&a, i, high)
+    a.swapAt(i, high)
     return i
   }
 
-  func randomizedSelect<T: Comparable>(inout a: [T], _ low: Int, _ high: Int, _ k: Int) -> T {
+  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
     if low < high {
       let p = randomizedPartition(&a, low, high)
       if k == p {

From 2924b2dced521f2ccf3a0f276f3f58f57822f914 Mon Sep 17 00:00:00 2001
From: i303071 <adam.borbas@sap.com>
Date: Mon, 29 Jan 2018 11:04:29 +0100
Subject: [PATCH 1378/1679] HashTable CustomStringConvertible conformance in
 protocol

---
 .../Sources/HashTable.swift                   | 38 ++++++++++---------
 1 file changed, 20 insertions(+), 18 deletions(-)

diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
index 2383b8192..476a51174 100644
--- a/Hash Table/HashTable.playground/Sources/HashTable.swift	
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -30,7 +30,7 @@
  Insert:  O(1)     O(n)
  Delete:  O(1)     O(n)
  */
-public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
+public struct HashTable<Key: Hashable, Value> {
     private typealias Element = (key: Key, value: Value)
     private typealias Bucket = [Element]
     private var buckets: [Bucket]
@@ -41,23 +41,6 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
     /// A Boolean value that indicates whether the hash table is empty.
     public var isEmpty: Bool { return count == 0 }
 
-    /// A string that represents the contents of the hash table.
-    public var description: String {
-        let pairs = buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }
-        return pairs.joined(separator: ", ")
-    }
-
-    /// A string that represents the contents of
-    /// the hash table, suitable for debugging.
-    public var debugDescription: String {
-        var str = ""
-        for (i, bucket) in buckets.enumerated() {
-            let pairs = bucket.map { e in "\(e.key) = \(e.value)" }
-            str += "bucket \(i): " + pairs.joined(separator: ", ") + "\n"
-        }
-        return str
-    }
-
     /**
      Create a hash table with the given capacity.
      */
@@ -151,3 +134,22 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         return abs(key.hashValue) % buckets.count
     }
 }
+
+extension HashTable: CustomStringConvertible {
+    /// A string that represents the contents of the hash table.
+    public var description: String {
+        let pairs = buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }
+        return pairs.joined(separator: ", ")
+    }
+    
+    /// A string that represents the contents of
+    /// the hash table, suitable for debugging.
+    public var debugDescription: String {
+        var str = ""
+        for (i, bucket) in buckets.enumerated() {
+            let pairs = bucket.map { e in "\(e.key) = \(e.value)" }
+            str += "bucket \(i): " + pairs.joined(separator: ", ") + "\n"
+        }
+        return str
+    }
+}

From 5beb84acec563fefef04ce87683484e4359f5350 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Wed, 31 Jan 2018 23:40:15 +0800
Subject: [PATCH 1379/1679] Update README.markdown

when k > n/2 ,  we just need random select a.count - k elements and remove them from the original array
---
 Selection Sampling/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index ff80791e1..741f592f4 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -193,7 +193,7 @@ print(output.count)
 
 The performance of this second algorithm is **O(n)** as it may require a pass through the entire input array.
 
-> **Note:** If `k > n/2`, then it's more efficient to do it the other way around and choose `k` items to remove.
+> **Note:** If `k > n/2`, then it's more efficient to do it the other way around and choose `a.count - k` items to remove.
 
 Based on code from Algorithm Alley, Dr. Dobb's Magazine, October 1993.
 

From f34ccf2f6fb873bbf1b21fa39841534dbb5a04c4 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 7 Feb 2018 02:11:29 -0800
Subject: [PATCH 1380/1679] English Edit

---
 Introsort/README.markdown | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/Introsort/README.markdown b/Introsort/README.markdown
index c4ee6f804..376703cf7 100644
--- a/Introsort/README.markdown
+++ b/Introsort/README.markdown
@@ -6,7 +6,7 @@ IntroSort is the algorithm used by swift to sort a collection. Introsort is an h
 
 The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
 
-Here's an implementation in Pseudocode:
+Here's an implementation in pseudocode:
 
 ```
 procedure sort(A : array):
@@ -32,9 +32,9 @@ Let's walk through the example. The array is initially:
 	[ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 
 
-for this example let's assume that `maxDepth` is **2** and that the size of the partition for the insertionSort to kick in is **5**
+For this example let's assume that `maxDepth` is **2** and that the size of the partition for the insertionSort to kick in is **5**
 
-At the first iteration we run introSort on the full collection that counts 13 elements. the maxDepth is 2, therefore we fall in the else case where quicksort acts.
+The first iteration of introsort begins by attempting to use insertionSort. The collection has 13 elements, so it tries to do heapsort instead. The condition for heapsort to occur is if `maxdepth == 0` evaluates true. Since `maxdepth` is currently **2** for the first iteration, introsort will default to quicksort.
 
 The `partition`  method picks the first element, the median and the last, it sorts them and uses the new median as pivot.
 
@@ -106,5 +106,6 @@ The array is now successfully sorted
 
 [Introsort on Wikipedia](https://en.wikipedia.org/wiki/Introsort)
 [Introsort comparison with other sorting algorithms](http://agostini.tech/2017/12/18/swift-sorting-algorithm/)
+[Introsort implementation from the Swift standard library](https://github.com/apple/swift/blob/09f77ff58d250f5d62855ea359fc304f40b531df/stdlib/public/core/Sort.swift.gyb)
 
 *Written for Swift Algorithm Club by Giuseppe Lanza*

From b59cd5f6b28130146cd03384e926ac5c4ff2622d Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 23 Feb 2018 15:30:42 -0600
Subject: [PATCH 1381/1679] working on readme.. finally finishing this PR

---
 Genetic/README.markdown                      | 169 ++++++++++++++++++-
 Genetic/gen.playground/Contents.swift        |  91 ++++++++++
 Genetic/gen.playground/contents.xcplayground |   4 +
 Genetic/gen.swift                            |  38 +++--
 4 files changed, 282 insertions(+), 20 deletions(-)
 create mode 100644 Genetic/gen.playground/Contents.swift
 create mode 100644 Genetic/gen.playground/contents.xcplayground

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 7cad649cb..fd208a19d 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -1,2 +1,167 @@
-# todo
-refactoring https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba for swift 4. Creating a tutorial and writing in more playground friendly format
+# Genetic Algorthim
+
+## What is it?
+
+A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), mutation and crossover. To understand more, let's walk through these process in terms of biology:
+
+### Selection
+>**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors. [Britannica](britannica)
+
+In other words, survival of the fittest. Organism that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank offspring and give them a better chance for reproduction.
+
+### Mutation
+>**Mutation**, an alteration in the genetic material (the genome) of a cell of a living organism or of a virus that is more or less permanent and that can be transmitted to the cell’s or the virus’s descendants. [Britannica](https://www.britannica.com/science/mutation-genetics)
+
+The randomization that allows for organisms to change over time. In GAs we build a randomization process that will mutate offspring in a populate in order to randomly introduce fitness variance.
+
+### Crossover
+>**Chromosomal crossover** (or crossing over) is the exchange of genetic material between homologous chromosomes that results in recombinant chromosomes during sexual reproduction [Wikipedia](https://en.wikipedia.org/wiki/Chromosomal_crossover)
+
+Simply reproduction. A generation will a mixed representation of the previous generation, with offspring taking data (DNA) from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
+
+### Resources:
+* [Wikipedia]()
+
+
+## The Code
+
+### Problem
+For this quick and dirty example, we are going to obtain a optimize string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
+
+We will be creating a bio-inspired world where the absolute existence is string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible.  
+
+### Define the Universe
+
+Before we dive into the core processes we need to set up our "universe". First let's define a lexicon, a set of everything that exists in our universe.
+
+```swift
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+```
+
+To make things easier, we are actually going to work in ASCII values, so let's define a String extension to help with that.
+
+```swift
+extension String {
+  var asciiArray: [UInt8] {
+    return [UInt8](self.utf8)
+  }
+}
+```
+
+ Now, let's define a few global variables for the universe:
+
+ ```swift
+// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+
+// The length of the string in our population. Organisms need to be similar
+let DNA_SIZE = OPTIMAL.count
+
+// size of each generation
+let POP_SIZE = 50
+
+// max number of generations, script will stop when it reach 5000 if the optimal value is not found
+let GENERATIONS = 5000
+
+// The chance in which a random nucleotide can mutate (1/n)
+let MUTATION_CHANCE = 100
+ ```
+
+ The last piece we need for set up is a function to give us a random ASCII value from our lexicon:
+
+ ```swift
+ func randomChar(from lexicon: [UInt8]) -> UInt8 {
+     let len = UInt32(lexicon.count-1)
+     let rand = Int(arc4random_uniform(len))
+     return lexicon[rand]
+ }
+ ```
+
+ ### Population Zero
+
+ Before selecting, mutating and reproduction, we need population to start with. Now that we have the universe defined we can write that function:
+
+ ```swift
+ func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+
+    let len = UInt32(lexicon.count)
+
+    var pop = [[UInt8]]()
+
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let char = randomChar(from: lexicon)
+            dna.append(char)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+ ```
+
+### Selection
+
+There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using ASCII values:
+
+```swift
+func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+    var fitness = 0
+    for c in 0...dna.count-1 {
+        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    }
+    return fitness
+}
+```
+
+The above is a very simple fitness calculation, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
+
+The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or not be able to reproduce.
+
+Let's take a second and ask why on this one. Why would you not always want to select the most fit from a population? It's hard to see from this simple example, but let's think about dog breeding, because breeders remove this process and hand select dogs for the next generation. As a result you get improved desired characteristics, but the individuals will also continue to carry genetic disorders that come along with those traits. This is essentially leading the evolution down a linear path. A certain "branch" of evolution may beat out the current fittest solution at a later time.
+
+ok, back to code. Here is our weighted choice function:
+
+```swift
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+
+    let total = items.reduce(0.0) { return $0 + $1.weight}
+
+    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
+
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+```
+
+The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value.
+
+## Mutation
+
+The all powerful mutation. The great randomization that turns bacteria into humans, just add time. So powerful yet so simple:
+
+```swift
+func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+    var outputDna = dna
+
+    for i in 0..<dna.count {
+        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        if rand == 1 {
+            outputDna[i] = randomChar()
+        }
+    }
+
+    return outputDna
+}
+```
+
+Takes a mutation chance and a individual and returns that individual with mutations, if any.
+
+This allows for a population to explore all the possibilities of it's building blocks and randomly stumble on a better solution. If there is too much mutation, the evolution process will get nowhere. If there is too little the populations will become too similar and never be able to branch out of a defect to meet their changing environment.
+
+## Crossover
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
new file mode 100644
index 000000000..b84fd13e3
--- /dev/null
+++ b/Genetic/gen.playground/Contents.swift
@@ -0,0 +1,91 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+extension String {
+    var asciiArray: [UInt8] {
+        return [UInt8](self.utf8)
+    }
+}
+
+
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+
+// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+
+// The length of the string in our population. Organisms need to be similar
+let DNA_SIZE = OPTIMAL.count
+
+// size of each generation
+let POP_SIZE = 50
+
+// max number of generations, script will stop when it reach 5000 if the optimal value is not found
+let GENERATIONS = 5000
+
+// The chance in which a random nucleotide can mutate (1/n)
+let MUTATION_CHANCE = 100
+
+func randomChar(from lexicon: [UInt8]) -> UInt8 {
+    let len = UInt32(lexicon.count-1)
+    let rand = Int(arc4random_uniform(len))
+    return lexicon[rand]
+}
+
+func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+    
+    let len = UInt32(lexicon.count)
+    
+    var pop = [[UInt8]]()
+    
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let char = randomChar(from: lexicon)
+            dna.append(char)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+
+randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+
+func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+    
+    var fitness = 0
+    for c in 0...dna.count-1 {
+        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    }
+    return fitness
+}
+
+calculateFitness(dna: "Hillo, World".asciiArray, optimal: "Hello, World".asciiArray)
+
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+
+    let total = items.reduce(0.0) { return $0 + $1.weight}
+    
+    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
+    
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+
+func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+    var outputDna = dna
+    
+    for i in 0..<dna.count {
+        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        if rand == 1 {
+            outputDna[i] = randomChar()
+        }
+    }
+    
+    return outputDna
+}
diff --git a/Genetic/gen.playground/contents.xcplayground b/Genetic/gen.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Genetic/gen.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index 72830b8a7..17df6d002 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -14,14 +14,16 @@ extension String {
     }
 }
 
+let lex = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".map {  }
+
 /*
     helper function to return a random character string
 */
 func randomChar() -> UInt8 {
-    
+
     let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
     let len = UInt32(letters.count-1)
-    
+
     let rand = Int(arc4random_uniform(len))
     return letters[rand]
 }
@@ -40,7 +42,7 @@ let MUTATION_CHANCE = 100
     optimal string comparsion = 0
 */
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-    
+
     var fitness = 0
     for c in 0...dna.count-1 {
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
@@ -53,7 +55,7 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 */
 func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
     var outputDna = dna
-    
+
     for i in 0..<dnaSize {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
@@ -70,10 +72,10 @@ func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
 */
 func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
-    
+
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
-    
+
     return (
         [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
         [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
@@ -85,12 +87,12 @@ func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[
 returns a random population, used to start the evolution
 */
 func randomPopulation(populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-    
+
     let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
     let len = UInt32(letters.count)
 
     var pop = [[UInt8]]()
-    
+
     for _ in 0..<populationSize {
         var dna = [UInt8]()
         for _ in 0..<dnaSize {
@@ -112,7 +114,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
     for itemTuple in items {
         weightTotal += itemTuple.weight;
     }
-    
+
     var n = Double(arc4random_uniform(UInt32(weightTotal * 1000000.0))) / 1000000.0
 
     for itemTuple in items {
@@ -133,36 +135,36 @@ func main() {
 
     for generation in 0...GENERATIONS {
         print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
-        
+
         var weightedPopulation = [(item:[UInt8], weight:Double)]()
-        
+
         // calulcated the fitness of each individual in the population
         // and add it to the weight population (weighted = 1.0/fitness)
         for individual in population {
             let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
-            
+
             let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
-            
+
             weightedPopulation.append(pair)
         }
-        
+
         population = []
-        
+
         // create a new generation using the individuals in the origional population
         for _ in 0...POP_SIZE/2 {
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
-            
+
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
             population.append(mutate(dna: offspring.dna1, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
             population.append(mutate(dna: offspring.dna2, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
         }
-        
+
         fittest = population[0]
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
-        
+
         // parse the population for the fittest string
         for indv in population {
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)

From c6381646601bb162f650106c2e8ddcd4c9cb86f6 Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 23 Feb 2018 16:05:01 -0600
Subject: [PATCH 1382/1679] readme updates

---
 Genetic/README.markdown                       | 30 +++++++++++++++++--
 Genetic/gen.playground/Contents.swift         | 19 ++++++++++--
 .../contents.xcworkspacedata                  |  7 +++++
 3 files changed, 50 insertions(+), 6 deletions(-)
 create mode 100644 Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index fd208a19d..6ebbf2cf7 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -114,7 +114,9 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 }
 ```
 
-The above is a very simple fitness calculation, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
+The above will produce a fitness value to an individual. The perfect solution, "Hello, World" will have a fitness of 0. "Gello, World" will have a fitness of 1 since it is one ASCII value off from the optimal.
+
+This example is very, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
 
 The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or not be able to reproduce.
 
@@ -146,13 +148,13 @@ The above function takes a list of individuals with their calculated fitness. Th
 The all powerful mutation. The great randomization that turns bacteria into humans, just add time. So powerful yet so simple:
 
 ```swift
-func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
     for i in 0..<dna.count {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
-            outputDna[i] = randomChar()
+            outputDna[i] = randomChar(from: lexicon)
         }
     }
 
@@ -165,3 +167,25 @@ Takes a mutation chance and a individual and returns that individual with mutati
 This allows for a population to explore all the possibilities of it's building blocks and randomly stumble on a better solution. If there is too much mutation, the evolution process will get nowhere. If there is too little the populations will become too similar and never be able to branch out of a defect to meet their changing environment.
 
 ## Crossover
+
+Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents:
+
+```swift
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
+
+    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+
+    return (
+        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
+        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
+    )
+}
+```
+
+The above is used to generate a completely new generation based on the current generation.
+
+## Putting it all together -- Running the Genetic Algorithm
+
+We now have all the methods we need to kick off the process. What is missing a `main()` function that loops though each generation of the GA.
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index b84fd13e3..50d4c4fc8 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -60,7 +60,7 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
     return fitness
 }
 
-calculateFitness(dna: "Hillo, World".asciiArray, optimal: "Hello, World".asciiArray)
+calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
 
 func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
 
@@ -77,15 +77,28 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
     return items[1]
 }
 
-func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
     
     for i in 0..<dna.count {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
-            outputDna[i] = randomChar()
+            outputDna[i] = randomChar(from: lexicon)
         }
     }
     
     return outputDna
 }
+
+
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
+    
+    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+    
+    return (
+        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
+        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
+    )
+}
diff --git a/Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata b/Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 247c308a0ae5c4c18a89f5b58be5e770a673be22 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Tue, 27 Feb 2018 20:51:41 +0900
Subject: [PATCH 1383/1679] :tada: Add Myers Difference Algorithm directory and
 playground

---
 .../MyersDifferenceAlgorithm.playground/Contents.swift     | 5 +++++
 .../contents.xcplayground                                  | 4 ++++
 .../timeline.xctimeline                                    | 6 ++++++
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata  | 7 +++++++
 4 files changed, 22 insertions(+)
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline

diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift
new file mode 100644
index 000000000..c9a67424b
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift	
@@ -0,0 +1,5 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+
+var str = "Hello, playground"
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 142713e62..5d5bf1906 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -51,6 +51,13 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "group:Myers Difference Algorithm"
+      name = "Myers Difference Algorithm">
+      <FileRef
+         location = "group:MyersDifferenceAlgorithm.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "container:"
       name = "3Sum and 4Sum">

From 574a19e22890585752b505f9905e2c2dbcd185b4 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Tue, 27 Feb 2018 21:54:29 +0900
Subject: [PATCH 1384/1679] :sparkles: Add Myers Algorithm source code

---
 .../Contents.swift                            | 21 +++++-
 .../Sources/MyersDifferenceAlgorithm.swift    | 67 +++++++++++++++++++
 .../timeline.xctimeline                       |  6 --
 .../MyersDifferenceAlgorithm.swift            | 67 +++++++++++++++++++
 Myers Difference Algorithm/README.md          |  2 +
 .../contents.xcworkspacedata                  |  6 ++
 6 files changed, 161 insertions(+), 8 deletions(-)
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift
 delete mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.swift
 create mode 100644 Myers Difference Algorithm/README.md

diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift
index c9a67424b..113487acc 100644
--- a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift	
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift	
@@ -1,5 +1,22 @@
 //: Playground - noun: a place where people can play
+import Foundation
 
-import UIKit
+let shortestEditDistance: ([String], [String]) -> Int = MyersDifferenceAlgorithm.calculateShortestEditDistance(from:to:)
 
-var str = "Hello, playground"
+/***
+ All elements are same, so any scripts do not need.
+ So, the edit distance is 0
+ ***/
+shortestEditDistance(["1", "2", "3"], ["1", "2", "3"])
+
+/***
+ Last element "3" should be inserted.
+ So, the edit distance is 1
+ ***/
+shortestEditDistance(["1", "2"], ["1", "2", "3"])
+
+/***
+ First, remove "1", then insert "1" after "2".
+ So, the edit distance is 2
+***/
+shortestEditDistance(["1", "2", "3"], ["2", "1", "3"])
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift
new file mode 100644
index 000000000..aedbf3e71
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift	
@@ -0,0 +1,67 @@
+//
+//  MyersDifferenceAlgorithm.swift
+//
+//  Created by Yuya Horita on 2018/02/27.
+//  Copyright © 2018年 hy. All rights reserved.
+//
+
+import Foundation
+
+public struct MyersDifferenceAlgorithm<E: Equatable> {
+    public static func calculateShortestEditDistance(from fromArray: Array<E>, to toArray: Array<E>) -> Int {
+        let fromCount = fromArray.count
+        let toCount = toArray.count
+        let totalCount = toCount + fromCount
+        var furthestReaching = Array(repeating: 0, count: 2 * totalCount + 1)
+        
+        let isReachedAtSink: (Int, Int) -> Bool = { x, y in
+            return x == fromCount && y == toCount
+        }
+        
+        let snake: (Int, Int, Int) -> Int = { x, D, k in
+            var _x = x
+            while _x < fromCount && _x - k < toCount && fromArray[_x] == toArray[_x - k] {
+                _x += 1
+            }
+            return _x
+        }
+        
+        for D in 0...totalCount {
+            for k in stride(from: -D, through: D, by: 2) {
+                let index = k + totalCount
+                
+                // (x, D, k) => the x position on the k_line where the number of scripts is D
+                // scripts means insertion or deletion
+                var x = 0
+                if D == 0 { }
+                    // k == -D, D will be the boundary k_line
+                    // when k == -D, moving right on the Edit Graph(is delete script) from k - 1_line where D - 1 is unavailable.
+                    // when k == D, moving bottom on the Edit Graph(is insert script) from k + 1_line where D - 1 is unavailable.
+                    // furthestReaching x position has higher calculating priority. (x, D - 1, k - 1), (x, D - 1, k + 1)
+                else if k == -D || k != D && furthestReaching[index - 1] < furthestReaching[index + 1] {
+                    // Getting initial x position
+                    // ,using the furthestReaching X position on the k + 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k + 1) + moving bottom + snake
+                    // this moving bottom on the edit graph is compatible with insert script
+                    x = furthestReaching[index + 1]
+                } else {
+                    // Getting initial x position
+                    // ,using the futrhest X position on the k - 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k - 1) + moving right + snake
+                    // this moving right on the edit graph is compatible with delete script
+                    x = furthestReaching[index - 1] + 1
+                }
+                
+                // snake
+                // diagonal moving can be performed with 0 cost.
+                // `same` script is needed ?
+                let _x = snake(x, D, k)
+                
+                if isReachedAtSink(_x, _x - k) { return D }
+                furthestReaching[index] = _x
+            }
+        }
+        
+        fatalError("Never comes here")
+    }
+}
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift
new file mode 100644
index 000000000..aedbf3e71
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift	
@@ -0,0 +1,67 @@
+//
+//  MyersDifferenceAlgorithm.swift
+//
+//  Created by Yuya Horita on 2018/02/27.
+//  Copyright © 2018年 hy. All rights reserved.
+//
+
+import Foundation
+
+public struct MyersDifferenceAlgorithm<E: Equatable> {
+    public static func calculateShortestEditDistance(from fromArray: Array<E>, to toArray: Array<E>) -> Int {
+        let fromCount = fromArray.count
+        let toCount = toArray.count
+        let totalCount = toCount + fromCount
+        var furthestReaching = Array(repeating: 0, count: 2 * totalCount + 1)
+        
+        let isReachedAtSink: (Int, Int) -> Bool = { x, y in
+            return x == fromCount && y == toCount
+        }
+        
+        let snake: (Int, Int, Int) -> Int = { x, D, k in
+            var _x = x
+            while _x < fromCount && _x - k < toCount && fromArray[_x] == toArray[_x - k] {
+                _x += 1
+            }
+            return _x
+        }
+        
+        for D in 0...totalCount {
+            for k in stride(from: -D, through: D, by: 2) {
+                let index = k + totalCount
+                
+                // (x, D, k) => the x position on the k_line where the number of scripts is D
+                // scripts means insertion or deletion
+                var x = 0
+                if D == 0 { }
+                    // k == -D, D will be the boundary k_line
+                    // when k == -D, moving right on the Edit Graph(is delete script) from k - 1_line where D - 1 is unavailable.
+                    // when k == D, moving bottom on the Edit Graph(is insert script) from k + 1_line where D - 1 is unavailable.
+                    // furthestReaching x position has higher calculating priority. (x, D - 1, k - 1), (x, D - 1, k + 1)
+                else if k == -D || k != D && furthestReaching[index - 1] < furthestReaching[index + 1] {
+                    // Getting initial x position
+                    // ,using the furthestReaching X position on the k + 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k + 1) + moving bottom + snake
+                    // this moving bottom on the edit graph is compatible with insert script
+                    x = furthestReaching[index + 1]
+                } else {
+                    // Getting initial x position
+                    // ,using the futrhest X position on the k - 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k - 1) + moving right + snake
+                    // this moving right on the edit graph is compatible with delete script
+                    x = furthestReaching[index - 1] + 1
+                }
+                
+                // snake
+                // diagonal moving can be performed with 0 cost.
+                // `same` script is needed ?
+                let _x = snake(x, D, k)
+                
+                if isReachedAtSink(_x, _x - k) { return D }
+                furthestReaching[index] = _x
+            }
+        }
+        
+        fatalError("Never comes here")
+    }
+}
diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
new file mode 100644
index 000000000..def447593
--- /dev/null
+++ b/Myers Difference Algorithm/README.md	
@@ -0,0 +1,2 @@
+#  Myers Difference Algorithm
+
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5d5bf1906..5b8dd996f 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -54,9 +54,15 @@
    <Group
       location = "group:Myers Difference Algorithm"
       name = "Myers Difference Algorithm">
+      <FileRef
+         location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
+      </FileRef>
       <FileRef
          location = "group:MyersDifferenceAlgorithm.playground">
       </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
    </Group>
    <Group
       location = "container:"

From 4e61fa1287d9a1caf1adcc4eb9fa71c4d65ce505 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Tue, 27 Feb 2018 22:11:02 +0900
Subject: [PATCH 1385/1679] :sparkles: EditGraph Images were added

---
 .../Images/EditGraph.png                       | Bin 0 -> 193070 bytes
 .../Images/EditGraph_k_move.png                | Bin 0 -> 206377 bytes
 .../contents.xcworkspacedata                   |   7 +++++++
 3 files changed, 7 insertions(+)
 create mode 100644 Myers Difference Algorithm/Images/EditGraph.png
 create mode 100644 Myers Difference Algorithm/Images/EditGraph_k_move.png

diff --git a/Myers Difference Algorithm/Images/EditGraph.png b/Myers Difference Algorithm/Images/EditGraph.png
new file mode 100644
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diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5b8dd996f..ea6bdfa32 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -54,6 +54,13 @@
    <Group
       location = "group:Myers Difference Algorithm"
       name = "Myers Difference Algorithm">
+      <Group
+         location = "container:"
+         name = "Images">
+         <FileRef
+            location = "group:Myers Difference Algorithm/Images/EditGraph_k_move.png">
+         </FileRef>
+      </Group>
       <FileRef
          location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
       </FileRef>

From be679572a9403d8c4c6fb8219b9f08dbda4f0f8c Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Wed, 28 Feb 2018 01:14:33 +0900
Subject: [PATCH 1386/1679] :pencil: README

---
 Myers Difference Algorithm/README.md          | 145 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   3 +
 2 files changed, 148 insertions(+)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index def447593..4e48a704f 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,2 +1,147 @@
 #  Myers Difference Algorithm
 
+Myers Difference Algorithm is the algorithm to find a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences by a simple O(ND) time, where N is the sum of the lengths of the two sequences. Common subsequence is the sequence of elements that appear in the same order in both sequences. Edit script will be discussed below.
+
+For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", 2]` has elements are included in both, but the appearing order is not correct.
+
+## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
+
+### Edit Graph
+
+Myers Algorithm uses Edit Graph for solving LCS/SES problem. Edit Graph is the graph like below.
+
+<img src='Images/EditGraph.png' height="250">
+
+Here, we think about the length of the LCS of sequences `X = [A, B, C, A, B, B, A]`, `Y = [C, B, A, B, A, C]`.
+
+In Myers Algorithm, edit graph are prepared by
+
+1. Line the element of sequence `X` on the x axis. And do for `Y` on the y axis.
+2. Make grid and vertex at each point in the grid (x, y), `x in [0, N] and y in [0, M]`. `N` is the length of sequence `X`, `M` is of `Y`
+3. Line for `x - y = k`, this line called k-line. Pink line is this.
+3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point.
+4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, then diagonal edge appears.
+
+> **Note:** Here, the sequences' start index is 1 not 0, so `X[1] = A`, `Y[1] = C`
+
+We discuss about which path is the shortest from `source` to `sink`. Can move on the edges on the graph. I mean we can move on  the grid, horizontal and vertical edges, and the diagonal edges.
+
+The movements are compatible with the `Edit Scripts`, insert or delete. The word `Edit Scripts` appeared here, as referred at Introduction SES is Shortest Edit Scripts.
+
+Let's get back on track. On this edit graph, the horizontal movement to vertex `(i, j)` is compatible with the script  `delete at index i from X`, the vertical movement to vertex `(i, j)` is compatible with the script `insert the element of Y at index j to immediately after the element of X at index i`. How about for the diagonal movement?. This movement to vertex `(i, j)` means `X[i] = Y[j]`, so no script needs.
+
+- horizontal movement -> delete
+- vertical movement -> insert
+- diagonal movement -> no script because both are same.
+
+Next, add cost 1 for non-diagonal movement, because they can be compatible with script. And 0 for diagonal movement, same means no script.
+
+The total cost for the minimum path, exploring from `source` to `sink`, is the same as the length of the Longest Common Subsequence or Shortest Edit Script.
+
+So, LSC/SES problem can be solved by finding the shortest path from `source` to `sink`.
+
+### Myers Algorithm
+
+As mentioned above, the problem of finding a shortest edit script can be reduced to finding a path from `source (0, 0)` to `sink (N, M)` with the fewest number of horizontal and vertical edges. Let `D-path` be a path starting at `source` that has exactly `D` non-diagonal edges, or must move non-diagonally D-times.
+
+For example, A 0-path consists solely of diagonal edges. This means both sequences are completely same.
+
+By a simple induction, D-path must consist of a (D-1)-path followed by a non-diagonal edge and then diagonal edges, which called `snake`. The minimum value of D is 0, both sequences being same. To the contrary, the maximum value of D is N + M because delete all elements from X and insert all elements from Y to X is the worst case edit scripts. For getting D, or the length of SES, running loop from 0 to N + M is enough.
+
+```swift
+for D in 0...N + M
+```
+
+Next, thinking about, where is the furthest reaching point for D-path on k-line. Like below, moving horizontally from k-line reaches (k+1)-line, moving vertically from k-line reaches (k-1)-line.
+
+<img src='Images/EditGraph_k_move.png' height="250">
+
+So, threre are several end points of D-path, or D-path can end on several k-line. We need the information to get the next path ((D+1)-path) as mentioned above. In fact, D-path must end on
+k-line, where k in { -D, -D + 2, ....., D - 2, D }. This is so simple, starting point, `source` is `(0, 0)` on (k=0)-line. D is the number of non-diagonal edges and non-diagonal movement changes current k-line to (kpm1)-line. Because 0 is even number, if D is even number D-path will end on (even_k)-line, if D is odd number D-path will end on (odd_k)-line.
+
+Searching loop outline will be below.
+
+```swift
+for D in 0...N + M {
+    for k in stride(from: -D, through: D, by: 2) {
+        //Find the end point of the furthest reaching D-path in k-line.
+        if furthestReachingX == N && furthestReachingY == M {
+            // The D-path is the shortest path
+            // D is the length of Shortest Edit Script
+            return
+        }
+    }
+}
+```
+
+The D-path on k-line can be decomposed into
+- a furthest reaching (D-1)-path on (k-1)-line, followed by a horizontal edge, followed by `snake`.
+- a furthest reaching (D-1)-path on (k+1)-line, followed by a vertical edge, followed by `snake`.
+as discussed above.
+
+The Myers Algorithm key point are these.
+- D-path must end on k-line, where k in { -D, -D + 2, ....., D - 2, D }
+- The D-path on k-line can be decomposed into two patterns
+
+thanks for these, the number of calculation become less.
+
+```swift
+public struct MyersDifferenceAlgorithm<E: Equatable> {
+    public static func calculateShortestEditDistance(from fromArray: Array<E>, to toArray: Array<E>) -> Int {
+        let fromCount = fromArray.count
+        let toCount = toArray.count
+        let totalCount = toCount + fromCount
+        var furthestReaching = Array(repeating: 0, count: 2 * totalCount + 1)
+
+        let isReachedAtSink: (Int, Int) -> Bool = { x, y in
+            return x == fromCount && y == toCount
+        }
+
+        let snake: (Int, Int, Int) -> Int = { x, D, k in
+            var _x = x
+            while _x < fromCount && _x - k < toCount && fromArray[_x] == toArray[_x - k] {
+                _x += 1
+            }
+            return _x
+        }
+
+        for D in 0...totalCount {
+            for k in stride(from: -D, through: D, by: 2) {
+                let index = k + totalCount
+            
+                // (x, D, k) => the x position on the k_line where the number of scripts is D
+                // scripts means insertion or deletion
+                var x = 0
+                if D == 0 { }
+                    // k == -D, D will be the boundary k_line
+                    // when k == -D, moving right on the Edit Graph(is delete script) from k - 1_line where D - 1 is unavailable.
+                    // when k == D, moving bottom on the Edit Graph(is insert script) from k + 1_line where D - 1 is unavailable.
+                    // furthestReaching x position has higher calculating priority. (x, D - 1, k - 1), (x, D - 1, k + 1)
+                else if k == -D || k != D && furthestReaching[index - 1] < furthestReaching[index + 1] {
+                    // Getting initial x position
+                    // ,using the furthestReaching X position on the k + 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k + 1) + moving bottom + snake
+                    // this moving bottom on the edit graph is compatible with insert script
+                    x = furthestReaching[index + 1]
+                } else {
+                    // Getting initial x position
+                    // ,using the futrhest X position on the k - 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k - 1) + moving right + snake
+                    // this moving right on the edit graph is compatible with delete script
+                    x = furthestReaching[index - 1] + 1
+                }
+                
+                // snake
+                // diagonal moving can be performed with 0 cost.
+                // `same` script is needed ?
+                let _x = snake(x, D, k)
+                
+                if isReachedAtSink(_x, _x - k) { return D }
+                furthestReaching[index] = _x
+            }
+        }
+
+        fatalError("Never comes here")
+    }
+}
+```
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ea6bdfa32..724755669 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -60,6 +60,9 @@
          <FileRef
             location = "group:Myers Difference Algorithm/Images/EditGraph_k_move.png">
          </FileRef>
+         <FileRef
+            location = "group:Myers Difference Algorithm/Images/EditGraph.png">
+         </FileRef>
       </Group>
       <FileRef
          location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">

From b22d54af4185f54947cf143e2bf03359eb2263b8 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Wed, 28 Feb 2018 01:36:54 +0900
Subject: [PATCH 1387/1679] :hammer: fix typo and description

---
 Myers Difference Algorithm/README.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index 4e48a704f..2f6c3c579 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -2,7 +2,7 @@
 
 Myers Difference Algorithm is the algorithm to find a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences by a simple O(ND) time, where N is the sum of the lengths of the two sequences. Common subsequence is the sequence of elements that appear in the same order in both sequences. Edit script will be discussed below.
 
-For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", 2]` has elements are included in both, but the appearing order is not correct.
+For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", "2"]` has elements are included in both, but the appearing order is not correct.
 
 ## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
 
@@ -10,7 +10,7 @@ For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2"
 
 Myers Algorithm uses Edit Graph for solving LCS/SES problem. Edit Graph is the graph like below.
 
-<img src='Images/EditGraph.png' height="250">
+<img src='Images/EditGraph.png' height="400">
 
 Here, we think about the length of the LCS of sequences `X = [A, B, C, A, B, B, A]`, `Y = [C, B, A, B, A, C]`.
 
@@ -18,15 +18,15 @@ In Myers Algorithm, edit graph are prepared by
 
 1. Line the element of sequence `X` on the x axis. And do for `Y` on the y axis.
 2. Make grid and vertex at each point in the grid (x, y), `x in [0, N] and y in [0, M]`. `N` is the length of sequence `X`, `M` is of `Y`
-3. Line for `x - y = k`, this line called k-line. Pink line is this.
-3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point.
-4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, then diagonal edge appears.
+3. Line for `x - y = k`, this line called k-line. Black dot line is this and pink number is the value of k.
+3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point, light green one.
+4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, where `(i, j)` is match point, then diagonal edge appears.
 
 > **Note:** Here, the sequences' start index is 1 not 0, so `X[1] = A`, `Y[1] = C`
 
 We discuss about which path is the shortest from `source` to `sink`. Can move on the edges on the graph. I mean we can move on  the grid, horizontal and vertical edges, and the diagonal edges.
 
-The movements are compatible with the `Edit Scripts`, insert or delete. The word `Edit Scripts` appeared here, as referred at Introduction SES is Shortest Edit Scripts.
+The movements are compatible with the `Edit Scripts`, insert or delete. The word `Edit Scripts` appeared here, as referred at Introduction, SES is Shortest Edit Scripts.
 
 Let's get back on track. On this edit graph, the horizontal movement to vertex `(i, j)` is compatible with the script  `delete at index i from X`, the vertical movement to vertex `(i, j)` is compatible with the script `insert the element of Y at index j to immediately after the element of X at index i`. How about for the diagonal movement?. This movement to vertex `(i, j)` means `X[i] = Y[j]`, so no script needs.
 
@@ -38,7 +38,7 @@ Next, add cost 1 for non-diagonal movement, because they can be compatible with
 
 The total cost for the minimum path, exploring from `source` to `sink`, is the same as the length of the Longest Common Subsequence or Shortest Edit Script.
 
-So, LSC/SES problem can be solved by finding the shortest path from `source` to `sink`.
+So, LCS/SES problem can be solved by finding the shortest path from `source` to `sink`.
 
 ### Myers Algorithm
 
@@ -52,9 +52,9 @@ By a simple induction, D-path must consist of a (D-1)-path followed by a non-dia
 for D in 0...N + M
 ```
 
-Next, thinking about, where is the furthest reaching point for D-path on k-line. Like below, moving horizontally from k-line reaches (k+1)-line, moving vertically from k-line reaches (k-1)-line.
+Next, thinking about, where is the furthest reaching point for D-path on k-line. Like below, moving horizontally from k-line reaches (k+1)-line, moving vertically from k-line reaches (k-1)-line. Red chalky line shows that.
 
-<img src='Images/EditGraph_k_move.png' height="250">
+<img src='Images/EditGraph_k_move.png' height="400">
 
 So, threre are several end points of D-path, or D-path can end on several k-line. We need the information to get the next path ((D+1)-path) as mentioned above. In fact, D-path must end on
 k-line, where k in { -D, -D + 2, ....., D - 2, D }. This is so simple, starting point, `source` is `(0, 0)` on (k=0)-line. D is the number of non-diagonal edges and non-diagonal movement changes current k-line to (kpm1)-line. Because 0 is even number, if D is even number D-path will end on (even_k)-line, if D is odd number D-path will end on (odd_k)-line.

From 81befa64507475361183cd52d29b14ce65da2e03 Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Mon, 5 Mar 2018 09:22:32 -0600
Subject: [PATCH 1388/1679] tutorial; weighted choice

---
 Genetic/README.markdown               |  49 +++++++-
 Genetic/gen.playground/Contents.swift |  52 +++++++++
 Genetic/gen.swift                     | 154 +++++++++++---------------
 3 files changed, 167 insertions(+), 88 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 6ebbf2cf7..fdc6d5d92 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -188,4 +188,51 @@ The above is used to generate a completely new generation based on the current g
 
 ## Putting it all together -- Running the Genetic Algorithm
 
-We now have all the methods we need to kick off the process. What is missing a `main()` function that loops though each generation of the GA.
+We now have all the functions we need to kick off the algorthim. Let's start from the beginning, first we need a random population to serve as a starting point. We will also initialize a fittest variable to hold the fittest individual, we will initialize it with the first individual of our random population.
+
+```swift
+var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+var fittest = population[0]
+```
+
+Now for the meat, the remainder of the code will take place in the generation loop, running once for every generation:
+
+```swift
+for generation in 0...GENERATIONS {
+  // run
+}
+```
+
+Now, for each individual in the population, we need to calculate its fitness and weighted value. For weighted choice we store the fitness as a percent `1 / fitness`.
+
+```swift
+var weightedPopulation = [(item:[UInt8], weight:Double)]()
+
+for individual in population {
+  let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+  let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+  weightedPopulation.append(pair)
+}
+```
+
+To understand weighted choice, let walk though a smaller example, let's say we have the following population, where 0 is the best fitness:
+
+```txt
+1: 10
+2: 5
+3: 4
+4: 7
+5: 11
+```
+
+Now here is the weight of each:
+
+```txt
+1:
+2:
+3:
+4:
+5:
+
+total =
+```
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 50d4c4fc8..4c67f8bd1 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -102,3 +102,55 @@ func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[
         [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
     )
 }
+
+func main() {
+    
+    // generate the starting random population
+    var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+    // print("population: \(population), dnaSize: \(DNA_SIZE) ")
+    var fittest = [UInt8]()
+    
+    for generation in 0...GENERATIONS {
+        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        
+        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        
+        // calulcated the fitness of each individual in the population
+        // and add it to the weight population (weighted = 1.0/fitness)
+        for individual in population {
+            let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+            
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            
+            weightedPopulation.append(pair)
+        }
+        
+        population = []
+        
+        // create a new generation using the individuals in the origional population
+        for _ in 0...POP_SIZE/2 {
+            let ind1 = weightedChoice(items: weightedPopulation)
+            let ind2 = weightedChoice(items: weightedPopulation)
+            
+            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+            
+            // append to the population and mutate
+            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
+        }
+        
+        fittest = population[0]
+        var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
+        
+        // parse the population for the fittest string
+        for indv in population {lex
+            let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+            if indvFitness < minFitness {
+                fittest = indv
+                minFitness = indvFitness
+            }
+        }
+        if minFitness == 0 { break; }
+    }
+    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+}
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index 17df6d002..f664fd5f7 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -1,46 +1,56 @@
-/*
-  base .. to be refactored
-*/
+//: Playground - noun: a place where people can play
 
 import Foundation
 
-// HELPERS
-/*
-    String extension to convert a string to ascii value
-*/
 extension String {
     var asciiArray: [UInt8] {
-        return unicodeScalars.filter{$0.isASCII}.map{UInt8($0.value)}
+        return [UInt8](self.utf8)
     }
 }
 
-let lex = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".map {  }
 
-/*
-    helper function to return a random character string
-*/
-func randomChar() -> UInt8 {
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
 
-    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
-    let len = UInt32(letters.count-1)
+// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
 
-    let rand = Int(arc4random_uniform(len))
-    return letters[rand]
-}
+// The length of the string in our population. Organisms need to be similar
+let DNA_SIZE = OPTIMAL.count
 
-// END HELPERS
+// size of each generation
+let POP_SIZE = 200
 
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
-let DNA_SIZE = OPTIMAL.count
-let POP_SIZE = 50
+// max number of generations, script will stop when it reach 5000 if the optimal value is not found
 let GENERATIONS = 5000
+
+// The chance in which a random nucleotide can mutate (1/n)
 let MUTATION_CHANCE = 100
 
-/*
-    calculated the fitness based on approximate string matching
-    compares each character ascii value difference and adds that to a total fitness
-    optimal string comparsion = 0
-*/
+func randomChar(from lexicon: [UInt8]) -> UInt8 {
+    let len = UInt32(lexicon.count-1)
+    let rand = Int(arc4random_uniform(len))
+    return lexicon[rand]
+}
+
+func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+
+    let len = UInt32(lexicon.count)
+
+    var pop = [[UInt8]]()
+
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let char = randomChar(from: lexicon)
+            dna.append(char)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+
+randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 
     var fitness = 0
@@ -50,26 +60,37 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
     return fitness
 }
 
-/*
-    randomly mutate the string
-*/
-func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
+calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
+
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+
+    let total = items.reduce(0.0) { return $0 + $1.weight}
+
+    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
+
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+
+func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
-    for i in 0..<dnaSize {
+    for i in 0..<dna.count {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
-            outputDna[i] = randomChar()
+            outputDna[i] = randomChar(from: lexicon)
         }
     }
 
     return outputDna
 }
 
-/*
-    combine two parents to create an offspring
-    parent = xy & yx, offspring = xx, yy
-*/
+
 func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
 
@@ -82,59 +103,15 @@ func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[
     )
 }
 
-
-/*
-returns a random population, used to start the evolution
-*/
-func randomPopulation(populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-
-    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
-    let len = UInt32(letters.count)
-
-    var pop = [[UInt8]]()
-
-    for _ in 0..<populationSize {
-        var dna = [UInt8]()
-        for _ in 0..<dnaSize {
-            let rand = arc4random_uniform(len)
-            let nextChar = letters[Int(rand)]
-            dna.append(nextChar)
-        }
-        pop.append(dna)
-    }
-    return pop
-}
-
-
-/*
-function to return random canidate of a population randomally, but weight on fitness.
-*/
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
-    var weightTotal = 0.0
-    for itemTuple in items {
-        weightTotal += itemTuple.weight;
-    }
-
-    var n = Double(arc4random_uniform(UInt32(weightTotal * 1000000.0))) / 1000000.0
-
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
-        }
-        n = n - itemTuple.weight
-    }
-    return items[1]
-}
-
 func main() {
 
     // generate the starting random population
-    var population:[[UInt8]] = randomPopulation(populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+    var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
     // print("population: \(population), dnaSize: \(DNA_SIZE) ")
     var fittest = [UInt8]()
 
     for generation in 0...GENERATIONS {
-        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
 
         var weightedPopulation = [(item:[UInt8], weight:Double)]()
 
@@ -143,7 +120,7 @@ func main() {
         for individual in population {
             let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
 
-            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : Double(100/POP_SIZE)/Double( fitnessValue ) )
 
             weightedPopulation.append(pair)
         }
@@ -158,15 +135,15 @@ func main() {
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
-            population.append(mutate(dna: offspring.dna1, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
-            population.append(mutate(dna: offspring.dna2, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
+            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
         }
 
         fittest = population[0]
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
 
         // parse the population for the fittest string
-        for indv in population {
+        for indv in population {lex
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
             if indvFitness < minFitness {
                 fittest = indv
@@ -174,6 +151,9 @@ func main() {
             }
         }
         if minFitness == 0 { break; }
+        if generation % 1000 == 0 {
+          print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+        }
     }
     print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
 }

From 66f75d2c51b97f51259e8e6706433773e4a6e1af Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 14:50:30 -0600
Subject: [PATCH 1389/1679] tutotial complete

---
 Genetic/README.markdown               | 143 +++++++++++++++++++++-----
 Genetic/gen.playground/Contents.swift |  25 ++---
 Genetic/gen.swift                     |  21 ++--
 3 files changed, 139 insertions(+), 50 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index fdc6d5d92..92f121daa 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -1,4 +1,4 @@
-# Genetic Algorthim
+individual# Genetic Algorthim
 
 ## What is it?
 
@@ -20,7 +20,9 @@ The randomization that allows for organisms to change over time. In GAs we build
 Simply reproduction. A generation will a mixed representation of the previous generation, with offspring taking data (DNA) from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
 
 ### Resources:
-* [Wikipedia]()
+* [Genetic Algorithms in Search Optimization, and Machine Learning](https://www.amazon.com/Genetic-Algorithms-Optimization-Machine-Learning/dp/0201157675/ref=sr_1_sc_1?ie=UTF8&qid=1520628364&sr=8-1-spell&keywords=Genetic+Algortithms+in+search)
+* [Wikipedia](https://en.wikipedia.org/wiki/Genetic_algorithm)
+* [My Original Gist](https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba)
 
 
 ## The Code
@@ -141,7 +143,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
 }
 ```
 
-The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value.
+The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value. The horrible 1,000,000 multiplication and division is to insure precision by calculating decimals. `arc4random` only uses integers so this is required to convert to a precise Double, it's not perfect, but enough for our example.
 
 ## Mutation
 
@@ -168,19 +170,16 @@ This allows for a population to explore all the possibilities of it's building b
 
 ## Crossover
 
-Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents:
+Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents.
 
 ```swift
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
 
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
 
-    return (
-        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
-        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
-    )
+    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 ```
 
@@ -203,7 +202,7 @@ for generation in 0...GENERATIONS {
 }
 ```
 
-Now, for each individual in the population, we need to calculate its fitness and weighted value. For weighted choice we store the fitness as a percent `1 / fitness`.
+Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weighted value. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
 
 ```swift
 var weightedPopulation = [(item:[UInt8], weight:Double)]()
@@ -215,24 +214,118 @@ for individual in population {
 }
 ```
 
-To understand weighted choice, let walk though a smaller example, let's say we have the following population, where 0 is the best fitness:
+From here we can start to build the next generation.
 
-```txt
-1: 10
-2: 5
-3: 4
-4: 7
-5: 11
+```swift
+var nextGeneration = []
+```
+
+The below loop is where we pull everything together. We loop for `POP_SIZE`, selecting 2 individuals by weighted choice, crossover their values to produce a offspring, then finial subject the new individual to mutation. Once completed we have a completely new generation based on the last generation.
+
+```swift
+0...POP_SIZE).forEach { _ in
+    let ind1 = weightedChoice(items: weightedPopulation)
+    let ind2 = weightedChoice(items: weightedPopulation)
+
+    let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+
+    // append to the population and mutate
+    nextGeneration.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
+}
+```
+
+The final piece to the main loop is to select the fittest individual of a population:
+
+```swift
+fittest = population[0]
+var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
+
+for indv in population {lex
+    let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+    if indvFitness < minFitness {
+        fittest = indv
+        minFitness = indvFitness
+    }
+}
+if minFitness == 0 { break; }
+print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
 ```
 
-Now here is the weight of each:
+Since we know the fittest string, I've added a `break` to kill the program if we find it. At the end of a loop at a print statement for the fittest string:
 
-```txt
-1:
-2:
-3:
-4:
-5:
+```swift
+print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
+```
 
-total =
+Now we can run the program! Playgrounds are a nice place to develop, but are going to run this program **very slow**. I highly suggest running in Terminal: `swift gen.swift`. When running you should see something like this and it should not take too long to get `Hello, World`:
+
+```text
+0: RXclh F HDko
+1: DkyssjgElk];
+2: TiM4u) DrKvZ
+3: Dkysu) DrKvZ
+4: -kysu) DrKvZ
+5: Tlwsu) DrKvZ
+6: Tlwsu) Drd}k
+7: Tlwsu) Drd}k
+8: Tlwsu) Drd}k
+9: Tlwsu) Drd}k
+10: G^csu) |zd}k
+11: G^csu) |zdko
+12: G^csu) |zdko
+13: Dkysu) Drd}k
+14: G^wsu) `rd}k
+15: Dkysu) `rdko
+16: Dkysu) `rdko
+17: Glwsu) `rdko
+18: TXysu) `rdkc
+19: U^wsu) `rdko
+20: G^wsu) `rdko
+21: Glysu) `rdko
+22: G^ysu) `rdko
+23: G^ysu) `ryko
+24: G^wsu) `rdko
+25: G^wsu) `rdko
+26: G^wsu) `rdko
+...
+1408: Hello, Wormd
+1409: Hello, Wormd
+1410: Hello, Wormd
+1411: Hello, Wormd
+1412: Hello, Wormd
+1413: Hello, Wormd
+1414: Hello, Wormd
+1415: Hello, Wormd
+1416: Hello, Wormd
+1417: Hello, Wormd
+1418: Hello, Wormd
+1419: Hello, Wormd
+1420: Hello, Wormd
+1421: Hello, Wormd
+1422: Hello, Wormd
+1423: Hello, Wormd
+1424: Hello, Wormd
+1425: Hello, Wormd
+1426: Hello, Wormd
+1427: Hello, Wormd
+1428: Hello, Wormd
+1429: Hello, Wormd
+1430: Hello, Wormd
+1431: Hello, Wormd
+1432: Hello, Wormd
+1433: Hello, Wormd
+1434: Hello, Wormd
+1435: Hello, Wormd
+fittest string: Hello, World
 ```
+
+How long it takes will vary since this is based on randomization, but it should almost always finish in under 5000 generations. Woo!
+
+
+## Now What?
+
+We did it, we have a running simple genetic algorithm. Take some time a play around with the global variables, `POP_SIZE`, `OPTIMAL`, `MUTATION_CHANCE`, `GENERATIONS`. Just make sure to only add characters that are in the lexicon, but go ahead and update too!
+
+For an example let's try something much longer: `Ray Wenderlich's Swift Algorithm Club Rocks`. Plug that string into `OPTIMAL` and change `GENERATIONS` to `10000`. You'll be able to see that the we are getting somewhere, but you most likely will not reach the optimal string in 10,000 generations. Since we have a larger string let's raise our mutation chance to `200` (1/2 as likely to mutate). You may not get there, but you should get a lot closer than before. With a longer string, too much mutate can make it hard for fit strings to survive. Now try either upping `POP_SIZE` or increase `GENERATIONS`. Either way you should eventually get the value, but there will be a "sweet spot" for an individual of a certain size.
+
+Please submit any kind of update to this tutorial or add more examples!
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 4c67f8bd1..8e1976ca6 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -63,7 +63,7 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
 
 func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
-
+    
     let total = items.reduce(0.0) { return $0 + $1.weight}
     
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
@@ -91,16 +91,13 @@ func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
 }
 
 
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
     
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
     
-    return (
-        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
-        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
-    )
+    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 
 func main() {
@@ -111,7 +108,7 @@ func main() {
     var fittest = [UInt8]()
     
     for generation in 0...GENERATIONS {
-        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
         
         var weightedPopulation = [(item:[UInt8], weight:Double)]()
         
@@ -120,7 +117,7 @@ func main() {
         for individual in population {
             let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
             
-            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : Double(100/POP_SIZE)/Double( fitnessValue ) )
             
             weightedPopulation.append(pair)
         }
@@ -128,15 +125,14 @@ func main() {
         population = []
         
         // create a new generation using the individuals in the origional population
-        for _ in 0...POP_SIZE/2 {
+        (0...POP_SIZE).forEach { _ in
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
             
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
             
             // append to the population and mutate
-            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
-            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
         }
         
         fittest = population[0]
@@ -151,6 +147,11 @@ func main() {
             }
         }
         if minFitness == 0 { break; }
+        print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+        
     }
-    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+    print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
 }
+
+main()
+
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index f664fd5f7..a2a1b1410 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -18,7 +18,7 @@ let OPTIMAL:[UInt8] = "Hello, World".asciiArray
 let DNA_SIZE = OPTIMAL.count
 
 // size of each generation
-let POP_SIZE = 200
+let POP_SIZE = 50
 
 // max number of generations, script will stop when it reach 5000 if the optimal value is not found
 let GENERATIONS = 5000
@@ -91,16 +91,13 @@ func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
 }
 
 
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
 
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
 
-    return (
-        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
-        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
-    )
+    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 
 func main() {
@@ -128,15 +125,14 @@ func main() {
         population = []
 
         // create a new generation using the individuals in the origional population
-        for _ in 0...POP_SIZE/2 {
+        (0...POP_SIZE).forEach { _ in
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
 
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
-            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
-            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
         }
 
         fittest = population[0]
@@ -151,11 +147,10 @@ func main() {
             }
         }
         if minFitness == 0 { break; }
-        if generation % 1000 == 0 {
-          print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
-        }
+        print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+
     }
-    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+    print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
 }
 
 main()

From ca6f0f0c71773a9117db63546b7c94b0c8de3a0e Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 15:32:58 -0600
Subject: [PATCH 1390/1679] readme updates

---
 Genetic/README.markdown | 79 ++++++++++++++++++++---------------------
 1 file changed, 38 insertions(+), 41 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 92f121daa..d6a474a10 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -2,35 +2,34 @@ individual# Genetic Algorthim
 
 ## What is it?
 
-A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), mutation and crossover. To understand more, let's walk through these process in terms of biology:
+A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), crossover and mutation. To understand more, let's walk through these processes in terms of biology:
 
 ### Selection
 >**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors. [Britannica](britannica)
 
-In other words, survival of the fittest. Organism that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank offspring and give them a better chance for reproduction.
-
-### Mutation
->**Mutation**, an alteration in the genetic material (the genome) of a cell of a living organism or of a virus that is more or less permanent and that can be transmitted to the cell’s or the virus’s descendants. [Britannica](https://www.britannica.com/science/mutation-genetics)
-
-The randomization that allows for organisms to change over time. In GAs we build a randomization process that will mutate offspring in a populate in order to randomly introduce fitness variance.
+In other words, survival of the fittest. Organisms that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank individuals and give them a better chance for reproduction.
 
 ### Crossover
 >**Chromosomal crossover** (or crossing over) is the exchange of genetic material between homologous chromosomes that results in recombinant chromosomes during sexual reproduction [Wikipedia](https://en.wikipedia.org/wiki/Chromosomal_crossover)
 
-Simply reproduction. A generation will a mixed representation of the previous generation, with offspring taking data (DNA) from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
+Simply reproduction. A generation will be a mixed representation of the previous generation, with offspring taking DNA from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
+
+### Mutation
+>**Mutation**, an alteration in the genetic material (the genome) of a cell of a living organism or of a virus that is more or less permanent and that can be transmitted to the cell’s or the virus’s descendants. [Britannica](https://www.britannica.com/science/mutation-genetics)
+
+The randomization that allows for organisms to change over time. In GAs we build a randomization process that will mutate offspring in a population in order to introduce fitness variance.
 
 ### Resources:
 * [Genetic Algorithms in Search Optimization, and Machine Learning](https://www.amazon.com/Genetic-Algorithms-Optimization-Machine-Learning/dp/0201157675/ref=sr_1_sc_1?ie=UTF8&qid=1520628364&sr=8-1-spell&keywords=Genetic+Algortithms+in+search)
 * [Wikipedia](https://en.wikipedia.org/wiki/Genetic_algorithm)
 * [My Original Gist](https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba)
 
-
 ## The Code
 
 ### Problem
-For this quick and dirty example, we are going to obtain a optimize string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
+For this quick and dirty example, we are going to produce an optimized string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
 
-We will be creating a bio-inspired world where the absolute existence is string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible.  
+We will be creating a bio-inspired world where the absolute existence is the string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible to ensure survival. 
 
 ### Define the Universe
 
@@ -40,36 +39,32 @@ Before we dive into the core processes we need to set up our "universe". First l
 let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
 ```
 
-To make things easier, we are actually going to work in ASCII values, so let's define a String extension to help with that.
+To make things easier, we are actually going to work in [Unicode values](https://en.wikipedia.org/wiki/List_of_Unicode_characters), so let's define a String extension to help with that.
 
 ```swift
 extension String {
-  var asciiArray: [UInt8] {
+  var unicodeArray: [UInt8] {
     return [UInt8](self.utf8)
   }
 }
 ```
 
  Now, let's define a few global variables for the universe:
+ * `OPTIMAL`: This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+ * `DNA_SIZE`: The length of the string in our population. Organisms need to be similar
+ * `POP_SIZE`: Size of each generation
+ * `MAX_GENERATIONS`: Max number of generations, script will stop when it reach 5000 if the optimal value is not found
+ * `MUTATION_CHANCE`: The chance in which a random nucleotide can mutate (`1/MUTATION_CHANCE`)
 
  ```swift
-// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
-
-// The length of the string in our population. Organisms need to be similar
+let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 let DNA_SIZE = OPTIMAL.count
-
-// size of each generation
 let POP_SIZE = 50
-
-// max number of generations, script will stop when it reach 5000 if the optimal value is not found
-let GENERATIONS = 5000
-
-// The chance in which a random nucleotide can mutate (1/n)
+let MAX_GENERATIONS = 5000
 let MUTATION_CHANCE = 100
  ```
 
- The last piece we need for set up is a function to give us a random ASCII value from our lexicon:
+ The last piece we need for set up is a function to give us a random unicode value from our lexicon:
 
  ```swift
  func randomChar(from lexicon: [UInt8]) -> UInt8 {
@@ -78,10 +73,12 @@ let MUTATION_CHANCE = 100
      return lexicon[rand]
  }
  ```
+ 
+ **Note**: `arc4random_uniform` is strickly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
 
  ### Population Zero
 
- Before selecting, mutating and reproduction, we need population to start with. Now that we have the universe defined we can write that function:
+Before selecting, crossover and mutation, we need a population to start with. Now that we have the universe defined we can write that function:
 
  ```swift
  func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
@@ -90,9 +87,9 @@ let MUTATION_CHANCE = 100
 
     var pop = [[UInt8]]()
 
-    for _ in 0..<populationSize {
+    (0..<populationSize).forEach { _ in
         var dna = [UInt8]()
-        for _ in 0..<dnaSize {
+        (0..<dnaSize).forEach { _ in
             let char = randomChar(from: lexicon)
             dna.append(char)
         }
@@ -104,27 +101,27 @@ let MUTATION_CHANCE = 100
 
 ### Selection
 
-There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using ASCII values:
+There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using unicode values:
 
 ```swift
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
     var fitness = 0
-    for c in 0...dna.count-1 {
+    (0...dna.count-1).forEach { c in
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
     }
     return fitness
 }
 ```
 
-The above will produce a fitness value to an individual. The perfect solution, "Hello, World" will have a fitness of 0. "Gello, World" will have a fitness of 1 since it is one ASCII value off from the optimal.
+The above will produce a fitness value to an individual. The perfect solution, "Hello, World" will have a fitness of 0. "Gello, World" will have a fitness of 1 since it is one unicode value off from the optimal (`H->G`).
 
-This example is very, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
+This example is very simple, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using a GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival. In our example we will reach our goal, a fitness of 0.
 
-The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or not be able to reproduce.
+The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or be unable to reproduce.
 
-Let's take a second and ask why on this one. Why would you not always want to select the most fit from a population? It's hard to see from this simple example, but let's think about dog breeding, because breeders remove this process and hand select dogs for the next generation. As a result you get improved desired characteristics, but the individuals will also continue to carry genetic disorders that come along with those traits. This is essentially leading the evolution down a linear path. A certain "branch" of evolution may beat out the current fittest solution at a later time.
+Let's take a second and ask why on this one. Why would you not always want to select the most fit from a population? It's hard to see from this simple example, but let's think about dog breeding, because breeders remove this process and hand select dogs for the next generation. As a result you get improved desired characteristics, but the individuals will also continue to carry genetic disorders that come along with those traits. A certain "branch" of evolution may beat out the current fittest solution at a later time. This may be ok depending on the problem, but to keep this educational we will go with the bio-inspired way.
 
-ok, back to code. Here is our weighted choice function:
+With all that, here is our weight choice function:
 
 ```swift
 func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
@@ -147,13 +144,13 @@ The above function takes a list of individuals with their calculated fitness. Th
 
 ## Mutation
 
-The all powerful mutation. The great randomization that turns bacteria into humans, just add time. So powerful yet so simple:
+The all powerful mutation, the thing that introduces otherwise non exisitant fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achive the optimal solution.
 
 ```swift
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
-    for i in 0..<dna.count {
+    (0..<dna.count).forEach { i in
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
             outputDna[i] = randomChar(from: lexicon)
@@ -202,7 +199,7 @@ for generation in 0...GENERATIONS {
 }
 ```
 
-Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weighted value. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
+Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weight. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
 
 ```swift
 var weightedPopulation = [(item:[UInt8], weight:Double)]()
@@ -251,7 +248,7 @@ if minFitness == 0 { break; }
 print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
 ```
 
-Since we know the fittest string, I've added a `break` to kill the program if we find it. At the end of a loop at a print statement for the fittest string:
+Since we know the fittest string, I've added a `break` to kill the program if we find it. At the end of a loop add a print statement for the fittest string:
 
 ```swift
 print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
@@ -324,8 +321,8 @@ How long it takes will vary since this is based on randomization, but it should
 
 ## Now What?
 
-We did it, we have a running simple genetic algorithm. Take some time a play around with the global variables, `POP_SIZE`, `OPTIMAL`, `MUTATION_CHANCE`, `GENERATIONS`. Just make sure to only add characters that are in the lexicon, but go ahead and update too!
+We did it, we have a running simple genetic algorithm. Take some time a play around with the global variables, `POP_SIZE`, `OPTIMAL`, `MUTATION_CHANCE`, `GENERATIONS`. Just make sure to only add characters that are in the lexicon or update the lexicon.
 
-For an example let's try something much longer: `Ray Wenderlich's Swift Algorithm Club Rocks`. Plug that string into `OPTIMAL` and change `GENERATIONS` to `10000`. You'll be able to see that the we are getting somewhere, but you most likely will not reach the optimal string in 10,000 generations. Since we have a larger string let's raise our mutation chance to `200` (1/2 as likely to mutate). You may not get there, but you should get a lot closer than before. With a longer string, too much mutate can make it hard for fit strings to survive. Now try either upping `POP_SIZE` or increase `GENERATIONS`. Either way you should eventually get the value, but there will be a "sweet spot" for an individual of a certain size.
+For an example let's try something much longer: `Ray Wenderlich's Swift Algorithm Club Rocks`. Plug that string into `OPTIMAL` and change `GENERATIONS` to `10000`. You'll be able to see that the we are getting somewhere, but you most likely will not reach the optimal string in 10,000 generations. Since we have a larger string let's raise our mutation chance to `200` (1/2 as likely to mutate). You may not get there, but you should get a lot closer than before. With a longer string, too much mutation can make it hard for fit strings to survive. Now try either upping `POP_SIZE` or increase `GENERATIONS`. Either way you should eventually get the value, but there will be a "sweet spot" for an string of a certain size.
 
 Please submit any kind of update to this tutorial or add more examples!

From 6c6b46b330d68698f1d7826276895ddcae82ed98 Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 15:43:15 -0600
Subject: [PATCH 1391/1679] typos

---
 Genetic/README.markdown               | 30 +++++++-------
 Genetic/gen.playground/Contents.swift | 39 +++++++------------
 Genetic/gen.swift                     | 56 ++++++++++++---------------
 3 files changed, 53 insertions(+), 72 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index d6a474a10..07547c4b4 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -29,7 +29,7 @@ The randomization that allows for organisms to change over time. In GAs we build
 ### Problem
 For this quick and dirty example, we are going to produce an optimized string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
 
-We will be creating a bio-inspired world where the absolute existence is the string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible to ensure survival. 
+We will be creating a bio-inspired world where the absolute existence is the string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible to ensure survival.
 
 ### Define the Universe
 
@@ -73,8 +73,8 @@ let MUTATION_CHANCE = 100
      return lexicon[rand]
  }
  ```
- 
- **Note**: `arc4random_uniform` is strickly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
+
+ **Note**: `arc4random_uniform` is strictly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
 
  ### Population Zero
 
@@ -83,8 +83,6 @@ Before selecting, crossover and mutation, we need a population to start with. No
  ```swift
  func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
 
-    let len = UInt32(lexicon.count)
-
     var pop = [[UInt8]]()
 
     (0..<populationSize).forEach { _ in
@@ -96,7 +94,7 @@ Before selecting, crossover and mutation, we need a population to start with. No
         pop.append(dna)
     }
     return pop
-}
+ }
  ```
 
 ### Selection
@@ -124,17 +122,17 @@ Let's take a second and ask why on this one. Why would you not always want to se
 With all that, here is our weight choice function:
 
 ```swift
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
 
     let total = items.reduce(0.0) { return $0 + $1.weight}
 
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
 
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
+    for item in items {
+        if n < item.weight {
+            return item
         }
-        n = n - itemTuple.weight
+        n = n - item.weight
     }
     return items[1]
 }
@@ -144,7 +142,7 @@ The above function takes a list of individuals with their calculated fitness. Th
 
 ## Mutation
 
-The all powerful mutation, the thing that introduces otherwise non exisitant fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achive the optimal solution.
+The all powerful mutation, the thing that introduces otherwise non existent fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achieve the optimal solution.
 
 ```swift
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
@@ -184,7 +182,7 @@ The above is used to generate a completely new generation based on the current g
 
 ## Putting it all together -- Running the Genetic Algorithm
 
-We now have all the functions we need to kick off the algorthim. Let's start from the beginning, first we need a random population to serve as a starting point. We will also initialize a fittest variable to hold the fittest individual, we will initialize it with the first individual of our random population.
+We now have all the functions we need to kick off the algorithm. Let's start from the beginning, first we need a random population to serve as a starting point. We will also initialize a fittest variable to hold the fittest individual, we will initialize it with the first individual of our random population.
 
 ```swift
 var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
@@ -202,7 +200,7 @@ for generation in 0...GENERATIONS {
 Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weight. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
 
 ```swift
-var weightedPopulation = [(item:[UInt8], weight:Double)]()
+var weightedPopulation = [(dna:[UInt8], weight:Double)]()
 
 for individual in population {
   let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
@@ -224,7 +222,7 @@ The below loop is where we pull everything together. We loop for `POP_SIZE`, sel
     let ind1 = weightedChoice(items: weightedPopulation)
     let ind2 = weightedChoice(items: weightedPopulation)
 
-    let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+    let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
 
     // append to the population and mutate
     nextGeneration.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
@@ -237,7 +235,7 @@ The final piece to the main loop is to select the fittest individual of a popula
 fittest = population[0]
 var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
 
-for indv in population {lex
+population.forEach { indv in
     let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
     if indvFitness < minFitness {
         fittest = indv
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 8e1976ca6..79a398ceb 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -3,16 +3,16 @@
 import Foundation
 
 extension String {
-    var asciiArray: [UInt8] {
+    var unicodeArray: [UInt8] {
         return [UInt8](self.utf8)
     }
 }
 
 
-let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".unicodeArray
 
 // This is the end goal and what we will be using to rate fitness. In the real world this will not exist
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 
 // The length of the string in our population. Organisms need to be similar
 let DNA_SIZE = OPTIMAL.count
@@ -34,13 +34,11 @@ func randomChar(from lexicon: [UInt8]) -> UInt8 {
 
 func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
     
-    let len = UInt32(lexicon.count)
-    
     var pop = [[UInt8]]()
     
-    for _ in 0..<populationSize {
+    (0..<populationSize).forEach { _ in
         var dna = [UInt8]()
-        for _ in 0..<dnaSize {
+        (0..<dnaSize).forEach { _ in
             let char = randomChar(from: lexicon)
             dna.append(char)
         }
@@ -49,30 +47,25 @@ func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int)
     return pop
 }
 
-randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
-
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-    
     var fitness = 0
-    for c in 0...dna.count-1 {
+    (0...dna.count-1).forEach { c in
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
     }
     return fitness
 }
 
-calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
-
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
     
     let total = items.reduce(0.0) { return $0 + $1.weight}
     
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
     
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
+    for item in items {
+        if n < item.weight {
+            return item
         }
-        n = n - itemTuple.weight
+        n = n - item.weight
     }
     return items[1]
 }
@@ -80,7 +73,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
     
-    for i in 0..<dna.count {
+    (0..<dna.count).forEach { i in
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
             outputDna[i] = randomChar(from: lexicon)
@@ -108,9 +101,8 @@ func main() {
     var fittest = [UInt8]()
     
     for generation in 0...GENERATIONS {
-        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
         
-        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        var weightedPopulation = [(dna:[UInt8], weight:Double)]()
         
         // calulcated the fitness of each individual in the population
         // and add it to the weight population (weighted = 1.0/fitness)
@@ -129,7 +121,7 @@ func main() {
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
             
-            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+            let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
             
             // append to the population and mutate
             population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
@@ -139,7 +131,7 @@ func main() {
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
         
         // parse the population for the fittest string
-        for indv in population {lex
+        population.forEach { indv in
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
             if indvFitness < minFitness {
                 fittest = indv
@@ -154,4 +146,3 @@ func main() {
 }
 
 main()
-
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index a2a1b1410..aad499d04 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -3,16 +3,16 @@
 import Foundation
 
 extension String {
-    var asciiArray: [UInt8] {
+    var unicodeArray: [UInt8] {
         return [UInt8](self.utf8)
     }
 }
 
 
-let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".unicodeArray
 
 // This is the end goal and what we will be using to rate fitness. In the real world this will not exist
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 
 // The length of the string in our population. Organisms need to be similar
 let DNA_SIZE = OPTIMAL.count
@@ -34,45 +34,38 @@ func randomChar(from lexicon: [UInt8]) -> UInt8 {
 
 func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
 
-    let len = UInt32(lexicon.count)
-
-    var pop = [[UInt8]]()
-
-    for _ in 0..<populationSize {
-        var dna = [UInt8]()
-        for _ in 0..<dnaSize {
-            let char = randomChar(from: lexicon)
-            dna.append(char)
-        }
-        pop.append(dna)
-    }
-    return pop
+   var pop = [[UInt8]]()
+
+   (0..<populationSize).forEach { _ in
+       var dna = [UInt8]()
+       (0..<dnaSize).forEach { _ in
+           let char = randomChar(from: lexicon)
+           dna.append(char)
+       }
+       pop.append(dna)
+   }
+   return pop
 }
 
-randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
-
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-
     var fitness = 0
-    for c in 0...dna.count-1 {
+    (0...dna.count-1).forEach { c in
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
     }
     return fitness
 }
 
-calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
-
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
 
     let total = items.reduce(0.0) { return $0 + $1.weight}
 
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
 
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
+    for item in items {
+        if n < item.weight {
+            return item
         }
-        n = n - itemTuple.weight
+        n = n - item.weight
     }
     return items[1]
 }
@@ -80,7 +73,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
-    for i in 0..<dna.count {
+    (0..<dna.count).forEach { i in
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
             outputDna[i] = randomChar(from: lexicon)
@@ -108,9 +101,8 @@ func main() {
     var fittest = [UInt8]()
 
     for generation in 0...GENERATIONS {
-        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
 
-        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        var weightedPopulation = [(dna:[UInt8], weight:Double)]()
 
         // calulcated the fitness of each individual in the population
         // and add it to the weight population (weighted = 1.0/fitness)
@@ -129,7 +121,7 @@ func main() {
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
 
-            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+            let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
             population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
@@ -139,7 +131,7 @@ func main() {
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
 
         // parse the population for the fittest string
-        for indv in population {lex
+        population.forEach { indv in
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
             if indvFitness < minFitness {
                 fittest = indv

From e1074a1aa7ac3fab3e809b8563dec3cf1d9454bb Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 16:05:03 -0600
Subject: [PATCH 1392/1679] MAX_GENERATIONS

---
 Genetic/gen.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index aad499d04..a61e61785 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -21,7 +21,7 @@ let DNA_SIZE = OPTIMAL.count
 let POP_SIZE = 50
 
 // max number of generations, script will stop when it reach 5000 if the optimal value is not found
-let GENERATIONS = 5000
+let MAX_GENERATIONS = 5000
 
 // The chance in which a random nucleotide can mutate (1/n)
 let MUTATION_CHANCE = 100
@@ -100,7 +100,7 @@ func main() {
     // print("population: \(population), dnaSize: \(DNA_SIZE) ")
     var fittest = [UInt8]()
 
-    for generation in 0...GENERATIONS {
+    for generation in 0...MAX_GENERATIONS {
 
         var weightedPopulation = [(dna:[UInt8], weight:Double)]()
 

From 1bc39d21853c4fe869a6861354c54d213cd624bf Mon Sep 17 00:00:00 2001
From: Philip Ridgeway <philip.ridgeway@gmail.com>
Date: Sat, 10 Mar 2018 10:57:39 -0800
Subject: [PATCH 1393/1679] Replaces references to indexOf(_:) with index(of:).

The global function `indexOf(_:)` was replaced with
`Collection.index(of:)` in Swift 2.
---
 Binary Search/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 09b141e04..0cecce6cf 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -4,15 +4,15 @@ Goal: Quickly find an element in an array.
 
 Let's say you have an array of numbers and you want to determine whether a specific number is in that array, and if so, at which index.
 
-In most cases, Swift's `indexOf()` function is good enough for that:
+In most cases, Swift's `Collection.index(of:)` function is good enough for that:
 
 ```swift
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
-numbers.indexOf(43)  // returns 15
+numbers.index(of: 43)  // returns 15
 ```
 
-The built-in `indexOf()` function performs a [linear search](../Linear%20Search/). In code that looks something like this:
+The built-in `Collection.index(of:)` function performs a [linear search](../Linear%20Search/). In code that looks something like this:
 
 ```swift
 func linearSearch<T: Equatable>(_ a: [T], _ key: T) -> Int? {

From 0bcbd08988c5ab000a9901c6a6c03ab1a29aed6a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Mar 2018 12:59:19 -0700
Subject: [PATCH 1394/1679] Grammar fixes for first bit.

---
 Myers Difference Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index 2f6c3c579..a9d92a227 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,6 +1,6 @@
 #  Myers Difference Algorithm
 
-Myers Difference Algorithm is the algorithm to find a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences by a simple O(ND) time, where N is the sum of the lengths of the two sequences. Common subsequence is the sequence of elements that appear in the same order in both sequences. Edit script will be discussed below.
+Myers Difference Algorithm is an algorithm that finds a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. The edit scripts will be discussed below.
 
 For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", "2"]` has elements are included in both, but the appearing order is not correct.
 

From 90afdf77d5fe66f20f1d68f38c9cf24d8070f363 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Mar 2018 13:07:53 -0700
Subject: [PATCH 1395/1679] Couple more edits.

---
 Myers Difference Algorithm/README.md | 22 +++++++++++++++++-----
 1 file changed, 17 insertions(+), 5 deletions(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index a9d92a227..c1aa2da3a 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,20 +1,32 @@
 #  Myers Difference Algorithm
 
-Myers Difference Algorithm is an algorithm that finds a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. The edit scripts will be discussed below.
+Myers Difference Algorithm is an algorithm that finds a longest common subsequence(LCS) or shortest edit scripts(SES) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. 
 
-For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", "2"]` has elements are included in both, but the appearing order is not correct.
+For example, let's assume you have two arrays:
+
+```
+A = [1, 2, 3]
+B = [2, 3, 4]
+```
+
+The common subsequences of these two arrays are `[2]`, and `[2,3]`. The longest common sequence in this case is `[2,3]`.
 
 ## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
 
 ### Edit Graph
 
-Myers Algorithm uses Edit Graph for solving LCS/SES problem. Edit Graph is the graph like below.
+MDA uses an **Edit Graph** to solve the LCS/SES problem. Below is a illustration depicting an edit graph:
 
 <img src='Images/EditGraph.png' height="400">
 
-Here, we think about the length of the LCS of sequences `X = [A, B, C, A, B, B, A]`, `Y = [C, B, A, B, A, C]`.
+In this case, the arrays are:
+
+```
+X = [A, B, C, A, B, B, A]
+Y = [C, B, A, B, A, C]
+```
 
-In Myers Algorithm, edit graph are prepared by
+MDA generates the edit graph through the following steps:
 
 1. Line the element of sequence `X` on the x axis. And do for `Y` on the y axis.
 2. Make grid and vertex at each point in the grid (x, y), `x in [0, N] and y in [0, M]`. `N` is the length of sequence `X`, `M` is of `Y`

From 38966972f6a602cb1a855d674bae58197af14c77 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Mar 2018 13:11:57 -0700
Subject: [PATCH 1396/1679] Few more updates to the edit graph.

---
 Myers Difference Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index c1aa2da3a..6c242de88 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -19,7 +19,7 @@ MDA uses an **Edit Graph** to solve the LCS/SES problem. Below is a illustration
 
 <img src='Images/EditGraph.png' height="400">
 
-In this case, the arrays are:
+The x-axis at the top of the graph represents one of the sequences, `X`. The y-axis at the left side of the graph represents the other sequence, `Y`. Hence, the two sequences in question is the following:
 
 ```
 X = [A, B, C, A, B, B, A]

From 81534d54a2f890ab1a5032941e77838b5e585d4b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 14 Mar 2018 09:46:07 -0700
Subject: [PATCH 1397/1679] Update README.markdown

---
 Brute-Force String Search/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Brute-Force String Search/README.markdown b/Brute-Force String Search/README.markdown
index 4e967bcfb..599fe75ea 100644
--- a/Brute-Force String Search/README.markdown	
+++ b/Brute-Force String Search/README.markdown	
@@ -51,6 +51,6 @@ extension String {
 
 This looks at each character in the source string in turn. If the character equals the first character of the search pattern, then the inner loop checks whether the rest of the pattern matches. If no match is found, the outer loop continues where it left off. This repeats until a complete match is found or the end of the source string is reached.
 
-The brute-force approach works OK, but it's not very efficient (or pretty). It should work fine on small strings, though. For a smarter algorithm that works better with large chunks of text, check out [Boyer-Moore](../Boyer-Moore/) string search.
+The brute-force approach works OK, but it's not very efficient (or pretty). It should work fine on small strings, though. For a smarter algorithm that works better with large chunks of text, check out [Boyer-Moore](../Boyer-Moore-Horspool) string search.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 2d5d8d0f552044b54b61409a46bd5b007f2fd2a2 Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Sun, 18 Mar 2018 10:00:41 +0000
Subject: [PATCH 1398/1679] Add Sparse Table link to README

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 5706fc8e5..dc0fc1f57 100644
--- a/README.markdown
+++ b/README.markdown
@@ -162,6 +162,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
   - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 - kd-Tree
+- [Sparse Table](Sparse%20Table/). Another take on quickly computing a function over a portion of an array, but this time we'll make it even quicker!.
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - [Trie](Trie/). A special type of tree used to store associative data structures.

From 39da67cf7f5124fd3e5d270ea59361d86c512d78 Mon Sep 17 00:00:00 2001
From: Mike R <mike.rudoi@gmail.com>
Date: Sun, 25 Mar 2018 12:41:35 +0300
Subject: [PATCH 1399/1679] change function name for future code explanations

---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 84e278f5c..30dc8d922 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -375,7 +375,7 @@ As an exercise, see if you can implement filter and reduce.
 We can make the code more readable by defining some helper functions.
 
 ```swift
-  private func reconnectParentToNode(node: BinarySearchTree?) {
+  private func reconnectParentTo(node: BinarySearchTree?) {
     if let parent = parent {
       if isLeftChild {
         parent.left = node

From 8baf3549e597edbef432218eb3b52469a75c9df9 Mon Sep 17 00:00:00 2001
From: Daniel Strobusch <1847260+dastrobu@users.noreply.github.com>
Date: Sun, 25 Mar 2018 18:23:11 +0200
Subject: [PATCH 1400/1679] fixed typo

---
 DiningPhilosophers/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index ae84cb63b..cd9d86154 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -44,7 +44,7 @@ Based on the Chandy and Misra's analysis, a system of preference levels is deriv
 
 # Swift implementation
 
-This Swift 3.0 implementation of the Chandy/Misra solution is based on the GCD and Semaphore tecnique that can be built on both macOS and Linux.
+This Swift 3.0 implementation of the Chandy/Misra solution is based on the GCD and Semaphore technique that can be built on both macOS and Linux.
 
 The code is based on a ForkPair struct used for holding an array of DispatchSemaphore and a Philosopher struct for associate a couple of forks to each Philosopher.
 

From e4ce8d3f2894745ec4bd62d6fed82311bbe685ea Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Wed, 28 Mar 2018 19:21:44 +0100
Subject: [PATCH 1401/1679] Add Sparse Table

---
 Sparse Table/Images/idempotency.png           | Bin 0 -> 33715 bytes
 Sparse Table/Images/query.png                 | Bin 0 -> 25405 bytes
 Sparse Table/Images/query_example.png         | Bin 0 -> 29984 bytes
 Sparse Table/Images/recursion.png             | Bin 0 -> 78302 bytes
 Sparse Table/Images/recursion_examples.png    | Bin 0 -> 120693 bytes
 Sparse Table/Images/structure.png             | Bin 0 -> 100125 bytes
 Sparse Table/Images/structure_examples.png    | Bin 0 -> 157486 bytes
 Sparse Table/README.markdown                  | 310 ++++++++++++++++++
 .../Sparse Table.playground/Contents.swift    | 144 ++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 11 files changed, 465 insertions(+)
 create mode 100644 Sparse Table/Images/idempotency.png
 create mode 100644 Sparse Table/Images/query.png
 create mode 100644 Sparse Table/Images/query_example.png
 create mode 100644 Sparse Table/Images/recursion.png
 create mode 100644 Sparse Table/Images/recursion_examples.png
 create mode 100644 Sparse Table/Images/structure.png
 create mode 100644 Sparse Table/Images/structure_examples.png
 create mode 100644 Sparse Table/README.markdown
 create mode 100644 Sparse Table/Sparse Table.playground/Contents.swift
 create mode 100644 Sparse Table/Sparse Table.playground/contents.xcplayground
 create mode 100644 Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Sparse Table/Images/idempotency.png b/Sparse Table/Images/idempotency.png
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diff --git a/Sparse Table/Images/query_example.png b/Sparse Table/Images/query_example.png
new file mode 100644
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diff --git a/Sparse Table/Images/structure.png b/Sparse Table/Images/structure.png
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+# Sparse Table
+
+I'm excited to present **Sparse Tables**. Despite being somewhat niche, Sparse Tables are simple to implement and extremely powerful.
+
+### The Problem
+
+Let's suppose:
+- we have an array **a** of some type
+- we have some associative binary function **f** <sup>[\*]</sup>. The function can be: min, max, [gcd](../GCD/), boolean AND, boolean OR ...
+
+*<sup>[\*]</sup> where **f** is also "idempotent". Don't worry, I'll explain this in a moment.*
+
+Our task is as follows:
+
+- Given two indices **l** and **r**, answer a **query** for the interval `[l, r)` by performing `f(a[l], a[l + 1], a[l + 2], ..., a[r - 1])`; taking all the elements in the range and applying **f** to them
+- There will be a *huge* number **Q** of these queries to answer ... so we should be able to answer each query *quickly*!  
+
+For example, if we have an array of numbers:
+
+```swift
+var a = [ 20, 3, -1, 101, 14, 29, 5, 61, 99 ]
+```
+and our function **f** is the *min* function.
+
+Then we may be given a query for interval `[3, 8)`. That means we look at the elements:
+
+```
+101, 14, 29, 5, 61
+```
+
+because these are the elements of **a** with indices 
+that lie in our range `[3, 8)` – elements from index 3 up to, but not including, index 8.
+We then we pass all of these numbers into the min function, 
+which takes the minimum. The answer to the query is `5`, because that's the result of `min(101, 14, 29, 5, 61)`.
+
+Imagine we have millions of these queries to process.
+> - *Query 1*: Find minimum of all elements between 2 and 5
+> - *Query 2*: Find minimum of all elements between 3 and 9
+> - ...
+> - *Query 1000000*: Find minimum of all elements between 1 and 4
+
+And our array is very large. Here, let's say **Q** = 1000000 and **N** = 500000. Both numbers are *huge*. We want to make sure that we can answer each query really quickly, or else the number of queries will overwhelm us! 
+
+*So that's the problem.* 
+
+The naive solution to this problem is to perform a `for` loop
+to compute the answer for each query. However, for very large **Q** and very large **N** this 
+will be too slow. We can speed up the time to compute the answer by using a data structure called
+a **Sparse Table**. You'll notice that so far, our problem is exactly the same as that of the [Segment Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree) 
+(assuming you're familiar). However! ... there's one crucial difference between Segment Trees
+and Sparse Tables ... and it concerns our choice of **f**.
+
+
+### A small gotcha ... Idempotency
+
+Suppose we wanted to find the answer to **`[A, D)`**.
+And we already know the answer to two ranges  **`[A, B)`** and **`[C, D)`**.
+And importantly here, ... *these ranges overlap*!! We have **C** < **B**. 
+
+![Overlapping ranges](Images/idempotency.png)
+
+
+So what? Well, for **f** = minimum function, we can take our answers for **`[A, B)`** and **`[C, D)`** 
+and combine them!
+We can just take the minimum of the two answers: `result = min(x1, x2)` ... *voilà!*, we have the minimum for **`[A, D)`**.
+It didn't matter that the intervals overlap - we still found the correct minimum.
+But now suppose **f** is the addition operation `+`. Ok, so now we're taking sums over ranges.
+If we tried the same approach again, it wouldn't work. That is, 
+if we took our answers for **`[A, B)`** and **`[C, D)`** 
+and added them together we'd get a wrong answer for **`[A, D)`**.
+*Why?* Well, we'd have counted some elements twice because of the overlap.
+
+Later, we'll see that in order to answer queries, Sparse Tables use this very technique. 
+They combine answers in the same way as shown above. Unfortunately this means
+we have to exclude certain binary operators from being **f**, including `+`, `*`, XOR, ...
+because they don't work with this technique.
+In order to get the best speed of a Sparse Table, 
+we need to make sure that the **f** we're using is an **[idempotent](https://en.wikipedia.org/wiki/Idempotence)** binary operator.
+Mathematically, these are operators that satisfy `f(x, x) = x` for all possible **x** that could be in **a**. 
+Practically speaking, these are the only operators that work; allowing us to combine answers from overlapping ranges.
+Examples of idempotent **f**'s are min, max, gcd, boolean AND, boolean OR, bitwise AND and bitwise OR.
+Note that for Segment Trees, **f** does not have to be idempotent. That's the crucial difference between
+Segment Trees and Sparse Tables.
+
+*Phew!* Now that we've got that out of the way, let's dive in!
+
+## Structure of a Sparse Table
+
+Let's use **f** = min and use the array:
+
+```swift
+var a = [ 10, 6, 5, -7, 9, -8, 2, 4, 20 ]
+```
+
+In this case, the Sparse Table looks like this:
+
+![Sparse Table](Images/structure.png)
+
+What's going on here? There seems to be loads of intervals.
+*Correct!* Sparse tables are preloaded with the answers for lots of queries `[l, r)`.
+Here's the idea. Before we process our **Q** queries, we'll pre-populate our Sparse Table `table`
+with answers to loads of queries;
+making it act a bit like a *cache*. When we come to answer one of our queries, we can break the query
+down into smaller "sub-queries", each having an answer that's already in the cache. 
+We lookup the cached answers for the sub-queries in 
+`table` in constant time
+and combine the answers together 
+to give the overall answer to the original query in speedy time.
+
+The problem is, we can't store the answers for every single possible query that we could ever have ... 
+or else our table would be too big! After all, our Sparse Table needs to be *sparse*. So what do we do?
+We only pick the "best" intervals to store answers for. And as it turns out, the "best" intervals are those 
+that have a **width that is a power of two**!
+
+For example, the answer for the query `[10, 18)` is in our table 
+because the interval width: `18 - 10 = 8 = 2**3` is a power of two (`**` is the [exponentiation operator](https://en.wikipedia.org/wiki/Exponentiation)).
+Also, the answer for `[15, 31)` is in our table because its width: `31 - 15 = 16 = 2**4` is again a power of two.
+However, the answer for `[1, 6)` is *not* in there because the interval's width: `6 - 1 = 5` is *not* a power of two.
+Consequently, we don't store answers for *all* possible intervals that fit inside **a** –
+only the ones with a width that is a power of two. 
+This is true irrespective of where the interval starts within **a**.
+We'll gradually see that this approach works and that relatively speaking, it uses very little space.
+
+A **Sparse Table** is a table where `table[w][l]` contains the answer for `[l, l + 2**w)`.     
+It has entries `table[w][l]` where:
+- **w** tells us our **width** ... the number of elements or the *width* is `2**w`
+- **l** tells us the **lower bound** ... it's the starting point of our interval
+
+Some examples:
+- `table[3][0] = -8`: our width is `2**3`, we start at `l = 0` so our query is `[0, 0 + 2**3) = [0, 8)`.    
+   The answer for this query is `min(10, 6, 5, -7, 9, -8, 2, 4, 20) = -8`.
+- `table[2][1] = -7`: our width is `2**2`, we start at `l = 1` so our query is  `[1, 1 + 2**2) = [1, 5)`.    
+   The answer for this query is `min(6, 5, -7, 9) = -7`.
+- `table[1][7] = 4`: our width is `2**1`, we start at `l = 7` so our query is `[7, 7 + 2**1) = [7, 9)`.     
+   The answer for this query is `min(4, 20) = 4`.
+- `table[0][8] = 20`: our width is `2**0`, we start at `l = 8` so our query is`[8, 8 + 2**0) = [8, 9)`.    
+   The answer for this query is `min(20) = 20`.
+
+
+![Sparse Table](Images/structure_examples.png)
+
+
+A Sparse Table can be implemented using a [two-dimentional array](../2D%20Array).    
+
+```swift
+public class SparseTable<T> {
+  private var table: [[T]]
+
+  public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
+      table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
+  }
+  // ...    
+}
+```
+
+
+## Building a Sparse Table
+
+To build a Sparse Table, we compute each table entry starting from the bottom-left and moving up towards
+the top-right (in accordance with the diagram).
+First we'll compute all the intervals for  **w** = 0, then compute all the intervals
+and for **w**  = 1 and so on. We'll continue up until **w** is big enough such that our intervals are can cover at least half the array.
+For each **w**, we compute the interval for **l** = 0, 1, 2, 3, ... until we reach **N**.
+This is all achieved using a double `for`-`in` loop:
+
+```swift
+for w in 0..<W {
+  for l in 0..<N {
+    // compute table[w][l]
+  }
+}
+```
+
+To compute `table[w][l]`:
+
+- **Base Case (w = 0)**: Each interval has width `2**w = 1`. 
+    - We have *one* element intervals of the form: `[l, l + 1)`. 
+    - The answer is just `a[l]` (e.g. the minimum of over a list with one element 
+is just the element itself).
+      ```
+      table[w][l] = a[l]
+      ``` 
+- **Inductive Case (w > 0)**: We need to find out the answer to `[l, l + 2**w)` for some **l**. 
+This interval, like all of our intervals in our table has a width that
+is a power of two (e.g.  2, 4, 8, 16) ... so we can cut it into two equal halves.
+    - Our interval with width ``2**w`` is cut into two intervals, each of width ``2**(w - 1)``.
+    - Because each half has a width that is a power of two, we can look them up in our Sparse Table.
+    - We combine them together using **f**. 
+        ```
+        table[w][l] = f(table[w - 1][l], table[w - 1][l + 2 ** (w - 1)])
+        ```     
+
+
+![Sparse Table](Images/recursion.png)
+
+For example for `a = [ 10, 6, 5, -7, 9, -8, 2, 4, 20 ]` and **f** = *min*:
+
+- we compute `table[0][2] = 5`. We just had to look at `a[2]` because the range has a width of one.
+- we compute `table[1][7] = 4`. We looked at `table[0][7]` and `table[0][8]` and apply **f** to them.
+- we compute `table[3][1] = -8`. We looked at `table[2][1]` and `table[2][5]` and apply **f** to them.
+
+
+![Sparse Table](Images/recursion_examples.png)
+
+
+
+```swift
+public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
+ let N = array.count
+ let W = Int(ceil(log2(Double(N))))
+ table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
+ self.function = function
+ self.defaultT = defaultT
+
+ for w in 0..<W {
+   for l in 0..<N {
+     if w == 0 {
+       table[w][l] = array[l]
+     } else {
+       let first = self.table[w - 1][l]
+       let secondIndex = l + (1 << (w - 1))
+       let second = ((0..<N).contains(secondIndex)) ? table[w - 1][secondIndex] : defaultT
+       table[w][l] = function(first, second)
+     }
+   }
+ }
+}
+```
+
+Building a Sparse Table takes **O(NlogN)** time.    
+The table itself uses **O(NlgN)** additional space.
+
+## Getting Answers to Queries
+
+Suppose we've built our Sparse Table. And now we're going to process our **Q** queries.
+Here's where our work pays off.
+
+Let's suppose **f** = min and we have: 
+```swift
+var a = [ 10, 6, 5, -7, 9, -8, 2, 4, 20 ]
+```
+And we have a query `[3, 9)`.
+
+1. First let's find the largest power of two that fits inside `[3, 9)`. Our interval has width `9 - 3 = 6`. So the largest power of two    that fits inside is four. 
+2. We create two new queries of `[3, 7)` and `[5, 9)` that have a width of four.
+   And, we arrange them so that to that they span the whole interval without leaving any gaps.
+   ![Sparse Table](Images/query_example.png)
+
+3. Because these two intervals have a width that is exactly a power of two we can lookup their answers in the Sparse Table using the 
+   entries for **w** = 2. The answer to `[3, 7)` is given by `table[2][3]`, and the answer to `[5, 9)` is given by `table[2][5]`.
+   We compute and return `min(table[2][3], table[2][5])`. This is our final answer! :tada:. Although the two intervals overlap, it doesn't matter because the **f** = min we originally chose is idempotent.
+
+In general, for each query: `[l, r)` ...
+
+1. Find **W**, by looking for the largest width that fits inside the interval that's also a power of two. Let largest such width = `2**W`.
+2. Form two sub-queries of width `2**W` and arrange them to that they span the whole interval without leaving gaps.
+   To guarantee there are no gaps, we need to align one half to the left and the align other half to the right.
+   ![Sparse Table](Images/query.png)
+3. Compute and return `f(table[W][l], table[W][r - 2**W])`.
+
+      ```swift
+      public func query(from l: Int, until r: Int) -> T {
+        let width = r - l
+        let W = Int(floor(log2(Double(width))))
+        let lo = table[W][l]
+        let hi = table[W][r - (1 << W)]
+        return function(lo, hi)
+     }
+      ```
+
+Finding answers to queries takes **O(1)** time.
+
+## Analysing Sparse Tables
+
+- **Query Time** - Both table lookups take constant time. All other operations inside `query` take constant time. 
+So answering a single query also takes constant time: **O(1)**. But instead of one query we're actually answering **Q** queries, 
+and we'll need time to built the table before-hand.
+Overall time is: **O(NlgN + Q)** to build the table and answer all queries. 
+The naive approach is to do a for loop for each query. The overall time for the naive approach is: **O(NQ)**. 
+For very large **Q**, the naive approach will scale poorly. For example if `Q = O(N*N)`
+then the naive approach is `O(N*N*N)` where a Sparse Table takes time `O(N*N)`.
+- **Space**-  The number of possible **w** is **lgN** and the number of possible **i** our table is **N**. So the table
+has uses **O(NlgN)** additional space.
+
+### Comparison with Segment Trees
+
+- **Pre-processing** - Segment Trees take **O(N)** time to build and use **O(N)** space. Sparse Tables take **O(NlgN)** time to build and use **O(NlgN)** space.
+- **Queries** - Segment Tree queries are **O(lgN)** time for any **f** (idempotent or not idempotent). Sparse Table queries are **O(1)** time if **f** is idempotent and are not supported if **f** is not idempotent. <sup>[†]</sup>
+- **Replacing Items** - Segment Trees allow us to efficiently update an element in **a** and update the segment tree in **O(lgN)** time. Sparse Tables do not allow this to be done efficiently. If we were to update an element in **a**, we'd have to rebuild the Sparse Table all over again in **O(NlgN)** time.
+
+
+<sup>[†]</sup> *Although technically, it's possible to rewrite the `query` method 
+to add support for non-idempotent functions. But in doing so, we'd bump up the time up from O(1) to O(lgn), 
+completely defeating the original purpose of Sparse Tables - supporting lightening quick queries. 
+In such a case, we'd be better off using a Segment Tree (or a Fenwick Tree)*
+
+## Summary
+
+That's it! See the playground for more examples involving Sparse Tables.
+You'll see examples for: min, max, gcd, boolean operators and logical operators. 
+
+### See also
+
+- [Segment Trees (Swift Algorithm Club)](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree)
+- [How to write O(lgn) time query function to support non-idempontent functions (GeeksForGeeks)](https://www.geeksforgeeks.org/range-sum-query-using-sparse-table/) 
+- [Fenwick Trees / Binary Indexed Trees (TopCoder)](https://www.topcoder.com/community/data-science/data-science-tutorials/binary-indexed-trees/) 
+- [Semilattice (Wikipedia)](https://en.wikipedia.org/wiki/Semilattice)
+
+*Written for Swift Algorithm Club by [James Lawson](https://github.com/jameslawson)*
+
diff --git a/Sparse Table/Sparse Table.playground/Contents.swift b/Sparse Table/Sparse Table.playground/Contents.swift
new file mode 100644
index 000000000..4eae8a6c2
--- /dev/null
+++ b/Sparse Table/Sparse Table.playground/Contents.swift	
@@ -0,0 +1,144 @@
+//
+//  Swift Algorithm Club - Sparse Table
+//  Author: James Lawson (github.com/jameslawson)
+//
+
+import Foundation
+
+// Last checked with Xcode Version 9.2 (9C40b)
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+public class SparseTable<T> {
+  private var defaultT: T
+  private var table: [[T]]
+  private var function: (T, T) -> T
+  
+  public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
+    let N = array.count
+    let W = Int(ceil(log2(Double(N))))
+    table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
+    self.function = function
+    self.defaultT = defaultT
+    
+    for w in 0..<W {
+      for l in 0..<N {
+        if w == 0 {
+          table[w][l] = array[l]
+        } else {
+          let first = self.table[w - 1][l]
+          let secondIndex = l + (1 << (w - 1))
+          let second = ((0..<N).contains(secondIndex)) ? table[w - 1][secondIndex] : defaultT
+          table[w][l] = function(first, second)
+        }
+      }
+    }
+  }
+  
+  public func query(from l: Int, until r: Int) -> T {
+    let width = r - l
+    let N = table[0].count
+    if width <= 0 || l >= N {
+      return defaultT
+    }
+    let r = min(N, r)
+    let W = Int(floor(log2(Double(width))))
+    let lo = table[W][l]
+    let hi = table[W][r - (1 << W)]
+    return function(lo, hi)
+  }
+}
+
+print("---------------------------- EXAMPLE 1 -------------------------------------")
+// Here we have an array of integers and we're repeatedly
+// finding the minimum over various ranges
+
+let intArray = [1, -11, -7, 3, 2, 4]
+let minIntTable = SparseTable<Int>(array: intArray, function: min, defaultT: Int.max)
+print(minIntTable.query(from: 0, until: 6)) // min(1, 3, -11, 3, 2, 4) = -11
+print(minIntTable.query(from: 3, until: 5)) // min(3, 2) = 2
+print(minIntTable.query(from: 2, until: 6)) // min(-7, 3, 2, 4) = -7
+print(minIntTable.query(from: 0, until: 1)) // min(1) = 1
+print(minIntTable.query(from: 0, until: 0)) // min(<empty range>) = Int.max
+print("----------------------------------------------------------------------------\n\n")
+
+
+print("---------------------------- EXAMPLE 2 -------------------------------------")
+// Now we have an array of doubles and we're repeatedly
+// finding the maximum over various ranges
+
+let doubleArray = [1.5, 20.0, 3.5, 15.0, 18.0, -10.0, 5.5]
+let maxDoubleTable = SparseTable<Double>(array: doubleArray, function: max, defaultT: -.infinity)
+print(maxDoubleTable.query(from: 0, until: 4)) // max(1.5, 20.0, 3.5, 15.0) = 20.0
+print(maxDoubleTable.query(from: 3, until: 4)) // max(3.5, 15.0) = 15.0
+print(maxDoubleTable.query(from: 4, until: 6)) // max(18.0, -10.0, 5.5) = 18.0
+print(maxDoubleTable.query(from: 1, until: 2)) // max(20.0) = 20.0
+print(maxDoubleTable.query(from: 0, until: 0)) // max(<empty range>) = -inf
+print("----------------------------------------------------------------------------\n\n")
+
+
+print("---------------------------- EXAMPLE 3 -------------------------------------")
+// An array of booleans and we're repeatedly
+// finding the boolean AND over various ranges
+
+let boolArray = [true, false, true, true, true, false, false]
+func and(_ x: Bool, _ y: Bool) -> Bool { return x && y }
+
+let maxBoolTable = SparseTable<Bool>(array: boolArray, function: and, defaultT: false)
+print(maxBoolTable.query(from: 0, until: 4)) // and(T, F, T, T) = F
+print(maxBoolTable.query(from: 2, until: 5)) // and(T, T, T) = T
+print(maxBoolTable.query(from: 2, until: 6)) // and(T, T, T, F) = F
+print(maxBoolTable.query(from: 0, until: 1)) // and(T) = T
+print(maxBoolTable.query(from: 1, until: 2)) // and(F) = F
+print(maxBoolTable.query(from: 0, until: 0)) // and(<empty range>) = F
+print("----------------------------------------------------------------------------\n\n")
+
+print("---------------------------- EXAMPLE 4 -------------------------------------")
+// An array of positive integers and we're repeatedly finding
+// the gcd (greatest common divisor) over various ranges. The gcd operator is
+// associative and idempontent so we can use it with sparse tables
+
+let posIntArray = [7, 2, 3, 4, 6, 5, 25, 75, 100]
+func gcd(_ m: Int, _ n: Int) -> Int {
+  var a = 0
+  var b = max(m, n)
+  var r = min(m, n)
+  
+  while r != 0 {
+    a = b
+    b = r
+    r = a % b
+  }
+  return b
+}
+
+let gcdTable = SparseTable<Int>(array: posIntArray, function: gcd, defaultT: 1)
+print(gcdTable.query(from: 0, until: 4)) // gcd(7, 2, 3) = 1
+print(gcdTable.query(from: 3, until: 5)) // gcd(4, 6) = 2
+print(gcdTable.query(from: 5, until: 7)) // gcd(5, 25, 75) = 5
+print(gcdTable.query(from: 6, until: 9)) // gcd(25, 75, 100) = 25
+print(gcdTable.query(from: 3, until: 4)) // gcd(4) = 4
+print(gcdTable.query(from: 0, until: 0)) // gcd(<empty range>) = 1
+print("------------------------------------------------------------------------\n\n")
+
+
+
+print("---------------------------- EXAMPLE 5 -------------------------------------")
+// An array of nonnegative integers where for each integer we consider its binary representation.
+// We're repeatedly finding the binary OR (|) over various ranges. The binary operator is
+// associative and idempontent so we can use it with sparse tables
+
+let binArray = [0b1001, 0b1100, 0b0000, 0b0001, 0b0010, 0b0100, 0b0000, 0b1111]
+
+
+let orTable = SparseTable<Int>(array: binArray, function: |, defaultT: 0b0000)
+print(String(orTable.query(from: 0, until: 2), radix: 2)) // binary_or(1001, 1100) = 1101
+print(String(orTable.query(from: 3, until: 5), radix: 2)) // binary_or(0001, 0010) = 0011
+
+print(String(orTable.query(from: 3, until: 6), radix: 2)) // binary_or(0001, 0010, 0100) = 0111
+print(String(orTable.query(from: 6, until: 8), radix: 2)) // binary_or(0000, 1111) = 1111
+print(String(orTable.query(from: 1, until: 5), radix: 2)) // binary_or(1100, 0000, 0001, 0010) = 1111
+print(String(orTable.query(from: 0, until: 1), radix: 2)) // binary_or(1001) = 1001
+print(String(orTable.query(from: 0, until: 0), radix: 2)) // binary_or(<empty range>) = 0000
+print("----------------------------------------------------------------------------\n\n")
diff --git a/Sparse Table/Sparse Table.playground/contents.xcplayground b/Sparse Table/Sparse Table.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Sparse Table/Sparse Table.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata b/Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 7d759ee1a1b2983fb887e514341509842a26a60d Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Wed, 28 Mar 2018 19:29:45 +0100
Subject: [PATCH 1402/1679] Fix typo. Rename varaible from i to l

---
 Sparse Table/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Sparse Table/README.markdown b/Sparse Table/README.markdown
index 701a33f21..31bd5a781 100644
--- a/Sparse Table/README.markdown	
+++ b/Sparse Table/README.markdown	
@@ -279,7 +279,7 @@ Overall time is: **O(NlgN + Q)** to build the table and answer all queries.
 The naive approach is to do a for loop for each query. The overall time for the naive approach is: **O(NQ)**. 
 For very large **Q**, the naive approach will scale poorly. For example if `Q = O(N*N)`
 then the naive approach is `O(N*N*N)` where a Sparse Table takes time `O(N*N)`.
-- **Space**-  The number of possible **w** is **lgN** and the number of possible **i** our table is **N**. So the table
+- **Space**-  The number of possible **w** is **lgN** and the number of possible **l** our table is **N**. So the table
 has uses **O(NlgN)** additional space.
 
 ### Comparison with Segment Trees

From 11a5e7cb24279b86da99c8ffcd791c2bbfbe6b58 Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Wed, 28 Mar 2018 19:33:16 +0100
Subject: [PATCH 1403/1679] Fix typo "Idempotent"

---
 Sparse Table/Sparse Table.playground/Contents.swift | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Sparse Table/Sparse Table.playground/Contents.swift b/Sparse Table/Sparse Table.playground/Contents.swift
index 4eae8a6c2..ef83263b0 100644
--- a/Sparse Table/Sparse Table.playground/Contents.swift	
+++ b/Sparse Table/Sparse Table.playground/Contents.swift	
@@ -14,14 +14,14 @@ public class SparseTable<T> {
   private var defaultT: T
   private var table: [[T]]
   private var function: (T, T) -> T
-  
+
   public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
     let N = array.count
     let W = Int(ceil(log2(Double(N))))
     table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
     self.function = function
     self.defaultT = defaultT
-    
+
     for w in 0..<W {
       for l in 0..<N {
         if w == 0 {
@@ -35,7 +35,7 @@ public class SparseTable<T> {
       }
     }
   }
-  
+
   public func query(from l: Int, until r: Int) -> T {
     let width = r - l
     let N = table[0].count
@@ -97,14 +97,14 @@ print("-------------------------------------------------------------------------
 print("---------------------------- EXAMPLE 4 -------------------------------------")
 // An array of positive integers and we're repeatedly finding
 // the gcd (greatest common divisor) over various ranges. The gcd operator is
-// associative and idempontent so we can use it with sparse tables
+// associative and idempotent so we can use it with sparse tables
 
 let posIntArray = [7, 2, 3, 4, 6, 5, 25, 75, 100]
 func gcd(_ m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
   var r = min(m, n)
-  
+
   while r != 0 {
     a = b
     b = r
@@ -127,7 +127,7 @@ print("------------------------------------------------------------------------\
 print("---------------------------- EXAMPLE 5 -------------------------------------")
 // An array of nonnegative integers where for each integer we consider its binary representation.
 // We're repeatedly finding the binary OR (|) over various ranges. The binary operator is
-// associative and idempontent so we can use it with sparse tables
+// associative and idempotent so we can use it with sparse tables
 
 let binArray = [0b1001, 0b1100, 0b0000, 0b0001, 0b0010, 0b0100, 0b0000, 0b1111]
 

From eda68c40eba5aef49b3f23b8fccf9bab62eb6e9d Mon Sep 17 00:00:00 2001
From: Stephen Clark <contact.stephenclark@gmail.com>
Date: Fri, 30 Mar 2018 16:15:25 +0100
Subject: [PATCH 1404/1679] Convex Hull: Clarified Readme, and small code
 clarity changes.

Began to clarify Convex Hull readme, and code. (Needs more work!!)
---
 .../Convex Hull.xcodeproj/project.pbxproj      |  6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist      |  8 ++++++++
 Convex Hull/Convex Hull/View.swift             | 12 ++----------
 Convex Hull/README.md                          | 18 ++++++++++++++----
 4 files changed, 27 insertions(+), 17 deletions(-)
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index 651a5bed3..c11cbf4d6 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -149,7 +149,7 @@
 					};
 					8E6D68B51E59989400161780 = {
 						CreatedOnToolsVersion = 8.2.1;
-						DevelopmentTeam = 7C4LVS3ZVC;
+						DevelopmentTeam = 4SQG5NJNPF;
 						ProvisioningStyle = Automatic;
 					};
 				};
@@ -384,7 +384,7 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				DEVELOPMENT_TEAM = 4SQG5NJNPF;
 				INFOPLIST_FILE = "Convex Hull/Info.plist";
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
@@ -397,7 +397,7 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				DEVELOPMENT_TEAM = 4SQG5NJNPF;
 				INFOPLIST_FILE = "Convex Hull/Info.plist";
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
diff --git a/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index a50cc247a..33d1426c3 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -11,20 +11,12 @@ import UIKit
 class View: UIView {
 
   let MAX_POINTS = 100
-
   var points = [CGPoint]()
-
   var convexHull = [CGPoint]()
 
   override init(frame: CGRect) {
     super.init(frame: frame)
-
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-    
-    generatePoints()
+    generateRandomPoints()
     quickHull(points: points)
   }
 
@@ -32,7 +24,7 @@ class View: UIView {
     fatalError("init(coder:) has not been implemented")
   }
 
-  func generatePoints() {
+  func generateRandomPoints() {
     for _ in 0..<MAX_POINTS {
       let offset: CGFloat = 50
       let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index 2e1fbe6a3..d27027a45 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -1,14 +1,23 @@
 # Convex Hull
 
-There are multiple Convex Hull algorithms. This particular implementation uses the Quickhull algorithm.
+Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points. In comparing different solutions to this problem we can describe each algorithm in terms of it's big-O time complexity.
 
-Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
+There are multiple Convex Hull algorithms but this solution is called Quickhull, is comes from the work of both W. Eddy in 1977 and also separately A. Bykat in 1978, this algorithm has an expected time complexity of O(n log n), but it's worst-case time-complexity can be O(n^2) . With average conditions the algorithm has ok efficiency, but it's time-complexity can start to head become more exponential in cases of high symmetry or where there are points lying on the circumference of a circle for example.
 
 ## Quickhull
 
 The quickhull algorithm works as follows:
-The algorithm takes an input of a collection of points. These points should be ordered on their x-coordinate value. We pick the two points A and B with the smallest(A) and the largest(B) x-coordinate. These of course have to be part of the hull. Imagine a line from point A to point B. All points to the right of this line are grouped in an array S1. Imagine now a line from point B to point A. (this is of course the same line as before just with opposite direction) Again all points to the right of this line are grouped in an array, S2 this time.
-We now define the following recursive function:
+
+- The algorithm takes an input of a collection of points. These points should be ordered on their x-coordinate value. 
+- We first find the two points A and B with the minimum(A) and the maximum(B) x-coordinates (as these will obviously be part of the hull). 
+- Use the line formed by the two points to divide the set in two subsets of points, which will be processed recursively.
+- Determine the point, on one side of the line, with the maximum distance from the line. The two points found before along with this one form a triangle.
+- The points lying inside of that triangle cannot be part of the convex hull and can therefore be ignored in the next steps.
+- Repeat the previous two steps on the two lines formed by the triangle (not the initial line).
+- Keep on doing so on until no more points are left, the recursion has come to an end and the points selected constitute the convex hull.
+
+
+Our functioni will have the following defininition:
 
 `findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`
 
@@ -18,6 +27,7 @@ findHull(S2, B, A)
 ```
 
 What this function does is the following:
+
 1. If `points` is empty we return as there are no points to the right of our line to add to our hull.
 2. Draw a line from `p1` to `p2`.
 3. Find the point in `points` that is furthest away from this line. (`maxPoint`)

From 2ce84e9dc6c7cba09192d621c0fb76e0d6cfb729 Mon Sep 17 00:00:00 2001
From: Aamir Anwar <aamir.anwar021193@gmail.com>
Date: Sat, 31 Mar 2018 14:12:06 +0530
Subject: [PATCH 1405/1679] Fixed broken youtube link in splay tree readme

---
 Splay Tree/readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index f3b852f22..75c3c0389 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -263,7 +263,7 @@ If the rotations would had been taking first the parent and not the grandparent
 
 [Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
 
-[Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
+[Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=8Zs1lj_bUV0)
 
 
 ----------------

From 3bf65574bf04db1e0540494ece247f2beba79a5c Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Sat, 7 Apr 2018 03:30:09 +0900
Subject: [PATCH 1406/1679] add explanation

---
 Myers Difference Algorithm/README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index 6c242de88..e6137e8ce 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -34,6 +34,11 @@ MDA generates the edit graph through the following steps:
 3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point, light green one.
 4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, where `(i, j)` is match point, then diagonal edge appears.
 
+Each elements on the figure shows that,
+- `Red number and dotted lines`: The red number is the value of k and dotted lines are k-line.
+- `Green dots: The match points`, which is the point `(i, j)` where `X[i] == Y[j]`
+- `Blue line`: The shortest path from source to sink, which is the path we are going to find finally.
+
 > **Note:** Here, the sequences' start index is 1 not 0, so `X[1] = A`, `Y[1] = C`
 
 We discuss about which path is the shortest from `source` to `sink`. Can move on the edges on the graph. I mean we can move on  the grid, horizontal and vertical edges, and the diagonal edges.

From 6bf3a160912dd4b7bf91379175549321fd45cecc Mon Sep 17 00:00:00 2001
From: Jorge <minuscorp@gmail.com>
Date: Wed, 11 Apr 2018 19:17:12 +0200
Subject: [PATCH 1407/1679] Update Combinatorics to match Swift 4 API

---
 Combinatorics/README.markdown | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index b365b389b..a2432a680 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -99,17 +99,17 @@ Here's a recursive algorithm by Niklaus Wirth:
 
 ```swift
 func permuteWirth<T>(_ a: [T], _ n: Int) {
-  if n == 0 {
-    print(a)   // display the current permutation
-  } else {
-    var a = a
-    permuteWirth(a, n - 1)
-    for i in 0..<n {
-      swap(&a[i], &a[n])
-      permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
+    if n == 0 {
+        print(a)   // display the current permutation
+    } else {
+        var a = a
+        permuteWirth(a, n - 1)
+        for i in 0..<n {
+            a.swapAt(i, n)
+            permuteWirth(a, n - 1)
+            a.swapAt(i, n)
+        }
     }
-  }
 }
 ```
 

From 7e1c2891d309fb0c2a875d6d3f3a872d8e3ee470 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 17 Apr 2018 08:46:31 -0400
Subject: [PATCH 1408/1679] Added link to Swift Alg Club book

---
 ...DataStructuresAndAlgorithmsInSwiftBook.png | Bin 0 -> 136406 bytes
 README.markdown                               |  26 ++++--------------
 2 files changed, 6 insertions(+), 20 deletions(-)
 create mode 100644 Images/DataStructuresAndAlgorithmsInSwiftBook.png

diff --git a/Images/DataStructuresAndAlgorithmsInSwiftBook.png b/Images/DataStructuresAndAlgorithmsInSwiftBook.png
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diff --git a/README.markdown b/README.markdown
index dc0fc1f57..481e25f62 100644
--- a/README.markdown
+++ b/README.markdown
@@ -206,32 +206,18 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Dining Philosophers](DiningPhilosophers/)
 - [Egg Drop Problem](Egg%20Drop%20Problem/)
 - [Encoding and Decoding Binary Tree](Encode%20and%20Decode%20Tree/)
-## Learn more!
 
-For more information, check out these great books:
+## Learn more!
 
-- [Introduction to Algorithms](https://mitpress.mit.edu/books/introduction-algorithms) by Cormen, Leiserson, Rivest, Stein
-- [The Algorithm Design Manual](http://www.algorist.com) by Skiena
-- [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
-- [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
-- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava
+Like what you see? Check out [Data Structures & Algorithms in Swift](https://store.raywenderlich.com/products/data-structures-and-algorithms-in-swift), the official book by the Swift Algorithm Club team!
 
-The following books are available for free online:
+![Data Structures & Algorithms in Swift Book](Images/DataStructuresAndAlgorithmsInSwift.png)
 
-- [Algorithms](http://www.beust.com/algorithms.pdf) by Dasgupta, Papadimitriou, Vazirani
-- [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
-- [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
-- Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
-- [Open Data Structures](http://opendatastructures.org) by Pat Morin
-- [Wikibooks: Algorithms and Implementations](https://en.wikibooks.org/wiki/Algorithm_Implementation)
+You’ll start with the fundamental structures of linked lists, queues and stacks, and see how to implement them in a highly Swift-like way. Move on to working with various types of trees, including general purpose trees, binary trees, AVL trees, binary search trees, and tries. 
 
-Other algorithm repositories:
+Go beyond bubble and insertion sort with better-performing algorithms, including mergesort, radix sort, heap sort, and quicksort. Learn how to construct directed, non-directed and weighted graphs to represent many real-world models, and traverse graphs and trees efficiently with breadth-first, depth-first, Dijkstra’s and Prim’s algorithms to solve problems such as finding the shortest path or lowest cost in a network.
 
-- [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
-- [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
-- [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
-- [AlgorithmVisualizer](http://jasonpark.me/AlgorithmVisualizer/). Visualize algorithms on your browser.
-- [Swift Structures](https://github.com/waynewbishop/SwiftStructures) Data Structures with directions on how to use them [here](http://waynewbishop.com/swift)
+By the end of this book, you’ll have hands-on experience solving common issues with data structures and algorithms — and you’ll be well on your way to developing your own efficient and useful implementations!
 
 ## Credits
 

From 8010ec629e93228bd960da271b406420d6cb9cb0 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 17 Apr 2018 08:47:31 -0400
Subject: [PATCH 1409/1679] Fixed typo in link

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 481e25f62..783750fbc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -211,7 +211,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 
 Like what you see? Check out [Data Structures & Algorithms in Swift](https://store.raywenderlich.com/products/data-structures-and-algorithms-in-swift), the official book by the Swift Algorithm Club team!
 
-![Data Structures & Algorithms in Swift Book](Images/DataStructuresAndAlgorithmsInSwift.png)
+![Data Structures & Algorithms in Swift Book](Images/DataStructuresAndAlgorithmsInSwiftBook.png)
 
 You’ll start with the fundamental structures of linked lists, queues and stacks, and see how to implement them in a highly Swift-like way. Move on to working with various types of trees, including general purpose trees, binary trees, AVL trees, binary search trees, and tries. 
 

From 12471a2f8ed0586269c8cb693efc5a33e31c45c0 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 17 Apr 2018 08:48:25 -0400
Subject: [PATCH 1410/1679] Added final link to book

---
 README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.markdown b/README.markdown
index 783750fbc..919f1b67f 100644
--- a/README.markdown
+++ b/README.markdown
@@ -219,6 +219,8 @@ Go beyond bubble and insertion sort with better-performing algorithms, including
 
 By the end of this book, you’ll have hands-on experience solving common issues with data structures and algorithms — and you’ll be well on your way to developing your own efficient and useful implementations!
 
+You can find the book on the [raywenderlich.com store](https://store.raywenderlich.com/products/data-structures-and-algorithms-in-swift).
+
 ## Credits
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).

From 730059ec7ba7dd16115f09d5d58a01b068df9beb Mon Sep 17 00:00:00 2001
From: APKaramyshev <38246803+APKaramyshev@users.noreply.github.com>
Date: Sat, 21 Apr 2018 21:54:58 +0300
Subject: [PATCH 1411/1679] Fixed two misspellings in O(n!) example

---
 Big-O Notation.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 19a1ddbde..257f80462 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -132,9 +132,9 @@ Below are some examples for each category of performance:
   The most trivial example of function that takes O(n!) time is given below.
 
   ```swift
-  func nFacFunc(n: Int) {
+  func nFactFunc(n: Int) {
     for i in stride(from: 0, to: n, by: 1) {
-      nFactFunc(n - 1)
+      nFactFunc(n: n - 1)
     }
   }
   ```

From a0cfcee54c015e1110ca7ab102d9ba84bda0ae85 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 22 Apr 2018 18:29:44 -0700
Subject: [PATCH 1412/1679] Update README.markdown

---
 Genetic/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 07547c4b4..18afb9639 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -1,4 +1,4 @@
-individual# Genetic Algorthim
+# Genetic Algorthim
 
 ## What is it?
 

From 83b08626a172030777db1924513599ad55c32f34 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Mon, 23 Apr 2018 15:31:04 +0800
Subject: [PATCH 1413/1679] Update README.markdown

Here should be right.  Bottom-left corner of the matrix is `matrix[0][m+1]`
---
 Longest Common Subsequence/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index 4cd2c2fcb..a62c562a6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -99,7 +99,7 @@ And so on... this is how `lcsLength(_:)` fills in the entire matrix.
 
 ## Backtracking to find the actual subsequence
 
-So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-left corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
+So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-right corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
 
 Having the length of every combination of substrings makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
 

From e0c0200ba34960f7b48dc742a33fd2a966843a83 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Mon, 23 Apr 2018 16:18:23 +0800
Subject: [PATCH 1414/1679] Update README.markdown

Fix typo: top-right -> top-left
---
 Longest Common Subsequence/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index a62c562a6..8a4a763c6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -156,7 +156,7 @@ func backtrack(_ matrix: [[Int]]) -> String {
 }
 ```  
 
-This backtracks from `matrix[n+1][m+1]` (bottom-right corner) to `matrix[1][1]` (top-right corner), looking for characters that are common to both strings. It adds those characters to a new string, `lcs`.
+This backtracks from `matrix[n+1][m+1]` (bottom-right corner) to `matrix[1][1]` (top-left corner), looking for characters that are common to both strings. It adds those characters to a new string, `lcs`.
 
 The `charInSequence` variable is an index into the string given by `self`. Initially this points to the last character of the string. Each time we decrement `i`, we also move back `charInSequence`. When the two characters are found to be equal, we add the character at `self[charInSequence]` to the new `lcs` string. (We can't just write `self[i]` because `i` may not map to the current position inside the Swift string.)
 

From 898db6fd3f266812be8387a2b2478d5f072cf872 Mon Sep 17 00:00:00 2001
From: Sergey Pugach <sergei.pygach@gmail.com>
Date: Mon, 30 Apr 2018 04:37:26 +0300
Subject: [PATCH 1415/1679] Refactors LinkedList implementation to be more
 Swifty. (#705)

* fix versions merge

* replace if to guard check
---
 .../LinkedList.playground/Contents.swift      | 585 ++++++++--------
 Linked List/LinkedList.swift                  | 263 ++++---
 Linked List/Tests/LinkedListTests.swift       | 662 +++++++++---------
 3 files changed, 779 insertions(+), 731 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 2ce3b4d66..4b58bb65e 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -9,371 +9,364 @@ print("Hello, Swift 4!")
 #endif
 
 public final class LinkedList<T> {
-
-  /// Linked List's Node Class Declaration
-  public class LinkedListNode<T> {
-    var value: T
-    var next: LinkedListNode?
-    weak var previous: LinkedListNode?
-
-    public init(value: T) {
-      self.value = value
+    
+    /// Linked List's Node Class Declaration
+    public class LinkedListNode<T> {
+        var value: T
+        var next: LinkedListNode?
+        weak var previous: LinkedListNode?
+        
+        public init(value: T) {
+            self.value = value
+        }
     }
-  }
-
-  /// Typealiasing the node class to increase readability of code
-  public typealias Node = LinkedListNode<T>
-
-  /// The head of the Linked List
-  fileprivate var head: Node?
-
-  /// Default initializer
-  public init() {}
-
-  /// Computed property to check if the linked list is empty
-  public var isEmpty: Bool {
-    return head == nil
-  }
-
-  /// Computed property to get the first node in the linked list (if any)
-  public var first: Node? {
-    return head
-  }
-
-  /// Computed property to iterate through the linked list and return the last node in the list (if any)
-  public var last: Node? {
-    guard var node = head else {
-      return nil
+    
+    /// Typealiasing the node class to increase readability of code
+    public typealias Node = LinkedListNode<T>
+    
+    
+    /// The head of the Linked List
+    private(set) var head: Node?
+    
+    /// Computed property to iterate through the linked list and return the last node in the list (if any)
+    public var last: Node? {
+        guard var node = head else {
+            return nil
+        }
+        
+        while let next = node.next {
+            node = next
+        }
+        return node
     }
     
-    while let next = node.next {
-      node = next
+    /// Computed property to check if the linked list is empty
+    public var isEmpty: Bool {
+        return head == nil
     }
-    return node
-  }
-
-  /// Computed property to iterate through the linked list and return the total number of nodes
-  public var count: Int {
-    guard var node = head else {
-      return 0
+    
+    /// Computed property to iterate through the linked list and return the total number of nodes
+    public var count: Int {
+        guard var node = head else {
+            return 0
+        }
+        
+        var count = 1
+        while let next = node.next {
+            node = next
+            count += 1
+        }
+        return count
     }
     
-    var count = 1
-    while let next = node.next {
-      node = next
-      count += 1
+    /// Default initializer
+    public init() {}
+    
+    
+    /// Subscript function to return the node at a specific index
+    ///
+    /// - Parameter index: Integer value of the requested value's index
+    public subscript(index: Int) -> T {
+        let node = self.node(at: index)
+        return node.value
     }
-    return count
-  }
-
-  /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameter index: Integer value of the node's index to be returned
-  /// - Returns: Optional LinkedListNode
-  public func node(at index: Int) -> Node {
-    assert(head != nil, "List is empty")
-    assert(index >= 0, "index must be greater than 0")
     
-    if index == 0 {
-        return head!
-    } else {
-        var node = head!.next
-        for _ in 1..<index {
-            node = node?.next
-            if node == nil {
-                break
+    /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the node's index to be returned
+    /// - Returns: LinkedListNode
+    public func node(at index: Int) -> Node {
+        assert(head != nil, "List is empty")
+        assert(index >= 0, "index must be greater than 0")
+        
+        if index == 0 {
+            return head!
+        } else {
+            var node = head!.next
+            for _ in 1..<index {
+                node = node?.next
+                if node == nil {
+                    break
+                }
             }
+            
+            assert(node != nil, "index is out of bounds.")
+            return node!
         }
-        
-        assert(node != nil, "index is out of bounds.")
-        return node!
     }
-  }
-
-  /// Subscript function to return the node at a specific index
-  ///
-  /// - Parameter index: Integer value of the requested value's index
-  public subscript(index: Int) -> T {
-    let node = self.node(at: index)
-    return node.value
-  }
-
-  /// Append a value to the end of the list
-  ///
-  /// - Parameter value: The data value to be appended
-  public func append(_ value: T) {
-    let newNode = Node(value: value)
-    self.append(newNode)
-  }
-
-  /// Append a copy of a LinkedListNode to the end of the list.
-  ///
-  /// - Parameter node: The node containing the value to be appended
-  public func append(_ node: Node) {
-    let newNode = node
-    if let lastNode = last {
-      newNode.previous = lastNode
-      lastNode.next = newNode
-    } else {
-      head = newNode
+    
+    /// Append a value to the end of the list
+    ///
+    /// - Parameter value: The data value to be appended
+    public func append(_ value: T) {
+        let newNode = Node(value: value)
+        append(newNode)
+    }
+    
+    /// Append a copy of a LinkedListNode to the end of the list.
+    ///
+    /// - Parameter node: The node containing the value to be appended
+    public func append(_ node: Node) {
+        let newNode = node
+        if let lastNode = last {
+            newNode.previous = lastNode
+            lastNode.next = newNode
+        } else {
+            head = newNode
+        }
+    }
+    
+    /// Append a copy of a LinkedList to the end of the list.
+    ///
+    /// - Parameter list: The list to be copied and appended.
+    public func append(_ list: LinkedList) {
+        var nodeToCopy = list.head
+        while let node = nodeToCopy {
+            append(node.value)
+            nodeToCopy = node.next
+        }
+    }
+    
+    /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - value: The data value to be inserted
+    ///   - index: Integer value of the index to be insterted at
+    public func insert(_ value: T, at index: Int) {
+        let newNode = Node(value: value)
+        insert(newNode, at: index)
+    }
+    
+    /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - node: The node containing the value to be inserted
+    ///   - index: Integer value of the index to be inserted at
+    public func insert(_ newNode: Node, at index: Int) {
+        if index == 0 {
+            newNode.next = head
+            head?.previous = newNode
+            head = newNode
+        } else {
+            let prev = node(at: index - 1)
+            let next = prev.next
+            newNode.previous = prev
+            newNode.next = next
+            next?.previous = newNode
+            prev.next = newNode
+        }
     }
-  }
-
-  /// Append a copy of a LinkedList to the end of the list.
-  ///
-  /// - Parameter list: The list to be copied and appended.
-  public func append(_ list: LinkedList) {
-    var nodeToCopy = list.head
-    while let node = nodeToCopy {
-      self.append(node.value)
-      nodeToCopy = node.next
+    
+    /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - list: The LinkedList to be copied and inserted
+    ///   - index: Integer value of the index to be inserted at
+    public func insert(_ list: LinkedList, at index: Int) {
+        if list.isEmpty { return }
+        
+        if index == 0 {
+            list.last?.next = head
+            head = list.head
+        } else {
+            let prev = node(at: index - 1)
+            let next = prev.next
+            
+            prev.next = list.head
+            list.head?.previous = prev
+            
+            list.last?.next = next
+            next?.previous = list.last?.next
+        }
     }
-  }
-
-  /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameters:
-  ///   - value: The data value to be inserted
-  ///   - index: Integer value of the index to be insterted at
-  public func insert(_ value: T, at index: Int) {
-    let newNode = Node(value: value)
-    self.insert(newNode, at: index)
-  }
-
-  /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameters:
-  ///   - node: The node containing the value to be inserted
-  ///   - index: Integer value of the index to be inserted at
-  public func insert(_ newNode: Node, at index: Int) {
-    if index == 0 {
-      newNode.next = head
-      head?.previous = newNode
-      head = newNode
-    } else {
-      let prev = node(at: index-1)
-      let next = prev.next
-      newNode.previous = prev
-      newNode.next = next
-      next?.previous = newNode
-      prev.next = newNode
+    
+    /// Function to remove all nodes/value from the list
+    public func removeAll() {
+        head = nil
     }
-  }
     
-  /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameters:
-  ///   - list: The LinkedList to be copied and inserted
-  ///   - index: Integer value of the index to be inserted at
-  public func insert(_ list: LinkedList, at index: Int) {
-    if list.isEmpty { return }
+    /// Function to remove a specific node.
+    ///
+    /// - Parameter node: The node to be deleted
+    /// - Returns: The data value contained in the deleted node.
+    @discardableResult public func remove(node: Node) -> T {
+        let prev = node.previous
+        let next = node.next
+        
+        if let prev = prev {
+            prev.next = next
+        } else {
+            head = next
+        }
+        next?.previous = prev
+        
+        node.previous = nil
+        node.next = nil
+        return node.value
+    }
     
-    if index == 0 {
-      list.last?.next = head
-      head = list.head
-    } else {
-      let prev = node(at: index-1)
-      let next = prev.next
-
-      prev.next = list.head
-      list.head?.previous = prev
-
-      list.last?.next = next
-      next?.previous = list.last?.next
+    /// Function to remove the last node/value in the list. Crashes if the list is empty
+    ///
+    /// - Returns: The data value contained in the deleted node.
+    @discardableResult public func removeLast() -> T {
+        assert(!isEmpty)
+        return remove(node: last!)
     }
-  }
-
-  /// Function to remove all nodes/value from the list
-  public func removeAll() {
-    head = nil
-  }
-
-  /// Function to remove a specific node.
-  ///
-  /// - Parameter node: The node to be deleted
-  /// - Returns: The data value contained in the deleted node.
-  @discardableResult public func remove(node: Node) -> T {
-    let prev = node.previous
-    let next = node.next
-
-    if let prev = prev {
-      prev.next = next
-    } else {
-      head = next
+    
+    /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the index of the node to be removed
+    /// - Returns: The data value contained in the deleted node
+    @discardableResult public func remove(at index: Int) -> T {
+        let node = self.node(at: index)
+        return remove(node: node)
     }
-    next?.previous = prev
-
-    node.previous = nil
-    node.next = nil
-    return node.value
-  }
-
-  /// Function to remove the last node/value in the list. Crashes if the list is empty
-  ///
-  /// - Returns: The data value contained in the deleted node.
-  @discardableResult public func removeLast() -> T {
-    assert(!isEmpty)
-    return remove(node: last!)
-  }
-
-  /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameter index: Integer value of the index of the node to be removed
-  /// - Returns: The data value contained in the deleted node
-  @discardableResult public func remove(at index: Int) -> T {
-    let node = self.node(at: index)
-    return remove(node: node)
-  }
 }
 
 //: End of the base class declarations & beginning of extensions' declarations:
 
 // MARK: - Extension to enable the standard conversion of a list to String 
 extension LinkedList: CustomStringConvertible {
-  public var description: String {
-    var s = "["
-    var node = head
-    while node != nil {
-      s += "\(node!.value)"
-      node = node!.next
-      if node != nil { s += ", " }
+    public var description: String {
+        var s = "["
+        var node = head
+        while let nd = node {
+            s += "\(nd.value)"
+            node = nd.next
+            if node != nil { s += ", " }
+        }
+        return s + "]"
     }
-    return s + "]"
-  }
 }
 
 // MARK: - Extension to add a 'reverse' function to the list
 extension LinkedList {
-  public func reverse() {
-    var node = head
-    while let currentNode = node {
-      node = currentNode.next
-      swap(&currentNode.next, &currentNode.previous)
-      head = currentNode
+    public func reverse() {
+        var node = head
+        while let currentNode = node {
+            node = currentNode.next
+            swap(&currentNode.next, &currentNode.previous)
+            head = currentNode
+        }
     }
-  }
 }
 
 // MARK: - An extension with an implementation of 'map' & 'filter' functions
 extension LinkedList {
-  public func map<U>(transform: (T) -> U) -> LinkedList<U> {
-    let result = LinkedList<U>()
-    var node = head
-    while node != nil {
-      result.append(transform(node!.value))
-      node = node!.next
+    public func map<U>(transform: (T) -> U) -> LinkedList<U> {
+        let result = LinkedList<U>()
+        var node = head
+        while let nd = node {
+            result.append(transform(nd.value))
+            node = nd.next
+        }
+        return result
     }
-    return result
-  }
-
-  public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
-    let result = LinkedList<T>()
-    var node = head
-    while node != nil {
-      if predicate(node!.value) {
-        result.append(node!.value)
-      }
-      node = node!.next
+    
+    public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
+        let result = LinkedList<T>()
+        var node = head
+        while let nd = node {
+            if predicate(nd.value) {
+                result.append(nd.value)
+            }
+            node = nd.next
+        }
+        return result
     }
-    return result
-  }
 }
 
 // MARK: - Extension to enable initialization from an Array
 extension LinkedList {
-  convenience init(array: Array<T>) {
-    self.init()
-
-    for element in array {
-      self.append(element)
+    convenience init(array: Array<T>) {
+        self.init()
+        
+        array.forEach { append($0) }
     }
-  }
 }
 
 // MARK: - Extension to enable initialization from an Array Literal
 extension LinkedList: ExpressibleByArrayLiteral {
-  public convenience init(arrayLiteral elements: T...) {
-    self.init()
-
-    for element in elements {
-      self.append(element)
+    public convenience init(arrayLiteral elements: T...) {
+        self.init()
+        
+        elements.forEach { append($0) }
     }
-  }
 }
 
 // MARK: - Collection
-extension LinkedList : Collection {
-  
-  public typealias Index = LinkedListIndex<T>
-  
-  /// The position of the first element in a nonempty collection.
-  ///
-  /// If the collection is empty, `startIndex` is equal to `endIndex`.
-  /// - Complexity: O(1)
-  public var startIndex: Index {
-    get {
-      return LinkedListIndex<T>(node: head, tag: 0)
+extension LinkedList: Collection {
+    
+    public typealias Index = LinkedListIndex<T>
+    
+    /// The position of the first element in a nonempty collection.
+    ///
+    /// If the collection is empty, `startIndex` is equal to `endIndex`.
+    /// - Complexity: O(1)
+    public var startIndex: Index {
+        get {
+            return LinkedListIndex<T>(node: head, tag: 0)
+        }
+    }
+    
+    /// The collection's "past the end" position---that is, the position one
+    /// greater than the last valid subscript argument.
+    /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+    ///   to the last node in the collection.
+    public var endIndex: Index {
+        get {
+            if let h = self.head {
+                return LinkedListIndex<T>(node: h, tag: count)
+            } else {
+                return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+            }
+        }
     }
-  }
-  
-  /// The collection's "past the end" position---that is, the position one
-  /// greater than the last valid subscript argument.
-  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
-  ///   to the last node in the collection.
-  public var endIndex: Index {
-    get {
-      if let h = self.head {
-        return LinkedListIndex<T>(node: h, tag: count)
-      } else {
-        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
-      }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
     }
-  }
-  
-  public subscript(position: Index) -> T {
-    get {
-      return position.node!.value
+    
+    public func index(after idx: Index) -> Index {
+        return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag + 1)
     }
-  }
-  
-  public func index(after idx: Index) -> Index {
-    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
-  }
 }
 
 // MARK: - Collection Index
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable {
-  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
-  fileprivate let tag: Int
-  
-  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag == rhs.tag)
-  }
-  
-  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag < rhs.tag)
-  }
+public struct LinkedListIndex<T>: Comparable {
+    fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
 }
 //: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
-list.first                    // nil
+list.head                    // nil
 list.last                     // nil
 
 list.append("Hello")
 list.isEmpty                  // false
-list.first!.value             // "Hello"
+list.head!.value             // "Hello"
 list.last!.value              // "Hello"
 list.count                    // 1
 
 list.append("World")
-list.first!.value             // "Hello"
+list.head!.value             // "Hello"
 list.last!.value              // "World"
 list.count                    // 2
 
-list.first!.previous          // nil
-list.first!.next!.value       // "World"
+list.head!.previous          // nil
+list.head!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
@@ -409,7 +402,7 @@ m    // [8, 6, 5]
 let f = list.filter { s in s.count > 5 }
 f    // [Universe, Swifty]
 
-list.remove(node: list.first!) // "Universe"
+list.remove(node: list.head!) // "Universe"
 list.count                     // 2
 list[0]                        // "Swifty"
 list[1]                        // "Hello"
@@ -464,7 +457,7 @@ let value = collection[index2] // 3
 // Iterating in a for loop, since the Sequence protocol allows this.
 var sum = 0
 for element in collection {
-  sum += element
+    sum += element
 }
 // sum is 15
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 569cea82b..285c85588 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,29 +1,24 @@
 public final class LinkedList<T> {
-
+    
+    /// Linked List's Node Class Declaration
     public class LinkedListNode<T> {
         var value: T
         var next: LinkedListNode?
         weak var previous: LinkedListNode?
-
+        
         public init(value: T) {
             self.value = value
         }
     }
-
+    
+    /// Typealiasing the node class to increase readability of code
     public typealias Node = LinkedListNode<T>
-
-    fileprivate var head: Node?
-
-    public init() {}
-
-    public var isEmpty: Bool {
-        return head == nil
-    }
-
-    public var first: Node? {
-        return head
-    }
-
+    
+    
+    /// The head of the Linked List
+    private(set) var head: Node?
+    
+    /// Computed property to iterate through the linked list and return the last node in the list (if any)
     public var last: Node? {
         guard var node = head else {
             return nil
@@ -34,7 +29,13 @@ public final class LinkedList<T> {
         }
         return node
     }
-
+    
+    /// Computed property to check if the linked list is empty
+    public var isEmpty: Bool {
+        return head == nil
+    }
+    
+    /// Computed property to iterate through the linked list and return the total number of nodes
     public var count: Int {
         guard var node = head else {
             return 0
@@ -48,9 +49,26 @@ public final class LinkedList<T> {
         return count
     }
     
+    /// Default initializer
+    public init() {}
+    
+    
+    /// Subscript function to return the node at a specific index
+    ///
+    /// - Parameter index: Integer value of the requested value's index
+    public subscript(index: Int) -> T {
+        let node = self.node(at: index)
+        return node.value
+    }
+    
+    /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the node's index to be returned
+    /// - Returns: LinkedListNode
     public func node(at index: Int) -> Node {
         assert(head != nil, "List is empty")
         assert(index >= 0, "index must be greater than 0")
+        
         if index == 0 {
             return head!
         } else {
@@ -66,17 +84,18 @@ public final class LinkedList<T> {
             return node!
         }
     }
-
-    public subscript(index: Int) -> T {
-        let node = self.node(at: index)
-        return node.value
-    }
-
+    
+    /// Append a value to the end of the list
+    ///
+    /// - Parameter value: The data value to be appended
     public func append(_ value: T) {
         let newNode = Node(value: value)
-        self.append(newNode)
+        append(newNode)
     }
-
+    
+    /// Append a copy of a LinkedListNode to the end of the list.
+    ///
+    /// - Parameter node: The node containing the value to be appended
     public func append(_ node: Node) {
         let newNode = node
         if let lastNode = last {
@@ -86,27 +105,40 @@ public final class LinkedList<T> {
             head = newNode
         }
     }
-
+    
+    /// Append a copy of a LinkedList to the end of the list.
+    ///
+    /// - Parameter list: The list to be copied and appended.
     public func append(_ list: LinkedList) {
         var nodeToCopy = list.head
         while let node = nodeToCopy {
-            self.append(node.value)
+            append(node.value)
             nodeToCopy = node.next
         }
     }
-
+    
+    /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - value: The data value to be inserted
+    ///   - index: Integer value of the index to be insterted at
     public func insert(_ value: T, at index: Int) {
         let newNode = Node(value: value)
-        self.insert(newNode, at: index)
+        insert(newNode, at: index)
     }
-
+    
+    /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - node: The node containing the value to be inserted
+    ///   - index: Integer value of the index to be inserted at
     public func insert(_ newNode: Node, at index: Int) {
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let prev = node(at: index-1)
+            let prev = node(at: index - 1)
             let next = prev.next
             newNode.previous = prev
             newNode.next = next
@@ -115,14 +147,19 @@ public final class LinkedList<T> {
         }
     }
     
+    /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - list: The LinkedList to be copied and inserted
+    ///   - index: Integer value of the index to be inserted at
     public func insert(_ list: LinkedList, at index: Int) {
-        if list.isEmpty { return }
+        guard !list.isEmpty else { return }
         
         if index == 0 {
             list.last?.next = head
             head = list.head
         } else {
-            let prev = self.node(at: index-1)
+            let prev = node(at: index - 1)
             let next = prev.next
             
             prev.next = list.head
@@ -133,50 +170,66 @@ public final class LinkedList<T> {
         }
     }
     
+    /// Function to remove all nodes/value from the list
     public func removeAll() {
         head = nil
     }
-
+    
+    /// Function to remove a specific node.
+    ///
+    /// - Parameter node: The node to be deleted
+    /// - Returns: The data value contained in the deleted node.
     @discardableResult public func remove(node: Node) -> T {
         let prev = node.previous
         let next = node.next
-
+        
         if let prev = prev {
             prev.next = next
         } else {
             head = next
         }
         next?.previous = prev
-
+        
         node.previous = nil
         node.next = nil
         return node.value
     }
-
+    
+    /// Function to remove the last node/value in the list. Crashes if the list is empty
+    ///
+    /// - Returns: The data value contained in the deleted node.
     @discardableResult public func removeLast() -> T {
         assert(!isEmpty)
         return remove(node: last!)
     }
-
+    
+    /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the index of the node to be removed
+    /// - Returns: The data value contained in the deleted node
     @discardableResult public func remove(at index: Int) -> T {
         let node = self.node(at: index)
         return remove(node: node)
     }
 }
 
+//: End of the base class declarations & beginning of extensions' declarations:
+
+// MARK: - Extension to enable the standard conversion of a list to String
 extension LinkedList: CustomStringConvertible {
     public var description: String {
         var s = "["
         var node = head
-        while node != nil {
-            s += "\(node!.value)"
-            node = node!.next
+        while let nd = node {
+            s += "\(nd.value)"
+            node = nd.next
             if node != nil { s += ", " }
         }
         return s + "]"
     }
 }
 
+// MARK: - Extension to add a 'reverse' function to the list
 extension LinkedList {
     public func reverse() {
         var node = head
@@ -188,99 +241,101 @@ extension LinkedList {
     }
 }
 
+// MARK: - An extension with an implementation of 'map' & 'filter' functions
 extension LinkedList {
     public func map<U>(transform: (T) -> U) -> LinkedList<U> {
         let result = LinkedList<U>()
         var node = head
-        while node != nil {
-            result.append(transform(node!.value))
-            node = node!.next
+        while let nd = node {
+            result.append(transform(nd.value))
+            node = nd.next
         }
         return result
     }
-
+    
     public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
         let result = LinkedList<T>()
         var node = head
-        while node != nil {
-            if predicate(node!.value) {
-                result.append(node!.value)
+        while let nd = node {
+            if predicate(nd.value) {
+                result.append(nd.value)
             }
-            node = node!.next
+            node = nd.next
         }
         return result
     }
 }
 
+// MARK: - Extension to enable initialization from an Array
 extension LinkedList {
     convenience init(array: Array<T>) {
         self.init()
-
-        for element in array {
-            self.append(element)
-        }
+        
+        array.forEach { append($0) }
     }
 }
 
+// MARK: - Extension to enable initialization from an Array Literal
 extension LinkedList: ExpressibleByArrayLiteral {
-  public convenience init(arrayLiteral elements: T...) {
-    self.init()
-
-    for element in elements {
-      self.append(element)
+    public convenience init(arrayLiteral elements: T...) {
+        self.init()
+        
+        elements.forEach { append($0) }
     }
-  }
 }
 
-extension LinkedList : Collection {
-  
-  public typealias Index = LinkedListIndex<T>
-  
-  /// The position of the first element in a nonempty collection.
-  ///
-  /// If the collection is empty, `startIndex` is equal to `endIndex`.
-  /// - Complexity: O(1)
-  public var startIndex: Index {
-    get {
-      return LinkedListIndex<T>(node: head, tag: 0)
+// MARK: - Collection
+extension LinkedList: Collection {
+    
+    public typealias Index = LinkedListIndex<T>
+    
+    /// The position of the first element in a nonempty collection.
+    ///
+    /// If the collection is empty, `startIndex` is equal to `endIndex`.
+    /// - Complexity: O(1)
+    public var startIndex: Index {
+        get {
+            return LinkedListIndex<T>(node: head, tag: 0)
+        }
+    }
+    
+    /// The collection's "past the end" position---that is, the position one
+    /// greater than the last valid subscript argument.
+    /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+    ///   to the last node in the collection.
+    public var endIndex: Index {
+        get {
+            if let h = self.head {
+                return LinkedListIndex<T>(node: h, tag: count)
+            } else {
+                return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+            }
+        }
     }
-  }
-  
-  /// The collection's "past the end" position---that is, the position one
-  /// greater than the last valid subscript argument.
-  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
-  ///   to the last node in the collection.
-  public var endIndex: Index {
-    get {
-      if let h = self.head {
-        return LinkedListIndex<T>(node: h, tag: count)
-      } else {
-        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
-      }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
     }
-  }
-  
-  public subscript(position: Index) -> T {
-    get {
-      return position.node!.value
+    
+    public func index(after idx: Index) -> Index {
+        return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag + 1)
     }
-  }
-  
-  public func index(after idx: Index) -> Index {
-    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
-  }
 }
 
+// MARK: - Collection Index
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable {
-  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
-  fileprivate let tag: Int
-  
-  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag == rhs.tag)
-  }
-  
-  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag < rhs.tag)
-  }
+public struct LinkedListIndex<T>: Comparable {
+    fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
 }
+
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 9ed698849..b16af05ba 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -1,339 +1,339 @@
 import XCTest
 
 class LinkedListTest: XCTestCase {
-  let numbers = [8, 2, 10, 9, 7, 5]
-
-  fileprivate func buildList() -> LinkedList<Int> {
-    let list = LinkedList<Int>()
-    for number in numbers {
-      list.append(number)
+    let numbers = [8, 2, 10, 9, 7, 5]
+    
+    fileprivate func buildList() -> LinkedList<Int> {
+        let list = LinkedList<Int>()
+        for number in numbers {
+            list.append(number)
+        }
+        return list
     }
-    return list
-  }
-
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
-  func testEmptyList() {
-    let list = LinkedList<Int>()
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    XCTAssertFalse(list.isEmpty)
-    XCTAssertEqual(list.count, 1)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertNil(list.first!.previous)
-    XCTAssertNil(list.first!.next)
-    XCTAssertEqual(list.first!.value, 123)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertNil(list.last!.previous)
-    XCTAssertNil(list.last!.next)
-    XCTAssertEqual(list.last!.value, 123)
-
-    XCTAssertTrue(list.first === list.last)
-  }
-
-  func testListWithTwoElements() {
-    let list = LinkedList<Int>()
-    list.append(123)
-    list.append(456)
-
-    XCTAssertEqual(list.count, 2)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertEqual(list.first!.value, 123)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertEqual(list.last!.value, 456)
-
-    XCTAssertTrue(list.first !== list.last)
-
-    XCTAssertNil(list.first!.previous)
-    XCTAssertTrue(list.first!.next === list.last)
-    XCTAssertTrue(list.last!.previous === list.first)
-    XCTAssertNil(list.last!.next)
-  }
-
-  func testListWithThreeElements() {
-    let list = LinkedList<Int>()
-    list.append(123)
-    list.append(456)
-    list.append(789)
-
-    XCTAssertEqual(list.count, 3)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertEqual(list.first!.value, 123)
-
-    let second = list.first!.next
-    XCTAssertNotNil(second)
-    XCTAssertEqual(second!.value, 456)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertEqual(list.last!.value, 789)
-
-    XCTAssertNil(list.first!.previous)
-    XCTAssertTrue(list.first!.next === second)
-    XCTAssertTrue(second!.previous === list.first)
-    XCTAssertTrue(second!.next === list.last)
-    XCTAssertTrue(list.last!.previous === second)
-    XCTAssertNil(list.last!.next)
-  }
-
-  func testNodeAtIndexInListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let node = list.node(at: 0)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node.value, 123)
-    XCTAssertTrue(node === list.first)
-  }
-
-  func testNodeAtIndex() {
-    let list = buildList()
-
-    let nodeCount = list.count
-    XCTAssertEqual(nodeCount, numbers.count)
-
-    let first = list.node(at: 0)
-    XCTAssertNotNil(first)
-    XCTAssertTrue(first === list.first)
-    XCTAssertEqual(first.value, numbers[0])
-
-    let last = list.node(at: nodeCount - 1)
-    XCTAssertNotNil(last)
-    XCTAssertTrue(last === list.last)
-    XCTAssertEqual(last.value, numbers[nodeCount - 1])
-
-    for i in 0..<nodeCount {
-      let node = list.node(at: i)
-      XCTAssertNotNil(node)
-      XCTAssertEqual(node.value, numbers[i])
+    
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
     }
-  }
-
-  func testSubscript() {
-    let list = buildList()
-    for i in 0 ..< list.count {
-      XCTAssertEqual(list[i], numbers[i])
+    
+    func testEmptyList() {
+        let list = LinkedList<Int>()
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        XCTAssertFalse(list.isEmpty)
+        XCTAssertEqual(list.count, 1)
+        
+        XCTAssertNotNil(list.first)
+        XCTAssertNil(list.head!.previous)
+        XCTAssertNil(list.head!.next)
+        XCTAssertEqual(list.head!.value, 123)
+        
+        XCTAssertNotNil(list.last)
+        XCTAssertNil(list.last!.previous)
+        XCTAssertNil(list.last!.next)
+        XCTAssertEqual(list.last!.value, 123)
+        
+        XCTAssertTrue(list.head === list.last)
+    }
+    
+    func testListWithTwoElements() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        list.append(456)
+        
+        XCTAssertEqual(list.count, 2)
+        
+        XCTAssertNotNil(list.first)
+        XCTAssertEqual(list.head!.value, 123)
+        
+        XCTAssertNotNil(list.last)
+        XCTAssertEqual(list.last!.value, 456)
+        
+        XCTAssertTrue(list.head !== list.last)
+        
+        XCTAssertNil(list.head!.previous)
+        XCTAssertTrue(list.head!.next === list.last)
+        XCTAssertTrue(list.last!.previous === list.head)
+        XCTAssertNil(list.last!.next)
+    }
+    
+    func testListWithThreeElements() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        list.append(456)
+        list.append(789)
+        
+        XCTAssertEqual(list.count, 3)
+        
+        XCTAssertNotNil(list.first)
+        XCTAssertEqual(list.head!.value, 123)
+        
+        let second = list.head!.next
+        XCTAssertNotNil(second)
+        XCTAssertEqual(second!.value, 456)
+        
+        XCTAssertNotNil(list.last)
+        XCTAssertEqual(list.last!.value, 789)
+        
+        XCTAssertNil(list.head!.previous)
+        XCTAssertTrue(list.head!.next === second)
+        XCTAssertTrue(second!.previous === list.head)
+        XCTAssertTrue(second!.next === list.last)
+        XCTAssertTrue(list.last!.previous === second)
+        XCTAssertNil(list.last!.next)
+    }
+    
+    func testNodeAtIndexInListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        let node = list.node(at: 0)
+        XCTAssertNotNil(node)
+        XCTAssertEqual(node.value, 123)
+        XCTAssertTrue(node === list.head)
+    }
+    
+    func testNodeAtIndex() {
+        let list = buildList()
+        
+        let nodeCount = list.count
+        XCTAssertEqual(nodeCount, numbers.count)
+        
+        let first = list.node(at: 0)
+        XCTAssertNotNil(first)
+        XCTAssertTrue(first === list.head)
+        XCTAssertEqual(first.value, numbers[0])
+        
+        let last = list.node(at: nodeCount - 1)
+        XCTAssertNotNil(last)
+        XCTAssertTrue(last === list.last)
+        XCTAssertEqual(last.value, numbers[nodeCount - 1])
+        
+        for i in 0..<nodeCount {
+            let node = list.node(at: i)
+            XCTAssertNotNil(node)
+            XCTAssertEqual(node.value, numbers[i])
+        }
+    }
+    
+    func testSubscript() {
+        let list = buildList()
+        for i in 0 ..< list.count {
+            XCTAssertEqual(list[i], numbers[i])
+        }
+    }
+    
+    func testInsertAtIndexInEmptyList() {
+        let list = LinkedList<Int>()
+        list.insert(123, at: 0)
+        
+        XCTAssertFalse(list.isEmpty)
+        XCTAssertEqual(list.count, 1)
+        
+        let node = list.node(at: 0)
+        XCTAssertNotNil(node)
+        XCTAssertEqual(node.value, 123)
+    }
+    
+    func testInsertAtIndex() {
+        let list = buildList()
+        let prev = list.node(at: 2)
+        let next = list.node(at: 3)
+        let nodeCount = list.count
+        
+        list.insert(444, at: 3)
+        
+        let node = list.node(at: 3)
+        XCTAssertNotNil(node)
+        XCTAssertEqual(node.value, 444)
+        XCTAssertEqual(nodeCount + 1, list.count)
+        
+        XCTAssertFalse(prev === node)
+        XCTAssertFalse(next === node)
+        XCTAssertTrue(prev.next === node)
+        XCTAssertTrue(next.previous === node)
     }
-  }
-
-  func testInsertAtIndexInEmptyList() {
-    let list = LinkedList<Int>()
-    list.insert(123, at: 0)
-
-    XCTAssertFalse(list.isEmpty)
-    XCTAssertEqual(list.count, 1)
-
-    let node = list.node(at: 0)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node.value, 123)
-  }
-
-  func testInsertAtIndex() {
-    let list = buildList()
-    let prev = list.node(at: 2)
-    let next = list.node(at: 3)
-    let nodeCount = list.count
-
-    list.insert(444, at: 3)
-
-    let node = list.node(at: 3)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node.value, 444)
-    XCTAssertEqual(nodeCount + 1, list.count)
-
-    XCTAssertFalse(prev === node)
-    XCTAssertFalse(next === node)
-    XCTAssertTrue(prev.next === node)
-    XCTAssertTrue(next.previous === node)
-  }
-
-  func testInsertListAtIndex() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.insert(list2, at: 2)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 1).value, 2)
-    XCTAssertEqual(list.node(at: 2).value, 99)
-    XCTAssertEqual(list.node(at: 3).value, 102)
-    XCTAssertEqual(list.node(at: 4).value, 10)
-  }
-
-  func testInsertListAtFirstIndex() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.insert(list2, at: 0)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 0).value, 99)
-    XCTAssertEqual(list.node(at: 1).value, 102)
-    XCTAssertEqual(list.node(at: 2).value, 8)
-  }
-
-  func testInsertListAtLastIndex() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.insert(list2, at: list.count)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 5).value, 5)
-    XCTAssertEqual(list.node(at: 6).value, 99)
-    XCTAssertEqual(list.node(at: 7).value, 102)
-  }
-
-  func testAppendList() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.append(list2)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 5).value, 5)
-    XCTAssertEqual(list.node(at: 6).value, 99)
-    XCTAssertEqual(list.node(at: 7).value, 102)
-  }
-
-  func testAppendListToEmptyList() {
-    let list = LinkedList<Int>()
-    let list2 = LinkedList<Int>()
-    list2.append(5)
-    list2.append(10)
-    list.append(list2)
-    XCTAssertTrue(list.count == 2)
-    XCTAssertEqual(list.node(at: 0).value, 5)
-    XCTAssertEqual(list.node(at: 1).value, 10)
-  }
-
-  func testRemoveAtIndexOnListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let value = list.remove(at: 0)
-    XCTAssertEqual(value, 123)
-
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testRemoveAtIndex() {
-    let list = buildList()
-    let prev = list.node(at: 2)
-    let next = list.node(at: 3)
-    let nodeCount = list.count
-
-    list.insert(444, at: 3)
-
-    let value = list.remove(at: 3)
-    XCTAssertEqual(value, 444)
-
-    let node = list.node(at: 3)
-    XCTAssertTrue(next === node)
-    XCTAssertTrue(prev.next === node)
-    XCTAssertTrue(node.previous === prev)
-    XCTAssertEqual(nodeCount, list.count)
-  }
-
-  func testRemoveLastOnListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let value = list.removeLast()
-    XCTAssertEqual(value, 123)
-
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testRemoveLast() {
-    let list = buildList()
-    let last = list.last
-    let prev = last!.previous
-    let nodeCount = list.count
-
-    let value = list.removeLast()
-    XCTAssertEqual(value, 5)
-
-    XCTAssertNil(last!.previous)
-    XCTAssertNil(last!.next)
-
-    XCTAssertNil(prev!.next)
-    XCTAssertTrue(list.last === prev)
-    XCTAssertEqual(nodeCount - 1, list.count)
-  }
-
-  func testRemoveAll() {
-    let list = buildList()
-    list.removeAll()
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testReverseLinkedList() {
-    let list = buildList()
-    let first = list.first
-    let last = list.last
-    let nodeCount = list.count
-
-    list.reverse()
-
-    XCTAssertTrue(first === list.last)
-    XCTAssertTrue(last === list.first)
-    XCTAssertEqual(nodeCount, list.count)
-  }
-
-  func testArrayLiteralInitTypeInfer() {
-    let arrayLiteralInitInfer: LinkedList = [1.0, 2.0, 3.0]
-
-    XCTAssertEqual(arrayLiteralInitInfer.count, 3)
-    XCTAssertEqual(arrayLiteralInitInfer.first?.value, 1.0)
-    XCTAssertEqual(arrayLiteralInitInfer.last?.value, 3.0)
-    XCTAssertEqual(arrayLiteralInitInfer[1], 2.0)
-    XCTAssertEqual(arrayLiteralInitInfer.removeLast(), 3.0)
-    XCTAssertEqual(arrayLiteralInitInfer.count, 2)
-  }
-
-  func testArrayLiteralInitExplicit() {
-    let arrayLiteralInitExplicit: LinkedList<Int> = [1, 2, 3]
-
-    XCTAssertEqual(arrayLiteralInitExplicit.count, 3)
-    XCTAssertEqual(arrayLiteralInitExplicit.first?.value, 1)
-    XCTAssertEqual(arrayLiteralInitExplicit.last?.value, 3)
-    XCTAssertEqual(arrayLiteralInitExplicit[1], 2)
-    XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
-    XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
-  }
-  
-  func testConformanceToCollectionProtocol() {
-    let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
-    let index2 = collection.index(collection.startIndex, offsetBy: 2)
-    let value = collection[index2]
     
-    XCTAssertTrue(value == 3)
-  }
+    func testInsertListAtIndex() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.insert(list2, at: 2)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 1).value, 2)
+        XCTAssertEqual(list.node(at: 2).value, 99)
+        XCTAssertEqual(list.node(at: 3).value, 102)
+        XCTAssertEqual(list.node(at: 4).value, 10)
+    }
+    
+    func testInsertListAtFirstIndex() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.insert(list2, at: 0)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 0).value, 99)
+        XCTAssertEqual(list.node(at: 1).value, 102)
+        XCTAssertEqual(list.node(at: 2).value, 8)
+    }
+    
+    func testInsertListAtLastIndex() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.insert(list2, at: list.count)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 5).value, 5)
+        XCTAssertEqual(list.node(at: 6).value, 99)
+        XCTAssertEqual(list.node(at: 7).value, 102)
+    }
+    
+    func testAppendList() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.append(list2)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 5).value, 5)
+        XCTAssertEqual(list.node(at: 6).value, 99)
+        XCTAssertEqual(list.node(at: 7).value, 102)
+    }
+    
+    func testAppendListToEmptyList() {
+        let list = LinkedList<Int>()
+        let list2 = LinkedList<Int>()
+        list2.append(5)
+        list2.append(10)
+        list.append(list2)
+        XCTAssertTrue(list.count == 2)
+        XCTAssertEqual(list.node(at: 0).value, 5)
+        XCTAssertEqual(list.node(at: 1).value, 10)
+    }
+    
+    func testRemoveAtIndexOnListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        let value = list.remove(at: 0)
+        XCTAssertEqual(value, 123)
+        
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testRemoveAtIndex() {
+        let list = buildList()
+        let prev = list.node(at: 2)
+        let next = list.node(at: 3)
+        let nodeCount = list.count
+        
+        list.insert(444, at: 3)
+        
+        let value = list.remove(at: 3)
+        XCTAssertEqual(value, 444)
+        
+        let node = list.node(at: 3)
+        XCTAssertTrue(next === node)
+        XCTAssertTrue(prev.next === node)
+        XCTAssertTrue(node.previous === prev)
+        XCTAssertEqual(nodeCount, list.count)
+    }
+    
+    func testRemoveLastOnListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        let value = list.removeLast()
+        XCTAssertEqual(value, 123)
+        
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testRemoveLast() {
+        let list = buildList()
+        let last = list.last
+        let prev = last!.previous
+        let nodeCount = list.count
+        
+        let value = list.removeLast()
+        XCTAssertEqual(value, 5)
+        
+        XCTAssertNil(last!.previous)
+        XCTAssertNil(last!.next)
+        
+        XCTAssertNil(prev!.next)
+        XCTAssertTrue(list.last === prev)
+        XCTAssertEqual(nodeCount - 1, list.count)
+    }
+    
+    func testRemoveAll() {
+        let list = buildList()
+        list.removeAll()
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testReverseLinkedList() {
+        let list = buildList()
+        let first = list.head
+        let last = list.last
+        let nodeCount = list.count
+        
+        list.reverse()
+        
+        XCTAssertTrue(first === list.last)
+        XCTAssertTrue(last === list.head)
+        XCTAssertEqual(nodeCount, list.count)
+    }
+    
+    func testArrayLiteralInitTypeInfer() {
+        let arrayLiteralInitInfer: LinkedList = [1.0, 2.0, 3.0]
+        
+        XCTAssertEqual(arrayLiteralInitInfer.count, 3)
+        XCTAssertEqual(arrayLiteralInitInfer.head?.value, 1.0)
+        XCTAssertEqual(arrayLiteralInitInfer.last?.value, 3.0)
+        XCTAssertEqual(arrayLiteralInitInfer[1], 2.0)
+        XCTAssertEqual(arrayLiteralInitInfer.removeLast(), 3.0)
+        XCTAssertEqual(arrayLiteralInitInfer.count, 2)
+    }
+    
+    func testArrayLiteralInitExplicit() {
+        let arrayLiteralInitExplicit: LinkedList<Int> = [1, 2, 3]
+        
+        XCTAssertEqual(arrayLiteralInitExplicit.count, 3)
+        XCTAssertEqual(arrayLiteralInitExplicit.head?.value, 1)
+        XCTAssertEqual(arrayLiteralInitExplicit.last?.value, 3)
+        XCTAssertEqual(arrayLiteralInitExplicit[1], 2)
+        XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
+        XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
+    }
+    
+    func testConformanceToCollectionProtocol() {
+        let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
+        let index2 = collection.index(collection.startIndex, offsetBy: 2)
+        let value = collection[index2]
+        
+        XCTAssertTrue(value == 3)
+    }
 }

From 444b993d571d955b36aa0aa64cd03dd1a31761b3 Mon Sep 17 00:00:00 2001
From: Bill Barbour <bill.barbour@oracle.com>
Date: Tue, 8 May 2018 15:24:10 -0400
Subject: [PATCH 1416/1679] Updated number to be prime; and Swift 4 update

---
 Rabin-Karp/Rabin-Karp.playground/Contents.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index 739b74e2a..40cd176a6 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -8,7 +8,7 @@ print("Hello, Swift 4!")
 import UIKit
 
 struct Constants {
-    static let hashMultiplier = 69069
+    static let hashMultiplier = 69061
 }
 
 precedencegroup PowerPrecedence { higherThan: MultiplicationPrecedence }
@@ -30,8 +30,8 @@ extension Character {
 // Find first position of pattern in the text using Rabin Karp algorithm
 public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.flatMap { $0.asInt }
-    let textArray = text.flatMap { $0.asInt }
+    let patternArray = pattern.compactMap { $0.asInt }
+    let textArray = text.compactMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1

From 65e3d4d18485598b030068be0ab4b82c1c21b823 Mon Sep 17 00:00:00 2001
From: Ruslan Skorb <ruslan@rsk-lab.com>
Date: Mon, 30 Apr 2018 10:11:12 +0300
Subject: [PATCH 1417/1679] [Binary Search Tree] [enum] Fix `height`.

https://en.wikipedia.org/wiki/Tree_\(data_structure\)\#Terminology
---
 Binary Search Tree/README.markdown                   | 4 ++--
 Binary Search Tree/Solution 2/BinarySearchTree.swift | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 30dc8d922..0b382f204 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -615,8 +615,8 @@ This implementation is recursive, and each case of the enum will be treated diff
 
   public var height: Int {
     switch self {
-    case .Empty: return 0
-    case .Leaf: return 1
+    case .Empty: return -1
+    case .Leaf: return 0
     case let .Node(left, _, right): return 1 + max(left.height, right.height)
     }
   }
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.swift
index 272b86368..23b1c8aca 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.swift	
@@ -20,8 +20,8 @@ public enum BinarySearchTree<T: Comparable> {
   /* Distance of this node to its lowest leaf. Performance: O(n). */
   public var height: Int {
     switch self {
-    case .empty: return 0
-    case .leaf: return 1
+    case .empty: return -1
+    case .leaf: return 0
     case let .node(left, _, right): return 1 + max(left.height, right.height)
     }
   }

From 9b7ecd6a47e4522ae0b48ae4d938dc97a31f8a22 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:23:20 +0200
Subject: [PATCH 1418/1679] Closest Pair of points algorithm

---
 .../ClosestPair.playground/Contents.swift     | 224 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 +
 .../UserInterfaceState.xcuserstate            | Bin 0 -> 10014 bytes
 .../Images/1200px-Closest_pair_of_points.png  | Bin 0 -> 17683 bytes
 Closest Pair/Images/Case.png                  | Bin 0 -> 17660 bytes
 Closest Pair/Images/Strip.png                 | Bin 0 -> 18824 bytes
 Closest Pair/README.markdown                  |  88 +++++++
 9 files changed, 331 insertions(+)
 create mode 100644 Closest Pair/ClosestPair.playground/Contents.swift
 create mode 100644 Closest Pair/ClosestPair.playground/contents.xcplayground
 create mode 100644 Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Closest Pair/ClosestPair.playground/playground.xcworkspace/xcuserdata/admin.xcuserdatad/UserInterfaceState.xcuserstate
 create mode 100644 Closest Pair/Images/1200px-Closest_pair_of_points.png
 create mode 100644 Closest Pair/Images/Case.png
 create mode 100644 Closest Pair/Images/Strip.png
 create mode 100644 Closest Pair/README.markdown

diff --git a/Closest Pair/ClosestPair.playground/Contents.swift b/Closest Pair/ClosestPair.playground/Contents.swift
new file mode 100644
index 000000000..c11c1770b
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/Contents.swift	
@@ -0,0 +1,224 @@
+//Created by Ahmed Nader (github: AhmedNader42) on 4/4/18.
+
+func ClosestPairOf(points: [Point]) -> (minimum:Double, firstPoint:Point, secondPoint:Point) {
+    var innerPoints = mergeSort(points, sortAccording : true)
+    let result = ClosestPair(&innerPoints, innerPoints.count)
+    return (result.minValue, result.firstPoint, result.secondPoint)
+}
+
+func ClosestPair(_ p : inout [Point],_ n : Int) -> (minValue: Double,firstPoint: Point,secondPoint: Point)
+{
+    // Brute force if only 3 points (To end recursion)
+    if n <= 3
+    {
+        var i=0, j = i+1
+        var minDist = Double.infinity
+        var newFirst:Point? = nil
+        var newSecond:Point? = nil
+        while i<n
+        {
+            j = i+1
+            while j < n
+            {
+                if dist(p[i], p[j]) <= minDist
+                {
+                    minDist = dist(p[i], p[j])
+                    newFirst = p[i]
+                    newSecond = p[j]
+                }
+                j+=1
+            }
+            i+=1
+            
+        }
+        return (minDist, newFirst ?? Point(0,0), newSecond ?? Point(0,0))
+    }
+    
+    
+    
+    let mid:Int = n/2
+    let line:Double = (p[mid].x + p[mid+1].x)/2
+    
+    // Split the array.
+    var leftSide = [Point]()
+    var rightSide = [Point]()
+    for s in 0..<mid
+    {
+        leftSide.append(p[s])
+    }
+    for s in mid..<p.count
+    {
+        rightSide.append(p[s])
+    }
+    
+    
+    // Recurse on the left and right part of the array.
+    let valueFromLeft = ClosestPair(&leftSide, mid)
+    let minLeft:Double = valueFromLeft.minValue
+    let valueFromRight = ClosestPair(&rightSide, n-mid)
+    let minRight:Double = valueFromRight.minValue
+    
+    // Starting current min must be the largest possible to not affect the real calculations.
+    var min = Double.infinity
+    
+    var first:Point
+    var second:Point
+    
+    // Get the minimum between the left and the right.
+    if minLeft < minRight {
+        min = minLeft
+        first = valueFromLeft.firstPoint
+        second = valueFromLeft.secondPoint
+    }
+    else {
+        min = minRight
+        first = valueFromRight.firstPoint
+        second = valueFromRight.secondPoint
+    }
+    
+    // Sort the array according to Y.
+    p = mergeSort(p, sortAccording: false)
+    
+    
+    var strip = [Point]()
+    
+    // If the value is less than the min distance away in X from the line then take it into consideration.
+    var i=0, j = 0
+    while i<n
+    {
+        if abs(p[i].x - line) < min
+        {
+            strip.append(p[i])
+            j+=1
+        }
+        i+=1
+    }
+    
+    
+    i=0
+    var x = i+1
+    var temp = min
+    var tempFirst:Point = Point(0,0)
+    var tempSecond:Point = Point(0,0)
+    // Get the values between the points in the strip but only if it is less min dist in Y.
+    while i<j
+    {
+        x = i+1
+        while x < j
+        {
+            if (abs(strip[x].y - strip[i].y)) > min { break }
+            if dist(strip[i], strip[x]) < temp
+            {
+                temp = dist(strip[i], strip[x])
+                tempFirst = strip[i]
+                tempSecond = strip[x]
+            }
+            x+=1
+        }
+        i+=1
+    }
+    
+    if temp < min
+    {
+        min = temp;
+        first = tempFirst
+        second = tempSecond
+    }
+    return (min, first, second)
+}
+
+
+
+
+// MergeSort the array (Taken from Swift Algorithms Club with
+// minor addition)
+// sortAccodrding : true -> x, false -> y.
+func mergeSort(_ array: [Point], sortAccording : Bool) -> [Point] {
+    guard array.count > 1 else { return array }
+    let middleIndex = array.count / 2
+    let leftArray = mergeSort(Array(array[0..<middleIndex]), sortAccording: sortAccording)
+    let rightArray = mergeSort(Array(array[middleIndex..<array.count]), sortAccording: sortAccording)
+    return merge(leftPile: leftArray, rightPile: rightArray, sortAccording: sortAccording)
+}
+
+
+private func merge(leftPile: [Point], rightPile: [Point], sortAccording: Bool) -> [Point] {
+    
+    var compare : (Point, Point) -> Bool
+    
+    // Choose to compare with X or Y.
+    if sortAccording
+    {
+        compare = { p1,p2 in
+            return p1.x < p2.x
+        }
+    }
+    else
+    {
+        compare = { p1, p2 in
+            return p1.y < p2.y
+        }
+    }
+    
+    var leftIndex = 0
+    var rightIndex = 0
+    var orderedPile = [Point]()
+    if orderedPile.capacity < leftPile.count + rightPile.count {
+        orderedPile.reserveCapacity(leftPile.count + rightPile.count)
+    }
+    
+    while true {
+        guard leftIndex < leftPile.endIndex else {
+            orderedPile.append(contentsOf: rightPile[rightIndex..<rightPile.endIndex])
+            break
+        }
+        guard rightIndex < rightPile.endIndex else {
+            orderedPile.append(contentsOf: leftPile[leftIndex..<leftPile.endIndex])
+            break
+        }
+        
+        if compare(leftPile[leftIndex], rightPile[rightIndex]) {
+            orderedPile.append(leftPile[leftIndex])
+            leftIndex += 1
+        } else {
+            orderedPile.append(rightPile[rightIndex])
+            rightIndex += 1
+        }
+    }
+    return orderedPile
+}
+
+
+// Structure to represent a point.
+struct Point
+{
+    var x: Double
+    var y: Double
+    
+    init(_ x:Double,_ y:Double) {
+        self.x = x
+        self.y = y
+    }
+}
+// Get the distance between two points a, b.
+func dist(_ a: Point,_ b: Point) -> Double
+{
+    let equation:Double = (((a.x-b.x)*(a.x-b.x))) + (((a.y-b.y)*(a.y-b.y)))
+    return equation.squareRoot()
+}
+
+
+var a = Point(0,2)
+var b = Point(6,67)
+var c = Point(43,71)
+var d = Point(1000,1000)
+var e = Point(39,107)
+var f = Point(2000,2000)
+var g = Point(3000,3000)
+var h = Point(4000,4000)
+
+
+var points = [a,b,c,d,e,f,g,h]
+let endResult = ClosestPairOf(points: points)
+print("Minimum Distance : \(endResult.minimum), The two points : (\(endResult.firstPoint.x ),\(endResult.firstPoint.y)), (\(endResult.secondPoint.x),\(endResult.secondPoint.y))")
+
diff --git a/Closest Pair/ClosestPair.playground/contents.xcplayground b/Closest Pair/ClosestPair.playground/contents.xcplayground
new file mode 100644
index 000000000..a93d4844a
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata b/Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcuserdata/admin.xcuserdatad/UserInterfaceState.xcuserstate b/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcuserdata/admin.xcuserdatad/UserInterfaceState.xcuserstate
new file mode 100644
index 0000000000000000000000000000000000000000..82b1303405d67c83db2a30dbba741c883e40fdff
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diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
new file mode 100644
index 000000000..57786c7ff
--- /dev/null
+++ b/Closest Pair/README.markdown	
@@ -0,0 +1,88 @@
+# ClosestPair
+
+Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
+
+![Given points and we're required to find the two red ones](../Closest Pair/Images/1200px-Closest_pair_of_points.png)
+
+As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
+
+Here is the main algorithm (Steps) we'll follow.
+
+- Sort the array according to their position on the X-axis so that they are sorted in the array as they are naturally in math.
+
+```swift
+var innerPoints = mergeSort(points, sortAccording : true)
+```
+
+- Divide the points into two arrays Left, Right and keep dividing until you reach to only having 3 points in your array.
+
+- The base case is you have less than 3 points compare those against each other (Brute force) then return the minimum distance you found and the two points.
+
+- Now we get the first observation in the below image, There could be 2 points both very close to each other and indeed those two are the closest pair but since our algorithm so far divides from the middle
+ 
+```swift
+let line:Double = (p[mid].x + p[mid+1].x)/2
+```
+
+and just recursively calls itself until it reaches the base case we don't detect those points.
+
+![ Points lying near the division line](../Closest Pair/Images/Case.png)
+
+- To solve this we start by sorting the array on the Y-axis to get the points in their natural order and then we start getting the difference between the X position of the point and the line we drew to divide and if it is less than the min we got so far from the recursion we add it to the strip 
+
+```swift
+var strip = [Point]()   
+var i=0, j = 0
+while i<n
+{
+	if abs(p[i].x - line) < min
+	{
+		strip.append(p[i])
+		j+=1
+	}
+	i+=1
+}
+```
+
+- After you insert the points that could possibly give you a better min distance we get to another observation in the image below.
+
+![The strip with 4 points shown](..//Closest Pair/Images/Strip.png)
+
+- Searching the strip is a brute force loop (But doesn't that just destroy everything we did? You ask) but it has an advantage it could never iterate on more than 8 points (worst case).
+
+- The reason is that the strip is constructed as a rectangle with sides of length = min that we got from the recursion and we ignore any points that have a Y difference bigger than min distance so to be able to place them ALL inside the rectangle with these conditions they'll have to be in the shape above with each one of them EXACTLY min distance away from the other which gives us 4 possible points for each one and 8 in total.
+
+```swift
+while i<j
+    {
+        x = i+1
+        while x < j
+        {
+            if (abs(strip[x].y - strip[i].y)) > min { break }
+            if dist(strip[i], strip[x]) < temp
+            {
+                temp = dist(strip[i], strip[x])
+                tempFirst = strip[i]
+                tempSecond = strip[x]
+            }
+            x+=1
+        }
+        i+=1
+    }
+```
+
+- Of course not every time you end up with the same shape but this is the worst case and it's rare to happen so in reality you end up with far less points valid for comparison and this is why the algorithm gets performance in addition to the sorting tricks we did.
+
+- Compare the points in the strip and if you find a smaller distance replace the current one with it.
+
+
+So this is the rundown of how the algorithm works and you could see the fun little math tricks used to optimize this and we end up with O(nlogn) complexity mainly because of the sorting.
+
+
+## See also
+
+See the playground to play around with the implementation of the algorithm
+
+[Wikipedia](https://en.wikipedia.org/wiki/Closest_pair_of_points_problem)
+
+*Written for Swift Algorithm Club by [Ahmed Nader](https://github.com/ahmednader42)*

From 9b0a3c517d1e26ced6bd506b42af25bf2b99d287 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:24:32 +0200
Subject: [PATCH 1419/1679] Images

---
 Closest Pair/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 57786c7ff..35ea15653 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](../Closest Pair/Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](Closest Pair/Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 
@@ -26,7 +26,7 @@ let line:Double = (p[mid].x + p[mid+1].x)/2
 
 and just recursively calls itself until it reaches the base case we don't detect those points.
 
-![ Points lying near the division line](../Closest Pair/Images/Case.png)
+![ Points lying near the division line](Closest Pair/Images/Case.png)
 
 - To solve this we start by sorting the array on the Y-axis to get the points in their natural order and then we start getting the difference between the X position of the point and the line we drew to divide and if it is less than the min we got so far from the recursion we add it to the strip 
 
@@ -46,7 +46,7 @@ while i<n
 
 - After you insert the points that could possibly give you a better min distance we get to another observation in the image below.
 
-![The strip with 4 points shown](..//Closest Pair/Images/Strip.png)
+![The strip with 4 points shown](Closest Pair/Images/Strip.png)
 
 - Searching the strip is a brute force loop (But doesn't that just destroy everything we did? You ask) but it has an advantage it could never iterate on more than 8 points (worst case).
 

From 4de991b7a6d0984eadd77341a6ea83ca4dafe2f7 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:26:43 +0200
Subject: [PATCH 1420/1679] Update README.markdown

---
 Closest Pair/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 35ea15653..3ce08dd49 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](Closest Pair/Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](../Closest\ Pair/Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 

From a018f72d59fd33a3990f343725dfd823f84a0340 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:30:35 +0200
Subject: [PATCH 1421/1679] Update README.markdown

---
 Closest Pair/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 3ce08dd49..5224bcef4 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](../Closest\ Pair/Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](../Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 

From 4174a840c332ee07f875306b098f710c0e3601bb Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:31:20 +0200
Subject: [PATCH 1422/1679] Update README.markdown

---
 Closest Pair/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 5224bcef4..a4de4a28b 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](../Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 
@@ -26,7 +26,7 @@ let line:Double = (p[mid].x + p[mid+1].x)/2
 
 and just recursively calls itself until it reaches the base case we don't detect those points.
 
-![ Points lying near the division line](Closest Pair/Images/Case.png)
+![ Points lying near the division line](Images/Case.png)
 
 - To solve this we start by sorting the array on the Y-axis to get the points in their natural order and then we start getting the difference between the X position of the point and the line we drew to divide and if it is less than the min we got so far from the recursion we add it to the strip 
 
@@ -46,7 +46,7 @@ while i<n
 
 - After you insert the points that could possibly give you a better min distance we get to another observation in the image below.
 
-![The strip with 4 points shown](Closest Pair/Images/Strip.png)
+![The strip with 4 points shown](Images/Strip.png)
 
 - Searching the strip is a brute force loop (But doesn't that just destroy everything we did? You ask) but it has an advantage it could never iterate on more than 8 points (worst case).
 

From bcb037d505afcc80a245db5ea43041b63a1d7c3f Mon Sep 17 00:00:00 2001
From: Abbey Jackson <abbey@abbeyjackson.ca>
Date: Tue, 22 May 2018 11:43:26 -0700
Subject: [PATCH 1423/1679] Fixed broken link

Link to shortest path example was broken
---
 Breadth-First Search/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index b2298822f..097f4278d 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -151,7 +151,7 @@ This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
 
 Breadth-first search can be used to solve many problems. A small selection:
 
-* Computing the [shortest path](../Shortest%20Path/) between a source node and each of the other nodes (only for unweighted graphs).
+* Computing the [shortest path](../Shortest%20Path%20(Unweighted)/) between a source node and each of the other nodes (only for unweighted graphs).
 * Calculating the [minimum spanning tree](../Minimum%20Spanning%20Tree%20(Unweighted)/) on an unweighted graph.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*

From bcdd28236d981f8763fdda9ebe41b699ea624579 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 4 Jun 2018 21:01:09 -0700
Subject: [PATCH 1424/1679] Updates maintainer list.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 919f1b67f..f5fc4247a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -225,7 +225,7 @@ You can find the book on the [raywenderlich.com store](https://store.raywenderli
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
 
-It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL) and [Ross O'brien](https://www.raywenderlich.com/u/narrativium).
+It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), and [Kelvin Lau](https://github.com/kelvinlauKL).
 
 The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 

From f4afbabffe020f8c81dc84a74e90e49f5ef90061 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 8 Jun 2018 01:47:25 -0700
Subject: [PATCH 1425/1679] Refactors first blurb.

---
 Myers Difference Algorithm/README.md | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index e6137e8ce..6be30ecda 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,15 +1,13 @@
 #  Myers Difference Algorithm
 
-Myers Difference Algorithm is an algorithm that finds a longest common subsequence(LCS) or shortest edit scripts(SES) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. 
-
-For example, let's assume you have two arrays:
+Myers Difference Algorithm(MDA) is an algorithm that finds a longest common subsequence(LCS) or shortest edit scripts(SES) of two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. For example, let's assume you have two arrays:
 
 ```
-A = [1, 2, 3]
-B = [2, 3, 4]
+let firstArray = [1, 2, 3]
+let secondArray = [2, 3, 4]
 ```
 
-The common subsequences of these two arrays are `[2]`, and `[2,3]`. The longest common sequence in this case is `[2,3]`.
+The common subsequences of these two arrays are `[2]`, and `[2, 3]`. The longest common sequence in this case is `[2, 3]`. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. 
 
 ## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
 

From 66db524690e73646b183eb28d3bb4ae77490b80b Mon Sep 17 00:00:00 2001
From: Ta-Cuong Nguyen <cuongnt04230@gmail.com>
Date: Sat, 9 Jun 2018 11:19:49 +0700
Subject: [PATCH 1426/1679] Update README.markdown

Update document for Hoare's partitioning scheme
---
 Quicksort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index b8a908985..a9356f921 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -288,7 +288,7 @@ func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
     repeat { i += 1 } while a[i] < pivot
     
     if i < j {
-      swap(&a[i], &a[j])
+      a.swapAt(i, j)
     } else {
       return j
     }

From 22e44960a9e5f8ec0010c8ed3a3cb0d3c23c724e Mon Sep 17 00:00:00 2001
From: augustoavelino <augusto_avelino@icloud.com>
Date: Mon, 11 Jun 2018 16:29:05 -0300
Subject: [PATCH 1427/1679] Fixed issue in LinkedList insert(_:, at:) method
 where next?.previous was referencing next itself.

---
 Linked List/LinkedList.playground/Contents.swift | 2 +-
 Linked List/LinkedList.swift                     | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 4b58bb65e..cfa3a8b45 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -176,7 +176,7 @@ public final class LinkedList<T> {
             list.head?.previous = prev
             
             list.last?.next = next
-            next?.previous = list.last?.next
+            next?.previous = list.last
         }
     }
     
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 285c85588..7c2cbb3b1 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -166,7 +166,7 @@ public final class LinkedList<T> {
             list.head?.previous = prev
             
             list.last?.next = next
-            next?.previous = list.last?.next
+            next?.previous = list.last
         }
     }
     

From 4528471976af69ce2e98dada083bd32b3fe9fd7f Mon Sep 17 00:00:00 2001
From: Denis Litvin <den.litvinn@gmail.com>
Date: Thu, 14 Jun 2018 14:23:11 +0300
Subject: [PATCH 1428/1679] Fix

---
 Rabin-Karp/Rabin-Karp.playground/Contents.swift           | 6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 11 insertions(+), 3 deletions(-)
 create mode 100644 Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index 739b74e2a..f5d4137c4 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -1,6 +1,6 @@
 //: Taking our rabin-karp algorithm for a walk
 
-// last checked with Xcode 9.0b4
+// last checked with Xcode 9.4
 #if swift(>=4.0)
 print("Hello, Swift 4!")
 #endif
@@ -30,8 +30,8 @@ extension Character {
 // Find first position of pattern in the text using Rabin Karp algorithm
 public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.flatMap { $0.asInt }
-    let textArray = text.flatMap { $0.asInt }
+    let patternArray = pattern.compactMap { $0.asInt }
+    let textArray = text.compactMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1
diff --git a/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From bf51c93414900e44baffbb2c7bd57aca76b22909 Mon Sep 17 00:00:00 2001
From: Milad Taghavi <mitghi@me.com>
Date: Wed, 20 Jun 2018 12:34:14 +0200
Subject: [PATCH 1429/1679] Add Simulated annealing to README

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index f5fc4247a..90b310752 100644
--- a/README.markdown
+++ b/README.markdown
@@ -119,6 +119,7 @@ Bad sorting algorithms (don't use these!):
 - Neural Networks
 - PageRank
 - [Naive Bayes Classifier](Naive%20Bayes%20Classifier/)
+- [Simulated annealing](Simulated%20annealing/). Probabilistic technique for approximating the global maxima in a (often discrete) large search space.
 
 ## Data structures
 

From 88f75eb2d05ff4a0e9ba18d4824158f7e9b1e84e Mon Sep 17 00:00:00 2001
From: Weslie <iwesliechen@gmail.com>
Date: Mon, 30 Jul 2018 11:22:18 +0800
Subject: [PATCH 1430/1679] [Swift 4 Update]add parentheses

Single argument function types require parentheses
---
 Binary Tree/BinaryTree.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index 102f23e06..6146880b4 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -29,7 +29,7 @@ extension BinaryTree: CustomStringConvertible {
 }
 
 extension BinaryTree {
-  public func traverseInOrder(process: T -> Void) {
+  public func traverseInOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
       left.traverseInOrder(process: process)
       process(value)
@@ -37,7 +37,7 @@ extension BinaryTree {
     }
   }
 
-  public func traversePreOrder(process: T -> Void) {
+  public func traversePreOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
       process(value)
       left.traversePreOrder(process: process)
@@ -45,7 +45,7 @@ extension BinaryTree {
     }
   }
 
-  public func traversePostOrder(process: T -> Void) {
+  public func traversePostOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
       left.traversePostOrder(process: process)
       right.traversePostOrder(process: process)

From 2b932ac83689f2e29e387a763f104e47aa6ae1c2 Mon Sep 17 00:00:00 2001
From: Jen <Jchangho@grubhub.com>
Date: Fri, 3 Aug 2018 13:57:38 -0400
Subject: [PATCH 1431/1679] Fixes Issue#371: Simulated Annealing demo crashes

---
 Simulated annealing/simann.swift         | 16 ++---------
 Simulated annealing/simann_example.swift | 36 +++++++-----------------
 2 files changed, 13 insertions(+), 39 deletions(-)

diff --git a/Simulated annealing/simann.swift b/Simulated annealing/simann.swift
index 8adfbf817..5dc624d04 100644
--- a/Simulated annealing/simann.swift	
+++ b/Simulated annealing/simann.swift	
@@ -22,16 +22,6 @@
   import Glibc
 #endif
 
-public extension Double {  
-  public static func random(_ lower: Double, _ upper: Double) -> Double {
-    #if os(OSX)
-      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #elseif os(Linux)
-      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #endif
-  }
-}
-
 protocol Clonable {
   init(current: Self)
 }
@@ -85,13 +75,13 @@ func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRat
   
   while temp > 1 {    
     let newSolution: T = currentSolution.clone()
-    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
-    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos1: Int = Int.random(in: 0 ..< newSolution.count)
+    let pos2: Int = Int.random(in: 0 ..< newSolution.count)
     newSolution.randSwap(a: pos1, b: pos2)
     let currentEnergy: Double  = currentSolution.currentEnergy()
     let newEnergy: Double = newSolution.currentEnergy()
     
-    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(in: 0 ..< 1) {
       currentSolution = newSolution.clone()
     }
     if currentSolution.currentEnergy() < bestSolution.currentEnergy() {
diff --git a/Simulated annealing/simann_example.swift b/Simulated annealing/simann_example.swift
index a0dfaa19a..0e07e0024 100644
--- a/Simulated annealing/simann_example.swift	
+++ b/Simulated annealing/simann_example.swift	
@@ -18,21 +18,11 @@
 
 #if os(OSX)
   import Foundation
+  import Cocoa
 #elseif os(Linux)
   import Glibc
 #endif
 
-public extension Double {
-  
-  public static func random(_ lower: Double, _ upper: Double) -> Double {
-    #if os(OSX)
-      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #elseif os(Linux)
-      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #endif
-  }
-}
-
 protocol Clonable {
   init(current: Self)
 }
@@ -96,8 +86,8 @@ extension Point {
   static func <-> (left: Point, right: Point) -> Double {
     let xDistance = (left.x - right.x)
     let yDistance = (left.y - right.y)
-    
-    return Double(sqrt(Double((xDistance * xDistance) + (yDistance * yDistance))))
+
+    return Double((xDistance * xDistance) + (yDistance * yDistance)).squareRoot()
   }
 }
 
@@ -128,15 +118,6 @@ extension Tour {
     self[a] = cpos2
     self[b] = cpos1
   }
-  
-  func shuffle() {
-    for i in stride(from:  self.count - 1, through: 1, by: -1) {
-      let j = Int(arc4random()) % (i + 1)
-      if i != j {
-        swap(&self.tour[i], &self.tour[j])
-      }
-    }
-  }
 
   func currentEnergy() -> Double {
     if self.energy == 0 {
@@ -155,7 +136,10 @@ extension Tour {
     }
     return self.energy
   }
-  
+
+  func shuffle() {
+    self.shuffle()
+  }
 }
 
 // MARK: - subscript to manipulate elements of Tour.
@@ -180,13 +164,13 @@ func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRat
   
   while temp > 1 {
     let newSolution: T = currentSolution.clone()
-    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
-    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos1: Int = Int.random(in: 0 ..< newSolution.count)
+    let pos2: Int = Int.random(in: 0 ..< newSolution.count)
     newSolution.randSwap(a: pos1, b: pos2)
     let currentEnergy: Double  = currentSolution.currentEnergy()
     let newEnergy: Double = newSolution.currentEnergy()
     
-    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(in: 0 ..< 1) {
       currentSolution = newSolution.clone()
     }
     if currentSolution.currentEnergy() < bestSolution.currentEnergy() {

From 8e207266be665e4a7426db2a7c30bc79bda93274 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Mon, 10 Sep 2018 20:51:35 -0700
Subject: [PATCH 1432/1679] Update maintainers list.

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 90b310752..7d3156ae7 100644
--- a/README.markdown
+++ b/README.markdown
@@ -226,7 +226,7 @@ You can find the book on the [raywenderlich.com store](https://store.raywenderli
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
 
-It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), and [Kelvin Lau](https://github.com/kelvinlauKL).
+It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL), and [Richard Ash](https://github.com/richard-ash).
 
 The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 

From 380bfc27b505ab14abd336465cade9d6ede57c57 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Wed, 26 Sep 2018 00:10:14 -0700
Subject: [PATCH 1433/1679] Update README.markdown

Fix contributors link to point to the raywenderlich repo instead of the rwenderlich fork
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 7d3156ae7..ff8bfe778 100644
--- a/README.markdown
+++ b/README.markdown
@@ -228,7 +228,7 @@ The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://
 
 It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL), and [Richard Ash](https://github.com/richard-ash).
 
-The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
+The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/raywenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 
 ## License
 

From b3ba0467b88ff48eaf6221482b05ca8908ab5bb0 Mon Sep 17 00:00:00 2001
From: Andy Ron <randy.njfu@gmail.com>
Date: Thu, 27 Sep 2018 17:34:40 +0800
Subject: [PATCH 1434/1679] Update README.md

---
 B-Tree/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/B-Tree/README.md b/B-Tree/README.md
index f6924aadc..10a06853e 100644
--- a/B-Tree/README.md
+++ b/B-Tree/README.md
@@ -133,7 +133,7 @@ Else:
 
 ![Moving Key](Images/MovingKey.png)
 
-####Merging two nodes
+#### Merging two nodes
 
 Let's say we want to merge the child `c1` at index `i` in its parent's children array.
 

From 106b65ede0191fe7c6ba78fcd519334b7ea56e6a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 15:33:23 -0300
Subject: [PATCH 1435/1679] addition of Bubble sort algorithm

---
 .../MyPlayground.playground/Contents.swift    | 27 ++++++++++++
 .../Sources/BubbleSort.swift                  | 42 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 .../contents.xcworkspacedata                  |  7 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 6 files changed, 96 insertions(+)
 create mode 100644 Bubble Sort/MyPlayground.playground/Contents.swift
 create mode 100644 Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
 create mode 100644 Bubble Sort/MyPlayground.playground/contents.xcplayground
 create mode 100644 Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
new file mode 100644
index 000000000..d0cf07ab3
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -0,0 +1,27 @@
+import Foundation
+
+public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+    var array = elements
+    
+    for i in 0..<array.count {
+        for j in i+1..<array.count {
+            if array[j] < array[i] {
+                let tmp = array[i]
+                array[i] = array[j]
+                array[j] = tmp
+            }
+        }
+    }
+    
+    return array
+}
+
+
+var array = [Int]()
+
+for _ in 0...10 {
+    array.append(Int.random(in: 0...500))
+}
+
+print("before:",array)
+print("after:",BubbleSort(array))
diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
new file mode 100644
index 000000000..8f1ec80f8
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -0,0 +1,42 @@
+//
+//  BubbleSort.swift
+//
+//  Created by Julio Brazil on 1/10/18.
+//
+//  Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
+//  associated documentation files (the "Software"), to deal in the Software without restriction, including
+//  without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//  copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the
+//  following conditions:
+//
+//  The above copyright notice and this permission notice shall be included in all copies or substantial
+//  portions of the Software.
+//
+//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
+//  LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
+//  EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+//  AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
+//  OR OTHER DEALINGS IN THE SOFTWARE.
+//
+
+import Foundation
+
+/// Performs the bubble sort algorithm in the array
+///
+/// - Parameter elements: the array to be sorted
+/// - Returns: an array with the same elements but in order
+public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+    var array = elements
+    
+    for i in 0..<array.count {
+        for j in i+1..<array.count {
+            if array[j] < array[i] {
+                let tmp = array[i]
+                array[i] = array[j]
+                array[j] = tmp
+            }
+        }
+    }
+    
+    return array
+}
diff --git a/Bubble Sort/MyPlayground.playground/contents.xcplayground b/Bubble Sort/MyPlayground.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 44711ad86d5fafc1f6db40bfebb5e94e277377b1 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 15:57:40 -0300
Subject: [PATCH 1436/1679] addition of convenience method

---
 .../SelectionSort.playground/Contents.swift   |  1 +
 .../Sources/SelectionSort.swift               | 26 +++++++++++++++++--
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++++
 3 files changed, 33 insertions(+), 2 deletions(-)
 create mode 100644 Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index e0bfdf259..b16dadb8d 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -6,5 +6,6 @@ print("Hello, Swift 4!")
 #endif
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
+selectionSort(list)
 selectionSort(list, <)
 selectionSort(list, >)
diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index 3015fde9b..b0bdfab55 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -1,4 +1,4 @@
-public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
 
   var a = array
@@ -7,7 +7,7 @@ public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T)
     // Find the lowest value in the rest of the array.
     var lowest = x
     for y in x + 1 ..< a.count {
-      if isOrderedBefore(a[y], a[lowest]) {
+      if a[y] < a[lowest] {
         lowest = y
       }
     }
@@ -19,3 +19,25 @@ public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T)
   }
   return a
 }
+
+public func selectionSort<T>(_ array: [T], _ isLowerThan: (T, T) -> Bool) -> [T] {
+    guard array.count > 1 else { return array }
+    
+    var a = array
+    for x in 0 ..< a.count - 1 {
+        
+        // Find the lowest value in the rest of the array.
+        var lowest = x
+        for y in x + 1 ..< a.count {
+            if isLowerThan(a[y], a[lowest]) {
+                lowest = y
+            }
+        }
+        
+        // Swap the lowest value with the current array index.
+        if x != lowest {
+            a.swapAt(x, lowest)
+        }
+    }
+    return a
+}
diff --git a/Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From d078c50bc281d92f0369fe3b6bac5508988e175a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 16:02:04 -0300
Subject: [PATCH 1437/1679] addition of function description

---
 .../Sources/SelectionSort.swift                        | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index b0bdfab55..3a27ef9dd 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -1,3 +1,7 @@
+/// Performs the Selection sort algorithm on a array
+///
+/// - Parameter array: array of elements that conform to the Comparable protocol
+/// - Returns: an array in ascending order
 public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
 
@@ -20,6 +24,12 @@ public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
   return a
 }
 
+/// Performs the Selection sort algorithm on a array using the provided comparisson method
+///
+/// - Parameters:
+///   - array: array of elements that conform to the Comparable protocol
+///   - isLowerThan: returns true if the two provided elements are in the correct order
+/// - Returns: a sorted array
 public func selectionSort<T>(_ array: [T], _ isLowerThan: (T, T) -> Bool) -> [T] {
     guard array.count > 1 else { return array }
     

From d82954fc2c7533181c72cd800cd892a4bf7ab987 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 19:22:36 -0300
Subject: [PATCH 1438/1679] added convenience method

---
 .../InsertionSort.playground/Contents.swift   | 35 +++++++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 Insertion Sort/InsertionSort.swift            | 14 ++++++++
 3 files changed, 47 insertions(+), 10 deletions(-)
 create mode 100644 Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 91e18640f..6c84a4a3e 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -6,19 +6,34 @@ print("Hello, Swift 4!")
 #endif
 
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  var a = array
-  for x in 1..<a.count {
-    var y = x
-    let temp = a[y]
-    while y > 0 && isOrderedBefore(temp, a[y - 1]) {
-      a[y] = a[y - 1]
-      y -= 1
+    var a = array
+    for x in 1..<a.count {
+        var y = x
+        let temp = a[y]
+        while y > 0 && isOrderedBefore(temp, a[y - 1]) {
+            a[y] = a[y - 1]
+            y -= 1
+        }
+        a[y] = temp
     }
-    a[y] = temp
-  }
-  return a
+    return a
+}
+
+func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
+    var a = array
+    for x in 1..<a.count {
+        var y = x
+        let temp = a[y]
+        while y > 0 && temp < a[y - 1] {
+            a[y] = a[y - 1]
+            y -= 1
+        }
+        a[y] = temp
+    }
+    return a
 }
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
+insertionSort(list)
 insertionSort(list, <)
 insertionSort(list, >)
diff --git a/Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 5d8a9565b..362c8565a 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -13,3 +13,17 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   }
   return a
 }
+
+func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
+    var a = array
+    for x in 1..<a.count {
+        var y = x
+        let temp = a[y]
+        while y > 0 && temp < a[y - 1] {
+            a[y] = a[y - 1]
+            y -= 1
+        }
+        a[y] = temp
+    }
+    return a
+}

From 06e894bf80c8940fa20db172c291fa9be713350a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 19:26:55 -0300
Subject: [PATCH 1439/1679] added primitive documentation

---
 Insertion Sort/InsertionSort.swift                     | 10 ++++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist              |  8 ++++++++
 2 files changed, 18 insertions(+)
 create mode 100644 Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 362c8565a..2d623adc9 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -1,3 +1,9 @@
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameters:
+///   - array: the array of elements to be sorted
+///   - isOrderedBefore: returns true if the elements provided are in the corect order
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   guard array.count > 1 else { return array }
 
@@ -14,6 +20,10 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   return a
 }
 
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     var a = array
     for x in 1..<a.count {
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 46742c7998828cf4e4ed8a49925bee046c3ae268 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 22:05:20 -0300
Subject: [PATCH 1440/1679] fixing dumb mistake

---
 .../InsertionSort.playground/Contents.swift    | 18 +++++++++++++++---
 .../contents.xcplayground                      |  2 +-
 Insertion Sort/InsertionSort.swift             |  2 ++
 3 files changed, 18 insertions(+), 4 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 6c84a4a3e..9a10ec04a 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -5,7 +5,15 @@
 print("Hello, Swift 4!")
 #endif
 
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameters:
+///   - array: the array of elements to be sorted
+///   - isOrderedBefore: returns true if the elements provided are in the corect order
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+    guard array.count > 1 else { return array }
+    
     var a = array
     for x in 1..<a.count {
         var y = x
@@ -19,6 +27,10 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
     return a
 }
 
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     var a = array
     for x in 1..<a.count {
@@ -34,6 +46,6 @@ func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
 }
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
-insertionSort(list)
-insertionSort(list, <)
-insertionSort(list, >)
+print(insertionSort(list))
+print(insertionSort(list, <))
+print(insertionSort(list, >))
diff --git a/Insertion Sort/InsertionSort.playground/contents.xcplayground b/Insertion Sort/InsertionSort.playground/contents.xcplayground
index 06828af92..9f9eecc96 100644
--- a/Insertion Sort/InsertionSort.playground/contents.xcplayground	
+++ b/Insertion Sort/InsertionSort.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 2d623adc9..9faf9dc42 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -25,6 +25,8 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 /// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
+    guard array.count > 1 else { return array }
+
     var a = array
     for x in 1..<a.count {
         var y = x

From a9b6c5f68e9d7ac0989e6f42c0bd98265740bc36 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 2 Oct 2018 11:49:32 -0300
Subject: [PATCH 1441/1679] correction in the algorithm

---
 .../MyPlayground.playground/Contents.swift       | 16 ++++++----------
 .../Sources/BubbleSort.swift                     |  8 ++++----
 2 files changed, 10 insertions(+), 14 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
index d0cf07ab3..16466e0bc 100644
--- a/Bubble Sort/MyPlayground.playground/Contents.swift	
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -4,10 +4,11 @@ public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
     var array = elements
     
     for i in 0..<array.count {
-        for j in i+1..<array.count {
-            if array[j] < array[i] {
-                let tmp = array[i]
-                array[i] = array[j]
+        for j in 1..<array.count-i {
+            print(array,"comparing [\(j-1)] with [\(j)]")
+            if array[j] < array[j-1] {
+                let tmp = array[j-1]
+                array[j-1] = array[j]
                 array[j] = tmp
             }
         }
@@ -16,12 +17,7 @@ public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
     return array
 }
 
-
-var array = [Int]()
-
-for _ in 0...10 {
-    array.append(Int.random(in: 0...500))
-}
+var array = [4,2,1,3]
 
 print("before:",array)
 print("after:",BubbleSort(array))
diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
index 8f1ec80f8..5ce18ef9b 100644
--- a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -29,10 +29,10 @@ public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
     var array = elements
     
     for i in 0..<array.count {
-        for j in i+1..<array.count {
-            if array[j] < array[i] {
-                let tmp = array[i]
-                array[i] = array[j]
+        for j in 1..<array.count-i {
+            if array[j] < array[j-1] {
+                let tmp = array[j-1]
+                array[j-1] = array[j]
                 array[j] = tmp
             }
         }

From b90632c00634d276312c23ea4bb462060cd5225a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 2 Oct 2018 13:36:20 -0300
Subject: [PATCH 1442/1679] added imlementation information on readme

---
 Bubble Sort/README.markdown | 72 ++++++++++++++++++++++++++++++++++++-
 1 file changed, 71 insertions(+), 1 deletion(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index 93d370827..80161ce56 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Bubble Sort
 
-Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
+Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.Sometimes this algorithm is refered as Sinking sort, due to the larger, or heavier elements sinking to the end of the array.
 
 ##### Runtime:
 - Average: O(N^2)
@@ -12,3 +12,73 @@ Bubble sort is a sorting algorithm that is implemented by starting in the beginn
 ### Implementation:
 
 The implementation will not be shown as the average and worst runtimes show that this is a very inefficient algorithm. However, having a grasp of the concept will help you understand the basics of simple sorting algorithms.
+
+Bubble sort is a very simple sorting algorithm, it consists in comparing pairs of adjacent elements in the array, if the first element is larger, swap them, otherwise, you do nothing and go for the next comparison.
+This is accomplished by looking through the array `n` times, `n` being the amount of elements in the array.
+
+#### Example
+Let us take the array `[5, 1, 4, 2, 8]`, and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required.
+
+##### First Pass
+[ **5 1** 4 2 8 ] -> [ **1 5** 4 2 8 ], Here, algorithm compares the first two elements, and swaps since 5 > 1.
+
+[ 1 **5 4** 2 8 ] -> [ 1 **4 5** 2 8 ], Swap since 5 > 4 
+
+[ 1 4 **5 2** 8 ] -> [ 1 4 **2 5** 8 ], Swap since 5 > 2 
+
+[ 1 4 2 **5 8** ] -> [ 1 4 2 **5 8** ], Now, since these elements are already in order (8 > 5), algorithm does not swap them.
+
+##### Second Pass
+[ **1 4** 2 5 8 ] -> [ **1 4** 2 5 8 ]
+
+[ 1 **4 2** 5 8 ] -> [ 1 **2 4** 5 8 ], Swap since 4 > 2 
+
+[ 1 2 **4 5** 8 ] -> [ 1 2 **4 5** 8 ]
+
+[ 1 2 4 **5 8** ] -> [ 1 2 4 **5 8** ]
+Now, the array is already sorted, but the algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted.
+
+##### Third Pass
+[ **1 2** 4 5 8 ] -> [ **1 2** 4 5 8 ]
+
+[ 1 **2 4** 5 8 ] -> [ 1 **2 4** 5 8 ]
+
+[ 1 2 **4 5** 8 ] -> [ 1 2 **4 5** 8 ]
+
+[ 1 2 4 **5 8** ] -> [ 1 2 4 **5 8** ]
+
+This is the same for the forth and fifth passes.
+
+#### Code
+```swift
+for i in 0..<array.count {
+for j in 1..<array.count {
+if array[j] < array[i] {
+let tmp = array[i]
+array[i] = array[j]
+array[j] = tmp
+}
+}
+}
+return array
+```
+
+#### Optimization
+The bubble sort algorithm can be easily optimized by observing that the `n-th` pass finds the `n-th` largest element and puts it into its final place. So, the inner loop can avoid looking at the last `n-1` items when running for the `n-th` time:
+
+```swift
+for i in 0..<array.count {
+for j in 1..<array.count - i {
+if array[j] < array[i] {
+let tmp = array[i]
+array[i] = array[j]
+array[j] = tmp
+}
+}
+}
+return array
+```
+
+The only change made was on the second line, changing the interval from `1..<array.count` to `1..<array.count - i`, effectively cutting the number of comparisons by half.
+
+That said, this is still a terribly inefficient sorting algorithm.

From a2493d861d5fc09e3b73269e653b0c74f344b09b Mon Sep 17 00:00:00 2001
From: Daniil Subbotin <mail@subdan.ru>
Date: Wed, 3 Oct 2018 21:35:49 +0300
Subject: [PATCH 1443/1679] [Swift 4.2] Update Binary Search

---
 Binary Search/BinarySearch.playground/Contents.swift        | 5 -----
 Binary Search/BinarySearch.playground/contents.xcplayground | 2 +-
 2 files changed, 1 insertion(+), 6 deletions(-)

diff --git a/Binary Search/BinarySearch.playground/Contents.swift b/Binary Search/BinarySearch.playground/Contents.swift
index 715fb5dc2..f673f25c4 100644
--- a/Binary Search/BinarySearch.playground/Contents.swift	
+++ b/Binary Search/BinarySearch.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // An unsorted array of numbers
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
diff --git a/Binary Search/BinarySearch.playground/contents.xcplayground b/Binary Search/BinarySearch.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Binary Search/BinarySearch.playground/contents.xcplayground	
+++ b/Binary Search/BinarySearch.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 7457400c6df02091f0943296335933a4645e58e1 Mon Sep 17 00:00:00 2001
From: Daniil Subbotin <mail@subdan.ru>
Date: Wed, 3 Oct 2018 22:06:41 +0300
Subject: [PATCH 1444/1679] [Swift 4.2] Update Shuffle

---
 Shuffle/README.markdown                          | 8 ++------
 Shuffle/Shuffle.playground/Contents.swift        | 5 -----
 Shuffle/Shuffle.playground/Sources/Shuffle.swift | 9 ++-------
 3 files changed, 4 insertions(+), 18 deletions(-)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index ced138572..63868767b 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -33,8 +33,6 @@ You should see three different arrangements -- or [permutations](../Combinatoric
 
 This shuffle works *in place*, it modifies the contents of the original array. The algorithm works by creating a new array, `temp`, that is initially empty. Then we randomly choose an element from the original array and append it to `temp`, until the original array is empty. Finally, the temporary array is copied back into the original one.
 
-> **Note:** `random()` is a helper function that returns a random integer between 0 and the given maximum.
-
 This code works just fine but it's not very efficient. Removing an element from an array is an **O(n)** operation and we perform this **n** times, making the total algorithm **O(n^2)**. We can do better!
 
 ## The Fisher-Yates / Knuth shuffle
@@ -45,7 +43,7 @@ Here is a much improved version of the shuffle algorithm:
 extension Array {
   public mutating func shuffle() {
     for i in stride(from: count - 1, through: 1, by: -1) {
-      let j = random(i + 1)
+      let j = Int.random(in: 0...i)
       if i != j {
         swap(&self[i], &self[j])
       }
@@ -56,8 +54,6 @@ extension Array {
 
 Again, this picks objects at random. In the naive version we placed those objects into a new temporary array so we could keep track of which objects were already shuffled and which still remained to be done. In this improved algorithm, however, we'll move the shuffled objects to the end of the original array. 
 
-> **Note**: When you write `random(x)`, the largest number it will return is `x - 1`. We want to have `j <= i`, not `j < i`, so the largest number from the random number generator needs to be `i`, not `i - 1`. That's why we do `random(i + 1)`. If we didn't add that 1 to compensate, it would make some shuffle orders more likely to occur than others.
-
 Let's walk through the example. We have the array:
 
 	[ "a", "b", "c", "d", "e", "f", "g" ]
@@ -99,7 +95,7 @@ Here is the code:
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
-    let j = random(i + 1)
+    let j = Int.random(in: 0...i)
     if i != j {
       a[i] = a[j]
     }
diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index ac9181660..9c3cabd27 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 var list = [ "a", "b", "c", "d", "e", "f", "g" ]
diff --git a/Shuffle/Shuffle.playground/Sources/Shuffle.swift b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
index 553832d43..500d3c245 100644
--- a/Shuffle/Shuffle.playground/Sources/Shuffle.swift
+++ b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
@@ -1,10 +1,5 @@
 import Foundation
 
-/* Returns a random integer between 0 and n-1. */
-public func random(_ n: Int) -> Int {
-  return Int(arc4random_uniform(UInt32(n)))
-}
-
 extension Array {
   /*
    Randomly shuffles the array in-place
@@ -13,7 +8,7 @@ extension Array {
    */
   public mutating func shuffle() {
     for i in (1...count-1).reversed() {
-      let j = random(i + 1)
+      let j = Int.random(in: 0...i)
       if i != j {
         let t = self[i]
         self[i] = self[j]
@@ -29,7 +24,7 @@ extension Array {
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
-    let j = random(i + 1)
+    let j = Int.random(in: 0...i)
     if i != j {
       a[i] = a[j]
     }

From 04127deb3d50256856e9d41ebff580d662747dbb Mon Sep 17 00:00:00 2001
From: mmcbee1 <meghankmcbee@gmail.com>
Date: Wed, 3 Oct 2018 21:49:24 -0700
Subject: [PATCH 1445/1679] [Swift 4.2] Update Stack

---
 Stack/Stack.playground/Contents.swift        | 6 ------
 Stack/Stack.playground/contents.xcplayground | 2 +-
 2 files changed, 1 insertion(+), 7 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index e9e3e9a57..1eb705f20 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,9 +1,3 @@
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*
   Stack
 
diff --git a/Stack/Stack.playground/contents.xcplayground b/Stack/Stack.playground/contents.xcplayground
index 5da2641c9..a40c0f554 100644
--- a/Stack/Stack.playground/contents.xcplayground
+++ b/Stack/Stack.playground/contents.xcplayground
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
+<playground version='5.0' target-platform='ios' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From c2d0169719cf1c76533c9402fcd96248e3e6978e Mon Sep 17 00:00:00 2001
From: Ashish Kakkad <ashishkakkad8@gmail.com>
Date: Thu, 4 Oct 2018 22:07:39 +0530
Subject: [PATCH 1446/1679] Swift 4.2 [Array2D]

---
 Array2D/Array2D.playground/Contents.swift     | 5 -----
 Array2D/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 2 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 77c0b364c..d31d77540 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*
  Two-dimensional array with a fixed number of rows and columns.
  This is mostly handy for games that are played on a grid, such as chess.
diff --git a/Array2D/Tests/Tests.xcodeproj/project.pbxproj b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
index a0fb1480b..af9b7c3b8 100644
--- a/Array2D/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
@@ -226,7 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -238,7 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};

From c7d17128ccda1f80da11e85e5a381102e1fab8c6 Mon Sep 17 00:00:00 2001
From: Ashish Kakkad <ashishkakkad8@gmail.com>
Date: Thu, 4 Oct 2018 22:51:29 +0530
Subject: [PATCH 1447/1679] [Swift 4.2] Graph

---
 Graph/Graph.playground/Contents.swift              |  6 ------
 Graph/Graph.playground/timeline.xctimeline         |  2 +-
 Graph/Graph.xcodeproj/project.pbxproj              | 14 +++++++++-----
 .../xcshareddata/xcschemes/Graph.xcscheme          |  2 +-
 .../xcshareddata/xcschemes/GraphTests.xcscheme     |  2 +-
 Graph/GraphTests/GraphTests.swift                  |  7 -------
 6 files changed, 12 insertions(+), 21 deletions(-)

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index 0410942f8..fde396e64 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,11 +1,5 @@
 import Graph
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
-
 for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 
   let v1 = graph.createVertex(1)
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph.playground/timeline.xctimeline
index 6afe06b6f..59717856a 100644
--- a/Graph/Graph.playground/timeline.xctimeline
+++ b/Graph/Graph.playground/timeline.xctimeline
@@ -3,7 +3,7 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Graph/Graph.playground#CharacterRangeLen=12&amp;CharacterRangeLoc=1322&amp;EndingColumnNumber=4&amp;EndingLineNumber=45&amp;StartingColumnNumber=7&amp;StartingLineNumber=44&amp;Timestamp=523289935.918656"
+         documentLocation = "file:///Users/ashishkakkad/Ashish/iOS/GitHub/swift-algorithm-club/Graph/Graph.playground#CharacterRangeLen=12&amp;CharacterRangeLoc=1238&amp;EndingColumnNumber=4&amp;EndingLineNumber=39&amp;StartingColumnNumber=7&amp;StartingLineNumber=38&amp;Timestamp=560365411.415967"
          selectedRepresentationIndex = "1"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index 17a5a7d6b..790f6ac18 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -158,7 +158,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					49BFA2FC1CDF886B00522D66 = {
@@ -251,12 +251,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -289,7 +291,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -308,12 +310,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -339,7 +343,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -364,7 +368,7 @@
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -386,7 +390,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index a12d85dad..73524effc 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index 28df1be50..873f1d7b4 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 92a4ce828..289d9aa64 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -10,13 +10,6 @@ import XCTest
 
 class GraphTests: XCTestCase {
 
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()

From 7442c10f596fec191eacbec644fcf8d5fae7f30a Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 22:34:48 +0500
Subject: [PATCH 1448/1679] Update Z-Algorithm up to Swift 4.2.

---
 Z-Algorithm/README.markdown                         |  5 ++---
 Z-Algorithm/ZAlgorithm.swift                        |  3 +--
 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift | 10 ++--------
 Z-Algorithm/ZetaAlgorithm.swift                     |  2 +-
 4 files changed, 6 insertions(+), 14 deletions(-)

diff --git a/Z-Algorithm/README.markdown b/Z-Algorithm/README.markdown
index 8b84c28bf..a6423be03 100644
--- a/Z-Algorithm/README.markdown
+++ b/Z-Algorithm/README.markdown
@@ -28,8 +28,7 @@ This a simple description of the idea that is behind this algorithm. There are a
 Here is the code of the function that computes the Z-array:
 ```swift
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-    let pattern = Array(ptrn.characters)
+    let pattern = Array(ptrn)
     let patternLength: Int = pattern.count
 
     guard patternLength > 0 else {
@@ -131,7 +130,7 @@ The Z-Algorithm discussed above leads to the simplest linear-time string matchin
 extension String {
 
     func indexesOf(pattern: String) -> [Int]? {
-        let patternLength: Int = pattern.characters.count
+        let patternLength: Int = pattern.count
         /* Let's calculate the Z-Algorithm on the concatenation of pattern and text */
         let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
index 969a3599b..65acaabd1 100644
--- a/Z-Algorithm/ZAlgorithm.swift
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -9,8 +9,7 @@
 import Foundation
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-  let pattern = Array(ptrn.characters)
+  let pattern = Array(ptrn)
   let patternLength = pattern.count
 
   guard patternLength > 0 else {
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index d057080a1..56aa92170 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -1,13 +1,7 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-  let pattern = Array(ptrn.characters)
+  let pattern = Array(ptrn)
   let patternLength = pattern.count
 
   guard patternLength > 0 else {
@@ -65,7 +59,7 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
 extension String {
 
   func indexesOf(pattern: String) -> [Int]? {
-    let patternLength = pattern.characters.count
+    let patternLength = pattern.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
     guard zeta != nil else {
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
index e60c1617f..f2c453364 100644
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -11,7 +11,7 @@ import Foundation
 extension String {
 
   func indexesOf(pattern: String) -> [Int]? {
-    let patternLength = pattern.characters.count
+    let patternLength = pattern.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
     guard zeta != nil else {

From 3c3168ea6e8d01972727d8db5ebea10f4aa794d3 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:13:45 +0500
Subject: [PATCH 1449/1679] Update Deque up to Swift 4.2.

---
 Deque/Deque-Simple.swift              | 2 +-
 Deque/Deque.playground/Contents.swift | 5 -----
 Deque/README.markdown                 | 2 +-
 3 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/Deque/Deque-Simple.swift b/Deque/Deque-Simple.swift
index f4f5f0409..fc0fcb2b2 100644
--- a/Deque/Deque-Simple.swift
+++ b/Deque/Deque-Simple.swift
@@ -21,7 +21,7 @@ public struct Deque<T> {
   }
 
   public mutating func enqueueFront(_ element: T) {
-    array.insert(element, atIndex: 0)
+    array.insert(element, at: 0)
   }
 
   public mutating func dequeue() -> T? {
diff --git a/Deque/Deque.playground/Contents.swift b/Deque/Deque.playground/Contents.swift
index df9b57a5e..9e7b22c02 100644
--- a/Deque/Deque.playground/Contents.swift
+++ b/Deque/Deque.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 public struct Deque<T> {
   private var array = [T]()
 
diff --git a/Deque/README.markdown b/Deque/README.markdown
index fda1de5f8..f3172e16e 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -23,7 +23,7 @@ public struct Deque<T> {
   }
 
   public mutating func enqueueFront(_ element: T) {
-    array.insert(element, atIndex: 0)
+    array.insert(element, at: 0)
   }
 
   public mutating func dequeue() -> T? {

From ed155f211d5b98fc54e3de40b55680367b5e1e93 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:21:00 +0500
Subject: [PATCH 1450/1679] Remove notice from GCD playground.

---
 GCD/GCD.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index f0fceb0da..c44f28310 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Recursive version
 func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b

From 945c7cbe8e6f79dd31f4e0f3468d22d0f5f024c2 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:28:36 +0500
Subject: [PATCH 1451/1679] Remove notice from FixedSizeArray playground.

---
 Fixed Size Array/FixedSizeArray.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 8b5bc1147..616f8443d 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 /*
  An unordered array with a maximum size.
  

From 8ea8a6590457b2ba931444ea75506e329850e788 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:34:40 +0500
Subject: [PATCH 1452/1679] Update Insertion Sort up to Swift 4.2.

---
 .../InsertionSort.playground/Contents.swift   |  5 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 26 ++++++++++++++++---
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 23 insertions(+), 10 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 9a10ec04a..184fc36e4 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /// Performs the Insertion sort algorithm to a given array
 ///
 /// - Parameters:
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj
index ee3ca1cae..e9ea3bc53 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,12 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -145,14 +145,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -191,14 +199,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -230,7 +246,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -242,7 +259,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..afd69e6a7 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 8943b0925cc937b7e87c5d5b7f39e9ca00e750d1 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:49:35 +0200
Subject: [PATCH 1453/1679] Update project with Xcode 10.

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 24 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 29 insertions(+), 5 deletions(-)
 create mode 100644 Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj
index 6493fd153..f0649ba26 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -141,14 +141,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -188,14 +196,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -228,7 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -240,7 +256,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..afd69e6a7 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 06cdc9f9f779ca3c18fca97419060de0bde350ea Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:50:05 +0200
Subject: [PATCH 1454/1679] Remove use of deprecated `characters` property.

---
 Bloom Filter/Tests/BloomFilterTests.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 30df702a7..d88ec0a31 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -6,7 +6,7 @@ import XCTest
 func djb2(_ x: String) -> Int {
   var hash = 5381
 
-  for char in x.characters {
+  for char in x {
     hash = ((hash << 5) &+ hash) &+ char.hashValue
   }
 
@@ -16,7 +16,7 @@ func djb2(_ x: String) -> Int {
 func sdbm(_ x: String) -> Int {
   var hash = 0
 
-  for char in x.characters {
+  for char in x {
     hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
   }
 

From 6ef7a6e6ad07781320418d276a67eaa4e3d635d7 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:57:46 +0200
Subject: [PATCH 1455/1679] Xcode 10 automated changes.

---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Bloom Filter/BloomFilter.playground/timeline.xctimeline   | 6 ------
 2 files changed, 8 insertions(+), 6 deletions(-)
 create mode 100644 Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Bloom Filter/BloomFilter.playground/timeline.xctimeline

diff --git a/Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bloom Filter/BloomFilter.playground/timeline.xctimeline b/Bloom Filter/BloomFilter.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Bloom Filter/BloomFilter.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 4201fb4fc8bfefe4ab9651f5c393c55ddfd5f294 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:58:26 +0200
Subject: [PATCH 1456/1679] Update for Swift 4.2.

* Remove the top code snippet, as per instructions.
* Remove use of deprecated `characters` property.
---
 Bloom Filter/BloomFilter.playground/Contents.swift | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 9e4a89351..7a3719d57 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Playground - noun: a place where people can play
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+
 public class BloomFilter<T> {
   fileprivate var array: [Bool]
   private var hashFunctions: [(T) -> Int]
@@ -54,7 +51,7 @@ public class BloomFilter<T> {
 
 func djb2(x: String) -> Int {
   var hash = 5381
-  for char in x.characters {
+  for char in x {
     hash = ((hash << 5) &+ hash) &+ char.hashValue
   }
   return Int(hash)
@@ -62,7 +59,7 @@ func djb2(x: String) -> Int {
 
 func sdbm(x: String) -> Int {
   var hash = 0
-  for char in x.characters {
+  for char in x {
     hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
   }
   return Int(hash)

From 849309c5eb5d2ef29918940536cc1b011b665b3c Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 21:45:50 +0200
Subject: [PATCH 1457/1679] Add note about Hasher in README.

* Adds a section about another Bloom filter approach, using only a single hashing function with Swift 4.2's `Hasher`.
* Adds links to some more documentation and a blog post implementing the Bloom filter in this way.
* Adds my name as updater.
---
 Bloom Filter/README.markdown | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index 3fff0a379..4364db857 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -100,4 +100,29 @@ public func query(_ value: T) -> Bool {
 
 If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop.
 
-*Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans.*
+## Another approach
+
+Another approach to create different hashes of an element for use in the Bloom filter, is to use the same hash function for every iteration, but combine it with different random numbers. This can help, because finding good hashing functions is hard, but combining them is equally non-trivial.
+
+```
+hash("Hello world!") >> hash(987654321) // would flip bit 8
+hash("Hello world!") >> hash(123456789) // would flip bit 2
+```
+
+Since Swift 4.2, `Hasher` is now included in the Standard library, which is designed to reduce multiple hashes to a single hash in an efficient manner. This makes combining the hashes trivial.
+
+```
+private func computeHashes(_ value: T) -> [Int] {
+  return randomSeeds.map() { seed in
+		let hasher = Hasher()
+		hasher.combine(seed)
+		hasher.combine(value)
+		let hashValue = hasher.finalize()
+		return abs(hashValue % array.count)
+	}
+}
+```
+
+If you want to learn more about this approach, you can read about the [Hasher documentation](https://developer.apple.com/documentation/swift/hasher) or Soroush Khanlou's [Swift 4.2 Bloom filter](http://khanlou.com/2018/09/bloom-filters/) implementation.
+
+*Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans. Updated by Bruno Scheele.*

From a56b88370d49aaf0d5640ca59d955f61178108f8 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:33:32 -0400
Subject: [PATCH 1458/1679] [Swift 4.2] Update Binary Search Tree

---
 .../Contents.swift                            |  5 --
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 47 ++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Contents.swift                            |  5 --
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++
 .../Sources/BinarySearch.swift                | 52 -------------------
 .../contents.xcworkspacedata                  |  7 ---
 9 files changed, 64 insertions(+), 78 deletions(-)
 create mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
 delete mode 100644 Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 8c06ae9e1..ec9902283 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index f4c3f65c7..ff594fff8 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 46;
+	objectVersion = 51;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -83,17 +83,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 3.2";
+			compatibilityVersion = "Xcode 10.0";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -141,13 +141,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -185,13 +195,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +230,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -218,10 +239,15 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -230,10 +256,15 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..afd69e6a7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index afa4338a9..2b5dcc341 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift b/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
deleted file mode 100644
index d6623e355..000000000
--- a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift	
+++ /dev/null
@@ -1,52 +0,0 @@
-/**
- Binary Search
- 
- Recursively splits the array in half until the value is found.
- 
- If there is more than one occurrence of the search key in the array, then
- there is no guarantee which one it finds.
- 
- Note: The array must be sorted!
- **/
-
-import Foundation
-
-// The recursive version of binary search.
-
-public func binarySearch<T: Comparable>(_ a: [T], key: T, range: Range<Int>) -> Int? {
-    if range.lowerBound >= range.upperBound {
-        return nil
-    } else {
-        let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
-        if a[midIndex] > key {
-            return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
-        } else if a[midIndex] < key {
-            return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
-        } else {
-            return midIndex
-        }
-    }
-}
-
-/**
- The iterative version of binary search.
- 
- Notice how similar these functions are. The difference is that this one
- uses a while loop, while the other calls itself recursively.
- **/
-
-public func binarySearch<T: Comparable>(_ a: [T], key: T) -> Int? {
-    var lowerBound = 0
-    var upperBound = a.count
-    while lowerBound < upperBound {
-        let midIndex = lowerBound + (upperBound - lowerBound) / 2
-        if a[midIndex] == key {
-            return midIndex
-        } else if a[midIndex] < key {
-            lowerBound = midIndex + 1
-        } else {
-            upperBound = midIndex
-        }
-    }
-    return nil
-}
diff --git a/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata	
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>

From 54ac83543efd7bb47d1a976fcf9016ac618c3793 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:38:01 -0400
Subject: [PATCH 1459/1679] [Swift 4.2] Update Binary Search Tree

---
 .../Contents.swift                            |  5 ++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 47 ++++---------------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ----
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Contents.swift                            |  5 ++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ----
 7 files changed, 19 insertions(+), 64 deletions(-)
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index ec9902283..8c06ae9e1 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index ff594fff8..f4c3f65c7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 51;
+	objectVersion = 46;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -83,17 +83,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 1000;
+				LastUpgradeCheck = 0720;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 1000;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 10.0";
+			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -141,23 +141,13 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
-				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
-				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
-				CLANG_WARN_STRICT_PROTOTYPES = YES;
-				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -195,23 +185,13 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
-				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
-				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
-				CLANG_WARN_STRICT_PROTOTYPES = YES;
-				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -230,7 +210,6 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -239,15 +218,10 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = (
-					"$(inherited)",
-					"@executable_path/../Frameworks",
-					"@loader_path/../Frameworks",
-				);
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.2;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -256,15 +230,10 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = (
-					"$(inherited)",
-					"@executable_path/../Frameworks",
-					"@loader_path/../Frameworks",
-				);
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.2;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index afd69e6a7..8ef8d8581 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1000"
+   LastUpgradeVersion = "0720"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 2b5dcc341..afa4338a9 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>

From d6099b34226cef00bc5e83fa503437c88fbd39b2 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:38:36 -0400
Subject: [PATCH 1460/1679] [Swift 4.2] Dijkstra Algorithm

---
 Dijkstra Algorithm/Dijkstra.playground/Contents.swift     | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../VisualizedDijkstra.playground/Contents.swift          | 5 -----
 .../VisualizedDijkstra.playground/Sources/Window.swift    | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 5 files changed, 17 insertions(+), 11 deletions(-)
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 1cd1254b1..7c7f1a4b0 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,11 +1,6 @@
 //: Playground - noun: a place where people can play
 import Foundation
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
diff --git a/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
index 8e61ef49b..de6b49834 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
@@ -9,11 +9,6 @@
 import UIKit
 import PlaygroundSupport
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*:
  First of all, let's set up colors for our window and graph. The visited color will be applied to visited vertices. The checking color will be applied to an edge and an edge neighbor every time the algorithm is checking some vertex neighbors. And default colors are just initial colors for elements.
  */
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
index 73c512e6b..9a169b8c7 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -134,7 +134,7 @@ public class Window: UIView, GraphDelegate {
         let origin = CGPoint(x: center.x - 25, y: 100)
         let activityIndicatorFrame = CGRect(origin: origin, size: size)
         activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
-        activityIndicator.activityIndicatorViewStyle = .whiteLarge
+        activityIndicator.style = .whiteLarge
     }
 
     @objc private func createGraphButtonTap() {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From e6a2aa77f23a515081d8bc806e46efc81d785321 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:43:56 -0400
Subject: [PATCH 1461/1679] [Swift 4.2] Update Binary Search Tree

---
 .../Contents.swift                            |  5 ---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 31 ++++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Contents.swift                            |  5 ---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 7 files changed, 52 insertions(+), 15 deletions(-)
 create mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 8c06ae9e1..ec9902283 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index f4c3f65c7..d7c687e0c 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -141,13 +141,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -185,13 +195,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +230,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -221,7 +242,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -233,7 +255,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..afd69e6a7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index afa4338a9..2b5dcc341 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 1d452b31d82f06ad964ae5acd6d0bd7e8b2cadd8 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 22:01:22 -0400
Subject: [PATCH 1462/1679] [Swift 4.2] Queue

---
 Queue/Tests/Tests.xcodeproj/project.pbxproj   | 26 ++++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 31 insertions(+), 5 deletions(-)
 create mode 100644 Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
index a554fd16e..f7fc3e048 100644
--- a/Queue/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -141,14 +141,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -187,14 +195,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -226,7 +242,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -238,7 +255,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..afd69e6a7 100644
--- a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 8eb0b26584b69603ca64ae634cfee1859a72be69 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 22:05:37 -0400
Subject: [PATCH 1463/1679] [Swift 4.2] Queue

---
 Queue/Queue.playground/Contents.swift                     | 6 ------
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Queue/Tests/Tests.xcodeproj/project.pbxproj               | 4 ++--
 3 files changed, 10 insertions(+), 8 deletions(-)
 create mode 100644 Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 22d2a84ca..08327783f 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -1,9 +1,3 @@
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*
   Queue
 
diff --git a/Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
index f7fc3e048..f927aba0d 100644
--- a/Queue/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -242,7 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
@@ -255,7 +255,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Release;

From 01ba34cc5084c7f70beb3955d71918f75fb30bd0 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 22:17:58 -0400
Subject: [PATCH 1464/1679] [Swift 4.2] Merge Sort

---
 Merge Sort/MergeSort.playground/Contents.swift            | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index b05332bfe..ca1347890 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 /* Top-down recursive version */
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
diff --git a/Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 3f0bdc6ec0009bf08251458a04b11631d13cb7c7 Mon Sep 17 00:00:00 2001
From: danielchick <daniel.chick@hotmail.com>
Date: Thu, 4 Oct 2018 22:44:53 -0500
Subject: [PATCH 1465/1679] [Swift 4.2] Update Tree

---
 Tree/Tree.playground/Contents.swift        | 4 ++--
 Tree/Tree.playground/contents.xcplayground | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 49cf41054..06f992fa8 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -1,8 +1,8 @@
 //: Playground - noun: a place where people can play
 
 // last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
+#if swift(>=4.2)
+print("Hello, Swift 4.2!")
 #endif
 
 let tree = TreeNode<String>(value: "beverages")
diff --git a/Tree/Tree.playground/contents.xcplayground b/Tree/Tree.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Tree/Tree.playground/contents.xcplayground
+++ b/Tree/Tree.playground/contents.xcplayground
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From f24a004b0420dcd3dc3156b368852e30b9841e89 Mon Sep 17 00:00:00 2001
From: imvm <imvm@cin.ufpe.br>
Date: Fri, 5 Oct 2018 02:51:06 -0300
Subject: [PATCH 1466/1679] Remove notice from Strassen Multiplication Matrix
 playground

---
 .../StrassensMatrixMultiplication.playground/Contents.swift  | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 409e28c52..6b9314557 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 var A = Matrix(rows: 2, columns: 4, initialValue: 0)

From 6ab163e4431ba09a6870b4b101dc536cffcf759d Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:34:07 +0200
Subject: [PATCH 1467/1679] Update to Xcode 10.

---
 Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj         | 6 +++++-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme | 4 +---
 3 files changed, 14 insertions(+), 4 deletions(-)
 create mode 100644 Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 84a305784..6df507720 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,7 +83,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -145,12 +145,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -197,12 +199,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 538a6f4fa..afd69e6a7 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From bd0c74e0f4342d3a303779b6fb93beac96eed428 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:49:56 +0200
Subject: [PATCH 1468/1679] Refactor to remove dependency on pre-Swift 4.

The code used to depend on pre-Swift 4's optional operators, which have since been replaced. Now, the one possible case for comparing a potential `nil` maximum value has been handled.
---
 Bucket Sort/BucketSort.swift | 31 +++++--------------------------
 1 file changed, 5 insertions(+), 26 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 108073288..4c2abd372 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -20,31 +20,6 @@
 //
 //
 
-import Foundation
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-  switch (lhs, rhs) {
-  case let (l?, r?):
-    return l < r
-  case (nil, _?):
-    return true
-  default:
-    return false
-  }
-}
-
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-  switch (lhs, rhs) {
-  case let (l?, r?):
-    return l >= r
-  default:
-    return !(lhs < rhs)
-  }
-}
-
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
@@ -87,7 +62,11 @@ private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> B
     let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
 
-    return totalCapacity >= maximumValue
+    guard let max = maximumValue else {
+        return false
+    }
+    
+    return totalCapacity >= max
 }
 
 //////////////////////////////////////

From 8f2bf19304b379d60551359f913080e22b8d7ed3 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:55:40 +0200
Subject: [PATCH 1469/1679] Change playground as well.

---
 .../Sources/BucketSort.swift                  | 31 +++----------------
 .../contents.xcplayground                     |  2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 3 files changed, 14 insertions(+), 27 deletions(-)
 create mode 100644 Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index bafd216fa..64408eca4 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -20,31 +20,6 @@
 //
 //
 
-import Foundation
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-    switch (lhs, rhs) {
-    case let (l?, r?):
-        return l < r
-    case (nil, _?):
-        return true
-    default:
-        return false
-    }
-}
-
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-    switch (lhs, rhs) {
-    case let (l?, r?):
-        return l >= r
-    default:
-        return !(lhs < rhs)
-    }
-}
-
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
@@ -87,7 +62,11 @@ private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> B
     let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
     
-    return totalCapacity >= maximumValue
+    guard let max = maximumValue else {
+        return false
+    }
+    
+    return totalCapacity >= max
 }
 
 //////////////////////////////////////
diff --git a/Bucket Sort/BucketSort.playground/contents.xcplayground b/Bucket Sort/BucketSort.playground/contents.xcplayground
index 5da2641c9..9f5f2f40c 100644
--- a/Bucket Sort/BucketSort.playground/contents.xcplayground	
+++ b/Bucket Sort/BucketSort.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From f28973201916ac83c3b95f4115215a09715d22b7 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:58:24 +0200
Subject: [PATCH 1470/1679] Add credit to README.

---
 Bucket Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index f572fc9a1..f2708d71e 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -256,4 +256,4 @@ The following are some of the variation to the general [Bucket Sort](https://en.
 - [Postman Sort](https://en.wikipedia.org/wiki/Bucket_sort#Postman.27s_sort)
 - [Shuffle Sort](https://en.wikipedia.org/wiki/Bucket_sort#Shuffle_sort)
 
-*Written for Swift Algorithm Club by Barbara Rodeker. Images from Wikipedia.*
+*Written for Swift Algorithm Club by Barbara Rodeker. Images from Wikipedia. Updated by Bruno Scheele.*

From 184786db68a17e40cfe2e4de6f7f212a84db42d4 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Fri, 5 Oct 2018 21:27:02 -0400
Subject: [PATCH 1471/1679] [Swift 4.2] Threaded Binary Tree

---
 .../ThreadedBinaryTree.playground/Contents.swift          | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index 4ce9d8157..ece1966e0 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From cafba43a1c38bad9f62400e42ef46b9f51c60df3 Mon Sep 17 00:00:00 2001
From: Aleph Retamal <retamal.ph@gmail.com>
Date: Sat, 6 Oct 2018 18:11:50 +1000
Subject: [PATCH 1472/1679] [Swift 4.2] Update K-Means

---
 K-Means/KMeans.swift                          |  2 +-
 K-Means/Tests/KMeansTests.swift               |  7 ------
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 24 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 5 files changed, 30 insertions(+), 13 deletions(-)
 create mode 100644 K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 4a89a3fae..bccc6efd3 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -12,7 +12,7 @@ class KMeans<Label: Hashable> {
   }
 
   private func indexOfNearestCenter(_ x: Vector, centers: [Vector]) -> Int {
-    var nearestDist = DBL_MAX
+    var nearestDist = Double.greatestFiniteMagnitude
     var minIndex = 0
 
     for (idx, center) in centers.enumerated() {
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index e6f4b08a1..7e0c93004 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,13 +10,6 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
   func genPoints(_ numPoints: Int, numDimensions: Int) -> [Vector] {
     var points = [Vector]()
     for _ in 0..<numPoints {
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 139f6baf5..1cbd139e5 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,11 +85,11 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				TargetAttributes = {
 					B80894DF1C852D100018730E = {
 						CreatedOnToolsVersion = 7.2.1;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -137,12 +137,20 @@
 		B80894D91C852CDC0018730E /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -162,12 +170,20 @@
 		B80894DA1C852CDC0018730E /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -229,7 +245,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -271,7 +287,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 2b401e86e..73ba8f37d 100644
--- a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 8ed7739498a2a3fa2c8974ab48eecfcec8863cbf Mon Sep 17 00:00:00 2001
From: Aleph Retamal <retamal.ph@gmail.com>
Date: Sat, 6 Oct 2018 19:28:22 +1000
Subject: [PATCH 1473/1679] [Swift 4.2] Update Egg Drop Problem

---
 Egg Drop Problem/EggDrop.playground/Contents.swift        | 4 ----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../xcshareddata/WorkspaceSettings.xcsettings             | 5 +++++
 3 files changed, 13 insertions(+), 4 deletions(-)
 create mode 100644 Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
index 0b707da98..decaacdca 100644
--- a/Egg Drop Problem/EggDrop.playground/Contents.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -1,7 +1,3 @@
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 drop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
 drop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
 drop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
diff --git a/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..0c67376eb
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,5 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict/>
+</plist>

From 2d60bb78c249085c47714474d27d97297a09fa2f Mon Sep 17 00:00:00 2001
From: askari01 <farrukh.askari01@gmail.com>
Date: Sat, 6 Oct 2018 23:02:19 +0500
Subject: [PATCH 1474/1679] 2 sum problem with swift 4.2

---
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift | 5 +----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift | 5 +----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 4 files changed, 18 insertions(+), 8 deletions(-)
 create mode 100644 Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 26bfae449..00a39b04a 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Two Sum
-// Last checked with: Version 9.0 (9A235)
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// Last checked with: Version 10.0 (10A255)
 
 func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
     var dict = [Int: Int]()
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index 4cb3d9283..469c15b5f 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Playground - noun: a place where people can play
-// Last checked with: Version 9.0 beta 4 (9M189t)
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// Last checked with: Version 10.0 (10A255)
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From f0ce485316036d977470c7d38e9a1959e8a60f08 Mon Sep 17 00:00:00 2001
From: askari01 <farrukh.askari01@gmail.com>
Date: Sat, 6 Oct 2018 23:08:23 +0500
Subject: [PATCH 1475/1679] updated readme for 2 sum problem with swift 4.2

---
 Two-Sum Problem/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 4d8ffcd95..bbd033343 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -168,4 +168,4 @@ I'm quite enamored by this little algorithm. It shows that with some basic prepr
 
 * [3Sum / 4Sum](https://github.com/raywenderlich/swift-algorithm-club/tree/master/3Sum%20and%204Sum)
 
-*Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser*
+*Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser updated to swift 4.2 by Farrukh Askari*

From 86d6cd114d34a602f987ab0f7a7b21d1ff7580ee Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 19:06:01 +1100
Subject: [PATCH 1476/1679] [Swift 4.2] Update Karatsuba multiplication

Changed the way the characters in a String were accessed since `characters` was deprecated on Swift 4.0.
Removed the code snippet at the beggining of the file.
---
 .../Contents.swift                              | 17 +++++++----------
 .../xcshareddata/IDEWorkspaceChecks.plist       |  8 ++++++++
 .../KaratsubaMultiplication.swift               | 12 ++++++------
 3 files changed, 21 insertions(+), 16 deletions(-)
 create mode 100644 Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 04aff1ec4..e0ce23b19 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -1,10 +1,7 @@
 //: Playground - noun: a place where people can play
 
 import Foundation
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4")
-#endif
+
 precedencegroup ExponentiativePrecedence {
   higherThan: MultiplicationPrecedence
   lowerThan: BitwiseShiftPrecedence
@@ -18,8 +15,8 @@ func ^^ (radix: Int, power: Int) -> Int {
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
-  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
+  let num1Array = String(num1).reversed().map { Int(String($0))! }
+  let num2Array = String(num2).reversed().map { Int(String($0))! }
   
   var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
   
@@ -38,14 +35,14 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
 
 // Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
+  let num1String = String(num1)
+  let num2String = String(num2)
   
-  guard num1Array.count > 1 && num2Array.count > 1 else {
+  guard num1String.count > 1 && num2String.count > 1 else {
     return multiply(num1, by: num2)
   }
   
-  let n = max(num1Array.count, num2Array.count)
+  let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
   
   let a = num1 / 10^^nBy2
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index fb20a667d..a82e82658 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -20,14 +20,14 @@ func ^^ (radix: Int, power: Int) -> Int {
 }
 
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
+  let num1String = String(num1)
+  let num2String = String(num2)
   
-  guard num1Array.count > 1 && num2Array.count > 1 else {
-    return num1 * num2
+  guard num1String.count > 1 && num2String.count > 1 else {
+    return multiply(num1, by: num2)
   }
-  
-  let n = max(num1Array.count, num2Array.count)
+
+  let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
   
   let a = num1 / 10^^nBy2

From ab20d205384c4fc40908f99dcfb941d485cac3c6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 19:22:09 +1100
Subject: [PATCH 1477/1679] [Swift 4.2] Update README.md for Karatsuba
 multiplication

---
 Karatsuba Multiplication/README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index c86f69831..3a48ed39d 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -71,15 +71,15 @@ Here's the full implementation. Note that the recursive algorithm is most effici
 
 ```swift
 // Karatsuba Multiplication
-func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
+  func karatsuba(_ num1: Int, by num2: Int) -> Int {
+  let num1String = String(num1)
+  let num2String = String(num2)
   
-  guard num1Array.count > 1 && num2Array.count > 1 else {
-    return num1*num2
+  guard num1String.count > 1 && num2String.count > 1 else {
+  return multiply(num1, by: num2)
   }
   
-  let n = max(num1Array.count, num2Array.count)
+  let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
   
   let a = num1 / 10^^nBy2

From 2d1d22316401f52ac6a08325c781e812e40542c5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 20:20:30 +1100
Subject: [PATCH 1478/1679] [Swift 4.2] added tests

---
 .travis.yml                                   |   1 +
 .../KaratsubaMultiplication.swift             |  31 +-
 .../Tests/KaratsubaMultiplicationTests.swift  |  17 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 305 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++++
 .../Tests/Tests/Info.plist                    |  22 ++
 .../contents.xcworkspacedata                  |   7 +
 7 files changed, 434 insertions(+), 5 deletions(-)
 create mode 100644 Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift
 create mode 100644 Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Karatsuba Multiplication/Tests/Tests/Info.plist

diff --git a/.travis.yml b/.travis.yml
index edf1cf89f..56e205656 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -48,6 +48,7 @@ script:
 - xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Karatsuba\ Multiplication/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 
 after_success:
 
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index a82e82658..3d14a243a 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -19,27 +19,48 @@ func ^^ (radix: Int, power: Int) -> Int {
   return Int(pow(Double(radix), Double(power)))
 }
 
+// Long Multiplication - O(n^2)
+func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
+  let num1Array = String(num1).reversed().map { Int(String($0))! }
+  let num2Array = String(num2).reversed().map { Int(String($0))! }
+
+  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
+    }
+    product[i + num2Array.count] += carry
+  }
+
+  return Int(product.reversed().map { String($0) }.reduce("", +))!
+}
+
+// Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1String = String(num1)
   let num2String = String(num2)
-  
+
   guard num1String.count > 1 && num2String.count > 1 else {
     return multiply(num1, by: num2)
   }
 
   let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
-  
+
   let a = num1 / 10^^nBy2
   let b = num1 % 10^^nBy2
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
-  
+
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
   let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-  
+
   let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-  
+
   return product
 }
diff --git a/Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift b/Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift
new file mode 100644
index 000000000..379c9e812
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift	
@@ -0,0 +1,17 @@
+//
+//  KaratsubaMultiplicationTests.swift
+//  Tests
+//
+//  Created by Afonso Graça on 8/10/18.
+//
+
+import XCTest
+
+final class KaratsubaMultiplicationTests: XCTestCase {
+
+    func testReadmeExample() {
+        let subject = karatsuba(1234, by: 5678)
+
+        XCTAssertEqual(subject, 7006652)
+    }
+}
diff --git a/Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj b/Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..ef23067ee
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,305 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 50;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		6AF099AC216B54E200F69B16 /* KaratsubaMultiplication.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AF099AB216B54E200F69B16 /* KaratsubaMultiplication.swift */; };
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+			);
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+		};
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+				GCC_NO_COMMON_BLOCKS = YES;
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+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
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+				);
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+			};
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+		};
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+			buildSettings = {
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+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
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+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				CODE_SIGN_STYLE = Automatic;
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
+				MACOSX_DEPLOYMENT_TARGET = 10.14;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				MTL_FAST_MATH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
+				SWIFT_VERSION = 4.2;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		6AF0999B216B545D00F69B16 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				6AF0999C216B545D00F69B16 /* Debug */,
+				6AF0999D216B545D00F69B16 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		6AF099A8216B54D500F69B16 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				6AF099A9216B54D500F69B16 /* Debug */,
+				6AF099AA216B54D500F69B16 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 6AF09998216B545D00F69B16 /* Project object */;
+}
diff --git a/Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..1288fd9a8
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "1000"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "6AF099A1216B54D500F69B16"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Karatsuba Multiplication/Tests/Tests/Info.plist b/Karatsuba Multiplication/Tests/Tests/Info.plist
new file mode 100644
index 000000000..6c40a6cd0
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>$(DEVELOPMENT_LANGUAGE)</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 142713e62..9305ae37c 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1472,6 +1472,13 @@
       <FileRef
          location = "group:README.markdown">
       </FileRef>
+      <Group
+         location = "group:"
+         name = "Tests">
+         <FileRef
+            location = "group:Tests/Tests.xcodeproj">
+         </FileRef>
+      </Group>
    </Group>
    <Group
       location = "group:Knuth-Morris-Pratt"

From 34526e97eb792f62a942c8379968f0494ae084c1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 20:31:20 +1100
Subject: [PATCH 1479/1679] [Swift 4.2] Update Fizz Buzz

There was no need to update the source code, simply removed the code snippet.
---
 Fizz Buzz/FizzBuzz.playground/Contents.swift              | 5 +----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 9 insertions(+), 4 deletions(-)
 create mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index 37acdab61..ae966bbcc 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,7 +1,4 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// last checked with Xcode 10.0 (10A255)
 
 func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 409e85fdc8968230758ef703804f51956dc524a7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9F=D0=B0=D0=BD=D0=BA=D0=BE=D0=B2=D0=B0=20=D0=9C=D0=B0?=
 =?UTF-8?q?=D1=80=D0=B8=D1=8F=20=D0=92=D0=B8=D1=82=D0=B0=D0=BB=D1=8C=D0=B5?=
 =?UTF-8?q?=D0=B2=D0=BD=D0=B0?= <mv.pankova@2Gis.ru>
Date: Mon, 8 Oct 2018 21:49:03 +0700
Subject: [PATCH 1480/1679] [Swift 4.2] Update Convex Hull

---
 .../Convex Hull.xcodeproj/project.pbxproj     | 26 +++++++++++++++----
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +--
 .../AppIcon.appiconset/Contents.json          |  5 ++++
 Convex Hull/Convex Hull/View.swift            |  4 +--
 4 files changed, 29 insertions(+), 10 deletions(-)

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index c11cbf4d6..27ca4eb25 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -139,7 +139,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0900;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = Workmoose;
 				TargetAttributes = {
 					1CB6142C1F89456C00A14493 = {
@@ -254,7 +254,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGETED_DEVICE_FAMILY = "1,2";
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
 			};
@@ -281,7 +281,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGETED_DEVICE_FAMILY = "1,2";
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
 			};
@@ -296,15 +296,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -346,15 +354,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -389,7 +405,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -402,7 +418,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 1f93a0c4f..8f04a0f51 100644
--- a/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -10,7 +10,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -31,7 +30,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"
diff --git a/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json
index 1d060ed28..d8db8d65f 100644
--- a/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json	
@@ -84,6 +84,11 @@
       "idiom" : "ipad",
       "size" : "83.5x83.5",
       "scale" : "2x"
+    },
+    {
+      "idiom" : "ios-marketing",
+      "size" : "1024x1024",
+      "scale" : "1x"
     }
   ],
   "info" : {
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 33d1426c3..e75c73ed0 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -27,8 +27,8 @@ class View: UIView {
   func generateRandomPoints() {
     for _ in 0..<MAX_POINTS {
       let offset: CGFloat = 50
-      let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
-      let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
+      let xrand = CGFloat(arc4random()) / CGFloat(UInt32.max) * (self.frame.width - offset) + 0.5 * offset
+      let yrand = CGFloat(arc4random()) / CGFloat(UInt32.max) * (self.frame.height - offset) + 0.5 * offset
       let point = CGPoint(x: xrand, y: yrand)
       points.append(point)
     }

From 0e83ef2e5d287d737153a4c14d15ff8ed2cf7fca Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 8 Oct 2018 19:30:25 -0300
Subject: [PATCH 1481/1679] removed duplicate implementation

---
 .../MyPlayground.playground/Contents.swift      | 17 -----------------
 1 file changed, 17 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
index 16466e0bc..8d27d801e 100644
--- a/Bubble Sort/MyPlayground.playground/Contents.swift	
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -1,22 +1,5 @@
 import Foundation
 
-public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
-    var array = elements
-    
-    for i in 0..<array.count {
-        for j in 1..<array.count-i {
-            print(array,"comparing [\(j-1)] with [\(j)]")
-            if array[j] < array[j-1] {
-                let tmp = array[j-1]
-                array[j-1] = array[j]
-                array[j] = tmp
-            }
-        }
-    }
-    
-    return array
-}
-
 var array = [4,2,1,3]
 
 print("before:",array)

From da34da5b85a2f40869305e8c03d3e78e7b04a5e7 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 8 Oct 2018 19:30:58 -0300
Subject: [PATCH 1482/1679] changed tab width to 2 spaces instead of 4

---
 .../Sources/BubbleSort.swift                  | 24 +++++++++----------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
index 5ce18ef9b..9c091b661 100644
--- a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -26,17 +26,17 @@ import Foundation
 /// - Parameter elements: the array to be sorted
 /// - Returns: an array with the same elements but in order
 public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
-    var array = elements
-    
-    for i in 0..<array.count {
-        for j in 1..<array.count-i {
-            if array[j] < array[j-1] {
-                let tmp = array[j-1]
-                array[j-1] = array[j]
-                array[j] = tmp
-            }
-        }
+  var array = elements
+  
+  for i in 0..<array.count {
+    for j in 1..<array.count-i {
+      if array[j] < array[j-1] {
+        let tmp = array[j-1]
+        array[j-1] = array[j]
+        array[j] = tmp
+      }
     }
-    
-    return array
+  }
+  
+  return array
 }

From ab3b6cdd61031bfd8a03803f6258f3369db0fa74 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 8 Oct 2018 20:16:55 -0300
Subject: [PATCH 1483/1679] updated readme to conform with changes requested

---
 Bubble Sort/README.markdown | 75 +++++++++++++++++++++++++++++--------
 1 file changed, 59 insertions(+), 16 deletions(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index 80161ce56..e55129d93 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Bubble Sort
 
-Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.Sometimes this algorithm is refered as Sinking sort, due to the larger, or heavier elements sinking to the end of the array.
+Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array. Sometimes this algorithm is refered as Sinking sort, due to the larger, or heavier elements sinking to the end of the array.
 
 ##### Runtime:
 - Average: O(N^2)
@@ -16,6 +16,10 @@ The implementation will not be shown as the average and worst runtimes show that
 Bubble sort is a very simple sorting algorithm, it consists in comparing pairs of adjacent elements in the array, if the first element is larger, swap them, otherwise, you do nothing and go for the next comparison.
 This is accomplished by looking through the array `n` times, `n` being the amount of elements in the array.
 
+![animated gif of the bubble sort algorithm](https://s3.amazonaws.com/codecademy-content/programs/tdd-js/articles/BubbleSort.gif)
+
+This GIF shows a inverted implementation than 
+
 #### Example
 Let us take the array `[5, 1, 4, 2, 8]`, and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required.
 
@@ -52,13 +56,13 @@ This is the same for the forth and fifth passes.
 #### Code
 ```swift
 for i in 0..<array.count {
-for j in 1..<array.count {
-if array[j] < array[i] {
-let tmp = array[i]
-array[i] = array[j]
-array[j] = tmp
-}
-}
+  for j in 1..<array.count {
+    if array[j] < array[i] {
+      let tmp = array[i]
+      array[i] = array[j]
+      array[j] = tmp
+    }
+  }
 }
 return array
 ```
@@ -68,17 +72,56 @@ The bubble sort algorithm can be easily optimized by observing that the `n-th` p
 
 ```swift
 for i in 0..<array.count {
-for j in 1..<array.count - i {
-if array[j] < array[i] {
-let tmp = array[i]
-array[i] = array[j]
-array[j] = tmp
-}
-}
+  for j in 1..<array.count - i {
+    if array[j] < array[i] {
+      let tmp = array[i]
+      array[i] = array[j]
+      array[j] = tmp
+    }
+  }
 }
 return array
 ```
 
 The only change made was on the second line, changing the interval from `1..<array.count` to `1..<array.count - i`, effectively cutting the number of comparisons by half.
 
-That said, this is still a terribly inefficient sorting algorithm.
+The ordering with the optimized code would look something like this for the array  `[5, 1, 4, 2, 8]`:
+
+##### First Pass
+[ **5 1** 4 2 8 ] -> [ **1 5** 4 2 8 ], Swaps since 5 > 1
+
+[ 1 **5 4** 2 8 ] -> [ 1 **4 5** 2 8 ], Swap since 5 > 4 
+
+[ 1 4 **5 2** 8 ] -> [ 1 4 **2 5** 8 ], Swap since 5 > 2 
+
+[ 1 4 2 **5 8** ] -> [ 1 4 2 **5 8** ], Now, since these elements are already in order (8 > 5), algorithm does not swap them. 
+
+*by the end of the first pass, the last element is guaranteed to be the largest*
+
+##### Second Pass
+[ **1 4** 2 5 8 ] -> [ **1 4** 2 5 8 ]
+
+[ 1 **4 2** 5 8 ] -> [ 1 **2 4** 5 8 ], Swap since 4 > 2 
+
+[ 1 2 **4 5** 8 ] -> [ 1 2 **4 5** 8 ], As the first loop has occured once, the inner loop stops here, not comparing 5 with 8
+
+##### Third Pass
+[ **1 2** 4 5 8 ] -> [ **1 2** 4 5 8 ]
+
+[ 1 **2 4** 5 8 ] -> [ 1 **2 4** 5 8 ] again, stoping one comparison short
+
+##### Fourth Pass
+[ **1 2** 4 5 8 ] -> [ **1 2** 4 5 8 ]
+
+There is no Fifth pass
+
+#### Conclusion
+
+Even with the proposed optimizations, this is still a terribly inefficient sorting algorithm. A good alternative is [Merge Sort](), that not only is better performing, has a similar degree of dificulty to implement.
+
+*Updated for the Swift Algorithm Club by Julio Brazil*
+
+##### Supporting Links
+[Code Pumpkin](https://codepumpkin.com/bubble-sort/)
+[Wikipedia](https://en.wikipedia.org/wiki/Bubble_sort)
+[GeeksforGeeks](https://www.geeksforgeeks.org/bubble-sort/)

From 39971b49661a7179117511ddfc6c79e1bde12378 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=95=D0=BA=D0=B0=D1=82=D0=B5=D1=80=D0=B8=D0=BD=D0=B0=20?=
 =?UTF-8?q?=D0=91=D0=B0=D1=82=D0=B5=D0=B5=D0=B2=D0=B0?= <bateeva-k@mail.ru>
Date: Wed, 10 Oct 2018 22:39:38 +0300
Subject: [PATCH 1484/1679] [Swift 4.2] Update Boyer-Moore-Horspool

---
 .../BoyerMooreHorspool.playground/Contents.swift          | 6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../BoyerMooreHorspool.playground/timeline.xctimeline     | 6 +++---
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift             | 6 +++---
 4 files changed, 17 insertions(+), 9 deletions(-)
 create mode 100644 Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index e88a1b93d..5817cc41f 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -16,13 +16,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
index 89bc76f90..2688d72c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=37&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616217"
+         documentLocation = "file:///Users/neifmetus/Documents/Projects/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=560891520.806637"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=26&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.61657"
+         documentLocation = "file:///Users/neifmetus/Documents/Projects/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=560891520.806855"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=25&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616725"
+         documentLocation = "file:///Users/neifmetus/Documents/Projects/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=560891520.807023"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index af8aea9d9..dbd738740 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -9,13 +9,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 

From 8e6c983cd0c5ae26a68531bb54521b85f3926120 Mon Sep 17 00:00:00 2001
From: Varun <varunkapoor989@gmail.com>
Date: Thu, 11 Oct 2018 13:41:40 +0530
Subject: [PATCH 1485/1679] updated LinkedList.playground to swift 4.2

---
 Linked List/LinkedList.playground/Contents.swift        | 4 ----
 Linked List/LinkedList.playground/contents.xcplayground | 2 +-
 2 files changed, 1 insertion(+), 5 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index cfa3a8b45..894b2d37f 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,10 +3,6 @@
 // For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
 //: Linked List Class Declaration:
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 public final class LinkedList<T> {
     
diff --git a/Linked List/LinkedList.playground/contents.xcplayground b/Linked List/LinkedList.playground/contents.xcplayground
index 3de2b51ba..5e28f2dd0 100644
--- a/Linked List/LinkedList.playground/contents.xcplayground	
+++ b/Linked List/LinkedList.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' display-mode='rendered'>
+<playground version='5.0' target-platform='osx' display-mode='rendered' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 3f0ee826265621d22205316a3f52f22d7e5ee39f Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:17:34 +0200
Subject: [PATCH 1486/1679] Update to Swift 4.2.

Also removed unused Tests group from project.
---
 .../project.pbxproj                           | 22 ++++++++-----------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 2 files changed, 17 insertions(+), 13 deletions(-)
 create mode 100644 DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
index ecb060026..97f3c4847 100755
--- a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -27,13 +27,6 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
-		OBJ_10 /* Tests */ = {
-			isa = PBXGroup;
-			children = (
-			);
-			path = Tests;
-			sourceTree = "<group>";
-		};
 		OBJ_11 /* Products */ = {
 			isa = PBXGroup;
 			children = (
@@ -42,15 +35,13 @@
 			name = Products;
 			sourceTree = BUILT_PRODUCTS_DIR;
 		};
-		OBJ_5 /*  */ = {
+		OBJ_5 = {
 			isa = PBXGroup;
 			children = (
 				OBJ_6 /* Package.swift */,
 				OBJ_7 /* Sources */,
-				OBJ_10 /* Tests */,
 				OBJ_11 /* Products */,
 			);
-			name = "";
 			sourceTree = "<group>";
 		};
 		OBJ_7 /* Sources */ = {
@@ -96,6 +87,11 @@
 			isa = PBXProject;
 			attributes = {
 				LastUpgradeCheck = 9999;
+				TargetAttributes = {
+					OBJ_13 = {
+						LastSwiftMigration = 1000;
+					};
+				};
 			};
 			buildConfigurationList = OBJ_2 /* Build configuration list for PBXProject "DiningPhilosophers" */;
 			compatibilityVersion = "Xcode 3.2";
@@ -104,7 +100,7 @@
 			knownRegions = (
 				en,
 			);
-			mainGroup = OBJ_5 /*  */;
+			mainGroup = OBJ_5;
 			productRefGroup = OBJ_11 /* Products */;
 			projectDirPath = "";
 			projectRoot = "";
@@ -139,7 +135,7 @@
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = SWIFT_PACKAGE;
 				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
 				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGET_NAME = DiningPhilosophers;
 			};
 			name = Debug;
@@ -157,7 +153,7 @@
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = SWIFT_PACKAGE;
 				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
 				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGET_NAME = DiningPhilosophers;
 			};
 			name = Release;
diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 6c48b3d493b4e6f023b006871f58fbe485db96b1 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:18:45 +0200
Subject: [PATCH 1487/1679] Add README.md to project.

This makes it easier to read along with the code.
---
 DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
index 97f3c4847..7699219de 100755
--- a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -11,6 +11,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
+		232D7939216F76F700831A74 /* README.md */ = {isa = PBXFileReference; lastKnownFileType = net.daringfireball.markdown; path = README.md; sourceTree = "<group>"; };
 		OBJ_12 /* DiningPhilosophers */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; path = DiningPhilosophers; sourceTree = BUILT_PRODUCTS_DIR; };
 		OBJ_6 /* Package.swift */ = {isa = PBXFileReference; explicitFileType = sourcecode.swift; path = Package.swift; sourceTree = "<group>"; };
 		OBJ_9 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = "<group>"; };
@@ -38,6 +39,7 @@
 		OBJ_5 = {
 			isa = PBXGroup;
 			children = (
+				232D7939216F76F700831A74 /* README.md */,
 				OBJ_6 /* Package.swift */,
 				OBJ_7 /* Sources */,
 				OBJ_11 /* Products */,

From f2c04f7ac0ed2634221eca58ed303e3a3b239cd9 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:18:54 +0200
Subject: [PATCH 1488/1679] Add credit to README.md.

---
 DiningPhilosophers/README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index cd9d86154..aed9dfe59 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -57,3 +57,4 @@ A background DispatchQueue is then used to let any Philosopher run asyncrounosly
 Dining Philosophers on Wikipedia https://en.wikipedia.org/wiki/Dining_philosophers_problem
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi
+Swift 4.2 check by Bruno Scheele

From eeb116e4073a0b1a0a9d13701bbe27d29e1ec6bb Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:26:17 +0200
Subject: [PATCH 1489/1679] Update to Swift 4.2.

---
 Red-Black Tree/RedBlackTree.playground/Contents.swift     | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
index f14f18e58..d1133bc98 100644
--- a/Red-Black Tree/RedBlackTree.playground/Contents.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -2,11 +2,6 @@
 // Test for  the RedBlackTree implementation provided in the Source folder of this Playground
 import Foundation
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let redBlackTree = RedBlackTree<Double>()
 
 let randomMax = Double(0x10000000)
diff --git a/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From af9a6564f87da3390d9c0287995ba213f47c94ad Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:26:34 +0200
Subject: [PATCH 1490/1679] Add credit to README.md.

---
 Red-Black Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 74fffa415..fd6c4db18 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -186,4 +186,4 @@ The overall runtime of delete is O(log n).
 ## Resources:
 [CLRS]  T. Cormen, C. Leiserson, R. Rivest, and C. Stein. "Introduction to Algorithms", Third Edition. 2009
 
-*Written for Swift Algorithm Club by Ute Schiehlen. Updated from Jaap Wijnen and Ashwin Raghuraman's contributions.*
+*Written for Swift Algorithm Club by Ute Schiehlen. Updated from Jaap Wijnen and Ashwin Raghuraman's contributions. Swift 4.2 check by Bruno Scheele.*

From d3d382f1d2f76c91a14a9b61b02375f7c6388265 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=95=D0=BA=D0=B0=D1=82=D0=B5=D1=80=D0=B8=D0=BD=D0=B0=20?=
 =?UTF-8?q?=D0=91=D0=B0=D1=82=D0=B5=D0=B5=D0=B2=D0=B0?= <bateeva-k@mail.ru>
Date: Fri, 12 Oct 2018 23:06:22 +0300
Subject: [PATCH 1491/1679] Fix HarversineDistance pi parameter in "Converts
 from degrees to radians"

---
 HaversineDistance/HaversineDistance.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 5b3f591d6..7aa686645 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -16,7 +16,7 @@ func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radi
     
     // Converts from degrees to radians
     let dToR = { (angle: Double) -> Double in
-        return (angle / 360) * 2 * M_PI
+        return (angle / 360) * 2 * .pi
     }
     
     let lat1 = dToR(la1)

From acb21c32df8cc6c2ba8c153497902c24a661fff4 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Fri, 12 Oct 2018 17:18:55 -0400
Subject: [PATCH 1492/1679] Updated MST to Swift 4.2

---
 .../MinimumSpanningTree.playground/Contents.swift         | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
index c4f0a811b..7e3532429 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -3,11 +3,6 @@
  Kruskal's and Prim's algorithms.
  */
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
     var cost: Int = 0
     var tree = Graph<T>()
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From e0c6676601b6de0b093d3a171bf7497c73947522 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Fri, 12 Oct 2018 17:37:17 -0400
Subject: [PATCH 1493/1679] Updated MST (Unweighted) to Swift 4.2

---
 .../Contents.swift                                        | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 65aa9fbc4..8ad04379c 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 45cca894960b5aab35f8e675c1e2066025e7df91 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Fri, 12 Oct 2018 17:40:24 -0400
Subject: [PATCH 1494/1679] Updated MST (Unweighted) tests to Swift 4.2

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 31 ++++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 36 insertions(+), 5 deletions(-)
 create mode 100644 Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
index a066b7a71..afb3b8acb 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
@@ -89,12 +89,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -149,13 +149,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,13 +203,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -218,6 +238,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -231,7 +252,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -244,7 +266,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..afd69e6a7 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 685b315c166d9fa8ee8af81ffb7029d242b03921 Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 10:59:37 +0300
Subject: [PATCH 1495/1679] update Huffman Coding to Swift 4.2

---
 Huffman Coding/Huffman.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index 6242ad272..2d59908e9 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 let s1 = "so much words wow many compression"

From 85738885f0ec2e2f6041eb8545a4cfa99233e783 Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:21:15 +0300
Subject: [PATCH 1496/1679] Update Quad Tree to Swift 4.2

---
 QuadTree/QuadTree.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
index f0d8cb2ef..ad8ee31f8 100644
--- a/QuadTree/QuadTree.playground/Contents.swift
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b5
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))

From 61400ea88862429ea588cf07e396377ca485d9b0 Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:31:57 +0300
Subject: [PATCH 1497/1679] Update Multiset to Swift 4.2

---
 Multiset/Multiset.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index b4f64ee1f..64b729df1 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 import Cocoa
 
 var set = Multiset<String>()

From bb9ae3b6629da9b837c4cf33f9dfd977b13a635d Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:39:24 +0300
Subject: [PATCH 1498/1679] Update Monty Hall to Swift 4.2

---
 Monty Hall Problem/MontyHall.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Monty Hall Problem/MontyHall.playground/Contents.swift b/Monty Hall Problem/MontyHall.playground/Contents.swift
index 4bfff2340..a809410c7 100644
--- a/Monty Hall Problem/MontyHall.playground/Contents.swift	
+++ b/Monty Hall Problem/MontyHall.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 func random(_ n: Int) -> Int {

From 33a50920ebefc92ce844d6f024e8c4a49f2eb3ef Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:49:26 +0300
Subject: [PATCH 1499/1679] Update Ring Buffer to Swift 4.2

---
 Ring Buffer/RingBuffer.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index f9ddb9c99..adcf146b4 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 public struct RingBuffer<T> {
   fileprivate var array: [T?]
   fileprivate var readIndex = 0

From 2a2971800f986286b098928f0cce0199a749ba9e Mon Sep 17 00:00:00 2001
From: NORMANDY REAL <mandy@NORMANDYs-MacBook-Pro.local>
Date: Sat, 13 Oct 2018 22:25:30 +0800
Subject: [PATCH 1500/1679] Migrate to Swift 4.2

---
 Ordered Array/OrderedArray.playground/Contents.swift | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 5b6be6420..e48af22e2 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -1,9 +1,6 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+
 
 public struct OrderedArray<T: Comparable> {
   fileprivate var array = [T]()

From 58af4187be04c17586a3bb37f30fd269bffd2692 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Sat, 13 Oct 2018 10:32:59 -0400
Subject: [PATCH 1501/1679] Updated LRU Cache to Swift 4.2

---
 LRU Cache/LRUCache.playground/Contents.swift              | 5 -----
 .../playground.xcworkspace/contents.xcworkspacedata       | 7 +++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 15 insertions(+), 5 deletions(-)
 create mode 100644 LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/LRU Cache/LRUCache.playground/Contents.swift b/LRU Cache/LRUCache.playground/Contents.swift
index 2ebc03242..35dcc5d59 100644
--- a/LRU Cache/LRUCache.playground/Contents.swift	
+++ b/LRU Cache/LRUCache.playground/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let cache = LRUCache<String>(2)
 cache.set("a", val: 1)
 cache.set("b", val: 2)
diff --git a/LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata b/LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 4130f3502c344e0b43f09c0ba6cef0221ef1ff92 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 01:37:22 -0300
Subject: [PATCH 1502/1679] Updated Bit Set to Swift 4.2

---
 Bit Set/BitSet.playground/Contents.swift                  | 4 ----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 4 deletions(-)
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 95253ea27..568202a33 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From d4d5b473774e68a24d3320865749d3dfe257da88 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 01:51:54 -0300
Subject: [PATCH 1503/1679] Updated Kth largest element to Swift 4.2

---
 Kth Largest Element/kthLargest.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index e6fca2ceb..a27dfce7d 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 let a = [5, 1, 3, 2, 7, 6, 4]
 

From 75182345961675c51823a5d8ec514d85e91c7de8 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 02:02:21 -0300
Subject: [PATCH 1504/1679] Revert "Updated Bit Set to Swift 4.2"

This reverts commit 4130f3502c344e0b43f09c0ba6cef0221ef1ff92.
---
 Bit Set/BitSet.playground/Contents.swift                  | 4 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 --------
 2 files changed, 4 insertions(+), 8 deletions(-)
 delete mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 568202a33..95253ea27 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,5 +1,9 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>

From f7b3996dd301816a66618fc497edb546706e68d0 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 02:09:18 -0300
Subject: [PATCH 1505/1679] Updated Knuth-Morris-Pratt to Swift 4.2

---
 .../KnuthMorrisPratt.playground/Contents.swift           | 9 ++-------
 1 file changed, 2 insertions(+), 7 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index 6609c9abe..9b4a50fa0 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -1,13 +1,8 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift4!")
-#endif
-
 func ZetaAlgorithm(ptnr: String) -> [Int]? {
   
-  let pattern = Array(ptnr.characters)
+  let pattern = Array(ptnr)
   let patternLength: Int = pattern.count
   
   guard patternLength > 0 else {
@@ -65,7 +60,7 @@ extension String {
   
   func indexesOf(ptnr: String) -> [Int]? {
     
-    let text = Array(self.characters)
+    let text = Array(self)
     let pattern = Array(ptnr.characters)
     
     let textLength: Int = text.count

From 6c2aa24b0674a97e755bf8c0acf480d6e107e756 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 02:23:51 -0300
Subject: [PATCH 1506/1679] Updated AVL Tree to Swift 4.2

---
 AVL Tree/AVLTree.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 04ef78d07..34c1e6ddd 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 let tree = AVLTree<Int, String>()
 

From 6536cd7af049eec810033f9611e6e8e5767a8a54 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 15 Oct 2018 13:17:08 +1100
Subject: [PATCH 1507/1679] fix indentation typos in the README.md

---
 Karatsuba Multiplication/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index 3a48ed39d..aef0d744a 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -71,12 +71,12 @@ Here's the full implementation. Note that the recursive algorithm is most effici
 
 ```swift
 // Karatsuba Multiplication
-  func karatsuba(_ num1: Int, by num2: Int) -> Int {
+func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1String = String(num1)
   let num2String = String(num2)
   
   guard num1String.count > 1 && num2String.count > 1 else {
-  return multiply(num1, by: num2)
+    return multiply(num1, by: num2)
   }
   
   let n = max(num1String.count, num2String.count)

From 32fe7e84c0378daacf3e4048cf2f4d55bdb22c65 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 15 Oct 2018 13:25:42 +1100
Subject: [PATCH 1508/1679] [Swift 4.2] Update Miller-Rabin Primality Test

References #748
There were no necessary code changes for Swift 4.2.
Removed the  snippet requested
---
 .../MRPrimality.playground/Contents.swift                 | 5 -----
 .../playground.xcworkspace/contents.xcworkspacedata       | 4 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 12 insertions(+), 5 deletions(-)
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index d8fd7fad8..98032bd59 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Real primes
 mrPrimalityTest(5)
 mrPrimalityTest(439)
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..94b2795e2
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+</Workspace>
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 027dc783bb15853c40f15bfd11daa9dcb7771120 Mon Sep 17 00:00:00 2001
From: Pragati <44121852+pragatiahuja@users.noreply.github.com>
Date: Mon, 15 Oct 2018 23:50:03 +0530
Subject: [PATCH 1509/1679] final README

Add recursive implementation for reversing a singly linked list.
---
 Linked List/README.markdown | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0c8431157..0998349fc 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -471,6 +471,7 @@ This will print the list like so:
 
 How about reversing a list, so that the head becomes the tail and vice versa? There is a very fast algorithm for that:
 
+Iterative Approach:
 ```swift
   public func reverse() {
     var node = head
@@ -482,6 +483,18 @@ How about reversing a list, so that the head becomes the tail and vice versa? Th
     }
   }
 ```
+Recursive Approach:
+```swift
+  public func reverse(node: head) {
+    if (!head || !(head.next)) {
+      return head
+    }
+    let temp = reverse(head.next)
+    head.next.next = head;
+    head.next = NULL;
+    return temp;
+  }
+```
 
 This loops through the entire list and simply swaps the `next` and `previous` pointers of each node. It also moves the `head` pointer to the very last element. (If you had a tail pointer you'd also need to update it.) You end up with something like this:
 

From 75783274fd291f6f9e6e801734c1eefa3b77eb38 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 16 Oct 2018 11:35:51 -0300
Subject: [PATCH 1510/1679] replaced repetitive implementation with call

---
 .../Sources/SelectionSort.swift               | 20 +------------------
 1 file changed, 1 insertion(+), 19 deletions(-)

diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index 3a27ef9dd..e7c66481d 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -3,25 +3,7 @@
 /// - Parameter array: array of elements that conform to the Comparable protocol
 /// - Returns: an array in ascending order
 public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
-  guard array.count > 1 else { return array }
-
-  var a = array
-  for x in 0 ..< a.count - 1 {
-
-    // Find the lowest value in the rest of the array.
-    var lowest = x
-    for y in x + 1 ..< a.count {
-      if a[y] < a[lowest] {
-        lowest = y
-      }
-    }
-
-    // Swap the lowest value with the current array index.
-    if x != lowest {
-      a.swapAt(x, lowest)
-    }
-  }
-  return a
+  return insertionSort(array, <)
 }
 
 /// Performs the Selection sort algorithm on a array using the provided comparisson method

From 35ca62c82b39506203e551c8d05938113aec3e2f Mon Sep 17 00:00:00 2001
From: TaeJoongYoon <tryump225@gmail.com>
Date: Wed, 17 Oct 2018 04:05:46 +0900
Subject: [PATCH 1511/1679] Add CounterClockWise(CCW)

---
 .../Contents.swift                            |  76 +++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 ++
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 ++
 CounterClockWise/CounterClockWise.swift       |  50 ++++++++
 CounterClockWise/Images/Pentagon_img.png      | Bin 0 -> 20639 bytes
 CounterClockWise/Images/Quadrilateral_img.jpg | Bin 0 -> 9081 bytes
 CounterClockWise/Images/Shoelace.png          | Bin 0 -> 77353 bytes
 CounterClockWise/Images/Triangle_img.jpg      | Bin 0 -> 10346 bytes
 CounterClockWise/Images/pentagon.png          | Bin 0 -> 25285 bytes
 CounterClockWise/Images/quadrilateral.png     | Bin 0 -> 22372 bytes
 CounterClockWise/Images/triangle.png          | Bin 0 -> 19654 bytes
 CounterClockWise/README.md                    | 118 ++++++++++++++++++
 README.markdown                               |   1 +
 14 files changed, 264 insertions(+)
 create mode 100644 CounterClockWise/CounterClockWise.playground/Contents.swift
 create mode 100644 CounterClockWise/CounterClockWise.playground/contents.xcplayground
 create mode 100644 CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 CounterClockWise/CounterClockWise.swift
 create mode 100644 CounterClockWise/Images/Pentagon_img.png
 create mode 100644 CounterClockWise/Images/Quadrilateral_img.jpg
 create mode 100644 CounterClockWise/Images/Shoelace.png
 create mode 100644 CounterClockWise/Images/Triangle_img.jpg
 create mode 100644 CounterClockWise/Images/pentagon.png
 create mode 100644 CounterClockWise/Images/quadrilateral.png
 create mode 100644 CounterClockWise/Images/triangle.png
 create mode 100644 CounterClockWise/README.md

diff --git a/CounterClockWise/CounterClockWise.playground/Contents.swift b/CounterClockWise/CounterClockWise.playground/Contents.swift
new file mode 100644
index 000000000..ffa91ecbb
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/Contents.swift
@@ -0,0 +1,76 @@
+/*
+ CounterClockWise(CCW) Algorithm
+ The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
+ and subtracts it from the surrounding polygon to find the area of the polygon within.
+ This code is based on the "Shoelace formula" by Carl Friedrich Gauss
+ https://en.wikipedia.org/wiki/Shoelace_formula
+ */
+
+import Foundation
+
+// MARK : Point struct for defining 2-D coordinate(x,y)
+public struct Point{
+  // Coordinate(x,y)
+  var x: Int
+  var y: Int
+  
+  public init(x: Int ,y: Int){
+    self.x = x
+    self.y = y
+  }
+}
+
+// MARK : Function that determine the area of a simple polygon whose vertices are described
+//        by their Cartesian coordinates in the plane.
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+  
+  // Take the first x-coordinate and multiply it by the second y-value,
+  // then take the second x-coordinate and multiply it by the third y-value,
+  // and repeat as many times until it is done for all wanted points.
+  for i in 0..<polygon{
+      orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+                      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+  
+  // If the points are labeled sequentially in the counterclockwise direction,
+  // then the sum of the above determinants is positive and the absolute value signs can be omitted
+  // if they are labeled in the clockwise direction, the sum of the determinants will be negative.
+  // This is because the formula can be viewed as a special case of Green's Theorem.
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
+
+// A few simple tests
+
+
+// Triangle
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+
+// Quadrilateral
+var p4 = Point(x: 5, y: 8)
+var p5 = Point(x: 2, y: 3)
+var p6 = Point(x: 6, y: 1)
+var p7 = Point(x: 9, y: 3)
+
+print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
+
+// Pentagon
+var p8 = Point(x: 5, y: 11)
+var p9 = Point(x: 3, y: 4)
+var p10 = Point(x: 5, y: 6)
+var p11 = Point(x: 9, y: 5)
+var p12 = Point(x: 12, y: 8)
+
+print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
diff --git a/CounterClockWise/CounterClockWise.playground/contents.xcplayground b/CounterClockWise/CounterClockWise.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/CounterClockWise/CounterClockWise.swift b/CounterClockWise/CounterClockWise.swift
new file mode 100644
index 000000000..07c422ea5
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.swift
@@ -0,0 +1,50 @@
+/*
+ CounterClockWise(CCW) Algorithm
+ The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
+ and subtracts it from the surrounding polygon to find the area of the polygon within.
+ This code is based on the "Shoelace formula" by Carl Friedrich Gauss
+ https://en.wikipedia.org/wiki/Shoelace_formula
+ */
+
+
+import Foundation
+
+// MARK : Point struct for defining 2-D coordinate(x,y)
+public struct Point{
+  // Coordinate(x,y)
+  var x: Int
+  var y: Int
+  
+  public init(x: Int ,y: Int){
+    self.x = x
+    self.y = y
+  }
+}
+
+// MARK : Function that determine the area of a simple polygon whose vertices are described
+//        by their Cartesian coordinates in the plane.
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+  
+  // Take the first x-coordinate and multiply it by the second y-value,
+  // then take the second x-coordinate and multiply it by the third y-value,
+  // and repeat as many times until it is done for all wanted points.
+  for i in 0..<polygon{
+    orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+  
+  // If the points are labeled sequentially in the counterclockwise direction,
+  // then the sum of the above determinants is positive and the absolute value signs can be omitted
+  // if they are labeled in the clockwise direction, the sum of the determinants will be negative.
+  // This is because the formula can be viewed as a special case of Green's Theorem.
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
diff --git a/CounterClockWise/Images/Pentagon_img.png b/CounterClockWise/Images/Pentagon_img.png
new file mode 100644
index 0000000000000000000000000000000000000000..44d8583036420e6a63fd0c339f65845632ebf28c
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diff --git a/CounterClockWise/README.md b/CounterClockWise/README.md
new file mode 100644
index 000000000..6b6c1a1da
--- /dev/null
+++ b/CounterClockWise/README.md
@@ -0,0 +1,118 @@
+# CounterClockWise
+
+Goal : Determine what direction to take when multiple points are given.
+
+CounterClockWise(CCW) is based on [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula#Examples) by Carl Friedrich Gauss.
+
+
+
+1. Take the first x-coordinate and multiply it by the second y-value, then take the second x-coordinate and multiply it by the third y-value, and repeat as many times until it is done for all wanted points.
+2. If the points are labeled sequentially in the counterclockwise direction, then the sum of the above determinants is positive and the absolute value signs can be omitted if they are labeled in the clockwise direction, the sum of the determinants will be negative. This is because the formula can be viewed as a special case of [Green's theorem](https://en.wikipedia.org/wiki/Green%27s_theorem).
+
+![Shoelace](./Images/Shoelace.png)
+
+
+
+Here's an implementation in Swift that should be easy to understand:
+
+```swift
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+
+  for i in 0..<polygon{
+    orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+    
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
+```
+
+Put this code in a playground and test it like so:
+
+```swift
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+```
+
+Here's how it works. When given an `[Photo]`, `ccw(points:)` calculates the direction of the given points according to the Shoelaces formula.
+
+
+
+`orientation` is less than 0, the direction is clockwise. 
+
+`orientation` is equal to 0, the direction is parallel. 
+
+`orientation` is greater than 0, the direction is counterclockwise. 
+
+
+
+## An example
+
+**In Triangle**
+
+```swift
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+```
+
+![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Triangle_img.jpg)
+
+![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/triangle.png)
+
+
+
+**In Quadrilateral**
+
+```swift
+var p4 = Point(x: 5, y: 8)
+var p5 = Point(x: 2, y: 3)
+var p6 = Point(x: 6, y: 1)
+var p7 = Point(x: 9, y: 3)
+
+print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
+```
+
+![Quadrilateral](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Quadrilateral_img.jpg)
+
+![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/quadrilateral.png)
+
+
+
+**In Pentagon**
+
+```swift
+var p8 = Point(x: 5, y: 11)
+var p9 = Point(x: 3, y: 4)
+var p10 = Point(x: 5, y: 6)
+var p11 = Point(x: 9, y: 5)
+var p12 = Point(x: 12, y: 8)
+
+print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
+```
+
+![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Pentagon_img.png)
+
+![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/pentagon.png)
+
+
+
+You probably won't need to use the CCW in any real-world problems, but it's cool to play around with geometry algorithm. The formula was described by Meister (1724-1788) in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles, and can be considered to be a special case of Green's theorem.
+
+
+
+*Written for Swift Algorithm Club by TaeJoong Yoon*
\ No newline at end of file
diff --git a/README.markdown b/README.markdown
index 90b310752..efe89edc0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -109,6 +109,7 @@ Bad sorting algorithms (don't use these!):
 - [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
 - [Strassen's Multiplication Matrix](Strassen%20Matrix%20Multiplication/). Efficient way to handle matrix multiplication.
+- [CounterClockWise](/CounterClockWise/). Determining the area of a simple polygon.
 
 ### Machine learning
 

From e48117cd2cd5efaec539eb83c44d47089edc5054 Mon Sep 17 00:00:00 2001
From: TaeJoong Yoon <tryump225@gmail.com>
Date: Wed, 17 Oct 2018 04:22:34 +0900
Subject: [PATCH 1512/1679] Update README.md

---
 CounterClockWise/README.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/CounterClockWise/README.md b/CounterClockWise/README.md
index 6b6c1a1da..2d15eba53 100644
--- a/CounterClockWise/README.md
+++ b/CounterClockWise/README.md
@@ -70,9 +70,9 @@ var p3 = Point(x: 3, y: 6)
 print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
 ```
 
-![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Triangle_img.jpg)
+![triangle](./Images/Triangle_img.jpg)
 
-![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/triangle.png)
+![triangleExpression](./Images/triangle.png)
 
 
 
@@ -87,9 +87,9 @@ var p7 = Point(x: 9, y: 3)
 print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
 ```
 
-![Quadrilateral](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Quadrilateral_img.jpg)
+![Quadrilateral](./Images/Quadrilateral_img.jpg)
 
-![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/quadrilateral.png)
+![triangleExpression](./Images/quadrilateral.png)
 
 
 
@@ -105,9 +105,9 @@ var p12 = Point(x: 12, y: 8)
 print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
 ```
 
-![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Pentagon_img.png)
+![triangle](./Images/Pentagon_img.png)
 
-![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/pentagon.png)
+![triangleExpression](./Images/pentagon.png)
 
 
 
@@ -115,4 +115,4 @@ You probably won't need to use the CCW in any real-world problems, but it's cool
 
 
 
-*Written for Swift Algorithm Club by TaeJoong Yoon*
\ No newline at end of file
+*Written for Swift Algorithm Club by TaeJoong Yoon*

From d321542c220e94607b056644c491c7436553103b Mon Sep 17 00:00:00 2001
From: Alex Persian <alex_persian@me.com>
Date: Tue, 16 Oct 2018 22:28:13 -0400
Subject: [PATCH 1513/1679] Changes class to enum and clarifies the reason why
 a copy is made

---
 Linked List/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0c8431157..e81e00b9f 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -555,7 +555,7 @@ enum ListNode<T> {
 }
 ```
 
-The big difference with the class-based version is that any modification you make to this list will result in a *new copy* being created. Whether that's what you want or not depends on the application.
+The big difference with the enum-based version is that any modification you make to this list will result in a *new copy* being created because of [Swift's value semantics](https://developer.apple.com/swift/blog/?id=10). Whether that's what you want or not depends on the application.
 
 [I might fill out this section in more detail if there's a demand for it.]
 

From f95093e7338bc66d73ff81b52f959ec0f4fdd2b5 Mon Sep 17 00:00:00 2001
From: Michael Pchelnikov <m.pchelnikov@gmail.com>
Date: Thu, 18 Oct 2018 00:28:16 +0300
Subject: [PATCH 1514/1679] Update Sorted Set to Swift 4.2

---
 .../Pages/Example 1.xcplaygroundpage/Contents.swift          | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index 45af5f99d..c81f4d915 100644
--- a/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 //: # Example 1 with type Int
 
 var mySet = SortedSet<Int>()

From 0c93543179946a42b44a11fb79061a6126a8d8b5 Mon Sep 17 00:00:00 2001
From: Erik Strottmann <erik.strottmann@gmail.com>
Date: Wed, 17 Oct 2018 22:01:48 -0700
Subject: [PATCH 1515/1679] Update Trie to Swift 4.2

Removes `#if swift(>=4.0)` checks and calls to deprecated
`String.characters` property, and enables Xcode 10 recommended warnings.
---
 Trie/ReadMe.md                                |  4 +--
 Trie/Trie/Trie.xcodeproj/project.pbxproj      | 33 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 Trie/Trie/Trie/Trie.swift                     | 11 ++-----
 Trie/Trie/Trie/ViewController.swift           |  5 ---
 Trie/Trie/TrieTests/TrieTests.swift           |  5 ---
 6 files changed, 39 insertions(+), 27 deletions(-)
 create mode 100644 Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 34b9beb9c..8e473a619 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -33,7 +33,7 @@ func contains(word: String) -> Bool {
 	var currentNode = root
   
 	// 2
-	var characters = Array(word.lowercased().characters)
+	var characters = Array(word.lowercased())
 	var currentIndex = 0
  
 	// 3
@@ -74,7 +74,7 @@ func insert(word: String) {
   var currentNode = root
 
   // 2
-  for character in word.lowercased().characters {
+  for character in word.lowercased() {
     // 3
     if let childNode = currentNode.children[character] {
       currentNode = childNode
diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 90c5734cc..1e3602eea 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -195,20 +195,23 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0810;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Rick Zaccone";
 				TargetAttributes = {
 					EB798DF91DFEF79900F0628D = {
 						CreatedOnToolsVersion = 8.1;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 					};
 					EB798E0A1DFEF79900F0628D = {
 						CreatedOnToolsVersion = 8.1;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 						TestTargetID = EB798DF91DFEF79900F0628D;
 					};
 					EB798E151DFEF79900F0628D = {
 						CreatedOnToolsVersion = 8.1;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 						TestTargetID = EB798DF91DFEF79900F0628D;
 					};
@@ -326,15 +329,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_SUSPICIOUS_MOVES = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
@@ -376,15 +387,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_SUSPICIOUS_MOVES = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
@@ -418,7 +437,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.Trie;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -431,7 +450,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.Trie;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
@@ -445,7 +464,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Trie.app/Contents/MacOS/Trie";
 			};
 			name = Debug;
@@ -460,7 +479,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Trie.app/Contents/MacOS/Trie";
 			};
 			name = Release;
@@ -474,7 +493,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieUITests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_TARGET_NAME = Trie;
 			};
 			name = Debug;
@@ -488,7 +507,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieUITests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_TARGET_NAME = Trie;
 			};
 			name = Release;
diff --git a/Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 1a7017c4c..fbc933138 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -6,11 +6,6 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 /// A node in the trie
@@ -105,7 +100,7 @@ extension Trie {
       return
     }
     var currentNode = root
-    for character in word.lowercased().characters {
+    for character in word.lowercased() {
       if let childNode = currentNode.children[character] {
         currentNode = childNode
       } else {
@@ -130,7 +125,7 @@ extension Trie {
       return false
     }
     var currentNode = root
-    for character in word.lowercased().characters {
+    for character in word.lowercased() {
       guard let childNode = currentNode.children[character] else {
         return false
       }
@@ -148,7 +143,7 @@ extension Trie {
   /// search failed.
   private func findLastNodeOf(word: String) -> Node? {
       var currentNode = root
-      for character in word.lowercased().characters {
+      for character in word.lowercased() {
           guard let childNode = currentNode.children[character] else {
               return nil
           }
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index 9c5e66163..928b01f4c 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -6,11 +6,6 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 import Cocoa
 
 class ViewController: NSViewController {
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 45be03aad..b69c5666e 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -6,11 +6,6 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 import XCTest
 @testable import Trie
 

From 5a200e0709ba32a7bd898336502264977b356f77 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:25:37 +0200
Subject: [PATCH 1516/1679] renaming Palindromes to Palindrome

also removing one implementation, moving the one on root level to the playground to reduce the number of implementations to maintain
---
 .../Sources/Palindrome.swift                  | 38 +++++++++++++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 .../Palindrome.swift}                         |  2 +-
 Palindromes/Test/Palindromes.swift            | 26 -------------
 .../Test/Test.xcodeproj/project.pbxproj       | 16 +++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 6 files changed, 65 insertions(+), 33 deletions(-)
 create mode 100644 Palindromes/Palindromes.playground/Sources/Palindrome.swift
 create mode 100644 Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 rename Palindromes/{Palindromes.swift => Test/Palindrome.swift} (93%)
 delete mode 100644 Palindromes/Test/Palindromes.swift
 create mode 100644 Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Palindromes/Palindromes.playground/Sources/Palindrome.swift b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
new file mode 100644
index 000000000..a6d2274bf
--- /dev/null
+++ b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
@@ -0,0 +1,38 @@
+import Foundation
+
+/**
+ Validate that a string is a plaindrome
+ - parameter str: The string to validate
+ - returns: `true` if string is plaindrome, `false` if string is not
+ */
+func isPalindrome(_ str: String) -> Bool {
+    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+    let length = strippedString.count
+    
+    if length > 1 {
+        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+    }
+    return false
+}
+
+/**
+ Compares a strings left side character against right side character following
+ - parameter str: The string to compare characters of
+ - parameter left: Index of left side to compare, must be less than or equal to right
+ - parameter right: Index of right side to compare, must be greater than or equal to left
+ - returns: `true` if left side and right side have all been compared and they all match, `false` if a left and right aren't equal
+ */
+private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
+    if left >= right {
+        return true
+    }
+    
+    let lhs = str[str.index(str.startIndex, offsetBy: left)]
+    let rhs = str[str.index(str.startIndex, offsetBy: right)]
+    
+    if lhs != rhs {
+        return false
+    }
+    
+    return palindrome(str, left: left + 1, right: right - 1)
+}
diff --git a/Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Test/Palindrome.swift
similarity index 93%
rename from Palindromes/Palindromes.swift
rename to Palindromes/Test/Palindrome.swift
index 9ddd04c80..16af14fdb 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Test/Palindrome.swift
@@ -2,7 +2,7 @@ import Foundation
 
 func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-    let length = strippedString.characters.count
+    let length = strippedString.count
 
     if length > 1 {
         return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
diff --git a/Palindromes/Test/Palindromes.swift b/Palindromes/Test/Palindromes.swift
deleted file mode 100644
index 9ddd04c80..000000000
--- a/Palindromes/Test/Palindromes.swift
+++ /dev/null
@@ -1,26 +0,0 @@
-import Foundation
-
-func isPalindrome(_ str: String) -> Bool {
-    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-    let length = strippedString.characters.count
-
-    if length > 1 {
-        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-    }
-    return false
-}
-
-private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-    if left >= right {
-        return true
-    }
-
-    let lhs = str[str.index(str.startIndex, offsetBy: left)]
-    let rhs = str[str.index(str.startIndex, offsetBy: right)]
-
-    if lhs != rhs {
-        return false
-    }
-
-    return palindrome(str, left: left + 1, right: right - 1)
-}
diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
index 07aae3e63..6af90d5c2 100644
--- a/Palindromes/Test/Test.xcodeproj/project.pbxproj
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -8,11 +8,11 @@
 
 /* Begin PBXBuildFile section */
 		9437D8841E0D960A00A38FB8 /* Test.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8831E0D960A00A38FB8 /* Test.swift */; };
-		9437D88B1E0D969500A38FB8 /* Palindromes.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8791E0D948A00A38FB8 /* Palindromes.swift */; };
+		9437D88B1E0D969500A38FB8 /* Palindrome.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8791E0D948A00A38FB8 /* Palindrome.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		9437D8791E0D948A00A38FB8 /* Palindromes.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Palindromes.swift; sourceTree = "<group>"; };
+		9437D8791E0D948A00A38FB8 /* Palindrome.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Palindrome.swift; sourceTree = "<group>"; };
 		9437D8811E0D960A00A38FB8 /* Test.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Test.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		9437D8831E0D960A00A38FB8 /* Test.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Test.swift; sourceTree = "<group>"; };
 		9437D8851E0D960A00A38FB8 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
@@ -32,7 +32,7 @@
 		9437D8651E0D945200A38FB8 = {
 			isa = PBXGroup;
 			children = (
-				9437D8791E0D948A00A38FB8 /* Palindromes.swift */,
+				9437D8791E0D948A00A38FB8 /* Palindrome.swift */,
 				9437D8821E0D960A00A38FB8 /* Test */,
 				9437D86F1E0D945200A38FB8 /* Products */,
 			);
@@ -87,6 +87,7 @@
 				TargetAttributes = {
 					9437D8801E0D960A00A38FB8 = {
 						CreatedOnToolsVersion = 8.2;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 					};
 				};
@@ -123,7 +124,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				9437D88B1E0D969500A38FB8 /* Palindromes.swift in Sources */,
+				9437D88B1E0D969500A38FB8 /* Palindrome.swift in Sources */,
 				9437D8841E0D960A00A38FB8 /* Test.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
@@ -229,7 +230,8 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -243,7 +245,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = self.edu.Test;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
@@ -266,6 +269,7 @@
 				9437D8881E0D960A00A38FB8 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 73b0fc92b71fa5a40a8b6ddc6a664ede35d09858 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:26:50 +0200
Subject: [PATCH 1517/1679] removing duplicate implementation

---
 .../Palindromes.playground/Contents.swift     | 42 -------------------
 1 file changed, 42 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index 44662745a..ee43cce33 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -1,49 +1,7 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
-/**
- Validate that a string is a plaindrome
- - parameter str: The string to validate
- - returns: `true` if string is plaindrome, `false` if string is not
- */
-func isPalindrome(_ str: String) -> Bool {
-    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-    let length = strippedString.characters.count
-
-    if length > 1 {
-        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-    }
-    return false
-}
-
-/**
- Compares a strings left side character against right side character following
- - parameter str: The string to compare characters of
- - parameter left: Index of left side to compare, must be less than or equal to right
- - parameter right: Index of right side to compare, must be greater than or equal to left
- - returns: `true` if left side and right side have all been compared and they all match, `false` if a left and right aren't equal
- */
-private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-    if left >= right {
-        return true
-    }
-
-    let lhs = str[str.index(str.startIndex, offsetBy: left)]
-    let rhs = str[str.index(str.startIndex, offsetBy: right)]
-
-    if lhs != rhs {
-        return false
-    }
-
-    return palindrome(str, left: left + 1, right: right - 1)
-}
-
 //true
 isPalindrome("A man, a plan, a canal, Panama!")
 isPalindrome("abbcbba")

From 66509650d57cd11deeb081359cbc0e4f68877b8e Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:27:09 +0200
Subject: [PATCH 1518/1679] updating recommended project settings

---
 .../Test/Test.xcodeproj/project.pbxproj        | 18 +++++++++++++++++-
 .../xcshareddata/xcschemes/Test.xcscheme       |  2 +-
 2 files changed, 18 insertions(+), 2 deletions(-)

diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
index 6af90d5c2..8125d1f8d 100644
--- a/Palindromes/Test/Test.xcodeproj/project.pbxproj
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -82,7 +82,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0820;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Joshua Alvarado";
 				TargetAttributes = {
 					9437D8801E0D960A00A38FB8 = {
@@ -141,15 +141,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -188,15 +196,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
diff --git a/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme b/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
index 9a1b39e69..72ae3d696 100644
--- a/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
+++ b/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From e9ed7947a90efd5fb42ed5757df1f89758778351 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:28:36 +0200
Subject: [PATCH 1519/1679] setting SWIFT_SWIFT3_OBJC_INFERENCE to default

---
 Palindromes/Test/Test.xcodeproj/project.pbxproj | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
index 8125d1f8d..f01f6f061 100644
--- a/Palindromes/Test/Test.xcodeproj/project.pbxproj
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -246,7 +246,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
@@ -261,7 +261,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = self.edu.Test;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Release;

From d3acedfb063b65327d503a50e86dfbaeb545b90e Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:31:39 +0200
Subject: [PATCH 1520/1679] making isPalindrome(_:) public

---
 Palindromes/Palindromes.playground/Sources/Palindrome.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/Palindromes.playground/Sources/Palindrome.swift b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
index a6d2274bf..3652dbb1f 100644
--- a/Palindromes/Palindromes.playground/Sources/Palindrome.swift
+++ b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
@@ -5,7 +5,7 @@ import Foundation
  - parameter str: The string to validate
  - returns: `true` if string is plaindrome, `false` if string is not
  */
-func isPalindrome(_ str: String) -> Bool {
+public func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
     let length = strippedString.count
     

From 5fe31fff9a5717815cb524b16eb3433fde20926b Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:31:42 +0200
Subject: [PATCH 1521/1679] cleanup

---
 Palindromes/Palindromes.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index ee43cce33..49f767982 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -2,7 +2,7 @@
 
 import Foundation
 
-//true
+// true
 isPalindrome("A man, a plan, a canal, Panama!")
 isPalindrome("abbcbba")
 isPalindrome("racecar")

From 93a4d2d24689ebc6beec1df55e28dc4e94318a96 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:55:39 +0200
Subject: [PATCH 1522/1679] updating README

---
 Palindromes/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 69520a132..e4012d8da 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -26,7 +26,7 @@ Here is a recursive implementation of this in Swift:
 ```swift
 func isPalindrome(_ str: String) -> Bool {
   let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-  let length = strippedString.characters.count
+  let length = strippedString.count
 
   if length > 1 {
     return palindrome(strippedString.lowercased(), left: 0, right: length - 1)

From c4a89a24bee0269733f2ac8ed9605ae0f1574eaa Mon Sep 17 00:00:00 2001
From: Stefan Pleava <stefan_pleava1@hotmail.com>
Date: Thu, 18 Oct 2018 11:45:46 -0400
Subject: [PATCH 1523/1679] Update README.markdown

I think it should say minimum not maximum in the description.
---
 Egg Drop Problem/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index b2f45d09e..416984193 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -12,7 +12,7 @@ If the object is incredibly resilient, and you may need to do the testing on the
 
 ## Description
 
-You're in a building with **m** floors and you are given **n** eggs. What is the maximum number of attempts it will take to find out the floor that breaks the egg?
+You're in a building with **m** floors and you are given **n** eggs. What is the minimum number of attempts it will take to find out the floor that breaks the egg?
 
 For convenience, here are a few rules to keep in mind:
 

From 4c718b4023565795675de2b2755db3226b3cd55e Mon Sep 17 00:00:00 2001
From: vp4 <vishwadatha_p@intuit.com>
Date: Fri, 19 Oct 2018 18:24:40 +0530
Subject: [PATCH 1524/1679] Remove semicolon

---
 Linked List/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0998349fc..d6f1fc986 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -490,9 +490,9 @@ Recursive Approach:
       return head
     }
     let temp = reverse(head.next)
-    head.next.next = head;
-    head.next = NULL;
-    return temp;
+    head.next.next = head
+    head.next = NULL
+    return temp
   }
 ```
 

From 66d0b867e22378465d83aecce1c30609906538d5 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Mon, 22 Oct 2018 03:05:09 +1100
Subject: [PATCH 1525/1679] Updated Radix Sort to Swift 4.2

---
 Radix Sort/RadixSort.playground/Contents.swift    | 15 ++-------------
 .../RadixSort.playground/Sources/radixSort.swift  |  1 -
 2 files changed, 2 insertions(+), 14 deletions(-)

diff --git a/Radix Sort/RadixSort.playground/Contents.swift b/Radix Sort/RadixSort.playground/Contents.swift
index 941723c37..0b549fc9e 100644
--- a/Radix Sort/RadixSort.playground/Contents.swift	
+++ b/Radix Sort/RadixSort.playground/Contents.swift	
@@ -1,21 +1,10 @@
 //: Playground - noun: a place where people can play
 
-import Cocoa
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Test Radix Sort with small array of ten values
 var array: [Int] = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
 radixSort(&array)
 
 // Test Radix Sort with large array of 1000 random values
-var bigArray = [Int](repeating: 0, count: 1000)
-var i = 0
-while i < 1000 {
-  bigArray[i] = Int(arc4random_uniform(1000) + 1)
-  i += 1
-}
+var bigArray = (0..<1000).map { _ in Int.random(in: 1...1000) }
+bigArray
 radixSort(&bigArray)
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
index 424d33fb9..af382f481 100644
--- a/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -3,7 +3,6 @@
  Sorting Algorithm that sorts an input array of integers digit by digit.
  
  */
-import Foundation
 
 // NOTE: This implementation does not handle negative numbers
 public func radixSort(_ array: inout [Int] ) {

From 36ae366ea4faeb4bf96380df3d58ca4da34525c6 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Mon, 22 Oct 2018 04:01:21 +1100
Subject: [PATCH 1526/1679] Updated Radix Sort Tests to Swift 4.2

---
 Radix Sort/Tests/RadixSortTests.swift | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/Radix Sort/Tests/RadixSortTests.swift b/Radix Sort/Tests/RadixSortTests.swift
index 9b881318a..688bcdcb8 100644
--- a/Radix Sort/Tests/RadixSortTests.swift	
+++ b/Radix Sort/Tests/RadixSortTests.swift	
@@ -9,13 +9,6 @@
 import XCTest
 
 class RadixSortTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-  
   func testCombSort() {
     let expectedSequence: [Int] = [2, 9, 19, 32, 55, 67, 89, 101, 912, 4242]
     var sequence = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]

From eab858255456bc4c3be0229cf852d91720ac3361 Mon Sep 17 00:00:00 2001
From: Rahul Sharma <rahulrs0029@gmail.com>
Date: Tue, 23 Oct 2018 18:08:08 +0530
Subject: [PATCH 1527/1679] [Swift 4.2] Updated Linear Search

The code worked fine in Xcode 10. I removed code snippet at the top of playground file.
---
 Linear Search/LinearSearch.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 8ac0e9a71..8c616ded4 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
     for (index, obj) in array.enumerated() where obj == object {
         return index

From d4fdc7bfa84715fcae452439e874740fc6759d7f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20C=2E=20Kr=C3=BCger?= <simon.krueger@intive.com>
Date: Tue, 23 Oct 2018 15:32:33 +0200
Subject: [PATCH 1528/1679] Adds binary recursive stein algorithm to the GCD
 class

* Improves the LCM by passing the used GCD algorithm into the function.
* Find an easy GCD function if possible.
---
 GCD/GCD.playground/Contents.swift             | 165 +++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 +
 GCD/GCD.playground/timeline.xctimeline        |   6 -
 GCD/GCD.swift                                 | 141 ++++++++++++---
 GCD/README.markdown                           |  68 ++++----
 5 files changed, 296 insertions(+), 92 deletions(-)
 create mode 100644 GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 GCD/GCD.playground/timeline.xctimeline

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index c44f28310..9dfd7cca9 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,39 +1,148 @@
 //: Playground - noun: a place where people can play
 
-// Recursive version
-func gcd(_ a: Int, _ b: Int) -> Int {
-  let r = a % b
-  if r != 0 {
-    return gcd(b, r)
-  } else {
+/*
+ Iterative approach based on the Euclidean algorithm.
+ The Euclidean algorithm is based on the principle that the greatest
+ common divisor of two numbers does not change if the larger number
+ is replaced by its difference with the smaller number.
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd if m and n
+ */
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+    
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
     return b
-  }
 }
 
 /*
-// Iterative version
-func gcd(m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
-
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+ Recursive approach based on the Euclidean algorithm.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Note: The recursive version makes only tail recursive calls.
+ Most compilers for imperative languages do not optimize these.
+ The swift compiler as well as the obj-c compiler is able to do
+ optimizations for tail recursive calls, even though it still ends
+ up to be the same in terms of complexity. That said, tail call
+ elimination is not mutually exclusive to recursion.
+ */
+func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+    let r: Int = m % n
+    if r != 0 {
+        return gcdRecursiveEuklid(n, r)
+    } else {
+        return n
+    }
+}
+
+/*
+ The binary GCD algorithm, also known as Stein's algorithm,
+ is an algorithm that computes the greatest common divisor of two
+ nonnegative integers. Stein's algorithm uses simpler arithmetic
+ operations than the conventional Euclidean algorithm; it replaces
+ division with arithmetic shifts, comparisons, and subtraction.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Complexity: worst case O(n^2), where n is the number of bits
+ in the larger of the two numbers. Although each step reduces
+ at least one of the operands by at least a factor of 2,
+ the subtract and shift operations take linear time for very
+ large integers
+ */
+func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+    if let easySolution = findEasySolution(m, n) { return easySolution }
+    
+    if (m & 1) == 0 {
+        // m is even
+        if (n & 1) == 1 {
+            // and n is odd
+            return gcdBinaryRecursiveStein(m >> 1, n)
+        } else {
+            // both m and n are even
+            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
+        }
+    } else if (n & 1) == 0 {
+        // m is odd, n is even
+        return gcdBinaryRecursiveStein(m, n >> 1)
+    } else if (m > n) {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((m - n) >> 1, n)
+    } else {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((n - m) >> 1, m)
+    }
+}
+
+/*
+ Finds an easy solution for the gcd.
+ - Note: It might be relevant for different usecases to
+ try finding an easy solution for the GCD calculation
+ before even starting more difficult operations.
+ */
+func findEasySolution(_ m: Int, _ n: Int) -> Int? {
+    if m == n {
+        return m
+    }
+    if m == 0 {
+        return n
+    }
+    if n == 0 {
+        return m
+    }
+    return nil
 }
-*/
 
-func lcm(_ m: Int, _ n: Int) -> Int {
-  return m / gcd(m, n) * n // we divide before multiplying to avoid integer overflow
+
+enum LCMError: Error {
+    case divisionByZero
+    case lcmEmptyList
+}
+
+/*
+ Calculates the lcm for two given numbers using a specified gcd algorithm.
+ 
+ - Parameter m: First natural number.
+ - Parameter n: Second natural number.
+ - Parameter using: The used gcd algorithm to calculate the lcm.
+ - Throws: Can throw a `divisionByZero` error if one of the given
+ attributes turns out to be zero or less.
+ - Returns: The least common multiplier of the two attributes as
+ an unsigned integer
+ */
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
+    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+    return m / gcdAlgorithm(m, n) * n
 }
 
-gcd(52, 39)       // 13
-gcd(228, 36)      // 12
-gcd(51357, 3819)  // 57
-gcd(841, 299)     // 1
+gcdIterativeEuklid(52, 39)       // 13
+gcdIterativeEuklid(228, 36)      // 12
+gcdIterativeEuklid(51357, 3819)  // 57
+gcdIterativeEuklid(841, 299)     // 1
 
-lcm(2, 3)   // 6
-lcm(10, 8)  // 40
+gcdRecursiveEuklid(52, 39)       // 13
+gcdRecursiveEuklid(228, 36)      // 12
+gcdRecursiveEuklid(51357, 3819)  // 57
+gcdRecursiveEuklid(841, 299)     // 1
+
+gcdBinaryRecursiveStein(52, 39)       // 13
+gcdBinaryRecursiveStein(228, 36)      // 12
+gcdBinaryRecursiveStein(51357, 3819)  // 57
+gcdBinaryRecursiveStein(841, 299)     // 1
+
+do {
+    try lcm(2, 3, using: gcdIterativeEuklid)   // 6
+    try lcm(10, 8, using: gcdIterativeEuklid)  // 40
+} catch {
+    dump(error)
+}
diff --git a/GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/GCD/GCD.playground/timeline.xctimeline b/GCD/GCD.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/GCD/GCD.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index bd903e58a..85b7681f0 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -1,34 +1,125 @@
+
 /*
-  Euclid's algorithm for finding the greatest common divisor
-*/
-func gcd(_ m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
+ Iterative approach based on the Euclidean algorithm.
+ The Euclidean algorithm is based on the principle that the greatest
+ common divisor of two numbers does not change if the larger number
+ is replaced by its difference with the smaller number.
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd if m and n
+ */
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+    
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
+    return b
+}
 
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+/*
+ Recursive approach based on the Euclidean algorithm.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Note: The recursive version makes only tail recursive calls.
+ Most compilers for imperative languages do not optimize these.
+ The swift compiler as well as the obj-c compiler is able to do
+ optimizations for tail recursive calls, even though it still ends
+ up to be the same in terms of complexity. That said, tail call
+ elimination is not mutually exclusive to recursion.
+ */
+func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+    let r: Int = m % n
+    if r != 0 {
+        return gcdRecursiveEuklid(n, r)
+    } else {
+        return n
+    }
 }
 
 /*
-// Recursive version
-func gcd(_ a: Int, _ b: Int) -> Int {
-  let r = a % b
-  if r != 0 {
-    return gcd(b, r)
-  } else {
-    return b
-  }
+ The binary GCD algorithm, also known as Stein's algorithm,
+ is an algorithm that computes the greatest common divisor of two
+ nonnegative integers. Stein's algorithm uses simpler arithmetic
+ operations than the conventional Euclidean algorithm; it replaces
+ division with arithmetic shifts, comparisons, and subtraction.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Complexity: worst case O(n^2), where n is the number of bits
+ in the larger of the two numbers. Although each step reduces
+ at least one of the operands by at least a factor of 2,
+ the subtract and shift operations take linear time for very
+ large integers
+ */
+func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+    if let easySolution = findEasySolution(m, n) { return easySolution }
+    
+    if (m & 1) == 0 {
+        // m is even
+        if (n & 1) == 1 {
+            // and n is odd
+            return gcdBinaryRecursiveStein(m >> 1, n)
+        } else {
+            // both m and n are even
+            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
+        }
+    } else if (n & 1) == 0 {
+        // m is odd, n is even
+        return gcdBinaryRecursiveStein(m, n >> 1)
+    } else if (m > n) {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((m - n) >> 1, n)
+    } else {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((n - m) >> 1, m)
+    }
+}
+
+/*
+ Finds an easy solution for the gcd.
+ - Note: It might be relevant for different usecases to
+ try finding an easy solution for the GCD calculation
+ before even starting more difficult operations.
+ */
+func findEasySolution(_ m: Int, _ n: Int) -> Int? {
+    if m == n {
+        return m
+    }
+    if m == 0 {
+        return n
+    }
+    if n == 0 {
+        return m
+    }
+    return nil
+}
+
+
+enum LCMError: Error {
+    case divisionByZero
+    case lcmEmptyList
 }
-*/
 
 /*
-  Returns the least common multiple of two numbers.
-*/
-func lcm(_ m: Int, _ n: Int) -> Int {
-  return m / gcd(m, n) * n
+ Calculates the lcm for two given numbers using a specified gcd algorithm.
+ 
+ - Parameter m: First natural number.
+ - Parameter n: Second natural number.
+ - Parameter using: The used gcd algorithm to calculate the lcm.
+ - Throws: Can throw a `divisionByZero` error if one of the given
+ attributes turns out to be zero or less.
+ - Returns: The least common multiplier of the two attributes as
+ an unsigned integer
+ */
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
+    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+    return m / gcdAlgorithm(m, n) * n
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index d7e9304bd..a23aea190 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -1,8 +1,8 @@
 # Greatest Common Divisor
 
-The *greatest common divisor* (or Greatest Common Factor) of two numbers `a` and `b` is the largest positive integer that divides both `a` and `b` without a remainder.
+The *greatest common divisor* (or Greatest Common Factor) of two numbers `a` and `b` is the largest positive integer that divides both `a` and `b` without a remainder. The GCD.swift file contains three different algorithms of how to calculate the greatest common divisor.
 
-For example, `gcd(39, 52) = 13` because 13 divides 39 (`39/13 = 3`) as well as 52 (`52/13 = 4`). But there is no larger number than 13 that divides them both.
+For example, `gcdIterativeEuklid(39, 52) = 13` because 13 divides 39 (`39/13 = 3`) as well as 52 (`52/13 = 4`). But there is no larger number than 13 that divides them both.
 
 You've probably had to learn about this in school at some point. :-)
 
@@ -17,25 +17,25 @@ where `a % b` calculates the remainder of `a` divided by `b`.
 Here is an implementation of this idea in Swift:
 
 ```swift
-func gcd(_ a: Int, _ b: Int) -> Int {
-  let r = a % b
-  if r != 0 {
-    return gcd(b, r)
-  } else {
-    return b
-  }
+func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+    let r: Int = m % n
+    if r != 0 {
+        return gcdRecursiveEuklid(n, r)
+    } else {
+        return n
+    }
 }
 ```
 
 Put it in a playground and try it out with these examples:
 
 ```swift
-gcd(52, 39)        // 13
-gcd(228, 36)       // 12
-gcd(51357, 3819)   // 57
+gcdBinaryRecursiveStein(52, 39)        // 13
+gcdRecursiveEuklid(228, 36)       // 12
+gcdIterativeEuklid(51357, 3819)   // 57
 ```
 
-Let's step through the third example:
+Let's step through the third example using gcd as a representation of the gcdRecursiveEuklid here:
 
 	gcd(51357, 3819)
 
@@ -47,10 +47,10 @@ because the remainder of `51357 % 3819` is `1710`. If you work out this division
 
 So `gcd(51357, 3819)` is the same as `gcd(3819, 1710)`. That's useful because we can keep simplifying:
 
-	gcd(3819, 1710) = gcd(1710, 3819 % 1710) = 
-	gcd(1710, 399)  = gcd(399, 1710 % 399)   = 
-	gcd(399, 114)   = gcd(114, 399 % 114)    = 
-	gcd(114, 57)    = gcd(57, 114 % 57)      = 
+	gcd(3819, 1710) = gcd(1710, 3819 % 1710) =
+	gcd(1710, 399)  = gcd(399, 1710 % 399)   =
+	gcd(399, 114)   = gcd(114, 399 % 114)    =
+	gcd(114, 57)    = gcd(57, 114 % 57)      =
 	gcd(57, 0)
 
 And now can't divide any further. The remainder of `114 / 57` is zero because `114 = 57 * 2` exactly. That means we've found the answer:
@@ -68,17 +68,17 @@ gcd(841, 299)     // 1
 Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop.
 
 ```swift
-func gcd(_ m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
-
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
+    return b
 }
 ```
 
@@ -88,9 +88,9 @@ The `max()` and `min()` at the top of the function make sure we always divide th
 
 An idea related to the GCD is the *least common multiple* or LCM.
 
-The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. 
+The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. The example implementation of the LCM takes two numbers and a specification which GCD algorithm is used.
 
-For example: `lcm(2, 3) = 6` because 6 can be divided by 2 and also by 3.
+For example: `lcm(2, 3, using: gcdIterativeEuklid) = 6` because 6 can be divided by 2 and also by 3.
 
 We can calculate the LCM using Euclid's algorithm too:
 
@@ -101,17 +101,19 @@ We can calculate the LCM using Euclid's algorithm too:
 In code:
 
 ```swift
-func lcm(_ m: Int, _ n: Int) -> Int {
-  return m / gcd(m, n) * n
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
+    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+    return m / gcdAlgorithm(m, n) * n
 }
 ```
 
 And to try it out in a playground:
 
 ```swift
-lcm(10, 8)    // 40
+lcm(10, 8, using: gcdIterativeEuklid)    // 40
 ```
 
 You probably won't need to use the GCD or LCM in any real-world problems, but it's cool to play around with this ancient algorithm. It was first described by Euclid in his [Elements](http://publicdomainreview.org/collections/the-first-six-books-of-the-elements-of-euclid-1847/) around 300 BC. Rumor has it that he discovered this algorithm while he was hacking on his Commodore 64.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
+*Extended by Simon Krüger*
\ No newline at end of file

From 0f08fa9ddb315a55cca92d1fbabecb48a406cee8 Mon Sep 17 00:00:00 2001
From: Rahul <rahulrs0029@gmail.com>
Date: Tue, 23 Oct 2018 19:02:39 +0530
Subject: [PATCH 1529/1679] [Swift 4.2] Updated Selection Sort

---
 Selection Sort/SelectionSort.playground/Contents.swift       | 5 -----
 .../SelectionSort.playground/Sources/SelectionSort.swift     | 2 +-
 2 files changed, 1 insertion(+), 6 deletions(-)

diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index b16dadb8d..a552c9edb 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 selectionSort(list)
 selectionSort(list, <)
diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index e7c66481d..e157319b4 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -3,7 +3,7 @@
 /// - Parameter array: array of elements that conform to the Comparable protocol
 /// - Returns: an array in ascending order
 public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
-  return insertionSort(array, <)
+  return selectionSort(array, <)
 }
 
 /// Performs the Selection sort algorithm on a array using the provided comparisson method

From e0c8738b1f1a16184d79158df9b65c6d42fc1568 Mon Sep 17 00:00:00 2001
From: Rahul <rahulrs0029@gmail.com>
Date: Tue, 23 Oct 2018 19:21:46 +0530
Subject: [PATCH 1530/1679] [Swift 4.2] Updated Linked List

---
 Linked List/LinkedList.playground/Contents.swift | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index cfa3a8b45..76b911310 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,10 +3,6 @@
 // For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
 //: Linked List Class Declaration:
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 public final class LinkedList<T> {
     
@@ -459,7 +455,7 @@ var sum = 0
 for element in collection {
     sum += element
 }
-// sum is 15
+sum //15
 
 // Another way of achieving the same result though 'reduce', another method defined in an extension of Sequence. Collections are Sequences.
 let result = collection.reduce(0) {$0 + $1} // 15

From 71b20f41f8e1926a3c4f10a8fc3eca05d98ab193 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 22:25:10 -0500
Subject: [PATCH 1531/1679] Removes Swift 4.0 checks and updates the Swift
 version to 4.2.

---
 Comb Sort/Comb Sort.playground/Contents.swift |  6 +----
 Comb Sort/Tests/CombSortTests.swift           |  1 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 22 ++++++++++++++++---
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 4 files changed, 22 insertions(+), 9 deletions(-)

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index 39e24248a..1f7723838 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -2,11 +2,7 @@
 // Created by Stephen Rutstein
 // 7-16-2016
 
-import Cocoa
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+import Foundation
 
 // Test Comb Sort with small array of ten values
 let array = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index e972c0a57..783fbd150 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -17,6 +17,7 @@ class CombSortTests: XCTestCase {
             print("Hello, Swift 4!")
         #endif
     }
+    
     override func setUp() {
         super.setUp()
         sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
index 7530acbdc..14d059271 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -82,7 +82,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0820;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					056E92741E2483D300B30F52 = {
@@ -142,15 +142,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -192,15 +200,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -235,7 +251,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -248,7 +264,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 55e697ad3..48faa2df7 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 17a1e4c1dec24be6b10cdf8ad7ecddfa520418c1 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 22:40:49 -0500
Subject: [PATCH 1532/1679] Updates tests to check for Swift 4.2. Updates build
 settings to use Swift 4.2.

---
 Comb Sort/Tests/CombSortTests.swift             | 6 +++---
 Comb Sort/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index 783fbd150..166065484 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -12,9 +12,9 @@ class CombSortTests: XCTestCase {
     var sequence: [Int]!
     let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
 
-    func testSwift4(){
-        #if swift(>=4.0)
-            print("Hello, Swift 4!")
+    func testSwiftVersion(){
+        #if swift(>=4.2)
+            print("Hello, Swift 4.2!")
         #endif
     }
     
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
index 14d059271..4582b3f2d 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -187,7 +187,7 @@
 				SDKROOT = macosx;
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -237,7 +237,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};

From 8da637c1d1c92cc65ea3eeb63275dc6117432b67 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:32:46 -0500
Subject: [PATCH 1533/1679] Removes Swift 4.0 check. Removes unused import.
 Refactors an if statement into a guard to be more Swift-y.

---
 Slow Sort/SlowSort.playground/Contents.swift | 5 -----
 Slow Sort/SlowSort.swift                     | 7 ++-----
 2 files changed, 2 insertions(+), 10 deletions(-)

diff --git a/Slow Sort/SlowSort.playground/Contents.swift b/Slow Sort/SlowSort.playground/Contents.swift
index 95bf80739..7c686782c 100644
--- a/Slow Sort/SlowSort.playground/Contents.swift	
+++ b/Slow Sort/SlowSort.playground/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var numberList = [1, 12, 9, 17, 13, 12]
 
 slowsort(0, numberList.count-1, &numberList)
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 9f264a057..c68a53455 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,12 +6,9 @@
 //
 //
 
-import Foundation
-
 public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  if i>=j {
-    return
-  }
+  guard i<j else { return }
+    
   let m = (i+j)/2
   slowsort(i, m, &numberList)
   slowsort(m+1, j, &numberList)

From 1a3a13c94b9ca1fb1ab8c4ec4c4a9b58f700fcdc Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:41:43 -0500
Subject: [PATCH 1534/1679] Removes Swift 4.0 check. Removes unused import.
 Refactors an if statement into a guard to be more Swift-y. Removes
 unnecessarily explicitly defining the function as public.

---
 Slow Sort/SlowSort.playground/Contents.swift | 7 +------
 Slow Sort/SlowSort.swift                     | 8 ++------
 2 files changed, 3 insertions(+), 12 deletions(-)

diff --git a/Slow Sort/SlowSort.playground/Contents.swift b/Slow Sort/SlowSort.playground/Contents.swift
index 95bf80739..54c1e61ea 100644
--- a/Slow Sort/SlowSort.playground/Contents.swift	
+++ b/Slow Sort/SlowSort.playground/Contents.swift	
@@ -1,9 +1,4 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var numberList = [1, 12, 9, 17, 13, 12]
 
-slowsort(0, numberList.count-1, &numberList)
+slowSort(0, numberList.count-1, &numberList)
 print(numberList)
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 9f264a057..217733daa 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,12 +6,8 @@
 //
 //
 
-import Foundation
-
-public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  if i>=j {
-    return
-  }
+func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  guard if i < j else { return }
   let m = (i+j)/2
   slowsort(i, m, &numberList)
   slowsort(m+1, j, &numberList)

From 7add278a6acf10b19e2f8f035441b4a490d0125c Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:43:25 -0500
Subject: [PATCH 1535/1679] Renames function to use camel case.

---
 Slow Sort/SlowSort.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 217733daa..c6e705fc7 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -9,12 +9,12 @@
 func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
   guard if i < j else { return }
   let m = (i+j)/2
-  slowsort(i, m, &numberList)
-  slowsort(m+1, j, &numberList)
+  slowSort(i, m, &numberList)
+  slowSort(m+1, j, &numberList)
   if numberList[j] < numberList[m] {
     let temp = numberList[j]
     numberList[j] = numberList[m]
     numberList[m] = temp
   }
-  slowsort(i, j-1, &numberList)
+  slowSort(i, j-1, &numberList)
 }

From 227d6d9899d7f9abcc120fc04adc4a72119ee4ef Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:50:21 -0500
Subject: [PATCH 1536/1679] Renames function to use camel case.

---
 Slow Sort/README.markdown                          | 14 ++++++--------
 .../SlowSort.playground/Sources/SlowSort.swift     | 13 ++++++-------
 2 files changed, 12 insertions(+), 15 deletions(-)

diff --git a/Slow Sort/README.markdown b/Slow Sort/README.markdown
index f8cc743cc..f7742b6a3 100644
--- a/Slow Sort/README.markdown	
+++ b/Slow Sort/README.markdown	
@@ -17,19 +17,17 @@ We can decompose the problem of sorting n numbers in ascending order into
 Here is an implementation of slow sort in Swift:
 
 ```swift
-public func slowsort(_ i: Int, _ j: Int) {
-    if i>=j {
-        return
-    }
+func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+    guard if i < j else { return }
     let m = (i+j)/2
-    slowsort(i,m)
-    slowsort(m+1,j)
+    slowSort(i, m, &numberList)
+    slowSort(m+1, j, &numberList)
     if numberList[j] < numberList[m] {
         let temp = numberList[j]
         numberList[j] = numberList[m]
         numberList[m] = temp
     }
-    slowsort(i,j-1)
+    slowSort(i, j-1, &numberList)
 }
 ```
 
@@ -47,4 +45,4 @@ public func slowsort(_ i: Int, _ j: Int) {
 
 *Written for Swift Algorithm Club by Lukas Schramm*
 
-(used the Insertion Sort Readme as template)
\ No newline at end of file
+(used the Insertion Sort Readme as template)
diff --git a/Slow Sort/SlowSort.playground/Sources/SlowSort.swift b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift
index 32bb38505..cf09dcc5d 100644
--- a/Slow Sort/SlowSort.playground/Sources/SlowSort.swift	
+++ b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift	
@@ -1,16 +1,15 @@
 import Foundation
 
-public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  if i>=j {
-    return
-  }
+public func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  guard i < j else { return }
+    
   let m = (i+j)/2
-  slowsort(i, m, &numberList)
-  slowsort(m+1, j, &numberList)
+  slowSort(i, m, &numberList)
+  slowSort(m+1, j, &numberList)
   if numberList[j] < numberList[m] {
     let temp = numberList[j]
     numberList[j] = numberList[m]
     numberList[m] = temp
   }
-  slowsort(i, j-1, &numberList)
+  slowSort(i, j-1, &numberList)
 }

From d3de867354ef9f639e991259e8722b9b9bb4e202 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Wed, 24 Oct 2018 18:31:38 -0500
Subject: [PATCH 1537/1679] Updates build settings to use Swift 4.2. Removes
 references to checking for Swift version 4.0. Removes unused import.

---
 Quicksort/Quicksort.playground/Contents.swift          |  5 -----
 Quicksort/Tests/QuicksortTests.swift                   |  7 -------
 Quicksort/Tests/SortingTestHelpers.swift               |  1 -
 .../Tests/Tests-Quicksort.xcodeproj/project.pbxproj    | 10 +++++++---
 .../xcshareddata/xcschemes/Tests-Quicksort.xcscheme    |  4 +---
 5 files changed, 8 insertions(+), 19 deletions(-)

diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 94d9f8e45..f0427731f 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 // *** Simple but inefficient version of quicksort ***
diff --git a/Quicksort/Tests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
index 0a8f1a2a8..c8d9a62e6 100644
--- a/Quicksort/Tests/QuicksortTests.swift
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -1,13 +1,6 @@
 import XCTest
 
 class QuicksortTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-  
   func testQuicksort() {
     checkSortAlgorithm(quicksort)
   }
diff --git a/Quicksort/Tests/SortingTestHelpers.swift b/Quicksort/Tests/SortingTestHelpers.swift
index d699ec1e4..0c47cde4e 100644
--- a/Quicksort/Tests/SortingTestHelpers.swift
+++ b/Quicksort/Tests/SortingTestHelpers.swift
@@ -1,4 +1,3 @@
-import Foundation
 import XCTest
 
 func randomArray(_ size: Int) -> [Int] {
diff --git a/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
index c1b14e727..923195121 100644
--- a/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
@@ -86,7 +86,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -149,12 +149,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -187,7 +189,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -203,12 +205,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -234,7 +238,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
index 5b67c6f70..ec81527d1 100644
--- a/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -10,7 +10,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -31,7 +30,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From b5d5c89353857a26589d2e03bd72f442b45e1aa9 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 12:17:59 +0200
Subject: [PATCH 1538/1679] Updated Binary Tree to Swift 4.2

---
 Binary Tree/BinaryTree.playground/Contents.swift          | 5 -----
 Binary Tree/BinaryTree.playground/contents.xcplayground   | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 9 insertions(+), 6 deletions(-)
 create mode 100644 Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index 9da194fed..b0bff577a 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 public indirect enum BinaryTree<T> {
   case node(BinaryTree<T>, T, BinaryTree<T>)
   case empty
diff --git a/Binary Tree/BinaryTree.playground/contents.xcplayground b/Binary Tree/BinaryTree.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Binary Tree/BinaryTree.playground/contents.xcplayground	
+++ b/Binary Tree/BinaryTree.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 016ae7c90bc525246f925480b6c6aa92eab47e4f Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 12:21:05 +0200
Subject: [PATCH 1539/1679] Update BitSet to Swift 4.2

---
 Bit Set/BitSet.playground/Contents.swift                  | 5 -----
 Bit Set/BitSet.playground/contents.xcplayground           | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 9 insertions(+), 6 deletions(-)
 create mode 100644 Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 95253ea27..d11b36e8c 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
 
diff --git a/Bit Set/BitSet.playground/contents.xcplayground b/Bit Set/BitSet.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Bit Set/BitSet.playground/contents.xcplayground	
+++ b/Bit Set/BitSet.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 6d8e795377902dc7dbdc6ad0a2231f62ba3a0d49 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 12:31:47 +0200
Subject: [PATCH 1540/1679] Update Bounded Priority Queue to Swift 4.2

---
 .../BoundedPriorityQueue.playground/Contents.swift        | 5 -----
 .../BoundedPriorityQueue.playground/contents.xcplayground | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj                 | 6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 5 files changed, 20 insertions(+), 9 deletions(-)
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index f8e219c13..d6204abec 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 struct Message: Comparable, CustomStringConvertible {
   let name: String
   let priority: Int
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground b/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 842c51695..11f907b47 100644
--- a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,7 +86,7 @@
 				TargetAttributes = {
 					B80004B21C83E342001FE2D7 = {
 						CreatedOnToolsVersion = 7.2.1;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -226,7 +226,7 @@
 				SDKROOT = macosx;
 				SWIFT_OBJC_BRIDGING_HEADER = "";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -269,7 +269,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OBJC_BRIDGING_HEADER = "";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 57f25c429638b6a607d3e67f9e70f3633e2a1045 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:16:15 +0200
Subject: [PATCH 1541/1679] Update Boyer Moore to Swift 4.2

---
 .../BoyerMooreHorspool.playground/Contents.swift   | 11 +++--------
 .../xcshareddata/IDEWorkspaceChecks.plist          |  8 ++++++++
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift      |  6 +++---
 Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift   |  4 ++--
 .../Tests/Tests.xcodeproj/project.pbxproj          | 14 ++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist          |  8 ++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme          |  4 +---
 .../contents.xcworkspacedata                       |  6 +++---
 8 files changed, 36 insertions(+), 25 deletions(-)
 create mode 100644 Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index e88a1b93d..1666549c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 /*
   Boyer-Moore string search
 
@@ -16,13 +11,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index af8aea9d9..dbd738740 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -9,13 +9,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
diff --git a/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift b/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
index 9efe60874..436173127 100755
--- a/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
+++ b/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
@@ -26,8 +26,8 @@ class BoyerMooreTest: XCTestCase {
         XCTAssertNotNil(index)
 
         let startIndex = index!
-        let endIndex = string.index(index!, offsetBy: pattern.characters.count)
-        let match = string.substring(with: startIndex..<endIndex)
+        let endIndex = string.index(index!, offsetBy: pattern.count)
+        let match = String(string[startIndex..<endIndex])
         XCTAssertEqual(match, pattern)
     }
 
diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
index ab93d46a0..d29ac95f5 100644
--- a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
@@ -78,12 +78,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0900;
+						LastSwiftMigration = "";
 					};
 				};
 			};
@@ -157,12 +157,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -210,12 +212,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -252,8 +256,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -265,8 +268,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 538a6f4fa..afd69e6a7 100644
--- a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 9305ae37c..04d4ac573 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -612,16 +612,16 @@
       location = "group:Boyer-Moore"
       name = "Boyer-Moore">
       <FileRef
-         location = "group:BoyerMoore.playground">
+         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.playground">
       </FileRef>
       <FileRef
-         location = "group:BoyerMoore.swift">
+         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>
       <Group
-         location = "group:Tests"
+         location = "group:Boyer-Moore-Horspool/Tests"
          name = "Tests">
          <FileRef
             location = "group:BoyerMooreHorspoolTests.swift">

From 7384ec29e4e95cbae0b6a93dc6ae2ffe66eecffb Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:20:32 +0200
Subject: [PATCH 1542/1679] Update Boyer Moore to Swift 4.2

---
 .../contents.xcworkspacedata                           | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 04d4ac573..d85d538b3 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -609,19 +609,19 @@
       </Group>
    </Group>
    <Group
-      location = "group:Boyer-Moore"
+      location = "group:Boyer-Moore-Horspool"
       name = "Boyer-Moore">
       <FileRef
-         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.playground">
+         location = "group:BoyerMooreHorspool.playground">
       </FileRef>
       <FileRef
-         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.swift">
+         location = "group:BoyerMooreHorspool.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>
       <Group
-         location = "group:Boyer-Moore-Horspool/Tests"
+         location = "group:Tests"
          name = "Tests">
          <FileRef
             location = "group:BoyerMooreHorspoolTests.swift">
@@ -633,7 +633,7 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:Tests.xcodeproj">
+            location = "group:/Users/mroedder/workspace/swift-algorithm-club/Boyer-Moore-Horspool/Tests/Tests.xcodeproj">
          </FileRef>
       </Group>
    </Group>

From 402f23669b3f5c06dbd64adfe885d873e3a23f65 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:24:39 +0200
Subject: [PATCH 1543/1679] Update Boyer Moore to Swift 4.2

---
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index d85d538b3..a37dac494 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -633,7 +633,7 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:/Users/mroedder/workspace/swift-algorithm-club/Boyer-Moore-Horspool/Tests/Tests.xcodeproj">
+            location = "group:Tests/Tests.xcodeproj">
          </FileRef>
       </Group>
    </Group>

From 6ead6d0dcb0e77f51cbda0582a1b6f56c1d0ebd0 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:27:09 +0200
Subject: [PATCH 1544/1679] Update README to use Swift 4.2

---
 Boyer-Moore-Horspool/README.markdown | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Boyer-Moore-Horspool/README.markdown b/Boyer-Moore-Horspool/README.markdown
index f5e21ea41..8879d8df6 100644
--- a/Boyer-Moore-Horspool/README.markdown
+++ b/Boyer-Moore-Horspool/README.markdown
@@ -38,13 +38,13 @@ extension String {
     func index(of pattern: String) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
@@ -162,13 +162,13 @@ extension String {
     func index(of pattern: String) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
+        let patternLength = pattern.count
         guard patternLength > 0, patternLength <= characters.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 

From 13d152600da95a0864d14edae72c0d93c161781c Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:41:18 +0200
Subject: [PATCH 1545/1679] Update Breadth First Search to Swift 4.2

---
 .../Contents.swift                            |  4 ---
 .../Sources/Graph.swift                       |  2 +-
 .../contents.xcplayground                     |  2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 30 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 7 files changed, 44 insertions(+), 12 deletions(-)
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 3986a0cee..cf22ebb25 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
index 87e21897c..0343120f8 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -5,7 +5,7 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(_ label: String) -> Node {
+  @discardableResult public func addNode(_ label: String) -> Node {
     let node = Node(label)
     nodes.append(node)
     return node
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground
index 513c2e7e9..f635e9804 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
@@ -1,2 +1,2 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='6.0' target-platform='ios' display-mode='raw'/>
\ No newline at end of file
+<playground version='6.0' target-platform='ios' display-mode='raw' last-migration='1000'/>
\ No newline at end of file
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index f86abf86e..a7f04e00a 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -59,7 +59,6 @@
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
 			name = Tests;
-			path = TestsTests;
 			sourceTree = "<group>";
 		};
 /* End PBXGroup section */
@@ -89,12 +88,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -149,13 +148,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,13 +202,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -218,6 +237,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -231,7 +251,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -244,7 +264,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index dfcf6de42..afd69e6a7 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 56e054717532036d5d42df76295a9633af3e231a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20C=2E=20Kr=C3=BCger?= <simon.krueger@intive.com>
Date: Fri, 26 Oct 2018 14:33:49 +0200
Subject: [PATCH 1546/1679] Extended Miller-Rabin Primality test [code]

* Adds a more readable documentation and clear naming for variables to the Miller-Rabin Primality Test example
   * Miller-Rabin can fail under certain situations. These have to throw an error.
* Updates the relevant playground files
* Add name to documentation
---
 .../MRPrimality.playground/Contents.swift     |  46 ++---
 .../Sources/MRPrimality.swift                 | 111 ------------
 .../Sources/MillerRabin.swift                 | 100 +++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 +
 Miller-Rabin Primality Test/MRPrimality.swift | 169 ++++++++----------
 Miller-Rabin Primality Test/README.markdown   |   5 +-
 7 files changed, 221 insertions(+), 225 deletions(-)
 delete mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index d8fd7fad8..1e4113c15 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -5,25 +5,27 @@
 print("Hello, Swift 4!")
 #endif
 
-// Real primes
-mrPrimalityTest(5)
-mrPrimalityTest(439)
-mrPrimalityTest(1201)
-mrPrimalityTest(143477)
-mrPrimalityTest(1299869)
-mrPrimalityTest(15487361)
-mrPrimalityTest(179426363)
-mrPrimalityTest(32416187747)
-
-// Fake primes
-mrPrimalityTest(15)
-mrPrimalityTest(435)
-mrPrimalityTest(1207)
-mrPrimalityTest(143473)
-mrPrimalityTest(1291869)
-mrPrimalityTest(15487161)
-mrPrimalityTest(178426363)
-mrPrimalityTest(32415187747)
-
-// With iteration
-mrPrimalityTest(32416190071, iteration: 10)
+do {
+    // Real primes
+    try checkWithMillerRabin(5)
+    try checkWithMillerRabin(439)
+    try checkWithMillerRabin(1201)
+    try checkWithMillerRabin(143477)
+    try checkWithMillerRabin(1299869)
+    try checkWithMillerRabin(15487361)
+    try checkWithMillerRabin(179426363)
+    
+    // Fake primes
+    try checkWithMillerRabin(15)
+    try checkWithMillerRabin(435)
+    try checkWithMillerRabin(1207)
+    try checkWithMillerRabin(143473)
+    try checkWithMillerRabin(1291869)
+    try checkWithMillerRabin(15487161)
+    try checkWithMillerRabin(178426363)
+    
+    // Specifying accuracy
+    try checkWithMillerRabin(179426363, accuracy: 10)
+} catch {
+    dump(error)
+}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
deleted file mode 100644
index ee2ace8b9..000000000
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
+++ /dev/null
@@ -1,111 +0,0 @@
-//
-//  MRPrimality.swift
-//  
-//
-//  Created by Sahn Cha on 2016. 10. 18..
-//
-//
-
-import Foundation
-
-/*
-  Miller-Rabin Primality Test.
-  One of the most used algorithms for primality testing.
-  Since this is a probabilistic algorithm, it needs to be executed multiple times to increase accuracy.
-  
-  Inputs:
-    n: UInt64 { target integer to be tested for primality }
-    k: Int    { optional. number of iterations }
- 
-  Outputs:
-    true      { probably prime }
-    false     { composite }
- */
-public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
-  guard n > 2 && n % 2 == 1 else { return false }
-
-  var d = n - 1
-  var s = 0
-
-  while d % 2 == 0 {
-    d /= 2
-    s += 1
-  }
-
-  let range = UInt64.max - UInt64.max % (n - 2)
-  var r: UInt64 = 0
-  repeat {
-    arc4random_buf(&r, MemoryLayout.size(ofValue: r))
-  } while r >= range
-
-  r = r % (n - 2) + 2
-
-  for _ in 1 ... k {
-    var x = powmod64(r, d, n)
-    if x == 1 || x == n - 1 { continue }
-
-    if s == 1 { s = 2 }
-
-    for _ in 1 ... s - 1 {
-      x = powmod64(x, 2, n)
-      if x == 1 { return false }
-      if x == n - 1 { break }
-    }
-
-    if x != n - 1 { return false }
-  }
-
-  return true
-}
-
-/*
-  Calculates (base^exp) mod m.
- 
-  Inputs:
-    base: UInt64  { base }
-    exp: UInt64   { exponent }
-    m: UInt64     { modulus }
- 
-  Outputs:
-    the result
- */
-private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
-  if m == 1 { return 0 }
-
-  var result: UInt64 = 1
-  var b = base % m
-  var e = exp
-
-  while e > 0 {
-    if e % 2 == 1 { result = mulmod64(result, b, m) }
-    b = mulmod64(b, b, m)
-    e >>= 1
-  }
-
-  return result
-}
-
-/*
-  Calculates (first * second) mod m, hopefully without overflow. :]
- 
-  Inputs:
-    first: UInt64   { first integer }
-    second: UInt64  { second integer }
-    m: UInt64       { modulus }
- 
-  Outputs:
-    the result
- */
-private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64 {
-  var result: UInt64 = 0
-  var a = first
-  var b = second
-
-  while a != 0 {
-    if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
-    a >>= 1
-    b = (b << 1) % m
-  }
-
-  return result
-}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift
new file mode 100644
index 000000000..03daac1fa
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift	
@@ -0,0 +1,100 @@
+//
+//  MRPrimality.swift
+//
+//
+//  Created by Sahn Cha on 2016. 10. 18..
+//
+//
+
+import Foundation
+
+enum MillerRabinError: Error {
+    case primeLowAccuracy
+    case primeLowerBorder
+    case uIntOverflow
+}
+
+/*
+ The Miller–Rabin test relies on an equality or set of equalities that
+ hold true for prime values, then checks whether or not they hold for
+ a number that we want to test for primality.
+ 
+ - Parameter n: an odd integer to be tested for primality;
+ - Parameter k: a parameter that determines the accuracy of the test
+ - throws: Can throw an error of type `MillerRabinError`.
+ - Returns: composite if n is composite, otherwise probably prime
+ */
+public func checkWithMillerRabin(_ n: UInt, accuracy k: UInt = 1) throws -> Bool {
+    guard k > 0 else { throw MillerRabinError.primeLowAccuracy }
+    guard n > 0 else { throw MillerRabinError.primeLowerBorder }
+    guard n > 3 else { return true }
+    
+    // return false for all even numbers bigger than 2
+    if n % 2 == 0 {
+        return false
+    }
+    
+    let s: UInt = UInt((n - 1).trailingZeroBitCount)
+    let d: UInt = (n - 1) >> s
+    
+    guard UInt(pow(2.0, Double(s))) * d == n - 1 else { throw MillerRabinError.primeLowerBorder }
+    
+    /// Inspect whether a given witness will reveal the true identity of n.
+    func tryComposite(_ a: UInt, d: UInt, n: UInt) throws -> Bool? {
+        var x = try calculateModularExponentiation(base: a, exponent: d, modulus: n)
+        if x == 1 || x == (n - 1) {
+            return nil
+        }
+        for _ in 1..<s {
+            x = try calculateModularExponentiation(base: x, exponent: 2, modulus: n)
+            if x == 1 {
+                return false
+            } else if x == (n - 1) {
+                return nil
+            }
+        }
+        return false
+    }
+    
+    for _ in 0..<k {
+        let a = UInt.random(in: 2..<n-2)
+        if let composite = try tryComposite(a, d: d, n: n) {
+            return composite
+        }
+    }
+    
+    return true
+}
+
+/*
+ Calculates the modular exponentiation based on `Applied Cryptography by Bruce Schneier.`
+ in `Schneier, Bruce (1996). Applied Cryptography: Protocols, Algorithms,
+ and Source Code in C, Second Edition (2nd ed.). Wiley. ISBN 978-0-471-11709-4.`
+ 
+ - Parameter base: The natural base b.
+ - Parameter base: The natural exponent e.
+ - Parameter base: The natural modulus m.
+ - Throws: Can throw a `uIntOverflow` if the modulus' square exceeds the memory
+ limitations of UInt on the current system.
+ - Returns: The modular exponentiation c.
+ */
+private func calculateModularExponentiation(base: UInt, exponent: UInt, modulus: UInt) throws -> UInt {
+    guard modulus > 1 else { return 0 }
+    guard !(modulus-1).multipliedReportingOverflow(by: (modulus-1)).overflow else {
+        throw MillerRabinError.uIntOverflow
+    }
+    
+    var result: UInt = 1
+    var exponentCopy = exponent
+    var baseCopy = base % modulus
+    
+    while exponentCopy > 0 {
+        if exponentCopy % 2 == 1 {
+            result = (result * baseCopy) % modulus
+        }
+        exponentCopy = exponentCopy >> 1
+        baseCopy = (baseCopy * baseCopy) % modulus
+    }
+    
+    return result
+}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Miller-Rabin Primality Test/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.swift
index ee2ace8b9..24b9c674c 100644
--- a/Miller-Rabin Primality Test/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.swift	
@@ -1,6 +1,6 @@
 //
 //  MRPrimality.swift
-//  
+//
 //
 //  Created by Sahn Cha on 2016. 10. 18..
 //
@@ -8,104 +8,93 @@
 
 import Foundation
 
-/*
-  Miller-Rabin Primality Test.
-  One of the most used algorithms for primality testing.
-  Since this is a probabilistic algorithm, it needs to be executed multiple times to increase accuracy.
-  
-  Inputs:
-    n: UInt64 { target integer to be tested for primality }
-    k: Int    { optional. number of iterations }
- 
-  Outputs:
-    true      { probably prime }
-    false     { composite }
- */
-public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
-  guard n > 2 && n % 2 == 1 else { return false }
-
-  var d = n - 1
-  var s = 0
-
-  while d % 2 == 0 {
-    d /= 2
-    s += 1
-  }
-
-  let range = UInt64.max - UInt64.max % (n - 2)
-  var r: UInt64 = 0
-  repeat {
-    arc4random_buf(&r, MemoryLayout.size(ofValue: r))
-  } while r >= range
-
-  r = r % (n - 2) + 2
-
-  for _ in 1 ... k {
-    var x = powmod64(r, d, n)
-    if x == 1 || x == n - 1 { continue }
-
-    if s == 1 { s = 2 }
-
-    for _ in 1 ... s - 1 {
-      x = powmod64(x, 2, n)
-      if x == 1 { return false }
-      if x == n - 1 { break }
-    }
-
-    if x != n - 1 { return false }
-  }
-
-  return true
+enum MillerRabinError: Error {
+    case primeLowAccuracy
+    case primeLowerBorder
+    case uIntOverflow
 }
 
 /*
-  Calculates (base^exp) mod m.
- 
-  Inputs:
-    base: UInt64  { base }
-    exp: UInt64   { exponent }
-    m: UInt64     { modulus }
- 
-  Outputs:
-    the result
- */
-private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
-  if m == 1 { return 0 }
+ The Miller–Rabin test relies on an equality or set of equalities that
+ hold true for prime values, then checks whether or not they hold for
+ a number that we want to test for primality.
+
+ - Parameter n: an odd integer to be tested for primality;
+ - Parameter k: a parameter that determines the accuracy of the test
+ - throws: Can throw an error of type `MillerRabinError`.
+ - Returns: composite if n is composite, otherwise probably prime
+*/
+func checkWithMillerRabin(_ n: UInt, accuracy k: UInt = 1) throws -> Bool {
+    guard k > 0 else { throw MillerRabinError.primeLowAccuracy }
+    guard n > 0 else { throw MillerRabinError.primeLowerBorder }
+    guard n > 3 else { return true }
+
+    // return false for all even numbers bigger than 2
+    if n % 2 == 0 {
+        return false
+    }
 
-  var result: UInt64 = 1
-  var b = base % m
-  var e = exp
+    let s: UInt = UInt((n - 1).trailingZeroBitCount)
+    let d: UInt = (n - 1) >> s
+
+    guard UInt(pow(2.0, Double(s))) * d == n - 1 else { throw EncryptionError.primeLowerBorder }
+
+    /// Inspect whether a given witness will reveal the true identity of n.
+    func tryComposite(_ a: UInt, d: UInt, n: UInt) throws -> Bool? {
+        var x = try calculateModularExponentiation(base: a, exponent: d, modulus: n)
+        if x == 1 || x == (n - 1) {
+            return nil
+        }
+        for _ in 1..<s {
+            x = try calculateModularExponentiation(base: x, exponent: 2, modulus: n)
+            if x == 1 {
+                return false
+            } else if x == (n - 1) {
+                return nil
+            }
+        }
+        return false
+    }
 
-  while e > 0 {
-    if e % 2 == 1 { result = mulmod64(result, b, m) }
-    b = mulmod64(b, b, m)
-    e >>= 1
-  }
+    for _ in 0..<k {
+        let a = UInt.random(in: 2..<n-2)
+        if let composite = try tryComposite(a, d: d, n: n) {
+            return composite
+        }
+    }
 
-  return result
+    return true
 }
 
 /*
-  Calculates (first * second) mod m, hopefully without overflow. :]
- 
-  Inputs:
-    first: UInt64   { first integer }
-    second: UInt64  { second integer }
-    m: UInt64       { modulus }
- 
-  Outputs:
-    the result
- */
-private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64 {
-  var result: UInt64 = 0
-  var a = first
-  var b = second
+ Calculates the modular exponentiation based on `Applied Cryptography by Bruce Schneier.`
+ in `Schneier, Bruce (1996). Applied Cryptography: Protocols, Algorithms,
+ and Source Code in C, Second Edition (2nd ed.). Wiley. ISBN 978-0-471-11709-4.`
+
+ - Parameter base: The natural base b.
+ - Parameter base: The natural exponent e.
+ - Parameter base: The natural modulus m.
+ - Throws: Can throw a `uIntOverflow` if the modulus' square exceeds the memory
+  limitations of UInt on the current system.
+ - Returns: The modular exponentiation c.
+*/
+private func calculateModularExponentiation(base: UInt, exponent: UInt, modulus: UInt) throws -> UInt {
+    guard modulus > 1 else { return 0 }
+    guard !(modulus-1).multipliedReportingOverflow(by: (modulus-1)).overflow else {
+        throw MillerRabinError.uIntOverflow
+    }
 
-  while a != 0 {
-    if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
-    a >>= 1
-    b = (b << 1) % m
-  }
+    var result: UInt = 1
+    var exponentCopy = exponent
+    var baseCopy = base % modulus
+
+    while exponentCopy > 0 {
+        if exponentCopy % 2 == 1 {
+            result = (result * baseCopy) % modulus
+        }
+        exponentCopy = exponentCopy >> 1
+        baseCopy = (baseCopy * baseCopy) % modulus
+    }
 
-  return result
+    return result
 }
diff --git a/Miller-Rabin Primality Test/README.markdown b/Miller-Rabin Primality Test/README.markdown
index 07acb9e18..9cc677a2e 100644
--- a/Miller-Rabin Primality Test/README.markdown	
+++ b/Miller-Rabin Primality Test/README.markdown	
@@ -27,8 +27,8 @@ The following pseudo code is excerpted from Wikipedia[3]:
 ## Usage
 
 ```swift
-mrPrimalityTest(7)                      // test if 7 is prime. (default iteration = 1)
-mrPrimalityTest(7, iteration: 10)       // test if 7 is prime && iterate 10 times.
+checkWithMillerRabin(7)                      // test if 7 is prime. (default iteration = 1)
+checkWithMillerRabin(7, accuracy: 10)       // test if 7 is prime && iterate 10 times.
 ```
 
 ## Reference
@@ -37,6 +37,7 @@ mrPrimalityTest(7, iteration: 10)       // test if 7 is prime && iterate 10 time
 3. Miller–Rabin primality test - Wikipedia, the free encyclopedia
 
 _Written for Swift Algorithm Club by **Sahn Cha**, @scha00_
+_Code updated by **Simon C. Krüger**._
 
 [1]: https://cs.uwaterloo.ca/research/tr/1975/CS-75-27.pdf
 [2]: http://www.sciencedirect.com/science/article/pii/0022314X80900840

From b47eb3e80afffc20c5e540e33fec66ae7a65bec0 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall
 <44420971+laurentaylormarshall@users.noreply.github.com>
Date: Fri, 26 Oct 2018 18:56:13 -0500
Subject: [PATCH 1547/1679] Update SlowSort.swift

---
 Slow Sort/SlowSort.swift | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index c68a53455..813f3b7a9 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -5,10 +5,8 @@
 //  Created by Pope Lukas Schramm (Dabendorf Orthodox Religion) on 16-07-16.
 //
 //
-
-public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  guard i<j else { return }
-    
+func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  guard if i < j else { return }
   let m = (i+j)/2
   slowsort(i, m, &numberList)
   slowsort(m+1, j, &numberList)

From 231f5629f4147d5808c70607cf9ad94c1cb89152 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall
 <44420971+laurentaylormarshall@users.noreply.github.com>
Date: Fri, 26 Oct 2018 19:11:33 -0500
Subject: [PATCH 1548/1679] Updates function name.

---
 Slow Sort/SlowSort.swift | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 813f3b7a9..3b762042a 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -1,19 +1,19 @@
 //
 //  SlowSort.swift
-//  
+//
 //
 //  Created by Pope Lukas Schramm (Dabendorf Orthodox Religion) on 16-07-16.
 //
 //
 func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  guard if i < j else { return }
-  let m = (i+j)/2
-  slowsort(i, m, &numberList)
-  slowsort(m+1, j, &numberList)
-  if numberList[j] < numberList[m] {
-    let temp = numberList[j]
-    numberList[j] = numberList[m]
-    numberList[m] = temp
-  }
-  slowsort(i, j-1, &numberList)
+    guard if i < j else { return }
+    let m = (i+j)/2
+    slowSort(i, m, &numberList)
+    slowSort(m+1, j, &numberList)
+    if numberList[j] < numberList[m] {
+        let temp = numberList[j]
+        numberList[j] = numberList[m]
+        numberList[m] = temp
+    }
+    slowSort(i, j-1, &numberList)
 }

From 22efd0d33aa9d3bfacf3c84701dc157bb10e5aa7 Mon Sep 17 00:00:00 2001
From: Erik Strottmann <erik.strottmann@gmail.com>
Date: Sat, 27 Oct 2018 10:26:54 -0700
Subject: [PATCH 1549/1679] Standardize Trie indentation to 2 spaces

2 spaces is recommended by the Ray Wenderlich Swift Style Guide.
---
 Trie/ReadMe.md                           |  40 +--
 Trie/Trie/Trie.xcodeproj/project.pbxproj |   2 +
 Trie/Trie/Trie/AppDelegate.swift         |  12 +-
 Trie/Trie/Trie/Trie.swift                | 118 ++++----
 Trie/Trie/Trie/ViewController.swift      |  16 +-
 Trie/Trie/TrieTests/TrieTests.swift      | 340 +++++++++++------------
 Trie/Trie/TrieUITests/TrieUITests.swift  |  34 +--
 7 files changed, 280 insertions(+), 282 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 8e473a619..8d0c45c8a 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -27,29 +27,29 @@ Tries are very useful for certain situations. Here are some of the advantages:
 
 ```swift
 func contains(word: String) -> Bool {
-	guard !word.isEmpty else { return false }
+  guard !word.isEmpty else { return false }
 
-	// 1
-	var currentNode = root
+  // 1
+  var currentNode = root
   
-	// 2
-	var characters = Array(word.lowercased())
-	var currentIndex = 0
+  // 2
+  var characters = Array(word.lowercased())
+  var currentIndex = 0
  
-	// 3
-	while currentIndex < characters.count, 
-	  let child = currentNode.children[characters[currentIndex]] {
-
-	  currentNode = child
-	  currentIndex += 1
-	}
-
-	// 4
-	if currentIndex == characters.count && currentNode.isTerminating {
-	  return true
-	} else {
-	  return false
-	}
+  // 3
+  while currentIndex < characters.count, 
+    let child = currentNode.children[characters[currentIndex]] {
+
+    currentNode = child
+    currentIndex += 1
+  }
+
+  // 4
+  if currentIndex == characters.count && currentNode.isTerminating {
+    return true
+  } else {
+    return false
+  }
 }
 ```
 
diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 1e3602eea..6b7cc9b61 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -87,7 +87,9 @@
 				EB798E191DFEF79900F0628D /* TrieUITests */,
 				EB798DFB1DFEF79900F0628D /* Products */,
 			);
+			indentWidth = 2;
 			sourceTree = "<group>";
+			tabWidth = 2;
 		};
 		EB798DFB1DFEF79900F0628D /* Products */ = {
 			isa = PBXGroup;
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
index b2c46695b..48dc24673 100644
--- a/Trie/Trie/Trie/AppDelegate.swift
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -11,12 +11,12 @@ import Cocoa
 @NSApplicationMain
 class AppDelegate: NSObject, NSApplicationDelegate {
 
-    func applicationDidFinishLaunching(_ aNotification: Notification) {
-        // Insert code here to initialize your application
-    }
+  func applicationDidFinishLaunching(_ aNotification: Notification) {
+    // Insert code here to initialize your application
+  }
 
-    func applicationWillTerminate(_ aNotification: Notification) {
-        // Insert code here to tear down your application
-    }
+  func applicationWillTerminate(_ aNotification: Notification) {
+    // Insert code here to tear down your application
+  }
 
 }
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index fbc933138..accc7b61c 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -43,54 +43,53 @@ class TrieNode<T: Hashable> {
 /// A trie data structure containing words.  Each node is a single
 /// character of a word.
 class Trie: NSObject, NSCoding {
-    typealias Node = TrieNode<Character>
-    /// The number of words in the trie
-    public var count: Int {
-        return wordCount
-    }
-    /// Is the trie empty?
-    public var isEmpty: Bool {
-        return wordCount == 0
-    }
-    /// All words currently in the trie
-    public var words: [String] {
-        return wordsInSubtrie(rootNode: root, partialWord: "")
-    }
-    fileprivate let root: Node
-    fileprivate var wordCount: Int
-
-    /// Creates an empty trie.
-    override init() {
-        root = Node()
-        wordCount = 0
-        super.init()
-    }
+  typealias Node = TrieNode<Character>
+  /// The number of words in the trie
+  public var count: Int {
+    return wordCount
+  }
+  /// Is the trie empty?
+  public var isEmpty: Bool {
+    return wordCount == 0
+  }
+  /// All words currently in the trie
+  public var words: [String] {
+    return wordsInSubtrie(rootNode: root, partialWord: "")
+  }
+  fileprivate let root: Node
+  fileprivate var wordCount: Int
+
+  /// Creates an empty trie.
+  override init() {
+    root = Node()
+    wordCount = 0
+    super.init()
+  }
 
-    // MARK: NSCoding
+  // MARK: NSCoding
 
-    /// Initializes the trie with words from an archive
-    ///
-    /// - Parameter decoder: Decodes the archive
-    required convenience init?(coder decoder: NSCoder) {
-        self.init()
-        let words = decoder.decodeObject(forKey: "words") as? [String]
-        for word in words! {
-            self.insert(word: word)
-        }
+  /// Initializes the trie with words from an archive
+  ///
+  /// - Parameter decoder: Decodes the archive
+  required convenience init?(coder decoder: NSCoder) {
+    self.init()
+    let words = decoder.decodeObject(forKey: "words") as? [String]
+    for word in words! {
+      self.insert(word: word)
     }
+  }
 
-    /// Encodes the words in the trie by putting them in an array then encoding
-    /// the array.
-    ///
-    /// - Parameter coder: The object that will encode the array
-    func encode(with coder: NSCoder) {
-        coder.encode(self.words, forKey: "words")
-    }
+  /// Encodes the words in the trie by putting them in an array then encoding
+  /// the array.
+  ///
+  /// - Parameter coder: The object that will encode the array
+  func encode(with coder: NSCoder) {
+    coder.encode(self.words, forKey: "words")
+  }
 }
 
 // MARK: - Adds methods: insert, remove, contains
 extension Trie {
-
   /// Inserts a word into the trie.  If the word is already present,
   /// there is no change.
   ///
@@ -142,14 +141,14 @@ extension Trie {
   /// - Returns: the node where the search ended, nil if the
   /// search failed.
   private func findLastNodeOf(word: String) -> Node? {
-      var currentNode = root
-      for character in word.lowercased() {
-          guard let childNode = currentNode.children[character] else {
-              return nil
-          }
-          currentNode = childNode
+    var currentNode = root
+    for character in word.lowercased() {
+      guard let childNode = currentNode.children[character] else {
+        return nil
       }
-      return currentNode
+      currentNode = childNode
+    }
+    return currentNode
   }
 
   /// Attempts to walk to the terminating node of a word.  The
@@ -160,10 +159,9 @@ extension Trie {
   /// search failed.
   private func findTerminalNodeOf(word: String) -> Node? {
     if let lastNode = findLastNodeOf(word: word) {
-        return lastNode.isTerminating ? lastNode : nil
+      return lastNode.isTerminating ? lastNode : nil
     }
     return nil
-
   }
 
   /// Deletes a word from the trie by starting with the last letter
@@ -237,17 +235,17 @@ extension Trie {
   ///   - prefix: the letters for word prefix
   /// - Returns: the words in the subtrie that start with prefix
   func findWordsWithPrefix(prefix: String) -> [String] {
-      var words = [String]()
-      let prefixLowerCased = prefix.lowercased()
-      if let lastNode = findLastNodeOf(word: prefixLowerCased) {
-          if lastNode.isTerminating {
-              words.append(prefixLowerCased)
-          }
-          for childNode in lastNode.children.values {
-              let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefixLowerCased)
-              words += childWords
-          }
+    var words = [String]()
+    let prefixLowerCased = prefix.lowercased()
+    if let lastNode = findLastNodeOf(word: prefixLowerCased) {
+      if lastNode.isTerminating {
+        words.append(prefixLowerCased)
+      }
+      for childNode in lastNode.children.values {
+        let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefixLowerCased)
+        words += childWords
       }
-      return words
+    }
+    return words
   }
 }
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index 928b01f4c..8ce34f6c7 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -10,16 +10,16 @@ import Cocoa
 
 class ViewController: NSViewController {
 
-    override func viewDidLoad() {
-        super.viewDidLoad()
+  override func viewDidLoad() {
+    super.viewDidLoad()
 
-        // Do any additional setup after loading the view.
-    }
+    // Do any additional setup after loading the view.
+  }
 
-    override var representedObject: Any? {
-        didSet {
-        // Update the view, if already loaded.
-        }
+  override var representedObject: Any? {
+    didSet {
+      // Update the view, if already loaded.
     }
+  }
 
 }
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index b69c5666e..0c5bc69c6 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -10,186 +10,184 @@ import XCTest
 @testable import Trie
 
 class TrieTests: XCTestCase {
-    var wordArray: [String]?
-    var trie = Trie()
-
-    /// Makes sure that the wordArray and trie are initialized before each test.
-    override func setUp() {
-        super.setUp()
-        createWordArray()
-        insertWordsIntoTrie()
+  var wordArray: [String]?
+  var trie = Trie()
+
+  /// Makes sure that the wordArray and trie are initialized before each test.
+  override func setUp() {
+    super.setUp()
+    createWordArray()
+    insertWordsIntoTrie()
+  }
+
+  /// Don't need to do anything here because the wordArray and trie should
+  /// stay around.
+  override func tearDown() {
+    super.tearDown()
+  }
+
+  /// Reads words from the dictionary file and inserts them into an array.  If
+  /// the word array already has words, do nothing.  This allows running all
+  /// tests without repeatedly filling the array with the same values.
+  func createWordArray() {
+    guard wordArray == nil else {
+      return
     }
-
-    /// Don't need to do anything here because the wordArray and trie should
-    /// stay around.
-    override func tearDown() {
-        super.tearDown()
-    }
-
-    /// Reads words from the dictionary file and inserts them into an array.  If
-    /// the word array already has words, do nothing.  This allows running all
-    /// tests without repeatedly filling the array with the same values.
-    func createWordArray() {
-        guard wordArray == nil else {
-            return
-        }
-        let resourcePath = Bundle.main.resourcePath! as NSString
-        let fileName = "dictionary.txt"
-        let filePath = resourcePath.appendingPathComponent(fileName)
-
-        var data: String?
-        do {
-            data = try String(contentsOfFile: filePath, encoding: String.Encoding.utf8)
-        } catch let error as NSError {
-            XCTAssertNil(error)
-        }
-        XCTAssertNotNil(data)
-        let dictionarySize = 162825
-        wordArray = data!.components(separatedBy: "\n")
-        XCTAssertEqual(wordArray!.count, dictionarySize)
-    }
-
-    /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
-    func insertWordsIntoTrie() {
-        guard let wordArray = wordArray, trie.count == 0 else { return }
-        for word in wordArray {
-            trie.insert(word: word)
-        }
-    }
-
-    /// Tests that a newly created trie has zero words.
-    func testCreate() {
-        let trie = Trie()
-        XCTAssertEqual(trie.count, 0)
-    }
-
-    /// Tests the insert method
-    func testInsert() {
-        let trie = Trie()
-        trie.insert(word: "cute")
-        trie.insert(word: "cutie")
-        trie.insert(word: "fred")
-        XCTAssertTrue(trie.contains(word: "cute"))
-        XCTAssertFalse(trie.contains(word: "cut"))
-        trie.insert(word: "cut")
-        XCTAssertTrue(trie.contains(word: "cut"))
-        XCTAssertEqual(trie.count, 4)
-    }
-
-    /// Tests the remove method
-    func testRemove() {
-        let trie = Trie()
-        trie.insert(word: "cute")
-        trie.insert(word: "cut")
-        XCTAssertEqual(trie.count, 2)
-        trie.remove(word: "cute")
-        XCTAssertTrue(trie.contains(word: "cut"))
-        XCTAssertFalse(trie.contains(word: "cute"))
-        XCTAssertEqual(trie.count, 1)
+    let resourcePath = Bundle.main.resourcePath! as NSString
+    let fileName = "dictionary.txt"
+    let filePath = resourcePath.appendingPathComponent(fileName)
+
+    var data: String?
+    do {
+      data = try String(contentsOfFile: filePath, encoding: String.Encoding.utf8)
+    } catch let error as NSError {
+      XCTAssertNil(error)
     }
-
-    /// Tests the words property
-    func testWords() {
-        let trie = Trie()
-        var words = trie.words
-        XCTAssertEqual(words.count, 0)
-        trie.insert(word: "foobar")
-        words = trie.words
-        XCTAssertEqual(words[0], "foobar")
-        XCTAssertEqual(words.count, 1)
+    XCTAssertNotNil(data)
+    let dictionarySize = 162825
+    wordArray = data!.components(separatedBy: "\n")
+    XCTAssertEqual(wordArray!.count, dictionarySize)
+  }
+
+  /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
+  func insertWordsIntoTrie() {
+    guard let wordArray = wordArray, trie.count == 0 else { return }
+    for word in wordArray {
+      trie.insert(word: word)
     }
-
-    /// Tests the performance of the insert method.
-    func testInsertPerformance() {
-        self.measure {
-            let trie = Trie()
-            for word in self.wordArray! {
-                trie.insert(word: word)
-            }
-        }
-        XCTAssertGreaterThan(trie.count, 0)
-        XCTAssertEqual(trie.count, wordArray?.count)
+  }
+
+  /// Tests that a newly created trie has zero words.
+  func testCreate() {
+    let trie = Trie()
+    XCTAssertEqual(trie.count, 0)
+  }
+
+  /// Tests the insert method
+  func testInsert() {
+    let trie = Trie()
+    trie.insert(word: "cute")
+    trie.insert(word: "cutie")
+    trie.insert(word: "fred")
+    XCTAssertTrue(trie.contains(word: "cute"))
+    XCTAssertFalse(trie.contains(word: "cut"))
+    trie.insert(word: "cut")
+    XCTAssertTrue(trie.contains(word: "cut"))
+    XCTAssertEqual(trie.count, 4)
+  }
+
+  /// Tests the remove method
+  func testRemove() {
+    let trie = Trie()
+    trie.insert(word: "cute")
+    trie.insert(word: "cut")
+    XCTAssertEqual(trie.count, 2)
+    trie.remove(word: "cute")
+    XCTAssertTrue(trie.contains(word: "cut"))
+    XCTAssertFalse(trie.contains(word: "cute"))
+    XCTAssertEqual(trie.count, 1)
+  }
+
+  /// Tests the words property
+  func testWords() {
+    let trie = Trie()
+    var words = trie.words
+    XCTAssertEqual(words.count, 0)
+    trie.insert(word: "foobar")
+    words = trie.words
+    XCTAssertEqual(words[0], "foobar")
+    XCTAssertEqual(words.count, 1)
+  }
+
+  /// Tests the performance of the insert method.
+  func testInsertPerformance() {
+    self.measure {
+      let trie = Trie()
+      for word in self.wordArray! {
+        trie.insert(word: word)
+      }
     }
-
-    /// Tests the performance of the insert method when the words are already
-    /// present.
-    func testInsertAgainPerformance() {
-        self.measure {
-            for word in self.wordArray! {
-                self.trie.insert(word: word)
-            }
-        }
+    XCTAssertGreaterThan(trie.count, 0)
+    XCTAssertEqual(trie.count, wordArray?.count)
+  }
+
+  /// Tests the performance of the insert method when the words are already
+  /// present.
+  func testInsertAgainPerformance() {
+    self.measure {
+      for word in self.wordArray! {
+        self.trie.insert(word: word)
+      }
     }
-
-    /// Tests the performance of the contains method.
-    func testContainsPerformance() {
-        self.measure {
-            for word in self.wordArray! {
-                XCTAssertTrue(self.trie.contains(word: word))
-            }
-        }
+  }
+
+  /// Tests the performance of the contains method.
+  func testContainsPerformance() {
+    self.measure {
+      for word in self.wordArray! {
+        XCTAssertTrue(self.trie.contains(word: word))
+      }
     }
+  }
 
-    /// Tests the performance of the remove method.  Since setup has already put
-    /// words into the trie, remove them before measuring performance.
-    func testRemovePerformance() {
-        for word in self.wordArray! {
-            self.trie.remove(word: word)
-        }
-        self.measure {
-            self.insertWordsIntoTrie()
-            for word in self.wordArray! {
-                self.trie.remove(word: word)
-            }
-        }
-        XCTAssertEqual(trie.count, 0)
+  /// Tests the performance of the remove method.  Since setup has already put
+  /// words into the trie, remove them before measuring performance.
+  func testRemovePerformance() {
+    for word in self.wordArray! {
+      self.trie.remove(word: word)
     }
-
-    /// Tests the performance of the words computed property.  Also tests to see
-    /// if it worked properly.
-    func testWordsPerformance() {
-        var words: [String]?
-        self.measure {
-            words = self.trie.words
-        }
-        XCTAssertEqual(words?.count, trie.count)
-        for word in words! {
-            XCTAssertTrue(self.trie.contains(word: word))
-        }
+    self.measure {
+      self.insertWordsIntoTrie()
+      for word in self.wordArray! {
+        self.trie.remove(word: word)
+      }
     }
-
-    /// Tests the archiving and unarchiving of the trie.
-    func testArchiveAndUnarchive() {
-        let resourcePath = Bundle.main.resourcePath! as NSString
-        let fileName = "dictionary-archive"
-        let filePath = resourcePath.appendingPathComponent(fileName)
-        NSKeyedArchiver.archiveRootObject(trie, toFile: filePath)
-        let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
-        XCTAssertEqual(trieCopy?.count, trie.count)
-
+    XCTAssertEqual(trie.count, 0)
+  }
+
+  /// Tests the performance of the words computed property.  Also tests to see
+  /// if it worked properly.
+  func testWordsPerformance() {
+    var words: [String]?
+    self.measure {
+      words = self.trie.words
     }
-
-    func testFindWordsWithPrefix() {
-        let trie = Trie()
-        trie.insert(word: "test")
-        trie.insert(word: "another")
-        trie.insert(word: "exam")
-        let wordsAll = trie.findWordsWithPrefix(prefix: "")
-        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"])
-        let words = trie.findWordsWithPrefix(prefix: "ex")
-        XCTAssertEqual(words, ["exam"])
-        trie.insert(word: "examination")
-        let words2 = trie.findWordsWithPrefix(prefix: "exam")
-        XCTAssertEqual(words2, ["exam", "examination"])
-        let noWords = trie.findWordsWithPrefix(prefix: "tee")
-        XCTAssertEqual(noWords, [])
-        let unicodeWord = "😬😎"
-        trie.insert(word: unicodeWord)
-        let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
-        XCTAssertEqual(wordsUnicode, [unicodeWord])
-        trie.insert(word: "Team")
-        let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
-        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
-
+    XCTAssertEqual(words?.count, trie.count)
+    for word in words! {
+      XCTAssertTrue(self.trie.contains(word: word))
     }
+  }
+
+  /// Tests the archiving and unarchiving of the trie.
+  func testArchiveAndUnarchive() {
+    let resourcePath = Bundle.main.resourcePath! as NSString
+    let fileName = "dictionary-archive"
+    let filePath = resourcePath.appendingPathComponent(fileName)
+    NSKeyedArchiver.archiveRootObject(trie, toFile: filePath)
+    let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
+    XCTAssertEqual(trieCopy?.count, trie.count)
+  }
+
+  func testFindWordsWithPrefix() {
+    let trie = Trie()
+    trie.insert(word: "test")
+    trie.insert(word: "another")
+    trie.insert(word: "exam")
+    let wordsAll = trie.findWordsWithPrefix(prefix: "")
+    XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"])
+    let words = trie.findWordsWithPrefix(prefix: "ex")
+    XCTAssertEqual(words, ["exam"])
+    trie.insert(word: "examination")
+    let words2 = trie.findWordsWithPrefix(prefix: "exam")
+    XCTAssertEqual(words2, ["exam", "examination"])
+    let noWords = trie.findWordsWithPrefix(prefix: "tee")
+    XCTAssertEqual(noWords, [])
+    let unicodeWord = "😬😎"
+    trie.insert(word: unicodeWord)
+    let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
+    XCTAssertEqual(wordsUnicode, [unicodeWord])
+    trie.insert(word: "Team")
+    let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
+    XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
+  }
 }
diff --git a/Trie/Trie/TrieUITests/TrieUITests.swift b/Trie/Trie/TrieUITests/TrieUITests.swift
index acb3b1756..380bf3092 100644
--- a/Trie/Trie/TrieUITests/TrieUITests.swift
+++ b/Trie/Trie/TrieUITests/TrieUITests.swift
@@ -10,27 +10,27 @@ import XCTest
 
 class TrieUITests: XCTestCase {
 
-    override func setUp() {
-        super.setUp()
+  override func setUp() {
+    super.setUp()
 
-        // Put setup code here. This method is called before the invocation of each test method in the class.
+    // Put setup code here. This method is called before the invocation of each test method in the class.
 
-        // In UI tests it is usually best to stop immediately when a failure occurs.
-        continueAfterFailure = false
-        // UI tests must launch the application that they test. Doing this in setup will make sure it happens for each test method.
-        XCUIApplication().launch()
+    // In UI tests it is usually best to stop immediately when a failure occurs.
+    continueAfterFailure = false
+    // UI tests must launch the application that they test. Doing this in setup will make sure it happens for each test method.
+    XCUIApplication().launch()
 
-        // In UI tests it’s important to set the initial state - such as interface orientation - required for your tests before they run. The setUp method is a good place to do this.
-    }
+    // In UI tests it’s important to set the initial state - such as interface orientation - required for your tests before they run. The setUp method is a good place to do this.
+  }
 
-    override func tearDown() {
-        // Put teardown code here. This method is called after the invocation of each test method in the class.
-        super.tearDown()
-    }
+  override func tearDown() {
+    // Put teardown code here. This method is called after the invocation of each test method in the class.
+    super.tearDown()
+  }
 
-    func testExample() {
-        // Use recording to get started writing UI tests.
-        // Use XCTAssert and related functions to verify your tests produce the correct results.
-    }
+  func testExample() {
+    // Use recording to get started writing UI tests.
+    // Use XCTAssert and related functions to verify your tests produce the correct results.
+  }
 
 }

From 41eb9c1ee1591472c24b49108295261f698a3f1b Mon Sep 17 00:00:00 2001
From: Samwel Charles <younggeeks101@gmail.com>
Date: Mon, 29 Oct 2018 00:22:43 +0300
Subject: [PATCH 1550/1679] update union-find to swift 4.2

---
 Union-Find/UnionFind.playground/Contents.swift            | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 6ac3b4c4e..b1f7fb4e1 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {
diff --git a/Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From cb76b97e3f295d171267044ca599d27db113a7ee Mon Sep 17 00:00:00 2001
From: Samwel Charles <younggeeks101@gmail.com>
Date: Mon, 29 Oct 2018 01:01:09 +0300
Subject: [PATCH 1551/1679] add link to merge sort algorithm in buble sort
 algorith README.md file

---
 Bubble Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index e55129d93..c4b2c37c8 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -117,7 +117,7 @@ There is no Fifth pass
 
 #### Conclusion
 
-Even with the proposed optimizations, this is still a terribly inefficient sorting algorithm. A good alternative is [Merge Sort](), that not only is better performing, has a similar degree of dificulty to implement.
+Even with the proposed optimizations, this is still a terribly inefficient sorting algorithm. A good alternative is [Merge Sort](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Merge%20Sort), that not only is better performing, has a similar degree of dificulty to implement.
 
 *Updated for the Swift Algorithm Club by Julio Brazil*
 

From 299a67caeb984577561aaf1921271015558bfd6e Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 29 Oct 2018 11:45:21 -0300
Subject: [PATCH 1552/1679] addition of convenience method

---
 Bubble Sort/MyPlayground.playground/Contents.swift     |  4 +++-
 .../MyPlayground.playground/Sources/BubbleSort.swift   | 10 +++++++---
 2 files changed, 10 insertions(+), 4 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
index 8d27d801e..6188a0763 100644
--- a/Bubble Sort/MyPlayground.playground/Contents.swift	
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -3,4 +3,6 @@ import Foundation
 var array = [4,2,1,3]
 
 print("before:",array)
-print("after:",BubbleSort(array))
+print("after:", bubbleSort(array))
+print("after:", bubbleSort(array, <))
+print("after:", bubbleSort(array, >))
diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
index 9c091b661..09e01542b 100644
--- a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -23,14 +23,18 @@ import Foundation
 
 /// Performs the bubble sort algorithm in the array
 ///
-/// - Parameter elements: the array to be sorted
+/// - Parameter elements: a array of elements that implement the Comparable protocol
 /// - Returns: an array with the same elements but in order
-public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+public func bubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+  return bubbleSort(elements, <)
+}
+
+public func bubbleSort<T> (_ elements: [T], _ comparison: (T,T) -> Bool) -> [T]  {
   var array = elements
   
   for i in 0..<array.count {
     for j in 1..<array.count-i {
-      if array[j] < array[j-1] {
+      if comparison(array[j], array[j-1]) {
         let tmp = array[j-1]
         array[j-1] = array[j]
         array[j] = tmp

From 7793fb4582dedafaa65f9de78bd9fcb96f9dd5d5 Mon Sep 17 00:00:00 2001
From: cr0ss <kayoslab@users.noreply.github.com>
Date: Tue, 30 Oct 2018 10:11:48 +0100
Subject: [PATCH 1553/1679] Removing unnecessary Error case for empty list

* Was intended to be a second example, but is not yet implemented
---
 GCD/GCD.playground/Contents.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 9dfd7cca9..175d26639 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -106,7 +106,6 @@ func findEasySolution(_ m: Int, _ n: Int) -> Int? {
 
 enum LCMError: Error {
     case divisionByZero
-    case lcmEmptyList
 }
 
 /*

From 34a6067355c2596754500ad309eb79bf540f135c Mon Sep 17 00:00:00 2001
From: cr0ss <kayoslab@users.noreply.github.com>
Date: Tue, 30 Oct 2018 10:12:34 +0100
Subject: [PATCH 1554/1679] Also removes the lcmEmptyList from the actual code
 file

---
 GCD/GCD.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index 85b7681f0..f4b390e63 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -105,7 +105,6 @@ func findEasySolution(_ m: Int, _ n: Int) -> Int? {
 
 enum LCMError: Error {
     case divisionByZero
-    case lcmEmptyList
 }
 
 /*

From 1e8e231d3cceb8d57a5bdf6838b4f8b544cdfe65 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Thu, 1 Nov 2018 06:55:11 +1100
Subject: [PATCH 1555/1679] Updated Run-Length Encoding to Swift 4.2

---
 Run-Length Encoding/RLE.playground/Contents.swift | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index fc2d82505..8d6a0a403 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 let originalString = "aaaaabbbcdeeeeeeef"
@@ -64,7 +59,7 @@ func testBufferWithoutSpans() -> Bool {
     // data ends up being longer.
     var bytes: [UInt8] = []
     for i in 0..<1024 {
-        bytes.append(UInt8(i%256))
+        bytes.append(UInt8(i % 256))
     }
     return encodeAndDecode(bytes)
 }

From d454cf1e1b3a9b60bc005a8b3051be1d328d1932 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Thu, 1 Nov 2018 07:25:19 +1100
Subject: [PATCH 1556/1679] Confirmed Linear Regression to work with Swift 4.2

---
 .../LinearRegression.playground/Contents.swift             | 7 +------
 Linear Regression/README.markdown                          | 2 +-
 2 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 3e4135794..a093ef566 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -2,11 +2,6 @@
 
 import Foundation
 
-// last checked with Xcode 4.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let carAge: [Double] = [10, 8, 3, 3, 2, 1]
 let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
 var intercept = 0.0
@@ -22,7 +17,7 @@ let numberOfCarAdvertsWeSaw = carPrice.count
 let numberOfIterations = 100
 let alpha = 0.0001
 
-for n in 1...numberOfIterations {
+for _ in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
         let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference
diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 29ac2e321..4f9d030db 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -62,7 +62,7 @@ let numberOfCarAdvertsWeSaw = carPrice.count
 let numberOfIterations = 100
 let alpha = 0.0001
 
-for n in 1...numberOfIterations {
+for _ in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
         let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference

From 8683fb16eee6102c207694f96beadbb63438ee75 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Thu, 1 Nov 2018 07:35:17 +1100
Subject: [PATCH 1557/1679] Updated Minimum Edit Distance Playground for Swift
 4.2

---
 .../MinimumEditDistance.playground/Contents.swift    | 12 ++++--------
 Minimum Edit Distance/README.markdown                |  4 ++--
 2 files changed, 6 insertions(+), 10 deletions(-)

diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
index 967e73182..5db0aeb0d 100644
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,15 +1,11 @@
 
 // Minimum Edit Distance
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 extension String {
     
     public func minimumEditDistance(other: String) -> Int {
-        let m = self.characters.count
-        let n = other.characters.count
+        let m = self.count
+        let n = other.count
         var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
         
         // initialize matrix
@@ -24,8 +20,8 @@ extension String {
         }
         
         // compute Levenshtein distance
-        for (i, selfChar) in self.characters.enumerated() {
-            for (j, otherChar) in other.characters.enumerated() {
+        for (i, selfChar) in self.enumerated() {
+            for (j, otherChar) in other.enumerated() {
                 if otherChar == selfChar {
                     // substitution of equal symbols with cost 0
                     matrix[i + 1][j + 1] = matrix[i][j]
diff --git a/Minimum Edit Distance/README.markdown b/Minimum Edit Distance/README.markdown
index b8880b2d4..c8e5e2f6d 100755
--- a/Minimum Edit Distance/README.markdown	
+++ b/Minimum Edit Distance/README.markdown	
@@ -37,8 +37,8 @@ Then in each cell the minimum of the cost of insertion, deletion, or substitutio
 
 ```swift
 // compute Levenshtein distance
-for (i, selfChar) in self.characters.enumerated() {
-    for (j, otherChar) in other.characters.enumerated() {
+for (i, selfChar) in self.enumerated() {
+    for (j, otherChar) in other.enumerated() {
         if otherChar == selfChar {
             // substitution of equal symbols with cost 0
             matrix[i + 1][j + 1] = matrix[i][j]

From eea4cfc6eaba53d86c3a383b1dce9c3c374b3ebd Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 22:56:29 -0300
Subject: [PATCH 1558/1679] Counting Sort working with Swift 4.2

---
 Counting Sort/CountingSort.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 4d918e384..dc375512a 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 enum CountingSortError: Error {
   case arrayEmpty
 }

From 43e76adfc53c5cadde2511e9fc80fa3c59114be9 Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 23:10:55 -0300
Subject: [PATCH 1559/1679] Union Find working with Swift 4.2 and Xcode 10

---
 Union-Find/UnionFind.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 6ac3b4c4e..b1f7fb4e1 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {

From 6707ce26934addaceff3d54ee417632e210443df Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 23:16:04 -0300
Subject: [PATCH 1560/1679] Shunting Yard working fine with Swift 4.2 and Xcode
 10

---
 Shunting Yard/ShuntingYard.playground/Contents.swift      | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index ddd73de59..38431f5e2 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 internal enum OperatorAssociativity {
   case leftAssociative
   case rightAssociative
diff --git a/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From a1d65fcba404f8a59897c46480e54cadbe491b63 Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 23:25:54 -0300
Subject: [PATCH 1561/1679] Updated random number generation to Swift 4.2

---
 Set Cover (Unweighted)/SetCover.playground/Contents.swift  | 7 ++-----
 .../SetCover.playground/Sources/RandomArrayOfSets.swift    | 4 ++--
 2 files changed, 4 insertions(+), 7 deletions(-)

diff --git a/Set Cover (Unweighted)/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
index d61b9c84a..065f5fd4d 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
@@ -1,10 +1,5 @@
 // SetCover
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let universe1 = Set(1...7)
 let array1 = randomArrayOfSets(covering: universe1)
 let cover1 = universe1.cover(within: array1)
@@ -36,3 +31,5 @@ let emptySet = Set<Int>()
 let coverTest1 = emptySet.cover(within: array1)
 let coverTest2 = universe1.cover(within: Array<Set<Int>>())
 let coverTest3 = emptySet.cover(within: Array<Set<Int>>())
+
+
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift
index 9454c6383..ac4ff063e 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
@@ -14,10 +14,10 @@ public func randomArrayOfSets<T>(covering universe: Set<T>,
 
   while true {
     var generatedSet = Set<T>()
-    let targetSetSize = Int(arc4random_uniform(UInt32(maxSetSize)) + 1)
+    let targetSetSize = Int.random(in: 0...maxSetSize) + 1
 
     while true {
-      let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
+      let randomUniverseIndex = Int.random(in: 0...universe.count)
       for (setIndex, value) in universe.enumerated() {
         if setIndex == randomUniverseIndex {
           generatedSet.insert(value)

From f37fb19f054c95b654e07186d5f6fc5cf56bb12d Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 1 Nov 2018 20:55:17 +0100
Subject: [PATCH 1562/1679] Update README according to comments.

---
 Bloom Filter/README.markdown | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index 4364db857..5f2ede069 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -102,7 +102,9 @@ If you're coming from another imperative language, you might notice the unusual
 
 ## Another approach
 
-Another approach to create different hashes of an element for use in the Bloom filter, is to use the same hash function for every iteration, but combine it with different random numbers. This can help, because finding good hashing functions is hard, but combining them is equally non-trivial.
+In the previous section, you learnt about how using multiple different hash functions can help reduce the chance of collisions in the bloom filter. However, good hash functions are difficult to design. A simple alternative to multiple hash functions is to use a set of random numbers.
+
+As an example, let's say a bloom filter wants to hash each element 15 times during insertion. Instead of using 15 different hash functions, you can rely on just one hash function. The hash value can then be combined with 15 different values to form the indices for flipping. This bloom filter would initialize a set of 15 random numbers ahead of time and use these values during each insertion.
 
 ```
 hash("Hello world!") >> hash(987654321) // would flip bit 8

From f9133844436bd6336595e0f6b66038f676dd3b3a Mon Sep 17 00:00:00 2001
From: gmotzespina <gmotzespina@icloud.com>
Date: Mon, 5 Nov 2018 19:00:34 -0600
Subject: [PATCH 1563/1679] Swift 4.2 Migration #748 - Depth First Search
 migrated to Swift 4.2

---
 .../APSP/APSP.xcodeproj/project.pbxproj                   | 8 +++++---
 .../Pages/Simple Example.xcplaygroundpage/Contents.swift  | 5 +----
 Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj  | 4 ++--
 3 files changed, 8 insertions(+), 9 deletions(-)

diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index 78df3fb76..908d32785 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -196,7 +196,7 @@
 					};
 					493D8DF01CDD5B960089795A = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 				};
 			};
@@ -420,7 +420,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -442,7 +443,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 99f20a729..c83f52af8 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,4 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// last checked with Xcode 10.1
 
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
     var nodesExplored = [source.label]
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 8f6058600..2b433bd96 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -234,7 +234,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -247,7 +247,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};

From 0f739b5230f7fe0df655fac82941e9111d346b90 Mon Sep 17 00:00:00 2001
From: gmotzespina <gmotzespina@icloud.com>
Date: Mon, 5 Nov 2018 19:08:43 -0600
Subject: [PATCH 1564/1679] Swift 4.2 support Depth-First Search

---
 .../DepthFirstSearch.playground/Edge.o          | Bin 0 -> 7016 bytes
 .../DepthFirstSearch.playground/Graph.o         | Bin 0 -> 21488 bytes
 .../DepthFirstSearch.playground/Node.o          | Bin 0 -> 19288 bytes
 .../xcshareddata/IDEWorkspaceChecks.plist       |   8 ++++++++
 .../xcshareddata/WorkspaceSettings.xcsettings   |   8 ++++++++
 5 files changed, 16 insertions(+)
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Edge.o
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Graph.o
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Node.o
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Depth-First Search/DepthFirstSearch.playground/Edge.o b/Depth-First Search/DepthFirstSearch.playground/Edge.o
new file mode 100644
index 0000000000000000000000000000000000000000..ab1e89b3aa83ed547413ba061a5edfd5dc918137
GIT binary patch
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diff --git a/Depth-First Search/DepthFirstSearch.playground/Graph.o b/Depth-First Search/DepthFirstSearch.playground/Graph.o
new file mode 100644
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diff --git a/Depth-First Search/DepthFirstSearch.playground/Node.o b/Depth-First Search/DepthFirstSearch.playground/Node.o
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z__uD`7xreDbPv%y8=0TuH{sR`rD4L;U~~7_Vec-=go1mDklh&FvE33oybhZm8JT7U
zuhnAzw7~|vW~+Ba=snw(ZDNt3;zlQSG)s{O3MLWDE$H^`^oaqscd5*7YAVoXy#os_
z6?mV#vehMdg#jqmUwn<&jhhSX$?it*GW*2-U?CUG304zK_WDCwauf9?Ty<I}y*@48
zZ}#D4fq$h!)7Ew3rR#O!P(-io3<tXsiP{HroYl4@Ts8h=Fd1r>$Ik7Vr$+Us66*tv
zk>u?)+oewHlFhWl$yyk!c^Y`)+jTyT^z97$yF|tcgK9Qt;@KdW)B_QEX`PSNo_IXi
z*Czs`ZHy&1?hT6tSSOQH_(VUBQQlho>lk`(?cQ$uGd#78biH+-zsujY!5h|l^hk2+
zzWaB2wdDOp6cuhr`yg~S2><$P*5mmJZ>Yl;dOQ{l!%sMW>0LCH-`}ex+lz-7TR7EO
zFZ2XmH9=Zy6W&IT2g72;y&V|Me81}syLoE-R+$=?)|Lu|lc9)=6f1LWNF_V#>hXL9
z-zMwvl6`VRDB<zfH#YkH8)MqWy&FTW%v6QG<vSb<&175&&h?tJP}JU6g+9#`Is6+$
zAG}P^U=9BuN(BFmNr!fam8hd*PKM>$kV~$oNfYlQ=}>)Jx@twF{+AI?)Ks_NU$WYg
WO2$%2gh>zf&_PY60#Acy_5T4cZe^PQ

literal 0
HcmV?d00001

diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>

From 07732e85027602ed909f9afbd9ebb2869ba18632 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Francisco=20Salda=C3=B1a?= <pako7797@icloud.com>
Date: Mon, 5 Nov 2018 19:18:53 -0600
Subject: [PATCH 1565/1679] fix deprecated methods and return type

---
 .../BoyerMooreHorspool.playground/Contents.swift       | 10 +++++-----
 .../xcshareddata/IDEWorkspaceChecks.plist              |  8 ++++++++
 .../BoyerMooreHorspool.playground/timeline.xctimeline  |  6 +++---
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift          | 10 +++++-----
 4 files changed, 21 insertions(+), 13 deletions(-)
 create mode 100644 Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index e88a1b93d..c51070caf 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -13,16 +13,16 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= self.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
@@ -57,7 +57,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k }
+                if let k = backwards() { return k.encodedOffset }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
index 89bc76f90..431d4a349 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=37&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616217"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556089"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=26&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.61657"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.5563149"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=25&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616725"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556504"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index af8aea9d9..92d2ee4c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -6,16 +6,16 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= self.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
@@ -50,7 +50,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k }
+                if let k = backwards() { return k.encodedOffset }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.

From 17990d8b52ae03bae0570f5e97e18d5f75485136 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Francisco=20Salda=C3=B1a?= <pako7797@icloud.com>
Date: Mon, 5 Nov 2018 19:37:55 -0600
Subject: [PATCH 1566/1679] change return type

---
 .../BoyerMooreHorspool.playground/Contents.swift            | 4 ++--
 .../BoyerMooreHorspool.playground/timeline.xctimeline       | 6 +++---
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift               | 4 ++--
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index c51070caf..eba2a5806 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -13,7 +13,7 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.count
@@ -57,7 +57,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k.encodedOffset }
+                if let k = backwards() { return k }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
index 431d4a349..5eb7f2337 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556089"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563161016.665907"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.5563149"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563161016.666045"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556504"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563161016.666169"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index 92d2ee4c1..1dd37873a 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -6,7 +6,7 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.count
@@ -50,7 +50,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k.encodedOffset }
+                if let k = backwards() { return k }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.

From a7047d8bbb8cbdc023c8979dcfa22d15ba6ed21f Mon Sep 17 00:00:00 2001
From: Morgan Davison <morgan.davison@gmail.com>
Date: Tue, 6 Nov 2018 20:09:29 -0500
Subject: [PATCH 1567/1679] Compile for Swift 4.2

---
 B-Tree/BTree.playground/Contents.swift        |  5 +---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 B-Tree/Tests/Tests.xcodeproj/project.pbxproj  | 24 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 5 files changed, 38 insertions(+), 9 deletions(-)
 create mode 100644 B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index a0643586f..f6325513a 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -2,10 +2,7 @@
 
 import Foundation
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// last checked with Xcode 10.0
 
 let bTree = BTree<Int, Int>(order: 1)!
 
diff --git a/B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
index 3e12b9ac3..66eb85190 100644
--- a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
+++ b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,12 +85,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Viktor Szilárd Simkó";
 				TargetAttributes = {
 					C66702771D0EEE25008CD769 = {
 						CreatedOnToolsVersion = 7.3.1;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -144,14 +144,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -192,14 +200,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -234,7 +250,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -247,7 +263,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 9d6c542ae..d1555acfb 100644
--- a/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From b4ec5b84731a4cef0319e74d8109bbf8bc101a0e Mon Sep 17 00:00:00 2001
From: alextakahashi <alextakahashi@berkeley.edu>
Date: Wed, 7 Nov 2018 22:38:11 -0800
Subject: [PATCH 1568/1679] Added Markdown Documentation to Stack playground

This might be overkill for such a small file, but I wish I started using Swift Markdown early in my iOS career.  Option click is too convenient to ignore!
---
 Stack/Stack.playground/Contents.swift | 28 +++++++++++++++++++++++++--
 1 file changed, 26 insertions(+), 2 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 1eb705f20..13774d7d1 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,4 +1,4 @@
-/*
+/**
   Stack
 
   A stack is like an array but with limited functionality. You can only push
@@ -9,27 +9,51 @@
   last is the first one to come off with the next pop.
 
   Push and pop are O(1) operations.
+ 
+  ## Usage
+  ```
+  var myStack = Stack(array: [])
+  myStack.push(10)
+  myStack.push(3)
+  myStack.push(57)
+  myStack.pop() // 57
+  myStack.pop() // 3
+ ```
 */
-
 public struct Stack<T> {
+    
+  /// Datastructure consisting of a generic item.
   fileprivate var array = [T]()
 
+  /// The number of items in the stack.
   public var count: Int {
     return array.count
   }
 
+  /// Verifies if the stack is empty.
   public var isEmpty: Bool {
     return array.isEmpty
   }
 
+  /**
+     Pushes an item to the top of the stack.
+     
+     - Parameter element: The item being pushed.
+  */
   public mutating func push(_ element: T) {
     array.append(element)
   }
 
+  /**
+     Removes and returns the item at the top of the sack.
+     
+     - Returns: The item at the top of the stack.
+  */
   public mutating func pop() -> T? {
     return array.popLast()
   }
 
+  /// Returns the item at the top of the stack.
   public var top: T? {
     return array.last
   }

From eb228cc1d18d860ad825c7d79063524121555bce Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:24:07 -0500
Subject: [PATCH 1569/1679] [Swift 4.2] Updated Hash Set

---
 Hash Set/HashSet.playground/Contents.swift                | 4 ----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 16 insertions(+), 4 deletions(-)
 create mode 100644 Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Hash Set/HashSet.playground/Contents.swift b/Hash Set/HashSet.playground/Contents.swift
index 5edb76bb4..551c6dc86 100644
--- a/Hash Set/HashSet.playground/Contents.swift	
+++ b/Hash Set/HashSet.playground/Contents.swift	
@@ -1,8 +1,4 @@
 //: Playground - noun: a place where people can play
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 var set = HashSet<String>()
 
diff --git a/Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 67ecddaafb2e7637da0b24787ece79cadd82603c Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:37:44 -0500
Subject: [PATCH 1570/1679] [Swift 4.2] Updated Hash Table

---
 Hash Table/HashTable.playground/Contents.swift            | 3 ---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 3 deletions(-)
 create mode 100644 Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index 273113440..121fb6032 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Playground - noun: a place where people can play
 
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 // Playing with hash values
 
 "firstName".hashValue
diff --git a/Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 70d26fccdea4e655986b0fe36cec2d2dae2ab8e8 Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:44:55 -0500
Subject: [PATCH 1571/1679] [Swift 4.2] Updated Heap Sort

---
 Heap Sort/Tests/HeapSortTests.swift           |  6 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 31 +++++++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +--
 4 files changed, 31 insertions(+), 18 deletions(-)
 create mode 100644 Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Heap Sort/Tests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
index b36f605e3..dae1f8a68 100644
--- a/Heap Sort/Tests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,12 +1,6 @@
 import XCTest
 
 class HeapSortTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
   
   func testSort() {
     var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index ff1f4937f..62e6d4e3f 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 46;
+	objectVersion = 51;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -86,17 +86,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1010;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 3.2";
+			compatibilityVersion = "Xcode 10.0";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -149,12 +149,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -201,12 +203,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -230,7 +234,8 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
 			};
 			name = Release;
 		};
@@ -239,10 +244,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -251,10 +260,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 538a6f4fa..1608804f9 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 0a2793fa925812cb71458c8447b988b897e126bb Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:49:37 -0500
Subject: [PATCH 1572/1679] [Swift 4.2] Updated Heap

---
 Heap/Tests/HeapTests.swift                    |  7 -----
 Heap/Tests/Tests.xcodeproj/project.pbxproj    | 31 +++++++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +--
 4 files changed, 31 insertions(+), 19 deletions(-)
 create mode 100644 Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 1ed15c726..ecf143778 100755
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -7,13 +7,6 @@ import XCTest
 
 class HeapTests: XCTestCase {
   
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-  
   fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
     for i in 0..<h.count {
       let left = h.leftChildIndex(ofIndex: i)
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
index 51433ee64..0ab48ba3b 100755
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 46;
+	objectVersion = 51;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -83,17 +83,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0920;
+				LastUpgradeCheck = 1010;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 3.2";
+			compatibilityVersion = "Xcode 10.0";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -145,12 +145,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -197,12 +199,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -226,7 +230,8 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
 			};
 			name = Release;
 		};
@@ -235,10 +240,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -247,10 +256,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 77d01bebc..1608804f9 100755
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0920"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 9374c513f34170a1fd5db63398718507a8937c70 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Nov 2018 23:00:22 -0500
Subject: [PATCH 1573/1679] Update Contents.swift

---
 HaversineDistance/HaversineDistance.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 7aa686645..3d8d60f54 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,8 +1,4 @@
 import UIKit
-// last checked with Xcode 9.04
-#if swift(>=4)
-print("Hello, Swift 4!")
-#endif
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
     

From ef4e890fd9f5b0ddf15cfa289fc2993ee46a9e04 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Nov 2018 23:01:46 -0500
Subject: [PATCH 1574/1679] Updates Contents.swift

---
 .../BoyerMooreHorspool.playground/Contents.swift             | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index 5817cc41f..1666549c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 /*
   Boyer-Moore string search
 

From 9ba8b54dc580cc6cb3803a1a2cd2a9efcd5bf6ab Mon Sep 17 00:00:00 2001
From: gmotzespina <gmotzespina@icloud.com>
Date: Mon, 12 Nov 2018 19:53:38 -0600
Subject: [PATCH 1575/1679] Bubble Sort Readme Code Issue #838 solved

---
 Bubble Sort/README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index e55129d93..648b9f324 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -57,9 +57,9 @@ This is the same for the forth and fifth passes.
 ```swift
 for i in 0..<array.count {
   for j in 1..<array.count {
-    if array[j] < array[i] {
-      let tmp = array[i]
-      array[i] = array[j]
+    if array[j] < array[j-1] {
+      let tmp = array[j-1]
+      array[j-1] = array[j]
       array[j] = tmp
     }
   }
@@ -73,9 +73,9 @@ The bubble sort algorithm can be easily optimized by observing that the `n-th` p
 ```swift
 for i in 0..<array.count {
   for j in 1..<array.count - i {
-    if array[j] < array[i] {
-      let tmp = array[i]
-      array[i] = array[j]
+    if array[j] < array[j-1] {
+      let tmp = array[j-1]
+      array[j-1] = array[j]
       array[j] = tmp
     }
   }

From 71c228a2b63a091a7bd521dc6f2c3bf219a9b6c7 Mon Sep 17 00:00:00 2001
From: Daniel Chick <daniel.chick@hotmail.com>
Date: Tue, 27 Nov 2018 14:22:02 -0600
Subject: [PATCH 1576/1679] Removing version check

---
 Tree/Tree.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 06f992fa8..1fad157a0 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.2)
-print("Hello, Swift 4.2!")
-#endif
-
 let tree = TreeNode<String>(value: "beverages")
 
 let hotNode = TreeNode<String>(value: "hot")

From f1363dd983ccacf1e48d9d393022f3ce68ba3c39 Mon Sep 17 00:00:00 2001
From: Francesco Scalise <f.scalise@eco-mind.eu>
Date: Tue, 4 Dec 2018 19:31:26 +0100
Subject: [PATCH 1577/1679] [Swift 4.2] Count occurences

---
 Count Occurrences/CountOccurrences.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index 6138b74ac..a34e3485f 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,7 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
 
 func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {

From a2953343f16129995f90cfc6cf49236b3bcb9ae5 Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Sun, 16 Dec 2018 21:46:06 +0000
Subject: [PATCH 1578/1679] Implement bit shift operations in BitSet

---
 Bit Set/BitSet.playground/Contents.swift      | 20 ++++++++
 .../BitSet.playground/Sources/BitSet.swift    | 46 +++++++++++++++++-
 Bit Set/BitSet.swift                          | 47 ++++++++++++++++++-
 3 files changed, 111 insertions(+), 2 deletions(-)

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index d11b36e8c..2c5edcd84 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -89,3 +89,23 @@ z.all1()        // false
 
 //var bigBits = BitSet(size: 10000)
 //print(bigBits)
+
+var smallBitSet = BitSet(size: 16)
+smallBitSet[5] = true
+smallBitSet[10] = true
+print( smallBitSet >> 3 )
+print( smallBitSet << 6 ) // one bit shifts off the end
+
+var bigBitSet = BitSet( size: 120 )
+bigBitSet[1] = true
+bigBitSet[3] = true
+bigBitSet[7] = true
+bigBitSet[32] = true
+bigBitSet[55] = true
+bigBitSet[64] = true
+bigBitSet[80] = true
+print( bigBitSet )
+print( bigBitSet << 32 )
+print( bigBitSet << 64 )
+print( bigBitSet >> 32 )
+print( bigBitSet >> 64 )
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index 59306f5a5..85f5da505 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -9,7 +9,7 @@ public struct BitSet {
     We store the bits in a list of unsigned 64-bit integers.
     The first entry, `words[0]`, is the least significant word.
   */
-  private let N = 64
+  fileprivate let N = 64
   public typealias Word = UInt64
   fileprivate(set) public var words: [Word]
 
@@ -221,6 +221,50 @@ prefix public func ~ (rhs: BitSet) -> BitSet {
   return out
 }
 
+// MARK: - Bit shift operations
+
+/*
+ Note: For bitshift operations, the assumption is that any bits that are
+ shifted off the end of the end of the declared size are not still set.
+ In other words, we are maintaining the original number of bits.
+ */
+
+public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsLeft / lhs.N
+    let shift = numBitsLeft % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i - offset >= 0 ) {
+            out.words[i] = lhs.words[i - offset] << shift
+        }
+        if( i - offset - 1 >= 0 ) {
+            out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
+public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsRight / lhs.N
+    let shift = numBitsRight % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i + offset < lhs.words.count ) {
+            out.words[i] = lhs.words[i + offset] >> shift
+        }
+        if( i + offset + 1 < lhs.words.count ) {
+            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
 // MARK: - Debugging
 
 extension UInt64 {
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index cfe8517b5..83829c6c5 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -9,7 +9,7 @@ public struct BitSet {
    We store the bits in a list of unsigned 64-bit integers.
    The first entry, `words[0]`, is the least significant word.
    */
-  private let N = 64
+  fileprivate let N = 64
   public typealias Word = UInt64
   fileprivate(set) public var words: [Word]
   
@@ -221,6 +221,51 @@ prefix public func ~ (rhs: BitSet) -> BitSet {
   return out
 }
 
+// MARK: - Bit shift operations
+
+/*
+ Note: For bitshift operations, the assumption is that any bits that are
+ shifted off the end of the end of the declared size are not still set.
+ In other words, we are maintaining the original number of bits.
+ */
+
+public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsLeft / lhs.N
+    let shift = numBitsLeft % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i - offset >= 0 ) {
+            out.words[i] = lhs.words[i - offset] << shift
+        }
+        if( i - offset - 1 >= 0 ) {
+            out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
+public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsRight / lhs.N
+    let shift = numBitsRight % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i + offset < lhs.words.count ) {
+            out.words[i] = lhs.words[i + offset] >> shift
+        }
+        if( i + offset + 1 < lhs.words.count ) {
+            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
+
 // MARK: - Debugging
 
 extension UInt64 {

From dd182db605004ecdea85cf9b95de13b4006d52e3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 20 Dec 2018 19:36:18 -0500
Subject: [PATCH 1579/1679] Fixes a typo

---
 A-Star/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/A-Star/README.md b/A-Star/README.md
index f362bb61e..b373d25fc 100644
--- a/A-Star/README.md
+++ b/A-Star/README.md
@@ -16,7 +16,7 @@ On the first step we expand the root node on the left (blue). We set the cost `g
 
 ![Step 1](Images/step1.png)
 
-We put the first not in the closed list (light blue) so that we don't try expanding it again if there were to be loops in the graph. Next we take the node on the open list with the smallest value of `g + h` where `g` is the current cost (0) plus the edge cost (1). Since all nodes in the open list have the same value we choose the top one.
+We put the first node in the closed list (light blue) so that we don't try expanding it again if there were to be loops in the graph. Next we take the node on the open list with the smallest value of `g + h` where `g` is the current cost (0) plus the edge cost (1). Since all nodes in the open list have the same value we choose the top one.
 
 ![Step 2](Images/step2.png)
 

From 1f15eda576530fdf76bb8245eecb99a5b4233a48 Mon Sep 17 00:00:00 2001
From: Andrzej Michnia <amichnia@gmail.com>
Date: Sun, 16 Dec 2018 22:44:30 +0100
Subject: [PATCH 1580/1679] Fixed error in description

---
 Comb Sort/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Comb Sort/README.markdown b/Comb Sort/README.markdown
index d30d429b3..20c939307 100644
--- a/Comb Sort/README.markdown	
+++ b/Comb Sort/README.markdown	
@@ -64,8 +64,8 @@ This will sort the values of the array into ascending order -- increasing in val
 ## Performance
 
 Comb Sort was created to improve upon the worst case time complexity of Bubble Sort. With Comb 
-Sort, the worst case scenario for performance is exponential -- O(n^2). At best though, Comb Sort 
-performs at O(n logn) time complexity. This creates a drastic improvement over Bubble Sort's performance. 
+Sort, the worst case scenario for performance is polynomial -- O(n^2). At best though, Comb Sort 
+performs at O(n logn) time complexity -- loglinear. This creates a drastic improvement over Bubble Sort's performance. 
 
 Similar to Bubble Sort, the space complexity for Comb Sort is constant -- O(1). 
 This is extremely space efficient as it sorts the array in place. 

From a9c311588b2ecee2420af4cfee91217db427f450 Mon Sep 17 00:00:00 2001
From: Mac Bellingrath <macbellingrath@users.noreply.github.com>
Date: Wed, 26 Dec 2018 15:27:08 -0500
Subject: [PATCH 1581/1679] Update README.md

---
 Convex Hull/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index d27027a45..ab263f00d 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -2,7 +2,7 @@
 
 Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points. In comparing different solutions to this problem we can describe each algorithm in terms of it's big-O time complexity.
 
-There are multiple Convex Hull algorithms but this solution is called Quickhull, is comes from the work of both W. Eddy in 1977 and also separately A. Bykat in 1978, this algorithm has an expected time complexity of O(n log n), but it's worst-case time-complexity can be O(n^2) . With average conditions the algorithm has ok efficiency, but it's time-complexity can start to head become more exponential in cases of high symmetry or where there are points lying on the circumference of a circle for example.
+There are multiple Convex Hull algorithms but this solution is called Quickhull, is comes from the work of both W. Eddy in 1977 and also separately A. Bykat in 1978, this algorithm has an expected time complexity of O(n log n), but it's worst-case time-complexity can be O(n^2) . With average conditions the algorithm has ok efficiency, but it's time-complexity can start to become more exponential in cases of high symmetry or where there are points lying on the circumference of a circle for example.
 
 ## Quickhull
 

From c1b704dfbe27b96a67a34949055bcc55a47ca7c3 Mon Sep 17 00:00:00 2001
From: Mac Bellingrath <macbellingrath@users.noreply.github.com>
Date: Thu, 27 Dec 2018 09:14:45 -0500
Subject: [PATCH 1582/1679] Update README.md

---
 Convex Hull/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index d27027a45..71a470f56 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -17,7 +17,7 @@ The quickhull algorithm works as follows:
 - Keep on doing so on until no more points are left, the recursion has come to an end and the points selected constitute the convex hull.
 
 
-Our functioni will have the following defininition:
+Our function will have the following defininition:
 
 `findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`
 

From 611253f617661d54280dd2861dfe57b3e4568b4e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20C=2E=20Kr=C3=BCger?= <simon.krueger@intive.com>
Date: Fri, 11 Jan 2019 10:43:51 +0100
Subject: [PATCH 1583/1679] GCD improvements after review

- Default parameter values
- umbrella for different gcd implementations with generic gcd(_: _:) function
- better structure of readme file including all 3 algorithms
---
 GCD/GCD.playground/Contents.swift          | 154 ++-------------------
 GCD/{ => GCD.playground/Sources}/GCD.swift |  35 +++--
 GCD/README.markdown                        | 146 ++++++++++++++-----
 3 files changed, 151 insertions(+), 184 deletions(-)
 rename GCD/{ => GCD.playground/Sources}/GCD.swift (73%)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 175d26639..bb8d49055 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,147 +1,21 @@
-//: Playground - noun: a place where people can play
+gcd(52, 39)       // 13
+gcd(228, 36)      // 12
+gcd(51357, 3819)  // 57
+gcd(841, 299)     // 1
 
-/*
- Iterative approach based on the Euclidean algorithm.
- The Euclidean algorithm is based on the principle that the greatest
- common divisor of two numbers does not change if the larger number
- is replaced by its difference with the smaller number.
- - Parameter m: First natural number
- - Parameter n: Second natural number
- - Returns: The natural gcd if m and n
- */
-func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
-    var a: Int = 0
-    var b: Int = max(m, n)
-    var r: Int = min(m, n)
-    
-    while r != 0 {
-        a = b
-        b = r
-        r = a % b
-    }
-    return b
-}
-
-/*
- Recursive approach based on the Euclidean algorithm.
- 
- - Parameter m: First natural number
- - Parameter n: Second natural number
- - Returns: The natural gcd of m and n
- - Note: The recursive version makes only tail recursive calls.
- Most compilers for imperative languages do not optimize these.
- The swift compiler as well as the obj-c compiler is able to do
- optimizations for tail recursive calls, even though it still ends
- up to be the same in terms of complexity. That said, tail call
- elimination is not mutually exclusive to recursion.
- */
-func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
-    let r: Int = m % n
-    if r != 0 {
-        return gcdRecursiveEuklid(n, r)
-    } else {
-        return n
-    }
-}
-
-/*
- The binary GCD algorithm, also known as Stein's algorithm,
- is an algorithm that computes the greatest common divisor of two
- nonnegative integers. Stein's algorithm uses simpler arithmetic
- operations than the conventional Euclidean algorithm; it replaces
- division with arithmetic shifts, comparisons, and subtraction.
- 
- - Parameter m: First natural number
- - Parameter n: Second natural number
- - Returns: The natural gcd of m and n
- - Complexity: worst case O(n^2), where n is the number of bits
- in the larger of the two numbers. Although each step reduces
- at least one of the operands by at least a factor of 2,
- the subtract and shift operations take linear time for very
- large integers
- */
-func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
-    if let easySolution = findEasySolution(m, n) { return easySolution }
-    
-    if (m & 1) == 0 {
-        // m is even
-        if (n & 1) == 1 {
-            // and n is odd
-            return gcdBinaryRecursiveStein(m >> 1, n)
-        } else {
-            // both m and n are even
-            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
-        }
-    } else if (n & 1) == 0 {
-        // m is odd, n is even
-        return gcdBinaryRecursiveStein(m, n >> 1)
-    } else if (m > n) {
-        // reduce larger argument
-        return gcdBinaryRecursiveStein((m - n) >> 1, n)
-    } else {
-        // reduce larger argument
-        return gcdBinaryRecursiveStein((n - m) >> 1, m)
-    }
-}
-
-/*
- Finds an easy solution for the gcd.
- - Note: It might be relevant for different usecases to
- try finding an easy solution for the GCD calculation
- before even starting more difficult operations.
- */
-func findEasySolution(_ m: Int, _ n: Int) -> Int? {
-    if m == n {
-        return m
-    }
-    if m == 0 {
-        return n
-    }
-    if n == 0 {
-        return m
-    }
-    return nil
-}
-
-
-enum LCMError: Error {
-    case divisionByZero
-}
-
-/*
- Calculates the lcm for two given numbers using a specified gcd algorithm.
- 
- - Parameter m: First natural number.
- - Parameter n: Second natural number.
- - Parameter using: The used gcd algorithm to calculate the lcm.
- - Throws: Can throw a `divisionByZero` error if one of the given
- attributes turns out to be zero or less.
- - Returns: The least common multiplier of the two attributes as
- an unsigned integer
- */
-func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
-    guard (m & n) != 0 else { throw LCMError.divisionByZero }
-    return m / gcdAlgorithm(m, n) * n
-}
-
-gcdIterativeEuklid(52, 39)       // 13
-gcdIterativeEuklid(228, 36)      // 12
-gcdIterativeEuklid(51357, 3819)  // 57
-gcdIterativeEuklid(841, 299)     // 1
-
-gcdRecursiveEuklid(52, 39)       // 13
-gcdRecursiveEuklid(228, 36)      // 12
-gcdRecursiveEuklid(51357, 3819)  // 57
-gcdRecursiveEuklid(841, 299)     // 1
+gcd(52, 39, using: gcdRecursiveEuklid)       // 13
+gcd(228, 36, using:  gcdRecursiveEuklid)      // 12
+gcd(51357, 3819, using: gcdRecursiveEuklid)  // 57
+gcd(841, 299, using: gcdRecursiveEuklid)     // 1
 
-gcdBinaryRecursiveStein(52, 39)       // 13
-gcdBinaryRecursiveStein(228, 36)      // 12
-gcdBinaryRecursiveStein(51357, 3819)  // 57
-gcdBinaryRecursiveStein(841, 299)     // 1
+gcd(52, 39, using: gcdBinaryRecursiveStein)       // 13
+gcd(228, 36, using: gcdBinaryRecursiveStein)      // 12
+gcd(51357, 3819, using: gcdBinaryRecursiveStein)  // 57
+gcd(841, 299, using: gcdBinaryRecursiveStein)     // 1
 
 do {
-    try lcm(2, 3, using: gcdIterativeEuklid)   // 6
-    try lcm(10, 8, using: gcdIterativeEuklid)  // 40
+    try lcm(2, 3)   // 6
+    try lcm(10, 8, using: gcdRecursiveEuklid)  // 40
 } catch {
     dump(error)
 }
diff --git a/GCD/GCD.swift b/GCD/GCD.playground/Sources/GCD.swift
similarity index 73%
rename from GCD/GCD.swift
rename to GCD/GCD.playground/Sources/GCD.swift
index f4b390e63..4eb0c7621 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.playground/Sources/GCD.swift
@@ -1,3 +1,17 @@
+/*
+ Finds the largest positive integer that divides both
+ m and n without a remainder.
+
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Parameter using: The used algorithm to calculate the gcd.
+                    If nothing provided, the Iterative Euclidean
+                    algorithm is used.
+ - Returns: The natural gcd of m and n.
+ */
+public func gcd(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int) = gcdIterativeEuklid) -> Int {
+    return gcdAlgorithm(m, n)
+}
 
 /*
  Iterative approach based on the Euclidean algorithm.
@@ -6,9 +20,9 @@
  is replaced by its difference with the smaller number.
  - Parameter m: First natural number
  - Parameter n: Second natural number
- - Returns: The natural gcd if m and n
+ - Returns: The natural gcd of m and n.
  */
-func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+public func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
     var a: Int = 0
     var b: Int = max(m, n)
     var r: Int = min(m, n)
@@ -26,7 +40,7 @@ func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
  
  - Parameter m: First natural number
  - Parameter n: Second natural number
- - Returns: The natural gcd of m and n
+ - Returns: The natural gcd of m and n.
  - Note: The recursive version makes only tail recursive calls.
  Most compilers for imperative languages do not optimize these.
  The swift compiler as well as the obj-c compiler is able to do
@@ -34,7 +48,7 @@ func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
  up to be the same in terms of complexity. That said, tail call
  elimination is not mutually exclusive to recursion.
  */
-func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+public func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
     let r: Int = m % n
     if r != 0 {
         return gcdRecursiveEuklid(n, r)
@@ -59,7 +73,7 @@ func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
  the subtract and shift operations take linear time for very
  large integers
  */
-func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+public func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
     if let easySolution = findEasySolution(m, n) { return easySolution }
     
     if (m & 1) == 0 {
@@ -85,6 +99,9 @@ func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
 
 /*
  Finds an easy solution for the gcd.
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: A natural gcd of m and n if possible.
  - Note: It might be relevant for different usecases to
  try finding an easy solution for the GCD calculation
  before even starting more difficult operations.
@@ -103,7 +120,7 @@ func findEasySolution(_ m: Int, _ n: Int) -> Int? {
 }
 
 
-enum LCMError: Error {
+public enum LCMError: Error {
     case divisionByZero
 }
 
@@ -113,12 +130,14 @@ enum LCMError: Error {
  - Parameter m: First natural number.
  - Parameter n: Second natural number.
  - Parameter using: The used gcd algorithm to calculate the lcm.
+                    If nothing provided, the Iterative Euclidean
+                    algorithm is used.
  - Throws: Can throw a `divisionByZero` error if one of the given
  attributes turns out to be zero or less.
  - Returns: The least common multiplier of the two attributes as
  an unsigned integer
  */
-func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
-    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+public func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int) = gcdIterativeEuklid) throws -> Int {
+    guard m & n != 0 else { throw LCMError.divisionByZero }
     return m / gcdAlgorithm(m, n) * n
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index a23aea190..07a3f0f4d 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -1,14 +1,19 @@
 # Greatest Common Divisor
 
 The *greatest common divisor* (or Greatest Common Factor) of two numbers `a` and `b` is the largest positive integer that divides both `a` and `b` without a remainder. The GCD.swift file contains three different algorithms of how to calculate the greatest common divisor.
+For example, `gcd(39, 52) = 13` because 13 divides 39 (`39 / 13 = 3`) as well as 52 (`52 / 13 = 4`). But there is no larger number than 13 that divides them both.
+You've probably had to learn about this in school at some point. :-)
 
-For example, `gcdIterativeEuklid(39, 52) = 13` because 13 divides 39 (`39/13 = 3`) as well as 52 (`52/13 = 4`). But there is no larger number than 13 that divides them both.
+You probably won't need to use the GCD or LCM in any real-world problems, but it's cool to play around with this ancient algorithm. It was first described by Euklid in his [Elements](http://publicdomainreview.org/collections/the-first-six-books-of-the-elements-of-euclid-1847/) around 300 BC. Rumor has it that he discovered this algorithm while he was hacking on his Commodore 64.
 
-You've probably had to learn about this in school at some point. :-)
+## Different Algorithms
 
-The laborious way to find the GCD of two numbers is to first figure out the factors of both numbers, then take the greatest number they have in common. The problem is that factoring numbers is quite difficult, especially when they get larger. (On the plus side, that difficulty is also what keeps your online payments secure.)
+This example includes three different algorithms to find the same result. 
 
-There is a smarter way to calculate the GCD: Euclid's algorithm. The big idea here is that,
+### Iterative Euklidean
+
+The laborious way to find the GCD of two numbers is to first figure out the factors of both numbers, then take the greatest number they have in common. The problem is that factoring numbers is quite difficult, especially when they get larger. (On the plus side, that difficulty is also what keeps your online payments secure.)
+There is a smarter way to calculate the GCD: Euklid's algorithm. The big idea here is that,
 
 	gcd(a, b) = gcd(b, a % b)
 
@@ -16,6 +21,33 @@ where `a % b` calculates the remainder of `a` divided by `b`.
 
 Here is an implementation of this idea in Swift:
 
+```swift
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
+    return b
+}
+```
+
+Put it in a playground and try it out with these examples:
+
+```swift
+gcd(52, 39, using: gcdIterativeEuklid)        // 13
+gcd(228, 36, using: gcdIterativeEuklid)       // 12
+gcd(51357, 3819, using: gcdIterativeEuklid)   // 57
+```
+
+### Recursive Euklidean
+
+Here is a slightly different implementation of Euklid's algorithm. Unlike the first version this doesn't use a `while` loop, but leverages recursion.
+
 ```swift
 func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
     let r: Int = m % n
@@ -27,19 +59,21 @@ func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
 }
 ```
 
-Put it in a playground and try it out with these examples:
+Put it in a playground and compare it with the results of the iterative Eulidean gcd. They should return the same results:
 
 ```swift
-gcdBinaryRecursiveStein(52, 39)        // 13
-gcdRecursiveEuklid(228, 36)       // 12
-gcdIterativeEuklid(51357, 3819)   // 57
+gcd(52, 39, using: gcdRecursiveEuklid)        // 13
+gcd(228, 36, using: gcdRecursiveEuklid)       // 12
+gcd(51357, 3819, using: gcdRecursiveEuklid)   // 57
 ```
 
-Let's step through the third example using gcd as a representation of the gcdRecursiveEuklid here:
+The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+
+Let's step through the third example using the *recursive Euklidean algorithm* here:
 
 	gcd(51357, 3819)
 
-According to Euclid's rule, this is equivalent to,
+According to Euklid's rule, this is equivalent to,
 
 	gcd(3819, 51357 % 3819) = gcd(3819, 1710)
 
@@ -57,7 +91,7 @@ And now can't divide any further. The remainder of `114 / 57` is zero because `1
 
 	gcd(3819, 51357) = gcd(57, 0) = 57
 
-So in each step of Euclid's algorithm the numbers become smaller and at some point it ends when one of them becomes zero.
+So in each step of Euklid's algorithm the numbers become smaller and at some point it ends when one of them becomes zero.
 
 By the way, it's also possible that two numbers have a GCD of 1. They are said to be *relatively prime*. This happens when there is no number that divides them both, for example:
 
@@ -65,55 +99,95 @@ By the way, it's also possible that two numbers have a GCD of 1. They are said t
 gcd(841, 299)     // 1
 ```
 
-Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop.
+### Binary Recursive Stein
+
+The binary GCD algorithm, also known as Stein's algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm is very similar to the recursive Eulidean algorithm, but uses arithmetical operations, which are simpler for computers to perform, than the conventional Euclidean algorithm does. It replaces division with arithmetic shifts, comparisons, and subtraction.
 
 ```swift
-func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
-    var a: Int = 0
-    var b: Int = max(m, n)
-    var r: Int = min(m, n)
+func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+    if let easySolution = findEasySolution(m, n) { return easySolution }
+
+    if (m & 1) == 0 {
+        // m is even
+        if (n & 1) == 1 {
+            // and n is odd
+            return gcdBinaryRecursiveStein(m >> 1, n)
+        } else {
+            // both m and n are even
+            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
+        }
+    } else if (n & 1) == 0 {
+        // m is odd, n is even
+        return gcdBinaryRecursiveStein(m, n >> 1)
+    } else if (m > n) {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((m - n) >> 1, n)
+    } else {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((n - m) >> 1, m)
+    }
+}
+```
 
-    while r != 0 {
-        a = b
-        b = r
-        r = a % b
+Depending on your application and your input expectations, it might be reasonable to also search for an "easy solution" using the other gcd implementations:
+
+```swift
+func findEasySolution(_ m: Int, _ n: Int) -> Int? {
+    if m == n {
+        return m
     }
-    return b
+    if m == 0 {
+        return n
+    }
+    if n == 0 {
+        return m
+    }
+    return nil
 }
+
 ```
 
-The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+Put it in a playground and compare it with the results of the other gcd implementations:
+
+```swift
+gcd(52, 39, using: gcdBinaryRecursiveStein)        // 13
+gcd(228, 36, using: gcdBinaryRecursiveStein)       // 12
+gcd(51357, 3819, using: gcdBinaryRecursiveStein)   // 57
+```
 
-## Least Common Multiple
+### Least Common Multiple
 
-An idea related to the GCD is the *least common multiple* or LCM.
+Another algorithm related to the GCD is the *least common multiple* or LCM.
 
-The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. The example implementation of the LCM takes two numbers and a specification which GCD algorithm is used.
+The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. The example implementation of the LCM takes two numbers and an optional specification which GCD algorithm is used.
 
-For example: `lcm(2, 3, using: gcdIterativeEuklid) = 6` because 6 can be divided by 2 and also by 3.
+For example: `lcm(2, 3, using: gcdRecursiveEuklid) = 6` , which tells us that 6 is the smallest number that can be devided by 2 as well as 3.
 
-We can calculate the LCM using Euclid's algorithm too:
+We can calculate the LCM using Euklid's algorithm too:
 
-	              a * b
-	lcm(a, b) = ---------
-	            gcd(a, b)
+a * b
+lcm(a, b) = ---------
+gcd(a, b)
 
 In code:
 
 ```swift
-func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
-    guard (m & n) != 0 else { throw LCMError.divisionByZero }
-    return m / gcdAlgorithm(m, n) * n
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int) = gcdIterativeEuklid) throws -> Int {
+guard (m & n) != 0 else { throw LCMError.divisionByZero }
+return m / gcdAlgorithm(m, n) * n
 }
 ```
 
 And to try it out in a playground:
 
 ```swift
-lcm(10, 8, using: gcdIterativeEuklid)    // 40
+lcm(10, 8)    // 40
 ```
 
-You probably won't need to use the GCD or LCM in any real-world problems, but it's cool to play around with this ancient algorithm. It was first described by Euclid in his [Elements](http://publicdomainreview.org/collections/the-first-six-books-of-the-elements-of-euclid-1847/) around 300 BC. Rumor has it that he discovered this algorithm while he was hacking on his Commodore 64.
+## Discussion
+
+While these algorithms all calculate the same result, comparing their plane complexity might not be enough to decide for one of them, though. The original iterative Euklidean algorithm is easier to understand. The recursive Euklidean and Stein's algorithm, while being generally faster, their runtime is heavily dependend on the environment they are running on.
+_If a fast calculation of the gcd is necessary, a runtime comparison for the specific platform and compiler optimization level should be done for the rekursive Euklidean and Stein's algorithm._
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
-*Extended by Simon Krüger*
\ No newline at end of file
+*Extended by Simon C. Krüger*

From 15f27793c56cd27788576deb0ef2c8ed901385d2 Mon Sep 17 00:00:00 2001
From: cr0ss <kayoslab@users.noreply.github.com>
Date: Fri, 11 Jan 2019 10:51:27 +0100
Subject: [PATCH 1584/1679] Linebreak in README

---
 GCD/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/GCD/README.markdown b/GCD/README.markdown
index 07a3f0f4d..4c459eff0 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -190,4 +190,5 @@ While these algorithms all calculate the same result, comparing their plane comp
 _If a fast calculation of the gcd is necessary, a runtime comparison for the specific platform and compiler optimization level should be done for the rekursive Euklidean and Stein's algorithm._
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
+
 *Extended by Simon C. Krüger*

From c5ff4084bd0f42ef7106a3139c217454aca28015 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Tue, 15 Jan 2019 15:27:38 -0800
Subject: [PATCH 1585/1679] Fix typo in Stack playground

---
 Stack/Stack.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 13774d7d1..e0632f8b4 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -45,7 +45,7 @@ public struct Stack<T> {
   }
 
   /**
-     Removes and returns the item at the top of the sack.
+     Removes and returns the item at the top of the stack.
      
      - Returns: The item at the top of the stack.
   */

From 0f2e9e1ebc22de221f508504c6e10bd34a76d919 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 28 Jan 2019 07:57:44 +0100
Subject: [PATCH 1586/1679] Update hyperlinks

Link to author profiles were missing
---
 AVL Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index e7515d99f..4e974ba71 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -88,4 +88,4 @@ The interesting bits are in the `balance()` method which is called after inserti
 
 AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black%20Tree/) seems to be more popular.
 
-*Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*
+*Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi) and [Matthijs Hollemans](https://github.com/hollance)*

From ff780b6ff7d25b2aa79cbeef5ac72de6ce76b77e Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Wed, 30 Jan 2019 17:16:49 -0800
Subject: [PATCH 1587/1679] Update README

Updated supported Xcode version to 10 and swift version to 4.2
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index ff8bfe778..88ea35949 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Code is compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
+Code is compatible with **Xcode 10** and **Swift 4.2**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From fa656f090ec4de0b7c9e8bd8eeb2e808c3d7f32c Mon Sep 17 00:00:00 2001
From: Andriy Makukha <andriy.makukha@gmail.com>
Date: Fri, 1 Feb 2019 10:20:10 +0800
Subject: [PATCH 1588/1679] reserveCapacity was missing in README (11% faster
 with it)

---
 Merge Sort/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 7ad6fd95e..d86f062f4 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -79,6 +79,7 @@ func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
 
   // 2
   var orderedPile = [Int]()
+  orderedPile.reserveCapacity(leftPile.count + rightPile.count)
 
   // 3
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
@@ -115,7 +116,7 @@ This method may look scary, but it is quite straightforward:
 
 1. You need two indexes to keep track of your progress for the two arrays while merging.
 
-2. This is the merged array. It is empty right now, but you will build it up in subsequent steps by appending elements from the other arrays.
+2. This is the merged array. It is empty right now, but you will build it up in subsequent steps by appending elements from the other arrays. Since you already know number of elements that will end up in this array, you reserve capacity to avoid reallocation overhead later.
 
 3. This while-loop will compare the elements from the left and right sides and append them into the `orderedPile` while making sure that the result stays in order.
 

From d4b9091af6f83f55e9681a5a11b6374bd2ac8cff Mon Sep 17 00:00:00 2001
From: Morgan Davison <morgan.davison@gmail.com>
Date: Sun, 3 Feb 2019 20:45:28 -0500
Subject: [PATCH 1589/1679] Check with Xcode 10.1

No changes needed
---
 3Sum and 4Sum/3Sum.playground/Contents.swift              | 4 ++++
 .../playground.xcworkspace/contents.xcworkspacedata       | 7 +++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3Sum and 4Sum/4Sum.playground/Contents.swift              | 5 +++++
 .../playground.xcworkspace/contents.xcworkspacedata       | 7 +++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 6 files changed, 39 insertions(+)
 create mode 100644 3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 2581da6e7..d172aed1f 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -1,3 +1,7 @@
+// last checked with Xcode 10.1
+#if swift(>=4.2)
+print("Hello, Swift 4.2!")
+#endif
 
 extension Collection where Element: Equatable {
   
diff --git a/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index 86b530224..37f75918c 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 10.1
+#if swift(>=4.2)
+print("Hello, Swift 4.2!")
+#endif
+
 extension Collection where Element: Equatable {
   
   /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
diff --git a/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 2f92aef01b0d7e6b57e4ae8a9de79467dd7598d9 Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Wed, 6 Feb 2019 21:34:53 +0000
Subject: [PATCH 1590/1679] fix bracket formatting

---
 Bit Set/BitSet.playground/Contents.swift       | 14 +++++++-------
 Bit Set/BitSet.playground/Sources/BitSet.swift |  8 ++++----
 Bit Set/BitSet.swift                           |  8 ++++----
 3 files changed, 15 insertions(+), 15 deletions(-)

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 2c5edcd84..70d5ca5e8 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -93,8 +93,8 @@ z.all1()        // false
 var smallBitSet = BitSet(size: 16)
 smallBitSet[5] = true
 smallBitSet[10] = true
-print( smallBitSet >> 3 )
-print( smallBitSet << 6 ) // one bit shifts off the end
+print(smallBitSet >> 3)
+print(smallBitSet << 6) // one bit shifts off the end
 
 var bigBitSet = BitSet( size: 120 )
 bigBitSet[1] = true
@@ -104,8 +104,8 @@ bigBitSet[32] = true
 bigBitSet[55] = true
 bigBitSet[64] = true
 bigBitSet[80] = true
-print( bigBitSet )
-print( bigBitSet << 32 )
-print( bigBitSet << 64 )
-print( bigBitSet >> 32 )
-print( bigBitSet >> 64 )
+print(bigBitSet)
+print(bigBitSet << 32)
+print(bigBitSet << 64)
+print(bigBitSet >> 32)
+print(bigBitSet >> 64)
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index 85f5da505..258bce457 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -235,10 +235,10 @@ public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
     let shift = numBitsLeft % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i - offset >= 0 ) {
+        if (i - offset >= 0) {
             out.words[i] = lhs.words[i - offset] << shift
         }
-        if( i - offset - 1 >= 0 ) {
+        if (i - offset - 1 >= 0) {
             out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
         }
     }
@@ -253,10 +253,10 @@ public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
     let shift = numBitsRight % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i + offset < lhs.words.count ) {
+        if (i + offset < lhs.words.count) {
             out.words[i] = lhs.words[i + offset] >> shift
         }
-        if( i + offset + 1 < lhs.words.count ) {
+        if (i + offset + 1 < lhs.words.count) {
             out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
         }
     }
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index 83829c6c5..19413f424 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -235,10 +235,10 @@ public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
     let shift = numBitsLeft % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i - offset >= 0 ) {
+        if (i - offset >= 0) {
             out.words[i] = lhs.words[i - offset] << shift
         }
-        if( i - offset - 1 >= 0 ) {
+        if (i - offset - 1 >= 0) {
             out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
         }
     }
@@ -253,10 +253,10 @@ public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
     let shift = numBitsRight % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i + offset < lhs.words.count ) {
+        if (i + offset < lhs.words.count) {
             out.words[i] = lhs.words[i + offset] >> shift
         }
-        if( i + offset + 1 < lhs.words.count ) {
+        if (i + offset + 1 < lhs.words.count) {
             out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
         }
     }

From 27efddaa9ceaa4f1675dc69433d253ce028596f1 Mon Sep 17 00:00:00 2001
From: Larissa Laich <llaich@ethz.ch>
Date: Thu, 7 Feb 2019 20:47:01 +0100
Subject: [PATCH 1591/1679] fixed error in linear regression formula

---
 Linear Regression/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 4f9d030db..db04bf8a2 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -75,7 +75,7 @@ for _ in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope.carAge + intercept) - carPrice)) ^ 2`.
+We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope * carAge + intercept) - carPrice)) ^ 2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 

From 6d936e461435783e2a19afcf6b817e1b9c0ceb5f Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Tue, 12 Feb 2019 14:38:02 +0530
Subject: [PATCH 1592/1679] Update Karatsuba README

---
 Karatsuba Multiplication/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index aef0d744a..02e54a1bf 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -115,10 +115,10 @@ What about the running time of this algorithm? Is all this extra work worth it?
  
 ## Resources
 
-[Wikipedia] (https://en.wikipedia.org/wiki/Karatsuba_algorithm)
+[Wikipedia](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
 
-[WolframMathWorld] (http://mathworld.wolfram.com/KaratsubaMultiplication.html) 
+[WolframMathWorld](http://mathworld.wolfram.com/KaratsubaMultiplication.html) 
 
-[Master Theorem] (https://en.wikipedia.org/wiki/Master_theorem)
+[Master Theorem](https://en.wikipedia.org/wiki/Master_theorem)
 
 *Written for Swift Algorithm Club by Richard Ash*

From deae79c2010d1e7341b24314819c9736cdfc4387 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Tue, 12 Feb 2019 15:07:50 +0530
Subject: [PATCH 1593/1679] Update README

Replace "minimise" with "minimize"
---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index db04bf8a2..d07bf1497 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -21,7 +21,7 @@ Let's start by looking at the data plotted out:
 
 We could imagine a straight line drawn through the points on this graph. It's not (in this case) going to go exactly through every point, but we could place the line so that it goes as close to all the points as possible.
 
-To say this in another way, we want to make the distance from the line to each point as small as possible. This is most often done by minimising the square of the distance from the line to each point.
+To say this in another way, we want to make the distance from the line to each point as small as possible. This is most often done by minimizing the square of the distance from the line to each point.
 
 We can describe the straight line in terms of two variables:
 
@@ -75,7 +75,7 @@ for _ in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope * carAge + intercept) - carPrice)) ^ 2`.
+We want to minimize the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope * carAge + intercept) - carPrice)) ^ 2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 

From a88c984a388c456de27302af796180bf25b15529 Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Fri, 15 Feb 2019 18:19:58 +0000
Subject: [PATCH 1594/1679] remove duplicate source file, update README

---
 Bit Set/BitSet.swift    | 293 ----------------------------------------
 Bit Set/README.markdown |  84 ++++++++++++
 2 files changed, 84 insertions(+), 293 deletions(-)
 delete mode 100644 Bit Set/BitSet.swift

diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
deleted file mode 100644
index 19413f424..000000000
--- a/Bit Set/BitSet.swift	
+++ /dev/null
@@ -1,293 +0,0 @@
-/*
- A fixed-size sequence of n bits. Bits have indices 0 to n-1.
- */
-public struct BitSet {
-  /* How many bits this object can hold. */
-  private(set) public var size: Int
-  
-  /*
-   We store the bits in a list of unsigned 64-bit integers.
-   The first entry, `words[0]`, is the least significant word.
-   */
-  fileprivate let N = 64
-  public typealias Word = UInt64
-  fileprivate(set) public var words: [Word]
-  
-  private let allOnes = ~Word()
-  
-  /* Creates a bit set that can hold `size` bits. All bits are initially 0. */
-  public init(size: Int) {
-    precondition(size > 0)
-    self.size = size
-    
-    // Round up the count to the next multiple of 64.
-    let n = (size + (N-1)) / N
-    words = [Word](repeating: 0, count: n)
-  }
-  
-  /* Converts a bit index into an array index and a mask inside the word. */
-  private func indexOf(_ i: Int) -> (Int, Word) {
-    precondition(i >= 0)
-    precondition(i < size)
-    let o = i / N
-    let m = Word(i - o*N)
-    return (o, 1 << m)
-  }
-  
-  /* Returns a mask that has 1s for all bits that are in the last word. */
-  private func lastWordMask() -> Word {
-    let diff = words.count*N - size
-    if diff > 0 {
-      // Set the highest bit that's still valid.
-      let mask = 1 << Word(63 - diff)
-      // Subtract 1 to turn it into a mask, and add the high bit back in.
-      return (Word)(mask | (mask - 1))
-    } else {
-      return allOnes
-    }
-  }
-  
-  /*
-   If the size is not a multiple of N, then we have to clear out the bits
-   that we're not using, or bitwise operations between two differently sized
-   BitSets will go wrong.
-   */
-  fileprivate mutating func clearUnusedBits() {
-    words[words.count - 1] &= lastWordMask()
-  }
-  
-  /* So you can write bitset[99] = ... */
-  public subscript(i: Int) -> Bool {
-    get { return isSet(i) }
-    set { if newValue { set(i) } else { clear(i) } }
-  }
-  
-  /* Sets the bit at the specified index to 1. */
-  public mutating func set(_ i: Int) {
-    let (j, m) = indexOf(i)
-    words[j] |= m
-  }
-  
-  /* Sets all the bits to 1. */
-  public mutating func setAll() {
-    for i in 0..<words.count {
-      words[i] = allOnes
-    }
-    clearUnusedBits()
-  }
-  
-  /* Sets the bit at the specified index to 0. */
-  public mutating func clear(_ i: Int) {
-    let (j, m) = indexOf(i)
-    words[j] &= ~m
-  }
-  
-  /* Sets all the bits to 0. */
-  public mutating func clearAll() {
-    for i in 0..<words.count {
-      words[i] = 0
-    }
-  }
-  
-  /* Changes 0 into 1 and 1 into 0. Returns the new value of the bit. */
-  public mutating func flip(_ i: Int) -> Bool {
-    let (j, m) = indexOf(i)
-    words[j] ^= m
-    return (words[j] & m) != 0
-  }
-  
-  /* Determines whether the bit at the specific index is 1 (true) or 0 (false). */
-  public func isSet(_ i: Int) -> Bool {
-    let (j, m) = indexOf(i)
-    return (words[j] & m) != 0
-  }
-  
-  /*
-   Returns the number of bits that are 1. Time complexity is O(s) where s is
-   the number of 1-bits.
-   */
-  public var cardinality: Int {
-    var count = 0
-    for var x in words {
-      while x != 0 {
-        let y = x & ~(x - 1)  // find lowest 1-bit
-        x = x ^ y             // and erase it
-        count += 1
-      }
-    }
-    return count
-  }
-  
-  /* Checks if all the bits are set. */
-  public func all1() -> Bool {
-    for i in 0..<words.count - 1 {
-      if words[i] != allOnes { return false }
-    }
-    return words[words.count - 1] == lastWordMask()
-  }
-  
-  /* Checks if any of the bits are set. */
-  public func any1() -> Bool {
-    for x in words {
-      if x != 0 { return true }
-    }
-    return false
-  }
-  
-  /* Checks if none of the bits are set. */
-  public func all0() -> Bool {
-    for x in words {
-      if x != 0 { return false }
-    }
-    return true
-  }
-}
-
-// MARK: - Equality
-
-extension BitSet: Equatable {
-}
-
-public func == (lhs: BitSet, rhs: BitSet) -> Bool {
-  return lhs.words == rhs.words
-}
-
-// MARK: - Hashing
-
-extension BitSet: Hashable {
-  /* Based on the hashing code from Java's BitSet. */
-  public var hashValue: Int {
-    var h = Word(1234)
-    for i in stride(from: words.count, to: 0, by: -1) {
-      h ^= words[i - 1] &* Word(i)
-    }
-    return Int((h >> 32) ^ h)
-  }
-}
-
-// MARK: - Bitwise operations
-
-extension BitSet {
-  public static var allZeros: BitSet {
-    return BitSet(size: 64)
-  }
-}
-
-private func copyLargest(_ lhs: BitSet, _ rhs: BitSet) -> BitSet {
-  return (lhs.words.count > rhs.words.count) ? lhs : rhs
-}
-
-/*
- Note: In all of these bitwise operations, lhs and rhs are allowed to have a
- different number of bits. The new BitSet always has the larger size.
- The extra bits that get added to the smaller BitSet are considered to be 0.
- That will strip off the higher bits from the larger BitSet when doing &.
- */
-
-public func & (lhs: BitSet, rhs: BitSet) -> BitSet {
-  let m = max(lhs.size, rhs.size)
-  var out = BitSet(size: m)
-  let n = min(lhs.words.count, rhs.words.count)
-  for i in 0..<n {
-    out.words[i] = lhs.words[i] & rhs.words[i]
-  }
-  return out
-}
-
-public func | (lhs: BitSet, rhs: BitSet) -> BitSet {
-  var out = copyLargest(lhs, rhs)
-  let n = min(lhs.words.count, rhs.words.count)
-  for i in 0..<n {
-    out.words[i] = lhs.words[i] | rhs.words[i]
-  }
-  return out
-}
-
-public func ^ (lhs: BitSet, rhs: BitSet) -> BitSet {
-  var out = copyLargest(lhs, rhs)
-  let n = min(lhs.words.count, rhs.words.count)
-  for i in 0..<n {
-    out.words[i] = lhs.words[i] ^ rhs.words[i]
-  }
-  return out
-}
-
-prefix public func ~ (rhs: BitSet) -> BitSet {
-  var out = BitSet(size: rhs.size)
-  for i in 0..<rhs.words.count {
-    out.words[i] = ~rhs.words[i]
-  }
-  out.clearUnusedBits()
-  return out
-}
-
-// MARK: - Bit shift operations
-
-/*
- Note: For bitshift operations, the assumption is that any bits that are
- shifted off the end of the end of the declared size are not still set.
- In other words, we are maintaining the original number of bits.
- */
-
-public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
-    var out = lhs
-    let offset = numBitsLeft / lhs.N
-    let shift = numBitsLeft % lhs.N
-    for i in 0..<lhs.words.count {
-        out.words[i] = 0
-        if (i - offset >= 0) {
-            out.words[i] = lhs.words[i - offset] << shift
-        }
-        if (i - offset - 1 >= 0) {
-            out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
-        }
-    }
-    
-    out.clearUnusedBits()
-    return out
-}
-
-public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
-    var out = lhs
-    let offset = numBitsRight / lhs.N
-    let shift = numBitsRight % lhs.N
-    for i in 0..<lhs.words.count {
-        out.words[i] = 0
-        if (i + offset < lhs.words.count) {
-            out.words[i] = lhs.words[i + offset] >> shift
-        }
-        if (i + offset + 1 < lhs.words.count) {
-            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
-        }
-    }
-    
-    out.clearUnusedBits()
-    return out
-}
-
-
-// MARK: - Debugging
-
-extension UInt64 {
-  /* Writes the bits in little-endian order, LSB first. */
-  public func bitsToString() -> String {
-    var s = ""
-    var n = self
-    for _ in 1...64 {
-      s += ((n & 1 == 1) ? "1" : "0")
-      n >>= 1
-    }
-    return s
-  }
-}
-
-extension BitSet: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    for x in words {
-      s += x.bitsToString() + " "
-    }
-    return s
-  }
-}
-
diff --git a/Bit Set/README.markdown b/Bit Set/README.markdown
index 6bb6e7c89..365950d06 100644
--- a/Bit Set/README.markdown	
+++ b/Bit Set/README.markdown	
@@ -329,6 +329,90 @@ This is the original value but with the lowest 1-bit removed.
 
 We keep repeating this process until the value consists of all zeros. The time complexity is **O(s)** where **s** is the number of 1-bits.
 
+## Bit Shift Operations
+
+Bit shifts are a common and very useful mechanism when dealing with bitsets. Here is the right-shift function:
+
+```
+public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsRight / lhs.N
+    let shift = numBitsRight % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        
+        if (i + offset < lhs.words.count) {
+            out.words[i] = lhs.words[i + offset] >> shift
+        }
+        
+        if (i + offset + 1 < lhs.words.count) {
+            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
+        }
+    }
+
+    out.clearUnusedBits()
+    return out
+}
+```
+
+Let's start with this line:
+
+```swift
+for i in 0..<lhs.words.count {
+```
+
+This indicates our strategy: we want to go through each word of the result and assign the correct bits.
+
+The two internal if-statements inside this loop are assigning some bits from one place in the source number and bitwise OR-ing them with some bits from a second place in the source number. The key insight here is that the bits for any one word of the result comes from at most two source words in the input. So the only remaining trick is to calculate which ones. For this, we need these two numbers:
+
+```swift
+let offset = numBitsRight / lhs.N
+let shift = numBitsRight % lhs.N
+```
+
+Offset gives us how many words away from the source word we start getting our bits (with the remainder coming from it's neighbour). Shift gives us how many bits we need to shift within that word. Note that both of these are calcuated using the word size `lhs.N`.
+
+All that's left if a little bit of protection against reading outside the bounds of the input. So these two if conditions protect against that:
+```swift
+if (i + offset < lhs.words.count) {
+```
+and
+```swift
+if (i + offset + 1 < lhs.words.count) {
+```
+
+Let's work through an example. Suppose our word length has been reduced to 8 bits, and we'd like to right-shift the following number by 10 bits:
+
+    01000010 11000000 00011100      >> 10
+
+I've grouped each part of the number by word to make it easier to see what happens. The for-loop goes from least significant word to most significant. So for index zero we're want to know what bits will make up our least significant word. Let's calculate our offset and shift values:
+
+    offset = 10 / 8 = 1     (remember this is integer division)
+    shift = 10 % 8 = 2
+
+So we consult the word at offset 1 to get some of our bits:
+
+    11000000 >> 2 = 00110000
+
+And we get the rest of them from the word one further away:
+
+    01000010 << (8 - 2) = 10000000
+    
+And we bitwise OR these together to get our least significant term
+
+    00110000
+    10000000
+    -------- OR
+    10110000
+
+We repeat this for the 2nd least significant term and obtain:
+
+    00010000
+
+The last term can't get any bits because they are past the end of our number so those are all zeros. Our result is:
+
+    00000000 00010000 10110000
+
 ## See also
 
 [Bit Twiddling Hacks](http://graphics.stanford.edu/~seander/bithacks.html)

From a10a15bab9934520d1762b5a71f357e6b112bc2a Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Sat, 16 Feb 2019 09:49:47 +0000
Subject: [PATCH 1595/1679] remove reference to old source file

---
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index a37dac494..12be3d827 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -549,9 +549,6 @@
       <FileRef
          location = "group:BitSet.playground">
       </FileRef>
-      <FileRef
-         location = "group:BitSet.swift">
-      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From aa2a318bfbf24223a26a609d8a23dba3accba935 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad@yelp.com>
Date: Sun, 24 Feb 2019 14:53:47 -0800
Subject: [PATCH 1596/1679] [Swift 4.2] Update All-Pairs Shortest Paths to
 Swift 4.2

---
 .../APSP/APSP.playground/Contents.swift       |  5 ----
 .../APSP.playground/contents.xcplayground     |  2 +-
 .../APSP/APSP.xcodeproj/project.pbxproj       | 26 ++++++++++++++-----
 .../xcshareddata/xcschemes/APSP.xcscheme      |  2 +-
 .../xcshareddata/xcschemes/APSPTests.xcscheme |  2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++++
 .../APSP/APSPTests/APSPTests.swift            |  8 ------
 .../xcshareddata/xcschemes/Graph.xcscheme     |  2 +-
 .../xcschemes/GraphTests.xcscheme             |  2 +-
 9 files changed, 33 insertions(+), 24 deletions(-)
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
index b1b499b39..24c27cac8 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Graph
 import APSP
 
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground b/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground
index 06828af92..d5a8d0e3f 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1010'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index 908d32785..dc8e509a1 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -187,12 +187,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1010;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					493D8DDF1CDD2A1C0089795A = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 					493D8DF01CDD5B960089795A = {
 						CreatedOnToolsVersion = 7.3;
@@ -302,14 +302,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -349,14 +357,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -388,7 +404,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -400,7 +416,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
@@ -420,7 +436,6 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
 				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
@@ -443,7 +458,6 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
 				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme
index e313c4b88..944957d8f 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme
index 5797cbf9c..481baffd8 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
index c2f64e239..ce0dfcf32 100644
--- a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -19,14 +19,6 @@ struct TestCase<T> where T: Hashable {
 }
 
 class APSPTests: XCTestCase {
-
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
   /**
    See Figure 25.1 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 690
    */
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index 73524effc..84c688e66 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1000"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index 873f1d7b4..7aa65b0e4 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1000"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From d89bf25bba0367bab880a3f18f2c78ec39fcd179 Mon Sep 17 00:00:00 2001
From: bbvch13531 <bbvch13531@gmail.com>
Date: Mon, 25 Feb 2019 22:08:56 +0900
Subject: [PATCH 1597/1679] Fix wrong description

Signed-off-by: bbvch13531 <bbvch13531@gmail.com>
---
 Linked List/LinkedList.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 7c2cbb3b1..de8a42c93 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -67,7 +67,7 @@ public final class LinkedList<T> {
     /// - Returns: LinkedListNode
     public func node(at index: Int) -> Node {
         assert(head != nil, "List is empty")
-        assert(index >= 0, "index must be greater than 0")
+        assert(index >= 0, "index must be greater or equal to 0")
         
         if index == 0 {
             return head!

From 8a6d99aa19f0888b51969bc10c0463aa98c1a94e Mon Sep 17 00:00:00 2001
From: bbvch13531 <bbvch13531@gmail.com>
Date: Mon, 25 Feb 2019 22:09:44 +0900
Subject: [PATCH 1598/1679] Fix typo

Signed-off-by: bbvch13531 <bbvch13531@gmail.com>
---
 Insertion Sort/InsertionSort.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 9faf9dc42..2ad607ac8 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -22,7 +22,7 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
 /// Performs the Insertion sort algorithm to a given array
 ///
-/// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
+/// - Parameter array: the array to be sorted, containing elements that conform to the Comparable protocol
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     guard array.count > 1 else { return array }

From de935b700ab32492791dbd9771a3fc841ad4044c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 5 Mar 2019 22:37:29 -0500
Subject: [PATCH 1599/1679] Updates README.markdown

* now using new `random` API from the Swift collection protocols, instead of creating a new function that uses `arc4random`
* updates code to Swift 4.2
* fixes some inconsistencies between terms begin used - such as `MAX_GENERATIONS` and `GENERATIONS`
---
 Genetic/README.markdown | 60 ++++++++++++++++-------------------------
 1 file changed, 23 insertions(+), 37 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 18afb9639..5dc4747f2 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -5,7 +5,7 @@
 A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), crossover and mutation. To understand more, let's walk through these processes in terms of biology:
 
 ### Selection
->**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors. [Britannica](britannica)
+>**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors.
 
 In other words, survival of the fittest. Organisms that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank individuals and give them a better chance for reproduction.
 
@@ -60,35 +60,23 @@ extension String {
 let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 let DNA_SIZE = OPTIMAL.count
 let POP_SIZE = 50
-let MAX_GENERATIONS = 5000
+let GENERATIONS = 5000
 let MUTATION_CHANCE = 100
  ```
 
- The last piece we need for set up is a function to give us a random unicode value from our lexicon:
-
- ```swift
- func randomChar(from lexicon: [UInt8]) -> UInt8 {
-     let len = UInt32(lexicon.count-1)
-     let rand = Int(arc4random_uniform(len))
-     return lexicon[rand]
- }
- ```
-
- **Note**: `arc4random_uniform` is strictly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
-
  ### Population Zero
 
 Before selecting, crossover and mutation, we need a population to start with. Now that we have the universe defined we can write that function:
 
  ```swift
  func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-
+    guard lexicon.count > 1 else { return [] }
     var pop = [[UInt8]]()
 
     (0..<populationSize).forEach { _ in
         var dna = [UInt8]()
         (0..<dnaSize).forEach { _ in
-            let char = randomChar(from: lexicon)
+            let char = lexicon.randomElement()! // guaranteed to be non-nil by initial guard statement
             dna.append(char)
         }
         pop.append(dna)
@@ -102,10 +90,11 @@ Before selecting, crossover and mutation, we need a population to start with. No
 There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using unicode values:
 
 ```swift
-func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+func calculateFitness(dna: [UInt8], optimal: [UInt8]) -> Int {
+    guard dna.count == optimal.count else { return -1 }
     var fitness = 0
-    (0...dna.count-1).forEach { c in
-        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    for index in dna.indices {
+        fitness += abs(Int(dna[index]) - Int(optimal[index]))
     }
     return fitness
 }
@@ -121,13 +110,11 @@ Let's take a second and ask why on this one. Why would you not always want to se
 
 With all that, here is our weight choice function:
 
-```swift
-func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
-
-    let total = items.reduce(0.0) { return $0 + $1.weight}
-
-    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
-
+func weightedChoice(items: [(dna: [UInt8], weight: Double)]) -> (dna: [UInt8], weight: Double) {
+    
+    let total = items.reduce(0) { $0 + $1.weight }
+    var n = Double.random(in: 0..<(total * 1000000)) / 1000000.0
+    
     for item in items {
         if n < item.weight {
             return item
@@ -136,25 +123,24 @@ func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weigh
     }
     return items[1]
 }
-```
 
-The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value. The horrible 1,000,000 multiplication and division is to insure precision by calculating decimals. `arc4random` only uses integers so this is required to convert to a precise Double, it's not perfect, but enough for our example.
+
+The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value. The horrible 1,000,000 multiplication and division is to insure precision by calculating decimals. `Double.random` only uses integers so this is required to convert to a precise Double, it's not perfect, but enough for our example.
 
 ## Mutation
 
 The all powerful mutation, the thing that introduces otherwise non existent fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achieve the optimal solution.
 
 ```swift
-func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
+func mutate(lexicon: [UInt8], dna: [UInt8], mutationChance: Int) -> [UInt8] {
     var outputDna = dna
-
     (0..<dna.count).forEach { i in
-        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        let rand = Int.random(in: 0..<mutationChance)
         if rand == 1 {
-            outputDna[i] = randomChar(from: lexicon)
+            outputDna[i] = lexicon.randomElement()!
         }
     }
-
+    
     return outputDna
 }
 ```
@@ -168,12 +154,12 @@ This allows for a population to explore all the possibilities of it's building b
 Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents.
 
 ```swift
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
-    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
-
+func crossover(dna1: [UInt8], dna2: [UInt8], dnaSize: Int) -> [UInt8] {
+    let pos = Int.random(in: 0..<dnaSize)
+    
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
-
+    
     return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 ```

From a1e2e9d03ba34c7e9f74cebea34258dce5bdac00 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 5 Mar 2019 22:38:53 -0500
Subject: [PATCH 1600/1679] Updates code to Swift 4.2

---
 Genetic/gen.playground/Contents.swift | 192 +++++++++++---------------
 1 file changed, 84 insertions(+), 108 deletions(-)

diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 79a398ceb..d76342f56 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -1,14 +1,12 @@
-//: Playground - noun: a place where people can play
 
-import Foundation
 
 extension String {
-    var unicodeArray: [UInt8] {
-        return [UInt8](self.utf8)
-    }
+  
+  var unicodeArray: [UInt8] {
+    return [UInt8](self.utf8)
+  }
 }
 
-
 let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".unicodeArray
 
 // This is the end goal and what we will be using to rate fitness. In the real world this will not exist
@@ -17,132 +15,110 @@ let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 // The length of the string in our population. Organisms need to be similar
 let DNA_SIZE = OPTIMAL.count
 
-// size of each generation
+// Size of each generation
 let POP_SIZE = 50
 
-// max number of generations, script will stop when it reach 5000 if the optimal value is not found
+// Max number of generations, script will stop when it reaches 5000 if the optimal value is not found
 let GENERATIONS = 5000
 
 // The chance in which a random nucleotide can mutate (1/n)
 let MUTATION_CHANCE = 100
 
-func randomChar(from lexicon: [UInt8]) -> UInt8 {
-    let len = UInt32(lexicon.count-1)
-    let rand = Int(arc4random_uniform(len))
-    return lexicon[rand]
-}
-
 func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-    
-    var pop = [[UInt8]]()
-    
-    (0..<populationSize).forEach { _ in
-        var dna = [UInt8]()
-        (0..<dnaSize).forEach { _ in
-            let char = randomChar(from: lexicon)
-            dna.append(char)
-        }
-        pop.append(dna)
+  var pop = [[UInt8]]()
+  
+  (0..<populationSize).forEach { _ in
+    var dna = [UInt8]()
+    (0..<dnaSize).forEach { _ in
+      let char = lexicon.randomElement()!
+      dna.append(char)
     }
-    return pop
+    pop.append(dna)
+  }
+  return pop
 }
 
-func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-    var fitness = 0
-    (0...dna.count-1).forEach { c in
-        fitness += abs(Int(dna[c]) - Int(optimal[c]))
-    }
-    return fitness
+func calculateFitness(dna: [UInt8], optimal: [UInt8]) -> Int {
+  var fitness = 0
+  for index in dna.indices {
+    fitness += abs(Int(dna[index]) - Int(optimal[index]))
+  }
+  return fitness
 }
 
-func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
-    
-    let total = items.reduce(0.0) { return $0 + $1.weight}
-    
-    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
-    
-    for item in items {
-        if n < item.weight {
-            return item
-        }
-        n = n - item.weight
+func weightedChoice(items: [(dna: [UInt8], weight: Double)]) -> (dna: [UInt8], weight: Double) {
+  
+  let total = items.reduce(0) { $0 + $1.weight }
+  var n = Double.random(in: 0..<(total * 1000000)) / 1000000.0
+  
+  for item in items {
+    if n < item.weight {
+      return item
     }
-    return items[1]
+    n = n - item.weight
+  }
+  return items[1]
 }
 
-func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
-    var outputDna = dna
-    
-    (0..<dna.count).forEach { i in
-        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
-        if rand == 1 {
-            outputDna[i] = randomChar(from: lexicon)
-        }
+func mutate(lexicon: [UInt8], dna: [UInt8], mutationChance: Int) -> [UInt8] {
+  var outputDna = dna
+  (0..<dna.count).forEach { i in
+    let rand = Int.random(in: 0..<mutationChance)
+    if rand == 1 {
+      outputDna[i] = lexicon.randomElement()!
     }
-    
-    return outputDna
+  }
+  
+  return outputDna
 }
 
-
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
-    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
-    
-    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
-    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
-    
-    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
+func crossover(dna1: [UInt8], dna2: [UInt8], dnaSize: Int) -> [UInt8] {
+  let pos = Int.random(in: 0..<dnaSize)
+  
+  let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+  let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+  
+  return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 
+var population: [[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+var fittest = population[0]
+import Foundation
+
 func main() {
+  for generation in 0...GENERATIONS {
+    var weightedPopulation = [(dna: [UInt8], weight: Double)]()
+    
+    for individual in population {
+      let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+      let pair = (individual, fitnessValue == 0 ? 1.0 : 1.0/Double(fitnessValue))
+      weightedPopulation.append(pair)
+    }
+    
+    population = []
+    
+    (0...POP_SIZE).forEach { _ in
+      let ind1 = weightedChoice(items: weightedPopulation)
+      let ind2 = weightedChoice(items: weightedPopulation)
+      
+      let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
+      population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
+    }
     
-    // generate the starting random population
-    var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
-    // print("population: \(population), dnaSize: \(DNA_SIZE) ")
-    var fittest = [UInt8]()
+    fittest = population[0]
+    var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
     
-    for generation in 0...GENERATIONS {
-        
-        var weightedPopulation = [(dna:[UInt8], weight:Double)]()
-        
-        // calulcated the fitness of each individual in the population
-        // and add it to the weight population (weighted = 1.0/fitness)
-        for individual in population {
-            let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
-            
-            let pair = ( individual, fitnessValue == 0 ? 1.0 : Double(100/POP_SIZE)/Double( fitnessValue ) )
-            
-            weightedPopulation.append(pair)
-        }
-        
-        population = []
-        
-        // create a new generation using the individuals in the origional population
-        (0...POP_SIZE).forEach { _ in
-            let ind1 = weightedChoice(items: weightedPopulation)
-            let ind2 = weightedChoice(items: weightedPopulation)
-            
-            let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
-            
-            // append to the population and mutate
-            population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
-        }
-        
-        fittest = population[0]
-        var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
-        
-        // parse the population for the fittest string
-        population.forEach { indv in
-            let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
-            if indvFitness < minFitness {
-                fittest = indv
-                minFitness = indvFitness
-            }
-        }
-        if minFitness == 0 { break; }
-        print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
-        
+    population.forEach { indv in
+      let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+      if indvFitness < minFitness {
+        fittest = indv
+        minFitness = indvFitness
+      }
     }
-    print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
+    
+    if minFitness == 0 { break }
+    print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+  }
+  print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
 }
-
 main()

From b41a01d824674cb6efc9859e4e3fbadf05e622cc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 5 Mar 2019 22:46:10 -0500
Subject: [PATCH 1601/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 88ea35949..064a4616c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -100,7 +100,7 @@ Bad sorting algorithms (don't use these!):
 - [Convex Hull](Convex%20Hull/).
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
-
+- [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 04b2d3010b3db16b1bfd472e9686364bbf785a94 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 8 Mar 2019 23:13:13 -0500
Subject: [PATCH 1602/1679] Updates for Swift 5.0

Removes unnecessary equatable implementations, since default implementations of `Equatable` has identical result.
---
 .../Points Lines Planes/2D/Line2D.swift       | 20 -------------------
 1 file changed, 20 deletions(-)

diff --git a/Points Lines Planes/Points Lines Planes/2D/Line2D.swift b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift
index c92cbdbed..c23040b14 100644
--- a/Points Lines Planes/Points Lines Planes/2D/Line2D.swift	
+++ b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift	
@@ -14,27 +14,11 @@ struct Line2D: Equatable {
     enum Slope: Equatable {
         case finite(slope: Double)
         case infinite(offset: Double)
-        
-        static func ==(lhs: Slope, rhs: Slope) -> Bool {
-            switch (lhs, rhs) {
-            case (.finite(let slope1), .finite(let slope2)): return slope1 == slope2
-            case (.infinite(let offset1), .infinite(let offset2)): return offset1 == offset2
-            default: return false
-            }
-        }
     }
     
     enum Direction: Equatable {
         case increasing
         case decreasing
-        
-        static func ==(lhs: Direction, rhs: Direction) -> Bool {
-            switch (lhs, rhs) {
-            case (.increasing, .increasing): return true
-            case (.decreasing, .decreasing): return true
-            default: return false
-            }
-        }
     }
     
     init(from p1: Point2D, to p2: Point2D) {
@@ -154,8 +138,4 @@ struct Line2D: Equatable {
             return Line2D(slope: .finite(slope: 0), offset: p.y, direction: dir)
         }
     }
-    
-    static func ==(lhs: Line2D, rhs: Line2D) -> Bool {
-        return lhs.slope == rhs.slope && lhs.offset == rhs.offset && lhs.direction == rhs.direction
-    }
 }

From 339cc1489b3b70e7464db4af7e8f398d45ce50db Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 8 Mar 2019 23:13:42 -0500
Subject: [PATCH 1603/1679] Updates to Swift 5.0

Removes `Equatable` impl.
---
 Points Lines Planes/Points Lines Planes/2D/Point2D.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Points Lines Planes/Points Lines Planes/2D/Point2D.swift b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift
index f51ffd64d..bbd8305f8 100644
--- a/Points Lines Planes/Points Lines Planes/2D/Point2D.swift	
+++ b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift	
@@ -9,10 +9,6 @@ struct Point2D: Equatable {
     var x: Double
     var y: Double
     
-    static func ==(lhs: Point2D, rhs: Point2D) -> Bool {
-        return lhs.x == rhs.x && lhs.y == rhs.y
-    }
-    
     // returns true if point is on or right of line
     func isRight(of line: Line2D) -> Bool {
         switch line.slope {

From 5e55f9261bc4095df3424fdd9f238513e0eae8e5 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 9 Mar 2019 19:39:32 -0500
Subject: [PATCH 1604/1679] Adds Myers Difference Algorithm to Readme

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 064a4616c..97917a320 100644
--- a/README.markdown
+++ b/README.markdown
@@ -101,6 +101,7 @@ Bad sorting algorithms (don't use these!):
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 - [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
+- [Myers Difference Algorithm](Myers\ Difference\ Algorithm/). Finding the longest common subsequence of two sequences.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 46c22ac590f580268a5c1fce288f6f8a720b37bb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 9 Mar 2019 19:40:06 -0500
Subject: [PATCH 1605/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 97917a320..c94716242 100644
--- a/README.markdown
+++ b/README.markdown
@@ -101,7 +101,7 @@ Bad sorting algorithms (don't use these!):
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 - [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
-- [Myers Difference Algorithm](Myers\ Difference\ Algorithm/). Finding the longest common subsequence of two sequences.
+- [Myers Difference Algorithm](Myers Difference Algorithm/). Finding the longest common subsequence of two sequences.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 3849a1d6113ddb7d8ac24be2a1e9fc4b7677efd6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 9 Mar 2019 19:41:21 -0500
Subject: [PATCH 1606/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index c94716242..d66eee5d8 100644
--- a/README.markdown
+++ b/README.markdown
@@ -101,7 +101,7 @@ Bad sorting algorithms (don't use these!):
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 - [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
-- [Myers Difference Algorithm](Myers Difference Algorithm/). Finding the longest common subsequence of two sequences.
+- [Myers Difference Algorithm](Myers%20Difference%20Algorithm/). Finding the longest common subsequence of two sequences.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 0d5e1b94e49311607fc0b30cc379304fe2123798 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 14 Mar 2019 22:44:36 -0400
Subject: [PATCH 1607/1679] Update README.markdown

Adds a reference to the GitHub page via #720
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index d66eee5d8..44879e8f8 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Code is compatible with **Xcode 10** and **Swift 4.2**. We'll keep this updated with the latest version of Swift.
+Code is compatible with **Xcode 10** and **Swift 4.2**. We'll keep this updated with the latest version of Swift. If you're interested in a GitHub pages version of the repo, check out [this](https://aquarchitect.github.io/swift-algorithm-club/).
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From 56e2fc9047a4523d62d3f1fe4eac679b20382509 Mon Sep 17 00:00:00 2001
From: bbvch13531 <bbvch13531@gmail.com>
Date: Fri, 15 Mar 2019 19:52:09 +0900
Subject: [PATCH 1608/1679] Change return type to brief type.

Fixes :#865

Signed-off-by: bbvch13531 <bbvch13531@gmail.com>
---
 .../Sources/BinarySearchTree.swift                            | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 34ade3896..2d0eb7e57 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -235,7 +235,7 @@ extension BinarySearchTree {
   /*
     Finds the node whose value precedes our value in sorted order.
   */
-  public func predecessor() -> BinarySearchTree<T>? {
+  public func predecessor() -> BinarySearchTree? {
     if let left = left {
       return left.maximum()
     } else {
@@ -251,7 +251,7 @@ extension BinarySearchTree {
   /*
     Finds the node whose value succeeds our value in sorted order.
   */
-  public func successor() -> BinarySearchTree<T>? {
+  public func successor() -> BinarySearchTree? {
     if let right = right {
       return right.minimum()
     } else {

From 7065c1a2d0aa0633188cdb27de69c11ab8d740d5 Mon Sep 17 00:00:00 2001
From: Dmitry Cherednikov <dmitry.cherednikov@tachos.ru>
Date: Sat, 16 Mar 2019 15:44:00 +0400
Subject: [PATCH 1609/1679] Implement getPredecessor().

---
 Red-Black Tree/README.markdown                |  1 +
 .../Sources/RedBlackTree.swift                | 27 ++++++++++++++++++-
 2 files changed, 27 insertions(+), 1 deletion(-)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index fd6c4db18..352588056 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -29,6 +29,7 @@ From [CLRS]
 ## Methods
 
 Nodes:
+* `nodeX.getPredecessor()` Returns the inorder predecessor of nodeX
 * `nodeX.getSuccessor()` Returns the inorder successor of nodeX
 * `nodeX.minimum()` Returns the node with the minimum key of the subtree of nodeX
 * `nodeX.maximum()` Returns the node with the maximum key of the subtree of nodeX
diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 59633031d..b88cd7cf5 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -60,6 +60,10 @@ public class RBTreeNode<T: Comparable>: Equatable {
     self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
     self.color = .black
   }
+
+  public func getKey() -> T? {
+    return key
+  }
   
   var isRoot: Bool {
     return parent == nil
@@ -120,9 +124,30 @@ extension RBTreeNode {
   }
 }
 
-// MARK: - Finding a nodes successor
+// MARK: - Finding a nodes successor and predecessor
 
 extension RBTreeNode {
+  /*
+  * Returns the inorder predecessor node of a node
+  * The predecessor is a node with the next smaller key value of the current node
+  */
+  public func getPredecessor() -> RBNode? {
+    // if node has left child: predecessor is min of this left tree
+    if let leftChild = leftChild, !leftChild.isNullLeaf {
+      return leftChild.maximum()
+    }
+    // else go upward while node is left child
+    var currentNode = self
+    var parent = currentNode.parent
+    while currentNode.isLeftChild {
+      if let parent = parent {
+        currentNode = parent
+      }
+      parent = currentNode.parent
+    }
+    return parent
+  }
+
   /*
    * Returns the inorder successor node of a node
    * The successor is a node with the next larger key value of the current node

From 6e8b5cdc37324a4120abee841d89cef36ab6352f Mon Sep 17 00:00:00 2001
From: TL <tommylohz@gmail.com>
Date: Wed, 20 Mar 2019 16:09:34 +0800
Subject: [PATCH 1610/1679] Update Shuffle
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

according to https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle

`checks if j ≠ i may be omitted`, and also remove checking logic will optimise performance(tested by 100000 times random).
---
 Shuffle/README.markdown | 3 ---
 Shuffle/Shuffle.swift   | 3 ---
 2 files changed, 6 deletions(-)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index 63868767b..d8ab7ff78 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -96,9 +96,6 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
     let j = Int.random(in: 0...i)
-    if i != j {
-      a[i] = a[j]
-    }
     a[j] = i
   }
   return a
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index 3e4292d56..a921e5ec3 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -30,9 +30,6 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
     let j = random(i + 1)
-    if i != j {
-      a[i] = a[j]
-    }
     a[j] = i  // insert next number from the sequence
   }
   return a

From 91b7bb1d1d16f4cbe64399de156b2045ebf6d5be Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 21 Mar 2019 10:17:06 -0400
Subject: [PATCH 1611/1679] Update SlowSort.swift

---
 Slow Sort/SlowSort.swift | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index bd8288b18..546a36395 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -7,14 +7,14 @@
 //
 
 func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-    guard if i < j else { return }
-    let m = (i+j)/2
-    slowSort(i, m, &numberList)
-    slowSort(m+1, j, &numberList)
-    if numberList[j] < numberList[m] {
-        let temp = numberList[j]
-        numberList[j] = numberList[m]
-        numberList[m] = temp
-    }
-    slowSort(i, j-1, &numberList)
+  guard if i < j else { return }
+  let m = (i+j)/2
+  slowSort(i, m, &numberList)
+  slowSort(m+1, j, &numberList)
+  if numberList[j] < numberList[m] {
+      let temp = numberList[j]
+      numberList[j] = numberList[m]
+      numberList[m] = temp
+  }
+  slowSort(i, j-1, &numberList)
 }

From 7457ceb7e9ec688ac11db158ac3d32118df49b0f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 21 Mar 2019 10:25:04 -0400
Subject: [PATCH 1612/1679] Two-spaced indents

---
 Comb Sort/Tests/CombSortTests.swift | 32 ++++++++++++-----------------
 1 file changed, 13 insertions(+), 19 deletions(-)

diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index 166065484..1d83af002 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -9,26 +9,20 @@
 import XCTest
 
 class CombSortTests: XCTestCase {
-    var sequence: [Int]!
-    let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
-
-    func testSwiftVersion(){
-        #if swift(>=4.2)
-            print("Hello, Swift 4.2!")
-        #endif
-    }
+  var sequence: [Int]!
+  let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
     
-    override func setUp() {
-        super.setUp()
-        sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
-    }
+  override func setUp() {
+    super.setUp()
+    sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
+  }
 
-    override func tearDown() {
-        super.tearDown()
-    }
+  override func tearDown() {
+    super.tearDown()
+  }
 
-    func testCombSort() {
-        let sortedSequence = combSort(sequence)
-        XCTAssertEqual(sortedSequence, expectedSequence)
-    }
+  func testCombSort() {
+    let sortedSequence = combSort(sequence)
+    XCTAssertEqual(sortedSequence, expectedSequence)
+  }
 }

From fdab1a2d7a9f9797ed7be27c5023f284c47f38ea Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 21 Mar 2019 10:25:24 -0400
Subject: [PATCH 1613/1679] two spaced indents

---
 Slow Sort/SlowSort.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 546a36395..968f6841b 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -12,9 +12,9 @@ func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
   slowSort(i, m, &numberList)
   slowSort(m+1, j, &numberList)
   if numberList[j] < numberList[m] {
-      let temp = numberList[j]
-      numberList[j] = numberList[m]
-      numberList[m] = temp
+    let temp = numberList[j]
+    numberList[j] = numberList[m]
+    numberList[m] = temp
   }
   slowSort(i, j-1, &numberList)
 }

From 7405c64e2cf7c035dce15207bba0fe7434010b55 Mon Sep 17 00:00:00 2001
From: Priyanka- <khiladis@Priyankas-MacBook-Pro.local>
Date: Sun, 24 Mar 2019 12:20:31 -0700
Subject: [PATCH 1614/1679] Kth Largest Element: updated to use Int.random API
 which has been introduced with Swift 4.2

---
 .../kthLargest.playground/Sources/kthLargest.swift        | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift
index 397c43a38..aad15eac6 100644
--- a/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift	
@@ -16,12 +16,6 @@ public func kthLargest(_ a: [Int], _ k: Int) -> Int? {
 
 // MARK: - Randomized selection
 
-/* Returns a random integer in the range min...max, inclusive. */
-public func random(min: Int, max: Int) -> Int {
-  assert(min < max)
-  return min + Int(arc4random_uniform(UInt32(max - min + 1)))
-}
-
 /*
   Returns the i-th smallest element from the array.
 
@@ -39,7 +33,7 @@ public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
   func randomPivot<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> T {
-    let pivotIndex = random(min: low, max: high)
+    let pivotIndex = Int.random(in: low...high)
     a.swapAt(pivotIndex, high)
     return a[high]
   }

From b6e9a40652d489605772f284ad2dac4a033fd216 Mon Sep 17 00:00:00 2001
From: TL <tommylohz@gmail.com>
Date: Tue, 26 Mar 2019 15:34:12 +0800
Subject: [PATCH 1615/1679] Update Shuffle

---
 Shuffle/README.markdown | 4 ++++
 Shuffle/Shuffle.swift   | 1 +
 2 files changed, 5 insertions(+)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index d8ab7ff78..5a2a07a98 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -96,6 +96,8 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
     let j = Int.random(in: 0...i)
+    // for the Fisher–Yates_shuffle's pseudo code implement in wiki, it will check if i != j
+    a[i] = a[j]
     a[j] = i
   }
   return a
@@ -112,6 +114,8 @@ This returns something like `[3, 0, 9, 1, 8, 5, 2, 6, 7, 4]`. As you can see, ev
 
 The `shuffledArray()` function first creates a new array with `n` zeros. Then it loops `n` times and in each step adds the next number from the sequence to a random position in the array. The trick is to make sure that none of these numbers gets overwritten with the next one, so it moves the previous number out of the way first!
 
+For this function, `The condition that checks if j ≠ i may be omitted in languages that have no problems accessing uninitialized array values, and for which assigning is cheaper than comparing.`, you can check it in wiki. And also remove checking logic will optimise performance.
+
 The algoritm is quite clever and I suggest you walk through an example yourself, either on paper or in the playground. (Hint: Again it splits the array into two regions.)
 
 ## See also
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index a921e5ec3..1d2758c11 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -30,6 +30,7 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
     let j = random(i + 1)
+    a[i] = a[j]
     a[j] = i  // insert next number from the sequence
   }
   return a

From 114becb9f856a765e58ebf890b2140a73899ce08 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 28 Apr 2019 13:19:59 -0400
Subject: [PATCH 1616/1679] Adds Closest Pair

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 44879e8f8..3e0174576 100644
--- a/README.markdown
+++ b/README.markdown
@@ -208,6 +208,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Dining Philosophers](DiningPhilosophers/)
 - [Egg Drop Problem](Egg%20Drop%20Problem/)
 - [Encoding and Decoding Binary Tree](Encode%20and%20Decode%20Tree/)
+- [Closest Pair](Closest%20Pair/)
 
 ## Learn more!
 

From 721af5d569661effa976e88fc65a14fd3961b826 Mon Sep 17 00:00:00 2001
From: Vladislav Badulin <vladislav@badulin.com>
Date: Mon, 29 Apr 2019 21:24:24 +0200
Subject: [PATCH 1617/1679] This fixes the unlikely event that the generated
 hashValue happens to be the equal to Int.min, in which case the abs value of
 it would be Int.max + 1 causing overflow.

---
 Hash Table/HashTable.playground/Sources/HashTable.swift | 2 +-
 Hash Table/README.markdown                              | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
index 476a51174..f2a1be040 100644
--- a/Hash Table/HashTable.playground/Sources/HashTable.swift	
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -131,7 +131,7 @@ public struct HashTable<Key: Hashable, Value> {
      Returns the given key's array index.
      */
     private func index(forKey key: Key) -> Int {
-        return abs(key.hashValue) % buckets.count
+        return abs(key.hashValue % buckets.count)
     }
 }
 
diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 9c4065a51..fb0bda788 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -141,7 +141,7 @@ The hash table does not do anything yet, so let's add the remaining functionalit
 
 ```swift
   private func index(forKey key: Key) -> Int {
-    return abs(key.hashValue) % buckets.count
+    return abs(key.hashValue % buckets.count)
   }
 ```
 

From 15db2b6d953d1130acb711a358a79f5237979d02 Mon Sep 17 00:00:00 2001
From: Vanderlei Alves <39912609+vzanshin@users.noreply.github.com>
Date: Fri, 3 May 2019 15:47:53 -0300
Subject: [PATCH 1618/1679] Fix typo and grammar

---
 .github/CONTRIBUTING.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index e5d00c17b..29f4ca7e1 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -6,7 +6,7 @@ Want to help out with the Swift Algorithm Club? Great! While we don't have stric
 
 Our repo is all about learning. The `README` file is the cake, and the sample code is the cherry on top. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
 
-> When choosing between brievity and performance, err to the side of brievity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things. 
+> When choosing between brevity and performance, err to the side of brevity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things. 
 
 **API Design Guidelines**
 
@@ -22,7 +22,7 @@ We follow the following Swift [style guide](https://github.com/raywenderlich/swi
 
 Unit tests. Fixes for typos. No contribution is too small. :-)
 
-The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library is most welcomed. 
+The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library are most welcome.
 
 ### New Contributions
 

From 3f1d661b2d95eb0349d824277447c63c0aa3ecf1 Mon Sep 17 00:00:00 2001
From: Vanderlei Alves <39912609+vzanshin@users.noreply.github.com>
Date: Wed, 8 May 2019 16:39:15 -0300
Subject: [PATCH 1619/1679] Fix minor typo at Heap/README

---
 Heap/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 76d2bee39..6c65fe9c8 100755
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -29,7 +29,7 @@ As a result of this heap property, a max-heap always stores its largest item at
 
 ## How does a heap compare to regular trees?
 
-A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
+A heap is not a replacement for a binary search tree, and there are similarities and differences between them. Here are some main differences:
 
 
 **Order of the nodes.** In a [binary search tree (BST)](../Binary%20Search%20Tree/), the left child must be smaller than its parent, and the right child must be greater. This is not true for a heap. In a max-heap both children must be smaller than the parent, while in a min-heap they both must be greater.

From 78a7ceeff6c59a740428c6fae41a79f660c5a58c Mon Sep 17 00:00:00 2001
From: Kenny Schlagel <schlagelk@aetna.com>
Date: Sun, 7 Jul 2019 19:52:11 -0600
Subject: [PATCH 1620/1679] Improvements to Count Occurrences

---
 .../Contents.swift                            | 20 +++++++--------
 Count Occurrences/CountOccurrences.swift      | 25 ++++++++++---------
 Count Occurrences/README.markdown             | 12 ++++-----
 3 files changed, 29 insertions(+), 28 deletions(-)

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index a34e3485f..6ab4c00f3 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,11 +1,11 @@
 
-func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
-  func leftBoundary() -> Int {
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+  var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] < key {
+      if array[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -14,12 +14,12 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  func rightBoundary() -> Int {
+  var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] > key {
+      if array[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -28,13 +28,13 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  return rightBoundary() - leftBoundary()
+  return rightBoundary - leftBoundary
 }
 
 // Simple test
 
 let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
-countOccurrencesOfKey(3, inArray: a)
+countOccurrences(of: 3, in: a)
 
 // Test with arrays of random size and contents (see debug output)
 
@@ -59,6 +59,6 @@ for _ in 0..<10 {
 
   // Note: we also test -1 and 6 to check the edge cases.
   for k in -1...6 {
-    print("\t\(k): \(countOccurrencesOfKey(k, inArray: a))")
+    print("\t\(k): \(countOccurrences(of: k, in: a))")
   }
 }
diff --git a/Count Occurrences/CountOccurrences.swift b/Count Occurrences/CountOccurrences.swift
index 10dd12c4f..532e3810e 100644
--- a/Count Occurrences/CountOccurrences.swift	
+++ b/Count Occurrences/CountOccurrences.swift	
@@ -1,14 +1,15 @@
-/*
-  Counts the number of times a value appears in an array in O(lg n) time.
-  The array must be sorted from low to high.
-*/
-func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
-  func leftBoundary() -> Int {
+/// Counts the number of times a value appears in an array in O(log n) time.  The array must be sorted from low to high.
+///
+/// - Parameter key: the key to be searched for in the array
+/// - Parameter array: the array to search
+/// - Returns: the count of occurences of the key in the given array
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+  var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] < key {
+      if array[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -17,12 +18,12 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  func rightBoundary() -> Int {
+  var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] > key {
+      if array[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -31,5 +32,5 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  return rightBoundary() - leftBoundary()
+  return rightBoundary - leftBoundary
 }
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 85b77d2d0..297bc4b0f 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,8 +22,8 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
-  func leftBoundary() -> Int {
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+  var leftBoundary: Int {
     var low = 0
     var high = a.count
     while low < high {
@@ -37,7 +37,7 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  func rightBoundary() -> Int {
+  var rightBoundary: Int {
     var low = 0
     var high = a.count
     while low < high {
@@ -51,11 +51,11 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  return rightBoundary() - leftBoundary()
+  return rightBoundary - leftBoundary
 }
 ```
 
-Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.
+Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an array of Strings, Ints or other types that conform to the Swift Comparable protocol.
 
 To test this algorithm, copy the code to a playground and then do:
 
@@ -113,7 +113,7 @@ The right boundary is at index 7. The difference between the two boundaries is 7
 
 Each binary search took 4 steps, so in total this algorithm took 8 steps. Not a big gain on an array of only 12 items, but the bigger the array, the more efficient this algorithm becomes. For a sorted array with 1,000,000 items, it only takes 2 x 20 = 40 steps to count the number of occurrences for any particular value.
 
-By the way, if the value you're looking for is not in the array, then `rightBoundary()` and `leftBoundary()` return the same value and so the difference between them is 0.
+By the way, if the value you're looking for is not in the array, then `rightBoundary` and `leftBoundary` return the same value and so the difference between them is 0.
 
 This is an example of how you can modify the basic binary search to solve other algorithmic problems as well. Of course, it does require that the array is sorted.
 

From 6e64f07b43971ba04b85887bf3bf2d616243c21a Mon Sep 17 00:00:00 2001
From: ygit <ygit@users.noreply.github.com>
Date: Wed, 10 Jul 2019 02:38:29 +0530
Subject: [PATCH 1621/1679] added Big O computation comparison graph

---
 Big-O Notation.markdown | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 257f80462..9509331a5 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -18,6 +18,11 @@ Big-O | Name | Description
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
 
 
+
+![Comparison of Big O computations](https://upload.wikimedia.org/wikipedia/commons/7/7e/Comparison_computational_complexity.svg)
+
+
+
 Below are some examples for each category of performance:
 
 **O(1)**

From 762de527ad71e07f36ca9fd417819d733d298bdd Mon Sep 17 00:00:00 2001
From: markgz <markgzpccw@gmail.com>
Date: Thu, 8 Aug 2019 17:09:28 +0800
Subject: [PATCH 1622/1679] The code of O(2^n) isn't correct which is O(n)

Need solve two smaller problems in one recursive call
---
 Big-O Notation.markdown | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 9509331a5..c3f020df2 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -124,9 +124,8 @@ Below are some examples for each category of performance:
   func solveHanoi(n: Int, from: String, to: String, spare: String) {
     guard n >= 1 else { return }
     if n > 1 {
-      solveHanoi(n: n - 1, from: from, to: spare, spare: to)
-    } else {
-      solveHanoi(n: n - 1, from: spare, to: to, spare: from)
+        solveHanoi(n: n - 1, from: from, to: spare, spare: to)
+        solveHanoi(n: n - 1, from: spare, to: to, spare: from)
     }
   }
   ```

From eb9424d3f69d18a311c474907c2775f2a07d2852 Mon Sep 17 00:00:00 2001
From: abuzeid ibrahim <abuzeid7@gmail.com>
Date: Thu, 15 Aug 2019 14:21:38 +0200
Subject: [PATCH 1623/1679] rename variables with convenience names

---
 Insertion Sort/InsertionSort.swift | 42 +++++++++++++++---------------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 2ad607ac8..926dad302 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -2,22 +2,22 @@
 ///
 /// - Parameters:
 ///   - array: the array of elements to be sorted
+///   - sortedArray: copy the array to save stability
 ///   - isOrderedBefore: returns true if the elements provided are in the corect order
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  guard array.count > 1 else { return array }
-
-  var a = array
-  for x in 1..<a.count {
-    var y = x
-    let temp = a[y]
-    while y > 0 && isOrderedBefore(temp, a[y - 1]) {
-      a[y] = a[y - 1]
-      y -= 1
+    guard array.count > 1 else { return array }
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0, isOrderedBefore(temp, sortedArray[currentIndex - 1]) {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
+        }
+        sortedArray[currentIndex] = temp
     }
-    a[y] = temp
-  }
-  return a
+    return sortedArray
 }
 
 /// Performs the Insertion sort algorithm to a given array
@@ -27,15 +27,15 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     guard array.count > 1 else { return array }
 
-    var a = array
-    for x in 1..<a.count {
-        var y = x
-        let temp = a[y]
-        while y > 0 && temp < a[y - 1] {
-            a[y] = a[y - 1]
-            y -= 1
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0, temp < sortedArray[currentIndex - 1] {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
         }
-        a[y] = temp
+        sortedArray[currentIndex] = temp
     }
-    return a
+    return sortedArray
 }

From 92e797ac998b3f7a00cb1c2247c01d927cfa5414 Mon Sep 17 00:00:00 2001
From: abuzeid ibrahim <abuzeid7@gmail.com>
Date: Thu, 15 Aug 2019 14:31:22 +0200
Subject: [PATCH 1624/1679] rename variables in the playground

---
 .../InsertionSort.playground/Contents.swift   | 36 +++++++++----------
 .../contents.xcplayground                     |  2 +-
 2 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 184fc36e4..e1d3a312e 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -9,17 +9,17 @@
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
     guard array.count > 1 else { return array }
     
-    var a = array
-    for x in 1..<a.count {
-        var y = x
-        let temp = a[y]
-        while y > 0 && isOrderedBefore(temp, a[y - 1]) {
-            a[y] = a[y - 1]
-            y -= 1
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0 && isOrderedBefore(temp, sortedArray[currentIndex - 1]) {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
         }
-        a[y] = temp
+        sortedArray[currentIndex] = temp
     }
-    return a
+    return sortedArray
 }
 
 /// Performs the Insertion sort algorithm to a given array
@@ -27,17 +27,17 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 /// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
-    var a = array
-    for x in 1..<a.count {
-        var y = x
-        let temp = a[y]
-        while y > 0 && temp < a[y - 1] {
-            a[y] = a[y - 1]
-            y -= 1
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0 && temp < sortedArray[currentIndex - 1] {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
         }
-        a[y] = temp
+        sortedArray[currentIndex] = temp
     }
-    return a
+    return sortedArray
 }
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
diff --git a/Insertion Sort/InsertionSort.playground/contents.xcplayground b/Insertion Sort/InsertionSort.playground/contents.xcplayground
index 9f9eecc96..06828af92 100644
--- a/Insertion Sort/InsertionSort.playground/contents.xcplayground	
+++ b/Insertion Sort/InsertionSort.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
+<playground version='5.0' target-platform='osx'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 6dc91c4a7bee34ff2b4fe9f4f2d5d77d3d42e55c Mon Sep 17 00:00:00 2001
From: Abuzeid-Ibrahim <abuzeid7@gmail.com>
Date: Thu, 15 Aug 2019 14:35:33 +0200
Subject: [PATCH 1625/1679] Update README.markdown

---
 Insertion Sort/README.markdown | 32 ++++++++++++++++----------------
 1 file changed, 16 insertions(+), 16 deletions(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 4bad29aa1..8c2a5c1a0 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -91,15 +91,15 @@ Here is an implementation of insertion sort in Swift:
 
 ```swift
 func insertionSort(_ array: [Int]) -> [Int] {
-    var a = array			 // 1
-    for x in 1..<a.count {		 // 2
-        var y = x
-        while y > 0 && a[y] < a[y - 1] { // 3
-            a.swapAt(y - 1, y)
-            y -= 1
+    var sortedArray = array			 // 1
+    for index in 1..<sortedArray.count {		 // 2
+        var currentIndex = index
+        while currentIndex > 0 && sortedArray[currentIndex] < sortedArray[currentIndex - 1] { // 3
+            sortedArray.swapAt(currentIndex - 1, currentIndex)
+            currentIndex -= 1
         }
     }
-    return a
+    return sortedArray
 }
 
 
@@ -154,17 +154,17 @@ In code that looks like this:
 
 ```swift
 func insertionSort(_ array: [Int]) -> [Int] {
-  var a = array
-  for x in 1..<a.count {
-    var y = x
-    let temp = a[y]
-    while y > 0 && temp < a[y - 1] {
-      a[y] = a[y - 1]                // 1
-      y -= 1
+  var sortedArray = array
+  for index in 1..<sortedArray.count {
+    var currentIndex = index
+    let temp = sortedArray[currentIndex]
+    while currentIndex > 0 && temp < sortedArray[currentIndex - 1] {
+      sortedArray[currentIndex] = sortedArray[currentIndex - 1]                // 1
+      currentIndex -= 1
     }
-    a[y] = temp                      // 2
+    sortedArray[currentIndex] = temp                      // 2
   }
-  return a
+  return sortedArray
 }
 ```
 

From dfea1d68dd6151f88221c6be34a0a78002c50537 Mon Sep 17 00:00:00 2001
From: Pavel <Peeoner174@gmail.com>
Date: Sat, 31 Aug 2019 11:12:51 +0500
Subject: [PATCH 1626/1679] Update Queue-Optimized.swift

---
 Queue/Queue-Optimized.swift | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index 7dff91698..aedf9c67f 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -23,7 +23,7 @@ public struct Queue<T> {
   }
 
   public mutating func dequeue() -> T? {
-    guard head < array.count, let element = array[head] else { return nil }
+    guard let element = array[guarded: head] else { return nil }
 
     array[head] = nil
     head += 1
@@ -45,3 +45,14 @@ public struct Queue<T> {
     }
   }
 }
+
+extension Array {
+    
+    subscript(guarded idx: Int) -> Element? {
+        guard (startIndex..<endIndex).contains(idx) else {
+            return nil
+        }
+        return self[idx]
+    }
+    
+}

From 70fdd27222f6ed42f958b78d906b4a0b0d4fb66f Mon Sep 17 00:00:00 2001
From: abuzeid ibrahim <abuzeid7@gmail.com>
Date: Tue, 3 Sep 2019 16:14:28 +0200
Subject: [PATCH 1627/1679] move documentation to func body

---
 Insertion Sort/InsertionSort.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 926dad302..e24ede905 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -2,11 +2,11 @@
 ///
 /// - Parameters:
 ///   - array: the array of elements to be sorted
-///   - sortedArray: copy the array to save stability
 ///   - isOrderedBefore: returns true if the elements provided are in the corect order
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
     guard array.count > 1 else { return array }
+    ///   - sortedArray: copy the array to save stability
     var sortedArray = array
     for index in 1..<sortedArray.count {
         var currentIndex = index

From 0299a1cb92c516ade55a0095467376a79d116f86 Mon Sep 17 00:00:00 2001
From: PavelKochenda
 <kpa@napoleonit.rukpa@napoleonit.rukpa@napoleonit.rukpa@napoleonit.rukpa@napoleonit.ru>
Date: Fri, 6 Sep 2019 11:39:57 +0500
Subject: [PATCH 1628/1679] Added changed by opened discussions

---
 Queue/Queue-Optimized.swift | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index aedf9c67f..3b17b98cb 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -47,12 +47,10 @@ public struct Queue<T> {
 }
 
 extension Array {
-    
     subscript(guarded idx: Int) -> Element? {
         guard (startIndex..<endIndex).contains(idx) else {
             return nil
         }
         return self[idx]
     }
-    
 }

From adc0360746e75aa6922c9a7bc1e65139d9c36204 Mon Sep 17 00:00:00 2001
From: Perris Davis <WikipediaBrown@users.noreply.github.com>
Date: Fri, 6 Sep 2019 13:18:40 -0700
Subject: [PATCH 1629/1679] Updated broken link

Updated link to Boyer-Moore-Horspool algorithm.
---
 Knuth-Morris-Pratt/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Knuth-Morris-Pratt/README.markdown b/Knuth-Morris-Pratt/README.markdown
index 95fdea9e9..2e4d5360b 100644
--- a/Knuth-Morris-Pratt/README.markdown
+++ b/Knuth-Morris-Pratt/README.markdown
@@ -14,7 +14,7 @@ let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
 concert.indexesOf(ptnr: "🎻🎷")   // Output: [6]
 ```
 
-The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm) is considered one of the best algorithms for solving the pattern matching problem. Although in practice [Boyer-Moore](../Boyer-Moore/) is usually preferred, the algorithm that we will introduce is simpler, and has the same (linear) running time.
+The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm) is considered one of the best algorithms for solving the pattern matching problem. Although in practice [Boyer-Moore](../Boyer-Moore-Horspool/) is usually preferred, the algorithm that we will introduce is simpler, and has the same (linear) running time.
 
 The idea behind the algorithm is not too different from the [naive string search](../Brute-Force%20String%20Search/) procedure. As it, Knuth-Morris-Pratt aligns the text with the pattern and goes with character comparisons from left to right. But, instead of making a shift of one character when a mismatch occurs, it uses a more intelligent way to move the pattern along the text. In fact, the algorithm features a pattern pre-processing stage where it acquires all the informations that will make the algorithm skip redundant comparisons, resulting in larger shifts.
 

From da2085fc5bd7b08aec0b061301218e90fdf3d35e Mon Sep 17 00:00:00 2001
From: Joe Soultanis <jsoultanis@uber.com>
Date: Tue, 29 Oct 2019 16:55:50 -0700
Subject: [PATCH 1630/1679] updaing incorrect big-O performance documentation
 of heap removal

---
 Heap/Heap.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index cf39fb8a5..7560bc7b9 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -212,7 +212,7 @@ extension Heap where T: Equatable {
     return nodes.index(where: { $0 == node })
   }
   
-  /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
+  /** Removes the first occurrence of a node from the heap. Performance: O(n). */
   @discardableResult public mutating func remove(node: T) -> T? {
     if let index = index(of: node) {
       return remove(at: index)

From 519a57ae2946033608bda0fe24d428e189212df4 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 29 Oct 2019 22:35:24 -0400
Subject: [PATCH 1631/1679] Removes the workspace.

---
 .../contents.xcworkspacedata                  | 2914 -----------------
 .../xcshareddata/IDEWorkspaceChecks.plist     |    8 -
 .../xcshareddata/WorkspaceSettings.xcsettings |    8 -
 3 files changed, 2930 deletions(-)
 delete mode 100644 swift-algorithm-club.xcworkspace/contents.xcworkspacedata
 delete mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 03d06d2f7..000000000
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ /dev/null
@@ -1,2914 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <Group
-      location = "container:"
-      name = "Sorted Set">
-      <FileRef
-         location = "group:Sorted Set/README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:Sorted Set/SortedSet.playground">
-      </FileRef>
-      <FileRef
-         location = "group:Sorted Set/SortedSet.swift">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Egg Drop Problem"
-      name = "Egg Drop Problem">
-      <FileRef
-         location = "group:/Users/arkalyk/Desktop/SwiftAlgorithmClub/swift-algorithm-club/Egg Drop Problem/EggDrop.swift">
-      </FileRef>
-      <FileRef
-         location = "group:EggDrop.playground">
-      </FileRef>
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-   </Group>
-   <FileRef
-      location = "group:README.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:LICENSE.txt">
-   </FileRef>
-   <FileRef
-      location = "group:Algorithm Design.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:Big-O Notation.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:.github/CONTRIBUTING.md">
-   </FileRef>
-   <FileRef
-      location = "group:Under Construction.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:What are Algorithms.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:Why Algorithms.markdown">
-   </FileRef>
-   <Group
-      location = "group:Myers Difference Algorithm"
-      name = "Myers Difference Algorithm">
-      <Group
-         location = "container:"
-         name = "Images">
-         <FileRef
-            location = "group:Myers Difference Algorithm/Images/EditGraph_k_move.png">
-         </FileRef>
-         <FileRef
-            location = "group:Myers Difference Algorithm/Images/EditGraph.png">
-         </FileRef>
-      </Group>
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-         location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
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-         location = "group:MyersDifferenceAlgorithm.playground">
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-            location = "group:TopologicalSortTests.swift">
-         </FileRef>
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-      <FileRef
-         location = "group:Topological Sort.playground">
-      </FileRef>
-      <FileRef
-         location = "group:TopologicalSort1.swift">
-      </FileRef>
-      <FileRef
-         location = "group:TopologicalSort2.swift">
-      </FileRef>
-      <FileRef
-         location = "group:TopologicalSort3.swift">
-      </FileRef>
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-      location = "group:Treap"
-      name = "Treap">
-      <Group
-         location = "group:Treap"
-         name = "Treap">
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-            name = "Treap">
-            <FileRef
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-            </FileRef>
-            <FileRef
-               location = "group:TreapTests.swift">
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-         location = "group:Treap.swift">
-      </FileRef>
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-      </FileRef>
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-      name = "Tree">
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-         name = "Images">
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-            location = "group:Cycles.png">
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-      </FileRef>
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-         location = "group:Tree.playground">
-      </FileRef>
-      <FileRef
-         location = "group:Tree.swift">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Trie"
-      name = "Trie">
-      <Group
-         location = "group:images"
-         name = "images">
-         <FileRef
-            location = "group:trie.png">
-         </FileRef>
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-         name = "Trie">
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-            name = "Trie">
-            <FileRef
-               location = "group:AppDelegate.swift">
-            </FileRef>
-            <Group
-               location = "group:Assets.xcassets"
-               name = "Assets.xcassets">
-               <Group
-                  location = "group:AppIcon.appiconset"
-                  name = "AppIcon.appiconset">
-                  <FileRef
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-                  </FileRef>
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-               name = "Base.lproj">
-               <FileRef
-                  location = "group:Main.storyboard">
-               </FileRef>
-            </Group>
-            <FileRef
-               location = "group:dictionary.txt">
-            </FileRef>
-            <FileRef
-               location = "group:Info.plist">
-            </FileRef>
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-            </FileRef>
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-            name = "TrieTests">
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-            <FileRef
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-               location = "group:Info.plist">
-            </FileRef>
-            <FileRef
-               location = "group:TrieUITests.swift">
-            </FileRef>
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-   </Group>
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-      location = "group:Two-Sum Problem"
-      name = "Two-Sum Problem">
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-      </FileRef>
-      <Group
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-         name = "Solution 1">
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-         name = "Solution 2">
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-            location = "group:2Sum.playground">
-         </FileRef>
-      </Group>
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-   <Group
-      location = "group:Union-Find"
-      name = "Union-Find">
-      <Group
-         location = "group:Images"
-         name = "Images">
-         <FileRef
-            location = "group:AfterFind.png">
-         </FileRef>
-         <FileRef
-            location = "group:AfterUnion.png">
-         </FileRef>
-         <FileRef
-            location = "group:BeforeFind.png">
-         </FileRef>
-         <FileRef
-            location = "group:BeforeUnion.png">
-         </FileRef>
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-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:UnionFind.playground">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Z-Algorithm"
-      name = "Z-Algorithm">
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:ZAlgorithm.swift">
-      </FileRef>
-      <FileRef
-         location = "group:ZetaAlgorithm.playground">
-      </FileRef>
-      <FileRef
-         location = "group:ZetaAlgorithm.swift">
-      </FileRef>
-   </Group>
-</Workspace>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
deleted file mode 100644
index 08de0be8d..000000000
--- a/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
-	<false/>
-</dict>
-</plist>

From ed5fca001429674c1f13557a166a19b73e7ba5e0 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.lau@instacart.com>
Date: Wed, 30 Oct 2019 14:43:34 -0400
Subject: [PATCH 1632/1679] Removes travis.yml

---
 .travis.yml | 55 -----------------------------------------------------
 1 file changed, 55 deletions(-)
 delete mode 100644 .travis.yml

diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index 56e205656..000000000
--- a/.travis.yml
+++ /dev/null
@@ -1,55 +0,0 @@
-language: objective-c
-osx_image: xcode9
-# sudo: false
-
-install:
-
-- gem install xcpretty-travis-formatter
-# - ./install_swiftlint.sh
-
-script:
-
-- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0' | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Test-Quicksort | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Karatsuba\ Multiplication/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-
-after_success:
-
-- if [[ "$TRAVIS_BRANCH" == "master" ]]; then ./gfm-render.sh; fi

From 7b08311b01bb7f4f2a261286e93e9cf7abe6da1b Mon Sep 17 00:00:00 2001
From: Robert Manson <robmanson@gmail.com>
Date: Sun, 3 Nov 2019 17:36:22 -0800
Subject: [PATCH 1633/1679] Fix infinite recursion in DFS

Fixes infinite recursion in the DFS algorithm for topological sort caused by graphs with cycles.
For example the following graph would previously have recursed indefinitely `a->b->a`.
---
 Topological Sort/TopologicalSort1.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 2ad9b51a0..05f1ab887 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -1,6 +1,7 @@
 extension Graph {
   private func depthFirstSearch(_ source: Node, visited: inout [Node : Bool]) -> [Node] {
     var result = [Node]()
+    visited[source] = true
 
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
@@ -10,7 +11,6 @@ extension Graph {
       }
     }
 
-    visited[source] = true
     return [source] + result
   }
 

From 0904c23f746bbbbfc5525ce32cf5c181c1eafe8e Mon Sep 17 00:00:00 2001
From: freak4pc <freak4pc@gmail.com>
Date: Sat, 9 Nov 2019 18:58:19 +0200
Subject: [PATCH 1634/1679] Use swapAt for Lomuto's partitioning

---
 Quicksort/Quicksort.playground/Contents.swift | 4 ++--
 Quicksort/README.markdown                     | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 94d9f8e45..bbe5d9b7d 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -42,12 +42,12 @@ func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
-      (a[i], a[j]) = (a[j], a[i])
+      a.swapAt(i, j)
       i += 1
     }
   }
 
-  (a[i], a[high]) = (a[high], a[i])
+  a.swapAt(i, high)
   return i
 }
 
diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index f4145af5b..120ddc346 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -137,12 +137,12 @@ func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
-      (a[i], a[j]) = (a[j], a[i])
+	  a.swapAt(i, j)
       i += 1
     }
   }
 
-  (a[i], a[high]) = (a[high], a[i])
+  a.swapAt(i, high)
   return i
 }
 ```

From ce280b64b2315cef04b5c0b0924d4ca9d9a6599e Mon Sep 17 00:00:00 2001
From: Fabian Terh <fabianterh@gmail.com>
Date: Wed, 27 Nov 2019 17:22:04 +0800
Subject: [PATCH 1635/1679] Update Heap.swift

Time complexity of remove() is O(n + log n), which simplifies to O(n).
---
 Heap/Heap.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index cf39fb8a5..7560bc7b9 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -212,7 +212,7 @@ extension Heap where T: Equatable {
     return nodes.index(where: { $0 == node })
   }
   
-  /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
+  /** Removes the first occurrence of a node from the heap. Performance: O(n). */
   @discardableResult public mutating func remove(node: T) -> T? {
     if let index = index(of: node) {
       return remove(at: index)

From 7762f6a884daa51e4acdb5677c664bec38273f5c Mon Sep 17 00:00:00 2001
From: TL <tommylohz@gmail.com>
Date: Fri, 29 Nov 2019 18:52:19 +0800
Subject: [PATCH 1636/1679] fix: add use case

---
 Skip-List/SkipList.playground/Contents.swift        | 13 +++++++++++++
 .../SkipList.playground/Sources/SkipList.swift      |  2 +-
 Skip-List/SkipList.swift                            |  2 +-
 3 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/Skip-List/SkipList.playground/Contents.swift b/Skip-List/SkipList.playground/Contents.swift
index 1b4847c0e..55b9d3a23 100644
--- a/Skip-List/SkipList.playground/Contents.swift
+++ b/Skip-List/SkipList.playground/Contents.swift
@@ -5,3 +5,16 @@ print("Hello, Swift 4!")
 
 // SkipList is ready for Swift 4.
 // TODO: Add Test
+
+let k = SkipList<Int, String>()
+k.insert(key: 10, data: "10")
+k.insert(key: 12, data: "12")
+k.insert(key: 13, data: "13")
+k.insert(key: 20, data: "20")
+k.insert(key: 24, data: "24")
+
+if let value = k.get(key: 20) {
+  print(value)
+} else {
+  print("not found!")
+}
diff --git a/Skip-List/SkipList.playground/Sources/SkipList.swift b/Skip-List/SkipList.playground/Sources/SkipList.swift
index f626da0f8..186286977 100644
--- a/Skip-List/SkipList.playground/Sources/SkipList.swift
+++ b/Skip-List/SkipList.playground/Sources/SkipList.swift
@@ -212,7 +212,7 @@ extension SkipList {
     }
   }
 
-  func insert(key: Key, data: Payload) {
+  public func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
         // replace, in case of key already exists.
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index fc635d0f2..8a1959f70 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -212,7 +212,7 @@ extension SkipList {
     }
   }
 
-  func insert(key: Key, data: Payload) {
+  public func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
         // replace, in case of key already exists.

From b513c0331b79a520cd30569913a624eaae8fa7bb Mon Sep 17 00:00:00 2001
From: Kyle Nicol <54515183+TRGoCPftF@users.noreply.github.com>
Date: Tue, 10 Dec 2019 12:30:45 -0500
Subject: [PATCH 1637/1679] Update simann_example.swift

Corrected definition where shuffle() was invoking self.shuffle() instead of self.tour.shuffle(), which would left the example in a infinite loop of shuffle() invocation
---
 Simulated annealing/simann_example.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Simulated annealing/simann_example.swift b/Simulated annealing/simann_example.swift
index 0e07e0024..e7933c89a 100644
--- a/Simulated annealing/simann_example.swift	
+++ b/Simulated annealing/simann_example.swift	
@@ -138,7 +138,7 @@ extension Tour {
   }
 
   func shuffle() {
-    self.shuffle()
+    self.tour.shuffle()
   }
 }
 

From 809cb974dc0b105407500f42e675c55f55e1588b Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Wed, 22 Jan 2020 17:51:05 +0100
Subject: [PATCH 1638/1679] Typos corrected

---
 Count Occurrences/README.markdown | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 297bc4b0f..95f020e90 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -25,10 +25,10 @@ In code this looks as follows:
 func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
   var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] < key {
+      if array[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -39,10 +39,10 @@ func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
 
   var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] > key {
+      if array[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -62,7 +62,7 @@ To test this algorithm, copy the code to a playground and then do:
 ```swift
 let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 
-countOccurrencesOfKey(3, inArray: a)  // returns 4
+countOccurrences(of: 3, in: a)  // returns 4
 ```
 
 > **Remember:** If you use your own array, make sure it is sorted first!

From 8a7db67f4f0e1706a3a91054f1b7aecc6ac95761 Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Wed, 22 Jan 2020 19:57:53 +0100
Subject: [PATCH 1639/1679] Update README.markdown

---
 Count Occurrences/README.markdown | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 95f020e90..2e48d1020 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,13 +22,13 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
   var leftBoundary: Int {
     var low = 0
-    var high = array.count
+    var high = a.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if array[midIndex] < key {
+      if a[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -39,10 +39,10 @@ func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
 
   var rightBoundary: Int {
     var low = 0
-    var high = array.count
+    var high = a.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if array[midIndex] > key {
+      if a[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -55,7 +55,9 @@ func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
 }
 ```
 
-Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an array of Strings, Ints or other types that conform to the Swift Comparable protocol.
+Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an 
+
+y of Strings, Ints or other types that conform to the Swift Comparable protocol.
 
 To test this algorithm, copy the code to a playground and then do:
 

From 467503c623c0fa781ea337b68a2ee5251d9a20bc Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Wed, 22 Jan 2020 19:58:38 +0100
Subject: [PATCH 1640/1679] Update README.markdown

---
 Count Occurrences/README.markdown | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 2e48d1020..4deb9990e 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -55,9 +55,7 @@ func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
 }
 ```
 
-Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an 
-
-y of Strings, Ints or other types that conform to the Swift Comparable protocol.
+Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an array of Strings, Ints or other types that conform to the Swift Comparable protocol.
 
 To test this algorithm, copy the code to a playground and then do:
 

From 43181f5b4c8790fa887c4a6bd5ea8e94b0279eb5 Mon Sep 17 00:00:00 2001
From: Satveer Singh <satveer.y.singh@gmail.com>
Date: Thu, 6 Feb 2020 19:30:24 +1100
Subject: [PATCH 1641/1679] Fix typo in Heap Sort README lg -> log

---
 Heap Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index a45dad6f9..5bec58626 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -42,7 +42,7 @@ As you can see, the largest items are making their way to the back. We repeat th
 
 > **Note:** This process is very similar to [selection sort](../Selection%20Sort/), which repeatedly looks for the minimum item in the remainder of the array. Extracting the minimum or maximum value is what heaps are good at.
 
-Performance of heap sort is **O(n lg n)** in best, worst, and average case. Because we modify the array directly, heap sort can be performed in-place. But it is not a stable sort: the relative order of identical elements is not preserved.
+Performance of heap sort is **O(n log n)** in best, worst, and average case. Because we modify the array directly, heap sort can be performed in-place. But it is not a stable sort: the relative order of identical elements is not preserved.
 
 Here's how you can implement heap sort in Swift:
 

From f664af1f502ec7f6692e8dcb34d5848ce3af4e60 Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Mon, 10 Feb 2020 20:01:47 +0100
Subject: [PATCH 1642/1679] Renamed array

---
 Count Occurrences/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 4deb9990e..8e935ea58 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,10 +22,10 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
   var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
       if a[midIndex] < key {
@@ -39,7 +39,7 @@ func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
 
   var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
       if a[midIndex] > key {

From 901aaeac47c2275d0e5facbf9c5525882eb4f7ea Mon Sep 17 00:00:00 2001
From: Paul Anguiano <paul@gentleworks.com>
Date: Thu, 5 Mar 2020 18:10:39 -0800
Subject: [PATCH 1643/1679] Modified Trie to add prefix support to boolean
 contains(), plus unit tests.

---
 Trie/Trie/Trie/Trie.swift           |  9 ++++++---
 Trie/Trie/TrieTests/TrieTests.swift | 27 ++++++++++++++++++++++++++-
 2 files changed, 32 insertions(+), 4 deletions(-)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index accc7b61c..3d5031cf3 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -117,9 +117,12 @@ extension Trie {
 
   /// Determines whether a word is in the trie.
   ///
-  /// - Parameter word: the word to check for
+  /// - Parameters:
+  ///   - word: the word to check for
+  ///   - matchPrefix: whether the search word should match
+  ///   if it is only a prefix of other nodes in the trie
   /// - Returns: true if the word is present, false otherwise.
-  func contains(word: String) -> Bool {
+  func contains(word: String, matchPrefix: Bool = false) -> Bool {
     guard !word.isEmpty else {
       return false
     }
@@ -130,7 +133,7 @@ extension Trie {
       }
       currentNode = childNode
     }
-    return currentNode.isTerminating
+    return matchPrefix || currentNode.isTerminating
   }
 
   /// Attempts to walk to the last node of a word.  The
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 0c5bc69c6..59da2cd9b 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -167,7 +167,8 @@ class TrieTests: XCTestCase {
     let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
     XCTAssertEqual(trieCopy?.count, trie.count)
   }
-
+  
+  /// Tests whether word prefixes are properly found and returned.
   func testFindWordsWithPrefix() {
     let trie = Trie()
     trie.insert(word: "test")
@@ -190,4 +191,28 @@ class TrieTests: XCTestCase {
     let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
     XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
   }
+
+  /// Tests whether word prefixes are properly detected on a boolean contains() check.
+  func testContainsWordMatchPrefix() {
+    let trie = Trie()
+    trie.insert(word: "test")
+    trie.insert(word: "another")
+    trie.insert(word: "exam")
+    let wordsAll = trie.contains(word: "", matchPrefix: true)
+    XCTAssertEqual(wordsAll, true)
+    let words = trie.contains(word: "ex", matchPrefix: true)
+    XCTAssertEqual(words, true)
+    trie.insert(word: "examination")
+    let words2 = trie.contains(word: "exam", matchPrefix: true)
+    XCTAssertEqual(words2, true)
+    let noWords = trie.contains(word: "tee", matchPrefix: true)
+    XCTAssertEqual(noWords, false)
+    let unicodeWord = "😬😎"
+    trie.insert(word: unicodeWord)
+    let wordsUnicode = trie.contains(word: "😬", matchPrefix: true)
+    XCTAssertEqual(wordsUnicode, true)
+    trie.insert(word: "Team")
+    let wordsUpperCase = trie.contains(word: "Te", matchPrefix: true)
+    XCTAssertEqual(wordsUpperCase, true)
+  }
 }

From 510f3da1a0e445c3c1ec4aec69f1731a86acfbc4 Mon Sep 17 00:00:00 2001
From: Mick Bennett <mjbennett31@gmail.com>
Date: Fri, 27 Mar 2020 00:00:03 -0700
Subject: [PATCH 1644/1679] updated depricated hashable values to hash into
 methods

---
 Graph/Graph/Edge.swift   | 10 ++++------
 Graph/Graph/Vertex.swift |  5 +++--
 2 files changed, 7 insertions(+), 8 deletions(-)

diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index ac5ed6a25..b69937895 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,12 +29,10 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
-  public var hashValue: Int {
-    var string = "\(from.description)\(to.description)"
-    if weight != nil {
-      string.append("\(weight!)")
-    }
-    return string.hashValue
+  public func hash(into hasher: inout Hasher) {
+    hasher.combine(from.description)
+    hasher.combine(to.description)
+    hasher.combine(weight)
   }
 }
 
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 758a367bb..47499dcc6 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,8 +24,9 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-  public var hashValue: Int {
-    return "\(data)\(index)".hashValue
+  public func hash(into hasher: inout Hasher) {
+    hasher.combine(data)
+    hasher.combine(index)
   }
 
 }

From 47356447f47fc353cb95dcdcc9a4d296b1a1b816 Mon Sep 17 00:00:00 2001
From: Mick Bennett <mjbennett31@gmail.com>
Date: Thu, 9 Apr 2020 16:47:58 -0700
Subject: [PATCH 1645/1679] updated lcs string extension to access string
 directly

---
 .../Contents.swift                                 | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index c8d413e7f..0e78b7043 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,4 +1,4 @@
-// last checked with Xcode 9.0b4
+// last checked with Xcode 11.4
 #if swift(>=4.0)
 print("Hello, Swift 4!")
 #endif
@@ -7,10 +7,10 @@ extension String {
   public func longestCommonSubsequence(_ other: String) -> String {
 
     func lcsLength(_ other: String) -> [[Int]] {
-      var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.characters.count+1), count: self.characters.count+1)
+      var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.count+1), count: self.count+1)
 
-      for (i, selfChar) in self.characters.enumerated() {
-        for (j, otherChar) in other.characters.enumerated() {
+      for (i, selfChar) in self.enumerated() {
+        for (j, otherChar) in other.enumerated() {
           if otherChar == selfChar {
             matrix[i+1][j+1] = matrix[i][j] + 1
           } else {
@@ -22,8 +22,8 @@ extension String {
     }
 
     func backtrack(_ matrix: [[Int]]) -> String {
-      var i = self.characters.count
-      var j = other.characters.count
+      var i = self.count
+      var j = other.count
       var charInSequence = self.endIndex
 
       var lcs = String()
@@ -41,7 +41,7 @@ extension String {
           lcs.append(self[charInSequence])
         }
       }
-      return String(lcs.characters.reversed())
+      return String(lcs.reversed())
     }
 
     return backtrack(lcsLength(other))

From 5b0861c2eca8ec37ed3f2667ada5de7e850cd75e Mon Sep 17 00:00:00 2001
From: Azhar Anwar <azharcodes@gmail.com>
Date: Tue, 28 Apr 2020 15:52:03 +0530
Subject: [PATCH 1646/1679] fixes: typo and punctuation

---
 Shuffle/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index 5a2a07a98..d9c35868a 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -37,7 +37,7 @@ This code works just fine but it's not very efficient. Removing an element from
 
 ## The Fisher-Yates / Knuth shuffle
 
-Here is a much improved version of the shuffle algorithm:
+Here is a much-improved version of the shuffle algorithm:
 
 ```swift
 extension Array {
@@ -52,7 +52,7 @@ extension Array {
 }
 ```
 
-Again, this picks objects at random. In the naive version we placed those objects into a new temporary array so we could keep track of which objects were already shuffled and which still remained to be done. In this improved algorithm, however, we'll move the shuffled objects to the end of the original array. 
+Again, this picks objects at random. In the naive version, we placed those objects into a new temporary array so we could keep track of which objects were already shuffled and which still remained to be done. In this improved algorithm, however, we'll move the shuffled objects to the end of the original array. 
 
 Let's walk through the example. We have the array:
 
@@ -116,7 +116,7 @@ The `shuffledArray()` function first creates a new array with `n` zeros. Then it
 
 For this function, `The condition that checks if j ≠ i may be omitted in languages that have no problems accessing uninitialized array values, and for which assigning is cheaper than comparing.`, you can check it in wiki. And also remove checking logic will optimise performance.
 
-The algoritm is quite clever and I suggest you walk through an example yourself, either on paper or in the playground. (Hint: Again it splits the array into two regions.)
+The algorithm is quite clever and I suggest you walk through an example yourself, either on paper or in the playground. (Hint: Again it splits the array into two regions.)
 
 ## See also
 

From 409ffd6921441afb56a7ea68c73a0f2c9516c809 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sarp=20G=C3=BCney=20Ba=C5=9Faraner?=
 <sarpbasaraner@gmail.com>
Date: Thu, 7 May 2020 10:35:45 +0300
Subject: [PATCH 1647/1679] fix typo

Dinstance -> Distance
---
 HaversineDistance/HaversineDistance.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 3d8d60f54..ed89b4462 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,6 +1,6 @@
 import UIKit
 
-func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
+func haversineDistance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
     
     let haversin = { (angle: Double) -> Double in
         return (1 - cos(angle))/2
@@ -27,4 +27,4 @@ let amsterdam = (52.3702, 4.8952)
 let newYork = (40.7128, -74.0059)
 
 // Google says it's 5857 km so our result is only off by 2km which could be due to all kinds of things, not sure how google calculates the distance or which latitude and longitude google uses to calculate the distance.
-haversineDinstance(la1: amsterdam.0, lo1: amsterdam.1, la2: newYork.0, lo2: newYork.1)
+haversineDistance(la1: amsterdam.0, lo1: amsterdam.1, la2: newYork.0, lo2: newYork.1)

From 7a77f3fa8abbdc0ee68b77b84d56b3e1eaf61087 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 11:57:00 -0500
Subject: [PATCH 1648/1679] Update Readme for code modification

Update to reflect alternative of using .isMultiple(of:) method instead of modulo (%) operator
---
 Fizz Buzz/README.markdown | 97 ++++++++++++++++++++++++++++-----------
 1 file changed, 69 insertions(+), 28 deletions(-)

diff --git a/Fizz Buzz/README.markdown b/Fizz Buzz/README.markdown
index 8c250da27..be516bd46 100644
--- a/Fizz Buzz/README.markdown	
+++ b/Fizz Buzz/README.markdown	
@@ -16,46 +16,48 @@ The modulus operator `%` is the key to solving fizz buzz.
 
 The modulus operator returns the remainder after an integer division. Here is an example of the modulus operator:
 
-| Division      | Division Result            | Modulus         | Modulus Result  |
-| ------------- | -------------------------- | --------------- | ---------------:|
-| 1 / 3       | 0 with a remainder of 3  | 1 % 3         | 1             |
-| 5 / 3       | 1 with a remainder of 2  | 5 % 3         | 2             |
-| 16 / 3      | 5 with a remainder of 1  | 16 % 3        | 1             |
+| Division    | Division Result       | Modulus       | Modulus Result|
+| ----------- | --------------------- | ------------- | :-----------: |
+| 1 / 3       | 0 with a remainder of 3 | 1 % 3         | 1             |
+| 5 / 3       | 1 with a remainder of 2 | 5 % 3         | 2             |
+| 16 / 3      | 5 with a remainder of 1 | 16 % 3        | 1             |
 
 A common approach to determine if a number is even or odd is to use the modulus operator:
 
-| Modulus       | Result          | Swift Code                      | Swift Code Result | Comment                                       |
-| ------------- | ---------------:| ------------------------------- | -----------------:| --------------------------------------------- |
-| 6 % 2       | 0               | `let isEven = (number % 2 == 0)`  | `true`            | If a number is divisible by 2 it is *even*    |
-| 5 % 2       | 1               | `let isOdd = (number % 2 != 0)`   | `true`            | If a number is not divisible by 2 it is *odd* |
+| Modulus  | Result | Swift Code                       | Swift Code<br>Result | Comment                                    |
+| -------- | :-----:| -------------------------------- | :----------------:| --------------------------------------------- |
+| 6 % 2    | 0      | `let isEven = (number % 2 == 0)` | `true`            | If a number is divisible by 2 it is *even*    |
+| 5 % 2    | 1      | `let isOdd = (number % 2 != 0)`  | `true`            | If a number is not divisible by 2 it is *odd* |
+
+Alternatively, Swift's built in function .isMultiple(of:) can be used, i.e. 6.isMultiple(of: 2) will return true, 5.isMultiple(of: 2) will return false
 
 ## Solving fizz buzz
 
-Now we can use the modulus operator `%` to solve fizz buzz.
+Now we can use the modulus operator `%` or .isMultiple(of:) method to solve fizz buzz.
 
 Finding numbers divisible by three:
 
-| Modulus | Modulus Result | Swift Code    | Swift Code Result |
-| ------- | --------------:| ------------- |------------------:|
-| 1 % 3 | 1            | `1 % 3 == 0`  | `false`           |
-| 2 % 3 | 2            | `2 % 3 == 0`  | `false`           |
-| 3 % 3 | 0            | `3 % 3 == 0`  | `true`            |
-| 4 % 3 | 1            | `4 % 3 == 0`  | `false`           |
+| Modulus | Modulus<br>Result | Swift Code<br>using Modulo | Swift Code<br>using .isMultiple(of:) | Swift Code<br>Result |
+| ------- | :---------------: | -------------------------- | ------------------------------------ | ------------------- |
+|1 % 3    | 1                 | `1 % 3 == 0`               | `1.isMultiple(of: 3)`                | `false`              |
+|2 % 3    | 2                 | `2 % 3 == 0`               | `2.isMultiple(of: 3)`                | `false`              |
+|3 % 3    | 0                 | `3 % 3 == 0`               | `3.isMultiple(of: 3)`                | `true`               |
+|4 % 3    | 1                 | `4 % 3 == 0`               | `4.isMultiple(of: 3)`                | `false`              |
 
 Finding numbers divisible by five:
 
-| Modulus | Modulus Result | Swift Code    | Swift Code Result |
-| ------- | --------------:| ------------- |------------------:|
-| 1 % 5 | 1            | `1 % 5 == 0`  | `false`           |
-| 2 % 5 | 2            | `2 % 5 == 0`  | `false`           |
-| 3 % 5 | 3            | `3 % 5 == 0`  | `false`           |
-| 4 % 5 | 4            | `4 % 5 == 0`  | `false`           |
-| 5 % 5 | 0            | `5 % 5 == 0`  | `true`            |
-| 6 % 5 | 1            | `6 % 5 == 0`  | `false`           |
+| Modulus | Modulus<br>Result | Swift Code<br>using Modulo | Swift Code<br>using .isMultiple(of:) | Swift Code<br>Result |
+| ------- | :---------------: | -------------------------- | ------------------------------------ | -------------------- |
+| 1 % 5   | 1                 | `1 % 5 == 0`               | `1.isMultiple(of: 5)`                | `false`              |
+| 2 % 5   | 2                 | `2 % 5 == 0`               | `2.isMultiple(of: 5)`                | `false`              |
+| 3 % 5   | 3                 | `3 % 5 == 0`               | `3.isMultiple(of: 5)`                | `false`              |
+| 4 % 5   | 4                 | `4 % 5 == 0`               | `4.isMultiple(of: 5)`                | `false`              |
+| 5 % 5   | 0                 | `5 % 5 == 0`               | `5.isMultiple(of: 5)`                | `true`               |
+| 6 % 5   | 1                 | `6 % 5 == 0`               | `6.isMultiple(of: 5)`                | `false`              |
 
 ## The code
 
-Here is a simple implementation in Swift:
+Here is a simple implementation in Swift using Modulus approach
 
 ```swift
 func fizzBuzz(_ numberOfTurns: Int) {
@@ -79,7 +81,31 @@ func fizzBuzz(_ numberOfTurns: Int) {
 }
 ```
 
-Put this code in a playground and test it like so:
+Here is simple implementation in Swift using .isMultiple(of:) and switch statement
+
+```swift
+func fizzBuzz(_ numberOfTurns: Int) {
+    guard numberOfTurns >= 1 else {
+        print("Number of turns must be >= 1")
+        return
+    }
+    
+    for i in 1...numberOfTurns {
+        switch (i.isMultiple(of: 3), i.isMultiple(of: 5)) {
+        case (false, false):
+            print("\(i)")
+        case (true, false):
+            print("Fizz")
+        case (false, true):
+            print("Buzz")
+        case (true, true):
+            print("Fizz Buzz")
+        }
+    }
+}
+```
+
+Put either code in a playground and test it like so:
 
 ```swift
 fizzBuzz(15)
@@ -87,10 +113,25 @@ fizzBuzz(15)
 
 This will output:
 
-	1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, Fizz Buzz
+1    
+2   
+Fizz   
+4   
+Buzz    
+Fizz  
+7   
+8   
+Fizz   
+Buzz   
+11   
+Fizz  
+13   
+14    
+Fizz Buzz  
 
 ## See also
 
 [Fizz buzz on Wikipedia](https://en.wikipedia.org/wiki/Fizz_buzz)
 
-*Written by [Chris Pilcher](https://github.com/chris-pilcher)*
+*Originally written by [Chris Pilcher](https://github.com/chris-pilcher)*<br>
+*Updated by [Lance Rettberg](https://github.com/l-rettberg)*

From 99d769d03c0cfee1b92b63aeeb1b203811eaddc8 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 12:02:06 -0500
Subject: [PATCH 1649/1679] Update FizzBuzz

Update to 1) add guard, 2) use .isMultiple(of:), 3) use switch statement
---
 Fizz Buzz/FizzBuzz.swift | 32 +++++++++++++++++---------------
 1 file changed, 17 insertions(+), 15 deletions(-)

diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index b6bb410e7..704ea7c6b 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,19 +1,21 @@
-func fizzBuzz(_ numberOfTurns: Int) {
-  for i in 1...numberOfTurns {
-    var result = ""
+// Updated for Xcode Version 11.4.1 (11E503a)
 
-    if i % 3 == 0 {
-      result += "Fizz"
+func fizzBuzz2(_ numberOfTurns: Int) {
+    guard numberOfTurns >= 1 else {
+        print("Number of turns must be >= 1")
+        return
     }
-
-    if i % 5 == 0 {
-      result += (result.isEmpty ? "" : " ") + "Buzz"
-    }
-
-    if result.isEmpty {
-      result += "\(i)"
+    
+    for i in 1...numberOfTurns {
+        switch (i.isMultiple(of: 3), i.isMultiple(of: 5)) {
+        case (false, false):
+            print("\(i)")
+        case (true, false):
+            print("Fizz")
+        case (false, true):
+            print("Buzz")
+        case (true, true):
+            print("Fizz Buzz")
+        }
     }
-
-    print(result)
-  }
 }

From 71431b12042a2dc17eb9c170a9fa5c731942462d Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 12:09:54 -0500
Subject: [PATCH 1650/1679] Update

---
 Fizz Buzz/FizzBuzz.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index 704ea7c6b..2e66b26f4 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,6 +1,6 @@
 // Updated for Xcode Version 11.4.1 (11E503a)
 
-func fizzBuzz2(_ numberOfTurns: Int) {
+func fizzBuzz(_ numberOfTurns: Int) {
     guard numberOfTurns >= 1 else {
         print("Number of turns must be >= 1")
         return

From f94bccc68d017bbc61cb774f7642dd25b25f1d4a Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 14:41:39 -0500
Subject: [PATCH 1651/1679] Updates to 1) add guard, 2) use .isMultiple(of:)
 and 3) use switch statement

---
 Fizz Buzz/FizzBuzz.playground/Contents.swift | 34 ++++++++++----------
 Fizz Buzz/FizzBuzz.swift                     |  4 +--
 2 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index ae966bbcc..2ab13b362 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,23 +1,23 @@
-// last checked with Xcode 10.0 (10A255)
+// Last checked with Xcode Version 11.4.1 (11E503a)
 
 func fizzBuzz(_ numberOfTurns: Int) {
-  for i in 1...numberOfTurns {
-    var result = ""
-
-    if i % 3 == 0 {
-      result += "Fizz"
+    guard numberOfTurns >= 1 else {
+        print("Number of turns must be >= 1")
+        return
     }
-
-    if i % 5 == 0 {
-      result += (result.isEmpty ? "" : " ") + "Buzz"
+    
+    for i in 1...numberOfTurns {
+        switch (i.isMultiple(of: 3), i.isMultiple(of: 5)) {
+        case (false, false):
+            print("\(i)")
+        case (true, false):
+            print("Fizz")
+        case (false, true):
+            print("Buzz")
+        case (true, true):
+            print("Fizz Buzz")
+        }
     }
-
-    if result.isEmpty {
-      result += "\(i)"
-    }
-
-    print(result)
-  }
 }
 
-fizzBuzz(100)
+fizzBuzz(15)
diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index 2e66b26f4..bf753e648 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,4 +1,4 @@
-// Updated for Xcode Version 11.4.1 (11E503a)
+// Last checked with Xcode Version 11.4.1 (11E503a)
 
 func fizzBuzz(_ numberOfTurns: Int) {
     guard numberOfTurns >= 1 else {
@@ -18,4 +18,4 @@ func fizzBuzz(_ numberOfTurns: Int) {
             print("Fizz Buzz")
         }
     }
-}
+}
\ No newline at end of file

From 6a9ec9628099601714655ad42237d8948b2cfc05 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 16:45:31 -0500
Subject: [PATCH 1652/1679] Remove file

---
 Fizz Buzz/FizzBuzz.playground/contents.xcplayground | 4 ----
 1 file changed, 4 deletions(-)
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/contents.xcplayground

diff --git a/Fizz Buzz/FizzBuzz.playground/contents.xcplayground b/Fizz Buzz/FizzBuzz.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Fizz Buzz/FizzBuzz.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file

From e3b3126f819ec57b9759cd4b80f639b1d39b440a Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 16:47:18 -0500
Subject: [PATCH 1653/1679] Delete IDEWorkspaceChecks.plist

---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 --------
 1 file changed, 8 deletions(-)
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>

From 51b0c2b5a2abed1a90241e64869ccd173b54a1e7 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 16:47:30 -0500
Subject: [PATCH 1654/1679] Delete contents.xcworkspacedata

---
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 -------
 1 file changed, 7 deletions(-)
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata	
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>

From 4617d9401be60101c12e100f428c0b460de0a210 Mon Sep 17 00:00:00 2001
From: jinthislife <8064873+jinthislife@users.noreply.github.com>
Date: Mon, 11 May 2020 15:30:38 +1000
Subject: [PATCH 1655/1679] Update README.markdown

remove duplicate parameter
---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 0b382f204..57d1f4bff 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -557,7 +557,7 @@ As a result, doing `tree.search(100)` gives nil.
 You can check whether a tree is a valid binary search tree with the following method:
 
 ```swift
-  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
+  public func isBST(minValue: T, maxValue: T) -> Bool {
     if value < minValue || value > maxValue { return false }
     let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
     let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true

From bf3f3d5d690fe0a6e3cd7fc549781551477a8c6b Mon Sep 17 00:00:00 2001
From: Jagdeep Matharu <jagdeepmatharu88@gmail.com>
Date: Sun, 31 May 2020 19:54:14 -0400
Subject: [PATCH 1656/1679] Updating Counting sort for stability

---
 Counting Sort/CountingSort.playground/Contents.swift | 7 ++++++-
 Counting Sort/CountingSort.swift                     | 5 ++++-
 Counting Sort/README.markdown                        | 7 +++++--
 3 files changed, 15 insertions(+), 4 deletions(-)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index dc375512a..839b16bc8 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -29,12 +29,17 @@ func countingSort(array: [Int]) throws -> [Int] {
 
   // Step 3
   // Place the element in the final array as per the number of elements before it
+  // Loop through the array in reverse to keep the stability of the new array
+  // (i.e. 7, is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
   var sortedArray = [Int](repeating: 0, count: array.count)
-  for element in array {
+  for index in stride(from: array.count - 1, through: 0, by: -1) {
+    let element = array[index]
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }
+    
   return sortedArray
 }
 
 try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
+
diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index 725a634a4..68dcf5c0d 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -29,8 +29,11 @@ func countingSort(_ array: [Int])-> [Int] {
 
   // Step 3
   // Place the element in the final array as per the number of elements before it
+  // Loop through the array in reverse to keep the stability of the new sorted array
+  // (For Example: 7 is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
   var sortedArray = [Int](repeating: 0, count: array.count)
-  for element in array {
+  for index in stride(from: array.count - 1, through: 0, by: -1) {
+    let element = array[index]
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }
diff --git a/Counting Sort/README.markdown b/Counting Sort/README.markdown
index 959becc8c..93d6635bd 100644
--- a/Counting Sort/README.markdown	
+++ b/Counting Sort/README.markdown	
@@ -50,7 +50,9 @@ The code for step 2 is:
 
 ### Step 3:
 
-This is the last step in the algorithm. Each element in the original array is placed at the position defined by the output of step 2. For example, the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array.
+This is the last step in the algorithm. Each element in the original array is placed at the position defined by the output of step 2. For example, the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array. 
+We also have to loop through the array in reverse to keep the stability of the new sorted array.
+For Example: 7 is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6.
 
 The final output would be:
 
@@ -63,7 +65,8 @@ Here is the code for this final step:
 
 ```swift
   var sortedArray = [Int](repeating: 0, count: array.count)
-  for element in array {
+  for index in stride(from: array.count - 1, through: 0, by: -1) {
+    let element = array[index]
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }

From d06b7e3c5e45a65b2f275a7dd81bfc77520788c6 Mon Sep 17 00:00:00 2001
From: Jagdeep Matharu <jagdeepmatharu88@gmail.com>
Date: Sun, 31 May 2020 19:54:43 -0400
Subject: [PATCH 1657/1679] Updating Counting sort tests project to support
 Swift 5

---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Counting Sort/Tests/Tests.xcodeproj/project.pbxproj       | 5 +++--
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 19 insertions(+), 2 deletions(-)
 create mode 100644 Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj
index 5cbb0d4aa..aaa6c1b6b 100644
--- a/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -97,6 +97,7 @@
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
+				English,
 				en,
 				Base,
 			);
@@ -226,7 +227,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 5.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +239,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 5.0;
 			};
 			name = Release;
 		};
diff --git a/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From bf38b12ddc30c6e396a50e61e3dc342ced28e538 Mon Sep 17 00:00:00 2001
From: Jagdeep Matharu <jagdeepmatharu88@gmail.com>
Date: Sun, 31 May 2020 19:58:21 -0400
Subject: [PATCH 1658/1679] Minor change in comment

---
 Counting Sort/CountingSort.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 839b16bc8..99178f85d 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -30,7 +30,7 @@ func countingSort(array: [Int]) throws -> [Int] {
   // Step 3
   // Place the element in the final array as per the number of elements before it
   // Loop through the array in reverse to keep the stability of the new array
-  // (i.e. 7, is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
+  // i.e. 7, is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
   var sortedArray = [Int](repeating: 0, count: array.count)
   for index in stride(from: array.count - 1, through: 0, by: -1) {
     let element = array[index]

From d8d165208465c8c725eda950e8cb2ddb3d7cfdca Mon Sep 17 00:00:00 2001
From: Yossa Bourne <cybercanonx@gmail.com>
Date: Thu, 11 Jun 2020 09:56:40 +0700
Subject: [PATCH 1659/1679] Fix Swift (language) typos

---
 Introsort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Introsort/README.markdown b/Introsort/README.markdown
index 376703cf7..3e596ee89 100644
--- a/Introsort/README.markdown
+++ b/Introsort/README.markdown
@@ -2,7 +2,7 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-IntroSort is the algorithm used by swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
+IntroSort is the algorithm used by Swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the Swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
 
 The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
 

From 9bc6aad9aaa56ce53ea7319f52c25585651e737a Mon Sep 17 00:00:00 2001
From: Roberto Efrain Hernandez <reh9019@gmail.com>
Date: Wed, 10 Jun 2020 23:44:40 -0700
Subject: [PATCH 1660/1679] Updating how String can be casted into an Array.

Just wanted to update the syntax from Array(self.characters) to Array(self). Similarly for casting of the ptnr String.
---
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 81bc65278..be0cd961d 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -12,8 +12,8 @@ extension String {
   
   func indexesOf(ptnr: String) -> [Int]? {
     
-    let text = Array(self.characters)
-    let pattern = Array(ptnr.characters)
+    let text = Array(self)
+    let pattern = Array(ptnr)
     
     let textLength: Int = text.count
     let patternLength: Int = pattern.count

From abfa66b02d35b6320a5e404241db94d4317386d6 Mon Sep 17 00:00:00 2001
From: msalvacion <mcsalvacion@gmail.com>
Date: Thu, 11 Jun 2020 15:32:05 -0700
Subject: [PATCH 1661/1679] Fix: Typos in Heap README.markdown

Added missing word and fixed a typo
---
 Heap/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 6c65fe9c8..fee881129 100755
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -82,7 +82,7 @@ array[parent(i)] >= array[i]
 
 Verify that this heap property holds for the array from the example heap.
 
-As you can see, these equations allow us to find the parent or child index for any node without the need for pointers. It is complicated than just dereferencing a pointer, but that is the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
+As you can see, these equations allow us to find the parent or child index for any node without the need for pointers. It is more complicated than just dereferencing a pointer, but that is the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
 
 It is important to understand this relationship between array index and position in the tree. Here is a larger heap which has 15 nodes divided over four levels:
 
@@ -164,7 +164,7 @@ All of the above take time **O(log n)** because shifting up or down is expensive
 
 - `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you are smart about this, it can be done in **O(n)** time.
 
-- [Heap sort](../Heap%20Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
+- [Heap sort](../Heap%20Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n log n).**
 
 The heap also has a `peek()` function that returns the maximum (max-heap) or minimum (min-heap) element, without removing it from the heap. Time: **O(1)**.
 

From f30e53c3cb45af31f8b80c35a8c4ee781d1ee311 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 15 Jun 2020 18:23:10 -0400
Subject: [PATCH 1662/1679] Fixes a few typos

---
 Introsort/README.markdown | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Introsort/README.markdown b/Introsort/README.markdown
index 3e596ee89..280950928 100644
--- a/Introsort/README.markdown
+++ b/Introsort/README.markdown
@@ -2,7 +2,9 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-IntroSort is the algorithm used by Swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the Swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
+IntroSort is the algorithm used by Swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. 
+
+The classic implementation of introsort uses a recursive Quicksort with a fallback to Heapsort in the case where the recursion depth level reached a certain maximum value. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the Swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
 
 The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
 

From f4fb2fc0eb04ab6a7862ae903f258741896f9ec1 Mon Sep 17 00:00:00 2001
From: nghiahoang <vannghia.hoang@ocha.vn>
Date: Thu, 25 Jun 2020 13:17:01 +0700
Subject: [PATCH 1663/1679] fix: SplayTree.remove is broken

---
 .../SplayTree.playground/Contents.swift       |  33 +----
 .../Sources/SplayTree.swift                   | 122 ++++-------------
 Splay Tree/SplayTree.swift                    | 124 ++++--------------
 Splay Tree/readme.md                          |   7 +-
 4 files changed, 57 insertions(+), 229 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
index a8a0bc5c6..28a201b37 100644
--- a/Splay Tree/SplayTree.playground/Contents.swift	
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -5,29 +5,10 @@
 print("Hello, Swift 4!")
 #endif
 
-let splayTree = SplayTree(value: 1)
-splayTree.insert(value: 2)
-splayTree.insert(value: 10)
-splayTree.insert(value: 6)
-
-splayTree.remove(value: 10)
-splayTree.remove(value: 6)
-
-splayTree.insert(value: 55)
-splayTree.insert(value: 559)
-splayTree.remove(value: 2)
-splayTree.remove(value: 1)
-splayTree.remove(value: 55)
-splayTree.remove(value: 559)
-
-splayTree.insert(value: 1843000)
-splayTree.insert(value: 1238)
-splayTree.insert(value: -1)
-splayTree.insert(value: 87)
-
-splayTree.minimum()
-splayTree.maximum()
-
-
-
-
+var tree = SplayTree<Int>(value: 0)
+tree.insert(value: 2)
+tree.insert(value: 3)
+tree.insert(value: 4)
+tree.insert(value: 7)
+_ = tree.search(value: 2)
+tree.remove(value: 2)
diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index 9e484129c..f450eaced 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -289,120 +289,42 @@ extension Node {
      - Node     Resulting from the deletion and the splaying of the removed node
      
      */
-    public func remove(value: T) -> Node<T>? {
-        let replacement: Node<T>?
+    fileprivate func remove(value: T) -> Node<T>? {
+        guard let target = search(value: value) else { return self }
         
-        if let v = self.value, v == value {
+        if let left = target.left, let right = target.right {
+            let largestOfLeftChild = left.maximum()
+            left.parent = nil
+            right.parent = nil
             
-            var parentToSplay: Node<T>?
-            if let left = left {
-                if let right = right {
-                    
-                    replacement = removeNodeWithTwoChildren(left, right)
-                    
-                    if let replacement = replacement,
-                        let replacementParent = replacement.parent,
-                        replacementParent.value != self.value {
-                        
-                        parentToSplay = replacement.parent
-                        
-                    } else if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                    
-                } else {
-                    // This node only has a left child. The left child replaces the node.
-                    replacement = left
-                    if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                }
-            } else if let right = right {
-                // This node only has a right child. The right child replaces the node.
-                replacement = right
-                if self.parent != nil {
-                    parentToSplay = self.parent
-                } else {
-                    parentToSplay = replacement
-                }
-            } else {
-                // This node has no children. We just disconnect it from its parent.
-                replacement = nil
-                parentToSplay = parent
-            }
-            
-            reconnectParentTo(node: replacement)
+            SplayOperation.splay(node: largestOfLeftChild)
+            largestOfLeftChild.right = right
             
-            // performs the splay operation
-            if let parentToSplay = parentToSplay {
-                SplayOperation.splay(node: parentToSplay)
-            }
+            return largestOfLeftChild
             
-            // The current node is no longer part of the tree, so clean it up.
-            parent = nil
-            left = nil
-            right = nil
+        } else if let left = target.left {
+            replace(node: target, with: left)
+            return left
             
-            return parentToSplay
+        } else if let right = target.right {
+            replace(node: target, with: right)
+            return right
             
-        } else if let v = self.value, value < v {
-            if left != nil {
-                return left!.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
         } else {
-            if right != nil {
-                return right?.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
+            return nil
         }
     }
     
-    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
+    private func replace(node: Node<T>, with newNode: Node<T>?) {
+        guard let sourceParent = sourceNode.parent else { return }
         
-        // Connect our left child with the new node.
-        successor.left = left
-        left.parent = successor
-        
-        // Connect our right child with the new node. If the right child does
-        // not have any left children of its own, then the in-order successor
-        // *is* the right child.
-        if right !== successor {
-            successor.right = right
-            right.parent = successor
+        if sourceNode.isLeftChild {
+            sourceParent.left = newNode
         } else {
-            successor.right = nil
+            sourceParent.right = newNode
         }
         
-        // And finally, connect the successor node to our parent.
-        return successor
-    }
-    
-    private func reconnectParentTo(node: Node?) {
-        if let parent = parent {
-            if isLeftChild {
-                parent.left = node
-            } else {
-                parent.right = node
-            }
-        }
-        node?.parent = parent
+        newNode?.parent = sourceParent
     }
 }
 
diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index a7b20743d..0f1fa48f0 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -44,7 +44,7 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
+    public static func operation<T>(forNode node: Node<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -289,120 +289,42 @@ extension Node {
             - Node     Resulting from the deletion and the splaying of the removed node
      
      */
-    public func remove(value: T) -> Node<T>? {
-        let replacement: Node<T>?
+    fileprivate func remove(value: T) -> Node<T>? {
+        guard let target = search(value: value) else { return self }
         
-        if let v = self.value, v == value {
+        if let left = target.left, let right = target.right {
+            let largestOfLeftChild = left.maximum()
+            left.parent = nil
+            right.parent = nil
             
-            var parentToSplay: Node<T>?
-            if let left = left {
-                if let right = right {
-                    
-                    replacement = removeNodeWithTwoChildren(left, right)
-                    
-                    if let replacement = replacement,
-                        let replacementParent = replacement.parent,
-                        replacementParent.value != self.value {
-                        
-                        parentToSplay = replacement.parent
-                        
-                    } else if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                    
-                } else {
-                    // This node only has a left child. The left child replaces the node.
-                    replacement = left
-                    if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                }
-            } else if let right = right {
-                // This node only has a right child. The right child replaces the node.
-                replacement = right
-                if self.parent != nil {
-                    parentToSplay = self.parent
-                } else {
-                    parentToSplay = replacement
-                }
-            } else {
-                // This node has no children. We just disconnect it from its parent.
-                replacement = nil
-                parentToSplay = parent
-            }
+            SplayOperation.splay(node: largestOfLeftChild)
+            largestOfLeftChild.right = right
             
-            reconnectParentTo(node: replacement)
+            return largestOfLeftChild
             
-            // performs the splay operation
-            if let parentToSplay = parentToSplay {
-                SplayOperation.splay(node: parentToSplay)
-            }
+        } else if let left = target.left {
+            replace(node: target, with: left)
+            return left
             
-            // The current node is no longer part of the tree, so clean it up.
-            parent = nil
-            left = nil
-            right = nil
-
-            return parentToSplay
+        } else if let right = target.right {
+            replace(node: target, with: right)
+            return right
             
-        } else if let v = self.value, value < v {
-            if left != nil {
-                return left!.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
         } else {
-            if right != nil {
-                return right?.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
+            return nil
         }
     }
     
-    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
+    private func replace(node: Node<T>, with newNode: Node<T>?) {
+        guard let sourceParent = sourceNode.parent else { return }
         
-        // Connect our left child with the new node.
-        successor.left = left
-        left.parent = successor
-        
-        // Connect our right child with the new node. If the right child does
-        // not have any left children of its own, then the in-order successor
-        // *is* the right child.
-        if right !== successor {
-            successor.right = right
-            right.parent = successor
+        if sourceNode.isLeftChild {
+            sourceParent.left = newNode
         } else {
-            successor.right = nil
+            sourceParent.right = newNode
         }
         
-        // And finally, connect the successor node to our parent.
-        return successor
-    }
-    
-    private func reconnectParentTo(node: Node?) {
-        if let parent = parent {
-            if isLeftChild {
-                parent.left = node
-            } else {
-                parent.right = node
-            }
-        }
-        node?.parent = parent
+        newNode?.parent = sourceParent
     }
 }
 
diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 75c3c0389..8a852c950 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -102,8 +102,11 @@ To insert a value:
 
 To delete a value: 
 
-- Delete it as in a binary search tree 
-- Splay the parent of the removed node to the root 
+- Perform search for the value, after performed search function if the tree contains the value, it'll be the root of the new tree.
+- If the tree has only left child, change left child to the root of the tree, remove the old root node
+- If the tree has only right child, change right child to the root of the tree, remove the old root node
+- Else, the tree has both two children, set parent of two children to nil, so that they're two new trees (left-tree and right-tree).
+- Splay the minimum node of right-tree (or minimum node of left-tree), then set left-tree as left child of new root of right-tree (or set right-tree as right child of new root of left-tree), return right-tree
 
 ### Search 
 

From 73f009209e99eaed53a6c81bf72dae83a5397cb4 Mon Sep 17 00:00:00 2001
From: Ahmed Abdulkareem Rezik <ahmedrezq100@hotmail.com>
Date: Thu, 9 Jul 2020 14:33:03 +0200
Subject: [PATCH 1664/1679] Fixed Hashable Conformance to hash(into:)

---
 Graph/Graph/Edge.swift   | 14 +++++++-------
 Graph/Graph/Vertex.swift |  6 ++++--
 2 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index ac5ed6a25..61cb576d1 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,13 +29,13 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
-  public var hashValue: Int {
-    var string = "\(from.description)\(to.description)"
-    if weight != nil {
-      string.append("\(weight!)")
-    }
-    return string.hashValue
-  }
+    public func hash(into hasher: inout Hasher) {
+           hasher.combine(from)
+           hasher.combine(to)
+        if weight != nil {
+             hasher.combine(weight)
+          }
+         }
 }
 
 public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 758a367bb..cdf39ba62 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,8 +24,10 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-  public var hashValue: Int {
-    return "\(data)\(index)".hashValue
+  public func hasher(into hasher: inout Hasher){
+      
+      hasher.combine(data)
+      hasher.combine(index)
   }
 
 }

From 0513f7d1d0432d844357f5b931bfc5e0d1940870 Mon Sep 17 00:00:00 2001
From: Ahmed Abdulkareem Rezik <ahmedrezq100@hotmail.com>
Date: Thu, 9 Jul 2020 14:37:37 +0200
Subject: [PATCH 1665/1679] Fixed Conformance to Hashable Protocol in Vertex
 and Edge structs

---
 Graph/Graph/Edge.swift   | 14 ++++++++------
 Graph/Graph/Vertex.swift | 12 +++++++-----
 2 files changed, 15 insertions(+), 11 deletions(-)

diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 61cb576d1..1f29e07dd 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,13 +29,15 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
+
     public func hash(into hasher: inout Hasher) {
-           hasher.combine(from)
-           hasher.combine(to)
-        if weight != nil {
-             hasher.combine(weight)
-          }
-         }
+              hasher.combine(from)
+              hasher.combine(to)
+           if weight != nil {
+                hasher.combine(weight)
+             }
+            }
+    
 }
 
 public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index cdf39ba62..45b2c3088 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,11 +24,13 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-  public func hasher(into hasher: inout Hasher){
-      
-      hasher.combine(data)
-      hasher.combine(index)
-  }
+
+    
+    public func hasher(into hasher: inout Hasher){
+        
+        hasher.combine(data)
+        hasher.combine(index)
+    }
 
 }
 

From 4311cad2e332b9454c1189bddcbbca5f156a3d4c Mon Sep 17 00:00:00 2001
From: Samuel Huang <samhuang91@gmail.com>
Date: Wed, 22 Jul 2020 13:26:35 -0700
Subject: [PATCH 1666/1679] Update BTree.swift

Fix spelling of swift markers - rename `Travelsals` to `Traversals`
---
 B-Tree/BTree.playground/Sources/BTree.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/B-Tree/BTree.playground/Sources/BTree.swift b/B-Tree/BTree.playground/Sources/BTree.swift
index 2693eb308..2ed0b2593 100644
--- a/B-Tree/BTree.playground/Sources/BTree.swift
+++ b/B-Tree/BTree.playground/Sources/BTree.swift
@@ -86,7 +86,7 @@ extension BTreeNode {
   }
 }
 
-// MARK: BTreeNode extension: Travelsals
+// MARK: BTreeNode extension: Traversals
 
 extension BTreeNode {
 
@@ -443,7 +443,7 @@ public class BTree<Key: Comparable, Value> {
   }
 }
 
-// MARK: BTree extension: Travelsals
+// MARK: BTree extension: Traversals
 
 extension BTree {
   /**

From 617187bf4c36ab57948592d403e295cf8127d664 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:37:23 -0700
Subject: [PATCH 1667/1679] Update style of Graph

---
 .../xcshareddata/IDEWorkspaceChecks.plist         |  8 ++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist         |  8 ++++++++
 Graph/Graph/Edge.swift                            | 15 +++++++--------
 3 files changed, 23 insertions(+), 8 deletions(-)
 create mode 100644 Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 3c95f9666..9ddd4e23d 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,14 +29,13 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
-    public func hash(into hasher: inout Hasher) {
-              hasher.combine(from)
-              hasher.combine(to)
-           if weight != nil {
-                hasher.combine(weight)
-             }
-            }
-    
+  public func hash(into hasher: inout Hasher) {
+    hasher.combine(from)
+    hasher.combine(to)
+    if weight != nil {
+      hasher.combine(weight)
+    }
+  }
 
 }
 

From d951e67ec24167c9518bcab4e91946ce956978f3 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:57:25 -0700
Subject: [PATCH 1668/1679] Update README.markdown

---
 README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.markdown b/README.markdown
index 3e0174576..093c5b9e7 100644
--- a/README.markdown
+++ b/README.markdown
@@ -195,6 +195,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 - [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
+- [A*](A-star/)
 
 ## Puzzles
 

From 7bba2b28da53b3764f24c7fa455fe37065948530 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:58:06 -0700
Subject: [PATCH 1669/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 093c5b9e7..b8b59bbcc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -195,7 +195,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 - [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
-- [A*](A-star/)
+- [A-star](A-star/)
 
 ## Puzzles
 

From cf518c04b31013a4f1b468648967eb7a7a3694b6 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:58:47 -0700
Subject: [PATCH 1670/1679] Update README.markdown

---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index b8b59bbcc..e87fe0335 100644
--- a/README.markdown
+++ b/README.markdown
@@ -195,7 +195,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 - [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
-- [A-star](A-star/)
+- [A-Star](A-Star/)
 
 ## Puzzles
 

From e515919e305371cbff38319e00d21c90b35188e4 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 14:24:59 -0700
Subject: [PATCH 1671/1679] Update Vertex.swift

---
 Graph/Graph/Vertex.swift | 14 ++++----------
 1 file changed, 4 insertions(+), 10 deletions(-)

diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index f74b38396..48645f0fa 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,16 +24,10 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-
-
-    
-    public func hasher(into hasher: inout Hasher){
-        
-        hasher.combine(data)
-        hasher.combine(index)
-    }
-
-
+  public func hasher(into hasher: inout Hasher) {
+    hasher.combine(data)
+    hasher.combine(index)
+  }
 
 }
 

From 81e2726f03ea14a5f92ddafe2e093cba9bee84c1 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 14:35:34 -0700
Subject: [PATCH 1672/1679] Update Linked List/README.markdown

---
 Linked List/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index d6f1fc986..c80b11d6f 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -491,7 +491,7 @@ Recursive Approach:
     }
     let temp = reverse(head.next)
     head.next.next = head
-    head.next = NULL
+    head.next = nil
     return temp
   }
 ```

From 15229cf1b57bd5bd95e81a19a0fd7de9abe0bb6f Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 14:38:06 -0700
Subject: [PATCH 1673/1679] Update Linked List/README.markdown

---
 Linked List/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c80b11d6f..fdbc2ee84 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -486,7 +486,7 @@ Iterative Approach:
 Recursive Approach:
 ```swift
   public func reverse(node: head) {
-    if (!head || !(head.next)) {
+    if !head || !head.next {
       return head
     }
     let temp = reverse(head.next)

From d664df8cb4fea0aad54d2e693f01684cec0590f9 Mon Sep 17 00:00:00 2001
From: Hashem <hashemp206@yahoo.com>
Date: Mon, 29 Mar 2021 15:58:37 +0400
Subject: [PATCH 1674/1679] Update README.markdown

`sort()` is in place sort. in reveres `sorted()` returns a sorted copy of the original array
---
 Insertion Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 8c2a5c1a0..1c41aa91d 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -114,7 +114,7 @@ insertionSort(list)
 
 Here is how the code works.
 
-1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sort()`, the `insertionSort()` function will return a sorted *copy* of the original array.
+1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sorted()`, the `insertionSort()` function will return a sorted *copy* of the original array.
 
 2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `x` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `x` -- is always sorted. The rest, from index `x` until the last element, is the unsorted pile.
 

From 90e23a6790f1f0a0e3704314a08be02114bcdf11 Mon Sep 17 00:00:00 2001
From: Coskun Deniz <c.deniz@gmail.com>
Date: Sat, 21 Aug 2021 19:44:58 +0100
Subject: [PATCH 1675/1679] declare 'index' as variable

---
 Insertion Sort/InsertionSort.swift | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index e24ede905..5f0b6c2b4 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -28,14 +28,13 @@ func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     guard array.count > 1 else { return array }
 
     var sortedArray = array
-    for index in 1..<sortedArray.count {
-        var currentIndex = index
-        let temp = sortedArray[currentIndex]
-        while currentIndex > 0, temp < sortedArray[currentIndex - 1] {
-            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
-            currentIndex -= 1
+    for var index in 1..<sortedArray.count {
+        let temp = sortedArray[index]
+        while index > 0, temp < sortedArray[index - 1] {
+            sortedArray[index] = sortedArray[index - 1]
+            index -= 1
         }
-        sortedArray[currentIndex] = temp
+        sortedArray[index] = temp
     }
     return sortedArray
 }

From 5ad2c68e359c6676df6b3b95315fe8d2b8d70d81 Mon Sep 17 00:00:00 2001
From: Aaron Watkins <ac.watkins80@gmail.com>
Date: Fri, 26 Nov 2021 16:35:21 -0500
Subject: [PATCH 1676/1679] legacy variables names correct legacy variable name
 `x` to be `index` so reader isnt wasting time scratching their head and can
 focus more on understanding the insertion sort algorithm.

---
 Insertion Sort/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 1c41aa91d..f37bfeaef 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -116,9 +116,9 @@ Here is how the code works.
 
 1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sorted()`, the `insertionSort()` function will return a sorted *copy* of the original array.
 
-2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `x` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `x` -- is always sorted. The rest, from index `x` until the last element, is the unsorted pile.
+2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `index` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `index` -- is always sorted. The rest, from index `index` until the last element, is the unsorted pile.
 
-3. The inner loop looks at the element at position `x`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
+3. The inner loop looks at the element at position `index`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
 
 > **Note:** The outer loop starts at index 1, not 0. Moving the very first element from the pile to the sorted portion doesn't actually change anything, so we might as well skip it. 
 

From eb4e151b55ff846c28be5d2357b7ab2f776a9dce Mon Sep 17 00:00:00 2001
From: Aaron Watkins <ac.watkins80@gmail.com>
Date: Fri, 26 Nov 2021 16:45:21 -0500
Subject: [PATCH 1677/1679] correct index to currentIndex

---
 Insertion Sort/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index f37bfeaef..f7b933b92 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -116,9 +116,9 @@ Here is how the code works.
 
 1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sorted()`, the `insertionSort()` function will return a sorted *copy* of the original array.
 
-2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `index` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `index` -- is always sorted. The rest, from index `index` until the last element, is the unsorted pile.
+2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `currentIndex` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `currentIndex` -- is always sorted. The rest, from index `currentIndex` until the last element, is the unsorted pile.
 
-3. The inner loop looks at the element at position `index`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
+3. The inner loop looks at the element at position `currentIndex`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
 
 > **Note:** The outer loop starts at index 1, not 0. Moving the very first element from the pile to the sorted portion doesn't actually change anything, so we might as well skip it. 
 

From 6af57a839d59db84ded9e95315d4a9aeff8a9d64 Mon Sep 17 00:00:00 2001
From: Namratha2604 <gundanamratha@gmail.com>
Date: Thu, 26 Sep 2024 14:25:05 +0530
Subject: [PATCH 1678/1679] #986-corrected the comment

---
 Bloom Filter/BloomFilter.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 7a3719d57..8ed808a06 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -79,4 +79,4 @@ bloom.insert("Bloom Filterz")
 print(bloom.array)
 
 bloom.query("Bloom Filterz")   // true
-bloom.query("Hello WORLD")     // true
+bloom.query("Hello WORLD")     // false or true: It may return true due to a false positive, but it's not guaranteed.

From 5e8c02913c04d86d3b41ebf47210b9f974ad7d26 Mon Sep 17 00:00:00 2001
From: Nitesh J <jnitesh1463@gmail.com>
Date: Mon, 7 Oct 2024 14:05:17 +0530
Subject: [PATCH 1679/1679] issue resolved  #997 and #998

Correction of the README.markdown and Selection Sampling code improvement #998
---
 Selection Sampling/README.markdown         | 2 +-
 Selection Sampling/SelectionSampling.swift | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index 741f592f4..5c2ff5e25 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -12,7 +12,7 @@ func select<T>(from a: [T], count k: Int) -> [T] {
   for i in 0..<k {
     let r = random(min: i, max: a.count - 1)
     if i != r {
-      swap(&a[i], &a[r])
+      a.swapAt(i, r) // Corrected line in README
     }
   }
   return Array(a[0..<k])
diff --git a/Selection Sampling/SelectionSampling.swift b/Selection Sampling/SelectionSampling.swift
index 52aa5988b..711460f47 100644
--- a/Selection Sampling/SelectionSampling.swift	
+++ b/Selection Sampling/SelectionSampling.swift	
@@ -17,7 +17,7 @@ func select<T>(from a: [T], count k: Int) -> [T] {
   for i in 0..<k {
     let r = random(min: i, max: a.count - 1)
     if i != r {
-      swap(&a[i], &a[r])
+      a.swapAt(i, r) // Corrected line
     }
   }
   return Array(a[0..<k])